Chapter B.3, Problem 71E

Mental Tasks and Drugs. Refer to Exercise B.68 regarding the experiment involving a person's ability to perform a mental task before and after taking one of four drugs. In that exercise, we considered the regression of after (the mental task score after taking a drug; on the predictor variables before (the mental task score before taking the drug) and the three variables druga, drugc, and drugd (the indicator variables for drugs A, C. and D. respectively). Drug B was a placebo. Use the technology of your choice to obtain output similar to that in Outputs B.57–B.61 on pages B-93–B-96.

1. a. Obtain the plot of after versus before, using a different plot symbol for each drug. Based on this plot, does it appear that drug is a useful predictor variable? Explain your answer.
2. b. Obtain the regression analysis of after on before and the three indicator variables, druga, drugc, and drugd. Conduct the individual t-tests for the utility of the four predictor variables at the 5% level of significance. Interpret your results.
3. c. Explain what the t-test for the utility of the indicator variable druga means in terms of comparing the effect of drug A to the effect of the placebo (drug B) on the after mental task scores.
4. d. Which drugs have an effect on the after mental task score that is different from the placebo?
5. e. Based on the output in part (b), obtain the individual regression equations relating after to before for each of the four drugs.
6. f. Obtain plots of residuals versus filled values, residuals versus before, and residuals versus each indicator variable, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
7. g. Provide a plot of after versus before with the separate regression lines for each of the four drugs. Based on this plot and your residual analysis in part (f), do you feel that this model fits the data well? Explain your answer.
8. h. To check for possible interactions between before score and drug, perform the regression analysis of after on before, druga, drugc, drugd, druga·before, drugc·before, and drugd·before. Is there an interaction between drug and before score, that is, are any of the cross-product terms useful predictor variables in the regression equation that contains the other terms in the model? Use α = 0.05.