http://www.physlab-wiki.com/ 2026-04-22T17:48:13+00:00 http://www.physlab-wiki.com/ http://www.physlab-wiki.com/lib/tpl/UChicago/images/favicon.ico text/html 2023-09-14T13:29:51+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.physlab-wiki.com/phylabs/lab_courses/supplemental-material/physics-and-mathematics-references/least_squares_fitting/start?rev=1694712591&do=diff 1 Linear Least-Squares Fitting ---------- (This discussion follows Chapter 15 of Numerical Recipes in C++ 2nd Edition by W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Cambridge University Press, 2002. ) 1.1 Analytic linear least-squares fitting $N$$x_i,y_i$$y_i$$\sigma_i$$f(x) = a + b(x)$$a$$b$$\chi^2 = \displaystyle\sum_{t=0}^{N-1}\left( \dfrac{y_i-(a + bx_i)}{\sigma_i}\right)^2$$a$$b$$0 = \dfrac{\partial\chi^2}{\partial a} = -2 \displaystyle\sum_{t=0}^{N-1} \dfrac{y_i-…