Statisticians use a measure called the correlation coefficient to determine the strength of the linear relationship between two variables. There are several types of correlation coefficients.

The Population Correlation Coefficient, denoted by the Greek letter \(\rho\), is the correlation computed by using all possible pairs of data values \((x,y)\) taken from a population.

The Linear Correlation Coefficient computed from the sample data measures the strength and direction of a linear relationship between two quantitative variables. The symbol for the sample correlation coefficient is \(r\).

Formula for the linear Correlation Coefficient:

\[r=\frac{n\left(\sum xy\right)-\left(\sum x\right)\left(\sum y\right)}{\sqrt{\left| n\left(\sum x^2\right)-\left(\sum x\right)^2\right|\cdot\left|n\left(\sum y^2\right)-\left(\sum y\right)^2 \right|}}\]

where \(n\) is the number of data pairs.