What measure indicates the linear correlation between two variables commonly called x and y?

The Pearson correlation coefficient (PCC) is the measure that specifically indicates the linear correlation between two numerical variables, commonly referred to as x and y. It assesses how well the relationship between these two variables can be described using a linear equation. The PCC ranges from -1 to 1, where a value of 1 implies a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 suggests no linear correlation at all.

This measure is particularly useful in various fields, including data analysis, statistics, and many scientific disciplines, when quantifying the degree of correlation between two distinct numerical measurements. It requires both variables to be continuous and normally distributed to produce meaningful results.

The other choices listed, while also measures of association, are not focused solely on linear relationships. For instance, Spearman's rank correlation coefficient assesses monotonic relationships, which can be non-linear, and Kendall's tau also measures ordinal correlations. The Chi-squared statistic, on the other hand, is used primarily for categorical data to assess how expected frequencies compare to observed frequencies, rather than measuring relationships between continuous variables. Therefore, the PCC stands out as the standard method for evaluating linear correlations.