The square of correlation coefficient between the observed value y of the dependent variable Y and the corresponding estimated value ŷ of y by the regression line ŷ = a + bx is called the coefficient of determination. It Is denoted by R².

Thus, R² = [Coy (y, ŷ)]²

= [Cov(y, a + bx)]²

= [Cov(y, x)]²

= r²

Uses:
(i) To determine the reliability of estimates obtained from the regression lines:

• If R² = 1, estimates obtained on the basis of regression line are 100 % reliable. There is perfect linear correlation between the variable Y and X.
• If R² = 0 estimates obtained on the basis of regression line are not reliable. There is lack of linear correlation between the variables Y and X.

(ii) For the interpretation regarding the assumption of linear regression between two random variables X and Y:

• If the value of R² obtained is close to 1 (i.e., 0.5 ≤ R² < 1), then it can be said that correlation between variables Y and X is close to the perfect linear correlation and hence it is said that the assumption of linear regression between variables X and Y is proper.
• If the value of R² obtained is close to zero (0) (i.e., 0 ≤ R² < 0.5) then it can be said that the correlation between variables Y and X is far from the perfect linear correlation and hence it is said that the assumption of linear regression between variables X and Y is not proper.