linear correlation coefficient, r


A measures the strength and direction of a linear relationship between two variables or two data sets 

The linear correlation is sometimes referred to as the Pearson product moment correlation coefficient in honor of its developer Karl Pearson.

When two sets of data are strongly linked together we say they have a High Correlation.The word Correlation is made of Co- (meaning “together”), and Relation

  • Correlation is Positive when the values increase together, and
  • Correlation is Negative when one value decreases as the other increases

Correlation can have a value:

  • 1 is a perfect positive correlation
  • 0 is no correlation (the values don’t seem linked at all)
  • -1 is a perfect negative correlation

The value shows how good the correlation is (not how steep the line is), and if it is positive or negative.

How to calculate

  • Step 1: Find the mean of x, and the mean of y
  • Step 2: Subtract the mean of x from every x value (call them “a“), do the same for y (call them “b“)
  • Step 3: Calculate: a × ba2 and b2 for every value
  • Step 4: Sum up a × b, sum up a2 and sum up b2
  • Step 5: Divide the sum of a × b by the square root of [(sum of a2) × (sum of b2)]

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