category: Economic-mathematical modeling

Ministry of Education

Ivanovo State University

Physics Department

Department of Theoretical Physics,

mathematical and computer modeling

Term papers on the topic

"**Using** **regression** **analysis** for the **processing** of **economic** **statistics**"

Finished: 3 rd year student at Lone AV < p> Supervisor: Associate Professor Ozerov VM

Ivanovo 2002

CONTENTS

1. Introduction

2. Role korrelyatsonno-**regression** **analysis** in the **processing** of **economic** data

3. Regression **analysis** and its possible

4. Background correlation and **regression** **analysis**

5. Package Analysis Microsoft Excel

6. Conclusion

7. Literature

Introduction

**processing** of statistical data has long been used in mostvarious types of human activity. Generally speaking, it is difficultcalled the sphere in which it would not be used. But, perhaps, or inone area of knowledge and practice of statistical **processing**data does not play a very large role in the economythat deals with **processing** and analyzing large volumes of informationsocio-**economic** phenomena and processes. Comprehensive and thorough**analysis** of this information, the so-called statistical data, suggestsuse of various special techniques, an important place among themis correlation and **regression** **analysis** of statisticaldata.

in **economic** research often face the challenge of identifying factorsdetermining the level and dynamics of the **economic** process. This problem oftensolved by methods of correlation and **regression** **analysis**. Forauthentic reflection of objective **economic** processesto identify significant relationships and not only identify, but also toquantified. This approach requires the opening of the causaldependencies. Under the causal dependence refers to a relationship betweenprocesses when a change in one of them is a consequence of changesanother.

main objectives are to assess the correlation **analysis** of the couplingand verification of statistical hypotheses about the presence and strength of correlation. Notall factors affecting the **economic** processes that are randomvalues, so the **analysis** of **economic** phenomena are usuallyexamines the links between random and nonrandom quantities. Suchconnection called **regression**, and the method of mathematical **statistics**, theirstudent, called **regression** **analysis**.

**Using** the capabilities of modern computer technologyequipped with software packages of computer **processing** of statistical informationcomputer, makes feasible rapid problem solving learningcorrelation between the exchange rates of the methods of correlation -**regression** **analysis**.

When machining background information on a computer equipped with packagesstandard programs of **analysis**, calculation of the parameters usedmathematical function is performed by quickly counting operation.

This paper studies the possibility of statisticaldata exchange rates of the methods of correlation and **regression** **analysis** withusing the software package Microsoft Excel.

Role korrelyatsonno-**regression** **analysis** in the **processing** of **economic** data

correlation **analysis** and **regression** **analysis** are relatedsections of mathematical **statistics**, and provide for the study ofselected according to statistical dependence of a number of variables, some ofwhich are random. In the statistical dependence of the notfunctionally related, but as random variables defined jointprobability distribution. Study of the relationship of random variablesexchange rate leads to the theory of correlation, as the theory of sectionprobability and correlation **analysis**, as a section of mathematical**statistics**. Investigation of the dependence of random variables leads to models**regression** and **regression** **analysis** based on sample data. Theoryprobability and mathematical **statistics** represent only a tool forstudy of statistical dependence, but do not aim to establishcausation. Representations and the hypothesis of a causal relationship must bebeen introduced from some other theory, which allows meaningfulexplain the phenomenon.

Formally, the correlation model of the relationship system of random variables

can be represented as follows:, where Z - a setrandom variables that influence the studied random variables.

Economic data is almost always presented in tabular form. Numericdata contained in the tables are usually between an overt (known)or implicit (hidden) connection.

clearly related indicators, which were obtained by methods of direct calculation, thatie calculated on pre-known formulas. For example, the percent ofplan levels, specific gravity, deviations in the amount of deviation in percentagegrowth rates, growth rates, indexes, etc.

Communications of the second type (implicit) are unknown. However, it mustbe able to explain and predict (predict) the complex phenomena in orderto manage them. Therefore, experts with the help of observations tendreveal hidden dependencies and express them in the form of formulas, ie,mathematically simulate the phenomena or processes. One suchprovides opportunities **regression** **analysis**.

Mathematical models are constructed and used for the three generalizedgoals:

? to explain;

? predicting;

? Management.

Introduction of **economic** and other data in spreadsheets inToday was a simple and natural. Room same spreadsheetmeans of **regression** **analysis** contributes to that ofof complex, deeply scientific and therefore rarely used, almostexotic methods, **regression** **analysis** turns tospecialist in the daily, efficient and rapid analyticaltool. However, because of its complexity, its development requires muchconsiderable knowledge and effort than the development of simple spreadsheets.

**Using** the methods of **regression** **analysis**, analystsmeasure the closeness relations indicators using correlation coefficient. Whenfound this regard, different in strength (strong, weak, moderate andetc.) and different direction (forward, backward). If the connection willsignificant, it is advisable to find their mathematical expression ina **regression** model and to evaluate the statistical significance of the model. InEconomy meaningful equation is typically used to predictphenomenon under study or indicator.

**regression** **analysis** is called the main method of modernmathematical **statistics** to identify the implicit and subtle relationshipsbetween the observational data. Spreadsheets make such an **analysis** is easilyavailable. Thus, the **regression** calculation and selection of goodequations - is a valuable, versatile research tool in mostvarious branches of business and scientific activities (marketing, trademedicine, etc.). Mastered the technology of using this tool, you canapply it as necessary, to acquire knowledge about hidden connections,improve analytical support to decision-making and increasing theirvalidity.

**regression** **analysis** is considered one of the main methodsmarketing, along with the optimization calculations, as well as mathematical andgraphical modeling of trends (trends). Widely used assingle-factor and multiple **regression** models.

**regression** **analysis** and its possible

Correlation **analysis** is one of the methods of statisticalanalyzing the relationship of several characters.

It is defined as a method used when the data monitoringcan be considered random and selected from the general population,distributed according to multivariate normal distribution. The main taskcorrelation **analysis** (which is the main and in **regression** **analysis**)is to evaluate the **regression** equation.

correlation - a statistical dependence between randomvalues that do not have a strictly functional nature, in whichchange one of the random variables leads to a change in the mathematical1. Pair correlation - the relationship between two characters (and the resultant factor or two-factor).

2. Partial correlation - correlation between efficiency and a factor variables at a fixed value of other factor variables.

3. Multiple correlation - the dependence of the effective and two or more factor variables included in the study.

correlation **analysis** has the task of quantificationcloseness between the two traits (paired communication) and betweenresultant variable and the set of factor variables (withmultifactor communication).

crowded regard quantitatively expressed by the value of the coefficientscorrelation. The correlation coefficients, representing quantitativecharacterization of the closeness between features, enable us to determine

"Usefulness" factor variables in constructing the equations of multiple**regression**. The magnitude of correlation coefficients is also the assessmentConformity **regression** equation identified causative factors.

Initially correlation studies were carried out in biology, andlater spread to other areas, including the socio -**economic**. Simultaneously with the beginning of the correlation used**regression**. Correlation and **regression** are closely linked: the firstestimates of (overcrowding), the statistical relationship, the second examines its shape. Andcorrelation and **regression** are used to establish relationships between the phenomenaand to determine the presence or absence of communication between them.

Background correlation and **regression** **analysis**

Before examining the assumptions of correlation and **regression****analysis**, it must be said that the general condition, allowing a morestable results in the construction of correlation and **regression** modelsexchange rates is to require the homogeneity of the initial information. Thisinformation should be treated for abnormal, ie, sharplyevolved from an array of data observations. This procedure is performed forby quantifying the homogeneity of the aggregate to anyone-dimensional or multidimensional criteria (depending on the initialinformation) and has a goal of the observed objects, in which the best (orworst) the modalities through no fault or slightly beyondreasons.

After **processing** the data for "abnormality" should bechecks how the remaining information satisfies the prerequisites forusing a static apparatus for the construction of models, since evenminor deviations from these assumptions are often reduced to zerothe resulting effect. It should be borne in mind that the probability orStatistical solution to every **economic** problem must be based ondetailed understanding of mathematical concepts and the initial assumptionscorrectness and objectivity of the collection of baseline information, in constantcombined with the tightness of connection of **economic** and mathematical-statistical**analysis**.

To use correlation **analysis** requires that allconsidered variables were random and had a normal lawdistribution. Moreover, the implementation of these conditions is necessary onlyprobabilistic assessment revealed the closeness relation.

Consider the simplest case of detection of distress communication - two-dimensionalmodel of correlation **analysis**.

To characterize the closeness of the relationship between two variables is usuallyuse the pair correlation coefficient, if we considergeneral population, or its assessment - selected pair coefficient

If the study sample. Doubles coefficientcorrelation in the case of the linear form of connection is calculated by the formula

, and its selective value - according to the formula

a small number of observations of a sample correlation coefficient is convenientcalculated by the following formula:

magnitude of the correlation coefficient varies in the range.

In between the two variables exists a functional relationship with

?- Direct functional relationship. If, then the value of X and Y insample are uncorrelated, if the system of random variablesa two-dimensional normal distribution, the value of X and Y willindependent.

If the correlation coefficient is in the range, somewhere betweenvalues of X and Y there is an inverse correlation. This isconfirmed by visual **analysis** and background information. In this case,deviation of Y from the mean value taken with the opposite sign.

If each pair of values of X and Y are often simultaneouslyis above (below) the corresponding mean values, betweenvalues there is a direct correlation and correlation coefficientis in the interval.

If the deviation of X from the mean value equally oftencause deviations of Y down from the average value whiledeviations are always different, we can assume thatcorrelation coefficient tends to zero.

should be noted that the correlation coefficient does not depend onunits of measurement and the choice of the origin. This means that if the variables

X and Y decrease (increase) in time to either one and the same number of C, thencorrelation coefficient does not change.

Package Analysis Microsoft Excel

The structure of Microsoft Excel includes a set of data **analysis** tools (socalled packet **analysis**), designed to solve complexstatistical and engineering tasks. To analyze the data usingthese tools should specify the input data and select options;**analysis** will be conducted using appropriate statistical or engineeringmacro functions and the result will be placed in the output range. Othertools allow to provide an **analysis** in graphical form.

graphic images are used primarily to illustratepresentation of statistical data, thanks to them much easiertheir perception and understanding. Essentially their role and when it comes toControl of completeness and accuracy of statistical source materialused for **processing** and **analysis**.

**statistics** are provided in the form of long and complexstatistical tables (eg, see Table 1), so is very difficultdetect them available inaccuracies and errors.

same graphical representation of statistical data helps themquickly identify unjustified peaks and troughs, obviously not relevantdepicted **statistics**, anomalies and deviations. The graphbuilt according to Table 1 (Fig. 1) clearly shows the distributionrate of exchange rates depending on the time of the transaction and pricetransactions in rubles.

Graphical representation of statistical data is not onlymeans of an illustration of statistical data and monitor their accuracy andreliability. Thanks to its properties, it is an important toolinterpretation and **analysis** of statistical data, and in some cases --unique and irreplaceable way of their synthesis and cognition. In particular,it is indispensable, while the study of several interrelated**economic** phenomena, as it allows at first sight to establishrelations existing between them and respect the difference and similarity, as well asidentify the characteristics of their changes over time.

However, to make better use of graphicsstatistical data, you must master the methods and techniques ofconstruction. It should be added that the graphicimage **statistics** of exchange rates in mostcorresponds to the nature and content depicted data setproblem **analysis**.

| Time | Deal Price |

| | Rubles |

| 11:16:45 | 99,45 |

| 11:21:53 | 99,4 |

| 11:23:09 | 99,31 |

| 11:23:37 | 99,31 |

| 11:24:49 | 99 |

| 11:24:57 | 99 |

| 11:48:40 | 98,61 |

| 11:49:45 | 98,99 |

| 11:53:51 | 98,66 |

| 11:55:05 | 98,65 |

| 11:55:24 | 98,7 |

| 11:58:18 | 98,8 |

| 11:58:18 | 98,8 |

| 11:58:24 | 98,65 |

| 11:58:35 | 98,8 |

Table 1. Choose an exchange rate on the time of committingtransaction and the transaction price in rubles for one day of stock exchange

Fig.1 Rasbution rate of exchange rates depending on the timetransaction and the sale price in rubles.

Correlation - a tool for **analysis** package Microsoft Excel.

Used to quantify the relationship of the two sets of datapresented in dimensionless form. Correlation coefficient selectionrepresents the covariance of two data sets divided by the producttheir standard deviations.

Correlation **analysis** can establish whether the associatedsets of data on size, that is: large values of one setdata associated with large values of the other (positivecorrelation), or, conversely, small values of one set are associated with largevalues of the other (negative correlation), or data of the two rangesunrelated (correlation close to zero).

**regression** is also a tool for data **analysis** package of Microsoft

Excel .. Linear **regression** **analysis** is to select the schedule forset of observations using the method of least squares. Regressionused to analyze the impact on a separate dependent variablevalues of one or more independent variables. For example, the rate of exchangerate is influenced by several factors, including such as the time oftransaction and its price. Regression proportionally distributes a quality measure forthese two factors on the basis of the functioning of the course of exchange rates.

The **regression** results can be used to predict the qualitiesnew, not yet committed exchange transactions. For example, using the resultsTable 1, you can use **regression** to predict the price of these transactions.

| Monitoring | predicted transaction price in | Remains |

| | Rubles | |

| 1 | 72,22015 | 27,22985 |

| 2 | 72,76796 | 26,63204 |

| 3 | 72,90313 | 26,40687 |

| 4 | 72,95293 | 26,35707 |

| 5 | 73,08099 | 25,91901 |

| 6 | 73,09522 | 25,90478 |

| 7 | 75,62617 | 22,98383 |

| 8 | 75,74178 | 23,24822 |

| 9 | 76,17932 | 22,48068 |

| 10 | 76,31094 | 22,33906 |

| 11 | 76,34473 | 22,35527 |

| 12 | 76,65421 | 22,14579 |

| 13 | 76,65421 | 22,14579 |

| 14 | 76,66488 | 21,98512 |

| 15 | 76,68444 | 22,11556 |

Table 2. The predicted transaction price in rubles

Conclusion

most difficult phase, the final **regression** **analysis**, isinterpretation of the results, ie translate them from the language of **statistics** andmathematics into the language of **economic**s.

interpretation of **regression** models by the methods of the industryknowledge, to which the phenomenon under investigation. Any interpretationbegins with a statistical evaluation of the **regression** equation as a whole and evaluatesignificance within the model of factor variables, ie to examine how theyaffect the value of the effective characteristic. The greater the value**regression** coefficient, the greater the impact of this trait insimulated **processing** of exchange rates. Of particular significance here is the signbefore the **regression** coefficients. Signs of **regression** coefficients indicatenature of the effect on the resultant variable statistical **analysis**If the factor has a plus sign, then the increasethis factor increases the resultant variable if the factor traitminus sign, then, with its resultant increase in the sign of decreasing.

The interpretation of these symbols is completely determined by socio-**economic**content of the simulated trait. If its value changes in the directionincrease, then the positive signs of factor variables have positiveinfluence. When you change the effective sign of downwardpositive values are minus signs factor variables. IfEconomic theory suggests that the factor should have a signpositive value, and he with a minus sign, then you should checkcalculate the **regression** equation.

correlation and **regression** **analysis** to determine the dependencebetween factors, as well as trace the influence of factors involved. Theseindicators are widely used in the compilation of **statistics** forachieve the best indicators of exchange rates.

Literature

1. VA Coleman, O. Staroverov, VB Turundaevskaya "Probability theory and mathematical satistika" / M., 1991.

2. "Theory of Statistics, edited by RA Shmoilova / "FIS", 1998.

3. "Multivariate statistical **analysis** of EBM using package Microsoft Excel? / M., 1997.

4. AA Frenkel, EV Adam "Correlation **regression** **analysis** in **economic** applications" / M., 1987.

5. I. D. Odintsov, "Theory of Statistics" / M., 1998.

6. AN Klenin, KK Shevchenko, "Mathematical Statistics for Economists, Statisticians / M., 1990.

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