Math Problem Statement

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

Estimated Salary=21,640.90+2456.42(Years of Experience)

What is the estimated salary for an employee with 18 years of experience?

Solution

To estimate the salary for an employee with 18 years of experience, we simply substitute the value of "Years of Experience" into the given regression equation.

The equation is:

Estimated Salary=21,640.90+2,456.42×(Years of Experience)\text{Estimated Salary} = 21,640.90 + 2,456.42 \times (\text{Years of Experience})

Substituting 18 years of experience into the equation:

Estimated Salary=21,640.90+2,456.42×18\text{Estimated Salary} = 21,640.90 + 2,456.42 \times 18

Now, calculate the result:

2,456.42×18=44,229.562,456.42 \times 18 = 44,229.56

Then,

Estimated Salary=21,640.90+44,229.56=65,870.46\text{Estimated Salary} = 21,640.90 + 44,229.56 = 65,870.46

So, the estimated salary for an employee with 18 years of experience is $65,870.46.

Would you like further details on how this regression equation works or have any questions about other types of predictions?

Related Questions:

  1. What is the interpretation of the coefficients in a regression equation?
  2. How would you interpret the significance of the intercept in this regression equation?
  3. How would you estimate the salary for someone with 5 years of experience?
  4. What is the purpose of regression analysis in predicting salary?
  5. How would you calculate the predicted salary for employees with extreme years of experience (e.g., 0 or 40 years)?

Tip: In regression equations, the intercept (21,640.90) represents the estimated salary when the years of experience is 0. The coefficient for years of experience (2,456.42) shows how the salary increases with each additional year of experience.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Algebra

Formulas

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

Theorems

Simple Linear Regression

Suitable Grade Level

Grades 10-12