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Lecture+29--Linear+regression

# Lecture+29--Linear+regression - Least Squares Approximation...

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Least Squares Approximation Minimizing Residuals: least squares (linear, quadratic, ….): ei = = - - = = n 1 i 2 i 1 0 i n 1 i 2 i r x a a y e S ) (

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Linear Least Squares Minimize total square-error Straight line approximation Impossible to pass all points if n > 2 ) , ( , , ) , ( , ) , ( , ) , ( 3 3 2 2 1 1 n n y x y x y x y x i 1 0 i i 1 0 x a a x f y x a a x f + = = + = ) ( ) (
Linear Least Squares Total square-error function: sum of the squares of the residuals Minimizing square-error Sr ( a0 ,a1 ) Solve for ( a0 ,a1 ) ) , ( , , ) , ( , ) , ( , ) , ( 3 3 2 2 1 1 n n y x y x y x y x = = - - = = n 1 i 2 i 1 0 i n 1 i 2 i r x a a y e S ) ( = = 0 a S 0 a S 1 r 0 r

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Linear Least Squares Minimize Solve a0 & a1 : = - - = n 1 i 2 i 1 0 i 1 0 r x a a y a a S ) ( ) , ( ( 29 ( 29 0 1 1 0 0 1 1 1 0 2 0 2 n r i i i n r i i i i S y a a x a S y a a x x a = = = = - - - = = - - - 0 0 1 n i a na = = 0 1 1 1 2 0 1 1 1 1 n n i i i i n n n i i i i i i i na x a y x a x a x y = = = = = + = ÷ + = ÷ ÷
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Lecture+29--Linear+regression - Least Squares Approximation...

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