{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Importing necessary packages" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# pip install ... in your terminal! \n", "import numpy as np\n", "import pandas as pd\n", "from matplotlib.pyplot import subplots\n", "import statsmodels.api as sm\n", "from ISLP import load_data\n", "from ISLP.models import (ModelSpec as MS, summarize , poly)\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple Linear Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basic Introduction on fitting the model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a simple loading function `load_data` in ISLP package:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Load the Boston housing data\n", "Boston = load_data('Boston')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Index(['crim', 'zn', 'indus', 'chas', 'nox', 'rm', 'age', 'dis', 'rad', 'tax',\n", " 'ptratio', 'lstat', 'medv'],\n", " dtype='object')\n" ] } ], "source": [ "# Inspect the data\n", "print(Boston.columns)\n", "\n", "# Type Boston? to find out more about these data. \n", "# you can use command + / to quickly comment/uncomment a line of code:\n", "\n", "# Boston?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We know the following:\n", "1. `medv` is median value of owner-occupied homes in thousands\n", "2. `lstat` is lower status of the population\n", "\n", "we can fit a model with `medv` as response variable and `lstat` as independent variable" ] }, { "cell_type": "code", "execution_count": 12, "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", "
interceptlstat
01.04.98
11.09.14
21.04.03
31.02.94
\n", "
" ], "text/plain": [ " intercept lstat\n", "0 1.0 4.98\n", "1 1.0 9.14\n", "2 1.0 4.03\n", "3 1.0 2.94" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# For this model, we can create the model matrix by hand.\n", "# Define the model specification\n", "X = pd.DataFrame({'intercept': np.ones(Boston.shape[0]),\n", "'lstat': Boston['lstat']})\n", "# and displays the first 4 rows\n", "X[:4]\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# extract the response and fit the model:\n", "y = Boston['medv']\n", "model = sm.OLS(y, X)\n", "results = model.fit()" ] }, { "cell_type": "code", "execution_count": 17, "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", "
coefstd errtP>|t|
intercept34.55380.56361.4150.0
lstat-0.95000.039-24.5280.0
\n", "
" ], "text/plain": [ " coef std err t P>|t|\n", "intercept 34.5538 0.563 61.415 0.0\n", "lstat -0.9500 0.039 -24.528 0.0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# looking into the summary:\n", "summarize(results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "note that the `summarize` function shows a quick summary of information using built-in function from ISLP package, for a more detailed summary, people could use `summary()` function in python:" ] }, { "cell_type": "code", "execution_count": 7, "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: 0.544
Model: OLS Adj. R-squared: 0.543
Method: Least Squares F-statistic: 601.6
Date: Fri, 06 Sep 2024 Prob (F-statistic): 5.08e-88
Time: 15:02:56 Log-Likelihood: -1641.5
No. Observations: 506 AIC: 3287.
Df Residuals: 504 BIC: 3295.
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 34.5538 0.563 61.415 0.000 33.448 35.659
lstat -0.9500 0.039 -24.528 0.000 -1.026 -0.874
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 137.043 Durbin-Watson: 0.892
Prob(Omnibus): 0.000 Jarque-Bera (JB): 291.373
Skew: 1.453 Prob(JB): 5.36e-64
Kurtosis: 5.319 Cond. No. 29.7


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified." ], "text/latex": [ "\\begin{center}\n", "\\begin{tabular}{lclc}\n", "\\toprule\n", "\\textbf{Dep. Variable:} & medv & \\textbf{ R-squared: } & 0.544 \\\\\n", "\\textbf{Model:} & OLS & \\textbf{ Adj. R-squared: } & 0.543 \\\\\n", "\\textbf{Method:} & Least Squares & \\textbf{ F-statistic: } & 601.6 \\\\\n", "\\textbf{Date:} & Fri, 06 Sep 2024 & \\textbf{ Prob (F-statistic):} & 5.08e-88 \\\\\n", "\\textbf{Time:} & 15:02:56 & \\textbf{ Log-Likelihood: } & -1641.5 \\\\\n", "\\textbf{No. Observations:} & 506 & \\textbf{ AIC: } & 3287. \\\\\n", "\\textbf{Df Residuals:} & 504 & \\textbf{ BIC: } & 3295. \\\\\n", "\\textbf{Df Model:} & 1 & \\textbf{ } & \\\\\n", "\\textbf{Covariance Type:} & nonrobust & \\textbf{ } & \\\\\n", "\\bottomrule\n", "\\end{tabular}\n", "\\begin{tabular}{lcccccc}\n", " & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]} \\\\\n", "\\midrule\n", "\\textbf{intercept} & 34.5538 & 0.563 & 61.415 & 0.000 & 33.448 & 35.659 \\\\\n", "\\textbf{lstat} & -0.9500 & 0.039 & -24.528 & 0.000 & -1.026 & -0.874 \\\\\n", "\\bottomrule\n", "\\end{tabular}\n", "\\begin{tabular}{lclc}\n", "\\textbf{Omnibus:} & 137.043 & \\textbf{ Durbin-Watson: } & 0.892 \\\\\n", "\\textbf{Prob(Omnibus):} & 0.000 & \\textbf{ Jarque-Bera (JB): } & 291.373 \\\\\n", "\\textbf{Skew:} & 1.453 & \\textbf{ Prob(JB): } & 5.36e-64 \\\\\n", "\\textbf{Kurtosis:} & 5.319 & \\textbf{ Cond. No. } & 29.7 \\\\\n", "\\bottomrule\n", "\\end{tabular}\n", "%\\caption{OLS Regression Results}\n", "\\end{center}\n", "\n", "Notes: \\newline\n", " [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: medv R-squared: 0.544\n", "Model: OLS Adj. R-squared: 0.543\n", "Method: Least Squares F-statistic: 601.6\n", "Date: Fri, 06 Sep 2024 Prob (F-statistic): 5.08e-88\n", "Time: 15:02:56 Log-Likelihood: -1641.5\n", "No. Observations: 506 AIC: 3287.\n", "Df Residuals: 504 BIC: 3295.\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "intercept 34.5538 0.563 61.415 0.000 33.448 35.659\n", "lstat -0.9500 0.039 -24.528 0.000 -1.026 -0.874\n", "==============================================================================\n", "Omnibus: 137.043 Durbin-Watson: 0.892\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 291.373\n", "Skew: 1.453 Prob(JB): 5.36e-64\n", "Kurtosis: 5.319 Cond. No. 29.7\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, we could use built-in functions `fit` and `transform` to fit the model and transform X:" ] }, { "cell_type": "code", "execution_count": 8, "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", "
interceptlstat
01.04.98
11.09.14
21.04.03
31.02.94
\n", "
" ], "text/plain": [ " intercept lstat\n", "0 1.0 4.98\n", "1 1.0 9.14\n", "2 1.0 4.03\n", "3 1.0 2.94" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "design = MS(['lstat'])\n", "design = design.fit(Boston)\n", "X = design.transform(Boston)\n", "X[:4]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "we could also merge the `design.fit` and `transform` into one step:" ] }, { "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", " \n", " \n", " \n", "
interceptlstat
01.04.98
11.09.14
21.04.03
31.02.94
\n", "
" ], "text/plain": [ " intercept lstat\n", "0 1.0 4.98\n", "1 1.0 9.14\n", "2 1.0 4.03\n", "3 1.0 2.94" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "design = MS(['lstat'])\n", "X = design.fit_transform(Boston)\n", "X[:4]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fitted coefficients can also be retrieved as the `params` attribute of\n", "results:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "intercept 34.553841\n", "lstat -0.950049\n", "dtype: float64" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predictions using the fitted model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `get_prediction()` method can be used to obtain predictions, and produce confidence intervals and prediction intervals for the prediction of medv for given values of lstat.\n", "\n", "We first create a new data frame, in this case containing only the variable\n", "`lstat`, with the values for this variable at which we wish to make\n", "predictions. We then use the `transform()` method of design to create the\n", "corresponding model matrix." ] }, { "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", "
interceptlstat
01.05
11.010
21.015
\n", "
" ], "text/plain": [ " intercept lstat\n", "0 1.0 5\n", "1 1.0 10\n", "2 1.0 15" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# for example for 3 values of lstat = 5, 10, 15\n", "new_df = pd.DataFrame({'lstat':[5, 10, 15]})\n", "newX = design.transform(new_df)\n", "newX" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we compute the predictions at `newX`, and view them by extracting\n", "the predicted_mean attribute." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([29.80359411, 25.05334734, 20.30310057])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "new_predictions = results.get_prediction(newX)\n", "new_predictions.predicted_mean" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can produce confidence intervals for the predicted values." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[29.00741194, 30.59977628],\n", " [24.47413202, 25.63256267],\n", " [19.73158815, 20.87461299]])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "new_predictions.conf_int(alpha=0.05)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Prediction intervals are computing by setting `obs=True`:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[17.56567478, 42.04151344],\n", " [12.82762635, 37.27906833],\n", " [ 8.0777421 , 32.52845905]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "new_predictions.conf_int(obs=True , alpha=0.05)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For instance, the 95% confidence interval associated with an lstat value of\n", "10 is (24.47, 25.63), and the 95% prediction interval is (12.82, 37.28). As\n", "expected, the confidence and prediction intervals are centered around the\n", "same point (a predicted value of 25.05 for medv when lstat equals 10), but\n", "the latter are substantially wider." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the data and the model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will now plot `medv` and `lstat` using `DataFrame.plot.scatter()`, and add the regression line to the resulting plot, we will first define a function `abline` that adds a linear regression fitted model to graphs:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def abline(ax, b, m, *args , **kwargs):\n", " xlim = ax.get_xlim()\n", " ylim = [m * xlim[0] + b, m * xlim[1] + b]\n", " ax.plot(xlim , ylim , *args , **kwargs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function has arguments `ax`, `b`, `m` where\n", "`ax` is an axis object for an exisiting plot, `b` is the intercept and `m` is the slope of the desired line. The addition of `*args` allows any number of non-named arguments to abline, while `*kwargs` allows any number of named arguments (such as\n", "linewidth=3) to abline." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "we can now plot the graph as:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/0h/0qf279212tbbfjv71z01qdkc0000gn/T/ipykernel_49203/2616703611.py:3: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n", " results.params[0],\n", "/var/folders/0h/0qf279212tbbfjv71z01qdkc0000gn/T/ipykernel_49203/2616703611.py:4: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n", " results.params[1],\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = Boston.plot.scatter('lstat', 'medv')\n", "abline(ax,\n", "results.params[0],\n", "results.params[1],\n", "'r--',\n", "linewidth=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could also perform some diagnosis on the fitted model by plotting the residuals:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = subplots(figsize=(8,8))[1]\n", "ax.scatter(results.fittedvalues , results.resid)\n", "ax.set_xlabel('Fitted value')\n", "ax.set_ylabel('Residual')\n", "ax.axhline(0, c='k', ls='--');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the basis of the residual plot (not shown), there is some evidence\n", "of non-linearity." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi-variate Linear Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to fit a model on `medv` using both `age` and `lstat`:" ] }, { "cell_type": "code", "execution_count": 18, "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", "
coefstd errtP>|t|
intercept33.22280.73145.4580.000
lstat-1.03210.048-21.4160.000
age0.03450.0122.8260.005
\n", "
" ], "text/plain": [ " coef std err t P>|t|\n", "intercept 33.2228 0.731 45.458 0.000\n", "lstat -1.0321 0.048 -21.416 0.000\n", "age 0.0345 0.012 2.826 0.005" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = MS(['lstat', 'age']).fit_transform(Boston)\n", "model1 = sm.OLS(y, X)\n", "results1 = model1.fit()\n", "summarize(results1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to fit a model on `medv` using all the variables:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Index(['crim', 'zn', 'indus', 'chas', 'nox', 'rm', 'age', 'dis', 'rad', 'tax',\n", " 'ptratio', 'lstat'],\n", " dtype='object')" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "terms = Boston.columns.drop('medv')\n", "terms" ] }, { "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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
coefstd errtP>|t|
intercept41.61734.9368.4310.000
crim-0.12140.033-3.6780.000
zn0.04700.0143.3840.001
indus0.01350.0620.2170.829
chas2.84000.8703.2640.001
nox-18.75803.851-4.8700.000
rm3.65810.4208.7050.000
age0.00360.0130.2710.787
dis-1.49080.202-7.3940.000
rad0.28940.0674.3250.000
tax-0.01270.004-3.3370.001
ptratio-0.93750.132-7.0910.000
lstat-0.55200.051-10.8970.000
\n", "
" ], "text/plain": [ " coef std err t P>|t|\n", "intercept 41.6173 4.936 8.431 0.000\n", "crim -0.1214 0.033 -3.678 0.000\n", "zn 0.0470 0.014 3.384 0.001\n", "indus 0.0135 0.062 0.217 0.829\n", "chas 2.8400 0.870 3.264 0.001\n", "nox -18.7580 3.851 -4.870 0.000\n", "rm 3.6581 0.420 8.705 0.000\n", "age 0.0036 0.013 0.271 0.787\n", "dis -1.4908 0.202 -7.394 0.000\n", "rad 0.2894 0.067 4.325 0.000\n", "tax -0.0127 0.004 -3.337 0.001\n", "ptratio -0.9375 0.132 -7.091 0.000\n", "lstat -0.5520 0.051 -10.897 0.000" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = MS(terms).fit_transform(Boston)\n", "model = sm.OLS(y, X)\n", "results = model.fit()\n", "summarize(results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "if we want to fit a model on `medv` on all variables but `age`:" ] }, { "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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
coefstd errtP>|t|
intercept41.52514.9208.4410.000
crim-0.12140.033-3.6830.000
zn0.04650.0143.3790.001
indus0.01350.0620.2170.829
chas2.85280.8683.2870.001
nox-18.48513.714-4.9780.000
rm3.68110.4118.9510.000
dis-1.50680.193-7.8250.000
rad0.28790.0674.3220.000
tax-0.01270.004-3.3330.001
ptratio-0.93460.132-7.0990.000
lstat-0.54740.048-11.4830.000
\n", "
" ], "text/plain": [ " coef std err t P>|t|\n", "intercept 41.5251 4.920 8.441 0.000\n", "crim -0.1214 0.033 -3.683 0.000\n", "zn 0.0465 0.014 3.379 0.001\n", "indus 0.0135 0.062 0.217 0.829\n", "chas 2.8528 0.868 3.287 0.001\n", "nox -18.4851 3.714 -4.978 0.000\n", "rm 3.6811 0.411 8.951 0.000\n", "dis -1.5068 0.193 -7.825 0.000\n", "rad 0.2879 0.067 4.322 0.000\n", "tax -0.0127 0.004 -3.333 0.001\n", "ptratio -0.9346 0.132 -7.099 0.000\n", "lstat -0.5474 0.048 -11.483 0.000" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "minus_age = Boston.columns.drop(['medv', 'age'])\n", "Xma = MS(minus_age).fit_transform(Boston)\n", "model1 = sm.OLS(y, Xma)\n", "summarize(model1.fit())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Add in interaction terms to the equation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Please also review the interpretation of coefficients when using interaction terms" ] }, { "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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
coefstd errtP>|t|
intercept36.08851.47024.5530.000
lstat-1.39210.167-8.3130.000
age-0.00070.020-0.0360.971
lstat:age0.00420.0022.2440.025
\n", "
" ], "text/plain": [ " coef std err t P>|t|\n", "intercept 36.0885 1.470 24.553 0.000\n", "lstat -1.3921 0.167 -8.313 0.000\n", "age -0.0007 0.020 -0.036 0.971\n", "lstat:age 0.0042 0.002 2.244 0.025" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = MS(['lstat',\n", "'age',\n", "('lstat', 'age')]).fit_transform(Boston)\n", "model2 = sm.OLS(y, X)\n", "summarize(model2.fit())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Qualitative Predictors:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we use the `Carseats` data, which is included in the ISLP package. We\n", "will attempt to predict Sales (child car seat sales) in 400 locations based\n", "on a number of predictors." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Index(['Sales', 'CompPrice', 'Income', 'Advertising', 'Population', 'Price',\n", " 'ShelveLoc', 'Age', 'Education', 'Urban', 'US'],\n", " dtype='object')" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Carseats = load_data('Carseats')\n", "Carseats.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The predictor `ShelveLoc` takes on three possible values, `Bad`, `Medium`, and `Good`. Given a qualitative variable such as ShelveLoc, `ModelSpec()` generates dummy variables automatically." ] }, { "cell_type": "code", "execution_count": 24, "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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
coefstd errtP>|t|
intercept6.57561.0096.5190.000
CompPrice0.09290.00422.5670.000
Income0.01090.0034.1830.000
Advertising0.07020.0233.1070.002
Population0.00020.0000.4330.665
Price-0.10080.007-13.5490.000
ShelveLoc[Good]4.84870.15331.7240.000
ShelveLoc[Medium]1.95330.12615.5310.000
Age-0.05790.016-3.6330.000
Education-0.02090.020-1.0630.288
Urban[Yes]0.14020.1121.2470.213
US[Yes]-0.15760.149-1.0580.291
Income:Advertising0.00080.0002.6980.007
Price:Age0.00010.0000.8010.424
\n", "
" ], "text/plain": [ " coef std err t P>|t|\n", "intercept 6.5756 1.009 6.519 0.000\n", "CompPrice 0.0929 0.004 22.567 0.000\n", "Income 0.0109 0.003 4.183 0.000\n", "Advertising 0.0702 0.023 3.107 0.002\n", "Population 0.0002 0.000 0.433 0.665\n", "Price -0.1008 0.007 -13.549 0.000\n", "ShelveLoc[Good] 4.8487 0.153 31.724 0.000\n", "ShelveLoc[Medium] 1.9533 0.126 15.531 0.000\n", "Age -0.0579 0.016 -3.633 0.000\n", "Education -0.0209 0.020 -1.063 0.288\n", "Urban[Yes] 0.1402 0.112 1.247 0.213\n", "US[Yes] -0.1576 0.149 -1.058 0.291\n", "Income:Advertising 0.0008 0.000 2.698 0.007\n", "Price:Age 0.0001 0.000 0.801 0.424" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "allvars = list(Carseats.columns.drop('Sales'))\n", "y = Carseats['Sales']\n", "\n", "# adding in some interaction effect\n", "final = allvars + [('Income', 'Advertising'), \n", "('Price', 'Age')]\n", "X = MS(final).fit_transform(Carseats)\n", "model = sm.OLS(y, X)\n", "summarize(model.fit())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Quick explanation of the above results:*\n", "\n", "In the first line above, we made allvars a list, so that we could add the\n", "interaction terms two lines down. Our model-matrix builder has created a\n", "`ShelveLoc[Good]` dummy variable that takes on a value of 1 if the shelving\n", "location is good, and 0 otherwise. It has also created a `ShelveLoc[Medium]`\n", "dummy variable that equals 1 if the shelving location is medium, and 0 otherwise.\n", "A bad shelving location corresponds to a zero for each of the two\n", "dummy variables. The fact that the coefficient for `ShelveLoc[Good]` in the\n", "regression output is positive indicates that a good shelving location is associated\n", "with high sales (relative to a bad location). And `ShelveLoc[Medium]`\n", "has a smaller positive coefficient, indicating that a medium shelving location\n", "leads to higher sales than a bad shelving location, but lower sales than\n", "a good shelving location." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 2 }