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 ) 1 ( 2 2 = i i mx b y b ( ) = 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 = ( ) ( ) = 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 and m 2 both equal to zero to minimize 2 . 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. You can do this by solving for one variable and substituting back into the other equation, but it is far easier to solve the equations in matrix form.
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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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Minimizing-Chi-Squared - University of Pennsylvania...

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