Chapter B.3, Problem 73E

Television Viewing. The results of a study on television viewing can be found in the Minitab worksheet TVhrs.mtw, which comes with Minitab. In the following table, we have reproduced the data on age (in years), weekly TV viewing time (in hours), and college-grad status for the participants in the study who are 50 years old or over.

  We want to regress weekly TV viewing time on the two predictor variables age and college-grad status. The indicator variable for college-grad status is

   $grad=\{\begin{array}{l}1,\text{if}\text{college}\text{grad};\hfill \\ 0,\text{if}\text{not}\text{college}\text{grad}.\hfill \end{array}$

Use the technology of your choice to do the following.

1. a. Obtain the scatterplot of TV viewing time versus age, using a different plot symbol for those who have graduated from college and those who have not. Based on the plot, docs it appear that college-grad status is a useful predictor variable? Explain your answer.
2. b. Obtain the regression analysis of TV viewing time on age and grad. Conduct t-tests for the individual utility of the two predictor variables at the 5% level of significance. Interpret your results.
3. c. Based on the output in part (b), obtain the individual regression equations relating TV viewing time to age for grads and non-grads.
4. d. Obtain plots of residuals versus fitted values, residuals versus age, and residuals versus grad, 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.
5. e. Provide a scatterplot of TV viewing time versus age with the regression lines for grads and non-grads. Based on this plot and your residual analysis in part (d), do you feel that this model fits the data well? Explain your answer.
6. f. To check for possible interaction between the two predictor variables, perform the regression analysis of TV viewing time on age, grad, and the cross-product term involving grad and age. Is there an interaction between age and college-grad status? Use α =0.05.