# Coefficient of Determination

**Definition: **The **Coefficient of determination** is the square of the coefficient of correlation r^{2} which is calculated to interpret the value of the correlation. It is useful because it explains the level of variance in the dependent variable caused or explained by its relationship with the independent variable.

The coefficient of determination explains the proportion of the explained variation or the relative reduction in variance corresponding to the regression equation rather than about the mean of the dependent variable. For example, if the value of r = 0.8, then r^{2} will be 0.64, which means that 64% of the variation in the dependent variable is explained by the independent variable while 36% remains unexplained.

Thus, the coefficient of determination is the ratio of explained variance to the total variance that tells about the strength of linear association between the variables, say X and Y. The value of **r ^{2} **lies between

**0 and 1**and observes the following relationship with

**‘r’**.

- With the decrease in the value of ‘r’ from its maximum value of 1, the ‘r
^{2}’ also decreases much more rapidly. - The value of ‘r’ will always be greater than ‘r
^{2}’ unless the r^{2}=0 or 1.

The coefficient of determination also explains that how well the regression line fits the statistical data. The closer the regression line to the points plotted on a scatter diagram, the more likely it explains all the variation and the farther the line from the points the lesser is the ability to explain the variance.