- #1
nickerst
- 9
- 0
1. Homework Statement
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. Homework 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?
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. Homework 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?