The concept of correlation-regression analysis implies the carrying out of a number of operations, namely: the determination of the tightness of the connection, its direction and the establishment of an equation describing the form of communication. This type of analysis contains two separate components: correlation and regression analysis.
The meaning and major steps in the process of correlation and regression analysis of economic phenomena
Correlation and regression analysis is one of the ways to solve problems and find information. It allows you to determine the joint effect of many interrelated and simultaneously operating characteristics, and separate the influence of each characteristic of the economic phenomenon (the process). Thanks to this type of analysis can assess the degree of interaction between multiple characteristics, between characteristics and results obtained, as well as to simulate the regression equation describing the shape of the relationship.
Stages of analysis
Correlation-regression analysis of economic processes is divided into several stages:
- Definition of arguments and preliminary processing of conditional information.
- Definition of the tightness and form of the relationship between several characteristics.
- Modeling of the presented economic process and analysis of the obtained model.
- Application of the final results to improve the planning and management of the model.
Statistical homogeneity of information can be determined using two techniques. First we need to define and to discard the importance of factors differ sharply from all quantities. Then carried out a statistical study of homogeneity with the test of independence of sampling and belonging to the only together with a normal distribution.
The regression model is determined by the least squares method, which ensures the best approximation of the evaluation of the result, determined through the regression equation, to its factors.
Correlation-regression analysis: parameters of the created model
The most important factors determining the characteristics of the model, it is customary to consider:
- The coefficients of pair correlation (demonstrate the strength of the relationship of the two factors).
- Coefficient of multiple correlation (determines the relationship between the result and factors).
- The private coefficients of determination (show the effect of variation of the argument for variation of the desired characteristic).
- The coefficient of multiple determination (indicates the proportion of all arguments on the variation of the desired characteristic).
- Private elasticities (characterize the influence of factors on the result, expressed in the same scale in percent).
Purpose of analysis
The main objectives of the correlation-regression analysis are to identify factors that significantly affect the economic outcome of a phenomenon or process, and to use the information obtained to improve the planning of an economic process or phenomenon.
Parametric analysis methods
All production processes are in close interconnection. This relationship is stochastic (the result depends on many factors) and functional (the result is changed to the same value as the factor). Stochastic dependence most often has a correlation character, that is, the value of the factor simultaneously corresponds to several values of the result having absolutely different directions.
The correlation lattice
The correlation relationship can have one or more factors-attributes, have a positive or negative orientation, be rectilinear or curvilinear (depending on the expression). It is possible to determine the type of the relationship by means of a correlation lattice. It is built within rectangular coordinate axes.
The frequencies placed close to the diagonals indicate a high interrelation of the signs. Frequencies placed close to the diagonal passing through the left lower and upper right corners indicate a positive direction, and those passing through the upper left and lower right corner are about the opposite direction. Frequencies in the form of an arc indicate a curvilinear relationship, and randomly scattered - the absence of an interconnection at all.
The main method of correlation analysis is the linear correlation coefficient. It can take values from -1 to 1. The closer the value is to 1, the stronger the Association between the factor and the result. Positive values show direct relationship, and negative otherwise. The coefficient takes the value “zero” in that case, if between the signs is not the relationship.
Nonparametric methods of analysis
A number of methods make it possible to evaluate the interconnection of phenomena without the quantitative expression of the trait and, accordingly, the distribution parameters. They are called nonparametric. Among them are:
- The rank correlation coefficient of Kendall (defines the relationship of the quantitative and qualitative values of indicators in case they are subject to ranking).
- The Spearman rank correlation coefficient (assigns grades to each argument and result, on the basis of which are determined by difference and calculated index).
- The correlation coefficient signs Fechner (determines the number of matches and mismatches of the variances of the arguments and of results from their mean value).
- Another important method of correlation-regression analysis — least squares Method, to determine analytical expression of the relationship of resultant variable and its factor. It is the construction of a system of equations and determine the parameters of these equations.
Correlation-regression analysis: example
In statistics and economics are used a variety of types and objects of analysis. Statistical methods of analysis are aimed at studying repetitive processes in order to make long-term predictions of the behavior of economic phenomena.
For example, in order to analyze the socio-economic development of the territory, it is necessary to study the indicators of the standard of living of the population. Correlation-regression analysis in statistics allows us to create a regression equation and determine the correlation coefficients that demonstrate the relationship between the standard of living and the development of the territory. The standard of living is determined by income, and the main source of income is the salary. In this case, the factor is the level of wages, and the result is the population with low incomes.
To facilitate calculations, you can conduct a correlation analysis in Excel. In this program there are a number of tools that help to facilitate calculations. Among them, the function "Correlation", which allows to form a matrix of coefficients and different parameters. It is displayed in the form of a table. Correlation coefficients are used as columns and rows. Based on the obtained data of the table, it will be necessary to perform a correlation analysis. Example of the sequence of analysis:
- In the "Tools" command, select the "Data analysis" item.
- Select "Correlation" as the analysis tool.
- In the window that appears in the line "Input interval" to specify a range of data to be analyzed, select "Group" in the "output Settings", enter the output range of the results and click OK.
The result is a correlation matrix located in the output range. Inside, the linear correlation coefficient, which estimates the tightness and form of the relationship between the indices, will be indicated.
Conducting analysis in Excel
In MS Excel, the "Correlation" function is used to perform a correlation-regression analysis. An example of calculating the coefficients will be considered below. This function forms a matrix with coefficients of tightness of the relationship between different parameters. As a result, a square table is formed, containing the correlation coefficients at the intersection of rows and columns.
For carrying out the analysis, it will be necessary to perform a number of specific actions:
- Open the "Tools" command, and in it the "Data analysis" item.
- In the window that appears, specify the item "Correlation" in the list of "Analysis Tools".
- In the opened window "Correlation" to indicate the input interval range of cells containing the analyzed information (it needs to be at least two columns), put a checkmark in "Group" and in the "output Settings" to choose the top-left cell where to begin on the correlation matrix.
- Press the OK button.
As a result of the calculations, a square table with correlation coefficients appears.
Regression analysis in MS Excel
In order to calculate the linear regression equation describing the relationship between the factors and the result in MS Excel to apply the function "LINEST". In order to use it, you must:
- Select an empty area in which the analysis results will be displayed.
- Open the "Wizard of Functions", in it to find the category "Statistical", and in it the function "Line" and click OK.
- In the field "Known values of y» Enter the range of results to be analyzed, in the field "Known values of x» - range of factors analyzed.
- In the field "Constant" indicates the presence of the free term of the equation (1 – Yes, 0 – no), and the "Statistics" – whether to display additional information (1 – there will be more information, a 0 will appear only parameter estimates). By default, you can specify in both fields 1.
- Press the OK button.
The first element of the table appears at the top of the previously selected area. In order to open all the data, you need to press F2, and then simultaneously Ctrl + Shift + Enter.
As a result, the regression information will be displayed as a table of two columns and five rows: