It is not clear whether you want
1. To fit the sampled data containing noise and measurement error as closely as possible
or
2. To fit a larger population of data containing noise and measurement error from which the sampled data is considered to be representative.
For example, consider a sample of N = 20 points from a contaminated linear model
y = a*x + b + c*randn(1,N).
The sample data can be represented exactly by a 19th order polynomial with Np = 20 estimated coefficients. However, that polynomial is usually not a good represenative model for the population.
In the latter case functions like STEPWISE and STEPWISEFIT that can automatically choose a more reasonable polynomial order are more appropriate.
Regardless of the model, it is usually wise to use as few estimated parameters, Np, as possible to increase the confidence in the parameter estimates (Search Occam's Razor). A useful rule of thumb is to assume N > Np is necessary and N >> Np is sufficient.
In the case of nonlinear neural network models, trial and error is a relatively straightforward approach. However, more advanced techniques like regularization and validation set stopping tend to be used by frequent practicioners.
Hope this helps.
Greg
