Coefficient of Determination (r^{2})
If the regression line calculated by the least square method were to fit the actual observations perfectly, then all observed points would lie on the regression line. The coefficient of determination, r^{2}, explains the amount of variation in Y which is explained by the introduction of X in the model. A perfect linear relationship between X and Y would result in r^{2} being equal to 1.r^{2} = (explained variation)/(Total variation) = [∑(Y - ý)^{2}] / [∑ (Y- ý)^{2}]
Where:
ý is the mean value of Y For computation purposes r^{2} can be given byr^{2} = (n ∑ xy - ∑ x ∑x)^{2 } [n ∑x^{2 } -( ∑x)^{2}] [n ∑y^{2} – (∑y)^{2}]