chaobin/Linear Regression - simple regression.ipynb

## Linear Regression - simple regression.ipynb
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the plot setup\n",
      "%pylab inline\n",
      "#import mpld3\n",
      "#mpld3.enable_notebook()\n",
      "import matplotlib.pyplot as plt\n",
      "from pylab import rcParams\n",
      "rcParams['figure.figsize'] = 8, 5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# data tools\n",
      "\n",
      "import math\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "from pandas import DataFrame, Series"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# use data below to experiment with\n",
      "# http://onlinestatbook.com/2/case_studies/data/sat.txt\n",
      "\n",
      "URL_GPA = \"http://onlinestatbook.com/2/case_studies/data/sat.txt\"\n",
      "\n",
      "def online_gpa():\n",
      "    import urllib2\n",
      "    source = urllib2.urlopen(URL_GPA)\n",
      "    df = DataFrame.from_csv(source, sep=' ', header=0, index_col=None)\n",
      "    return df\n",
      "df_gpa = online_gpa()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df_gpa.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>high_GPA</th>\n",
        "      <th>math_SAT</th>\n",
        "      <th>verb_SAT</th>\n",
        "      <th>comp_GPA</th>\n",
        "      <th>univ_GPA</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 3.45</td>\n",
        "      <td> 643</td>\n",
        "      <td> 589</td>\n",
        "      <td> 3.76</td>\n",
        "      <td> 3.52</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 2.78</td>\n",
        "      <td> 558</td>\n",
        "      <td> 512</td>\n",
        "      <td> 2.87</td>\n",
        "      <td> 2.91</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 2.52</td>\n",
        "      <td> 583</td>\n",
        "      <td> 503</td>\n",
        "      <td> 2.54</td>\n",
        "      <td> 2.40</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 3.67</td>\n",
        "      <td> 685</td>\n",
        "      <td> 602</td>\n",
        "      <td> 3.83</td>\n",
        "      <td> 3.47</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 3.24</td>\n",
        "      <td> 592</td>\n",
        "      <td> 538</td>\n",
        "      <td> 3.29</td>\n",
        "      <td> 3.47</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "   high_GPA  math_SAT  verb_SAT  comp_GPA  univ_GPA\n",
        "0      3.45       643       589      3.76      3.52\n",
        "1      2.78       558       512      2.87      2.91\n",
        "2      2.52       583       503      2.54      2.40\n",
        "3      3.67       685       602      3.83      3.47\n",
        "4      3.24       592       538      3.29      3.47"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def std_deviation(data):\n",
      "    \"\"\"\n",
      "    Calculates the standard deviation of data.\n",
      "    \n",
      "    Note pandas has std() itself.\n",
      "    \n",
      "    data\n",
      "        pandas.DataFrame\n",
      "    \n",
      "    return\n",
      "        numpy.float\n",
      "    \"\"\"\n",
      "    normalizer = data.shape[0] - 1 # because the data could be a sample of a larger parent set\n",
      "    std = (data - data.mean()).pow(2).sum() / normalizer\n",
      "    assert np.round(np.sqrt(std), 6) == np.round(data.std(), 6)\n",
      "    return np.sqrt(std)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "std_deviation(df_gpa.high_GPA)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "0.51659782715214253"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def pearson_r(col_x, col_y):\n",
      "    \"\"\"\n",
      "    Calculate the Pearson Correlation between x and y.\n",
      "    \n",
      "    http://onlinestatbook.com/2/describing_bivariate_data/calculation.html\n",
      "    \n",
      "    col_x and col_y\n",
      "        pandas.DataFrame, or pandas.Series\n",
      "        \n",
      "    return\n",
      "        float, r\n",
      "    \"\"\"\n",
      "    \n",
      "    # calulate the variances\n",
      "    var_x = col_x - col_x.mean()\n",
      "    # assert var_x == col_x.var()\n",
      "    var_y = col_y - col_y.mean()\n",
      "    # assert var_y == col_y.var()\n",
      "    \n",
      "    # calculate Pearson's r\n",
      "    r = (var_x * var_y).sum() / (np.sqrt(var_x.pow(2).sum() * var_y.pow(2).sum()))\n",
      "    return r\n",
      "\n",
      "# the correlation with itself should always be 1.0\n",
      "assert pearson_r(df_gpa.univ_GPA, df_gpa.univ_GPA) == 1.0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pearson_r(df_gpa.univ_GPA, df_gpa.high_GPA)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "0.77956312054891597"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df_gpa.high_GPA.corr(df_gpa.univ_GPA, method=\"pearson\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "0.77956312054891608"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# now the regression\n",
      "def fit(X, Y):\n",
      "    \"\"\"\n",
      "    Calculate a straigt line that best fits the Xs and Ys.\n",
      "    The definition of a line being best fitting is that this line\n",
      "    minimizes the sum of all squared errors (the distance between the predicted\n",
      "    value and its actual value).\n",
      "    \n",
      "    X and Y\n",
      "        pandas.DataFrame, or pandas.Series\n",
      "    \n",
      "    return\n",
      "        a function, the straigt line function.\n",
      "        \n",
      "        The function of a straight line is given below:\n",
      "    \n",
      "        Y' = bX + A\n",
      "    \n",
      "        where b is the slope, and A being the intercept.\n",
      "    \"\"\"\n",
      "    \n",
      "    # b = r * (std(Y) / std(X))\n",
      "    r = pearson_r(X, Y)\n",
      "    std_x = std_deviation(X)\n",
      "    std_y = std_deviation(Y)\n",
      "    \n",
      "    b = r * (std_y / std_x)\n",
      "    \n",
      "    # A = M(Y) - bM(X)\n",
      "    A = Y.mean() - b * X.mean()\n",
      "    \n",
      "    def line(x):\n",
      "        \"\"\"\n",
      "        The function of the best fitting line.\n",
      "        \n",
      "        return\n",
      "            float, a prediction\n",
      "        \"\"\"\n",
      "        return b * x + A\n",
      "    \n",
      "    return line"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "predictor = fit(df_gpa.high_GPA, df_gpa.univ_GPA)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot our best fitting line against the original data\n",
      "# I better leave this here to help draw the line : )\n",
      "# ('o', 'v', '^', '<', '>', '8', 's', 'p', '*', 'h', 'H', 'D', 'd')\n",
      "plot(df_gpa.high_GPA, df_gpa.univ_GPA, 'ko', fillstyle='none')\n",
      "plot(df_gpa.high_GPA, df_gpa.high_GPA.apply(predictor), 'g-')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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Mo25KUjabVTKZ1IoVK2y/x7n5QZFWzO5jnjPQgdHRUctmymblvabZPOTKfsqVGty2bduq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\nQRolAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b4285d0>"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "predictor(2.78)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "2.9728504133781488"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# now a wrapped up version of the fitting function using\n",
      "# linear algebra tools from inside Pandas\n",
      "# as you can see just how little of code you need\n",
      "# to write to train a predictor\n",
      "\n",
      "def fit2(X, Y):\n",
      "    b = X.corr(Y, method=\"pearson\") * (Y.std() / X.std())\n",
      "    A = (Y.mean() - b * X.mean())\n",
      "    \n",
      "    def line(x):\n",
      "        return b*x + A\n",
      "    return line\n",
      "\n",
      "# a pure Python implementation\n",
      "\n",
      "def fit3(X, Y):\n",
      "    \n",
      "    def mean(Xs):\n",
      "        return sum(Xs) / len(Xs)\n",
      "    m_X = mean(X)\n",
      "    m_Y = mean(Y)\n",
      "    \n",
      "    def std(Xs, m):\n",
      "        normalizer = len(Xs) - 1\n",
      "        return math.sqrt(sum((pow(x - m, 2) for x in Xs)) / normalizer)\n",
      "    # assert np.round(Series(X).std(), 6) == np.round(std(X, m_X), 6)\n",
      "    \n",
      "    def pearson_r(Xs, Ys):\n",
      "        \n",
      "        sum_xy = 0\n",
      "        sum_sq_v_x = 0\n",
      "        sum_sq_v_y = 0\n",
      "        \n",
      "        for (x, y) in zip(Xs, Ys):\n",
      "            var_x = x - m_X\n",
      "            var_y = y - m_Y\n",
      "            sum_xy += var_x * var_y\n",
      "            sum_sq_v_x += pow(var_x, 2)\n",
      "            sum_sq_v_y += pow(var_y, 2)\n",
      "        return sum_xy / math.sqrt(sum_sq_v_x * sum_sq_v_y)\n",
      "    # assert np.round(Series(X).corr(Series(Y)), 6) == np.round(pearson_r(X, Y), 6)\n",
      "    \n",
      "    r = pearson_r(X, Y)\n",
      "\n",
      "    b = r * (std(Y, m_Y) / std(X, m_X))\n",
      "    A = m_Y - b * m_X\n",
      "    \n",
      "    def line(x):\n",
      "        return b * x + A\n",
      "    return line"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "predictor2 = fit2(df_gpa.high_GPA, df_gpa.univ_GPA)\n",
      "predictor3 = fit3(df_gpa.high_GPA, df_gpa.univ_GPA)\n",
      "predictor2(2.78), predictor3(2.78)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "(2.972850413378147, 2.9728504133781488)"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the two\n",
      "\n",
      "plt.xlabel(\"High School GPA\")\n",
      "plt.ylabel(\"University GPA\")\n",
      "plot(df_gpa.high_GPA, df_gpa.univ_GPA, \"ko\", fillstyle='none'),\n",
      "plot(df_gpa.high_GPA, df_gpa.high_GPA.apply(predictor2), 'r-', antialiased=True)\n",
      "plot(df_gpa.high_GPA, df_gpa.high_GPA.apply(predictor3), 'g-', antialiased=True)\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HJzCS+6sOxlVMg+ekbm7OPdfGLiLSCE6vFb878HI9d95ASuxSM6uE/sTxCfY7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\nIiIiIiIiIiIiIlLW/wet9tdtLPelgQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b409590>"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# To Do\n",
      "# Perhaps to perform an amount of prediction using the trained\n",
      "# predictor. Observe the correlation between:\n",
      "# \n",
      "# 1. training data set size, mean(sum of squared errors)\n",
      "# 2. std(x), mean(sum of squared errors)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}