Qocayeva N.
Nakhchivan State University

Abstract
This study presents a comparative analysis of linear and non-linear correlation methods within statistical modeling, employing synthetic datasets to explore their effectiveness under varying data conditions. Linear correlation, quantified by Pearson’s r, was found to be more effective in homoscedastic datasets, where the variance of one variable remains constant across the range of another. In contrast, non-linear correlation methods, particularly Spearman’s rho and Kendall’s tau, exhibited superior performance in heteroscedastic datasets, characterized by varying variances and more complex relationships. The research underscores the importance of selecting the appropriate correlation analysis method based on the specific characteristics of the dataset, as the use of an unsuitable method can lead to misinterpretation of data and analytical errors. These findings advocate for a nuanced, context-specific approach to correlation analysis, especially relevant in fields where understanding variable relationships is critical. The study also highlights the potential for future research, including the application of these findings to real-world data, the exploration of more complex data structures, and the integration of machine learning techniques for advanced correlation analysis.

Keywords: Correlation Analysis, Linear and Non-Linear Models, Statistical Modeling, Homoscedasticity, Heteroscedasticity.