{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Simple Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We used the correlation function to measure the strength of the linear relationship between two variables. For most applications, knowing that such a linear relationship exists isn’t enough. We’ll want to be able to understand the nature of the relationship. This is where we’ll use simple linear regression.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## The Model\n",
    "\n",
    "$$y_i = \\beta x_i + \\alpha + \\epsilon_i$$\n",
    "\n",
    "\n",
    "where \n",
    "\n",
    "- $y_i$ is the number of minutes user i spends on the site daily, \n",
    "- $x_i$ is the number of friends user i has\n",
    "- $\\alpha$ is the constant when x = 0.\n",
    "- $ε_i$ is a (hopefully small) error term representing the fact that there are other factors not accounted for by this simple model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Least Squares Fit\n",
    "\n",
    "最小二乘法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$ y_i = X_i^T w$$\n",
    "\n",
    "The constant could be represent by 1 in X\n",
    "\n",
    "The squared error could be written as: \n",
    "\n",
    "$$ \\sum_{i = 1}^m (y_i -X_i^T w)^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "If we know $\\alpha$ and $\\beta$, then we can make predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T07:00:38.067857Z",
     "start_time": "2018-11-14T07:00:38.062774Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Since we know the actual output $y_i$ we can compute the error for each pair."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Since the negative errors cancel out with the positive ones, we use squared errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The least squares solution is to choose the $\\alpha$ and $\\beta$ that make **sum_of_squared_errors** as small as possible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The choice of beta means that when the input value increases by standard_deviation(x), the prediction increases by correlation(x, y) * standard_deviation(y). \n",
    "\n",
    "- In the case when x and y are perfectly positively correlated, a one standard deviation increase in x results in a one-standard-deviation-of-y increase in the prediction.\n",
    "- When they’re perfectly negatively correlated, the increase in x results in a decrease in the prediction. \n",
    "- And when the correlation is zero, beta is zero, which means that changes in x don’t affect the prediction at all."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "> In this case, the slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. \n",
    "\n",
    "$$ y_i = \\alpha + \\beta x_i + \\varepsilon_i $$\n",
    "\n",
    "$$ \\hat\\varepsilon_i =y_i-a -b x_i $$\n",
    "\n",
    "$$ \\text{Find }\\min_{a,\\, b} Q(a, b), \\quad \\text{for } Q(a, b) = \\sum_{i=1}^n\\hat\\varepsilon_i^{\\,2} = \\sum_{i=1}^n (y_i -a - b x_i)^2\\ $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "By expanding to get a quadratic expression in $a$ and $b$, we can derive values of $a$ and $b$ that minimize the objective function $Q$ (these minimizing values are denoted $\\hat{\\alpha}$ and $\\hat{\\beta}$):\n",
    "\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    " \\hat\\alpha & = \\bar{y} - \\hat\\beta\\,\\bar{x}, \\\\\n",
    "  \\hat\\beta &= \\frac{ \\sum_{i=1}^n (x_i - \\bar{x})(y_i - \\bar{y}) }{ \\sum_{i=1}^n (x_i - \\bar{x})^2 } = \\frac{ \\operatorname{Cov}(x, y) }{ \\operatorname{Var}(x) } = r_{xy} \\frac{s_y}{s_x}. \\\\[6pt]\n",
    "\\end{align}\n",
    "\n",
    "- $r_{xy}$ as the sample correlation coefficient between x and y\n",
    "- $s_x$ and $s_y$ as the uncorrected sample standard deviations of x and y\n",
    "\n",
    "\n",
    "> Kenney, J. F. and Keeping, E. S. (1962) \"Linear Regression and Correlation.\" Ch. 15 in ''Mathematics of Statistics'', Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 252–285"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Substituting the above expressions for $\\hat{\\alpha}$ and $\\hat{\\beta}$ into\n",
    "\n",
    "$$f = \\hat{\\alpha} + \\hat{\\beta} x,$$\n",
    "\n",
    "yields\n",
    "\n",
    "$$\\frac{ f - \\bar{y}}{s_y} = r_{xy} \\frac{ x - \\bar{x}}{s_x}  .$$\n",
    "\n",
    "\n",
    "> Kenney, J. F. and Keeping, E. S. (1962) \"Linear Regression and Correlation.\" Ch. 15 in ''Mathematics of Statistics'', Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 252–285"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-08T13:54:24.977792Z",
     "start_time": "2019-06-08T13:54:24.954921Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "num_friends_good = [49,41,40,25,21,21,19,19,18,18,16,15,15,15,15,14,14,13,13,13,13,12,12,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,8,8,8,8,8,8,8,8,8,8,8,8,8,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]\n",
    "daily_minutes_good = [68.77,51.25,52.08,38.36,44.54,57.13,51.4,41.42,31.22,34.76,54.01,38.79,47.59,49.1,27.66,41.03,36.73,48.65,28.12,46.62,35.57,32.98,35,26.07,23.77,39.73,40.57,31.65,31.21,36.32,20.45,21.93,26.02,27.34,23.49,46.94,30.5,33.8,24.23,21.4,27.94,32.24,40.57,25.07,19.42,22.39,18.42,46.96,23.72,26.41,26.97,36.76,40.32,35.02,29.47,30.2,31,38.11,38.18,36.31,21.03,30.86,36.07,28.66,29.08,37.28,15.28,24.17,22.31,30.17,25.53,19.85,35.37,44.6,17.23,13.47,26.33,35.02,32.09,24.81,19.33,28.77,24.26,31.98,25.73,24.86,16.28,34.51,15.23,39.72,40.8,26.06,35.76,34.76,16.13,44.04,18.03,19.65,32.62,35.59,39.43,14.18,35.24,40.13,41.82,35.45,36.07,43.67,24.61,20.9,21.9,18.79,27.61,27.21,26.61,29.77,20.59,27.53,13.82,33.2,25,33.1,36.65,18.63,14.87,22.2,36.81,25.53,24.62,26.25,18.21,28.08,19.42,29.79,32.8,35.99,28.32,27.79,35.88,29.06,36.28,14.1,36.63,37.49,26.9,18.58,38.48,24.48,18.95,33.55,14.24,29.04,32.51,25.63,22.22,19,32.73,15.16,13.9,27.2,32.01,29.27,33,13.74,20.42,27.32,18.23,35.35,28.48,9.08,24.62,20.12,35.26,19.92,31.02,16.49,12.16,30.7,31.22,34.65,13.13,27.51,33.2,31.57,14.1,33.42,17.44,10.12,24.42,9.82,23.39,30.93,15.03,21.67,31.09,33.29,22.61,26.89,23.48,8.38,27.81,32.35,23.84]\n",
    "alpha, beta = 22.9475, 0.90386\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-08T13:54:49.498421Z",
     "start_time": "2019-06-08T13:54:48.852023Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(num_friends_good, daily_minutes_good)\n",
    "plt.plot(num_friends_good, [alpha + beta*i for i in num_friends_good], 'b-')\n",
    "plt.xlabel('# of friends', fontsize = 20)\n",
    "plt.ylabel('minutes per day', fontsize = 20)\n",
    "plt.title('simple linear regression model', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Of course, we need a better way to figure out how well we’ve fit the data than staring at the graph. \n",
    "\n",
    "A common measure is the coefficient of determination (or R-squared), which measures the fraction of the total variation in the dependent variable that is captured by the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-07T05:42:35.575216Z",
     "start_time": "2018-11-07T05:42:35.570042Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Multiple Regression using Matrix Method\n",
    "\n",
    "Machine Learning in Action\n",
    "\n",
    "https://github.com/computational-class/machinelearninginaction/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$ y_i = X_i^T w$$\n",
    "\n",
    "The constant could be represent by 1 in X\n",
    "\n",
    "The squared error could be written as: \n",
    "\n",
    "$$ \\sum_{i = 1}^m (y_i -X_i^T w)^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can also write this in matrix notation as $(y-Xw)^T(y-Xw)$. \n",
    "\n",
    "If we take the derivative of this with respect to w, we’ll get $X^T(y-Xw)$. \n",
    "\n",
    "We can set this to zero and solve for w to get the following equation:\n",
    "\n",
    "$$\\hat w = (X^T X)^{-1}X^T y$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-09T02:31:35.132677Z",
     "start_time": "2019-06-09T02:31:35.115627Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y</th>\n",
       "      <th>x3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.067732</td>\n",
       "      <td>3.176513</td>\n",
       "      <td>1.384291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.427810</td>\n",
       "      <td>3.816464</td>\n",
       "      <td>1.354246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.995731</td>\n",
       "      <td>4.550095</td>\n",
       "      <td>1.801504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.738336</td>\n",
       "      <td>4.256571</td>\n",
       "      <td>1.374716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.981083</td>\n",
       "      <td>4.560815</td>\n",
       "      <td>1.637240</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    x1        x2         y        x3\n",
       "0  1.0  0.067732  3.176513  1.384291\n",
       "1  1.0  0.427810  3.816464  1.354246\n",
       "2  1.0  0.995731  4.550095  1.801504\n",
       "3  1.0  0.738336  4.256571  1.374716\n",
       "4  1.0  0.981083  4.560815  1.637240"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://github.com/computational-class/machinelearninginaction/blob/master/Ch08/regression.py\n",
    "import pandas as pd\n",
    "import random\n",
    "\n",
    "dat = pd.read_csv('../data/ex0.txt', sep = '\\t', names = ['x1', 'x2', 'y'])\n",
    "dat['x3'] = [yi*.3 + .5*random.random() for yi in dat['y']]\n",
    "dat.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-09T02:31:58.107318Z",
     "start_time": "2019-06-09T02:31:58.098246Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from numpy import mat, linalg, corrcoef\n",
    "\n",
    "def standRegres(xArr,yArr):\n",
    "    xMat = mat(xArr); yMat = mat(yArr).T\n",
    "    xTx = xMat.T*xMat\n",
    "    if linalg.det(xTx) == 0.0:\n",
    "        print(\"This matrix is singular, cannot do inverse\")\n",
    "        return\n",
    "    ws = xTx.I * (xMat.T*yMat)\n",
    "    return ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-09T02:32:02.126263Z",
     "start_time": "2019-06-09T02:32:02.105970Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.0, 0.067732, 1.3842912829135907], [1.0, 0.42781, 1.3542457458385966]]\n",
      "[[2.88936235]\n",
      " [1.63851705]\n",
      " [0.10238664]]\n"
     ]
    }
   ],
   "source": [
    "xs = [[dat.x1[i], dat.x2[i], dat.x3[i]] for i in dat.index]\n",
    "y = dat.y\n",
    "print(xs[:2])\n",
    "ws = standRegres(xs, y)\n",
    "print(ws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-08T14:13:25.237796Z",
     "start_time": "2019-06-08T14:13:25.230467Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "xMat=mat(xs)\n",
    "yMat=mat(y)\n",
    "yHat = xMat*ws\n",
    "\n",
    "xCopy=xMat.copy()\n",
    "xCopy.sort(0)\n",
    "yHat=xCopy*ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-08T14:13:31.245040Z",
     "start_time": "2019-06-08T14:13:31.046248Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(xMat[:,1].flatten().A[0], yMat.T[:,0].flatten().A[0])\n",
    "ax.plot(xCopy[:,1],yHat, 'r-')\n",
    "plt.ylim(0, 5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-07T12:48:32.415464Z",
     "start_time": "2018-11-07T12:48:32.409103Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.98666465],\n",
       "       [ 0.98666465,  1.        ]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yHat = xMat*ws\n",
    "corrcoef(yHat.T, yMat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Doing Statistics with statsmodels\n",
    "\n",
    "http://www.statsmodels.org/stable/index.html\n",
    "\n",
    "statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T05:37:53.042411Z",
     "start_time": "2018-11-14T05:37:51.646856Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T05:41:58.692475Z",
     "start_time": "2018-11-14T05:41:58.679427Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y</th>\n",
       "      <th>x3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.067732</td>\n",
       "      <td>3.176513</td>\n",
       "      <td>0.885553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.427810</td>\n",
       "      <td>3.816464</td>\n",
       "      <td>1.100010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.995731</td>\n",
       "      <td>4.550095</td>\n",
       "      <td>1.323654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.738336</td>\n",
       "      <td>4.256571</td>\n",
       "      <td>1.267457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.981083</td>\n",
       "      <td>4.560815</td>\n",
       "      <td>1.300163</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    x1        x2         y        x3\n",
       "0  1.0  0.067732  3.176513  0.885553\n",
       "1  1.0  0.427810  3.816464  1.100010\n",
       "2  1.0  0.995731  4.550095  1.323654\n",
       "3  1.0  0.738336  4.256571  1.267457\n",
       "4  1.0  0.981083  4.560815  1.300163"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dat = pd.read_csv('ex0.txt', sep = '\\t', names = ['x1', 'x2', 'y'])\n",
    "dat['x3'] = [yi*.3 - .1*random.random() for yi in y]\n",
    "dat.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T05:42:03.424640Z",
     "start_time": "2018-11-14T05:42:03.357545Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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>   0.986</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.986</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   7167.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 14 Nov 2018</td> <th>  Prob (F-statistic):</th> <td>1.04e-184</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:42:03</td>     <th>  Log-Likelihood:    </th> <td>  284.06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   200</td>      <th>  AIC:               </th> <td>  -562.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   197</td>      <th>  BIC:               </th> <td>  -552.2</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>Intercept</th> <td>    1.7146</td> <td>    0.093</td> <td>   18.372</td> <td> 0.000</td> <td>    1.531</td> <td>    1.899</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>        <td>    0.9264</td> <td>    0.057</td> <td>   16.228</td> <td> 0.000</td> <td>    0.814</td> <td>    1.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>        <td>    1.5151</td> <td>    0.109</td> <td>   13.909</td> <td> 0.000</td> <td>    1.300</td> <td>    1.730</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 4.027</td> <th>  Durbin-Watson:     </th> <td>   1.852</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.134</td> <th>  Jarque-Bera (JB):  </th> <td>   2.762</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.112</td> <th>  Prob(JB):          </th> <td>   0.251</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.469</td> <th>  Cond. No.          </th> <td>    58.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.986\n",
       "Model:                            OLS   Adj. R-squared:                  0.986\n",
       "Method:                 Least Squares   F-statistic:                     7167.\n",
       "Date:                Wed, 14 Nov 2018   Prob (F-statistic):          1.04e-184\n",
       "Time:                        13:42:03   Log-Likelihood:                 284.06\n",
       "No. Observations:                 200   AIC:                            -562.1\n",
       "Df Residuals:                     197   BIC:                            -552.2\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.7146      0.093     18.372      0.000       1.531       1.899\n",
       "x2             0.9264      0.057     16.228      0.000       0.814       1.039\n",
       "x3             1.5151      0.109     13.909      0.000       1.300       1.730\n",
       "==============================================================================\n",
       "Omnibus:                        4.027   Durbin-Watson:                   1.852\n",
       "Prob(Omnibus):                  0.134   Jarque-Bera (JB):                2.762\n",
       "Skew:                          -0.112   Prob(JB):                        0.251\n",
       "Kurtosis:                       2.469   Cond. No.                         58.2\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = smf.ols('y ~ x2 + x3', data=dat).fit()\n",
    "\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T05:42:06.382425Z",
     "start_time": "2018-11-14T05:42:05.862926Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "fig = sm.graphics.plot_partregress_grid(results, fig = fig)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T05:58:41.909065Z",
     "start_time": "2018-11-14T05:58:41.893565Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.329\n",
      "Model:                            OLS   Adj. R-squared:                  0.326\n",
      "Method:                 Least Squares   F-statistic:                     98.60\n",
      "Date:                Wed, 14 Nov 2018   Prob (F-statistic):           3.68e-19\n",
      "Time:                        13:58:41   Log-Likelihood:                -711.76\n",
      "No. Observations:                 203   AIC:                             1428.\n",
      "Df Residuals:                     201   BIC:                             1434.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "x1             0.9039      0.091      9.930      0.000       0.724       1.083\n",
      "const         22.9476      0.846     27.133      0.000      21.280      24.615\n",
      "==============================================================================\n",
      "Omnibus:                       26.873   Durbin-Watson:                   2.027\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):                7.541\n",
      "Skew:                           0.004   Prob(JB):                       0.0230\n",
      "Kurtosis:                       2.056   Cond. No.                         13.9\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "X = np.array(num_friends_good)\n",
    "X = sm.add_constant(X, prepend=False)\n",
    "\n",
    "mod = sm.OLS(daily_minutes_good, X)\n",
    "res = mod.fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T05:59:29.913876Z",
     "start_time": "2018-11-14T05:59:29.553693Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6,8))\n",
    "fig = sm.graphics.plot_partregress_grid(res, fig = fig)\n",
    "plt.show()"
   ]
  }
 ],
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