Chapter 14, Problem 41PS

In Problem 14.5 on page 542, you developed a multiple regression model to predict wine quality for red wings. 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 (m), do not include an interaction team.

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 $10\%$ a red wine that has $10\%$ alcohol. Construct a $95\%$ prediction interval.

d. Perform a residual analysis on the model 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 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 13.4 on page 493. Explain the difference in the results.

i. Compare and interpret the meaning of the coefficient of multiple determination, $r^2.$

j. Compute and interpret the adjusted $r^2.$

k. Compare $r^2$ with the $r^2$ value computed in Problem 13.16 (a) on page 499.

l. Compute the coefficients of partial determination and interpret their meaning.

m. What assumption about the slope of type wine with quality do you need to make in this problem?

n. 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.

o. On the basis of the result of (f) and (n), which model most appropriate? Explain.

p. What conclusions can you reach concerning the effect of alcohol percentage and type of wine on wine quality?