Methods of mathematical statistics. Regression analysis

The term "multiple regression analysis" was used by Pearson in his works, dating back to 1908. He described it on the example of the work of an agent selling real estate. In his notes, the house trade specialist kept a record of a wide range of input data for each particular building. Based on the results of trading, it was determined which factor had the greatest impact on the transaction price.

Analysis of a large number of transactions gave interesting results. The final cost was influenced by many factors, sometimes leading to paradoxical conclusions and even to explicit "emissions", when a house with a high initial potential was sold at a low price.

A second example of the application of this analysis is the work of a human resources specialist, who was entrusted with determining the remuneration of employees. The complexity of the task consisted in the fact that it was not necessary to distribute a fixed amount to everyone, but a strict correspondence of its value to a specifically performed work. The emergence of many problems that have a practically similar solution would require more detailed study of them at the mathematical level.

In mathematical statistics, a significant place was assigned to the section "regression analysis", it combined the practical methods used to study the dependencies that fall under the concept of regression. These relationships are observed between the data obtained in the course of statistical studies.

Regression analysis among the set of solved problems, the main three goals are: definition for the general regression equation ; Constructing estimates of parameters that are unknown, which are part of the regression equation; Check statistical regression hypotheses. In the course of studying the connection between a pair of quantities obtained as a result of experimental observations and making up a series (type) of the type (x1, y1), ..., (xn, yn), they rely on the provisions of regression theory and assume that for one quantity Y there is a certain probability distribution, while the other X remains fixed.

The result of Y depends on the value of the variable X, this dependence can be determined by various regularities, while the accuracy of the results obtained is influenced by the nature of the observations and the purpose of the analysis. The experimental model is based on certain assumptions that are simplistic, but plausible. The main condition is that the parameter X is the controlled quantity. Its values are set before the experiment begins.

If a pair of uncontrolled XY values is used during the experiment, the regression analysis is performed in the same way, but for the interpretation of the results, during which the relationship of the investigated random variables is studied, the methods of correlation analysis are applied . Methods of mathematical statistics are not an abstract topic. They find their application in life in the most diverse spheres of human activity.

In the scientific literature, the term linear regression analysis has found wide application for determining the above method. For the variable X, the term regressor or predictor is used, and the dependent Y variables are also called criterial. In this terminology, only the mathematical dependence of variables is reflected, but not the causal relationship.

Regression analysis is the most common method that is used in the processing of the results of a variety of observations. Physical and biological dependencies are studied using the means of this method, it is implemented both in the economy and in technology. Many other areas use regression analysis models. Dispersion analysis, experiment planning, multivariate statistical analysis work closely with this method of study.