For a linear regression model, the data for a continuous input variable X is such that 90% of the data lie at a value far short of the maximum possible. For example, say the range of X (in months) is between 1 and 100,the median of X is 25 and the 90th percentile is 60 months. Most of the input X values (90% in the example) lie before a value only a little over half the maximum possible.
The outcome variable Y is a percentage. The trend of Y vs X is as follows: Y shows a very small increasing trend ( nearly flat looking ) vs X, upto the 65 month mark. After this, there is a very sharp downward trend.
However, the regression coefficient for X is a very small positive number (close to zero) and not negative.
I should mention the regression is weighted by another variable W, which is in currency units. However, even without the weighting, I still get nearly the same coefficient from my regression. My guess is that the regression is influenced by the fact that most data is in the slightly upward trending part.
For our application, it is very important to capture the negative trend. Binning the variable X is not possible due to the nature of the application - it has to be continuous. Is there any other transformation of X that could help ? or any other method that could be used in this situation to capture the downward trend at the end?
Thanks for any advice!