The regression line = 3 + 2X has been fitted to the data points (4,14),(2,7),and (1,4).The sum of the residuals squared will be 8.0.

Question

The regression line  = 3 + 2X has been fitted to the data points (4,14),(2,7),and (1,4).The sum of the residuals squared will be 8.0.

Quizplus · Accepted Answer

To find the sum of residuals squared, we need to first calculate the predicted values of y using the regression equation:
For (4,14):
y = 3 + 2x = 3 + 2(4) = 11
Residual = actual y - predicted y = 14 - 11 = 3
Residual squared = 3^2 = 9

For (2,7):
y = 3 + 2x = 3 + 2(2) = 7
Residual = actual y - predicted y = 7 - 7 = 0
Residual squared = 0^2 = 0

For (1,4):
y = 3 + 2x = 3 + 2(1) = 5
Residual = actual y - predicted y = 4 - 5 = -1
Residual squared = (-1)^2 = 1

Sum of residuals squared = 9 + 0 + 1 = 10, not 8. Therefore, the statement is false and the answer is B.

The Regression Line = 3 + 2X Has Been