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Chapter 5 · Data Analysis: A Concise Overview of Statistical Techniques · Slide 211/274

Linear Correlation Coefficient

The (Pearson) linear correlation coefficient measures the strength of the linear relationship between two variables.

5.2.3 · Relationship between Two VariablesCorrelation Coefficient

Linear Correlation Coefficient

Properties:
  • Values of the linear correlation coefficient always lie between −1 and 1.
  • When r = +1 there is a perfect positive linear relationship between the variables.
  • When r = −1 there is a perfect negative linear relationship between the variables.
  • The closer r is to +1 or −1, the stronger the respective relationship.
  • If r is close to 0, there is little evidence of a linear relationship — but this does not mean there is no relationship at all, just no linear.
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Linear Correlation Coefficient

The (Pearson) linear correlation coefficient measures the strength of the linear relationship between two variables.

r = Sum (x_i − x̄)(y_i − ȳ) divided by Sqrt(Sum (x_i − x̄)²) times Sqrt(Sum (y_i − ȳ)²)
QUESTIONSTAR · Dr. Paul Marx211 / 274
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