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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 mathematicalematical 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 mathematicalematical 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 mathematicalematical 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 mathematicalematical model to the relating data which can't deduce a mechanism models.
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| 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.
|
Exempli
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.
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.
|
| a1
, a2 and a3 - |
Respectively
is Coefficient
of Model.
|
| k1
, k2 , k3 and k4 - |
Respectively
is power
of
Model. |
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