# Lab 5 is due todays plan chi squared least squared

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No LABS . Lab 5 is due.

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Today’s Plan: Chi-Squared, least-squared fitting Experiment #4 Next week: Review Lecture
LEAST SQUARES FITTING (Ch.8) Purpose: 1) Agreement with theory? 2) Parameters 0 5 10 15 20 25 x 0 10 20 30 y = f(x) y(x) = Bx

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LINEAR FIT y(x) = A +Bx : A – intercept with y axis B – slope 0 5 10 15 20 25 x 0 10 20 30 y(x) x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 A θ where B=tan θ
LINEAR FIT: y(x) = A + Bx 0 5 10 15 20 25 x 0 10 20 30 y(x) y 3 -yfit 3 y 4 -yfit 4 [y j -yfit j ] Σ 2 Quality of the fit Method of linear regression, aka the least-squares fit….

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LINEAR FIT: y(x) = A + Bx 0 5 10 15 20 25 x 0 10 20 30 y(x) y 3 -(A+Bx 3 ) y 4 -(A+Bx 4 ) [y j -(A+Bx j )] Σ 2 minimize Method of linear regression, aka the least-squares fit….
What about error bars? Not all data points are created equal! 0 5 10 15 20 25 x 0 10 20 30 y(x)

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Weight-adjusted average: N x x x N x x N i + + + = = ... 2 1 N N N i i i w w w x w x w x w w x w x + + + + + + = = ... ... 2 1 2 2 1 1 Reminder: Typically the average value of x is given as: Sometimes we want to weigh data points with some “weight factors” w 1 , w 2 etc: You already KNOW this – e. g. your grade: % 25 5 * % 15 % 25 % 15 + × + × = FINAL LABS GRADE Weights: 25 for Final Exam, 15 for each of 5 labs
More precise data points should carry more weight!

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