If A has 0.75 correlation with B+C , shouldn't we have the same correlation between A and B/C?

Question

I have a set of data A , B , C

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

I thought that I would find the same type of correlation with A ~ B/C

Am I totally wrong in thinking that correlation should survive the ratio B/C ?

thank you

Answer 1

Suppose $B = C$. Then $A$ has a high correlation with $2B$.

But $B / C = B / B = 1$. Does $A$ have a high correlation with the constant $1$? If $B$ is not constant, I'd say no.

Answer 2

Supose that A = { y(i) i=1,...,n }. B = { x(i)^2 i=1,...,n } and C={x(i) i=1,...,n}. If y(i) has a strong correlation with x(i)^2, it should has a strong correlation with B and with B+C, but not with B/C = C.

The answer is: a correlation with B+C does not imply a correlation with B/C.

Answer 3

thanks for your answer , may be I was unclear in my question or may be I have trouble understanding your answers.

I think you misunderstood B+C as an addition where in fact it is the explanatory variable of a multiple linear regression model.

It will help me if I use an example:

if A is the average salary per year for every US company B is the number of men in each company C is the number of women in each company

If I find a multiple correlation of A with B and C , aka the average salary in a company depends on the number of men and women

Does it make sense that I find no correlation of A with the ratio of men/women in each company ?

let's say than men earn more in average, in my mind the effect of more men in the company should also translate in the ratio men/women