Soft narrate

 

People will obtain many relating data of two or more than two dimension during experiments and production. These data will help them to solve problems of reality on contrary, which need data processing to make them become mathematics model reflecting the data variation regulation. The application of the Least Square Method can only make linear regression, but to the nonlinear problems it must construct relating mathematics relationship expression, namely mechanism model through procedure supposing to do linearization processing of mechanism model and then do regression modeling computation. Some relating data of the recursive models are good, but the data of reality are changeable, some deduce mechanism models. After the linear process the correlation property of the regression model is not good, and some relating data even can't deduce in the mechanism model. It is even more harder to build mathematics  models.

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 mathematics model to the relating data which can't deduce a mechanism models.

Soft nomenclature

Sample: The system in acquisition data for each data collection point, every time collection all data, called a sample.
Sample Quantity: Times of experiment, xi, yi are individually the numerical value of arbitrary group of experiment number x, y.
Dimension: The relating characters which influence each other in some process.
Variant: the variants influence some properties in some process.
Objective function: Objective characteristics in some process.
Element: In variant made up of objective function and variants, every term which contain variant at the side of the variant side is called a variable.

Explanation

 

Two Dimensions Function:(x1 , x2)

During the regression computing while x1 is the variant, then x2 is the objective function, if x2 is the variant, x1 is the objective function.  

 

Three Dimensions Function:(x1 , x2 , x3)

During the regression computing, when x1 and x2 are variants, x3 is the objective function; if x2 and x3 are variants, then x1 is the objective function.

Four Dimensions Function:(x1 , x2 , x3 , x4)

During the regression computing, when x1, x2 and  x3 are variants, x4 is the objective function, if x2, x3 and x4 are variants, then x1 is the objective function.

Exempli gratia

 

y = a0  +  a1 x1k1  +  a2 x2k2   +   a3 x1k3 x2k4                   Formula 1

 

Function in Formula 1,

x1   and   x2 -

Respectively is Variant.

y -

Is Objective function.

x1 x2   and   y -

Respectively is Dimension.

x1k1  ,    x2k2   and    x1k3 x2k4 -

Respectively is Element.

a0 - Respectively is Constant of Model.
a,   a2   and   a3 - Respectively is Coefficient of Model.
k1 ,   k2 ,   k3   and   k4 - Respectively is power of Model.