# Multiple regression with dummy variables and interaction term

We have done a multiple regression analysis to see how gender and experience affect salary. We used a dummy variable for gender and then we also added the interaction variable (female work experience). I am having a hard time interpreting the results. Could someone please help me?

• What is your dependent variable? Jan 22, 2019 at 21:54
• Our dependent variable is salary.
– user234982
Jan 22, 2019 at 22:03
• Welcome to the site, jessxx! I have edited your first two sentences. Please take a look and make sure they still match your intent. Jan 22, 2019 at 22:10
• Do you want to study the how gender and experience cause changes in salary? Or is it enough to simply describe the trends? Jan 22, 2019 at 22:12
• I am not sure if I understand what you're trying to say but I think we want to describe the trends. I am not really sure how to interpret the coefficients.
– user234982
Jan 22, 2019 at 22:14

[For simplicity, I'm ignoring values after the decimal]

1) For a hypothetical man with zero years of experience, the salary is 908 units (don't know what the units are here) on average.

2) For a hypothetical woman with zero years of experience, the salary is 908 - 60 = 848 units on average.

3) For every additional year of experience, a man's salary increase by 15 units relative to their baseline of 908 (on average). So the average man with (i) 1 year of experience gets a salary of 908 + 15 = 923 units, and with (ii) 5 years of experience gets a salary of 908 + (15 x 5) = 983 units.

4) For every additional year of experience, a woman's salary increases by 15 - 5 = 10 units relative to their baseline of 848 (on average). This is because the interaction coefficient (-5) tells you that for each additional year of experience, a woman gets 5 units less than a man does for the same additional year of experience. So the average woman with (i) 1 year of experience gets a salary of 848 + 10 = 858 units, and with (ii) 5 years of experience gets a salary of 848 + (10 x 5) = 898 units.

• So that interaction coefficient (-5.32) doesn't tell you anything on its own?
– user234982
Jan 23, 2019 at 14:13
• @jessxx It tells you that for each additional year of experience, a woman gets 5.32 units less than a man does for the same additional year of experience. Since the man gets 15.99 more for each additional year, a woman gets 15.99 - 5.32 = 10.67. Note that all of this is on average.
– mkt
Jan 23, 2019 at 15:02

Assuming your indicator variable for Female is coded 0=Male, 1=Female...

For Males: Each year of experience is associated with 16 units higher salary

For Females: Each year of experience is associated with 16-5=11 units higher salary

For a person with 10 years work experience, being Female is associated with 60.59+(10*5.33)=113.9 units lower salary.

For a person with 25 years work experience, being Female is associated with 60.59+(25*5.33)=193.8 units lower salary.

Because of the interaction term, you can not compute an overall effect of Male vs. Female salaries. It depends on experience. And you can not compute an overall effect of salary, it depends on Male vs. Female

P.S. You can plug is zero years experience and compute that Females make 60.59 units lower salary, with no experience. The difference between Females and Males only increases from there!

Quickly spoken:

• Females seem to have lower salary but statistically not significant (at 95%).
• The more work experience the higher the salary (statistically significant at 95%)
• The effect of work experience depends on the gender of the person. If the person is female, the effect of work experience diminishes compared to a guy. (significant at 95%).
• How do you interpret this by using the actual coefficient outputs. Does that mean that "For every additional year of work experience, the salary goes up by 16 or does it mean that it goes up 16\$ more for men compared to women? What about interpreting the interaction coefficient?
– user234982
Jan 22, 2019 at 22:24