14-LinearModels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1><center> Linear Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "Linear (regression) modelling is a method of predicting the value of an output value as a linear combination of weight input values.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Imports \n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Statmodels & patsy\n",
    "import patsy\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# Linear Models with sklearn\n",
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Generate some correlated data\n",
    "corr = 0.75\n",
    "covs = [[1, corr], [corr, 1]]\n",
    "\n",
    "means = [0, 0]\n",
    "\n",
    "dat = np.random.multivariate_normal(means, covs, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PHhzoqWJsU/Dpx8f4w1TKtxZdf/Wzs038SGpnx1gRJJKyZ9L0I6QiDeyw2Ilv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aAAAG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105d2ee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check out the data we generated\n",
    "plt.scatter(dat[:, 0], dat[:, 1], alpha=0.5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Put data into a DataFrame\n",
    "df = pd.DataFrame(dat, columns=['D1', 'D2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.502209</td>\n",
       "      <td>0.581489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.091061</td>\n",
       "      <td>-0.483754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.191680</td>\n",
       "      <td>0.170911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.284596</td>\n",
       "      <td>0.794369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.534975</td>\n",
       "      <td>-1.700292</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         D1        D2\n",
       "0  0.502209  0.581489\n",
       "1 -1.091061 -0.483754\n",
       "2  1.191680  0.170911\n",
       "3 -0.284596  0.794369\n",
       "4 -0.534975 -1.700292"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Eye ball the data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Models with Statsmodels & Patsy\n",
    "<br>\n",
    "<div class=\"alert alert-success\">\n",
    "Statsmodels is a module for statistical analyses in Python. <br>\n",
    "Patsy is a useful package to work with and describe statistical models.\n",
    "</div>\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "Statsmodels - http://www.statsmodels.org/stable/index.html <br>\n",
    "Patsy - https://patsy.readthedocs.io/en/latest/\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Patsy gives us an easy way to construct design matrices\n",
    "#  For our purpose, 'design matrices' are just organized matrices of our predictor and output variables\n",
    "outcome, predictors = patsy.dmatrices('D1 ~ D2', df)\n",
    "\n",
    "# Use statsmodels to intialize the OLS model\n",
    "mod = sm.OLS(outcome, predictors)\n",
    "\n",
    "# Fit the model\n",
    "res = mod.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     D1   R-squared:                       0.562\n",
      "Model:                            OLS   Adj. R-squared:                  0.561\n",
      "Method:                 Least Squares   F-statistic:                     1279.\n",
      "Date:                Fri, 19 May 2017   Prob (F-statistic):          5.36e-181\n",
      "Time:                        19:11:22   Log-Likelihood:                -1001.5\n",
      "No. Observations:                1000   AIC:                             2007.\n",
      "Df Residuals:                     998   BIC:                             2017.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0205      0.021      0.983      0.326        -0.020     0.061\n",
      "D2             0.7403      0.021     35.769      0.000         0.700     0.781\n",
      "==============================================================================\n",
      "Omnibus:                        0.847   Durbin-Watson:                   1.949\n",
      "Prob(Omnibus):                  0.655   Jarque-Bera (JB):                0.925\n",
      "Skew:                          -0.041   Prob(JB):                        0.630\n",
      "Kurtosis:                       2.875   Cond. No.                         1.02\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Check out the results\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statsmodels gives us a lot of information! Perhaps most notably, the middle of the above print out gives a the coef's and p-values of our predictors, in this case, 'Intercept', and 'D2'. We see that D2 has a coef a significant coefficient that is approximately the correlation value we generated our data with!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using multiple predictors\n",
    "\n",
    "We can also use more than 1 predictor variable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.502209</td>\n",
       "      <td>0.581489</td>\n",
       "      <td>-0.276967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.091061</td>\n",
       "      <td>-0.483754</td>\n",
       "      <td>0.867106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.191680</td>\n",
       "      <td>0.170911</td>\n",
       "      <td>1.191308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.284596</td>\n",
       "      <td>0.794369</td>\n",
       "      <td>-0.287994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.534975</td>\n",
       "      <td>-1.700292</td>\n",
       "      <td>1.003555</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         D1        D2        D3\n",
       "0  0.502209  0.581489 -0.276967\n",
       "1 -1.091061 -0.483754  0.867106\n",
       "2  1.191680  0.170911  1.191308\n",
       "3 -0.284596  0.794369 -0.287994\n",
       "4 -0.534975 -1.700292  1.003555"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a new column of data to df\n",
    "df['D3'] = pd.Series(np.random.randn(1000), index=df.index)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Predict D1 from D2 and D3\n",
    "outcome, predictors = patsy.dmatrices('D1 ~ D2 + D3', df)\n",
    "mod = sm.OLS(outcome, predictors)\n",
    "res = mod.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     D1   R-squared:                       0.562\n",
      "Model:                            OLS   Adj. R-squared:                  0.561\n",
      "Method:                 Least Squares   F-statistic:                     640.0\n",
      "Date:                Fri, 19 May 2017   Prob (F-statistic):          1.57e-179\n",
      "Time:                        19:11:22   Log-Likelihood:                -1001.1\n",
      "No. Observations:                1000   AIC:                             2008.\n",
      "Df Residuals:                     997   BIC:                             2023.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0197      0.021      0.946      0.345        -0.021     0.061\n",
      "D2             0.7397      0.021     35.724      0.000         0.699     0.780\n",
      "D3            -0.0195      0.021     -0.928      0.354        -0.061     0.022\n",
      "==============================================================================\n",
      "Omnibus:                        0.815   Durbin-Watson:                   1.945\n",
      "Prob(Omnibus):                  0.665   Jarque-Bera (JB):                0.897\n",
      "Skew:                          -0.043   Prob(JB):                        0.639\n",
      "Kurtosis:                       2.882   Cond. No.                         1.06\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression with sklearn\n",
    "\n",
    "Scikit-learn also has implementations of Linear Regression models. \n",
    "\n",
    "<br>\n",
    "<div class=\"alert alert-info\">\n",
    "Linear Regression in sklearn: http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Convert data into shape for easier use with sklearn\n",
    "d1 = np.reshape(df.D1.values, [len(df.D1), 1])\n",
    "d2 = np.reshape(df.D2.values, [len(df.D2), 1])\n",
    "d3 = np.reshape(df.D3.values, [len(df.D3), 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Initialize linear regression model\n",
    "reg = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the linear regression model\n",
    "reg.fit(d2, d1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0205115074726\n",
      "0.74025630917\n"
     ]
    }
   ],
   "source": [
    "# Check the results of this\n",
    "#  If you compare these to what we got with statsmodels above, they are indeed the same\n",
    "print(reg.intercept_[0])\n",
    "print(reg.coef_[0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using multiple predictors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initialize and fit linear model\n",
    "reg = linear_model.LinearRegression()\n",
    "reg.fit(np.hstack([d2, d3]), d1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: \t 0.0197398584329\n",
      "Theta D2 :\t 0.73969506124\n",
      "Theta D3 :\t -0.0194792007873\n"
     ]
    }
   ],
   "source": [
    "# Check the results of this\n",
    "#  If you compare these to what we got with statsmodels above, they are indeed the same\n",
    "print('Intercept: \\t', reg.intercept_[0])\n",
    "print('Theta D2 :\\t', reg.coef_[0][0])\n",
    "print('Theta D3 :\\t', reg.coef_[0][1])"
   ]
  }
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