Active.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gender Imbalance in STEM Majors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fernando Mazzoni\n",
    "## June 5th 2018"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Background"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using \"Bachelors’ Degrees by Major and Sex, Massachusetts, 2015-2016\"\n",
    "by The National Center for Education Statistics , the following journal shows the sex distribution of Massachusetts college students in stem fields "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Dataset = pd.read_csv(\"bachelors_major_ma_2015_16.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UnitID</th>\n",
       "      <th>Institution Name</th>\n",
       "      <th>City location of institution (HD2015)</th>\n",
       "      <th>Institution open to the general public (HD2015)</th>\n",
       "      <th>Applicants total (ADM2015_RV)</th>\n",
       "      <th>Admissions total (ADM2015_RV)</th>\n",
       "      <th>Enrolled total (ADM2015_RV)</th>\n",
       "      <th>Unnamed: 7</th>\n",
       "      <th>Grand total (C2016_A  First major  Agriculture  Agriculture Operations and Related Sciences  Bachelor's degree)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Agriculture  Agriculture Operations and Related Sciences  Bachelor's degree)</th>\n",
       "      <th>...</th>\n",
       "      <th>Grand total women (C2016_A  First major  Health Professions and Related Programs  Bachelor's degree)</th>\n",
       "      <th>Grand total (C2016_A  First major  Business  Management  Marketing  and Related Support Services  Bachelor's degree)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Business  Management  Marketing  and Related Support Services  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  Business  Management  Marketing  and Related Support Services  Bachelor's degree)</th>\n",
       "      <th>Grand total (C2016_A  First major  History  Bachelor's degree)</th>\n",
       "      <th>Grand total men (C2016_A  First major  History  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  History  Bachelor's degree)</th>\n",
       "      <th>Grand total (C2016_A  First major  Grand total  Bachelor's degree)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Grand total  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  Grand total  Bachelor's degree)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>419147</td>\n",
       "      <td>Ailano School of Cosmetology</td>\n",
       "      <td>Brockton</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>476735</td>\n",
       "      <td>Alexander Academy</td>\n",
       "      <td>Fitchburg</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>487144</td>\n",
       "      <td>American Academy of Personal Training-Boston C...</td>\n",
       "      <td>Boston</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>164447</td>\n",
       "      <td>American International College</td>\n",
       "      <td>Springfield</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2060.0</td>\n",
       "      <td>1301.0</td>\n",
       "      <td>355.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>85.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>279.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>168.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>164465</td>\n",
       "      <td>Amherst College</td>\n",
       "      <td>Amherst</td>\n",
       "      <td>1.0</td>\n",
       "      <td>8568.0</td>\n",
       "      <td>1210.0</td>\n",
       "      <td>477.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>29.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>432.0</td>\n",
       "      <td>224.0</td>\n",
       "      <td>208.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 125 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   UnitID                                   Institution Name  \\\n",
       "0  419147                       Ailano School of Cosmetology   \n",
       "1  476735                                  Alexander Academy   \n",
       "2  487144  American Academy of Personal Training-Boston C...   \n",
       "3  164447                     American International College   \n",
       "4  164465                                    Amherst College   \n",
       "\n",
       "  City location of institution (HD2015)  \\\n",
       "0                              Brockton   \n",
       "1                             Fitchburg   \n",
       "2                                Boston   \n",
       "3                           Springfield   \n",
       "4                               Amherst   \n",
       "\n",
       "   Institution open to the general public (HD2015)  \\\n",
       "0                                              1.0   \n",
       "1                                              1.0   \n",
       "2                                              1.0   \n",
       "3                                              1.0   \n",
       "4                                              1.0   \n",
       "\n",
       "   Applicants total (ADM2015_RV)  Admissions total (ADM2015_RV)  \\\n",
       "0                            NaN                            NaN   \n",
       "1                            NaN                            NaN   \n",
       "2                            NaN                            NaN   \n",
       "3                         2060.0                         1301.0   \n",
       "4                         8568.0                         1210.0   \n",
       "\n",
       "   Enrolled total (ADM2015_RV)  Unnamed: 7  \\\n",
       "0                          NaN         NaN   \n",
       "1                          NaN         NaN   \n",
       "2                          NaN         NaN   \n",
       "3                        355.0         NaN   \n",
       "4                        477.0         NaN   \n",
       "\n",
       "   Grand total (C2016_A  First major  Agriculture  Agriculture Operations and Related Sciences  Bachelor's degree)  \\\n",
       "0                                                NaN                                                                 \n",
       "1                                                NaN                                                                 \n",
       "2                                                NaN                                                                 \n",
       "3                                                NaN                                                                 \n",
       "4                                                NaN                                                                 \n",
       "\n",
       "   Grand total men (C2016_A  First major  Agriculture  Agriculture Operations and Related Sciences  Bachelor's degree)  \\\n",
       "0                                                NaN                                                                     \n",
       "1                                                NaN                                                                     \n",
       "2                                                NaN                                                                     \n",
       "3                                                NaN                                                                     \n",
       "4                                                NaN                                                                     \n",
       "\n",
       "                                     ...                                     \\\n",
       "0                                    ...                                      \n",
       "1                                    ...                                      \n",
       "2                                    ...                                      \n",
       "3                                    ...                                      \n",
       "4                                    ...                                      \n",
       "\n",
       "   Grand total women (C2016_A  First major  Health Professions and Related Programs  Bachelor's degree)  \\\n",
       "0                                                NaN                                                      \n",
       "1                                                NaN                                                      \n",
       "2                                                NaN                                                      \n",
       "3                                               85.0                                                      \n",
       "4                                                NaN                                                      \n",
       "\n",
       "   Grand total (C2016_A  First major  Business  Management  Marketing  and Related Support Services  Bachelor's degree)  \\\n",
       "0                                                NaN                                                                      \n",
       "1                                                NaN                                                                      \n",
       "2                                                NaN                                                                      \n",
       "3                                               45.0                                                                      \n",
       "4                                                NaN                                                                      \n",
       "\n",
       "   Grand total men (C2016_A  First major  Business  Management  Marketing  and Related Support Services  Bachelor's degree)  \\\n",
       "0                                                NaN                                                                          \n",
       "1                                                NaN                                                                          \n",
       "2                                                NaN                                                                          \n",
       "3                                               33.0                                                                          \n",
       "4                                                NaN                                                                          \n",
       "\n",
       "   Grand total women (C2016_A  First major  Business  Management  Marketing  and Related Support Services  Bachelor's degree)  \\\n",
       "0                                                NaN                                                                            \n",
       "1                                                NaN                                                                            \n",
       "2                                                NaN                                                                            \n",
       "3                                               12.0                                                                            \n",
       "4                                                NaN                                                                            \n",
       "\n",
       "   Grand total (C2016_A  First major  History  Bachelor's degree)  \\\n",
       "0                                                NaN                \n",
       "1                                                NaN                \n",
       "2                                                NaN                \n",
       "3                                                3.0                \n",
       "4                                               29.0                \n",
       "\n",
       "   Grand total men (C2016_A  First major  History  Bachelor's degree)  \\\n",
       "0                                                NaN                    \n",
       "1                                                NaN                    \n",
       "2                                                NaN                    \n",
       "3                                                3.0                    \n",
       "4                                               17.0                    \n",
       "\n",
       "   Grand total women (C2016_A  First major  History  Bachelor's degree)  \\\n",
       "0                                                NaN                      \n",
       "1                                                NaN                      \n",
       "2                                                NaN                      \n",
       "3                                                0.0                      \n",
       "4                                               12.0                      \n",
       "\n",
       "   Grand total (C2016_A  First major  Grand total  Bachelor's degree)  \\\n",
       "0                                                NaN                    \n",
       "1                                                NaN                    \n",
       "2                                                NaN                    \n",
       "3                                              279.0                    \n",
       "4                                              432.0                    \n",
       "\n",
       "   Grand total men (C2016_A  First major  Grand total  Bachelor's degree)  \\\n",
       "0                                                NaN                        \n",
       "1                                                NaN                        \n",
       "2                                                NaN                        \n",
       "3                                              111.0                        \n",
       "4                                              224.0                        \n",
       "\n",
       "   Grand total women (C2016_A  First major  Grand total  Bachelor's degree)  \n",
       "0                                                NaN                         \n",
       "1                                                NaN                         \n",
       "2                                                NaN                         \n",
       "3                                              168.0                         \n",
       "4                                              208.0                         \n",
       "\n",
       "[5 rows x 125 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dataset[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Particulary Engineering, Physical Sciences, and Math majors are sampled in this journal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Enrolled total (ADM2015_RV)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Engineering  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  Engineering  Bachelor's degree)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Physical Sciences  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  Physical Sciences  Bachelor's degree)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.00000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1550.687500</td>\n",
       "      <td>164.312500</td>\n",
       "      <td>63.000000</td>\n",
       "      <td>22.62500</td>\n",
       "      <td>16.125000</td>\n",
       "      <td>26.062500</td>\n",
       "      <td>14.875000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1226.493306</td>\n",
       "      <td>175.746681</td>\n",
       "      <td>73.965758</td>\n",
       "      <td>23.38625</td>\n",
       "      <td>13.744696</td>\n",
       "      <td>34.607261</td>\n",
       "      <td>16.280356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>114.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>800.750000</td>\n",
       "      <td>14.500000</td>\n",
       "      <td>3.750000</td>\n",
       "      <td>6.00000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1347.000000</td>\n",
       "      <td>103.000000</td>\n",
       "      <td>35.000000</td>\n",
       "      <td>15.00000</td>\n",
       "      <td>11.500000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>10.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1665.000000</td>\n",
       "      <td>294.000000</td>\n",
       "      <td>80.750000</td>\n",
       "      <td>31.75000</td>\n",
       "      <td>28.250000</td>\n",
       "      <td>31.500000</td>\n",
       "      <td>14.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4702.000000</td>\n",
       "      <td>519.000000</td>\n",
       "      <td>232.000000</td>\n",
       "      <td>76.00000</td>\n",
       "      <td>39.000000</td>\n",
       "      <td>125.000000</td>\n",
       "      <td>57.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Enrolled total (ADM2015_RV)  \\\n",
       "count                    16.000000   \n",
       "mean                   1550.687500   \n",
       "std                    1226.493306   \n",
       "min                     114.000000   \n",
       "25%                     800.750000   \n",
       "50%                    1347.000000   \n",
       "75%                    1665.000000   \n",
       "max                    4702.000000   \n",
       "\n",
       "       Grand total men (C2016_A  First major  Engineering  Bachelor's degree)  \\\n",
       "count                                          16.000000                        \n",
       "mean                                          164.312500                        \n",
       "std                                           175.746681                        \n",
       "min                                             0.000000                        \n",
       "25%                                            14.500000                        \n",
       "50%                                           103.000000                        \n",
       "75%                                           294.000000                        \n",
       "max                                           519.000000                        \n",
       "\n",
       "       Grand total women (C2016_A  First major  Engineering  Bachelor's degree)  \\\n",
       "count                                          16.000000                          \n",
       "mean                                           63.000000                          \n",
       "std                                            73.965758                          \n",
       "min                                             0.000000                          \n",
       "25%                                             3.750000                          \n",
       "50%                                            35.000000                          \n",
       "75%                                            80.750000                          \n",
       "max                                           232.000000                          \n",
       "\n",
       "       Grand total men (C2016_A  First major  Physical Sciences  Bachelor's degree)  \\\n",
       "count                                           16.00000                              \n",
       "mean                                            22.62500                              \n",
       "std                                             23.38625                              \n",
       "min                                              0.00000                              \n",
       "25%                                              6.00000                              \n",
       "50%                                             15.00000                              \n",
       "75%                                             31.75000                              \n",
       "max                                             76.00000                              \n",
       "\n",
       "       Grand total women (C2016_A  First major  Physical Sciences  Bachelor's degree)  \\\n",
       "count                                          16.000000                                \n",
       "mean                                           16.125000                                \n",
       "std                                            13.744696                                \n",
       "min                                             0.000000                                \n",
       "25%                                             6.000000                                \n",
       "50%                                            11.500000                                \n",
       "75%                                            28.250000                                \n",
       "max                                            39.000000                                \n",
       "\n",
       "       Grand total men (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)  \\\n",
       "count                                          16.000000                                       \n",
       "mean                                           26.062500                                       \n",
       "std                                            34.607261                                       \n",
       "min                                             0.000000                                       \n",
       "25%                                             3.000000                                       \n",
       "50%                                            12.000000                                       \n",
       "75%                                            31.500000                                       \n",
       "max                                           125.000000                                       \n",
       "\n",
       "       Grand total women (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)  \n",
       "count                                          16.000000                                        \n",
       "mean                                           14.875000                                        \n",
       "std                                            16.280356                                        \n",
       "min                                             0.000000                                        \n",
       "25%                                             4.500000                                        \n",
       "50%                                            10.000000                                        \n",
       "75%                                            14.750000                                        \n",
       "max                                            57.000000                                        "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Major = Dataset[['Institution Name','Enrolled total (ADM2015_RV)',\"Grand total men (C2016_A  First major  Engineering  Bachelor's degree)\",\"Grand total women (C2016_A  First major  Engineering  Bachelor's degree)\",\"Grand total men (C2016_A  First major  Physical Sciences  Bachelor's degree)\",\"Grand total women (C2016_A  First major  Physical Sciences  Bachelor's degree)\", \"Grand total men (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)\",\"Grand total women (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)\"]]\n",
    "Major = Major.dropna()\n",
    "\n",
    "Major.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[\"Bard College at Simon's Rock\" 117.0 3.0 1.0 1.0 1.0 3.0 2.0]\n",
      " ['Boston University' 3629.0 276.0 101.0 43.0 33.0 57.0 41.0]\n",
      " ['Eastern Nazarene College' 114.0 4.0 0.0 1.0 0.0 0.0 1.0]\n",
      " ['Harvard University' 1660.0 40.0 37.0 62.0 27.0 125.0 57.0]\n",
      " ['Massachusetts Institute of Technology' 1106.0 236.0 232.0 50.0 36.0 58.0\n",
      "  14.0]\n",
      " ['Merrimack College' 828.0 24.0 3.0 3.0 1.0 3.0 10.0]\n",
      " ['Northeastern University' 2797.0 519.0 148.0 28.0 24.0 23.0 17.0]\n",
      " ['Smith College' 609.0 0.0 33.0 0.0 39.0 0.0 12.0]\n",
      " ['Suffolk University' 1334.0 17.0 4.0 8.0 3.0 3.0 0.0]\n",
      " ['Tufts University' 1360.0 110.0 60.0 22.0 14.0 13.0 10.0]\n",
      " ['University of Massachusetts-Amherst' 4702.0 388.0 74.0 76.0 32.0 70.0\n",
      "  38.0]\n",
      " ['University of Massachusetts-Boston' 1680.0 7.0 1.0 18.0 7.0 11.0 9.0]\n",
      " ['University of Massachusetts-Dartmouth' 1430.0 137.0 23.0 9.0 9.0 11.0\n",
      "  5.0]\n",
      " ['University of Massachusetts-Lowell' 1633.0 348.0 62.0 22.0 18.0 20.0 7.0]\n",
      " ['Western New England University' 719.0 96.0 21.0 7.0 7.0 2.0 3.0]\n",
      " ['Worcester Polytechnic Institute' 1093.0 424.0 208.0 12.0 7.0 18.0 12.0]]\n"
     ]
    }
   ],
   "source": [
    "unis = Major[0 :1]\n",
    "for x in range(len(Major)):\n",
    "    unis = np.vstack((unis , Major[x+1 :(x+2 )] ))\n",
    "\n",
    "print(unis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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cSe7nMDOro0oSxGnAWmCIbAC/7wAfmGyjiPgJcH+FcRwJXBoRGyLij8BtwHMr3NbMrGUU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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cbd552b978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#first trial\n",
    "\n",
    "for i in range(len(unis[:,1])):\n",
    "    name = (unis[i,0])\n",
    "    enroll = (unis[i,1])\n",
    "   \n",
    "    m_engin = (unis[i,2])\n",
    "    w_engin =(unis[i,3])\n",
    "    \n",
    "    m_phys = (unis[i,4])\n",
    "    w_phys =(unis[i,5])\n",
    "    \n",
    "    m_math = (unis[i,6])\n",
    "    w_math = (unis[i,7])\n",
    "    \n",
    "    plt.plot(m_engin, w_engin , color='green', marker='o')\n",
    "    plt.plot(m_phys,w_phys , color='blue', marker='o')\n",
    "    plt.plot(m_math, w_math , color='black', marker='o')\n",
    "    \n",
    "plt.title(\"Sex distribution in a given college\")\n",
    "plt.xlabel('# of male students')\n",
    "plt.ylabel('# of female students')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 'null hypothisis' is that women and men are present in the stem field equally. To test this out I plotted and gathered the statistics of each major."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing the  Null Hypothosis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To constrain the dataset to just the majors of interest and remove any NaNs, I did the following"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Institution Name</th>\n",
       "      <th>Enrolled total (ADM2015_RV)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Engineering  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  Engineering  Bachelor's degree)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Physical Sciences  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  Physical Sciences  Bachelor's degree)</th>\n",
       "      <th>Grand total men (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)</th>\n",
       "      <th>Grand total women (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Bard College at Simon's Rock</td>\n",
       "      <td>117.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>Boston University</td>\n",
       "      <td>3629.0</td>\n",
       "      <td>276.0</td>\n",
       "      <td>101.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>Eastern Nazarene College</td>\n",
       "      <td>114.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>Harvard University</td>\n",
       "      <td>1660.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>62.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>125.0</td>\n",
       "      <td>57.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>Massachusetts Institute of Technology</td>\n",
       "      <td>1106.0</td>\n",
       "      <td>236.0</td>\n",
       "      <td>232.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         Institution Name  Enrolled total (ADM2015_RV)  \\\n",
       "11           Bard College at Simon's Rock                        117.0   \n",
       "28                      Boston University                       3629.0   \n",
       "47               Eastern Nazarene College                        114.0   \n",
       "68                     Harvard University                       1660.0   \n",
       "96  Massachusetts Institute of Technology                       1106.0   \n",
       "\n",
       "    Grand total men (C2016_A  First major  Engineering  Bachelor's degree)  \\\n",
       "11                                                3.0                        \n",
       "28                                              276.0                        \n",
       "47                                                4.0                        \n",
       "68                                               40.0                        \n",
       "96                                              236.0                        \n",
       "\n",
       "    Grand total women (C2016_A  First major  Engineering  Bachelor's degree)  \\\n",
       "11                                                1.0                          \n",
       "28                                              101.0                          \n",
       "47                                                0.0                          \n",
       "68                                               37.0                          \n",
       "96                                              232.0                          \n",
       "\n",
       "    Grand total men (C2016_A  First major  Physical Sciences  Bachelor's degree)  \\\n",
       "11                                                1.0                              \n",
       "28                                               43.0                              \n",
       "47                                                1.0                              \n",
       "68                                               62.0                              \n",
       "96                                               50.0                              \n",
       "\n",
       "    Grand total women (C2016_A  First major  Physical Sciences  Bachelor's degree)  \\\n",
       "11                                                1.0                                \n",
       "28                                               33.0                                \n",
       "47                                                0.0                                \n",
       "68                                               27.0                                \n",
       "96                                               36.0                                \n",
       "\n",
       "    Grand total men (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)  \\\n",
       "11                                                3.0                                       \n",
       "28                                               57.0                                       \n",
       "47                                                0.0                                       \n",
       "68                                              125.0                                       \n",
       "96                                               58.0                                       \n",
       "\n",
       "    Grand total women (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)  \n",
       "11                                                2.0                                        \n",
       "28                                               41.0                                        \n",
       "47                                                1.0                                        \n",
       "68                                               57.0                                        \n",
       "96                                               14.0                                        "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Major = Dataset[['Institution Name','Enrolled total (ADM2015_RV)',\"Grand total men (C2016_A  First major  Engineering  Bachelor's degree)\",\"Grand total women (C2016_A  First major  Engineering  Bachelor's degree)\",\"Grand total men (C2016_A  First major  Physical Sciences  Bachelor's degree)\",\"Grand total women (C2016_A  First major  Physical Sciences  Bachelor's degree)\", \"Grand total men (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)\",\"Grand total women (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)\"]]\n",
    "Major = Major.dropna()\n",
    "\n",
    "Major.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Engineer Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data is then further constrained to just Men Engineering Majors and to just Women engineering Majors. To see if there is a linear relationship between the # of Men and Women engineering Majors a regression fit was performed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ferna\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1334: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=16\n",
      "  \"anyway, n=%i\" % int(n))\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>d_w_engin</td>    <th>  R-squared:         </th> <td>   0.558</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.527</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   17.69</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 07 Jun 2018</td> <th>  Prob (F-statistic):</th> <td>0.000880</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:45:28</td>     <th>  Log-Likelihood:    </th> <td> -84.508</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    16</td>      <th>  AIC:               </th> <td>   173.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    14</td>      <th>  BIC:               </th> <td>   174.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   11.3304</td> <td>   17.684</td> <td>    0.641</td> <td> 0.532</td> <td>  -26.598</td> <td>   49.259</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>d_m_engin</th> <td>    0.3145</td> <td>    0.075</td> <td>    4.206</td> <td> 0.001</td> <td>    0.154</td> <td>    0.475</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>16.156</td> <th>  Durbin-Watson:     </th> <td>   1.841</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  14.172</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.698</td> <th>  Prob(JB):          </th> <td>0.000837</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.119</td> <th>  Cond. No.          </th> <td>    329.</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:              d_w_engin   R-squared:                       0.558\n",
       "Model:                            OLS   Adj. R-squared:                  0.527\n",
       "Method:                 Least Squares   F-statistic:                     17.69\n",
       "Date:                Thu, 07 Jun 2018   Prob (F-statistic):           0.000880\n",
       "Time:                        11:45:28   Log-Likelihood:                -84.508\n",
       "No. Observations:                  16   AIC:                             173.0\n",
       "Df Residuals:                      14   BIC:                             174.6\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     11.3304     17.684      0.641      0.532     -26.598      49.259\n",
       "d_m_engin      0.3145      0.075      4.206      0.001       0.154       0.475\n",
       "==============================================================================\n",
       "Omnibus:                       16.156   Durbin-Watson:                   1.841\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               14.172\n",
       "Skew:                           1.698   Prob(JB):                     0.000837\n",
       "Kurtosis:                       6.119   Cond. No.                         329.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_m_engin = Major[\"Grand total men (C2016_A  First major  Engineering  Bachelor's degree)\"]\n",
    "d_w_engin = Major[\"Grand total women (C2016_A  First major  Engineering  Bachelor's degree)\"]\n",
    "\n",
    "\n",
    "engin_model = smf.ols(formula = 'd_w_engin ~ d_m_engin', data = Major)\n",
    "\n",
    "est = engin_model.fit()\n",
    "est.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following shows a plot of Engineering  Men v. Women Majors. Shown in black is the expected trend if there was an equal # of Male and Female students. Shown in red is the trend for engineering majors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zJkeBJIh/4IzM2ktVd+Hc4TwyqFEZE2LWrl3LlVdeySOPPMKtt97K6tWr6dq1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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cbd552b048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(d_m_engin, d_w_engin, color='green', marker='o')\n",
    "plt.title(\"Sex distribution in a given college (Engineering)\")\n",
    "plt.xlabel('# of male students')\n",
    "plt.ylabel('# of female students')\n",
    "\n",
    "o_x = np.linspace(0,500,100) # 100 linearly spaced numbers\n",
    "o_y = 11.3304 + 0.3145*o_x\n",
    "plt.plot(o_x , o_y, color = 'red')\n",
    "\n",
    "\n",
    "p_x = o_x\n",
    "plt.plot(p_x , p_x, color = 'black')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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V2ZKk0TmkI0k9YeBLUk8Y+JLUEwa+JPWEgS9JPWHgS1JPGPiS1BMGviT1hIEvST1h4EtS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\nhIEvST1h4EtSTxj4ktQTBr4k9cT/B/xzd5Dq/E4nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cbd5499f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(d_m_engin, color = 'blue')\n",
    "plt.hist(d_w_engin, color = 'red')\n",
    "#plt.axvline(x=-1.96, color = 'r')\n",
    "#plt.axvline(x=1.96, color = 'r')\n",
    "plt.xlabel('# of students')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The statistics can be obtained and then used to see if the null hypothesis is a valid model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample difference: 101.3125\n",
      "Expected population difference: 0\n",
      "Standard Error: 46.1556231973\n",
      "Z =  2.19501965268\n"
     ]
    }
   ],
   "source": [
    "n_obs = len(d_w_engin)\n",
    "\n",
    "\n",
    "mean_w = np.mean(d_w_engin)\n",
    "std_w = np.std(d_w_engin)\n",
    "\n",
    "\n",
    "mean_m =  np.mean(d_m_engin)\n",
    "std_m = np.std(d_m_engin)\n",
    "\n",
    "\n",
    "obs_diff = np.abs( mean_w - mean_m )\n",
    "\n",
    "# Expected difference is that there is no difference\n",
    "#(testing null hypothesis)\n",
    "exp_diff = 0\n",
    "\n",
    "\n",
    "#vng = (sd_g**2/n_g)\n",
    "#vnb = (sd_b**2/n_b)\n",
    "std_err = np.sqrt( ((std_w**2)/n_obs) + ((std_m**2)/n_obs)   )\n",
    "\n",
    "z = (obs_diff - exp_diff)/std_err\n",
    "\n",
    "#print(mean_w)\n",
    "print('Sample difference:' , obs_diff)\n",
    "print('Expected population difference:' , exp_diff)\n",
    "print('Standard Error:' , std_err)\n",
    "print('Z = ' , z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same can then be performed for the physcial sciences and Math majors. It seems like a function could have been made to more quickly obtain the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Physical Sciences Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ferna\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1334: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=16\n",
      "  \"anyway, n=%i\" % int(n))\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>d_w_phys</td>     <th>  R-squared:         </th> <td>   0.449</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.410</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   11.42</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 07 Jun 2018</td> <th>  Prob (F-statistic):</th>  <td>0.00449</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:47:20</td>     <th>  Log-Likelihood:    </th> <td> -59.345</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    16</td>      <th>  AIC:               </th> <td>   122.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    14</td>      <th>  BIC:               </th> <td>   124.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    7.2122</td> <td>    3.731</td> <td>    1.933</td> <td> 0.074</td> <td>   -0.791</td> <td>   15.215</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>d_m_phys</th>  <td>    0.3939</td> <td>    0.117</td> <td>    3.379</td> <td> 0.004</td> <td>    0.144</td> <td>    0.644</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>20.491</td> <th>  Durbin-Watson:     </th> <td>   2.232</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  21.263</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 2.040</td> <th>  Prob(JB):          </th> <td>2.41e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.904</td> <th>  Cond. No.          </th> <td>    45.3</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               d_w_phys   R-squared:                       0.449\n",
       "Model:                            OLS   Adj. R-squared:                  0.410\n",
       "Method:                 Least Squares   F-statistic:                     11.42\n",
       "Date:                Thu, 07 Jun 2018   Prob (F-statistic):            0.00449\n",
       "Time:                        11:47:20   Log-Likelihood:                -59.345\n",
       "No. Observations:                  16   AIC:                             122.7\n",
       "Df Residuals:                      14   BIC:                             124.2\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      7.2122      3.731      1.933      0.074      -0.791      15.215\n",
       "d_m_phys       0.3939      0.117      3.379      0.004       0.144       0.644\n",
       "==============================================================================\n",
       "Omnibus:                       20.491   Durbin-Watson:                   2.232\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               21.263\n",
       "Skew:                           2.040   Prob(JB):                     2.41e-05\n",
       "Kurtosis:                       6.904   Cond. No.                         45.3\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_m_phys = Major[\"Grand total men (C2016_A  First major  Physical Sciences  Bachelor's degree)\"]\n",
    "d_w_phys = Major[\"Grand total women (C2016_A  First major  Physical Sciences  Bachelor's degree)\"]\n",
    "\n",
    "\n",
    "phys_model = smf.ols(formula = 'd_w_phys ~ d_m_phys', data = Major)\n",
    "\n",
    "est = phys_model.fit()\n",
    "est.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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06dOHRx55hA0bNtC0aVNLAiYkgkkEZ/RH825MUys04RiTux05coROnTpx4403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\ngTHG5HL/D/kXX5TjXmlxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cbd5460ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ln_inc_edu = plt.figure()\n",
    "plt.scatter(d_m_phys, d_w_phys, color='Blue', marker='o')\n",
    "plt.title(\"Sex distribution in a given college (Physical Sciences)\")\n",
    "plt.xlabel('# of male students')\n",
    "plt.ylabel('# of female students')\n",
    "\n",
    "o_x = np.linspace(0,80,100) # 100 linearly spaced numbers\n",
    "o_y = 7.2122 + 0.3939*o_x\n",
    "plt.plot(o_x , o_y, color = 'red')\n",
    "\n",
    "\n",
    "p_x = o_x\n",
    "plt.plot(p_x , p_x, color = 'black')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cbd5460550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(d_m_phys, color = 'blue')\n",
    "plt.hist(d_w_phys, color = 'red')\n",
    "#plt.axvline(x=-1.96, color = 'r')\n",
    "#plt.axvline(x=1.96, color = 'r')\n",
    "plt.title('Distribution')\n",
    "plt.xlabel('# of students')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample difference: 6.5\n",
      "Expected population difference: 0\n",
      "Standard Error: 6.5662191842\n",
      "Z =  0.989915173048\n"
     ]
    }
   ],
   "source": [
    "n_obs = len(d_w_engin)\n",
    "\n",
    "\n",
    "mean_w = np.mean(d_w_phys)\n",
    "std_w = np.std(d_w_phys)\n",
    "\n",
    "\n",
    "mean_m =  np.mean(d_m_phys)\n",
    "std_m = np.std(d_m_phys)\n",
    "\n",
    "\n",
    "obs_diff = np.abs( mean_w - mean_m )\n",
    "\n",
    "# Expected difference is that there is no difference\n",
    "#(testing null hypothesis)\n",
    "exp_diff = 0\n",
    "\n",
    "\n",
    "#vng = (sd_g**2/n_g)\n",
    "#vnb = (sd_b**2/n_b)\n",
    "std_err = np.sqrt( ((std_w**2)/n_obs) + ((std_m**2)/n_obs)   )\n",
    "\n",
    "z = (obs_diff - exp_diff)/std_err\n",
    "\n",
    "\n",
    "print('Sample difference:' , obs_diff)\n",
    "print('Expected population difference:' , exp_diff)\n",
    "print('Standard Error:' , std_err)\n",
    "print('Z = ' , z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Math Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ferna\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1334: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=16\n",
      "  \"anyway, n=%i\" % int(n))\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>d_w_math</td>     <th>  R-squared:         </th> <td>   0.853</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.842</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   81.05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 07 Jun 2018</td> <th>  Prob (F-statistic):</th> <td>3.37e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:45:36</td>     <th>  Log-Likelihood:    </th> <td> -51.503</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    16</td>      <th>  AIC:               </th> <td>   107.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    14</td>      <th>  BIC:               </th> <td>   108.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    3.5532</td> <td>    2.048</td> <td>    1.735</td> <td> 0.105</td> <td>   -0.840</td> <td>    7.946</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>d_m_math</th>  <td>    0.4344</td> <td>    0.048</td> <td>    9.003</td> <td> 0.000</td> <td>    0.331</td> <td>    0.538</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.127</td> <th>  Durbin-Watson:     </th> <td>   2.327</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.345</td> <th>  Jarque-Bera (JB):  </th> <td>   0.496</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.186</td> <th>  Prob(JB):          </th> <td>   0.780</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.778</td> <th>  Cond. No.          </th> <td>    53.8</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               d_w_math   R-squared:                       0.853\n",
       "Model:                            OLS   Adj. R-squared:                  0.842\n",
       "Method:                 Least Squares   F-statistic:                     81.05\n",
       "Date:                Thu, 07 Jun 2018   Prob (F-statistic):           3.37e-07\n",
       "Time:                        11:45:36   Log-Likelihood:                -51.503\n",
       "No. Observations:                  16   AIC:                             107.0\n",
       "Df Residuals:                      14   BIC:                             108.6\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      3.5532      2.048      1.735      0.105      -0.840       7.946\n",
       "d_m_math       0.4344      0.048      9.003      0.000       0.331       0.538\n",
       "==============================================================================\n",
       "Omnibus:                        2.127   Durbin-Watson:                   2.327\n",
       "Prob(Omnibus):                  0.345   Jarque-Bera (JB):                0.496\n",
       "Skew:                          -0.186   Prob(JB):                        0.780\n",
       "Kurtosis:                       3.778   Cond. No.                         53.8\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_m_math = Major[\"Grand total men (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)\"]\n",
    "d_w_math = Major[\"Grand total women (C2016_A  First major  Mathematics and Statistics  Bachelor's degree)\"]\n",
    "\n",
    "\n",
    "math_model = smf.ols(formula = 'd_w_math ~ d_m_math', data = Major)\n",
    "\n",
    "est = math_model.fit()\n",
    "est.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9ejTVq1f3O6zCQxXWr88YDXXhQtdyqFgxo8B8yy1WYDYRwxKEyZGq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\nxhhjgvr/Dze/BQb++RQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cbd5720da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ln_inc_edu = plt.figure()\n",
    "plt.scatter(d_m_math, d_w_math, color='black', marker='o')\n",
    "plt.title(\"Sex distribution in a given college (Math)\")\n",
    "plt.xlabel('# of male students')\n",
    "plt.ylabel('# of female students')\n",
    "\n",
    "o_x = np.linspace(0,120,100) # 100 linearly spaced numbers\n",
    "o_y = 3.5532 + 0.4344*o_x\n",
    "plt.plot(o_x , o_y, color = 'red')\n",
    "\n",
    "\n",
    "p_x = o_x\n",
    "plt.plot(p_x , p_x, color = 'black')\n",
    "\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UEwa+JPWEgS9JPWHgS1JPGPiS1BMGviT1hIEvST3R5Zy2pya5K8k1XbUhSRpcl1f4pwGH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\n8f8BnbVKWXq+PKcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1cbd5820a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(d_m_math, color = 'blue')\n",
    "plt.hist(d_w_math, color = 'red')\n",
    "#plt.axvline(x=-1.96, color = 'r')\n",
    "#plt.axvline(x=1.96, color = 'r')\n",
    "plt.title('Distribution')\n",
    "plt.xlabel('# of students')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample difference: 11.1875\n",
      "Expected population difference: 0\n",
      "Standard Error: 9.25774327506\n",
      "Z =  1.20844785469\n"
     ]
    }
   ],
   "source": [
    "n_obs = len(d_w_engin)\n",
    "\n",
    "\n",
    "mean_w = np.mean(d_w_math)\n",
    "std_w = np.std(d_w_math)\n",
    "\n",
    "\n",
    "mean_m =  np.mean(d_m_math)\n",
    "std_m = np.std(d_m_math)\n",
    "\n",
    "\n",
    "obs_diff = np.abs( mean_w - mean_m )\n",
    "\n",
    "# Expected difference is that there is no difference\n",
    "#(testing null hypothesis)\n",
    "exp_diff = 0\n",
    "\n",
    "\n",
    "#vng = (sd_g**2/n_g)\n",
    "#vnb = (sd_b**2/n_b)\n",
    "std_err = np.sqrt( ((std_w**2)/n_obs) + ((std_m**2)/n_obs)   )\n",
    "\n",
    "z = (obs_diff - exp_diff)/std_err\n",
    "\n",
    "\n",
    "print('Sample difference:' , obs_diff)\n",
    "print('Expected population difference:' , exp_diff)\n",
    "print('Standard Error:' , std_err)\n",
    "print('Z = ' , z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots show that many colleges in Massachusetss do have more Stem Male majors than female Majors. A challenge was repeating/copy&pasting the code for each major."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Junk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.hist?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b8c07cb7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3637.0\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(unis[:,1])):\n",
    "    name = (unis[i,0])\n",
    "    enroll = (unis[i,1])\n",
    "   \n",
    "    m_engin = (unis[i,2])\n",
    "    w_engin =(unis[i,3])\n",
    "    \n",
    "    loc_engin = m_engin + w_engin\n",
    "    tot_engin = tot_engin + loc_engin\n",
    "    \n",
    "    if m_engin or w_engin > 0:\n",
    "        plt.plot(m_engin, w_engin , color='green', marker='o')\n",
    "    \n",
    "plt.show()   \n",
    "\n",
    "print(tot_engin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA12SWuL/AkOfqX83/hbjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b8c07cb320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "620.0\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(unis[:,1])):    \n",
    "    m_phys = (unis[i,4])\n",
    "    w_phys =(unis[i,5])\n",
    "    \n",
    "    loc_phys = m_phys + w_phys\n",
    "    tot_phys = tot_phys + loc_phys\n",
    "    \n",
    "    if m_phys or w_phys > 0:\n",
    "        plt.plot(m_phys, w_phys, color='blue', marker='o')\n",
    "plt.show()\n",
    "\n",
    "print(tot_phys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'float' object cannot be interpreted as an integer",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-19-c861b2f2ddf9>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     17\u001b[0m     \u001b[0mpcent_w\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mw_math\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mloc_math\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     18\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 19\u001b[1;33m     \u001b[0mconcatenate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0munis\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m6\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mm_math\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     20\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     21\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpcent_w\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbins\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m30\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: 'float' object cannot be interpreted as an integer"
     ]
    }
   ],
   "source": [
    "\n",
    "m_math = (unis[0,6])\n",
    "w_math = (unis[0,7])\n",
    "    \n",
    "loc_math = m_math + w_math\n",
    "pcent_w = w_math/loc_math\n",
    "\n",
    "\n",
    "for i in range(len(unis[:,1])-1):   \n",
    "    \n",
    "    \n",
    "    \n",
    "    m_math = (unis[i+1,6])\n",
    "    w_math = (unis[i+1,7])\n",
    "    \n",
    "    loc_math = m_math + w_math\n",
    "    pcent_w = w_math/loc_math\n",
    "\n",
    "    concatenate((unis[0,6]),m_math)\n",
    "        \n",
    "plt.hist(pcent_w, bins = 30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IzAPAiWp/0j1A9+uRL6lbH/4M+HRm/gLwGrp9qUUfIuJG4PeBZmbeAlxF974Dk17/h4E7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b8c07cb780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "655.0\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(unis[:,1])):   \n",
    "    m_math = (unis[i,6])\n",
    "    w_math = (unis[i,7])\n",
    "    \n",
    "    loc_math = m_math + w_math\n",
    "    tot_math = tot_math + loc_math\n",
    "    if m_math or w_math > 0:\n",
    "        plt.plot(m_math, w_math , color='black', marker='o')\n",
    "    \n",
    "plt.show()\n",
    "\n",
    "print(tot_math)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Ailano School of Cosmetology' nan nan nan nan nan nan nan]\n",
      "[['Ailano School of Cosmetology' nan nan ..., nan nan nan]\n",
      " ['Alexander Academy' nan nan ..., nan nan nan]\n",
      " ['American Academy of Personal Training-Boston Campus' nan nan ..., nan\n",
      "  nan nan]\n",
      " ..., \n",
      " ['Williams College' 551.0 nan ..., 38.0 22.0 14.0]\n",
      " ['Worcester Polytechnic Institute' 1093.0 424.0 ..., 7.0 18.0 12.0]\n",
      " ['Worcester State University' 814.0 nan ..., 8.0 3.0 3.0]]\n"
     ]
    }
   ],
   "source": [
    "print(unis[0,:])\n",
    "print(unis[:,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bu = Major[28:29]\n",
    "uml = Major[177:178]\n",
    "uma = Major[173:174]\n",
    "wpi = Major[189:190]\n",
    "wit = Major[182:183]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3637.0 620.0 655.0\n"
     ]
    }
   ],
   "source": [
    "tot_m_engin = 0\n",
    "tot_w_engin = 0\n",
    "tot_engin = 0\n",
    "\n",
    "tot_m_math = 0\n",
    "tot_w_math = 0\n",
    "tot_math = 0\n",
    "\n",
    "tot_m_phys = 0\n",
    "tot_w_phys = 0\n",
    "tot_phys = 0\n",
    "\n",
    "for i in range(len(unis[:,1])):\n",
    "    name = (unis[i,0])\n",
    "    enroll = (unis[i,1])\n",
    "   \n",
    "    m_engin = (unis[i,2])\n",
    "    w_engin =(unis[i,3])\n",
    "    \n",
    "    loc_engin = m_engin + w_engin\n",
    "    tot_engin = tot_engin + loc_engin\n",
    "    \n",
    "    \n",
    "    m_phys = (unis[i,4])\n",
    "    w_phys =(unis[i,5])\n",
    "    \n",
    "    loc_phys = m_phys + w_phys\n",
    "    tot_phys = tot_phys + loc_phys\n",
    "    \n",
    "    \n",
    "    m_math = (unis[i,6])\n",
    "    w_math = (unis[i,7])\n",
    "    \n",
    "    loc_math = m_math + w_math\n",
    "    tot_math = tot_math + loc_math\n",
    "    \n",
    "    \"\"\"\n",
    "    plt.plot(enroll, (m_engin + w_engin) , color='green', marker='o')\n",
    "    plt.plot(enroll, (m_phys + w_phys) , color='blue', marker='o')\n",
    "    plt.plot(enroll,(m_math + w_math) , color='black', marker='o')\n",
    "    \n",
    "    plt.show()\"\"\"\n",
    "\n",
    "print(tot_engin, tot_phys, tot_math)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}