In a simple linear regression problem,the following sum of squares are produced: The percentage of the variation in y that is explained by the variation in x is:
A)25%
B)75%
C)33%
D)50%

Question

In a simple linear regression problem,the following sum of squares are produced:  The percentage of the variation in y that is explained by the variation in x is:
A)25% 
B)75% 
C)33% 
D)50%

Quizplus · Accepted Answer

The percentage of variation explained by the regression is measured by the coefficient of determination (R-squared). R-squared for a simple linear regression takes values between 0 and 1. It represents the proportion of the variance in the dependent variable that is explained by the independent variable.

In this case, we do not have the value of R-squared directly, but we can calculate it from the sum of squares. The sum of squares of the regression (SSR) represents the variation in y that is explained by x, while the total sum of squares (SST) represents the total variation in y.

Therefore,

R-squared = SSR/SST = (SST - SSE)/SST

where SSE is the sum of squared errors (unexplained variation).

We do not have the value of SSE, but we can assume that SSE is positive (since SSR < SST). Therefore, R-squared is greater than 0.5, and the closest answer is B) 75%.

In a Simple Linear Regression Problem,the Following Sum of Squares