The production of wine is a multibillion dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine experts, data was collected from red wine variants of Portuguese “ Vinho Verde” wine. A sample of 50 wines is stored in VinhoVerde. (Data extracted from P. Cortez,
A. Cerdeira, F. Almeida, T. Matos, and J. Reis, “ Modeling Wine Preferences by Data Mining from Physiochemical Properties,” Decision Support Systems, 47, 2009, pp. 547–553 and bit.ly/9xKlEa.) Develop a multiple linear regression model to predict wine quality, measured on a scale from 0 (very bad) to 10 (excellent) based on alcohol content (%) and the amount of chlorides.
a. State the multiple regression equation.
b. Interpret the meaning of the slopes, b1 and b2, in this problem.
c. Explain why the regression coefficient, b0, has no practical meaning in the context of this problem.
d. Predict the mean wine quality rating for wines that have 10% alcohol and chlorides of 0.08.
e. Construct a 95% confidence interval estimate for the mean wine quality rating for wines that have 10% alcohol and chlorides of 0.08.
f. Construct a 95% prediction interval for the wine quality rating for an individual wine that has 10% alcohol and chlorides of 0.08.
g. What conclusions can you reach concerning this regression model?