# Help please in interpreting interaction variables

1. Apr 10, 2007

### statsfanatic

hi,
i used stata to regress these two models,
the problem is about gender and wage descrimination and stuff like that.
experience and gender are the predictors for salary.

so here are the multiple regression results, also gender is a dummy variable with 1 = male and 0 = female:

model 1 without interaction:
regress salary exp gender

Source | SS df MS Number of obs = 12
-------------+------------------------------ F( 2, 9) = 112.51
Model | 4.5962e+09 2 2.2981e+09 Prob > F = 0.0000
Residual | 183835117 9 20426124.2 R-squared = 0.9615
Total | 4.7801e+09 11 434552604 Root MSE = 4519.5

------------------------------------------------------------------------------
salary | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exp | 3534.216 320.6494 11.02 0.000 2808.857 4259.576
gender | 26550.33 2609.35 10.18 0.000 20647.57 32453.09
_cons | 13711.1 3792.469 3.62 0.006 5131.935 22290.26

Model 2 with interaction:

.generate cross=gender*exp

. regress salary exp gender cross

Source | SS df MS Number of obs = 12
-------------+------------------------------ F( 3, 8) = 1813.92
Model | 4.7731e+09 3 1.5910e+09 Prob > F = 0.0000
Residual | 7016925.79 8 877115.724 R-squared = 0.9985
Total | 4.7801e+09 11 434552604 Root MSE = 936.54

------------------------------------------------------------------------------
salary | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exp | 2590.805 93.96821 27.57 0.000 2374.114 2807.496
gender | 7053.171 1475.829 4.78 0.001 3649.902 10456.44
cross | 1886.822 132.8911 14.20 0.000 1580.375 2193.27
_cons | 23459.68 1043.569 22.48 0.000 21053.2 25866.15

the bold points are the new predictor values. cross is the interaction variable between experience and gender.
please help me understand how to interpret the new values of the variables for model 2 and what they mean for female and male salaries?

Last edited: Apr 10, 2007
2. Apr 20, 2007

### EnumaElish

I will assume exp is measured as a positive continuous variable (e.g. "years employed").

Your 2nd equation is really like two equations:
for gender = 0: salary = 23459 + 2590 exp
for gender = 1: salary = (23459 + 7053) + (2590 + 1886) exp

You should verify that you get the above two equations by setting gender to either of its two possible values.

Therefore:
expected salary for gender = 0 with no experience (exp = 0) is about 23459.
expected salary for gender = 0 increases about 2590 with each additional year.
expected salary for gender = 1 with no experience (exp = 0) is about 23459 + 7053.
expected salary for gender = 1 increases about (2590 + 1886) with each additional year.

Last edited: Apr 20, 2007