Interpreting LOG-LINEAR(ratio) Model

rmk

New Member
#1
Hello,

I ve a linear regression model. The dependent variable is log transformed ln_EBIT (EBIT is in Million EUR). The independent variable is a ratio between RD / Sales (both in million EUR).
The Coefficient is around -2,5.

If we change RD/SALES by 1 (unit), we’d expect EBIT to change by -2,5% or -250% percent?

Is the effect now -2,5% or -250%? I´m not quite sure if I have to multiple the coefficient with 100 because it is already a ratio?

Thanks in Advance,
rmk
 

hlsmith

Not a robit
#2
My old notes say the following:


A one-unit change in X1 is associated with a (eB1 – 1) * 100 percentage change in Y,


this is approximately equal to 100(B1): If, -0.1 < β1 < 0.1, 0.1 is a rule of thumb.


So if I am correct, which seem to be quite a bit off from -250, I believe the *100 is a generalization, then for a ratio change of 1 you would have a -92% change in Y. Now the next question is, that I think Y is now on the geometric mean scale so, perhaps the results is:


For a 1 unit change in X1, you would expect a 92% decrease in the median of Y. Whew, not as clear as we usually think if I did that right.