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!

Homework Help: Least Squares Fitting

  1. Feb 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose two variables x and y are known to satisfy a relation y=Bx. That is a graph of x vs. y is a line through the origin. Suppose further that you have N measurements (xi,yi)and that the uncertainties in x are negligible and those in y are equal. Prove the best estimate for B is B= [Sum(xy)]/[Sum(x^2)]

    2. Relevant equations

    B= [(N Sum(xy))-(Sum(x))*(Sum(y))]/[Del]

    Del = [N(Sum(x^2))] - (Sum(x))^2]

    3. The attempt at a solution[/b]

    So I plugged the equation of Del into the equation for B so I can try to simplify it and therefor show the best estimate. But it just gets more and more complicated. Is that for sure where I should start?
     
  2. jcsd
  3. Feb 27, 2010 #2
    I simplified the expression for B into...

    [Sum(x)Sum(y)] * [(N - 1)] / [Sum(x^2)] [N - Sum(x^2)]

    This almost gives me what I want but I'm not sure what to do with the N - 1 and N - Sum(x^2). Might it be that when N = 0 (at the origin) it reduces the expression to just the best estimate for B?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook