# When and how to transform data in regression tasks [duplicate]

I'm studying linear regression tasks and some transformation of data, in order to make the model linear, and to make the L-I-N-E assumption of linear regression met.

I know that if we have a non-linear population model, something like this : $$y = \alpha x^c$$
We can perform log-transformation of both predictor and response variable and get a linear relationship between $$log(x)$$ and $$log(y)$$. $$log(y) = log(a) + clog(x)$$

Or if the population model was originally like this : $$y = \alpha e^{cx}$$ , then one proper step to get to linear model is to transform the response $$y$$ variable and we get : $$log(y) = log(a) + c \times x$$ Hence, optain a linear relationship between $$log(y)$$ and $$x$$ .

Here is my question: Most of regression tasks, we never have the population equation, so that we do not know what is the exact non-linear relationship of the original data. So after detecting that we have to use some non-linear model ( by residual plot as I study ), how do we know the appropriate transformation to use? When should we transform the predictor $$X$$, or the response $$y$$ , or both.