part 11.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$m = \\frac{\\overline{X} \\cdot \\overline{Y} - \\overline{XY}}{(\\overline{X})^2 - \\overline{X^2}}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Math\n",
    "Math(r'm = \\frac{\\overline{X} \\cdot \\overline{Y} - \\overline{XY}}{(\\overline{X})^2 - \\overline{X^2}}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$b = \\overline{Y} - m \\overline{X}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Math(r'b = \\overline{Y} - m \\overline{X}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from statistics import mean\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import style\n",
    "%matplotlib inline\n",
    "style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HH33U1k5NTdWUKVO0Z88erVixwq/FWJbV6X1c10Mltf0MyuW5Kcvy+KGqvq0rc9qfDfT5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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6cf5b61c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.array([1,2,3,4,5,6], dtype=np.float64)\n",
    "ys = np.array([5,4,6,5,6,7], dtype=np.float64)\n",
    "\n",
    "plt.scatter(xs, ys)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.42857142857142866, 4.0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def best_fit_slope_and_intercept(xs, ys):\n",
    "    m = (\n",
    "         ((mean(xs) * mean(ys)) - mean(xs*ys))\n",
    "         / \n",
    "         ((mean(xs))**2 - mean(xs**2))\n",
    "        )\n",
    "    b = mean(ys) - m*mean(xs)\n",
    "    return m, b\n",
    "\n",
    "m, b = best_fit_slope_and_intercept(xs, ys)\n",
    "m, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "regression_line = [(m*x)+b for x in xs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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s+PtC3sLhp8fixYtx9OhRlJaW4vvvv8cf/vAHNDY2YsaMGQCApUuXYsKECe3b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\n4iqCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6cf5b8ef60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(xs, ys)\n",
    "plt.plot(xs, regression_line)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$r^2 = 1 - \\frac{SE\\hat{y}}{SE\\overline{y}}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Math(r'r^2 = 1 - \\frac{SE\\hat{y}}{SE\\overline{y}}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5844155844155845"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def squared_error(ys_orig, ys_line):\n",
    "    return sum((ys_line-ys_orig)**2)\n",
    "\n",
    "def coefficcient_of_determination(ys_orig, ys_line):\n",
    "    y_mean_line = [mean(ys_orig) for y in ys_orig]\n",
    "    squared_error_regr = squared_error(ys_orig, ys_line)\n",
    "    squared_error_y_mean = squared_error(ys_orig, y_mean_line)\n",
    "    return 1 - (squared_error_regr / squared_error_y_mean)\n",
    "\n",
    "r_squared = coefficcient_of_determination(ys, regression_line)\n",
    "r_squared"
   ]
  }
 ],
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