Question

Assume one has estimated a regression equation of salary (dependent variable) against years of education independent variable). How would one go about expanding the regression model to also estimate the gender effect (i.e., the average difference between male and female salary, given the same level of education? Explain how you would construct the additional variable and how you would interpret it, given how you construct it. How would you construct a hypothesis test to determine if the estimated gender-based differential is statistically significant?

Answer 1

Assume one has estimated a regression equation of salary (dependent variable) against years of education independent variable).

We are given:

Dependent variable is salary.

Independent variable is years of education

A simple linear regression equation is:

y = b₀ + b₁x

where y = dependent variable

x = independent variable

The estimated regression equation is:

Salary = b₀ + b₁*Years of education

How would one go about expanding the regression model to also estimate the gender effect (i.e., the average difference between male and female salary, given the same level of education?

One can introduce a new independent variable which is a gender of the person into the estimated regression equation to estimate the gender effect.

Explain how you would construct the additional variable and how you would interpret it, given how you construct it.

We would introduce a new independent variable which is a gender of the person into the estimated regression equation.

The estimated regression equation is:

Salary = b₀ + b₁*Years of education + b₂*Gender

We also notice that this new variable will help us determine the gender-based salary of a person without changing the other variable years of education.

Interpretation:

If the gender of a person is Female, then we will put Gender value as one into our regression equation.

If the gender of a person is Male, then we will put Gender value as zero into our regression equation.

How would you construct a hypothesis test to determine if the estimated gender-based differential is statistically significant?

We will conduct a regression test taking Salary as a dependent variable and Gender and Years of education as the independent variables.

We would compare the p-value for the independent variable Gender at a reasonable significance level to check whether the estimated gender-based differential is statistically significant. If we find the p-value to be less than a reasonable significance level, there is sufficient evidence to say that estimated gender-based differential is statistically significant.