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 SE23A 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 SE23B (page 655) and Table SE23C (page 656). 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 Cp 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 Cp 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 Cp 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.
x1
|
Number of bins
|
x13
|
Breadth-to-thickness ratio
|
x2
|
Maximum required concrete per hour
|
x14
|
Perimeter of complex
|
x3
|
Height
|
x15
|
Mixer capacity
|
x4
|
Sliding rate of the slipform (m/day)
|
x16
|
Density of stored material
|
x5
|
Number of construction stages
|
x17
|
Waste percent in reinforcing steel
|
x6
|
Perimeter of slipform
|
x18
|
Waste percent in concrete
|
x7
|
Volume of silo complex
|
x19
|
Number of workers in concrete crew
|
x8
|
Surface area of silo walls
|
x20
|
Wall thickness (cm)
|
x9
|
Volume of one bin
|
x21
|
Number of reinforcing steel crews
|
x10
|
Wall-to-floor areas
|
x22
|
Number of workers in forms crew
|
x11
|
Number of lifting jacks
|
x23
|
Length-to-breadth ratio
|
x12
|
Length-to-thickness ratio
|
|
|
TABLE SE23B Data for Exercise 23
y
|
z
|
w
|
x1
|
x2
|
x3
|
x4
|
x5
|
x6
|
x7
|
x8
|
x9
|
x10
|
x11
|
1,850
|
9,520
|
476
|
33
|
4.5
|
19.8
|
4.0
|
4
|
223
|
11,072
|
14,751
|
335
|
26.1
|
72
|
932
|
4,272
|
268
|
24
|
3.5
|
22.3
|
4.0
|
2
|
206
|
2,615
|
8,875
|
109
|
27.9
|
64
|
556
|
3,296
|
206
|
18
|
2.7
|
20.3
|
5.0
|
2
|
130
|
2,500
|
5,321
|
139
|
28.4
|
48
|
217
|
1,088
|
68
|
9
|
3.2
|
11.0
|
4.5
|
1
|
152
|
1,270
|
1,675
|
141
|
11.6
|
40
|
199
|
2,587
|
199
|
2
|
1.0
|
23.8
|
5.0
|
1
|
79
|
1,370
|
7,260
|
685
|
17.1
|
21
|
56
|
1,560
|
120
|
2
|
0.5
|
16.6
|
5.0
|
1
|
43
|
275
|
1,980
|
137
|
22.0
|
15
|
64
|
1,534
|
118
|
2
|
0.5
|
18.4
|
5.0
|
1
|
43
|
330
|
825
|
165
|
23.6
|
12
|
397
|
2,660
|
133
|
14
|
3.0
|
16.0
|
4.0
|
1
|
240
|
5,200
|
18,525
|
371
|
12.8
|
74
|
1,926
|
11,020
|
551
|
42
|
3.5
|
16.0
|
4.0
|
4
|
280
|
15,500
|
3,821
|
369
|
12.8
|
88
|
724
|
3,090
|
103
|
15
|
7.8
|
15.0
|
3.5
|
1
|
374
|
4,500
|
5,600
|
300
|
12.2
|
114
|
711
|
2,860
|
143
|
25
|
5.0
|
16.0
|
3.5
|
1
|
315
|
2,100
|
6,851
|
87
|
24.8
|
60
|
1,818
|
9,900
|
396
|
28
|
4.8
|
22.0
|
4.0
|
3
|
230
|
13,500
|
13,860
|
482
|
17.6
|
44
|
619
|
2,626
|
202
|
12
|
3.0
|
18.0
|
5.0
|
1
|
163
|
1,400
|
2,935
|
115
|
26.4
|
36
|
375
|
2,060
|
103
|
12
|
5.8
|
15.0
|
3.5
|
1
|
316
|
4,200
|
4,743
|
350
|
11.8
|
93
|
214
|
1,600
|
80
|
12
|
3.5
|
15.0
|
4.5
|
1
|
193
|
1,300
|
2,988
|
105
|
20.6
|
40
|
300
|
1,820
|
140
|
6
|
2.1
|
14.0
|
5.0
|
1
|
118
|
800
|
1,657
|
133
|
17.0
|
24
|
771
|
3,328
|
256
|
30
|
3.0
|
14.0
|
5.0
|
3
|
165
|
2,800
|
2,318
|
92
|
19.9
|
43
|
189
|
1,456
|
91
|
12
|
4.0
|
17.0
|
4.5
|
1
|
214
|
2,400
|
3,644
|
200
|
13.6
|
53
|
494
|
4,160
|
320
|
27
|
3.3
|
20.0
|
4.5
|
3
|
178
|
6,750
|
3,568
|
250
|
14.0
|
44
|
389
|
1,520
|
95
|
6
|
4.1
|
19.0
|
4.0
|
1
|
158
|
2,506
|
3,011
|
401
|
11.8
|
38
|
441
|
1,760
|
110
|
6
|
4.0
|
22.0
|
5.0
|
1
|
154
|
2,568
|
3,396
|
428
|
14.1
|
35
|
768
|
3,040
|
152
|
12
|
5.0
|
24.0
|
4.0
|
1
|
275
|
5,376
|
6,619
|
448
|
14.5
|
65
|
797
|
3,180
|
159
|
9
|
5.0
|
25.0
|
4.0
|
1
|
216
|
4,514
|
5,400
|
501
|
14.8
|
52
|
261
|
1,131
|
87
|
3
|
3.0
|
17.5
|
4.0
|
1
|
116
|
1,568
|
2,030
|
522
|
10.5
|
24
|
524
|
1,904
|
119
|
6
|
4.4
|
18.8
|
4.0
|
1
|
190
|
3,291
|
3,572
|
548
|
9.8
|
42
|
1,262
|
5,070
|
169
|
15
|
7.0
|
24.6
|
3.5
|
1
|
385
|
8,970
|
9,490
|
598
|
12.9
|
92
|
839
|
7,080
|
354
|
9
|
5.2
|
25.5
|
4.0
|
1
|
249
|
5,845
|
6,364
|
649
|
13.9
|
60
|
1,003
|
3,500
|
175
|
9
|
5.7
|
27.7
|
4.0
|
1
|
246
|
6,095
|
6,248
|
677
|
15.1
|
60
|
TABLE SE23C Data for Exercise 23
x12
|
x13
|
x14
|
x15
|
x16
|
x17
|
x18
|
x19
|
x20
|
x21
|
x22
|
x23
|
19.6
|
17.6
|
745
|
0.50
|
800
|
6.00
|
5.50
|
10
|
24
|
7
|
20
|
1.12
|
16.0
|
16.0
|
398
|
0.25
|
600
|
7.00
|
5.00
|
10
|
20
|
6
|
20
|
1.00
|
15.3
|
13.5
|
262
|
0.25
|
850
|
7.00
|
4.50
|
8
|
20
|
5
|
18
|
1.13
|
17.0
|
13.8
|
152
|
0.25
|
800
|
5.00
|
4.00
|
8
|
25
|
6
|
16
|
1.23
|
28.1
|
27.5
|
79
|
0.15
|
800
|
7.50
|
3.50
|
5
|
20
|
4
|
14
|
1.02
|
20.3
|
20.0
|
43
|
0.15
|
600
|
5.00
|
4.00
|
5
|
15
|
1
|
12
|
1.02
|
24.0
|
18.3
|
43
|
0.15
|
600
|
5.05
|
4.25
|
5
|
15
|
2
|
12
|
1.31
|
27.5
|
23.0
|
240
|
0.25
|
600
|
6.00
|
4.00
|
8
|
20
|
7
|
22
|
1.20
|
27.5
|
23.0
|
1121
|
0.25
|
800
|
8.00
|
4.00
|
10
|
20
|
9
|
24
|
1.20
|
21.2
|
18.4
|
374
|
0.75
|
800
|
5.00
|
3.50
|
10
|
25
|
12
|
24
|
1.15
|
10.6
|
10.0
|
315
|
0.50
|
800
|
6.00
|
4.00
|
10
|
25
|
11
|
20
|
1.06
|
20.0
|
20.0
|
630
|
0.50
|
800
|
7.00
|
5.00
|
10
|
25
|
9
|
18
|
1.00
|
13.7
|
13.9
|
163
|
0.25
|
600
|
6.00
|
4.50
|
8
|
18
|
11
|
18
|
1.20
|
20.4
|
20.4
|
316
|
0.50
|
800
|
6.50
|
3.50
|
10
|
25
|
6
|
14
|
1.00
|
13.6
|
10.2
|
193
|
0.50
|
800
|
5.00
|
3.50
|
10
|
25
|
4
|
14
|
1.33
|
13.6
|
12.8
|
118
|
0.25
|
800
|
5.00
|
3.75
|
8
|
25
|
6
|
14
|
1.06
|
13.6
|
9.6
|
424
|
0.25
|
800
|
5.00
|
3.75
|
8
|
25
|
6
|
14
|
1.42
|
18.5
|
16.0
|
214
|
0.50
|
600
|
6.00
|
4.00
|
8
|
20
|
4
|
14
|
1.15
|
19.5
|
16.0
|
472
|
0.25
|
600
|
6.50
|
4.50
|
10
|
20
|
3
|
14
|
1.20
|
21.0
|
12.8
|
158
|
0.50
|
800
|
5.50
|
3.50
|
6
|
25
|
8
|
14
|
1.30
|
20.8
|
16.0
|
154
|
0.50
|
800
|
7.00
|
4.00
|
8
|
36
|
8
|
14
|
1.35
|
23.4
|
17.3
|
275
|
0.50
|
600
|
7.50
|
5.50
|
8
|
22
|
11
|
16
|
1.40
|
16.8
|
15.4
|
216
|
0.50
|
800
|
8.00
|
5.50
|
8
|
28
|
12
|
16
|
1.10
|
26.8
|
17.8
|
116
|
0.25
|
850
|
6.50
|
3.00
|
6
|
25
|
5
|
14
|
1.50
|
23.6
|
16.1
|
190
|
0.50
|
850
|
6.50
|
4.50
|
5
|
28
|
9
|
16
|
1.45
|
23.6
|
16.6
|
385
|
0.75
|
800
|
8.00
|
6.50
|
15
|
25
|
16
|
20
|
1.43
|
25.6
|
16.0
|
249
|
0.50
|
600
|
8.00
|
5.50
|
12
|
25
|
13
|
16
|
1.60
|
22.3
|
14.3
|
246
|
0.50
|
800
|
8.50
|
6.00
|
8
|
28
|
16
|
16
|
1.55
|
The article referred to in Exercise 23 presents values for the dependent and independent variables for 10 additional construction jobs. These values are presented in Tables SE24A and SE24B (page 657).
a. Using the equation constructed in part (a) of Exercise 23, predict the concrete quantity (y) for each of these 10 jobs.
b. Denoting the predicted values by
10 and the observed values by y1, . . . , y10, compute the quantities
These are the prediction errors.
c. Now compute the fitted values
from the data in Exercise 23. Using the observed values y1, .. . , y28 from those data, compute the residuals
d. On the whole, which are larger, the residuals or the prediction errors? Why will this be true in general?
TABLE SE24A Data for Exercise 24
y
|
z
|
w
|
x1
|
x2
|
x3
|
x4
|
x5
|
x6
|
x7
|
x8
|
x9
|
x10
|
x11
|
1,713
|
3,400
|
170
|
6
|
4.2
|
27.0
|
4.0
|
1
|
179
|
4,200
|
4,980
|
700.0
|
15.1
|
42
|
344
|
1,616
|
101
|
3
|
3.4
|
20.0
|
5.0
|
1
|
133
|
2,255
|
2,672
|
751.5
|
16.7
|
30
|
474
|
2,240
|
140
|
3
|
3.4
|
28.0
|
5.0
|
1
|
116
|
2,396
|
3,259
|
798.8
|
17.0
|
24
|
1,336
|
5,700
|
190
|
15
|
7.0
|
26.0
|
3.5
|
1
|
344
|
12,284
|
9,864
|
818.9
|
16.0
|
86
|
1,916
|
9,125
|
365
|
18
|
5.6
|
26.5
|
3.5
|
2
|
307
|
15,435
|
8,140
|
852.5
|
12.4
|
68
|
1,280
|
11,980
|
599
|
9
|
2.1
|
28.3
|
4.0
|
1
|
283
|
8,064
|
8,156
|
896.0
|
14.0
|
68
|
1,683
|
6,390
|
213
|
12
|
7.9
|
29.0
|
3.5
|
1
|
361
|
11,364
|
10,486
|
947.0
|
13.4
|
87
|
901
|
2,656
|
166
|
6
|
5.4
|
29.5
|
4.5
|
1
|
193
|
5,592
|
5,696
|
932.0
|
14.8
|
39
|
460
|
2,943
|
150
|
3
|
3.0
|
30.0
|
5.0
|
1
|
118
|
2,943
|
3,540
|
981.0
|
17.2
|
26
|
826
|
3,340
|
167
|
6
|
4.9
|
29.8
|
4.5
|
1
|
211
|
6,000
|
6,293
|
1,000.0
|
15.1
|
50
|
TABLE SE24B Data for Exercise 24
x12
|
x13
|
x14
|
x15
|
x16
|
x17
|
x18
|
x19
|
x20
|
x21
|
x22
|
x23
|
22.5
|
14.8
|
179
|
0.50
|
850
|
8.0
|
5.0
|
6
|
28
|
11
|
16
|
1.52
|
32.0
|
18.8
|
133
|
0.25
|
800
|
7.5
|
3.0
|
10
|
25
|
7
|
14
|
1.70
|
24.6
|
15.0
|
116
|
0.25
|
800
|
9.0
|
4.0
|
10
|
28
|
9
|
14
|
1.65
|
20.2
|
21.1
|
344
|
0.75
|
850
|
8.5
|
6.5
|
12
|
28
|
19
|
18
|
1.72
|
30.0
|
13.2
|
540
|
0.50
|
600
|
6.5
|
7.0
|
15
|
25
|
12
|
18
|
1.75
|
25.3
|
14.3
|
283
|
0.25
|
800
|
7.5
|
6.5
|
14
|
30
|
20
|
16
|
1.80
|
22.7
|
14.0
|
361
|
0.75
|
800
|
9.0
|
7.0
|
10
|
30
|
25
|
18
|
1.42
|
20.5
|
16.0
|
193
|
0.50
|
850
|
9.5
|
5.5
|
10
|
30
|
15
|
16
|
1.20
|
26.0
|
20.1
|
118
|
0.25
|
600
|
10.0
|
4.0
|
10
|
25
|
8
|
14
|
1.30
|
32.0
|
20.0
|
211
|
0.50
|
600
|
9.5
|
5.0
|
10
|
25
|
13
|
16
|
1.90
|