Chapter 14.3, Problem 35PB

Regression of weight gain on diet Refer to the previous exercise.

1. a. Set up indicator variables for protein source and for protein level and specify a regression model with the effects both of protein level and protein source on weight gain.
2. b. Fit the model in part a and explain how to interpret the parameter estimate for the protein level indicator variable.
3. c. Show how you could test a hypothesis about beta parameters in the model in part a to analyze the effect of protein source on weight gain.
4. d. Using the fit of the model, find the estimated mean for each of the six diets. Explain what it means when we say that these estimated means do not allow for interaction between protein level and source in their effects on weight loss.

14.34 Diet and weight gain A randomized experiment⁴ measured weight gain (in grams) of male rats under six diets varying by source of protein (beef, cereal, pork) and level of protein (high, low). Ten rats were assigned to each diet. The data are shown in the table that follows and are also available in the Protein and Weight Gain data file on the book’s website.

1. a. Conduct a two-way ANOVA that assumes a lack of interaction. Report the F test statistic and the P-value for testing the effect of the protein level. Interpret.
2. b. Now conduct a two-way ANOVA that also considers potential interaction. Report the hypotheses, test statistic, and P-value for a test of no interaction. What do you conclude at the 0.05 significance level? Explain.
3. c. Refer to part b. Allowing interaction, construct a 95% confidence interval to compare the mean weight gain for the two protein levels, for the beef source of protein.