🚀 go-pugleaf

  I need some help with the following:

  Let's say that, in a linear regression model, I have a dependent
  variable Y, and that I want to predict Y by using P as an 
  independent variable. P is expressed in percentage.

  Let's now say that some theory leads me to believe that for
  P, as it relates to Y, 50% is a special value, i.e., I suspect 
  that for the below-50% group and for the above-50% group of
  observations, the regression slopes are the same but the 
  intercepts are different. 

  To model that "jump" in the values of Y around P=50, I decide
  to add a second variable in my linear regression model, which
  I call D. D is such that D=0 for P<50% and D=1 for P>=50%.

  Thus, my model accounts for the trend (P) and for the jump (D).

  The fact, however, that D is directly derived from P makes me
  nervous about using both D and P in the same regression model.
  Should I be nervous? After all, it is not unusual to use, say,
  X and X^2 in the same set of independent variables? Is my model 
  okay as long as the correlation between P and D is not too high?
  Would a similar approach be used when modeling a health condition,              for instance, with its own trend, and the application of a
  medical treatment expected to create a "jump" but no change in 
  the slope of the trend? 

  I'd appreciate any thoughts and comments about this.

  Thanks,

  Philippe