The 2000 U.S. presidential election was one of the most controversial in history with the final outcome ultimately being decided in a court of law rather than in the voting booth. At issue were the election results in Palm Beach, Florida. Palm Beach County used a so-called "butterfly" ballot where the candidates' names were arranged to the left and right of a center row of holes. Voters were to specify their preference by "punching" the appropriate hole next to the desired candidate. According to several news accounts, many voters in Palm Beach, Florida claimed they were confused by the ballot structure and may have inadvertently voted for Pat Buchanan when in fact they intended to vote for Al Gore. This allegedly contributed to Gore not obtaining enough votes to overtake George W. Bush's slim margin of victory in Florida-and ultimately cost Gore the election.

The file Votes.xlsx contains the original vote totals by Florida county for Gore, Bush, and Buchanan as of November 8, 2000. (These data reflect the results prior to the hand recount that was done due to other problems with the election in Florida (e.g., the “hanging chad” problem).) Use the data in this file to answer the following questions.

1. What was George W. Bush's margin of victory in Florida?
2. Prepare a scatter plot showing the relationship between the number of votes received by Gore (X-axis) and Buchanan (Y-axis) in each county. Does there appear to be any outliers? If so, for what counties?
3. Estimate the parameters for a simple linear regression model for predicting the number of votes for Buchanan in each county (excluding Palm Beach County) as a function of the number of votes for Gore. What is the estimated regression equation?
4. Interpret the value for R2 obtained using the equation from question 3.
5. Using the regression results from question 3, develop a 99% prediction interval for the number of votes you expect Buchanan to receive in Palm Beach County. What are the upper and lower limits of that interval? How does this compare with the actual number of votes reported for Buchanan in Palm Beach County?
6. Prepare a scatter plot showing the relationship between the number of votes received by Bush (X-axis) and Buchanan (Y-axis) in each county. Does there appear to be any outliers? If so, for what counties?
7. Estimate the parameters for a simple linear regression model for predicting the number of votes for Buchanan in each county (excluding Palm Beach County) as a function of the number of votes for Bush. What is the estimated regression equation?
8. Interpret the value for R2 obtained using the equation from question 7.
9. Using the regression results from question 7, develop a 99% prediction interval for the number of votes you expect Buchanan to receive in Palm Beach County. What are the upper and lower limits of that interval? How does this compare with the actual number of votes reported for Buchanan in Palm Beach County?
10. What do these results suggest? What assumptions are being made by using regression analysis in this way?