Coefficient of Determination or Goodness of Fit

The coefficient of determination is a statistical measure that represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s) in a regression model. It is often referred to as the "R-squared" value.

1. Goodness of Fit

2. Diagram Explanation

3. Deviation of the observed value of Y into two component Firstly, it is explained by the regression line variation Secondly, the unexplained variation. That is

4. TSS or Total variation The total variation of the dependent variable by comparing each value of Y to the mean Ȳ and adding all the resulting deviations. That is

5. RSS or Unexplained variable This is a part of the variation of the dependent variable which is not explained by the regression line. Thus the sum of the squared residuals gives the total unexplained variation of the dependent variable Y around its mean. That is