2.4. Pearson Correlation

Correlation analysis is a quantitative study of the relationships between two or more variables, aiming to reveal the strength of their association. The Pearson correlation coefficient is a classic statistical tool for measuring the linear relationship between two variables, commonly denoted by the letter r. This method quantifies the degree of linear dependence between variables by calculating the value of the correlation coefficient. Given n pairs of data xi,yi for i = 1, 2, …, n, the Pearson correlation coefficient is calculated using the following formula:

where x¯ and y¯ represent the sample means of x and y, respectively. This formula provides a numerical value that ranges from −1 to 1, indicating the strength and direction of the linear relationship between the variables. A value close to 1 suggests a strong positive linear relationship, a value close to −1 indicates a strong negative linear relationship, and a value close to 0 implies little to no linear relationship.