Factor analysis formula. Factor analysis as a data classification method

Perform a factorial analysis of the phenomenon on a cartoon model using the method relative differences, absolute differences, the method of chain substitutions and formalization of the indecomposable remainder and the logarithmic method.

a) absolute change: b) relative change:

Calculations

3,62*5,02*2,92*5,82=308,829

76,7807

=0,00

Examination

У4.52*5.02*4.02*5.72=521.7521

3,62*5,02*2,92*5,82=308,829

521,721-308,829=212,92

CONCLUSION: factor analysis calculations show that under the influence of all independent factors A, B, C, D, the effective factor Y increased by 212.92 units. At the same time, factors such as B and D also had a negative impact on the productive factor Y. Of these greatest influence factor D had, and its change caused a decrease in the effective factor Y by 9.12 units. At the same time, factors A and C had a positive impact on factor Y, of which factor C had the greatest influence, its change caused an increase in the effective factor Y by 145.264 units.

2) the method of "indecomposable remainder"

Isolated influence of factors

For factor A \u003d 0.9 * 5.02 * 2.92 * 5.82 \u003d 76.7807

B \u003d 0.00 * 3.62 * 2.92 * 5.82 \u003d 0.00

C \u003d 1.1 * 3.62 * 5.02 * 5.82 \u003d 116.3397

D \u003d -0.10 * 3.62 * 5.02 * 5.82 \u003d -10.5763

"Indecomposable residue" is determined by the formula

NO \u003d No \u003d 212.92-182.5441 \u003d 30.38

CONCLUSION: factor analysis calculations show that under the influence of all independent factors A, B, C, D, the effective factor Y increased by 182.5441 units. At the same time, factors such as B and D also had a negative impact on the effective factor Y. Of these, factor D had the greatest influence, and its change caused a decrease in the effective factor Y by 10.5763 units. At the same time, factors A and C had a positive impact on factor Y, of which factor C had the greatest influence, its change caused an increase in the effective factor Y by 116.3397 units. The error was 30.38.

3) Logarithmic method.

I Lg (i) i /Lg (i) y

For factor A = 0.09643*212.92/0.22775=90.151

For factor B = 0.00*212.92/0.22775=0.00

For factor С = 0.13884*212.92/0.22775=129.8

For factor D = -0.00753*212.92/0.22775=-7.0397

90,151+0,00+129,8+(-7,0397)= 212,9113

CONCLUSION: factor analysis calculations show that under the influence of all independent factors A, B, C, D, the effective factor U increased by 212.9113 units (the error in the calculations is associated with rounding off the change in the factor) At the same time, factor D had a negative impact on the effective factor Y , and its change caused a decrease in the effective factor Y by 7.03997 units. At the same time, factors A and C had a positive impact on factor Y, of which factor C had the greatest influence, its change caused an increase in the effective factor Y by 129.8 units.

4) The method of absolute differences. Y= A*B*S*D

b) general change in the results of factors

Decision

0,9*5,02*2,92*5,82=76,781

4,52*0,00*2,92*5,82=0,00

4,52*5,02*1,1*5,82=145,2639

4,52*5,02*4,02*(-0,1)= -9,1215

76,781+0,00+145,2639+(-9,1215)= 212,923

Checking the results:

У4.52*5.02*4.02*5.72=521.7521

3,62*5,02*2,92*5,82=308,829

521,721-308,829=212,92

CONCLUSION: factor analysis calculations show that under the influence of all independent factors A, B, C, D, the effective factor Y increased by 212.923 units. At the same time, factor D had a negative impact on the effective factor Y, and its change caused a decrease in the effective factor Y by 9.12 units. At the same time, factors A and C had a positive effect on factor Y, of which factor C had the greatest influence, its change caused an increase in the effective factor Y by 145.2639 units.

5) the method of chain substitutions.

All phenomena and processes of economic activity of enterprises are interconnected and interdependent. Some of them are directly related, 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 affect the change in the effective indicator.

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

Deterministic factor analysis is a methodology for studying the influence of factors, the relationship of which with the performance indicator is of a functional nature.

The main properties of the deterministic approach to analysis:

building a deterministic model by logical analysis;

the presence of a complete (rigid) relationship between indicators;

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

study of interrelations in the short term.

There are four types of deterministic models:

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

Such models, for example, include cost indicators in conjunction with production cost elements 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 divisions.

Multiplicative Models in a generalized form can be represented by the formula

.

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

,

where H - average headcount workers;

CB is the average output per worker.

Multiple Models:

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

,

where W T- average stock of goods; O R- one-day sales volume.

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

Examples of such models are cost indicators for 1 ruble. marketable products, profitability indicators, etc.

To study the relationship between indicators and to quantify the many factors that influenced the performance indicator, we present general model conversion rules to include new factor indicators.

To refine 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 original factorial model , and , then the model takes the form .

To isolate a certain number of new factors and construct the factor indicators necessary for calculations, the method 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 method of reducing factor models is used. When using this technique, the numerator and denominator are divided by the same number.

.

The detailing 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. They are based on the following principles:

the place of each factor in the model should 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 the factors, usually qualitative ones, into components;

when writing a multivariate model formula, the 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, a method for assessing the influence of factors is determined.

Method of chain substitutions consists in determining a number of intermediate values ​​of the generalizing indicator by successively replacing the basic values ​​of the factors with the reporting ones. This method based on elimination. Eliminate- means to eliminate, exclude the influence of all factors on the value of the effective indicator, except for one. At the same time, 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 rest remain unchanged, and so on.

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

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

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

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

The total change ∆ y=y 1 -y 0 is the sum of the changes in the resulting indicator due to changes in each factor with fixed values ​​of the other factors:

Consider an example:

Table 2 - Initial data for factor analysis

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

Then the impact 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 of 5 people in the number of employees, which caused an increase in production by 730 thousand rubles. 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 total influence of the two factors led to an increase in production by 480 thousand rubles.

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

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of the factor expansion have different values. 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 assessing factors is neglected, highlighting the relative importance of the influence of one or another factor. However, there are certain rules that determine the sequence of substitution:

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

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 (the number of workers, machine tools, raw materials, etc.).

Qualitative Factors determine personal traits, signs and features of the studied phenomena (labor productivity, product quality, average working day, etc.).

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

Relative difference method is used to measure the influence of factors on the growth of the effective indicator in multiplicative and mixed models of the form y \u003d (a - c) . with. It is used in cases where the initial data contain previously defined relative deviations of factorial indicators in percent.

For multiplicative models like y = a . in . with the analysis technique is as follows:

find the relative deviation of each factor indicator:

determine the deviation of the effective indicator at for each factor

Example. Using the data in Table. 2, we will analyze by the method of relative differences. The relative deviations of the considered factors will be:

Let us calculate the impact on the volume of marketable output of each factor:

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

integral method allows you to avoid the disadvantages inherent in the method of chain substitution, and does not require the use of techniques for the distribution of the indecomposable remainder by factors, since it has a logarithmic law of redistribution of factor loadings. The integral method allows you to achieve a complete decomposition of the effective indicator by factors and is universal in nature, i.e. applicable to multiplicative, multiple, and mixed models. The operation of calculating a definite integral is solved with the help of a PC and is reduced to the construction of integrands that depend on the type of function or model of the factorial system.

You can also use the already formed working formulas given in the special literature ∆ 4∆ :

1. View model:

2. View model :

3. View Model :

4. View Model :

Consider the possibility of using the main methods of deterministic analysis, summarizing the above in the form of a matrix (Table 3).

Table 3 - Matrix of applying methods of deterministic factor analysis

Questions for self-control

What management tasks are solved through economic analysis?

Describe the subject of economic analysis.

What kind distinctive features characterize the method of economic analysis?

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

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

Explain how to build deterministic factorial models.

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

Describe the advantages and describe the algorithm for applying the integral method.

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

Factor analysis of profit allows you to evaluate the impact of each factor separately on the financial result as a whole. Read how to conduct it, and also download the methodology.

The essence of factor analysis

The essence of the factorial method is to determine the influence of each factor individually on the result as a whole. This is quite difficult to do, since the factors influence each other, and if the factor is not quantitative (for example, service), then its weight is estimated by an expert, which leaves an imprint of subjectivity on the whole analysis. In addition, when there are too many factors affecting the result, the data cannot be processed and calculated without special mathematical modeling programs.

One of the most important financial indicators enterprises is profit. As part of factor analysis, it is better to analyze marginal profit, where fixed costs absent, or profit from sales.

Factor analysis by chain substitution

In factor analysis, economists usually use the chain substitution method, but mathematically this method is incorrect and produces highly skewed results that differ significantly depending on which variables are substituted first and which are substituted after (for example, in Table 1).

Table 1. Analysis of revenue depending on the price and quantity of products sold

In the first variant, the revenue due to the price increased by 500 rubles, and in the second, by 600 rubles; revenue due to the quantity in the first increased by 300 rubles, and in the second by only 200 rubles. Thus, the results vary significantly depending on the order of substitution. .

It is possible to more correctly distribute the factors influencing the final result depending on the markup (Nats) and the number of sales (Col) (see Figure 1).

Picture 1

The formula for profit growth due to the markup: P nat = ∆ Nat * (Col (current) + Col (base)) / 2

The formula for profit growth due to quantity: P count \u003d ∆ Col * (Nat (current) + Nat (base)) / 2

An example of a two-way analysis

Consider an example in Table 2.

table 2. Example of two-way revenue analysis

The averaged values ​​between the variants of chain substitutions were obtained (see Table 1).

Excel model for factor analysis of revenue

Download the finished model in Excel, it will calculate how revenue has changed in the reporting period compared to the previous period or plan. The model will help to assess how the sales volume, price and sales structure affected the revenue.

Three-factor model for profit analysis

The three-factor model is much more complicated than the two-factor one (Figure 2).

Figure 2

The formula that determines the influence of each factor in a 3-factor model (for example, margin, quantity, nomenclature) on the overall result is similar to the formula in a two-factor model, but more complicated.

P nat \u003d ∆Nat * ((Col (current) * Nom (current) + Nom (base) * Nom (base)) / 2 - ∆Col * ∆Nom / 6)

P count \u003d ∆Col * ((Nat (current) * Nom (act) + Nat (base) * Nom (base)) / 2 - ∆Nat * ∆Nom / 6)

P nom \u003d ∆Nom * ((Nat (current) * Number (act) + Nat (base) * Number (base)) / 2 - ∆Nat * ∆Col / 6)

Analysis example

In the table we have given an example of using a three-factor model.

Table 3. An example of calculating revenue using a three-factor model

If you look at the results of the analysis of revenue by the factorial method, then the largest increase in revenue occurred due to price increases. Prices increased by (15 / 10 - 1) * 100% = 50%, the next most important was the increase in the range from 3 to 4 units - the growth rate was (4 / 3 - 1) * 100% = 33% and last place the "amount" that has only increased by (120/100-1)*100% = 20%. Thus, the factors affect profit in proportion to the growth rate.

Four-factor model

Unfortunately, for a function of the form Pr = Kol sr * Nom * (Price - Seb), simple formulas calculation of the influence of each individual factor on the indicator.

Pr - profit;

Kol av - the average quantity per unit of the nomenclature;

Nom - the number of item positions;

Price - price;

There is a calculation method based on the Lagrange finite increments theorem, using differential and integral calculus, but it is so complicated and laborious that it is practically not applicable in real life.

Therefore, to isolate each individual factor, first the more general factors are calculated according to the usual two-factor model, and then their components are calculated in the same way.

The general formula of profit: Pr \u003d Kol * Nat (Nat - markup on a unit of production). Accordingly, we determine the influence of two factors: quantity and markup. In turn, the number of products sold depends on the range and the number of sales per item on average.

We get Qty \u003d Qty cf * Nom. And the markup depends on the price and cost, i.e. Nat = Price - Seb. In turn, the impact of the cost on the change in profit depends on the number of products sold and on the change in the cost itself.

Thus, we need to separately determine the influence of 4 factors on the change in profit: Call, Price, Seb, Nom, using 4 equations:

1. Pr \u003d Number * Nat
2. Qty \u003d Qty cf * Nom
3. Cost \u003d Qty * Seb.
4. Ex = Qty * Price

An example of a four-way model analysis

Let's look at this with an example. Initial data and calculations in the table

Table 4. An example of profit analysis using a 4-factor model

Note: figures in Excel spreadsheet may differ by several units from the data in text description, because in the table they are rounded to tenths.

1. First, according to the two-factor model (described at the very beginning), we decompose the change in profit into a quantitative factor and a margin factor. These are first order factors.

Pr \u003d Number * Nat

Col ∆ \u003d ∆Q * (H 1 + H 0) / 2 \u003d (220 - 180) * (3.9 + 4.7) / 2 \u003d 172

National ∆ = ∆H * (Q 1 + Q 0) / 2 = (4.7 - 3.9) * (220 + 180) / 2 = 168

Check: ∆Pr = Col ∆ + Nat ∆ = 172+168 = 340

2. We calculate the dependence on the cost parameter. To do this, we decompose the costs into quantity and cost according to the same formula, but with a minus sign, since the cost reduces profit.

Cost \u003d Number * Seb

Seb∆ \u003d - ∆С * (Q1 + Q0) / 2 \u003d - (7.2 - 6.4) * (180 + 220) / 2 \u003d -147

3. We calculate the dependence on the price. To do this, we decompose the revenue into quantity and price using the same formula.

Ext = Qty*Price

Price ∆ = ∆P * (Q1 + Q0) / 2 = (11.9 - 10.3) * (220 + 180) / 2 = 315

Check: Nat∆ = Price∆ - Seb∆ = 315 - 147 = 168

4. We calculate the impact of the nomenclature on profit. To do this, we decompose the number of products sold by the number of units in the assortment and the average quantity per one unit of the nomenclature. So we will determine the ratio of the quantity factor and the nomenclature in physical terms. After that, we multiply the obtained data by the average annual margin and convert it into rubles.

Number = Nom * Number (avg)

Nom ∆ = ∆N * (Q (cf 0) + Q (cf 1)) / 2 * (H 1 + H 0) / 2 = (3 - 2) (73 + 90) / 2 * (4.7 + 3.9) = 352

Col (av) \u003d ∆Q (av) * (N 1 + N 0) / 2 * (H 1 + H 0) / 2 \u003d (73 - 90) * (2 + 3) / 2 * (4.7 + 3.9) = -180

Check: Col ∆ = Nom ∆ + Col (av) = 352-180 = 172

The above four-factor analysis showed that profit increased compared to the previous year due to:

• price increases by 315 thousand rubles;
• changes in the nomenclature by 352 thousand rubles.

And decreased due to:

• cost growth by 147 thousand rubles;
• drop in the number of sales by 180 thousand rubles.

It seems like a paradox: total units sold this year compared to the previous year increased by 40 units, but the quantity factor shows a negative result. This is because sales growth occurred due to the increase in nomenclature units. If last year there were only 2 of them, then this year one more has been added. At the same time, in terms of quantity, goods “B” were sold in the reporting year by 20 units. less than in the previous one.

This suggests that product C, introduced in the new year, partially replaced product B, but attracted new customers that product B did not have. If next year product "B" continues to lose its position, then it can be removed from the assortment.

As for prices, their increase by (11.9 / 10.3 - 1) * 100% = 15.5% did not greatly affect sales in general. Judging by product "A", which was not affected by structural changes in the assortment, its sales increased by 20%, despite the price increase by 33%. This means that price increases are not critical for the firm.

Everything is clear with the cost price: it has grown and profit has decreased.

Factor analysis of sales profit

Evgeny Shagin, Financial Director of Management Company "RusCherMet"

To conduct a factor analysis, you must:

• choose the basis for analysis - sales revenue, profit;
• select the factors whose influence is to be assessed. Depending on the chosen basis of analysis, they can be: sales volume, cost, operating expenses, non-operating income, interest on a loan, taxes;
• evaluate the impact of each factor on the final indicator. In the base calculation for the previous period, substitute the value of the selected factor from the reporting period and adjust the final indicator taking into account these changes;
• determine the influence of the factor. Subtract from received intermediate value the estimated indicator is its actual value for the previous period. If the figure is positive, the change in the factor had a positive impact, a negative one - a negative one.

Example of Factor Analysis of Sales Profit

Let's look at an example. Let us substitute the value of sales for the current period (571,513,512 rubles instead of 488,473,087 rubles) into the statement of financial results of Alfa for the previous period, all other indicators will remain the same (see table 5). As a result, net profit increased by RUB 83,040,425. (116,049,828 rubles - 33,009,403 rubles). This means that if in the previous period the company managed to sell products for the same amount as in this one, then its net profit would increase by just these 83,040,425 rubles.

Table 5. Factor analysis of profit by sales volume

Using a similar scheme, it is possible to evaluate the influence of each factor and recalculate net profit, and summarize the final results in one table (see table 6).

Table 6. Influence of factors on profit, rub.

As can be seen from Table 6, sales growth (83,040,425 rubles) had the greatest impact in the analyzed period. The sum of the influence of all factors coincides with the actual change in profit over the past period. From this we can conclude that the results of the analysis are correct.

Conclusion

In conclusion, I would like to understand: what should profits be compared with in factor analysis? With last year, with the base year, with competitors, with the plan? How to understand whether the company has worked well this year or not? For example, an enterprise has doubled its profit for the current year, it would seem that this is an excellent result! But at this time, competitors carried out a technical re-equipment of the enterprise and from next year they will force the lucky ones out of the market. And if compared with competitors, then they have less income, because. instead of, say, advertising or expanding the range, they invested in modernization. Thus, everything depends on the goals and plans of the enterprise. From which it follows that the actual profit must be compared, first of all, with the planned one.

All business processes of enterprises are interconnected and interdependent. Some of them are directly related to each other, some are manifested indirectly. Thus, important issue in economic analysis is the assessment of the influence of a factor on a particular economic indicator For this, factor analysis is used.

Factor analysis of the enterprise. Definition. Goals. Kinds

Factor analysis refers to scientific literature to the section of multivariate statistical analysis, where the estimation of the observed variables is carried out using covariance or correlation matrices.

Factor analysis was first used in psychometrics and is currently used in almost all sciences, from psychology to neurophysiology and political science. The basic concepts of factor analysis were defined by the English psychologist Galton and then developed by Spearman, Thurstone, and Cattell.

Can be distinguished 2 goals of factor analysis:
- determination of the relationship between variables (classification).
— reduction of the number of variables (clustering).

Factor analysis of the enterprise – complex methodology systematic study and assessment of the impact of factors on the value of the effective indicator.

The following can be distinguished types of factor analysis:

1. Functional, where the performance indicator is defined as a product or algebraic sum factors.
2. Correlation (stochastic) - the relationship between the performance indicator and factors is probabilistic.
3. Direct / Reverse - from general to specific and vice versa.
4. Single stage / multi stage.
5. Retrospective / prospective.

Let's take a closer look at the first two.

In order to be able to factor analysis is necessary:
All factors must be quantitative.
- The number of factors is 2 times more than the performance indicators.
— Homogeneous sample.
— Normal distribution factors.

Factor analysis carried out in several stages:
Stage 1. Selected factors.
Stage 2. Factors are classified and systematized.
Stage 3. The relationship between the performance indicator and factors is modeled.
Stage 4. Evaluation of the influence of each factor on the performance indicator.
Stage 5 Practical use of the model.

Methods of deterministic factor analysis and methods of stochastic factor analysis are singled out.

Deterministic factor analysis- a study in which factors affect the performance indicator functionally. Methods of deterministic factor analysis - the method of absolute differences, the method of logarithm, the method of relative differences. This type of analysis is the most common due to its ease of use and allows you to understand the factors that need to be changed to increase / decrease the effective indicator.

Stochastic factor analysis- a study in which factors affect the performance indicator probabilistically, i.e. when a factor changes, there may be several values ​​(or a range) of the resulting indicator. Methods of stochastic factor analysis - game theory, mathematical programming, multiple correlation analysis, matrix models.

In order to find out how profitable or unprofitable an enterprise is, it is not enough just to count the money. To understand this for sure, and most importantly, to help increase profits, you need to regularly carry out the work of the enterprise as a whole. And for this you need to have some skills in the accounting field and certain information. It is worth considering that the company worked both at the time of inflation and during the crisis. The prices changed constantly. Now you understand why the banal counting of money does not make it possible to objectively assess the situation with profit or costs? After all, you need to take into account the price factor.

So, many find it difficult to make an example of our analysis, we hope it will help them to make their own - by analogy this species diagnostics is very fast. It is in the form of a table. First, let's make a header for our factor analysis. We draw a table with 5 columns and 9 rows. Make the first column wider - it will contain the names of the articles of the enterprise, not numbers. It will be called - "Indicators", which you should write in the first line of the column. In it, fill in all the lines according to the sample: 1 - the name, 2 - put the number 1 - the numbering of the columns, in the 3rd line write down - "Sales revenue", 4 - "Cost". In the fifth line of the first column, put the item - "Business expenses". In 6, write - "Expenses for managing the process." The seventh line is called - and 8 - "Index of price changes", and the last line, 9 - "Sale at comparable prices."

Next, we proceed to the design of 2 columns: in 1 line we write - "Previous period, thousand rubles." (you can write other monetary units - euro, dollar, etc. - it depends on what currency you will be calculating in), and in the second line we write the number - 2. Go to the 3rd column - in it 1 line has the name - "Reporting period", thousand rubles. And the second one is filled with the number 3. Next, we draw up our factorial analysis of revenue and go to column 4. In the first line we enter - "Absolute change, thousand rubles", and the second line contains a small formula: 4 \u003d 3-2. This means that the numbers that you will write in subsequent rows will be the result of subtracting the numbers in the second column from the numbers in the third. We proceed to the design of the last - 5th column. In it, in 1 line, you need to write: "Relative changes%", which means that in this column all data will be written as a percentage. In the second line, the formula is: 5=(4/2)*100%. Everything, we have designed the header, it remains only to fill in each item of the table with the relevant data. We carry out factor analysis, an example of which we give you. First of all, we calculate the price change index - this is perhaps the most important figure in our calculations. We write the numbers of different periods in the corresponding columns. In columns 4 and 5 we carry out the necessary calculations. Factor analysis, of which you can view an example, assumes precision in numbers. Therefore, only reliable information should be written in 3 lines of each column. In 4 and 5, we again carry out calculations. As you understand, the factorial is mainly carried out in lines 5 and 6: try to add there the most real, not underestimated, numbers. In the 4th and 5th columns of these lines, again carry out calculations using formulas. Next, we perform a factor analysis of revenue in column 7 - profit. We write reliable numbers in columns 2 and 3, and in columns 4 and 5 we again consider everything according to the formulas. And the last column remains: we write the data, we calculate. Bottom line: the factor analysis, of which we give you an example, shows what is the impact of each of the factors described in the articles on profit or production costs. Now you see the weaknesses and can correct the situation in order to get as much profit as possible.

You have done all the calculations to perform factor analysis, but they will not help you in any way if you do not analyze the data thoroughly.