Lecture28 - Advantage of Least Squares Positive differences...

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Advantage of Least Squares Positive differences do not cancel negative differences Differentiation is straightforward Weighted differences Small differences become smaller and large differences are magnified
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Linear Least Squares Use sum( ) in MATLAB S nS S S nS a S nS S S S S a S S a a S S S n y S y x S x S x S let 2 x xx y x xy 1 2 x xx x xy y xx 0 xy y 1 0 xx x x n 1 i i y i n 1 i i xy n 1 i i x n 1 i 2 i xx - - = - - = = = = = = = = = = , , , ,
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Correlation Coefficient Sum of squares of the residuals with respect to the mean Sum of squares of the residuals with respect to the regression line Coefficient of determination Correlation coefficient perfect fit: S r =0 =>r=1 = = = - = n i i n i i t y n y y y S 1 2 1 1 ; ) ( 2 n 1 i i 1 0 i r x a a y S ) ( = - - = t r t S S S r - = t r t S S S r / ) ( 2 - =
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Correlation Coefficient Alternative formulation of correlation coefficient More convenient for computer implementation ( 29 - - - = 2 i 2 i 2 i 2 i i i i i y y n x x n y x y x n r ) ( ) ( ) )( (
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Standard Error of the Estimate If the data spread about the line is normal Standard deviation ” for the regression line 2 n S S r x y - = / Standard error of the estimate 0 1
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Lecture28 - Advantage of Least Squares Positive differences...

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