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.
>Source
This is fictitious data. , 0
1, 0
5 8,9 0, 0
00
4 4 0, 0
, 0
0
3 3 ,700
,3 0
3 3 ,300
,200
2 3 ,0 , 0
10
3 2 ,4 , 0
0
3 3 0
,590
3 4 , 0
, 0
0
4 4 ,050
,250
2 3 , 0
3 3 0
,800
0
3 4 , 0
,060
1670 3 4 ,040
,470
0
3 3 ,010
,120
0
2 1 0
0
0
3 4 , 0
, 0
4 5 ,300
,140
0
3 4 ,230
0
2 3 0
,140
4 3 , 0
2 3 ,610
4 4 0
,610
0
2 2 ,050
0
4 3 0
4 3 ,550
0
0
5 4 ,500
5
4 4 ,360
,990
3 3 ,650
1650 3 3 2 2 ,270
0
4 3 ,860
4 4 , 0
3 3 ,530
0
2 1 ,070
0
3 4 ,570
0
3 4 0
2 3 0
1700 3 2 4 4 ,330
1590 2 2 0
3 2 3 2 0
,030
5 6 4 4 1730 2 1 ,170
0
2 2 0
4 4 , 0
0
3 3 , 0
4 3 ,930
,410
2 3 1700 3 3 2 3 1910 3 3 1610 2 1 , 1470 2 1 ,540
3 4 1650 2 2 2 1 4 5 2 1 3 3 0
3 4 ,340
2 1 0
3 4 1780 3 2 2 1 2040 4 4 5 4 2170 4 3 0
2 3 3 2 0
0
2 1 2100 5 6 1610 2 2 1950 4 4 5 4 0
3 2 ,720
1920 4 4 1920 4 3 2 1 2 1 1650 3 2 4 5 3 4 1820 3 4 3 2 ,070
1460 2 1 1530 3 2 2 3 1950 3 2 3 2 2050 4 4 3 2 1540 2 3 3 4 ,830
2 1 3 4 ,040
1700 3 3 4 5 1850 3 4 2 3 2 1 4 5 1890 4 4 133,270 1640 2 3 2070 3 3 1810 3 2 1460 2 1 1410 2 2 4 3 ,890
3 4 3 3 1930 3 3 1930 4 5 1820 3 4 1480 2 1 1600 2 1 1880 3 2 1780 3 2 1920 3 2 1830 4 3 1470 2 3 3 4 1930 4 5 2 3 1530 2 2 2030 5 6 1830 3 3 2070 3 4 2 3 1580 3 2 3 4 1810 4 5 3 2 1890 3 3 1640 2 1 147,530 4 4 1730 3 3 4 3 1750 4 5 1660 3 3 5 6 1700 2 3 1660 3 4 4 5 1430 2 2 1710 4 5 1580 2 1
2
Data
House
Appraised Value
Selling Price
Square Feet
Bedrooms
Bathrooms
1
11
9
3
7
12
8
70
20
5
4
2
14
30
15
25
22
3
13
39
122
78
1
59
4
1
35
1
44
50
18
6
5
1
26
1
16
12
10
6
1
37
80
139
49
17
7
1
23
90
115
73
1
67
8
150,
83
1
40
1780
9
123
48
120
29
1
52
10
1
32
1
47
1830
11
148
21
152,2
60
1700
12
139,
53
144
1
72
13
114
34
107
14
140
147
1
65
15
1
36
135
1
61
16
140,
93
140,
24
1
57
17
132
42
129
89
1650
18
118
121
1
64
19
122,140
111
142
20
149,
82
1
45
2070
21
1
28
91
139,010
1610
22
134
129,340
1910
23
121,
99
113
1
41
24
150,500
141
1
86
25
142,
87
152,900
1990
26
1
55
157,
79
2
27
27
128
135,570
1
96
28
1
43
1
51
1820
29
119
120,530
30
122,570
118,640
1470
31
145
149,510
1
85
32
149,730
1
46
2170
33
147,700
143
88
1930
34
117
118,520
1
38
35
140,
130
146
1
81
36
136
135,350
1
76
37
130,440
121,
54
1530
38
118,130
132,
98
39
130,980
147,530
1980
40
131
128,490
41
141,
100
141,930
1
74
42
117,870
123,550
1730
43
160,
58
1
62
2100
44
151,100
157,390
2040
45
120,150
114,550
46
133
139,540
1
68
47
140,160
149,
92
2050
48
124
56
122,080
1
75
49
127
97
136,510
1870
50
101
109
1330
51
131,470
127,290
52
121,270
120,450
1460
53
143,550
151,960
54
136,890
132,540
55
106
110
114,330
56
137
141,320
1810
57
134,330
83,760
58
127,590
118,200
1520
59
137,440
140,200
1920
60
114,090
113,550
1410
61
145,460
156,520
2030
62
141,900
137,350
1
95
63
116
110,610
1340
64
149,200
153,
69
1850
65
141,810
153,330
66
116,440
111,950
1440
67
137,740
143,460
68
144,700
142,130
2160
69
149,660
155,460
70
118,170
135,440
1
71
71
137,660
127,300
1640
72
119,700
113,
77
138
73
143,120
141,110
74
129,910
130,080
75
141,780
139,350
76
159,190
160,030
2080
77
156,130
152,
84
1960
78
126
122,270
79
133,220
145,880
80
118,090
115,470
1490
81
141,630
135,720
1600
82
138,560
136,160
83
134,100
144,920
1890
84
132,240
131,290
1620
85
145,820
138,530
86
127,150
124,050
1750
87
105
107,900
88
127,200
123,450
89
111,560
111,700
1540
90
150,410
145,140
91
129,150
120,440
1480
92
130,310
136,870
93
129,230
140,300
1660
94
105,060
113,780
95
134,210
141,230
1720
96
109,250
104
1400
97
127,350
118,790
1578
98
104,010
112
99
133,940
137,270
1880
100
141,130
145,710
101
136,530
138,380
1430
102
118,040
109,460
1390
103
153,700
144,680
2130
104
126,310
133,270
105
134,020
106
141,560
150,380
107
142,960
135,260
108
118,530
112,600
109
121,590
114,230
110
146,400
153,240
2190
111
141,250
125
1580
112
130,730
135,620
1840
113
132,650
138,820
114
125,570
129,430
115
125,740
136,450
116
120,220
126,740
117
128,290
130,090
118 136,890
132,680
119
142,430
142,890
120
119,310
127,040
121
120,370
131,450
122
118,830
114,570
123
124,490
129,560
1690
124
140,570
149,550
125
133,620
140,820
1970
126
105,050
111,550
127
147,090
142,760
128
115,430
124,250
129
125,370
132,320
130
115,970
121,450
1630
131
125,210
132,450
132
130,370
135,830
1760
133
119,750
125,760
134
120,930
125,840
1710
135
126,800
135,320
136
118,820
120,140
137
144,080
2010
138
142,490
144,940
139
140,550
136,010
1770
140
130,360
119,330
141
124,270
131,150
142
167,730
172,360
2510
143
129,190
137,170
144
125,180
124,710
145
157,510
148,650
2110
146
126,670
128,520
147
137,570
132,020
148
133,460
128,030
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