In a simple linear regression analysis, the following sums of squares are produced: The proportion of the variation in Y that is explained by the variation in X is:
A) 20%
B) 80%
C) 25%
D) 50%
E) none of these choices

Question

In a simple linear regression analysis, the following sums of squares are produced:  The proportion of the variation in Y that is explained by the variation in X is:
A) 20% 
B) 80% 
C) 25% 
D) 50% 
E) none of these choices

Quizplus · Accepted Answer

The proportion of the variation in Y that is explained by the variation in X is represented by the coefficient of determination (R-squared), which is the ratio of the explained variation to the total variation. R-squared ranges from 0 to 1, where 0 indicates that there is no linear relationship between X and Y, and 1 indicates that all the variation in Y is explained by X. Therefore, the answer is 80% (0.8) as the sum of squares explained divided by the total sum of squares equals 0.8.

In a Simple Linear Regression Analysis, the Following Sums of Squares