Fitting multi-datasets sharing same parameters?

[haze (Masahiro Haze)]

I have three data sets and three fitting functions.
I want to fit three curves in the same time, because these fitting curves share the fitting parameters.

The figure is one example.
I have three data sets (blue, red, green).
Blue ones should be fitted by the function y=ax^2.
Red ones should be fitted by the function y=ax+b.
Green ones should be fitted by the function y=bx+2a.

In this kind of situation I want to find the best a and b.
normal “Findfit” allows only one functions.

Does anyone have ideas to solve?

[jbaldwinpsw (Jim Baldwin)]

See the excellent answer by @SjoerdSmit on MultiNonlinearModelFit.

I believe (and I certainly could be wrong) that when using MultiNonlinearModelFit one must be able to assume (as opposed to just willing to assume) that all regressions have the same error variance and that all of the errors are independent of each other.

If you what you need doesn’t allow you to make those assumptions, please edit your question with the details.