Exercise 22 (Section 3.3) of Chapter 3 gave SAS output from a regression of amount of oil recovered from wheat straw on amount of oil added.

a. Does the simple linear regression model appear to specify a useful relationship between these two variables? State the relevant hypotheses, and carry out a test in two different ways.

b. If the roles of the two variables were reversed, so that the amount of oil recovered from wheat straw was the independent variable, what would be the value of the t-ratio for testing model utility? (Answer without actually carrying out another regression analysis, and explain your reasoning.)

Exercise 22

A four-factor factorial design was used to investigate the effect of fabric (A), type of exposure (B), level of exposure (C), and fabric direction (D) on the extent of color change as measured by a spectrocolorimeter (from “Accelerated Weathering of Marine Fabrics,” J. Testing and Eval., 1992: 139–143). Two observations were made at each combination of the factor levels. The resulting mean squares were MSA 2,207.329, MSB 47.255, MSC 491.783, MSD .44, MS(AB) 15.303, MS(AC) 275.446, MS(AD) .470, MS(BC) 2.141, MS(BD) .273, MS(CD) .247, MS(ABC) 3.714, MS(ABD) 4.072, MS(ACD) .767, MS(BCD) .280, and MSE .977. Perform an analysis of variance using .01 for all tests, and summarize your conclusions.