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.
