If the coefficient of determination is 0.32 and = 150,then what is the sum of squares residual for an analysis of regression?
A)48
B)102
C)150
D)There is not enough information to answer this question.

Question

If the coefficient of determination is 0.32 and  = 150,then what is the sum of squares residual for an analysis of regression?
A)48 
B)102 
C)150 
D)There is not enough information to answer this question.

Quizplus · Accepted Answer

The coefficient of determination (R-squared) is the proportion of the variability in the dependent variable that is explained by the independent variable(s). Therefore, the remaining proportion of the variability (1-0.32=0.68) is unexplained and is captured by the sum of squares residual.

We can use the formula: 
Sum of squares residual = (1-R-squared)*Sum of squares total 
where Sum of squares total is the total variation in the dependent variable.

Since 11eaab06_0afc_4671_ac44_056ceb290a31_TB6823_11 represents the sum of squares total in this case, we can solve for the sum of squares residual:

Sum of squares residual = (1-0.32)*150 = 102

Therefore, the sum of squares residual is 102 and the best choice is B.

If the Coefficient of Determination Is 0