Page 552 Problem 1

1. Explore the relationship between the selling prices ( Y) and the appraised values ( X) of the 148 homes in the file P02_ 11. xlsx by estimating a simple linear regression model. Interpret the standard error of estimate s e and R2 and the least squares line for these data.
a. Is there evidence of a linear relationship between the selling price and appraised value? If so, characterize the relationship. Is it positive or negative? Is it weak or strong?
b. For which of the three remaining variables, the size of the home, the number of bedrooms, and the number of bathrooms, is the relationship with the home’s selling price stronger? Justify your choice with additional simple linear regression models.

2

>Source

This is fictitious data.

Data

,

0

1,

0

5

2

8,9

0,

0

00

4 4

3

0,

0

,

0

0

3 3

4

,700

,3

0

3 3

5

,300

,200

2 3

6

,0

,

0

10

3 2

7

,4

,

0

0

3 3

8

0

,590

3 4

9

,

0

,

0

0

4 4

10

,050

,250

2 3

11

,

0

3 3

12

0

,800

0

3 4

13

,

0

,060

1670 3 4

14

,040

,470

0

3 3

15

,010

,120

0

2 1

16

0

0

0

3 4

17

,

0

,

0

4 5

18

,300

,140

0

3 4

,230

0

2 3

20

0

,140

4 3

21

,

0

2 3

22

,610

4 4

23

0

,610

0

2 2

24

,050

0

4 3

25

0

4 3

26

,550

0

0

5 4

27

,500

5

4 4

28

,360

,990

3 3

29

,650

1650 3 3

30

2 2

,270

0

4 3

32

,860

4 4

,

0

3 3

34

,530

0

2 1

35

,070

0

3 4

36

,570

0

3 4

37

0

2 3

38

0

1700 3 2

39

4 4

40

,330

1590 2 2

41

0

3 2

42

3 2

43

0

,030

5 6

44

4 4

45

1730 2 1

46

,170

0

2 2

47

0

4 4

48

,

0

0

3 3

49

,

0

4 3

50

,930

,410

2 3

51

1700 3 3

52

2 3

53

1910 3 3

54

1610 2 1

55

,

1470 2 1

56

,540

3 4

57

1650 2 2

58

2 1

59

4 5

60

2 1

61

3 3

62

0

3 4

,340

2 1

64

0

3 4

65

1780 3 2

2 1

67

2040 4 4

68

5 4

69

2170 4 3

70

0

2 3

71

3 2

72

0

0

2 1

73

2100 5 6

74

1610 2 2

75

1950 4 4

76

5 4

77

0

3 2

78

,720

1920 4 4

79

1920 4 3

80

2 1

81

2 1

82

1650 3 2

83

4 5

84

3 4

85

1820 3 4

86

3 2

87

,070

1460 2 1

88

1530 3 2

89

2 3

90

1950 3 2

91

3 2

92

2050 4 4

93

3 2

1540 2 3

95

3 4

96

,830

2 1

97

3 4

98

,040

1700 3 3

99

4 5

100

1850 3 4

101

2 3

2 1

4 5

104

1890 4 4

105

133,270 1640 2 3

106

2070 3 3

107

1810 3 2

1460 2 1

109

1410 2 2

110

4 3

111

,890

3 4

112

3 3

113

1930 3 3

114

1930 4 5

115

1820 3 4

116

1480 2 1

117

1600 2 1

118 136,890

1880 3 2

119

1780 3 2

120

1920 3 2

121

1830 4 3

122

1470 2 3

123

3 4

124

1930 4 5

125

2 3

126

1530 2 2

127

2030 5 6

128

1830 3 3

129

2070 3 4

130

2 3

131

1580 3 2

132

3 4

133

1810 4 5

134

3 2

135

1890 3 3

136

1640 2 1

137

147,530

4 4

138

1730 3 3

139

4 3

140

1750 4 5

141

1660 3 3

142

5 6

143

1700 2 3

144

1660 3 4

145

4 5

146

1430 2 2

147

1710 4 5

148

1580 2 1

House Appraised Value Selling Price Square Feet Bedrooms Bathrooms
1 11 9 3 7 12 8 70 20 5 4
14 30 15 25 22
13 39 122 78 1

59
1

35 1

44 50 18 6
1

26 1

16 12

10
1

37 80 139 49 17
1

23 90 115 73 1

67
150,

83 1

40 1780
123 48 120 29 1

52
1

32 1

47 1830
148 21 152,2

60 1700
139,

53 144 1

72
114 34 107
140 147 1

65
1

36 135 1

61
140,

93 140,

24 1

57
132 42 129 89 1650
118 121 1

64
19 122,140 111 142
149,

82 1

45 2070
1

28 91 139,010 1610
134 129,340 1910
121,

99 113 1

41
150,500 141 1

86
142,

87 152,900 1990
1

55 157,

79 2

27
128 135,570 1

96
1

43 1

51 1820
119 120,530
122,570 118,640 1470
31 145 149,510 1

85
149,730 1

46 2170
33 147,700 143 88 1930
117 118,520 1

38
140,

130 146 1

81
136 135,350 1

76
130,440 121,

54 1530
118,130 132,

98
130,980 147,530 1980
131 128,490
141,

100 141,930 1

74
117,870 123,550 1730
160,

58 1

62 2100
151,100 157,390 2040
120,150 114,550
133 139,540 1

68
140,160 149,

92 2050
124 56 122,080 1

75
127 97 136,510 1870
101 109 1330
131,470 127,290
121,270 120,450 1460
143,550 151,960
136,890 132,540
106 110 114,330
137 141,320 1810
134,330 83,760
127,590 118,200 1520
137,440 140,200 1920
114,090 113,550 1410
145,460 156,520 2030
141,900 137,350 1

95
63 116 110,610 1340
149,200 153,

69 1850
141,810 153,330
66 116,440 111,950 1440
137,740 143,460
144,700 142,130 2160
149,660 155,460
118,170 135,440 1

71
137,660 127,300 1640
119,700 113,

77 138
143,120 141,110
129,910 130,080
141,780 139,350
159,190 160,030 2080
156,130 152,

84 1960
126 122,270
133,220 145,880
118,090 115,470 1490
141,630 135,720 1600
138,560 136,160
134,100 144,920 1890
132,240 131,290 1620
145,820 138,530
127,150 124,050 1750
105 107,900
127,200 123,450
111,560 111,700 1540
150,410 145,140
129,150 120,440 1480
130,310 136,870
129,230 140,300 1660
94 105,060 113,780
134,210 141,230 1720
109,250 104 1400
127,350 118,790 1578
104,010 112
133,940 137,270 1880
141,130 145,710
136,530 138,380 1430
102 118,040 109,460 1390
103 153,700 144,680 2130
126,310 133,270
134,020
141,560 150,380
142,960 135,260
108 118,530 112,600
121,590 114,230
146,400 153,240 2190
141,250 125 1580
130,730 135,620 1840
132,650 138,820
125,570 129,430
125,740 136,450
120,220 126,740
128,290 130,090
132,680
142,430 142,890
119,310 127,040
120,370 131,450
118,830 114,570
124,490 129,560 1690
140,570 149,550
133,620 140,820 1970
105,050 111,550
147,090 142,760
115,430 124,250
125,370 132,320
115,970 121,450 1630
125,210 132,450
130,370 135,830 1760
119,750 125,760
120,930 125,840 1710
126,800 135,320
118,820 120,140
144,080 2010
142,490 144,940
140,550 136,010 1770
130,360 119,330
124,270 131,150
167,730 172,360 2510
129,190 137,170
125,180 124,710
157,510 148,650 2110
126,670 128,520
137,570 132,020
133,460 128,030
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