The 2000 U.S. presidential election was very close, especially in the state of Florida. Indeed, newscasters were unable to predict a winner the day after the election because they could not decide who was going to win Florida’s 25 electoral votes. Many voters in Palm Beach County complained that they were confused by the design of the ballot and might have voted for Patrick Buchanan instead of Al Gore, as they had intended. Table 11.32 displays the official bailot counts (after all official recounts) for each county. There was no reason, prior to the election, to think that Patrick Buchanan would gather a significantly higher percent of the vote in Palm Beach County than in any other Florida county.
a. Draw a plot of the vote count for Patrick Buchanan against the total vote count with one point for each county. Identify the point corresponding to Palm Beach County.
b. Given the complaints about the Palm Beach bailot, it might be sensible to treat the data point for Palm Beach County as being different from the others. Fit a simple linear regression model with Y being the vote for Buchanan and X being the total vote in each county, excluding Palm Beach County.
c. Plot the residuals from the regression in part (b) against the X variable. Do you notice any pattern in the plot?
d. The variance of the vote for each candidate in a county ought to depend on the total vote in the county. The larger the total vote, the more variance you expect in the vote for each candidate. For this reason, the assumptions of the simple linear regression model would not hold. As an Alternative, fit a simple linear regression with Y being the logarithm of the vote for Buchanan and X being the logarithm of the total vote in each county. Continue to exclude Palm Beach County.
e. Plot the residuals from the regression in part (d) against the X variable. Do you notice any pattern in the plot?
f. Using the model fit in part (d), form a 99 percent prediction interval for the Buchanan vote (not the logarithm of the Buchanan vote) in Palm Beach County.
g. Let B be the upper endpoint of the interval you found in part (f). Just suppose that the actual number of people in Palm Beach County who voted for Buchanan had actually been B instead of 3411. Also suppose that the remaining 3411− B voters had actually voted for Gore. Would this have changed the winner of the total popular vote for the State of Florida?