# 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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