<s>[INST] ### Overview

When I Perform Regression on the data, I get R-squared around .80, so when I project the Predicted Values I'm getting a lot of values above the Actual values for a particular column. The main reason is I've been told is due to "Regression towards the mean". This is a common phenomenon in regression analysis where the predicted values are more towards the mean of the predictor variable, or in other words, they tend to be average. This makes sense, because my Y is continuous and naturally distributed.

So in order to address this issue of regression towards the mean, I was told I could try to transform the data prior to regression, so I can get better calibrated estimates. The most common transformation is to log the independent variable, which is perfectly normal. BUT, the problem is that the nature of the column I'm trying to predict is Exponential and very Heteroscedastic. Taking log of an Exponential distribution and doing regression will shift the mean, not the Variance, hence after exp transformation the predicted values will be again far from actuals.

This summary provides context and background on why the current approach (non-log transformed) regression's predicted value run high. How can I best overcome the issue of regression towards the mean (RTM) when exponential data shows values at or below 2 in the majority of cases, and values at or far above 100 in a minority of cases.

### Questions

* What does RTM mean in regression analysis?[/INST]