I have to fit a curve to predict Y on the basis of X. 50 pair of (x,y) is given. On free hand plot the curve it is seen (and otherwise known also) that Y and X has 1:1 relationship. The basic nature of movement of Y is quite composite and found involving x^a, sin(c+bx), d^x , one additive constant, and different constant multipliers of the first 3 terms. Here constants are real valued . That is, Y= p + q.x^a+ r.sin(c+dx) + s.d^x What I did is to start with arbitrary values of a,b,c,d and find p,q,r,s by least squares and calculate the residual sum of squares (rss). Now I varied 'a' and compared rss till it is minimum. Then repeated the same with others, one at a time and came back to 'a' ..and so on. This resulted in a nice fit but the rss value never seem to stabilize.. it is decreasing (but of course it is not becoming 0). My question is when should I stop ... is there any objective method or a value of rss (or value of R^2) which can be used as cut off when I can say the fit is satisfactory? PS: Frequency distributions cannot be formed to test goodness of fit. Any idea is appreciated.