# Regression to Classification and back to Regression

Is it reasonable to transform regression problem into classification by binning target variable into classes and construct regression curve separately on each class?\

Precisely, if my goal is to solve regression problem are the following steps reasonable:

1. If my target variable is $$Y$$, Create $$m$$ classes $$Y_1 =\{Y:Y.
2. Construct classifier $$p_j(x)=Pr(Y \in Y_j|X=x)$$.
3. Construct regression curves for each class separately $$E[Y|Y_j,X=x]=f_j(x)$$.
4. Estimate final regression curve by $$E[Y|X=x]=\sum_{i=1}^m p_j(x)f_j(x).$$

Theoretically, if our goal is to construct regression curve $$E[Y|X=x]$$ than from identity $$E[Y|X=x]= \sum_{i=1}^m Pr(Y \in Y_j|X=x) E[Y|Y_j,X=x]=\sum_{i=1}^m p_j(x)f_j(x)$$ it looks like steps described above are just a waste of time. But it’s possible that the estimation of $$p_j(x)f_j(x)$$ could be done more effectively. Any literature or comment would be helpful.

• Why do you want this? Binning is loosing information: Binning is loosing. – kjetil b halvorsen Aug 8 at 9:31
• I can't think of a statistical principle that would make one want to do this. – Frank Harrell Aug 8 at 11:18
• @kjetilbhalvorsen binning predictors is not a good idea, I'm interested on binning target variable – Dato Gogolashvili Aug 8 at 14:18
• Binning the target variable neither is a good idea! Better tell us what is your ultimate modeling goal. – kjetil b halvorsen Aug 8 at 14:31