A process engineer is interested in determining if there is a difference in the breaking strength of a monofilament fiber produced using three different machines for a textile company (Montgomery 1991). However, the strength of the fiber is also related to its diameter, with thicker fibers being stronger than thinner ones. Random samples of five fiber specimens each were selected from each machine, and the breaking strength y (in pounds) and the diameter x (in 10−3 inches) (to be used as a covariate)

are measured.

Machine 1 Machine 2 Machine 3 y x y x y x 36 20 45 22 35 21 41 25 52 28 37 23 39 24 44 22 42 26 42 25 49 30 34 21 48 32 51 28 32 15 Use proc glm in SAS and the one-way covariance model to analyze this data. Extract numbers from the SAS output and write your own answers to the following questions:

a. Write an appropriate model for analyzing these data so that it is possible to perform a test of the equality of the slopes from your analysis. Construct an “adjusted” analysis of variance table to test the hypothesis of equal means (or effects) corresponding to the machines. State your conclusion based on the p-value.

b. Provide estimates of the regression coefficients of the straight lines if it is determined that their slopes are different.

c. Calculate 95% confidence intervals on all differences in pair of means

(e.g., μi − μj ) adjusted at the mean value of x.

d. Include a proc step in your SAS program to obtain a scatter plot of y versus x, superimposed by the fitted regression lines.