Error-Proof - University of Pennsylvania Proof of Formulae...

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University of Pennsylvania Error Proof. 1 Proof of Formulae for Error in Slope and Intercept of Best Fit Line This is a derivation of the propagation of the error in the dependent variable, y σ , through the formulae for the slope and the intercept to get equations for the error in the slope and the intercept, mentioned in the Least Squares Fitting with Excel document. ( ) ( ) = = ∑ ∑ ∑∑ ∑∑ i i i i i i i i i y x x x y x x y x b 2 2 where () = 2 2 i i x x N 2 b = 2 2 i y y b = ( ) 2 2 2 ∑∑ i i i i i y y x x x y = 2 2 2 i i i y x x x = 2 2 2 2 i i i y x x x = 2 2 2 2 i i i y x x x = () () + 2 2 2 2 2 2 2 2 i i i i i i y x x x x x x = ( )() + 2 2 2 2 2 2 2 2 i i i i i i y x x x x x x = + 2 2 2 2 2 2 2 2 2 i i i i i y x x x x x N = 2 2 2 2 2 2 2
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This note was uploaded on 12/14/2009 for the course PHYS PHYS-102 taught by Professor Kikkawa during the Spring '09 term at UPenn.

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Error-Proof - University of Pennsylvania Proof of Formulae...

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