I am estimating a model of the following form:
log(y) = b1 x + b2 x^2 + b3 log(z1) + b4 z2
This is an econometric model with a focus on the impact of
x^2 (the inverted U relationship), where
x ranges from 0 to 1. I included the other variables
z1 and z2 just to be clear that there are other controls (some which are log-transformed and some not).
I get a clear inverted U relationship - slope check at end points and a marginal plot confirms that.
My question is the following: How can I say something about the change in x impacting y (not log(y))? This article (https://library.virginia.edu/data/articles/interpreting-log-transformations-in-a-linear-model) provides a nice way to interpret in case I don't have the
x^2 term. How to do this correctly when I have the
For example, if I am able to do one of the following that will be wonderful:
- If x increases by 0.1 from its current sample mean what will be impact on y?
- If x increases by 10% from its current sample mean, what will be the impact on y?