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
E) none of these

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 
E) none of these

Quizplus · Accepted Answer

Using the formula for the least squares estimates of the slope and y-intercept, we have:
slope = (nΣ(XY) - ΣXΣY) / (nΣ(X^2) - (ΣX)^2)
y-intercept = (ΣY - slopeΣX) / n

Plugging in the values from the sample, we get:
slope = (10(155) - (65)(33)) / (10(81.4) - (65)^2) = 2.5
y-intercept = (33 - (2.5)(65)) / 10 = -5

Therefore, the least squares estimates of the slope and y-intercept are 2.5 and -5, respectively, which corresponds to answer choice D.

In a Simple Linear Regression Problem, the Following Statistics Are