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 using the regression line, and then subtract them from the actual values to get the residuals. Then we square each residual, and add them up.

Using the regression line 11eb06d9_cc89_1e47_8177_adf4b08f8323_TB1387_11 = 3 + 2X, we get:
- For the point (4, 14):
Predicted value = 3 + 2(4) = 11
Residual = actual - predicted = 14 - 11 = 3
Residual squared = 3^2 = 9

- For the point (2, 7):
Predicted value = 3 + 2(2) = 7
Residual = actual - predicted = 7 - 7 = 0
Residual squared = 0^2 = 0

- For the point (1, 4):
Predicted value = 3 + 2(1) = 5
Residual = actual - predicted = 4 - 5 = -1
Residual squared = (-1)^2 = 1

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

The Regression Line = 3 + 2X Has Been