Let (1) = ( (1) ,..., (n) ), where (i) denotes the estimate of E(Y

Let π̂^(–1) = (π̂^(–1),...,π̂^(–n)), where π̂^(–i) denotes the estimate of E(Y_i) for binary observation i after fitting the model without that observation. Cross-validation declares a model to have good predictive power if corr(π̂^(–), y) is high. Consider the model logit(π_i) = α for all i. Show that π̂_i = y̅ and hence π̂^(–i) = [n/(n – 1)][y̅ – (1/n)y_i], and hence corr(π̂^(–), y) = – 1 regardless of how well the model fits. Thus cross-validation can be misleading with binary data.