Table B. 11 presents data on the quality of Pinot Noir wine.

a. Build a regression model relating quality \(y\) to flavor \(x_{4}\) that incorporates the region information given in the last column. Does the region have an impact on wine quality?
b. Perform a residual analysis for this model and comment on model adequacy.
c. Are there any outliers or influential observations in this data set?
d. Modify the model in part a to include interaction terms between flavor and the region variables. Is this model superior to the one you found in part a?

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Clarity, X Aroma, X Body, X3 Flavor, X4 Oakiness, X's Quality, y Region 3.3 2.8 4.4 4.9 3.9 5.3 3.9 2.6 5.6 5.1 4.6 4.7 4.8 4.8 4.8 5.3 4.5 4.3 4.3 3.9 4.3 3.9 4.7 5.1 4.3 4.5 1 0.9 0.9 99-88---8-289 0.5 3.3 5.4 4.3 ECECEECECE 3.1 4.1 9.8 3.5 3.9 12.6 1 4.8 4.7 11.9 1 3.1 3.6 11.1 5.5 5.1 13.3 4.1 12.8 3.3 12.8 1 4.3 5.2 12 1 2.9 13.6 3 3.9 13.9 1 3.6 14.4 3.6 12.3 0.8 5.9 5.7 4.1 16.1 0.7 7.7 6.6 6.7 3.7 16.1 7.1 4.4 5.8 4.1 15.5 0.9 5.5 5.6 5.6 6.3 5.4 4.8 5.5 5.5 4.6 4.1 4.3 3.4 5 3.4 6.4 5.5 5.4 5.3 6.6 5.3 0.7 4.7 4.1 5 0.7 4.1 4 4.1 6 5.4 5.7 4.3 4.6 4.7 3.9 4 5.1 5.1 4.9 3.9 4.4 4.5 3.7 5.2 4.3 0.8 4.2 3.8 94738 1 3 1 3.3 3.5 4.3 1 0.8 0.8 0.8 0.8 65372 6.8 5 5.7 5.5 4.7 4.2 4.3 5.5 3.5 4.8 5.7 5257 783988-99889869929383 1 8 8 8 6 7 8 95002007 6 8 7 3 8 8 8 8 7 6 8 8 7+37 16 4.4 15.5 4.6 13.8 4.1 13.8 3 3.1 11.3 1 3.4 7.9 2 4.8 15.1 13.5 10.8 4 9.5 4.7 12.7 4.9 11.6 5.1 11.7 5.1 11.9 4.4 10.8 8.5 10.7 133223212222- 4.7 9.1 1 4.5 12.1 1 5.2 14.9 3 4.8 13.5 1 12.2 1 5.8 10.3 1 3.5 13.2 1