Obtaining semi-partial correlations and standardized betas after decomposing a categorical by continuous interaction in multiple regression

[Chloe Boyle]

Hello and thank you in advance for your time.

I am using Stata SE/16.1. I would like to obtain standardized betas and semi-partial correlations after decomposing a categorical by continuous interaction in multiple regression. I do not typically use standardized betas or semi-partial correlation coefficients, but need to at the request of a colleague.

I am using the regress command with one continuous covariate, one categorical predictor, one continuous predictor, and a categorical by continuous predictor interaction. In the sample auto.dta dataset it would look like:

regress price c.mpg i.foreign##c.turn , beta

I tested the interaction using:

margins foreign, dydx(turn)

This yields the beta coefficient for each group in foreign (i.e., slope of turn in domestic cars, slope of turn in foreign cars).
My coauthor would like the standardized beta and semi-partial correlation coefficient for each group of foreign. I realize that I can get an approximation of both by testing each group individually with the following two commands:

regress price c.mpg c.turn if foreign==1, beta

pcorr price c.turn c.mpg if foreign==1

This is the approach colleagues have used. I am not convinced this is entirely accurate - I believe the estimates are slightly different if a covariate is in the model? Am I wrong here? If not, is there a way to obtain the standardized betas and semi-partials following the margins command?

Thank you for your help and patience, even if this is an inane question.
Chloe