Exercise 8.25 Stat 121 KJ Wang. Votes for Bush and Buchanan in all Florida Counties Palm Beach...
-
Upload
karen-henry -
Category
Documents
-
view
214 -
download
1
Transcript of Exercise 8.25 Stat 121 KJ Wang. Votes for Bush and Buchanan in all Florida Counties Palm Beach...
Exercise 8.25
Stat 121
KJ Wang
Votes for Bush and Buchanan in all Florida Counties
0 50000 100000 150000 200000 250000 300000
bush2000
0
1000
2000
3000
buch
anan
2000
Quantiles of Standard Normal
Res
idua
ls
-2 -1 0 1 2-1
000
010
0020
00
36
13
67
Palm Beach County (outlier)
Log Transformation
7 8 9 10 11 12 13
logbush
2
4
6
8
logb
ucha
nan
Data excluding Palm Beach County
0 50000 100000 150000 200000 250000 300000
bush2000
0
200
400
600
800
1000bu
chan
an20
00
S Plus Model for data w/o Palm Beach County
• *** Linear Model ***
• Call: lm(formula = buchanan2000 ~ bush2000, data = ex0825, na.action = na.exclude)
• Residuals:• Min 1Q Median 3Q Max • -512.4 -47.97 -17.09 41.78 305.5
• Coefficients:• Value Std. Error t value Pr(>|t|) • (Intercept) 65.5735 17.3304 3.7837 0.0003 • bush2000 0.0035 0.0003 13.9226 0.0000
• Residual standard error: 112.5 on 64 degrees of freedom• Multiple R-Squared: 0.7518 • F-statistic: 193.8 on 1 and 64 degrees of freedom, the p-value is 0
CI Attempt 1• Formula: Buchanan Votes = (0.0035)Bush Votes + 66• 95% CI = fitted +/- t*SE(fitted)• Intercept = 66 +/- 17.3*(1.99773) = 100.5, 31.5• Coefficient = 0.0035 +/- 0.0003(1.99773) = 0.0041, 0.0029• Bush = 152846
– Predicted High with 95% CI: 152846 *0.0041 + 100.5 = 727
– Predicted Low with 95% CI: 152846 * 0.0029 + 31.5 = 475
• THEREFORE: Predicted number of votes Buchanan should have received in Palm Beach County based on the number of votes Bush received is 475-727
• Buchanan actually received 3407 votes in Palm Beach County• IF the statistically extra Buchanan votes were intended for Gore, then Gore should
have received at least (3407-727 =) 2680 more votes.
CI Attempt 2• Formula: Buchanan Votes = (0.0035)Bush Votes + 66• 95% CI = fitted +/- t*SE(predicted)• SE(predicted) = square root(σ^2 + SE(fit)^2)• σ = Residual Standard Error = 112.5• SE(fit) = 31.05• Buchanan(predicted) =597.77• SE(pred) = root(112.5^2 + 31.05^2) = 116.7058• qt(.975, 64) = 1.99773; qt(.975,64)*SE(pred) = 233.0965• Buchanan(predict) = 597.77 +/- 233.0965
• THEREFORE: Predicted number of votes Buchanan should have received in Palm Beach County based on the number of votes Bush received is 365 - 831
• Buchanan actually received 3407 votes in Palm Beach County• IF the statistically extra Buchanan votes were intended for Gore, then Gore should
have received at least (3407-831 =) 2576 more votes.
FINAL CONCLUSION
• Gore would have won the election if the voters in Palm Beach followed the same statistical model as the rest of the state
• 2576 extra votes is more than Bush’s initial margin of victory of 1738 votes
• BUT TOO BAD!