How can I interpret the coefficient of a logit transformed explanatory variable in linear regression? I fit a linear regression model with continuous response. One of my predictor variables is given in percentage. So I transformed the predictor with logit transformation. My question is how can I interpret the coefficient of this transformed predictor? You can consider the following model as example:
$Y = b_0 + b_1 logit(X) + e$
How to interpret $b_1$?
 A: Welcome to the site, user248399.
As @Heteroskedastic Jim states, b1 allows you to calculate the expected change in Y for a given change in logit(X).
If the coefficient b1 is significantly different from 0 (check the standard error on the estimate of b1 and calculate confidence intervals, or check the p-value for b1), then it appears that logit(X) is a useful predictor for Y.
A couple of things to consider:


*

*Have you tried the regression with the untransformed values of X, and checked to see if the residuals are normally distributed and without obvious patterns in the residual vs. fitted values plot? i.e. is the transformation necessary?

*In the dataset you have used to fit the relationship, do you have any values very close to (or at) 0% or 100%? If you don't have these,  be extra careful - you cannot be confident that the relationship will hold outside of the values of logit(X) for which you had data. It could be particularly dangerous to extrapolate to values close to 0% or 100%, because the tails of the logit transformation are quite severe, so at small or large percentages, you will get quite large changes in logit(X) (and therefore the predicted value of Y) for only a small change in X.
Less severe alternatives to the logit transformation are available - e.g. folded roots, see here, here and here.
