Regression-Basics.ipynb

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    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Machine Learning: Regression Basics",
     "level": 1
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "This is a series of notebooks to document my learning, and hopefully to help others learn machine learning. I would love suggestions / corrections / feedback for these notebooks.\n\nVisit <a href=\"http://rmdk.ca\">my webpage</a> for more notebooks like this. \n\nEmail me: <a href=\"mailto:email.ryan.kelly@gmail.com?Subject=Hey\" target=\"_top\">email.ryan.kelly@gmail.com</a>\n\nI'd love if you shared this"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "social()",
     "prompt_number": 6,
     "outputs": [
      {
       "output_type": "pyout",
       "html": "\n    <a style='float:left; margin-right:5px;' href=\"https://twitter.com/share\" class=\"twitter-share-button\" data-text=\"Check this out\" data-via=\"Ryanmdk\">Tweet</a>\n<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n    <a style='float:left; margin-right:5px;' href=\"https://twitter.com/Ryanmdk\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Ryanmdk</a>\n<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n    <a style='float:left; margin-right:5px;'target='_parent' href=\"http://www.reddit.com/submit\" onclick=\"window.location = 'http://www.reddit.com/submit?url=' + encodeURIComponent(window.location); return false\"> <img src=\"http://www.reddit.com/static/spreddit7.gif\" alt=\"submit to reddit\" border=\"0\" /> </a>\n<script src=\"//platform.linkedin.com/in.js\" type=\"text/javascript\">\n  lang: en_US\n</script>\n<script type=\"IN/Share\"></script>\n",
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       "prompt_number": 6,
       "text": "<IPython.core.display.HTML at 0x103f94610>"
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     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "This notebook covers or includes:",
     "level": 2
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "- Linear Regression OLS\n- Multiple Regression\n- Best Practices"
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Data Sources:",
     "level": 2
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "- <a target=\"_parent\" href=\"http://en.wikipedia.org/wiki/Regression_analysis\">Wikipedia</a> (introduction content)"
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "TO DO:",
     "level": 6
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "- Improve flow"
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Getting Started",
     "level": 1
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Pulled directly from <a target=\"_parent\" href=\"http://en.wikipedia.org/wiki/Regression_analysis\">wikipedia</a>: \n\nIn statistics, regression analysis is a **supervised learning** statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.\n\nRegression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable; for example, correlation does not imply causation.\n\nLet's grab some data and get going."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "import pandas as pd\nimport numpy as np\n\n# Advertising Sales data\ndf = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)\nprint df.info()",
     "prompt_number": 5,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "<class 'pandas.core.frame.DataFrame'>\nInt64Index: 200 entries, 1 to 200\nData columns (total 4 columns):\nTV           200 non-null float64\nRadio        200 non-null float64\nNewspaper    200 non-null float64\nSales        200 non-null float64\ndtypes: float64(4)None\n"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "df.describe()",
     "prompt_number": 166,
     "outputs": [
      {
       "output_type": "pyout",
       "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>TV</th>\n      <th>Radio</th>\n      <th>Newspaper</th>\n      <th>Sales</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>count</th>\n      <td> 200.000000</td>\n      <td> 200.000000</td>\n      <td> 200.000000</td>\n      <td> 200.000000</td>\n    </tr>\n    <tr>\n      <th>mean</th>\n      <td> 147.042500</td>\n      <td>  23.264000</td>\n      <td>  30.554000</td>\n      <td>  14.022500</td>\n    </tr>\n    <tr>\n      <th>std</th>\n      <td>  85.854236</td>\n      <td>  14.846809</td>\n      <td>  21.778621</td>\n      <td>   5.217457</td>\n    </tr>\n    <tr>\n      <th>min</th>\n      <td>   0.700000</td>\n      <td>   0.000000</td>\n      <td>   0.300000</td>\n      <td>   1.600000</td>\n    </tr>\n    <tr>\n      <th>25%</th>\n      <td>  74.375000</td>\n      <td>   9.975000</td>\n      <td>  12.750000</td>\n      <td>  10.375000</td>\n    </tr>\n    <tr>\n      <th>50%</th>\n      <td> 149.750000</td>\n      <td>  22.900000</td>\n      <td>  25.750000</td>\n      <td>  12.900000</td>\n    </tr>\n    <tr>\n      <th>75%</th>\n      <td> 218.825000</td>\n      <td>  36.525000</td>\n      <td>  45.100000</td>\n      <td>  17.400000</td>\n    </tr>\n    <tr>\n      <th>max</th>\n      <td> 296.400000</td>\n      <td>  49.600000</td>\n      <td> 114.000000</td>\n      <td>  27.000000</td>\n    </tr>\n  </tbody>\n</table>\n<p>8 rows × 4 columns</p>\n</div>",
       "metadata": {},
       "prompt_number": 166,
       "text": "               TV       Radio   Newspaper       Sales\ncount  200.000000  200.000000  200.000000  200.000000\nmean   147.042500   23.264000   30.554000   14.022500\nstd     85.854236   14.846809   21.778621    5.217457\nmin      0.700000    0.000000    0.300000    1.600000\n25%     74.375000    9.975000   12.750000   10.375000\n50%    149.750000   22.900000   25.750000   12.900000\n75%    218.825000   36.525000   45.100000   17.400000\nmax    296.400000   49.600000  114.000000   27.000000\n\n[8 rows x 4 columns]"
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     "metadata": {},
     "cell_type": "markdown",
     "source": "So, what types of questions could we answer with regards to this dataset? \n\n- *Is there a relationship between the types of advertising, and sales?*\n- *How strong is this relationship?*\n- *What variables contribute to more sales?*\n- *How well can we predict sales?*\n- *Is there synergy among variables that contributes to the amount of sales?*\n\n**I will not be going over all the theory of regression, but I will demonstrate a workflow which checks assumptions and describes the required steps and considerations.**\n\nThe first step is to split our data into training and testing data."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "from sklearn.cross_validation import train_test_split\n#Help for train test spit\n#train_test_split?\n\nx = df[['TV', 'Radio', 'Newspaper']]\ny = df['Sales']\n\nx_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.33, random_state=123)",
     "prompt_number": 171,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Interpreting significance, influence, and the coefficients:",
     "level": 2
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Now lets get a sense about how our independent variables are related to the dependent variable (`Sales`). We do this by examining the p values and coefficients of univariate regressions between each predictor and dependent variable (DV).\n\nThe questions we want to ask are:\n\n- \"Which variables are significant?\"\n- \"What type of relationship do the predictors have with the DV? (positive / negative)\"\n- \"What is the strength of this relationship\"\n- \"Does this make intuitive sense?\"\n\nThe last point is particularly important. As is the case with any modeling, accurate intuition about your data takes paramount importance over the dataset on hand. For example, if the data revealed that a increases in a predictor variable, `smoking`, was found to be negatively related to lung cancer, it would likely not be satisfactory to include `smoking` in the model."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Is there a potential relationship between the predictors and the response variable?",
     "level": 3
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "from sklearn.feature_selection import f_regression\n#f_regression?\n# Perform univariate regression and report p values\np_values = f_regression(x_train, y_train)\np_values",
     "prompt_number": 172,
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 172,
       "metadata": {},
       "text": "(array([ 201.74678914,   50.60657905,    7.68597105]),\n array([  2.29293230e-28,   6.44463252e-11,   6.37042164e-03]))"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Great! All of our predictors are significant ( `p < 0.05` ) in a univariate regression. The `F` values are also > 1 which suggests that all the predictors are related to sales. This is not often the case and has only happened because this dataset is tailored for machine learning analysis.\n\nNow we can take a look at the coefficients. We will build a customized function that runs several linear models to do this."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "What do the coefficients tell us?",
     "level": 3
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "def coefs(x_train, y_train, x_test, y_test):\n    lr = LinearRegression(fit_intercept=True)\n    \n    feature_names = df.columns\n    coef_list = []\n    \n    for col in xrange(len(x_train[1])):\n        # Iterate through columns, \n        # LinearRegression expects 2D inputs for x\n        # So we add a new blank axis\n        x = x_train[:, np.newaxis]\n        x = x[:, :, col]\n        \n        lr.fit(x, y_train)\n        coef_list.append([feature_names[col], lr.coef_[0]])\n        \n    return coef_list\n        \ncoefs(x_train, y_train, x_test, y_test)",
     "prompt_number": 174,
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 174,
       "metadata": {},
       "text": "[['TV', 0.046984295187230886],\n ['Radio', 0.18498775661674768],\n ['Newspaper', 0.05350821976042866]]"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "While we can begin to interpret the magnitude of these coefficients, the important thing at this stage is directionality. If there were any variables here which intuitively disagreed with a *known* reality in terms of direction, we would want to exclude them from the model. However, keep in mind that many times we do not know the expected behaviour, so we should not remove any variables in that case.\n\n- Here, we see that as expected, all three types of advertising have a positive effect on sales.\n\nIn this notebook, we will not get into interpreting magnitudes of the coefficients beyond this. The problem is similar to one we have experienced before in classification whereby we are currently mixing our units and it would not make sense (in most cases) to interpret the coefficients this way. If the predictors shared the same unit, say in dollars of advertising spent, you could begin exploring the magnitude of the relationships with some confidence."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Assessing Model Accuracy",
     "level": 2
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "There are two metrics typically used to asses model fit for linear regression: \n\n- Residual standard error (RSE)\n- R^2\n\nThe RSE is a measure of the average difference between the predicted y and our observed y, while R^2 is a measure of predictive power by measuring the proportion of explained variance.\n\nLet's modify our function from above to include these new metrics."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "def models(x_train, y_train, x_test, y_test):\n    \n    lr = LinearRegression(fit_intercept=True)\n    \n    feature_names = df.columns\n    \n    coef_list = []\n    error_list = []\n    r2_list = []\n    feature_list = []\n    \n    for col in xrange(len(feature_names)-1):\n        # Iterate through columns, \n        # LinearRegression expects 2D inputs for x\n        # So we add a new blank axis\n        xtrain = x_train[:, np.newaxis]\n        xtrain = xtrain[:, :, col]\n        \n        xtest = x_test[:, np.newaxis]\n        xtest = xtest[:, :, col]\n        \n        lr.fit(xtrain, y_train)\n        \n        # Compute RSE\n        error_list.append(np.sum(lr.predict(xtest) - y_test)**2)\n        r2_list.append(lr.score(xtest, y_test))\n        coef_list.append(lr.coef_[0])\n        feature_list.append(feature_names[col])\n        \n    out = zip(feature_list, r2_list, error_list, coef_list, )\n    \n    return out\n\nmodel_outs = models(x_train, y_train, x_test, y_test)\nmodel_outs",
     "prompt_number": 176,
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 176,
       "metadata": {},
       "text": "[('TV', 0.62450810246495947, 326.33971180270174, 0.046984295187230886),\n ('Radio', 0.43882257063230956, 79.574614380832173, 0.18498775661674768),\n ('Newspaper', 0.038253869337874224, 830.59166804447102, 0.05350821976042866)]"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Now we have a pretty good sense of how our predictors interact with `sales`. For example, `TV` advertising can explain ~62% of the variation in the data, yet the `RSE` error is rather high, which means that the deviation of this parameter can be quite variable (possibly due to some outliers).\n\nLet's use this information to build a multiple regression model that improves our R^2 value, thus our future predictive power."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Switching python packages:",
     "level": 3
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "scikit-learn is best for doing machine learning with emphasis on predictive modeling, often with large and sparse data.\n\n\n`statsmodels` on the other hand is better at \"traditional\" statistics and econometrics, with much stronger emphasis on parameter estimation and (statistical) testing. `statsmodels` will help us understand the basics more clearly before we move onto more complex regression techniques.\n\nBefore we get into the modeling, we need to check if our dependent variable `sales` is normally distributed, and thus satisfies the assumptions of our regression."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "# Plot the results thus far\nfrom ggplot import *\n# Enable inline plotting\n%matplotlib inline\n\nqplot(y)+geom_histogram()",
     "prompt_number": 177,
     "outputs": [
      {
       "output_type": "display_data",
       "metadata": {},
       "png": 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OxSOPPBI33HBDbN26NTZu3Bijo6Or9qnVajE9Pd2xpuapr68vlpeX8y4DgI+Y\nqampvEs460JqybIsRkZGurb+Z1kW4+PjbZ9nYmLigq6nLOv/mb60dMxaB1tZWYmDBw/G+vXr4+ab\nb46IiHq9HvV6/Zx9p6amSvGoM8uyUlwHAJeWIq09rdTSbDYLVXvKhdT3UV7/1xwUjx8/Hs8//3xc\nddVV8dBDD0VExC233BLXXXddx4oDACA/aw6Kmzdvjm9/+9sdLAUAgCLxzSwAACQJigAAJAmKAAAk\nCYoAACQJigAAJAmKAAAkCYoAACQJigAAJAmKAAAkCYoAACQJigAAJAmKAAAkCYoAACQJigAAJAmK\nAAAkCYoAACQJigAAJAmKAAAkCYoAACQJigAAJGXdHmBpaSmq1WpkWdeH+kCzs7Ntj99sNmNxcbHt\nWprNZgwNDbV1jk5cDwCXhmazWZh7/oXW0mg04sSJExehovYNDAx86D49PT0XtF/RVSqVlo/p+k9e\nf39/zM7ORqPR6PZQHyjLshgfH2/rHBMTE22f48x52g2cnboeAIqvSPf8ItXSKReyJg8MDHTkw6K8\nVavVlo/x6BkAgCRBEQCAJEERAIAkQREAgCRBEQCAJEERAIAkQREAgCRBEQCAJEERAIAkQREAgCRB\nEQCAJEERAIAkQREAgCRBEQCAJEERAIAkQREAgCRBEQCAJEERAIAkQREAgKRsrQcePXo0fvzjH8fK\nykps3749du7c2cm6AADI2Zo+UTx9+nQ8/vjjsWfPnvjTP/3TeOGFF2JqaqrTtQEAkKM1BcU33ngj\nPvaxj8XIyEj09vbGZz7zmXjppZc6XRsAADla06PnmZmZ+I3f+I2z/1+v1+ONN96ImZmZmJubW7Vv\nrVaLLFvzE+6OaDQauY7/ftVqta3ji3Y9AHCpupA1ube3t+21uwjWkscqKysrK60e9B//8R/xX//1\nXzE+Ph4REc8991y88cYbMTAwEJOTk6v23bx5c/zhH/5h1Ov1louje2ZmZuLw4cOxY8cOvSkQfSkm\nfSkmfSkuvSmmtfRlTR/1DQ0NxcmTJ1cNXK/X44YbbojR0dGz26empuKxxx6Lubk5PygFMzc3F5OT\nkzE6Oqo3BaIvxaQvxaQvxaU3xbSWvqwpKH784x+Pt99+O6anp2NoaChefPHF2L17d9TrdT8QAAAl\nsaag2NvbG3feeWf8wz/8Q5w+fTq2b98e69ev73RtAADkaM1/ZXLdddfFdddd18laAAAokN5vf/vb\n3+7WyVcpnS3wAAAFlUlEQVRWVuKyyy6La665Jvr6+ro1DGugN8WkL8WkL8WkL8WlN8W0lr6s6a+e\nAQAov67+A4e+5q+YvvOd70RfX1/09PRET09P3H///XmX9JF04MCBOHr0aAwODsbevXsjImJhYSH2\n798f77zzTgwPD8dXvvKVGBgYyLnSj55Ub/793/89nnnmmRgcHIyIiFtuucWv31xkJ0+ejMceeyzm\n5+cjImLHjh3x+c9/3rzJ2Qf1xZzJV6PRiL//+7+PZrMZp06diuuvvz5uvfXWludL14Lima/5u/fe\ne6Ner8fDDz8co6Oj/uilACqVSnzta1+LdevW5V3KR9q2bdvic5/7XDz22GNntx06dCiuvfba2Llz\nZxw6dCgOHToUt912W45VfjSlelOpVOLmm2+O3/qt38qxso+2np6e+NKXvhQbNmyI5eXlePjhh2PL\nli3x7LPPmjc5+qC+mDP5qlar8dWvfjUuu+yyOHXqVHzve9+L1157LY4cOdLSfFnTV/hdCF/zB+e3\nefPm6O/vX7XtyJEj8dnPfjYiIm688UZzJiep3pC/oaGh2LBhQ0RE9PX1xRVXXBEzMzPmTc4+qC/k\n77LLLouIiFOnTsXKykoMDAy0PF+69oniB33NH8Xw/e9/PyqVStx0002xY8eOvMvh/zc/Px+1Wi0i\nfv31l2ce5VAMv/jFL+K5556Lj3/843H77bd7vJmj6enpePPNN+MTn/iEeVMg7+3L66+/bs7k7PTp\n0/Hd7343pqen46abboorr7yy5fnStaBYqVS6dWra9I1vfCOGhoZifn4+vv/978cVV1wRmzdvzrss\n3sccKpabbropdu3aFRER//Zv/xZPPPFE3H333TlX9dG0vLwcjzzySNxxxx3n/OWmeZOf9/fFnMlf\nT09PPPDAA7G0tBQ/+MEP4tVXX131+oXMl649ev6gr/kjf0NDQxERMTg4GFu3bvVJb4EMDg7G7Oxs\nRETMzs6e/SVw8ler1aJSqUSlUont27ebNzk5depUPPLII3HDDTfE1q1bI8K8KYJUX8yZ4ujv749P\nfepTceLEiZbnS9eC4nu/5q/ZbMaLL7646nugyce7774by8vLZ//75ZdfjiuvvDLnqjhjdHQ0nnvu\nuYiI+OUvfxnXX399zhVxxpkba0TESy+9ZN7kYGVlJQ4ePBjr16+Pm2+++ex28yZfH9QXcyZf8/Pz\nsbi4GBG//gvol19+OTZs2NDyfOnqv6N45p/HOfM1f1/4whe6NRQXaHp6Ov7pn/4pIn79uws33HCD\nvuRk//79cezYsVhYWIharRZjY2MxOjoajz76aJw8edI/85Gj9/fmi1/8Yhw7dizefPPNqFQqMTw8\nHHfdddfZ3/Ph4njttdfi7/7u7+Kqq646+8jslltuiY0bN5o3OfqgvrzwwgvmTI7+93//Nx577LFY\nWVmJlZWVuPHGG+O3f/u3Y2FhoaX54h/cBgAgqWuPngEAuLQJigAAJAmKAAAkCYoAACQJigAAJAmK\nAAAkCYoAACQJigAAJAmKAAAkCYoAH+Dll1+Oyy+/PJ599tmIiDhx4kSsX78+fvazn+VcGcDFISgC\nfIAtW7bEX/3VX8WePXticXExvv71r8fXv/71+J3f+Z28SwO4KHzXM8CHuPvuu+OVV16J3t7eePrp\np6NareZdEsBF4RNFgA/xzW9+M371q1/Fn/3ZnwmJwEeKTxQBzmNubi5uvPHGuOWWW+Lxxx+PF154\nIUZGRvIuC+CiEBQBzuMb3/hGLCwsxA9/+MP41re+Fe+880788z//c95lAVwUHj0DfICDBw/GE088\nEX/7t38bERH79u2LZ555Jn74wx/mXBnAxeETRQAAknyiCABAkqAIAECSoAgAQJKgCABAkqAIAECS\noAgAQJKgCABAkqAIAEDS/wf/pVU5fm2ICwAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x10c96e710>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 177,
       "metadata": {},
       "text": "<ggplot: (281636577)>"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "This is probably as close to normal as we can get (despite the right skew), however, under circumstances with very non-normal data, you can transform the data to coerce it to be normally distributed. We will do that another day apparently. \n\nThere is generally a misconception surrounding statistical analysis that requires a normality assumption. It is not very useful to test for normality using a statistical test like `Shapiro's` or `Anderson Darling`. This is because for small datasets, even large deviances from normality are not detected, and for large datasets, even the smallest departure from normality will lead to a rejected null. <a href = \"http://www.r-bloggers.com/normality-tests-don’t-do-what-you-think-they-do/\"> See more here</a>."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "import statsmodels.api as sm\n\n# Recall our data\nx = df[['TV', 'Radio', 'Newspaper']]\ny = df['Sales']",
     "prompt_number": 218,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "# Add intercept\nX = sm.add_constant(x)\nmodel = sm.OLS(y, X).fit()\nprint model.summary2()",
     "prompt_number": 226,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "            Results: Ordinary least squares\n======================================================\nModel:              OLS   AIC:                778.3941\nDependent Variable: Sales BIC:                788.2891\nNo. Observations:   200   Log-Likelihood:     -386.20 \nDf Model:           2     F-statistic:        859.6   \nDf Residuals:       197   Prob (F-statistic): 4.83e-98\nR-squared:          0.897 Scale:              2.8270  \nAdj. R-squared:     0.896                             \n------------------------------------------------------\n          Coef.  Std.Err.    t    P>|t|  [0.025 0.975]\n------------------------------------------------------\nconst     2.9211   0.2945  9.9192 0.0000 2.3403 3.5019\nTV        0.0458   0.0014 32.9087 0.0000 0.0430 0.0485\nRadio     0.1880   0.0080 23.3824 0.0000 0.1721 0.2038\n------------------------------------------------------\nOmnibus:          60.022   Durbin-Watson:      2.081  \nProb(Omnibus):    0.000    Jarque-Bera (JB):   148.679\nSkew:             -1.323   Prob(JB):           0.000  \nKurtosis:         6.292    Condition No.:      425    \n======================================================\n\n"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "As you can see, `statsmodels` provides a much more descriptive output, and it well suited for these basic statistic stats."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Interpreting the output and variable selection:",
     "level": 2
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "This is a very important part! Here is what you need to know. \n\nFirst, we can examine the model's F statistic and p-value. If our F statistic is greater than 1 we can conclude that *at least* one of our variables is related to housing price and we can continue with our analysis. There are special cases when  `n`  is small, or when we have more predictors than  `n` , but we will cover this later.\n\nNow, we are more concerned about **which** variables are related, and how they are related.\n\nBelow, we can see the `coefficients` and `p-values` of the individual independent variables. These `p-values` judge whether each individual predictor is related to the dependent variable, **after** adjusting for the other predictors. Simply put, it measures the *partial effect* of adding that particular variable to the model, in the presence of other variables.\n\nWhat we are talking about here are the considerations for *variable selection*. Since we want only the predictors that actually influence the prediction of our dependent variable. While there are very complex methods of variable selection (`AIC BIC`), we will explore the basics here.\n\nThe two most basic methods are:\n\n- **Forward Selection**. Begin with a null model of an intercept and no predictors. Fit univariate regressions for all available predictors. Add the predictor with the lowest `RSS` to the model. The next variables added will be the one that results in the lowest RSS for the new 2-variable model. This is continued until some stopping rule.\n\n\n- **Backward Selection**. Start will all variables in the model, then remove the variable with the largest `p-value` (the least significant). Refit the model and repeat the processes until all remaining variables have `p` < some defined threshold (often < 0.05 or 0.1).\n\nThere are also ways to combine these two techniques, which is how I prefer to do it. This is called **mixed selection**. Starting with no variables in the model, add the variable that provides the best fit (highest `R^2` from the univariate regression). When then continue adding variables by next highest `R^2` as long as their `p-value` in the multiple regression model are significant.\n\nLastly, we need some way to judge overall model performance. Recall that `RSE` and `R^2` are the most common measures of model fit. An `R^2` of `1` would indicate that the predictor variables explain all the variation of the dependent variable (not realistic to find this in nature). We can add this idea to our variable selection technique. We will only include variables which also increase `R^2` by at least some threshold (perhaps 0.5% or 1%).\n<hr>"
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "So what does all this mean for our model?",
     "level": 3
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Notice that when we include all three advertising types into the model that `newspaper` changes from significant in our univariate regression to  insignificant in multiple regression. We can therefor conclude that newspaper has no influence (positive or negative) on sales. This is a common situation when using real-life data. \n\nConsider the correlation between `newspaper` and `radio`:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "from scipy.stats.stats import pearsonr\n\npearsonr(X['Radio'], X['Newspaper'])",
     "prompt_number": 186,
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 186,
       "metadata": {},
       "text": "(0.35410375076117517, 2.688835078719089e-07)"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "As we can see, these two variables correlated. This means that there is a tendency to spend more on `newspaper` advertising in the same markets where more is spent on `radio` advertising. What this means is that `newspaper` appears to be related to `sales`, but it is only piggy-backing on the affect of `radio` advertising.\n\nThe classic example of this effect is the relationship between ice cream sales and shark attacks, which suggests that closing down ice cream parlours would reduce incidents. However, the increased shark attacks is facilitated by increasing temperatures, which drives more people to the beach, who also purchase ice cream.\n\nLet's exclude newspaper from our model."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "df = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)\n\nx = df[['TV', 'Radio']]\ny = df['Sales']\n\nX = sm.add_constant(x)\n\nmodel = sm.OLS(y, X).fit()\n# print model error\nprint model.mse_resid\nprint model.summary2()",
     "prompt_number": 353,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "2.82697451811\n            Results: Ordinary least squares\n======================================================\nModel:              OLS   AIC:                778.3941\nDependent Variable: Sales BIC:                788.2891\nNo. Observations:   200   Log-Likelihood:     -386.20 \nDf Model:           2     F-statistic:        859.6   \nDf Residuals:       197   Prob (F-statistic): 4.83e-98\nR-squared:          0.897 Scale:              2.8270  \nAdj. R-squared:     0.896                             \n------------------------------------------------------\n          Coef.  Std.Err.    t    P>|t|  [0.025 0.975]\n------------------------------------------------------\nconst     2.9211   0.2945  9.9192 0.0000 2.3403 3.5019\nTV        0.0458   0.0014 32.9087 0.0000 0.0430 0.0485\nRadio     0.1880   0.0080 23.3824 0.0000 0.1721 0.2038\n------------------------------------------------------\nOmnibus:          60.022   Durbin-Watson:      2.081  \nProb(Omnibus):    0.000    Jarque-Bera (JB):   148.679\nSkew:             -1.323   Prob(JB):           0.000  \nKurtosis:         6.292    Condition No.:      425    \n======================================================\n\n"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<hr>\nGreat! As you can see, we really did not lose any predictive power by removing `newspaper`. However, there could also be some problems that cannot be diagnosed using these numbers or tests. One of the more robust and simple ways to assess the quality of our model is to plot the residuals, which is the error term, computed from the difference of the predicted and observed data.\n\nFor linear regression, we expect that the residuals (predicted values) are evenly distributed around zero."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "qplot(y=model.resid, x = xrange(len(y)))+geom_point() \\\n+ geom_smooth(size=2,color='blue', se=False)",
     "prompt_number": 284,
     "outputs": [
      {
       "output_type": "display_data",
       "metadata": {},
       "png": 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0Gg2cnJwQGxtrUtvLgIAA5OTk6JYlEgmSkpJKTPSaN2+OJ0+e6K0LDAzUXThN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\n",
       "text": "<matplotlib.figure.Figure at 0x11ac9b890>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 284,
       "metadata": {},
       "text": "<ggplot: (297961477)>"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "We can see that there is a negative skew on these residuals, which suggests that there is some bias towards under prediction in the model. Further we can see a very subtle negative-to-positive-to-negative trend. This suggests a non-linear pattern whereby two or more variables are interacting with some synergistic effects. In other words, sometimes combining `TV` and `Radio` advertising can work together to boost sales more than using any single medium. \n\nWe will discuss this in more later."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Prediction:",
     "level": 2
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Once we have fit a satisfactory multiple regression model, we can quickly begin to predict the response of `y` using new values for the predictors. Yet, we should utilize a confidence interval to quantify the uncertainty of out prediction of sales. Using this method we can predict that the true `sales` will be within some 95% confidence interval given any `TV` or `Radio` spending."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Other Regression Considerations:",
     "level": 2
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "What we have discussed thus far is very basic regression techniques. In the real world we have many **different types of data sources**, and **non-linear relationships**."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Dealing with Quantitative Variables:",
     "level": 3
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "url = 'http://www-bcf.usc.edu/~gareth/ISL/Credit.csv'\n\ndf = pd.read_csv(url)\ndf.info()",
     "prompt_number": 6,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "<class 'pandas.core.frame.DataFrame'>\nInt64Index: 400 entries, 0 to 399\nData columns (total 12 columns):\nUnnamed: 0    400 non-null int64\nIncome        400 non-null float64\nLimit         400 non-null int64\nRating        400 non-null int64\nCards         400 non-null int64\nAge           400 non-null int64\nEducation     400 non-null int64\nGender        400 non-null object\nStudent       400 non-null object\nMarried       400 non-null object\nEthnicity     400 non-null object\nBalance       400 non-null int64\ndtypes: float64(1), int64(7), object(4)"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "In this dataset we have several qualitative variables, along with some quantitative. Let's see how this data is coded."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "df.head()",
     "prompt_number": 316,
     "outputs": [
      {
       "output_type": "pyout",
       "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>Unnamed: 0</th>\n      <th>Income</th>\n      <th>Limit</th>\n      <th>Rating</th>\n      <th>Cards</th>\n      <th>Age</th>\n      <th>Education</th>\n      <th>Gender</th>\n      <th>Student</th>\n      <th>Married</th>\n      <th>Ethnicity</th>\n      <th>Balance</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td> 1</td>\n      <td>  14.891</td>\n      <td> 3606</td>\n      <td> 283</td>\n      <td> 2</td>\n      <td> 34</td>\n      <td> 11</td>\n      <td>   Male</td>\n      <td>  No</td>\n      <td> Yes</td>\n      <td> Caucasian</td>\n      <td> 333</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td> 2</td>\n      <td> 106.025</td>\n      <td> 6645</td>\n      <td> 483</td>\n      <td> 3</td>\n      <td> 82</td>\n      <td> 15</td>\n      <td> Female</td>\n      <td> Yes</td>\n      <td> Yes</td>\n      <td>     Asian</td>\n      <td> 903</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td> 3</td>\n      <td> 104.593</td>\n      <td> 7075</td>\n      <td> 514</td>\n      <td> 4</td>\n      <td> 71</td>\n      <td> 11</td>\n      <td>   Male</td>\n      <td>  No</td>\n      <td>  No</td>\n      <td>     Asian</td>\n      <td> 580</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td> 4</td>\n      <td> 148.924</td>\n      <td> 9504</td>\n      <td> 681</td>\n      <td> 3</td>\n      <td> 36</td>\n      <td> 11</td>\n      <td> Female</td>\n      <td>  No</td>\n      <td>  No</td>\n      <td>     Asian</td>\n      <td> 964</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td> 5</td>\n      <td>  55.882</td>\n      <td> 4897</td>\n      <td> 357</td>\n      <td> 2</td>\n      <td> 68</td>\n      <td> 16</td>\n      <td>   Male</td>\n      <td>  No</td>\n      <td> Yes</td>\n      <td> Caucasian</td>\n      <td> 331</td>\n    </tr>\n  </tbody>\n</table>\n<p>5 rows × 12 columns</p>\n</div>",
       "metadata": {},
       "prompt_number": 316,
       "text": "   Unnamed: 0   Income  Limit  Rating  Cards  Age  Education  Gender Student  \\\n0           1   14.891   3606     283      2   34         11    Male      No   \n1           2  106.025   6645     483      3   82         15  Female     Yes   \n2           3  104.593   7075     514      4   71         11    Male      No   \n3           4  148.924   9504     681      3   36         11  Female      No   \n4           5   55.882   4897     357      2   68         16    Male      No   \n\n  Married  Ethnicity  Balance  \n0     Yes  Caucasian      333  \n1     Yes      Asian      903  \n2      No      Asian      580  \n3      No      Asian      964  \n4     Yes  Caucasian      331  \n\n[5 rows x 12 columns]"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "We can see that the data for the qualitative variables (also known as factors) are coded as text strings. Factors such as `Gender`, `Student` and  `Married` only have two `levels`, for example: `male` or `female`. To incorporate these into a regression model, we can create a `dummy variable` that takes on two values based on the two levels of the factor. To convert `Gender` to a dummy variable we simple create a new variable:\n\n- `Gender` = **1** if person is male, **0** if person is female.\n\nIn the regression model, if a person is female we simply do not compute a coefficient, since in our model, being female is represented as an absence of being male, thus the `Gender` variable can be modeled by only investigating the properties of either being male, or not being male. In this example, being female is considered the `baseline` condition, which is associated with *B*0, or the regression intercept.\n\nβ0+β1+εi if the person is Male\n\nβ0+εi if the person is Female\n\nNow β0 can be interpreted as average credit score among females, β0 + β1 as the average credit score among males, and β1 as the average difference in credit balance between males and females.\n\nCoding males at 1 is arbitrary, you could have chosen females to be equal to 1; the only difference is in how you interpret the coefficients."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "# Create new dummy variable\ndf['Males'] = 1\ndf['Males'][df['Gender']=='Female'] = 0 \n\nx = df[['Males']]\ny = df['Balance']\n\nX = sm.add_constant(x)\nmodel = sm.OLS(y, X).fit()\n# print model error\nprint 'p-values:'\nprint model.pvalues\nprint 'R^2:'\nprint model.rsquared_adj",
     "prompt_number": 317,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "p-values:\nconst    3.312981e-47\nMales    6.685161e-01\ndtype: float64\nR^2:\n-0.00205027122403\n"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "As we can see, thus far there is no significant relationship between being male or female."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Qualitative predictors with more than two levels:",
     "level": 3
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Considered the variable `Ethnicity`, which has three levels. A single dummy variable cannot represent all the possible values. Instead we create two dummy variables.\n\n1. Asian: if Asian = 1, otherwise 0\n2. Caucasian: if Caucasian = 1, otherwise 0\n\nNotice we do not need a third dummy variable, because African American is accounted for by the baseline condition (intercept) similar to how females was in the previous example.\n\nβ0+β1+εi if the person is Asian\n\nβ0+β2+εi if the person is Caucasian\n\nβ0+εi if the person is African American\n\nNow β0 is the average credit balance for African Americans, β1 is the difference in the average balance between Asian and African Americans, and β2 is the difference in the average balance between Caucasian and African American's.\n\nThus we now can think about this as comparing the baseline condition β0 to the other conditions."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "# Create dummy variables easily in pandas!\nx = pd.core.reshape.get_dummies(df['Ethnicity'])\n# Remove the African American variable\nx = x[['Asian', 'Caucasian']]\nx.head()",
     "prompt_number": 318,
     "outputs": [
      {
       "output_type": "pyout",
       "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>Asian</th>\n      <th>Caucasian</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td> 0</td>\n      <td> 1</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td> 1</td>\n      <td> 0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td> 1</td>\n      <td> 0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td> 1</td>\n      <td> 0</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td> 0</td>\n      <td> 1</td>\n    </tr>\n  </tbody>\n</table>\n<p>5 rows × 2 columns</p>\n</div>",
       "metadata": {},
       "prompt_number": 318,
       "text": "   Asian  Caucasian\n0      0          1\n1      1          0\n2      1          0\n3      1          0\n4      0          1\n\n[5 rows x 2 columns]"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "X = sm.add_constant(x)\nmodel = sm.OLS(y, X).fit()\nmodel.summary()",
     "prompt_number": 352,
     "outputs": [
      {
       "output_type": "pyout",
       "html": "<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>Sales</td>      <th>  R-squared:         </th> <td>   0.897</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.896</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   859.6</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Mon, 26 May 2014</td> <th>  Prob (F-statistic):</th> <td>4.83e-98</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>19:14:51</td>     <th>  Log-Likelihood:    </th> <td> -386.20</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>   200</td>      <th>  AIC:               </th> <td>   778.4</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>   197</td>      <th>  BIC:               </th> <td>   788.3</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     2</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>[95.0% Conf. Int.]</th> \n</tr>\n<tr>\n  <th>const</th> <td>    2.9211</td> <td>    0.294</td> <td>    9.919</td> <td> 0.000</td> <td>    2.340     3.502</td>\n</tr>\n<tr>\n  <th>TV</th>    <td>    0.0458</td> <td>    0.001</td> <td>   32.909</td> <td> 0.000</td> <td>    0.043     0.048</td>\n</tr>\n<tr>\n  <th>Radio</th> <td>    0.1880</td> <td>    0.008</td> <td>   23.382</td> <td> 0.000</td> <td>    0.172     0.204</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>60.022</td> <th>  Durbin-Watson:     </th> <td>   2.081</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 148.679</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td>-1.323</td> <th>  Prob(JB):          </th> <td>5.19e-33</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 6.292</td> <th>  Cond. No.          </th> <td>    425.</td>\n</tr>\n</table>",
       "metadata": {},
       "prompt_number": 352,
       "text": "<class 'statsmodels.iolib.summary.Summary'>\n\"\"\"\n                            OLS Regression Results                            \n==============================================================================\nDep. Variable:                  Sales   R-squared:                       0.897\nModel:                            OLS   Adj. R-squared:                  0.896\nMethod:                 Least Squares   F-statistic:                     859.6\nDate:                Mon, 26 May 2014   Prob (F-statistic):           4.83e-98\nTime:                        19:14:51   Log-Likelihood:                -386.20\nNo. Observations:                 200   AIC:                             778.4\nDf Residuals:                     197   BIC:                             788.3\nDf Model:                           2                                         \n==============================================================================\n                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n------------------------------------------------------------------------------\nconst          2.9211      0.294      9.919      0.000         2.340     3.502\nTV             0.0458      0.001     32.909      0.000         0.043     0.048\nRadio          0.1880      0.008     23.382      0.000         0.172     0.204\n==============================================================================\nOmnibus:                       60.022   Durbin-Watson:                   2.081\nProb(Omnibus):                  0.000   Jarque-Bera (JB):              148.679\nSkew:                          -1.323   Prob(JB):                     5.19e-33\nKurtosis:                       6.292   Cond. No.                         425.\n==============================================================================\n\"\"\""
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "We can see that the baseline credit balance for `African Americans` is 531. It is also estimated that `Asians` have **~\\$18** less debt than `African Americans` and `Caucasians` will have **~\\$12** less debt than `African Americans`.\n\nHowever, it turns out that this factor is not significant in our model of credit balance, since the `p-values` are insignificant and the `F` statistic is close to `1`, which suggests that there is no relationship between the variables (accepts the null hypothesis)."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Non-Linear effects:",
     "level": 3
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "While a linear regression model often may produce good results, the assumptions that the relationship between the predictors and the response is both _additive_ and _linear_ is often violated. The additive assumption means that the effect of changes in predictor ***X*** *j* on the response ***Y*** is independent of the values of the other predictors. While the linear assumption means that change in the response variable is constant per unit of the predictor variable. \n\nThere are however, some basic ways to relax some of these assumptions:"
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Removing the Additive Assumption:",
     "level": 4
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Recall in the Advertising sales data we concluded that `TV` and `Radio` have an effect on `Sales`. Under additive linear assumptions, the effect of `TV` on sales is independent of the amount spent on `Radio` advertising. \n\nHowever, it may be the the case that spending money on `Radio` advertising increases the effectiveness of `TV`.\n\nFrom a marketing perspective it could mean that splitting the advertising funds between `Radio` and `TV` could be more effective than spending it all on `TV`."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "# import formula api as alias smf\nimport statsmodels.formula.api as smf\n\n# formula: response ~ predictor + predictor\nmodel = smf.ols(formula='Sales ~ 1 + TV + Radio + TV * Radio', data=df).fit()\nmodel.summary()",
     "prompt_number": 354,
     "outputs": [
      {
       "output_type": "pyout",
       "html": "<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>Sales</td>      <th>  R-squared:         </th> <td>   0.968</td> \n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.967</td> \n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1963.</td> \n</tr>\n<tr>\n  <th>Date:</th>             <td>Mon, 26 May 2014</td> <th>  Prob (F-statistic):</th> <td>6.68e-146</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>19:15:19</td>     <th>  Log-Likelihood:    </th> <td> -270.14</td> \n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>   200</td>      <th>  AIC:               </th> <td>   548.3</td> \n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>   196</td>      <th>  BIC:               </th> <td>   561.5</td> \n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     3</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>[95.0% Conf. Int.]</th> \n</tr>\n<tr>\n  <th>Intercept</th> <td>    6.7502</td> <td>    0.248</td> <td>   27.233</td> <td> 0.000</td> <td>    6.261     7.239</td>\n</tr>\n<tr>\n  <th>TV</th>        <td>    0.0191</td> <td>    0.002</td> <td>   12.699</td> <td> 0.000</td> <td>    0.016     0.022</td>\n</tr>\n<tr>\n  <th>Radio</th>     <td>    0.0289</td> <td>    0.009</td> <td>    3.241</td> <td> 0.001</td> <td>    0.011     0.046</td>\n</tr>\n<tr>\n  <th>TV:Radio</th>  <td>    0.0011</td> <td> 5.24e-05</td> <td>   20.727</td> <td> 0.000</td> <td>    0.001     0.001</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>128.132</td> <th>  Durbin-Watson:     </th> <td>   2.224</td> \n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1183.719</td> \n</tr>\n<tr>\n  <th>Skew:</th>          <td>-2.323</td>  <th>  Prob(JB):          </th> <td>9.09e-258</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td>13.975</td>  <th>  Cond. No.          </th> <td>1.80e+04</td> \n</tr>\n</table>",
       "metadata": {},
       "prompt_number": 354,
       "text": "<class 'statsmodels.iolib.summary.Summary'>\n\"\"\"\n                            OLS Regression Results                            \n==============================================================================\nDep. Variable:                  Sales   R-squared:                       0.968\nModel:                            OLS   Adj. R-squared:                  0.967\nMethod:                 Least Squares   F-statistic:                     1963.\nDate:                Mon, 26 May 2014   Prob (F-statistic):          6.68e-146\nTime:                        19:15:19   Log-Likelihood:                -270.14\nNo. Observations:                 200   AIC:                             548.3\nDf Residuals:                     196   BIC:                             561.5\nDf Model:                           3                                         \n==============================================================================\n                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n------------------------------------------------------------------------------\nIntercept      6.7502      0.248     27.233      0.000         6.261     7.239\nTV             0.0191      0.002     12.699      0.000         0.016     0.022\nRadio          0.0289      0.009      3.241      0.001         0.011     0.046\nTV:Radio       0.0011   5.24e-05     20.727      0.000         0.001     0.001\n==============================================================================\nOmnibus:                      128.132   Durbin-Watson:                   2.224\nProb(Omnibus):                  0.000   Jarque-Bera (JB):             1183.719\nSkew:                          -2.323   Prob(JB):                    9.09e-258\nKurtosis:                      13.975   Cond. No.                     1.80e+04\n==============================================================================\n\nWarnings:\n[1] The condition number is large, 1.8e+04. This might indicate that there are\nstrong multicollinearity or other numerical problems.\n\"\"\""
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "It turns out we were right! The synergistic effect increased our `R^2` by about **6%**. There may be examples where the individual effects may be insignificant after adding an interaction term, however it is still good practice to keep in these individual terms. This is because leaving them out tends to alter the meaning of the interaction.\n\nInteraction tends to be an important consideration for qualitative variables as well. Recall the Credit Card dataset. It is likely that changes in `income` would have different effects on `students` vs. `non-students`. Thus we can multiply `income` with the student dummy variable. In terms of the model fit, this means that the slopes of the lines between `students` and `non-students` will be different when estimating `credit balance` using `income`. We could eventually conclude that `non-students` may have larger `credit balances` as `income` increases, compared to individuals that are `students`."
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Non-Linear Relationships:",
     "level": 4
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "In some cases, the true relatioship between the predictors and the response variable could be non-linear. We can extend the linear model to accomodate non-linear effects using **Polynomial Regression**. There are however, other more advanced techniques that will be discussed later that may be better suited to this type of application.\n\nMore on polynomial fitting can be found in my other notebook <a target = '_self' href='http://rmdk.ca/machine-learning-curve-fitting/'>here</a>."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "url = 'http://www-bcf.usc.edu/~gareth/ISL/Auto.csv'\ndf = pd.read_csv(url)\n\ndf.info()",
     "prompt_number": 27,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "<class 'pandas.core.frame.DataFrame'>\nInt64Index: 397 entries, 0 to 396\nData columns (total 9 columns):\nmpg             397 non-null float64\ncylinders       397 non-null int64\ndisplacement    397 non-null float64\nhorsepower      397 non-null object\nweight          397 non-null int64\nacceleration    397 non-null float64\nyear            397 non-null int64\norigin          397 non-null int64\nname            397 non-null object\ndtypes: float64(3), int64(4), object(2)"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "# Make horsepower into integer\ndf2 = df[df['horsepower']!='?']\ndf2['horsepower'] = df2['horsepower'].astype(int)\n# formula: response ~ predictor + predictor\n# I makes sure operation is done before fitting the model\n\nmodel1 = smf.ols(formula='mpg ~ 1 + horsepower', data=df2).fit()\nprint model1.rsquared_adj\nmodel2 = smf.ols(formula='mpg ~ 1 + horsepower + I(horsepower**2)', data=df2).fit()\nprint model2.rsquared_adj",
     "prompt_number": 30,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "0.604937868807\n0.685952650207\n"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "heading",
     "source": "Potential Problems:",
     "level": 2
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "These are some things to keep out for while performing linear regression. Some of this we have already covered.\n\n1. Non-Linearity of the response-predictor relationships.\n2. Correlation of the error terms.\n3. Non-constant variance of error terms.\n4. Outliers.\n5. High -leverage points.\n6. Multicollinearity.\n<hr>"
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "**Non-Linear Relationships:**\n\nLinear regression assumes that there is a linear relationship between the predictors and response. If the actual relationship is very non-linear, then most of the conclusions that we draw from the model are less robust, and model prediction accuracy would be diminished. \n\nResidual plots are the first step for testing this assumption. Here we plot residuals vs. predicted values for `mpg ~ horsepower` and `mpg ~ horsepower + horsepower^2`. We can see that the quadratic version has much less pattern in the residuals, which suggests that the quadratic fit improves the model. If it looks like the predictors are non-linear, a simple approach is to use non-linear transformations. We will discuss more advanced techniques.\n\n**Non-constant variance of error terms:**\n\nNon-constant variance is when there is a distinct trend in the variance, whereby the variance may increase with the value of the response. This can also be viewed with a `residual vs fitted plot`. The resulting plot will take on a *funnel shape* under this condition, called `heteroscedasticity`. In this case, a simple fix is often transforming the response variable to assume a more normal distribution. If this still doesn't work, you may have to explore weighted least squares regression, which proportionally weights the model by the inverse of the variances."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "qplot(y=model1.resid, x=model1.fittedvalues)+geom_point()+geom_smooth()",
     "prompt_number": 337,
     "outputs": [
      {
       "output_type": "display_data",
       "metadata": {},
       "png": 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OKS2BkpKSEBMTI/3RxsTE4J///CfCw8M98npKpRKTJ0/2yLWLE4vFApPJBIVC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\nIsWxKCUiIiIixf0f477zDtGKZJQAAAAASUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0x11a548610>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 337,
       "metadata": {},
       "text": "<ggplot: (299288717)>"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "qplot(y=model2.resid, x=model2.fittedvalues)+geom_point()+geom_smooth()",
     "prompt_number": 336,
     "outputs": [
      {
       "output_type": "display_data",
       "metadata": {},
       "png": 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dOHCg3eMjRoyo5EiIiFxP0X3ujUYjzp07hxYtWpTreoIgICsry+rYrVu3yh0fEVFFuUxP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\nKQAAAIyjlAIAAMC4/wcYTqLhkEMpCQAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x11e6d2990>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 336,
       "metadata": {},
       "text": "<ggplot: (299286513)>"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<hr>\n**Correlation of error terms:**\n\nOne of the assumptions of linear regression is that the error terms (residuals) are uncorrelated. Important indicators:`p-values` `standard errors` and `R^2` all depend on this assumption. Time series data often has correlated error terms, and there are many ways to deal with it.\n\nFor us, a simple plot of the residuals can reveal if there is any noticeable trend. These errors are fairly evenly distributed around 0, thats good. If they are not, this can often be remedied by transforming our dependent variable to a more normal distribution. However, sources of dependent error terms are often due to experimental design and data sources/collection. For example: a study of predicting individuals heights are predicted from weight could be skewed if many of the study members are of the same family, or are on the same diet."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "qplot(y=model2.resid, x=xrange(len(y)))+geom_point()+geom_smooth()",
     "prompt_number": 340,
     "outputs": [
      {
       "output_type": "display_data",
       "metadata": {},
       "png": 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CPWDAAHTr1g0JCQnQ6/VwdHTEjh07Gig6Yg0SiQT79+8XOgxi4/bs2YPk5GRkZWWhd+/e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\nFbrvhx9+qAYNGsjlcqlJkyaWz6GJ0sXFxWnLli3auHGjtm/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2ZWdnW1SNv8TERL+zfCXJ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\nAgAAwCj/Dwp9GkzAjzyQAAAAAElFTkSuQmCC\n",
       "text": "<matplotlib.figure.Figure at 0x11e6c0b50>"
      },
      {
       "output_type": "pyout",
       "prompt_number": 340,
       "metadata": {},
       "text": "<ggplot: (300335109)>"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<hr>\n**Outliers:**\n\nAn outlier is a any record whose predicted value is far-off from the observed value. Outliers often arise from incorrect data recording. There are many ways to identify outliers, and removing them from the model will often result in an improvement in predictive power and reduced error. However, we have to be careful to understand if a record is actually an outlier (error) or just a rare occurrence in the data, which we should not remove. Outliers can also indicate model deficiency; perhaps a missing predictor could account for the missing response."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "# Using stats models\nmodel.outlier_test()",
     "prompt_number": 344,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "**High Leverage Points:**\n\nLeverage points are unusual values in predictor variables, rather than response variables. Removing high leverage points often has a great effect on the model fit. Here is an influence plot of the advertising data model. This plot takes into account outliers and high leverage. We can see several points here that seem to deviate from the average influence, yet again it is up to our discretion if we choose to remove these points or not based on our knowledge of the data, and it's source."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "fig = sm.graphics.influence_plot(model2, criterion=\"cooks\")\nprint fig",
     "prompt_number": 365,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Figure(480x320)\n"
      },
      {
       "output_type": "display_data",
       "metadata": {},
       "png": 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MLKsQw4gCwOHYxMUXdy/nVWs0mvOJcmkYlStX5tChQwghSExMZPXq1cFzBw4c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cN1Hn646GCEs4nMzEySkpJISkoiNTUNj8dPWJiTBg3qEx8fT/369c9q01OwWD29zzImT55Mjx49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\nptmajIxY9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COPyKeffrpE557MGbnDWLJkCTfdpArx3XTTTSxatKjAmLVr19K8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\nSUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0x11eca4c50>"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "**Collinearity:**\n\nThis occurs when two or more predictors are closely related to each other. Collinearity will cause the standard error to grow, since it reduces the accuracy of the regression coefficients, which may cause us to improperly reject the null hypothesis (since the standard error effects the `t-value` and `p-value`). The probability of detecting a non-zero coefficient ( a relationship) is reduced by collinearity, thus we may not find a relationship that exists. Simply speaking, the importance of a variable may be missed due to collinearity.\n\nWe can test collinearity using a correlation matrix between the predictors, which we can use to eliminate variables within the model fitting process. If two variables are highly correlated, it is usual practise to remove the predictor with the lower R^2. However, **multicollinearity** exists when here is correlation between three or more variables. We use the `variance inflation factor` (VIF) to address this issue. This statistic shows us the ratio of the variation to the coefficients. The smallest value for VIF is 1, and as a rule of thumb, we should remove variables that have a VIF value  that exceeds 5.\n\nAn alternative solution is to combine the correlated variables into a single feature. For example, one could take the average standardized versions of two predictors in order to make a new index all together. The construction of this new variable is more of an art than a science, and will be explored in a future lesson."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "# Grab a few columns\ndata_to_check = df2.ix[:, 0:-4]\n# Check correlation and VIF\nprint data_to_check.corr()",
     "prompt_number": 82,
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "                   mpg  cylinders  displacement  horsepower    weight\nmpg           1.000000  -0.777618     -0.805127   -0.778427 -0.832244\ncylinders    -0.777618   1.000000      0.950823    0.842983  0.897527\ndisplacement -0.805127   0.950823      1.000000    0.897257  0.932994\nhorsepower   -0.778427   0.842983      0.897257    1.000000  0.864538\nweight       -0.832244   0.897527      0.932994    0.864538  1.000000\n\n[5 rows x 5 columns]\n"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "It turns out that VIF is not well implimented in python for basic OLS regression. I will update when it is properly supported in statsmodels or scikit learn."
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "from IPython.core.display import HTML\n\n\ndef css_styling():\n    styles = open(\"/users/ryankelly/desktop/custom_notebook.css\", \"r\").read()\n    return HTML(styles)\ncss_styling()",
     "prompt_number": 5,
     "outputs": [
      {
       "output_type": "pyout",
       "html": "\n<style>\nbody {\n    font-family: Century Gothic, sans;\n\n}\n\n\ndiv.text_cell_render h1 { /* Main titles bigger, centered */\nfont-size: 2.2em;\nline-height:1.4em;\ntext-align:center;\n}\n\n/*Input and output cells formatting*/\ndiv.prompt.input_prompt, div.prompt.output_prompt {\n    visibility: hidden;\n    /*font-family: Consolas;*/\n    color: #575748;\n    /*background-color: #CCCCCC;*/\n    border: 0px;\n    width: 6.5em;\n    float:left;\n}\n\n\ndiv.output_subarea.output_text.output_stream.output_stdout,div.output_subarea.output_text {\n    margin-left: 1.5em;\n    padding-top: 1em;\n    padding-bottom: 0.5em;\n    margin-top: 8px; /*This is for getting the box-shadow property of the parent to display properly;*/\n}\n\ndiv.cell { /* Tunes the space between cells */\nmargin-top:1em;\nmargin-bottom:1em;\nwidth:100%;\nmargin-right:auto;\noverflow-x:hidden;\n}\n\ndiv.text_cell_render{\n    overflow-x:hidden;\n      \n}\n\n\ndiv.input{\nmargin-right:1%;\n}\n\n</style>\n \n\n\n\n",
       "metadata": {},
       "prompt_number": 5,
       "text": "<IPython.core.display.HTML at 0x105cad5d0>"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "def social():\n    code = \"\"\"\n    <a style='float:left; margin-right:5px;' href=\"https://twitter.com/share\" class=\"twitter-share-button\" data-text=\"Check this out\" data-via=\"Ryanmdk\">Tweet</a>\n<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n    <a style='float:left; margin-right:5px;' href=\"https://twitter.com/Ryanmdk\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Ryanmdk</a>\n<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n    <a style='float:left; margin-right:5px;'target='_parent' href=\"http://www.reddit.com/submit\" onclick=\"window.location = 'http://www.reddit.com/submit?url=' + encodeURIComponent(window.location); return false\"> <img src=\"http://www.reddit.com/static/spreddit7.gif\" alt=\"submit to reddit\" border=\"0\" /> </a>\n<script src=\"//platform.linkedin.com/in.js\" type=\"text/javascript\">\n  lang: en_US\n</script>\n<script type=\"IN/Share\"></script>\n\"\"\"\n    return HTML(code)",
     "prompt_number": 3,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    }
   ],
   "metadata": {}
  }
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