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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 σ = 2 2 i y y b σ = ( ) ( ) 2 2 2 ∑ ∑ i i i i i y y x x x y σ = ( ) ( ) 2 2 2 ∑ ∑ i i i y x x x σ = ( ) ( ) 2 2 2 2 ∑ ∑ i i i y x x x σ = ( ) ( ) 2 2 2 2 ∑ ∑ i i i y x x x σ = ( ) ( ) ( ) + 2 2 2 2 2 2 2 2 i i i i i i y x x x x x x σ = ( ) ( ) ( ) ( ) ∑ ∑ + 2 2 2 2 2 2 2 2 i i i i i i y x x x x x x σ = ( ) ( ) ( ) ( )
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