Coefficient of Determination
The coefficient of determination is the measurement applied to determine the variability of one factor caused by its relationship with another related factor. The correlation is termed as the goodness of fit and is represented by values between 0.0 and 1.0. Therefore, the coefficient of determination is the square of correlation (R) between the predicted Y and actual Y sores, ranging between 0 and 1. In linear regression, the coefficient of determination equals the square of the correlation between X and Y scores. Also, the coefficient of determination cannot be negative because it results from the squaring correlation coefficient.
It should be noted that even if the correlation is negative, squaring results in a positive number. For example, since R is always between -1 and 1, R-squared is the square of correlation. It then measures the proportion of variation in the single variables. Thus, correlation R=0.9; R squared will be 0.81.