7.55 The following variables were recorded for several counties in Minnesota in 1977: y = average rent paid per acre of land with alfalfa x₁ = average rent paid per acre for all land x₂ = average number of dairy cows per square mile x3 = proportion of farmland in pasture The data for 34 counties are given in Table 7.5 (Weisberg 1985, p. 162). Can rent for alfalfa land be predicted from the other three variables? (a) Find and s². (b) Find , and ß, using Sex and syx as in (7.46) and (7.47). (c) Find R² and R².

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TABLE 7.5 Land Rent Data
X1
15.50
22.29
y
18.38
20.00
11.50
25.00
52.50
82.50
25.00
30.67
12.00
61.25
60.00
57.50
31.00
60.00
72.50
60.33
49.75
12.36
31.84
83.90
72.25
27.14
40.41
12.42
69.42
48.46
69.00
26.09
62.83
77.06
58.83
59.48
x2
17.25
18.51
11.13
5.54
5.44
20.37
31.20
4.29
8.69
6.63
27.40
31.23
28.50
29.98
13.59
45.46
35.90
X3
.24
.20
.12
.12
.04
.05
.27
.10
.41
.04
.12
.08
.21
.17
.05
.16
.32
y
8.50
36.50
60.00
16.25
50.00
11.50
35.00
75.00
31.56
48.50
77.50
21.67
19.75
56.00
25.00
40.00
56.67
X1
9.00
20.64
81.40
18.92
50.32
21.33
46.85
65.94
38.68
51.19
59.42
24.64
26.94
46.20
26.86
20.00
62.52
X2
8.89
23.81
4.54
29.62
21.36
1.53
5.42
22.10
14.55
7.59
49.86
11.46
2.48
31.62
53.73
40.18
15.89
X3
.08
.24
.05
.72
.19
.10
.08
.09
.17
.13
.13
.21
.10
.26
43
.56
.05
Transcribed Image Text:TABLE 7.5 Land Rent Data X1 15.50 22.29 y 18.38 20.00 11.50 25.00 52.50 82.50 25.00 30.67 12.00 61.25 60.00 57.50 31.00 60.00 72.50 60.33 49.75 12.36 31.84 83.90 72.25 27.14 40.41 12.42 69.42 48.46 69.00 26.09 62.83 77.06 58.83 59.48 x2 17.25 18.51 11.13 5.54 5.44 20.37 31.20 4.29 8.69 6.63 27.40 31.23 28.50 29.98 13.59 45.46 35.90 X3 .24 .20 .12 .12 .04 .05 .27 .10 .41 .04 .12 .08 .21 .17 .05 .16 .32 y 8.50 36.50 60.00 16.25 50.00 11.50 35.00 75.00 31.56 48.50 77.50 21.67 19.75 56.00 25.00 40.00 56.67 X1 9.00 20.64 81.40 18.92 50.32 21.33 46.85 65.94 38.68 51.19 59.42 24.64 26.94 46.20 26.86 20.00 62.52 X2 8.89 23.81 4.54 29.62 21.36 1.53 5.42 22.10 14.55 7.59 49.86 11.46 2.48 31.62 53.73 40.18 15.89 X3 .08 .24 .05 .72 .19 .10 .08 .09 .17 .13 .13 .21 .10 .26 43 .56 .05
7.55 The following variables were recorded for several counties in Minnesota in
1977:
y = average rent paid per acre of land with alfalfa
X₁ = - average rent paid per acre for all land
x₂ = average number of dairy cows per square mile
x3 = proportion of farmland in pasture
The data for 34 counties are given in Table 7.5 (Weisberg 1985, p. 162). Can
rent for alfalfa land be predicted from the other three variables?
(a) Find 3 and ².
(b) Find , and ß using Sex and sx as in (7.46) and (7.47).
(c) Find R² and R2.
Transcribed Image Text:7.55 The following variables were recorded for several counties in Minnesota in 1977: y = average rent paid per acre of land with alfalfa X₁ = - average rent paid per acre for all land x₂ = average number of dairy cows per square mile x3 = proportion of farmland in pasture The data for 34 counties are given in Table 7.5 (Weisberg 1985, p. 162). Can rent for alfalfa land be predicted from the other three variables? (a) Find 3 and ². (b) Find , and ß using Sex and sx as in (7.46) and (7.47). (c) Find R² and R2.
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