I think many of us have at least once been interested in artificial intelligence and neural networks. Factor analysis occupies an important place in the theory of neural networks. It is designed to highlight the so-called hidden factors. This analysis has many methods. A special feature is the method of principal components, the distinctive feature of which is a complete mathematical justification. To be honest, when I started reading the articles on the links above, I felt uneasy because I didn’t understand anything. My interest subsided, but, as usually happens, understanding came on its own, unexpectedly.

So let's take a look Arabic numerals from 0 to 9. In this case, 5x7 format, which were taken from a project for LCD from Nokia 3310.

Black pixels correspond to 1, white pixels to 0. Thus, we can represent each digit as a 5x7 matrix. For example the matrix below:

Let's assume that from each pixel, of which we have 5x7=35, the signal enters a certain black box, and the output is a signal that corresponds to the input digit. What happens in the black box? And in the black box, from all 35 signals, those 4 are selected that are fed to the input of the decoder and allow you to unambiguously determine the number at the input. Now it’s clear why we were looking for combinations without matches. After all, if 4 signals of the first combination were selected in a black box, then the numbers 0 and 5 for such a system would simply be indistinguishable. We have minimized the task, because instead of 35 signals, it is enough to process only 4. Those 4 pixels are the minimum set of hidden factors that characterize this array of numbers. Very interesting feature has this set. If you look closely at the values ​​in the columns, you will notice that the number 8 is the opposite of the number 4, 7 is 5, 9 is 3, 6 is 2, and 0 is 1. The attentive reader will ask, what does neural networks have to do with it? And the peculiarity of neural networks is that it itself is capable of identifying these factors, without the intervention of a reasonable person. You just periodically show her the numbers, and she finds those 4 hidden signals and switches it with one of her 10 outputs. How can we apply those similar signals that we discussed at the beginning? And they can serve as a mark for a set of numbers. For example, Roman numerals will have their own set of maximums and minimums, and letters will have their own. Based on similarity signals, you can separate numbers from letters, but recognizing characters within a set is only possible based on maximum difference.

The functioning of any socio-economic system (which includes an operating enterprise) occurs in conditions of complex interaction of a complex of internal and external factors. Factor- this is the cause, the driving force of a process or phenomenon, determining its character or one of its main features.

Under factor analysis understands the methodology for a comprehensive and systematic study and measurement of the impact of factors on the value of performance indicators.

In general, the following main ones can be distinguished: stages (tasks) factor analysis:

Setting the purpose of the analysis.

Selection of factors that determine the performance indicators under study.

Classification and systematization of factors in order to provide an integrated and systematic approach to the study of their influence on results economic activity.

Determination of the form of dependence between factors and the performance indicator.

Modeling the relationships between performance and factor indicators.

Calculation of the influence of factors and assessment of the role of each of them in changing the value of the performance indicator.

Working with the factor model (its practical use for managing economic processes).

In other words, method task- transition from real large number signs or reasons that determine the observed variability in a small number of the most important variables (factors) with minimal loss of information (methods that are similar in essence, but not in mathematical terms - component analysis, canonical analysis, etc.).

The method arose and was initially developed in problems of psychology and anthropology (at the turn of the 19th and 20th centuries), but now the scope of its application is much wider.

Purpose of factor analysis

Factor analysis- determining the influence of factors on the result - is one of the strongest methodological solutions in the analysis of the economic activities of companies for decision making. For managers - an additional argument, an additional “angle of view”.

The feasibility of using factor analysis

As you know, you can analyze everything ad infinitum. It is advisable at the first stage to implement an analysis of deviations, and where necessary and justified, to apply the factor analysis method. In many cases, a simple analysis of deviations is enough to understand that the deviation is “critical”, and when it is not at all necessary to know the degree of its influence.

Factors are divided into internal and external, depending on whether the activities of a given enterprise affect them or not. The analysis focuses on internal factors that the enterprise can influence.

Factors are divided into objective, independent of will and people's desires, And subjective, influenced by the activities of legal entities and individuals.

According to the degree of prevalence, factors are divided into general and specific. General factors operate in all sectors of the economy. Specific factors operate within a specific industry or specific enterprise.

Types of factor analysis

The following types of factor analysis exist:

1) Deterministic (functional) – the effective indicator is presented in in the form of a work, quotient or algebraic sum of factors.

2) Stochastic (correlation) - the relationship between the effective and factor indicators is incomplete or probabilistic.

3) Direct (deductive) – from the general to the specific.

4) Reverse (inductive) – from the particular to the general.

5) Single-stage and multi-stage.

6) Static and dynamic.

7) Retrospective and prospective.

Depending on the type of factor model, there are two main types of factor analysis - deterministic and stochastic.

Deterministic factor analysis is a technique for studying the influence of factors whose connection with the effective indicator is functional in nature, that is, when the effective indicator of the factor model is presented in the form of a product, quotient or algebraic sum of factors.

This type of factor analysis is the most common, since, being quite simple to use (compared to stochastic analysis), it allows you to understand the logic of the action of the main factors of enterprise development, quantify their influence, understand which factors and in what proportion it is possible and advisable to change to increase production efficiency.

Deterministic factor analysis has a fairly strict sequence of procedures:

1.building an economically sound deterministic factor model;

2. choosing a method of factor analysis and preparing conditions for its implementation;

3.implementation of counting procedures for model analysis;

Basic methods of deterministic factor analysis

Chain substitution method; Absolute difference method; Relative difference method; Integral method; Logarithm method.

Stochastic Analysis is a methodology for studying factors whose connection with a performance indicator, unlike a functional one, is incomplete and probabilistic (correlation). The essence of the stochastic method is to measure the influence of stochastic dependencies with uncertain and approximate factors. Stochastic method It is advisable to use for economic research with incomplete (probabilistic) correlation: for example, for marketing problems. If with a functional (complete) dependence with a change in the argument there is always a corresponding change in the function, then with a correlation connection a change in the argument can give several values ​​of the increase in the function depending on the combination of other factors that determine this indicator. For example, labor productivity at the same level of capital-labor ratio may be different at different enterprises. This depends on the optimal combination of other factors affecting this indicator.

Stochastic modeling is, to a certain extent, a complement and deepening of deterministic factor analysis. In factor analysis, these models are used according to three main reasons:

It is necessary to study the influence of factors for which it is impossible to build a strictly determined factor model (for example, the level of financial leverage);

It is necessary to study the influence of complex factors that cannot be combined in the same strictly deterministic model;

It is necessary to study the influence of complex factors that cannot be expressed in one quantitative indicator (for example, the level of scientific and technological progress).

It is also necessary to distinguish static And dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Finally, factor analysis can be retrospective, which studies the reasons for the increase in performance indicators over past periods, and promising, which examines the behavior of factors and performance indicators in perspective.

Factor analysis can be single-stage or multi-stage. The first type is used to study factors of only one level (one level) of subordination without detailing them into their component parts. For example, . In multi-stage factor analysis, factors a and b are detailed into their component elements in order to study their behavior. The detailing of factors can be continued further. In this case, the influence of factors at different levels of subordination is studied.

It is also necessary to distinguish between static and dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Called factor analysis. The main types of factor analysis are deterministic analysis and stochastic analysis.

Deterministic factor analysis is based on a methodology for studying the influence of such factors, the relationship of which with a general economic indicator is functional. The latter means that the generalizing indicator is either a product, a quotient of division, or an algebraic sum of individual factors.

Stochastic factor analysis is based on a methodology for studying the influence of such factors, the relationship of which with a general economic indicator is probabilistic, otherwise - correlation.

In the presence of a functional relationship with a change in the argument, there is always a corresponding change in the function. If there is a probabilistic relationship, a change in the argument can be combined with several values ​​of the change in the function.

Factor analysis is also divided into straight, otherwise deductive analysis and back(inductive) analysis.

First type of analysis carries out the study of the influence of factors by a deductive method, that is, in the direction from the general to the specific. In reverse factor analysis the influence of factors is studied inductively - in the direction from particular factors to general economic indicators.

Classification of factors influencing the efficiency of an organization

The factors whose influence is studied during the study are classified according to various criteria. First of all, they can be divided into two main types: internal factors , depending on the activity of this, and external factors, independent of this organization.

Internal factors, depending on the magnitude of their impact on, can be divided into major and minor. The main ones include factors related to the use of materials and materials, as well as factors determined by supply and sales activities and some other aspects of the functioning of the organization. The main factors have a fundamental impact on general economic indicators. External factors beyond the control of a given organization are determined by natural-climatic (geographical), socio-economic, and foreign economic conditions.

Depending on the duration of their impact on economic indicators, we can distinguish constant and variable factors. The first type of factors has an impact on economic indicators that is not limited in time. Variable factors affect economic indicators only over a certain period of time.

Factors can be divided into extensive (quantitative) and intensive (qualitative) based on the essence of their influence on economic indicators. So, for example, if the influence of labor factors on the volume of output is studied, then a change in the number of workers will be an extensive factor, and a change in the labor productivity of one worker will be an intensive factor.

Factors influencing economic indicators, according to the degree of their dependence on the will and consciousness of the organization’s employees and other persons, can be divided into objective and subjective factors. Objective factors may include weather conditions, natural disasters, which do not depend on human activity. Subjective factors depend entirely on people. The vast majority of factors should be classified as subjective.

Factors can also be divided depending on the scope of their action into factors of unlimited and factors of limited action. The first type of factors operates everywhere, in all industries. National economy. The second type of factors influences only within an industry or even a separate organization.

According to their structure, factors are divided into simple and complex. The overwhelming majority of factors are complex, including several components. At the same time, there are also factors that cannot be separated. For example, capital productivity can serve as an example of a complex factor. The number of days the equipment was used during a given period is a simple factor.

According to the nature of the influence on general economic indicators, they are distinguished direct and indirect factors. Thus, a change in products sold, although it has an inverse effect on the amount of profit, should be considered direct factors, that is, a first-order factor. The change in value material costs has an indirect effect on profit, i.e. affects profit not directly, but through cost, which is a first-order factor. Based on this, the level of material costs should be considered a second-order factor, that is, an indirect factor.

Depending on whether it is possible to quantify the influence of a given factor on a general economic indicator, a distinction is made between measurable and unmeasurable factors.

This classification is closely interconnected with the classification of reserves for increasing the efficiency of economic activities of organizations, or, in other words, reserves for improving the analyzed economic indicators.

Factor economic analysis

Those signs that characterize the cause are called factorial, independent. The same signs that characterize the investigation are usually called resultant, dependent.

The set of factor and resultant characteristics that are in the same cause-and-effect relationship is called factor system. There is also the concept of a factor system model. It characterizes the relationship between the resultant characteristic, denoted as y, and the factor characteristics, denoted as . In other words, the factor system model expresses the relationship between general economic indicators and individual factors influencing this indicator. In this case, other economic indicators act as factors, representing the reasons for changes in the general indicator.

Factor system model can be expressed mathematically using the following formula:

Establishing dependencies between generalizing (resulting) and influencing factors is called economic-mathematical modeling.

We study two types of relationships between generalizing indicators and the factors influencing them:

• functional (otherwise - functionally determined, or strictly determined connection.)
• stochastic (probabilistic) connection.

Functional connection- this is a relationship in which each value of a factor (factorial characteristic) corresponds to a completely definite non-random value of a generalizing indicator (resultative characteristic).

Stochastic communication- this is a relationship in which each value of a factor (factor characteristic) corresponds to a set of values ​​of a general indicator (resultative characteristic). Under these conditions, for each value of factor x, the values ​​of the general indicator y form a conditional statistical distribution. As a result, a change in the value of factor x only on average causes a change in the general indicator y.

In accordance with the two types of relationships considered, a distinction is made between methods of deterministic factor analysis and methods of stochastic factor analysis. Consider the following diagram:

The greatest completeness and depth of analytical research, the greatest accuracy of analysis results is ensured by the use of economic and mathematical research methods.

These methods have a number of advantages over traditional and statistical methods analysis.

Thus, they provide a more accurate and detailed calculation of the influence of individual factors on changes in the values ​​of economic indicators and also make it possible to solve a number of analytical problems that cannot be done without the use of economic and mathematical methods.

All phenomena and processes of economic activity of enterprises are interconnected and interdependent. Some of them are directly related to each other, others indirectly. Hence, an important methodological issue in economic analysis is the study and measurement of the influence of factors on the value of the studied economic indicators.

Under economic factor analysis is understood as a gradual transition from the initial factor system to the final factor system, the disclosure of a full set of direct, quantitatively measurable factors that influence the change in the performance indicator.

Based on the nature of the relationship between indicators, methods of deterministic and stochastic factor analysis are distinguished.

Deterministic factor analysis is a methodology for studying the influence of factors whose connection with the performance indicator is functional in nature.

The main properties of the deterministic approach to analysis:
· construction of a deterministic model through logical analysis;
· the presence of a complete (hard) connection between indicators;
· the impossibility of separating the results of the influence of simultaneously acting factors that cannot be combined in one model;
· study of relationships in the short term.

There are four types of deterministic models:

Additive Models represent an algebraic sum of indicators and have the form

Such models, for example, include cost indicators in relation to elements of production costs and cost items; an indicator of the volume of production in its relationship with the volume of output of individual products or the volume of output in individual departments.

Multiplicative models can be summarized by the formula

.

An example of a multiplicative model is a two-factor model of sales volume

,

Where H - average number workers;

C.B.- average output per employee.

Multiple models:

An example of a multiple model is the indicator of the turnover period of goods (in days). T OB.T:

,

Where Z T- average stock of goods; O R- one-day sales volume.

Mixed models are a combination of the above models and can be described using special expressions:

Examples of such models are cost indicators per 1 ruble. commercial products, profitability indicators, etc.

To study the relationship between indicators and quantitatively measure the many factors that influenced the effective indicator, we present general model transformation rules in order to include new factor indicators.

To detail the generalizing factor indicator into its components, which are of interest for analytical calculations, the method of lengthening the factor system is used.

If the initial factor model is , a , then the model will take the form .

To identify a certain number of new factors and construct the factor indicators necessary for calculations, the technique of expanding factor models is used. In this case, the numerator and denominator are multiplied by the same number:

.

To construct new factor indicators, the technique of reducing factor models is used. When using this technique, the numerator and denominator are divided by the same number.

.

The detail of factor analysis is largely determined by the number of factors whose influence can be quantified, therefore great importance in the analysis have multifactorial multiplicative models. Their construction is based on the following principles:
· the place of each factor in the model must correspond to its role in the formation of the effective indicator;
· the model should be built from a two-factor complete model by sequentially dividing factors, usually qualitative, into components;
· when writing a formula for a multifactor model, factors should be arranged from left to right in the order of their replacement.

Building a factor model is the first stage of deterministic analysis. Next, determine the method for assessing the influence of factors.

Chain substitution method consists in determining a number of intermediate values ​​of the generalizing indicator by sequentially replacing the basic values ​​of the factors with the reporting ones. This method is based on elimination. Eliminate- means to eliminate, exclude the influence of all factors on the value of the effective indicator, except one. Moreover, based on the fact that all factors change independently of each other, i.e. First, one factor changes, and all the others remain unchanged. then two change while the others remain unchanged, etc.

IN general view The application of the chain production method can be described as follows:

where a 0, b 0, c 0 are the basic values ​​of factors influencing the general indicator y;

a 1, b 1, c 1 - actual values ​​of factors;

y a, y b, are intermediate changes in the resulting indicator associated with changes in factors a, b, respectively.

The total change D у = у 1 – у 0 consists of the sum of changes in the resulting indicator due to changes in each factor with fixed values ​​of the remaining factors:

Let's look at an example:

table 2

Initial data for factor analysis

We will analyze the impact of the number of workers and their output on the volume of marketable output using the method described above based on the data in Table 2. The dependence of the volume of commercial products on these factors can be described using a multiplicative model:

Then the effect of a change in the number of employees on the general indicator can be calculated using the formula:

Thus, the change in the volume of marketable products positive influence had a change in the number of employees by 5 people, which caused an increase in production volume by 730 thousand rubles. And bad influence had a decrease in output by 10 thousand rubles, which caused a decrease in volume by 250 thousand rubles. The combined influence of two factors led to an increase in production volume by 480 thousand rubles.

Advantages this method: versatility of application, ease of calculations.

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of factor decomposition have different meanings. This is due to the fact that as a result of applying this method, a certain indecomposable residue is formed, which is added to the magnitude of the influence of the last factor. In practice, the accuracy of factor assessment is neglected, highlighting the relative importance of the influence of one or another factor. However, there are certain rules that determine the substitution sequence:
· if there are quantitative and qualitative indicators in the factor model, the change in quantitative factors is considered first;
· if the model is represented by several quantitative and qualitative indicators, the substitution sequence is determined by logical analysis.

Under quantitative factors in analysis they understand those that express the quantitative certainty of phenomena and can be obtained by direct accounting (number of workers, machines, raw materials, etc.).

Qualitative factors determine the internal qualities, signs and characteristics of the phenomena being studied (labor productivity, product quality, average duration working day, etc.).

Absolute difference method is a modification of the chain substitution method. The change in the effective indicator due to each factor using the method of differences is defined as the product of the deviation of the factor being studied by the basic or reporting value of another factor, depending on the selected substitution sequence:

Relative difference method used to measure the influence of factors on the growth of a performance indicator in multiplicative and mixed models of the form y = (a – c) . With. It is used in cases where the source data contains previously determined relative deviations of factor indicators in percentages.

For multiplicative models like y = a . V . The analysis technique is as follows:

· find the relative deviation of each factor indicator:

· determine the deviation of the performance indicator at due to each factor

Example. Using the data in table. 2, we will analyze using the method of relative differences. The relative deviations of the factors under consideration will be:

Let's calculate the impact of each factor on the volume of commercial output:

The calculation results are the same as when using the previous method.

Integral method allows you to avoid the disadvantages inherent in the chain substitution method, and does not require the use of techniques for distributing the indecomposable remainder among factors, because it has a logarithmic law of redistribution of factor loads. The integral method makes it possible to achieve a complete decomposition of the effective indicator into factors and is universal in nature, i.e. applicable to multiplicative, multiple and mixed models. The operation of calculating a definite integral is solved using a PC and is reduced to constructing integrand expressions that depend on the type of function or model of the factor system.
1. What management problems are solved through economic analysis?
2. Describe the subject of economic analysis.
3. What distinctive features characterize the method of economic analysis?
4. What principles underlie the classification of techniques and methods of analysis?
5. What role does the method of comparison play in economic analysis?
6. Explain how to construct deterministic factor models.
7. Describe the algorithm for applying the most simple ways deterministic factor analysis: method of chain substitutions, method of differences.
8. Characterize the advantages and describe the algorithm for using the integral method.
9. Give examples of problems and factor models to which each of the methods of deterministic factor analysis is applied.

This may be of interest (selected paragraphs):

All phenomena and processes of economic activity of enterprises are interconnected and interdependent. Some of them are directly related to each other, others indirectly. Hence, an important methodological issue in economic analysis is the study and measurement of the influence of factors on the value of the economic indicators under study.

Under economic factor analysis is understood as a gradual transition from the initial factor system to the final factor system, the disclosure of a full set of direct, quantitatively measurable factors that influence the change in the performance indicator.

Based on the nature of the relationship between indicators, methods of deterministic and stochastic factor analysis are distinguished.

Deterministic factor analysis is a methodology for studying the influence of factors whose connection with the performance indicator is functional in nature.

The main properties of the deterministic approach to analysis:

· construction of a deterministic model through logical analysis;

· the presence of a complete (hard) connection between indicators;

· the impossibility of separating the results of the influence of simultaneously acting factors that cannot be combined in one model;

· study of relationships in the short term.

There are four types of deterministic models:

Additive Models represent an algebraic sum of indicators and have the form

Such models, for example, include cost indicators in relation to elements of production costs and cost items; an indicator of the volume of production in its relationship with the volume of output of individual products or the volume of output in individual departments.

Multiplicative models can be summarized by the formula

.

An example of a multiplicative model is a two-factor model of sales volume

,

Where H- average number of employees;

C.B.- average output per employee.

Multiple models:

An example of a multiple model is the indicator of the turnover period of goods (in days). T OB.T:

,

Where Z T- average stock of goods; O R- one-day sales volume.

Mixed models are a combination of the above models and can be described using special expressions:

; Y = ; Y = ; Y = .

Examples of such models are cost indicators per 1 ruble. commercial products, profitability indicators, etc.

To study the relationship between indicators and quantitatively measure the many factors that influenced the effective indicator, we present general model transformation rules in order to include new factor indicators.

To detail the generalizing factor indicator into its components, which are of interest for analytical calculations, the technique of lengthening the factor system is used.

If the initial factor model is , a , then the model will take the form .

To identify a certain number of new factors and construct the factor indicators necessary for calculations, the technique of expanding factor models is used. In this case, the numerator and denominator are multiplied by the same number:

.

To construct new factor indicators, the technique of reducing factor models is used. When using this technique, the numerator and denominator are divided by the same number.

.

The detail of factor analysis is largely determined by the number of factors whose influence can be quantitatively assessed, therefore multifactorial multiplicative models are of great importance in the analysis. Their construction is based on the following principles:

· the place of each factor in the model must correspond to its role in the formation of the effective indicator;

· the model should be built from a two-factor complete model by sequentially dividing factors, usually qualitative, into components;

· when writing a formula for a multifactor model, factors should be arranged from left to right in the order of their replacement.

Building a factor model is the first stage of deterministic analysis. Next, determine the method for assessing the influence of factors.

Chain substitution method consists in determining a number of intermediate values ​​of the generalizing indicator by sequentially replacing the basic values ​​of the factors with the reporting ones. This method is based on elimination. Eliminate- means to eliminate, exclude the influence of all factors on the value of the effective indicator, except one. Moreover, based on the fact that all factors change independently of each other, i.e. First, one factor changes, and all the others remain unchanged. then two change while the others remain unchanged, etc.

In general, the application of the chain production method can be described as follows:

y 0 = a 0 . b 0 . c 0 ;

y a = a 1 . b 0 . c 0 ;

y b = a 1 . b 1. c 0 ;

y 1 = a 1 . b 1. c 1,

where a 0, b 0, c 0 are the basic values ​​of factors influencing the general indicator y;

a 1 , b 1 , c 1 - actual values factors;

y a, y b, are intermediate changes in the resulting indicator associated with changes in factors a, b, respectively.

The total change Dу=у 1 –у 0 consists of the sum of changes in the resulting indicator due to changes in each factor with fixed values ​​of the other factors:

Dу = SDу (а, b, с) = Dу a + Dу b + Dу c

Dу а = у а – у 0 ; Dу b = у в – у а; Dу с = у 1 – у в.

Let's look at an example:

table 2

Initial data for factor analysis

We will analyze the impact of the number of workers and their output on the volume of marketable output using the method described above based on the data in Table 2. The dependence of the volume of commercial products on these factors can be described using a multiplicative model:

TP o = Ch o. NE o = 20. 146 = 2920 (thousand rubles).

Then the effect of a change in the number of employees on the general indicator can be calculated using the formula:

TP conv 1 = Ch 1. NE o = 25. 146 = 3650 (thousand rubles),

DTPusl 1 = TPusl 1 – TP o = 3650 – 2920 = 730 (thousand rubles).

TP 1 = Ch 1. CB 1 = 25. 136 = 3400 (thousand rubles),

DTP cond 2 = TP 1 – TPusl 1 = 3400 – 3650 = - 250 (thousand rubles).

Thus, the change in the volume of commercial output was positively influenced by a change in 5 people. number of employees, which caused an increase in production volume by 730 tons. rub. and a negative impact was exerted by a decrease in output by 10 thousand rubles, which caused a decrease in volume by 250 thousand rubles. The combined influence of two factors led to an increase in production volume by 480 thousand rubles.

The advantages of this method: versatility of application, ease of calculations.

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of factor decomposition have different meanings. This is due to the fact that as a result of applying this method, a certain indecomposable residue is formed, which is added to the magnitude of the influence of the last factor. In practice, the accuracy of factor assessment is neglected, highlighting the relative importance of the influence of one or another factor. However, there are certain rules that determine the substitution sequence:

· if there are quantitative and qualitative indicators in the factor model, the change in quantitative factors is considered first;

· if the model is represented by several quantitative and qualitative indicators, the substitution sequence is determined by logical analysis.

Under quantitative factors in analysis they understand those that express the quantitative certainty of phenomena and can be obtained by direct accounting (number of workers, machines, raw materials, etc.).

Qualitative factors determine the internal qualities, signs and characteristics of the phenomena being studied (labor productivity, product quality, average working hours, etc.).

Absolute difference method is a modification of the chain substitution method. The change in the effective indicator due to each factor using the method of differences is defined as the product of the deviation of the factor being studied by the basic or reporting value of another factor, depending on the selected substitution sequence:

y 0 = a 0 . b 0 . c 0 ;

Dу а = Da. b 0 . c 0 ;

Dу b = Db. a 1. c 0 ;

Dу с = Dс. a 1. b 1 ;

y 1 = a 1 . b 1. c 1 ;

Dу = Dу а + Dу b + Dу c.

Relative difference method used to measure the influence of factors on the growth of a performance indicator in multiplicative and mixed models of the form y = (a – b) . With. It is used in cases where the source data contains previously determined relative deviations of factor indicators in percentages.

For multiplicative models like y = a . V . The analysis technique is as follows:

· find the relative deviation of each factor indicator:

· determine the deviation of the performance indicator at due to each factor

Example. Using the data in table. 2, we will analyze using the method of relative differences. The relative deviations of the factors under consideration will be:

Let's calculate the impact of each factor on the volume of commercial output:

The calculation results are the same as when using the previous method.

Integral method allows you to avoid the disadvantages inherent in the chain substitution method, and does not require the use of techniques for distributing the indecomposable remainder among factors, because it has a logarithmic law of redistribution of factor loads. The integral method makes it possible to achieve a complete decomposition of the effective indicator into factors and is universal in nature, i.e. applicable to multiplicative, multiple and mixed models. The operation of calculating a definite integral is solved using a PC and is reduced to constructing integrand expressions that depend on the type of function or model of the factor system.

Questions for self-control

1. What management problems are solved through economic analysis?

2. Describe the subject of economic analysis.

3. What distinctive features characterize the method of economic analysis?

4. What principles underlie the classification of techniques and methods of analysis?

5. What role does the method of comparison play in economic analysis?

6. Explain how to construct deterministic factor models.

7. Describe the algorithm for using the simplest methods of deterministic factor analysis: the method of chain substitutions, the method of differences.

8. Characterize the advantages and describe the algorithm for using the integral method.

9. Give examples of problems and factor models to which each of the methods of deterministic factor analysis is applied.