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I have a data set consisting of crop biomass measurements ("response" variable) and corresponding spectral vegetation indices measurements (predictor variables). The measurements have been made on two crop varieties. I fitted three regression models -

  1. combined data set
  2. variety one only
  3. variety two only.

    Since I do not have a theory behind my experiment I tested both linear and exponential models in each case and selected those with the lower RMSE. Also, I tested the different predictors (one at a time) and selected in each case the best one. Now I have three models fitted to different data sets (different observations and different predictors) and of different type (linear or exponential).

I want to know can I use F test (or other test) to say whether there is significant difference between the fitted combined model and the fitted separate models for each of the two varieties. In other words, is there a necessity to split the data set and model each crop variety separately or I can develop combined model applicable to both varieties.

I found a textbook where it was explained how to use F test to say whether a treatment change the dose-response curve. But they are comparing two versions of the same model (Hill equation). In my case the equations are different - linear and exponential.

An alternative that I am also thinking of is just to compare the RMSE, but do not know how.

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  • $\begingroup$ As I recall, Fisher originally created the "F" test to do exactly this, decide which equation to use as a model. $\endgroup$ – James Phillips Jun 4 '18 at 16:39

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