Least Squares Fitting

nickerst

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?

nickerst

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?