Correlation Coefficient

The correlation coefficient, usually denoted by r, measures the direction and strength of a linear relationship between two variables. It can take on values between -1 and 1. Values near -1 mean that the correlation is strong and negative, while values close to 1 are strong and positive. Values close to 0 represent a weak or very weak correlation, but r=0 represents no correlation.

When there is a linear model that describes the relationship between two variables well, the correlation coefficient indicates how close the points are to the line of best fit. The closer the value r is to -1 or 1, the closer the points to the line of best fit.

Keep in mind that the correlation coefficient is useful only when a linear model describes the data well. In addition to understanding the meaning of the correlation coefficient, while a graphing calculator is able to find the line of best fit, it is beneficial to learn how to calculate it by hand. Consider the following formula.

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Formula for Finding the Pearson Correlation Coefficient

Given a data set with n points {(x_1,y_1),...,(x_n,y_n)}, the Pearson correlation coefficient can be found by dividing the covariance of x and y by the product of their standard deviations. r = Cov(x,y)/σ(x)σ(y) Alternatively, the formula can be rewritten as follows.

Although there are different types of correlation coefficients, the most commonly used is the Pearson correlation coefficient.