Perhaps this question is silly but I need to clarify a doubt I have:

As far as I understand the number of variables refers to those parameters which have been "guessed" in the fit and it is limited by the number of independent points.

If I have a group of variables but only set to guess a few of them while fixing the others, then fix some of the obtained values and guess other variables; I might include a large number of parameters in the resulting fit (even more than the independent points) without increasing the Number of variables of each individual fit. This also would keep reduced chi2 from increasing too much.

Would this be cheating? 

The total number of parameters included is always restricted by the Number of independent points?

or

Can I include all the parameters I want as long as I set to guess no more that the number of independent points at the time?

Thank you in advance as always,

Yours 

Jesús

esús