Correllation

The direction and strength of the linear relationship between two variables can be described numerically by their correlation(r). The correlation of two variables, x(explanatory) and y(response) is given by the formula:


Where Sx and Sy are the standard deviations of the variables x and y.

Note that the formula standardises the values of the x and y variables. This is done so that units of measurement never need to be taken into consideration.

r is a positive number when the two variables are positively associated, and negative when the variables are negatively associated.

r is always a number ≥ -1 and ≤ 1.
Values near -1 and 1 indicate that the linear relationship between the variables is strong, while values near 0 indicate that it’s weak.

r is not resistant, that is, it is significantly affected by the presence of outliers.