An article in Quality Engineering (The Catapult Problem: Enhanced Engineering Modeling Using Experimental Design, Vol. 4, 1992) conducted an experiment with a catapult to determine the effects of hook (x 1 ), arm length

(x 2 ), start angle (x3 ), and stop angle (x 4 ) on the distance that the catapult throws a ball. They threw the ball three times for each setting of the factors. Table E3. 7 summarizes the experimental results.

a. Fit a regression model to the data and perform a residual analysis for the model.

b. Use the sample variances as the basis for weighted least squares estimation of the original data (not the sample means).

c. Fit an appropriate model to the sample variances. Use this model to develop the appropriate weights and repeat part b.