BSD131 Multiple Regression

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BSD131

Multiple Regression

Tutorial Question

Question 1

The Equal Opportunity Commission is investigating questions around unequal pay rates and discriminatory remuneration in various industries. The Pay Equity tab in the excel workbook contains information on 100 employees from a particular industry. Information includes:

•     Salary ($)

•     Gender

•     Years of Education

•     Years of Experience

•     Age

Investigate the following questions.

a.    Run a multiple regression analysis looking at the relationship between salary and years of education and years of experience.

i.      What proportion of variation in salary can be explained by these two variables?

ii.       Conduct atest of the overall significance of the model.

iii.      Test  both the  Education  and  Experience variables separately. Do both contribute to explaining the variation in salaries?

iv.      Write out the estimated equation and interpret all coefficients.

b.    In order to answer the question of pay equity, include the variable Gender. Use Male as the reference point i.e. M = 0.

i.      To what extent has including Gender increased the explanatory power of the model?

ii.      Conduct a test on each of the three variables to see if each contributes to the explanatory power of the model.

iii.       Based on the results of the tests does this mean that there is no difference in salaries between males and females? Is there another test you could suggest to determine if there is a difference?

c.    Include the age variable to the analysis and create a correlation matrix for all four variables. Does age appear to have a significant correlation with Salary? Is it likely to increase the explanatory power of the model?

d.    Run the regression adding in Age.

i.      What is the change in the Adjusted R2? Has age added anything?

ii.      Conduct at test each of the coefficients to determine if they are significant interpret the coefficients.

iii.      Are the results of the last two questions consistent with part c.? What is the likely issue?

       e.    Exclude all of the non-significant variables and run the regression again. What salary would you expect for a

38 year old female with 20 years education and 10 years work experience in the marketing division?