.Least Cubic Method

[eaihua]

Least Square Method is method for data regression, but in actual application exsit Deduce the complicacy problem and the relativity is not high Problem etc.Least Cubic Method solves problems that Least Square Method data regression met in the regression of relating data. Since the computers are widely used and applied in experiment, designing and production, it makes the regression computation based on the theory of Least Cubic Method into reality. people can not only process the mechanism model through the regression linearization processing better, but can also give a sound mathematicalematical model to the relating data which can't deduce a mechanism models.

[sqh]

I have a chart(as follows), want regression analysis to a model (formula), "Least Cubic Method" can do it?

[eaihua]

Hi sqh

Chart of you sent me at below, processing methods such as the following steps.

step 1: Confirm the factor value and goal calculating value (goal function).

Step 2: from the chart to Read abundance data.

Step 3: Use DRS software to enter data and Finally dimension as the objective function.

Step 4: Calculation of regression.

Format of enter data(factor value1,factor value2,goal function)

150 200 200

100 3 300

300 45 400

..... ..... .....

200 0.7 450

300 0.8 600

300 0.025 700

[eaihua]

QUOTE (eaihua @ May 1 2008, 11:44 PM)

Least Square Method is method for data regression, but in actual application exsit Deduce the complicacy problem and the relativity is not high Problem etc.Least Cubic Method solves problems that Least Square Method data regression met in the regression of relating data. Since the computers are widely used and applied in experiment, designing and production, it makes the regression computation based on the theory of Least Cubic Method into reality. people can not only process the mechanism model through the regression linearization processing better, but can also give a sound mathematicalematical model to the relating data which can't deduce a mechanism models.

Least Cubic Method (Generalized Least Square Method)

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.

The Method to do multivariate nonlinear model chart

Download1:

Download2: http://fbn.skycn.com/down/eDRS2008.zip

Web address:

[mes]

QUOTE (eaihua @ May 1 2008, 11:44 PM)

Least Square Method is method for data regression, but in actual application exsit Deduce the complicacy problem and the relativity is not high Problem etc.Least Cubic Method solves problems that Least Square Method data regression met in the regression of relating data. Since the computers are widely used and applied in experiment, designing and production, it makes the regression computation based on the theory of Least Cubic Method into reality. people can not only process the mechanism model through the regression linearization processing better, but can also give a sound mathematicalematical model to the relating data which can't deduce a mechanism models.

I have the 8-dimensional data，Regression model can it?

[eaihua]

QUOTE (mes @ Oct 29 2008, 02:51 PM)

I have the 8-dimensional data，Regression model can it?

Certainly, we can do more multidimensional nonlinear data regression , you can send us the data.

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