Template:The Correlation Coefficient Calculation: Difference between revisions
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(Created page with ''''The Correlation Coefficient''' The estimator of <math>\rho </math> is the sample correlation coefficient, <math>\hat{\rho }</math> , given by: ::<math>\hat{\rho }=\frac{…') |
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'''The Correlation Coefficient''' | '''The Correlation Coefficient''' | ||
The estimator of <math>\rho </math> is the sample correlation coefficient, <math>\hat{\rho }</math> , given by: | The estimator of <math>\rho \,\!</math> is the sample correlation coefficient, <math>\hat{\rho }\,\!</math> , given by: | ||
::<math>\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> | ::<math>\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> | ||
Revision as of 03:33, 28 August 2012
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]