In modern data analysis and data mining, there are many applicable regression procedures, however, the most frequently used ones include classical linear regression, decision trees, random forest model, support vector method and artificial neural networks. Most of these algorithms are powerful approximation tools that can model the complex relationships and patterns in data. One of the reasons for redundant structure within such procedures is the use of a too-large feature vector for a given task. This paper aimed to investigate and compare the selected methods of significance analysis and then reduce the size of the feature vector through supervised learning models. Based on the obtained results, it seems that the Shap analysis and the Sobol global sensitivity analysis method are the most reliable methods for determining the significance of feature vector elements and thus for reducing the feature vector dimension in regression problems.