On Mar 31, 4:33 am, SChapman <sumant...@googlemail.com> wrote: > Sorry, my question wasn't clear. > > Why is that in Generalised Linear Model we don't predict individual response variable values Yi? We only predict the conditional expectation E[Yi]. > > In a general linear model (simple linear regression) however all text books give formula for predicting Yi as well as E[Yi].
If b is the vector of estimated model coefficients and x is a vector of predictor scores for an individual then g(x'b) is the predicted response for that individual, where g() is the inverse link function.
If C is the estimated covariance matrix of the coefficients and z is the 1-alpha/2 quantile of the standard normal distribution then g(x'b +/- z*sqrt(x'Cx)) is a 1-alpha confidence interval for the response.