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

Akash Yadav · Accepted Answer

Final Answer : D, Explanation :  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) / nPlugging in the values from the sample, we get:slope = (10(155) - (65)(33)) / (10(81.4) - (65)^2) = 2.5y-intercept = (33 - (2.5)(65)) / 10 = -5Therefore, 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 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

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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 0.5B) 2.5 and 1.5C) 1.5 and 2.5D) 2.5 and -5.0E) none of these

Definitions

Learning Objectives

Learning Objectives

Related questions

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