604 - data pairs: x1 y1 x2 y2 xi yi (height weight) Method...

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1 data pairs: x 1 y 1 x 2 y 2 # x i y i # (height weight) Method of least squares : to find the “least-square line” y = a 0 + a 1 x to best fit the data in the sense that the error sum of squares is minimized. Let v 1 = [ 1 1 " 1 ] T , v 2 = [ x 1 x 2 " x n ] T , y = [ y 1 y 2 " y n ] T , a = [ a 0 a 1 ] T and C = [ v 1 v 2 ]. Then E = || y ( a 0 v 1 + a 1 v 2 ) || 2 = || y C a || 2 Mathematical formulation of the method of least squares: given y and C , wish to find a which minimizes || y C a || , where C = [ v 1 v 2 ], and (in general) B = { v 1 , v 2 } is L.I., or equivalently, wish to find a such that C a = P W y , the orthogonal projection of y on W = Span B . Comparing Theorem 6.8 and the mathematical formulation of the least-squares method, we see that the vector a that minimizes || y C a || is which is the solution of the normal equation
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2 Example: the best linear approximation between the finished weight y and the rough weight x is y = 0.056 +0.745
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This note was uploaded on 10/16/2010 for the course EE 155 taught by Professor Fong during the Spring '09 term at National Taiwan University.

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604 - data pairs: x1 y1 x2 y2 xi yi (height weight) Method...

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