Method For Constructing Correlation Dependences For Functions Of Many Variables Used Finite Differences

The article considers a method for constructing correlation models for finite-type functions using a set of variables. The use of the method of unknown squares in the construction of correlation models and the construction of higher-quality models is also justified. The proposed correlation models are considered on the example of statistical data of the Bukhara region of the Republic of Uzbekistan.


INTRODUCTION
When it comes to the method of constructing correlation models, researchers usually use the method of unnamed squares and get the dependence Υ = f(x), but these obtained dependences do not give the real Parin of the actual process. Of course, correlation dependences are not functional dependence. But sometimes the model values are so different from the real ones that make it difficult to use them in planning and forecasting practice, this explains the not very wide use of economic and mathematical models in forecasting practice and other calculations of the economy. In our works [1,2,3,4], some attempts were made to obtain a better quality dependence of the type Υ = ( ); namely, the rejection of traditional methods based on obtaining the relationship between the factors of feathering; namely, rejection of traditional methods based on obtaining the relationship between factors operating in advance known х mathematical formulas such as Υ = о = в х , = Ае, = A -L etc. we proposed to find the relationship from the nature of the most data available to us.

Method For Constructing Correlation Dependences For Functions Of Many Variables Used Finite Differences
In mathematical analysis, we know that lim ∆ →0 Instead of what we have at our disposal, we can obtain finite differences of a certain order or we can calculate the value y i−1− y i Δx ≈ 1 ( ) Now, instead of getting the dependency Υ = ( ), we will build a function of 1 = (х) based on this data. Integrating this function and solving the Cauchy problem, we obtain the desired correlation dependence of the type Υ = ( ).
We will consider the methodology for constructing correlations using the proposed method using a specific example, using the example of real statistical data of the Bukhara region of the Republic of Uzbekistan in the period 2014-2019. Let = ( ) the volume of GDP in the region х 1 ( ) -the number of households producing agricultural products (thousand) х 2 ( ) the volume of production by farms.
All data for calculating carrying out in  For traditional methods, we look for the dependence = (х 1 ; х 2 ) in the form = а о + а 1 х 1 + а 2 х 2 and find the specific form of the function by the name-squares method = -26477,3+68,2х 1 +1,94х 2 And so we have two functions of the correlation dependence = (х 1 х 2 ) formula (1) is obtained by the proposed method and formula (2) by the traditional method. For a drive comparison, all the calculations in the following table are here γ ф -the actual value of GDP in the area, γ p -obtained by the proposed method and the value γ т − obtained by the traditional method The proposed method is an alternative method for constructing correlation dependences to the existing ones.

CONCLUSION
The main task set before us when writing work [1; 2; 3] and this work is the development of alternative methods to the existing one, such as the method of unnamed squares and others. Here, the correlation between the factors is not known in advance for specific mathematical functions, but is determined based on the nature of the available data.
In mathematical analysis it is assumed that the derivative function gives the saw characteristics of the antiderivative of the function. Based on the methods of obtaining functional dependencies in other industries at uni, we also wanted to apply this method in mathematical statistics. And the conducted research has shown the possibility and effectiveness of this attempt.
Here is one of the simplest examples of which gives hope to use the proposed method in mathematical statistics and econometrics.
Let the following data be obtained as a result of observation, which are given in the following table. The task is to obtain the dependence = f (x) by the finite difference method.
And so we have In our work, for simplicity, we basically stopped the computation process at the first step. And having received dy dx = ( ) immediately after integration, we obtained the required dependence = f (x