A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model: Salary = β₀ + β₁ Service + ε. The following ANOVA table summarizes a portion of the regression results. How much of the variation in Salary is unexplained by the sample regression equation? A) 1% B) 2% C) 18.39% D) 77.94%

Question

Quizplus · Accepted Answer

The ANOVA table shows that the total variation in Salary is 100%. The percentage of variation explained by the regression model (R-squared) is 22.06%. Therefore, the percentage of variation in Salary that is unexplained by the regression model is 100% - 22.06% = 77.94%. This means that 77.94% of the variation in Salary is due to factors other than length of service, as captured by the sample regression equation.

A Manager at a Local Bank Analyzed the Relationship Between