An online clothing retailer examined their transactional database to see if total yearly Purchases ($) were related to customers’ Incomes ($). (You may assume that the assumptions and conditions for regression are met.)

The least squares linear regression is:

Purchases = —31.6 + 0.012 Income.

a) Interpret the intercept in the linear model.

b) Interpret the slope in the linear model.

c) If a customer has an Income of $20,000, what is his predicted total yearly Purchases?

d) This customer’s yearly Purchases were actually $ 100. What is the residual using this linear model? Did the model provide an underestimate or overestimate for this customer?