# Overfitting and data transformations

Ok, if we put together too much independent variables, primary looking for better fits (for exemple, higher R², lower AIC, [...]), the model could be very unreal, or unable to predict something. The coefficients could have a difficult interpretation too (considering a ceteris paribus interpretation as a desirable thing).

That is, we don't really have a better model if it demands too many crucial information entered by the user (and much more objections).

Is it possible that data transformations could lead to some of that problems?

For exemple: I discover a better fit between $y$ and $x_i, i={1,2,3...}$, using $x_1$ and $x_6$ transformations like

$x_1._1 = x_1^{0.58}$ instead of tradicional $x_1._1 = x_1^{0.5} = sqrt(x_1)$

(after testing $0.57, 0.56, 0.55, [...];$ and $0.59, 0.6, 0.61, [...]$)

or

$x_6._1 = 2.6^{x_6}$ instead of $x_6._1 = e^{x_6} = 2.718^{x_6}$

(You can imagine other non-usual transformations)

I know that the interpretation will be like less "visual", but assuming that I have all the hypothesis verified and more precision, doing that should be considered as overfitting too?

The real variables could have a strange relation in the population, after all. Is that reasonable?