I ran a screening experiment for six numerical parameters to determine if they influence the response $Y$.
However, one factor, $A$, is confusing me. I visualized its effect on $Y$ and got the following plot:
However, when I plotted the effect of the parameter on $Z = \ln(1+Y)$, I got that its ifluence was quite different:
I transformed $Y$ in order to get normally distributed and homoscedasticit residuals for a mixed model for the response (and after transformation, the residuals were normally distributed and homoscedasticit).
How should I interpret this parameter's effect and why does the curve look so different for $\ln(1+Y)$? Instead of peaking and $A=0$, it drops from $A=-1$ to $A=0$ and it seems that its values at $A=1$ are almost the same as for $A=0$. Comparing to what I got for $\ln Y$, this is pretty different behavior.
EDIT 1: Here are the scatter plots for $Y$:
and $Z = \ln(1+Y)$: