1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# of measurments in order to find parameters

  1. Nov 21, 2011 #1

    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


  2. jcsd
  3. Nov 21, 2011 #2
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook