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Answer» The square of correlation coefficient between the observed value y of the dependent variable Y and
the corresponding estimated value y of Y by the regression line y = a + bx is called the coefficient of determination. It is denoted by R2. Thus, R2 = [Cor (y, ŷ)]2
= [Cor (y, a + bx)]2
= [Cor (y, x)]2 - 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.
- If R2 is near to 1 (i.e., 0.5 ≤ R2 < 1), then the assumption of linear regression is said to be proper and estimates obtained by regression line are reliable,
- If R2 is near to ‘0’ (i.e., 0 ≤ R2 < 0.5), then the assumption of linear regression is said to be improper and the estimates obtained by regression line are not reliable.
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