Lec3 LeastSquaresFit

# Lec3 LeastSquaresFit - Gaussian Distribution Physics 257...

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Physics 257 Lecture 3: Least Squares Fit Prof. Matt Dobbs Physics Department, McGill U. Prof. M. Dobbs, Physics 257 Sept 27, 2007 2 Gaussian Distribution Question from last class: where does the Gauss distribution come from? ± Used in the 1730s by de Moivre as the limiting case for large N binomial distributions. Later extended by Laplace Æ Theorem of Moivre-Laplace ± Legendre introduced method of least squares in 1805 – Gauss gave a formal justification for the method in 1809 by assuming the errors were distributed in according to the Normal Distribution. Prof. M. Dobbs, Physics 257 Sept 27, 2007 3 Summary - Distributions ± Flat (roll of a die) ± Gaussian or normal (average heart rate of Canadian males) z Central limit theorem means that nature produces Gaussian distributions OFTEN. ± Poisson (counting – number of heads or tails) Prof. M. Dobbs, Physics 257 Sept 27, 2007 4 Review: Central Limit Theorem ± http://www.math.csusb.edu/faculty/stanton/probst at/clt.html

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Prof. M. Dobbs, Physics 257 Sept 27, 2007 5 Outline ± Questions ? ± Intro to χ 2 ± Least squares fitting to straight lines ± Why Δ x= ±1/ 12 z When doesn’t this apply? Prof. M. Dobbs, Physics 257 Sept 27, 2007 6 Lab / Asst Feedback ± Remember the checklists for graphing and read the instructions carefully . ± Discussions: z Quote the result (but do not repeat all details) z Discuss the experimental results and errors. z Were your results consistent with expectation? If not, why not? How can the expt be improved? ± Always show example calculation or spreadsheet. z You can use software like MS Equation Editor or a typesetter like Latex. z If you’re not comfortable with these, you may write the example calculation equations carefully and clearly by hand. (Everything else, including graphs, must be computer generated for the lab reports).
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## This note was uploaded on 04/29/2008 for the course PHYS 257 taught by Professor Dobbs during the Fall '07 term at McGill.

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Lec3 LeastSquaresFit - Gaussian Distribution Physics 257...

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