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Coefficient of Determination (r2)
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, r2, 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 r2 being equal to 1.r2 = (explained variation)/(Total variation) = [∑(Y - ý)2] / [∑ (Y- ý)2]
Where:
ý is the mean value of Y For computation purposes r2 can be given byr2 = (n ∑ xy - ∑ x ∑x)2 [n ∑x2 -( ∑x)2] [n ∑y2 – (∑y)2]
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