Homework 1. Which of two things is larger? (SOLUTIONS)

Due: Thursday, September 19, 11:59 PM

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Useful libraries for this assignment

In [8]:
# special IPython command to prepare the notebook for matplotlib
%matplotlib inline 

from fnmatch import fnmatch

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import requests
from pattern import web

# set some nicer defaults for matplotlib
from matplotlib import rcParams

#these colors come from colorbrewer2.org. Each is an RGB triplet
dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),
                (0.8509803921568627, 0.37254901960784315, 0.00784313725490196),
                (0.4588235294117647, 0.4392156862745098, 0.7019607843137254),
                (0.9058823529411765, 0.1607843137254902, 0.5411764705882353),
                (0.4, 0.6509803921568628, 0.11764705882352941),
                (0.9019607843137255, 0.6705882352941176, 0.00784313725490196),
                (0.6509803921568628, 0.4627450980392157, 0.11372549019607843),
                (0.4, 0.4, 0.4)]

rcParams['figure.figsize'] = (10, 6)
rcParams['figure.dpi'] = 150
rcParams['axes.color_cycle'] = dark2_colors
rcParams['lines.linewidth'] = 2
rcParams['axes.grid'] = True
rcParams['axes.facecolor'] = '#eeeeee'
rcParams['font.size'] = 14
rcParams['patch.edgecolor'] = 'none'


This was the XKCD comic after the 2012 Presidential election:

The comic refers to the fact that Nate Silver's statistical model (which is based mostly on combining information from pre-election polls) correctly predicted the outcome of the 2012 presidential race in all 50 states.

Polling data isn't a perfect predictor for the future, and some polls are more accurate than others. This means that election forecastors must consider prediction uncertainty when building models.

In this first assignment, you will perform a simple analysis of polling data about the upcoming Governor races. The assignment has three main parts:

First you will build some tools to download historical polling data from the web, and parse it into a more convenient format.

Next you will use these tools to aggregate and visualize several past Governor races

Finally you will run a bootstrap analysis to estimate the probable outcome of current Governor races, given the level of precision of historical polls.

Part 1: Collect and Clean

The Real Clear Politics website archives many political polls. In addition, they combine related polls to form an "RCP average" estimate of public opinion over time. For example, the chart on this page shows historical polling data for the Obama-Romney presidential race. The chart is an average of the polling data table below the chart.

The data used to generate plots like this are stored as XML pages, with URLs like:


Here, [id] is a unique integer, found at the end of the URL of the page that displays the graph. The id for the Obama-Romney race is 1171:


Opening this page in Google Chrome or Firefox will show you the XML content in an easy-to-read format. Notice that XML tags are nested inside each other, hierarchically (the jargony term for this is the "Document Object Model", or "DOM"). The first step of webscraping is almost always exploring the HTML/XML source in a browser, and getting a sense of this hierarchy.

Problem 0

The above XML page includes 5 distinct tags (one, for example, is chart). List these tags, and depict how they nest inside each other using an indented list. For example:

  • Page
    • Section
      • Paragraph
    • Conclusion
  • chart
    • series
      • value
    • graphs
      • graph
        • value

Problem 1

We want to download and work with poll data like this. Like most programming tasks, we will break this into many smaller, easier pieces

Fill in the code for the get_poll_xml function, that finds and downloads an XML page discussed above


requests.get("http://www.google.com").text downloads the text from Google's homepage

In [9]:

Given a poll_id, return the XML data as a text string

poll_id : int
    The ID of the poll to fetch

xml : str
    The text of the XML page for that poll_id

>>> get_poll_xml(1044)
u'<?xml version="1.0" encoding="UTF-8"?><chart><series><value xid=\'0\'>1/27/2009</value>
#your code here    

def get_poll_xml(poll_id):
    url = "http://charts.realclearpolitics.com/charts/%i.xml" % int(poll_id)
    return requests.get(url).text

Here are some other functions we'll use later. plot_colors contains hints about parsing XML data.

In [10]:
# "r"egular "e"xpressions is kind of a mini-language to
# do pattern matching on text
import re

def _strip(s):
    """This function removes non-letter characters from a word
    for example _strip('Hi there!') == 'Hi there'
    return re.sub(r'[\W_]+', '', s)

def plot_colors(xml):
    Given an XML document like the link above, returns a python dictionary
    that maps a graph title to a graph color.
    Both the title and color are parsed from attributes of the <graph> tag:
    <graph title="the title", color="#ff0000"> -> {'the title': '#ff0000'}
    These colors are in "hex string" format. This page explains them:
    >>> plot_colors(get_poll_xml(1044))
    {u'Approve': u'#000000', u'Disapprove': u'#FF0000'}
    dom = web.Element(xml)
    result = {}
    for graph in dom.by_tag('graph'):
        title = _strip(graph.attributes['title'])
        result[title] = graph.attributes['color']
    return result

Problem 2

Even though get_poll_xml pulls data from the web into Python, it does so as a block of text. This still isn't very useful. Use the web module in pattern to parse this text, and extract data into a pandas DataFrame.


  • You might want create python lists for each column in the XML. Then, to turn these lists into a DataFrame, run

pd.DataFrame({'column_label_1': list_1, 'column_label_2':list_2, ...})

  • use the pandas function pd.to_datetime to convert strings into dates
In [11]:

    Extract poll information from an XML string, and convert to a DataFrame

    xml : str
        A string, containing the XML data from a page like 
    A pandas DataFrame with the following columns:
        date: The date for each entry
        title_n: The data value for the gid=n graph (take the column name from the `title` tag)
    This DataFrame should be sorted by date
    Consider the following simple xml page:
    <value xid="0">1/27/2009</value>
    <value xid="1">1/28/2009</value>
    <graph gid="1" color="#000000" balloon_color="#000000" title="Approve">
    <value xid="0">63.3</value>
    <value xid="1">63.3</value>
    <graph gid="2" color="#FF0000" balloon_color="#FF0000" title="Disapprove">
    <value xid="0">20.0</value>
    <value xid="1">20.0</value>
    Given this string, rcp_poll_data should return
    result = pd.DataFrame({'date': pd.to_datetime(['1/27/2009', '1/28/2009']), 
                           'Approve': [63.3, 63.3], 'Disapprove': [20.0, 20.0]})
#your code here
def rcp_poll_data(xml): 
    dom = web.Element(xml)
    result = {}
    dates = dom.by_tag('series')[0]    
    dates = {n.attributes['xid']: str(n.content) for n in dates.by_tag('value')}
    keys = dates.keys()
    result['date'] = pd.to_datetime([dates[k] for k in keys])
    for graph in dom.by_tag('graph'):
        name = graph.attributes['title']
        data = {n.attributes['xid']: float(n.content) 
                if n.content else np.nan for n in graph.by_tag('value')}
        result[name] = [data[k] for k in keys]
    result = pd.DataFrame(result)    
    result = result.sort(columns=['date'])
    return result

The output from rcp_poll_data is much more useful for analysis. For example, we can plot with it:

In [12]:
def poll_plot(poll_id):
    Make a plot of an RCP Poll over time
    poll_id : int
        An RCP poll identifier

    # hey, you wrote two of these functions. Thanks for that!
    xml = get_poll_xml(poll_id)
    data = rcp_poll_data(xml)
    colors = plot_colors(xml)

    #remove characters like apostrophes
    data = data.rename(columns = {c: _strip(c) for c in data.columns})

    #normalize poll numbers so they add to 100%    
    norm = data[colors.keys()].sum(axis=1) / 100    
    for c in colors.keys():
        data[c] /= norm
    for label, color in colors.items():
        plt.plot(data.date, data[label], color=color, label=label)        
    plt.ylabel("Normalized Poll Percentage")

If you've done everything right so far, the following code should reproduce the graph on this page

In [13]:
plt.title("Obama Job Approval")
<matplotlib.text.Text at 0x10661b290>

Part 2: Aggregate and Visualize

Problem 3

Unfortunately, these data don't have any error bars. If a candidate leads by 10% in the RCP average, is she a shoo-in to win? Or is this number too close to call? Does a 10% poll lead mean more 1 day before a race than it does 1 week before? Without error estimates, these questions are impossible to answer.

To get a sense of how accurate the RCP polls are, you will gather data from many previous Governor races, where the outcome is known.

This url has links to many governer races.


Notice that each link to a governor race has the following URL pattern:


Write a function that scans html for links to URLs like this

Hint The fnmatch function is useful for simple string matching tasks.

In [14]:

    Find and return links to RCP races on a page like
    html : str
        The HTML content of a page to scan
    A list of urls for Governer race pages
    For a page like
    <a href="http://www.realclearpolitics.com/epolls/2010/governor/ma/massachusetts_governor_baker_vs_patrick_vs_cahill-1154.html"></a>
    <a href="http://www.realclearpolitics.com/epolls/2010/governor/ca/california_governor_whitman_vs_brown-1113.html"></a>
    find_governor_races would return
#your code here

def is_gov_race(l):
    """return True if a URL refers to a Governor race"""    
    pattern = 'http://www.realclearpolitics.com/epolls/????/governor/??/*-*.html'
    return fnmatch(l, pattern)
def find_governor_races(html):
    dom = web.Element(html)
    links = [a.attributes.get('href', '') for a in dom.by_tag('a')] 
    links = [l for l in links if is_gov_race(l)]
    #eliminate duplicates!
    links = list(set(links))
    return links

Problem 4

At this point, you have functions to find a collection of governor races, download historical polling data from each one, parse them into a numerical DataFrame, and plot this data.

The main question we have about these data are how accurately they predict election outcomes. To answer this question, we need to grab the election outcome data.

Write a function that looks up and returns the election result on a page like this one.

Remember to look at the HTML source!

You can do this by selection view->developer->view source in Chrome, or Tools -> web developer -> page source in Firefox. Altenatively, you can right-click on a part of the page, and select "inspect element"

In [15]:

    Return the actual voting results on a race page
    url : string
        The website to search through
    A dictionary whose keys are candidate names,
    and whose values is the percentage of votes they received.
    If necessary, normalize these numbers so that they add up to 100%.
    >>> url = 'http://www.realclearpolitics.com/epolls/2010/governor/ca/california_governor_whitman_vs_brown-1113.html'
    >>> race_result(url)
    {'Brown': 56.0126582278481, 'Whitman': 43.9873417721519}
#your code here
def race_result(url):
    dom = web.Element(requests.get(url).text)
    table = dom.by_tag('div#polling-data-rcp')[0]
    result_data = table.by_tag('tr.final')[0]
    td = result_data.by_tag('td')

    results = [float(t.content) for t in td[3:-1]]
    tot = sum(results) / 100
    #get table headers
    headers = table.by_tag('th')
    labels = [str(t.content).split('(')[0].strip() for t in headers[3:-1]]
    return {l:r / tot for l, r in zip(labels, results)}

Here are some more utility functions that take advantage of what you've done so far.

In [16]:
def id_from_url(url):
    """Given a URL, look up the RCP identifier number"""
    return url.split('-')[-1].split('.html')[0]

def plot_race(url):
    """Make a plot summarizing a senate race
    Overplots the actual race results as dashed horizontal lines
    #hey, thanks again for these functions!
    id = id_from_url(url)
    xml = get_poll_xml(id)    
    colors = plot_colors(xml)

    if len(colors) == 0:
    #really, you shouldn't have
    result = race_result(url)
    plt.ylabel("Polling Percentage")
    for r in result:
        plt.axhline(result[r], color=colors[_strip(r)], alpha=0.6, ls='--')

Now that this is done, we can easily visualize many historical Governer races. The solid line plots the poll history, the dotted line reports the actual result.

If this code block fails, you probably have a bug in one of your functions.

In [17]:
page = requests.get('http://www.realclearpolitics.com/epolls/2010/governor/2010_elections_governor_map.html').text.encode('ascii', 'ignore')

for race in find_governor_races(page):