Exhibit 14-4
The following information regarding a dependent variable (Y) and an independent variable (X) is provided. SSE = 6
SST = 16
-Refer to Exhibit 14-4. The least squares estimate of the Y intercept is
A)1
B)2
C)3

Question

Exhibit 14-4
The following information regarding a dependent variable (Y) and an independent variable (X) is provided.  SSE = 6
SST = 16
-Refer to Exhibit 14-4. The least squares estimate of the Y intercept is
A)1 
B)2 
C)3

Quizplus · Accepted Answer

The least squares estimate of the Y intercept is equal to the sample mean of Y minus the slope multiplied by the sample mean of X. Since SST = 16, we know that the total variation in Y is 16 units. Since SSE = 6, we know that the explained variation due to X is 10 units. Therefore, the remaining unexplained variation (due to factors not included in our model) is 6 units. Since the slope is the ratio of the explained variation to the variation in X (or 10/4 = 2.5), we can use the formula for the Y intercept to solve for b: b = Y¯ − bX¯ = 2 − 2.5(1) = -0.5. Therefore, the best choice for the least squares estimate of the Y intercept is 2.

Exhibit 14-4 the Following Information Regarding a Dependent Variable (Y) and an and an Independent