stat 516 hw

STAT 516 – Spring 2023 – Homework 3
Due before class on Thursday, February 2nd
The file http://www.stat.sc.edu/~habing/courses/data/DATATAB_1_2_Complete.txt contains
the observations in Table 1.2 that have responses to all of the variables. The full data set
(which includes some incomplete observations) is described on pages 6-11 in the text.
(1) Make the scatterplot for predicting price from size (including the estimated regression line)
and the residual plots for that regression.
(2) Check the assumptions for the linear regression for predicting price from size based on
some or all of your graphs in (1). Be sure to clearly identify which graphs you used, what you
looked for, and why each particular assumption seemed to be met pretty well or not. It is ok,
for example, to annotate the graphs as a big part of your answer. If you are unable to check
one of the assumptions using those graphs, say what other graphs you would want and what
you would look for in them. (You do not need to make any missing graphs to actually check).
(3) Find an appropriate transformation to price for correcting the violation of assumption(s)
you noted in (2). Fit the linear regression using your transformation of price. Give the
estimated model equation and show from the residual plot that the assumptions are now met
(or at least much, much closer to being met).
(4) Give the 95% prediction interval for predicting the transformation of price you used in (3)
for a house with 1500 sq.ft. Use that interval to make a 95% prediction interval for price.
obs
1
2
3
4
5
6
8
9
10
11
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
30
31
33
35
36
37
38
39
40
41
42
43
44
45
46
47
48
zip
3
3
4
3
1
2
4
1
3
4
3
1
4
3
3
3
4
2
1
4
2
4
4
4
4
1
2
3
4
4
4
4
4
1
4
2
4
2
2
4
3
4
2
age
21
21
7
6
51
19
27
51
1
32
25
31
29
16
20
18
28
27
8
19
3
5
5
27
33
4
36
5
27
23
25
24
1
34
26
26
31
24
29
21
10
3
9
bed
3
3
1
3
3
3
3
2
3
3
2
3
3
3
3
4
3
3
3
3
3
3
4
3
2
3
3
4
4
4
3
4
3
3
4
3
3
4
5
3
3
3
3
bath
3
2
1
2
1
2
1
1
2
2
2
1.5
2
2
2
2
2
2
2
2
2
2
2
1.5
2
2
2.5
2.5
2
2.5
2
2
2.5
2
2
2
2
2.5
2.5
2
2
2
2.5
size
951
1036
676
1456
1186
1456
994
1176
1216
1410
1064
1770
1524
1750
1152
1770
1624
1540
1532
1647
1344
1550
1752
1450
1312
1636
1800
1972
2082
2463
2572
2113
2016
1852
2670
2336
1980
2483
2809
2036
2298
2038
2370
lot
exter garage fp
64904 other 0
0
217800
frame 0
54450 other 2
0
51836 other 0
1
10857 other 1
0
40075 frame 0
0
11016 frame 1
0
6259 frame 1
1
11348 other 0
0
25450 brick 0
0
218671
other 0
19602 brick 0
1
12720 brick 2
1
130680
frame 0
104544
other 2
10640 other 0
0
12700 brick 2
1
5679 brick 2
1
6900 brick 2
1
6900 brick 2
0
43560 other 1
0
6575 brick 2
1
8193 brick 2
0
11300 brick 1
1
7150 brick 0
1
6097 brick 1
0
83635 brick 2
1
7667 brick 2
0
13500 brick 3
1
10747 brick 2
1
7090 brick 2
1
7200 brick 2
1
9000 brick 2
1
13500 brick 2
0
9158 brick 2
1
5408 brick 0
1
8325 brick 2
1
10295 brick 2
1
15927 brick 2
1
16910 brick 2
1
10950 brick 2
1
7000 brick 2
0
10796 brick 2
1
price
30000
0
39900
46500
48600
51500
56990
62500
65500
69000
76900
0
79900
79950
82900
0
84900
0
85000
87900
89900
89900
93500
94900
95800
98500
99500
99900
102000
106000
109900
110000
114900
119900
119900
122900
123938
124900
126900
129900
132900
134900
135900
139500
139990
144900
147600
49
52
53
54
55
56
57
59
60
61
62
63
65
66
67
68
69
2
4
3
4
2
4
4
4
2
3
4
2
4
4
4
4
4
29
1
27
5
32
29
1
33
25
16
2
2
0
20
18
3
5
5
4
3
3
4
3
3
3
4
3
4
4
3
4
5
4
4
3.5
2
2
2.5
3.5
3
3
4
2.5
2.5
4.5
3.5
2.5
3
4
4.5
3.5
2921
2436
1920
2949
3310
2805
2553
3627
3056
3045
3253
4106
2992
3055
3846
3314
3472
11992 brick
52000 brick
226512
11950 brick
10500 brick
16500 brick
8610 brick
17760 brick
10400 other
168576
54362 brick
44737 brick
14500 other
250034
23086 brick
43734 brick
130723
2
1
2
1
frame 4
2
1
2
1
2
1
2
1
3
1
2
1
brick 3
3
2
3
1
3
1
brick 3
4
3
3
1
brick 2
149990
164000
1
167500
169900
175000
179000
179900
199000
216000
1
229900
285000
328900
327300
0
349900
370000
380000
2
395000