Estimation of two parameters - R

Question

this is more a general statistics problem. My aim is to determine the relationship between two unknown parameters: k and a, in this equation:

k = f(T,t0)*a + g(T,t0)

Assuming that in the scenario I am considering this equation holds, I thought that the best I can do is to estimate the relationship between k and a. So my idea is to compute a lot of values of f and g, varying (almost) randomly T and t0, then assign (almost) random values to a, calculate respective k, so finding N points (a,k) and plotting k against a. From there do some sort of regression and estimate a relationship between the parameters, which can be linear or non linear.

I could implement it in R and got an interesting plot, which looked more like bands, made me think to discrete energy levels. I would report the graph and the code here but all the work got lost. Whatever, nothing like a continuos function between k and a. Maybe there could be some other relation explainable with some more advanced function or tool, or most likely my assumptions on the validity of the equations were wrong. Or otherwise there is a mistake in my method.

However theoretically, I have the feeling that there is a smarter and more appropriate way to approach the problem, although I don't find any logical mistakes in my way.

Any experienced opinion would be highly appreciated

Thanks!

question from:https://stackoverflow.com/questions/65884584/estimation-of-two-parameters-r

Answer 1

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