Statistics for Environmental Engineers

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171


16.1


-3.06


-1.13


0.014


0.971


19966


289


D


186


7.1


-3.06


0.143


0.968


19912


343


E


98


20.9


-0.65


-1.13


-0.08


0.864


17705


2550


F


113


11.9


-0.65


-0.08


0.858


17651


2605


G


117


16.1


-0.97


-1.13


0.849


17416


2840


H


132


7.1


-0.97


0.844


17362


2894

Note: () indicates t ratios of the estimated parameters. [] indicates standard errors of the estimated parameters.


residual mean square (RMS = 308.8/6 = 51.5) are the key statistics in comparing this model with simpler models.


The regression sum of squares (RegSS) shows how much of the total variation (i.e., how much of the Total SS) has been explained by the fitted equation. For this model, RegSS = 20,255.5.


The coefficient of determination, commonly denoted as R2, is the regression sum of squares expressed as a fraction of the total sum of squares. For the complete six-parameter model (Model A in Table 38.3), R = (20256/20564) = 0.985, so it can be said that this model accounts for 98.5% of the total variation in the data.


It is natural to be fascinated by high R2 values and this tempts us to think that the goal of model building is to make R as high as possible. Obviously, this can be done by putting more high-order terms into a model, but it should be equally obvious that this does not necessarily improve the predictions that will be made using the model. Increasing R2 is the wrong goal. Instead of worrying about R2 values, we should seek the simplest adequate model.

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