CEVAP:

In correlation and regression problems, the coefficient of determination measures the proportion of the variance of dependent variable (y), given by independent variable (x), when y is expressed as a linear regression on x.  In brief, the coefficient of determination shows the amount of the variability of dependent variable (y) is explained by the independent variable (x). There may be more than one independent variable to explain the total variability of dependent variable y. It is not feasible to think that one variable will explain all the variability in dependent variable.

The coefficient of determination is calculated by using the square of Pearson’s correlation coefficient, r2. Remember Pearson’s correlation coefficient takes values between -1 and +1, therefore it is easy to see that the coefficient of determination takes values between 0 and +1. For example, let’s say that Pearson’s correlation coefficient is -0.48 in a problem. Therefore, we know that there is a negative moderate correlation between the variables. The coefficient of determination in the same problem is r2= (-0.48)2 = 0.23. The practical
meaning of this result can be written as follows: “the independent variable in this problem explains the 23% of the variability of the dependent variable”. If we consider the total variability of dependent variable as 100%, it means that there is still 77% of unaccounted variability for the dependent variable. There must be some other effects on the variability of the dependent variable.