Question

Which of the following are feasible equations of a least squares regression line for number of dollars left in an endowment providing college scholarships in each of its first ten years if it was entirely funded by a single donation?

a. y ˆ =269,000+8300x
b. y ˆ =69,000−8300x
c. y ˆ =−269,000−8300x
d. y ˆ =269,000−8300x
e. y ˆ =0−8300x

Answer 1

d. y ˆ =269,000−8300x

Explanation:

If the regression describes the amount of dollars left after a single donation as a function of time, the regression must consist of a positive lump sum subtracted by an yearly rate. This rules out alternatives a, c, and e.

Since this equation must represent the amount left after 10 years, it must yield a positive value up to at least x = 10.

For equation b., when x = 10:

`y=69,000-8,300*10\\y=-14,000`

For equation d., when x = 10:

`y=269,000-8,300*10\\y=186,000`

Therefore, the only possible answer is d. y ˆ =269,000−8300x