The article ??Estimating Resource Requirements at Conceptual Design Stage Using Neural Networks?? (A. Elazouni, I. Nosair, et al., Journal of Computing in Civil Engineering, 1997:217??223) suggests that certain resource requirements in the construction of concrete silos can be predicted from a model. These include the quantity of concrete in m³(y), the number of crew-days of labor (z), or the number of concrete mixer hours (w) needed for a particular job. Table SE23 A defines 23 potential independent variables that can be used to predict y, z, or w. Values of the dependent and independent variables, collected on 28 construction jobs, are presented in Table SE23 B (page 659) and Table SE23C (page 660). Unless otherwise stated, lengths are in meters, areas in m², and volumes in m³.

a. Using best subsets regression, find the model that is best for predicting y according to the adjusted R² criterion.

b. Using best subsets regression, find the model that is best for predicting y according to the minimum Mallows C_p criterion.

c. Find a model for predicting y using stepwise regression. Explain the criterion you are using to determine which variables to add to or drop from the model.

d. Using best subsets regression, find the model that is best for predicting z according to the adjusted R² criterion.

e. Using best subsets regression, find the model that is best for predicting z according to the minimum Mallows C_p criterion.

f. Find a model for predicting z using stepwise regression. Explain the criterion you are using to determine which variables to add to or drop from the model.

g. Using best subsets regression, find the model that is best for predicting w according to the adjusted R² criterion.

h. Using best subsets regression, find the model that is best for predicting w according to the minimum Mallows C_p criterion.

i. Find a model for predicting w using stepwise regression. Explain the criterion you are using to determine which variables to add to or drop from the model.

TABLE SE23A Descriptions of Variables for Exercise 23

TABLE SE23B Data for Exercise 23

TABLE SE23C Data for Exercise 23

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Number of bins Maximum required concrete per hour Height Sliding rate of the slipform (m/day) Number of construction stages X6 Perimeter of slipform Volume of silo complex X13 Breadth-to-thickness ratio X2 X14 Perimeter of complex X15 Mixer capacity X3 Density of stored material Waste percent in reinforcing steel Waste percent in concrete Number of workers in concrete crew Wall thickness (cm) X4 X16 X5 X17 X18 X7 X19 Xg Surface area of silo walls X20 Volume of one bin Number of reinforcing steel crews Number of workers in forms crew X9 X21 X10 Wall-to-floor areas X11 Number of lifting jacks X12 Length-to-thickness ratio X22 X23 Length-to-breadth ratio