Simple Linear Correlation (Pearson r)

Pearson correlation (hereafter called correlation):
  • Assumes that the two variables are measured on at least interval scales.

  • Determines the extent to which values of the two variables are proportional to each other.

The value of correlation (correlation coefficient) does not depend on the specific measurement units used. For example, the correlation between height and weight will be identical regardless of whether inches and pounds, or centimeters and kilograms are used as measurement units.

Proportional means linearly related, that is, the correlation is high if it can be summarized by a straight line (sloped upwards or downwards).

This line is called the regression line or least squares line, because the sum of the squared distances of all the data points from the line is the lowest possible.

The concept of squared distances will have important functional consequences on how the value of the correlation coefficient reacts to various specific arrangements of data.