Answered: Diam. Volume Height (feet) Volume Diam.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Pine Tree Volume. We provided data on volume and diameter for 70 shortleaf pine trees and used the method of transformations in an attempt to predict volume based on diameter. In this exercise, we include the observed heights of the 70 pine trees and propose using a second-order polynomial regression equation in diameter and height to predict volume. The data are given in the following table.

a. Obtain a scatterplot matrix for the observed values of volume, diameter, and height. What do these plots indicate about the relationship between volume and diameter? between volume and height?

b. Obtain a three-dimensional scatterplot of volume versus diameter andheight. What does this plot indicate about the relationship between volume and the two predictor variables diameter and height?

c. Obtain the correlation coefficients between volume and the firstand second-order terms in the centered predictor variables diameterc andheightc. Which terms are most highly correlated with volume? What are the correlation coefficients between the firstand second-order terms? Will these correlations adversely affect the ability to assess the effect of a term in the presence of the other terms? Explain your answer.

d. Perform a second-order polynomial regression analysis for volume using the centered predictor variables diameterc and heightc. Based on the t-tests for the utility of each term in the model, which terms would you retain in the regression equation? Is it appropriate to use the t-tests here?

e. Obtain plots of residuals versus fitted values, residuals versus diameterc, and residuals versus heightc, and also a normal probability plot of the residuals. Assess the appropriateness of the second-order polynomial regression equation, the assumption of constant conditional standard deviations, and the assumption of normality of the conditional distributions. Check for outliers and influential observations.

f. Does your analysis in part (e) reveal any violations of the assumptions for regression inferences? Explain.

g. To address the problems found in part (f), what would you suggest as the next step in the analysis?

h. Referring to part (g), carry out your suggestion in an attempt to obtain a model that meets the assumptions for regression inferences.

Diam.
Volume
Height
(feet)
Volume
Diam.
Height
(feet)
(inches)
(cu. ft.)
(inches)
(cu. ft.)
4.4
38
2.0
11.0
71
25.8
4.6
33
2.2
11.1
81
32.8
5.0
40
3.0
11.2
91
35.4
5.1
49
4.3
11.5
66
26.0
5.1
37
3.0
11.7
65
29.0
5.2
41
2.9
12.0
72
30.2
5.2
41
3.5
12.2
66
28.2
5.5
39
3.4
12.2
72
32.4
5.5
50
5.0
12.5
90
41.3
5.6
69
7.2
12.9
88
45.2
5.9
58
6.4
13.0
63
31.5
5.9
50
5.6
13.1
69
37.8
7.5
45
7.7
13.1
65
31.6
7.6
51
10.3
13.4
73
43.1
7.6
49
8.0
13.8
69
36.5
7.8
59
12.1
13.8
77
43.3
8.0
56
11.1
14.3
64
41.3
8.1
86
16.8
14.3
77
58.9
8.4
59
13.6
14.6
91
65.6
59.3
8.6
78
16.6
14.8
90
8.9
93
20.2
14.9
68
41.4
9.1
65
17.0
15.1
96
61.5
9.2
67
17.7
15.2
91
66.7

Diam.
Height
(feet)
Volume
Diam.
Height
(feet)
Volume
(inches)
(cu. ft.)
(inches)
(cu. ft.)
9.3
76
19.4
15.2
97
68.2
9.3
64
17.1
15.3
95
73.2
9.8
71
23.9
15.4
89
65.9
9.9
72
22.0
15.7
73
55.5
9.9
79
23.1
15.9
99
73.6
9.9
69
22.6
16.0
90
65.9
10.1
71
22.0
16.8
90
71.4
10.2
80
27.0
17.8
91
80.2
10.2
82
27.0
18.3
96
93.8
10.3
81
27.4
18.3
100
97.9
10.4
75
25.2
19.4
94
107.0
10.6
75
25.5
23.4
104
163.5

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