Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 13

For a binary response y, let be the proportion of ones in the sample (which is equal to the sample average of the yi.). Let be the percent correctly predicted for the outcome y = 0 and let be the percent correctly predicted for the outcome y = 1. If is the overall percent correctly predicted, show that is a weighted average of and :
(ii) In a sample of 300, suppose that =.70, so that there are 210 outcomes with yi = 1 and 90 with yi = 0. Suppose that the percent correctly predicted when y = 0 is 80, and the percent correctly predicted when y = 1 is 40. Find the overall percent correctly predicted.