07_Seminar_08032016-Copy1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from datascience import *\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "data = Table.read_table(\"https://github.com/data-8/history-connector/raw/gh-pages/Data4.csv\")\n",
    "\n",
    "def standard_units(any_numbers):\n",
    "    \"Convert any array of numbers to standard units.\"\n",
    "    return (any_numbers - np.mean(any_numbers))/np.std(any_numbers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Last time, we looked at the relationships between grain-workers and relief payments, and between wage-earners and relief payments.\n",
    "\n",
    "This time, we will continue our discussion about association by looking at:\n",
    "\n",
    "/1/ The effect of an outlier on the r value\n",
    "\n",
    "/2/ Deriving the regression line\n",
    "\n",
    "/3/ Interpreting the slope and the intercept\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## /1/ Outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember from last class that we discovered that one parish has exceptionally high unemployment, around 60%, and several are around 30% (Greece's unemployment rate is about 25% nowadays, a figure typical during the Great Depression as the table below of US unemployment shows):\n",
    "\n",
    "Y\t1929\t1930\t1931\t1932\t1933\t1934\t1935\t1936\t1937\n",
    "%U\t3.1\t     8.7\t15.8\t23.5\t24.8\t21.6\t20\t    16.8\t14.2\n",
    " \n",
    "\n",
    "Y\t1938\t1939\t1940\t1941\n",
    "%U\t18.9\t17.1\t14.5\t9.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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H0FkSl3rNnWMciByDCV8kb7z9MdTqNnh6ekKtbsPWPf82rrOfMF9n1+lsU7ez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\n3jEJPDVtRXsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2214ba2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.scatter (\"UNEMP\", \"RELIEF\", s=10)\n",
    "#plots.scatter(data.column(\"UNEMP\"), data.column(\"RELIEF\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Last time, we also calculated the *r* with all 311 parishes. Let's compare that to the *r* *without* the outlier parish. There must be a very, very strong reason to do this in research, and we are doing it here as a learning exercise.\n",
    "\n",
    "For instance, we might have a strong theoretical reason for dropping exceptionally high and exceptionally low values -- some unemployment is, what economists call, natural (people changing jobs), and unemployment beyond a certain level signifies a process that goes beyond usual labor market fluctuations (natural disaster).\n",
    "\n",
    "URT3= data.select([\"UNEMP\", \"RELIEF\"]).where(np.logical_and(data.column(\"UNEMP\") >0.03, data.column(\"UNEMP\") <0.30))\n",
    "\n",
    "URT3.scatter(\"UNEMP\", \"RELIEF\", fit_line=True)\n",
    "URT3.hist(\"UNEMP\", bins=np.arange(0, 0.5, 0.01))\n",
    "\n",
    "\n",
    "We will use the function standard_units that we defined last class to do this, once again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "keyword can't be an expression (<ipython-input-7-314c779054e4>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-7-314c779054e4>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    data.where(data.colum(\"COUNTY\")=1)\u001b[0m\n\u001b[1;37m              ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m keyword can't be an expression\n"
     ]
    }
   ],
   "source": [
    "data.where(data.colum(\"COUNTY\")=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>UNEMP</th> <th>RELIEF</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0.14 </td> <td>20.36 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.07 </td> <td>29.09 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.05 </td> <td>14.93 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.06 </td> <td>24.12 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.03 </td> <td>18.21 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.1  </td> <td>20.73 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.07 </td> <td>8.12  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.01 </td> <td>14.02 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.08 </td> <td>18.42 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>0.26 </td> <td>34.55 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (300 rows omitted)</p"
      ],
      "text/plain": [
       "UNEMP | RELIEF\n",
       "0.14  | 20.36\n",
       "0.07  | 29.09\n",
       "0.05  | 14.93\n",
       "0.06  | 24.12\n",
       "0.03  | 18.21\n",
       "0.1   | 20.73\n",
       "0.07  | 8.12\n",
       "0.01  | 14.02\n",
       "0.08  | 18.42\n",
       "0.26  | 34.55\n",
       "... (300 rows omitted)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 0: Drop the outlier; for ease, Unemployment Relief Trimmed can just be shortened to URT\n",
    "#Another acronym may be more intuitive to you.\n",
    "\n",
    "#Question: How may rows do we expect?\n",
    "\n",
    "URT = data.select([\"UNEMP\", \"RELIEF\"]).where(data.column(\"UNEMP\")<0.40)\n",
    "URT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NiJTC6ROAIAg2f//666/R0tLis0aR56SkGMyDypI6MRUO/vqqMB2RXBSxDoACl5rvgllC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\n4YcfxqxZs2yOy/Wz4kpb7JHrZ6W7u9v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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2248a1278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Check visually, and do you easily notice a difference?\n",
    "\n",
    "URT.scatter('UNEMP', 'RELIEF', s=10)\n",
    "\n",
    "#Alternative: plots.scatter(URT.column('UNEMP'), URT.column('RELIEF'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Step 1: Get the data you're concerned with in standard units\n",
    "\n",
    "URT_su = URT.with_columns\n",
    "    ......\n",
    "    ]).select(['UNEMP', 'RELIEF', 'UNEMP (su)','RELIEF (su)'])\n",
    "URT_su\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Step 3: Find the product of your SU columns\n",
    "\n",
    "URT_product = URT_su.column(\"UNEMP (su)\") * URT_su.column(\"RELIEF (su)\")\n",
    "URT_product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Step 4: Find the mean, which is your r\n",
    "r = np.mean(URT_product)\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that last time, the r we calculated (without trimming the outlier) was ~0.365 (or, more precisley, 0.36475785072022804).\n",
    "\n",
    "What does this difference between the two correlation coefficients tell you? What do you think happens if we drop other values? \n",
    "\n",
    "Try “dropping” some values, and justify your choice (you can do this in the cells above, by modifying your code - no need to re-do it all)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## /2/ Regression Line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Last time, we included a ‘fit_line=True’ to convince ourselves that the r was, in fact, positive, and in section 3 we will actually derive the line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Try several options with plots!\n",
    "\n",
    "URT_su.scatter(\"UNEMP (su)\", \"RELIEF (su)\", 0, fit_line=True, s=10)\n",
    "_ = plots.plot([...], [....], color='r', lw=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Compare to rounded standard units of UNEMP and RELIEF\n",
    "\n",
    "rounded = URT_su.with_columns([\"UNEMP SU rounded\", np.round(URT_su.column(\"UNEMP (su)\")),\n",
    "                              \"RELIEF SU rounded\", np.round(URT_su.column(\"RELIEF (su)\"))]).select([\"UNEMP SU rounded\", \"RELIEF (su)\"])\n",
    "\n",
    "rounded.scatter(0, fit_line=True, s=10)\n",
    "_ = plots.plot([-1, 3], [-1 * r, 3 * r], color='g', lw=2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the differences between these two plots, and how would the results change if you included the outlier, or dropped a different series of outliers? Dropping values go get a better fit requires a strong justification; you can see some of the manipulation of results, sometimes called 'p-hacking', that goes on in research:\n",
    "\n",
    "(http://fivethirtyeight.com/features/science-isnt-broken/#part2; and\n",
    "http://www.nature.com/news/scientific-method-statistical-errors-1.14700)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## /3/ Interpreting the values of the slope and intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the social sciences, one way to describe relationships is in terms of so-called marginal effects – how much does Y change when X changes by 1? \n",
    "\n",
    "Since both UNEMP and RELIEF are quantitative variables, it makes sense to talk about how much does RELIEF change as, on average, proportion UNEMP increases by 1 percent or even 10 percent. To do this, we need to calculate the slope and the intercept:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Find the equation of the regression line. In standard units, r is the slope. What is the intercept in SU?\n",
    "\n",
    "intercept_su = np.mean(URT_su.column(\"RELIEF (su)\")) - r * np.mean(URT_su.column(\"UNEMP (su)\"))\n",
    "intercept_su"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just write the equation, in terms of variables we have defined, for the best-fit line in standard units:\n",
    "\n",
    "y = r * x + intercept_su\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Now, calculate these values for our original units:\n",
    "slope = r * np.std(URT.column(\"....\"))/np.std(URT.column(\"....\"))\n",
    "intercept = np.mean(URT.column(\"....\")) - slope * np.mean(URT.column(\"....\"))\n",
    "\n",
    "#Display the slope and the intercept in a list\n",
    "[slope, intercept]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions and Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "/1/ What does the intercept signify and how is it different from the mean/average? Does the intercept necessarily have a meaningul interpretation? Think of the examples discussed in class, namely Galton's findings about the heights of father's and son's."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*double-click and enter your answer here*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "/2/ Complete this statement: On average, a one-unit increase in the proportion of unemployed wage-laborers is associated with an increase in relief payments of ____ shillings.   \n",
    "\n",
    "*(double-click to edit)*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "/3/ Do the same as above, but for GRAIN and RELIEF. What intuition do you gain by thinking in terms of r, the slope and intercept?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*(Add as many cells as you need!)* "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "/4/ How about WEALTH and POP? Does it look like a linear regression would be a good fit here?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*(Add as many cells as you need!)* "
   ]
  }
 ],
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   "file_extension": ".py",
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