The following information regarding a dependent variable (y) and an independent variable (x) is provided.
SSE = 1.9
SST = 6.8

The least squares estimate of the slope is
A) 1.
B) 3.4.
C) 3.
D) .7.

Question

The following information regarding a dependent variable (y) and an independent variable (x) is provided. ​  ​
SSE = 1.9
SST = 6.8
​
The least squares estimate of the slope is
A) 1. 
B) 3.4. 
C) 3. 
D) .7.

Quizplus · Accepted Answer

The least squares estimate of the slope (b1) is given by: 
b1 = SS(xy) / SS(x) where SS(xy) is the sum of cross-products of deviations of x and y from their respective means, and SS(x) is the sum of squares of deviations of x from its mean.

SS(xy) = SST - SSE = 6.8 - 1.9 = 4.9 
SS(x) = SST - SS(y) = SST - SSE = 6.8 - 1.9 = 4.9

Therefore, 
b1 = SS(xy) / SS(x) = 4.9 / 7.9 = 0.62 ≈ 0.7

Thus, the least squares estimate of the slope is D) 0.7.

The Following Information Regarding a Dependent Variable (Y) and an Independent