The study of objectively existing links between socio-economic phenomena and processes is the most important task of the theory of statistics. In the process

Statistical study of dependencies reveals cause-and-effect relationships between phenomena, which makes it possible to identify factors (signs) that have a major impact on the variation of the studied phenomena and processes. Cause-and-effect relations are such a connection of phenomena and processes when a change in one of them - the cause - leads to a change in the other - the effect.

Financial and economic processes are the result of the simultaneous impact of a large number of causes. Therefore, when studying these processes, it is necessary to identify the main, main causes, abstracting from secondary ones.

At the heart of the first stage of the statistical study of communication is qualitative analysis associated with the analysis of the nature of a social or economic phenomenon by methods economic theory, sociology, concrete economics. The second stage is the construction of a communication model, based on statistical methods: groupings, averages, and so on. The third and last stage, the interpretation of the results, is again associated with the qualitative features of the phenomenon under study. Statistics has developed many methods for studying relationships. The choice of the method of studying the connection depends on the cognitive purpose and objectives of the study.

According to their essence and significance for the study of the relationship, signs are divided into two classes. Signs that cause changes in other related signs are called factorial, or simply factors. Traits that change under the influence of factor traits are called productive.

In statistics, functional and stochastic dependencies are distinguished. functional such a relationship is called in which one and only one value of the effective attribute corresponds to a certain value of the factor attribute.

If causal dependence does not appear in each individual case, but in general, on average, with large numbers observations, then such a relationship is called stochastic. A special case of a stochastic connection is correlation a connection in which the change in the average value of the effective attribute is due to the change in factor signs.

Relationships between phenomena and their features are classified according to the degree of tightness,

direction and analytic expression.

According to the degree of closeness of communication, they distinguish:

With an increase or decrease in the values ​​of the factor attribute, an increase or decrease in the values ​​of the effective attribute occurs. Thus, the growth of production volumes contributes to an increase in the profit of the enterprise. When reverse connections of the value of the effective attribute change under the influence of the factor, but in the opposite direction compared to the change in the factor attribute, that is reverse- this is a relationship in which with an increase or decrease in the values ​​of one attribute, a decrease or increase in the values ​​of another attribute occurs. Thus, a decrease in the unit cost of production entails an increase in profitability.

According to the analytical expression, connections are distinguished rectilinear(or simply whether-

natural) and non-linear. If a statistical relationship between phenomena can be

roughly expressed by the equation of a straight line, it is called linear type connection.

Social phenomena, including legally significant ones, are interconnected, depend on each other and determine each other. The existing relationships are realized in the form of causality, functional connection, state connection, etc. Special Role in the interconnections of social phenomena belongs to causality, that is, to a particle of universal connection, but not subjective, but objectively real. This objectively necessary connection, in which one or more interrelated phenomena, called a cause (factor), give rise to another phenomenon, called a consequence (result), and can be called causation.

Legal sciences concretize this concept in relation to phenomena and processes legally. meaningful nature. Among the legal disciplines in the study of causality, criminology has advanced the furthest - the science of crime, its causes and prevention, criminal law, where the establishment of a causal relationship between an action and a consequence is a necessary condition for the onset of criminal liability. But questions of causality are important in administrative, civil, and other branches of law.

Between causality in criminology and law is not only commonality, but also significant differences. The causal relationship between criminogenic factors and the commission of a crime (causes and crime) precedes in time the causal relationship between a socially dangerous action (inaction) and criminal consequences. The latter is characterized mainly by dynamic patterns and functional relationships, and between criminogenic factors and criminal behavior, there are mainly statistical patterns and correlations.

Any regular connection presupposes repetition, sequence and order in phenomena, but the considered connections manifest themselves in different ways: functional - in each single case, and correlation - in a large mass of phenomena. For example, there is a direct causal functional relationship between stabbing and bodily injury (unless, of course, the injury is complicated by infection of the wound, unskilled medical care, etc.). Functional dependence is characterized by the fact that a change in any one feature that is a function is associated with a change in another feature. This relationship is equally manifested in all units of any population.

If a blow with a knife causes a wound to the body (we abstract from the type of knife, the force of the blow, its place, the nature of the wound and other specific circumstances), then whoever this blow is inflicted, the relationship between it and the wound will manifest itself everywhere. Having established it once, we use this dependence in all similar cases. Based on the knowledge of this dependence, medical and forensic examinations are built. Attributing the relationship between stabbing and wounding to a functional relationship is rather arbitrary. This form of dependence is not identical to the functional connection in physics or mathematics.

In the exact sciences, functional relationships are usually expressed by formulas. For example, in the formula S = kya 2 area of ​​a circle S(resultant sign) is directly proportional to the square

its radius R(factorial sign). Formula I= - decoded-

torn more difficult: strength electric current(/) is directly proportional to the voltage (U) and inversely proportional to the resistance (R). In this case, the effective feature is determined by two factor features with opposite effects. The current will be greater, the higher the voltage or the lower the resistance. Functional dynamic linkage is accurately calculated. Therefore, it is both complete and accurate. It operates in all autonomous, little dependent on external influences systems with a relatively small number of elements.

Legal sciences deal mainly with social and legal phenomena and processes, where there are no such rigid, uniquely complete and precise connections. The causation of a crime, and even more crime, as a mass social phenomenon, is associated with a huge set of interdependent circumstances that, with a change in the action of at least one of them, can change the nature of the entire interaction as a whole. The number of circumstances that influence the commission of crimes reaches 450 or more.

The causal relationship between each sign-factor and the sign-consequence is characterized by ambiguity: one or another sign-consequence changes under the influence of a complex of signs-factors, and each value of the sign-factor corresponds (under the influence of other signs-factors) to several values ​​of the sign-consequence. Therefore, the relationship between the cause (a set of causes) and the effect (crime or crime) is multi-valued and has a probabilistic character.

The ambiguity lies not only in the fact that each offense (and offense in general) is the result of the action of many causes, but also in the fact that each cause, interacting with one or another set of other causes, can give rise to not one, but several consequences, in including - different kinds illegal and lawful behavior.

The probabilistic side of the ambiguity of causality in criminology and the sociology of law "consists in the fact that when replacing any condition, even for the same reason, a different result is obtained" . This form of causality, in which the cause determines the effect not uniquely, but only with a certain degree of probability, is incomplete and is called a correlation. It reflects a statistical regularity and operates in all non-autonomous, dependent on constantly changing external conditions systems with a very large number of elements (factors).

The causes of a crime, for example, are "dissolved" in the total mass of positive influences, "distributed" in the structure of a person's activity and "stretched" throughout his life. Therefore, the effect of one cause or another can be detected only in a very large mass of cases. But even at the mass statistical level, where the influence of random factors is somehow leveled by mutual annihilation, the discovered dependencies cannot be complete and accurate, i.e., functional. The effect of unaccounted for, unknown, and often well-known, but hardly perceptible factors is manifested in the fact that the studied relationships turn out to be not only incomplete, but also approximate.

It is reasonably believed that raising a child without one or both parents is a criminogenic factor. Does this mean that every person brought up in such conditions will commit a crime in the future? No way. Behind the generalized factor - upbringing without parents - there may be a huge number of other factors, criminogenic and anticriminogenic, which are different for each child. But when studying a large number of people brought up by parents and without parents, in all countries of the world, a statistical deviation is established with a pattern: people brought up without one or both parents commit crimes much more often than those brought up in a complete family.

Between criminogenic factors and crime there is direct correlation(with a "+" sign). For example, the higher the level of alcoholization in society, the higher the crime, and the crime is specific (“drunk”). Between anti-criminogenic factors and crime, there is a inverse correlation(with a "-" sign). For example, the higher the social control in a society, the lower the crime rate. Both direct and feedback can be straight and curvilinear.

Rectilinear (linear) relationships appear when, with an increase in the values ​​of the attribute-factor, there is an increase (direct) or decrease (reverse) in the value of the attribute-consequence. Mathematically, such a relationship is expressed by a straight line equation (regression equation):

where at - sign-consequence; a and b - corresponding coupling coefficients; x is a sign-factor.

We have already referred to this formula when aligning the dynamic range in a straight line.

Curvilinear connections are different. An increase in the value of a factor attribute has an uneven effect on the value of the resulting attribute. Initially, this relationship can be direct, and then reverse. In legal science, such connections have hardly been studied, but they are present. Famous example- the relationship of crimes with the age of offenders. Initially, the criminal activity of persons grows in direct proportion to the increase in the age of offenders (up to approximately 30 years), and then, with increasing age, criminal activity decreases. Moreover, the peak of the distribution curve of offenders by age is shifted from the average to the left (toward a younger age) and is asymmetric.

A more complex example: with the expansion of social control, the level of illegal behavior decreases, but further totalization of control turns it from an anti-criminogenic factor into a criminogenic one. Therefore, "tightening the screws" in society is socially useful only to a certain extent. Such connections are statistically described by the equations of curved lines (hyperbolas, parabolas, etc.).

Correlation rectilinear relationships can be single-factorial, when the relationship between one sign-factor and one sign-consequence is investigated (pair correlation). They can be multifactorial when the influence of many interacting signs-factors on the sign-consequence (multiple correlation) is studied.

Pair correlation has long been used in legal statistics, and multiple correlation practically not used, although in criminology, delictology and sociology of law, multifactorial connections, one might say, dominate. This is due to a number of difficulties: poor accounting of signs-factors, insufficient mathematical, statistical and sociological training of lawyers and other circumstances of an objective nature.

Correlations of some phenomena with others are already visible at the first stages of statistical data processing. A summary and grouping of statistical indicators, the calculation of relative and average values, the construction of variational, dynamic, parallel series makes it possible to establish the existence of a relationship between the phenomena under study and even its nature (direct and reverse). If by building variation series criminals by age, we find that the main frequencies are grouped in the interval of youth age, we have sufficient reason to believe that youth is the most criminogenic age. Although age (as we have established in previous chapters) does not appear in its own meaning, but only as an integrated exponent of criminogenic conditions that interact with the corresponding age-related changes in a person.

Let us turn to the state of intoxication, which in all countries of the world is considered a criminogenic factor and, therefore, is statistically monitored. In Russia in 1996, it was recorded: in a state of intoxication, offenders committed 39% of all recorded crimes, including 77.6% - rape, 73.5% - premeditated murders, 69.8% - hooligan actions, 59.7% - robbery, 57.0% - robbery, 37.7% - theft and 0% - bribery. The given percentages indicate a direct correlation between crimes and drunkenness (except for bribery). Since these figures are repeated almost from year to year, they indicate not only the presence of this connection, but to a certain extent the degree of influence of drunkenness on various types of acts. For a more accurate measurement of relationships, statistics has a large set of different methods.

• See: Kudryavtsev VN Causality in criminology. M., 1968; Tsereteli T.V. Causality in criminal law. M, 1963.
• See: Model of Regional Criminological and Criminal Law Forecast. M., 1994.
• Kudryavtsev VN Causality in criminology. S. 9.
• See: Luneev VV Crime of the XX century. World, regional and Russian trends. pp. 775-840.

An important place in the statistical study of relationships is occupied by following methods:

1. Method of reduction of parallel data. 2. Method of analytical groupings. 3. Graphic method 4. Balance method. 5. Index method. 6. Correlation-regression.

1. The essence of the parallel data reduction method is as follows:

The initial data on the basis of X are arranged in ascending or descending order, and on the basis of Y, the corresponding indicators are recorded. By comparing the values ​​of X and Y, a conclusion is made about the presence and direction of dependence.

3. The essence of the graphical method is a visual representation of the presence and direction of relationships between features. To do this, the value of the factor attribute X is located along the abscissa axis, and the value of the resulting attribute along the ordinate axis. According to the joint arrangement of points on the graph, a conclusion is made about the direction and the presence of dependence. In this case, the following options are possible:

a \, b / (up), c \ (down).

If the points on the graph are arranged randomly (a), then there is no relationship between the studied features.

If the points on the graph are concentrated around the straight line (b) /, the relationship between the signs is direct.

If the points are concentrated around the straight line (c) \, then this indicates the presence of an inverse relationship.

Based on the method of parallel data and the graphical method, indicators can be calculated that characterize the degree of closeness of the correlation dependence.

The most multiple of them is the Fechner sign coefficient. It is calculated by the formula:

C - the sum of the coinciding signs of the deviations of the individual values ​​of the attribute from the average.

H - sum of mismatches

This coefficient varies within (-1;1).

The value of KF=0 indicates the absence of dependence between the studied features.

If KF=±1, then this indicates the presence of a functional direct (+) and inverse (-) dependence. With a value of KF>½0.6½, it is concluded that there is a strong direct (inverse) relationship between the features. In addition, on the basis of the initial data on factor and resultant features, the Spearman rank correlation coefficient can be calculated, which is determined by the formula:

Rank difference squares, (R2-R1), n ​​- number of rank pairs

This coefficient, like the previous one, varies within the same limits and has the same economic interpretation as KF.

In cases where the value of X or Y is expressed by the same indicators, the rank correlation coefficient is calculated using the following formula:

tj - the same number of ranks in the j - row

If the relationship between three or more mathematical features is being investigated, then the concordance coefficient is used to study it, which is determined by the formula:

m - number of factors n - number of observations S - deviation of the sum of squares of ranks from the mean of squares of ranks

Balance method in statistics- the most important method of processing and analyzing statistical data, which allows you to mutually link resources and their use, to identify the proportions and relationships that develop in the process of reproduction. The balance method in statistics received wide use. Great importance This method is determined by the nature of the economy and follows from the law of the planned development of the national economy. By means of the balance method, it is possible to identify not only economic ties and proportions in national economy but also to reveal disproportions where they exist.

Index Methodindex in statistics called a relative indicator that characterizes the change in the magnitude of a phenomenon (simple or complex) in time, space or in comparison with any standard. The main element of the index relation is the indexed value. Indexed value- the value of the attribute of the statistical population. According to the content of the studied quantities indices are divided into indices of quantitative and indices of qualitative indicators. Indices of quantitative indicators– indices of physical volume. All indexed indicators of these indices are voluminous because they characterize total, total size (volume) of this or that phenomenon and are expressed as absolute values. When calculating such indices, the quantities are evaluated in the same, comparable prices. Quality indexes- indices of the exchange rate, prices, cost, labor productivity, wages, etc. The indexed indicators of these indices characterize the level of the phenomenon per one or another unit of the population. Such indicators are called quality. They do not measure volume, but intensity, efficiency phenomenon or process. Typically, they are either average, or relative quantities. By the degree of coverage of population units indexes are divided into: individual and general. At the same time, under complex phenomenon understand such statistical population, whose individual elements are not directly summable. If indexes do not cover all elements complex phenomenon, but only a part, they are called group or sub-indices. By calculation methods distinguish between aggregate and average indices . Calculation individual indices is simple, they are determined by calculating the ratio of two indexed quantities: individual index of physical volume of production i q is calculated by the formula: , where q 1 , q 0- the quantity (volume) of goods produced in the current (reporting) and base periods, respectively; individual price index i р: , where p 1 , p 0- the price of a unit of the same product in the reporting and base periods, respectively. Many statistical indicators are in a certain relationship with each other (often in the form of a product). The form of the relationship between such indicators is revealed on the basis of theoretical analysis. Statistics characterizes these relationships quantitatively. The relationship between economic indicators forms index systems. Let's consider the construction of interrelated indexes using the example price indices, physical volume of production(if we are talking about selling prices) or physical volume of trade(if we are talking about retail prices) and the index production cost(goods turnover in actual prices). Indices of physical volume and prices are factorial to production cost index(goods turnover in actual prices): , or . T o, the product of the price index by the index of the physical volume of production gives the index of the cost of production (turnover in actual prices), i.e. forms an index system of these three indices.

Correlation-regression method of analysis– a comprehensive study of correlations, incl. finding the level of regression, measuring the tightness and direction of the connection, as well as determining possible errors, both parameters of the level of regression and indicators of the tightness of the connection. For analytical purposes, the correlation is represented by means of Math. functions, i.e. give it shape. Form of communication - trend, which is manifested in a change in the effective attribute due to a change in the factor attribute. Construction and analysis of the correlation model of communication impl. using correlation-regression analysis, which consists of the following steps: 1. preliminary a priori analysis; 2.collection of information and its primary processing; 3. building a model (regression equation); 4. evaluation and analysis of the model. The choice of the form of connection is decided on the basis of a theoretical analysis of the essence of the phenomena under study and studies of empirical data. empirical research forms of communication includes: construction of correlation fields; empirical regression lines; analysis of the parallel series method. The study of empirical material makes it possible to establish the direction and form of communication.

1. Types and forms of connections between phenomena.

2. Methods for studying relationships.

3. Correlation-regression modeling.

4. Evaluation of KRM for adequacy.

1. All phenomena of the objective world, including social ones, are in constant interconnection and interaction with each other, in continuous change and development. The most important task of statistics, along with assessing the state of mass phenomena and identifying the patterns of their development, is to study the relationships between them.

The connections of mass social phenomena are established on the basis of a theoretical analysis of their essence, the study of patterns and driving forces development, assessment of the conditions for their functioning. In this case, categories, concepts and previously accumulated knowledge of other sciences are used. The task of statistics is to identify the very existence of a connection in specific conditions, as well as to obtain indicators characterizing its strength, degree and nature.

Of theoretical and practical interest, first of all, are causal relationships, when some phenomena (factors) cause changes in others (results). Their analysis allows, firstly, to explain the actual state of affairs, and secondly, by influencing the factors, to achieve a change in the results in the desired direction.

Types of connections:

I. By nature:

1) functional. The relationship between phenomena is called functional, if a change in the factor indicator x by one corresponds to a strictly defined change in the resultant attribute y. Such connections are expressed by formulas that are valid in all cases. An example is the change in wages (at the same hourly rate) depending on the number of hours worked, the change in fuel costs depending on its consumption in kind (at constant prices), etc.

2) statistical (correlation). Statistical (correlation) are called connections in which a strictly defined change in the factor attribute x corresponds to a whole series (statistical distribution) of changes in the result y, which are not completely defined, subject to random fluctuations. These connections are manifested only on the average, in mass phenomena; In addition to the factor under study, other reasons also affect the result, including those of a random nature. For example, with an increase in the doses of applied fertilizers, crop yields increase on average, but not always and not by the same amount.

II. In terms of expression:

1) direct - with an increase in the factor sign, the productive one increases (for example, with an increase in the length of service of an employee, as a rule, the productivity of his labor increases);

2) reverse - changes go in the opposite direction (for example, with an increase in the productivity of animals and crop yields, the costs per unit of production are reduced on average).

III. According to the analytical expression:

1) rectilinear - with an increase in one attribute for any of its initial values, the other changes on average by the same amount;

2) curvilinear - these changes themselves change (increase, decrease or even change their sign).

IV. Depending on the number of factor features included in the model:

1) paired (one-factor);

2) multiple (multifactorial).

2. To study functional relationships, use methods:

Balance connections. It is based on a simple functional relationship between the availability of some resource at the beginning and end of the period, its receipt and expenditure during this period. If any three of the specified indicators are known, the fourth one is determined automatically. Availability at the end of the year = Availability at the beginning of the year + Received - Departed.

For example, the annual consumption in the economy of products own production can be calculated like this:

Consumption = Availability at the beginning of the year + Production - Availability at the end of the year.

Index analysis.

To study correlations, one uses methods:

Matching parallel rows;

The simplest and most common technique is to match parallel rows. Its essence lies in the simultaneous consideration of the studied characteristics by units of the population or by periods (moments) of a dynamic series. The comparison is made purely visually, without special calculations (Table 9.3).

In this case, it is clearly seen that in the dynamics of the dose of organic and mineral fertilizers, up to 1990, they increase, and then decrease. A similar trend is also observed in grain yields: an increase until 1990 with a subsequent decline. On the contrary, there is no parallelism in potato yield with fertilizer application rates.

Comparison of parallel series (it is especially convenient to conduct it with the help of line graphs) allows you to establish the presence of a connection, its direction and, very approximately, its strength. Thus, changes in the doses of organic and mineral fertilizers are very closely related, their relationship with the yield of grain crops, although weak, is also present, it is direct and linear, but the relationship with the yield of potatoes is practically not traced.

The main disadvantage of this technique is the absence of any connection indicators. Comparison also does not resolve the issue of cause-and-effect relationships of the studied phenomena. From theory, for example, it is known that the application of fertilizers leads to an increase in yield. But potatoes are cultivated mainly in the households of the population, and its share in the structure of crops is small. Therefore, the rate of fertilizer application, on average per 1 ha of the entire sown area, and, moreover, in all categories of farms, is too general to show any connection with potato yield.

Graphical method (correlation field method);

It consists in plotting graph points on the coordinate plane, as well as determining the correlation field and the direction of the relationship between features.

Example: There are data:

Inverse relationship.

Method for constructing group correlation tables;

There are data:

Group boundaries for x:

Group boundaries for y:

1 gr.: 18-21.2;

2 gr.: 21.2-24.4;

3 gr.: 24.4-27.6;

4 gr.: 27.6-30.8;

5 gr.: 30.8-34.

Table - Group correlation table

Conclusion: the connection is direct unidirectional (because the frequencies are located diagonally).

Method of analytical groupings;

ANOVA method;

KPA method;

Method of non-parametric evaluation of relationships.

3. The method of correlation-regression modeling consists of two stages:

I. Regression– search for a connection equation that most fully characterizes the relationship between features, and determination of the parameters of this equation.

The conditional beginning is not subject to meaningful interpretation;

Regression coefficients showing how many units the resulting attribute will change when the factor attribute changes by one, provided that all other factor attributes remain unchanged.

II. Correlation - determination of indicators of tightness of communication.

Most often, the correlation is characterized by two indicators:

Correlation coefficient (characterizes the degree of closeness of the relationship between the resultant and all factor features; it is measured in the range from 0 to 1 modulo; the closer to 1, the closer the relationship between the features);

The coefficient of determination (shows the percentage of the factors included in the model explain the variation of the resulting attribute: it is measured in the range from 0 to 100%).

correlations

2. Coefficient. pair determination

2. Empirical coefficient. determi-

2. Coefficient. plural determinations

net regression coefficient for the i-th factor attribute;

Wed kV. deviations on the i-th factor sign.

In order to make the regression coefficients comparable and to determine the influence of each individual factor on the effective attribute, standardized coefficients are calculated:

1) Elasticity coefficients:

Elasticity coefficients show how many percent the resultant sign will change, with an increase in the factor sign by 1%.

show by how much the mean square deviations of the resulting feature will change when the factor factor is increased by its standard deviation.

3) Individual determination coefficients:

The coefficients of a separate definition of the definition show the contribution of each factor to the variation of the resulting attribute.

4. The adequacy of the KRM is an assessment of the constructed model in reality.

The assessment of the constructed model for adequacy is carried out using Fisher's F criterion:

n is the volume of the population;

k is the number of factor features in the equation;

Dispersion of the aligned values ​​of the resulting feature according to the regression equation.

Dispersion of deviations of the actual values ​​of the resulting attribute from those aligned according to the regression equation.

According to the table of values ​​of Fisher's F-test, its tabular value is determined at a significance level of 0.01; 0.05; or 0.1 and the number of degrees of freedom n-k-1. If - the model is adequate.

The significance of the regression coefficients is determined using Student's t-test.

Table 1 - Calculation of deviations Million national rubles.

1) Calculate and according to the following formulas:

2) Calculate the Fechner coefficient. Its calculation is based on a comparison of the signs of paired deviations in terms of factorial and resultant characteristics.

where C is the number of coinciding deviations, pcs.;

Since it is in the range from 0.3 to 0.5, the relationship can be considered weak

For further analysis of the relationship, we will compile Table 2

Table 2 - calculation of the value of the result according to the relation equation (y) Million national rubles

Where is the pairwise linear regression coefficient

This is the free parameter of the regression equation

1) Calculate the parameters of the paired linear regression

(million national rubles)

On average, in aggregate, an increase in the equity capital of commercial banks by 1 ruble leads to an increase in the amount of assets of commercial banks by 16 million national rubles.

(million national rubles)

In the reporting period, the average cumulative impact of unaccounted factors or the average for the group, the amount of assets of commercial banks increased by 288 million national rubles.

2) Let's make a regression equation with the calculated parameters

3) We get the following graph:

Calculate quantitative characteristics connection tightness:

1) The linear correlation coefficient () is a standardized regression coefficient, expressed not in absolute units of measurement of the attribute, but in fractions of the mean square change in the result.

The calculated value of the coefficient is from 0.7 to 1, which shows a direct strong relationship between the studied features.

2) Determination coefficient () - shows what part of the result variation is due to the variation of the studied factor.

The coefficient of determination shows that 73% of the variation in the amount of assets of commercial banks is due to the variation in the equity capital of commercial banks. It follows that 27% is accounted for by other factors (not included in the study)

3) Correlation ratio:

The calculated value of the correlation ratio is from 0.7 to 1, which shows a direct strong relationship between the studied features.

After calculating the coefficient of determination and the correlation ratio, the following condition must be met:

in my work the condition is fulfilled.

4) Elasticity coefficient:

With an increase of 1% in the average equity, on average in the aggregate leads to an increase in the amount of assets by 0.861%

Let's spend statistical evaluation reliability and accuracy of calculations of indicators of closeness of connection.

Where (n -2) is the number of degrees of freedom for the population under consideration

Let's compare the calculated values ​​of the F-criterion with the tabular

Table 3 - The value of t - Student's criterion at confidence levels of 0.5; 0.05; 0.01:

Comparison of the calculated values ​​with the tabular ones confirms the strong relationship of the signs, since it corresponds to a low probability level of 0 of the value of the tested indicators of the tightness of the connection.

ω 2 =0 - means that the use of a straight line to estimate the shape of the regression is justified.

5. Calculate the rank correlation coefficient

Confirms a strong direct relationship.

Let's carry out forecasting on the basis of the regression equation.

Let us estimate the change in the amount of assets of commercial banks, provided that in the next reporting period the equity capital of commercial banks will increase by 7%.

Y predict. =289.307+288.186+16.012*7.81=702.547

Because it was revealed that in the reporting period there were factors that positively affect the amount of assets of commercial banks, then the predicted increase in the studied factor, i.e. own capital of commercial banks, by 7% provides a further increase in the amount of assets of commercial banks.

CONCLUSION

This course work considers the statistical study of the relationship of socio-economic phenomena. The first chapter of my work is devoted to the essence of the study of the relationship of socio-economic characteristics, the second - the basic concepts of inflation, indicators of its measurement, as well as the calculation methodology. In the practical part, I studied the dependence of the amount of assets of commercial banks and equity.

In general, the task of statistics in the field of studying relationships is not only to quantify their presence, direction and strength of the connection, but also to determine the form of influence of factor characteristics on the resultant one. To solve it, methods of correlation and regression analysis are used.

The tasks of correlation analysis are reduced to measuring the tightness of a known relationship between varying features, determining unknown causation and evaluation of the factors that have the greatest impact on the resulting attribute.

The tasks of regression analysis are the choice of the type of model, the establishment of the degree of influence of independent variables on the dependent variable, and the determination of the calculated values ​​of the dependent variable.

The solution of all these problems leads to the need for the integrated use of these methods.

Based on the analysis of inflation, the following conclusions were made.

Inflation is a complex multi-profile process that causes serious damage to the country's economy and its population. Inflation now to some extent covers almost all countries of the world. Fighting it in order to reduce it requires a lot of effort and material costs.

All the progressive economic thought of mankind put a lot of effort into fighting inflation, but inflation was not finally defeated, because. new and more complex forms appeared.

Intense inflationary pressure always accompanies the transformation of the administrative-commercial system into a market one. Its roots are in the structural and systemic disproportions of the developing economy. To combat inflation, it is necessary to develop and implement a set of measures that combines monetary policy and state policy to stimulate economic growth, structural policy and social policy. It is necessary to overcome interdepartmental disagreements and decide on a method for calculating price increases. In order to more objectively reflect the situation with the rise in prices in the economy, it is advisable to calculate inflation also from the rise in wholesale prices.

At the end of the work, I want to emphasize that Russia has every opportunity to get out of the inflationary impasse, because, despite all the difficulties, it undoubtedly remains a superpower with enormous resources and largely determines the situation around the world.

The study of the dependence of the sum of assets of commercial banks and equity capital was carried out using a correlation-regression analysis of a paired linear dependence of features. The interpretation of the obtained indicators showed a strong direct relationship between the amount of assets and the equity capital of commercial banks. In the reporting period, reserves for increasing the amount of assets were identified, i.e. factors not taken into account in the study, which had a positive effect on the amount of assets of commercial banks. The forecast of changes in the amount of assets confirms the need to work with unaccounted factors.

LITERATURE

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