0

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

vincent
  • 3
  • it sounds like such a thing would be possible. – supinf Nov 21 '17 at 10:31
  • Multiple linear regression? Afaik, that should involve multiple variables. Purely from your phrasing, I get the impression that you're looking at the correlation between $A$ and $S=(B+C)$. Maybe I'm just not used to standard notations in that field... Would you mind clarifying that point? – N.Bach Nov 21 '17 at 10:35
  • B and C are two different explanatory variables , it is not the sum of B and C . I get why my notation can be confusing. I use the R software notation as I do not really know the "correct" mathematical one – vincent Nov 21 '17 at 11:13

1 Answers1

0

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 $R^2$.

mzp
  • 1,925
  • 2
  • 18
  • 41
  • thank you for your explanation. I will use the first regression then as it appears to give more information as you said. – vincent Nov 21 '17 at 12:53