fonction in python

[Duncan Smith]

Steven D'Aprano wrote:
> On Tue, 04 Jul 2006 03:06:37 -0700, aliassaf wrote:
> 
> 
>>Hello, 
>>  
>>If we write = x^2  and if I give to the program the values of x, it will
>>going to calculate the values of y, and also for x.   
>>
>>But it is possible ? that is if I give to the program the values of X and Y,
>>it will indicate to me the relation between the two variables, in the other
>>hand if I look to the program x=2 y=4, x=3 y=9 ect... it is going to show me
>>that f (t)!!! 
> 
> 
> You are asking for curve-fitting. There is a HUGE amount of work on
> curve-fitting in computer science and statistics.
> 
> Generally, you start with some data points (x, y). You generally have some
> idea of what sort of function you expect -- is it a straight line? A
> curve? What sort of curve? A polynomial, an exponential, a sine curve, a
> cubic spline, a Bezier curve?
> 
> You might like to google on "least squares curve fitting" and "linear
> regression". That's just two methods out of many.
> 
> Some curve-fitting methods also estimate the error between the predicted
> curve and the data points; you could then try all of the methods and pick
> the one with the least error.
> 

The problem being that complex enough models will fit the data
arbitrarily closely (i.e. over-fit).  The OP should take into account
any prior expectations over the type of function (as you indicate) and
apply Occam's razor (find a relatively simple model that gives a
reasonable fit to the data).

Duncan