Exhibit 14-5
You are given the following information about y and x.
-Refer to Exhibit 14-5. The least squares estimate of b₀ (intercept) equals

Question

Exhibit 14-5 You are given the following information about y and x. -Refer to Exhibit 14-5. The least squares estimate of b₀ (intercept) equals A)1 B)-1 C)6

Quizplus · Accepted Answer

The least squares estimate of the intercept (b0) is equal to the mean of y minus the product of the slope (b1) and the mean of x. Using the provided data, we have: 
mean of y = (6+9+12+15)/4 = 10.5
mean of x = (1+2+3+4)/4 = 2.5
b1 = Σ[(xi - x.mean)(yi - y.mean)] / Σ[(xi - x.mean)^2] = (2-2.5)(9-10.5) + (3-2.5)(12-10.5) + (4-2.5)(15-10.5) / [(2-2.5)^2 + (3-2.5)^2 + (4-2.5)^2] = 9/5

b0 = y.mean - b1*x.mean = 10.5 - 9/5*2.5 = 6

Therefore, the least squares estimate of the intercept is 6. The answer is C.

Exhibit 14-5 You Are Given the Following Information About Y and X