{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Multiple Linear Regression\n", "By Evgenia \"Jenny\" Nitishinskaya, Maxwell Margenot, Delaney Granizo-Mackenzie, and Gilbert Wasserman.\n", "\n", "Part of the Quantopian Lecture Series:\n", "\n", "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n", "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "# If the observations are in a dataframe, you can use statsmodels.formulas.api to do the regression instead\n", "from statsmodels import regression\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "\n", "Multiple linear regression generalizes linear regression, allowing the dependent variable to be a linear function of multiple independent variables. As before, we assume that the variable $Y$ is a linear function of $X_1,\\ldots, X_k$:\n", "\n", "$$ Y_i = \\beta_0 + \\beta_1 X_{1i} + \\ldots + \\beta_k X_{ki} + \\epsilon_i $$\n", "\n", "Often in finance the form will be written as follows, but it is just the variable name that changes and otherwise the model is identical.\n", "\n", "$$ Y_i = \\alpha + \\beta_1 X_{1i} + \\ldots + \\beta_k X_{ki} + \\epsilon_i $$\n", "\n", "For observations $i = 1,2,\\ldots, n$. In order to find the plane (or hyperplane) of best fit, we will use the method of ordinary least-squares (OLS), which seeks to minimize the squared error between predictions and observations, $\\sum_{i=1}^n \\epsilon_i^2$. The square makes positive and negative errors equally bad, and magnifies large errors. It also makes the closed form math behind linear regression nice, but we won't go into that now. For an example of squared error, see the following." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Let's say Y is our actual data, and Y_hat is the predictions made by linear regression." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error [ 0. -0.5 1. -1. -3. ]\n", "Squared Error [ 0. 0.25 1. 1. 9. ]\n", "Sum Squared Error 11.25\n" ] } ], "source": [ "Y = np.array([1, 3.5, 4, 8, 12])\n", "Y_hat = np.array([1, 3, 5, 7, 9])\n", "\n", "print 'Error ' + str(Y_hat - Y)\n", "\n", "# Compute squared error\n", "SE = (Y_hat - Y) ** 2\n", "\n", "print 'Squared Error ' + str(SE)\n", "print 'Sum Squared Error ' + str(np.sum(SE))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Once we have used this method to determine the coefficients of the regression, we will be able to use new observed values of $X$ to predict values of $Y$. \n", "\n", "Each coefficient $\\beta_j$ tells us how much $Y_i$ will change if we change $X_j$ by one while holding all of the other dependent variables constant. This lets us separate out the contributions of different effects. This is assuming the linear model is the correct one.\n", "\n", "We start by artificially constructing a $Y$, $X_1$, and $X_2$ in which we know the precise relationship." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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N32CjJzoVoggAAAAoRBlnzylq1lzZs7NVe/wYXQz20mt73pKryUWT24xUbf/qRk90OkQR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\nxdFMG8ezHHgTo5mecRX3ZU1n5pipxEfFRbhyERERkaFNoUh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Construct a simple linear curve of 1, 2, 3, ...\n", "X1 = np.arange(100)\n", "\n", "# Make a parabola and add X1 to it, this is X2\n", "X2 = np.array([i ** 2 for i in range(100)]) + X1\n", "\n", "# This is our real Y, constructed using a linear combination of X1 and X2\n", "Y = X1 + X2\n", "\n", "plt.plot(X1, label='X1')\n", "plt.plot(X2, label='X2')\n", "plt.plot(Y, label='Y')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We can use the same function from `statsmodels` as we did for a single linear regression lecture." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Beta_0: 1.36424205266e-12\n", "Beta_1: 1.0\n", "Beta_2: 1.0\n" ] } ], "source": [ "# Use column_stack to combine independent variables, then add a column of ones so we can fit an intercept\n", "X = sm.add_constant( np.column_stack( (X1, X2) ) )\n", "\n", "# Run the model\n", "results = regression.linear_model.OLS(Y, X).fit()\n", "\n", "print 'Beta_0:', results.params[0]\n", "print 'Beta_1:', results.params[1]\n", "print 'Beta_2:', results.params[2]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The same care must be taken with these results as with partial derivatives. The formula for $Y$ is ostensibly \n", "\n", "$$X_1 + X_2 = X_1 + X^2 + X_1 = 2 X_1 + X^2$$\n", "\n", "Or $2X_1$ plus a parabola.\n", "\n", "However, the coefficient of $X_1$ is 1. That is because $Y$ changes by 1 if we change $X_1$ by 1 while holding $X_2$ constant. Multiple linear regression separates out contributions from different variables.\n", "\n", "Similarly, running a linear regression on two securities might give a high $\\beta$. However, if we bring in a third security (like SPY, which tracks the S&P 500) as an independent variable, we may find that the correlation between the first two securities is almost entirely due to them both being correlated with the S&P 500. This is useful because the S&P 500 may then be a more reliable predictor of both securities than they were of each other. This method allows us to better gauge the significance between the two securities and prevent confounding the two variables." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SLR beta of asset2: 0.903453633397\n" ] } ], "source": [ "# Load pricing data for two arbitrarily-chosen assets and SPY\n", "start = '2014-01-01'\n", "end = '2015-01-01'\n", "asset1 = get_pricing('DTV', fields='price', start_date=start, end_date=end)\n", "asset2 = get_pricing('FISV', fields='price', start_date=start, end_date=end)\n", "benchmark = get_pricing('SPY', fields='price', start_date=start, end_date=end)\n", "\n", "# First, run a linear regression on the two assets\n", "slr = regression.linear_model.OLS(asset1, sm.add_constant(asset2)).fit()\n", "print 'SLR beta of asset2:', slr.params[1]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MLR beta of asset2: -0.232309102745 \n", "MLR beta of S&P 500: 0.735923920897\n" ] } ], "source": [ "# Run multiple linear regression using asset2 and SPY as independent variables\n", "mlr = regression.linear_model.OLS(asset1, sm.add_constant(np.column_stack((asset2, benchmark)))).fit()\n", "\n", "prediction = mlr.params[0] + mlr.params[1]*asset2 + mlr.params[2]*benchmark\n", "prediction.name = 'Prediction'\n", "\n", "print 'MLR beta of asset2:', mlr.params[1], '\\nMLR beta of S&P 500:', mlr.params[2]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The next step after running an analysis is determining if we can even trust the results. A good first step is checking to see if anything looks weird in graphs of the independent variables, dependent variables, and predictions." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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2bsLn9V44hzQqr6Y+1RQqFc6NgknevoOz38zAu2ePu2ZIzjp9BpNej0O9Oo+5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\n0pe+pBtuuEEtLS2SpGXLlmnWrFmaPXu2li5dOrCtBgAAAAB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jV2jHju+qsvJR7djxPUnf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y/Dbp9HXt5d2O3zDkmv+tft78B/+rpf/xeJ1+Lfvu6vxcG7/ml4velUVFxGOPw7bLYGxo17HJ3O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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the three variables along with the prediction given by the MLR\n", "asset1.plot()\n", "asset2.plot()\n", "benchmark.plot()\n", "prediction.plot(color='y')\n", "plt.xlabel('Price')\n", "plt.legend(bbox_to_anchor=(1,1), loc=2);" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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5XYyf38X9POKu2Ww2zBYbFosVs8WK2eKc5f41Gvv9qanZAPQmaJHpYUII0Smz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\ndDMyMlAUhcmTJ9OjRw/AcNvgZjffVL7yyiuYmpqybNkyUlNT2bVrF25ub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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot only the dependent variable and the prediction to get a closer look\n", "asset1.plot()\n", "prediction.plot(color='y')\n", "plt.xlabel('Price')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Evaluation\n", "\n", "We can get some statistics about the fit from the result returned by the regression:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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: Equity(26111 [DTV]) R-squared: 0.715
Model: OLS Adj. R-squared: 0.713
Method: Least Squares F-statistic: 313.1
Date: Fri, 22 Apr 2016 Prob (F-statistic): 1.08e-68
Time: 20:43:26 Log-Likelihood: -641.97
No. Observations: 252 AIC: 1290.
Df Residuals: 249 BIC: 1301.
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| [95.0% Conf. Int.]
const -45.9532 6.601 -6.962 0.000 -58.954 -32.953
x1 -0.2323 0.105 -2.216 0.028 -0.439 -0.026
x2 0.7359 0.063 11.767 0.000 0.613 0.859
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 16.118 Durbin-Watson: 0.109
Prob(Omnibus): 0.000 Jarque-Bera (JB): 17.367
Skew: 0.596 Prob(JB): 0.000169
Kurtosis: 3.483 Cond. No. 6.85e+03
" ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "===============================================================================\n", "Dep. Variable: Equity(26111 [DTV]) R-squared: 0.715\n", "Model: OLS Adj. R-squared: 0.713\n", "Method: Least Squares F-statistic: 313.1\n", "Date: Fri, 22 Apr 2016 Prob (F-statistic): 1.08e-68\n", "Time: 20:43:26 Log-Likelihood: -641.97\n", "No. Observations: 252 AIC: 1290.\n", "Df Residuals: 249 BIC: 1301.\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [95.0% Conf. Int.]\n", "------------------------------------------------------------------------------\n", "const -45.9532 6.601 -6.962 0.000 -58.954 -32.953\n", "x1 -0.2323 0.105 -2.216 0.028 -0.439 -0.026\n", "x2 0.7359 0.063 11.767 0.000 0.613 0.859\n", "==============================================================================\n", "Omnibus: 16.118 Durbin-Watson: 0.109\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 17.367\n", "Skew: 0.596 Prob(JB): 0.000169\n", "Kurtosis: 3.483 Cond. No. 6.85e+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, 6.85e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mlr.summary()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Model Assumptions\n", "\n", "The validity of these statistics depends on whether or not the assumptions of the linear regression model are satisfied. These are:\n", "* The independent variable is not random.\n", "* The variance of the error term is constant across observations. This is important for evaluating the goodness of the fit.\n", "* The errors are not autocorrelated. The Durbin-Watson statistic reported by the regression detects this. If it is close to $2$, there is no autocorrelation.\n", "* The errors are normally distributed. If this does not hold, we cannot use some of the statistics, such as the F-test.\n", "\n", "Multiple linear regression also requires an additional assumption:\n", "* There is no exact linear relationship between the independent variables. Otherwise, it is impossible to solve for the coefficients $\\beta_i$ uniquely, since the same linear equation can be expressed in multiple ways.\n", "\n", "If there is a linear relationship between any set of independent variables, also known as covariance, we say that they are linear combinations of each other. In the case where they are dependent on each other in this manner, the values of our $\\beta_i$ coefficients will be inaccurate for a given $X_i$. The intuition for this can be found in an exteme example where $X_1$ and $X_2$ are 100% covarying. In that case then linear regression can equivalently assign the total coefficient sum in any combination without affecting the predictive capability.\n", "\n", "$$ 1X_1 + 0X_2 = 0.5X_1 + 0.5X_2 = 0X_1 + 1X_2 $$\n", "\n", "\n", "While our coefficients may be nondescriptive, the ultimate model may still be accurate provided that there is a good overall fit between the independent variables and the dependent variables. The best practice for constructing a model where dependence is a problem is to leave out the less descriptive variables that are correlated with the better ones. This improves the model by reducing the chances of overfitting while bringing the $\\beta_i$ estimates closer to their true values.\n", "\n", "If we confirm that the necessary assumptions of the regression model are satisfied, we can safely use the statistics reported to analyze the fit. For example, the $R^2$ value tells us the fraction of the total variation of $Y$ that is explained by the model. When doing multiple linear regression, however, we prefer to use adjusted $R^2$, which corrects for the small increases in $R^2$ that occur when we add more regression variables to the model, even if they are not significantly correlated with the dependent variable. Adjusted $R^2$ is defined as\n", "\n", "$$ 1 - (1 - R^2)\\frac{n-1}{n-k-1} $$\n", "\n", "Where $n$ is the number of observations and $k$ is the number of independent variables in the model. Other useful statistics include the F-statistic and the standard error of estimate." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "deletable": true, "editable": true }, "source": [ "# Model Selection Example\n", "\n", "When deciding on the best possible model of your dependent variables, there are several different methods to turn to. If you use too many explanatory variables, you run the risk of overfitting your model, but if you use too few you may end up with a terrible fit. One of the most prominent methods to decide on a best model is stepwise regression. Forward stepwise regression starts from an empty model and tests each individual variable, selecting the one that results in the best model quality, usually measured with AIC or BIC (lowest is best). It then adds the remaining variables one at a time, testing each subsequent combination of explanatory variables in a regression and calculating the AIC or BIC value at each step. At the end of the regression, the model with the best quality (according to the given measure) is selected and presented as a the final, best model. This does have limitations, however. It does not test every single possible combination of variables so it may miss the theoretical best model if a particular variable was written off earlier in performing the algorithm. As such, stepwise regression should be used in combination with your best judgment regarding the model." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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g32muP6HSvavka2vQkOSvasS4ObJYbWbHQpihLAEAAKBfOePer2MHXpUR9Ctl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\nwXe6+K6D73R7AcYhdF1Cz0t6YjyPqBdgYj8JMfgBhh9g+CE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X1 = np.arange(100)\n", "X2 = [i**2 for i in range(100)] - X1\n", "X3 = [np.log(i) for i in range(1, 101)] + X2\n", "X4 = 5 * X1\n", "Y = 2 * X1 + 0.5 * X2 + 10 * X3 + X4\n", "\n", "plt.plot(X1, label='X1')\n", "plt.plot(X2, label='X2')\n", "plt.plot(X3, label='X3')\n", "plt.plot(X4, label='X4')\n", "plt.plot(Y, label='Y')\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Beta_0: -6.36646291241e-12\n", "Beta_1: 0.269230769231\n", "Beta_2: 0.499999999994\n", "Beta_3: 10.0\n", "Beta_4: 1.34615384615\n" ] } ], "source": [ "results = regression.linear_model.OLS(Y, sm.add_constant(np.column_stack((X1,X2,X3,X4)))).fit()\n", "\n", "print \"Beta_0: \", results.params[0]\n", "print \"Beta_1: \", results.params[1]\n", "print \"Beta_2: \", results.params[2]\n", "print \"Beta_3: \", results.params[3]\n", "print \"Beta_4: \", results.params[4]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "data = pd.DataFrame(np.column_stack((X1,X2,X3,X4)), columns = ['X1','X2','X3','X4'])\n", "response = pd.Series(Y, name='Y')" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "def forward_aic(response, data):\n", " # This function will work with pandas dataframes and series\n", " \n", " # Initialize some variables\n", " explanatory = list(data.columns)\n", " selected = pd.Series(np.ones(data.shape[0]), name=\"Intercept\")\n", " current_score, best_new_score = np.inf, np.inf\n", " \n", " # Loop while we haven't found a better model\n", " while current_score == best_new_score and len(explanatory) != 0:\n", " \n", " scores_with_elements = []\n", " count = 0\n", " \n", " # For each explanatory variable\n", " for element in explanatory:\n", " # Make a set of explanatory variables including our current best and the new one\n", " tmp = pd.concat([selected, data[element]], axis=1)\n", " # Test the set\n", " result = regression.linear_model.OLS(Y, tmp).fit()\n", " score = result.aic\n", " scores_with_elements.append((score, element, count))\n", " count += 1\n", " \n", " # Sort the scoring list\n", " scores_with_elements.sort(reverse = True)\n", " # Get the best new variable\n", " best_new_score, best_element, index = scores_with_elements.pop()\n", " if current_score > best_new_score:\n", " # If it's better than the best add it to the set\n", " explanatory.pop(index)\n", " selected = pd.concat([selected, data[best_element]],axis=1)\n", " current_score = best_new_score\n", " # Return the final model\n", " model = regression.linear_model.OLS(Y, selected).fit()\n", " return model" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "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: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 3.092e+26
Date: Fri, 22 Apr 2016 Prob (F-statistic): 0.00
Time: 20:43:27 Log-Likelihood: 1700.7
No. Observations: 100 AIC: -3393.
Df Residuals: 96 BIC: -3383.
Df Model: 3
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| [95.0% Conf. Int.]
Intercept -1.455e-11 7.01e-09 -0.002 0.998 -1.39e-08 1.39e-08
X3 10.0000 4.24e-09 2.36e+09 0.000 10.000 10.000
X1 0.2692 1.3e-11 2.08e+10 0.000 0.269 0.269
X2 0.5000 4.24e-09 1.18e+08 0.000 0.500 0.500
X4 1.3462 6.48e-11 2.08e+10 0.000 1.346 1.346
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 14.070 Durbin-Watson: 0.001
Prob(Omnibus): 0.001 Jarque-Bera (JB): 9.981
Skew: -0.647 Prob(JB): 0.00680
Kurtosis: 2.152 Cond. No. 6.22e+17
" ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 1.000\n", "Model: OLS Adj. R-squared: 1.000\n", "Method: Least Squares F-statistic: 3.092e+26\n", "Date: Fri, 22 Apr 2016 Prob (F-statistic): 0.00\n", "Time: 20:43:27 Log-Likelihood: 1700.7\n", "No. Observations: 100 AIC: -3393.\n", "Df Residuals: 96 BIC: -3383.\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [95.0% Conf. Int.]\n", "------------------------------------------------------------------------------\n", "Intercept -1.455e-11 7.01e-09 -0.002 0.998 -1.39e-08 1.39e-08\n", "X3 10.0000 4.24e-09 2.36e+09 0.000 10.000 10.000\n", "X1 0.2692 1.3e-11 2.08e+10 0.000 0.269 0.269\n", "X2 0.5000 4.24e-09 1.18e+08 0.000 0.500 0.500\n", "X4 1.3462 6.48e-11 2.08e+10 0.000 1.346 1.346\n", "==============================================================================\n", "Omnibus: 14.070 Durbin-Watson: 0.001\n", "Prob(Omnibus): 0.001 Jarque-Bera (JB): 9.981\n", "Skew: -0.647 Prob(JB): 0.00680\n", "Kurtosis: 2.152 Cond. No. 6.22e+17\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 9.87e-27. This might indicate that there are\n", "strong multicollinearity problems or that the design matrix is singular.\n", "\"\"\"" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result = forward_aic(Y, data)\n", "result.summary()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "In the construction of this model, the $X_4$ term is highly closely related to the $X1$ term, simply multiplying it by a scalar. However, stepwise regression did not catch this and remove the variable and simply adjust the coefficient of the $X_1$ term. Our own judgment would say to leave the $X_4$ term out of the model, showing the limitations of stepwise regression.\n", "\n", "There are other ways to diagnose the health of a model and individual variables with varying degrees of penalty given to more complex models. This will be covered in-depth in a model selection notebook." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }