Fundamentals of Mathematics in Medical Research: Theory and Cases

Correlation Theory

Author(s): Carlos Polanco * .

Pp: 57-69 (13)

DOI: 10.2174/9789815223132124010010

* (Excluding Mailing and Handling)

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.


Keywords: R2space, R 3 space, linear correlation on R 2 , multiple correlation on R 3 , non-linear correlation on R 2 , Pearson’s correlation factor, Spearman’s correlation factor.

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