2.1.8 - Preparing a data set for modeling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using a dataset of your choice, select an outcome variable and then pick four or five other variables (one to two categorical, three to four continuous) to act as the basis for features. Explore the variables using the univariate and bivariate methods you've learned so far.  \n",
    "\n",
    "### Next, based on what you learned via your data exploration, create ten new features. Explain the reasoning behind each one.  \n",
    "\n",
    "### Finally, use filtering methods to select the five best features and justify your choices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = (10.0, 5.0)\n",
    "plt.rcParams['font.size'] = (16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The chosen dataset are test scores for math, reading and writing along with some other student features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>race/ethnicity</th>\n",
       "      <th>parental level of education</th>\n",
       "      <th>lunch</th>\n",
       "      <th>test preparation course</th>\n",
       "      <th>math score</th>\n",
       "      <th>reading score</th>\n",
       "      <th>writing score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>female</td>\n",
       "      <td>group B</td>\n",
       "      <td>bachelor's degree</td>\n",
       "      <td>standard</td>\n",
       "      <td>none</td>\n",
       "      <td>72</td>\n",
       "      <td>72</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>female</td>\n",
       "      <td>group C</td>\n",
       "      <td>some college</td>\n",
       "      <td>standard</td>\n",
       "      <td>completed</td>\n",
       "      <td>69</td>\n",
       "      <td>90</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>female</td>\n",
       "      <td>group B</td>\n",
       "      <td>master's degree</td>\n",
       "      <td>standard</td>\n",
       "      <td>none</td>\n",
       "      <td>90</td>\n",
       "      <td>95</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>male</td>\n",
       "      <td>group A</td>\n",
       "      <td>associate's degree</td>\n",
       "      <td>free/reduced</td>\n",
       "      <td>none</td>\n",
       "      <td>47</td>\n",
       "      <td>57</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>male</td>\n",
       "      <td>group C</td>\n",
       "      <td>some college</td>\n",
       "      <td>standard</td>\n",
       "      <td>none</td>\n",
       "      <td>76</td>\n",
       "      <td>78</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   gender race/ethnicity parental level of education         lunch  \\\n",
       "0  female        group B           bachelor's degree      standard   \n",
       "1  female        group C                some college      standard   \n",
       "2  female        group B             master's degree      standard   \n",
       "3    male        group A          associate's degree  free/reduced   \n",
       "4    male        group C                some college      standard   \n",
       "\n",
       "  test preparation course  math score  reading score  writing score  \n",
       "0                    none          72             72             74  \n",
       "1               completed          69             90             88  \n",
       "2                    none          90             95             93  \n",
       "3                    none          47             57             44  \n",
       "4                    none          76             78             75  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import data into df_usd data frame\n",
    "df_scores = pd.read_csv('studentsperformance.csv')\n",
    "\n",
    "# print 1st 5 rows of df_usd (spot price)\n",
    "df_scores.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>race/ethnicity</th>\n",
       "      <th>parental level of education</th>\n",
       "      <th>lunch</th>\n",
       "      <th>test preparation course</th>\n",
       "      <th>math score</th>\n",
       "      <th>reading score</th>\n",
       "      <th>writing score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>female</td>\n",
       "      <td>group E</td>\n",
       "      <td>master's degree</td>\n",
       "      <td>standard</td>\n",
       "      <td>completed</td>\n",
       "      <td>88</td>\n",
       "      <td>99</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>male</td>\n",
       "      <td>group C</td>\n",
       "      <td>high school</td>\n",
       "      <td>free/reduced</td>\n",
       "      <td>none</td>\n",
       "      <td>62</td>\n",
       "      <td>55</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>female</td>\n",
       "      <td>group C</td>\n",
       "      <td>high school</td>\n",
       "      <td>free/reduced</td>\n",
       "      <td>completed</td>\n",
       "      <td>59</td>\n",
       "      <td>71</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>female</td>\n",
       "      <td>group D</td>\n",
       "      <td>some college</td>\n",
       "      <td>standard</td>\n",
       "      <td>completed</td>\n",
       "      <td>68</td>\n",
       "      <td>78</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>female</td>\n",
       "      <td>group D</td>\n",
       "      <td>some college</td>\n",
       "      <td>free/reduced</td>\n",
       "      <td>none</td>\n",
       "      <td>77</td>\n",
       "      <td>86</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     gender race/ethnicity parental level of education         lunch  \\\n",
       "995  female        group E             master's degree      standard   \n",
       "996    male        group C                 high school  free/reduced   \n",
       "997  female        group C                 high school  free/reduced   \n",
       "998  female        group D                some college      standard   \n",
       "999  female        group D                some college  free/reduced   \n",
       "\n",
       "    test preparation course  math score  reading score  writing score  \n",
       "995               completed          88             99             95  \n",
       "996                    none          62             55             55  \n",
       "997               completed          59             71             65  \n",
       "998               completed          68             78             77  \n",
       "999                    none          77             86             86  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scores.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Outcome Variable:  math score - Did the student get at least a C on the math score ?\n",
    "\n",
    "- Other variables:\n",
    "    - Categorical:\n",
    "        - gender\n",
    "        - race/ethnicity\n",
    "        - parent level of eduction\n",
    "        - lunch\n",
    "        - test preperation\n",
    "    - Discrete:\n",
    "        - reading score (ratio variable)\n",
    "        - writing score (ratio variable)\n",
    "    - Continuous:\n",
    "        - Any average for either of the 3 tests or average by gender, race, preparation, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring the data - Univariate:\n",
    "- How many variables do I have?\n",
    "    - 5 categorical and 3 continuous\n",
    "- How many datapoints?\n",
    "    - 1000 rows \n",
    "- Which variables are continuous (having an infinite number of possible values, such as age) and which are categorical (having a limited number of values, such as gender).\n",
    "    - (see above)\n",
    "- Do any of my variables have a known probability distribution (normal, Poisson, Gamma, etc)?\n",
    "    - all 3 continuous variables look like they have a normal probablity distribution. (see below)\n",
    "- Do I have missing data? If so, how much?\n",
    "    - no missing data\n",
    "- How much variance is there in each of my variables? If you’ve cleaned this dataset yourself, you’ll probably already know the answers to most of these questions.\n",
    "    - (see below for variances of each of the 3 continuous variables.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Making a three-panel plot.\n",
    "fig = plt.figure()\n",
    "\n",
    "fig.add_subplot(221)\n",
    "plt.hist(df_scores['math score'])\n",
    "plt.title('Math')\n",
    "plt.xlabel('Score')\n",
    "plt.ylabel('Number in each bin')\n",
    "\n",
    "fig.add_subplot(222)\n",
    "plt.hist(df_scores['reading score'])\n",
    "plt.title('Reading')\n",
    "plt.xlabel('Score')\n",
    "plt.ylabel('Number in each bin')\n",
    "\n",
    "plt.subplots_adjust(hspace=1.0, wspace=.5)\n",
    "\n",
    "fig.add_subplot(223)\n",
    "plt.hist(df_scores['writing score'])\n",
    "plt.title('Writing')\n",
    "plt.xlabel('Score')\n",
    "plt.ylabel('Number in each bin')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "math score       229.918998\n",
      "reading score    213.165605\n",
      "writing score    230.907992\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(df_scores.var(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "math score       15.163080\n",
      "reading score    14.600192\n",
      "writing score    15.195657\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(df_scores.std(axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring the data - Bivariate:\n",
    "- The scatterplot\n",
    "    - (see plots below)\n",
    "\n",
    "- The correlation coefficient\n",
    "    - r (math and reading) = **0.8175796636720539**\n",
    "    - r (math and writing) = **0.8026420459498083**\n",
    "    - r (reading and writitng) = **0.9545980771462479**\n",
    "    - (see below for calculations)\n",
    "- Look for: two-dimensional outliers that represent unusual combinations of values\n",
    "    - no significant outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Making a three-panel plot.\n",
    "fig = plt.figure()\n",
    "\n",
    "fig.add_subplot(221)\n",
    "plt.scatter(df_scores['math score'], df_scores['reading score'])\n",
    "plt.title('Math & Reading')\n",
    "plt.xlabel('Match Score')\n",
    "plt.ylabel('Reading Score')\n",
    "\n",
    "fig.add_subplot(222)\n",
    "plt.scatter(df_scores['math score'], df_scores['writing score'])\n",
    "plt.title('Math and Writing')\n",
    "plt.xlabel('Match Score')\n",
    "plt.ylabel('Reading Score')\n",
    "\n",
    "plt.subplots_adjust(hspace=1.2, wspace=.5)\n",
    "\n",
    "fig.add_subplot(223)\n",
    "plt.scatter(df_scores['reading score'], df_scores['writing score'])\n",
    "plt.title('Reading and Writing')\n",
    "plt.xlabel('Reading Score')\n",
    "plt.ylabel('Writing Score')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8175796636720539"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scores['math score'].corr(df_scores['reading score'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8026420459498083"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scores['math score'].corr(df_scores['writing score'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
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    "df_scores['reading score'].corr(df_scores['writing score'])"
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    "### 10 New Features\n",
    "- hair color\n",
    "    - categorical\n",
    "    - probably very little correlation\n",
    "- eye color\n",
    "    - categorical\n",
    "    - probably very little correlation\n",
    "- height\n",
    "    - categorical\n",
    "    - probably very little correlation\n",
    "- weight\n",
    "    - categorical\n",
    "    - probably very little correlation\n",
    "- all scores (math, reading, writing) in the prior year\n",
    "    - continuous - ratio\n",
    "    - these values would probably be highly correlated and highly predictive to current data\n",
    "- scores in other subjects such as history or chemistry\n",
    "    - continuous - ratio\n",
    "    - also would be highly correlated to scores in this dataset\n",
    "- income level of parents\n",
    "    - continuous - level\n",
    "    - may be correlated ---> possibly similar to comparison with 'lunch' data\n",
    "- brother or sister scores from years prior or the same year\n",
    "    - continuos - ratio\n",
    "    - probably highly correlated with this data since many other variable would be the same\n",
    "- do they have a tutor or have they had a tutor in the past\n",
    "    - categorical\n",
    "    - could be fairly correlated with scores data\n",
    "- number of times their parents helped them with their studies in the past year\n",
    "    - continuous - ratio\n",
    "    - probably correlated with scores\n",
    "- number of hours spent studying for the test\n",
    "    - continuous\n",
    "    - could be correlated with scores"
   ]
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    "### 5 Best Features - Scatterplots and r calculation could be use for all of these to justify. \n",
    "1.  Scores in other subjects. \n",
    "    - we know from the scatterplots that scores from one subject to the next are highly correlated.\n",
    "2.  Scores in previous year. \n",
    "    - Same student and most if not all of the same variables.\n",
    "3.  Scores in other subjects such as history or chemistry.\n",
    "    - Most likely, a good student in one subject will be a good student in another subject.\n",
    "4.  Number of hours spend studyting for the test.\n",
    "    - Not only would this activity likely yield better results, it also shows motivation and discipline.\n",
    "5.  Number of times parents helped with studies in past year.\n",
    "    - This shows parental support which is probably important."
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": []
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