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Data with two variables

Measuring the variability

With single variable data we calculated the measure of spread to quantify the variability in the data set (e.g. standard deviation).

  • The strength of the linear relationship between two variables is called the correlation coefficient (\(r\)).
  • You can calculate the correlation coefficient on most scientific calculators.
  • The correlation coefficient is a value that can only be between \(−1\) and \(1\).
  • The closer the correlation coefficient is to either \(-1\) or \(1\), the stronger the linear correlation will be.
  • A negative correlation coefficient means that the relationship is negative (as \(x\) increases, \(y\) decreases). A positive correlation coefficient means that the relationship is positive (as \(x\) increases, \(y\) increases).
  • For example the correlation coefficient is \(r \approx 0.966\).
  • This implies a strong positive relationship between the two variables. To note: the presence of a strong linear correlation does not imply a cause/effect relationship.