In the Department of Fisheries and Wildlife at Virginia Tech, an experiment was conducted to study the effect of stream characteristics on fish biomass. The regressor variables are as follows: average depth (of 50 cells),x1; area of in-stream cover (i.e., undercut banks, logs, boulders, etc.),x2; percent canopy cover (average of 12),x3; and area≥25 centimeters in depth,x4. The response isy, the fish biomass. The data are as follows:
Obs.
y
x1
x2
x3
x4
1
100
14.3
15
12.2
48
2
388
19.1
29.4
26
152.2
3
755
54.6
58
24.2
469.7
4
1288
28.8
42.6
26.1
485.9
5
230
16.1
15.9
31.6
87.6
6
0
10
56.4
23.3
6.9
7
551
28.5
95.1
13
192.9
8
345
13.8
60.6
7.5
105.8
9
10.7
35.2
40.3
348
25.9
52
116.6
(a) Fit a multiple linear regression including all four regression variables.
(b) UseCp,R2, ands2 to determine the best subset of variables. Compute these statistics for all possible subsets.
(c) Compare the appropriateness of the models in parts
(a) and (b) for predicting fish biomass.
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