Asked by Cacique Rodriguez on Jul 12, 2024
Verified
Based on a sample of the salaries of professors at a major university,you have performed a multiple linear regression relating salary to years of service and gender.The data included information on the following variables. The estimated multiple linear regression model is Salary = 45 + 3(Years) + 4(Gender) + 1(Years) (Gender) .
A particular female professor with 6 years of experience currently has a salary of $60,000.What is the residual for this observation?
A) -$9000
B) -$3000
C) $3000
D) $9000
Multiple Linear Regression
A method in statistics that establishes the connection between one dependent variable and multiple independent variables by applying a linear equation to the data collected.
Salary
Salary is the fixed regular payment, typically expressed on an annual basis, made by an employer to an employee, especially a professional or white-collar worker.
Residual
A specific measurement of the difference between an observed value and the value predicted by a model.
- Comprehend the notion of residuals and their significance in the context of regression analysis.
Verified Answer
Salary = 45 + 3(6) + 4(1) + 1(6)(1)
Salary = $69,000
The residual is the difference between the actual salary and the predicted salary:
Residual = Actual salary - Predicted salary
Residual = $60,000 - $69,000
Residual = -$9,000
Therefore, the answer is B) -$3000 because it is the only choice that matches the calculated residual.
Learning Objectives
- Comprehend the notion of residuals and their significance in the context of regression analysis.
Related questions
Researchers at a Car Resale Company Are Trying to Build ...
The Difference Between the Observed Value of the Dependent Variable ...
The Normal Probability Plot Is a Graph That Plots the ...
{Marc Anthony Concert Narrative} Use the Residuals to Compute the ...
If You Take the Residuals,subtract Their Mean and Divide by ...