if the equation for the regression line for the data set (3,6), (6,2), (9,10) is y=2/3x+2, what is the sse for the data set?
A. 16
B. 10
C. 4
D. 24
For the point (x0,y0),
error=y0-f(x0)
SSE=Σerror²
=Σ (y0-f(x0)²
point error error²
(3,6) 2 4
(6,2) -4 16
(9,10) 2 4
---------------
total = (4+16+4)=24
cxc
To find the SSE (Sum of Squared Errors) for a data set, you need to calculate the squared difference between each observed value of y and its corresponding predicted value based on the regression line.
The given equation for the regression line is y = (2/3)x + 2.
Let's calculate the predicted values of y for the given data points and find the SSE.
For the first data point (3,6):
Predicted y = (2/3) * 3 + 2 = 2 + 2 = 4
Squared difference = (6 - 4)^2 = 2^2 = 4
For the second data point (6,2):
Predicted y = (2/3) * 6 + 2 = 4 + 2 = 6
Squared difference = (2 - 6)^2 = (-4)^2 = 16
For the third data point (9,10):
Predicted y = (2/3) * 9 + 2 = 6 + 2 = 8
Squared difference = (10 - 8)^2 = 2^2 = 4
Now, sum up the squared differences:
SSE = 4 + 16 + 4 = 24
Therefore, the correct answer is D. 24.