General Concept About Correlation Relationships.

Аннотация

This annotation provides a comprehensive insight into the general concept of correlation relationships. It explores the fundamental principles and applications of correlations within various fields, emphasizing their significance in statistical analysis, predictive modeling, and decision-making processes. The annotation delves into the types of correlations, their mathematical representation, and the interpretation of correlation coefficients. Additionally, it discusses the strengths and limitations of correlational studies, shedding light on their role in establishing connections between variables and elucidating associations within datasets. The annotation aims to offer a foundational understanding of correlation relationships, serving as a valuable resource for researchers, analysts, and students exploring this critical statistical concept. 1 INTRODUCTION variable changes in a regular manner with the change in the average value of the other variable, then such a relationship is called a statistical or correlation Topic objective. To illustrate the relationship relationship. Correlation models are very important (dependence) between economic indicators. models in the group of economic-statistical models. In economics, technology, and other fields, it is In the simplest case, the relationship between two appropriate to study the relationships between various indicators or variables is tested. In this case, it is numerical and qualitative indicators. Among the called a simple correlation. If there is a relationship indicators, there are two types of relationships - between two or more indicators, then it is called a functional and correlation (or statistical) relationships. multiple correlation. In functional relationships, for any arbitrary value of If an indicator is related to other indicators, it is called one variable, there is a specific value of another a dependent indicator and is identified with it, as well variable that corresponds to it. Such relationships are as with the variables that are dependent on it, such as specifically studied in subjects such as mathematics, argument or factor variables or simply factors. physics, and chemistry. In this case, the correlation model is written as Topic objective. To illustrate the relationship follows: (dependence) between economic indicators. ~ In economics, technology, and other fields, it is у =a+bx i i appropriate to study the relationships between various The regression equation is a formula that expresses the numerical and qualitative indicators. Among the relationship between the dependent variable, which is indicators, there are two types of relationships - found through testing, the independent variables functional and correlation (or statistical) relationships. obtained from experiments, and the constant In functional relationships, for any arbitrary value of coefficients. They have the following economic one variable, there is a specific value of another meanings: a represents the significance of the variable that corresponds to it. Such relationships are unaccounted factors, b indicates how much y will specifically studied in subjects such as mathematics, increase when x increases by one unit. The correlation physics, and chemistry. is represented graphically as follows. [1] If there is such a relationship (correlation) between two random variables, and the average value of one Na+b N x = N y у = a+bx i=1 i i=1 i    (5) N N N correlation field ax +bx2 =x y  i i i i i=1 i=1 i=1 (5) Kramer left with a sad face. x O (1) Creating correlation models consists of several stages: N N y x 1) Formulating the problem; i i i=1 i=1 N N 2) Collecting statistical data;  x y  x2 i i i 3) Determining the form of the regression equation; a = i=1 i=1 N 4) Finding the strength of the relationship; N  x i i=1 5) Finding finite values for the parameters in the N N regression equation;  x  x2 i i 6) Applying the obtained result to economics. i=1 i=1 N Let's say we have a regression equation with an N  y ~ i unknown variable у =a+bx where the size of the i=1 i i N N sample is N. To find the equation a and b its   x x y coefficients, we will use the method of least squares: i i i b= i=1 i=1 [2] N 2 N S =( y − ~ y ) =min (2) N  x i i i i=1 i=1 N N у  x  x2 Here we - present the positive indicators that can i i i i=1 i=1 be obtained from experience: (1) and (2). N 2 S =( y −a−bx ) =min The correlation coefficient is used to determine the i i i=1 strength of the relationship. We obtain special properties with respect to the N normal distribution, i.e. x −x )( y −y ) i i r = i=1 S =−2 N ( y −a−bx ) =0  yx (N −1)  x  y a i i   i=1  (3) S =−2x  N ( y −a−bx ) =0   N ( x −x )2 b i i=1 i i    = i=1 i x (N −1) (3) Let's multiply the base of the triangle by (-2) and divide the system into both sides.  N (y −y)2 i  N ( y −a−bx ) =0   y = i=1 (N −1) i i   i=1  (4) x  N ( y −a−bx ) =0  If r yx is close to 1, it is called a strong con