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Lab 5 is due today’s plan chi-squared least-squared

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Unformatted text preview: Lab 5 is due. 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 5 10 15 20 25 x 10 20 30 y = f(x) y(x) = Bx LINEAR FIT y(x) = A +Bx : A – intercept with y axis B – slope 5 10 15 20 25 x 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 5 10 15 20 25 x 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…. LINEAR FIT: y(x) = A + Bx 5 10 15 20 25 x 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! 5 10 15 20 25 x 10 20 30 y(x) 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...
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Lab 5 is due Today’s Plan Chi-Squared least-squared...

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