The Criterion for the Sample Observations Completeness in the Construction of Regression Models

This article is devoted to the development of a new criterion for the adequacy of regression models. When constructing regression models, it often happens that there are no important observations in the sample. Therefore, a regression model estimated from such a sample, even with high approximation qualities, in practice may behave inadequately. Hence, there is a need to develop such a criterion for the adequacy of regression models, which would give a quantitative assessment of the degree of completeness of the sample available to the researcher. From the theory of experiment planning, it is known that in the presence of a small number of factors, a complete factorial experiment is often carried out, realizing all possible combinations of factor levels. Based on the ideas of implementing a full factorial experiment, a criterion for the sample observations completeness was developed. To find it, you first need to determine the intervals of possible values of the factors, then select the number of their levels and form the corresponding interval for each level. Then form all possible combinations of levels and set the number of observations belonging to each combination. Next, calculate the criterion for the completeness of observations, as the ratio of the number of combinations of levels, including at least one observation, to the total number of combinations. This criterion takes values from 0 to 1. The larger its value, the higher the completeness of sample observations. The proposed criterion can be used to analyze absolutely any data samples. In the article, the criterion is applied in solving the problem of modeling rail transportation in the Irkutsk region. The criterion made it possible not only to assess the completeness of the sample observations, but also to answer the question of which observations are contained in the sample in excess, and which are not at all.