I have two different predictors "A" and "B" that can be used (not at the same time) to affect a response variable, "C".
Previous data has shown a very strong linear relationship between A and C, and B and C. When SLR models were fit to these relationships, both had R-squared values above 95%. Scatterplots confirm the highly linear relationships.
A claim has been made that when predictor "B" is applied, there is a 5% increase in the response "C", compared to when "A" is applied.
The two linear models fit to (A~C) and (B~C) have different slopes and intercepts. So for lower levels of A (or B), one predictor is associated with higher "C" measurements, but this is slightly reversed at higher levels.
Does anyone have an idea on how to test the 5% claim mentioned above? I was thinking it might be appropriate to create a model like this one:
$C = (U + V*X)*(1 + Y*B)$, where $U, V$ and $Y $ are constants.
X is the predictor level (either A or B). "B" in this model is an indicator variable such that B = 1 if B is being used, or B = 0 if A is used. If the 5% claim were true, we would expect Y to be .05.
The problem is that this model is not linear in the parameters, and as far as I know cannot be calculated using the common least-squares matrix operations.
Can anyone think of how to validate this model, or offer a better alternative to test the desired claim?
Thanks a lot for your help.