Question

In: Statistics and Probability

Plot the data on air travel delays. Can you see seasonal patterns? Explain. Use Megastat to...

Plot the data on air travel delays. Can you see seasonal patterns? Explain. Use Megastat to calculate estimated seasonal indices and trend. Which months have the most delays? The fewest? Is this logical? Is there a trend in the deseasonalized data?

National Airspace Total System Delays, 2002-2006
Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2002 14,158 13,821 20,020 24,027 28,533 33,770 32,304 29,056 24,493 25,266 17,712 22,489
2003 16,159 18,260 25,387 17,474 26,544 27,413 32,833 37,066 28,882 21,422 34,116 31,332
2004 28,104 32,274 34,001 32,459 50,800 52,121 46,894 43,770 30,412 37,271 35,234 32,446
2005 32,121 30,176 34,633 25,887 30,920 48,922 58,471 45,328 32,949 34,221 34,273 29,766
2006 29,463 24,705 37,218 35,132 40,669 48,096 47,606 46,547 48,092 51,053 43,482

39,797

In Column Format
Year Month Delays
2002 Jan 14158
Feb 13821
Mar 20020
Apr 24027
May 28533
Jun 33770
Jul 32304
Aug 29056
Sep 24493
Oct 25266
Nov 17712
Dec 22489
2003 Jan 16159
Feb 18260
Mar 25387
Apr 17474
May 26544
Jun 27413
Jul 32833
Aug 37066
Sep 28882
Oct 21422
Nov 34116
Dec 31332
2004 Jan 28104
Feb 32274
Mar 34001
Apr 32459
May 50800
Jun 52121
Jul 46894
Aug 43770
Sep 30412
Oct 37271
Nov 35234
Dec 32446
2005 Jan 32121
Feb 30176
Mar 34633
Apr 25887
May 30920
Jun 48922
Jul 58471
Aug 45328
Sep 32949
Oct 34221
Nov 34273
Dec 29766
2006 Jan 29463
Feb 24705
Mar 37218
Apr 35132
May 40669
Jun 48096
Jul 47606
Aug 46547
Sep 48092
Oct 51053
Nov 43482
Dec 39797

Solutions

Expert Solution

The plot using Megastat is:

Yes, the seasonal patterns are observed.

The seasonal indexes are:

Centered
Moving Ratio to Seasonal Delays
t Year Quarter Delays Average CMA Indexes Deseasonalized
1 1 1 14,158 0.946 14,961.9
2 1 2 13,821 1.003 13,779.3
3 1 3 20,020 19803.38 1.011 1.073 18,663.8
4 1 4 24,027 24093.88 0.997 0.978 24,566.4
5 2 1 28,533 28123.00 1.015 0.946 30,153.2
6 2 2 33,770 30287.13 1.115 1.003 33,668.2
7 2 3 32,304 30410.75 1.062 1.073 30,115.7
8 2 4 29,056 28842.75 1.007 0.978 29,708.2
9 3 1 24,493 25955.75 0.944 0.946 25,883.8
10 3 2 25,266 23310.88 1.084 1.003 25,189.8
11 3 3 17,712 21448.25 0.826 1.073 16,512.2
12 3 4 22,489 19530.75 1.151 0.978 22,993.8
13 4 1 16,159 19614.38 0.824 0.946 17,076.5
14 4 2 18,260 19946.88 0.915 1.003 18,205.0
15 4 3 25,387 20618.13 1.231 1.073 23,667.3
16 4 4 17,474 23060.38 0.758 0.978 17,866.3
17 5 1 26,544 25135.25 1.056 0.946 28,051.2
18 5 2 27,413 28515.00 0.961 1.003 27,330.4
19 5 3 32,833 31256.25 1.050 1.073 30,608.9
20 5 4 37,066 30799.63 1.203 0.978 37,898.1
21 6 1 28,882 30211.13 0.956 0.946 30,522.0
22 6 2 21,422 29654.75 0.722 1.003 21,357.4
23 6 3 34,116 28840.75 1.183 1.073 31,805.0
24 6 4 31,332 30100.00 1.041 0.978 32,035.3
25 7 1 28,104 31442.13 0.894 0.946 29,699.8
26 7 2 32,274 31568.63 1.022 1.003 32,176.7
27 7 3 34,001 34546.50 0.984 1.073 31,697.7
28 7 4 32,459 39864.38 0.814 0.978 33,187.6
29 8 1 50,800 43956.88 1.156 0.946 53,684.5
30 8 2 52,121 46982.38 1.109 1.003 51,963.9
31 8 3 46,894 45847.75 1.023 1.073 43,717.4
32 8 4 43,770 41443.00 1.056 0.978 44,752.5
33 9 1 30,412 38129.25 0.798 0.946 32,138.9
34 9 2 37,271 35256.25 1.057 1.003 37,158.6
35 9 3 35,234 34054.38 1.035 1.073 32,847.2
36 9 4 32,446 33381.13 0.972 0.978 33,174.3
37 10 1 32,121 32419.13 0.991 0.946 33,944.9
38 10 2 30,176 31524.13 0.957 1.003 30,085.0
39 10 3 34,633 30554.13 1.133 1.073 32,286.9
40 10 4 25,887 32747.25 0.791 0.978 26,468.1
41 11 1 30,920 38070.25 0.812 0.946 32,675.7
42 11 2 48,922 43480.13 1.125 1.003 48,774.5
43 11 3 58,471 46163.88 1.267 1.073 54,510.1
44 11 4 45,328 44579.88 1.017 0.978 46,345.5
45 12 1 32,949 39717.50 0.830 0.946 34,819.9
46 12 2 34,221 34747.50 0.985 1.003 34,117.8
47 12 3 34,273 32366.50 1.059 1.073 31,951.3
48 12 4 29,766 30741.25 0.968 0.978 30,434.2
49 13 1 29,463 29919.88 0.985 0.946 31,136.0
50 13 2 24,705 30958.75 0.798 1.003 24,630.5
51 13 3 37,218 33030.25 1.127 1.073 34,696.8
52 13 4 35,132 37354.88 0.940 0.978 35,920.6
53 14 1 40,669 41577.25 0.978 0.946 42,978.3
54 14 2 48,096 44302.63 1.086 1.003 47,951.0
55 14 3 47,606 46657.38 1.020 1.073 44,381.1
56 14 4 46,547 47954.88 0.971 0.978 47,591.9
57 15 1 48,092 47809.00 1.006 0.946 50,822.8
58 15 2 51,053 46449.75 1.099 1.003 50,899.1
59 15 3 43,482 1.073 40,536.5
60 15 4 39,797 0.978 40,690.4
Calculation of Seasonal Indexes
1 2 3 4
1 1.011 0.997
2 1.015 1.115 1.062 1.007
3 0.944 1.084 0.826 1.151
4 0.824 0.915 1.231 0.758
5 1.056 0.961 1.050 1.203
6 0.956 0.722 1.183 1.041
7 0.894 1.022 0.984 0.814
8 1.156 1.109 1.023 1.056
9 0.798 1.057 1.035 0.972
10 0.991 0.957 1.133 0.791
11 0.812 1.125 1.267 1.017
12 0.830 0.985 1.059 0.968
13 0.985 0.798 1.127 0.940
14 0.978 1.086 1.020 0.971
15 1.006 1.099
mean: 0.946 1.003 1.072 0.978 3.998
adjusted: 0.946 1.003 1.073 0.978 4.000

Which months have the most delays?

July 2005, May 2004

The fewest?

February 2002, January 2002

Is this logical?

Yes

Is there a trend in the deseasonalized data?

Yes


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