In: Statistics and Probability
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 |
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