Correlation and regression methods for educational data in the systems analysis of the quality of training of vocational education teachers

Abstract

The article describes the integration of correlation and regression methods into the systems analysis of the quality of training of vocational education teachers, which enables automated processing of educational process monitoring results and provides feedback loops within the logical and physical models of the systems analysis of quality for the purpose of its optimization. The study theoretically substantiates the expediency of implementing correlation and regression methods for educational data in the systemic analysis of the quality of vocational education teachers’ training. It is shown that the effectiveness of correlation and regression methods can be increased by taking into account their relationships with other methods of Educational Data Mining (EDM), as well as through automatic processing of the results of correlation and regression analysis. The software implementation of correlation and regression methods intended for processing educational data was carried out in Python. The developed program consists of two modules that implement correlation analysis and regression analysis, respectively. Correlation analysis of educational data involves computing the linear relationship between two characteristics of the educational process, which are mathematically described as parameters X and Y, respectively. The relationship between parameters X and Y is quantitatively expressed by Pearson’s correlation coefficient (Corr). An example of correlation analysis of educational data is considered, namely semester grades of students in six subjects. The correlation coefficient Corr makes it possible to quantify the relationships between grades in different subjects and to purposefully investigate relationships with high Corr values. Regression analysis involves computing a regression equation that is approximated by a polynomial of degree p. To assess approximation accuracy, the root mean square error Rmse was used for the training sample and RmseV for the validation sample. The optimal polynomial degree pA was determined as the value of p for which the minimum approximation error RmseV was obtained on the validation sample. Using the resulting regression equation, the values of parameter Y were forecast based on parameter X, which makes it possible, for example, to predict students’ grades in a subject for the next semester based on their grades in the previous semester. The obtained regression model also enables the diagnosis of students’ educational achievements using the outlier detection method. In the context of analyzing educational achievements, an outlier means that a given student received a grade in a particular subject that is significantly higher or lower than the predicted one, and the learning outcomes of such a student require further investigation. It is shown that the developed program makes it possible to perform correlation and regression analysis, as well as forecasting, identification of relationships, and detection of outliers in educational data for a large sample (1,000 students). Implementing correlation and regression methods enables automated processing of educational process monitoring results in order to ensure the quality of training of vocational education teachers.