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Correlation coefficient

  • The population correlation coefficient ρ (rho) measures the strength of the association between the variables
  • The sample correlation coefficient r is an estimate of ρ and is used to measure the strength of the linear relationship in the sample observations
  • Features of ρ and r
    • Unit free
    • Range between -1 and 1
    • The closer to -1, the stronger the negative linear relationship
    • The closer to 1, the stronger the positive linear relationship
    • The closer to 0, the weaker the linear relationship

Examples of approximate r values

 

 

 

Calculating the correlation coefficient

  • Sample correlation coefficient:



 

  • or the algebraic equivalent:

 

 

 

  • Where:

r = Sample correlation coefficient

n = Sample size

x = Value of the independent variable

y = Value of the dependent variable

 





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