I have a set of data I'm analyzing in R with 2 explanatory variables (X1 and X2), and one response variable (Y).



My goal is to calculate an equation that will allow me to predict Y based on future X1 and Y1 values. In the past I have used a linear regression like so:


And then use this formula to predict Y

Y= coefficients(MyFit)[1]+coefficients(MyFit)[2]*X1+coefficients(MyFit)[3]*X2

In the above dummy set, Y is strongly driven by X1. But the issue with my real data is that at some point Y gets saturated, so that further increases in X1 do not bring about increases in Y (for this data the saturation value is 250, but the actual values begin to slow down and form a saturation curve as it approaches peak value, as opposed to an absolute saturation point). The result is that the linear model will always over-predict the peak Y values. This can be seen in a plot here:


How can I correct for this. Is it possible to do a multiple non-linear regression for this data? Or is there some other technique I can use here?

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    $\begingroup$ A side note: Instead of Y= coefficients(MyFit)[1]+coefficients(MyFit)[2]*X1+coefficients(MyFit)[3]*X2 simply use predict(object = MyFit) $\endgroup$ – Helix123 Mar 8 '16 at 17:27
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    $\begingroup$ If you've some theory to suggest an asymptote - rather than a mere tailing off - it could be worth looking at simple non-linear models. $\endgroup$ – Scortchi - Reinstate Monica Mar 8 '16 at 17:31
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    $\begingroup$ What are y, x1 and x2? $\endgroup$ – Roland Mar 9 '16 at 16:22
  • $\begingroup$ The above is dummy data that approximates an issue I'm having with an actual data set. So in this case Y is my response variable (Photosynthetic output), and X1 (Light) and X2 (wind) would be my explanatory variables. $\endgroup$ – Vinterwoo Mar 9 '16 at 23:41
  • $\begingroup$ Then theory & your dummy data concur in suggesting a hyperbolic growth curve for the relationship between photosynthetic rate & light intensity mightn't be a bad model. Wind, up to a point, presumably aids photosynthesis by increasing transpiration, but does it affect the saturated rate or the half-saturation constant, or both? You also need to think about the error structure - is variability in rate roughly the same after light & wind are accounted for? It'd be a good idea to include additional information in your question rather than in comments. $\endgroup$ – Scortchi - Reinstate Monica Mar 10 '16 at 12:53

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