Question: 1 (i) For a binary response y, let - y be the proportion of ones in the sample (which is equal to the sample average

1 (i) For a binary response y, let - y be the proportion of ones in the sample (which is equal to the sample average of the yi ). Let qˆ0 be the percent correctly predicted for the outcome y  0 and let qˆ1 be the percent correctly predicted for the outcome y  1. If pˆ is the overall percent correctly predicted, show that ˆ p is a weighted average of qˆ0 and qˆ1: pˆ  (1  - y) qˆ0  - yqˆ1. (ii) In a sample of 300, suppose that - y  .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.

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