In the 2000 U.S. presidential election, Palm Beach County in Florida was the focus of unusual voting patterns (including a large number of illegal double votes) apparently caused by a confusing €œbutterfly ballot.€ Many voters claimed that they voted mistakenly for the Reform Party candidate, Pat Buchanan, when they intended to vote for Al Gore. Figure 4.8 shows the total number of votes for Buchanan plotted against the number of votes for the Reform Party candidate in 1996 (Ross Perot), by county in Florida. 

a. In county i, let Ï€_i, denote the proportion of the vote for Buchanan and let x_i denote the proportion of the vote for Perot in 1996. For the linear probability model fitted to all counties except Palm Beach County, π̂_i = €“0.0003 + 0.0304x_i. Give the value of P in the interpretation: The estimated proportion vote for Buchanan in 2000 was roughly P% of that for Perot in 1996.

b. For Palm Beach County, π_i = 0.0079 and x_i = 0.0774. Does this result appear to be an outlier? Explain.

c. For Logistic regression, log[π̂_i/(1€“π̂_i)] = €“7.164 + 12.219 x_i. Find π̂_i in Palm Beach County. Is that county an outlier for this model.

Figure 4.8:

3500 O Palm Beach 3000 2500- 2000- 1500- 1000- 500- 10,000 20,000 30,000 40,000 Perot votes, 1996 Total vote, by county in Florida, for Reform Party candidates Buchanan in 2000 and Perot in 1996. Buchanan votes, 2000