# of measurments in order to find parameters

[ted1986]

Hi,

I've got a question about fitting a known function to a measured data.

Suppose I want to find X parameters by fitting a curve to some measurments - What is the minimum number of measurements needed?
Someone has told me that I need X+1 measurments, (because one degree of freedom), but I didn't understand it...
Could someone tell me if its true, and why


Thanks!

Ted
:-)

 

[gsal]

Well, I am no expert on curve-fitting, but let's think about it...

if you knew that your function is a straight line (order 1 "polynomial": ax+b), how many measurements would need to make? Well...you would just need to make 2 measurements so that you could put together 2 equations and 2 unknowns and solve for a and b...that was n+1, where n was the order of the "polynomial" representing your function (1 in this case...this is the highest power for x in the equation).

Now, if you knew that your function was a parabola (ax^2+bx+c)...how many measurements would you need to determine a, b, and c? You would need 3 values for x, plug them in the equation above and form a system of 3 equations and 3 unknowns and solve...that was n+1=3 measurements for a 2nd degree "polynomial"..

...starting to get the picture?

my 2 cents