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I have a rather simple question on error propagation - I have 2 sets of models, where the results from model are used as variables in the next model. I need to know how to carry forward errors from one to another.

Case -

Model 1: Y = a*exp(b*X) + c

The errors on X (which is a vector of about 100 samples) and Y (a vector of same size as X) are not know. From fitting the above non-linear model to the data and examining the residuals, I can calculate Mean Absolute Error, RMSE, etc. So, in the end I get a vector of Y values and a single error estimate from the model (e.g. RMSE).

Model 2: Z = s*(Y)^t + u

Where Y is the variable obtained from the results of Model 1. Applying Model 1 to a large number of new X values, I now have Y as a vector with > 10,000 elements. Each element in vector Y should have an associated error. My question is - what error should I give each element of vector Y? My next question is, once the error on each element of vector Y is known, how do I propagate this error to each element of vector Z? Finally, how do I calculate RMSE for Model 2?

All help will be much appreciated!

Thanks,

Yaal