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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Homework 1. Exploratory Data Analysis\n",
      "\n",
      "Due: Thursday, September 18, 2014 11:59 PM\n",
      "\n",
      "<a href=https://raw.githubusercontent.com/cs109/2014/master/homework/HW1.ipynb download=HW1.ipynb> Download this assignment</a>\n",
      "\n",
      "---"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Introduction\n",
      "\n",
      "In this homework we ask you three questions that we expect you to answer using data. For each question we ask you to complete a series of tasks that should help guide you through the data analysis. Complete these tasks and then write a short (100 words or less) answer to the question.\n",
      "\n",
      "#### Data\n",
      "For this assignment we will use two databases: \n",
      "\n",
      "1. The [Sean Lahman's Baseball Database](http://seanlahman.com/baseball-archive/statistics) which contains the \"complete batting and pitching statistics from 1871 to 2013, plus fielding statistics, standings, team stats, managerial records, post-season data, and more. For more details on the latest release, please [read the documentation](http://seanlahman.com/files/database/readme2012.txt).\"\n",
      "\n",
      "2. [Gapminder](http://www.gapminder.org) is a great resource that contains over [500 data sets](http://www.gapminder.org/data/) related to world indicators such as income, GDP and life expectancy. \n",
      "\n",
      "\n",
      "#### Purpose\n",
      "\n",
      "In this assignment, you will learn how to: \n",
      "\n",
      "a. Load in CSV files from the web. \n",
      "\n",
      "b. Create functions in python. \n",
      "\n",
      "C. Create plots and summary statistics for exploratory data analysis such as histograms, boxplots and scatter plots. \n",
      "\n",
      "\n",
      "#### Useful libraries for this assignment \n",
      "\n",
      "* [numpy](http://docs.scipy.org/doc/numpy-dev/user/index.html), for arrays\n",
      "* [pandas](http://pandas.pydata.org/), for data frames\n",
      "* [matplotlib](http://matplotlib.org/), for plotting\n",
      "\n",
      "---"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# special IPython command to prepare the notebook for matplotlib\n",
      "%matplotlib inline \n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "# For this assignment, we need to load in the following modules\n",
      "import requests\n",
      "import StringIO\n",
      "import zipfile\n",
      "import scipy.stats "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem 1\n",
      "\n",
      "In Lecture 1, we showed a plot that provided evidence that the 2002 and 2003 Oakland A's, a team that used data science, had a competitive advantage. Since, others teams have started using data science as well. Use exploratory data analysis to determine if the competitive advantage has since disappeared. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(a) \n",
      "Load in [these CSV files](http://seanlahman.com/files/database/lahman-csv_2014-02-14.zip) from the [Sean Lahman's Baseball Database](http://seanlahman.com/baseball-archive/statistics). For this assignment, we will use the 'Salaries.csv' and 'Teams.csv' tables. Read these tables into a pandas `DataFrame` and show the head of each table. \n",
      "\n",
      "**Hint** Use the [requests](http://docs.python-requests.org/en/latest/), [StringIO](http://docs.python.org/2/library/stringio.html) and [zipfile](https://docs.python.org/2/library/zipfile.html) modules to get from the web.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "def getZIP(zipFileName):\n",
      "    r = requests.get(zipFileName).content\n",
      "    s = StringIO.StringIO(r)\n",
      "    zf = zipfile.ZipFile(s, 'r') # Read in a list of zipped files\n",
      "    return zf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here, we use the requests, StringIO and zipfile modules to extract all the text files from the web.  The zipfile model can create, read, write, append, and list ZIP files.  You did not have to create a function, but I did to make the solution cleaner. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using the URL linking to the .zip file, we can print all the files listed in the zipped folder. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "url = 'http://seanlahman.com/files/database/lahman-csv_2014-02-14.zip'\n",
      "zf = getZIP(url)\n",
      "print zf.namelist()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "['SchoolsPlayers.csv', 'SeriesPost.csv', 'Teams.csv', 'TeamsFranchises.csv', 'TeamsHalf.csv', 'AllstarFull.csv', 'Appearances.csv', 'AwardsManagers.csv', 'AwardsPlayers.csv', 'AwardsShareManagers.csv', 'AwardsSharePlayers.csv', 'Batting.csv', 'BattingPost.csv', 'Fielding.csv', 'FieldingOF.csv', 'FieldingPost.csv', 'HallOfFame.csv', 'Managers.csv', 'ManagersHalf.csv', 'Master.csv', 'Pitching.csv', 'PitchingPost.csv', 'readme2013.txt', 'Salaries.csv', 'Schools.csv']\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tablenames = zf.namelist()\n",
      "tablenames[tablenames.index('Salaries.csv')]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "'Salaries.csv'"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we extract the 'Salaries.csv' file from the zipped folder. We use the `zf.open()` function to open a specific file and use `pd.read_csv()` to read the table into a pandas DataFrame. This table contains salaries labled by year, by player, by league and by team. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "salaries = pd.read_csv(zf.open(tablenames[tablenames.index('Salaries.csv')]))\n",
      "print \"Number of rows: %i\" % salaries.shape[0]\n",
      "salaries.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Number of rows: 23956\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>yearID</th>\n",
        "      <th>teamID</th>\n",
        "      <th>lgID</th>\n",
        "      <th>playerID</th>\n",
        "      <th>salary</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BAL</td>\n",
        "      <td> AL</td>\n",
        "      <td> murraed02</td>\n",
        "      <td> 1472819</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BAL</td>\n",
        "      <td> AL</td>\n",
        "      <td>  lynnfr01</td>\n",
        "      <td> 1090000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BAL</td>\n",
        "      <td> AL</td>\n",
        "      <td> ripkeca01</td>\n",
        "      <td>  800000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BAL</td>\n",
        "      <td> AL</td>\n",
        "      <td>  lacyle01</td>\n",
        "      <td>  725000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BAL</td>\n",
        "      <td> AL</td>\n",
        "      <td> flanami01</td>\n",
        "      <td>  641667</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "   yearID teamID lgID   playerID   salary\n",
        "0    1985    BAL   AL  murraed02  1472819\n",
        "1    1985    BAL   AL   lynnfr01  1090000\n",
        "2    1985    BAL   AL  ripkeca01   800000\n",
        "3    1985    BAL   AL   lacyle01   725000\n",
        "4    1985    BAL   AL  flanami01   641667"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finall, we extract the 'Teams.csv' file from the zipped folder. This table contains a large amount of information, but for our purposes, we are interested in the `yearID`, `teamID` and number of wins `W`. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "teams = pd.read_csv(zf.open(tablenames[tablenames.index('Teams.csv')]))\n",
      "teams = teams[['yearID', 'teamID', 'W']]\n",
      "print \"Number of rows: %i\" % teams.shape[0]\n",
      "teams.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Number of rows: 2745\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>yearID</th>\n",
        "      <th>teamID</th>\n",
        "      <th>W</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1871</td>\n",
        "      <td> PH1</td>\n",
        "      <td> 21</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1871</td>\n",
        "      <td> CH1</td>\n",
        "      <td> 19</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 1871</td>\n",
        "      <td> BS1</td>\n",
        "      <td> 20</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1871</td>\n",
        "      <td> WS3</td>\n",
        "      <td> 15</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1871</td>\n",
        "      <td> NY2</td>\n",
        "      <td> 16</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "   yearID teamID   W\n",
        "0    1871    PH1  21\n",
        "1    1871    CH1  19\n",
        "2    1871    BS1  20\n",
        "3    1871    WS3  15\n",
        "4    1871    NY2  16"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(b)\n",
      "\n",
      "Summarize the Salaries DataFrame to show the total salaries for each team for each year. Show the head of the new summarized DataFrame. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "totSalaries = salaries.groupby(['yearID','teamID'], as_index=False).sum()\n",
      "totSalaries.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>yearID</th>\n",
        "      <th>teamID</th>\n",
        "      <th>salary</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1985</td>\n",
        "      <td> ATL</td>\n",
        "      <td> 14807000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BAL</td>\n",
        "      <td> 11560712</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BOS</td>\n",
        "      <td> 10897560</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1985</td>\n",
        "      <td> CAL</td>\n",
        "      <td> 14427894</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1985</td>\n",
        "      <td> CHA</td>\n",
        "      <td>  9846178</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "   yearID teamID    salary\n",
        "0    1985    ATL  14807000\n",
        "1    1985    BAL  11560712\n",
        "2    1985    BOS  10897560\n",
        "3    1985    CAL  14427894\n",
        "4    1985    CHA   9846178"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(c)\n",
      "\n",
      "Merge the new summarized Salaries DataFrame and Teams DataFrame together to create a new DataFrame\n",
      "showing wins and total salaries for each team for each year year. Show the head of the new merged DataFrame.\n",
      "\n",
      "**Hint**: Merge the DataFrames using `teamID` and `yearID`."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To merge these two DataFrames, we can use the `merge` function to join together DataFrame objects `on` a set of column names (must be found in both DataFrames) and `how` (union, intersection, only rows from one data set or the other). Below, we use the arguments `how=\"inner\"` to take the intersection of the rows and `on=['yearID', 'teamID']` the column names `yearID` and `teamID` which can be found in both DataFrames. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "joined = pd.merge(totSalaries, teams, how=\"inner\", on=['yearID', 'teamID'])\n",
      "joined.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>yearID</th>\n",
        "      <th>teamID</th>\n",
        "      <th>salary</th>\n",
        "      <th>W</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1985</td>\n",
        "      <td> ATL</td>\n",
        "      <td> 14807000</td>\n",
        "      <td> 66</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BAL</td>\n",
        "      <td> 11560712</td>\n",
        "      <td> 83</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BOS</td>\n",
        "      <td> 10897560</td>\n",
        "      <td> 81</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1985</td>\n",
        "      <td> CAL</td>\n",
        "      <td> 14427894</td>\n",
        "      <td> 90</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1985</td>\n",
        "      <td> CHA</td>\n",
        "      <td>  9846178</td>\n",
        "      <td> 85</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "   yearID teamID    salary   W\n",
        "0    1985    ATL  14807000  66\n",
        "1    1985    BAL  11560712  83\n",
        "2    1985    BOS  10897560  81\n",
        "3    1985    CAL  14427894  90\n",
        "4    1985    CHA   9846178  85"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(d)\n",
      "\n",
      "How would you graphically display the relationship between total wins and total salaries for a given year? What kind of plot would be best? Choose a plot to show this relationship and specifically annotate the Oakland baseball team on the on the plot. Show this plot across multiple years. In which years can you detect a competitive advantage from the Oakland baseball team of using data science? When did this end? \n",
      "\n",
      "**Hints**: Use a `for` loop to consider multiple years. Use the `teamID` (three letter representation of the team name) to save space on the plot.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using our summarized DataFrame in 1(c), we will create a scatter plot to graphically display the relationship between total wins and total salaries for a given year. Because each team is represented by one point, we can annotate specific points by the team name. In this case, we will consider the Oakland baseball team.  The `teamID` for Oakland is OAK, so we will add the `OAK` annotation on the scatter plot.  You could have used any color, shapes, etc for the annotation of the team name. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "teamName = 'OAK'\n",
      "years = np.arange(2000, 2004)\n",
      "\n",
      "for yr in years: \n",
      "    df = joined[joined['yearID'] == yr]\n",
      "    plt.scatter(df['salary'] / 1e6, df['W'])\n",
      "    plt.title('Wins versus Salaries in year ' + str(yr))\n",
      "    plt.xlabel('Total Salary (in millions)')\n",
      "    plt.ylabel('Wins')\n",
      "    plt.xlim(0, 180)\n",
      "    plt.ylim(30, 130)\n",
      "    plt.grid()\n",
      "    plt.annotate(teamName, \n",
      "        xy = (df['salary'][df['teamID'] == teamName] / 1e6,  df['W'][df['teamID'] == teamName]), \n",
      "        xytext = (-20, 20), textcoords = 'offset points', ha = 'right', va = 'bottom',\n",
      "        bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),\n",
      "        arrowprops = dict(arrowstyle = '->', facecolor = 'black' , connectionstyle = 'arc3,rad=0'))\n",
      "    \n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V0aOfY//+heTlbeSDD7Zz6613l/FViIiTQikUW4HHgC/s4Y3A5IglqoC82CZZ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\nRERERERERERERERERERERERERKSi+n+quYMTVo76bQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1039b6e90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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n5OU9DlQDOpGfPzjsdZU103//+zk5OXcALYDa5OY+yscff16mZUYiVzQokz3C\n6aO4BngCqE9Br7kfKMu3tx4ChgA+TDPWjUAyMA1oivmm2ABgfxnWITGmb9/L2bJlHRs2bKBJkyac\nfPLJTkc6YdWr12XPnlWYkwb9JCauok6ddrasu0GDulSqtIqCr+2som7dOiXNIlKicE6X2gj0BSJ1\nM+NmmMtrnoFp0poGfAy0ATKAp4AHgVrA6JB5reY2kfD4fD6mTJnC2rU/07ZtGwYMGGDLpTVmz57N\nddeNxOcbgMezltNPz2Xhwi9suUBgRkYGKSnnsW9fW44cqYvHM4svv/yIzp07R33d4k52fI/iWyCS\n13yuDSzA3IDgd2AW8ALwItAd2IXpNE8DWofMq0IhYfP7/QwadCMffbSW7OxLSE6ew8CB5zFhgj13\nnVu+fDnz5s2jTp06DBgwgMqVK9uyXoDMzEymT59Obm4ul112Gaeddppt6xb3KWuhCMfzmL3+wZhm\nqGuAq8u4zJGYIrEbmGSN2xf0fFzIcICjZw4UZ968eU5H8Pv9fv+KFSv8c+fO9e/YscM1mYLZnWnV\nqlV+r7eRH7KtM6ky/VWq1PFv3rzZsUzhcGMmv9+duZQpPJTxrKdw+ihqALnAxSHjZ57gOk8D7sE0\nQWUC0zH9FcGK/cOGDx9+9EYwNWvWJCUlhdTUVKCgE8nu4QCn1p+amsqoUX9mwoR38HgaA1t49NGC\nVjunX5/A8LJlyxxYfzIQuNbRj8TFecnMzKRx48akpaWxbNky17w+bvo8FTXszPtX8rDev6KH09LS\nmDhxIkCpb5xVFCeu9TQQ6A3cbA3fgGmG6gFchDkFtwEwDzU9heWrr77i8stvIjt7Caauf0nNmtez\nd+/2Cn0fguzsbJo3b0NGxv34/VcSH/8eDRqMZ+PGn2xtBhJxWjQv4fGg9fvFIn5eONEVAmsxhSEJ\nE7wXsBqYAwyzphkGzC5ybjnGL7/8gvk2cw1rzEX8/vtecnNzHUzlvOTkZL7+ei4pKe9TvXpHOnWa\ny/z5n6pIiJRSSYUiEegMrAB+CPpZYv2cqOWYa0X9YC0b4HXMKbi9gXWYo4snyrAOW4UectqtXbt2\n+HyfU3CdxnepVaue6y4v7cTr1KpVK3788SsyM3eycOHnnHrqqY5nOh43ZgJ35lIme5TUR1ETeA5z\nGutPmLOfvrN+7y3jep+yfoLtxRxdSCl17NiRxx9/hAcfPAuPpzZer5/HHx/rdCwRKSfCabOqDJwD\nnItp3ziVSbjpAAAVHUlEQVQX80W4M6KYqzjqoyhBZmYmGRkZNG7c2Nb7XoiIu5W1jyKcs56SMN/C\nrmH9bKegyUhstnTpUt58810SEuIZOfJGzjzzzKPP1ahRgxo1apQwt4hI6ZXURzEe08w0FXMU8R1w\nLebu7TdGP1rssKtN8ttvv6Vbt4t56aWaPP98Ep07d2f58uWOZioNZQqPGzOBO3Mpkz1KOqJogml2\nWg9ss3507SUHjRnzL3JyniBwO5Ds7Bo89thzTJv2VpmXvXv3br766iu8Xi+9evXSmUEictTx2qzi\nMddgCvRPnAX8hrkW9N+iG61IFbqPomvXS1i0aBQQuA/yO1x22cd89NHUMi135cqVdOvWG5+vM37/\nbpo3h4ULv3DdWVMicmKifSvUwNVdP7F+vgVOB+4+0RXKibvppgF4vQ9i3oZ5eL1juPHGP5R5uTff\n/Ceyssby++8fcODAd6xffwovvmjP9ZBExP1KKhR3Y67xtBn4CuiHuYLsVZgL+4nFrjbJm28eweOP\n38Gpp95Bixb389JLY7n22mvKnGnLli34/YHrPsZx8OB5/PLL1rIHLkMmuyhT+NyYS5nsUVIfRTPg\nfeBPmDOdxGFxcXHcddco7rprVESX263bucyePY68vH8D+/B6J9K9+4PHnU9ExI2cvABjubV//35/\nt26X+D2eJL/HU9l/330P+30+n9OxSpSenu7v1q2Pv3btxv6uXXv5N2zYYOv6v/nmG3/r1p38deo0\n8V911RD//v37bV2/SGlQxqvHxtoV46y/WaLh999/JzEx0fVnPB06dIgWLdqzffswjhwZRHz8LOrV\ne5mNG3+ypQN+06ZNnHVWZ7KzXwU6kJj4Dy644Dc+//yDqK9b5EREuzNbwuDGNskTyVStWrWoFolI\nvU4///wz+/fHceTIQ0BzfL57ycmpzsqVK23J9OWXX+L3X4r5WtGp5OW9SlraJ+Tn55d6WZHKZAc3\n5lIme6hQSMypVq0a+fl7gWxrTC75+XuoVq2abeuPj99CwdH8NjyeyiQkJNiyfhG7qelJYo7f7+eG\nG0Yye/YKsrP7k5z8MZdcciozZrxjy/03Dh48yDnndGfjxkYcPNgBr/dN/v73e7j33ruivm6RE2HH\nPbPdRIVCAPD5fEyePJkVK1bRpk1rhg4dSny8fQfIOTk5jB8/nm3bdtKjR3f69Olj27pFSsuOe2a7\niYPnDRTPjffIVabwKFP43JhLmcJDGc96Uh+FiIiUKNYORaziKCIi4dLpsSIiElUqFBHgxvOmlSk8\nyhQ+N+ZSJnuoUMQIv9/P669PoFu3y7nssgH88MMPpV7G/Pnzufjia7jwwn5MnTotCilFpDxSH0WM\neOaZ5xkz5nWys/8J7CA5+W8sWpRGmzZtwpp/wYIF9Op1hXXjo2p4vQ/w6qt/Z+jQIVHNLSLO0/co\nKojGjduwdetbQGcA4uL+wv33+3jyycfCmn/o0FuYNKk15mLAAJ/Qrt3jLF8+Pyp5RcQ91JntAna0\nSZovk/mCxhwp8VvIoZnMtEcKzW/nF9TAnW23yhQ+N+ZSJnuoUMSIBx4Yhdc7FJhKXNyzeL1vcOON\nQ8Oe/847b8brfRJ4BZiE13s7o0ffXuS027Zt44svvuCXX34p8vmsrCzS0tJYunQpFfUIT6QiUdNT\nDJk0aTLvvDOT6tWTGTPmPtq1a1eq+RcuXMjjj7/IwYN53H77EK644opjppk2bTo33ngbiYltOXRo\nFf/3f49w//33HH1+1apVXHhhH/Lzm3DkyA569OjMrFmTdUE8ERdTH0UF4/f7ycvLi8rlwA8cOEC9\neo3JzU0D2gNbSUrqwIoV33H66acDkJJyAStWDMHvvwU4RHJyT15++Y8MGzYs4nlEJDLUR+ECdrVJ\n/uc/M6le/SS83qqccUYn0tPTI5ppx44dJCTUwhQJgFNITGxbqAlq06YN+P2XW0OVyc7uxfr1G8Ja\nvhvbbpUpfG7MpUz2UKGIEWvXrmXo0Fs5cOBTfL5DrFt3LX36XBPRdZxyyinExR0AvrTGrOTw4Z9o\n3br10Wnatm1HQsJEzDXG9pOcPIuUlPbHLkxEyg01PcWId955h1Gj5nLgwGRrjJ+EhCSysvZG9Paf\n8+bN44orBuL31yA/fw9vvPEq118/+Ojzmzdvpnv3y9izJ5v8/H3cdNNNvPTSv2y5D4SInJiyNj15\nIhdFounkk08GVgCHgMrATyQmViEpKSmi67nooovYuTOdzZs307BhQ6pXr17o+SZNmrB+/TI2bdpE\n9erVqV+/fkTXLyLuo6anCLCjTbJ379706NGWqlU7k5w8jKSk3rzxxmvF7smXJZPX66V169bHFIkA\nj8dDixYtSl0kSptp586djBnzKHfe+WfmzZtXqnmjlckObswE7sylTPbQEUWMiIuLY/bs95g7dy7b\nt2+nc+f7adu2rdOxomb37t20b9+VvXsvIz+/CW++OYQ33niGwYMHOR1NpMKJtYblCttHESuWLFnC\n8uXLyc7OpkWLFvTo0YPExMRSL+fxx59gzJiNHD483hozn1NOuZUtW1ZHNrBIBaA+CnGN0aPH8MIL\nb5Kb2xr4nsqV69Ky5UksWPA5ycnJpVpWdnYO+fnBTVsNyM3NjmheEQmP+igiwI1tknZnWrNmDS+8\n8Dq5uUuB/wHfc+jQHn7+uSHjxj1f6kxXXtmfKlVeB+YAK0hKupVBg/4Q8dx678LnxlzKZA+nCkVN\nYAawBlgNdAFqY7Yw64DPrGkkRmzZsoXExDOButaYFkAt8vLasmHDllIv75xzzmHmzHdo3fofNGo0\niFtu6cS4cY9HMrKIhMmpPoq3ga+ANzHNX8nAI0AG8BTwIFALGB0yn/ooXGr79u20aNGenJw5QFdg\nJnAHXm8DXnzxDkaMuNHhhCIVVyxe66kGsBQ4NWT8WqA7sAs4GUgDWodMo0LhYv/9738ZOHAYubl5\n+P0+EhKOcOuto3jxRX0hT8RJsXitp+bAHuAt4EdgPOaIoj6mSGD9jplvcrmxTdKJTH379iUzcxc7\nd24kI2MzWVl7eemlZ44WCb1O4XFjJnBnLmWyhxOFwgN0wNwYoQOQTRFNTNaPxBiPx0O9evWoU6dO\nRC8tIiLOceL02K3Wz/fW8AzgIWAnpslpJ9AA2F3UzMOHD6dZs2YA1KxZk5SUFFJTU4GCSq7hVFJT\nU12VJyAtLc01eUL3/NySx63DgXFuyaP3r/jhtLQ0Jk6cCHB0e1kWTjUczwduxpzhNBYI7Hr+BjyJ\nOcKoiTqzRUTKLBb7KADuBCYDy4F2wD+BJ4DemOLRwxqOCaF7Nm6gTOFRpvC5MZcy2cOpb2YvBzoV\nMb6X3UFERKRksXbOopqeRERKKVabnkREJEaoUESAG9sklSk8yhQ+N+ZSJnuoUIiISInURyEiUs6p\nj0JERKJKhSIC3NgmqUzhUabwuTGXMtlDhUJEREqkPgoRkXJOfRQiIhJVKhQR4MY2SWUKjzKFz425\nlMkeKhQiIlIi9VGIiJRz6qMQEZGoUqGIADe2SSpTeJQpfG7MpUz2UKEQEZESqY9CRKScUx+FiIhE\nlQpFBLixTVKZwqNM4XNjLmW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       "text": [
        "<matplotlib.figure.Figure at 0x10a0655d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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btm0MHTqKNWs20rnzmYwaNTzsndnBsPw6sxMTa5CWNkSd2SIeVN5C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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x103997490>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xOPfe+1dmzHg3aLnt1qFDByIjtwHfAt2BqVSrlkXr1q2pVq0an312Yt/2tlNE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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a44a350>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We see a competitive advantage can be detected in years 2001-2003 for the Oakland baseball team, because in those years Oakland spent much less in salary compared to other teams, but stood out with the number of wins.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(e):\n",
      "\n",
      "**For AC209 Students**: Fit a linear regression to the data from each year and obtain the residuals. Plot the residuals against time to detect patterns that support your answer in 1(d). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For each year, we perform the following: \n",
      "\n",
      "1. Calculate the least squares estimate of the coefficients in a linear regression model where x = salaries (in millions) and y = total wins. \n",
      "2. Calculate the residuals for each team: $$e_i = y_i - \\hat{y}_i$$\n",
      "3. Plot the residuals for each team across time. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "teamName = 'OAK'\n",
      "years = np.arange(1999, 2005)\n",
      "residData = pd.DataFrame()\n",
      "\n",
      "for yr in years: \n",
      "    df = joined[joined['yearID'] == yr]\n",
      "    x_list = df['salary'].values / 1e6\n",
      "    y_list = df['W'].values\n",
      "\n",
      "    # least squares estimates\n",
      "    A = np.array([x_list, np.ones(len(x_list))])\n",
      "    y = y_list\n",
      "    w = np.linalg.lstsq(A.T,y)[0] # coefficients\n",
      "    yhat = (w[0]*x_list+w[1]) # regression line\n",
      "    residData[yr] = y - yhat\n",
      "  \n",
      "residData.index = df['teamID']\n",
      "residData = residData.T\n",
      "residData.index = residData.index.format()\n",
      "\n",
      "residData.plot(title = 'Residuals from least squares estimates across years', figsize = (15, 8),\n",
      "               color=map(lambda x: 'blue' if x=='OAK' else 'gray',df.teamID))\n",
      "plt.xlabel('Year')\n",
      "plt.ylabel('Residuals')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tpqamEhISQp8+ffDx8WkQy200FtnZNUv2iorggQcqT/RMt7dpU3exVtY+U1Nh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Xfv3iU+Pp5Dhw4RHx8/5XYDAwN88cUXAJw8eXJZEhdFORyOGddYajQa2tra6O7uJjg4mE2bNuH7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       "text": [
        "<matplotlib.figure.Figure at 0x10a56c250>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Discussion for Problem 1\n",
      "\n",
      "*Write a brief discussion of your conclusions to the questions and tasks above in 100 words or less.*\n",
      "\n",
      "Considering the plots from 1(d) and 1(e), we see the Oakland baseball team stood out amongst the other baseball teams in terms of their ability to win a large amount of games with a small budget from 2001-2003.  Upon futher reading, we can attributed this to Billy Beane's effort to use \"sabermetrics\" (or the empirical analysis of baseball data) at the Oakland A's. He was able to find the most undervalued players and baseball and hire them on a reduced budget.  \n",
      "\n",
      "---\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem 2\n",
      "\n",
      "Several media reports have demonstrated the income inequality has increased in the US during this last decade. Here we will look at global data. Use exploratory data analysis to determine if the gap between Africa/Latin America/Asia and Europe/NorthAmerica has increased, decreased or stayed the same during the last two decades. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 2(a)\n",
      "\n",
      "Using the list of countries by continent from [World Atlas](http://www.worldatlas.com/cntycont.htm) data, load in the `countries.csv` file into a pandas DataFrame and name this data set as `countries`.  This data set can be found on Github in the 2014_data repository [here](https://github.com/cs109/2014_data/blob/master/countries.csv). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "url = \"https://raw.githubusercontent.com/cs109/2014_data/master/countries.csv\"\n",
      "s = StringIO.StringIO(requests.get(url).content)\n",
      "countries = pd.read_csv(s)\n",
      "countries.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Country</th>\n",
        "      <th>Region</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>  Algeria</td>\n",
        "      <td> AFRICA</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>   Angola</td>\n",
        "      <td> AFRICA</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>    Benin</td>\n",
        "      <td> AFRICA</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> Botswana</td>\n",
        "      <td> AFRICA</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>  Burkina</td>\n",
        "      <td> AFRICA</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "    Country  Region\n",
        "0   Algeria  AFRICA\n",
        "1    Angola  AFRICA\n",
        "2     Benin  AFRICA\n",
        "3  Botswana  AFRICA\n",
        "4   Burkina  AFRICA"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using the [data available on Gapminder](http://www.gapminder.org/data/), load in the [Income per person (GDP/capita, PPP$ inflation-adjusted)](https://spreadsheets.google.com/pub?key=phAwcNAVuyj1jiMAkmq1iMg&gid=0) as a pandas DataFrame and name this data set as `income`.\n",
      "\n",
      "**Hint**: Consider using the pandas function `pandas.read_excel()` to read in the .xlsx file directly."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "income_link = 'https://spreadsheets.google.com/pub?key=phAwcNAVuyj1jiMAkmq1iMg&output=xls'\n",
      "source = StringIO.StringIO(requests.get(income_link).content)\n",
      "income = pd.read_excel(source, sheetname = \"Data\")\n",
      "income.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>gdp pc test</th>\n",
        "      <th>1800</th>\n",
        "      <th>1801</th>\n",
        "      <th>1802</th>\n",
        "      <th>1803</th>\n",
        "      <th>1804</th>\n",
        "      <th>1805</th>\n",
        "      <th>1806</th>\n",
        "      <th>1807</th>\n",
        "      <th>1808</th>\n",
        "      <th>...</th>\n",
        "      <th>2003</th>\n",
        "      <th>2004</th>\n",
        "      <th>2005</th>\n",
        "      <th>2006</th>\n",
        "      <th>2007</th>\n",
        "      <th>2008</th>\n",
        "      <th>2009</th>\n",
        "      <th>2010</th>\n",
        "      <th>2011</th>\n",
        "      <th>2012</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>              Abkhazia</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>...</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>           Afghanistan</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td> 472.053500</td>\n",
        "      <td>...</td>\n",
        "      <td>  785.127571</td>\n",
        "      <td>  804.717458</td>\n",
        "      <td>  874</td>\n",
        "      <td>  887.914578</td>\n",
        "      <td>  983.652314</td>\n",
        "      <td>  984.805841</td>\n",
        "      <td> 1154.859365</td>\n",
        "      <td> 1214.613653</td>\n",
        "      <td> 1261.354184</td>\n",
        "      <td> 1349.696941</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> Akrotiri and Dhekelia</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>...</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>               Albania</td>\n",
        "      <td> 601.215222</td>\n",
        "      <td> 601.839631</td>\n",
        "      <td> 602.464688</td>\n",
        "      <td> 603.090394</td>\n",
        "      <td> 603.716751</td>\n",
        "      <td> 604.343757</td>\n",
        "      <td> 604.971415</td>\n",
        "      <td> 605.599725</td>\n",
        "      <td> 606.228687</td>\n",
        "      <td>...</td>\n",
        "      <td> 4855.210024</td>\n",
        "      <td> 5115.252837</td>\n",
        "      <td> 5369</td>\n",
        "      <td> 5652.049321</td>\n",
        "      <td> 5958.021197</td>\n",
        "      <td> 6365.530359</td>\n",
        "      <td> 6550.896164</td>\n",
        "      <td> 6746.445312</td>\n",
        "      <td> 6914.267317</td>\n",
        "      <td> 6969.306283</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>               Algeria</td>\n",
        "      <td> 766.253664</td>\n",
        "      <td> 766.234779</td>\n",
        "      <td> 766.215895</td>\n",
        "      <td> 766.197011</td>\n",
        "      <td> 766.178127</td>\n",
        "      <td> 766.159244</td>\n",
        "      <td> 766.140362</td>\n",
        "      <td> 766.121480</td>\n",
        "      <td> 766.102598</td>\n",
        "      <td>...</td>\n",
        "      <td> 5576.851564</td>\n",
        "      <td> 5790.967692</td>\n",
        "      <td> 6011</td>\n",
        "      <td> 6022.270940</td>\n",
        "      <td> 6133.782763</td>\n",
        "      <td> 6162.719840</td>\n",
        "      <td> 6173.729741</td>\n",
        "      <td> 6300.648214</td>\n",
        "      <td> 6354.640523</td>\n",
        "      <td> 6419.127829</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 214 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "             gdp pc test        1800        1801        1802        1803  \\\n",
        "0               Abkhazia         NaN         NaN         NaN         NaN   \n",
        "1            Afghanistan  472.053500  472.053500  472.053500  472.053500   \n",
        "2  Akrotiri and Dhekelia         NaN         NaN         NaN         NaN   \n",
        "3                Albania  601.215222  601.839631  602.464688  603.090394   \n",
        "4                Algeria  766.253664  766.234779  766.215895  766.197011   \n",
        "\n",
        "         1804        1805        1806        1807        1808     ...      \\\n",
        "0         NaN         NaN         NaN         NaN         NaN     ...       \n",
        "1  472.053500  472.053500  472.053500  472.053500  472.053500     ...       \n",
        "2         NaN         NaN         NaN         NaN         NaN     ...       \n",
        "3  603.716751  604.343757  604.971415  605.599725  606.228687     ...       \n",
        "4  766.178127  766.159244  766.140362  766.121480  766.102598     ...       \n",
        "\n",
        "          2003         2004  2005         2006         2007         2008  \\\n",
        "0          NaN          NaN   NaN          NaN          NaN          NaN   \n",
        "1   785.127571   804.717458   874   887.914578   983.652314   984.805841   \n",
        "2          NaN          NaN   NaN          NaN          NaN          NaN   \n",
        "3  4855.210024  5115.252837  5369  5652.049321  5958.021197  6365.530359   \n",
        "4  5576.851564  5790.967692  6011  6022.270940  6133.782763  6162.719840   \n",
        "\n",
        "          2009         2010         2011         2012  \n",
        "0          NaN          NaN          NaN          NaN  \n",
        "1  1154.859365  1214.613653  1261.354184  1349.696941  \n",
        "2          NaN          NaN          NaN          NaN  \n",
        "3  6550.896164  6746.445312  6914.267317  6969.306283  \n",
        "4  6173.729741  6300.648214  6354.640523  6419.127829  \n",
        "\n",
        "[5 rows x 214 columns]"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Transform the data set to have years as the rows and countries as the columns. Show the head of this data set when it is loaded. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "income.index=income[income.columns[0]] # Make the countries as the index\n",
      "income = income.drop(income.columns[0], axis = 1) \n",
      "income.columns = map(lambda x: int(x), income.columns) # Convert years from floats to ints\n",
      "income = income.transpose()\n",
      "income.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th>gdp pc test</th>\n",
        "      <th>Abkhazia</th>\n",
        "      <th>Afghanistan</th>\n",
        "      <th>Akrotiri and Dhekelia</th>\n",
        "      <th>Albania</th>\n",
        "      <th>Algeria</th>\n",
        "      <th>American Samoa</th>\n",
        "      <th>Andorra</th>\n",
        "      <th>Angola</th>\n",
        "      <th>Anguilla</th>\n",
        "      <th>Antigua and Barbuda</th>\n",
        "      <th>...</th>\n",
        "      <th>Western Sahara</th>\n",
        "      <th>Vietnam</th>\n",
        "      <th>Virgin Islands (U.S.)</th>\n",
        "      <th>Yemen Arab Republic (Former)</th>\n",
        "      <th>Yemen Democratic (Former)</th>\n",
        "      <th>Yemen, Rep.</th>\n",
        "      <th>Yugoslavia</th>\n",
        "      <th>Zambia</th>\n",
        "      <th>Zimbabwe</th>\n",
        "      <th>\u00c5land</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1800</th>\n",
        "      <td>NaN</td>\n",
        "      <td> 472.0535</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 601.215222</td>\n",
        "      <td> 766.253664</td>\n",
        "      <td> 674.453726</td>\n",
        "      <td> 1260.123256</td>\n",
        "      <td> 359.932582</td>\n",
        "      <td> 775.668711</td>\n",
        "      <td> 538.376199</td>\n",
        "      <td>...</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 459.708986</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 661.902376</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 364.464811</td>\n",
        "      <td> 372.818338</td>\n",
        "      <td>NaN</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1801</th>\n",
        "      <td>NaN</td>\n",
        "      <td> 472.0535</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 601.839631</td>\n",
        "      <td> 766.234779</td>\n",
        "      <td> 674.453726</td>\n",
        "      <td> 1262.214402</td>\n",
        "      <td> 359.932582</td>\n",
        "      <td> 775.668711</td>\n",
        "      <td> 538.376199</td>\n",
        "      <td>...</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 459.708986</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 662.058563</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 364.464811</td>\n",
        "      <td> 372.818338</td>\n",
        "      <td>NaN</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1802</th>\n",
        "      <td>NaN</td>\n",
        "      <td> 472.0535</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 602.464688</td>\n",
        "      <td> 766.215895</td>\n",
        "      <td> 674.453726</td>\n",
        "      <td> 1264.309018</td>\n",
        "      <td> 359.932582</td>\n",
        "      <td> 775.668711</td>\n",
        "      <td> 538.376199</td>\n",
        "      <td>...</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 459.708986</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 662.214787</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 364.464811</td>\n",
        "      <td> 372.818338</td>\n",
        "      <td>NaN</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1803</th>\n",
        "      <td>NaN</td>\n",
        "      <td> 472.0535</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 603.090394</td>\n",
        "      <td> 766.197011</td>\n",
        "      <td> 674.453726</td>\n",
        "      <td> 1266.407109</td>\n",
        "      <td> 359.932582</td>\n",
        "      <td> 775.668711</td>\n",
        "      <td> 538.376199</td>\n",
        "      <td>...</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 459.708986</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 662.371047</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 364.464811</td>\n",
        "      <td> 372.818338</td>\n",
        "      <td>NaN</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1804</th>\n",
        "      <td>NaN</td>\n",
        "      <td> 472.0535</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 603.716751</td>\n",
        "      <td> 766.178127</td>\n",
        "      <td> 674.453726</td>\n",
        "      <td> 1268.508683</td>\n",
        "      <td> 359.932582</td>\n",
        "      <td> 775.668711</td>\n",
        "      <td> 538.376199</td>\n",
        "      <td>...</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 459.708986</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 662.527345</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 364.464811</td>\n",
        "      <td> 372.818338</td>\n",
        "      <td>NaN</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 260 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "gdp pc test  Abkhazia  Afghanistan  Akrotiri and Dhekelia     Albania  \\\n",
        "1800              NaN     472.0535                    NaN  601.215222   \n",
        "1801              NaN     472.0535                    NaN  601.839631   \n",
        "1802              NaN     472.0535                    NaN  602.464688   \n",
        "1803              NaN     472.0535                    NaN  603.090394   \n",
        "1804              NaN     472.0535                    NaN  603.716751   \n",
        "\n",
        "gdp pc test     Algeria  American Samoa      Andorra      Angola    Anguilla  \\\n",
        "1800         766.253664      674.453726  1260.123256  359.932582  775.668711   \n",
        "1801         766.234779      674.453726  1262.214402  359.932582  775.668711   \n",
        "1802         766.215895      674.453726  1264.309018  359.932582  775.668711   \n",
        "1803         766.197011      674.453726  1266.407109  359.932582  775.668711   \n",
        "1804         766.178127      674.453726  1268.508683  359.932582  775.668711   \n",
        "\n",
        "gdp pc test  Antigua and Barbuda         ...           Western Sahara  \\\n",
        "1800                  538.376199         ...                      NaN   \n",
        "1801                  538.376199         ...                      NaN   \n",
        "1802                  538.376199         ...                      NaN   \n",
        "1803                  538.376199         ...                      NaN   \n",
        "1804                  538.376199         ...                      NaN   \n",
        "\n",
        "gdp pc test     Vietnam  Virgin Islands (U.S.)  Yemen Arab Republic (Former)  \\\n",
        "1800         459.708986                    NaN                           NaN   \n",
        "1801         459.708986                    NaN                           NaN   \n",
        "1802         459.708986                    NaN                           NaN   \n",
        "1803         459.708986                    NaN                           NaN   \n",
        "1804         459.708986                    NaN                           NaN   \n",
        "\n",
        "gdp pc test  Yemen Democratic (Former)  Yemen, Rep.  Yugoslavia      Zambia  \\\n",
        "1800                               NaN   661.902376         NaN  364.464811   \n",
        "1801                               NaN   662.058563         NaN  364.464811   \n",
        "1802                               NaN   662.214787         NaN  364.464811   \n",
        "1803                               NaN   662.371047         NaN  364.464811   \n",
        "1804                               NaN   662.527345         NaN  364.464811   \n",
        "\n",
        "gdp pc test    Zimbabwe  \u00c5land  \n",
        "1800         372.818338    NaN  \n",
        "1801         372.818338    NaN  \n",
        "1802         372.818338    NaN  \n",
        "1803         372.818338    NaN  \n",
        "1804         372.818338    NaN  \n",
        "\n",
        "[5 rows x 260 columns]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 2(b)\n",
      "\n",
      "Graphically display the distribution of income per person across all countries in the world for any given year (e.g. 2000).  What kind of plot would be best? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we use a histogram to plot the distribution of income per person in a given year across all the countries on the dollar scale and the log10(dollar) scale. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "year = 2000\n",
      "plt.plot(subplots=True)\n",
      "plt.hist(income.ix[year].dropna().values, bins = 20)\n",
      "plt.title('Year: %i' % year)\n",
      "plt.xlabel('Income per person')\n",
      "plt.ylabel('Frequency')\n",
      "plt.show()\n",
      "\n",
      "plt.hist(np.log10(income.ix[year].dropna().values), bins = 20)\n",
      "plt.title('Year: %i' % year)\n",
      "plt.xlabel('Income per person (log10 scale)')\n",
      "plt.ylabel('Frequency')\n",
      "plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10976c6d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1098b4050>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 2(c)\n",
      "\n",
      "Write a function to merge the `countries` and `income` data sets for any given year. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\"\n",
      "Function\n",
      "--------\n",
      "mergeByYear\n",
      "\n",
      "Return a merged DataFrame containing the income, \n",
      "country name and region for a given year. \n",
      "\n",
      "Parameters\n",
      "----------\n",
      "year : int\n",
      "    The year of interest\n",
      "\n",
      "Returns\n",
      "-------\n",
      "a DataFrame\n",
      "   A pandas DataFrame with three columns titled \n",
      "   'Country', 'Region', and 'Income'. \n",
      "\n",
      "Example\n",
      "-------\n",
      ">>> mergeByYear(2010)\n",
      "\"\"\"\n",
      "#your code here\n",
      "\n",
      "def mergeByYear(year):\n",
      "    data = pd.DataFrame(income.ix[year].values, columns = ['Income'])\n",
      "    data['Country'] = income.columns\n",
      "    joined = pd.merge(data, countries, how=\"inner\", on=['Country'])\n",
      "    joined.Income = np.round(joined.Income, 2)\n",
      "    return joined\n",
      "\n",
      "mergeByYear(2010).head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Income</th>\n",
        "      <th>Country</th>\n",
        "      <th>Region</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>  1214.61</td>\n",
        "      <td> Afghanistan</td>\n",
        "      <td>   ASIA</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>  6746.45</td>\n",
        "      <td>     Albania</td>\n",
        "      <td> EUROPE</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>  6300.65</td>\n",
        "      <td>     Algeria</td>\n",
        "      <td> AFRICA</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 33052.28</td>\n",
        "      <td>     Andorra</td>\n",
        "      <td> EUROPE</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>  5497.62</td>\n",
        "      <td>      Angola</td>\n",
        "      <td> AFRICA</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "     Income      Country  Region\n",
        "0   1214.61  Afghanistan    ASIA\n",
        "1   6746.45      Albania  EUROPE\n",
        "2   6300.65      Algeria  AFRICA\n",
        "3  33052.28      Andorra  EUROPE\n",
        "4   5497.62       Angola  AFRICA"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 2(d) \n",
      "\n",
      "Use exploratory data analysis tools such as histograms and boxplots to explore the distribution of the income per person by region data set from 2(c) for a given year. Describe how these change through the recent years?\n",
      "\n",
      "**Hint**: Use a `for` loop to consider multiple years.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "years = np.arange(1950, 2010, 10)\n",
      "\n",
      "for yr in years:\n",
      "    df = mergeByYear(yr)\n",
      "    df.boxplot('Income', by = 'Region', rot = 90)\n",
      "    plt.title(\"Year:\" + str(yr))\n",
      "    plt.ylabel('Income per person (log10 scale)')\n",
      "    plt.ylim(10**2, 10.5 **5)\n",
      "    plt.yscale('log')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gjeF3J3y/sXnz5lGr1ab0gSnTt35dU0R8iKKIKIqYP38+eFoj/DxgH6wB/THg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\n30t1uZUqi09Y2Dx5YfNxma3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       "text": [
        "<matplotlib.figure.Figure at 0x10a5304d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bMWMG1Wp1VLlvkb7165oikoUgCAiCgJkzZ0IP4zR6cRVwENaA/jTwBaxH1eFY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\nrHF4NvZQrWDfxqdhkxfOzyy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       "text": [
        "<matplotlib.figure.Figure at 0x10a703f10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/w1imcUKE9wIPJY0gCEI35XTOmbZKJWBkpOo7jMR1ei3zpgzpLEMawU86uylp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\nREREREREREREREREREREJA3/H0uWZlkzdYI8AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b2071d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yrio9bq7HShrHYjNRA/wBy0zae1SVWQj3UqSwXsG6Yz4LvBzbbu5X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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b2feb50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bdDhWlhY3i7AnjVOwkagB/ohlJs0tqorMh2spklsvY80xnwNeCq3X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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b559510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eCeW+qtMQEWktiiKiKGJgYAA8zRF+MbAnVoH+JPA5rEXV/lhF9ySsE9+XJvCZ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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b6a4e90>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In recent years, Africa and Asia have an upwards trend in average income per person while other continents have stayed more constant through the 20th century. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Discussion for Problem 2\n",
      "\n",
      "*Write a brief discussion of your conclusions to the questions and tasks above in 100 words or less.*\n",
      "\n",
      "In most continents (especially Africa and Asia), we see that the distribution of incomes is very skewed: most countries are in a group of low-income states with a fat tail of high-income countries that remains approximately constant throughout the 20th century.  In 2(b) we used a histogram to look at the income distribution of all countries in the world for a given year saw a non-normal distribution. In 2(d) we used boxplots to take a closer look at the income distribution of countries grouped by regions across decades.  We saw upward trends in average income per person across certain regions (e.g. Africa) as we moved through the 20th century.\n",
      "\n",
      "---\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem 3\n",
      "\n",
      "In general, if group A has larger values than group B on average, does this mean the largest values are from group A? Discuss after completing each of the problems below. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 3(a)\n",
      "\n",
      "Assume you have two list of numbers, X and Y, with distribution approximately normal. X and Y have standard deviation equal to 1, but the average of X is different from the average of Y.  If the difference in the average of X and the average of Y is larger than 0, how does the proportion of X > a compare to the proportion of Y > a? "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Write a function that analytically calculates the ratio of these two proportions: Pr(X > a)/Pr(Y > a) as function of the difference in the average of X and the average of Y. \n",
      "\n",
      "**Hint**: Use the `scipy.stats` module for useful functions related to a normal random variable such as the probability density function, cumulative distribution function and survival function. \n",
      "\n",
      "**Update**: Assume Y is normally distributed with mean equal to 0. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Show the curve for different values of a (a = 2,3,4 and 5)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\"\n",
      "Function\n",
      "--------\n",
      "ratioNormals\n",
      "\n",
      "Return ratio of these two proportions: \n",
      "    Pr(X > a)/Pr(Y > a) as function of \n",
      "    the difference in the average of X \n",
      "    and the average of Y. \n",
      "\n",
      "Parameters\n",
      "----------\n",
      "diff : difference in the average of X \n",
      "    and the average of Y. \n",
      "a : cutoff value\n",
      "\n",
      "Returns\n",
      "-------\n",
      "Returns ratio of these two proportions: \n",
      "    Pr(X > a)/Pr(Y > a)\n",
      "    \n",
      "Example\n",
      "-------\n",
      ">>> ratioNormals(diff = 1, a = 2)\n",
      "\"\"\"\n",
      "#your code here\n",
      "\n",
      "def ratioNormals(diff, a):\n",
      "    X = scipy.stats.norm(loc=diff, scale=1)\n",
      "    Y = scipy.stats.norm(loc=0, scale=1) \n",
      "    return X.sf(a) / Y.sf(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "# let diff range from 0 to 5 \n",
      "diffs = np.linspace(0, 5, 50)\n",
      "a_values = range(2,6)\n",
      "\n",
      "# Plot separate curves for \n",
      "# Pr(X > a) / Pr(Y > a) as a function of diff\n",
      "# for all given values of a\n",
      "plt.figure(figsize=(8,5));\n",
      "for a in a_values:\n",
      "    ratios = [ratioNormals(diff, a) for diff in diffs]\n",
      "    plt.plot(diffs, ratios)\n",
      "    \n",
      "# Labels\n",
      "plt.legend([\"a={}\".format(a) for a in a_values], loc=0);\n",
      "plt.xlabel('Diff');\n",
      "plt.ylabel('Pr(X>a) / Pr(Y>a)');\n",
      "plt.title('Ratio of Pr(X > a) to Pr(Y > a) as a Function of Diff');\n",
      "\n",
      "# Using a log scale so you can actually see the curves\n",
      "plt.yscale('log')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xk8PLubmc7+3NsyNGcJGvr+TEhc2yVEDvcdYxMTHxzLaM6S6E6Kxfqqr4b1YW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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d0265d0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 3(b)\n",
      "\n",
      "Now consider the distribution of income per person from two regions: Asia and South America. Estimate the average income per person across the countries in those two regions. Which region has the larger average of income per person across the countries in that region? \n",
      "\n",
      "**Update**: Use the year 2012. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "merged = mergeByYear(2012).groupby('Region', as_index=False).mean()\n",
      "merged = merged.loc[(merged.Region == \"ASIA\") | (merged.Region == \"SOUTH AMERICA\")]\n",
      "merged.Income = np.round(merged.Income, 2)\n",
      "merged"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Region</th>\n",
        "      <th>Income</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>          ASIA</td>\n",
        "      <td> 14510.04</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> SOUTH AMERICA</td>\n",
        "      <td>  9471.47</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "          Region    Income\n",
        "1           ASIA  14510.04\n",
        "5  SOUTH AMERICA   9471.47"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Asia has a larger income compared to South America. We can also create boxplots to see the income distribution of the two continents on the dollar scale and log10(dollar) scale. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = mergeByYear(2012)\n",
      "df = df.loc[(df.Region == \"ASIA\") | (df.Region == \"SOUTH AMERICA\")]\n",
      "df.boxplot('Income', by = 'Region', rot = 90)\n",
      "plt.ylabel('Income per person (dollars)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.text.Text at 0x10b09ba90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1ylcQyUuSNA6VUfMZT6z5jMA+H0lj1ep1PpIktZXJR21XHYIpdQrP2eKZfCRJ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\no5EkSZIkSZIkSZIkSZIkSZIkSXn6Pz4AZKU8OVyFAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a053a50>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = mergeByYear(2012)\n",
      "df = df.loc[(df.Region == \"ASIA\") | (df.Region == \"SOUTH AMERICA\")]\n",
      "df.boxplot('Income', by = 'Region', rot = 90)\n",
      "plt.ylabel('Income per person (log10 scale)')\n",
      "plt.yscale('log')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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erorHJOVseWL7M8Cn4vZWbD6FvSRtxprGYEoWDl9Ka2r6jSXEIqVx5gT3NYB3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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a3ff690>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 3(c) \n",
      "\n",
      "Calculate the proportion of countries with income per person that is greater than 10,000 dollars. Which region has a larger proportion of countries with income per person greater than 10,000 dollars? If the answer here is different from the answer in 3(b), explain why in light of your answer to 3(a).\n",
      "\n",
      "**Update**: Use the year 2012. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ratioCountries(groupedData, a):\n",
      "    prop = [len(group.Income[group.Income >= a]) / float(len(group.Income.dropna())) for key, group in groupedData]\n",
      "    z = pd.DataFrame(groupedData.mean().index, columns = ['Region'])\n",
      "    z['Mean'] = np.round(groupedData.mean().values,2)\n",
      "    z['P(X > %g)' % a] = np.round(prop, 4)\n",
      "    return z\n",
      "\n",
      "df = mergeByYear(2012).groupby('Region')\n",
      "df_ratio = ratioCountries(df, 1e4)\n",
      "df_ratio = df_ratio[(df_ratio.Region == 'ASIA') | (df_ratio.Region == 'SOUTH AMERICA')]\n",
      "df_ratio"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Region</th>\n",
        "      <th>Mean</th>\n",
        "      <th>P(X &gt; 10000)</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>          ASIA</td>\n",
        "      <td> 14510.04</td>\n",
        "      <td> 0.3684</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> SOUTH AMERICA</td>\n",
        "      <td>  9471.47</td>\n",
        "      <td> 0.4167</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "          Region      Mean  P(X > 10000)\n",
        "1           ASIA  14510.04        0.3684\n",
        "5  SOUTH AMERICA   9471.47        0.4167"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "South America has a larger proportion of countries greater than 10,000 dollars compared to Asia. This is different from the answer in 3(b). Because Asia does not have a normal distribution, the theory in Problem in 3(a) is not applicable here.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 3(d)\n",
      "\n",
      "**For AC209 Students**: Re-run this analysis in Problem 3 but compute the average income per person for each region, instead of the average of the reported incomes per person across countries in the region. Why are these two different? Hint: use this [data set](https://spreadsheets.google.com/pub?key=phAwcNAVuyj0XOoBL_n5tAQ&gid=0). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#your code here\n",
      "\n",
      "# First import the population data:\n",
      "population_link = 'https://spreadsheets.google.com/pub?key=phAwcNAVuyj0XOoBL_n5tAQ&output=xls'\n",
      "source = StringIO.StringIO(requests.get(population_link).content)\n",
      "population = pd.read_excel(source, sheetname = \"Data\")\n",
      "\n",
      "# Put years as index and countries as column names\n",
      "population.columns = ['Country'] + map(int, list(population.columns)[1:])\n",
      "population.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Country</th>\n",
        "      <th>1700</th>\n",
        "      <th>1730</th>\n",
        "      <th>1750</th>\n",
        "      <th>1785</th>\n",
        "      <th>1786</th>\n",
        "      <th>1787</th>\n",
        "      <th>1788</th>\n",
        "      <th>1789</th>\n",
        "      <th>1790</th>\n",
        "      <th>...</th>\n",
        "      <th>2004</th>\n",
        "      <th>2005</th>\n",
        "      <th>2006</th>\n",
        "      <th>2007</th>\n",
        "      <th>2008</th>\n",
        "      <th>2009</th>\n",
        "      <th>2010</th>\n",
        "      <th>2011</th>\n",
        "      <th>2012</th>\n",
        "      <th>2013</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>              Abkhazia</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>...</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>           Afghanistan</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>...</td>\n",
        "      <td> 26693486</td>\n",
        "      <td> 27614718</td>\n",
        "      <td> 28420974</td>\n",
        "      <td> 29145841</td>\n",
        "      <td> 29839994</td>\n",
        "      <td> 30577756</td>\n",
        "      <td> 31411743</td>\n",
        "      <td> 32358260</td>\n",
        "      <td> 33397058</td>\n",
        "      <td> 34499915</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> Akrotiri and Dhekelia</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>...</td>\n",
        "      <td>      NaN</td>\n",
        "      <td>    15700</td>\n",
        "      <td>      NaN</td>\n",
        "      <td>      NaN</td>\n",
        "      <td>    15700</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>               Albania</td>\n",
        "      <td>  300000</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>...</td>\n",
        "      <td>  3124861</td>\n",
        "      <td>  3141800</td>\n",
        "      <td>  3156607</td>\n",
        "      <td>  3169665</td>\n",
        "      <td>  3181397</td>\n",
        "      <td>  3192723</td>\n",
        "      <td>  3204284</td>\n",
        "      <td>  3215988</td>\n",
        "      <td>  3227373</td>\n",
        "      <td>  3238316</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>               Algeria</td>\n",
        "      <td> 1750000</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>...</td>\n",
        "      <td> 32396048</td>\n",
        "      <td> 32888449</td>\n",
        "      <td> 33391954</td>\n",
        "      <td> 33906605</td>\n",
        "      <td> 34428028</td>\n",
        "      <td> 34950168</td>\n",
        "      <td> 35468208</td>\n",
        "      <td> 35980193</td>\n",
        "      <td> 36485828</td>\n",
        "      <td> 36983924</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 233 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "                 Country     1700  1730  1750  1785  1786  1787  1788  1789  \\\n",
        "0               Abkhazia      NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
        "1            Afghanistan      NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
        "2  Akrotiri and Dhekelia      NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
        "3                Albania   300000   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
        "4                Algeria  1750000   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
        "\n",
        "   1790  ...       2004      2005      2006      2007      2008      2009  \\\n",
        "0   NaN  ...        NaN       NaN       NaN       NaN       NaN       NaN   \n",
        "1   NaN  ...   26693486  27614718  28420974  29145841  29839994  30577756   \n",
        "2   NaN  ...        NaN     15700       NaN       NaN     15700       NaN   \n",
        "3   NaN  ...    3124861   3141800   3156607   3169665   3181397   3192723   \n",
        "4   NaN  ...   32396048  32888449  33391954  33906605  34428028  34950168   \n",
        "\n",
        "       2010      2011      2012      2013  \n",
        "0       NaN       NaN       NaN       NaN  \n",
        "1  31411743  32358260  33397058  34499915  \n",
        "2       NaN       NaN       NaN       NaN  \n",
        "3   3204284   3215988   3227373   3238316  \n",
        "4  35468208  35980193  36485828  36983924  \n",
        "\n",
        "[5 rows x 233 columns]"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider we have $M$ regions.  Let $R_j$ be the number of countries in the $j^{th}$ region where $j = 1, \\ldots, M$.  \n",
      "\n",
      "If the income per person in a country $i$ is $I_i$, we previously calculated the average income per person over $R_j$ countries in the $j^{th}$ region using the following formula: \n",
      "    $$\\bar{S}_j = \\frac{1}{R_j}\\sum_{i=1}^{R_j} I_i$$\n",
      "Now, we want to consider the average income in a given region adjusting for each countries' population $N_i$. Therefore, we use the following formula to calculate an average income in a given region $R_j$ adjusting for the population in each country: \n",
      "     $$ \\bar{S}_j = \\frac{S_1 + S_2 + \\ldots + S_{R_j}}{N_1 + N_2 + \\ldots + N_{R_j} } = \\frac{N_1 * I_1 + N_2 * I_2 + \\ldots + N_{R_j} * I_{R_j}}{N_1 + N_2 + \\ldots + N_{R_j} }$$\n",
      "    \n",
      "We start by creating a function similar to `mergeByYear()` from 2(c) which merges the income for each country in a given region, but also includes the population for each country. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mergeByYearWithPop(year):\n",
      "\n",
      "    # income DataFrame\n",
      "    income_df = pd.DataFrame(income.ix[year].values, columns = ['Income'])\n",
      "    income_df['Country'] = income.columns\n",
      "\n",
      "    # merge income DataFrame and countries\n",
      "    joined = pd.merge(income_df, countries, how=\"inner\", on=['Country'])\n",
      "    \n",
      "    # population DataFrame\n",
      "    population_df = population[['Country',year]]\n",
      "\n",
      "    # merge population DataFrame and joined DataFrame \n",
      "    joined = pd.merge(joined, population_df, how=\"inner\", on=['Country'])\n",
      "    joined.columns = list(joined.columns[:-1])+['TotalPopulation']\n",
      "    joined.Income = np.round(joined.Income, 2)\n",
      "    \n",
      "    def func(df):\n",
      "        totPop = df.sum()['TotalPopulation']\n",
      "        dfout = df\n",
      "        dfout['AdjustedIncome'] = df.Income * df.TotalPopulation / float(totPop)\n",
      "        dfout.AdjustedIncome = np.round(dfout.AdjustedIncome, 2)\n",
      "        return dfout\n",
      "        \n",
      "    # Group by region\n",
      "    returnDataFrame = joined.groupby('Region').apply(func)\n",
      "        \n",
      "    return returnDataFrame\n",
      "\n",
      "mergeByYearWithPop(2012).head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Income</th>\n",
        "      <th>Country</th>\n",
        "      <th>Region</th>\n",
        "      <th>TotalPopulation</th>\n",
        "      <th>AdjustedIncome</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1349.70</td>\n",
        "      <td> Afghanistan</td>\n",
        "      <td>   ASIA</td>\n",
        "      <td> 33397058</td>\n",
        "      <td>  11.13</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 6969.31</td>\n",
        "      <td>     Albania</td>\n",
        "      <td> EUROPE</td>\n",
        "      <td>  3227373</td>\n",
        "      <td>  37.68</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 6419.13</td>\n",
        "      <td>     Algeria</td>\n",
        "      <td> AFRICA</td>\n",
        "      <td> 36485828</td>\n",
        "      <td> 246.02</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>     NaN</td>\n",
        "      <td>     Andorra</td>\n",
        "      <td> EUROPE</td>\n",
        "      <td>    87518</td>\n",
        "      <td>    NaN</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 5838.16</td>\n",
        "      <td>      Angola</td>\n",
        "      <td> AFRICA</td>\n",
        "      <td> 20162517</td>\n",
        "      <td> 123.65</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "    Income      Country  Region  TotalPopulation  AdjustedIncome\n",
        "0  1349.70  Afghanistan    ASIA         33397058           11.13\n",
        "1  6969.31      Albania  EUROPE          3227373           37.68\n",
        "2  6419.13      Algeria  AFRICA         36485828          246.02\n",
        "3      NaN      Andorra  EUROPE            87518             NaN\n",
        "4  5838.16       Angola  AFRICA         20162517          123.65"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = mergeByYearWithPop(2012).groupby('Region').sum()\n",
      "df.Income = mergeByYear(2012).groupby('Region').mean().Income\n",
      "df.Income = np.round(df.Income, 2)\n",
      "df = df.ix[['ASIA', 'SOUTH AMERICA']]\n",
      "df"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Income</th>\n",
        "      <th>TotalPopulation</th>\n",
        "      <th>AdjustedIncome</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>ASIA</th>\n",
        "      <td> 14510.04</td>\n",
        "      <td> 4048448110</td>\n",
        "      <td>  6731.66</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>SOUTH AMERICA</th>\n",
        "      <td>  9471.47</td>\n",
        "      <td>  400557572</td>\n",
        "      <td> 10550.87</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "                 Income  TotalPopulation  AdjustedIncome\n",
        "ASIA           14510.04       4048448110         6731.66\n",
        "SOUTH AMERICA   9471.47        400557572        10550.87"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In 3(b) we computed the average income per person in each of the regions. The first column in the table above contains the averages from 3(b) (i.e. without adjusting for population). Column 2 contains the total population in the given region. The last column is the average income per person in each of the regions (adjusted for population).  \n",
      "\n",
      "To compare the boxplots from 3(b), here we plot the income per person for a given region (adjusted for population) on the log10 scale. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = mergeByYearWithPop(2012)\n",
      "df.AdjustedIncome = df['AdjustedIncome']\n",
      "df = df[(df.Region == 'ASIA') | (df.Region == 'SOUTH AMERICA')]\n",
      "df.boxplot('AdjustedIncome', by = 'Region', rot = 90)\n",
      "plt.yscale('log')\n",
      "plt.ylabel('Income per person adjusted for population (log10 scale)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<matplotlib.text.Text at 0x10ba6d250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qQEREUtRqDqQLKyT+hk1lMtZtH3TnckFNWCIiyUtqKpM7gB08zmVBNZCUqElA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\nWCJSJF2R/YrbnsKWupU2UwE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       "text": [
        "<matplotlib.figure.Figure at 0x10a77af50>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next let's repeat the analysis in 3(c)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ratioCountries(groupedData, a):\n",
      "    prop = [len(group.AdjustedIncome[group.AdjustedIncome >= a]) / float(len(group.AdjustedIncome.dropna())) for key, group in groupedData]\n",
      "    z = pd.DataFrame(groupedData.mean().index, columns = ['Region'])\n",
      "    z['AdjustedIncome'] = np.round(groupedData.AdjustedIncome.sum().values,2)\n",
      "    z['P(X > %g)' % a] = np.round(prop,4)\n",
      "    return z"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = mergeByYearWithPop(2012).groupby('Region')\n",
      "df_ratio = ratioCountries(df, 1e4)\n",
      "df_ratio = df_ratio[(df_ratio.Region == 'ASIA') | (df_ratio.Region == 'SOUTH AMERICA')]\n",
      "df_ratio\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Region</th>\n",
        "      <th>AdjustedIncome</th>\n",
        "      <th>P(X &gt; 10000)</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>          ASIA</td>\n",
        "      <td>  6731.66</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> SOUTH AMERICA</td>\n",
        "      <td> 10550.87</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "          Region  AdjustedIncome  P(X > 10000)\n",
        "1           ASIA         6731.66             0\n",
        "5  SOUTH AMERICA        10550.87             0"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we lower the value `a` from 10,000 to 1,000:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = mergeByYearWithPop(2012).groupby('Region')\n",
      "df_ratio = ratioCountries(df, 1e3)\n",
      "df_ratio = df_ratio[(df_ratio.Region == 'ASIA') | (df_ratio.Region == 'SOUTH AMERICA')]\n",
      "df_ratio"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Region</th>\n",
        "      <th>AdjustedIncome</th>\n",
        "      <th>P(X &gt; 1000)</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>          ASIA</td>\n",
        "      <td>  6731.66</td>\n",
        "      <td> 0.0526</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> SOUTH AMERICA</td>\n",
        "      <td> 10550.87</td>\n",
        "      <td> 0.1667</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "          Region  AdjustedIncome  P(X > 1000)\n",
        "1           ASIA         6731.66       0.0526\n",
        "5  SOUTH AMERICA        10550.87       0.1667"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The solutions to Problem 3(d) are different because here we are correcting for the countries with the largest populations.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Discussion for Problem 3\n",
      "\n",
      "*Write a brief discussion of your conclusions to the questions and tasks above in 100 words or less.*\n",
      "\n",
      "---\n",
      "\n",
      "The start of Problem 3 asked: *If group A has larger values than group B on average, does this mean the largest values are from group A?*.  After completely Problem 3, we see the answer is no.  In 2012, Asia had a larger average income per person compared to South America, but because the distributions of Asia and South America are different (e.g. Asia is not normally distributed), we saw the probability of seeing extreme values in Asia is smaller than the probability of seeing extreme values in South America.  When we adjust the incomes for the population of each country, we are correcting for the problem of outliers or the countries with the largest populations. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    }
   ],
   "metadata": {}
  }
 ]
}