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 variability in the dependent variable that is explained by the independent variable(s).

R-squared = 0.32 means that 32% of the variability in the dependent variable is explained by the independent variable(s). Therefore, the remaining 68% is unexplained (or residual) variability.

The sum of squares (SS) total is the total amount of variation in the dependent variable.

SS_total = SS_regression + SS_residual

Since we know that SS_regression = R-squared * SS_total, we can calculate the value of SS_residual:

SS_residual = SS_total - SS_regression

Substituting the given values:

SS_residual = 150 - (0.32*150)

SS_residual = 102

Therefore, the sum of squares residual for this analysis of regression is 102.

The correct answer is B).

If the Coefficient of Determination Is 0