1 / 16

Notes on Weighted Least Squares Straight line Fit Passing Through The Origin

Notes on Weighted Least Squares Straight line Fit Passing Through The Origin. Amarjeet Bhullar. November 14, 2008. Data Set. For given {x i , y i } find line through them; i.e., find a and b in y = a+bx. (x 6 ,y 6 ). (x 3 ,y 3 ). (x 5 ,y 5 ). (x 1 ,y 1 ). (x 7 ,y 7 ). (x 4 ,y 4 ).

tangia
Download Presentation

Notes on Weighted Least Squares Straight line Fit Passing Through The Origin

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Notes onWeighted Least Squares Straight line FitPassing Through The Origin AmarjeetBhullar November 14, 2008

  2. Data Set • For given {xi, yi} find line through them;i.e., find a and b in y = a+bx (x6,y6) (x3,y3) (x5,y5) (x1,y1) (x7,y7) (x4,y4) (x2,y2)

  3. Least Squares • Universal formulation of fitting:minimize squares of differences betweendata and function • Example: for fitting a line, minimize Using appropriate a and b • General solution: take derivatives w.r.t. unknown variables, set equal to zero

  4. Linear Least Squares: Equal Weighting

  5. Linear Least Squares: Equal Weighting Data Reduction and Error Analysis for the Physical Sciences by Philip R Bevington (1969)

  6. Uncertainties or Estimation of Errors: In a & b • Using the propagation of errors:

  7. Uncertainty or Estimation of Error: In Calculated a The uncertainty in parameter a

  8. Uncertainty or Estimation of Error: In Calculated b The uncertainty in parameter b

  9. Uncertainties or Estimation of Errors: In Calculated a & b Intercept Uncertainty or Error Slope Uncertainty or Error Where &

  10. Linear Least Squares fit : • Linear least squares fitting and error of a straight line which MUST go through the origin (0, 0). • Partial derivative w. r. t. b is zero

  11. Uncertainty or Estimation of Error in b Where

  12. Weighted Least Squares Straight Line Fitting

  13. Uncertainties in a and b: Unequal Weighting Intercept Uncertainty or Error Slope Uncertainty or Error Where

  14. Weighted Least Squares Straight Line Fit: Eq (6) in draft should be Where Eq (7) in draft should be

  15. Uncertainty in b: Unequal Weighting Eq (8) in draft should be

  16. Conclusion Eq (6) Eq (7) Eq (8)

More Related