What does Pearson's correlation coefficient (r) quantify?

Pearson's correlation coefficient (r) quantifies the direction and strength of a linear relationship between two variables. It can take on values between -1 and 1. A value close to 1 indicates a strong positive linear correlation, where as one variable increases, the other also increases. A value close to -1 indicates a strong negative linear correlation, where as one variable increases, the other decreases. A value around 0 suggests no linear correlation. This correlation is useful for determining how closely related two datasets are, which is central to many statistical analyses.

The average of two variable datasets is not what r measures; rather, it focuses on the relationship between the two datasets. The number of data points in a scatterplot does not inform about the nature of the relationship but only quantifies the sample size. Lastly, the sum of squared residuals pertains to the accuracy of predictions in regression analysis and is not what the correlation coefficient indicates. Hence, the correct answer encapsulates the essential feature of Pearson's r as a measure of the relationship between two variables.