You're looking to estimate a function f: R² -> R
, therefore regression is the family of methods you should be looking into. Which kind of regression however depends largely on the relation between (x, y)
and mass
.
Generally described, a regression method defines a cost function c: R² x F -> R+
and a set F
of functions to choose from. Often the set F
is infinite and parametrized in some form. This leaves most regression methods with the problem of estimating the parameters that determine the optimal f
(what you referred to as 'estimating parameters').
In order to determine which regression method is most suitable, you'll have to find out the following things:
- what is a meaningful cost function
c
? - how to choose the set
F
of functions?
For example, linear regression chooses the linear least squares cost function and sets the defines F
to be the set of all linear functions f: R² x R
. This may or may not be what you want, depending on your setup.
Therefore, explaining the experimental setup under which the triplets (x, y, mass)
can be determined might help to shed some light on this.