If average salary is correlated with number of men and women in a company , should it be correlated with ratio of men/women?

Question

I study a large set of data (200 companies in the same sector)

A = average salary in the company , B = number of men in the company , C = number of women in the company

I find a very high correlation(0.75) with a multiple linear regression A ~ B + C

ie : the average salary is positively impacted by the number of men employed.

I computed the ratio of men/women in each company : R= B/C

I run an other multiple linear regression A ~ R and only get 0.25 correlation

Am I wrong somewhere or does it make sense from a mathematical point of view ?

thank you

Answer 1

You are using more information about the company in your first regression than in your second, so it makes sense that the $R^2$ is higher. When you include $B$ and $C$ separately you are trying to explain $A$ not only with the share of man to woman but also with the overall number of employees, which you lose when you run the regression using only the share. It seems that the size of the company (measured by numbers of employees) is also important in explaining average salaries leading to the higher $R^2$.