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 by

r² =   (n ∑ xy  - ∑ x ∑x)²
       [n ∑x²  -( ∑x)²]  [n ∑y² – (∑y)²]