Exercise 8.25 Stat 121 KJ Wang. Votes for Bush and Buchanan in all Florida Counties Palm Beach County (outlier)

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Presentation transcript:

Exercise 8.25 Stat 121 KJ Wang

Votes for Bush and Buchanan in all Florida Counties Palm Beach County (outlier)

Log Transformation

Data excluding Palm Beach County

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 Coefficients: Value Std. Error t value Pr(>|t|) (Intercept) bush Residual standard error: on 64 degrees of freedom Multiple R-Squared: F-statistic: on 1 and 64 degrees of freedom, the p-value is 0

CI Attempt 1 Formula: Buchanan Votes = (0.0035)Bush Votes % CI = fitted +/- t*SE(fitted) Intercept = 66 +/- 17.3*( ) = 100.5, 31.5 Coefficient = / ( ) = , Bush = –Predicted High with 95% CI: * = 727 –Predicted Low with 95% CI: * = 475 THEREFORE: Predicted number of votes Buchanan should have received in Palm Beach County based on the number of votes Bush received is 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 ( =) 2680 more votes.

CI Attempt 2 Formula: Buchanan Votes = (0.0035)Bush Votes % CI = fitted +/- t*SE(predicted) SE(predicted) = square root(σ^2 + SE(fit)^2) σ = Residual Standard Error = SE(fit) = Buchanan(predicted) = SE(pred) = root(112.5^ ^2) = qt(.975, 64) = ; qt(.975,64)*SE(pred) = Buchanan(predict) = / THEREFORE: Predicted number of votes Buchanan should have received in Palm Beach County based on the number of votes Bush received is 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 ( =) 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!