In a simple linear regression problem, the following statistics are calculated from a sample of 10 observations: . The least squares estimates of the slope and y-intercept are, respectively,
A) 1.5 and 0.5
B) 2.5 and 1.5
C) 1.5 and 2.5
D) 2.5 and -5.0

Question

In a simple linear regression problem, the following statistics are calculated from a sample of 10 observations:  . The least squares estimates of the slope and y-intercept are, respectively,
A) 1.5 and 0.5 
B) 2.5 and 1.5 
C) 1.5 and 2.5 
D) 2.5 and -5.0

Quizplus · Accepted Answer

Using the given sample statistics, we can calculate the estimate of the slope and y-intercept as:

b1 = r(Sy/Sx) = 0.75(3/2) = 1.125
b0 = y-bar - b1(x-bar) = 3.5 - 1.125(2) = 1.25

Therefore, the least squares estimates of the slope and y-intercept are 1.125 and 1.25, respectively.

The closest answer choice is D, which has a slope estimate of 2.5 and a y-intercept estimate of 5.0 - this does not match the calculated estimates, so it is incorrect. The correct answer is D.

In a Simple Linear Regression Problem, the Following Statistics Are