Polynomial - ∑ ∑ = = = j x y x a M i j i i M i k j i n k k ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ = = = = = = = = = = = =

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Regression and Correlation of Data Objective: Fit a polynomial with the Least Squares Method
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Fitting the polynomial with the least squares approach Regression and Correlation of Data n x a x a x a a x P n n + + + + = ... ) ( 2 2 1 0 Least squares method can also be sued to determine the coefficients: n ,...,a , a , a a 2 1 0 2 1 1 2 )] ( [ = = - = = n i i n i n i i x P y e SSE 0 ) ( = SSE a i i = 0, 1, 2, …, n (n+1 equations) (n+1 coefficients)
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Regression and Correlation of Data In this case, we wish to minimize: where: M is the number of data points minus 1 The minimization step leads to a system of n +1 normal equations in n +1 unknowns. The unknowns are the coefficients of the polynomial a 0 , a 1 , a 2 , … , a n ( 29 2 0 ) ( P = - M i i i x y
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n. ..., 1, , 0 where , 0 0 0 = =
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Unformatted text preview: ∑ ∑ = = + = j x y x a M i j i i M i k j i n k k ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ = = = = + + = = = + = = = = = = = = = + + + + = + + + + = + + + + M i M i n i i n i n M i M i n i n i M i n i M i M i i i n i n M i M i i i M i i M i M i i i n i n M i M i i i M i i x y x a x a x a x a x y x a x a x a x a x y x a x a x a x a 2 2 2 1 1 1 1 3 2 2 1 1 2 2 1 1 ... , ... , ... Regression and Correlation of Data • Gives a system of equations simultaneous equations that can be solved. Example 45...
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This note was uploaded on 02/13/2012 for the course MATH 2320 taught by Professor Glyn during the Fall '11 term at Minnesota.

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Polynomial - ∑ ∑ = = = j x y x a M i j i i M i k j i n k k ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ = = = = = = = = = = = =

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