I'm running a multiple linear regression. Let's suppose I really need to use the logarithmic transformation. However, all values of one variable are negative. I assume I have to do the following: X1 + constant. After that, I can use the logarithmic transformation and run a multiple regression.
I'd like to mention that I have done that before without the logarithmic transformation, running a simple linear regression and it has affected only an alpha coefficient (makes perfect sense for me).
For example, I have got the following results:
- y = 1,08 + 0,56*x1, original x1
- y = -0,03 + 0,56*(x1 + 2), x1 + constant
So I can use both equations for making predictions, getting the same results.
Is it still possible to interpret Beta coefficients? I am used to relying on elasticity and logarithmic transformation, showing how independent variables influence "Y". Do I need to take into account that I have added a "constant"? If I do, how?