The regression line Estimated y = 3 + 2x has been fitted to the data points (4,8), (2,5), and (1,2). The sum of the squared residuals will be:
A) 7.
B) 15.
C) 8.
D) 22.

Question

Quizplus · Accepted Answer

First, we need to calculate the predicted y values based on the regression line for each of the given x values:

For x = 4: 
Estimated y = 3 + 2(4) = 11

For x = 2:
Estimated y = 3 + 2(2) = 7

For x = 1:
Estimated y = 3 + 2(1) = 5

Next, we calculate the residuals (the difference between the actual y values and the estimated y values):

For (4, 8):
Residual = 8 - 11 = -3

For (2, 5):
Residual = 5 - 7 = -2

For (1, 2):
Residual = 2 - 5 = -3

Now, we square each of the residuals:

(-3)^2 = 9
(-2)^2 = 4
(-3)^2 = 9

Finally, we add up the squared residuals:

9 + 4 + 9 = 22

Therefore, the sum of the squared residuals is 22.

The Regression Line Estimated Y = 3 + 2x Has