Homework4 2019.docx-Stat 6214 Homework 4...
Homework4_2019.docx-Stat 6214 Homework 4 Due date:
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Homework4 2019.docx-Stat 6214 Homew...
Homework4_2019.docx-Stat 6214 Homework 4 Due date:
##### Page 1
Stat 6214
Homework 4
Due date: October.1
Name
15 points for each problem
Problem 1: According the following situation draw the graphs:
(You don’t need to draw the graphs from an actual data)
a.
There is a linear relationship between variable X and Y with uncorrelated errors.
b.
There is a linear relationship between variable X and Y with larger errors for large
X.
c.
There is a linear relationship between variable X and Y with a large outlier.
d.
There is almost no linear relationship between most pairs of X and Y, but there
exists a point making the data fitting a linear regression.
e.
There is no linear and also no non-linear relationship.
f.
There is a non-linear relation between X and Y with errors.
Problem 2,
a.
Read the following data in, generating an ID number, identify the unusual
observations and clarify as outliers, high-leverage, and/or high influential
observations
b.
What model should be used to mode the value Y?
Y
X1
X2
X3
X4
X5
X6
443
49
79
76
8
15
205
290
27
70
31
6
6
129
676
115
92
130
0
9
339
536
92
62
92
5
8
247
481
67
42
94
16
3
202
296
31
54
34
14
11
119
453
105
60
47
5
10
212
617
114
85
84
17
20
285
514
98
72
71
12
-1
242
400
15
59
99
15
11
174
473
62
62
81
9
1
207
157
25
11
7
9
9
45
440
45
65
84
19
13
195
480
92
75
63
9
20
232
316
27
26
82
4
17
134
530
111
52
93
11
13
256
610
78
102
84
5
7
266
617
106
87
82
18
7
276
600
97
98
71
12
8
266
480
67
65
62
13
12
196

##### Page 2
279
38
26
44
10
8
110
446
56
32
99
16
8
188
450
54
100
50
11
15
205
335
53
55
60
8
0
170
459
61
53
79
6
5
193
630
60
108
104
17
8
273
483
83
78
71
11
8
233
617
74
125
66
16
4
265
605
89
121
71
8
8
283
388
64
30
81
10
10
176
351
34
44
65
7
9
143
366
71
34
56
8
9
162
493
88
30
87
13
0
207
648
112
105
123
5
12
340
449
57
69
72
5
4
200
340
61
35
55
13
0
152
292
29
45
47
13
13
123
688
82
105
81
20
9
268
408
80
55
61
11
1
197
461
82
88
54
14
7
225
Problem 3
Consider the data used in Problem 2, suppose we use all six predictors X1 to X6 to fit
the linear regression model with Y as the outcome:
a.
What assumptions for using least squares seem to be violated?
b.
Compute residuals r
i
, C
i
, DFIT
i
, and h
i
. (residual, Cook’s D, DFFITS, Leverage)
c.
Construct the index plots for r
i
, C
i
, DFIT
i
, and h
i
d.
Identify the unusual observations in the data and identify the type of outliers.
e.
Using X1, X2 and X3 to fit a linear regression with the outcome Y.
f.
Should we add X4 to the model in e? If yes, keep it and justify your answer.
g.
Should we add X5 or X6 to the model in f? If yes, keep it and justify your answer.

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