{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# IntroStat Week 8\n", "\n", "Welcome to the 8th lecture in IntroStat\n", "\n", "During the lectures we will present both slides and notebooks. \n", "\n", "This is the notebook used in the lecture in week 8.\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import scipy.stats as stats\n", "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf\n", "import statsmodels.stats.power as smp\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Height and weight" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear regression with height and weight data" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# data\n", "x = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179]) # height data\n", "y = np.array([65.5, 58.3, 68.1, 85.7, 80.5, 63.4, 102.6, 91.4, 86.7, 78.9]) # weight data" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# make scatter plot:\n", "plt.scatter(x,y)\n", "plt.ylabel(\"weight\")\n", "plt.xlabel(\"height\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear relationship?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now lets put data into a **pandas dataframe**:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y\n", "0 168 65.5\n", "1 161 58.3\n", "2 167 68.1\n", "3 179 85.7\n", "4 184 80.5\n", "5 166 63.4\n", "6 198 102.6\n", "7 187 91.4\n", "8 191 86.7\n", "9 179 78.9\n" ] } ], "source": [ "student = pd.DataFrame({'x': x, 'y': y}) # \"import pandas as pd\"\n", "print(student)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we do a **linear regression model**:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# for now we just run the code, we will understand it later\n", "\n", "# fit the model\n", "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() # OBS: use the statsmodels.formula.api library (smf)\n", "\n", "# Get prediction and confidence intervals\n", "x_pred = pd.DataFrame({'x': np.arange(160,200, 1)})\n", "pred = fitStudents.get_prediction(x_pred).summary_frame(alpha=0.05)\n", "\n", "plt.scatter(x,y)\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.ylabel(\"weight\")\n", "plt.xlabel(\"height\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The red line is the **regression line**.\n", "\n", "The regression line is a trsight line.\n", "\n", "Is is defined by a **slope** and an **intercept** with the y-axis." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\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, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "# later today we will be able to estimate values for the parameters: intercept and slope\n", "print(fitStudents.summary(slim=True))\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# we will also be able to estimate standard error and conficence intervals for the parameters (also in table above)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# later today we will be able to make a prediction interval for \"future\" obervations (with other x-values)\n", "plt.scatter(x,y)\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"obs_ci_lower\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"obs_ci_upper\"], color=\"lightgrey\")\n", "plt.ylabel(\"weight\")\n", "plt.xlabel(\"height\")\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# and later today we will also be able to make a prediction interval for the mean at every value on the x-axis\n", "plt.scatter(x,y)\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"mean_ci_lower\"], color=\"grey\")\n", "plt.plot(x_pred, pred[\"mean_ci_upper\"], color=\"grey\")\n", "plt.plot(x_pred, pred[\"obs_ci_lower\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"obs_ci_upper\"], color=\"lightgrey\")\n", "plt.ylabel(\"weight\")\n", "plt.xlabel(\"height\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Estimating parameters $\\beta_0$ and $\\beta_1$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# First we compute som simulated data, so we know the \"real\" beta_0 and beta_1 (and sigma)\n", "np.random.seed(23498)\n", "\n", "beta_0 = 50\n", "beta_1 = 200\n", "sigma = 90\n", "\n", "# choose som random x-values:\n", "x = stats.uniform.rvs(size = 20, loc=-2, scale = 6)\n", "# simulate y-values from statistical model:\n", "y = beta_0 + beta_1*x + stats.norm.rvs(size = 20, loc=0, scale = sigma)\n", "\n", "plt.scatter(x,y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is now our \"Toy Data\" :-)\n", "\n", "Lets see if we can estimate the parameters " ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "13.795479789979595 225.76353862601528\n", "50 200\n" ] } ], "source": [ "# calculate estimates beta_0_hat and beta_1_hat:\n", "Sxx = np.sum((x - x.mean())**2)\n", "\n", "beta_1_hat = np.sum((x - x.mean())*(y - y.mean())) / Sxx\n", "beta_0_hat = y.mean() - beta_1_hat*x.mean()\n", "\n", "print(beta_0_hat, beta_1_hat)\n", "print(beta_0, beta_1)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot estimated model with data:\n", "plt.scatter(x,y)\n", "plt.plot([-2,4], [beta_0_hat + beta_1_hat*(-2), beta_0_hat + beta_1_hat*(4)], color=\"red\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Great! " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# also plot the \"true\" underlying model (this is *only* possible because we have simulated data - IRL one cannot plot the \"true\" model):\n", "plt.scatter(x,y)\n", "plt.plot([-2,4], [beta_0_hat + beta_1_hat*(-2), beta_0_hat + beta_1_hat*(4)], color=\"red\")\n", "plt.plot([-2,4], [beta_0 + beta_1*(-2), beta_0 + beta_1*(4)], color=\"red\", linestyle='--')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Variation of $\\beta_0$ and $\\beta_1$" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "73.84511187771452 194.84106802781554\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# repeat with new sample:\n", "y = beta_0 + beta_1*x + stats.norm.rvs(size = 20, loc=0, scale = sigma) # y-data with new values of residuals\n", "\n", "# re-calculate parameters\n", "Sxx = np.sum((x - x.mean())**2)\n", "beta_1_hat = np.sum((x - x.mean())*(y - y.mean())) / Sxx\n", "beta_0_hat = y.mean() - beta_1_hat*x.mean()\n", "print(beta_0_hat, beta_1_hat)\n", "\n", "#plot:\n", "plt.scatter(x,y)\n", "plt.plot([-2,4], [beta_0_hat + beta_1_hat*(-2), beta_0_hat + beta_1_hat*(4)], color=\"red\")\n", "plt.plot([-2,4], [beta_0 + beta_1*(-2), beta_0 + beta_1*(4)], color=\"red\", linestyle='--')\n", "plt.ylim([-400,1000])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Estimate parameters and their standard errors (height and weight data)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y\n", "0 168 65.5\n", "1 161 58.3\n", "2 167 68.1\n", "3 179 85.7\n", "4 184 80.5\n", "5 166 63.4\n", "6 198 102.6\n", "7 187 91.4\n", "8 191 86.7\n", "9 179 78.9\n" ] } ], "source": [ "# Recall the height and weigth data:\n", "print(student)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-119.95810730253355 1.11274217585693\n" ] } ], "source": [ "### 1 ### Estimate parameters beta_0_hat and bata_1_hat *manually*\n", "\n", "Sxx = np.sum((student[\"x\"] - student[\"x\"].mean())**2)\n", "\n", "beta_1_hat = np.sum((student[\"x\"] - student[\"x\"].mean())*(student[\"y\"] - student[\"y\"].mean())) / Sxx\n", "\n", "beta_0_hat = student[\"y\"].mean() - beta_1_hat*student[\"x\"].mean()\n", "\n", "print(beta_0_hat, beta_1_hat)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y y_pred residuals\n", "0 168 65.5 66.982578 -1.482578\n", "1 161 58.3 59.193383 -0.893383\n", "2 167 68.1 65.869836 2.230164\n", "3 179 85.7 79.222742 6.477258\n", "4 184 80.5 84.786453 -4.286453\n", "5 166 63.4 64.757094 -1.357094\n", "6 198 102.6 100.364844 2.235156\n", "7 187 91.4 88.124680 3.275320\n", "8 191 86.7 92.575648 -5.875648\n", "9 179 78.9 79.222742 -0.322742\n" ] } ], "source": [ "### 2 ### Estimate standard error for the parameters *manually* \n", "\n", "student[\"y_pred\"] = beta_0_hat + beta_1_hat*student[\"x\"]\n", "student[\"residuals\"] = student[\"y\"] - student[\"y_pred\"]\n", "print(student)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "18.897051763916973 0.10593909266894098\n" ] } ], "source": [ "RSS = np.sum(student[\"residuals\"]**2)\n", "sigma_hat = np.sqrt(RSS/(10-2))\n", "\n", "se_beta_0_hat = sigma_hat*np.sqrt(1/10 + student[\"x\"].mean()**2 / Sxx)\n", "\n", "se_beta_1_hat = sigma_hat*np.sqrt(1/Sxx)\n", "\n", "print(se_beta_0_hat, se_beta_1_hat)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\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, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "### automatic ### Do it all with inbuilt python function smf.ols\n", "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() # OBS: use the statsmodels.formula.api library (smf)\n", "print(fitStudents.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intercept -119.958107\n", "x 1.112742\n", "dtype: float64\n" ] } ], "source": [ "# Get parameters\n", "print(fitStudents.params)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intercept 18.897052\n", "x 0.105939\n", "dtype: float64\n" ] } ], "source": [ "# Get parameter standard errors\n", "print(fitStudents.bse)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "15.061388599105827\n", "15.06138859910578\n" ] } ], "source": [ "# get estimate of sigma^2:\n", "print(fitStudents.scale)\n", "print(sigma_hat**2) #compare to the one we calculated *manualy*" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 66.982578\n", "1 59.193383\n", "2 65.869836\n", "3 79.222742\n", "4 84.786453\n", "5 64.757094\n", "6 100.364844\n", "7 88.124680\n", "8 92.575648\n", "9 79.222742\n", "dtype: float64\n" ] } ], "source": [ "# get fitted values:\n", "print(fitStudents.fittedvalues)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot:\n", "plt.scatter(student[\"x\"], student[\"y\"])\n", "plt.plot(student[\"x\"], fitStudents.fittedvalues, color=\"red\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Hypothesis test for parameters" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\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, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() # OBS: use the statsmodels.formula.api library (smf)\n", "print(fitStudents.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intercept 0.000221\n", "x 0.000006\n", "dtype: float64\n" ] } ], "source": [ "# Warning!! The p-values appear to be zero but they are in reality only smaller than 0.000\n", "\n", "# print the pvalues seperately to be sure:\n", "print(fitStudents.pvalues)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-6.347997036566651\n" ] } ], "source": [ "# we can also do the test manually (here only for the intercept):\n", "\n", "# calculate \"t_obs\"\n", "t_obs_int = -119.9581/18.897\n", "print(t_obs_int)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.00022108433338164315\n" ] } ], "source": [ "# find corresponding pvalue:\n", "print(2*stats.t.cdf(t_obs_int, df=10-2)) # obs! df = n - 2 (2 is the number of parameters)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Confidence interval for parameters" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\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, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() \n", "print(fitStudents.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-163.53466013972562\n", "-76.38153986027439\n" ] } ], "source": [ "# we can also calculate CI *manually*\n", "\n", "# here only for the intercept:\n", "\n", "print(-119.9581 + stats.t.ppf(0.025, df=10-2)*18.897)\n", "print(-119.9581 - stats.t.ppf(0.025, df=10-2)*18.897)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Confidence interval for the line" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y\n", "0 0.507929 85.844021\n", "1 1.935535 519.486580\n", "2 1.619628 275.358640\n", "3 -1.996896 -477.868342\n", "4 -1.363155 -413.276293\n", "5 1.304766 131.195526\n", "6 3.004870 679.832200\n", "7 3.459938 764.296535\n", "8 2.056708 520.693047\n", "9 -0.629292 -84.292611\n", "10 0.506390 115.618570\n", "11 -0.562325 -101.450199\n", "12 1.056394 182.941453\n", "13 2.801986 729.915799\n", "14 -1.942645 -455.967857\n", "15 0.509977 188.065774\n", "16 3.968193 914.620017\n", "17 1.163689 385.099272\n", "18 -1.418796 -194.803230\n", "19 -0.938826 -92.997100\n" ] } ], "source": [ "# Simulated data from underlying linear model:\n", "np.random.seed(23498)\n", "\n", "beta_0 = 50\n", "beta_1 = 200\n", "sigma = 90\n", "\n", "# choose som random x-values:\n", "x = stats.uniform.rvs(size = 20, loc=-2, scale = 6)\n", "# simulate y-values from statistical model:\n", "y = beta_0 + beta_1*x + stats.norm.rvs(size = 20, loc=0, scale = sigma)\n", "\n", "data = pd.DataFrame({'x': x, 'y': y}) # OBS: use the pandas library (pd)\n", "print(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is new set of \"Toy data\"" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(data[\"x\"],data[\"y\"])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.963\n", "Model: OLS Adj. R-squared: 0.961\n", "No. Observations: 20 F-statistic: 468.9\n", "Covariance Type: nonrobust Prob (F-statistic): 2.43e-14\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 13.7955 19.969 0.691 0.498 -28.157 55.748\n", "x 225.7635 10.426 21.655 0.000 203.860 247.667\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "# fit a linear regression model\n", "linfit = smf.ols(formula = 'y ~ x', data=data).fit()\n", "print(linfit.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower \\\n", "0 -437.731597 34.066943 -509.303589 -366.159606 -624.530446 \n", "1 -435.473962 33.979179 -506.861567 -364.086357 -622.202241 \n", "2 -433.216327 33.891507 -504.419741 -362.012912 -619.874265 \n", "3 -430.958691 33.803930 -501.978113 -359.939269 -617.546521 \n", "4 -428.701056 33.716448 -499.536685 -357.865427 -615.219007 \n", "\n", " obs_ci_upper \n", "0 -250.932749 \n", "1 -248.745683 \n", "2 -246.558388 \n", "3 -244.370862 \n", "4 -242.183105 \n" ] } ], "source": [ "# Make predictions and confidence intervals\n", "x_pred = pd.DataFrame({'x': np.arange(-2,4,.01)})\n", "\n", "pred = linfit.get_prediction(x_pred).summary_frame(alpha=0.05) \n", "\n", "print(pred.head())" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot all the predictions:\n", "plt.scatter(data[\"x\"],data[\"y\"])\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"mean_ci_lower\"], color=\"grey\")\n", "plt.plot(x_pred, pred[\"mean_ci_upper\"], color=\"grey\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could also calculate this interval *manually* " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Prediction interval for parameters" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower \\\n", "0 -437.731597 34.066943 -509.303589 -366.159606 -624.530446 \n", "1 -435.473962 33.979179 -506.861567 -364.086357 -622.202241 \n", "2 -433.216327 33.891507 -504.419741 -362.012912 -619.874265 \n", "3 -430.958691 33.803930 -501.978113 -359.939269 -617.546521 \n", "4 -428.701056 33.716448 -499.536685 -357.865427 -615.219007 \n", "\n", " obs_ci_upper \n", "0 -250.932749 \n", "1 -248.745683 \n", "2 -246.558388 \n", "3 -244.370862 \n", "4 -242.183105 \n" ] } ], "source": [ "# Same data as above\n", "\n", "# now we want the prediction interval for individual (new/future) observations\n", "\n", "print(pred.head())" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot all the predictions:\n", "plt.scatter(data[\"x\"],data[\"y\"])\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"obs_ci_lower\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"obs_ci_upper\"], color=\"lightgrey\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot all the predictions:\n", "plt.scatter(data[\"x\"],data[\"y\"])\n", "plt.plot(x_pred, pred[\"mean\"], color=\"red\")\n", "plt.plot(x_pred, pred[\"obs_ci_lower\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"obs_ci_upper\"], color=\"lightgrey\")\n", "plt.plot(x_pred, pred[\"mean_ci_lower\"], color=\"grey\")\n", "plt.plot(x_pred, pred[\"mean_ci_upper\"], color=\"grey\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Correlation and $R^2$" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y y_pred residuals\n", "0 168 65.5 66.982578 -1.482578\n", "1 161 58.3 59.193383 -0.893383\n", "2 167 68.1 65.869836 2.230164\n", "3 179 85.7 79.222742 6.477258\n", "4 184 80.5 84.786453 -4.286453\n", "5 166 63.4 64.757094 -1.357094\n", "6 198 102.6 100.364844 2.235156\n", "7 187 91.4 88.124680 3.275320\n", "8 191 86.7 92.575648 -5.875648\n", "9 179 78.9 79.222742 -0.322742\n" ] } ], "source": [ "# Recall student height and weight data\n", "print(student)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.932\n", "Model: OLS Adj. R-squared: 0.924\n", "No. Observations: 10 F-statistic: 110.3\n", "Covariance Type: nonrobust Prob (F-statistic): 5.87e-06\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -119.9581 18.897 -6.348 0.000 -163.535 -76.381\n", "x 1.1127 0.106 10.504 0.000 0.868 1.357\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, 2.75e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\pydni\\AppData\\Local\\anaconda3\\envs\\pernille\\Lib\\site-packages\\scipy\\stats\\_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "fitStudents = smf.ols(formula = 'y ~ x', data=student).fit() # OBS: use the statsmodels.formula.api library (smf)\n", "print(fitStudents.summary(slim=True))" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0.96560343]\n", " [0.96560343 1. ]]\n", "[[1. 0.93238999]\n", " [0.93238999 1. ]]\n" ] } ], "source": [ "print(np.corrcoef(student[\"x\"], student[\"y\"]))\n", "print(np.corrcoef(student[\"x\"], student[\"y\"])**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "compare with R-squared in the table" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Model validation in Python" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(student[\"x\"], student[\"y\"])\n", "plt.plot(student[\"x\"], fitStudents.fittedvalues, color=\"red\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inspect the residuals (and assumption about normality):" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# residuals:\n", "residuals = fitStudents.resid\n", "fittedvalues = fitStudents.fittedvalues\n", "\n", "fig, (ax0, ax1, ax2) = plt.subplots(1,3,figsize=(12,4))\n", "\n", "# plot residuals versus x-values:\n", "ax0.scatter(student[\"x\"],student[\"residuals\"])\n", "ax0.set_xlabel(\"x\")\n", "ax0.set_ylabel(\"residuals\")\n", "\n", "# qq-plot of resiudals:\n", "sm.qqplot(residuals,ax=ax1, line='s')\n", "ax1.set_title(\"QQ plot of residuals\")\n", "\n", "# plot residuals versus fitted values:\n", "ax2.scatter(fittedvalues,residuals)\n", "ax2.set_xlabel(\"fitted values\")\n", "ax2.set_ylabel(\"residuals\")\n", "\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Another example:\n", "\n", "beta_0 = 50\n", "beta_1 = 200\n", "sigma = 90\n", "\n", "# choose som random x-values:\n", "x = stats.uniform.rvs(size = 90, loc=0, scale = 20)\n", "# simulate y-values from statistical model:\n", "y = beta_0 + beta_1*x + x*stats.norm.rvs(size = 90, loc=0, scale = sigma)\n", "\n", "plt.scatter(x,y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Is the normal assumption fulfilled here??" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "\n", "data = pd.DataFrame({'x': x, 'y': y}) # OBS: use the pandas library (pd)\n", "linfit = smf.ols(formula = 'y ~ x', data=data).fit()\n", "\n", "data[\"residuals\"] = linfit.resid\n", "fittedvalues = linfit.fittedvalues\n" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "fig, (ax0, ax1, ax2) = plt.subplots(1,3,figsize=(12,4))\n", "\n", "# plot residuals versus x-values:\n", "ax0.scatter(data[\"x\"],data[\"residuals\"])\n", "ax0.set_xlabel(\"x\")\n", "ax0.set_ylabel(\"residuals\")\n", "\n", "# qq-plot of resiudals:\n", "sm.qqplot(data[\"residuals\"],ax=ax1, line='s')\n", "ax1.set_title(\"QQ plot of residuals\")\n", "\n", "# plot residuals versus fitted values:\n", "ax2.scatter(fittedvalues,data[\"residuals\"])\n", "ax2.set_xlabel(\"fitted values\")\n", "ax2.set_ylabel(\"residuals\")\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "pernille", "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": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 2 }