The regression equation Salary = 25,000 + 3200 YearsExperience + 1400 YearsCollege describes employee salaries at Axolotl Corporation. The standard error is 2600. John has 10 years' experience and 4 years of college. His salary is $66,500. What is John's standardized residual?
A)-1.250
B)-0.240
C)+0.870
D)+1.500

Question

Quizplus · Accepted Answer

First, we need to calculate John's predicted salary based on the regression equation:

Salary = 25,000 + 3200(10) + 1400(4)
Salary = 62,000

Next, we can calculate John's residual:

Residual = Actual Salary - Predicted Salary
Residual = 66,500 - 62,000
Residual = 4,500

Finally, we can calculate John's standardized residual using the formula:

Standardized Residual = Residual / Standard Error
Standardized Residual = 4,500 / 2600
Standardized Residual = 1.73

Since the standardized residual is positive, we know that John's actual salary is higher than what we would predict based on the regression equation. A standardized residual of 1.73 indicates that his salary is roughly 1.73 standard deviations above the mean predicted salary for someone with his years of experience and college education. Therefore, the best choice is D.

The Regression Equation Salary = 25,000 + 3200 YearsExperience