ml-finance-python

python scripts for finance machine learning
git clone https://9o.is/git/ml-finance-python.git
notebook.ipynb

(174589B)
      1 {
      2  "cells": [
      3   {
      4    "cell_type": "markdown",
      5    "metadata": {
      6     "collapsed": true
      7    },
      8    "source": [
      9     "# Exercises: Linear Regression - Answer Key\n",
     10     "By Christopher van Hoecke, Max Margenot, and Delaney Mackenzie\n",
     11     "\n",
     12     "## Lecture Link : \n",
     13     "https://www.quantopian.com/lectures/linear-regression\n",
     14     "\n",
     15     "### IMPORTANT NOTE: \n",
     16     "This lecture corresponds to the Linear Regression lecture, which is part of the Quantopian lecture series. This homework expects you to rely heavily on the code presented in the corresponding lecture. Please copy and paste regularly from that lecture when starting to work on the problems, as trying to do them from scratch will likely be too difficult.\n",
     17     "\n",
     18     "Part of the Quantopian Lecture Series:\n",
     19     "\n",
     20     "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n",
     21     "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n",
     22     "\n",
     23     "Notebook released under the Creative Commons Attribution 4.0 License.\n",
     24     "\n",
     25     "----"
     26    ]
     27   },
     28   {
     29    "cell_type": "markdown",
     30    "metadata": {},
     31    "source": [
     32     "## Key Concepts"
     33    ]
     34   },
     35   {
     36    "cell_type": "code",
     37    "execution_count": 1,
     38    "metadata": {
     39     "collapsed": true
     40    },
     41    "outputs": [],
     42    "source": [
     43     "# Useful Functions\n",
     44     "def linreg(X,Y):\n",
     45     "    # Running the linear regression\n",
     46     "    X = sm.add_constant(X)\n",
     47     "    model = regression.linear_model.OLS(Y, X).fit()\n",
     48     "    a = model.params[0]\n",
     49     "    b = model.params[1]\n",
     50     "    X = X[:, 1]\n",
     51     "\n",
     52     "    # Return summary of the regression and plot results\n",
     53     "    X2 = np.linspace(X.min(), X.max(), 100)\n",
     54     "    Y_hat = X2 * b + a\n",
     55     "    plt.scatter(X, Y, alpha=0.3) # Plot the raw data\n",
     56     "    plt.plot(X2, Y_hat, 'r', alpha=0.9);  # Add the regression line, colored in red\n",
     57     "    plt.xlabel('X Value')\n",
     58     "    plt.ylabel('Y Value')\n",
     59     "    return model.summary()"
     60    ]
     61   },
     62   {
     63    "cell_type": "code",
     64    "execution_count": 2,
     65    "metadata": {},
     66    "outputs": [],
     67    "source": [
     68     "# Useful Libraries\n",
     69     "import math\n",
     70     "import numpy as np\n",
     71     "import matplotlib.pyplot as plt\n",
     72     "\n",
     73     "from statsmodels import regression\n",
     74     "from statsmodels.stats import diagnostic\n",
     75     "import statsmodels.regression as smr\n",
     76     "import statsmodels.api as sm\n",
     77     "from statsmodels.stats.diagnostic import het_breushpagan\n",
     78     "\n",
     79     "import scipy as sp\n",
     80     "import scipy.stats\n",
     81     "import seaborn\n"
     82    ]
     83   },
     84   {
     85    "cell_type": "markdown",
     86    "metadata": {},
     87    "source": [
     88     "---"
     89    ]
     90   },
     91   {
     92    "cell_type": "markdown",
     93    "metadata": {
     94     "collapsed": true
     95    },
     96    "source": [
     97     "# Exercise 1: Temperatures\n",
     98     "Given this set of Fahrenheit and Celsius values, find a model that expresses the relationship between the two temperature scales."
     99    ]
    100   },
    101   {
    102    "cell_type": "code",
    103    "execution_count": 3,
    104    "metadata": {},
    105    "outputs": [
    106     {
    107      "data": {
    108       "text/html": [
    109        "<table class=\"simpletable\">\n",
    110        "<caption>OLS Regression Results</caption>\n",
    111        "<tr>\n",
    112        "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   1.000</td> \n",
    113        "</tr>\n",
    114        "<tr>\n",
    115        "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   1.000</td> \n",
    116        "</tr>\n",
    117        "<tr>\n",
    118        "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>7.818e+06</td>\n",
    119        "</tr>\n",
    120        "<tr>\n",
    121        "  <th>Date:</th>             <td>Tue, 19 Jun 2018</td> <th>  Prob (F-statistic):</th> <td>8.33e-55</td> \n",
    122        "</tr>\n",
    123        "<tr>\n",
    124        "  <th>Time:</th>                 <td>18:08:12</td>     <th>  Log-Likelihood:    </th> <td> -26.373</td> \n",
    125        "</tr>\n",
    126        "<tr>\n",
    127        "  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>   56.75</td> \n",
    128        "</tr>\n",
    129        "<tr>\n",
    130        "  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>   58.83</td> \n",
    131        "</tr>\n",
    132        "<tr>\n",
    133        "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
    134        "</tr>\n",
    135        "<tr>\n",
    136        "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
    137        "</tr>\n",
    138        "</table>\n",
    139        "<table class=\"simpletable\">\n",
    140        "<tr>\n",
    141        "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
    142        "</tr>\n",
    143        "<tr>\n",
    144        "  <th>const</th> <td>   32.1905</td> <td>    0.195</td> <td>  165.172</td> <td> 0.000</td> <td>   31.783    32.598</td>\n",
    145        "</tr>\n",
    146        "<tr>\n",
    147        "  <th>x1</th>    <td>    1.7998</td> <td>    0.001</td> <td> 2795.998</td> <td> 0.000</td> <td>    1.798     1.801</td>\n",
    148        "</tr>\n",
    149        "</table>\n",
    150        "<table class=\"simpletable\">\n",
    151        "<tr>\n",
    152        "  <th>Omnibus:</th>       <td>53.344</td> <th>  Durbin-Watson:     </th> <td>   2.112</td>\n",
    153        "</tr>\n",
    154        "<tr>\n",
    155        "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 281.704</td>\n",
    156        "</tr>\n",
    157        "<tr>\n",
    158        "  <th>Skew:</th>          <td> 4.210</td> <th>  Prob(JB):          </th> <td>6.74e-62</td>\n",
    159        "</tr>\n",
    160        "<tr>\n",
    161        "  <th>Kurtosis:</th>      <td>18.844</td> <th>  Cond. No.          </th> <td>    303.</td>\n",
    162        "</tr>\n",
    163        "</table>"
    164       ],
    165       "text/plain": [
    166        "<class 'statsmodels.iolib.summary.Summary'>\n",
    167        "\"\"\"\n",
    168        "                            OLS Regression Results                            \n",
    169        "==============================================================================\n",
    170        "Dep. Variable:                      y   R-squared:                       1.000\n",
    171        "Model:                            OLS   Adj. R-squared:                  1.000\n",
    172        "Method:                 Least Squares   F-statistic:                 7.818e+06\n",
    173        "Date:                Tue, 19 Jun 2018   Prob (F-statistic):           8.33e-55\n",
    174        "Time:                        18:08:12   Log-Likelihood:                -26.373\n",
    175        "No. Observations:                  21   AIC:                             56.75\n",
    176        "Df Residuals:                      19   BIC:                             58.83\n",
    177        "Df Model:                           1                                         \n",
    178        "Covariance Type:            nonrobust                                         \n",
    179        "==============================================================================\n",
    180        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
    181        "------------------------------------------------------------------------------\n",
    182        "const         32.1905      0.195    165.172      0.000        31.783    32.598\n",
    183        "x1             1.7998      0.001   2795.998      0.000         1.798     1.801\n",
    184        "==============================================================================\n",
    185        "Omnibus:                       53.344   Durbin-Watson:                   2.112\n",
    186        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              281.704\n",
    187        "Skew:                           4.210   Prob(JB):                     6.74e-62\n",
    188        "Kurtosis:                      18.844   Cond. No.                         303.\n",
    189        "==============================================================================\n",
    190        "\n",
    191        "Warnings:\n",
    192        "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
    193        "\"\"\""
    194       ]
    195      },
    196      "execution_count": 3,
    197      "metadata": {},
    198      "output_type": "execute_result"
    199     },
    200     {
    201      "data": {
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67zyDSpK+x17D6re//S3r16/n9ttv53//93/ZsGEDffv2rYptkiSpqn3wQXCH\n6u9/D45zcoKgOvtsg0qSfsAew2rGjBl07NiRo48+mqOPPhqAMWPGVNkwSZJUhQoLg6CaNSs4PuWU\n4CV/eXkGlSTtgz2G1ZQpU/j9739P586d6datGy1btqzKXZIkqZKUlJRSUFDM1q3JHLryfdr8YyxJ\nb78d/GS7dsEdqvbtDSpJ+hH2GFZjxoyhqKiIF154gfz8fNLS0ujWrRuXXnop6enpVblRkiQdQAUF\nxfDuSk58YSiZC9+mLKGCpHPPDB6b3q5d2PMkKS794HussrOzufHGG7nxxhv58MMPmTZtGl27duWk\nk07iT3/6U1VtlCRJB0IkAnPmcOwv7iPjs3kAbGh1Fiu6Xkv7QReGPE6S4tteH17xjaOOOopmzZqx\naNEilixZUpmbJEnSgRSJwFtvBU/5mzuXhiUVrGvdgaWXDebrY3LIyFgd9kJJins/GFYVFRW8+eab\nTJ06lfnz53P++edz9913+34rSZLiQSQCr78eBFVhYXCuY0cS+/Vj2c7D2LY1mYz01eTmZoU6U5Kq\ngz2G1X333ceMGTNo3rw5l19+OX/+859JTU2tym2SJGl/RCLwj38ET/n74IPg3AUXBO+hat2aFCAv\n1IGSVP3sMazq1q3LpEmTOPzww6tyjyRJ2l+RCLz6anCH6qOPgnOdO8OgQdCqVbjbJKma22NYDRgw\noCp3SJKk/VVRAa+8EgTVp58Gj0m/5JIgqI47Lux1klQj7PPDKyRJUoypqIAZM2D4cFi4MAiqn/40\nCKrmzcNeJ0k1imElSVK8KS+HF18M3kO1eDEkJkK3bjBgABxzTNjrJKlGStzTT/Tu3ZsVK1ZU5RZJ\nkvRDyspgyhQ4+2z4+c9hyRK48srgUeojRxpVkhSiPd6x6tKlC9dddx2XX345N954IykpKVW5S5Ik\nfaOsDKZOhREjYNkySE6Gq68O7lA1aRL2OkkSP3DH6qc//SkvvPACX331FV26dOHtt99m5cqVu39I\nkqRKVloKkyZBXl7wvqlVq+Caa2D2bHjgAaNKkmLID77Hql69etx555386le/YuDAgWRkZBCJREhI\nSOC1116rqo2SJNUspaXwzDPBy/tWroSUFOjdG/r1g8aNw14nSfoePxhW77//Pr/73e9o06YNr732\nGhkZGVW1S5KkmqekJLhD9eCDsHo1pKZCnz5wyy3QqFHY6yRJP2CPYXXrrbeyaNEifvOb35CTk1OV\nmyRJqllYyU9AAAAgAElEQVR27YKJE2HUKFizBtLS4IYb4OabITs77HWSpH2wx7Bq3rw5999/P8nJ\nPpFdkqQDqaSklIKCYrZvLKPpnGc5ZuZ4EouLoXZt6Ns3+JGVFfZMSdKPsMdquvHGG6tyhyRJNcZ7\nb66gwXOv0ealh0nbvI5dtVOpffPNQVAdfHDY8yRJ+8HbUZIkVZVt22DsWFr/v1Gkbt5EWa10ll08\ngNWdf0qH7i3DXidJioJhJUlSZdu6FZ58Eh59FDZuJDm5NksvGcSK82+kLD2DjIzVYS+UJEXJsJIk\nqbJs3gxjxsBjj8GmTVC/Ptx6K8nX9mbDwp2wdRcZ6avJzfX9VJIU7wwrSZIOtM2b4fHHgx+bN0NG\nBtxxB1x3HdSvTyrBZ/5KkqoPw0qSpANl06YgpkaPhi1boGFDuOsu+NnPID097HWSpEpkWEmSFK2N\nG+Evfwle9rdtGxx0ENxzD/TuDXXrhr1OklQFDCtJkvbXhg3wyCPBgym2bw8+e+q226BXr+AzqSRJ\nNYZhJUnSj7VuXRBUY8fCjh2QnQ133gk9e0KtWmGvkySFwLCSJGlfFRXBww/DU0/Bzp3QqFHwkr8e\nPSAtLex1kqQQGVaSJO3N2rUwahSMHw8lJdC4MfTvD1ddBampYa+TJMUAw0qSpD358ssgqCZMgNJS\nOOIIGDAAuneHlJSw10mSYohhJUnSf1u5MgiqSZOCoDrqKBg4ELp2NagkSd/LsJIk6RsrVsDIkfDs\ns1BWBk2b/juokv1HpiRpz/ynhCRJy5YFQTV5MpSXwzHHwKBBcOmlBpUkaZ/4TwtJUs21ZAmMGAFT\np0JFBTRvDoMHw8UXQ1JS2OskSXHEsJIk1SglJaV8OPldUh8Zyq5F75KanEDCcccFd6g6d4bExLAn\nSpLikGElSao5PvuMDXf8gVZvz6K8rIzNTdtQ1PNaTsjvaVBJkqJiWEmSqr9PP4Vhw2DGDBruqmBz\nk5N469QrSb3oZySnFHOCUSVJilLchtV9993HggULSEhI4K677qJ169ZhT5IkxZqPPgqC6pVXguO2\nbfm8Qy+WN7uSfy1ZwjEJCaSnl4W7UZJULcRlWL333nusWLGCSZMmsWTJEu6++24mTZoU9ixJUqz4\n4IMgqP7+9+A4Jwfy8+Gss2hRWsamgi9JSlpDRkZtcnOzwt0qSaoW4jKs3nnnHTp06ABAs2bN2Lx5\nM9u2baNu3bohL5MkhWrePBg6FGbNCo5PPTUIqjPOgIQEAFJTU8jLa0ydOmvJyWkc4lhJUnUSl2G1\nfv16TjjhhN3HDRs2ZP369YaVJNVU778PDzwAb7wRHLdvHzw2vX373UElSVJlisuw+m+RSGSfvq6w\nsLCSlygeeB0IvA6qi7offUTWhAmkf/ABAFtPOoninj3Z9s37bufN+8Ff73Ug8DrQv3ktKBpxGVZZ\nWVmsX79+93FxcTGHHHLIXn9dTk5OZc5SHCgsLPQ6kNdBvItEYM6c4CV/77wTnOvQAYYMIfOUU8jc\nx7+N14HA60D/5rUgiC6u4/L5sqeffjozZ84E4JNPPiE7O5s6deqEvEqSVKkiEXjrLejSBa64Ioiq\n886D6dPhb3+DU04Je6EkqQaLyztWbdu2pVWrVlx11VUkJSXxq1/9KuxJkqTKEonA668Hd6i++S+J\nHTsG76E66aRQp0mS9I24DCuAIUOGhD1BklSZIhF47bXgsenz5wfnLrggCCo/u1CSFGPiNqwkSdVU\nJBJ8/tTQofDhh8G5zp2DoDr++HC3SZK0B4aVJCk2VFTAK68Ed6g++SR4TPqll8KgQdCyZdjrJEn6\nQYaVJClcFRUwYwYMHw4LF0JiYvCAioEDoXnzsNdJkrRPDCtJUjjKy+HFF4OgWrQoCKpu3YKgatYs\n7HWSJP0ohpUkqUqVbN/BF0PHc+ikMdRdu4zU2ikkXHllEFRHHRX2PEmS9othJUmqGmVl8Nxz7Pjd\nnzj6y9VEEpNZdUZPNvTszqlX5Ia9TpKkqBhWkqTKVVoKU6fCiBGwfDmpZYmsOrsXyzr3Y+chR5Cc\nXBT2QkmSomZYSZIqR2kpPPMMjBwJK1dCSgr87Gd8eMrlFCfn7P6y9PSyEEdKknRgGFaSpAOrpAQm\nTYIHH4TVqyE1Ffr0gX794NBDaVtSSkHBarZuTSY9vYzc3KywF0uSFDXDSpJ0YOzaBRMnwqhRsGYN\n1KoFN94IP/85ZGfv/rLU1BTy8hqHOFSSpAPPsJIkRWfnThg/Hh56CIqKoHbtIKb69oVDDgl7nSRJ\nVcKwkiTtnx07YNw4ePhhWLcO6tSBm28Ogurgg8NeJ0lSlTKsJEk/zrZtMHYsPPoorF8P6ekwYEDw\nsr/MzLDXSZIUCsNKkrRvtm6FJ58MgmrjRqhXDwYPhhtugIyMsNdJkhQqw0qS9MM2b4YxY+Cxx2DT\nJqhfH/Lzg6CqXz/sdZIkxQTDSpL0/TZvhscfD35s3hzclbrjDrjuOoNKkqT/YlhJkr5t06YgpkaP\nhi1bgvdN3X039O4dvJ9KkiR9h2ElSQps3Bi83G/MmOD9VAcfDIMGwbXXQt26Ya+TJCmmGVaSVNOt\nXx88kOLJJ2H7dsjKgltvhV69gs+kkiRJe2VYSVINUlJSSkFBMVu3JtOwdC0/KZxK8vjxwWdSZWfD\nnXdCz55Qq1bYUyVJiiuGlSTVIAUFxWxflszRLz/MEbPGUV6+g+QjD4N77oEePSAtLeyJkiTFJcNK\nkmqKNWto9ND/47B/Pk9iWQk7Mw/jX5deS5v7+kJqatjrJEmKa4aVJFV3q1fDqFEwcSJHbNvF9oOa\nsOziAXx5RncaHFxsVEmSdAAYVpJUXa1cCQ8+CE8/DaWl0KQJSbfcwieNz2DLzto0SC8mNzcr7JWS\nJFULhpUkVTcrVsDIkfDss1BWBk2bwsCB0LUrycnJnBH2PkmSqiHDSpKqi2XLgqCaPBnKy6FZMxg8\nGC69FJL9416SpMrkP2klKd4tWQIjRsDUqVBRAc2bB0F18cWQlBT2OkmSagTDSpLi1eLFMHw4vPAC\nRCLQsmUQVJ07Q2Ji2OskSapRDCtJijcLFwZ3qKZPD4Lq+ONhyBC44AKDSpKkkBhWkhQvPv0Uhg6F\nl14Kjlu3DoKqUydISAh3myRJNZxhJUmx7qOPgqCaOTM4PumkIKjOO8+gkiQpRhhWkhSrPvgAhg2D\nv/89OM7JCYLq7LMNKkmSYoxhJUmxprAwCKpZs4LjU06B/HzIyzOoJEmKUYaVJMWK996DBx6AN98M\njtu1C+5QtW9vUEmSFOMMK0kK27vvBu+hevvt4PiMM4LHprdrF+4uSZK0zwwrSQpDJAKzZwcv+Xvn\nneDcWWcFQXXqqeFukyRJP5phJUlVqGRXCQsfm86hE0eT8fl8UlMTSTj33CCocnLCnidJkvaTYSVJ\nVSESgddfZ8s999Lis08AKD7xfNb17MHJ/3N+yOMkSVK0DCtJqkyRCLz2WvCSv/nzqburguK2F7H0\nssFsOao1yclFYS+UJEkHgGElSZUhEoFXXw0eSvHRR8G5zp35JO9qvmx47u4vS08vC2mgJEk6kAwr\nSTqQKirglVeCoPr00+Ax6ZdcAoMGwXHH0bqklO0Fq9m6NZn09DJyc7PCXixJkg4Aw0qSDoSKCpgx\nA4YPh4ULITERunSBgQOhefPdX5aamkJeXuMQh0qSpMpgWElSNMrL4cUXg/dQLV4cBFW3bkFQNWsW\n9jpJklRFDCtJ2h9lZTBtWnCH6osvICkJuncPgqpp07DXSZKkKmZYSdKPUVYGU6fCiBGwbBkkJ8PV\nV8OAAdCkSdjrJElSSAwrSdoXpaUwZUoQVCtWQEoKXHMN9O8PRxwR9jpJkhQyw0qSfkhpKTz9NDz4\nIKxcGQRV797Qrx809iEUkiQpYFhJ0vcpKYG//S0Iqi+/hNRU6NMHbrkFGjUKe50kSYoxhpUk/add\nu2DixCCo1q6FtDS44Qa4+WbIzg57nSRJilGGlSQB7NwJ48fDQw9BURHUrg19+wY/svwQX0mS9MMM\nK0k12/btMG4cPPIIrFsHdeoEd6f69oWDDw57nSRJihOGlaSaads2GDs2CKoNGyA9PXhk+o03QmZm\n2OskSVKcMawk1RglJaW8/8+llDz+FNsKX6bOri0k1KsHgwcH76PKyAh7oiRJilOGlaSaYfNmVt49\njNbPTyJh80Yi9RqyrMv1HH3frVC/ftjrJElSnDOsJFVvX38No0fD44/TeN0mSutm8v65N7Djqtuh\n/g6ONqokSdIBYFhJqp42bYLHHw+iassWaNiQVb36sbj9IBatXssxdeqTkb4l7JWSJKmaMKwkVS8b\nN8Jf/gJjxgQPqDjoILjnHujdmyNTUllTUEzS2jVkZNQmN9fHqEuSpAPDsJJUPaxfD48+Ck8+GTxC\nPSsLbrsNevUKPpMKSAXy8hpTp85acnIahzpXkiRVL4aVpPhWXBwE1dixsGMHZGfDnXdCz55Qq1bY\n6yRJUg1hWEmKT0VF8NBD8NRTsGsXNGoUvOSvRw9ISwt7nSRJqmEMK0nxZc0aGDUKJkyAkhJo3Bj6\n94erroLU1LDXSZKkGsqwkhQfVq8OgmriRCgthSOOgAEDoHt3SEkJe50kSarhDCtJsW3lShg5Ep55\nJgiqJk1g4EC4/HKDSpIkxQzDSlJsWr48CKrJk6GsDJo2DYKqa1dI9o8uSZIUW/y3E0mxZdkyGDEC\npkyB8nI45hgYNAguvdSgkiRJMct/S5EUG774Igiq556Digpo0QIGD4bOnSEpKex1kiRJP8iwkhSu\nxYth2DCYNg0iETjuuCCoLroIEhPDXidJkrRPDCtJ4Vi4EIYPhxdfDIKqVSsYMgTOP9+gkiRJccew\nklQlSkpKKSgohk++4NgXHyV73hskALRpEwRVx46QkBD2TEmSpP1iWEmqEh9NfJ0m4yeSNX8mAF8d\n25LM/70TOnQwqCRJUtwzrCRVrvnzYdgwWs14FUhkU7Mcll42hK/bHseFHQ8Ne50kSdIBYVhJqhyF\nhTB0KPzznwBsPf4kFnW+m43HnwEJCWTUWx3yQEmSpAPHsJJ0YM2dGwTVm28Gx+3bw+DB1P/JKVTM\nXUfy1mLS08vIzc0Kd6ckSdIBZFhJOjDeeSd4bPrbbwfHZ5wRPJTitNMASAXy8hqHt0+SJKkSGVaS\n9l8kArNnB3eo3n03OHfWWUFQnXJKuNskSZKqkGEl6ceLROCtt4Kgmjs3OHfeeTBoEOTkhLtNkiQp\nBIaVpH0XiQQPoxg2LHg4BQSfPzV4MJx0UrjbJEmSQmRYSdq7SAT+8Y8gqD74IDh3wQVBULVuHe42\nSZKkGGBYSdqzSARefTV4yd9HHwXnOncOXvLXqlW42yRJkmKIYSXpuyoq4OWXgztUn34KCQlw6aVB\nULVsGfY6SZKkmBMTYfXcc88xYsQIjjzySABOP/10brrpJj777DN+85vfkJiYSIsWLfj1r38NwOjR\no5k5cyaJiYncfPPNnHXWWWHOl6qPigp48UUYPhw++wwSE6FLFxg4EJo3D3udJElSzIqJsAK46KKL\nuP3227917t577+WXv/wlrVq1Ij8/n7feeoumTZvy8ssv88wzz/D111/Ts2dPzjzzTBISEkJaLlUD\n5eUwfXoQVIsXB0HVrVsQVM2ahb1OkiQp5sVMWP230tJSVq9eTav/ex/Hueeey5w5cyguLubMM88k\nKSmJzMxMGjduzBdffMGxxx4b8mIpDpWVwQsvBEG1ZAkkJcGVV8KAAdC0adjrJEmS4kbMhNXcuXO5\n4YYbKCsr44477iAzM5MGDRrs/vnMzEyKi4tp2LAhmZmZ3zq/bt06w0r6McrKYOpUGDECli2D5GS4\n+uogqJo0CXudJElS3KnysHr22WeZPHkyCQkJRCIREhIS6Ny5M/379+ess87igw8+4LbbbuOvf/0r\nkUhkr3+/ffkaSVBSUsrc2atJnzmTo198jHob15CQkgK9ekG/fnDEEWFPlCRJiltVHlZXXHEFV1xx\nxR5//qSTTuKrr76iYcOGbNq0aff5oqIisrOzycrKYunSpd86n5WVtU+/d+E3H2iqGq1GXgdlZWx5\n/Hla/P0l6m1aS0VSMgtOO5vEAddSesghUFwc/KhBauR1oO/wOhB4HejfvBYUjZh4KeDo0aNp1KgR\nnTt3ZvHixWRmZpKSksLRRx/NvHnzOPnkk3n11Vfp1asXRx11FE888QQDBgxgw4YNFBcXc8wxx+zT\n75OTk1PJ34liXWFhYc26DkpK4G9/gwcfZOeyVVQk12LVBTewvHM/yg9J4MILssNeGIoadx3oe3kd\nCLwO9G9eC4Lo4jomwuqSSy7htttuY9KkSZSXl/OHP/wBgLvuuotf/epXRCIRTjzxRNq1awdA9+7d\n6dmzJwkJCfz2t78Nc7oUm3btgokT4cEHYe1aqFWLokt78Nk5d1DSMIipjPTVIY+UJEmqPmIirLKz\nsxk3btx3zjdr1owJEyZ853zPnj3p2bNnVUyT4suOHTB+PDz8MBQVQe3a8POfQ9++NGqQwb8KiqnY\nWkR6ehm5ufv2ElpJkiTtXUyElaQobd8O48bBI4/AunVQpw7ccgv07QsHHQRAKpCX1zjcnZIkSdWU\nYSXFs23bYOzYIKg2bID09OBDfW+4Af7jYwkkSZJUuQwrKR5t2QJPPgmPPgpffQX168OQIXD99ZCR\nEfY6SZKkGsewkuLJ5s3w17/CY4/B118HQZWfH9yhql8/7HWSJEk1lmElxYOvv4bRo+Hxx4O4ysiA\nO+6APn2gXr2w10mSJNV4hpUUy776Koipv/41ePlfw4Zw113ws58F76eSJElSTDCspFi0cWPw/qkn\nnggeUHHQQXDPPdC7N9StG/Y6SZIk/RfDSool69cHQfXkk8Ej1LOy4LbboFev4DOpJEmSFJMMKykW\nFBcHj0wfOxZ27oTsbLjzTujZE2rVCnudJEmS9sKwksJUVAQPPQRPPQW7dkGjRtCvH/ToAWlpYa+T\nJEnSPjKspDCsWQOjRsGECVBSAo0bw4ABcOWVkJoa9jpJkiT9SIaVVAVKSkopKCimdPk6jp05msPf\nmk5CaSkccQQMHAhXXAEpKWHPlCRJ0n4yrKQqMH/aBzSa+AyHvf0MieWlbGl0GPV/eRt07WpQSZIk\nVQOGlVSZli+HkSNpM/4ZEsor2J7VlKWXDmJ9XnsuuLhx2OskSZJ0gBhWUmVYtgxGjIApU6C8nJJG\nR7K48x2sPfVSSEoio8HqsBdKkiTpADKspAPpiy9g+HB4/nmoqIAWLWDwYGp37MTO9zeQvHU96ell\n5OZmhb1UkiRJB5BhJR0IixYFQTVtGkQicNxxMHgwXHQRJCaSCuTl+dI/SZKk6sqwkqKxcGEQVC++\nGATVCSfAkCHQqRMkJoa9TpIkSVXEsJL2xyefwLBh8NJLwfGJJwZB1aEDJCSEu02SJElVzrCSfowP\nP4ShQ+HVV4Pjtm2DoDr3XINKkiSpBjOspH0xf35wh+of/wiOc3IgPx/OOsugkiRJkmEl/aDCQnjg\nAXj99eA4NzcIqtNPN6gkSZK0m2ElfZ+5c4Ogeuut4Lh9++Apf+3bG1SSJEn6DsNK+k9z5gQv+Zs9\nOzg+44zgPVSnnRbuLkmSJMU0w0qKRIKQGjoU3n03OHf22cEdqlNOCXWaJEmS4oNhpZorEoE33wyC\n6r33gnPnnRcE1cknh7tNkiRJccWwUs0TicA//xm85K+wMDjXsWPwkr8TTwx3myRJkuKSYaUaoaSk\nlIJ3i1g/6Q2a3nIbDf/1GQkAF14Y3KE64YSwJ0qSJCmOGVaq/iIRFo98mpYTxlF76QKSk5NYe/o5\nNLr/bjj++LDXSZIkqRowrFR9VVTAyy/DsGEcM/9jIiTxeatz2dDr1+w8qiGNjs8Oe6EkSZKqCcNK\n1U95OcyYAcOHw2efQWIiG8+8gM8uuJsF2xM45vBjyEhfHfZKSZIkVSOGlaqP8nKYPj14KMXnn0Ni\nIlxxBQwYwMFHHElKQTFJ85eSkVGb3NyssNdKkiSpGjGsFP/KyuD554M7VEuXQlISXHklDBwIRx0F\nQCqQl9eYOnXWkpPTONS5kiRJqn4MK8Wv0lKYOhVGjIDlyyE5GXr0gP79oUmTsNdJkiSpBjGsFH9K\nS2HyZBg5ElasgJQU6NUrCKrD/397dxsU5Xm2cfxYFjERBFlhSeOTNhrbxtFHS+lIDcEKEzS2SSTK\nAqKmWuNLGk3FvJT6llpnjCZtjC0k1kKrrZoQcXRsk6glY4h9EDAmk8ZYNUo6RTTA4gLBFcF4PR92\nui3VNCa7sML+f5/ci2v3Pu/Zc+7x2Ot++Z9AVwcAAIAgRLBCz9HRIRUXewLV6dOeQDVrlvTww9LN\nNwe6OgAAAAQxghWuf+3t0rZtUn6+dOaM1LevNHu2J1DddFOgqwMAAAAIVriOtbX9K1B99JF0ww3S\n3LnSQw9JcTyDCgAAANcPghWuPxcuSFu2SAUFUn29dOONnjA1f74UGxvo6gAAAIArEKxw/XC7pc2b\npRdekJxOKTxcWrBAmjdPGjgw0NUBAAAAn4pghcA7f17atMkTqM6dkyIiPM+gmjtXio4OdHUAAADA\nZyJYIXA+/lj63e+kX/9acrmkyEhp8WLpwQelAQMCXR0AAABwzQhW6H4tLVJRkbRxo9Tc7AlUjz3m\nCVSRkYGuDgAAAPjcCFbocu3tHaqsrFdbnVu37f+DBpcWy/Lxx55Vqbw8z7Oo+vcPdJkAAADAF0aw\nQpc7XHpCA19+RV8uLVLohY/ljopU+NKl0ve/77meCgAAAOjhCFboOufOSRs2aGRBoaxtbWrvH6MT\nmYt0dvzdmnD/4EBXBwAAAPgNwQr+53RKGzZ47vTndsuER+t4ep5Op8zQ5b43asCA2kBXCAAAAPgV\nwQr+U1/vuWX65s1SW5sUFyctWaKwDIda3m1RSGuLIiPOKTHRHuhKAQAAAL8iWMF3dXVSQYH0hz9I\nFy9KX/qStHChNHWq1LevwiQlJ3NzCgAAAPReBCt8cWfPSvn50tatUnu7NGiQ9MgjUlaWFBYW6OoA\nAACAbkOwwudXW+sJVNu2SR0d0pe/7AlUDofUp0+gqwMAAAC6HcEK166mRvrlL6WXX/YEqltvlX70\nI2nyZAIVAAAAghrBCp/t73/3BKqSEunSJWnIEE+guv9+KZQWAgAAAPhfMT7dhx9K69dLO3ZIn3wi\nDR0q5eZK990nWa2Brg4AAAC4bhCscKWTJz2BaudO6fJl6etf9wSq732PQAUAAABcBcEK/3LihLRu\nnbR7t2SMNGyYJ1B997tSSEigqwMAAACuWwQrSH/7m/Tcc9Kf/uQJVCNGSIsXS+PHE6gAAACAa0Cw\nCmbvv+9ZoXr1Vc/rUaM8gequuySLJbC1AQAAAD0IwSoY/fWvnkC1d6/ndXy8J1ClphKoAAAAgC+A\nYBUE2ts7VFlZr5B3/6ahf/q17H/9P1kk6Vvfkh59VBo7lkAFAAAA+IBgFQSqDtToK0+tkv0dzwpV\n4/CRilm9TEpKIlABAAAAfkCwCgJtzouKPl6hc7ffoepJi/Xx/96miXfGBbosAAAAoNcgWAWBvjdH\n6o2Co97VqQERtQGuCAAAAOhduJd2EEhMtGtA9BmFhtZpwIBaJSbaA10SAAAA0KuwYhUEwsL6KDl5\nUKDLAAAAAHotVqwAAAAAwEcEKwAAAADwEcEKAAAAAHxEsAIAAAAAHxGsAAAAAMBHBCsAAAAA8BHB\nCgAAAAB8RLACAAAAAB8RrAAAAADARwQrAAAAAPARwQoAAAAAfESwAgAAAAAfEawAAAAAwEcEKwAA\nAADwEcEKAAAAAHxEsAIAAAAAHwUkWFVVVemOO+5QWVmZd+zYsWPKzs5WTk6OVq5c6R0vLCyUw+FQ\nVlaWd35ra6vmzZunnJwczZkzRy0tLd2+DwAAAADwT90erGpqarRp0yYlJCR0Gl+9erWWL1+ubdu2\nqaWlRQcOHNDp06f12muv6aWXXtILL7ygNWvWyBijTZs2KTExUdu2bVNaWpo2btzY3bsBAAAAAF7d\nHqzsdrsKCgoUERHhHevo6FBtba2GDx8uSUpNTVV5ebkqKys1duxYWa1W2Ww2DRo0SB988IEqKiqU\nlpYmSUpJSVF5eXl37wYAAAAAeIV29wb79u17xZjL5VJUVJT3tc1mU319vaKjo2Wz2bzjAwcOVEND\ng5xOp6Kjo71jTqez6wsHAAAAgE/RpcFq+/btKikpkcVikTFGFotFCxcuVFJS0hf6vMuXL18xZoy5\n5vcfPnz4C20XvQt9AIk+gAd9AIk+wL/QC/BFlwYrh8Mhh8PxmfNsNptcLpf3dV1dneLi4mS321Vd\nXX3VcafTqYiICNXV1clut3/mNv7zmi4AAAAA8JeA3m79n6tNoaGhGjJkiN5++21J0r59+5ScnKzE\nxESVlZXp0qVLqqurU319vYYOHaqkpCS99tprneYCAAAAQKBYzOc5l84PysrKVFhYqA8//FA2m02x\nsbEqKirSqVOntGLFChljNGrUKP34xz+WJG3dulW7d++WxWJRbm6uEhMT5Xa79fjjj6upqUmRkZF6\n5plnOt0MAwAAAAC6U7cHKwAAAADobQJ6KiAAAAAA9AYEKwAAAADwEcEKAAAAAHzUK4NVUVGR0tPT\n5XA4dOTIEUnSsWPHlJ2drZycHK1cudI7t7CwUA6HQ1lZWSorKwtUyegiTqdTo0eP1qFDhyTRB8Hm\nk08+UV5ennJycpSdne298yh9gKeeekrZ2dmaOnWq3nvvvUCXg27w9NNPKzs7Ww6HQ3/+85/10Ucf\nacaMGZo+fbpyc3PV0dEhSdq9e7cyMjKUlZWlkpKSAFcNf7t48aLS0tK0a9cueiCI7d69W5MmTdKU\nKVNUVlbmv14wvcwHH3xgpkyZYi5fvmyOHj1qfvWrXxljjJkxY4Y5cuSIMcaYxYsXmzfffNPU1NSY\nyeJqkFgAAAkISURBVJMnm0uXLpnGxkZz9913m8uXLweyfPjZE088YSZPnmyqqqqMMfRBsNmxY4dZ\nuXKlMcZzbMjIyDDG0AfBrqqqysybN88YY8zJkydNVlZWgCtCV6uoqDBz5841xhjjcrnMuHHjTF5e\nntmzZ48xxphnn33WvPjii8btdpsJEyaY1tZW09bWZu655x7T3NwcyNLhZ88++6zJyMgwO3fuNHl5\neWbv3r3ecXogOLhcLjN+/HjjdrtNQ0ODWb58ud96odetWO3fv18TJ06UxWLRsGHDtGDBAnV0dKi2\ntlbDhw+XJKWmpqq8vFyVlZUaO3asrFarbDabBg0apJMnTwZ4D+AvFRUVioiI0Ne+9jVJog+C0KRJ\nk5SXlyfJ8yDy5uZmdXR06PTp0/RBEDt48KDuuusuSdJtt92mlpYWnT9/PsBVoSuNHj1a69evlyRF\nRkbK7Xbr0KFDSk1NlSSlpKSovLxc7777rkaOHKnw8HD17dtX3/zmN70r3ej5qqurVV1dre985zsy\nxujQoUNKSUmRRA8Ek/LyciUlJenGG29UTEyMfvazn6mqqsovvdDrglVtba3OnDmjBx98ULNmzdKx\nY8fkcrkUFRXlnWOz2VRfX6/GxkbZbLZO4w0NDYEoG37W0dGhgoIC5ebmesfog+BjtVoVFhYmSdq8\nebPuvfdeuVwuDRgwwDuHPgg+Tqez03cdHR0tp9MZwIrQ1SwWi2644QZJUklJicaNG6cLFy6oT58+\nkqSBAwdyHAgCa9eu9f7YJokeCFK1tbW6cOGCHnroIU2fPl0HDx5UW1ubX3ohtEsr72Lbt29XSUmJ\nLBaLJMkYo8bGRiUnJ6uwsFCHDx/WsmXL9Pzzz8tcw+O6rmUOrj//3gfGGFksFt15553KzMy84sHR\n9EHvdbU+WLhwoZKSkrR161YdPXpUGzZsUGNj4zV9Hn0QPPiug0dpaal27NihoqIijR8/3jv+aT1A\nb/Qeu3btUnx8vAYNGnTVv9MDwcMYo6amJhUUFKi2tlYPPPBAp+/Zl17o0cHK4XDI4XB0GsvPz9eQ\nIUMkSQkJCTpz5owGDhyopqYm75y6ujrFxcXJbrerurq607jdbu+e4uE3V+uDqVOn6i9/+Yu2bNmi\nf/zjH3rvvff085//XM3Nzd459EHvcrU+kDyB64033tDzzz/vPc3P5XJ5/04fBB+73d5phaq+vl6x\nsbEBrAjd4cCBA9q4caOKiooUERGh8PBwtbe3KywsrNNx4N9/ka6rq1N8fHwAq4a/lJWV6fTp09q/\nf7/q6urUp08f9evXjx4IQjExMYqPj1dISIhuueUWhYeHKzQ01C+90OtOBUxOTtaBAwckSadOndJN\nN90kq9WqIUOGeM+L3Ldvn5KTk5WYmKiysjJdunRJdXV1qq+v19ChQwNZPvzkxRdf1EsvvaTi4mKN\nGzdOTz75pG6//XYNHjyYPggiNTU1Ki4uVn5+vneJPzQ0lONBkEtKStLevXslSe+//77i4uLUr1+/\nAFeFrtTa2qpnnnlGGzZsUP/+/SVJY8aM8fbB3r17lZycrJEjR+rIkSNqbW3V+fPn9c477yghISGQ\npcNP1q1bp+3bt6u4uFgZGRl6+OGHNWbMGO3Zs0cSPRBMkpKSVFlZKWOMXC6X3G6333qhR69YXc2o\nUaP05ptvKjs7W5L05JNPSpKWLFmiFStWyBijUaNGacyYMZKkzMxMTZs2TRaLpdNtl9E70QfBpaSk\nRM3NzZozZ4739MDf/va39EGQi4+P1/Dhw5WdnS2r1aoVK1YEuiR0sVdffVVNTU1atGiR91iwdu1a\nLV26VMXFxbr55pt1//33y2q16tFHH9UPfvADhYSEaOHChVecUo7e45FHHtETTzyhl19+mR4IInFx\ncZowYYIyMzNlsVi0YsUKjRgxwi+9YDGcPAoAAAAAPul1pwICAAAAQHcjWAEAAACAjwhWAAAAAOAj\nghUAAAAA+IhgBQAAAAA+IlgBAAAAgI8IVgCAHuPIkSNKS0vT+fPnvWOrVq3S008/3Wnejh07tGDB\ngivev3z5cm3cuPFTP3/nzp16/PHH/VcwACBoEKwAAD3GiBEjlJ6erjVr1kiS3nrrLR06dEiLFi3q\nNG/ixIl666231NTU5B1rb2/Xvn37NHny5P+6DYvF4v/CAQC9HsEKANCjzJ8/XydOnNDrr7+ulStX\nau3atQoLC+s0p1+/fkpLS9Mrr7ziHSstLVV8fLxiYmLU2Nio2bNna+bMmZoyZYp27dp1xXZSU1NV\nU1MjSaqqqlJOTo4k6ezZs5o/f75mzpypzMxMHTx4sAv3FgDQU4QGugAAAD4Pq9WqNWvWKD09XTNn\nztSwYcOuOm/KlClatWqVpk2bJknatWuXMjMzJUn19fWaPn26UlJS1NDQoHvvvVfp6en/dbv/XMn6\n6U9/qtmzZ2v06NFyOp3KzMxUaWmpQkL4rRIAghnBCgDQ4xw/fly33HKL3n777U+d841vfEMXL17U\nqVOnFBUVpePHjyslJUWSZLfbVVhYqN/85jeyWq1qbm6+5m1XVlbK7XZ7X4eFhamxsVGxsbFffIcA\nAD0ewQoA0KM0NDRo3bp12rJli9asWaPf//73euCBB646NyMjQzt37lRMTIzuueceWa1WSdJzzz2n\nW2+9Vb/4xS/kdruVkJBwxXv//Vqrjo4O77/DwsKUn5+vqKgoP+8ZAKAn47wFAECPsmzZMv3whz9U\nbGysli5dqk2bNnmvhfpP9913n15//XXt2bNHGRkZ3nGn06mhQ4dKkv74xz8qJCRE7e3tnd4bERGh\ns2fPSpIqKiq84wkJCd5rt86dO6fVq1f7df8AAD0TwQoA0GMUFxfLYrFo0qRJkiSbzabc3Fz95Cc/\nuep8m82mr371q7JarRo8eLB3fPr06Vq/fr1mz56t/v3769vf/rYee+yxTqtUs2bN0pIlSzRnzhz1\n69fPO7506VKVlpZq2rRpmj9/vsaMGdNFewsA6EksxhgT6CIAAAAAoCdjxQoAAAAAfESwAgAAAAAf\nEawAAAAAwEcEKwAAAADwEcEKAAAAAHxEsAIAAAAAHxGsAAAAAMBH/w+oowp7Mio6FgAAAABJRU5E\nrkJggg==\n",
    203       "text/plain": [
    204        "<matplotlib.figure.Figure at 0x7ffaec04d0d0>"
    205       ]
    206      },
    207      "metadata": {},
    208      "output_type": "display_data"
    209     }
    210    ],
    211    "source": [
    212     "fahrenheit = [-868, -778, -688, -598, -508, -418, -328, -238, -144, -58, 32, 122, 212, 302, 392, 482, \n",
    213     "              572, 662, 752, 842, 932]\n",
    214     "celsius    = [-500, -450, -400, -350, -300, -250, -200, -150, -100, -50, 0, 50, 100, 150, 200, 250, \n",
    215     "              300, 350, 400, 450, 500]\n",
    216     "\n",
    217     "## Your code goes here\n",
    218     "linreg(celsius, fahrenheit)"
    219    ]
    220   },
    221   {
    222    "cell_type": "markdown",
    223    "metadata": {},
    224    "source": [
    225     "<center>*We can clearly see from the table (and the graph) that    $f = 1.8c + 32$ *</center>"
    226    ]
    227   },
    228   {
    229    "cell_type": "markdown",
    230    "metadata": {},
    231    "source": [
    232     "----"
    233    ]
    234   },
    235   {
    236    "cell_type": "markdown",
    237    "metadata": {},
    238    "source": [
    239     "# Exercise 2 : Confidence Intervals\n",
    240     "## a. Visualizing Confidence Intervals \n",
    241     "Using the lecture series and the seaborn library, plot the regression line between the parameters and the $95\\%$ confidence interval."
    242    ]
    243   },
    244   {
    245    "cell_type": "code",
    246    "execution_count": 4,
    247    "metadata": {
    248     "scrolled": false
    249    },
    250    "outputs": [
    251     {
    252      "data": {
    253       "image/png": 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d4wTZA2WvT6rKLUXTGB4LYXg0hBsTi9CN9QNUJVHA/YdalpfFtaGr1QdhB1tm7zSGIiIi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\n",
    254       "text/plain": [
    255        "<matplotlib.figure.Figure at 0x7ffac4f0ecd0>"
    256       ]
    257      },
    258      "metadata": {},
    259      "output_type": "display_data"
    260     }
    261    ],
    262    "source": [
    263     "start = '2014-01-01'\n",
    264     "end = '2015-01-01'\n",
    265     "asset = get_pricing('KO', fields='price', start_date=start, end_date=end)\n",
    266     "benchmark = get_pricing('PEP', fields='price', start_date=start, end_date=end)\n",
    267     "\n",
    268     "returns1 = asset.pct_change()[1:]\n",
    269     "returns2 = benchmark.pct_change()[1:]\n",
    270     "\n",
    271     "## Your code goes here\n",
    272     "seaborn.regplot(returns1.values, returns2.values, ci=95);"
    273    ]
    274   },
    275   {
    276    "cell_type": "markdown",
    277    "metadata": {},
    278    "source": [
    279     "## b. Calculating Confidence Levels of Parameters. \n",
    280     "Let's directly calculate the $95\\%$ confidence intervals of our parameters. The formula for a given parameter is:\n",
    281     "\n",
    282     "$$ CI = \\left(\\beta - z \\cdot \\frac{s}{\\sqrt{n}}, \\beta + z \\cdot \\frac{s}{\\sqrt{n}}\\right) $$\n",
    283     "\n",
    284     "Where,  $\\beta$ is the coefficient, $z$ is the critical value*(t-statistic required to obtain a probability less than the alpha significance level)*, and $SE_{i,i}$ is the Standard Error Matrix. "
    285    ]
    286   },
    287   {
    288    "cell_type": "code",
    289    "execution_count": 5,
    290    "metadata": {},
    291    "outputs": [
    292     {
    293      "name": "stdout",
    294      "output_type": "stream",
    295      "text": [
    296       "0.343562222943 0.530358115519\n"
    297      ]
    298     }
    299    ],
    300    "source": [
    301     "start = '2014-01-01'\n",
    302     "end = '2015-01-01'\n",
    303     "asset = get_pricing('KO', fields='price', start_date=start, end_date=end)\n",
    304     "benchmark = get_pricing('PEP', fields='price', start_date=start, end_date=end)\n",
    305     "\n",
    306     "X = asset.pct_change()[1:]\n",
    307     "Y = benchmark.pct_change()[1:]\n",
    308     "\n",
    309     "result = sm.OLS(Y,X).fit()\n",
    310     "\n",
    311     "# Convert X to Matrix (adding columns of one)\n",
    312     "X = np.vstack((X, np.ones( X.size ) ))\n",
    313     "X = np.matrix( X )\n",
    314     "\n",
    315     "# Matrix Multiplication and inverse calculation\n",
    316     "C = np.linalg.inv( X * X.T )\n",
    317     "C *= result.mse_resid\n",
    318     "SE = np.sqrt(C) # Calucaltion of Standard Error. \n",
    319     "\n",
    320     "# Critical Values of the t-statistic\n",
    321     "N = result.nobs\n",
    322     "P = result.df_model\n",
    323     "dof = N - P - 1\n",
    324     "z = scipy.stats.t(dof).ppf(0.975)\n",
    325     "\n",
    326     "i = 0\n",
    327     "## Your code goes here\n",
    328     "\n",
    329     "# Fetch values of Beta and parameters of SE from the matrix\n",
    330     "beta = result.params[i]\n",
    331     "c = SE[i,i]\n",
    332     "\n",
    333     "print beta - z * c, beta + z * c"
    334    ]
    335   },
    336   {
    337    "cell_type": "markdown",
    338    "metadata": {},
    339    "source": [
    340     "----"
    341    ]
    342   },
    343   {
    344    "cell_type": "markdown",
    345    "metadata": {},
    346    "source": [
    347     "# Exercise 3 : $R^2$ Value\n",
    348     "\n",
    349     "$R^2$ is the measure of how closely your data points are to the regression line, and is defined as $$ R^2 = 1 - \\frac{\\Sigma((y_{predicted} - (y_{actual}))^2)}{\\Sigma( y_{predicited} - \\frac{\\Sigma y_{actual}}{len(y_{actual}})^2} $$ \n",
    350     "Given the information from exercise 1, calculate the value of $R^2$ manually.\n",
    351     "You can start by expressing f as a function of c from the data obtained from Exercise 1 (these are the predicted values of y). "
    352    ]
    353   },
    354   {
    355    "cell_type": "code",
    356    "execution_count": 6,
    357    "metadata": {},
    358    "outputs": [],
    359    "source": [
    360     "# Creat an empty numpy array (float values). \n",
    361     "# Find the predicted value of f for every c in celsius (given by f = 32 + 1.8c)\n",
    362     "fpred = np.array([])\n",
    363     "f = [32 + 1.8*a for a in celsius] ## Your code goes here (fill in the values of Beta, and X1)\n",
    364     "ypredicted = np.append(f, fpred)"
    365    ]
    366   },
    367   {
    368    "cell_type": "markdown",
    369    "metadata": {},
    370    "source": [
    371     "Using the values of $y_{predicted}$  and  $y_{actual}$, calculate the squared element by element difference of the two lists, and sum them."
    372    ]
    373   },
    374   {
    375    "cell_type": "code",
    376    "execution_count": 7,
    377    "metadata": {
    378     "collapsed": true
    379    },
    380    "outputs": [],
    381    "source": [
    382     "# Calucate the difference between the predicted values of y and the actual values of y, \n",
    383     "# Find the square of the difference\n",
    384     "# Sum the Squares\n",
    385     "\n",
    386     "ypred_yact = [a - b for a, b in zip(ypredicted, fahrenheit)] ## your code goes here (a - b)\n",
    387     "diff1squared = [a**2 for a in ypred_yact] ## Your code goes here (a**2)\n",
    388     "sumsquares1 = sum(diff1squared) ## Your code goes here "
    389    ]
    390   },
    391   {
    392    "cell_type": "markdown",
    393    "metadata": {},
    394    "source": [
    395     "Using the values of $y_{predicted}$ and mean, calculate the mean of the predicted values, along with the difference between $y_{predicted} - mean$. Square the values in the list obtained from the difference and sum them. "
    396    ]
    397   },
    398   {
    399    "cell_type": "code",
    400    "execution_count": 8,
    401    "metadata": {
    402     "collapsed": true
    403    },
    404    "outputs": [],
    405    "source": [
    406     "# Calucate the difference between the predicted values of y and mean of y. \n",
    407     "# Find the square of the difference\n",
    408     "# Sum the Squares\n",
    409     "\n",
    410     "mean = sum(fahrenheit)/len(fahrenheit) ## Your code goes here\n",
    411     "ypred_mean = [x - mean for x in ypredicted] ## Your code goes here (x-mean)\n",
    412     "ypred_meansquared = [a**2 for a in ypred_mean] ## Your code goes here (a**2)\n",
    413     "sumsquares2 = sum(ypred_meansquared) ## Your code goes here\n"
    414    ]
    415   },
    416   {
    417    "cell_type": "markdown",
    418    "metadata": {},
    419    "source": [
    420     "We can now calculate the R-Squared by subtracting one to the ratio of the two sums. "
    421    ]
    422   },
    423   {
    424    "cell_type": "code",
    425    "execution_count": 9,
    426    "metadata": {},
    427    "outputs": [
    428     {
    429      "name": "stdout",
    430      "output_type": "stream",
    431      "text": [
    432       "R-squared =  0.999997434664\n"
    433      ]
    434     }
    435    ],
    436    "source": [
    437     "## Your code goes here\n",
    438     "r = 1 - sumsquares1/sumsquares2\n",
    439     "\n",
    440     "print 'R-squared = ', r"
    441    ]
    442   },
    443   {
    444    "cell_type": "markdown",
    445    "metadata": {},
    446    "source": [
    447     "----"
    448    ]
    449   },
    450   {
    451    "cell_type": "markdown",
    452    "metadata": {},
    453    "source": [
    454     "# Exercise 4 : Residuals\n",
    455     "**Defintion : In statistics, the residuals are differences between the predicted values and the actual values**: \n",
    456     "\n",
    457     "$$e = y - ŷ$$\n",
    458     "\n",
    459     "## a. Residual Analysis I\n",
    460     "- Model the data given bellow as a linear regression. \n",
    461     "- Calculate and plot the residual of the data sets *(remember to use the coefficient and the value of x1 to find the predicted values of y)*\n",
    462     "- Print the sum of the residuals. \n",
    463     "- Discuss the choice of regression model. "
    464    ]
    465   },
    466   {
    467    "cell_type": "code",
    468    "execution_count": 10,
    469    "metadata": {
    470     "collapsed": true
    471    },
    472    "outputs": [],
    473    "source": [
    474     "asset1 = get_pricing('SPY', fields='price', start_date='2005-01-01', end_date='2010-01-01')\n",
    475     "asset2 = get_pricing('GS', fields='price', start_date='2005-01-01', end_date='2010-01-01')\n",
    476     "\n",
    477     "returns1 = asset1.pct_change()[1:]\n",
    478     "returns2 = asset2.pct_change()[1:]\n",
    479     "\n",
    480     "## Your code goes here\n",
    481     "results = smr.linear_model.OLS(returns1.values, sm.add_constant(returns2.values)).fit()"
    482    ]
    483   },
    484   {
    485    "cell_type": "markdown",
    486    "metadata": {},
    487    "source": [
    488     "Run the Breush-Pagan test to check for heteroskedasticity in the residuals. Note that the residuals of the model should have constant variance, presence of heteroskedasticity would indicate our choice of model is not optimal. "
    489    ]
    490   },
    491   {
    492    "cell_type": "code",
    493    "execution_count": 11,
    494    "metadata": {},
    495    "outputs": [
    496     {
    497      "name": "stdout",
    498      "output_type": "stream",
    499      "text": [
    500       "p-value for f-statistic of the breush-pagan test: 0.664407993179\n",
    501       "====\n",
    502       "Since the p-value obtained is greater than alpha (0.05), we can't reject the null hypothesis of the breush-pagan test, and state that there is no presence of heteroskedasticity\n"
    503      ]
    504     }
    505    ],
    506    "source": [
    507     "lm, p_lm, fv, p_fv = het_breushpagan(results.resid, results.model.exog)\n",
    508     "print 'p-value for f-statistic of the breush-pagan test:', p_fv\n",
    509     "print '===='  \n",
    510     "print \"Since the p-value obtained is greater than alpha (0.05), \\\n",
    511     "we can't reject the null hypothesis of the breush-pagan test, and state that there is \\\n",
    512     "no presence of heteroskedasticity\""
    513    ]
    514   },
    515   {
    516    "cell_type": "code",
    517    "execution_count": 12,
    518    "metadata": {},
    519    "outputs": [
    520     {
    521      "data": {
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06tVL8+fP15w5c5SXl6fS0lKFh4frr3/9q9q2bau2bdvqgQce0JgxY9S0aVMNGjRIt9xy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\n/7ASqMDCvEQA9VmFYWnbtm0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XX7xQaWneQ+4OV+k78R82V93vnVADoKEKeFj64osvNHTo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\n",
    523       "text/plain": [
    524        "<matplotlib.figure.Figure at 0x7ffae47068d0>"
    525       ]
    526      },
    527      "metadata": {},
    528      "output_type": "display_data"
    529     }
    530    ],
    531    "source": [
    532     "# Predicted values of asset1\n",
    533     "y = results.params[0] + results.params[1]*returns1.values\n",
    534     "\n",
    535     "plt.scatter(y, results.resid)\n",
    536     "plt.title('Scatter plot of Residuals to predicted model')\n",
    537     "plt.xlabel('Predicted Model')\n",
    538     "plt.ylabel('Residuals');"
    539    ]
    540   },
    541   {
    542    "cell_type": "markdown",
    543    "metadata": {},
    544    "source": [
    545     "Here we can clearly see the plot of the residuals obeys a random pattern, which would indicate that the choice of model was good. This is further accentuated by the near 0 value of the sum of residuals. "
    546    ]
    547   },
    548   {
    549    "cell_type": "markdown",
    550    "metadata": {},
    551    "source": [
    552     "## b. Residual Analysis II\n",
    553     "- Run the linear regression function for x and y\n",
    554     "- Find and plot the residual of the two data points. \n",
    555     "- Discuss the choice in model. "
    556    ]
    557   },
    558   {
    559    "cell_type": "code",
    560    "execution_count": 13,
    561    "metadata": {},
    562    "outputs": [],
    563    "source": [
    564     "p1 = get_pricing('SPY', start_date = '2005-01-01', \n",
    565     "                 end_date = '2010-01-01', \n",
    566     "                 fields = 'price').pct_change()[1:]\n",
    567     "p2 = get_pricing('XLF', start_date = '2005-01-01', \n",
    568     "                 end_date = '2010-01-01', \n",
    569     "                 fields = 'price').pct_change()[1:]\n",
    570     "\n",
    571     "## Your code goes here\n",
    572     "results2 = smr.linear_model.OLS(p1, sm.add_constant(p2)).fit()\n",
    573     "\n",
    574     "y = results2.params[0] + results2.params[1]*p1"
    575    ]
    576   },
    577   {
    578    "cell_type": "code",
    579    "execution_count": 14,
    580    "metadata": {},
    581    "outputs": [
    582     {
    583      "name": "stdout",
    584      "output_type": "stream",
    585      "text": [
    586       "p-value for f-statistic of the breush-pagan test: 5.66764037947e-08\n",
    587       "====\n",
    588       "Since the p-value obtained is less than alpha (0.05), we reject the null hypothesis of the breush-pagan test, and state that there is presence of heteroskedasticity\n"
    589      ]
    590     },
    591     {
    592      "data": {
    593       "image/png": 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sWMCvf/1r1qxZw6hRo/jLX/7CzTffzNtvv81//dd/cc011/CnP/2Jp556iieffJK3337b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\nNC1atMjl/vLycqWmpmrp0qVatmyZli5dqrNnzzruf/nllzVo0CBPNxs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6T5IWL16siRMn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\nRU5ErkJggg==\n",
    594       "text/plain": [
    595        "<matplotlib.figure.Figure at 0x7ffae46f3590>"
    596       ]
    597      },
    598      "metadata": {},
    599      "output_type": "display_data"
    600     }
    601    ],
    602    "source": [
    603     "res = results2.resid\n",
    604     "\n",
    605     "plt.scatter(y, res)\n",
    606     "plt.title('Scatter plot of Residuals to predicted model')\n",
    607     "plt.xlabel('Predicted Model')\n",
    608     "plt.ylabel('Residuals')\n",
    609     "\n",
    610     "lm, p_lm, fv, p_fv = het_breushpagan(results2.resid, results2.model.exog)\n",
    611     "print 'p-value for f-statistic of the breush-pagan test:', p_fv\n",
    612     "print '===='  \n",
    613     "print \"Since the p-value obtained is less than alpha (0.05), \\\n",
    614     "we reject the null hypothesis of the breush-pagan test, and state that there is \\\n",
    615     "presence of heteroskedasticity\""
    616    ]
    617   },
    618   {
    619    "cell_type": "markdown",
    620    "metadata": {},
    621    "source": [
    622     "Here, we can clearly see that the choice of model was not adapt for our data as the plot of the residuals gives us an exponential looking function (not random) and the sum of the residuals is much greater than 0. "
    623    ]
    624   },
    625   {
    626    "cell_type": "markdown",
    627    "metadata": {},
    628    "source": [
    629     "While checking for residual is a good way of checking the accuracy of our model choice, we must also check fot heteroscedasticity (checking if there are sub-populations that have different variabilities from others).  \n",
    630     "An assumption of the linear regression model is that there is no heteroscedasticity, OLS estimators are no longer the Best Linear Unbiased Estimators if this assumption is broken.  \n",
    631     "Read more about heteroscedasticity here https://en.wikipedia.org/wiki/Heteroscedasticity#Consequences"
    632    ]
    633   },
    634   {
    635    "cell_type": "markdown",
    636    "metadata": {},
    637    "source": [
    638     "---"
    639    ]
    640   },
    641   {
    642    "cell_type": "markdown",
    643    "metadata": {},
    644    "source": [
    645     "Congratulations on completing the Linear Regression exercise!\n",
    646     "\n",
    647     "As you learn more about writing trading algorithms and the Quantopian platform, be sure to check out the [Quantopian Daily Contest](https://www.quantopian.com/contest), in which you can compete for a cash prize every day.\n",
    648     "\n",
    649     "Start by going through the [Writing a Contest Algorithm](https://www.quantopian.com/tutorials/contest) Tutorial."
    650    ]
    651   },
    652   {
    653    "cell_type": "markdown",
    654    "metadata": {},
    655    "source": [
    656     "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company.  In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*"
    657    ]
    658   }
    659  ],
    660  "metadata": {
    661   "kernelspec": {
    662    "display_name": "Python 3.5",
    663    "language": "python",
    664    "name": "py35"
    665   },
    666   "language_info": {
    667    "codemirror_mode": {
    668     "name": "ipython",
    669     "version": 3
    670    },
    671    "file_extension": ".py",
    672    "mimetype": "text/x-python",
    673    "name": "python",
    674    "nbconvert_exporter": "python",
    675    "pygments_lexer": "ipython3",
    676    "version": "3.6.5"
    677   }
    678  },
    679  "nbformat": 4,
    680  "nbformat_minor": 2
    681 }