{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# R\u00e9gressions lin\u00e9aires avec Statsmodels et Scikit-Learn\n", "\n", "On peut r\u00e9aliser des r\u00e9gressions lin\u00e9aires de beaucoup de mani\u00e8res avec Python. \n", "On en a retenu 2, statsmodels et scikit-learn. Les deux librairies ont chacunes leurs qualit\u00e9s et leurs d\u00e9fauts, sachez que l'une est plus orient\u00e9 data science et l'autre plus pour des \u00e9conomistes. \n", "\n", "(inspir\u00e9 de la page [Linear Regression with Statsmodels and Scikit-Learn](http://marcharper.codes/2016-06-14/Linear+Regression+with+Statsmodels+and+Scikit-Learn.html))\n", "\n", "Par exemple, statsmodel vous fournira directement le tableau de regression, pour scikit c'est moins imm\u00e9diat \n", "On commence par charger tous les packages qui vont servir dans ce notebook : "]}, {"cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [{"data": {"text/html": ["
\n", ""], "text/plain": [""]}, "execution_count": 2, "metadata": {}, "output_type": "execute_result"}], "source": ["from jyquickhelper import add_notebook_menu\n", "add_notebook_menu()"]}, {"cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["c:\\Python36_x64\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n", " from pandas.core import datetools\n"]}], "source": ["%matplotlib inline\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy import stats\n", "import seaborn as sns\n", "import statsmodels.api as sm\n", "from sklearn import linear_model"]}, {"cell_type": "markdown", "metadata": {}, "source": ["On va utiliser la fameuse base des Iris qu'on peut appeler depuis la librairie seaborn.\n", "Pour chaque fleur, on a des informations sur la longueur et largeur de ses s\u00e9pales ainsi que de ses p\u00e9tales."]}, {"cell_type": "markdown", "metadata": {}, "source": ["Pour comprendre la diff\u00e9rence en image : [S\u00e9pale](http://idao.cirad.fr/content/adventoi/defs/235_fr.html)."]}, {"cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [{"data": {"text/html": ["\n", "\n", "
\n", " \n", " \n", " | \n", " sepal_length | \n", " sepal_width | \n", " petal_length | \n", " petal_width | \n", " species | \n", "
\n", " \n", " \n", " \n", " 0 | \n", " 5.1 | \n", " 3.5 | \n", " 1.4 | \n", " 0.2 | \n", " setosa | \n", "
\n", " \n", " 1 | \n", " 4.9 | \n", " 3.0 | \n", " 1.4 | \n", " 0.2 | \n", " setosa | \n", "
\n", " \n", " 2 | \n", " 4.7 | \n", " 3.2 | \n", " 1.3 | \n", " 0.2 | \n", " setosa | \n", "
\n", " \n", " 3 | \n", " 4.6 | \n", " 3.1 | \n", " 1.5 | \n", " 0.2 | \n", " setosa | \n", "
\n", " \n", " 4 | \n", " 5.0 | \n", " 3.6 | \n", " 1.4 | \n", " 0.2 | \n", " setosa | \n", "
\n", " \n", "
\n", "
"], "text/plain": [" sepal_length sepal_width petal_length petal_width species\n", "0 5.1 3.5 1.4 0.2 setosa\n", "1 4.9 3.0 1.4 0.2 setosa\n", "2 4.7 3.2 1.3 0.2 setosa\n", "3 4.6 3.1 1.5 0.2 setosa\n", "4 5.0 3.6 1.4 0.2 setosa"]}, "execution_count": 4, "metadata": {}, "output_type": "execute_result"}], "source": ["iris = sns.load_dataset(\"iris\")\n", "iris.head()"]}, {"cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [{"data": {"image/png": 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F48ozrjTErNUxxaHYdj1ma5Ej6VVCiMbMP38lhLge2t3E+/T/l1J2O7EdIqqwInJ+rfJ0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BXT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\nliB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jIjJLRFyveyAil4vID6uw3ctF5C22x7tFZHylt0ONq1Dseli+W0RWuDy3W0TGi8hY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\n", "text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["sns.pairplot(iris, hue=\"species\");"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Gr\u00e2ce \u00e0 ces graphiques, on observere une forte relation entre longeur et la largeur des p\u00e9tales. \n", "On r\u00e9alise une regression \u00e0 une variable entre la longueur et la largeur gr\u00e2ce \u00e0 seaborn. "]}, {"cell_type": "markdown", "metadata": {}, "source": ["## Regression \u00e0 une variable avec seaborn"]}, {"cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [{"data": {"image/png": 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Td7+yBYeAQ8AyEI0ZCvwuhud58bud7G8MdXse1afSngl3b5LbWhljXgcOpnAN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\nJ3fd2dWvAAAAAElFTkSuQmCC\n", "text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["sns.lmplot(x=\"petal_length\", y=\"petal_width\", data=iris);"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Si on observe bien qu'une relation existe, on ne connait pas grand chose d'autre. "]}, {"cell_type": "markdown", "metadata": {}, "source": ["## Regression en utilisant scikit-learn"]}, {"cell_type": "code", "execution_count": 6, "metadata": {"collapsed": true}, "outputs": [], "source": ["X = iris[[\"petal_length\"]]\n", "y = iris[\"petal_width\"]\n", "\n", "# On fit le modele\n", "model = linear_model.LinearRegression()\n", "results = model.fit(X, y)"]}, {"cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["-0.363075521319 [ 0.41575542]\n"]}], "source": ["print(results.intercept_, results.coef_)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["La meilleure approximation lin\u00e9aire est donc y=a+bx avec \n", "- a=\u22120.363075521319\n", "- b=0.41575542\n", "\n", "Mais en termes de pr\u00e9sentation de r\u00e9sultats, c'est un peu limit\u00e9... Pas de standard errors, pas de $R^2$ etc (du moins pas automatiquement) "]}, {"cell_type": "markdown", "metadata": {}, "source": ["## Regression en utilisant statsmodels\n", "\n", "Remarque : on invese X et y dans la sp\u00e9cification du mod\u00e8le pour cette librairie. "]}, {"cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": [" OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: petal_width R-squared: 0.967\n", "Model: OLS Adj. R-squared: 0.967\n", "Method: Least Squares F-statistic: 4417.\n", "Date: Sun, 24 Sep 2017 Prob (F-statistic): 1.22e-112\n", "Time: 20:12:37 Log-Likelihood: -8.7179\n", "No. Observations: 150 AIC: 19.44\n", "Df Residuals: 149 BIC: 22.45\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "petal_length 0.3365 0.005 66.463 0.000 0.327 0.347\n", "==============================================================================\n", "Omnibus: 19.720 Durbin-Watson: 0.857\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 23.498\n", "Skew: 0.957 Prob(JB): 7.90e-06\n", "Kurtosis: 3.311 Cond. No. 1.00\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"]}], "source": ["model = sm.OLS(y, X)\n", "results = model.fit()\n", "# Avec statsmodel, on a une sortie qui ressemble beaucoup \u00e0 celle de R\n", "print(results.summary())"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Si vous regardez de plus pr\u00e8s, vous observez que les coefficients des deux r\u00e9gressions sont proches mais pas \u00e9gaux. Probl\u00e8me de pr\u00e9cision ? Non...\n", "\n", "Il faut faire attention avec statsmodels, il n'inclut pas de lui-m\u00eame un intercept ($\\beta_0$) alors que scikit learn le fait. "]}, {"cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": [" OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: petal_width R-squared: 0.927\n", "Model: OLS Adj. R-squared: 0.927\n", "Method: Least Squares F-statistic: 1882.\n", "Date: Sun, 24 Sep 2017 Prob (F-statistic): 4.68e-86\n", "Time: 20:12:37 Log-Likelihood: 24.796\n", "No. Observations: 150 AIC: -45.59\n", "Df Residuals: 148 BIC: -39.57\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "x1 0.4158 0.010 43.387 0.000 0.397 0.435\n", "const -0.3631 0.040 -9.131 0.000 -0.442 -0.285\n", "==============================================================================\n", "Omnibus: 5.765 Durbin-Watson: 1.455\n", "Prob(Omnibus): 0.056 Jarque-Bera (JB): 5.555\n", "Skew: 0.359 Prob(JB): 0.0622\n", "Kurtosis: 3.611 Cond. No. 10.3\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"]}], "source": ["X = iris[\"petal_length\"]\n", "X = np.vander(X, 2) #ici on ajoute\n", "y = iris[\"petal_width\"]\n", "model = sm.OLS(y, X)\n", "results = model.fit()\n", "print(results.summary())"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Ca y est, les coefficients de scikit et de statsmodels sont quasi identiques (en r\u00e9alit\u00e9 si vous regardez apr\u00e8s la 10\u00e8me d\u00e9cimale, ils sont l\u00e9g\u00e8rement diff\u00e9rents...)\n", "\n", "Si on regadre le $R^2$, on se dit qu'on est plut\u00f4t pas mal pour cette r\u00e9gression (en m\u00eame temps, dire que pour un iris, la longueur et la largeur du p\u00e9tale sont corr\u00e9l\u00e9es, c'est un peu normal...)'\n", "\n", "Mais voyons si on peut aller encore plus loin, par exemple, en ajoutant l'information de l'esp\u00e8ce de l'iris, avec des variables cat\u00e9gorielles (qu'on ajoutera sous la forme d'indicatries ou dummies)"]}, {"cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [{"data": {"text/html": ["\n", "\n", "
\n", " \n", " \n", " | \n", " sepal_length | \n", " sepal_width | \n", " petal_length | \n", " petal_width | \n", " species | \n", " setosa | \n", " versicolor | \n", " virginica | \n", "
\n", " \n", " \n", " \n", " 0 | \n", " 5.1 | \n", " 3.5 | \n", " 1.4 | \n", " 0.2 | \n", " setosa | \n", " 1 | \n", " 0 | \n", " 0 | \n", "
\n", " \n", " 1 | \n", " 4.9 | \n", " 3.0 | \n", " 1.4 | \n", " 0.2 | \n", " setosa | \n", " 1 | \n", " 0 | \n", " 0 | \n", "
\n", " \n", " 2 | \n", " 4.7 | \n", " 3.2 | \n", " 1.3 | \n", " 0.2 | \n", " setosa | \n", " 1 | \n", " 0 | \n", " 0 | \n", "
\n", " \n", " 3 | \n", " 4.6 | \n", " 3.1 | \n", " 1.5 | \n", " 0.2 | \n", " setosa | \n", " 1 | \n", " 0 | \n", " 0 | \n", "
\n", " \n", " 4 | \n", " 5.0 | \n", " 3.6 | \n", " 1.4 | \n", " 0.2 | \n", " setosa | \n", " 1 | \n", " 0 | \n", " 0 | \n", "
\n", " \n", "
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"], "text/plain": [" sepal_length sepal_width petal_length petal_width species setosa \\\n", "0 5.1 3.5 1.4 0.2 setosa 1 \n", "1 4.9 3.0 1.4 0.2 setosa 1 \n", "2 4.7 3.2 1.3 0.2 setosa 1 \n", "3 4.6 3.1 1.5 0.2 setosa 1 \n", "4 5.0 3.6 1.4 0.2 setosa 1 \n", "\n", " versicolor virginica \n", "0 0 0 \n", "1 0 0 \n", "2 0 0 \n", "3 0 0 \n", "4 0 0 "]}, "execution_count": 11, "metadata": {}, "output_type": "execute_result"}], "source": ["dummies = pd.get_dummies(iris[\"species\"])\n", "iris = pd.concat([iris, dummies], axis=1)\n", "iris.head()"]}, {"cell_type": "markdown", "metadata": {}, "source": ["## La regression multi-lin\u00e9aire avec statsmodels"]}, {"cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": [" OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: petal_width R-squared: 0.946\n", "Model: OLS Adj. R-squared: 0.944\n", "Method: Least Squares F-statistic: 845.5\n", "Date: Sun, 24 Sep 2017 Prob (F-statistic): 4.88e-92\n", "Time: 20:12:38 Log-Likelihood: 46.704\n", "No. Observations: 150 AIC: -85.41\n", "Df Residuals: 146 BIC: -73.37\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "--------------------------------------------------------------------------------\n", "const 0.2501 0.098 2.561 0.011 0.057 0.443\n", "petal_length 0.2304 0.034 6.691 0.000 0.162 0.298\n", "setosa -0.3410 0.051 -6.655 0.000 -0.442 -0.240\n", "versicolor 0.0944 0.054 1.751 0.082 -0.012 0.201\n", "virginica 0.4967 0.096 5.150 0.000 0.306 0.687\n", "==============================================================================\n", "Omnibus: 6.210 Durbin-Watson: 1.736\n", "Prob(Omnibus): 0.045 Jarque-Bera (JB): 9.578\n", "Skew: -0.110 Prob(JB): 0.00832\n", "Kurtosis: 4.218 Cond. No. 1.69e+16\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The smallest eigenvalue is 9.68e-30. This might indicate that there are\n", "strong multicollinearity problems or that the design matrix is singular.\n"]}], "source": ["X = iris[[\"petal_length\", \"setosa\", \"versicolor\", \"virginica\"]]\n", "X = sm.add_constant(X) # une autre fa\u00e7ons d'ajouter une constante \n", "y = iris[\"petal_width\"]\n", "\n", "model = sm.OLS(y, X)\n", "results = model.fit()\n", "print(results.summary())"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Avec cette version, on s'am\u00e9liore en termes de $R^2$ mais la pr\u00e9cision de notre estimateur est plus faible..."]}, {"cell_type": "markdown", "metadata": {}, "source": ["Pour aller plus loin, de nombreux exemples sont disponibles l\u00e0 : \n", " \n", "- [OLS](http://www.statsmodels.org/dev/examples/notebooks/generated/ols.html)\n", "- [GLS](http://www.statsmodels.org/dev/examples/notebooks/generated/gls.html)\n", "- [Regression quantile](http://www.statsmodels.org/dev/examples/notebooks/generated/quantile_regression.html)"]}, {"cell_type": "code", "execution_count": 12, "metadata": {"collapsed": true}, "outputs": [], "source": []}], "metadata": {"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": "3.6.1"}}, "nbformat": 4, "nbformat_minor": 2}