For purpose of calibration, i suggest you carry out a linear/planar form of model fitting initially, and perform the appropriate statistical analyses including the model diagonstic tests, in case you find the linear / planar model poorly fitting your data, you can sequentially go for a higher order model that best fits your data using the stepwise selection of regressors algorithm.

An alternate approach is to use a neural network approach, design a neural network with pre chosen no. of parameters( connecting weights, bias values and no. of neurons in hidden layers etc. ) , use experimental data on process input and output as training set with an appropriate algorithm, e.g back propagation algorithm or genetic algorithm as the optimizer.

normally the number of parameters should be less than the number of data points.

Initially the fitting problem is based on how you choose the shape of the fitting equation and you search for the fitting parameters. If the data is hard to detect its shape you can assume a nonlinear equation of the second order and you raise the order gradually to the limit of the accepted accuracy. For some problems the model may be assumed as a polynomial have parameters on the numerator and others on the denumerators, You can rely easily on several published letters on my list of publications that cover this topic.

Good Luck

Prof. S. El-Rabaie

Agree with Qin that the number of parameters should not usually exceed the number of data points less one. Deviation from this can be justified only if you have information additional to your data, e.g. a theoretical reason why a certain function is relevant. More parameters, up to data-1, will give a better fit (i.e. reduced residuals) but not necessarily better understanding - see comments from others on how to assess this. The more parameters you have, the more poorly behaved the model is likely to be outside the range of data, or even between data points.