Relative newbie with quantitative analysis here, so forgive me if the question is naive or ill-specified. I have argued in a manuscript that along with using Beta values in linear multiple regression output to show the relative strength/magnitude of the influence of each independent variable on variation in the dependent variable, one can also remove independent variables separately (or as a category) note the reduction in adjusted r-squared values to compare the relative strength of each variable (or category). A reviewer of the manuscript questions if this last move is legitimate. I thought I read somewhere some months ago that this was a valid procedure, and it actually seemed like common sense to me, so I didn't bother to note the source. Now I can't find the source. Am I wrong in using change in adjusted r-squared when variables are removed from the regression model to evaluate the relative strength of variables?
I think in principle, using adjusted R-squared is more sensible than using standard errors of individual predictors. However 1, people tend to use a likelihood based metric such as AIC for variable selection, which you try to minimise in a variable search analagous to maximising adjusted R-squared. However 2 this is a massive topic in statistical research. The risk you run with any variable selection method is overfitting, that is to say, finding a combination of predictor variables in your dataset which works brilliantly well, but a model that doesn't work well if applied to a new dataset on the same phenomenon. Here is one source on variable selection methods that might explain it better than I can: https://towardsdatascience.com/stopping-stepwise-why-stepwise-selection-is-bad-and-what-you-should-use-instead-90818b3f52df