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 the above

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 the above

Quizplus · Accepted Answer

The proportion of the variation in Y that is explained by the variation in X is determined by the coefficient of determination (R-squared), which is the ratio of the explained variance to the total variance. R-squared ranges between 0 (no linear relationship between X and Y) and 1 (perfect linear relationship), so it can also be expressed as a percentage. In this case, we are not given the value of R-squared, but we can calculate it from the sums of squares using the formula: R-squared = 1 - (SSresid/SStotal), where SSresid is the sum of squared residuals (unexplained variance) and SStotal is the total sum of squares (total variance). Therefore, R-squared = 1 - (11/44) = 0.75 or 75%, which means that 75% of the variation in Y is explained by the variation in X. To convert this to a percentage, we multiply by 100, so the answer is B) 80%.

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