The new forums will be named Coin Return (based on the most recent vote)! You can check on the status and timeline of the transition to the new forums here.
The Guiding Principles and New Rules document is now in effect.
Least Squares Fit and Residuals Questions
StudioAudience
Registered User regular
Registered User regular
I'm working on a problem set right now, and I'm sort of stump on the following queries. I'm not looking for answers, but tips/hints would be awesome.
Given x1,x,2,x3,x4, and y1,y2,y3,y4 as data points, let yhat = a1(xi) + a0, i = 1,2,3,4 be the estimates of the least squares fit.
The problem wants me to show that the mean of the residuals (yhat - y) is equal to 0.
I have:
[(a1x1 + a0 - y1) + (a1x2 + a0 - y2) + (a1x3 + a0 - y3) + (a1x4 + a0 - y4)]/4 as being equal to the mean. I guess you can simplify this to:
[a1(x1+x2+x3+x4) + 4a0 - (y1+y2+y3+y4)]/4
However, this is as far as I can get before I'm stumped. How would I go about showing that this is equal to 0 when no definite values are given for any of the variables?
Given x1,x,2,x3,x4, and y1,y2,y3,y4 as data points, let yhat = a1(xi) + a0, i = 1,2,3,4 be the estimates of the least squares fit.
The problem wants me to show that the mean of the residuals (yhat - y) is equal to 0.
I have:
[(a1x1 + a0 - y1) + (a1x2 + a0 - y2) + (a1x3 + a0 - y3) + (a1x4 + a0 - y4)]/4 as being equal to the mean. I guess you can simplify this to:
[a1(x1+x2+x3+x4) + 4a0 - (y1+y2+y3+y4)]/4
However, this is as far as I can get before I'm stumped. How would I go about showing that this is equal to 0 when no definite values are given for any of the variables?
GFWL: studaud (for SF4)
StudioAudience on
0
Posts
Hint
http://mathworld.wolfram.com/LeastSquaresFitting.html
The answer to your problem is hidden somewhere between equation (1) and (6).
GFWL: studaud (for SF4)