In regression analysis, the coefficient of determination, $$R ^ { 2 }$$ , measures the amount of variation in y that is:
A) caused by the variation in x.
B) explained by the variation in x.
C) unexplained by the variation in x.
D) caused by the variation in x or explained by the variation in x.

Question

Quizplus · Accepted Answer

The coefficient of determination, $$R ^ { 2 }$$ , measures the proportion of the variance in the dependent variable (y) that is explained by the independent variable (x) in a regression model. Therefore, it measures the amount of variation in y that is explained (not just caused) by the variation in x. Option A is incorrect because the variation in x may not always cause variation in y. Option C is incorrect because unexplained variation has nothing to do with the coefficient of determination. Option D is incorrect because the coefficient of determination only measures the explained variation in y.

In Regression Analysis, the Coefficient of Determination R2R ^ { 2 }R2

In Regression Analysis, the Coefficient of Determination $R ^ { 2 }$