# Why/when should we use semi-partial correlations instead of regression coeffcients?

Research context:

(1) What's the effect of a binary X1 (gender) on a continuous Y (index for consumption of femine-gendered goods), controlling for demographics. (2) Is this relationship moderated by continuous X2, X3, X4 (gender salience, perceived differences between genders, amount of close friends from other gender).

Model:

I ran a hierarchical regression model using Stata. Most effects are small, but still interpretable. The effect structure makes substantially sense and is in line with expectations.

Problem:

A reviewer suggested to use squared semi-partial correlations as alternative effect size. I computed those (using Stata's pcorr). I was baffled. The semi-partial correlations suggest that the predictors (especially the interactions) do not explain any variance in Y (- most of them well below 1%).

I’m aware of the general argument that small changes in R² can still make a big difference in real life. However, I ask myself, whether the differences between (my interpretation of) the regression coefficients and the semi-partials aren't too large to be able to follow this argument?

Questions:

How could I explain the different results from the semi-partials ("only 2% variance uniquely explained by gender") and the raw regression coefficients b (e.g., "changing gender increases outcome by almost a third of its theoretical scale“)?

How could I justify that I still stick to the interpretation of regression coefficients?

From here, I understood that the unsquared semi-partial correlations are very similar to standardized regression coefficients (but not able to exceed 1). From here I learned that semi-partials are often used in the decision about the inclusion of predictors. Different to these discussions, I'm seeking for help in regard to:

Which statistic I should rely on in the interpretation of the substantial findings - the explained variance in Y, or the change in Y when X changes one unit?

What type of research questions lends itself towards one or the other statistic?

How could I convince the reviewer that the effect size I choose is the most informative in my context?