Properties of correlation coefficient

The properties of Karl Pearson’s Coefficient of Correlation are:

1. Karl Pearson’s Correlation coefficient r has no unit. It is a pure number. It means a unit of measurement is not a part of r. It is independent of the origin and scale.
2. The value of the correlation coefficient lies between {tex}- 1 \leq r \leq 1{/tex}. If the value of r lies outside this range, it indicates there is some error in the calculation.
3. A negative value of r indicates an inverse relation. A change in one variable is associated with change in the other variable in the opposite direction.
4. If r is positive it indicates a direct relation and the two variables move in the same direction.
5. The converse of the theorem,i.e.,r=0, is not true, that is uncorrelated variables and need not necessarily be independent. Uncorrelation between the variables X and Y simply imply the absence of a linear relationship between them.
6. Therefore, if the data is too large, step deviation method is used, which makes the calculation of correlation coefficient easy.