Question
1. 17.1 Xr17-01 A developer who specializes in summer cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner
1. 17.1 Xr17-01 A developer who specializes in summer cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner of the tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants to forecast the value of each lot. From previous experience, she knows that the most important factors affecting the price of a lot are size, number of mature trees, and distance to the lake. From a nearby area, she gathers the relevant data for 60 recently sold lots.
a. Find the regression equation.
b. What is the standard error of estimate? Interpret its value.
c. What is the coefficient of determination? What does this statistic tell you?
d. What is the coefficient of determination, adjusted for degrees of freedom? Why does this value differ from the coefficient of determination? What does this tell you about the model?
e. Test the validity of the model. What does the p-value of the test statistic tell you?
f. Interpret each of the coefficients.
g. Test to determine whether each of the independent variables is linearly related to the price of the lot in this model.
h.Is the normality requirement violated? Explain.
i. Is the variance of the error variable constant? Explain.
Price |
105.4
91.2
183.3
93.8
207.5
130.9
162.3
18.8
80.5
38.3
71.3
55.5
85.7
110.5
85.1
78.3
27.2
70.9
101.4
133.3
117.7
49.7
49.6
83.2
81.3
152.5
112.2
37.1
130.2
39.1
81.9
24.6
101.9
117.6
148.8
60.2
43.7
113.1
38.1
89.2
3
55.8
89.7
136.1
44.7
63.2
163.4
64.1
98.7
139.9
92
66.6
16.4
131.9
11
27.9
103.5
107
51.6
133.4
-----------------------------------------------------------------------------
Lot size
41.2
44.8
21.3
43.9
57.7
33.4
31.4
27.4
26.2
40
47.6
31.6
21.6
36.3
47.2
30.5
41.8
20.6
35.3
40.1
35.6
20.6
22.4
45.8
29.4
51.7
27.2
37
38.9
32.5
34
35.8
32.9
46.4
51.9
28.9
35.2
30.4
38.3
49.2
21.5
41.9
21.8
66.3
28.2
41.9
46.7
32.1
38.5
27.6
47
20.7
34
31.9
28
40
46.6
23.2
46.4
32.1
----------------------------------------------------------------------------
Trees
24
5
72
58
52
78
65
22
68
57
53
36
23
48
61
41
1
20
38
68
24
16
32
77
40
60
0
50
48
25
12
16
44
62
59
0
57
70
24
61
46
10
79
56
73
64
69
12
59
0
65
24
12
76
2
52
26
11
53
55
--------------------------------------------------------------------------
Distance
42
71
43
14
12
26
51
0
83
76
35
26
24
98
59
55
60
33
75
0
41
77
86
19
0
34
16
49
63
45
0
34
42
48
39
66
77
78
62
0
83
69
62
34
77
65
27
0
77
0
37
51
75
63
42
84
70
83
44
98
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Trigonometry, Enhanced
Authors: Cynthia Y Young
4th Edition
1119321131, 9781119321132
