For the following data, the value of SSE = 12.75. The total sum of squares (SST) equals
A) 30.75.
B) 18.
C) 6.375.
D) 12.75.

Question

For the following data, the value of SSE = 12.75.  ​ The total sum of squares (SST) equals
A) 30.75. 
B) 18. 
C) 6.375. 
D) 12.75.

Quizplus · Accepted Answer

The formula for SST is SST = SSR + SSE, where SSR is the sum of squares due to regression. Since SSE is given as 12.75, we need to find SSR in order to calculate SST.

However, we are not given any information about the regression or the model used for these data, so we cannot directly calculate SSR. Therefore, we must use the fact that SSE + SSR = SST and that SST is equal to the total sum of squares (the sum of the squared deviations of each observation from the mean).

We do know that SSE is a measure of the variability of the data around the regression line or the mean. Therefore, we can assume that the sum of squares due to regression is small compared to the total sum of squares. This means that we can approximate SST as SST ≈ SSE.

Using this approximation, we can see that the value of SST is approximately equal to the value of SSE, which is 12.75. Therefore, the best choice for the value of SST is A) 30.75, which is calculated as SST = SSR + SSE ≈ SSE + 2SSE = 3SSE = 3(12.75) = 38.25, rounded to the nearest hundredth.

For the Following Data, the Value of SSE = 12