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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Dec 2011 11:16:34 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/21/t13244842689axiefe94tiphsy.htm/, Retrieved Tue, 07 May 2024 09:14:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158861, Retrieved Tue, 07 May 2024 09:14:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact66

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [gemiddelde consum...] [2011-12-21 16:16:34] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20,98	
20,1	
20,61	
20,27	
20,08	
23,58	
22,31	
22,89	
21,78	
22,19	
22,58	
22,78	
25,06	
25,16	
25,47	
25,34	
24,2	
25,32	
25,57	
25,76	
24,79	
23,14	
22,66	
22,06	
24,26	
23,15	
22,92	
21,43	
21,56	
23,48	
24,35	
24,83	
24,19	
23,58	
23,58	
24,35	
27,18	
25,69	
24,81	
23,26	
23,49	
26,86	
27,12	
27,66	
26,26	
25,51	
24,63	
23,57	
27,63	
25,85	
26,09	
24,47	
24,19	
25,09	
25,26	
25,58	
24,76	
25,02	
24,24	
24,14	
28,69	
26,74	
26,48	
24,45	
23,88	
26,58	
26,23	
28,63	
26,81	
26,56	
26,64	
26,8	
28,37	
27,13	
28,44	
28,62	
27,28	
31,32	
31,26	
31,41	
31,76	
32,72	
32,15	
33,62	
35,97	
33,78	
33,77	
32,75	
32,55	
33,22	
32,88	
31,56	
30,27	
28,65	
27,89	
27,07	
30,8	
28,38	
27,5	
28	
28,02	
29,2	
27,59	
27,22	
27,16	
26,31	
25,67	
26,41	
28,34	
25,43	
23,72	
23,33	
23,8	
27,7	
26,28	
27,51	
27,93	
28,76	
28,65	
29,52	
31,23	
27,9	
27,87	
27,52	
27,59	
31,2	
30,22	
30,62	
31,52	
30,59	
31,42	
31,95

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158861&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158861&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158861&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.883697961283497
beta0.00882745161237523
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.883697961283497 \tabularnewline
beta & 0.00882745161237523 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158861&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.883697961283497[/C][/ROW]
[ROW][C]beta[/C][C]0.00882745161237523[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158861&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158861&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.883697961283497
beta0.00882745161237523
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325.0623.09880815695161.96119184304838
1425.1624.9492827768290.210717223171009
1525.4725.473859846772-0.00385984677201989
1625.3425.4510460200678-0.111046020067842
1724.224.4370230190868-0.237023019086763
1825.3225.6539975567251-0.33399755672508
1925.5725.40354129529020.166458704709775
2025.7626.0419638133318-0.281963813331792
2124.7924.34996790103110.440032098968899
2223.1425.0117421273316-1.87174212733159
2322.6623.6250689005515-0.965068900551469
2422.0622.9743395906984-0.91433959069845
2524.2624.6475627138803-0.387562713880271
2623.1524.1940641234365-1.04406412343653
2722.9223.5370810281972-0.617081028197159
2821.4322.94053609459-1.51053609458998
2921.5620.79357325496170.76642674503826
3023.4822.70497933555740.775020664442589
3124.3523.46224507314130.887754926858751
3224.8324.63918871410090.190811285899144
3324.1923.4757426116720.714257388327976
3423.5824.0732796841068-0.49327968410682
3523.5823.9895030049296-0.409503004929636
3624.3523.81552927750720.53447072249276
3727.1827.05690840753120.123091592468821
3825.6926.9211339291789-1.23113392917886
3924.8126.1540786875378-1.34407868753778
4023.2624.7579968954193-1.49799689541933
4123.4922.80625898869860.683741011301379
4226.8624.72154207828832.13845792171166
4327.1226.6764535900830.443546409917001
4427.6627.38709365638740.272906343612643
4526.2626.18595120306240.0740487969375891
4625.5126.0369791704932-0.526979170493149
4724.6325.938685283188-1.30868528318796
4823.5725.0701229371475-1.50012293714751
4927.6326.37303791033721.25696208966283
5025.8527.0467069658531-1.1967069658531
5126.0926.2686856462755-0.178685646275518
5224.4725.8384627578757-1.36846275787571
5324.1924.2076352355798-0.0176352355797746
5425.0925.674294511085-0.584294511084952
5525.2625.01011230368240.249887696317607
5625.5825.48529467050670.094705329493312
5724.7624.19250837877250.567491621227528
5825.0224.40449740370290.615502596297109
5924.2425.1912123764076-0.951212376407575
6024.1424.583235583678-0.443235583677964
6128.6927.19041545703951.49958454296045
6226.7427.7430830346453-1.0030830346453
6326.4827.2490426129749-0.769042612974875
6424.4526.1226660252037-1.67266602520368
6523.8824.3579968564897-0.477996856489749
6626.5825.31420146504341.26579853495657
6726.2326.3594405330033-0.129440533003262
6828.6326.47078128843272.15921871156733
6926.8126.8946882973538-0.0846882973538143
7026.5626.49375938036770.0662406196323069
7126.6426.59529351543680.0447064845632106
7226.826.9383525759331-0.138352575933141
7328.3730.3719565217112-2.0019565217112
7427.1327.5180349916875-0.388034991687526
7528.4427.57937199256660.860628007433448
7628.6227.71974795593250.900252044067521
7727.2828.3291712828706-1.04917128287057
7831.3229.19522905975652.12477094024345
7931.2630.78438024347250.475619756527511
8031.4131.7577427014818-0.347742701481824
8131.7629.51808030977522.24191969022476
8232.7231.12541238680731.59458761319273
8332.1532.5753423617925-0.425342361792467
8433.6232.53099769576371.08900230423633
8535.9737.6401896735595-1.6701896735595
8633.7835.0135167487711-1.23351674877114
8733.7734.5992519061968-0.829251906196795
8832.7533.1188594344454-0.368859434445355
8932.5532.30169472493910.248305275060879
9033.2235.0698470300967-1.84984703009672
9132.8832.9025667648813-0.0225667648813399
9231.5633.3431708742486-1.78317087424857
9330.2730.07968176562420.190318234375844
9428.6529.7878453054792-1.13784530547916
9527.8928.5821177837876-0.692117783787619
9627.0728.379371998322-1.30937199832203
9730.830.276538196010.523461803990003
9828.3829.7631734848052-1.38317348480515
9927.529.1168146307797-1.6168146307797
1002827.08479975125550.91520024874448
10128.0227.50583319102240.514166808977581
10229.229.899552042766-0.699552042765998
10327.5928.9706613870233-1.38066138702325
10427.2227.9260090984987-0.706009098498729
10527.1626.01254404443941.14745595556055
10626.3126.4491528518359-0.139152851835913
10725.6726.1663602539045-0.496360253904474
10826.4126.01122705121070.398772948789265
10928.3429.5263517387389-1.18635173873886
11025.4327.3418194874131-1.91181948741312
11123.7226.1150290004965-2.39502900049654
11223.3323.6993045163837-0.369304516383703
11323.822.9794659094670.820534090533044
11427.725.19399872347542.50600127652464
11526.2827.0162251604079-0.736225160407855
11627.5126.58868180596550.921318194034491
11727.9326.30507182298291.62492817701711
11828.7626.9887984744341.77120152556603
11928.6528.33155102768370.318448972316347
12029.5229.04452233807390.475477661926128
12131.2332.7822491662074-1.55224916620742
12227.930.0410368877134-2.14103688771344
12327.8728.5711011252227-0.701101125222728
12427.5227.8833745507818-0.363374550781753
12527.5927.26513717618260.324862823817387
12631.229.48137259189721.7186274081028
12730.2230.13713976085350.0828602391464521
12830.6230.688867675378-0.0688676753780264
12931.5229.48571122627312.03428877372691
13030.5930.44775063392160.142249366078417
13131.4230.15095794475721.2690420552428
13231.9531.75981632326110.190183676738879

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 25.06 & 23.0988081569516 & 1.96119184304838 \tabularnewline
14 & 25.16 & 24.949282776829 & 0.210717223171009 \tabularnewline
15 & 25.47 & 25.473859846772 & -0.00385984677201989 \tabularnewline
16 & 25.34 & 25.4510460200678 & -0.111046020067842 \tabularnewline
17 & 24.2 & 24.4370230190868 & -0.237023019086763 \tabularnewline
18 & 25.32 & 25.6539975567251 & -0.33399755672508 \tabularnewline
19 & 25.57 & 25.4035412952902 & 0.166458704709775 \tabularnewline
20 & 25.76 & 26.0419638133318 & -0.281963813331792 \tabularnewline
21 & 24.79 & 24.3499679010311 & 0.440032098968899 \tabularnewline
22 & 23.14 & 25.0117421273316 & -1.87174212733159 \tabularnewline
23 & 22.66 & 23.6250689005515 & -0.965068900551469 \tabularnewline
24 & 22.06 & 22.9743395906984 & -0.91433959069845 \tabularnewline
25 & 24.26 & 24.6475627138803 & -0.387562713880271 \tabularnewline
26 & 23.15 & 24.1940641234365 & -1.04406412343653 \tabularnewline
27 & 22.92 & 23.5370810281972 & -0.617081028197159 \tabularnewline
28 & 21.43 & 22.94053609459 & -1.51053609458998 \tabularnewline
29 & 21.56 & 20.7935732549617 & 0.76642674503826 \tabularnewline
30 & 23.48 & 22.7049793355574 & 0.775020664442589 \tabularnewline
31 & 24.35 & 23.4622450731413 & 0.887754926858751 \tabularnewline
32 & 24.83 & 24.6391887141009 & 0.190811285899144 \tabularnewline
33 & 24.19 & 23.475742611672 & 0.714257388327976 \tabularnewline
34 & 23.58 & 24.0732796841068 & -0.49327968410682 \tabularnewline
35 & 23.58 & 23.9895030049296 & -0.409503004929636 \tabularnewline
36 & 24.35 & 23.8155292775072 & 0.53447072249276 \tabularnewline
37 & 27.18 & 27.0569084075312 & 0.123091592468821 \tabularnewline
38 & 25.69 & 26.9211339291789 & -1.23113392917886 \tabularnewline
39 & 24.81 & 26.1540786875378 & -1.34407868753778 \tabularnewline
40 & 23.26 & 24.7579968954193 & -1.49799689541933 \tabularnewline
41 & 23.49 & 22.8062589886986 & 0.683741011301379 \tabularnewline
42 & 26.86 & 24.7215420782883 & 2.13845792171166 \tabularnewline
43 & 27.12 & 26.676453590083 & 0.443546409917001 \tabularnewline
44 & 27.66 & 27.3870936563874 & 0.272906343612643 \tabularnewline
45 & 26.26 & 26.1859512030624 & 0.0740487969375891 \tabularnewline
46 & 25.51 & 26.0369791704932 & -0.526979170493149 \tabularnewline
47 & 24.63 & 25.938685283188 & -1.30868528318796 \tabularnewline
48 & 23.57 & 25.0701229371475 & -1.50012293714751 \tabularnewline
49 & 27.63 & 26.3730379103372 & 1.25696208966283 \tabularnewline
50 & 25.85 & 27.0467069658531 & -1.1967069658531 \tabularnewline
51 & 26.09 & 26.2686856462755 & -0.178685646275518 \tabularnewline
52 & 24.47 & 25.8384627578757 & -1.36846275787571 \tabularnewline
53 & 24.19 & 24.2076352355798 & -0.0176352355797746 \tabularnewline
54 & 25.09 & 25.674294511085 & -0.584294511084952 \tabularnewline
55 & 25.26 & 25.0101123036824 & 0.249887696317607 \tabularnewline
56 & 25.58 & 25.4852946705067 & 0.094705329493312 \tabularnewline
57 & 24.76 & 24.1925083787725 & 0.567491621227528 \tabularnewline
58 & 25.02 & 24.4044974037029 & 0.615502596297109 \tabularnewline
59 & 24.24 & 25.1912123764076 & -0.951212376407575 \tabularnewline
60 & 24.14 & 24.583235583678 & -0.443235583677964 \tabularnewline
61 & 28.69 & 27.1904154570395 & 1.49958454296045 \tabularnewline
62 & 26.74 & 27.7430830346453 & -1.0030830346453 \tabularnewline
63 & 26.48 & 27.2490426129749 & -0.769042612974875 \tabularnewline
64 & 24.45 & 26.1226660252037 & -1.67266602520368 \tabularnewline
65 & 23.88 & 24.3579968564897 & -0.477996856489749 \tabularnewline
66 & 26.58 & 25.3142014650434 & 1.26579853495657 \tabularnewline
67 & 26.23 & 26.3594405330033 & -0.129440533003262 \tabularnewline
68 & 28.63 & 26.4707812884327 & 2.15921871156733 \tabularnewline
69 & 26.81 & 26.8946882973538 & -0.0846882973538143 \tabularnewline
70 & 26.56 & 26.4937593803677 & 0.0662406196323069 \tabularnewline
71 & 26.64 & 26.5952935154368 & 0.0447064845632106 \tabularnewline
72 & 26.8 & 26.9383525759331 & -0.138352575933141 \tabularnewline
73 & 28.37 & 30.3719565217112 & -2.0019565217112 \tabularnewline
74 & 27.13 & 27.5180349916875 & -0.388034991687526 \tabularnewline
75 & 28.44 & 27.5793719925666 & 0.860628007433448 \tabularnewline
76 & 28.62 & 27.7197479559325 & 0.900252044067521 \tabularnewline
77 & 27.28 & 28.3291712828706 & -1.04917128287057 \tabularnewline
78 & 31.32 & 29.1952290597565 & 2.12477094024345 \tabularnewline
79 & 31.26 & 30.7843802434725 & 0.475619756527511 \tabularnewline
80 & 31.41 & 31.7577427014818 & -0.347742701481824 \tabularnewline
81 & 31.76 & 29.5180803097752 & 2.24191969022476 \tabularnewline
82 & 32.72 & 31.1254123868073 & 1.59458761319273 \tabularnewline
83 & 32.15 & 32.5753423617925 & -0.425342361792467 \tabularnewline
84 & 33.62 & 32.5309976957637 & 1.08900230423633 \tabularnewline
85 & 35.97 & 37.6401896735595 & -1.6701896735595 \tabularnewline
86 & 33.78 & 35.0135167487711 & -1.23351674877114 \tabularnewline
87 & 33.77 & 34.5992519061968 & -0.829251906196795 \tabularnewline
88 & 32.75 & 33.1188594344454 & -0.368859434445355 \tabularnewline
89 & 32.55 & 32.3016947249391 & 0.248305275060879 \tabularnewline
90 & 33.22 & 35.0698470300967 & -1.84984703009672 \tabularnewline
91 & 32.88 & 32.9025667648813 & -0.0225667648813399 \tabularnewline
92 & 31.56 & 33.3431708742486 & -1.78317087424857 \tabularnewline
93 & 30.27 & 30.0796817656242 & 0.190318234375844 \tabularnewline
94 & 28.65 & 29.7878453054792 & -1.13784530547916 \tabularnewline
95 & 27.89 & 28.5821177837876 & -0.692117783787619 \tabularnewline
96 & 27.07 & 28.379371998322 & -1.30937199832203 \tabularnewline
97 & 30.8 & 30.27653819601 & 0.523461803990003 \tabularnewline
98 & 28.38 & 29.7631734848052 & -1.38317348480515 \tabularnewline
99 & 27.5 & 29.1168146307797 & -1.6168146307797 \tabularnewline
100 & 28 & 27.0847997512555 & 0.91520024874448 \tabularnewline
101 & 28.02 & 27.5058331910224 & 0.514166808977581 \tabularnewline
102 & 29.2 & 29.899552042766 & -0.699552042765998 \tabularnewline
103 & 27.59 & 28.9706613870233 & -1.38066138702325 \tabularnewline
104 & 27.22 & 27.9260090984987 & -0.706009098498729 \tabularnewline
105 & 27.16 & 26.0125440444394 & 1.14745595556055 \tabularnewline
106 & 26.31 & 26.4491528518359 & -0.139152851835913 \tabularnewline
107 & 25.67 & 26.1663602539045 & -0.496360253904474 \tabularnewline
108 & 26.41 & 26.0112270512107 & 0.398772948789265 \tabularnewline
109 & 28.34 & 29.5263517387389 & -1.18635173873886 \tabularnewline
110 & 25.43 & 27.3418194874131 & -1.91181948741312 \tabularnewline
111 & 23.72 & 26.1150290004965 & -2.39502900049654 \tabularnewline
112 & 23.33 & 23.6993045163837 & -0.369304516383703 \tabularnewline
113 & 23.8 & 22.979465909467 & 0.820534090533044 \tabularnewline
114 & 27.7 & 25.1939987234754 & 2.50600127652464 \tabularnewline
115 & 26.28 & 27.0162251604079 & -0.736225160407855 \tabularnewline
116 & 27.51 & 26.5886818059655 & 0.921318194034491 \tabularnewline
117 & 27.93 & 26.3050718229829 & 1.62492817701711 \tabularnewline
118 & 28.76 & 26.988798474434 & 1.77120152556603 \tabularnewline
119 & 28.65 & 28.3315510276837 & 0.318448972316347 \tabularnewline
120 & 29.52 & 29.0445223380739 & 0.475477661926128 \tabularnewline
121 & 31.23 & 32.7822491662074 & -1.55224916620742 \tabularnewline
122 & 27.9 & 30.0410368877134 & -2.14103688771344 \tabularnewline
123 & 27.87 & 28.5711011252227 & -0.701101125222728 \tabularnewline
124 & 27.52 & 27.8833745507818 & -0.363374550781753 \tabularnewline
125 & 27.59 & 27.2651371761826 & 0.324862823817387 \tabularnewline
126 & 31.2 & 29.4813725918972 & 1.7186274081028 \tabularnewline
127 & 30.22 & 30.1371397608535 & 0.0828602391464521 \tabularnewline
128 & 30.62 & 30.688867675378 & -0.0688676753780264 \tabularnewline
129 & 31.52 & 29.4857112262731 & 2.03428877372691 \tabularnewline
130 & 30.59 & 30.4477506339216 & 0.142249366078417 \tabularnewline
131 & 31.42 & 30.1509579447572 & 1.2690420552428 \tabularnewline
132 & 31.95 & 31.7598163232611 & 0.190183676738879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158861&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]25.06[/C][C]23.0988081569516[/C][C]1.96119184304838[/C][/ROW]
[ROW][C]14[/C][C]25.16[/C][C]24.949282776829[/C][C]0.210717223171009[/C][/ROW]
[ROW][C]15[/C][C]25.47[/C][C]25.473859846772[/C][C]-0.00385984677201989[/C][/ROW]
[ROW][C]16[/C][C]25.34[/C][C]25.4510460200678[/C][C]-0.111046020067842[/C][/ROW]
[ROW][C]17[/C][C]24.2[/C][C]24.4370230190868[/C][C]-0.237023019086763[/C][/ROW]
[ROW][C]18[/C][C]25.32[/C][C]25.6539975567251[/C][C]-0.33399755672508[/C][/ROW]
[ROW][C]19[/C][C]25.57[/C][C]25.4035412952902[/C][C]0.166458704709775[/C][/ROW]
[ROW][C]20[/C][C]25.76[/C][C]26.0419638133318[/C][C]-0.281963813331792[/C][/ROW]
[ROW][C]21[/C][C]24.79[/C][C]24.3499679010311[/C][C]0.440032098968899[/C][/ROW]
[ROW][C]22[/C][C]23.14[/C][C]25.0117421273316[/C][C]-1.87174212733159[/C][/ROW]
[ROW][C]23[/C][C]22.66[/C][C]23.6250689005515[/C][C]-0.965068900551469[/C][/ROW]
[ROW][C]24[/C][C]22.06[/C][C]22.9743395906984[/C][C]-0.91433959069845[/C][/ROW]
[ROW][C]25[/C][C]24.26[/C][C]24.6475627138803[/C][C]-0.387562713880271[/C][/ROW]
[ROW][C]26[/C][C]23.15[/C][C]24.1940641234365[/C][C]-1.04406412343653[/C][/ROW]
[ROW][C]27[/C][C]22.92[/C][C]23.5370810281972[/C][C]-0.617081028197159[/C][/ROW]
[ROW][C]28[/C][C]21.43[/C][C]22.94053609459[/C][C]-1.51053609458998[/C][/ROW]
[ROW][C]29[/C][C]21.56[/C][C]20.7935732549617[/C][C]0.76642674503826[/C][/ROW]
[ROW][C]30[/C][C]23.48[/C][C]22.7049793355574[/C][C]0.775020664442589[/C][/ROW]
[ROW][C]31[/C][C]24.35[/C][C]23.4622450731413[/C][C]0.887754926858751[/C][/ROW]
[ROW][C]32[/C][C]24.83[/C][C]24.6391887141009[/C][C]0.190811285899144[/C][/ROW]
[ROW][C]33[/C][C]24.19[/C][C]23.475742611672[/C][C]0.714257388327976[/C][/ROW]
[ROW][C]34[/C][C]23.58[/C][C]24.0732796841068[/C][C]-0.49327968410682[/C][/ROW]
[ROW][C]35[/C][C]23.58[/C][C]23.9895030049296[/C][C]-0.409503004929636[/C][/ROW]
[ROW][C]36[/C][C]24.35[/C][C]23.8155292775072[/C][C]0.53447072249276[/C][/ROW]
[ROW][C]37[/C][C]27.18[/C][C]27.0569084075312[/C][C]0.123091592468821[/C][/ROW]
[ROW][C]38[/C][C]25.69[/C][C]26.9211339291789[/C][C]-1.23113392917886[/C][/ROW]
[ROW][C]39[/C][C]24.81[/C][C]26.1540786875378[/C][C]-1.34407868753778[/C][/ROW]
[ROW][C]40[/C][C]23.26[/C][C]24.7579968954193[/C][C]-1.49799689541933[/C][/ROW]
[ROW][C]41[/C][C]23.49[/C][C]22.8062589886986[/C][C]0.683741011301379[/C][/ROW]
[ROW][C]42[/C][C]26.86[/C][C]24.7215420782883[/C][C]2.13845792171166[/C][/ROW]
[ROW][C]43[/C][C]27.12[/C][C]26.676453590083[/C][C]0.443546409917001[/C][/ROW]
[ROW][C]44[/C][C]27.66[/C][C]27.3870936563874[/C][C]0.272906343612643[/C][/ROW]
[ROW][C]45[/C][C]26.26[/C][C]26.1859512030624[/C][C]0.0740487969375891[/C][/ROW]
[ROW][C]46[/C][C]25.51[/C][C]26.0369791704932[/C][C]-0.526979170493149[/C][/ROW]
[ROW][C]47[/C][C]24.63[/C][C]25.938685283188[/C][C]-1.30868528318796[/C][/ROW]
[ROW][C]48[/C][C]23.57[/C][C]25.0701229371475[/C][C]-1.50012293714751[/C][/ROW]
[ROW][C]49[/C][C]27.63[/C][C]26.3730379103372[/C][C]1.25696208966283[/C][/ROW]
[ROW][C]50[/C][C]25.85[/C][C]27.0467069658531[/C][C]-1.1967069658531[/C][/ROW]
[ROW][C]51[/C][C]26.09[/C][C]26.2686856462755[/C][C]-0.178685646275518[/C][/ROW]
[ROW][C]52[/C][C]24.47[/C][C]25.8384627578757[/C][C]-1.36846275787571[/C][/ROW]
[ROW][C]53[/C][C]24.19[/C][C]24.2076352355798[/C][C]-0.0176352355797746[/C][/ROW]
[ROW][C]54[/C][C]25.09[/C][C]25.674294511085[/C][C]-0.584294511084952[/C][/ROW]
[ROW][C]55[/C][C]25.26[/C][C]25.0101123036824[/C][C]0.249887696317607[/C][/ROW]
[ROW][C]56[/C][C]25.58[/C][C]25.4852946705067[/C][C]0.094705329493312[/C][/ROW]
[ROW][C]57[/C][C]24.76[/C][C]24.1925083787725[/C][C]0.567491621227528[/C][/ROW]
[ROW][C]58[/C][C]25.02[/C][C]24.4044974037029[/C][C]0.615502596297109[/C][/ROW]
[ROW][C]59[/C][C]24.24[/C][C]25.1912123764076[/C][C]-0.951212376407575[/C][/ROW]
[ROW][C]60[/C][C]24.14[/C][C]24.583235583678[/C][C]-0.443235583677964[/C][/ROW]
[ROW][C]61[/C][C]28.69[/C][C]27.1904154570395[/C][C]1.49958454296045[/C][/ROW]
[ROW][C]62[/C][C]26.74[/C][C]27.7430830346453[/C][C]-1.0030830346453[/C][/ROW]
[ROW][C]63[/C][C]26.48[/C][C]27.2490426129749[/C][C]-0.769042612974875[/C][/ROW]
[ROW][C]64[/C][C]24.45[/C][C]26.1226660252037[/C][C]-1.67266602520368[/C][/ROW]
[ROW][C]65[/C][C]23.88[/C][C]24.3579968564897[/C][C]-0.477996856489749[/C][/ROW]
[ROW][C]66[/C][C]26.58[/C][C]25.3142014650434[/C][C]1.26579853495657[/C][/ROW]
[ROW][C]67[/C][C]26.23[/C][C]26.3594405330033[/C][C]-0.129440533003262[/C][/ROW]
[ROW][C]68[/C][C]28.63[/C][C]26.4707812884327[/C][C]2.15921871156733[/C][/ROW]
[ROW][C]69[/C][C]26.81[/C][C]26.8946882973538[/C][C]-0.0846882973538143[/C][/ROW]
[ROW][C]70[/C][C]26.56[/C][C]26.4937593803677[/C][C]0.0662406196323069[/C][/ROW]
[ROW][C]71[/C][C]26.64[/C][C]26.5952935154368[/C][C]0.0447064845632106[/C][/ROW]
[ROW][C]72[/C][C]26.8[/C][C]26.9383525759331[/C][C]-0.138352575933141[/C][/ROW]
[ROW][C]73[/C][C]28.37[/C][C]30.3719565217112[/C][C]-2.0019565217112[/C][/ROW]
[ROW][C]74[/C][C]27.13[/C][C]27.5180349916875[/C][C]-0.388034991687526[/C][/ROW]
[ROW][C]75[/C][C]28.44[/C][C]27.5793719925666[/C][C]0.860628007433448[/C][/ROW]
[ROW][C]76[/C][C]28.62[/C][C]27.7197479559325[/C][C]0.900252044067521[/C][/ROW]
[ROW][C]77[/C][C]27.28[/C][C]28.3291712828706[/C][C]-1.04917128287057[/C][/ROW]
[ROW][C]78[/C][C]31.32[/C][C]29.1952290597565[/C][C]2.12477094024345[/C][/ROW]
[ROW][C]79[/C][C]31.26[/C][C]30.7843802434725[/C][C]0.475619756527511[/C][/ROW]
[ROW][C]80[/C][C]31.41[/C][C]31.7577427014818[/C][C]-0.347742701481824[/C][/ROW]
[ROW][C]81[/C][C]31.76[/C][C]29.5180803097752[/C][C]2.24191969022476[/C][/ROW]
[ROW][C]82[/C][C]32.72[/C][C]31.1254123868073[/C][C]1.59458761319273[/C][/ROW]
[ROW][C]83[/C][C]32.15[/C][C]32.5753423617925[/C][C]-0.425342361792467[/C][/ROW]
[ROW][C]84[/C][C]33.62[/C][C]32.5309976957637[/C][C]1.08900230423633[/C][/ROW]
[ROW][C]85[/C][C]35.97[/C][C]37.6401896735595[/C][C]-1.6701896735595[/C][/ROW]
[ROW][C]86[/C][C]33.78[/C][C]35.0135167487711[/C][C]-1.23351674877114[/C][/ROW]
[ROW][C]87[/C][C]33.77[/C][C]34.5992519061968[/C][C]-0.829251906196795[/C][/ROW]
[ROW][C]88[/C][C]32.75[/C][C]33.1188594344454[/C][C]-0.368859434445355[/C][/ROW]
[ROW][C]89[/C][C]32.55[/C][C]32.3016947249391[/C][C]0.248305275060879[/C][/ROW]
[ROW][C]90[/C][C]33.22[/C][C]35.0698470300967[/C][C]-1.84984703009672[/C][/ROW]
[ROW][C]91[/C][C]32.88[/C][C]32.9025667648813[/C][C]-0.0225667648813399[/C][/ROW]
[ROW][C]92[/C][C]31.56[/C][C]33.3431708742486[/C][C]-1.78317087424857[/C][/ROW]
[ROW][C]93[/C][C]30.27[/C][C]30.0796817656242[/C][C]0.190318234375844[/C][/ROW]
[ROW][C]94[/C][C]28.65[/C][C]29.7878453054792[/C][C]-1.13784530547916[/C][/ROW]
[ROW][C]95[/C][C]27.89[/C][C]28.5821177837876[/C][C]-0.692117783787619[/C][/ROW]
[ROW][C]96[/C][C]27.07[/C][C]28.379371998322[/C][C]-1.30937199832203[/C][/ROW]
[ROW][C]97[/C][C]30.8[/C][C]30.27653819601[/C][C]0.523461803990003[/C][/ROW]
[ROW][C]98[/C][C]28.38[/C][C]29.7631734848052[/C][C]-1.38317348480515[/C][/ROW]
[ROW][C]99[/C][C]27.5[/C][C]29.1168146307797[/C][C]-1.6168146307797[/C][/ROW]
[ROW][C]100[/C][C]28[/C][C]27.0847997512555[/C][C]0.91520024874448[/C][/ROW]
[ROW][C]101[/C][C]28.02[/C][C]27.5058331910224[/C][C]0.514166808977581[/C][/ROW]
[ROW][C]102[/C][C]29.2[/C][C]29.899552042766[/C][C]-0.699552042765998[/C][/ROW]
[ROW][C]103[/C][C]27.59[/C][C]28.9706613870233[/C][C]-1.38066138702325[/C][/ROW]
[ROW][C]104[/C][C]27.22[/C][C]27.9260090984987[/C][C]-0.706009098498729[/C][/ROW]
[ROW][C]105[/C][C]27.16[/C][C]26.0125440444394[/C][C]1.14745595556055[/C][/ROW]
[ROW][C]106[/C][C]26.31[/C][C]26.4491528518359[/C][C]-0.139152851835913[/C][/ROW]
[ROW][C]107[/C][C]25.67[/C][C]26.1663602539045[/C][C]-0.496360253904474[/C][/ROW]
[ROW][C]108[/C][C]26.41[/C][C]26.0112270512107[/C][C]0.398772948789265[/C][/ROW]
[ROW][C]109[/C][C]28.34[/C][C]29.5263517387389[/C][C]-1.18635173873886[/C][/ROW]
[ROW][C]110[/C][C]25.43[/C][C]27.3418194874131[/C][C]-1.91181948741312[/C][/ROW]
[ROW][C]111[/C][C]23.72[/C][C]26.1150290004965[/C][C]-2.39502900049654[/C][/ROW]
[ROW][C]112[/C][C]23.33[/C][C]23.6993045163837[/C][C]-0.369304516383703[/C][/ROW]
[ROW][C]113[/C][C]23.8[/C][C]22.979465909467[/C][C]0.820534090533044[/C][/ROW]
[ROW][C]114[/C][C]27.7[/C][C]25.1939987234754[/C][C]2.50600127652464[/C][/ROW]
[ROW][C]115[/C][C]26.28[/C][C]27.0162251604079[/C][C]-0.736225160407855[/C][/ROW]
[ROW][C]116[/C][C]27.51[/C][C]26.5886818059655[/C][C]0.921318194034491[/C][/ROW]
[ROW][C]117[/C][C]27.93[/C][C]26.3050718229829[/C][C]1.62492817701711[/C][/ROW]
[ROW][C]118[/C][C]28.76[/C][C]26.988798474434[/C][C]1.77120152556603[/C][/ROW]
[ROW][C]119[/C][C]28.65[/C][C]28.3315510276837[/C][C]0.318448972316347[/C][/ROW]
[ROW][C]120[/C][C]29.52[/C][C]29.0445223380739[/C][C]0.475477661926128[/C][/ROW]
[ROW][C]121[/C][C]31.23[/C][C]32.7822491662074[/C][C]-1.55224916620742[/C][/ROW]
[ROW][C]122[/C][C]27.9[/C][C]30.0410368877134[/C][C]-2.14103688771344[/C][/ROW]
[ROW][C]123[/C][C]27.87[/C][C]28.5711011252227[/C][C]-0.701101125222728[/C][/ROW]
[ROW][C]124[/C][C]27.52[/C][C]27.8833745507818[/C][C]-0.363374550781753[/C][/ROW]
[ROW][C]125[/C][C]27.59[/C][C]27.2651371761826[/C][C]0.324862823817387[/C][/ROW]
[ROW][C]126[/C][C]31.2[/C][C]29.4813725918972[/C][C]1.7186274081028[/C][/ROW]
[ROW][C]127[/C][C]30.22[/C][C]30.1371397608535[/C][C]0.0828602391464521[/C][/ROW]
[ROW][C]128[/C][C]30.62[/C][C]30.688867675378[/C][C]-0.0688676753780264[/C][/ROW]
[ROW][C]129[/C][C]31.52[/C][C]29.4857112262731[/C][C]2.03428877372691[/C][/ROW]
[ROW][C]130[/C][C]30.59[/C][C]30.4477506339216[/C][C]0.142249366078417[/C][/ROW]
[ROW][C]131[/C][C]31.42[/C][C]30.1509579447572[/C][C]1.2690420552428[/C][/ROW]
[ROW][C]132[/C][C]31.95[/C][C]31.7598163232611[/C][C]0.190183676738879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158861&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158861&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325.0623.09880815695161.96119184304838
1425.1624.9492827768290.210717223171009
1525.4725.473859846772-0.00385984677201989
1625.3425.4510460200678-0.111046020067842
1724.224.4370230190868-0.237023019086763
1825.3225.6539975567251-0.33399755672508
1925.5725.40354129529020.166458704709775
2025.7626.0419638133318-0.281963813331792
2124.7924.34996790103110.440032098968899
2223.1425.0117421273316-1.87174212733159
2322.6623.6250689005515-0.965068900551469
2422.0622.9743395906984-0.91433959069845
2524.2624.6475627138803-0.387562713880271
2623.1524.1940641234365-1.04406412343653
2722.9223.5370810281972-0.617081028197159
2821.4322.94053609459-1.51053609458998
2921.5620.79357325496170.76642674503826
3023.4822.70497933555740.775020664442589
3124.3523.46224507314130.887754926858751
3224.8324.63918871410090.190811285899144
3324.1923.4757426116720.714257388327976
3423.5824.0732796841068-0.49327968410682
3523.5823.9895030049296-0.409503004929636
3624.3523.81552927750720.53447072249276
3727.1827.05690840753120.123091592468821
3825.6926.9211339291789-1.23113392917886
3924.8126.1540786875378-1.34407868753778
4023.2624.7579968954193-1.49799689541933
4123.4922.80625898869860.683741011301379
4226.8624.72154207828832.13845792171166
4327.1226.6764535900830.443546409917001
4427.6627.38709365638740.272906343612643
4526.2626.18595120306240.0740487969375891
4625.5126.0369791704932-0.526979170493149
4724.6325.938685283188-1.30868528318796
4823.5725.0701229371475-1.50012293714751
4927.6326.37303791033721.25696208966283
5025.8527.0467069658531-1.1967069658531
5126.0926.2686856462755-0.178685646275518
5224.4725.8384627578757-1.36846275787571
5324.1924.2076352355798-0.0176352355797746
5425.0925.674294511085-0.584294511084952
5525.2625.01011230368240.249887696317607
5625.5825.48529467050670.094705329493312
5724.7624.19250837877250.567491621227528
5825.0224.40449740370290.615502596297109
5924.2425.1912123764076-0.951212376407575
6024.1424.583235583678-0.443235583677964
6128.6927.19041545703951.49958454296045
6226.7427.7430830346453-1.0030830346453
6326.4827.2490426129749-0.769042612974875
6424.4526.1226660252037-1.67266602520368
6523.8824.3579968564897-0.477996856489749
6626.5825.31420146504341.26579853495657
6726.2326.3594405330033-0.129440533003262
6828.6326.47078128843272.15921871156733
6926.8126.8946882973538-0.0846882973538143
7026.5626.49375938036770.0662406196323069
7126.6426.59529351543680.0447064845632106
7226.826.9383525759331-0.138352575933141
7328.3730.3719565217112-2.0019565217112
7427.1327.5180349916875-0.388034991687526
7528.4427.57937199256660.860628007433448
7628.6227.71974795593250.900252044067521
7727.2828.3291712828706-1.04917128287057
7831.3229.19522905975652.12477094024345
7931.2630.78438024347250.475619756527511
8031.4131.7577427014818-0.347742701481824
8131.7629.51808030977522.24191969022476
8232.7231.12541238680731.59458761319273
8332.1532.5753423617925-0.425342361792467
8433.6232.53099769576371.08900230423633
8535.9737.6401896735595-1.6701896735595
8633.7835.0135167487711-1.23351674877114
8733.7734.5992519061968-0.829251906196795
8832.7533.1188594344454-0.368859434445355
8932.5532.30169472493910.248305275060879
9033.2235.0698470300967-1.84984703009672
9132.8832.9025667648813-0.0225667648813399
9231.5633.3431708742486-1.78317087424857
9330.2730.07968176562420.190318234375844
9428.6529.7878453054792-1.13784530547916
9527.8928.5821177837876-0.692117783787619
9627.0728.379371998322-1.30937199832203
9730.830.276538196010.523461803990003
9828.3829.7631734848052-1.38317348480515
9927.529.1168146307797-1.6168146307797
1002827.08479975125550.91520024874448
10128.0227.50583319102240.514166808977581
10229.229.899552042766-0.699552042765998
10327.5928.9706613870233-1.38066138702325
10427.2227.9260090984987-0.706009098498729
10527.1626.01254404443941.14745595556055
10626.3126.4491528518359-0.139152851835913
10725.6726.1663602539045-0.496360253904474
10826.4126.01122705121070.398772948789265
10928.3429.5263517387389-1.18635173873886
11025.4327.3418194874131-1.91181948741312
11123.7226.1150290004965-2.39502900049654
11223.3323.6993045163837-0.369304516383703
11323.822.9794659094670.820534090533044
11427.725.19399872347542.50600127652464
11526.2827.0162251604079-0.736225160407855
11627.5126.58868180596550.921318194034491
11727.9326.30507182298291.62492817701711
11828.7626.9887984744341.77120152556603
11928.6528.33155102768370.318448972316347
12029.5229.04452233807390.475477661926128
12131.2332.7822491662074-1.55224916620742
12227.930.0410368877134-2.14103688771344
12327.8728.5711011252227-0.701101125222728
12427.5227.8833745507818-0.363374550781753
12527.5927.26513717618260.324862823817387
12631.229.48137259189721.7186274081028
12730.2230.13713976085350.0828602391464521
12830.6230.688867675378-0.0688676753780264
12931.5229.48571122627312.03428877372691
13030.5930.44775063392160.142249366078417
13131.4230.15095794475721.2690420552428
13231.9531.75981632326110.190183676738879






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13335.248190894098533.128582515553337.3677992726437
13433.60813525994330.831715673623536.3845548462626
13534.327607075735330.926821149234637.7283930022361
13634.306177987476930.414302637291438.1980533376624
13734.051414949997729.743422970131538.3594069298638
13836.63598730867131.635908018641.636066598742
13935.406195193230830.200014950573540.6123754358881
14035.952746200951730.327707799465341.5777846024382
14134.889419311902429.093463750313740.6853748734911
14233.718545014439927.786302250363439.6507877785164
14333.388675069413527.200017869747639.5773322690793
14433.765263515836819.776183716687747.7543433149859

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 35.2481908940985 & 33.1285825155533 & 37.3677992726437 \tabularnewline
134 & 33.608135259943 & 30.8317156736235 & 36.3845548462626 \tabularnewline
135 & 34.3276070757353 & 30.9268211492346 & 37.7283930022361 \tabularnewline
136 & 34.3061779874769 & 30.4143026372914 & 38.1980533376624 \tabularnewline
137 & 34.0514149499977 & 29.7434229701315 & 38.3594069298638 \tabularnewline
138 & 36.635987308671 & 31.6359080186 & 41.636066598742 \tabularnewline
139 & 35.4061951932308 & 30.2000149505735 & 40.6123754358881 \tabularnewline
140 & 35.9527462009517 & 30.3277077994653 & 41.5777846024382 \tabularnewline
141 & 34.8894193119024 & 29.0934637503137 & 40.6853748734911 \tabularnewline
142 & 33.7185450144399 & 27.7863022503634 & 39.6507877785164 \tabularnewline
143 & 33.3886750694135 & 27.2000178697476 & 39.5773322690793 \tabularnewline
144 & 33.7652635158368 & 19.7761837166877 & 47.7543433149859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158861&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]133[/C][C]35.2481908940985[/C][C]33.1285825155533[/C][C]37.3677992726437[/C][/ROW]
[ROW][C]134[/C][C]33.608135259943[/C][C]30.8317156736235[/C][C]36.3845548462626[/C][/ROW]
[ROW][C]135[/C][C]34.3276070757353[/C][C]30.9268211492346[/C][C]37.7283930022361[/C][/ROW]
[ROW][C]136[/C][C]34.3061779874769[/C][C]30.4143026372914[/C][C]38.1980533376624[/C][/ROW]
[ROW][C]137[/C][C]34.0514149499977[/C][C]29.7434229701315[/C][C]38.3594069298638[/C][/ROW]
[ROW][C]138[/C][C]36.635987308671[/C][C]31.6359080186[/C][C]41.636066598742[/C][/ROW]
[ROW][C]139[/C][C]35.4061951932308[/C][C]30.2000149505735[/C][C]40.6123754358881[/C][/ROW]
[ROW][C]140[/C][C]35.9527462009517[/C][C]30.3277077994653[/C][C]41.5777846024382[/C][/ROW]
[ROW][C]141[/C][C]34.8894193119024[/C][C]29.0934637503137[/C][C]40.6853748734911[/C][/ROW]
[ROW][C]142[/C][C]33.7185450144399[/C][C]27.7863022503634[/C][C]39.6507877785164[/C][/ROW]
[ROW][C]143[/C][C]33.3886750694135[/C][C]27.2000178697476[/C][C]39.5773322690793[/C][/ROW]
[ROW][C]144[/C][C]33.7652635158368[/C][C]19.7761837166877[/C][C]47.7543433149859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158861&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158861&T=3

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13335.248190894098533.128582515553337.3677992726437
13433.60813525994330.831715673623536.3845548462626
13534.327607075735330.926821149234637.7283930022361
13634.306177987476930.414302637291438.1980533376624
13734.051414949997729.743422970131538.3594069298638
13836.63598730867131.635908018641.636066598742
13935.406195193230830.200014950573540.6123754358881
14035.952746200951730.327707799465341.5777846024382
14134.889419311902429.093463750313740.6853748734911
14233.718545014439927.786302250363439.6507877785164
14333.388675069413527.200017869747639.5773322690793
14433.765263515836819.776183716687747.7543433149859


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')