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statistics

 

 

Q1. [25] Let us consider the Hawkins-Bradu-Kass (1984) Data

 

Index
1 10.1 19.6 28.3 9.7
2 9.5 20.5 28.9 10.1
3 10.7 20.2 31.0 10.3
4 9.9 21.5 31.7 9.5
5 10.3 21a.1 31.1 10.0
6 10.8 20.4 29.2 10.0
7 10.5 20.9 29.1 10.8
8 9.9 19.6 28.8 10.3
9 9.7 20.7 31.0 9.6
10 9.3 19.7 30.3 9.9
11 11.0 24.0 35.0 -0.2
12 12.0 23.0 37.0 -0.4
13 12.0 26.0 34.0 0.7
14 11.0 34.0 34.0 0.1
15  3.4 2.9 2.1 -0.4
16 3.1 2.2 0.3 0.6
17 0.0 1.6 0.2 -0.2
18 2.3 1.6 2.0 0.0
19 0.8 2.9 1.6 0.1
20 3.1 3.4 2.2 0.4
21 2.6 2.2 1.9 0.9
22 0.4 3.2 1.9 0.3
23 2.0 2.3 0.8 -0.8
24 1.3 2.3 0.5 0.7
25 1.0 0.0 0.4 -0.3
26 0.9 3.3 2.5 -0.8
27 3.3 2.5 2.9 -0.7
28 1.8 0.8 2.0 0.3
29 1.2 0.9 0.8 0.3
30 1.2 0.7 3.4 -0.3
31 3.1 1.4 1.0 0.0
32 0.5 2.4 0.3 -0.4
33 1.5 3.1 1.5 -0.6
34 0.4 0.0 0.7 -0.7
35 3.1 2.4 3.0 0.3
36 1.1 2.2 2.7 -1.0
37 0.1 3.0 2.6 -0.6
38 1.5 1.2 0.2 0.9
39 2.1 0.0 1.2 -0.7
40 0.5 2.0 1.2 -0.5
41 3.4 1.6 2.9 -0.1
42 0.3 1.0 2.7 -0.7
43 0.1 3.3 0.9 0.6
44 1.8 0.5 3.2 -0.7
45 1.9 0.1 0.6 -0.5
46 1.8 0.5 3.0 -0.4
47 3.0 0.1 0.8 -0.9
48 3.1 1.6 3.0 0.1
49 3.1 2.5 1.9 0.9
50 2.1 2.8 2.9 -0.4
51 2.3 1.5 0.4 0.7
52 3.3 0.6 1.2 -0.5
53 0.3 0.4 3.3 0.7
54 1.1 3.0 0.3 0.7
55 0.5 2.4 0.9 0.0
56 1.8 3.2 0.9 0.1
57 1.8 0.7 0.7 0.7
58 2.4 3.4 1.5 -0.1
59 1.6 2.1 3.0 -0.3
60 0.3 1.5 3.3 -0.9
61 0.4 3.4 3.0 -0.3
62 0.9 0.1 0.3 0.6
63 1.1 2.7 0.2 -0.3
64 2.8 3.0 2.9 -0.9
65 2.0 0.7 2.7 0.6
66 0.2 1.8 0.8 -0.9
67 1.6 2.0 1.2 -0.7
68 0.1 0.0 1.1 0.6
69 2.0 0.6 0.3 0.2
70 1.0 2.2 2.9 0.7
71 2.2 2.5 2.3 0.2
72 0.6 2.0 1.5 -0.2
73 0.3 1.7 2.2 0.4
74 0.0 2.2 1.6 -0.9
75 0.3 0.4 2.6 0.2

 

  • [2] Fit the above data by the least squares method and compute the residuals.

 

 

  • [2] Use the normal probability plot of the residuals to comment on the normality of random errors.

 

 

  • [6] Compute the Jarque-Bera and the Rescaled Moments test for normality of errors and comment on your findings.

 

 

  • [2] Plot Y on . Which observations look unusual?

 

 

  • [2] Plot Y on . Which observations look unusual?

 

 

  • [2] Plot Y on . Which observations look unusual?

 

 

  • [2] Use Standardized and deleted Standardized residuals to identify outliers (if any).

 

 

  • [2] Use twice the mean rule and thrice the mean rule to identify high leverage points (if any).

 

 

  • [2] Use Cook’s distance and DFFITS to identify influential observations (if any).

 

 

  • [3] Do you think any of the above methods suffer from masking?
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