# Regression equation to test state variation

I'm an undergraduate student writing up a research proposal for a reserach-based class. I'm testing how LGBTQ discrimination in the labor market might vary in each state in the US (that's my research proposal, not actually collecting the data). This would be a correspondence study (bertrand style). I'm struggling with how my regression equation would work: Would something like this measure between-state variation or only within-state variation? probability of getting interview = a + b[being LGBTQ]+c[state 1] + d[state 2]+...+e[state 49] + f[state 1 x being LGBTQ] + g[state 2 x being LGBTQ]. Would the interaction terms represent the discrimination variation by state? Eg is f is very negative, state 1 discriminates a lot by LGBTQ status.

Or should I just do a simple linear regression for each state and compare?

I'm not sure what your variable is for LGBTQ, but the regression seems fine.

$$b$$ would measure the effect of being LGBTQ for the omitted state.

$$f$$ would measure the difference in the effect of being LGBTQ for state 1 relative to the omitted state.

$$g$$ would measure the difference in the effect of being LGBTQ for state 2 relative to the omitted state.

So your interpretation is correct, you just need to remember that you are estimating relative effects (to the baseline group) rather than effects in levels.

• Thank you! I see- so you are estimating relative effects to the baseline group. Then in that case, to then compare different states, could you rank the states by their interaction term?The state with smallest/most negative interaction term has the most lgbtq discrimination?
– Bob
May 2, 2022 at 14:35
• Yes, and the omitted state has a value of 0. May 2, 2022 at 19:23