1
$\begingroup$

I have a linear regression model with some variables log transformed:

Y = Beta1.Log(X1) + Beta2.Log(X2) + Beta3.X3

Y is a percentage variable (A credit card companies market share) and X3 is Premium spend as a percentage of total spend. Therefore both variables range from 0 to 100.

For a specific business reason (too long to explain), I need to interpret Beta3 as the percentage (Relative) change in Y due to a percentage (relative) change in X3. The standard interpretation would be 1% (point) change in X3 would lead to a 1% (point) change in Y.

How can I do this WITHOUT rerunning the model?

Can I take log on both sides such as :

log(Y) = Beta3.log(X3)?

If yes, how can I change Beta3 to represent a log transformed variable now instead of a linear one?

If this is incorrect, what other options do I have which do not require a model re-run?

Improve this question
$\endgroup$
3
  • $\begingroup$ If the change is 50% to 60%, then the percentage (Relative) change = 10% or (60-50)/50 = 20%? $\endgroup$
    – user158565
    Oct 28, 2018 at 17:27
  • $\begingroup$ Relative change would be 20% and point change 10% $\endgroup$
    – Karan
    Oct 29, 2018 at 1:44
  • $\begingroup$ Then your relative change is not only depended on X3 and Beta3. Other factors also contribute to relative change. $\endgroup$
    – user158565
    Oct 30, 2018 at 3:48

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.