Statistics for Environmental Engineers

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One approach to finding the simplest adequate model is to start with a simple tentative model and use diagnostic checks, such as residuals plots, for guidance. The alternate approach is to start by overfitting the data with a highly parameterized model and to then find appropriate simplifications. Each time a term is added or deleted from the model, a check is made on whether the difference in the regression sum of squares of the two models is large enough to justify modification of the model.

References


Berthouex, P. M. and D. K. Stevens (1982). “Computer Analysis of Settling Data,” J. Envr. Engr. Div., ASCE, 108, 1065-1069.


Camp, T. R. (1946). “Sedimentation and Design of Settling Tanks,” Trans. Am. Soc. Civil Engr., 3, 895-936. Draper, N. R. and H. Smith (1998). Applied Regression Analysis, 3rd ed., New York, John Wiley.

Exercises


38.1 Settling Test. Find a polynomial model that describes the following data. The initial suspended solids concentration was 560 mg/L. There are duplicate measurements at each time and depth.


Depth (ft)


Susp. Solids Conc. at Time t (min)


20


40


60


120


2


135


90


75


48


140


100


66


40


4


170


110


90


53


165


117


88


46


6


180


126


96


60


187


121


90


63

38.2    Solid Waste Fuel Value. Exercise 3.5 includes a table that relates solid waste composition to the fuel value. The fuel value was calculated from the Dulong model, which uses elemental composition instead of the percentages of paper, food, metal, and plastic. Develop a model to relate the percentages of paper, food, metals, glass, and plastic to the Dulong estimates of fuel value. One proposed model is E (Btu/lb) = 23 Food + 82.8 Paper + 160 Plastic. Compare your model to this.

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