# Is it ok to use polynomial model to fit logarithmically transformed data?

Can we use polynomial regression using logarithmically transformed data. I transformed both y and x1 and x2 variables by natural log. After this, I used polynomial regression to fit. when using poly(), fitting result is good when using other types of model, the results are not good. I wanna make sure if I can use polynomial regression on transformed data?

model form in R is:

mod <- lm(logy ~ poly(logx1 + logx2, 2, raw=TRUE)


Of course you can use. Not restricted to polynomial regression, depending on your data, you can use any suitable transformation. The question is about if that transformation fits your data well, or not. By using your model, you assume that your DV and IVs have the following relation: $$\log y=a+b\log{x_1}+c\log{x_2}+d\log{x_1}\log{x_2}+e(\log{x_1})^2+f(\log x_2)^2$$ or, in a different form: $$y=Ax_1^bx_2^cx_1^{d\log x_2+e\log{x_1}}x_2^{f\log x_2}$$