Consider the following population model for household​ consumption: cons = a + b 1 * inc+ b 2 * educ+ b 3 * hhsize + u where cons is​ consumption, inc is​ income, educ is the education level of...

Consider the following population model for household​ consumption:

cons = a + b₁
* inc+ b₂
* educ+ b₃* hhsize + u

where cons is​ consumption, inc is​ income, educ is the education level of household​ head, hhsize is the size of a household.

Suppose a researcher estimates the model and gets the predicted​ value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize.

Which of the following choice is correct and please explain why.

A) be certain that R^2 = 1

B) be certain that R^2 = 0

C) be certain that R^2 is less than 1 but greater than 0.

D) not be certain