Interpreting regression coefficients in linear regression

[Zain Kaleem]

Hi,

I am running a linear regression model where I have used log-transformed dependent and log-transformed independent variables for easier interpretation of the regression coefficients as a percentage change in the dependent variable with each unit change in the independent variable.

Is there a way I could transform the regression coefficient such that it represents the percentage change in the dependent variable with each IQR change in the independent variable?

[Clyde Schechter]

I am running a linear regression model where I have used log-transformed dependent and log-transformed independent variables for easier interpretation of the regression coefficients as a percentage change in the dependent variable with each unit change in the independent variable.

That is incorrect. With both the dependent and independent variables long transformed, the interpretation of the coefficients is (approximately) as a percentage change in the dependent variable with a 1% change in the independent variable, not a unit change in the independent variable.

Is there a way I could transform the regression coefficient such that it represents the percentage change in the dependent variable with each IQR change in the independent variable?

No. Nothing you can do to the coefficient of a log-log regression can do this. However, you can change the regression model as follows. Take the untransformed independent variable and calculate its median and IQR. Then calculate a new independent variable equal to the original untransformed variable minus the median, all divided by the IQR. Now regress the log-transformed dependent variable on this new variable. The coefficient will represent the (approximate) percent difference in the dependent variable associated with a 1 IQR difference in the independent variable.