If the sum of squares for error (SSE) is equal to zero, then the coefficient of determination ( ) must be:
A) 1.5
B) 1.0
C) 0.0
D) -1.0
E) 100

Question

If the sum of squares for error (SSE) is equal to zero, then the coefficient of determination (  ) must be:
A) 1.5 
B) 1.0 
C) 0.0 
D) -1.0 
E) 100

Quizplus · Accepted Answer

The sum of squares for error (SSE) measures the difference between the predicted values and the actual values, and a SSE of zero implies that there is no difference between the predicted and actual values.

The coefficient of determination (R-squared) is a measure of how well the regression line fits the data, and it is calculated as follows:

R-squared = 1 - (SSE/SST),

where SST is the total sum of squares.

If SSE is equal to zero, then R-squared is equal to:

R-squared = 1 - (0/SST) = 1,

which means that the regression line perfectly explains the variability in the data and fits the data with no errors. Therefore, the coefficient of determination (R-squared) must be equal to 1 or 100% (option B).

If the Sum of Squares for Error (SSE) Is Equal