multiple-linear-regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple Linear Regression\n",
    "\n",
    "Probably the single most used technique in modern quantitative finance. \n",
    "\n",
    "Multiple linear regression is just like single linear regression, except you can use many variables to predict one outcome and measure the relative contributions of each. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import yfinance as yf\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "from pandas_datareader import data as pdr\n",
    "from statsmodels import regression\n",
    "\n",
    "\n",
    "yf.pdr_override()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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.\n",
    "\n",
    "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta_0: 2.5579538487363607e-13\n",
      "Beta_1: 1.0000000000004086\n",
      "Beta_2: 0.9999999999999942\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": {},
   "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 <i>while holding $X_2$ constant</i>. 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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "SLR beta of asset2: -1.1982315073849126\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/numpy/core/fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "# Load pricing data for two arbitrarily-chosen assets and SPY\n",
    "start_date = '2014-01-01'\n",
    "end_date = '2015-01-01'\n",
    "asset1 = pdr.get_data_yahoo('BBI', start=start_date, end=end_date, interval = \"1d\")['Adj Close']\n",
    "asset2 = pdr.get_data_yahoo('FARM', start=start_date, end=end_date, interval = \"1d\")['Adj Close']\n",
    "benchmark = pdr.get_data_yahoo('SPY', start=start_date, end=end_date, interval = \"1d\")['Adj Close']\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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLR beta of asset2: -0.03602224186854651 \n",
      "MLR beta of S&P 500: -0.730501445742465\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": {},
   "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Brickell Biotech Inc. ending with:\n",
      "73.5\n",
      "Farmer Bros. Co. ending with:\n",
      "29.450000762939453\n",
      "SPY ending with:\n",
      "185.170166015625\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the three variables along with the prediction given by the MLR\n",
    "\n",
    "print('Brickell Biotech Inc. ending with:')\n",
    "print(asset1[-1])\n",
    "\n",
    "print('Farmer Bros. Co. ending with:')\n",
    "print(asset2[-1])\n",
    "\n",
    "print('SPY ending with:')\n",
    "print(benchmark[-1])\n",
    "\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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Brickell Biotech Inc. ending with:\n",
      "73.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot only the dependent variable and the prediction to get a closer look\n",
    "\n",
    "print('Brickell Biotech Inc. ending with:')\n",
    "print(asset1[-1])\n",
    "\n",
    "asset1.plot()\n",
    "prediction.plot(color='y')\n",
    "plt.xlabel('Price')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>Adj Close</td>    <th>  R-squared:         </th> <td>   0.412</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.407</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   87.24</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 08 Jun 2020</td> <th>  Prob (F-statistic):</th> <td>1.93e-29</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:03:07</td>     <th>  Log-Likelihood:    </th> <td> -849.62</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   252</td>      <th>  AIC:               </th> <td>   1705.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   249</td>      <th>  BIC:               </th> <td>   1716.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>  213.3664</td> <td>   10.893</td> <td>   19.588</td> <td> 0.000</td> <td>  191.913</td> <td>  234.820</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>   -0.0360</td> <td>    0.179</td> <td>   -0.201</td> <td> 0.841</td> <td>   -0.388</td> <td>    0.316</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>   -0.7305</td> <td>    0.077</td> <td>   -9.434</td> <td> 0.000</td> <td>   -0.883</td> <td>   -0.578</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>31.307</td> <th>  Durbin-Watson:     </th> <td>   0.230</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  47.105</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.754</td> <th>  Prob(JB):          </th> <td>5.91e-11</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.486</td> <th>  Cond. No.          </th> <td>4.24e+03</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 4.24e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:              Adj Close   R-squared:                       0.412\n",
       "Model:                            OLS   Adj. R-squared:                  0.407\n",
       "Method:                 Least Squares   F-statistic:                     87.24\n",
       "Date:                Mon, 08 Jun 2020   Prob (F-statistic):           1.93e-29\n",
       "Time:                        17:03:07   Log-Likelihood:                -849.62\n",
       "No. Observations:                 252   AIC:                             1705.\n",
       "Df Residuals:                     249   BIC:                             1716.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        213.3664     10.893     19.588      0.000     191.913     234.820\n",
       "x1            -0.0360      0.179     -0.201      0.841      -0.388       0.316\n",
       "x2            -0.7305      0.077     -9.434      0.000      -0.883      -0.578\n",
       "==============================================================================\n",
       "Omnibus:                       31.307   Durbin-Watson:                   0.230\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               47.105\n",
       "Skew:                           0.754   Prob(JB):                     5.91e-11\n",
       "Kurtosis:                       4.486   Cond. No.                     4.24e+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, 4.24e+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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta_0:  -2.5693225325085223e-11\n",
      "Beta_1:  0.2692307692305427\n",
      "Beta_2:  0.4999999999911324\n",
      "Beta_3:  10.000000000006139\n",
      "Beta_4:  1.3461538461538396\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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>8.784e+26</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 08 Jun 2020</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:03:08</td>     <th>  Log-Likelihood:    </th> <td>  1752.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>  -3498.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    96</td>      <th>  BIC:               </th> <td>  -3487.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td> 4.684e-11</td> <td> 4.16e-09</td> <td>    0.011</td> <td> 0.991</td> <td>-8.21e-09</td> <td>  8.3e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>X3</th>        <td>   10.0000</td> <td> 2.52e-09</td> <td> 3.97e+09</td> <td> 0.000</td> <td>   10.000</td> <td>   10.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>X1</th>        <td>    0.2692</td> <td> 7.69e-12</td> <td>  3.5e+10</td> <td> 0.000</td> <td>    0.269</td> <td>    0.269</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>X2</th>        <td>    0.5000</td> <td> 2.52e-09</td> <td> 1.99e+08</td> <td> 0.000</td> <td>    0.500</td> <td>    0.500</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>X4</th>        <td>    1.3462</td> <td> 3.85e-11</td> <td>  3.5e+10</td> <td> 0.000</td> <td>    1.346</td> <td>    1.346</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>14.003</td> <th>  Durbin-Watson:     </th> <td>   0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.001</td> <th>  Jarque-Bera (JB):  </th> <td>  10.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.651</td> <th>  Prob(JB):          </th> <td> 0.00666</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.156</td> <th>  Cond. No.          </th> <td>5.01e+17</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 1.52e-26. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\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:                 8.784e+26\n",
       "Date:                Mon, 08 Jun 2020   Prob (F-statistic):               0.00\n",
       "Time:                        17:03:08   Log-Likelihood:                 1752.9\n",
       "No. Observations:                 100   AIC:                            -3498.\n",
       "Df Residuals:                      96   BIC:                            -3487.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept   4.684e-11   4.16e-09      0.011      0.991   -8.21e-09     8.3e-09\n",
       "X3            10.0000   2.52e-09   3.97e+09      0.000      10.000      10.000\n",
       "X1             0.2692   7.69e-12    3.5e+10      0.000       0.269       0.269\n",
       "X2             0.5000   2.52e-09   1.99e+08      0.000       0.500       0.500\n",
       "X4             1.3462   3.85e-11    3.5e+10      0.000       1.346       1.346\n",
       "==============================================================================\n",
       "Omnibus:                       14.003   Durbin-Watson:                   0.001\n",
       "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               10.024\n",
       "Skew:                           0.651   Prob(JB):                      0.00666\n",
       "Kurtosis:                       2.156   Cond. No.                     5.01e+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 1.52e-26. 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": {},
   "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."
   ]
  }
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