I have a variable X1 = (a - b) / (a + b). This variable shows a higher correlation to Y that any of (a, Y) and (b, Y).
In a multiple regression model like Y ~ X1, X2, does it make sense to use the X1 formula, or should I always use the base variables a and b?
In this post somebody pointed out that
Intuitively you'd be a lot more confident about inferences from an observed ratio of 1 (boys to girls) if it came from seeing 100 boys and 100 girls than > from seeing 2 and 2. Consequently, if you have covariates you'll have more information about their effects and potentially a better predictive model.
Fine, but can the multiple linear model rebuild the same (X1, Y) predictive relationship just by a and b least square analysis?