8.17 Consider a 23 factorial experiment. Suppose that the response follows an exponential distribution and that the linear predictor is #(μ) = 8.0 +2.0χ1+3.0χ2+*3— 1.5xiX2> where the design variables are coded as +1.

(a) Use the inverse link and generate two replicates of this experiment using an exponential random number generator with the mean calculated from the link function and the linear predictor.

(b) Fit the GLM using the inverse 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. ( 0 Rework parts (b), (c), and

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