{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Laboratorio su Regressione Lineare\n", "\n", "La regressione lineare ci permette di modellare la relazione tra una **variabile dipendente** $y$ e una o più **variabili indipendenti** (o regressori) $x_i$. Ciò avviene definendo il seguente modello parametrico:\n", "\n", "$$\n", "y = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + \\ldots + \\beta_n x_n + \\epsilon\n", "$$\n", "\n", "dove:\n", " * $\\beta_0, \\ldots, \\beta_n$ sono i parametri del modello;\n", " * $\\beta_0$ è l'intercetta;\n", " * $\\beta_1, \\ldots, \\beta_n$ sono detti _coefficienti di regressione_;\n", " * $n$ è il numero di variabili indipendenti $x_i$;\n", " * $\\epsilon$ è il termine di errore (o rumore), ovvero la parte di $y$ che la regressione \"non riesce a spiegare\".\n", "\n", "Dato un insieme di dati, è possibile stimare i parametri ottimali $\\beta_0$ e $\\mathbf{\\beta}$ del regressore lineare mediante una procedura di ottimizzazione. Il regressore calcolato fornisce un modello in grado di spiegare le relazioni (lineari) tra le variabili indipendenti e la variabile dipendente." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inizieremo considerando il solito *height-weight* dataset:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "RangeIndex: 4231 entries, 0 to 4230\n", "Data columns (total 4 columns):\n", " # Column Non-Null Count Dtype \n", "--- ------ -------------- ----- \n", " 0 sex 4231 non-null object \n", " 1 BMI 4231 non-null float64\n", " 2 height 4231 non-null float64\n", " 3 weight 4231 non-null float64\n", "dtypes: float64(3), object(1)\n", "memory usage: 132.3+ KB\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " sex BMI height weight\n", "0 M 33.36 187.96 117.933920\n", "1 M 26.54 177.80 83.914520\n", "2 F 32.13 154.94 77.110640\n", "3 M 26.62 172.72 79.378600\n", "4 F 27.13 167.64 76.203456" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "data=pd.read_csv('http://antoninofurnari.it/downloads/height_weight.csv')\n", "data.info()\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regressione Lineare Semplice\n", "\n", "Vediamo un esempio di regressione semplice (ovvero rispetto a una sola variabile indipendente $x_1$). Consideriamo le variabili `weight` e `BMI`, cercando di prevedere i valori di `BMI` da `weight`. Costruiremo dunque un modello lineare di questo tipo:\n", "\n", "$$\n", "BMI = \\beta_0 + \\beta_1 \\cdot weight\n", "$$\n", "\n", "dove:\n", " * **weight** è la variabile indipendente;\n", " * **BMI** è la variabile dipendente;\n", " * $\\beta_1$ è il coefficiente di `weight`;\n", " * $\\beta_0$ è l'intercetta.\n", "\n", "Per definire e calcolare il modello di regressione lineare, utilizzeremo il metodo dei minimi quadrati (Ordinary Least Squares - OLS), implementato dalla libreria **statsmodels**:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Intercept 7.371959\n", "weight 0.252028\n", "dtype: float64" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from statsmodels.formula.api import ols\n", "#la notazione y ~ x indica che y è la variabile\n", "#dipendente e x è la variabile indipendente\n", "#le altre variabili del dataframe saranno scartate\n", "model = ols(\"BMI ~ weight\",data).fit()\n", "\n", "#visualizziamo i parametri del modello\n", "model.params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Abbiamo calcolato il modello lineare:\n", "\n", "$$\n", "BMI = 0.25 \\cdot weight + 7.37\n", "$$\n", "\n", "che ci permette di calcolare il valore di `BMI` dai valori di `weight`. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **🙋‍♂️ Domanda 1**\n", ">\n", "> Secondo il modello lineare trovato, che valore di BMI ha un soggetto che pesa 69 Kg? E per un soggetto che pesa 90 Kg?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il modello mette a disposizione il metodo **predict** per effettuare questo tipo di calcoli. Il metodo però vuole che specifichiamo il nome delle variabili indipendenti per le quali stiamo fornendo i valori. Ciò si può fare definendo al volo un dizionario:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 24.761904\n", "1 30.054496\n", "dtype: float64" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.predict({'weight':[69, 90]})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il modello calcolato non è altro che una retta che fa corrispondere valori di `weight` a valori di `BMI`. Possiamo facilmente visualizzare la retta utilizzando la libreria `seaborn`:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import seaborn as sns\n", "from matplotlib import pyplot as plt\n", "sns.regplot(x='BMI',y='weight',data=data)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **🙋‍♂️ Domanda 2**\n", ">\n", "> Cosa possiamo dire della retta visualizzata? Esistono valori per i quali l'errore commesso è maggiore? Qual è l'equazione della retta mostrata nel grafico?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Analisi di un regressore lineare semplice\n", "\n", "Analizziamo adesso il regrssore ottenuto e vediamo che interpretazione hanno i parametri individuati. Possiamo visualizzare un sommario sul regressore mediante il metodo `summary` dell'oggetto `ols`:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: BMI R-squared: 0.704
Model: OLS Adj. R-squared: 0.704
Method: Least Squares F-statistic: 1.006e+04
Date: Tue, 31 Oct 2023 Prob (F-statistic): 0.00
Time: 06:41:15 Log-Likelihood: -10476.
No. Observations: 4231 AIC: 2.096e+04
Df Residuals: 4229 BIC: 2.097e+04
Df Model: 1
Covariance Type: nonrobust
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coef std err t P>|t| [0.025 0.975]
Intercept 7.3720 0.203 36.253 0.000 6.973 7.771
weight 0.2520 0.003 100.290 0.000 0.247 0.257
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Omnibus: 342.463 Durbin-Watson: 2.007
Prob(Omnibus): 0.000 Jarque-Bera (JB): 467.107
Skew: 0.679 Prob(JB): 3.71e-102
Kurtosis: 3.896 Cond. No. 372.


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: BMI R-squared: 0.704\n", "Model: OLS Adj. R-squared: 0.704\n", "Method: Least Squares F-statistic: 1.006e+04\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 0.00\n", "Time: 06:41:15 Log-Likelihood: -10476.\n", "No. Observations: 4231 AIC: 2.096e+04\n", "Df Residuals: 4229 BIC: 2.097e+04\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 7.3720 0.203 36.253 0.000 6.973 7.771\n", "weight 0.2520 0.003 100.290 0.000 0.247 0.257\n", "==============================================================================\n", "Omnibus: 342.463 Durbin-Watson: 2.007\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 467.107\n", "Skew: 0.679 Prob(JB): 3.71e-102\n", "Kurtosis: 3.896 Cond. No. 372.\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il sommario presenta molte informazioni. Alcune di esse sono autoesplicative, come ad esempio \"Dep. Variable\", \"Model\", \"Method\", \"Date\", \"Time\", \"No. Observations\", \"coef\". Altre sono invece molto specifiche. Tra tutti i valori mostrati, alcuni importanti sono:\n", " * R-squared e Adjusted R-squared;\n", " * F-statistic e prob(F-statistic);\n", " * Valori $t$ dei singoli parametri e relativi valori di $P>|t|$ (p-value);\n", " * I valori trovati per i singoli parametri.\n", "Analizziamo il significato di ciascuno di questi valori:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il valore di $R^2$ indica che la conoscenza di `weight` permette di ridurre l'errore sulle predizioni di `BMI` del $70\\%$. Ciò vuol dire che, benché `weight` da sola non riesca a spiegare (linearmente) `BMI`, le due variabili sono piuttosto correlate. (Si noti che in realtà sappiamo che `BMI` si calcola a partire da `height` e `weight`, quindi questa non dovrebbe essere una scoperta sorprendente). Il valore della F-statistic è alto, mentre quello di Prob(F-statistic) è nullo. Possiamo concludere che il regressore è statisticamente significativo.\n", "\n", "I p-value relativi a entrambi i parametri sono nulli, pertanto entrambi i parametri sono statisticamente rilevanti. Il valore dell'intercetta è pari a $7.38$. Ciò indica che a un peso di $0\\ Kg$ corrisponde un BMI pari a $7.38$ secondo il modello trovato. Il valore del coefficiente di `weight` è pari a $0.25$. Ciò significa che incrementando il peso di un kilogrammo, il BMI aumenta di $0.25\\ Kg/m^2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regressione Lineare Multipla\n", "\n", "Vediamo adesso un esempio di regressione multipla. La regressione lineare multipla permette di studiare le relazioni tra una variabile dipendente e un insieme di variabili indipendenti. Calcoliamo un regressore lineare per predire i valori di `BMI` da quelli di `height` e `weight`:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: BMI R-squared: 0.986
Model: OLS Adj. R-squared: 0.986
Method: Least Squares F-statistic: 1.513e+05
Date: Fri, 26 Oct 2018 Prob (F-statistic): 0.00
Time: 19:48:28 Log-Likelihood: -3987.0
No. Observations: 4231 AIC: 7980.
Df Residuals: 4228 BIC: 7999.
Df Model: 2
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 55.8865 0.171 327.627 0.000 55.552 56.221
height -0.3310 0.001 -294.311 0.000 -0.333 -0.329
weight 0.3497 0.001 550.104 0.000 0.348 0.351
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Omnibus: 441.026 Durbin-Watson: 1.980
Prob(Omnibus): 0.000 Jarque-Bera (JB): 3489.395
Skew: 0.132 Prob(JB): 0.00
Kurtosis: 7.441 Cond. No. 3.36e+03


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.36e+03. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: BMI R-squared: 0.986\n", "Model: OLS Adj. R-squared: 0.986\n", "Method: Least Squares F-statistic: 1.513e+05\n", "Date: Fri, 26 Oct 2018 Prob (F-statistic): 0.00\n", "Time: 19:48:28 Log-Likelihood: -3987.0\n", "No. Observations: 4231 AIC: 7980.\n", "Df Residuals: 4228 BIC: 7999.\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 55.8865 0.171 327.627 0.000 55.552 56.221\n", "height -0.3310 0.001 -294.311 0.000 -0.333 -0.329\n", "weight 0.3497 0.001 550.104 0.000 0.348 0.351\n", "==============================================================================\n", "Omnibus: 441.026 Durbin-Watson: 1.980\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 3489.395\n", "Skew: 0.132 Prob(JB): 0.00\n", "Kurtosis: 7.441 Cond. No. 3.36e+03\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 3.36e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = ols('BMI ~ height + weight',data).fit()\n", "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il regressore lineare trovato ha un valore di $R^2$ molto alto ($0.986$), una F-statistic alta e un valore di Prob(F-statistic) nullo. Possiamo concludere che il regressore è significativo. I p-value dei parametri sono tutti nulli, il che significa che le variabili contribuiscono tutte significativamente alla regressione. \n", "\n", "L'intercetta ha un valore pari a $55.88$, il che indica che, idealmente, un soggetto di peso e altezza nulla avrebbe un `BMI` pari a $55.88\\ Kg/m^2$. Il coefficiente di `height` indica che quando l'altezza viene incrementata di un metro, il BMI viene decrementato di $0.33\\ Kg/m^2$. Analogamente, quando il peso viene incrementato di un kilogrammo, il BMI viene incrementato di $0.35\\ Kg/m^2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Boston House Pricing Dataset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vediamo adesso un esempio con un dataset più complesso. Utilizzeremo il dataset \"Boston\" che contiene osservazioni relativi ai prezzi di diverse case nei sobborghi di Boston. Carichiamo il dataset mediante la funzione `get_rdataset` di `statsmodels`, che permette di caricare dataset contenuti nelle librerie del linguaggio R:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "from statsmodels.datasets import get_rdataset\n", "boston = get_rdataset('Boston', package='MASS')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I dataset caricati mediante `get_rdataset` presentano la medesima struttura. Esiste una documentazione nella proprietà `__doc__`. Stampiamola per farci un'idea più precisa sul dataset:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ".. container::\n", "\n", " ====== ===============\n", " Boston R Documentation\n", " ====== ===============\n", "\n", " .. rubric:: Housing Values in Suburbs of Boston\n", " :name: Boston\n", "\n", " .. rubric:: Description\n", " :name: description\n", "\n", " The ``Boston`` data frame has 506 rows and 14 columns.\n", "\n", " .. rubric:: Usage\n", " :name: usage\n", "\n", " .. code:: R\n", "\n", " Boston\n", "\n", " .. rubric:: Format\n", " :name: format\n", "\n", " This data frame contains the following columns:\n", "\n", " ``crim``\n", " per capita crime rate by town.\n", "\n", " ``zn``\n", " proportion of residential land zoned for lots over 25,000 sq.ft.\n", "\n", " ``indus``\n", " proportion of non-retail business acres per town.\n", "\n", " ``chas``\n", " Charles River dummy variable (= 1 if tract bounds river; 0\n", " otherwise).\n", "\n", " ``nox``\n", " nitrogen oxides concentration (parts per 10 million).\n", "\n", " ``rm``\n", " average number of rooms per dwelling.\n", "\n", " ``age``\n", " proportion of owner-occupied units built prior to 1940.\n", "\n", " ``dis``\n", " weighted mean of distances to five Boston employment centres.\n", "\n", " ``rad``\n", " index of accessibility to radial highways.\n", "\n", " ``tax``\n", " full-value property-tax rate per $10,000.\n", "\n", " ``ptratio``\n", " pupil-teacher ratio by town.\n", "\n", " ``black``\n", " ``1000(Bk - 0.63)^2`` where ``Bk`` is the proportion of blacks by\n", " town.\n", "\n", " ``lstat``\n", " lower status of the population (percent).\n", "\n", " ``medv``\n", " median value of owner-occupied homes in $1000s.\n", "\n", " .. rubric:: Source\n", " :name: source\n", "\n", " Harrison, D. and Rubinfeld, D.L. (1978) Hedonic prices and the demand\n", " for clean air. *J. Environ. Economics and Management* **5**, 81–102.\n", "\n", " Belsley D.A., Kuh, E. and Welsch, R.E. (1980) *Regression\n", " Diagnostics. Identifying Influential Data and Sources of\n", " Collinearity.* New York: Wiley.\n", "\n" ] } ], "source": [ "print(boston.__doc__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il dataframe contenente le osservazioni si trova all'interno della proprietà `data`:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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crimzninduschasnoxrmagedisradtaxptratioblacklstatmedv
00.0063218.02.3100.5386.57565.24.0900129615.3396.904.9824.0
10.027310.07.0700.4696.42178.94.9671224217.8396.909.1421.6
20.027290.07.0700.4697.18561.14.9671224217.8392.834.0334.7
30.032370.02.1800.4586.99845.86.0622322218.7394.632.9433.4
40.069050.02.1800.4587.14754.26.0622322218.7396.905.3336.2
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" ], "text/plain": [ " crim zn indus chas nox rm age dis rad tax ptratio \\\n", "0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 \n", "1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 \n", "2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 \n", "3 0.03237 0.0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 \n", "4 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 \n", "\n", " black lstat medv \n", "0 396.90 4.98 24.0 \n", "1 396.90 9.14 21.6 \n", "2 392.83 4.03 34.7 \n", "3 394.63 2.94 33.4 \n", "4 396.90 5.33 36.2 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boston.data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Questo dataset è generalmente utilizzato come un dataset di regressione, nel quale l'obiettivo è quello di predire il valore di `medv` (prezzo medio delle case in migliaia di dollari) a partire dai valori delle altre variabili." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Regressori lineari, variabili categoriche e variabili dummy\n", "Notiamo che le variabili `rad` e `chas` sono categoriche. Quando si lavora con regressori lineari e variabili categoriche bisogna fare attenzione: \n", " * Le variabili categoriche non vanno utilizzate come variabili dipendenti di un regressore lineare; \n", " * Le variabili categoriche possono essere utilizzate invece come variabili indipendenti solo se binarie. \n", "`chas` è binaria, quindi possiamo includerla tra le variabili indipendenti. `rad` invece non è binaria, pertanto non può essere inclusa tra le variabili per la regressione. \n", "\n", "Se vogliamo includere `rad` tra le variabili per la regressione lineare, dobbiamo trasformarla in un insiem di variabili binarie \"dummy\". Ogni variabile \"dummy\" indicherà per ogni osservazione, se essa appartiene a una specifica classe tra quelle della variabile categorica considerata.\n", "\n", "Vediamo un esempio:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 A\n", "1 A\n", "2 B\n", "3 A\n", "4 C\n", "5 C\n", "6 B\n", "7 A\n", "8 C\n", "9 B\n", "dtype: object" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var = pd.Series(['A','A','B','A','C','C','B','A','C','B'])\n", "var" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Si consideri `var` come una variabile categorica che consta di $10$ osservazioni e $3$ classi. Possiamo sostituire la variabile `var` con tre variabili `A`,`B`,`C` tali che `A` sarà pari a $1$ solo quando `var` è uguale ad `A`, `C` sarà pari a $1$ solo quando `var` è uguale ad `C`. Possiamo ottenere queste tre variabili dummy mediante la funzione `get_dummies` di Pandas:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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ABC
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" ], "text/plain": [ " A B C\n", "0 1 0 0\n", "1 1 0 0\n", "2 0 1 0\n", "3 1 0 0\n", "4 0 0 1\n", "5 0 0 1\n", "6 0 1 0\n", "7 1 0 0\n", "8 0 0 1\n", "9 0 1 0" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pd.get_dummies(var)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Confrontiamo ad esempio l'osservazione di indice $5$ della serie e del DataFrame di variabili dummy:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C \n", "\n", "A 0\n", "B 0\n", "C 1\n", "Name: 5, dtype: uint8\n" ] } ], "source": [ "print(var[5],'\\n')\n", "print(pd.get_dummies(var).loc[5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il valore di `var` è $5$. In maniera corrispondente, la variabile dummy `C` è pari a $1$, mentre le altre sono pari a zero. Questo tipo di rappresentazione di `var` è tuttavia ridondante. Infatti, se sappiamo che $B=0$ e $C=0$, possiamo facilmente dedurre che $A=1$. Questa semplice ridondanza può creare problemi di clacolo numerico nell'ottimizzazione del regressore lineare. Per evitarla, generalmente si esclude una delle variabili dummy. Possiamo ottenere questo risultato come segue:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " B C\n", "0 0 0\n", "1 0 0\n", "2 1 0\n", "3 0 0\n", "4 0 1\n", "5 0 1\n", "6 1 0\n", "7 0 0\n", "8 0 1\n", "9 1 0" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pd.get_dummies(var,drop_first=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Possiamo convertire la variabile categorica `rad` in un insieme di variabili dummy come segue:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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crimzninduschasnoxrmagedistaxptratio...lstatmedvrad_2rad_3rad_4rad_5rad_6rad_7rad_8rad_24
00.0063218.02.3100.5386.57565.24.090029615.3...4.9824.000000000
10.027310.07.0700.4696.42178.94.967124217.8...9.1421.610000000
20.027290.07.0700.4697.18561.14.967124217.8...4.0334.710000000
30.032370.02.1800.4586.99845.86.062222218.7...2.9433.401000000
40.069050.02.1800.4587.14754.26.062222218.7...5.3336.201000000
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5 rows × 21 columns

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" ], "text/plain": [ " crim zn indus chas nox rm age dis tax ptratio ... \\\n", "0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 296 15.3 ... \n", "1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 242 17.8 ... \n", "2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 242 17.8 ... \n", "3 0.03237 0.0 2.18 0 0.458 6.998 45.8 6.0622 222 18.7 ... \n", "4 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 222 18.7 ... \n", "\n", " lstat medv rad_2 rad_3 rad_4 rad_5 rad_6 rad_7 rad_8 rad_24 \n", "0 4.98 24.0 0 0 0 0 0 0 0 0 \n", "1 9.14 21.6 1 0 0 0 0 0 0 0 \n", "2 4.03 34.7 1 0 0 0 0 0 0 0 \n", "3 2.94 33.4 0 1 0 0 0 0 0 0 \n", "4 5.33 36.2 0 1 0 0 0 0 0 0 \n", "\n", "[5 rows x 21 columns]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boston_mod=pd.get_dummies(boston.data, columns=['rad'],drop_first=True)\n", "boston_mod.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ispezioniamo i nomi delle colonne:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Index(['crim', 'zn', 'indus', 'chas', 'nox', 'rm', 'age', 'dis', 'tax',\n", " 'ptratio', 'black', 'lstat', 'medv', 'rad_2', 'rad_3', 'rad_4', 'rad_5',\n", " 'rad_6', 'rad_7', 'rad_8', 'rad_24'],\n", " dtype='object')" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boston_mod.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notiamo che `rad` è stata rimossa e sostituita da diverse variabili dummy, rappresentanti i vari valori assunti da `rad`. Possiamo adesso procedere al calcolo del regressore lineare multiplo:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: medv R-squared: 0.750
Model: OLS Adj. R-squared: 0.740
Method: Least Squares F-statistic: 72.70
Date: Tue, 31 Oct 2023 Prob (F-statistic): 8.29e-132
Time: 06:43:47 Log-Likelihood: -1489.6
No. Observations: 506 AIC: 3021.
Df Residuals: 485 BIC: 3110.
Df Model: 20
Covariance Type: nonrobust
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coef std err t P>|t| [0.025 0.975]
Intercept 35.2596 5.434 6.489 0.000 24.583 45.936
crim -0.1088 0.033 -3.329 0.001 -0.173 -0.045
zn 0.0549 0.014 3.880 0.000 0.027 0.083
indus 0.0238 0.064 0.373 0.709 -0.101 0.149
chas 2.5242 0.863 2.924 0.004 0.828 4.220
nox -17.5731 3.896 -4.510 0.000 -25.229 -9.917
rm 3.6655 0.421 8.703 0.000 2.838 4.493
age 0.0005 0.013 0.035 0.972 -0.026 0.026
dis -1.5545 0.202 -7.699 0.000 -1.951 -1.158
tax -0.0087 0.004 -2.246 0.025 -0.016 -0.001
ptratio -0.9724 0.144 -6.731 0.000 -1.256 -0.689
black 0.0094 0.003 3.531 0.000 0.004 0.015
lstat -0.5292 0.051 -10.451 0.000 -0.629 -0.430
rad_2 1.4889 1.478 1.008 0.314 -1.414 4.392
rad_3 4.6813 1.335 3.506 0.000 2.058 7.305
rad_4 2.5762 1.187 2.170 0.031 0.243 4.909
rad_5 2.9185 1.208 2.417 0.016 0.546 5.291
rad_6 1.1858 1.464 0.810 0.418 -1.691 4.062
rad_7 4.8790 1.571 3.105 0.002 1.792 7.966
rad_8 4.8398 1.492 3.245 0.001 1.909 7.771
rad_24 7.4617 1.789 4.172 0.000 3.947 10.976
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 183.890 Durbin-Watson: 1.089
Prob(Omnibus): 0.000 Jarque-Bera (JB): 858.805
Skew: 1.554 Prob(JB): 3.26e-187
Kurtosis: 8.575 Cond. No. 1.60e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.6e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: medv R-squared: 0.750\n", "Model: OLS Adj. R-squared: 0.740\n", "Method: Least Squares F-statistic: 72.70\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 8.29e-132\n", "Time: 06:43:47 Log-Likelihood: -1489.6\n", "No. Observations: 506 AIC: 3021.\n", "Df Residuals: 485 BIC: 3110.\n", "Df Model: 20 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 35.2596 5.434 6.489 0.000 24.583 45.936\n", "crim -0.1088 0.033 -3.329 0.001 -0.173 -0.045\n", "zn 0.0549 0.014 3.880 0.000 0.027 0.083\n", "indus 0.0238 0.064 0.373 0.709 -0.101 0.149\n", "chas 2.5242 0.863 2.924 0.004 0.828 4.220\n", "nox -17.5731 3.896 -4.510 0.000 -25.229 -9.917\n", "rm 3.6655 0.421 8.703 0.000 2.838 4.493\n", "age 0.0005 0.013 0.035 0.972 -0.026 0.026\n", "dis -1.5545 0.202 -7.699 0.000 -1.951 -1.158\n", "tax -0.0087 0.004 -2.246 0.025 -0.016 -0.001\n", "ptratio -0.9724 0.144 -6.731 0.000 -1.256 -0.689\n", "black 0.0094 0.003 3.531 0.000 0.004 0.015\n", "lstat -0.5292 0.051 -10.451 0.000 -0.629 -0.430\n", "rad_2 1.4889 1.478 1.008 0.314 -1.414 4.392\n", "rad_3 4.6813 1.335 3.506 0.000 2.058 7.305\n", "rad_4 2.5762 1.187 2.170 0.031 0.243 4.909\n", "rad_5 2.9185 1.208 2.417 0.016 0.546 5.291\n", "rad_6 1.1858 1.464 0.810 0.418 -1.691 4.062\n", "rad_7 4.8790 1.571 3.105 0.002 1.792 7.966\n", "rad_8 4.8398 1.492 3.245 0.001 1.909 7.771\n", "rad_24 7.4617 1.789 4.172 0.000 3.947 10.976\n", "==============================================================================\n", "Omnibus: 183.890 Durbin-Watson: 1.089\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 858.805\n", "Skew: 1.554 Prob(JB): 3.26e-187\n", "Kurtosis: 8.575 Cond. No. 1.60e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.6e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=ols(\"\"\"medv ~ crim + zn + indus + chas + nox + rm +age + dis + tax + \n", " ptratio + black + lstat + rad_2 + rad_3 + rad_4 + rad_5 + rad_6 + \n", " rad_7 + rad_8 + rad_24\"\"\", boston_mod).fit()\n", "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il regressore ottenuto presenta un valore di $R^2$ piuttosto alto. Ciò vuol dire che, globalmente, le variabili indipendenti sono correlate con la variabile dipendente. La F-statistic è alta e il p-value corrispondente è molto basso. Il regressore è, globalmente, statisticamente significativo. \n", "\n", "Passiamo all'analisi dei p-value dei singoli parametri trovati. I p-value delle seguenti variabili sono più alti di $0.05$:\n", " * `indus`;\n", " * `age`;\n", " * `rad2`;\n", " * `rad6`.\n", " \n", "Queste variabili non contribuiscono significativamente alla regressione. Analizziamo i valori dei parametri relativi a varabili che contribuiscono statisticamente alla regressione:\n", " * `intercept`: quando tutte le altre variabili assumono valori nulli, `medv` assume il valore $35.26$. Ricordiamo che `medv` esprime il prezzo medio delle case in migliaia di dollari, per cui il \"prezzo medio base\" delle case è di circa $35260$ dollari;\n", " * `crim`: l'incremento di una unità del tasso di criminalità pro-capite abbassa il valore delle case di cica $108$ dollari;\n", " * `zn`: l'incremento di una unità della proporzione di terre destinate a uso residenziale aumenta il valore delle case di circa $54$ dollari;\n", " * `chas`: quando la variabile è pari a $1$ (ricordiamo che si tratta di una variabile categorica), il prezzo delle case sale di circa $2500$ dollari. Possiamo dire che le case vicine al fiume tendono ad essere più care;\n", " * `nox`: l'aumento di una unità della concentrazione di ossido di azoto abbassa i prezzi delle case di circa $17500$ dollari. Questo può sembrare un numero altissimo, ma si noti che i valori di `nox` variano tra un minimo di $0.38$ a un massimo di $0.87$, per cui non si verificheranno decrementi dei prezzi delle case così grandi;\n", " * `rm`: l'incremento del numero di stanze di una unità incrementa il prezzo della casa di circa $3600$ dollari;\n", " * `dis`: l'incremento di una unità della distanza media dal centro diminuisce il prezzo delle case di circa $1500$ dollari (le case più distanti dal centro valgono di meno);\n", " * `tax`: l'aumento di un unità del tax-rate della proprietà ne diminuisce il valore di 8 dollari. Sembra un decremento trascurabile, tuttavia, si consideri che il range di `tax` è compreso tra $187$ e $711$;\n", " * `ptratio`: l'aumento di una unità del rapporto insegnante-alunni diminuisce il valore della proprietà di circa $1000$ dollari;\n", " * `black`: l'aumento di una unità del valore di `black` (una variabile dipendente dalla proporzione tra abitanti bianchi e neri) incrementa il valore delle case di pochi dollari. Si consideri che il range di `black` va da circa $0$ a $396$;\n", " * `lstat`: l'aumento di una unità del valore di questa variabile (percenutale di abitanti meno abbienti) diminuisce il prezzo delle case di circa $500$ dollari;\n", " * I coefficienti appresi per le variabili dummy di `rad` indicano che quando `rad` assume il valore 24, il valore delle case aumenta di circa $7500$ dollari. Altri valori di `rad` contribuiscono differentemente all'incremento del valore di `medv`;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **🙋‍♂️ Domanda 3**\n", ">\n", "> Dati i risultati del regressore lineare, qual è la variabile più influente nella regressione?" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: medv R-squared: 0.741
Model: OLS Adj. R-squared: 0.734
Method: Least Squares F-statistic: 108.1
Date: Tue, 31 Oct 2023 Prob (F-statistic): 6.72e-135
Time: 06:48:40 Log-Likelihood: -1498.8
No. Observations: 506 AIC: 3026.
Df Residuals: 492 BIC: 3085.
Df Model: 13
Covariance Type: nonrobust
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coef std err t P>|t| [0.025 0.975]
Intercept 36.4595 5.103 7.144 0.000 26.432 46.487
crim -0.1080 0.033 -3.287 0.001 -0.173 -0.043
zn 0.0464 0.014 3.382 0.001 0.019 0.073
indus 0.0206 0.061 0.334 0.738 -0.100 0.141
chas 2.6867 0.862 3.118 0.002 0.994 4.380
nox -17.7666 3.820 -4.651 0.000 -25.272 -10.262
rm 3.8099 0.418 9.116 0.000 2.989 4.631
age 0.0007 0.013 0.052 0.958 -0.025 0.027
dis -1.4756 0.199 -7.398 0.000 -1.867 -1.084
tax -0.0123 0.004 -3.280 0.001 -0.020 -0.005
ptratio -0.9527 0.131 -7.283 0.000 -1.210 -0.696
black 0.0093 0.003 3.467 0.001 0.004 0.015
lstat -0.5248 0.051 -10.347 0.000 -0.624 -0.425
rad 0.3060 0.066 4.613 0.000 0.176 0.436
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 178.041 Durbin-Watson: 1.078
Prob(Omnibus): 0.000 Jarque-Bera (JB): 783.126
Skew: 1.521 Prob(JB): 8.84e-171
Kurtosis: 8.281 Cond. No. 1.51e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.51e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: medv R-squared: 0.741\n", "Model: OLS Adj. R-squared: 0.734\n", "Method: Least Squares F-statistic: 108.1\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 6.72e-135\n", "Time: 06:48:40 Log-Likelihood: -1498.8\n", "No. Observations: 506 AIC: 3026.\n", "Df Residuals: 492 BIC: 3085.\n", "Df Model: 13 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 36.4595 5.103 7.144 0.000 26.432 46.487\n", "crim -0.1080 0.033 -3.287 0.001 -0.173 -0.043\n", "zn 0.0464 0.014 3.382 0.001 0.019 0.073\n", "indus 0.0206 0.061 0.334 0.738 -0.100 0.141\n", "chas 2.6867 0.862 3.118 0.002 0.994 4.380\n", "nox -17.7666 3.820 -4.651 0.000 -25.272 -10.262\n", "rm 3.8099 0.418 9.116 0.000 2.989 4.631\n", "age 0.0007 0.013 0.052 0.958 -0.025 0.027\n", "dis -1.4756 0.199 -7.398 0.000 -1.867 -1.084\n", "tax -0.0123 0.004 -3.280 0.001 -0.020 -0.005\n", "ptratio -0.9527 0.131 -7.283 0.000 -1.210 -0.696\n", "black 0.0093 0.003 3.467 0.001 0.004 0.015\n", "lstat -0.5248 0.051 -10.347 0.000 -0.624 -0.425\n", "rad 0.3060 0.066 4.613 0.000 0.176 0.436\n", "==============================================================================\n", "Omnibus: 178.041 Durbin-Watson: 1.078\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 783.126\n", "Skew: 1.521 Prob(JB): 8.84e-171\n", "Kurtosis: 8.281 Cond. No. 1.51e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.51e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=ols(\"\"\"medv ~ crim + zn + indus + chas + nox + rm +age + dis + tax + \n", " ptratio + black + lstat + rad\"\"\", boston.data).fit()\n", "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It should be noted that, when it is obvious that a variable is categorical, `statsmodels` automatically create dummy variables internally. For instance, let us modify the dataframe so that `rad` becomes text:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 1\n", "1 2\n", "2 2\n", "3 3\n", "4 3\n", " ..\n", "501 1\n", "502 1\n", "503 1\n", "504 1\n", "505 1\n", "Name: rad, Length: 506, dtype: object" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boston2 = boston.data.copy()\n", "boston2['rad'] = boston2['rad'].apply(str)\n", "boston2['rad']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we fit a linear regressor model on the modified dataset, `statsmodels` will introduce different dummy variables for the different values of `rad`:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: medv R-squared: 0.750
Model: OLS Adj. R-squared: 0.740
Method: Least Squares F-statistic: 72.70
Date: Tue, 31 Oct 2023 Prob (F-statistic): 8.29e-132
Time: 06:57:15 Log-Likelihood: -1489.6
No. Observations: 506 AIC: 3021.
Df Residuals: 485 BIC: 3110.
Df Model: 20
Covariance Type: nonrobust
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coef std err t P>|t| [0.025 0.975]
Intercept 35.2596 5.434 6.489 0.000 24.583 45.936
rad[T.2] 1.4889 1.478 1.008 0.314 -1.414 4.392
rad[T.24] 7.4617 1.789 4.172 0.000 3.947 10.976
rad[T.3] 4.6813 1.335 3.506 0.000 2.058 7.305
rad[T.4] 2.5762 1.187 2.170 0.031 0.243 4.909
rad[T.5] 2.9185 1.208 2.417 0.016 0.546 5.291
rad[T.6] 1.1858 1.464 0.810 0.418 -1.691 4.062
rad[T.7] 4.8790 1.571 3.105 0.002 1.792 7.966
rad[T.8] 4.8398 1.492 3.245 0.001 1.909 7.771
crim -0.1088 0.033 -3.329 0.001 -0.173 -0.045
zn 0.0549 0.014 3.880 0.000 0.027 0.083
indus 0.0238 0.064 0.373 0.709 -0.101 0.149
chas 2.5242 0.863 2.924 0.004 0.828 4.220
nox -17.5731 3.896 -4.510 0.000 -25.229 -9.917
rm 3.6655 0.421 8.703 0.000 2.838 4.493
age 0.0005 0.013 0.035 0.972 -0.026 0.026
dis -1.5545 0.202 -7.699 0.000 -1.951 -1.158
tax -0.0087 0.004 -2.246 0.025 -0.016 -0.001
ptratio -0.9724 0.144 -6.731 0.000 -1.256 -0.689
black 0.0094 0.003 3.531 0.000 0.004 0.015
lstat -0.5292 0.051 -10.451 0.000 -0.629 -0.430
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 183.890 Durbin-Watson: 1.089
Prob(Omnibus): 0.000 Jarque-Bera (JB): 858.805
Skew: 1.554 Prob(JB): 3.26e-187
Kurtosis: 8.575 Cond. No. 1.60e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.6e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: medv R-squared: 0.750\n", "Model: OLS Adj. R-squared: 0.740\n", "Method: Least Squares F-statistic: 72.70\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 8.29e-132\n", "Time: 06:57:15 Log-Likelihood: -1489.6\n", "No. Observations: 506 AIC: 3021.\n", "Df Residuals: 485 BIC: 3110.\n", "Df Model: 20 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 35.2596 5.434 6.489 0.000 24.583 45.936\n", "rad[T.2] 1.4889 1.478 1.008 0.314 -1.414 4.392\n", "rad[T.24] 7.4617 1.789 4.172 0.000 3.947 10.976\n", "rad[T.3] 4.6813 1.335 3.506 0.000 2.058 7.305\n", "rad[T.4] 2.5762 1.187 2.170 0.031 0.243 4.909\n", "rad[T.5] 2.9185 1.208 2.417 0.016 0.546 5.291\n", "rad[T.6] 1.1858 1.464 0.810 0.418 -1.691 4.062\n", "rad[T.7] 4.8790 1.571 3.105 0.002 1.792 7.966\n", "rad[T.8] 4.8398 1.492 3.245 0.001 1.909 7.771\n", "crim -0.1088 0.033 -3.329 0.001 -0.173 -0.045\n", "zn 0.0549 0.014 3.880 0.000 0.027 0.083\n", "indus 0.0238 0.064 0.373 0.709 -0.101 0.149\n", "chas 2.5242 0.863 2.924 0.004 0.828 4.220\n", "nox -17.5731 3.896 -4.510 0.000 -25.229 -9.917\n", "rm 3.6655 0.421 8.703 0.000 2.838 4.493\n", "age 0.0005 0.013 0.035 0.972 -0.026 0.026\n", "dis -1.5545 0.202 -7.699 0.000 -1.951 -1.158\n", "tax -0.0087 0.004 -2.246 0.025 -0.016 -0.001\n", "ptratio -0.9724 0.144 -6.731 0.000 -1.256 -0.689\n", "black 0.0094 0.003 3.531 0.000 0.004 0.015\n", "lstat -0.5292 0.051 -10.451 0.000 -0.629 -0.430\n", "==============================================================================\n", "Omnibus: 183.890 Durbin-Watson: 1.089\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 858.805\n", "Skew: 1.554 Prob(JB): 3.26e-187\n", "Kurtosis: 8.575 Cond. No. 1.60e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.6e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=ols(\"\"\"medv ~ crim + zn + indus + chas + nox + rm +age + dis + tax + \n", " ptratio + black + lstat + rad\"\"\", boston2).fit()\n", "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, we can instruct statsmodels to use a variable as a categorical one with the `C(variable)` tag:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: medv R-squared: 0.750
Model: OLS Adj. R-squared: 0.740
Method: Least Squares F-statistic: 72.70
Date: Tue, 31 Oct 2023 Prob (F-statistic): 8.29e-132
Time: 07:05:32 Log-Likelihood: -1489.6
No. Observations: 506 AIC: 3021.
Df Residuals: 485 BIC: 3110.
Df Model: 20
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 35.2596 5.434 6.489 0.000 24.583 45.936
C(rad)[T.2] 1.4889 1.478 1.008 0.314 -1.414 4.392
C(rad)[T.3] 4.6813 1.335 3.506 0.000 2.058 7.305
C(rad)[T.4] 2.5762 1.187 2.170 0.031 0.243 4.909
C(rad)[T.5] 2.9185 1.208 2.417 0.016 0.546 5.291
C(rad)[T.6] 1.1858 1.464 0.810 0.418 -1.691 4.062
C(rad)[T.7] 4.8790 1.571 3.105 0.002 1.792 7.966
C(rad)[T.8] 4.8398 1.492 3.245 0.001 1.909 7.771
C(rad)[T.24] 7.4617 1.789 4.172 0.000 3.947 10.976
crim -0.1088 0.033 -3.329 0.001 -0.173 -0.045
zn 0.0549 0.014 3.880 0.000 0.027 0.083
indus 0.0238 0.064 0.373 0.709 -0.101 0.149
chas 2.5242 0.863 2.924 0.004 0.828 4.220
nox -17.5731 3.896 -4.510 0.000 -25.229 -9.917
rm 3.6655 0.421 8.703 0.000 2.838 4.493
age 0.0005 0.013 0.035 0.972 -0.026 0.026
dis -1.5545 0.202 -7.699 0.000 -1.951 -1.158
tax -0.0087 0.004 -2.246 0.025 -0.016 -0.001
ptratio -0.9724 0.144 -6.731 0.000 -1.256 -0.689
black 0.0094 0.003 3.531 0.000 0.004 0.015
lstat -0.5292 0.051 -10.451 0.000 -0.629 -0.430
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 183.890 Durbin-Watson: 1.089
Prob(Omnibus): 0.000 Jarque-Bera (JB): 858.805
Skew: 1.554 Prob(JB): 3.26e-187
Kurtosis: 8.575 Cond. No. 1.60e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.6e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: medv R-squared: 0.750\n", "Model: OLS Adj. R-squared: 0.740\n", "Method: Least Squares F-statistic: 72.70\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 8.29e-132\n", "Time: 07:05:32 Log-Likelihood: -1489.6\n", "No. Observations: 506 AIC: 3021.\n", "Df Residuals: 485 BIC: 3110.\n", "Df Model: 20 \n", "Covariance Type: nonrobust \n", "================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "Intercept 35.2596 5.434 6.489 0.000 24.583 45.936\n", "C(rad)[T.2] 1.4889 1.478 1.008 0.314 -1.414 4.392\n", "C(rad)[T.3] 4.6813 1.335 3.506 0.000 2.058 7.305\n", "C(rad)[T.4] 2.5762 1.187 2.170 0.031 0.243 4.909\n", "C(rad)[T.5] 2.9185 1.208 2.417 0.016 0.546 5.291\n", "C(rad)[T.6] 1.1858 1.464 0.810 0.418 -1.691 4.062\n", "C(rad)[T.7] 4.8790 1.571 3.105 0.002 1.792 7.966\n", "C(rad)[T.8] 4.8398 1.492 3.245 0.001 1.909 7.771\n", "C(rad)[T.24] 7.4617 1.789 4.172 0.000 3.947 10.976\n", "crim -0.1088 0.033 -3.329 0.001 -0.173 -0.045\n", "zn 0.0549 0.014 3.880 0.000 0.027 0.083\n", "indus 0.0238 0.064 0.373 0.709 -0.101 0.149\n", "chas 2.5242 0.863 2.924 0.004 0.828 4.220\n", "nox -17.5731 3.896 -4.510 0.000 -25.229 -9.917\n", "rm 3.6655 0.421 8.703 0.000 2.838 4.493\n", "age 0.0005 0.013 0.035 0.972 -0.026 0.026\n", "dis -1.5545 0.202 -7.699 0.000 -1.951 -1.158\n", "tax -0.0087 0.004 -2.246 0.025 -0.016 -0.001\n", "ptratio -0.9724 0.144 -6.731 0.000 -1.256 -0.689\n", "black 0.0094 0.003 3.531 0.000 0.004 0.015\n", "lstat -0.5292 0.051 -10.451 0.000 -0.629 -0.430\n", "==============================================================================\n", "Omnibus: 183.890 Durbin-Watson: 1.089\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 858.805\n", "Skew: 1.554 Prob(JB): 3.26e-187\n", "Kurtosis: 8.575 Cond. No. 1.60e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.6e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=ols(\"\"\"medv ~ crim + zn + indus + chas + nox + rm +age + dis + tax + \n", " ptratio + black + lstat + C(rad)\"\"\", boston.data).fit()\n", "model.summary()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: weight R-squared: 0.990
Model: OLS Adj. R-squared: 0.990
Method: Least Squares F-statistic: 1.392e+05
Date: Tue, 31 Oct 2023 Prob (F-statistic): 0.00
Time: 06:54:01 Log-Likelihood: -8403.1
No. Observations: 4231 AIC: 1.681e+04
Df Residuals: 4227 BIC: 1.684e+04
Df Model: 3
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept -158.3473 0.670 -236.287 0.000 -159.661 -157.033
sex[T.M] 0.0592 0.079 0.753 0.451 -0.095 0.213
BMI 2.8199 0.005 546.155 0.000 2.810 2.830
height 0.9440 0.004 240.347 0.000 0.936 0.952
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 412.503 Durbin-Watson: 1.978
Prob(Omnibus): 0.000 Jarque-Bera (JB): 2913.710
Skew: 0.146 Prob(JB): 0.00
Kurtosis: 7.055 Cond. No. 4.27e+03


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 4.27e+03. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: weight R-squared: 0.990\n", "Model: OLS Adj. R-squared: 0.990\n", "Method: Least Squares F-statistic: 1.392e+05\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 0.00\n", "Time: 06:54:01 Log-Likelihood: -8403.1\n", "No. Observations: 4231 AIC: 1.681e+04\n", "Df Residuals: 4227 BIC: 1.684e+04\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -158.3473 0.670 -236.287 0.000 -159.661 -157.033\n", "sex[T.M] 0.0592 0.079 0.753 0.451 -0.095 0.213\n", "BMI 2.8199 0.005 546.155 0.000 2.810 2.830\n", "height 0.9440 0.004 240.347 0.000 0.936 0.952\n", "==============================================================================\n", "Omnibus: 412.503 Durbin-Watson: 1.978\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 2913.710\n", "Skew: 0.146 Prob(JB): 0.00\n", "Kurtosis: 7.055 Cond. No. 4.27e+03\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 4.27e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ols(\"weight ~ BMI + height + sex\",data).fit().summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, there is less control on which dummy variables to include or not in the model, as seen in the next section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Backward Elimination\n", "Il modello di regressione lineare calcolato è in generale buono, ma include alcune variabili che non contribuiscono significativamente alla regressione. In pratica, queste variabili possono inficiare il calcolo del regressore lineare e quindi sarebbe ideale non averle dentro. Potremmo rimuoverle tutte, ma non siamo sicuri che, in assenza di alcune, le altre non acquisiscano una qualche significatività. Esistono diverse tecniche per eliminare tali variabili. Una delle possibilità consiste nell'usare il metodo della **backward elimination**, che è definito come segue:\n", " \n", " 1. Si calcola il regressore lineare considerando tutte le variabili dipendenti;\n", " * Se tutte le variabili sono significative, il regressore trovato è quello finale;\n", " * Se qualche variabile non è significativa, si rimuove la variabile con p-value più alto, si ricalcola il regressore lineare e si va al punto 2.\n", " \n", "Alla fine del processo, otterremo un regressore in cui tutte le variabili sono significative. \n", "\n", "Applichiamo il processo al nostro esempio. La variabile con p-value più alto è `age`. Riomuoviamola e ricalcoliamo il regressore:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: medv R-squared: 0.750
Model: OLS Adj. R-squared: 0.740
Method: Least Squares F-statistic: 76.68
Date: Tue, 31 Oct 2023 Prob (F-statistic): 9.34e-133
Time: 06:44:13 Log-Likelihood: -1489.6
No. Observations: 506 AIC: 3019.
Df Residuals: 486 BIC: 3104.
Df Model: 19
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 35.2429 5.407 6.518 0.000 24.619 45.867
crim -0.1088 0.033 -3.333 0.001 -0.173 -0.045
zn 0.0548 0.014 3.900 0.000 0.027 0.082
indus 0.0238 0.064 0.374 0.709 -0.101 0.149
chas 2.5256 0.861 2.932 0.004 0.833 4.218
nox -17.5386 3.765 -4.659 0.000 -24.936 -10.142
rm 3.6682 0.414 8.869 0.000 2.856 4.481
dis -1.5566 0.193 -8.058 0.000 -1.936 -1.177
tax -0.0087 0.004 -2.250 0.025 -0.016 -0.001
ptratio -0.9719 0.144 -6.769 0.000 -1.254 -0.690
black 0.0094 0.003 3.544 0.000 0.004 0.015
lstat -0.5286 0.047 -11.130 0.000 -0.622 -0.435
rad_2 1.4910 1.475 1.011 0.313 -1.407 4.389
rad_3 4.6798 1.333 3.510 0.000 2.060 7.300
rad_4 2.5748 1.185 2.172 0.030 0.246 4.904
rad_5 2.9185 1.206 2.419 0.016 0.548 5.289
rad_6 1.1833 1.461 0.810 0.418 -1.687 4.053
rad_7 4.8767 1.568 3.110 0.002 1.795 7.958
rad_8 4.8423 1.488 3.253 0.001 1.918 7.767
rad_24 7.4563 1.780 4.188 0.000 3.958 10.954
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 184.084 Durbin-Watson: 1.088
Prob(Omnibus): 0.000 Jarque-Bera (JB): 861.138
Skew: 1.555 Prob(JB): 1.01e-187
Kurtosis: 8.583 Cond. No. 1.57e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.57e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: medv R-squared: 0.750\n", "Model: OLS Adj. R-squared: 0.740\n", "Method: Least Squares F-statistic: 76.68\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 9.34e-133\n", "Time: 06:44:13 Log-Likelihood: -1489.6\n", "No. Observations: 506 AIC: 3019.\n", "Df Residuals: 486 BIC: 3104.\n", "Df Model: 19 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 35.2429 5.407 6.518 0.000 24.619 45.867\n", "crim -0.1088 0.033 -3.333 0.001 -0.173 -0.045\n", "zn 0.0548 0.014 3.900 0.000 0.027 0.082\n", "indus 0.0238 0.064 0.374 0.709 -0.101 0.149\n", "chas 2.5256 0.861 2.932 0.004 0.833 4.218\n", "nox -17.5386 3.765 -4.659 0.000 -24.936 -10.142\n", "rm 3.6682 0.414 8.869 0.000 2.856 4.481\n", "dis -1.5566 0.193 -8.058 0.000 -1.936 -1.177\n", "tax -0.0087 0.004 -2.250 0.025 -0.016 -0.001\n", "ptratio -0.9719 0.144 -6.769 0.000 -1.254 -0.690\n", "black 0.0094 0.003 3.544 0.000 0.004 0.015\n", "lstat -0.5286 0.047 -11.130 0.000 -0.622 -0.435\n", "rad_2 1.4910 1.475 1.011 0.313 -1.407 4.389\n", "rad_3 4.6798 1.333 3.510 0.000 2.060 7.300\n", "rad_4 2.5748 1.185 2.172 0.030 0.246 4.904\n", "rad_5 2.9185 1.206 2.419 0.016 0.548 5.289\n", "rad_6 1.1833 1.461 0.810 0.418 -1.687 4.053\n", "rad_7 4.8767 1.568 3.110 0.002 1.795 7.958\n", "rad_8 4.8423 1.488 3.253 0.001 1.918 7.767\n", "rad_24 7.4563 1.780 4.188 0.000 3.958 10.954\n", "==============================================================================\n", "Omnibus: 184.084 Durbin-Watson: 1.088\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 861.138\n", "Skew: 1.555 Prob(JB): 1.01e-187\n", "Kurtosis: 8.583 Cond. No. 1.57e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.57e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=ols(\"\"\"medv ~ crim + zn + indus + chas + nox + rm + dis + tax + \n", " ptratio + black + lstat + rad_2 + rad_3 + rad_4 + rad_5 + rad_6 + \n", " rad_7 + rad_8 + rad_24\"\"\", boston_mod).fit()\n", "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notiamo che il valore di $R^2$ è rimasto invariato. Esistono ancora variabili non statisticamente rilevanti. Rimuoviamo `indus`, che ha il p-value più alto:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: medv R-squared: 0.750
Model: OLS Adj. R-squared: 0.741
Method: Least Squares F-statistic: 81.08
Date: Tue, 31 Oct 2023 Prob (F-statistic): 1.10e-133
Time: 06:44:17 Log-Likelihood: -1489.7
No. Observations: 506 AIC: 3017.
Df Residuals: 487 BIC: 3098.
Df Model: 18
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 35.1757 5.399 6.515 0.000 24.567 45.784
crim -0.1094 0.033 -3.355 0.001 -0.173 -0.045
zn 0.0541 0.014 3.891 0.000 0.027 0.081
chas 2.5593 0.856 2.990 0.003 0.878 4.241
nox -17.1366 3.605 -4.754 0.000 -24.219 -10.054
rm 3.6519 0.411 8.887 0.000 2.845 4.459
dis -1.5711 0.189 -8.312 0.000 -1.943 -1.200
tax -0.0081 0.004 -2.312 0.021 -0.015 -0.001
ptratio -0.9691 0.143 -6.765 0.000 -1.251 -0.688
black 0.0094 0.003 3.537 0.000 0.004 0.015
lstat -0.5275 0.047 -11.138 0.000 -0.621 -0.434
rad_2 1.5671 1.459 1.074 0.283 -1.300 4.435
rad_3 4.6605 1.331 3.501 0.001 2.045 7.276
rad_4 2.6052 1.182 2.205 0.028 0.284 4.927
rad_5 2.9000 1.204 2.408 0.016 0.534 5.266
rad_6 1.1244 1.451 0.775 0.439 -1.726 3.975
rad_7 4.8734 1.567 3.110 0.002 1.795 7.952
rad_8 4.7944 1.482 3.236 0.001 1.883 7.706
rad_24 7.3362 1.749 4.194 0.000 3.899 10.774
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 184.119 Durbin-Watson: 1.089
Prob(Omnibus): 0.000 Jarque-Bera (JB): 861.392
Skew: 1.555 Prob(JB): 8.93e-188
Kurtosis: 8.584 Cond. No. 1.56e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.56e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: medv R-squared: 0.750\n", "Model: OLS Adj. R-squared: 0.741\n", "Method: Least Squares F-statistic: 81.08\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 1.10e-133\n", "Time: 06:44:17 Log-Likelihood: -1489.7\n", "No. Observations: 506 AIC: 3017.\n", "Df Residuals: 487 BIC: 3098.\n", "Df Model: 18 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 35.1757 5.399 6.515 0.000 24.567 45.784\n", "crim -0.1094 0.033 -3.355 0.001 -0.173 -0.045\n", "zn 0.0541 0.014 3.891 0.000 0.027 0.081\n", "chas 2.5593 0.856 2.990 0.003 0.878 4.241\n", "nox -17.1366 3.605 -4.754 0.000 -24.219 -10.054\n", "rm 3.6519 0.411 8.887 0.000 2.845 4.459\n", "dis -1.5711 0.189 -8.312 0.000 -1.943 -1.200\n", "tax -0.0081 0.004 -2.312 0.021 -0.015 -0.001\n", "ptratio -0.9691 0.143 -6.765 0.000 -1.251 -0.688\n", "black 0.0094 0.003 3.537 0.000 0.004 0.015\n", "lstat -0.5275 0.047 -11.138 0.000 -0.621 -0.434\n", "rad_2 1.5671 1.459 1.074 0.283 -1.300 4.435\n", "rad_3 4.6605 1.331 3.501 0.001 2.045 7.276\n", "rad_4 2.6052 1.182 2.205 0.028 0.284 4.927\n", "rad_5 2.9000 1.204 2.408 0.016 0.534 5.266\n", "rad_6 1.1244 1.451 0.775 0.439 -1.726 3.975\n", "rad_7 4.8734 1.567 3.110 0.002 1.795 7.952\n", "rad_8 4.7944 1.482 3.236 0.001 1.883 7.706\n", "rad_24 7.3362 1.749 4.194 0.000 3.899 10.774\n", "==============================================================================\n", "Omnibus: 184.119 Durbin-Watson: 1.089\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 861.392\n", "Skew: 1.555 Prob(JB): 8.93e-188\n", "Kurtosis: 8.584 Cond. No. 1.56e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.56e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=ols(\"\"\"medv ~ crim + zn + chas + nox + rm + dis + tax + \n", " ptratio + black + lstat + rad_2 + rad_3 + rad_4 + rad_5 + rad_6 + \n", " rad_7 + rad_8 + rad_24\"\"\", boston_mod).fit()\n", "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notiamo che l'adjusted $R^2$ è leggermente salito. Ciò indica che il regressore trovato è leggermente migliore degli altri. Esistono ancora variabili non rilvanti statisticamente. Rimuoviamo `rad6` che ha il p-value più alto:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: medv R-squared: 0.749
Model: OLS Adj. R-squared: 0.741
Method: Least Squares F-statistic: 85.88
Date: Tue, 31 Oct 2023 Prob (F-statistic): 1.56e-134
Time: 06:44:22 Log-Likelihood: -1490.0
No. Observations: 506 AIC: 3016.
Df Residuals: 488 BIC: 3092.
Df Model: 17
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 36.0716 5.272 6.842 0.000 25.713 46.430
crim -0.1099 0.033 -3.375 0.001 -0.174 -0.046
zn 0.0529 0.014 3.830 0.000 0.026 0.080
chas 2.5397 0.855 2.970 0.003 0.860 4.220
nox -17.4021 3.587 -4.852 0.000 -24.449 -10.355
rm 3.6414 0.411 8.870 0.000 2.835 4.448
dis -1.5824 0.188 -8.400 0.000 -1.953 -1.212
tax -0.0077 0.003 -2.216 0.027 -0.014 -0.001
ptratio -0.9780 0.143 -6.851 0.000 -1.258 -0.698
black 0.0094 0.003 3.554 0.000 0.004 0.015
lstat -0.5262 0.047 -11.123 0.000 -0.619 -0.433
rad_2 0.9497 1.222 0.777 0.438 -1.452 3.351
rad_3 4.0559 1.078 3.762 0.000 1.938 6.174
rad_4 1.9660 0.846 2.324 0.021 0.304 3.628
rad_5 2.2505 0.865 2.603 0.010 0.552 3.949
rad_7 4.2718 1.360 3.140 0.002 1.599 6.945
rad_8 4.1634 1.237 3.365 0.001 1.732 6.595
rad_24 6.5600 1.434 4.575 0.000 3.743 9.377
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 183.149 Durbin-Watson: 1.089
Prob(Omnibus): 0.000 Jarque-Bera (JB): 853.017
Skew: 1.548 Prob(JB): 5.89e-186
Kurtosis: 8.557 Cond. No. 1.52e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.52e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: medv R-squared: 0.749\n", "Model: OLS Adj. R-squared: 0.741\n", "Method: Least Squares F-statistic: 85.88\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 1.56e-134\n", "Time: 06:44:22 Log-Likelihood: -1490.0\n", "No. Observations: 506 AIC: 3016.\n", "Df Residuals: 488 BIC: 3092.\n", "Df Model: 17 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 36.0716 5.272 6.842 0.000 25.713 46.430\n", "crim -0.1099 0.033 -3.375 0.001 -0.174 -0.046\n", "zn 0.0529 0.014 3.830 0.000 0.026 0.080\n", "chas 2.5397 0.855 2.970 0.003 0.860 4.220\n", "nox -17.4021 3.587 -4.852 0.000 -24.449 -10.355\n", "rm 3.6414 0.411 8.870 0.000 2.835 4.448\n", "dis -1.5824 0.188 -8.400 0.000 -1.953 -1.212\n", "tax -0.0077 0.003 -2.216 0.027 -0.014 -0.001\n", "ptratio -0.9780 0.143 -6.851 0.000 -1.258 -0.698\n", "black 0.0094 0.003 3.554 0.000 0.004 0.015\n", "lstat -0.5262 0.047 -11.123 0.000 -0.619 -0.433\n", "rad_2 0.9497 1.222 0.777 0.438 -1.452 3.351\n", "rad_3 4.0559 1.078 3.762 0.000 1.938 6.174\n", "rad_4 1.9660 0.846 2.324 0.021 0.304 3.628\n", "rad_5 2.2505 0.865 2.603 0.010 0.552 3.949\n", "rad_7 4.2718 1.360 3.140 0.002 1.599 6.945\n", "rad_8 4.1634 1.237 3.365 0.001 1.732 6.595\n", "rad_24 6.5600 1.434 4.575 0.000 3.743 9.377\n", "==============================================================================\n", "Omnibus: 183.149 Durbin-Watson: 1.089\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 853.017\n", "Skew: 1.548 Prob(JB): 5.89e-186\n", "Kurtosis: 8.557 Cond. No. 1.52e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.52e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=ols(\"\"\"medv ~ crim + zn + chas + nox + rm + dis + tax + \n", " ptratio + black + lstat + rad_2 + rad_3 + rad_4 + rad_5 + \n", " rad_7 + rad_8 + rad_24\"\"\", boston_mod).fit()\n", "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Proseguiamo rimuovendo `rad2`:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: medv R-squared: 0.749
Model: OLS Adj. R-squared: 0.741
Method: Least Squares F-statistic: 91.29
Date: Tue, 31 Oct 2023 Prob (F-statistic): 2.17e-135
Time: 06:44:23 Log-Likelihood: -1490.3
No. Observations: 506 AIC: 3015.
Df Residuals: 489 BIC: 3087.
Df Model: 16
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 36.5878 5.228 6.999 0.000 26.316 46.859
crim -0.1104 0.033 -3.393 0.001 -0.174 -0.046
zn 0.0528 0.014 3.829 0.000 0.026 0.080
chas 2.5090 0.854 2.938 0.003 0.831 4.187
nox -17.5190 3.582 -4.891 0.000 -24.557 -10.481
rm 3.6650 0.409 8.956 0.000 2.861 4.469
dis -1.5974 0.187 -8.527 0.000 -1.965 -1.229
tax -0.0082 0.003 -2.430 0.015 -0.015 -0.002
ptratio -0.9814 0.143 -6.881 0.000 -1.262 -0.701
black 0.0094 0.003 3.551 0.000 0.004 0.015
lstat -0.5240 0.047 -11.100 0.000 -0.617 -0.431
rad_3 3.7017 0.977 3.790 0.000 1.783 5.621
rad_4 1.6623 0.750 2.217 0.027 0.189 3.135
rad_5 1.9304 0.760 2.541 0.011 0.438 3.423
rad_7 3.9667 1.302 3.047 0.002 1.408 6.525
rad_8 3.8288 1.160 3.302 0.001 1.550 6.107
rad_24 6.4209 1.422 4.515 0.000 3.627 9.215
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 182.880 Durbin-Watson: 1.086
Prob(Omnibus): 0.000 Jarque-Bera (JB): 852.759
Skew: 1.545 Prob(JB): 6.69e-186
Kurtosis: 8.559 Cond. No. 1.51e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.51e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: medv R-squared: 0.749\n", "Model: OLS Adj. R-squared: 0.741\n", "Method: Least Squares F-statistic: 91.29\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 2.17e-135\n", "Time: 06:44:23 Log-Likelihood: -1490.3\n", "No. Observations: 506 AIC: 3015.\n", "Df Residuals: 489 BIC: 3087.\n", "Df Model: 16 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 36.5878 5.228 6.999 0.000 26.316 46.859\n", "crim -0.1104 0.033 -3.393 0.001 -0.174 -0.046\n", "zn 0.0528 0.014 3.829 0.000 0.026 0.080\n", "chas 2.5090 0.854 2.938 0.003 0.831 4.187\n", "nox -17.5190 3.582 -4.891 0.000 -24.557 -10.481\n", "rm 3.6650 0.409 8.956 0.000 2.861 4.469\n", "dis -1.5974 0.187 -8.527 0.000 -1.965 -1.229\n", "tax -0.0082 0.003 -2.430 0.015 -0.015 -0.002\n", "ptratio -0.9814 0.143 -6.881 0.000 -1.262 -0.701\n", "black 0.0094 0.003 3.551 0.000 0.004 0.015\n", "lstat -0.5240 0.047 -11.100 0.000 -0.617 -0.431\n", "rad_3 3.7017 0.977 3.790 0.000 1.783 5.621\n", "rad_4 1.6623 0.750 2.217 0.027 0.189 3.135\n", "rad_5 1.9304 0.760 2.541 0.011 0.438 3.423\n", "rad_7 3.9667 1.302 3.047 0.002 1.408 6.525\n", "rad_8 3.8288 1.160 3.302 0.001 1.550 6.107\n", "rad_24 6.4209 1.422 4.515 0.000 3.627 9.215\n", "==============================================================================\n", "Omnibus: 182.880 Durbin-Watson: 1.086\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 852.759\n", "Skew: 1.545 Prob(JB): 6.69e-186\n", "Kurtosis: 8.559 Cond. No. 1.51e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.51e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=ols(\"\"\"medv ~ crim + zn + chas + nox + rm + dis + tax + \n", " ptratio + black + lstat + rad_3 + rad_4 + rad_5 + \n", " rad_7 + rad_8 + rad_24\"\"\", boston_mod).fit()\n", "model.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Non ci sono più variabili non significative. Il regressore trovato è quello finale. Va notato che i coefficienti delle variabili sono leggermente cambiati rispetto al regressore che conteneva tutte le variabili." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **🙋‍♂️ Domanda 4**\n", ">\n", "> Si calcolino i valori MSE per il primo regressore trovato (quello contenente tutte le variabili) e l'ultimo (quello contenente solo variabili significative). Esistono differenze tra i due valori?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Residual Plots\n", "\n", "Possiamo visualizzare i residual plots e i Q-Q plot dei residui di un regressore lineare mediante `statsmodels`:" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import statsmodels.api as sm\n", "model=ols(\"\"\"medv ~ crim + zn + chas + nox + rm + dis + tax + \n", " ptratio + black + lstat + rad_3 + rad_4 + rad_5 + \n", " rad_7 + rad_8 + rad_24\"\"\", boston_mod).fit()\n", "\n", "#otteniamo i valori predetti dal modello:\n", "fitted = model.fittedvalues.fillna(0) #rimpiazzo eventuali NaN con zero\n", "\n", "plt.figure(figsize=(20,22))\n", "sns.residplot(x=fitted, y='medv', data=boston_mod.dropna(),lowess=True,line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8}, ax=plt.subplot(421))\n", "sm.qqplot(fitted-boston_mod.dropna()['medv'], line='45',fit=True, ax=plt.subplot(422))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estensioni al Modello Lineare\n", "La API `formula` di `statsmodels` rende semplice inserire deviazioni dal modello lineare. Vediamo degli esempi con il dataset **Auto MPG**. Carichiamo il dataset:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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displacementcylindershorsepowerweightaccelerationmodel_yearoriginmpg
0307.08130.0350412.070118.0
1350.08165.0369311.570115.0
2318.08150.0343611.070118.0
3304.08150.0343312.070116.0
4302.08140.0344910.570117.0
...........................
393140.0486.0279015.682127.0
39497.0452.0213024.682244.0
395135.0484.0229511.682132.0
396120.0479.0262518.682128.0
397119.0482.0272019.482131.0
\n", "

398 rows × 8 columns

\n", "
" ], "text/plain": [ " displacement cylinders horsepower weight acceleration model_year \\\n", "0 307.0 8 130.0 3504 12.0 70 \n", "1 350.0 8 165.0 3693 11.5 70 \n", "2 318.0 8 150.0 3436 11.0 70 \n", "3 304.0 8 150.0 3433 12.0 70 \n", "4 302.0 8 140.0 3449 10.5 70 \n", ".. ... ... ... ... ... ... \n", "393 140.0 4 86.0 2790 15.6 82 \n", "394 97.0 4 52.0 2130 24.6 82 \n", "395 135.0 4 84.0 2295 11.6 82 \n", "396 120.0 4 79.0 2625 18.6 82 \n", "397 119.0 4 82.0 2720 19.4 82 \n", "\n", " origin mpg \n", "0 1 18.0 \n", "1 1 15.0 \n", "2 1 18.0 \n", "3 1 16.0 \n", "4 1 17.0 \n", ".. ... ... \n", "393 1 27.0 \n", "394 2 44.0 \n", "395 1 32.0 \n", "396 1 28.0 \n", "397 1 31.0 \n", "\n", "[398 rows x 8 columns]" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from ucimlrepo import fetch_ucirepo \n", " \n", "# fetch dataset \n", "auto_mpg = fetch_ucirepo(id=9) \n", " \n", "# data (as pandas dataframes) \n", "X = auto_mpg.data.features \n", "y = auto_mpg.data.targets \n", " \n", "data = X.join(y)\n", "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calcoliamo un semplice regressore lineare:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: mpg R-squared: 0.706
Model: OLS Adj. R-squared: 0.705
Method: Least Squares F-statistic: 467.9
Date: Tue, 31 Oct 2023 Prob (F-statistic): 3.06e-104
Time: 07:08:31 Log-Likelihood: -1121.0
No. Observations: 392 AIC: 2248.
Df Residuals: 389 BIC: 2260.
Df Model: 2
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 45.6402 0.793 57.540 0.000 44.081 47.200
horsepower -0.0473 0.011 -4.267 0.000 -0.069 -0.026
weight -0.0058 0.001 -11.535 0.000 -0.007 -0.005
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 35.336 Durbin-Watson: 0.858
Prob(Omnibus): 0.000 Jarque-Bera (JB): 45.973
Skew: 0.683 Prob(JB): 1.04e-10
Kurtosis: 3.974 Cond. No. 1.15e+04


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.15e+04. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: mpg R-squared: 0.706\n", "Model: OLS Adj. R-squared: 0.705\n", "Method: Least Squares F-statistic: 467.9\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 3.06e-104\n", "Time: 07:08:31 Log-Likelihood: -1121.0\n", "No. Observations: 392 AIC: 2248.\n", "Df Residuals: 389 BIC: 2260.\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 45.6402 0.793 57.540 0.000 44.081 47.200\n", "horsepower -0.0473 0.011 -4.267 0.000 -0.069 -0.026\n", "weight -0.0058 0.001 -11.535 0.000 -0.007 -0.005\n", "==============================================================================\n", "Omnibus: 35.336 Durbin-Watson: 0.858\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 45.973\n", "Skew: 0.683 Prob(JB): 1.04e-10\n", "Kurtosis: 3.974 Cond. No. 1.15e+04\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.15e+04. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ols(\"mpg ~ horsepower + weight\", data).fit().summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il regressore è statisticamente lineare e ha un $R^2=0.706$. Visualizziamo residual e Q-Q plot:" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import statsmodels.api as sm\n", "model=ols(\"mpg ~ horsepower + weight\", data).fit()\n", "\n", "#otteniamo i valori predetti dal modello:\n", "fitted = model.fittedvalues.fillna(0) #rimpiazzo eventuali NaN con zero\n", "\n", "plt.figure(figsize=(20,22))\n", "sns.residplot(x=fitted, y='mpg', data=data.dropna(),lowess=True,line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8}, ax=plt.subplot(421))\n", "sm.qqplot(fitted-data.dropna()['mpg'], line='45',fit=True, ax=plt.subplot(422))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interaction terms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aggiungiamo un termine di interazione tra \"weight\" e \"horsepower\":" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: mpg R-squared: 0.748
Model: OLS Adj. R-squared: 0.746
Method: Least Squares F-statistic: 384.8
Date: Tue, 31 Oct 2023 Prob (F-statistic): 7.26e-116
Time: 07:17:40 Log-Likelihood: -1090.7
No. Observations: 392 AIC: 2189.
Df Residuals: 388 BIC: 2205.
Df Model: 3
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 63.5579 2.343 27.127 0.000 58.951 68.164
horsepower -0.2508 0.027 -9.195 0.000 -0.304 -0.197
weight -0.0108 0.001 -13.921 0.000 -0.012 -0.009
weight:horsepower 5.355e-05 6.65e-06 8.054 0.000 4.05e-05 6.66e-05
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 34.175 Durbin-Watson: 0.904
Prob(Omnibus): 0.000 Jarque-Bera (JB): 54.522
Skew: 0.577 Prob(JB): 1.45e-12
Kurtosis: 4.417 Cond. No. 4.77e+06


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 4.77e+06. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: mpg R-squared: 0.748\n", "Model: OLS Adj. R-squared: 0.746\n", "Method: Least Squares F-statistic: 384.8\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 7.26e-116\n", "Time: 07:17:40 Log-Likelihood: -1090.7\n", "No. Observations: 392 AIC: 2189.\n", "Df Residuals: 388 BIC: 2205.\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "=====================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "-------------------------------------------------------------------------------------\n", "Intercept 63.5579 2.343 27.127 0.000 58.951 68.164\n", "horsepower -0.2508 0.027 -9.195 0.000 -0.304 -0.197\n", "weight -0.0108 0.001 -13.921 0.000 -0.012 -0.009\n", "weight:horsepower 5.355e-05 6.65e-06 8.054 0.000 4.05e-05 6.66e-05\n", "==============================================================================\n", "Omnibus: 34.175 Durbin-Watson: 0.904\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 54.522\n", "Skew: 0.577 Prob(JB): 1.45e-12\n", "Kurtosis: 4.417 Cond. No. 4.77e+06\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 4.77e+06. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ols(\"mpg ~ horsepower + weight + weight*horsepower\", data).fit().summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il valore di $R^2$ si è alzato di un po' ed è ora $0.748$. La relazione introdotto è statisticamente rilevante. Visualizziamo i residual plot:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import statsmodels.api as sm\n", "model=ols(\"mpg ~ horsepower + weight + horsepower*weight\", data).fit()\n", "\n", "#otteniamo i valori predetti dal modello:\n", "fitted = model.fittedvalues.fillna(0) #rimpiazzo eventuali NaN con zero\n", "\n", "plt.figure(figsize=(20,22))\n", "sns.residplot(x=fitted, y='mpg', data=data.dropna(),lowess=True,line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8}, ax=plt.subplot(421))\n", "sm.qqplot(fitted-data.dropna()['mpg'], line='45',fit=True, ax=plt.subplot(422))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I residui sono meno correlati con la variabile predetta e il Q-Q plot mostra una deviazione minore dalla Gaussiana. Il modello \"spiega\" meglio i dati. \n", "\n", "### Modello Quadratico\n", "Proviamo a fare fit di un modello quadratico:" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: mpg R-squared: 0.688
Model: OLS Adj. R-squared: 0.686
Method: Least Squares F-statistic: 428.0
Date: Tue, 31 Oct 2023 Prob (F-statistic): 5.40e-99
Time: 07:25:55 Log-Likelihood: -1133.2
No. Observations: 392 AIC: 2272.
Df Residuals: 389 BIC: 2284.
Df Model: 2
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 56.9001 1.800 31.604 0.000 53.360 60.440
horsepower -0.4662 0.031 -14.978 0.000 -0.527 -0.405
I(horsepower ** 2) 0.0012 0.000 10.080 0.000 0.001 0.001
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 16.158 Durbin-Watson: 1.078
Prob(Omnibus): 0.000 Jarque-Bera (JB): 30.662
Skew: 0.218 Prob(JB): 2.20e-07
Kurtosis: 4.299 Cond. No. 1.29e+05


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.29e+05. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: mpg R-squared: 0.688\n", "Model: OLS Adj. R-squared: 0.686\n", "Method: Least Squares F-statistic: 428.0\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 5.40e-99\n", "Time: 07:25:55 Log-Likelihood: -1133.2\n", "No. Observations: 392 AIC: 2272.\n", "Df Residuals: 389 BIC: 2284.\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "======================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "--------------------------------------------------------------------------------------\n", "Intercept 56.9001 1.800 31.604 0.000 53.360 60.440\n", "horsepower -0.4662 0.031 -14.978 0.000 -0.527 -0.405\n", "I(horsepower ** 2) 0.0012 0.000 10.080 0.000 0.001 0.001\n", "==============================================================================\n", "Omnibus: 16.158 Durbin-Watson: 1.078\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 30.662\n", "Skew: 0.218 Prob(JB): 2.20e-07\n", "Kurtosis: 4.299 Cond. No. 1.29e+05\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.29e+05. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ols(\"mpg ~ horsepower + I(horsepower**2)\", data).fit().summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Da notare che è necessario specificare `I(horsepower**2)` per aggiungere il termine quadratico (semplicemente `horsepower**2` verrebbe ignorato). Il modello ha un $R^2$ inferiore al modello con termine di interazione, ma comunque superiore al modello base:" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: mpg R-squared: 0.606
Model: OLS Adj. R-squared: 0.605
Method: Least Squares F-statistic: 599.7
Date: Tue, 31 Oct 2023 Prob (F-statistic): 7.03e-81
Time: 07:27:30 Log-Likelihood: -1178.7
No. Observations: 392 AIC: 2361.
Df Residuals: 390 BIC: 2369.
Df Model: 1
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 39.9359 0.717 55.660 0.000 38.525 41.347
horsepower -0.1578 0.006 -24.489 0.000 -0.171 -0.145
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 16.432 Durbin-Watson: 0.920
Prob(Omnibus): 0.000 Jarque-Bera (JB): 17.305
Skew: 0.492 Prob(JB): 0.000175
Kurtosis: 3.299 Cond. No. 322.


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: mpg R-squared: 0.606\n", "Model: OLS Adj. R-squared: 0.605\n", "Method: Least Squares F-statistic: 599.7\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 7.03e-81\n", "Time: 07:27:30 Log-Likelihood: -1178.7\n", "No. Observations: 392 AIC: 2361.\n", "Df Residuals: 390 BIC: 2369.\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 39.9359 0.717 55.660 0.000 38.525 41.347\n", "horsepower -0.1578 0.006 -24.489 0.000 -0.171 -0.145\n", "==============================================================================\n", "Omnibus: 16.432 Durbin-Watson: 0.920\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 17.305\n", "Skew: 0.492 Prob(JB): 0.000175\n", "Kurtosis: 3.299 Cond. No. 322.\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ols(\"mpg ~ horsepower\", data).fit().summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vediamo i residual plot:" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "image/png": 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fotf3vw8ej9ujkyjoWRJJI00VPKWVda0qeBatLnV7aHGxsayGHJ+31bYcn5dNZTUujUhERERERGJiLbz6Khx9NJx2GlRXwyOPwMqVcNZZCpNSiKvPlDHmL8aYUmPMxy229THGvG6M+azxtLebYxRJJS0reIxxTn1ew5zFxW4PLS6G9M4Nu6zo4N65Lo1IRCR9GGOGGGP+a4z51BizyhhzudtjEhGRNPPf/7Jz3FFwyilsWvMFv/v+r/jn4wvg/PPB623/+pJU3I7+/gacvNe2a4D/WGsPAv7TeF5EopDuFTzTJ4/AH7TUNASw1jn1By3TJ49we2giIukgAFxlrT0EmAD83BjzFZfHJCIiKW7+shIuvvh+3j7gcDj+ePzF6/ntty7hG0VzmHvgFK554VPmLytxe5jSAa72ULLWLjbGDNtr82nAlMZ//x1YBFzddaMSSV1DeudSWlnX3GMI0quCZ8roQmbhVGJtKqthcJr1iBIRcZO1dguwpfHflcaYT4FBwCeuDkxERFLO/GUlzH5tDX0/XcFVbzzKn9YvZXteATd98yIeP+IU6jMymy9b6w8y+7U1ToNuSSnJ2JR7QOMXGqy1W4wxYY8UjTFFQBHA0KFDu3B4Islr+uQRzHxhFTUNAXJ8Xmr9wbSt4LFx2k86NzEXEemoxj/4jQPedXkoIiKSYuYvK+HvD87nxkX/4MR177Erpye/m/JjHhl3KrWZ2WGvs7m8totHKfGQjIFSVKy1c4G5AOPHj4/XsaVISkv3Cp6mpuM+r2nVdHwWdOg+xnt/IiLpwBjTA3gW+KW1dneY3+uPeiIiEt4nn9DzRz/j+Y8XU5GVx53Hnc9fj5xKdVbbMyb2L8jpogFKPCVjoLTNGLNfY3XSfkB6LE8l0kWmjC5M2zCkZdNxgNzMDGoaAsxZXNyh+xzv/YmIpDpjjA8nTHrMWvtcuMvoj3oiIrKPtWvhpptg3jyO8mVz3zHn8uevnc7u7B7tXjXH52XGSaO6YJASb8kYKL0A/B9we+PpP90djqQyTWdKLxvLaijI8bXa1pmm4/Hen4hIKjPGGODPwKfW2rvdHo+IiKSA9evh5pvhH/8g4MvkiePO5q7Dp1KW2yviVXweQ4/sDMpr/OxfkMOMk0apf1KKcjVQMsbMw2nA3c8Yswm4ASdIesoY81PgS+As90YoqUzTmdJPvJuOp3sT80RSWCuSlo4FfgisNMYsb9z2G2vty+4NSUREktLGjXDrrfDnP4PXy7pzfswFhcezKatn2IsbnB6ogxQgpRW3V3mbFuFX3+zSgUha0nSm9BPvpuPdqYl5PLkZ1irIEkkca+2bON/5RUREwtuyBW67DebMAWuhqAh+8xv+75E1lERorK0QKX153B6ASKJsLKshx+dttU3TmVLblNGFzJo6hsL8bCpq/RTmZzNr6pgOBwrx3l930TKsNcY59XkNcxYXJ/R2m4Ks0sq6VkHWotVqtSciIiKSUNu3w4wZMHIkPPgg/PCH8NlnzL/wNxzbRphkgLeuOV5hUppKxh5KInGh6UzpKd5Nx9O5iXmiuNV7SlWHIiIiIl2srAzuvBPuuw9qa+G882DmTOZX5nDj31ZRXutv8+pavS29KVCStKXpTKkl2qlMmvLkPrfCWjVRFxEREekiu3fDvffC3XdDRQX/OWwKvzvqHDb0H0rw4TXNPZHaotXb0p8CJUlbU0YXMgunqmFTWQ2DFT7EpCuDm2h78qjRenJwK6xV1aGIiIhIglVXwwMPwOzZsGsXm79xEj878DRW9Bnq/N46MVJ7YZL6JnUPCpQkrWk6U8d0dXAT7VQmTXlKDm6Ftao6FBEREUmQ2lr44x/h9tudfknf/jb//cEvuPBjS9C2Fx+1Nqggh7euOT5BA5VkokBJRPbR1cFNtFOZUmnKU7pPzXMjrFXVoYiIiEic1dfDww/Drbc6K7h985v87/zLuPyLbMpXtt0fKRxNc+teFCiJyD66OriJdipTqkx50tS8xFHVYXyle/ApIiIiEfj98Le/wS23wJdfwnHH8cas+7m0pCflq/1A7GFS71wfN3x3jKa5dSMetwcgIslnSO9cav3BVtsSGdxMnzwCf9BS0xDAWuc03FSmaC/ntpYVXsY4pz6vYc7iYreHJtKsKfgsraxrFXwuWl3q9tBEREQkUYJB+Mc/YPRoKCqCgQPhtdeYf+/jFH3Ro91V21oyjaeDCnK495wjWDbzWwqTuhlVKInIPrq6V020U5lSZcpTKk3Nk+5LPclERES6kVAInnoKbrwR1qyhfPSh3PqjW3h64OGYhX4sK2LanZpuCyhQEpEw3Ahuop3KlApTnlJlap50bwo+RUREugFrYf58mDkTPv4Yxozh3dlz+XH5IGoC0a3Y1iTH5+W2Mw5TiCTNFCiJSFipENwkK61GJqlAwaeIiEgasxZefpnyX11LweqVfN5nEPd9dwYvjZ5EaIeX6GMkh/ojSTgKlERE4ixVpuZJ96bgU0REJA1ZCwsWwPXXw7vvsrvXAG7+9hXMHzOFoMcb8+4UJElbFChJWtMKRuIWVXhJslPwKSIikmYWL3aCpMWLqRm4Pzef9AuePuwEAt7YD/u9xnDX2YcrSJI2KVCStKWl26W7UHAqHaXgU0REJA0sWeIESQsWwH77seLXN3Nu6DBqOxAkAfi8htlnKkyS9nncHoBIomjpdukOtPS7iIiISDf14Ydw6qkwcSIsX87KK2dyxI8e5DQzrsNhUu9cn8IkiZoqlCRtaQUj6Q7aWvq96ffdoXJJVVqpQc+TiIhIHKxcCTfcAM8/D717w+9+x6xhx/OXFTti3pWqkaQzFChJ2tIKRtIZqXLgGyk4/ay0MiWmfN6/YC0Pv7me6oYgeZleLpw0nMtOODimfWh6a2rQ8yQiItJJq1fDjTfCU09Bfj7ceCMvfeNsrvvvRso7ECap4bZ0lgIlSVtawUg6KpUOfCMFpw2BEL1ywlcuJfI+xBLE3b9gLfctXIfHQIbHGfd9C9cBxBQqtVWllWzPV3em50lERKSDPv8cZs2CRx8lkJXN3489m/u/ejoVtfnwcnTtPNRkWxJBPZQkbU0ZXcisqWMozM+motZPYX42s6aO0YGLtCuV+m9NnzwCf9BS0xDAWufUH7T4vIYcX+ulYRM95TPWfk4Pv7m+MUzy4DGexlNneyw2ltV0+X2V2Ol5EhERidEXX8BFF8GoUQSffJK/HHU6R134EDcf+0MqcvKj3o0BhUmSEKpQkrSWzCsYpcqUqu4olfpvRVr6fc7i4i6f8hlrBUp1Q5CMvf6s4THO9lhoemtq0PMkIiISnVf//SEV193E9z58BWvg8SO+zYMTzmJ7jz4d2t95E4YqTJKEUKAk4oJUmlLVHXXlgW88gsVIwWlXT/mMNYjLy3TG5TF7toWssz0Wmt6aGvQ8iYiItKO0lLcu/BVTXnkSbyjI04edyAPHnMOWnv07tLu8TC+3fu8whUmSMAqURFygXiLJrasOfBMZLEaqXErk66utIC5ccHbhpOHct3AdgVAIj3HCpJCFCycNj+l23bivEjs9TyIiIuH9678fs/m6WZz3/gtMCPh5bszx3H/suWwsGNih/anZtnQVBUqSVmKp9nBzylkqTanqjrrqwDfRwWJXT/mMFMRNHNEnfHA2dQyXH39gp1d5g+Se3ir7sm4PQEREJAn8a/EnbLjuVn707vPkNdTx4iGTue/YaRT3HdzhfZ4/YSi3nH5YHEcpEpkCJUkbsVR7uD3lTL1Ekl9XBBTpFiy21c8pUnA2r2hChwIkST1uf+6KiIgkg/nLSrh53hLOXfJPit57jlPrq3n54GO4d9IPWNt/WIf3q6okcYMCJUkbsVR7uD3lTL1EBFI7WIxU4RcuiLvunx+nVXAmHTNncTH+YJCdVQEagiEyvR565mRoqm8HGGNGApustfXGmCnAWOAf1tpyN8clIiKtzV9Wwo0vrKK81g9Atr+OHy39F/9+91n61u7m9QOP4t5J57FqwMiY963+SJIMFChJ2oil2sPtyhD1Ekkebk59TNVgMdZKEzeDM62mmDw+K62kosaPx2PwegyBkGVHZQP+YKXbQ0tFzwLjjTEHAn8GXgAeB77d2R0bY/4CfAcotdYe2tn9iYh0V/OXlTDj6RX4Q5asQAPTlr/Kz5c8Rf/qchYPG8fdx53P8v1HxbxfVSJJMlGgJEmpIweB4Q5ad1bXU10fZNIdC1vtJxkqQ9TzxX1uT8FJ1WAx1go/t4Izt59faa0hEAIDHuMs62cMhIx1tkusQtbagDHme8C91toHjDHL4rTvvwG/B/4Rp/2JiHRLN724CvwNnPfR6/z8nafYv3IHS4Ycys9Ov5YPBo+Jej/qiSTJTIGSJJ2OHgTufdC6s7qe0soG+vfI3Gc/qVoZIvHl9tRHSM1gMdYKv3gGZ7GEzcnw/MoePq+h1g+hkMUYsI2duTO9xt2BpSa/MWYa8H/Adxu3+dq4fNSstYuNMcPisS8Rke5q5rPLOGHJy1z29hMMqdjGh/uP5lff/iVvH3C48xeVKGhKm6QCBUqSdDp6ELj3QWt1fZD+PTLpn5+9z37mFU1IycoQiS+3pz6mqo5U+EUKzmJdmfFXz6ygqj5AMGTZUVXPr55ZwZ1nHh72Onp+k8vBA3qyfkcVlXV7eijlZ/sY3q+H20NLRT8GLgZutdauN8YMBx51eUwiIhIM8ofpN3PBcw8xomwzHw08kOtP/BmLRhwZVZCkEElSTdIGSsaYDUAlEAQC1trx7o5IYtGZviWdOQhsedA66Y6Fbe7H7coQ9XZxXzJMfUxF8arwi7Ua8fZXPqW8xo/XGLzGYENQXuPn9lc+TbreTU30Pt+j6XUzsFeGKkM7yVr7iTHmamBo4/n1wO1ddfvGmCKgCGDo0KFddbMiIskrFGLeNfdw5F/u5+c7v+TT/sO46IzreP3AoxUkSVrzuD2AdnzDWnuEwqTU0nSQWFpZ1+ogcdHq0qiuP6R3LrX+YKttHTkIjNd+EqGzj5HEx/TJI/AHLTUNAax1TnWA274powuZNXUMhfnZVNT6KczPZtbUMTEHJS2rEY1xTn1ew5zFxWEvv35nDR4DHo/BGIPHY/AYZ3s47T2/i1aXMm3uEibdsZBpc5fE/f2n93lr8XrdCBhjvgssB15tPH+EMeaFrrp9a+1ca+14a+34/v37d9XNiogkH2vhhRf44oDRTJv9Kzw2xM+nXs23f3w/rx80oc0wKS/Ty73nHMGG209l1ayTFSZJSkraCiVJXZ3tWxKv6odk7pOk3i776opKjnC3MWvqmJSf+uhGFUw8KvwSPSWtrd5NXdGwW+/zfbldGZpGbgSOAhYBWGuXN057ExGRrmAtvPYaZb+6ht6rVhDqvR+//M5VvHDIZEIeb8Sr+byG2WcervBI0kYyB0oW+LcxxgJzrLVz3R6QRKezB4nxauCbzCtoqbdLa11xcB/xNqaOYV7RhLjchhtSeSWzWKekjeiXx2elVRi7p6lzyMJB/fMi3kakAKMjYU+swZ3e55JAAWtthWn9l28bjx0bY+YBU4B+xphNwA3W2j/HY98iIqlq/rISrn3uI2r9ISZ+8RFXvvEoXyv5hOqehfzulMt47tBvEmwjSAJNa5P0lMyB0rHW2s3GmELgdWPMamvt4qZfav5+8opH35J4/RU7Wf8angy9XZJJV1RypGu1SCrfr7aqCMOFN1efPJoZz6ygsi5AIBgiw+Ohd66Pq08eHfNtxxr2dCS40/tcEuhjY8wPAK8x5iDgMuDteOzYWjstHvsREUkX85eVcOWTyxm36ROueuNRjvnyI7b06Mt137qEJ8eeiN/b/iKbx47sw2MXTeyC0Yp0raTtoWSt3dx4Wgo8j1Pa3fL3mr+fpNK1L008+62k62PUURvLasjxtf6rTrwrObriNtyQbPcrlvdJpJ46QNjeQwCzzzyccUN7s1+vHMYN7c3sCCu8tSfWHmux9nsCvc8loS4FxgD1wDxgN/BLNwckIpKO5i8r4a/3PsVfn5rJs4/9moN2fslN37yIKdMf4tFx31aYJN1eUlYoGWPyAI+1trLx398CZrk8rKSSzCsHJfNUs46K97SidHyMOqMrKjnStVokme5XR94n4aoIp81dErHqal7RhLi8T2LtsdaR6Wt6n0uiWGtrgN82/oiISAJcO/MfHD/vQf657l125fTktikX8I9x36E2Mzuq62dleLjj+2M1xU3SWlIGSsAA4PnG3gAZwOPW2lfjeQPJHMi0JxV6piTrVLOOSsS0onR7jDqjKxqoJ3OT9s5w636F+wyN1/ukK3oPxRr2dDS40/tc4skY8yJt9Eqy1k7twuGIiKSnTz7h3R/+gtuW/pfdWXncedz5/PXIqVRnRf/HOlUlSXeRlIGStbYYODxR+0+mQKYjwVYq90xJVWqum1hdUckRj9tIxiDajSqYSJ+h1fV+9uuV0+qyHXmfdFXVVSxhT7oGkpJy7nR7ACIi6eqeB19i2B/u4rRP/seYzGzun3gODx/1PXZn94hpPwqTpDtJykAp0ZIlkOlosKVwo+sl07SiREiGoKQrKjk6cxvJFETvraurYOYsLsYfDLKzKkBDMESm10PPnAz8QUutP9jp90kyhjeavibJwFr7P7fHICKSdtav59VzLuHSD/6N3+tj7tFnMOeoMyjL7RXTbnrn+rjhu2M0xU26lW4ZKHVFIBPNAXpHg610DzeSUTIe4MZLtEFJMoRObkqWIDoWiXrOPiutpKLGj8dj8HoMgZBlR2UDOZne5ibUnXmfJGt4o+lr4jZjzFPW2rONMSsJM/XNWjvWhWGJiKSk//fw6wz6w92c/dHrfMN4+PuR3+WPE85kR17vdq97/oSh3HL6YV0wSpHkljaBUiwHTokOZKI9QO9IsLVodSll1fVs2FmNz+NhQM8sMryetAk3klWyHuDGQzRBSTJX53SVVKsMTORz1hAIEbSWYNBiLTjt7hyzpo6Jy/tE4Y1IWJc3nn7H1VGIiKSyrVt5/uyfc/nbL2KsZd7hJ/OHiWexLb9fVFc/dmQfhUkijdIiUKqsC8R04JToapNoKxliDbZaHiAOLshhW2U9m8rrOLiwB9efOloHX10kYjfUFBVNUNKZ6pxow163KqCivd1krgxMZIPscEI2RKjFG8HaptOQgiCRBLLWbmn85yXW2qtb/s4Ycwdw9b7XEhERgJcXfsSW387iBx+8xHeDfp457AQeOOZcSnpF971Fq7aJ7Mvj9gDiYXtlffOBkzHOqc9rmLO4OOzlp4wuZNbUMRTmZ1NR66cwP5tZU8fE7SBoY1kNOT5vq23hKhmmTx7RPD3EWue0rWCr5QFiz5xMDirMZ1jfXApyM3UAl2BNYV5pZV2r0HLR6lK3h9ZpQ3rnUusPttq2d1AS7Wt6b9E+bm49vrHcbqzv164S6T6s3ba7Q89ZNDzGg9eAx4DBOfUaMCYt/ksRSQUnhtl2SpePQkQkyc1fVsLRv3qK3x9zDpNPmcAF7z7Py6OO4ZsX/YlrTrks6jDp2JF9WHPLKQqTRPaSFhVKDcFQzAdOifwr+pDeuWzYWcXu2tYNa4f1bb1CQKzTqFJtyk06ScX+OdGKpmKvo9U50T5ubj2+sdxusk57THSD7HAyMzzUNhg8HoMxToVSKGTJzFCgJJJIxpifAZcAI4wxH7X4VT7wljujEhFJPtfNX8n8/63mJx/8k9ffn0/P+mpeGn0c9xz7Az7vNyTq/RjgPPVLEokoLQKlTK+HHVX1VNbtOaDKz85geL/YlniMl4kj+vDehl14Gv+C3xAMUVrZwLSv9dnnsrEEW8k85SbdpXOYF01Q0tFpotE+bm49vrHebjJO50p0g+xwDirMZ83W3ZTX+glZ53OuIMfHQYX5Ea/T3Zu6i8TJ48ArwG3ANS22V1prd7kzJBGR5DF/WQnXPrKEC5a+yBvvPkfvukpeO2gC90w6j9WFw6Pez0GFebx+5ZTEDVQkTaRFoNQjy8v2qoZWAc72qgZ+cNS+AU5XeKd4F/17ZO4TcL1TvIvLOrHfdF5pLNkN6Z3L+h1VSRNaxlt7QUlHq3OiDUGH9M5l5aYyqhpCzdt6ZHo4bHD7q2x0RjqEtA2BEBjwNHbGNgZCxmlqFK8G2XtrCs29HoPPQMhCRV2AiSPCf+aqqbtIfFhrK4AKYJoxxgsMwPku18MY08Na+6WrAxQRccl181fy9Bufcf7yV3hjydP0q6lg4Yjx3H3c+Xw88MCo9+Mx8IOjVZEkEq20CJSq6oOMys/cZ4pZZwOcjtpYVkO/Hln0z89u3mat7XS1RbJOuekOwlWduRlauqEj1TlRh6A21CpMApzztvW2eEuHkNbnNdT6nSlnTdPPADK9JmEVVbGG5uk8ZVTiLBCAnTth2zYoLd33RwAwxvwCuBHYBjR9UFpgrFtjEhHpSvOXlXDtcx9R6w+RGfBzzkev8b93nmJg1S7ePOBw7j7ufJYOOiTq/akiSaRj0iJQqm4IsLs2QL8eWfRsnL7SMsDp6qkWiax6SMYpN93BO8W7KEyi0DJVRBuCvvdFedjrR9re1eNLZgcP6Bmmes6X0Oq5WEPzdJkyqml7nVRXFz4kavlTVgZ9+kBhYeufUaOc0z//2e17kSx+CYyy1u50eyAiIl1t/rISfvnkcjKCAc75+D9c+vYTDN69nXcHj+Hy787g3aGxVRedrx5JIh2WFoFSU8XI5opaAHrm+JoDnERMtWjvoCIdqh6ktY1lNfTNy6Jfj/hWnXUH0YSgwcY16BtnbQFOpU2w5dr0jRJ1UL/vLaWGps+bgb0yOvV5E8vjGmto3tblY30+3Qp1NG2vHTU1sHWrEwpt2xa+wqiuDvr3bx0UDRkC48c72wcMgL59wett//ZkI87UNxGRbufmf37EGR//h8vfmscB5VtZvt/BXHvypbwxbFzrL5NtyMv0cuv3DtOqbSKdlBaBUobHg8FgseyoqifDa5oPqOI91SKag4p0qHqQ1tKh104y83pM2PDI62n9pSDeB/WJDAmiDT46G5C09XkTyxhieRxiDc0jXX7iiD4x3a6boU63nrZXW7snJGr5U1q6J0Ty+51AaODAPWHRV74CX/+6s71/fygoiPqLvrSrGFhkjPkXUN+00Vp7t3tDEhFJsFCIJ2fcyVN/e4CRuzbx8YCR/OT7M1k48mtR/f+iEEkk/tIiUPJ6DPsXZFO6u466QIjC/OzmA6fr/vlxXKdaxHpQ0V7Vg6ZQpAZVnSXW1LEDeX75lub+Py23txTvg/q29tf0+468N6MNPuIdkLR8+GLZd6yPa6yheaTLx3q7boY66TJtbx9N09C2bt0TEm3b1rraqL5+T1A0YIDzc8ghMGWKs23gQMjPV1jUtb5s/Mls/BERSV/W8ti19/HVv9zHOds3sKbfUKaf/hv+ffAErPG0e3X1RxJJnLQIlOr8QbZX1tMr18ewvj2YVzSh+XfxXp0rmoOKrjiYVBDVtVR1llj3nPtVYCkvfLSVYMji9Rimjh3YuH2PeB/UR9rfZ6WVnQp6og0+4hGQRPocycv0Rr3vjjyusfZzC3f5WAP/jWU1eA0Ub69q/jzv1yOzzXHG67MyJasU6+tbh0Thqovq6loHRQMGwEEHwaRJe0KkXr0UFiUZa+1Nbo9BRCThrOUf1z/IuIfv4bxtn/N5n0Fc9t0ZvDR6EiFP+9OjVZEkknhpESgBVDcEqW4I4sU5gGg6YIj36lzRHFQk+mBSvTzcoYboiTW8Xw/yMr1UNwTJy/SGDX1jOaiPJkiItL+GQIheOR0PeqINaDoS5Ox9v8qq68N+jhTvqOagwtaPYaR9uxWWxHq7+VkZfFZahddj8HoMgZClpLxun/vZJJ6flUlXpRgKwa5dsGWLEww1nTb9lJY6fY2aehMNGOCEQyNHwrHH7gmRNA0tJRlj+gO/BsYAzc39rLXHuzYoEZF4sZbbrryfk576Iz/avIYvew3gqm9fwfwxUwi2EyQZ4Dw12RbpMmkRKFmc78MeYEeNv9UBQ7xX54rmoCKRB5PQzXt5xOj+BWt5+M31zSHFhZOGc9kJB7s9rJTQlVVw9y9Yy30L1+ExkOFxQoX7Fq4DaPV8RXtQH22QEGl/Pq8hx9f6C0sslVDRBiWxBirh7teGndX0yfWxtaKuVdVO076i2bdbYUmst2ub5kQ2ze2ze23fSzw/Kztapdjh91FDQ+uAaO/gqLQUevRwqogGDoT99nMaXH/ta875prDI0/5UAElJjwFPAt8BLgb+D9ju6ohERDph/rISZjy9nHFffMxVbzzKtRs/piS/P9ec9AueOewEAt72D1vvPecIVSOJdLG0CJQMkJ3hxVpLMOQcDDYdMMR7da5oDioSdTDZJJYgqjtPjYs2pGjS3mPVnR7Lrp6O+fCb6xufJ+fg12MgEArx8JvrWz1X0R7URxsktNXbpzMVO9EGJbEGKuHul9cYdlT5yczwtKraGdgzC3/QRrXvjjT2jsf7IdaQpqohyKCCbHZUNTSHZwN7ZFHdEAx7+XhPkYy1SjHi+8hapgzK2TckanlaWbmnP9F++zmnRxwBp5yyJzDKyurQ/ZC00Nda+2djzOXW2v8B/zPG/M/tQYmIRGv+shKufe4jav0hAMaVrOYvbzzKcV8sZ1uPPsw8YTpPHH4yDRm+dvbkOHZkH4VJIi5Ii0CJxmp9ayHT62l1wDCkdy4bdlbtU6E0rG/HeihB+wcViTqYBCck2VJRx6ayWjwG+uVlMqBXTtiD3e4+NS7akALaf6wS8Vgmc0DV1dMxqxuCZOxVSOExhA0KojmojyVIiLS/zlTsRBuUxBqohLtfhsZCnb2qdnpkZXDNKYfE1Dh7799Fej7P3FTOI0u+oLIuQCAUYkdlPTOeWcHsMw/vUKgU7XWaQvgR/fd8ftc0BCjMz27z8vGayhf1ezYYhO3befWxf3Psli0MqC2nz+6d9N69i/zyHQx4qAIG9doTFDWdfuUre8737avqImmLv/F0izHmVGAzMNjF8YiItGvvEAlgzNZ1XPnmY3zz8/fZmdOTm7/xUx4d923qfdH/0eR8TXETcU16BEoWQiFLCEu/HtmtDhjC9VAqrWxg2tc61kMpGok6mGyquGlaCitkobSqAX8oRH525j4Hu8k+NS7RgUosIUV7j1W8H8tkD/viOR1ze2Udlz2xjJ45vojPc16mE9p4WrRyCVln+96mzXmbd9aXNZ+fOLw386Yf0+oynQ0S4tGEPdqgpCOBSsv7FbCWrAwPGR6zT9VOZ/t+RXrd/2lxMQ2BEF6PIcPrwVooq/Fzx6urE/r6jTWEj+dUvpbv2UJvCM+G9Ty1/H36je7BoRm1rauLduyAPn04rtRS3bsf5b36srn/EFaNPJxd+X34wteTf888tbMPh3RvtxhjegFXAQ8APYEr3B2SiEh4TdPZWuRIjNq+gSvefIyT175DeXYP/t/kH/G3I79LTWZO1Ps9dmQfHrtoYgJGLCLRSotAyQLGA/vnZ5PhNa0OGN4p3kX/Hpn7rPL2ysdbead4V8LCjEQcTDZX3Hi9BEOWQChEyMLuuiD3nD0mLis3dZWuCFRiCSnae6zi/Vgme9gXr+mYu2v97KxuIGQtQ/vkRnyeL5w0nPsWriMQCuExzvMUss72lvYOkwDeWV/GtDlvtwqV4hEkJGMT9umTRzDjmRWUlNUSCIXI8HjwGEPvXB/9W1TptFW1E4tIq6rVNATJ9Bo8jc2cjQFrLMU7qjt9m22JNejrUDBoLZSV7TMFrerfS5m5o5T+1WVkNjRQ1rMP23v05pOSQg797lEwYcKe6qL+/cHn49G5S/Z5H8XruZHuzVr7UuM/K4BvuDkWEZFI5i8r4conl9MiR2Lkzo388s3HOXX1m1Rl5nDPsT/gL187jcqsvKj3q9XbRJJHVIGSMeaMMJsrgJXW2tL4Dil2w/rmMW5IbzaV1VCYn93qgGFjWQ39emS1OtjaXdvA2tIqhvXNTViYccUT7S+BHquWFTfOKkdeQjZEIBR+3G4uc91e9VFXBCrRhhTQ/mMV78cymcM+CB/I7KiqZ3N5LSN/83LEBud7P047quoJhSwWWLOtsnnK6d7Pc9N+2mugvneYFGl7PCqMkpUFMGCMAQPZXg/BUHS9kmIVaVU1N9cEizXo2+fywaATFLWsKGr5s20bZGe3no62//78+wCDf3wh5T37UpWbD8ZgraWi1s/ZF4ZfWCvpVoaTtGGM+St7Jro2s9b+xIXhiIg0C1eNBDC0bAuXvz2P01ctoi4jkz9OOJO5R51BRU5+1PvW1DaR5BNthdJPgYnAfxvPTwGWAAcbY2ZZax9JwNiilp+dwbyiCWF/Fy4I2LY7/DLb8QozrnhiKc8v39J8PhiyPL98Cy9+9DKXHX9gh1cZc5ZUD2BtEGudqgBjIC8z/NPo1sFMNNVHXRGoRBtSQPuPVbwfSzfDvmjsHcgA7K4NkOE1Ma/CFrLg8+4JJHZUNuAPVu5zm5edcHBcV+BLxgqjzpqzuJheOT7267WnHLymIYDPY+idlxX38CzSqmoZHiecNSHrVCc1hrUH9kuC129dXeugaO9/79wJvXs7QVFTaHTIIXD88XtWTMvd935sr9q32qi992w6B5viupda/Dsb+B5OH6VOM8acDNwHeIGHrbW3x2O/IpK+rpu/kkeXfBn2d/vvLuXSt57grJULCHgz+PP40/jThDPZldsrqn0b4DwFSSJJK9pAKQQcYq3dBmCMGQD8ETgaWAy4Gii1JWwQEAoxuKD1/Nx4hhkvfLQ17PZAyLa5ylh7vjm6f6ugylrAOtvDcetgJprqo64KVKINKdp7rOL9WCYy7ItXb6qWgczYG19rDJNiW4XNGIPX2ObrGQMhY2kIhPa5vXj31ErmpucdFSmIraj18+oV4UP1zmhvVbWq+kBzFWZBlo9rTjkk5tuI6Xmy1ln9bO+qopahUU3NnmCoKTA6+ug9AVJhIWTEPtu7o+/ZdAw2xX3W2mdbnjfGzAMWdHa/xhgv8AfgRGAT8L4x5gVr7Sed3beIpJ/5y0r45ZPLw/6usHInP1/yFOeueA2AR756Kg9OOIvtPdrvY6spbSKpI9pv1cOawqRGpcDB1tpdxhh/pCu54f4Fa/epSJk1dUyrIMDnMfhDrSvF4xlmBEP7VKE38xjCrjIWja27GyjIyWB3XYCQdfbVMzuDrbsbIl6nowcznTkYj6b6KBmngrT3WH20qZxVmyuobghSUevno03lHT5QTFTYl6jeVB1dhe3Im//tvF5bVLIAZHpbT5qKdtwTh/cOO+1t4vDeHdpfMojlvdbVlW2RVlU7qNAZZ2dfv3s/T9srarj78TfJO7I3X8tu2Dc02rrVWfmsZXXRwIFw2GF7tvXunZDV0VRtJEnuIGBoHPZzFLDOWlsMYIx5AjgNUKAkIkDb1UgAfavL+dmSpzl/+St4Q0GePuxEHjjmHLb0DP8HcICsDA93fH+sAiSRFBRtoPSGMeYl4OnG82cCi40xeUB5IgbWEU2roDlLxe+ZlnP58Qe2mhLXdBCTqDDD6zERQ6VIB+HR2Nh4EGPMnoNxa23c++509mA8moPeVDs4i/Tago5Vm0FiKhcS1ZsqlgbnLR08oCfrd1Tt1RTfx/B+PVpdLtpxT//6gXz45Qc0BPe8vzK9hulfP7BD+wN3K5lifa91dRDb1u3F/PoNhaC8HEpLnT5F27ax/vl3+b9t28iv2EXfyp30rdlNXU4eNQsGwNfHOgHRyJFw7LF7AqMePdq9qURRtZEkC2NMJY1rkjSebgWujsOuBwEbW5zfhFONvvftFwFFAEOHxiPHEpFk1V6A1KSgdjfT332O/1v6IlkBP8+NOZ77jz2XjQUDI15HPZFEUl+0gdLPgTOASThfXv4OPGudBhtJs7pI8ypoMU7LiXeYMXXswFZT05p4TXQH4ZF0VXVCZ0OJaA96U+ngLNrXlts62puqvSbysTQ4b6nptTCwV0abr4Voxz1ncTFD+uTus2rW3q/NaPfndiVTrO+1rg5io769UAh27doTFrUIjZr/vWOH05uosBAGDIDCQr6sg039D6TsgAJ29ujN9rze1Hsz6JWdwQfXfysh90kkHVhro+9iG5twPffDNf+eC8wFGD9+fOSybBFJSdGGSAA966r46fv/5CcfzCevoY4XD5nMfcdOo7jv4LCXz/AY7jzrcFUjiaSJqAIla601xrwFBHD6Kb1vm7u1Jo9YpuU0ScSdcA7EWzfmNoDHY6I6CI+kq6oTOtswO9Wqj6LRkdeWGzoSOkZqIr+14m0wnubKnaljB/Kf1dvbbXDe0pTRhZy5qXyfaah7vxaiHXe0r81o95fI1QbDTb/d+/HqyHutq4PYKQf3Y0ofnGCotBSWLoBXS1uHRzt2QH7+nrCoMTDiwAObz/9vl+VPS0paVYI9W7+MWn+wOagFIBRqVYEmIq0ZY3KA84CvNG76AHjGWht5/nv0NgFDWpwfTJyafYtI8pu/rIQrn1zOvp0u95VXX8MFH75I0XvP0au+mpcPPoZ7J/2Atf2Hhb+8+iKJpKWoAiVjzIXATGAhTjbyQOPqbn9J5OBiFe20nKaqBH8wSEWNny0VtSz9soyfTxkZt2qTe879Kvec2/qgMscX3UF4JJGCGoBpc5fEbcpOPCqhUqn6KBqxrrAXjURMtepI6NjURL7FTEqshXfWlzGyf15z5U5JeS33nzsupjEuWl3KM0tL6J+fxdDG8TyztISxgwtaT2WLctzRvjaj3V+iVhuMdoqk66v9BYNOGLR3NVFTeLR1q1N5VFDQqrKIAQNg9Og94VG/fpCZGfFmFq0uZear+1aCAWAhZFv02LKQuXd6KyIAGGMOA14E/gd8iPOd7CTgCmPMicCvrLXXdeIm3gcOMsYMB0qAc4EfdG7UIpIKznvoHd76fFe7l8v21/HDpS9z8bvP0Ld2N68feBT3TjqPVQNG7nNZ9UYSSX/RHg3PAMZZa3cCGGP6Am8DSREord5aybS5S/jm6P688NHWdqflzFlcjD8YZGeVH2PA5/UQDFn+sOjzfQ50O+rkexaxelt18/nRA/J49Yop+1yuo6FC09/vP9pUzjNLS+I6ZWfvg/EdVfWU1fipqPUzbe6SlK826ohYV9hrT6KmWnWkOqytJvItK3dKymr46T8+AIi6QinaCqBow9KJI/rwzNKSqKZTRvM4tBXodCbwizRF8o//+5x3infFfH86JBRywqItW/YNjJr+XVYGffo4IVFhodPgurAQDj10T3jUrx/4fO3fXhsivQ4A+uVnsrt2T4+tnnk+hvV1r0+SSJK7H7jIWvt6y43GmBOAj4FVndm5tTZgjPkF8BrgBf5ire3UPkUk+UUTJmUFGpi2/FUuWfI0hdVlLB42jruPO5/l+49qdbmDCvN4/copCRytiCSTaAOlTUBli/OVtG7a6KpMLDvKqykpr41qWs7GshoqapwwydNYluE1EAhZ5iwuBuhU5cjeYRLA6m3VnHzPolahUqyhQrjL/2HR5/TJ89ErJxuIz5Sdlgfjn23bTWV9kD55PvrmZSX1almJ1JEV9tqSyKlWsVaHtdVEvknp7jp21TgLOmZlmKibksdSAbT3uMO93p9ZWsKZXx3EO8W72g3Monkcpk8ewa+eWUFJeW1z/6geWRmcdvj+nQr8wk2RtNZS67eUVtZ16P7sIxBwQqEtW1j53qcseetjzLatHNCwm3EZNfSrqYBevfashlZY6Pz78MP3hEd9+4K3Yz3dYhHpdZDpNfi83nZ7bLXkZhN1kSSw395hEoC1dkHjqrvf6+wNWGtfBl7u7H5EJPlFEyT5gn7OWrmAX7z9JPtX7mDJkEO55PRr+GDwmFaXUzWSSPcUbaBUArxrjPln4/mpwHvGmCsBrLV3x3tgxpiTgftw/kL2sLX29kiX3W/HJv7wh0sJGEO1x8d3PZnUZGRRn5nFgLd6wytDnWawOTmQl8f/rdzCp7sD+LOyqc/Ios6XRY03i4asbGpqt3PvxhIqPRlUBLxRT4dreZCzqaw27GX2DpnaCxX2PnAqq67f5/LBkKWixk+/HtnN+43HlJ2mg/Fpc5e0quCIZ/CRSjaW1dArx4c/aJsrKXrl+Dr8OCdqqlVHNDWR37srWl7mnkRke1U94ARpHuOJuil5Z6Z0RXp/vFO8q9WqjZ1lAKwT+GANBnh55ZZOBX7hpt8GQ85txXR//H7YvBm+/HLPz8aNzunOndCnD5tze/NhmYfqXn2pOuBgluUWMCevD5dOm8TXx4ZviNnVhvTODbPaXwYHDejJ9Mkjoq6oW7S6lF89s4Kq+gDBkGVHVT2/emYFd555eLf6PJJuzWOMybLW1rfcaIzJBvzW2q7/T0REUk40Tbe9oSBnfLyQy95+giEV2/hw/9H86tu/5O0DDm/uk3DsyD48dtHErhiyiCSpaAOlzxt/mg45/9n474SsMmKM8QJ/AE7EqY563xjzgrX2k3CXLykcylVXzaGktAx/dR05DXVkBxrICdST7a9neV4PfjFhMNTUQE0Nkw/ys/3NtWTvLiXX30BW4+V6WT+++jrygvV46urJ9dcR8niozcik7sksSg/cj8LCAsjLc8KpxpBqXWWQ99eWMzYrm0NzclhdZan1ZVHry6bGl021L9sJrXzZrcbdVqgQrjpjw85qBhfktLp8VoaHukDrxtDx6MHSFGa9t2EXWV5DYc9s8rN9rcbYnfTI9LJuezVeY/AaQyBoKSmv48D+eRGv01Ylheu9c1poaiLfcpW3ow4ooKSivnkqVlMBk7dFo6VompJ3ppF8V4RucxYX0zPHx8Bee95XNQ0B1u+s4aDC1tOuYrntCycN597/fIY/2PrxKezRus9Qjs9Lyc4qKCkJHxqVljrVREOHOj8jR8KUKc6/BwyAjAyu2iv0bboPf1qyKWkCpYkj+vDehl2NgSQ0BENsr2rgB0f1iami7vZXPqW8xt/8PrQhKK/xc/srnypQku7iH8CzxphfWGs3ABhjhuFMhXvExXGJSAqIpiLJEwry3U8Xc/lb8xhRtpmPBh7I9Sf+jEUjjiQvK4N71VhbRFqItvPpy8AROKXUZwFnAmdaa2+y1t6UgHEdBayz1hY3rlryBHBapAsHKkqp+fw9dgW8VPqyqV/7AtvqS1lbOIwVA4bz0Nv/5oj5qxi5NJexa3px5ccr2HnqZOZMmsZdE7/P/b283HPsydw+7Tdce8YV/PyAofzk5J9yzk/u5f/O+i2/HnYANxw9lVsn/ZCt55/P7zZvZs3BB8PEiZQWFPDEqy9hqnfQv7aCwRs+Zsq7j/HdFa/yow9f4qr/Pszsp65mzjM38Mxjv6bmiCP4ZPBgqk44gTuevZ2fPPRbzpn9Y075+x18/ZmHmPzsA3zn8atZdvNsJq9+myM/eIn9nriJURtXMrxiG6FV71Dz0t2EqssByCtbS/77f6WqsgJrLRWfL6NywYP8aPwAAP79739TVFREXV2d80S+/DJFRUUEAk7/khdffJGioqLmx/L5559n2v9dyMwXVlFaWUdeyfv43v87m8vrqKzzU/3J/9jxn4eag49HHnmEGTNmNF//b3/7G9dee23z+Ycffpjrr7+++fyf/vQnbrppz0vm97//Pbfeemvz+XvvvZc77rij+fxdd93FXXfd1Xz+jjvu4N57720+f+utt/L73/+++fxNN93En/70p+bz119/PQ8//HDz+WuvvZa//e1vzednzJjBI4/s+Q5+xRVXMG/evObzl112GU8//TSmMUjJ+eCvZGz6oHlh5YrXH+TFF18EIBAIUFRUxMsvv8yi1aVc/9wyiuffTdbWjymtrOP6Zz7g7PN/zMKFC5k+eQQNNVWUvnI/tV+upKYhQENVBcHFc3j77bcB2Lp1K0VFRbz77rsAbNq0iaKiIj788EMANmzYQFFREStWrABg3bp1FBUVsWqV0+5izZo1FBUVsWbNGgBWrVpFUVER69Y5U9VWrFhBUVERGzZs4LQjBnNo5k76r/g74/qEmP71Azl/RAMNi/5E2c7teD2GrJ2f0eODv2Dqndmvnm2r6fXBXykvLwdg4cKFFBUVUVVVBTivvcfvvo7rThpJYX42O1e/S8OiP3HDt0cxZXRh2NfeJZdc0nw+f/MH7Hh9z3OZiNde8ev/IMfnTPna/f4/qVjyTPP5XUueo+K955ovv+udp8la82rz+bZee2MHF9Br1XPkrl/kPFZYBn/4KKPefYKJK/7Haf99kvPuu5ir7pnOww9fAdOn8+bFF7Pi+edh0CA46yxu6N2bZy69FObPh/vv55LiYp73+WDiRBg0iKJLLuHFF19kY1kN2V7Y+eoD1Hzu9LjKNkE+f/5u/v3vfwNQVVVFUVERCxcuBKC8vJyioiIWL14MwI4dOygqKkrYa++/S5bRZ+lfyarZTshC9u5N9Fn6V/639FPuX7CWwy/9E4efeCZjZ8zj/gVreffddykqKmLrVqdh/Ntvv+28Vjdvw2PAt30NOe/9GU+gBo+Bjave3+e1F+vnXsvX3tNPP81ll13WfH7evHlcccUVzee7y+dek0suuYTnn3+++XxRUVHYzz2Auro6ioqKEvba6+6stbcArwKLjTE7jDE7cBp0v26tvdnd0YlIMrpu/kqGXfMvhl3zrzbDJGNDnLL6TV79y6Xc99Jd1GdkctEZ13HWT+7j9N9cyIY7vsOqWScrTBKRVqKtUHoU+BVOw8doVpLsrEG07tG0CTi65QWMMUVAEUBOXj4NgbaH1RAIOastNQTZVF7LaGDO+Ufy4L8/YsMqDwN65nDV1DH84dXlrG1cxcsag9+bQaUvk2DPApZm9CFwyMFsKCykavx47i/L5w9rtpPddwjVwyYQLBhKf1uG3xOg8sBvEeg1CG/lFnqseZWqUSdz0MiR3P2NAubecw+/vOgiFr9XypK3P6DPhrcx+x9MlieTHhWbGAx4t23lK74d+HZtwbt1Az0XP0+GP4CnfDv51TvI/eRj6n05VIcChAKVBCoq2OXNhVANgdrtHP+vR2FJX/YvLubI4mI8r74KffrQc906BpSXOxURBQWY4L4VJpvKa8lsnO7TIyuDasBiKd1dR59gCGuJT9PgFFJZH2BQQTa7gVDIkuExDOyZRe3e88QaNU3XChqDMZCTmYFtMGypcKZDThldyDUnj+L29zzUNAQ5ID+baccO5KWSzjU/7oj3infx+w/WY2obyPAYdlbXM/OFVZw/Ag7ZryezfnYMT328mz889RnWQsiGCIZCeC3s1yu73f1PHlXItw4fyssv72L+/LV8PcpKkkkH9uOfn9Nc3dTQ+NqbOKIP0+YuYf2SdWTt3sWi1aUdrk7Jy8qg1h/cp1JsRL88yj63BIJNvY+ChEKWwwcXtLk/EwrBl1/yv4f/xfc2f85gu44hX3xC4a6tNJRtZlN+fyoaQuzqvx9LBwymdL+DuHTmrzl47BCeveIKjjrqKA6fNg2Asqefxma0/xE9pHcu2ypaT6et9QfJSvBKaeU1fm745yp2vLqTQltORmOPrXC2VdaR4fUwuHcuvt49afDksNvr4bPSSpYvXIcvECQbqA04vbnOGhJ+2rCIgLX298DvjTH5jecr27mKiHRD85eVcOWTy9s/cLOWE9a9x5VvPspXStezrs9gfj71al4efSznTRzGmtMP64rhikiKMjbCAXGrCxnzprV2UheMp+n2zgJOstZe2Hj+h8BR1tpLw10+f/Ao+52Zf+fd9TsJ2X2XPweaqw7A6f3i83g4fEjBPtORFq0uZfqjHxKy1plSYSGEpW9eJsP79WjudXL/grXcveCzsOMfkJ9FWU0DDcE9j224Vd7G3vgaVfWB5nE2jbtHVgZj9u8VdhpLptdDQW4mJTurGNHDy0VfLeTY/XOhurrtn6qqVv/esW0X2zbvxFRX4c3KpP+APvQZ0Ad69OD5zyoI5eZRl5VDXVYO5cZHacjHbm8mQ4YUcvLRI/nqmCHQo8een+xs8KTvUt/T5i5hw86q1qtR5WQwrG+PsP1vJt2xkIIcX3NlEzjBREWtnzeuPr4rh96uvftkgfNaK8zPbnXf7l+wloffXN9mw/twOtNEuem6Tf11mlZF83lNqyl0s6aO6VCo1HJq6d77gzZWiauqgi++gA0bWv+UlED//jy9w0t54SBK++5HaZ+BbOu7H1XZeWzdXcdBA3rG3oC7g/chHtPAwj1/QEy3Gek1tmFnTavV8MD5fM7xefnoxpP22c8p9y7ms9IqvB4nqLXWWaXwoMIevPLLyZ2+r5L8jDEfWmvHuz0O2WP8+PH2gw8+cHsYIoITIl373EfU+qP4+7+1fH39Uq5481GO2PIZ63vvx33H/oAXDplMyOPl/AlDuUVhkojQ9vevaCuUbjDGPAz8B2huBGmtfS7yVTplEzCkxfnBwOZIFx41MJ95RRO44omlYZsLm72vYC01/mBzk9itFXWtGm//fMpI/rDocwIhS1aGh/xsH5kZ3lZVOQ+/uT7i4Esr61s14wWoqgvsc7nqhiA+r8Fj9hxMhWyI6oZgxN4z1586Or4HoBkegrW1ZNTU8NuvD2HCgGw+fOxd6srK6RXyk1NfS3Z9LcNqqugX8nNWlh/eXAOvtQipqqqgvt7pKZWXtydkavnvlufDXabpNDOzeYzJtJLTxBF9mgNLAH8wSK0/yLSvDQ17eTd7JMX62EXbq+iyEw6OKkDaeyzRrpYWadwtLzdt7pKwzbLveHV1h14vLVc03CfkqapiynG9YONu2PQJPPnanv5GtbUwbBgccIBzetJJzunQoZCZyXNhApTahgAHDegZ14bi7d6HTor0/OX6PDE1LY/0eRYKWTIyWn9YttWb6+qTRzPjmRVU1gUIBENkeDz0zvVx9cmjO31fRUREUlE0Dbb3NvGLj7jyjUf5WsknbOpZyIxTLuO5Q79J0OMlL9PLreqTJCJRijZQ+jEwGvCxZ8qbBRIVKL0PHGSMGY6zwty5wA/au1K45sKG1hVLAP7G1ZZ2VjfgwZDhMQSt5Q+LPmfs4AIuO+Fgxg4uaPMAra1mxBYI7hVqbaqoZ9JtC3jz2hOat4VbCSpkne2JPEjce/WsjLw8anxZ3Pd5gAnfPJQT/q8wctVGpNsPBltXQoU7rapyVqZq+vfev6uqAo+HXSYTb0WQn2bn4M/OocabycYnslg/ZjDDD+jvNERv+mlava/l+ezs1tt9vn1fBDF6eeUWsM7rxrJnZbCXV24JG7J0phl1Z8QS4DSJNvzqSIVSeysZxjrucOFXIBhiw84ahvXNjfo+N9u9mynB7UwZWg5moxMW/b9NTnBUXw9Dhuz5OeII+O53YfBg6N+/zddUVz//sTS2jkWk5y/WpuWRPs8ue2JZxM/ASPuZfebhCflcFBERSSUdCZKO3PQJV73xKMd8+RFbevTlum9dwpNjT8Tv9akiSUQ6JNpA6XBrbZd9wlhrA8aYXwCvAV7gL9baVZEuX1kXYNLt/6Gkog5rIdfn5eLjR3DZCQdz/4K13LdwHYFQCI9hz2pVHvBg8DQeyXgN+IOh5gPd9g7Q8jK97A5TddSWTRX1TLpjYXMFxYWThu8ztpB1VoiCxB0ktleR0qEwy+uFnj2dHxqrTd4vZmNZJkN6F0R30GctNDTw6wcXUb2znN6hBrIb6sj012NraygNWq7af3+oq3NW7Nu506kUafqpqdnzu5bbg8HwwVPL8+2EVJmfrGJERib+zGzqfVnUZWRS48lg/c7YDqD3DlHiXYUVbYDTUjThR9P7yJme5ARO9y10mnu3FSpFW/00Z3Ex/mCQnVWtpxTuPe4hvXP3mXroD4Yi3+dR/aGiwgmKwv0EAk5VUVNo9LWvwRlnOP/u06fDQWQiA+FwOjodsT2Rnj8gbO+paCrwWmbt7X0GRrsfke7GGJMLXAUMtdZeZIw5CBhlrX3J5aGJSILENJ1tL2O3rOXKNx5jyvoP2Z5XwE3fvIjHjziF+oxMBUki0inRBkpLjDFfsdZ+ktDRtGCtfRlndbl2bdxVQ315XfP5Gn+Qe//j9DdqOqhqebA1ID+Drbvr9+m1lOX17HOgG+mg/8JJw8P2UGqqYImkVQXF1DFcfvyBCTkQbEs0FSmdCbM6UiUDOAfvWVmsbvBRULg/VXv1H3q71s9VP+hA/6FAYN/gqeX5vX+3bds+IdUF731Gtr+e7ECD8+OvJyMYoCHDB+/d0zqIysuDvDymNP7Qu3F635ptsMn53fulddz7v42UWh9VXh/Ld9cy45lKZp95eKdCh2gCnHCv6VlTx7QZfjz85vpWvW48xul18/Cb69t8vUZb/fRZaSVl1Q1O+aOFQChIXWOw1VLL5eczQwEKKivoWVXOCFvN8C9r6VlVTq+qcnpVlpFbsctZYNvna11pNHEinH228++Cgk5Xr0WSqEB4bx0N+6IR6fkb0S+P6oZg1BVYET8TYvwM7PBnS4ySbcqtSBh/BT4EJjae3wQ8DShQEklD5z30TpsrtEVySGkxV77xGCeue5ddOT25bcoF/GPcd6jLzOY8BUkiEgfRBkqTgP8zxqzH6aFkAGutHZuwkcUg2Ng0qfm4sPGv3E0Hu3v3fmlqvB20Fm9jY1droVeer9WBblsHL037e2DhZzT9oSArw8PPp4yM2KzbGaNpVUExr2hCwgOkvSV6Ok5HqmRainv/oYwMyM93ftrQfBDpr2FI/9YHkQ+FaQYcCgYZ0zuT+T89snVQFa4Z+tatrab5lb9fzPTKSvIa6sjx15EdaKDe68PzSC58ZfCeflR5eXv+nZu759/Z2U6/qaws57Tx59jqzWzdFcKXk03Q4yXk8VIVsIzqlQsVFSz+fBe3vLIWj89LQXZmqwP7tnr7VDcE2XvRsLZ63TTZ+7VWV+8Hv59LphwAZWXg90MgQMG2zeQ1NOALBskM+snx15MVqKfA+uGpMigvh+3bOWjhRzy4Yzv5leXk1tewOzefHTm92NWjAE9hIbt7FLC5/2BKs/LxDhzA5MtPch6zNNbRsC8abfVyg+grsNr6TIjlM7Czny3R6KrQSqSTRlprzzHGTAOw1tYak6B0XES6XGeqkQAO3PElV7z5GKeueYvdWXncedz5/PXIqRzxlcF8etHE9ncgIhKlaAOlkxM6igSJdLA7ZXRhc+NtfzBEltdDrzwfPm/rxtuRDl5aNgAeP6zvPgdST73/JZsq6ve5XZ93z3e9tvqNJFqip+NEO80pEjf6D7V3EBmuGXBBXha/nHo49O0b8+394rpXsNbibQwBjA2R0VBHrr+BJb+c6IRQNTXOT3X1nqCqqYKqvh4aGvacNv77l9t38/H6UrKCfnxYCAQxwSAH98uBFz3031jGvQE/PhvCEwphjQe/8WD/5OETXwY1IYMv08fgfvn07ZXjhHEZGfz+01Lq8WA9XkLGQ8DjJWCM8/srFzhTHjMy9px6PFBZyZTycp7ZuI1tX27FW7mbLK+Hfr3z6PVqY28rnw8yM5mxZgd+TwZ+jxe/N4NaXxa1GVn4fVmwPseZSjl6NC99mUfw6L7s7tmHqpx8rMfD7toGNpXXMaxv7r49v9I8TIKOh33RaOuz4v4Fa1m1uYLqhiAVtX4+2lQe8TOkrc+EWKbrdfazJRpdEVqJxEGDMSaHxqJoY8xIWiyaIiKpqbNB0rBdJVz+1jxO++R/1GRmc//Ec3j4qO9R36Mnd3x/rBpti0jcRRUoWWu/SPRAEiFcY9eWUxlG9MvDWkt1QzBsqNLRBsBvXnsCk25b0CpU8npg9MCezee7asWvSBI5HaezFUZd3X8G2j+ITHQzYGs81Pmyqc/McVYO66D9gDWrS/njXuPs0zjOi+5YSEGOD9NYZuWxIaqq69haVsWIgmxyvQZ/fQOhQJBfn3AgxwwrgGCQ7Ys/47G315NhQ/hsEBMK4QkGOXfcfvDVQc60wkDA6VcVCEAo5FSEFRRQ2PhDfr4TNoX5I/pl171CIBjC4lR/GeOUQWZ4PVx69SnNl9u1c9/V0zK8Hg4u7EFBbma3bNTcVnP/eAj3WRHrNLshvXObV9Vs6n2Vn51BhsfEvJ9Er57YFaGVSBzcALwKDDHGPAYcC1zg6ohEpMM60mC7pcEV27jsrXmc8fFC/F4fc48+g0cmncWM8ybxkUIkEUmgaCuUkpq38QDVtmi34jH7NnbduwqlqZLh5tMODXvwGe7gZdvu+qj+et1yNbem2+3qFb/cEo8Ko67qP9MkmoPIeI5peN9c1m2vxoTsnil0Fg7s1/kD47bG2eo1bQwh46WkNgRZudAznxqAPKhpCPDAmlqO+frhAPxoxAjKB+9bSXJWnKZrjuiXx2elVWS0mFIYDFlG9Mtrdbm2pmAlW4DUVX14OtPYuqNinWbXsveVx0BDMMT2qgYyGs9Hu5+uqF7sitBKpLOsta8bY5YCE3Dy98uttTtcHpaIxGj+shKufHI5HatHgoG7d/CLd57knI/+Tch4ePc7P+DYh+7k4gEDuDiuIxURCS8tAqUhfXLpX5DdepW3r4/Y54Ak1qkMYQ9eQiEGF+S0uly4v15Pm/M276wvaz4/ekAevfOyu0UFhRsVRp3V1QeR15xyCL96ZgVV9QGCIYvXYyjI8nHNKYe0uly8Q4lIB+SDC7JbXS7ca3rvXmTxFG5KYe9cH1efPLrV5VLltdWVfXjCLTyQ6Ob+sU6ze6d4F4X5ma1W5+uZk8GWinqyMkzU++mK59+NKbci0TLGfHWvTVsaT4caY4Zaa5d29ZhEpGM62mgboH9VGZcseYofLH8VYy1Lv/V9jn74bo4dpGokEelaxtq21iRLDePHj7cffPBBu5eb1HK6TyNrLRW1ft64es/qYS0P4ntkejHGUFUfYHDvXMqq6/GHbKvgoaYhQGF+dnNT473DpCYTh/dm3vRjOnNXtfpQgrQMAPbuw5Oox7fpuYx0YJyoMe19u+U1DTQEQ22+plteL1GvvfYej1Qybe6+U/NqGgL4PIbeeVkp//4de+Nr1PqDzZVF4FQW5fi8fHTjSftcPtJn76otu8nwmKj301XS6bWYbowxH1prx7s9DrcYY/7bxq+ttbYDS6F2TrTfwURkj46GSX1qKpj+7rP8aOm/yLIBPBdcANddB8OGxX2MIiJN2vr+lRYVShDdwW40VSjhp8WFmqfFRTN9LVyY1Nb2WO6jVh9KjGgqH9p7jcUauLQ3hS5RzYH3vt1oXtORXntnbirnneJdcQlIunqaYyJF7r9Wy7CQTfn3b6zT7CJ99g7qlc2W3fUxTdeL9X3WkSA0nV6Lkl6std9wewwi0nEdbbrds66Ki957nh9/+AK5/jo8558PM2fCgQcmaKQiItFJiwqlUYceYQf86J52KzmiqfiIVFnQslqjvb9eD7vmXxHHuuH2Uzt8P6MZmyTGotWle6ZkhZwpWfnZGcw+8/BWQWM8q4miragLN9ZYD6Dbe02He+1tr6yjrMbP4N45XVbVlSrCPV6flVaChYMG5Ddvq2kIkOn1UJCbmXJVS7GsztbW++OjTeVx2U+4x8yNykNJrO5eodTEGJMNXAJMwlnp7Q3gT9bauq4eiyqURKLTkaqkHvU1XLzsBaZ/+AK+qt1w9tlw441wyCHtXldEJF7SvkJpe2U9gyNUcgCtDq7P/Oog3ineFfHAuaubM8dzyex4Tklye2qdG7ff1m3e8epqymr8eD2GDK8Ha6Gsxs8dr65myujChFQThavq2FldT3V9kEl3LIxYJdWRKrb2XtPhXntN4Vp3X1493Osm2l5V0awamaxi6anVVgXglNGFUe8n1vdZoqr8RJLAP4BK4IHG89OAR4CzXBuRiIQ1f1kJM55eTixFSTkNdVy04l/84sPnyawoh9NPh5tugrFjEzVMEZEOSYtAqSHo9NxoKcfn5bPSyuaDa6+BZV+W8d6GnRzUv0dMK7tFas4cKYCYOLx3xB5KLXVk6e1IY4vndDi3p9a5cfvt3WbxjurGFaqcaiFjwBpL8Y5qoGNLjbcXmu0dSuysrqe0soH+PTIjPi6JOoAO99qrD4TI8rbuzNzdlleP+LqZOoZZU8e0ClAyvR4agq2/TUa7amQ6iEcQH+v7rCPvS5EUMcpae3iL8/81xqxwbTQiEtZ181fy6JIvo758lr+ee8qW8O1//R1KS+GUU2DWLBjf7QszRSRJedq/SPLL9Hqo9bdeFajWH6QhEMLnNQRDli0V9VjAawwbdtUw84VVLFpdus++pk8egT9oqWkIYK1zGm6Fn6YDydLKulYHkotWlzJv+jH7hEfhGnK3XHrbYzyNp872cNoaW8sgwRjn1Oc1zVVasYjnvjrCjdvv7G0O6Z0b9jUYaZW4tl4/TaaMLmTW1DEU5mdTUeunuj5I/x6Z9M/PjjjGjWU1YcPVzh5Ah3vteT2GXrmtD9Y7szLeotWlTJu7hEl3LGTa3CVh35+xXC7e1w2nrdfNlNGFzCuawBtXH8+8oglcffLofd+/oRAD8rNa7VOBR2Sxvs9ivbxICllmjGme626MORp4y8XxiEij6+avZPg1/2LYNf+KOkzKDPi5YNlLrHniUr7919lw2GHw9tvw8ssKk0QkqaVFoNQ/Pyts0NLUN2N7ZT2msbrEY5yAKVJYsPdBfGF+dth+G+0FEPOmH8OG209t/gm3ult1QxBP6xWz218yO8LY4hkkJCqUSObbb+82h/fNJRiy1PmD1PqD1PmDBEOW4X2dA9Nog8gm0QZYLUOJnjk++vVoO3wY0juXzeW1rNpcwcqSClZtrmBzeW2nD6DDvfZ+PmUkPq836vvclmgCtlgu15nbiEVbr5u9wytgn8fwoP49yNirykuBR2Sxvs9ivbxICjkaeNsYs8EYswF4B/i6MWalMeYjd4cm0j3NX1bCQb9xQqRoO9RmBAOcs+I1/vtQETf++08wYgT897+wYAFMnJjQ8YqIxENaTHnLz87YZ3pJU9VOaWUdDcEQ3sbkxlqnoqmtgCKaqRnxmEqRl+n0VmkZKoWssz2SSGOLZapee+K5r45w4/bbu81vH7Yf9yz4rNV1QtbZDtGtEtdSR14/0TwuA3tm8k6xv9UYd9X4Gdgzs51HIHpNX5LGDi5g7OCCuCyvHu1Uvc5M6euqPle1/iA9sjIiToVr2UA/mhX2ZI9Y32exXj5dxdKrT1LGyW4PQEQcHVm5zRMKcvoni7j8rXkcUL6VXYceAXc9Ciee6PRVEBFJEWkRKEHkoGXmC6vwGkMoZDFACEu/HtmdDijiEXrEuvQ2RO67E6kJcEcOTOO5r45w4/bbu813incxoGcWlXUBGoIhMr3OKm/vFO/issZ9xNIjpiOvn2gel/+s3t4cUFq75zvJf1Zvj/7BCKOtXkHxWGEw2oCtM0FuIvrpRHpOfB4bVXgVr8AjkYGB2w369xZrL6Z4LqKQimLt1SepwVr7hTGmNzCEFt/lrLVL3RuVSPcTa48kY0OcuvpNrnjzcUbu2kT56EPhkYfoc+qpCpJEJCWlTaAU6aBnFs4KXWtLq/B5Yf/8bDK8ptMBRTxCj6Yv8x1ZMjtcU+Z4/SXe7b/qu3H77d3mxrIa+vXIon/+nlW6rLUdDiM68vqJ5nGpbgji8xo8Zs80qpANRZxGGa1Er5YVbcDWmab5+VkZ1PqDca18i/ScXPfPj6MOryIFHtEGOYkMDNxu0J9oyRaWJULLXn3gTKsOhEI8/OZ6BUopzBhzM3AB8Dl7CkctcLxbYxLpbmIKk6zlpM/e4ZdvPs4h2zewbchIeOhZCk4/HTxp0YFERLqptAiUKusCbR70TBld2HzgsKmshsL87E4fOMQr9Ihl6e32Durj+Zd4t/+q78btt3WbQ3rnsn5H1T4VSsP79ejwbXXk9dPe49KRaZTRSPRqWdEGbNMnj+BXz6ygpLyWYMji9Rh6ZGVw/alfaXW5cEFIRa2fpoclnpVv4Z6TIYs7V8EYS5CTyMAg0UGim9I9LGtS3RAkY69jlbZ69UnKOBsYaa1tiNcOjTFnATcChwBHWWs/iNe+RdLNeQ+9w1uf72r/gtbyjeIPuPKNRzls2+es7zOI93/3e77264vB27nvZiIiySAtAqXtlfUMbuegJxEBRVeHHt1pCexkqxyYOKIP723Yhcc4B2MNwRDbqxr4wVF9OrzPRLx+OjKNMhpDeueyYWcVu2v3BGo9czIY1rdjgdreYgnYDIB1KsSwhnAF4uGCEACfx9A7LyuulW/hXqudrWCMJciJV2AQ7n6k82dOOodlLbUXMifbZ61E7WOgAOjcUpX77vMMYE4c9ymSVuYvK2HG08tpt12StRz7xQqueuMRvrp5DV/2GsCzl97M9+++huEZaXH4JSICpEmg1BAMuboqWVdxu1l2V0nGyoF3indRmJ+5T6DSsodSMoh1GmW0wgVqpZUNTPtaxwO1vUUTsM1ZXEzPHB8De+U0bwsXAkQKQipq/bx6Red7PjVpq7dUuIUCon39xhLkxKMqLdL9SMQ0wWSRzmFZS22FzMn4WStRuw1YZoz5GKhv2mitndrRHVprPwUw6uMiEla0U9yO2vgxV73xKEdv/JjyfgNhzhyG/vjHDPX52r2uiEiqSYtAKdPrSduDnpbcbpbdVZKxcmBjWQ3BoKXWHyRkIRhywppkPPiMZRpltN4p3kX/HpltNiXvCtGGAF0Vvrb1Wp1XNCHuq8eFG388qtIi3Q9rLf6gTcvPnO4S0LcVMk+buyTpPmslan8H7gBWAtEvLSUiHTJ/WUm7YdK4ktVc+cajHPfFcrb36M2KX9/M4bNmQFZWF41SRKTrpUWg1D8/q0MHPalW6u92s+yukoyVAwYorWrANP7bWuf8kN457VwzsiueWMoLH21t7gU0dexA7jn3q50e67Q5b/PO+rLm8xOH92be9GM6tc94NyXvqGhDgK4KXxP1Wo1l/PGoSmurouvm0w5Ny8+c7hLQQ+SQORk/ayVqO6y198d6JWPMAmBgmF/91lr7zxj2UwQUAQwdOjTWYYiknN8+vzLi78ZsXceVbz7GNz9/n125Pfn4ius59JZr6J+bXn+gEBEJJy0Cpe2V9eQ3BGgIhMj0Gg4a0LPdg55El/onKqxyu1l2V0jGyoEdVc6MAhthe6yueGIpzy/f0nw+GLKN55d2KlTaO0wCeGd9GdPmvN2pUCnRPZSiFW0IEI/wNZr3cKJeq7GOv7NVaW3dj3T9zOkuAX1bkvGzVqL2oTHmNuAFWk95W9rWlay1J8Tjxq21c4G5AOPHj9/7v0aRtDB/WQk3vrCK8lp/2N+P2r6BK958jJPXvkN5dg+e/N7FnPOP2fTp0bXfjURE3JQWgVIgFGJgz+xWB5fR9GJJVKm/+lJ0TjJWDjQELRkeZyqRtWCaewl17Hv0Cx9tBZz9NLHW2X7PuR0f595hUnvbo9UVPZSiEUsI0JkgJNr3cCJfq7GMv7MBdjK+57pCuoZl0equz3uaGNd42rIpnAWOd2EsImmnrVXcRuzcxC/fepzvfPoGVZk53HPsD1h11gU8fPmJXTxKERH3pUWg5DEGY0xMoVAiS/2TsQdQKknGyoGmxsdZ3j3LaQVCIXJ9HVvyNRgKH0RF2u62ruihFG0oEm0I0JmQJdr3cDK8VuMRYCfD/ZCup+c9dVlrvxHvfRpjvgc8APQH/mWMWW6tPSnetyOSjNqrRgIYWraFy9+ex+mrFlGXkckfJ5zJQ0edwY0XHMcV4wZ14WhFRJJHWgRKLUUbCiWy1D8d+lLcv2Bt3FcKi0WyVQ7Eo/FxS16PCRseeT3JubpOonsoxbuqr7P7i+U97PZrNV4Bttv3Q9yh5z11GWNOBcYAzR/M1tpZHd2ftfZ54Pk4DE0kpcxfVsKMp1fgj/BHvf13l3LpW09w5sf/Iejx8ufxpzHn6O+zM6+Ae885gtMVJolIN+Zp/yKpJdpQaPrkEc2NvK11TuNV6j+kdy61/mCHxpUM7l+wlvsWrqPWHyTDA9X1Ae5e8BmH3fAq0+YuYdHqUreH2OUuO+FgLj/+QHJ8XgIhJ1y4/PgDOxyyTR3r9ES1ds9Py+0dNXF475i2N1m0upRpc5cw6Y6FYZ/jRL+mW4YiTdWGPq9hzuJiV/aXSu/hjWU15OxVKZdqAbaIxMYY8yfgHOBSnLUizgIOcHVQIilo/rISrnhqedgwqbByJze9/kf+O7eIM1Yt5LEjTuG46Q/zu+N/ys68As6fMFRhkoh0e2lRoRSyFmttTP0fElnqn+p9KR5+cz0eAxkeD8GQJdSYdlQ3BLt1P6jONj5uyWm8Hf9V3uZNPybmVd6iqeZJ9Gs63lV9nd1fKr2H3WqsnGqrZIqkmWOstWONMR9Za28yxtwFPOf2oERSQXvT2/pWl/OzJU9z/vJX8IaCPH3Yifz+mLPZ3HPP/3HnTxjKLacf1lVDFhFJWmkRKGV4PFTU+mMOhRJV6p/qfSmqG5zKJHD6BDUJ2e7dDyreB9D3nPvVTjXgjqS91dz2vh9l1fXtTplK9Gs63qFIZ/eXSu9hN8IvLTwg4rraxtMaY8z+wE6gY3OwRbqR6+av5NElX4b9XUHtboree44LPnyRrICf58Ycz/3HnsvGgj3V471zfdzw3TGqTBIRaZQWgdKI/nm8cXVyLWySyn0pmhpQe8yeqVjgrO4F3XM6TSodQF/xROTKp3D3Y8POagYX5LTaR7jnOJ6v6b1DrYkj+vDM0pIOhyLx3h+kznvYjfCrrb5NTb9X5ZJIQr1kjCkAZgNLcVZ4e8jVEYkkuUhhUs+6Kn76/j/5yQfzyWuo48VDJnPfsdMo7ju4+TLHjuzDYxdN7MrhioikhLQIlCS+WjagBudbKkC/vEwgeXvJJFKqrNx3xRNLeX75lubzwZBtPL+Ue879atj74fN42FZZT8+czObrhXuO41WhFS7UemZpCUcO7cV/Vm9v1Qg+2tXcwu3vzK8O4p3iXUlfYRQPXR1+RZpS+Nm23SkTvIqkMmvtzY3/fNYY8xKQba2tcHNMIsls/rISHtsrTMptqOWCD19k+rvP0qu+mpcPPoZ7J/2Atf2HNV9GFUkiIm1LukDJGHMjcBGwvXHTb6y1L7s3ou6nqU/Qw2+upyoUAKAgJ4PCntlxbV6eSlJl5b4XPtoKgGmxWJy1zvZ7zg1/Pwb0zGJTeV2b1TzxrNAKF2ptr6zjpZVb8RqDwdIQCPHIki8YO7ig3f1HCvte+XgrBbmZhF+zJb109aqMkaYUNgQtvVIgeBVJVcaYrwEbrbVbG8//CPg+8IUx5kZr7S5XByiSRCL1Ssr21/HDpS9z8bvP0Ld2NwtGfo17jjufVQNGAuDzGmafebhCJBGRKCRdoNToHmvtnW4Pojtr2YC6qTKlO1R6ROJW4+NYBSMsedu0Pdz9yPB6OLiwBwW5mRGf43hWaIULtcpq/PiDFk+GIcPrwVpn2x2vrm53/+H2FwiG2LCzhmF9c5O+UqazlV9NqzI6jfSd1+V9C9cBxCVUCje+SH2bMjM8WnEuxai5esqZA5wAYIyZDNyOs9LbEcBc4EzXRiaSROYvK2HG0ytard6WFWhg2vJXuWTJ0xRWl7F42DjuPu58lu8/qvkyeZlebv3eYQqTRESilKyBkiSRVOklk0ipsuqX12PChkrexgZYke7H9aeObvM5jmeFVrhQqz7gTK/0NJZWGQPWWIp3VHdof9t2h280fserq5Pq4DkelV8tV2UEp9dZIBTi4TfXdzpQiji+qWOYNXXMPkHznMXFMQevCjTck0q94aSZt0UV0jnAXGvtszhT35a7NyyR5HLTi6uawyRf0M9ZKxfwi7efZP/KHSwZcig/P+1q3h9yaPPlNbVNRKRjkjVQ+kVjGfcHwFXW2rL2riCSSKmy6tfUsQN5fvmWVs3Um7ZD5Pvx0aZyLntiWcQpU/Gs0AoXagHNKwu2J6oG3KHQPo3Gk7FqKR6VXy1XZWziMc72RI5vXtGEsGOMJXhVoOGuVOkNJ614jTEZ1toA8E2gqMXvkvU7nUiXaTnNzRsKcsbHC7ns7ScYUrGND/cfza++/UvePuDw5t4A508Yyi2nH+byqEVEUpcrXz6MMQuAgWF+9Vvgj8DNOL2gbwbuAn4SZh9FNH6RGjp0aMLGKtIkFSq1nNXcIq/yBvvej2imTMWzQitcqFXfEGBrZQOhkHWqkyyELBzYb9/G4DOeWUFlXYBAKMSOynrWlVbywwkHtGrA7fOYVmXu4FQtebBsraijIRgi0+shPzvD1YPneFR+tVyVsUnIOtu7enyxBq8KNNyVKr3hpJV5wP+MMTuAWuANAGPMgYCacku3Nn9ZCdc+t5L6+gZO+3Qxl781jxFlm/lo4IFcf+LPWDTiyFZNJgtyfAqTREQ6yZVAyVp7QjSXM8Y8BLwUYR9zcfoFMH78+O7Qd1dcFu+pOYlqpHzPuV/lnnOjv3w0U6biXaG1d6i1aHUpl85bSnVDkJB1xpCX6eWaUw5pdb07Xl1NWY0fr6d1r6VXPt7KK7+c3Gp/ewdg9YEQHg8EghavMQSClp3VDQSCuzt0H+IhHpVfLVdl9BgnTApZZ7sb44sleFWg4a5U6Q0ne1hrbzXG/AfYD/i3tc31qB6cXkoi3dasf65kysr/ccWbj3Pwzi/5tP8wLjrjOl4/8OjWq5XgNN6+ceoYl0YqIpI+kq482hizn7W2ad3z7wEfuzkeEYj/1JxENlKONfiKdspUoiu0sn1e/EFLIBQiw+Mh27dvhU3xjmo8pv1eS+ECsC3ldfhDITyePdcNhSwNQffy6HhUfrVclTHe4WSie4cp0HBXqvSGk9astUvCbFvrxlhEutr8ZSXMfm0NJeW1GJzpDFjLCeve49E3H+UrpetZ12cwP596NS+PPhZr9p1Pr35JIiLxk3SBEvD/jDFH4PwfsQGY7upoRIj/1JxENVLuSPAV7ZSpRDZPnrO4GK/HOE3FrWn+d2emPu0dgI2/5XUqakKE7J5pdVjIjLZ5UwLEq/Kr5aqMyTi+SBRouCtVesOJiABcN38ljy35kqY/A1lrmbx+KVe++ShHbPmMDQX78cvvXMULh0wm5Nl3xdHbztDqbSIi8ZZ0gZK19oduj0Fkb/GempOoRsodCb6imTKV6ObJa7ftprzWTyjkJMmBYJC6QJBAMNTqcsP75rJuezWmnV5L4RxUmM+arY230zitriDHx0GF+Z0ef2cke2+uRI5PgYb7kv31JyLSstF2k4lffMSVbzzK10o+YVPPQn598mU8d+jxBLz7HtqoIklEJHGSLlASSUbxnpqTqEbKHQm+opkylejmybX+EMEQGBrbHFgIhqDG3zpQuuaUQ/jVMyuoqg80Nx0vyPLt02spnIkj+vDehl14PQZfY3BWURdg4og+nR6/dJwCDRERiWTvqqQjN33CVW88yjFffsTWHn247luX8OTYE/F7fWGvX5DjY9nMb3XdgEVEuhkFSiJRiPfUnEQ1Uu5o8NXelKmNZTV4DRRvr2peIa1fj8y4NU/2B1oERzbCdpzw4c4zD+9QRcs7xbvo3yOTyrpAq1Xe3inexWVxuRciIiISL/OXlTSHSWO3rOXKNx5jyvoP2Z5bwKzjL+KxI06m3pcV8foG1HhbRCTBFCiJRCHeU3MS1Ug5UT1pemR6Wbe9Gq8xzSuklZTXcWD/vE7tt4nHY8jAErLONDZjwGtobqDdUkcrWjaW1dCvRxb987Obt1lrtaKYRC2RfcRERKS12a+tYXRpMVe+8RgnrnuXXTk9uW3KBfxj3Heozcxu87oGOG/CUE1zExFJMAVKIlGK99ScRDRSTlRPGtO03K5p/AGwLbZ3UlNvJJ/HNPdGClrL8L77Vlbdv2Bth4K4Ib1zWb+jap8KpeH9esTlPkh6S3QfMRERaeGTT/jN327g1DVvsjsrjzuPO5+/HTmVqqzIFddNFd+DCnKYcdIohUkiIl1AgZJImvloUzmrNldQ3RCkotbPR5vKO33AW1kfYFBBNjuqGprDmIE9s6iqD8RlzNH2Rrp/wVruW7iucYU8ZzrffQvXAbQbKjX1UPIY50tnQzDE9qoGfnBUavVQUpWMOxLdR0xERIDPPoObboLHH+cbvmzun3gODx/1PXZnt/7jjxpti4gkB/fWyxaRuGsKXGr9wVaBy/0L1nZqv0N655Lh9TCifw9GD+zJiP49yPB6OtyUfG9NvZHGDenNwJ7ZjBvSmzvPPHyfA/WH31zfGCZ58BhP46mzvT3vFO+iMD+TTK+HkIVMr4fC/EzeKd4Vl/vQFZqqZEor61pVySxaXer20NLexrIacnz7LkOtKZMiInGwYQP85CdwyCHw3HMwYwaLXnmXP37zglZhkgHOnzCUZTO/pTBJRCQJqEJJJI20DFzAqcQJhEI8/Ob6Tk2vS1RvppaimVJY3eAEZS15jLO9PRvLauibl0W/HqnbQ0lVMu6J90qPIiICbNoEt94Kf/4zeDxw6aVwzTXM3xxg9mtrqPUH8RpD0FpNZRMRSUIKlETSSGcCl7YkqjdTS9FM5crLdMKslr26Q9bZ3p50CAQ2ltVQkNN6aWRVyXSNrghV3aAplCLiiq1b4bbbYM4cCIXgwgvht7+FQYOYv6yEa59bSa3f+e4StJYcn1dhkohIEtKUN5E0kpfpJWRbb4s2cGnPlNGFzCuawBtXH8+8oglxD5Oimcp14aThhKxTdRWyocZTZ3t7pk8egT9oqWkIYK1zmmqBwJDeuc1fsJukWiiWqqaMLmTW1DEU5mdTUeunMD+bWVPHpHT4oimUItLlduyAX/8aRoyAP/wBzj8f1q6FBx9sDpOuempF2P/rZr+2xqVBi4hIJKpQEkkjF04azn0L1xEIhZpXO4k2cHFTtFO5mqbtdWSVtymjCzlzU/k+102lQCBdq2RSRbxXenSbplCKSJcpK4O77oL77oPqaidImjkTDjyw+SJNlUlBa8PuYnN5bVeNVkREoqRASSSNdCZwcVMsU7kuO+HgDt2fRatLeWZpCf3zsxjaGMY8s7SEsYMLUubguSumHkr3oSmUIpJwu3c7IdJdd0FFBZx9Ntx4o9N8u4WmyqRIYRLA/gU5CR6siIjESoGSSJrpaODiplj6G92/YG2HArN0qcZItyoZcU869BWT+DHGzAa+CzQAnwM/ttaWuzooSV3V1fD738P/+3+waxecfjrcdBOMHQs4AdLs19ZQUl6LASLHSI6mHkoiIpJc1ENJJM0sWl3KtLlLmHTHQqbNXZIS/VCi7W90/4K13LdwHbV+p/l4rT/IfQvXcf+Cte3ehpZ9F2ktHfqKSVy9DhxqrR0LrAWudXk8kopqa+Gee5weSddcA0cfDe+/D88/3ypMuva5lZQ0TmFrL0zyGsNtZxymhtwiIklIgZJIGknVJrvRNjx++M31eAxkeDx4jKfx1NneHjW0blsqBpHSOenYaFw6zlr7b2ttoPHsEmCwm+ORFFNf7zTWPvBAuPJKOOwwePttePllGD++1UVnv7Zmn/+PI8nxebnr7MMVJomIJClNeRNJI6k8rSuaqVzVDU5lUkse42xvjxpaR9YURPq8plUQOQuS/nUjnaMplBLBT4An3R6EpAC/H/7+d7j5ZvjyS5g0CR57DKZMCXvx+ctKmiuT2qPKJBGR5KdASSSNpHuT3bxMJwjymD3bQtbZ3h41tI4slYNIST6LVpcyZ3ExG8tqGKL3WVIxxiwABob51W+ttf9svMxvgQDwWBv7KQKKAIYOHZqAkUrSCwad4GjWLPj8czjqKHjoITjxRDBmn4vPX1bCjS+sorzWH9Xuc3xehUkiIilAgZJIGkn3JrsXThrOfQvXEQiF8BgnTApZZ3s0VI0RXroHkdJ1VO2W3Ky1J7T1e2PM/wHfAb5pbeTltqy1c4G5AOPHj2+vBY6kk1AInn7aWalt9WoYNw5efBFOPXWfICnWxttNeuf6uOG7YxQmiYikAPVQEkkj6d5k97ITDuby4w8kx+clEHJCj8uPPzDlVrVLNuovJfHSstrNGOfU5zXMWVzs9tCkHcaYk4GrganWWqXJ0pq1TmPtI46Ac88FrxeefRY++AC+852wYVIsjbcBBhXkcO85R7Bs5rcUJomIpAhVKImkke4wreuyEw5WgBRn6i8l8aJqt5T2eyALeN044cASa+3F7g5JXGctvPIKXH89LF0KBx8Mjz8OZ5/thErsqUTaXF5LrxwfxkBZTXRT28AJkt665vhE3QMREUkgBUoiaUbTuiRW3SGIlK6R7tNu05m19kC3xyBJxFr4z3+cIGnJEhg+HP72NzjvPMjY8/5uqkRqqnKNtkdSkxyflxknjYrnyEVEpAspUBKRbkPNgiNTECnxoGo3kTSweLETJC1eDEOGwJw58OMfg8+3z0Vnv7ZmnynT0VKvJBGR1KdASUS6BTULbpvCNokHVbuJpLB333WCpNdfh4ED4YEH4KKLICsr4lU2N/ZIikZTY+5BBTnMOGmUgiQRkTSgQElEuoWWzYIBcjMzqGkIMGdxcbc/2FXYFh2FbtFRtZtIilm6FGbOhH/9C/r1gzvvhJ/9DHLbn6q6f0FOc+PttihEEhFJT1rlTUS6hY1lNeT4vK22qVmwQytzta8pdCutrGsVui1aXer20EREOmblSjjjDDjySHj7bfjd72D9erjqqqjCJIAZJ43a5//WlnJ8Xu495wjeuuZ4hUkiImlIFUoi0i2oWXBkWpmrfapwE5G0sWYN3HgjPPkk5Oc7//7lL6FXr6h3sffKbtk+D+U1/uZV3spr/OyvqiQRkbSnQElEugU1C45MYVv7FLqJSMr7/HOYNQsefRRycuCaa+BXv4I+fWLaTbiV3XJ8Xu455wiFRyIi3YymvIlItzBldCGzpo6hMD+bilo/hfnZzJo6RtUlOGGbP2ipaQhgrXOqsK21Ib1z91nJSKGbiKSEL7+EoiIYPRqeegquuAKKi50pbjGESfOXlXDs7Qv55ZPLw34ezn5tTbxHLiIiSU4VSiLSbahZcHhamat9qnATkZSzebMTGj30kHP+4ovhN7+B/faLeVd7VyWFvbkYVnwTEZH0oEBJREQUtrVDoZuIpIzSUrjjDnjwQQgE4Cc/gd/+FoYO7fAuZ7+2ps0wCZwV30REpHtRoCQiIhIFhW4iktR27oQ774QHHoDaWvjRj+D662FE5ysp26s+yvF5mXHSqE7fjoiIpBZXeigZY84yxqwyxoSMMeP3+t21xph1xpg1xpiT3BifiIiIiEhKqKiAG26A4cOdyqSpU+GTT+Cvf41LmARtVx8NKsjhtjMOU0NuEZFuyK0KpY+BM4A5LTcaY74CnAuMAfYHFhhjDrbWtl1jKyKSohatLmXO4mI2ltUwRNOoREQkWlVVcP/9TlVSWRl8//tw441w6KFxv6kZJ43ap4dSjs+rIElEpJtzpULJWvuptTbcUhCnAU9Ya+utteuBdcBRXTs6EZGusWh1KTNfWEVpZR0FOT5KK+uY+cIqFq0udXtoIiKSrGpqnBBp+HCnN9Kxx8LSpfDMMwkJkwBOHzeI2844jEEFORhUlSQiIo5k66E0CFjS4vymxm0iImlnzuJifF5DbqbzUZybmUFNQ4A5i4tVpSQiIq3V1cHcuXDbbbB1K3zrWzBrFhx9dJfc/OnjBilAEhGRVhIWKBljFgADw/zqt9baf0a6WphtNsL+i4AigKGdWLVCRMQtG8tqKMjxtdqW4/OyqazGpRGJiEjSaWhw+iHdcgts2gRf/zo89RQcd5zbIxMRkW4uYYGStfaEDlxtEzCkxfnBwOYI+58LzAUYP3582NBJRCSZDemdS2llXXOFEkCtP8jg3rkujkpERJJCIACPPOJUIW3YABMnwt/+BscfDybc32BFRES6lis9lNrwAnCuMSbLGDMcOAh4z+UxiYgkxPTJI/AHLTUNAax1Tv1By/TJ8VmVR0REUlAwCI8/Dl/5CvzkJ9C3L7z8Mrz1Fnzzm10WJs1fVsKxty9k+DX/4tjbFzJ/WUmX3K6IiKQOVwIlY8z3jDGbgInAv4wxrwFYa1cBTwGfAK8CP9cKbyKSrqaMLmTW1DEU5mdTUeunMD+bWVPHqH+SiEh3FAo5jbXHjoXzzoPsbJg/H95/H045pUurkuYvK+Ha51ZSUl6LBUrKa7n2uZUKlUREpBVXmnJba58Hno/wu1uBW7t2RCIi7pgyulABkohId2YtvPQSXH89rFgBo0fDk0/CmWeCx53JBLNfW0Otv/XfdGv9QWa/tkaNuUVEpFmyTXkTEREREUl/1sJrr8GECTB1KlRVOT2TPv4Yzj7btTAJYHN5bUzbRUSke1KgJCIiIiLSlRYtclZpO/lk2LYNHn4YPv0Uzj8fvF63R8f+BTkxbRcRke7JlSlvIiIiIiLdzttvO1PbFi6E/feHBx+En/4UMjNdHdb8ZSXMfm0Nm8tr2b8gh2+M7s+zH5a0mvaW4/My46RRLo5SRESSjSqUREREREQS6YMPnMbaxx7rTGm75x5Ytw5+9rOkCJP2bsD97IclfP/IQQwqyMEAgwpyuO2Mw9Q/SUREWlGFkoiIiIhIIqxYATNnwgsvQN++cMcd8POfQ16e2yNrFqkB939Xb+eta453aVQiIpIKFCiJiIiIiMTTJ5/AjTfC009Dr15w881w2WXQs6erw9p7atuMk0apAbeIiHSYAiURERGRbs4YczNwGhACSoELrLWb3R1VCvrsM7jpJnj8cacK6brr4MoroXdvt0fWPLWtqRqppLyWa59bSUGuj7Ia/z6XVwNuERFpj3ooiYiISFK7f8Faxt74GpkDRn7V7bGksdnW2rHW2iOAl4CZLo8ntWzY4DTXPuQQeO45mDED1q93KpOSIEyCyFPbrHUabrekBtwiIhINBUoiIiKStO5fsJb7Fq5rOhC2bo8nXVlrd7c4m4ce6+hs2uQ01j74YHjsMbj0UidIuuMO6NfP7dG1EmkKW0Wtn9vOOEwNuEVEJGaa8iYiIpIGFq0uZc7iYjaW1TCkdy7TJ49gyuhCt4fVaQ+/uR6PgQyP/gaWaMaYW4EfARXAN9q4XBFQBDB06NCuGVyy2boVbr8d/vQnCIXgwgvhN7+BwYPdHlnYPkmnjxvE/gU5lIQJlfYvyOH0cYMUIImISMz07UxERCTFLVpdyswXVlFaWUdBjo/SyjpmvrCKRatL3R5ap1U3BPEYt0eRHowxC4wxH4f5OQ3AWvtba+0Q4DHgF5H2Y62da60db60d379//64afnLYsQN+/WsYMQJ+/3s4/3xYuxYefDBpwqRrn1tJSXktlj19kuYvK2HGSaM0tU1EROJKFUoiIiIpbs7iYnxeQ26m8996bmYGNQ0B5iwuTvkqpbxML7V+hUrxYK09IcqLPg78C7ghgcNJLWVlcNddcN99UF0N550HN9wABx7o9shaidQnafZra3jrmuObL7N39ZKIiEhHKFASERFJcRvLaijI8bXaluPzsqmsxqURxc+Fk4Zz38J1BEIht4eS1owxB1lrP2s8OxVY7eZ4ksbu3U6IdNddUFEBZ58NN97oNN9OQpH6JDVt19Q2ERGJJwVKIiIiKW5I71xKK+uaK5TAqUoY3DvXxVHFx2UnHAw4vZQA1Sklzu3GmFFACPgCuNjl8birutqZ0vb//h/s2gWnnQY33QSHH+72yNrUVp8kERGReFMPJRERkRQ3ffII/EFLTUMAa51Tf9AyffIIt4cWF5edcDAf3XgSDds+X+r2WNKVtfb71tpDrbVjrbXftdaWuD0mV9TWwj33OD2SrrkGjj4a3n8f5s9P+jAJUJ8kERHpUgqUREREUtyU0YXMmjqGwvxsKmr9FOZnM2vqmJTvnyTSZerrncbaBx4IV14Jhx0Gb70FL78M48e7PbqonT5uELedcRiDCnIwwKCCHG474zBNcxMRkYTQlDcREZE0MGV0oQIkkVj5/fD3v8PNN8OXX8KkSfDYYzBlitsj6zD1SRIRka6iCiURERER6V6CQXjkEae59kUXwcCB8NprsHhxSodJIiIiXUmBkoiIiIh0D6EQPPkkHHoo/OhHkJ8PL74IS5bAt74FRn3fRUREoqVASURERETSm7VOY+0jjoBzzwWvF555Bj78EL7zHQVJIiIiHaAeSiIiIiKSnqyFV16BmTOd8Ojgg+Hxx+Hss51QKcXMX1bC7NfWsLm8lv0Lcphx0ij1SxIREdeoQklERERE0ou1sGABHHMMnHoq7NoFf/0rrFoF06albJh07XMrKSmvxQIl5bVc+9xK5i8rcXtoIiLSTSlQEhEREZH08cYb8I1vwIknwqZNMGcOrFkDF1wAGalbnD/7tTXU+oOtttX6g8x+bY1LIxIRke5OgZKIiIiIpL5333Uaa0+e7ARI998Pn30GRUXg87k9uk7bXF4b03YREZFEU6AkIiIiIqlr6VKnsfaECbBsGdx5J3z+OVx6KWRnuz26uNm/ICem7SIiIommQElEREREUs/HH8P3vw9HHglvvw2/+x2sXw9XXQW5uW6PLu5mnDSKHF/r3k85Pi8zThrl0ohERKS7S92J5CIiIiLS/axZAzfeCE8+Cfn5cMMNcMUV0KuX2yNLqKbV3LTKm4iIJAsFSiIiIiKS/IqLYdYseOQRyMmBa66BX/0K+vRxe2Rd5vRxgxQgiYhI0lCgJCIi3L9gLQ+/uZ7qhiB5mV4unDScy0442O1hiYjAl1/CLbfAX//qrNJ2xRXw619DYaHbI+uQ+ctKVGUkIiJpQYGSiEg3d/+Ctdy3cB0eAxkeZxnq+xauA1CoJCLu2bzZ6Yv00EPO+Ysvhmuvhf33d3dcnTB/WQnXPreSWn8QgJLyWq59biWAQiUREUk5rjTlNsacZYxZZYwJGWPGt9g+zBhTa4xZ3vjzJzfGJyLSnTz85vrGMMmDx3gaT53tIiJdrrTUaaw9ciTMmQMXXACffQYPPJDSYRI4/Y+awqQmtf4gs19b49KIREREOs6tCqWPgTOAOWF+97m19oiuHY6ISPdV3RAkY68/L3iMs11EpMvs2gWzZzvBUW0t/PCHMHMmjBjh9sjiZnN5bUzbRUREkpkrgZK19lMAY4wbNy8iIi3kZXqp9QfxtPhIDllnu4hIwlVUwD33wN13Q1UVnHuus3LbqFFujyzu9i/IoSRMeLR/QY4LoxEREekcV6a8tWO4MWaZMeZ/xpjjIl3IGFNkjPnAGPPB9u3bu3J8IiJp5cJJwwlZCIRChGyo8dTZLiKSMFVVTo+k4cPhppvgxBPho4/g8cfTMkwCmHHSKHJ8rcP6HJ+XGSel5/0VEZH0lrAKJWPMAmBgmF/91lr7zwhX2wIMtdbuNMYcCcw3xoyx1u7e+4LW2rnAXIDx48fbeI1bRKS7aWq8rVXeRKRL1NTAgw/CHXfAjh3wne/ArFkwbpzbI0u4psbbWuVNRETSQcICJWvtCR24Tj1Q3/jvD40xnwMHAx/EeXgiItLCZSccrABJRBKrvh7mznWqkrZuhW99ywmSjj7a7ZF1qdPHDVKAJCIiacGtptxhGWP6A7ustUFjzAjgIKDY5WGJiIiISEc1NMBf/wq33AKbNsHXvw5PPQXHRexsICIiIinAlR5KxpjvGWM2AROBfxljXmv81WTgI2PMCuAZ4GJr7S43xigiIiIinRAIwN/+5vRDuvhiGDIEFiyA//5XYZKIiEgacGuVt+eB58NsfxZ4tutHJCIiIiJxEQzCk086jbbXroUjj3R6Jp18MmiFXxERkbSRjKu8iYiIiEiqCYXg2Wdh7Fg47zzIyoLnn4f334dTTlGYJCIikmYUKImIiIhIx1kLL77oVCKdeaYTLD35JCxfDqefriBJREQkTSVVU24RERERSSG7d8OECfDeezByJPzjH/CDH4DX6/bIREREJMEUKImIiIhIx3z2GQwdCg8/DD/6Efh8bo9IREREuoix1ro9hk4zxmwHvnB7HDHqB+xwexDSip6T5KLnI7no+Ugu3fX5OMBa29/tQcgeKfodLBG663uyJT0GDj0ODj0Oegya6HFwpPLjEPH7V1oESqnIGPOBtXa82+OQPfScJBc9H8lFz0dy0fMhklz0ntRj0ESPg0OPgx6DJnocHOn6OKgpt4iIiIiIiIiIxESBkoiIiIiIiIiIxESBknvmuj0A2Yeek+Si5yO56PlILno+RJKL3pN6DJrocXDocdBj0ESPgyMtHwf1UBIRERERERERkZioQklERERERERERGKiQKkLGGP+YowpNcZ83GLbjcaYEmPM8safb7s5xu7EGDPEGPNfY8ynxphVxpjLG7f3Mca8boz5rPG0t9tj7Q7aeD70HnGBMSbbGPOeMWZF4/NxU+N2vT9c0sZzoveISJIwxtxsjPmo8b34b2PM/m6PyQ3GmNnGmNWNj8XzxpgCt8fkBmPMWY2f1yFjTNqt6tQWY8zJxpg1xph1xphr3B6PG8Id+3U3kb7fdzeRvsOlE0156wLGmMlAFfAPa+2hjdtuBKqstXe6ObbuyBizH7CftXapMSYf+BA4HbgA2GWtvb3xP8De1tqr3Rtp99DG83E2eo90OWOMAfKstVXGGB/wJnA5cAZ6f7iijefkZPQeEUkKxpie1trdjf++DPiKtfZil4fV5Ywx3wIWWmsDxpg7ALrj/xXGmEOAEDAH+JW19gOXh9QljDFeYC1wIrAJeB+YZq39xNWBdbFwx37dTaTv993wtRD2O5y1donLQ4sbVSh1AWvtYmCX2+MQh7V2i7V2aeO/K4FPgUHAacDfGy/2d5xQQxKsjedDXGAdVY1nfY0/Fr0/XNPGcyIiSaIpTGqURzd9j1pr/22tDTSeXQIMdnM8brHWfmqtXeP2OFxwFLDOWltsrW0AnsD5/tCt6NhP3++bdIfvcAqU3PWLxpLgv2j6iDuMMcOAccC7wABr7RZwPgSBQheH1i3t9XyA3iOuMMZ4jTHLgVLgdWut3h8ui/CcgN4jIknDGHOrMWYjcB4w0+3xJIGfAK+4PQjpUoOAjS3Ob6IbhgjSWpjv991KG9/h0oICJff8ERgJHAFsAe5ydTTdkDGmB/As8Mu9/rIoLgjzfOg94hJrbdBaewTOX5aPMsZ0y3LtZBLhOdF7RKQLGWMWGGM+DvNzGoC19rfW2iHAY8Av3B1t4rT3ODRe5rdAAOexSEvRPA7dkAmzLa2qMSQ2Ot5K/+/VGW4PoLuy1m5r+rcx5iHgJReH0+00zmF9FnjMWvtc4+Ztxpj9rLVbGuf9lro3wu4l3POh94j7rLXlxphFOL169P5IAv+/vfsP9auu4zj+fDGZLRsLpwSRNlvT0ciNpZJLYuWsiFhbJWkS6wf9gpr9cAQVWZZgP1iRJlEZkSzLIZSoiPbDWs5LtprmTEaiRlaWo2E5zZrv/jifb31d98e+6+77HbvPB1zu+X7O+XzO+3zPPfd+z/t+Pp/Tf076507yGpEOvqpatZ+bfhu4HrjwIIYzMlO9D0nWAa8BzqzDeLLWAX4eZpLfA8f1vX4O8IcRxaIRm+B+a8ba53P1YTNhuz2URqTdkPWs5TD6oTrUtcnRrgB+U1Ub+1ZdC6xry+uA7w87tploovPhNTIaSY7tPZUnyRxgFXAPXh8jM9E58RqRDh1JFvW9XE33e3PGSfIq4MPA6qraM+p4NHS3A4uSnJBkNnAO3ecHzTCT3G/NKJN8rj5s+JS3IUhyFbASOAZ4iO4/VivphikUcD/wrt78JDq4kpwBbAF+TfcEDoCP0I3rvRo4HvgdcHZVzegJ9YZhkvNxLl4jQ5fkZLpJt2fR/dPh6qq6KMl8vD5GYpJzciVeI9IhIck1wEl0f8ceAN5dVQ+ONqrhS/Jb4EhgVysam6FPu1sLXAocC+wGtlfVK0ca1JAkeTXwRbq/Wd+oqotHG9HwjXfvV1VXjDSoIZvo831V3TC6qIZvos9wo41qeplQkiRJkiRJ0kAc8iZJkiRJkqSBmFCSJEmSJEnSQEwoSZIkSZIkaSAmlCRJkiRJkjQQE0qSJEmSJEkaiAklSZIkSZpmSeYn2d6+/pTkwba8O8ndQ45lTZIX9L2+KMmqA2hnQZK7Jli3JMmPkuxMcm+STyaZ9vvNyY4lyS1JTpnufUoanwklSZIkSZpmVbWrqpZV1TLgK8AX2vIy4Mnp3l+SIyZZvQb4TxKmqj5eVT+Yxn3PAa4FLqmqE4EXAqcB50/XPvqs4SAei6T9Z0JJkiRJkoZrVpKvJdmR5KaWkCHJwiQ3JtmWZEuSxa38uUl+mOTO9v34Vv7NJBuT/Bj4zHj1k6wAVgOfaz2kFrZ6b2htnJpka5I7kvw8ydzWE2lLkl+2rxVTHM+bgFur6iaAqtoDvBfY0PbxiSQX9DZOcleSBW35ey3eHUne2bfN35Nc3OIaS/KsqY6lX5JXJLmtxb85yTNa+SVJ7m7v5ecHP3WSekwoSZIkSdJwLQK+XFVLgN3A61v5V4H3VdWLgAuAy1v5ZcC3qupkYBPwpb62TgRWVdWHxqtfVVvpeg9taD2m7u1VTDIb+C5wflUtBVYBjwF/Bs6qquXAG/fZ33iWANv6C9p+5iR55hR139biPQVYn2R+Kz8KGGtx/RR4x2TH0i/JMcDH2vuyHPgF8MEkRwNrgSXtvfz0FLFJmsRk3SIlSZIkSdPvvqra3pa3AQtaD5oVwOYkve2ObN9PB17Xlq8EPtvX1uaq2jtF/YmcBPyxqm4HqKpHAJIcBVyWZBmwly5pNZkANUH5VNYnWduWj6NLtu0CngCua+XbgLP2o62eF9MNi7u1vRezgduAR4DHga8nub6vfUkHwISSJEmSJA3XP/qW9wJz6EaP7G7zLE2lP3nzaPs+SP2eiRJBHwAeApa2dh+fop0dwEuf0nDyPODhqtqd5F88dXTM09o2K+l6RZ1eVXuS3NJbB/yzqnqx7WWwe9cAN1fVuf+zIjkNOBM4h25Y3ssHaFdSH4e8SZIkSdKItd5B9yU5GyCdpW31VroECMB5wM8GrP83YO44u70HeHaSU1uduW1y73l0PZeeBN4MzJoi/E3AGX1PW5tDN0zuwrb+fmB5W7ccOKGVzwP+2pJJi+l6Fk1lomPpNwa8JMnz2z6fnuTE1otrXlXdALyfboJ0SQfIhJIkSZIkHRrOA96e5A66Xj+vbeXrgbcmuZMuwTPR09Mmqv8dYEOSXyVZ2Nu4qp6gmyPp0lbnZroeQpcD65KM0Q13e5RJVNVjdJNlfzTJTuBhukm6N7VNrgGOTrIdeA+ws5XfCBzRjutTdImgqYx7LPvE8xfgLcBVre0xYDFdIuq6VvYTup5Ykg5Q/tuLUJIkSZKk/0+SNcBG4GVV9cCIw5F0kJhQkiRJkiRJ0kAc8iZJkiRJkqSBmFCSJEmSJEnSQEwoSZIkSZIkaSAmlCRJkiRJkjQQE0qSJEmSJEkaiAklSZIkSZIkDcSEkiRJkiRJkgbybzYguRrerZ77AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import statsmodels.api as sm\n", "import numpy as np\n", "model=ols(\"mpg ~ horsepower + I(horsepower**2)\", data).fit()\n", "\n", "#otteniamo i valori predetti dal modello:\n", "fitted = model.fittedvalues.fillna(0) #rimpiazzo eventuali NaN con zero\n", "\n", "plt.figure(figsize=(20,22))\n", "sns.residplot(x=fitted, y='mpg', data=data.dropna(),lowess=True,line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8}, ax=plt.subplot(421))\n", "sm.qqplot(fitted-data.dropna()['mpg'], line='45',fit=True, ax=plt.subplot(422))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Anche in questo caso, i residual plot sono \"migliori\" di quelli del modello base:" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import statsmodels.api as sm\n", "import numpy as np\n", "model=ols(\"mpg ~ horsepower\", data).fit()\n", "\n", "#otteniamo i valori predetti dal modello:\n", "fitted = model.fittedvalues.fillna(0) #rimpiazzo eventuali NaN con zero\n", "\n", "plt.figure(figsize=(20,22))\n", "sns.residplot(x=fitted, y='mpg', data=data.dropna(),lowess=True,line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8}, ax=plt.subplot(421))\n", "sm.qqplot(fitted-data.dropna()['mpg'], line='45',fit=True, ax=plt.subplot(422))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Regressione Polinomiale\n", "Sembra comunque che il modello con termini di interazione sia migliore di quello quadratico. Potremmo pensare di unire le due cose facendo fit di un regressore polinomiale:\n", "\n", "$$mpg = \\beta_0 + \\beta_1 horsepower^2 + \\beta_2 weight^2 + \\beta_3 horsepower\\cdot weight + \\beta_4 horsepower + \\beta_5 weight$$\n", "\n", "Ciò si fa facilmente in statsmodels come segue:" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: mpg R-squared: 0.749
Model: OLS Adj. R-squared: 0.746
Method: Least Squares F-statistic: 230.9
Date: Tue, 31 Oct 2023 Prob (F-statistic): 1.30e-113
Time: 07:31:26 Log-Likelihood: -1089.9
No. Observations: 392 AIC: 2192.
Df Residuals: 386 BIC: 2216.
Df Model: 5
Covariance Type: nonrobust
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coef std err t P>|t| [0.025 0.975]
Intercept 63.4053 2.939 21.572 0.000 57.626 69.184
I(horsepower ** 2) 0.0003 0.000 1.138 0.256 -0.000 0.001
I(weight ** 2) 2.438e-07 7.94e-07 0.307 0.759 -1.32e-06 1.8e-06
horsepower -0.2646 0.052 -5.093 0.000 -0.367 -0.162
weight -0.0102 0.003 -3.558 0.000 -0.016 -0.005
horsepower:weight 3.594e-05 2.53e-05 1.421 0.156 -1.38e-05 8.57e-05
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Omnibus: 31.272 Durbin-Watson: 0.917
Prob(Omnibus): 0.000 Jarque-Bera (JB): 50.516
Skew: 0.531 Prob(JB): 1.07e-11
Kurtosis: 4.402 Cond. No. 1.63e+08


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.63e+08. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: mpg R-squared: 0.749\n", "Model: OLS Adj. R-squared: 0.746\n", "Method: Least Squares F-statistic: 230.9\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 1.30e-113\n", "Time: 07:31:26 Log-Likelihood: -1089.9\n", "No. Observations: 392 AIC: 2192.\n", "Df Residuals: 386 BIC: 2216.\n", "Df Model: 5 \n", "Covariance Type: nonrobust \n", "======================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "--------------------------------------------------------------------------------------\n", "Intercept 63.4053 2.939 21.572 0.000 57.626 69.184\n", "I(horsepower ** 2) 0.0003 0.000 1.138 0.256 -0.000 0.001\n", "I(weight ** 2) 2.438e-07 7.94e-07 0.307 0.759 -1.32e-06 1.8e-06\n", "horsepower -0.2646 0.052 -5.093 0.000 -0.367 -0.162\n", "weight -0.0102 0.003 -3.558 0.000 -0.016 -0.005\n", "horsepower:weight 3.594e-05 2.53e-05 1.421 0.156 -1.38e-05 8.57e-05\n", "==============================================================================\n", "Omnibus: 31.272 Durbin-Watson: 0.917\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 50.516\n", "Skew: 0.531 Prob(JB): 1.07e-11\n", "Kurtosis: 4.402 Cond. No. 1.63e+08\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.63e+08. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ols(\"mpg ~ I(horsepower**2) + I(weight**2) + horsepower*weight + horsepower + weight\", data).fit().summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notiamo che i p-value dei termini quadratici e dell'interaction term sono alti. Applichiamo backward elimination e iniziamo rimuovendo il termine $horsepower^2$:" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: mpg R-squared: 0.749
Model: OLS Adj. R-squared: 0.746
Method: Least Squares F-statistic: 288.1
Date: Tue, 31 Oct 2023 Prob (F-statistic): 1.37e-114
Time: 07:32:20 Log-Likelihood: -1090.6
No. Observations: 392 AIC: 2191.
Df Residuals: 387 BIC: 2211.
Df Model: 4
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 62.7418 2.882 21.771 0.000 57.076 68.408
I(weight ** 2) -3.068e-07 6.3e-07 -0.487 0.626 -1.54e-06 9.31e-07
horsepower -0.2721 0.052 -5.281 0.000 -0.373 -0.171
weight -0.0095 0.003 -3.388 0.001 -0.015 -0.004
horsepower:weight 5.971e-05 1.43e-05 4.183 0.000 3.16e-05 8.78e-05
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 32.870 Durbin-Watson: 0.913
Prob(Omnibus): 0.000 Jarque-Bera (JB): 52.237
Skew: 0.560 Prob(JB): 4.54e-12
Kurtosis: 4.395 Cond. No. 1.60e+08


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.6e+08. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: mpg R-squared: 0.749\n", "Model: OLS Adj. R-squared: 0.746\n", "Method: Least Squares F-statistic: 288.1\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 1.37e-114\n", "Time: 07:32:20 Log-Likelihood: -1090.6\n", "No. Observations: 392 AIC: 2191.\n", "Df Residuals: 387 BIC: 2211.\n", "Df Model: 4 \n", "Covariance Type: nonrobust \n", "=====================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "-------------------------------------------------------------------------------------\n", "Intercept 62.7418 2.882 21.771 0.000 57.076 68.408\n", "I(weight ** 2) -3.068e-07 6.3e-07 -0.487 0.626 -1.54e-06 9.31e-07\n", "horsepower -0.2721 0.052 -5.281 0.000 -0.373 -0.171\n", "weight -0.0095 0.003 -3.388 0.001 -0.015 -0.004\n", "horsepower:weight 5.971e-05 1.43e-05 4.183 0.000 3.16e-05 8.78e-05\n", "==============================================================================\n", "Omnibus: 32.870 Durbin-Watson: 0.913\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 52.237\n", "Skew: 0.560 Prob(JB): 4.54e-12\n", "Kurtosis: 4.395 Cond. No. 1.60e+08\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.6e+08. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ols(\"mpg ~ I(weight**2) + horsepower*weight + horsepower + weight\", data).fit().summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rimuoviamo ora $weight^2$:" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: mpg R-squared: 0.748
Model: OLS Adj. R-squared: 0.746
Method: Least Squares F-statistic: 384.8
Date: Tue, 31 Oct 2023 Prob (F-statistic): 7.26e-116
Time: 07:32:46 Log-Likelihood: -1090.7
No. Observations: 392 AIC: 2189.
Df Residuals: 388 BIC: 2205.
Df Model: 3
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 63.5579 2.343 27.127 0.000 58.951 68.164
horsepower -0.2508 0.027 -9.195 0.000 -0.304 -0.197
weight -0.0108 0.001 -13.921 0.000 -0.012 -0.009
horsepower:weight 5.355e-05 6.65e-06 8.054 0.000 4.05e-05 6.66e-05
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 34.175 Durbin-Watson: 0.904
Prob(Omnibus): 0.000 Jarque-Bera (JB): 54.522
Skew: 0.577 Prob(JB): 1.45e-12
Kurtosis: 4.417 Cond. No. 4.77e+06


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 4.77e+06. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: mpg R-squared: 0.748\n", "Model: OLS Adj. R-squared: 0.746\n", "Method: Least Squares F-statistic: 384.8\n", "Date: Tue, 31 Oct 2023 Prob (F-statistic): 7.26e-116\n", "Time: 07:32:46 Log-Likelihood: -1090.7\n", "No. Observations: 392 AIC: 2189.\n", "Df Residuals: 388 BIC: 2205.\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "=====================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "-------------------------------------------------------------------------------------\n", "Intercept 63.5579 2.343 27.127 0.000 58.951 68.164\n", "horsepower -0.2508 0.027 -9.195 0.000 -0.304 -0.197\n", "weight -0.0108 0.001 -13.921 0.000 -0.012 -0.009\n", "horsepower:weight 5.355e-05 6.65e-06 8.054 0.000 4.05e-05 6.66e-05\n", "==============================================================================\n", "Omnibus: 34.175 Durbin-Watson: 0.904\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 54.522\n", "Skew: 0.577 Prob(JB): 1.45e-12\n", "Kurtosis: 4.417 Cond. No. 4.77e+06\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 4.77e+06. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ols(\"mpg ~ horsepower*weight + horsepower + weight\", data).fit().summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ci siamo ricondotti al modello con interaction term. Da qui deduciamo che un modello polinomiale non modella i dati meglio del modello con termini di interazione." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ridge e Lasso Regression\n", "È possibile eseguire la Ridge regression in `statsmodels` come segue:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
params
variables
Intercept21.314471
displacement-0.363361
cylinders-0.698638
horsepower-1.090416
weight-3.001519
acceleration-0.149495
model_year2.385728
origin1.028683
\n", "
" ], "text/plain": [ " params\n", "variables \n", "Intercept 21.314471\n", "displacement -0.363361\n", "cylinders -0.698638\n", "horsepower -1.090416\n", "weight -3.001519\n", "acceleration -0.149495\n", "model_year 2.385728\n", "origin 1.028683" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.stats import zscore\n", "from ucimlrepo import fetch_ucirepo \n", "from statsmodels.formula.api import ols\n", "import pandas as pd\n", " \n", "alpha = 0.1\n", "# fetch dataset \n", "auto_mpg = fetch_ucirepo(id=9) \n", " \n", "# data (as pandas dataframes) \n", "X = auto_mpg.data.features \n", "y = auto_mpg.data.targets \n", " \n", "data = X.join(y)\n", "\n", "# Apply z-scoring and drop NA\n", "data2=data.dropna().drop('mpg',axis=1).apply(zscore).join(data.dropna()['mpg'])\n", "\n", "model = ols(\"mpg ~ displacement + cylinders + horsepower + weight + acceleration + model_year + origin\", data2).fit_regularized(L1_wt=0, alpha=alpha)\n", "\n", "params = pd.DataFrame({'variables':['Intercept','displacement','cylinders' , 'horsepower' , 'weight' , 'acceleration' , 'model_year' , 'origin'], 'params':model.params}).set_index('variables')\n", "params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Si può ottenere un ridge regressor ponendo il parametro `L1_wt` a $1$:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
params
variables
Intercept23.345918
displacement0.000000
cylinders0.000000
horsepower-0.381223
weight-4.718045
acceleration0.000000
model_year2.646279
origin0.891852
\n", "
" ], "text/plain": [ " params\n", "variables \n", "Intercept 23.345918\n", "displacement 0.000000\n", "cylinders 0.000000\n", "horsepower -0.381223\n", "weight -4.718045\n", "acceleration 0.000000\n", "model_year 2.646279\n", "origin 0.891852" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = ols(\"mpg ~ displacement + cylinders + horsepower + weight + acceleration + model_year + origin\", data2).fit_regularized(L1_wt=1, alpha=alpha)\n", "\n", "params = pd.DataFrame({'variables':['Intercept','displacement','cylinders' , 'horsepower' , 'weight' , 'acceleration' , 'model_year' , 'origin'], 'params':model.params}).set_index('variables')\n", "params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Come si può vedere il lasso regressor ha impostato dei pesi esattamente a zero." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Esercizi\n", "> 🧑‍💻 Esercizio 1\n", "> \n", "> Si consideri il dataset delle iris di Fisher. Si effettui uno scatterplot per studiare le relazioni tra le variabili. Si calcoli la matrice di correlazione usando gli indici di correlazione di Pearson, Spearman e Kendall. Esistono correlazioni deboli, medie o forti? Si calcoli l'indice di correlazione di Pearson tra le due coppie di variabili che individuano le correlazioni più forti. Si tratta di correlazioni significative?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> 🧑‍💻 Esercizio 2\n", "> \n", "> Si effettui la normalizzazione **z-scoring** su tutte le variabili del dataset delle iris di Fisher. Si calcoli la matrice di covarianza delle variabili normalizzate. Si confronti la matrice ottenuta con la matrice di correlazione calcolata mediante l'indice di Pearson. Ci sono differenze tra le due matrici? Perché?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> 🧑‍💻 Esercizio 3\n", "> \n", "> Si consideri il dataset Titanic. Si calcoli un regressore lineare che predica i valori di `Fare` dai valori di `Survived`, `Pclass`, `Sex` e `Age`. Si inseriscano variabili dummy ove opportuno. Il regressore ottenuto è un buon regressore? Quali variabili contribuiscono significativamente alla regressione? Esistono variabili non rilevanti? Si eliminino tali variabili mediante la tecnica della backward elimination. Si discuta il significato dei coefficienti individuati." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> 🧑‍💻 Esercizio 4\n", "> \n", "> Si consideri il dataset Titanic. Si calcoli un regressore lineare che predica i valori di `Age` dai valori di `Survived`, `Pclass`, `Sex` e `Fare`. Si inseriscano variabili dummy ove opportuno. Il regressore ottenuto è un buon regressore? Si tratta di un regressore migliore o peggiore del regressore calcolato nell'esercizio precedente? Quali variabili contribuiscono significativamente alla regressione? Esistono variabili non rilevanti? Si eliminino tali variabili mediante la tecnica della backward elimination. Si discuta il significato dei coefficienti individuati." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> 🧑‍💻 Esercizio 5\n", "> \n", "> Si consideri il dataset Boston. Si calcoli un regressore lineare che predica i valori di `crim` dai valori delle altre variabili. Si inseriscano variabili dummy ove opportuno. Quali variabili contribuiscono significativamente alla regressione? Esistono variabili non rilevanti? Si eliminino tali variabili mediante la tecnica della backward elimination. Si discuta il significato dei coefficienti individuati." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 1 }