# 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

# 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