Logistic regression is another example of a generalized linear model where the response variable follows a Bernoulli distribution and a logit link function is used. Based on the definition of deviance given in class derive the formula for the deviance of a logistic regression model as well as the formula for a single deviance residual.

Deviance Deviance is a way of measuring the difference between a GLM's fit and the fit of the perfect model (i.e. where 0best = E(Y; |X) = Y;). It is defined as twice the log of the ratio between the likelihood of the perfect model and the likelihood of the given model, (Obest | Y) D = 2log ( 0 | Y) = 2(1(0best [ Y) - 1(0|Y) )