Statistics for Environmental Engineers

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5


12


32.6


20


34


2


4


40.8


39


17


5


12


24.5


28


35


2


4


24.5


43


18


5


12


24.5


12


36


2


4


8.2


48

Source: Cashion B. S. and T. M. Keinath, J. WPCF, 55, 1331-1338.

39

The Coefficient of Determination, R2


KEY WORDS coefficient of determination, coefficient of multiple correlation, confidence interval, F ratio, hapenstance data, lack of fit, linear regression, nested model, null model, prediction interval, pure error, R2, repeats, replication, regression, regression sum of squares, residual sum of squares, spurious correlation.


Regression analysis is so easy to do that one of the best-known statistics is the coefficient of determination, R2. Anderson-Sprecher (1994) calls it a measure many statistician’s love to hate.”


Every scientist knows that R is the coefficient of determination and R is that proportion of the total variability in the dependent variable that is explained by the regression equation. This is so seductively simple that we often assume that a high R2 signifies a useful regression equation and that a low signifies the opposite. We may even assume further that high R indicates that the observed relation between independent and dependent variables is true and can be used to predict new conditions.


Life is not this simple. Some examples will help us understand what R really reveals about how well the model fits the data and what important information can be overlooked if too much reliance is placed on the interpretation of R.

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