Template:The Correlation Coefficient Calculation

The Correlation Coefficient

The estimator of [math]\displaystyle{ \rho\,\! }[/math] is the sample correlation coefficient, [math]\displaystyle{ \hat{\rho }\,\! }[/math], given by:

[math]\displaystyle{ \hat{\rho }=\frac{\underset{i=1}{\overset{N}{\mathop{\sum }}}\,({{x}_{i}}-\overline{x})({{y}_{i}}-\overline{y})}{\sqrt{\underset{i=1}{\overset{N}{\mathop{\sum }}}\,{{({{x}_{i}}-\overline{x})}^{2}}\cdot \underset{i=1}{\overset{N}{\mathop{\sum }}}\,{{({{y}_{i}}-\overline{y})}^{2}}}}\,\! }[/math]