# Can adjusted r-squared (or r-squared) be used to compare the strength of independent variables in linear multiple regression?

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?

• No this is not appropriate. R-squared increases just by increasing the number of variables, and vice versa. – user2974951 Sep 20 '19 at 8:45
• The OP stated "adjusted R2", in other words, it would not improve merely by the addition of variables. – Paul Hewson Sep 20 '19 at 13:34
• You use "relative strength" in two completely different senses: effect size (size of estimated parameter) and statistical significance (as measured by reduction in adjusted R-squared). In light of this contradiction, could you clarify for us just what you mean by "relative strength"? – whuber Sep 20 '19 at 14:18
• @whuber Maybe I misunderstand, but I thought reduction in adjusted r-squared is not directly connected with statistical significance. I thought both Beta values and adjusted r-squared are more directly connected with effect size. – Ethan Sep 21 '19 at 0:12