# Converting linear variable's coefficient to log scale

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?

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