# Statistics for Environmental Engineers

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The test used above is valid to compare any two of the models that have one less parameter than Model A. To compare Models A and E, notice that omitting t2 decreases the regression sum of squares by 20256 — 17705 = 2551. The F statistic is 2551/51.5 = 49.5. Because 49.5 >> 5.99 (the upper 95% point of the F distribution with 1 and 6 degrees of freedom), this change is significant and t2 needs to be included in the model.

The test is modified slightly to compare Models A and D because Model D has two less terms than Model A. The decrease of 343 in the regression sum of squares results from dropping to terms (z2 and zt). The F statistic is now computed using 343/2 in the numerator and 51.5 in the denominator: F = (343/2)/51.5 = 3.33. The upper 95% point of the appropriate reference distribution is F = 5.14, which has 2 degrees of freedom for the numerator and 6 degrees of freedom for the denominator. Because for the model is less than the reference F (F = 3.33 < 5.14), the terms z2 and zt are not needed.

Model D is as good as Model A. Model D is the simplest adequate model:

Model D у = 186 + 7.12t- 3.06z + 0.143t2

This is the same model that was obtained by starting with the simplest possible model and adding terms to make up for inadequacies.