The coefficient of determination r2 is the ratio of the explained variation to the total variation. That is, r 2 = Explained variation Total variation
Example: The correlation coefficient for the data that represents the number of hours students watched television and the test scores of each student is r ≈ -0.831. Find the coefficient of determination. r 2 ≈ (−0.831)2 ≈ 0.691
About 69.1% of the variation in the test scores can be explained by the variation in the hours of TV watched. About 30.9% of the variation is unexplained. Pharmaceutical Biostatistics: Correlation & Regression
• Unlike the value of a test statistic, the coefficient of determination does not have a critical value that enables us to draw conclusions. • In general the higher the value of R2, the better the model fits the data. • r2 = 1: Perfect match between the line and the data points. • r2 = 0: There are no linear relationship between x and y.
Pharmaceutical Biostatistics: Correlation & Regression