8.15 Consider a 22 factorial experiment. Suppose that the response follows a Poisson distribution and that the linear predictor is #(μ) = 3.5 +2.0x\+\.5x2, where the design variables are coded as + 1.

(a) Use a log link and generate three replicates of this experiment using a Poisson random number generator with the mean calculated from the link function and the linear predictor.

(b) Fit the GLM using the log link.

(c) Find the covariance and correlation matrix of the estimated parameters. Comment on the variances and the correlations.

(d) Calculate the fitted values at each design point.

(e) Compare your empirical results and then compare to the theoretical results.

(f) Rework parts (b), (c), and

(d) using the square root link and comment on your results.