What does squaring the Pearson correlation coefficient (r²) tell us?

Squaring the Pearson correlation coefficient (r) gives us the value of r², which indicates the proportion of variance in one variable that can be explained by the other variable in a linear relationship. This means that if r² is, for example, 0.64, it implies that 64% of the variance in one variable is accounted for by the other variable, highlighting how closely related they are in terms of their variability. This shared variance is particularly useful in determining the strength of the relationship between the two variables and is a fundamental concept in regression analysis.

Understanding this concept is essential in fields like healthcare statistics, where it helps researchers and practitioners quantify the strength of relationships between different health outcomes and predictor variables, thereby guiding data-informed decisions and policies.