Statistics 550 Spring 2017 Exam 2 Take-home Questions

1. Using the Davis.txt data file, fit the following three regression models:

a. Fit a regression model with an intercept term (a column of 1's in the X matrix), and verify that the residuals sum to zero. Explain this result geometrically.
b. Fit a regression model without an intercept, and verify that the residuals do not sum to zero. Explain this result geometrically.
c. Fit a regression model without an intercept (so the X matrix has no column that is equal to 1), where the residuals do sum to zero. Explain this result geometrically.

2. The cereal data file has data on many brands of cereal.

Fit a model to predict the calories of a brand of cereal from the protein, fat, sodium, fiber, carbohydrates (carbo), sugars, and potassium (potass) variables. Check the studentized residuals, hat values, and Cook's D statistic and report on which observations (if any) exceeded the 'cutoff' values for each statistic.

3. Using the same data as in problem 2, obtain VIF and PCA information (no intercept) and interpret collinearity from this information. Also use these data to verify the identity on page 356 relating VIF values to PCA results for the 'protein' variable.

4. Problem 12.4 in the text.