Math Problem Statement

Suppose the following table was generated from a sample of 20 CEOs relating annual salary to years of experience and the industry in which they are employed. Indicator (dummy) variables were created for each industry (1 if the CEO works in that industry, 0 otherwise). The Health Care industry is considered the base-level industry.

Coefficients Standard Error t Stat P-Value Intercept 142712.946698 4039.569273 35.328753 0.000000 Experience 2885.800829 190.013764 15.187325 0.000000 Service 12526.980087 3792.667105 3.302947 0.004830 Financial −19574.362623 3849.361835 −5.085093 0.000134 Manufacturing 20351.863484 3776.640067 5.388881 0.000075

According to the results, if a CEO in the Health Care industry and a CEO in the Financial industry both have 6 years of experience, what is the estimated difference in annual salary between the two CEOs? Enter your answer below, rounded to two decimal places.

Solution

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Dummy Variables
Linear Algebra

Formulas

Salary = Intercept + (Experience Coefficient × Years of Experience) + Industry Coefficient
Difference = Salary_{Health Care} - Salary_{Financial}

Theorems

Ordinary Least Squares (OLS)
Interpretation of Coefficients in Multiple Linear Regression

Suitable Grade Level

Undergraduate