Problem

Refer to the data in Exercise 12.3. Suppose that another variable was controlled and that...

Refer to the data in Exercise 12.3. Suppose that another variable was controlled and that the first four squares at each speed were treated with a .2 concentration of protective coating, whereas the second four squares were treated with a .4 concentration of the same coating. x1 denotes the machine speed and x2 denotes the concentration of the protective coating. Fit these models using available statistical software. Which model seems to provide a better fit to the data? Why?

Exercise 12.3

A manufacturer tested the abrasive effect of a wear tester for experimental fabrics on a particular fabric while run at six different machine speeds. Forty-eight identical 5-inch-square pieces of fabric were cut, with eight squares randomly assigned to each of the six machine speeds, 100, 120, 140, 160, 180, and 200 revolutions per minute (rev/min). The order of assignment of the squares to the machine was random, with each square tested for a 3-minute period at the appropriate machine setting. The amount of wear was measured and recorded for each square. The data appear here.

a. Generate a graph of the data. (The variability within a speed is about the same for all speeds, so you can save time while still maintaining the trend by plotting the sample mean for each speed.)
b. What type of regression model appears appropriate?
c. Output for linear, quadratic, and cubic regression models is shown on the following pages. Which regression equation gives a better fit? Why?
d. Is there anything peculiar about the data? What might have happened?

LINEAR REGRESSION ANALYSIS FOR WEAR TESTER DATA