In Problem 13.5 on page 470, you developed a multiple regression model to predict wine quality for red wines. Now, you wish to determine whether there is an effect on wine quality due to whether the wine is white (0) or red (1). These data are organized and stored in RedandWhite . Develop a multiple regression model to predict wine quality based on the percentage of alcohol and the type of wine. For (a) through (l), do not include an interaction term.
a. State the multiple regression equation that predicts wine quality based on the percentage of alcohol and the type of wine.
b. Interpret the regression coefficients in (a).
c. Predict the mean quality for a red wine that has 10% alcohol. Construct a 95% confidence interval estimate and a 95% prediction interval.
d. Perform a residual analysis on the results and determine whether the regression assumptions are valid.
e. Is there a significant relationship between wine quality and the two independent variables (percentage of alcohol and the type of wine) at the 0.05 level of significance?
f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.
g. Construct and interpret 95% confidence interval estimates of the population slope for the relationship between wine quality and the percentage of alcohol and between wine quality and the type of wine.
h. Compare the slope in (b) with the slope for the simple linear regression model of Problem 12.4 on page 423. Explain the difference in the results.
i. Compute and interpret the meaning of the coefficient of multiple determination, r2.
j. Compute and interpret the adjusted r2.
k. Compare r2 with the r2 value computed in Problem 12.16 (a) on page 429.
l. What assumption about the slope of type of wine with wine quality do you need to make in this problem?
m. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.
n. On the basis of the results of (f) and (m), which model is most appropriate? Explain.
o. What conclusions can you reach concerning the effect of alcohol percentage and type of wine on wine quality?