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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 May 2011 04:09:55 +0000
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/May/20/t13058645333g0v37u54s4f8qc.htm/, Retrieved Mon, 13 May 2024 17:04:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122396, Retrieved Mon, 13 May 2024 17:04:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Exponential Smoot...] [2010-01-26 07:22:52] [702b109ff2d8b1c8a15cc31390408a4f]
- R PD  [Exponential Smoothing] [Sarah Geerts - Ex...] [2011-05-20 00:54:17] [38950998a23e7419c15b25db858fbdfd]
-   PD      [Exponential Smoothing] [Sarah Geerts - ex...] [2011-05-20 04:09:55] [0b99204a0dc37104849df68eb9128a1a] [Current]
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Dataseries X:
31.514
27.071
29.462
26.105
22.397
23.843
21.705
18.089
20.764
25.316
17.704
15.548
28.029
29.383
36.438
32.034
22.679
24.319
18.004
17.537
20.366
22.782
19.169
13.807
29.743
25.591
29.096
26.482
22.405
27.044
17.970
18.730
19.684
19.785
18.479
10.698
31.956
29.506
34.506
27.165
26.736
23.691
18.157
17.328
18.205
20.995
17.382
9.367
31.124
26.551
30.651
25.859
25.100
25.778
20.418
18.688
20.424
24.776
19.814
12.738
31.566
30.111
30.019
31.934
25.826
26.835
20.205
17.789
20.520
22.518
15.572
11.509
25.447
24.090
27.786
26.195
20.516
22.759
19.028
16.971
20.036
22.485
18.730
14.538
27.561
25.985
34.670
32.066
27.186
29.586
21.359
21.553
19.573
24.256
22.380
16.167
27.297
28.287




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122396&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122396&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122396&T=0

As an alternative you can also use a 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'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.217005798442115
beta0
gamma0.706425518435226

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.217005798442115 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.706425518435226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122396&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]0.217005798442115[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.706425518435226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122396&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122396&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.217005798442115
beta0
gamma0.706425518435226







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1328.02926.73908851391691.28991148608307
1429.38328.59406420526350.788935794736517
1536.43835.80631162444930.631688375550702
1632.03431.82775533593290.206244664067089
1722.67922.65419040399380.0248095960061718
1824.31924.3606438174574-0.0416438174574054
1918.00422.3785573631892-4.37455736318921
2017.53717.9358310666813-0.398831066681261
2120.36620.19508293531510.170917064684858
2222.78224.1677453379306-1.38574533793059
2319.16916.54899572450192.62000427549815
2413.80715.0451672854309-1.23816728543092
2529.74327.55254812255352.19045187744652
2625.59129.3363868270661-3.74538682706612
2729.09635.3166826509825-6.22068265098245
2826.48229.8987923348675-3.41679233486748
2922.40520.66708368517911.73791631482094
3027.04422.59258651548124.45141348451877
3117.9719.2246774176737-1.25467741767373
3218.7317.66100605447641.06899394552358
3319.68420.5929863670096-0.908986367009586
3419.78523.4708488064628-3.68584880646277
3518.47917.61701653946140.861983460538628
3610.69813.7597193612411-3.06171936124105
3731.95626.71572184808345.24027815191662
3829.50625.91824428498893.5877557150111
3934.50632.03228408752482.47371591247516
4027.16529.8280998545382-2.66309985453818
4126.73623.17902868743423.55697131256579
4223.69127.1549251810745-3.46392518107453
4318.15718.792354147262-0.635354147262028
4417.32818.6395403988487-1.31154039884874
4518.20519.9450910340095-1.74009103400945
4620.99521.0114609964673-0.0164609964672984
4717.38218.4173870906547-1.03538709065473
489.36711.9226303211818-2.55563032118179
4931.12429.40882550325481.71517449674517
5026.55126.9681106631271-0.417110663127108
5130.65131.2834339745109-0.632433974510921
5225.85926.0011792503858-0.142179250385752
5325.123.45497107025161.64502892974842
5425.77823.14183998042712.63616001957285
5520.41817.85724955442562.56075044557444
5618.68818.01011166603720.677888333962766
5720.42419.53048912285280.893510877147204
5824.77622.26322231831682.51277768168317
5919.81419.37153946533990.442460534660068
6012.73811.53236198504021.2056380149598
6131.56635.9404540057861-4.37445400578605
6230.11130.4358634100249-0.324863410024946
6330.01935.2387052155291-5.21970521552911
6431.93428.70190853669133.23209146330866
6525.82627.6463850319208-1.82038503192077
6626.83527.072576409823-0.23757640982301
6720.20520.6404261132437-0.435426113243729
6817.78919.0448944892686-1.25589448926862
6920.5220.27877599135620.241224008643751
7022.51823.751046718997-1.23304671899702
7115.57219.0367214045529-3.46472140455286
7211.50911.30388643827130.205113561728723
7325.44730.4742403876788-5.02724038767878
7424.0927.3001174930027-3.21011749300272
7527.78628.4355003726381-0.649500372638094
7626.19527.6009196306679-1.40591963066795
7720.51623.3065826792077-2.79058267920771
7822.75923.3108481180279-0.55184811802792
7919.02817.598485637691.42951436231003
8016.97116.18006675364190.790933246358104
8120.03618.46704348117741.56895651882258
8222.48521.19779218956631.28720781043368
8318.7316.05376762050672.67623237949332
8414.53811.60209861941582.9359013805842
8527.56129.4574897396373-1.89648973963727
8625.98527.812886453676-1.82788645367602
8734.6730.99458883078343.67541116921661
8832.06630.50829067249251.55770932750752
8927.18625.25903793669291.92696206330707
9029.58627.90667666058541.67932333941459
9121.35922.6892116506813-1.33021165068127
9221.55319.89353658012931.65946341987074
9319.57323.2965843081304-3.72358430813045
9424.25625.0248703741857-0.768870374185678
9522.3819.58053259414062.79946740585943
9616.16714.64232321417061.52467678582936
9727.29730.6626089672762-3.3656089672762
9828.28728.6351311159572-0.348131115957226

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 28.029 & 26.7390885139169 & 1.28991148608307 \tabularnewline
14 & 29.383 & 28.5940642052635 & 0.788935794736517 \tabularnewline
15 & 36.438 & 35.8063116244493 & 0.631688375550702 \tabularnewline
16 & 32.034 & 31.8277553359329 & 0.206244664067089 \tabularnewline
17 & 22.679 & 22.6541904039938 & 0.0248095960061718 \tabularnewline
18 & 24.319 & 24.3606438174574 & -0.0416438174574054 \tabularnewline
19 & 18.004 & 22.3785573631892 & -4.37455736318921 \tabularnewline
20 & 17.537 & 17.9358310666813 & -0.398831066681261 \tabularnewline
21 & 20.366 & 20.1950829353151 & 0.170917064684858 \tabularnewline
22 & 22.782 & 24.1677453379306 & -1.38574533793059 \tabularnewline
23 & 19.169 & 16.5489957245019 & 2.62000427549815 \tabularnewline
24 & 13.807 & 15.0451672854309 & -1.23816728543092 \tabularnewline
25 & 29.743 & 27.5525481225535 & 2.19045187744652 \tabularnewline
26 & 25.591 & 29.3363868270661 & -3.74538682706612 \tabularnewline
27 & 29.096 & 35.3166826509825 & -6.22068265098245 \tabularnewline
28 & 26.482 & 29.8987923348675 & -3.41679233486748 \tabularnewline
29 & 22.405 & 20.6670836851791 & 1.73791631482094 \tabularnewline
30 & 27.044 & 22.5925865154812 & 4.45141348451877 \tabularnewline
31 & 17.97 & 19.2246774176737 & -1.25467741767373 \tabularnewline
32 & 18.73 & 17.6610060544764 & 1.06899394552358 \tabularnewline
33 & 19.684 & 20.5929863670096 & -0.908986367009586 \tabularnewline
34 & 19.785 & 23.4708488064628 & -3.68584880646277 \tabularnewline
35 & 18.479 & 17.6170165394614 & 0.861983460538628 \tabularnewline
36 & 10.698 & 13.7597193612411 & -3.06171936124105 \tabularnewline
37 & 31.956 & 26.7157218480834 & 5.24027815191662 \tabularnewline
38 & 29.506 & 25.9182442849889 & 3.5877557150111 \tabularnewline
39 & 34.506 & 32.0322840875248 & 2.47371591247516 \tabularnewline
40 & 27.165 & 29.8280998545382 & -2.66309985453818 \tabularnewline
41 & 26.736 & 23.1790286874342 & 3.55697131256579 \tabularnewline
42 & 23.691 & 27.1549251810745 & -3.46392518107453 \tabularnewline
43 & 18.157 & 18.792354147262 & -0.635354147262028 \tabularnewline
44 & 17.328 & 18.6395403988487 & -1.31154039884874 \tabularnewline
45 & 18.205 & 19.9450910340095 & -1.74009103400945 \tabularnewline
46 & 20.995 & 21.0114609964673 & -0.0164609964672984 \tabularnewline
47 & 17.382 & 18.4173870906547 & -1.03538709065473 \tabularnewline
48 & 9.367 & 11.9226303211818 & -2.55563032118179 \tabularnewline
49 & 31.124 & 29.4088255032548 & 1.71517449674517 \tabularnewline
50 & 26.551 & 26.9681106631271 & -0.417110663127108 \tabularnewline
51 & 30.651 & 31.2834339745109 & -0.632433974510921 \tabularnewline
52 & 25.859 & 26.0011792503858 & -0.142179250385752 \tabularnewline
53 & 25.1 & 23.4549710702516 & 1.64502892974842 \tabularnewline
54 & 25.778 & 23.1418399804271 & 2.63616001957285 \tabularnewline
55 & 20.418 & 17.8572495544256 & 2.56075044557444 \tabularnewline
56 & 18.688 & 18.0101116660372 & 0.677888333962766 \tabularnewline
57 & 20.424 & 19.5304891228528 & 0.893510877147204 \tabularnewline
58 & 24.776 & 22.2632223183168 & 2.51277768168317 \tabularnewline
59 & 19.814 & 19.3715394653399 & 0.442460534660068 \tabularnewline
60 & 12.738 & 11.5323619850402 & 1.2056380149598 \tabularnewline
61 & 31.566 & 35.9404540057861 & -4.37445400578605 \tabularnewline
62 & 30.111 & 30.4358634100249 & -0.324863410024946 \tabularnewline
63 & 30.019 & 35.2387052155291 & -5.21970521552911 \tabularnewline
64 & 31.934 & 28.7019085366913 & 3.23209146330866 \tabularnewline
65 & 25.826 & 27.6463850319208 & -1.82038503192077 \tabularnewline
66 & 26.835 & 27.072576409823 & -0.23757640982301 \tabularnewline
67 & 20.205 & 20.6404261132437 & -0.435426113243729 \tabularnewline
68 & 17.789 & 19.0448944892686 & -1.25589448926862 \tabularnewline
69 & 20.52 & 20.2787759913562 & 0.241224008643751 \tabularnewline
70 & 22.518 & 23.751046718997 & -1.23304671899702 \tabularnewline
71 & 15.572 & 19.0367214045529 & -3.46472140455286 \tabularnewline
72 & 11.509 & 11.3038864382713 & 0.205113561728723 \tabularnewline
73 & 25.447 & 30.4742403876788 & -5.02724038767878 \tabularnewline
74 & 24.09 & 27.3001174930027 & -3.21011749300272 \tabularnewline
75 & 27.786 & 28.4355003726381 & -0.649500372638094 \tabularnewline
76 & 26.195 & 27.6009196306679 & -1.40591963066795 \tabularnewline
77 & 20.516 & 23.3065826792077 & -2.79058267920771 \tabularnewline
78 & 22.759 & 23.3108481180279 & -0.55184811802792 \tabularnewline
79 & 19.028 & 17.59848563769 & 1.42951436231003 \tabularnewline
80 & 16.971 & 16.1800667536419 & 0.790933246358104 \tabularnewline
81 & 20.036 & 18.4670434811774 & 1.56895651882258 \tabularnewline
82 & 22.485 & 21.1977921895663 & 1.28720781043368 \tabularnewline
83 & 18.73 & 16.0537676205067 & 2.67623237949332 \tabularnewline
84 & 14.538 & 11.6020986194158 & 2.9359013805842 \tabularnewline
85 & 27.561 & 29.4574897396373 & -1.89648973963727 \tabularnewline
86 & 25.985 & 27.812886453676 & -1.82788645367602 \tabularnewline
87 & 34.67 & 30.9945888307834 & 3.67541116921661 \tabularnewline
88 & 32.066 & 30.5082906724925 & 1.55770932750752 \tabularnewline
89 & 27.186 & 25.2590379366929 & 1.92696206330707 \tabularnewline
90 & 29.586 & 27.9066766605854 & 1.67932333941459 \tabularnewline
91 & 21.359 & 22.6892116506813 & -1.33021165068127 \tabularnewline
92 & 21.553 & 19.8935365801293 & 1.65946341987074 \tabularnewline
93 & 19.573 & 23.2965843081304 & -3.72358430813045 \tabularnewline
94 & 24.256 & 25.0248703741857 & -0.768870374185678 \tabularnewline
95 & 22.38 & 19.5805325941406 & 2.79946740585943 \tabularnewline
96 & 16.167 & 14.6423232141706 & 1.52467678582936 \tabularnewline
97 & 27.297 & 30.6626089672762 & -3.3656089672762 \tabularnewline
98 & 28.287 & 28.6351311159572 & -0.348131115957226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122396&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]28.029[/C][C]26.7390885139169[/C][C]1.28991148608307[/C][/ROW]
[ROW][C]14[/C][C]29.383[/C][C]28.5940642052635[/C][C]0.788935794736517[/C][/ROW]
[ROW][C]15[/C][C]36.438[/C][C]35.8063116244493[/C][C]0.631688375550702[/C][/ROW]
[ROW][C]16[/C][C]32.034[/C][C]31.8277553359329[/C][C]0.206244664067089[/C][/ROW]
[ROW][C]17[/C][C]22.679[/C][C]22.6541904039938[/C][C]0.0248095960061718[/C][/ROW]
[ROW][C]18[/C][C]24.319[/C][C]24.3606438174574[/C][C]-0.0416438174574054[/C][/ROW]
[ROW][C]19[/C][C]18.004[/C][C]22.3785573631892[/C][C]-4.37455736318921[/C][/ROW]
[ROW][C]20[/C][C]17.537[/C][C]17.9358310666813[/C][C]-0.398831066681261[/C][/ROW]
[ROW][C]21[/C][C]20.366[/C][C]20.1950829353151[/C][C]0.170917064684858[/C][/ROW]
[ROW][C]22[/C][C]22.782[/C][C]24.1677453379306[/C][C]-1.38574533793059[/C][/ROW]
[ROW][C]23[/C][C]19.169[/C][C]16.5489957245019[/C][C]2.62000427549815[/C][/ROW]
[ROW][C]24[/C][C]13.807[/C][C]15.0451672854309[/C][C]-1.23816728543092[/C][/ROW]
[ROW][C]25[/C][C]29.743[/C][C]27.5525481225535[/C][C]2.19045187744652[/C][/ROW]
[ROW][C]26[/C][C]25.591[/C][C]29.3363868270661[/C][C]-3.74538682706612[/C][/ROW]
[ROW][C]27[/C][C]29.096[/C][C]35.3166826509825[/C][C]-6.22068265098245[/C][/ROW]
[ROW][C]28[/C][C]26.482[/C][C]29.8987923348675[/C][C]-3.41679233486748[/C][/ROW]
[ROW][C]29[/C][C]22.405[/C][C]20.6670836851791[/C][C]1.73791631482094[/C][/ROW]
[ROW][C]30[/C][C]27.044[/C][C]22.5925865154812[/C][C]4.45141348451877[/C][/ROW]
[ROW][C]31[/C][C]17.97[/C][C]19.2246774176737[/C][C]-1.25467741767373[/C][/ROW]
[ROW][C]32[/C][C]18.73[/C][C]17.6610060544764[/C][C]1.06899394552358[/C][/ROW]
[ROW][C]33[/C][C]19.684[/C][C]20.5929863670096[/C][C]-0.908986367009586[/C][/ROW]
[ROW][C]34[/C][C]19.785[/C][C]23.4708488064628[/C][C]-3.68584880646277[/C][/ROW]
[ROW][C]35[/C][C]18.479[/C][C]17.6170165394614[/C][C]0.861983460538628[/C][/ROW]
[ROW][C]36[/C][C]10.698[/C][C]13.7597193612411[/C][C]-3.06171936124105[/C][/ROW]
[ROW][C]37[/C][C]31.956[/C][C]26.7157218480834[/C][C]5.24027815191662[/C][/ROW]
[ROW][C]38[/C][C]29.506[/C][C]25.9182442849889[/C][C]3.5877557150111[/C][/ROW]
[ROW][C]39[/C][C]34.506[/C][C]32.0322840875248[/C][C]2.47371591247516[/C][/ROW]
[ROW][C]40[/C][C]27.165[/C][C]29.8280998545382[/C][C]-2.66309985453818[/C][/ROW]
[ROW][C]41[/C][C]26.736[/C][C]23.1790286874342[/C][C]3.55697131256579[/C][/ROW]
[ROW][C]42[/C][C]23.691[/C][C]27.1549251810745[/C][C]-3.46392518107453[/C][/ROW]
[ROW][C]43[/C][C]18.157[/C][C]18.792354147262[/C][C]-0.635354147262028[/C][/ROW]
[ROW][C]44[/C][C]17.328[/C][C]18.6395403988487[/C][C]-1.31154039884874[/C][/ROW]
[ROW][C]45[/C][C]18.205[/C][C]19.9450910340095[/C][C]-1.74009103400945[/C][/ROW]
[ROW][C]46[/C][C]20.995[/C][C]21.0114609964673[/C][C]-0.0164609964672984[/C][/ROW]
[ROW][C]47[/C][C]17.382[/C][C]18.4173870906547[/C][C]-1.03538709065473[/C][/ROW]
[ROW][C]48[/C][C]9.367[/C][C]11.9226303211818[/C][C]-2.55563032118179[/C][/ROW]
[ROW][C]49[/C][C]31.124[/C][C]29.4088255032548[/C][C]1.71517449674517[/C][/ROW]
[ROW][C]50[/C][C]26.551[/C][C]26.9681106631271[/C][C]-0.417110663127108[/C][/ROW]
[ROW][C]51[/C][C]30.651[/C][C]31.2834339745109[/C][C]-0.632433974510921[/C][/ROW]
[ROW][C]52[/C][C]25.859[/C][C]26.0011792503858[/C][C]-0.142179250385752[/C][/ROW]
[ROW][C]53[/C][C]25.1[/C][C]23.4549710702516[/C][C]1.64502892974842[/C][/ROW]
[ROW][C]54[/C][C]25.778[/C][C]23.1418399804271[/C][C]2.63616001957285[/C][/ROW]
[ROW][C]55[/C][C]20.418[/C][C]17.8572495544256[/C][C]2.56075044557444[/C][/ROW]
[ROW][C]56[/C][C]18.688[/C][C]18.0101116660372[/C][C]0.677888333962766[/C][/ROW]
[ROW][C]57[/C][C]20.424[/C][C]19.5304891228528[/C][C]0.893510877147204[/C][/ROW]
[ROW][C]58[/C][C]24.776[/C][C]22.2632223183168[/C][C]2.51277768168317[/C][/ROW]
[ROW][C]59[/C][C]19.814[/C][C]19.3715394653399[/C][C]0.442460534660068[/C][/ROW]
[ROW][C]60[/C][C]12.738[/C][C]11.5323619850402[/C][C]1.2056380149598[/C][/ROW]
[ROW][C]61[/C][C]31.566[/C][C]35.9404540057861[/C][C]-4.37445400578605[/C][/ROW]
[ROW][C]62[/C][C]30.111[/C][C]30.4358634100249[/C][C]-0.324863410024946[/C][/ROW]
[ROW][C]63[/C][C]30.019[/C][C]35.2387052155291[/C][C]-5.21970521552911[/C][/ROW]
[ROW][C]64[/C][C]31.934[/C][C]28.7019085366913[/C][C]3.23209146330866[/C][/ROW]
[ROW][C]65[/C][C]25.826[/C][C]27.6463850319208[/C][C]-1.82038503192077[/C][/ROW]
[ROW][C]66[/C][C]26.835[/C][C]27.072576409823[/C][C]-0.23757640982301[/C][/ROW]
[ROW][C]67[/C][C]20.205[/C][C]20.6404261132437[/C][C]-0.435426113243729[/C][/ROW]
[ROW][C]68[/C][C]17.789[/C][C]19.0448944892686[/C][C]-1.25589448926862[/C][/ROW]
[ROW][C]69[/C][C]20.52[/C][C]20.2787759913562[/C][C]0.241224008643751[/C][/ROW]
[ROW][C]70[/C][C]22.518[/C][C]23.751046718997[/C][C]-1.23304671899702[/C][/ROW]
[ROW][C]71[/C][C]15.572[/C][C]19.0367214045529[/C][C]-3.46472140455286[/C][/ROW]
[ROW][C]72[/C][C]11.509[/C][C]11.3038864382713[/C][C]0.205113561728723[/C][/ROW]
[ROW][C]73[/C][C]25.447[/C][C]30.4742403876788[/C][C]-5.02724038767878[/C][/ROW]
[ROW][C]74[/C][C]24.09[/C][C]27.3001174930027[/C][C]-3.21011749300272[/C][/ROW]
[ROW][C]75[/C][C]27.786[/C][C]28.4355003726381[/C][C]-0.649500372638094[/C][/ROW]
[ROW][C]76[/C][C]26.195[/C][C]27.6009196306679[/C][C]-1.40591963066795[/C][/ROW]
[ROW][C]77[/C][C]20.516[/C][C]23.3065826792077[/C][C]-2.79058267920771[/C][/ROW]
[ROW][C]78[/C][C]22.759[/C][C]23.3108481180279[/C][C]-0.55184811802792[/C][/ROW]
[ROW][C]79[/C][C]19.028[/C][C]17.59848563769[/C][C]1.42951436231003[/C][/ROW]
[ROW][C]80[/C][C]16.971[/C][C]16.1800667536419[/C][C]0.790933246358104[/C][/ROW]
[ROW][C]81[/C][C]20.036[/C][C]18.4670434811774[/C][C]1.56895651882258[/C][/ROW]
[ROW][C]82[/C][C]22.485[/C][C]21.1977921895663[/C][C]1.28720781043368[/C][/ROW]
[ROW][C]83[/C][C]18.73[/C][C]16.0537676205067[/C][C]2.67623237949332[/C][/ROW]
[ROW][C]84[/C][C]14.538[/C][C]11.6020986194158[/C][C]2.9359013805842[/C][/ROW]
[ROW][C]85[/C][C]27.561[/C][C]29.4574897396373[/C][C]-1.89648973963727[/C][/ROW]
[ROW][C]86[/C][C]25.985[/C][C]27.812886453676[/C][C]-1.82788645367602[/C][/ROW]
[ROW][C]87[/C][C]34.67[/C][C]30.9945888307834[/C][C]3.67541116921661[/C][/ROW]
[ROW][C]88[/C][C]32.066[/C][C]30.5082906724925[/C][C]1.55770932750752[/C][/ROW]
[ROW][C]89[/C][C]27.186[/C][C]25.2590379366929[/C][C]1.92696206330707[/C][/ROW]
[ROW][C]90[/C][C]29.586[/C][C]27.9066766605854[/C][C]1.67932333941459[/C][/ROW]
[ROW][C]91[/C][C]21.359[/C][C]22.6892116506813[/C][C]-1.33021165068127[/C][/ROW]
[ROW][C]92[/C][C]21.553[/C][C]19.8935365801293[/C][C]1.65946341987074[/C][/ROW]
[ROW][C]93[/C][C]19.573[/C][C]23.2965843081304[/C][C]-3.72358430813045[/C][/ROW]
[ROW][C]94[/C][C]24.256[/C][C]25.0248703741857[/C][C]-0.768870374185678[/C][/ROW]
[ROW][C]95[/C][C]22.38[/C][C]19.5805325941406[/C][C]2.79946740585943[/C][/ROW]
[ROW][C]96[/C][C]16.167[/C][C]14.6423232141706[/C][C]1.52467678582936[/C][/ROW]
[ROW][C]97[/C][C]27.297[/C][C]30.6626089672762[/C][C]-3.3656089672762[/C][/ROW]
[ROW][C]98[/C][C]28.287[/C][C]28.6351311159572[/C][C]-0.348131115957226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122396&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122396&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1328.02926.73908851391691.28991148608307
1429.38328.59406420526350.788935794736517
1536.43835.80631162444930.631688375550702
1632.03431.82775533593290.206244664067089
1722.67922.65419040399380.0248095960061718
1824.31924.3606438174574-0.0416438174574054
1918.00422.3785573631892-4.37455736318921
2017.53717.9358310666813-0.398831066681261
2120.36620.19508293531510.170917064684858
2222.78224.1677453379306-1.38574533793059
2319.16916.54899572450192.62000427549815
2413.80715.0451672854309-1.23816728543092
2529.74327.55254812255352.19045187744652
2625.59129.3363868270661-3.74538682706612
2729.09635.3166826509825-6.22068265098245
2826.48229.8987923348675-3.41679233486748
2922.40520.66708368517911.73791631482094
3027.04422.59258651548124.45141348451877
3117.9719.2246774176737-1.25467741767373
3218.7317.66100605447641.06899394552358
3319.68420.5929863670096-0.908986367009586
3419.78523.4708488064628-3.68584880646277
3518.47917.61701653946140.861983460538628
3610.69813.7597193612411-3.06171936124105
3731.95626.71572184808345.24027815191662
3829.50625.91824428498893.5877557150111
3934.50632.03228408752482.47371591247516
4027.16529.8280998545382-2.66309985453818
4126.73623.17902868743423.55697131256579
4223.69127.1549251810745-3.46392518107453
4318.15718.792354147262-0.635354147262028
4417.32818.6395403988487-1.31154039884874
4518.20519.9450910340095-1.74009103400945
4620.99521.0114609964673-0.0164609964672984
4717.38218.4173870906547-1.03538709065473
489.36711.9226303211818-2.55563032118179
4931.12429.40882550325481.71517449674517
5026.55126.9681106631271-0.417110663127108
5130.65131.2834339745109-0.632433974510921
5225.85926.0011792503858-0.142179250385752
5325.123.45497107025161.64502892974842
5425.77823.14183998042712.63616001957285
5520.41817.85724955442562.56075044557444
5618.68818.01011166603720.677888333962766
5720.42419.53048912285280.893510877147204
5824.77622.26322231831682.51277768168317
5919.81419.37153946533990.442460534660068
6012.73811.53236198504021.2056380149598
6131.56635.9404540057861-4.37445400578605
6230.11130.4358634100249-0.324863410024946
6330.01935.2387052155291-5.21970521552911
6431.93428.70190853669133.23209146330866
6525.82627.6463850319208-1.82038503192077
6626.83527.072576409823-0.23757640982301
6720.20520.6404261132437-0.435426113243729
6817.78919.0448944892686-1.25589448926862
6920.5220.27877599135620.241224008643751
7022.51823.751046718997-1.23304671899702
7115.57219.0367214045529-3.46472140455286
7211.50911.30388643827130.205113561728723
7325.44730.4742403876788-5.02724038767878
7424.0927.3001174930027-3.21011749300272
7527.78628.4355003726381-0.649500372638094
7626.19527.6009196306679-1.40591963066795
7720.51623.3065826792077-2.79058267920771
7822.75923.3108481180279-0.55184811802792
7919.02817.598485637691.42951436231003
8016.97116.18006675364190.790933246358104
8120.03618.46704348117741.56895651882258
8222.48521.19779218956631.28720781043368
8318.7316.05376762050672.67623237949332
8414.53811.60209861941582.9359013805842
8527.56129.4574897396373-1.89648973963727
8625.98527.812886453676-1.82788645367602
8734.6730.99458883078343.67541116921661
8832.06630.50829067249251.55770932750752
8927.18625.25903793669291.92696206330707
9029.58627.90667666058541.67932333941459
9121.35922.6892116506813-1.33021165068127
9221.55319.89353658012931.65946341987074
9319.57323.2965843081304-3.72358430813045
9424.25625.0248703741857-0.768870374185678
9522.3819.58053259414062.79946740585943
9616.16714.64232321417061.52467678582936
9727.29730.6626089672762-3.3656089672762
9828.28728.6351311159572-0.348131115957226







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9935.661599893754432.062699227513739.2605005599952
10033.059694899405529.340485282150236.7789045166608
10127.426853142247123.650495835013331.2032104494809
10229.559148980674525.602316566640333.5159813947087
10322.21335682794618.33364235435826.0930713015341
10421.320657207117517.342804546376825.2985098678582
10521.311735248787317.208835723446825.4146347741278
10625.657563060736421.18071831007130.1344078114018
10722.13718944129617.781396569403426.4929823131886
10815.751607317931111.688634665340919.8145799705212
10928.637766461673823.341748086061933.9337848372857
11029.0155966083571-46.9237224842763104.95491570099

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
99 & 35.6615998937544 & 32.0626992275137 & 39.2605005599952 \tabularnewline
100 & 33.0596948994055 & 29.3404852821502 & 36.7789045166608 \tabularnewline
101 & 27.4268531422471 & 23.6504958350133 & 31.2032104494809 \tabularnewline
102 & 29.5591489806745 & 25.6023165666403 & 33.5159813947087 \tabularnewline
103 & 22.213356827946 & 18.333642354358 & 26.0930713015341 \tabularnewline
104 & 21.3206572071175 & 17.3428045463768 & 25.2985098678582 \tabularnewline
105 & 21.3117352487873 & 17.2088357234468 & 25.4146347741278 \tabularnewline
106 & 25.6575630607364 & 21.180718310071 & 30.1344078114018 \tabularnewline
107 & 22.137189441296 & 17.7813965694034 & 26.4929823131886 \tabularnewline
108 & 15.7516073179311 & 11.6886346653409 & 19.8145799705212 \tabularnewline
109 & 28.6377664616738 & 23.3417480860619 & 33.9337848372857 \tabularnewline
110 & 29.0155966083571 & -46.9237224842763 & 104.95491570099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122396&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]99[/C][C]35.6615998937544[/C][C]32.0626992275137[/C][C]39.2605005599952[/C][/ROW]
[ROW][C]100[/C][C]33.0596948994055[/C][C]29.3404852821502[/C][C]36.7789045166608[/C][/ROW]
[ROW][C]101[/C][C]27.4268531422471[/C][C]23.6504958350133[/C][C]31.2032104494809[/C][/ROW]
[ROW][C]102[/C][C]29.5591489806745[/C][C]25.6023165666403[/C][C]33.5159813947087[/C][/ROW]
[ROW][C]103[/C][C]22.213356827946[/C][C]18.333642354358[/C][C]26.0930713015341[/C][/ROW]
[ROW][C]104[/C][C]21.3206572071175[/C][C]17.3428045463768[/C][C]25.2985098678582[/C][/ROW]
[ROW][C]105[/C][C]21.3117352487873[/C][C]17.2088357234468[/C][C]25.4146347741278[/C][/ROW]
[ROW][C]106[/C][C]25.6575630607364[/C][C]21.180718310071[/C][C]30.1344078114018[/C][/ROW]
[ROW][C]107[/C][C]22.137189441296[/C][C]17.7813965694034[/C][C]26.4929823131886[/C][/ROW]
[ROW][C]108[/C][C]15.7516073179311[/C][C]11.6886346653409[/C][C]19.8145799705212[/C][/ROW]
[ROW][C]109[/C][C]28.6377664616738[/C][C]23.3417480860619[/C][C]33.9337848372857[/C][/ROW]
[ROW][C]110[/C][C]29.0155966083571[/C][C]-46.9237224842763[/C][C]104.95491570099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122396&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122396&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9935.661599893754432.062699227513739.2605005599952
10033.059694899405529.340485282150236.7789045166608
10127.426853142247123.650495835013331.2032104494809
10229.559148980674525.602316566640333.5159813947087
10322.21335682794618.33364235435826.0930713015341
10421.320657207117517.342804546376825.2985098678582
10521.311735248787317.208835723446825.4146347741278
10625.657563060736421.18071831007130.1344078114018
10722.13718944129617.781396569403426.4929823131886
10815.751607317931111.688634665340919.8145799705212
10928.637766461673823.341748086061933.9337848372857
11029.0155966083571-46.9237224842763104.95491570099



Parameters (Session):
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')