Polynomial Model Derivation

Polynomial Model Derivation - Polynomial Model Given ( , ),...

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Unformatted text preview: Polynomial Model Given ( , ), ( , given data set. ), ( , ), … , ( , = ), best fit − − − = + +⋯+ ( ≤ − 2) to a The residual at each data point is given by The sum of the square of the residuals then is = = ( −⋯− − − ⋯− ) where To find the constants of the polynomial model, we set the derivatives with respect to = 1, … , , equal to zero. = 2( − − − ⋯− )(−1) = 0 = = Then, + + + + 2( 2( − − + + + + − − ⋮ − ⋯− −⋯− + ⋯+ + ⋯+ + ⋯+ + ⋯+ )(− ) = 0 )(− = = = = )=0 ⋮ These equations in matrix form are given by ⋮ , ⋯ ⋮ ⋯ The above equations are then solved for ,⋯, ⋯ ⋯ ⋮ ⋮ = ⋮ ...
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