For a binary response y, let ỹ be the proportion of ones in the sample (which is equal to the (i) sample average of the y,). Let ĝo be the percent correctly predicted for the outcome y = 0 and let 9, be the percent correctly predicted for the outcome y = 1. If p is the overall percent correctly predicted, show that p is a weighted average of ĝo and q1: p = (1 – y)ao + 5ª1- (ii) In a sample of 300, suppose that ỹ = .70, so that there are 210 outcomes with y, = 1 and 90 with y; = 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.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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For a binary response y, let ỹ be the proportion of ones in the sample (which is equal to the
(i)
sample average of the y,). Let ĝo be the percent correctly predicted for the outcome y = 0 and let
9, be the percent correctly predicted for the outcome y = 1. If p is the overall percent correctly
predicted, show that p is a weighted average of ĝo and q1:
p = (1 – y)ao + 5ª1-
(ii) In a sample of 300, suppose that ỹ = .70, so that there are 210 outcomes with y, = 1 and 90
with y; = 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.
Transcribed Image Text:For a binary response y, let ỹ be the proportion of ones in the sample (which is equal to the (i) sample average of the y,). Let ĝo be the percent correctly predicted for the outcome y = 0 and let 9, be the percent correctly predicted for the outcome y = 1. If p is the overall percent correctly predicted, show that p is a weighted average of ĝo and q1: p = (1 – y)ao + 5ª1- (ii) In a sample of 300, suppose that ỹ = .70, so that there are 210 outcomes with y, = 1 and 90 with y; = 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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