The regression line has been fitted to the data points (28, 60), (20, 50), (10, 18), and (25, 55). The sum of the squared residuals will be:
A) 20.25
B) 16.00
C) 49.00
D) 94.25

Question

The regression line  has been fitted to the data points (28, 60), (20, 50), (10, 18), and (25, 55). The sum of the squared residuals will be:
A) 20.25 
B) 16.00 
C) 49.00 
D) 94.25

Quizplus · Accepted Answer

Using the formula for sum of squared residuals:
residual = observed y - predicted y
residual = y - ax - b

where a is the slope and b is the y-intercept of the regression line.

The regression line can be represented as:
y = 2.1x + 8.4

Using this equation, we can calculate the predicted values of y for each point:

(28, 60): 60 = 2.1(28) + 8.4 = 67.2
(20, 50): 50 = 2.1(20) + 8.4 = 50.4
(10, 18): 18 = 2.1(10) + 8.4 = 29.4
(25, 55): 55 = 2.1(25) + 8.4 = 62.4

Now we can calculate the residual for each point:

(28, 60): 60 - 67.2 = -7.2
(20, 50): 50 - 50.4 = -0.4
(10, 18): 18 - 29.4 = -11.4
(25, 55): 55 - 62.4 = -7.4

Then we square each residual and add them up:
(-7.2)^2 + (-0.4)^2 + (-11.4)^2 + (-7.4)^2 = 94.24

Therefore, the sum of the squared residuals is 94.24, which is closest to choice D: 94.25.

The Regression Line Has Been Fitted to the Data