I have 3 independent variables A, B, C and want to run a multiple linear regression to predict Y. After studying the correlations between:
1) A, Y
2) B, Y
3) A/B, Y
4) (A-B)/(A+B), Y
It turns out that 4) has the highest correlation than all other cases by at least > 0.10. Both 3) and 4) make sense to me as variables A and B are complementary: that is, they represent the items bought in store A versus store B and there are only 2 stores in this problem.
Now, in a simple linear regression I have little doubt that the higher the correlation of the single independent variable the better the fit. But in a multiple linear regression, does it make sense to select the independent variables by looking at the formulas or ratios that shows the highest correlations against Y? In this case using 4) in the regression over 1), 2) or 3) because it has the highest correlation.