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Minimizing-Chi-Squared

# Minimizing-Chi-Squared - University of Pennsylvania...

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University of Pennsylvania Minimizing Chi-Squared. 1 Details of Minimizing 2 χ to Get Equations for Slope and Intercept of Best Fit Line This is the derivation for the equations for the slope and intercept of the best fit line ( y = mx + b ) using the method of least squares fitting, mentioned in the Least Squares Fitting with Excel document. ( ) 2 2 = i i mx b y χ ( ) ( ) ) 1 ( 2 2 = i i mx b y b χ ( ) ( ) = i i mx b y 2 + + = i i mx b y 2 2 2 + + = i i x m Nb y 2 2 2 ( ) ( ) ) ( 2 2 i i i x mx b y m = χ ( ) ( ) = 2 2 i i i i mx bx y x = 2 2 2 2 i i i i mx bx y x = 2 2 2 2 i i i i x m x b y x Set b 2 χ and m 2 χ both equal to zero to minimize 2 χ . 0 2 2 2 = + + i i x m Nb y 0 = + + i i x m Nb y = + i i y x m Nb 0 2 2 2 2 = i i i i x m x b y x 0 2 = i i i i x m x b y x = + i i i i y x x m x b 2 Solve the two equations simultaneously.

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Minimizing-Chi-Squared - University of Pennsylvania...

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