Correlation coefficient (r)

How to read it

In OpenStax’s Introductory Statistics, values of r close to −1 or +1 mean a stronger linear relationship between x and y. r = 1 is perfect positive correlation and r = −1 perfect negative correlation, with all the points lying on a straight line. A positive r means y tends to increase as x increases, and a negative r means y tends to decrease. If r = 0 there is likely no linear correlation, but OpenStax warns that data with a curved pattern can also give a correlation of 0. r is calculated from sample data and estimates the population correlation coefficient ρ, which is unknown. A strong correlation, OpenStax adds, does not suggest that x causes y.

Also searched as: correlation coefficient symbol, correlation symbol, pearson correlation, r, r in statistics.

r and R

A capital R is the multiple correlation coefficient, for one variable against several others; Miller finds it in use at least since G. Udny Yule in 1896. Miller notes that R is now generally used for the sample coefficient, which he calls awkward, because the capital of ρ, the natural choice for the population, is the letter P. Squared, the two become the coefficient of determination, r² or R².

Where you’ll see it

OpenStax notes that spreadsheets, statistics software and many calculators compute r, and that on TI-83, TI-83+ and TI-84+ calculators it is the bottom item of the LinRegTTest output, under r².