The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

7.6 Logistic Regression 117

For each model, the value of R 2 describes the percentage of the
variance in the votes for Buchanan that can be explained by the predic-
tor variables. This is a measure of the goodness of fi t for the model.
The adjusted R 2 is slightly smaller and takes into account the fact that
the estimates have greater variability in prediction due their correlation
in estimation from a common data set.
Both the R 2 and adjusted R 2 are highest in model 3. The R 2 and
adjusted R 2 in models 1 and 2 are almost the same. But model 2 is
preferable to 1 because Gore ’ s coeffi cient is not statistically signifi cant.
Each model is highly predictive, as indicated by the p - value for the
overall F - test, which is 0.0001 in each case.
It appears that model 3 is the best. So we will use model 3 to predict
Buchanan ’ s total in Palm Beach County. Here are the predictions that
each model would give.

Model 1: 587.710 votes for Buchanan

Model 2: 649.389 votes for Buchanan

Model 3: 659.236 votes for Buchanan

We see that none of the models predict more than 660 votes for

Buchanan. Not mentioned in the section on simple linear regression

were the simple linear regression models. Without going into the details,

which can be found in Chernick and Friis ( 2003 ), the prediction for the

simple linear regression models ranged from 600 to 1076.

Recall that Palm Beach actually recorded 3407 votes for Buchanan.

This is more than three times the amount obtained by any of the predic-

tions. Subtracting the predictions from 3407, we see that Buchanan

received between 2331 = 3407 − 1076 and 2807 = 3407 − 600 that we

believe were mistakes. Our best estimate is 3407 − 660 = 2747. In any

case, if these votes should have gone to Gore, this swing would have

a signifi cant impact on the results.

7.6 LOGISTIC REGRESSION

Logistic regression is a method used to predict binary outcomes on the

basis of one or more predictor variables. The goals are the same as with

linear regression. We attempt to construct a model to best describe the