5.22 Schubert et al. (1992) conducted an experiment using a catapult to determine the effects of hook (x\)9 arm length (x2), start angle (x3), and stop angle (x4) on the distance that the catapult throws a ball. They threw the ball three times for each setting of the factors. The data follow. X[ X2 x$ X4 y - 1 - 1 - 1 - 1 - 1 1 - 1 1 1 - 1 1 - 1 1 1 1 1 - 1 - 1 1 1 - 1 1 1 - 1 - 1 1 1 - 1 - 1 - 1 1 1 28.0 46.3 21.9 52.9 75.0 127.7 86.2 195.0 27.1 43.5 21.0 53.7 73.1 126.9 86.5 195.9 26.1 46.5 20.1 52.0 74.3 128.7 87.0 195.7

(a) Use GLMs to fit an appropriate model for the variance.

(b) Use this model as a basis for a weighted least squares estimation of the model for the distance.

(c) Discuss your results.