Math Problem Statement

Suppose the following estimated regression equation was determined to predict salary based on years of experience.  

Estimated Salary=20,502.22+2705.91(Years of Experience)Estimated Salary=20,502.22+2705.91(Years of Experience) What is the estimated salary for an employee with 88 years of experience? 

Solution

To calculate the estimated salary for an employee with 88 years of experience using the regression equation:

Estimated Salary=20,502.22+2705.91×(Years of Experience)\text{Estimated Salary} = 20,502.22 + 2705.91 \times (\text{Years of Experience})

Substitute Years of Experience=88\text{Years of Experience} = 88:

Estimated Salary=20,502.22+2705.91×88\text{Estimated Salary} = 20,502.22 + 2705.91 \times 88

Step-by-Step Calculation:

  1. Calculate 2705.91×882705.91 \times 88: 2705.91×88=238,120.082705.91 \times 88 = 238,120.08

  2. Add the intercept: Estimated Salary=20,502.22+238,120.08=258,622.30\text{Estimated Salary} = 20,502.22 + 238,120.08 = 258,622.30

Final Answer:

The estimated salary for an employee with 88 years of experience is $258,622.30.

Would you like further clarification or have questions on related topics? Here are some ideas to explore further:

  1. How to interpret the slope in the regression equation?
  2. What is the role of the intercept in a regression equation?
  3. How can we calculate the residual if the actual salary is provided?
  4. What are the assumptions of linear regression?
  5. How would this regression model change if additional variables were added?

Tip: Always verify the assumptions of linear regression, such as linearity, homoscedasticity, and independence, to ensure the model's accuracy.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Algebra

Formulas

Estimated Salary = Intercept + Slope × (Years of Experience)

Theorems

Linear Regression Equation

Suitable Grade Level

Grades 9-12