In Example 24.1 the data show correlation between the income and age of the customer. This produces collinearity and makes the analysis tricky to interpret. The marketing research group could have removed this collinearity by collecting data in which these two variables were uncorrelated. For example, they could have identified two customers for each combination of incomes $60,000, $70,000, . . . , $120,000, and ages, 25, 35, 45, 55, and 65 years old. That would have given them 70 observations (7 income levels, with 10 in each).
(a) Explain why Income and Age would be uncorrelated for these data.
(b) Would the marginal slope be the same as the partial slope when analyzing these data?
(c) Would the marginal slope for Age when estimated for these data have a positive or negative sign?