While learning Econometrics, I got curious to know whether
A/B can make a better variable than separate
B, when constructing a linear regression model.
Variables are often changed to more appropriate form in linear regression like making it log(x) or changing its scale for better interpretation. So I thought, why not try taking a ratio of two variables and get rid of the original two? (To avoid multicollinearity of course.)
For an example, let's say I'm interested in stock price and make a linear regression on it. Would it be better to include original
book value and
market value as two separate variables in my model or make them into one variable like
book value/market value? or would it depend on the situation/purpose?