Generalized Least Square Method(Least Cubic Method)

[eaihua]

When studying the relating relations between the two variable numbers (x, y), we can get a series of binate data(x1, y1, x2, y2.....xm, ym), describing the data into the x - y orthogonal coordinate system(Chart), the points are found near a curve. suppose the one-variant non-linear variant of the curve such as (Formula 1)



y = a0 + a1 xi ^k (1)

There into, a0, a1 and k are arbitrary real numbers

To set the curve variant, the numbers of a0, a1 and k must be set. Use the same way with “The Least Square Method data regression” based on the square sum of the deviation of the true measure value yi and computing value.

Order:
φ = ∑(yi - y)^2 (2)

Take (Formula 1) to (Formula 2) to get :

φ = ∑(yi - a0 - a1 xik )^2 (3)

When the square of ∑(yi - a0 - a1 xik ) is the smallest, we can use functionφ to get the partial differential coefficients of a0, a1 and k, make the three partial differential coefficients zero.

(4)

(5)

(6)

Get three variant groups about a0,a1 and k which are the unknown numbers, solve the groups can get mathematical model.

Also, we can judge the right of the mathematical model with the help of correlation coefficient R, statistical variable F, residual standard deviation S to judge, it is better that R tends to 1,the absolute value of F is bigger and S tends to 0. the validation is good, but error of model computing sometimes are big, to improve the mathematical model farther, the biggest error, equal error and the equal relating error of computing model are computed to validate the model.

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