Table B. 11 presents 38 observations on wine quality.

a. Select four observations at random from this data set, then delete these observations and fit a model involving only the regressor flavor and the indicator variables for the region information to the remaining observations. Use this model to predict the deleted observations and calculate \(R^{2}\) for prediction.
b. Repeat part a 100 times and compute the average \(R^{2}\) for prediction for all 100 repetitions.
c. Fit the model to all 38 observations and calculate the \(R^{2}\) for prediction based on PRESS.
d. Comment on all three approaches from parts a-c above as measures of model validity.

Clarity, X Aroma, x Body, x3 Flavor, x4 Oakiness, X Quality, y Region 3.3 2.8 3.1 4.1 9.8 4.4 4.9 3.5 3.9 12.6 3.9 5.3 4.8 4.7 11.9 3.9 2.6 3.1 3.6 11.1 5.6 5.1 5.5 5.1 13.3 4.6 4.7 4.1 12.8 4.8 4.8 4.8 3.3 12.8 5.3 4.5 4.3 5.2 12 4.3 4.3 3.9 2.9 13.6 4.3 3.9 4.7 3.9 13.9 5.1 4.3 4.5 3.6 14.4 0.5 3.3 5.4 4.3 3.6 12.3 0.8 5.9 5.7 4.1 16.1 0.7 7.7 1 0.9 71 5.5 6.3 1 4.6 0.9 3.4 5 0.9 6.4 1 5.5 0.7 4.7 0.7 4.1 4 1 6 1 4.3 1 3.9 5.1 3.9 1 4.5 1 5.2 0.8 4.2 1 3.3 1 6.8 0.8 5 0.8 3.5 0.8 4.3 0.8 5.2 89 88 87 88 89-9898365934 6.6 6.7 3.7 16.1 4.4 5.8 4.1 15.5 5.6 5.6 4.4 15.5 5.4 4.8 4.6 13.8 5.5 5.5 4.1 13.8 4.1 4.3 3.1 11.3 3.4 3.4 7.9 5.4 6.6 5.3 5.3 63 4.8 15.1 3.8 13.5 4.1 5 3.7 10.8 4.1 4 9.5 5.7 4.7 12.7 4.7 4.9 11.6 5.1 5.1 11.7 5 5.1 11.9 4.4 5 4.4 10.8 3.7 2.9 3.9 8.5 5 6 10.7 3 4.7 9.1 1 4.3 4.5 12.1 1 6 5.2 14.9 5.7 5.5 4.8 13.5 4.7 4.2 3.3 12.2 5.5 3.5 5.8 10.3 5.7 3.5 13.2