Correlation Theory

Abstract

In this chapter, we examine the nature of correlations in Euclidean spaces, focusing on the two-dimensional space R 2 and the three-dimensional space R 3 . We begin by exploring linear correlations in R 2 , where we analyze calculation techniques and association measures to quantify the relationship between two continuous variables. Next, we delve into multiple correlations in R 3 , examining how several variables can be related simultaneously and how their strength and direction can be jointly measured. Subsequently, we address non-linear correlations in R 2 , expanding the focus beyond traditional linear relationships. We explore advanced methods and techniques for detecting and measuring non-linear correlations, allowing us to capture complex and non-linear patterns in the data. Furthermore, examples of practical applications are discussed where the presence of non-linear correlations is crucial for analysis and decision-making.

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