Statistical study of the relationships between socio-economic phenomena. Theory of statistics The concept of functional and correlation relationships
When studying various economic phenomena, we constantly come across cause-and-effect relationships, when some phenomena, called causes, give rise to another phenomenon, called a consequence (result). We will call the causes factor attributes or simply factors, and the result – the effective attribute. The study and measurement of relationships between cause and effect are carried out using statistical methods.
The main task of correlation analysis is to measure the closeness of the relationship between variables (random variables) by point and interval estimates of the corresponding coefficients (characteristics).
With the help of correlation analysis, factors are selected that have the most significant impact on the resulting characteristic (based on the degree of connection between them), and previously unknown causal relationships are discovered.
Correlation does not directly reveal causal connections between variables, but establishes the numerical value of the closeness of these connections and the reliability of judgments about their presence.
Let it be necessary to study the impact on an economic indicator Y factors X 1 ,X m .
Considering the relationship between the performance indicator Y and factor characteristics X 1 ,X m , two categories of connections can be identified:
1) Functional dependence;
2) Correlation dependence;
Functional connections are characterized by complete correspondence between changes in factor characteristics and changes in the resulting value, that is, each specific set of factor values corresponds to a certain value of the resulting characteristic.
In economics, we usually deal with phenomena and processes where there are no such rigid connections. The causality of economic phenomena is associated with a huge set of interdependent circumstances. The number of circumstances (factors) that influence the economic indicator being studied reaches several hundred.
The relationship between cause and effect is ambiguous and probabilistic. In this case, there is a correlation dependence.
There is no complete correspondence in the correlations between the measurement of factors and the resulting characteristic. The impact of individual factors appears only on average during mass observation of actual data. The fact is that the identified factors are not the only reason for changes in the performance indicator. Along with him by the amount Y influenced by many other reasons.
Therefore, for the same set of factor values, the value Y may turn out to be different. Thus, simultaneous influence on the studied trait Y a large number of very diverse factors leads to the fact that one set of factor values corresponds to a whole distribution of values of the resulting characteristic Y .
When comparing functional and correlation dependencies, it should be borne in mind that in the presence of a functional dependence, it is possible, knowing the value of the factors, to accurately determine the value Y . In the presence of a correlation dependence, only a trend of change is established Y when factors change.
When studying correlation dependencies, it is necessary:
1) Establish the existence of a connection, determine its directions and form;
2) Measure the degree of closeness of connection between characteristics;
3) Find an analytical expression for the relationship, that is, build a regression model;
4) Assess the adequacy of the model and give its interpretation.
In order for the results of correlation analysis to give the desired result, certain requirements must be met regarding the selection of the object of study and the characteristics-factors. One of the most important conditions for the correct application of correlation analysis methods is the requirement for the one-sidedness of those objects that are being studied. Another important requirement to ensure the reliability of the conclusions of correlation analysis is the requirement of a sufficient number of observations. In addition, the selection of factors influencing the performance indicator is of great importance. The factor-signs included in the consideration should be as independent from each other as possible, since the presence of a close connection between them indicates that they characterize the same aspects of the phenomenon under study and largely duplicate each other.
It should be noted that all the main provisions of correlation analysis are developed under the assumption of the normal nature of the distribution of the characteristics under consideration (random variables). In reality, we are faced with certain deviations from the initial premises. But this does not mean that one should abandon the use of correlation analysis methods.
In correlation analysis, the following dependency options are distinguished:
1) Pair correlation - a connection between two characteristics (resultative and factor or two factor);
2) Partial correlation - the dependence between the resultant and one factor characteristics with fixed values of other factor characteristics;
3) Multiple correlation – dependence between the resultant and two or more factor characteristics.
End of work -
This topic belongs to the section:
Subject, tasks and methods of econometrics
Goals and objectives of studying the topic.. study the subject of the task and methods of econometrics.. basic concepts of econometrics, measurement in economics, observation, summary and grouping of statistical data..
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