I want to find the best curve fitting for my model of type:
y=a1f1(x)+a2f2(x)+a3f3(x)
where, (xi,yi), i∈{1,2,...,n}
Now I need to find the parameter vector (a1ˆ,a2ˆ,a3ˆ) that best fits the data, assuming f1, f2 and f3 are any functions chosen from Powers, exponentials, sines, sigmoids, hyperbolic tangents, Gaussians
2) Also, choose points xi and simulate to generate data using the expression:
yi=a1f1(xi+∆xi)+a2f2(xi+∆xi)+a3f3(xi+∆xi)+∆yi
Generate the set of 2n values for ∆xi and ∆yi as small independent pseudo-random variables
My doubt here is how do I fit data to such a garden variety function