Schubert et al. [1992], conducted an experiment using a catapult to determine the effects of hook \(\left(x_{1}\right)\), arm length \(\left(x_{2}\right)\), start angle \(\left(x_{3}\right)\), and stop angle \(\left(x_{4}\right)\) on the distance that the catapult throws a ball. They threw the ball three times for each setting of the factors. The data follow.

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.

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X1 X2 X3 X4 y -1 -1 -1 -1 28.0 27.1 26.1 -1 -1 1 1 46.3 43.5 46.5 1 1 21.9 21.0 20.1 1 1 -1 52.9 53.7 52.0 1 1 75.0 73.1 74.3 1 1 127.7 126.9 128.7 1 1 -1 -1 86.2 86.5 87.0 1 1 1 1 195.0 195.9 195.7