Say I have a bunch of explanatory variables to predict a continuous independent variable. Below, a simple toy example:
I think it would be easiest to do a log-log transform and proceed with linear regression. Looks like that the explanatory variables are relatively highly correlated, and there might be a high collinearity between them. This, I would take care of later via e.g.,
- Lasso regression (or Ridge)
- feature selection algos
- Partial Least Squares
- Decision trees and feature importance
- Dimensionality reduction via principal component analysis
But back to the log-log-transform; now, the data looks like this:
To me, it looks like that x2, x3, and x4 are now better suited for a linear regression. However, x1 does not look "very linear" anymore. How would I best deal with x1 before I proceed?