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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 03 Dec 2010 19:14:24 +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/2010/Dec/03/t129140374334uubz0imogt6pp.htm/, Retrieved Tue, 07 May 2024 19:36:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104977, Retrieved Tue, 07 May 2024 19:36:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-12-03 19:14:24] [c9b1b69acb8f4b2b921fdfd5091a94b7] [Current]
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Dataseries X:
12008
9169
8788
8417
8247
8197
8236
8253
7733
8366
8626
8863
10102
8463
9114
8563
8872
8301
8301
8278
7736
7973
8268
9476
11100
8962
9173
8738
8459
8078
8411
8291
7810
8616
8312
9692
9911
8915
9452
9112
8472
8230
8384
8625
8221
8649
8625
10443
10357
8586
8892
8329
8101
7922
8120
7838
7735
8406
8209
9451
10041
9411
10405
8467
8464
8102
7627
7513
7510
8291
8064
9383
9706
8579
9474
8318
8213
8059
9111
7708
7680
8014
8007
8718
9486
9113
9025
8476
7952
7759
7835
7600
7651
8319
8812
8630




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104977&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104977&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104977&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0618419834147308
beta0
gamma0.322340313497252

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0618419834147308 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.322340313497252 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104977&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]0.0618419834147308[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.322340313497252[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104977&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104977&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
alpha0.0618419834147308
beta0
gamma0.322340313497252







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131010210040.433760683861.5662393162402
1484638403.5284350717659.4715649282425
1591149059.0769039743354.9230960256718
1685638529.7607532051333.2392467948721
1788728874.1452968581-2.14529685809612
1883018294.424923482676.57507651732703
1983018164.41050195957136.589498040431
2082788300.72809680264-22.7280968026425
2177367797.19317558775-61.1931755877531
2279738408.77949760859-435.77949760859
2382688611.7423251823-343.742325182295
2494768799.14691404673676.853085953275
251110010093.61849008401006.38150991604
2689628514.50897235092447.491027649075
2791739192.6778494662-19.6778494661939
2887388652.1908989179685.8091010820353
2984598989.12596304143-530.125963041428
3080788379.39131259644-301.391312596435
3184118269.64879929562141.351200704379
3282918358.08224692338-67.082246923379
3378107840.17230073919-30.1723007391902
3486168340.39980801158275.600191988422
3583128615.1883734454-303.188373445406
3696929113.73522726881578.264772731187
37991110501.7613282095-590.761328209517
3889158654.86941101666260.130588983337
3994529180.17680584806271.823194151941
4091128689.61676050825422.383239491748
4184728861.103686033-389.103686032995
4282308329.26089772807-99.260897728067
4383848365.9065887149818.0934112850191
4486258383.68597391713241.314026082870
4582217896.00965962521324.990340374787
4686498510.66861110863138.331388891374
4786258601.9389802379923.0610197620117
48104439387.218595239581055.78140476042
491035710451.2545903467-94.2545903467144
5085868892.3825826454-306.382582645396
5188929386.19159501558-494.191595015576
5283298893.78995931962-564.789959319616
5381018758.82950000134-657.829500001344
5479228298.01841584362-376.018415843619
5581208353.0375376632-233.037537663193
5678388422.78977342329-584.78977342329
5777357909.32979364573-174.329793645733
5884068436.66298295507-30.6629829550675
5982098482.623936501-273.623936501006
6094519561.85696016096-110.856960160962
611004110205.9677681594-164.967768159438
6294118578.57390800513832.42609199487
63104059086.014507333541318.98549266646
6484678684.39395953467-217.393959534669
6584648542.78142865477-78.781428654771
6681028203.00123047686-101.001230476862
6776278318.266257289-691.266257289006
6875138253.30868108957-740.308681089573
6975107854.35672547885-344.356725478853
7082918414.62083907508-123.620839075076
7180648381.3602080626-317.360208062602
7293839507.11022847005-124.110228470046
73970610134.0379869939-428.037986993937
7485798791.99337919066-212.993379190664
7594749381.9217196230992.0782803769125
7683188439.81620253703-121.816202537029
7782138346.03167141113-133.031671411134
7880597996.1771259159762.8228740840332
7991117943.073586533741167.92641346626
8077087978.26144211615-270.261442116152
8176807728.11644621713-48.1164462171328
8280148373.45253564256-359.452535642564
8380078267.01962824298-260.019628242977
8487189454.75568599356-736.755685993556
8594869951.88661121125-465.886611211248
8691138672.53218116372440.467818836281
8790259395.12740395928-370.127403959275
8884768359.7551637003116.244836299706
8979528277.30117263641-325.301172636413
9077597974.78391873713-215.783918737132
9178358238.64088847943-403.640888479433
9276007741.72305384134-141.723053841341
9376517566.7051395867284.294860413278
9483198126.07985893804192.920141061962
9588128083.87589607805728.124103921947
9686309188.55280672682-558.552806726819

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 10102 & 10040.4337606838 & 61.5662393162402 \tabularnewline
14 & 8463 & 8403.52843507176 & 59.4715649282425 \tabularnewline
15 & 9114 & 9059.07690397433 & 54.9230960256718 \tabularnewline
16 & 8563 & 8529.76075320513 & 33.2392467948721 \tabularnewline
17 & 8872 & 8874.1452968581 & -2.14529685809612 \tabularnewline
18 & 8301 & 8294.42492348267 & 6.57507651732703 \tabularnewline
19 & 8301 & 8164.41050195957 & 136.589498040431 \tabularnewline
20 & 8278 & 8300.72809680264 & -22.7280968026425 \tabularnewline
21 & 7736 & 7797.19317558775 & -61.1931755877531 \tabularnewline
22 & 7973 & 8408.77949760859 & -435.77949760859 \tabularnewline
23 & 8268 & 8611.7423251823 & -343.742325182295 \tabularnewline
24 & 9476 & 8799.14691404673 & 676.853085953275 \tabularnewline
25 & 11100 & 10093.6184900840 & 1006.38150991604 \tabularnewline
26 & 8962 & 8514.50897235092 & 447.491027649075 \tabularnewline
27 & 9173 & 9192.6778494662 & -19.6778494661939 \tabularnewline
28 & 8738 & 8652.19089891796 & 85.8091010820353 \tabularnewline
29 & 8459 & 8989.12596304143 & -530.125963041428 \tabularnewline
30 & 8078 & 8379.39131259644 & -301.391312596435 \tabularnewline
31 & 8411 & 8269.64879929562 & 141.351200704379 \tabularnewline
32 & 8291 & 8358.08224692338 & -67.082246923379 \tabularnewline
33 & 7810 & 7840.17230073919 & -30.1723007391902 \tabularnewline
34 & 8616 & 8340.39980801158 & 275.600191988422 \tabularnewline
35 & 8312 & 8615.1883734454 & -303.188373445406 \tabularnewline
36 & 9692 & 9113.73522726881 & 578.264772731187 \tabularnewline
37 & 9911 & 10501.7613282095 & -590.761328209517 \tabularnewline
38 & 8915 & 8654.86941101666 & 260.130588983337 \tabularnewline
39 & 9452 & 9180.17680584806 & 271.823194151941 \tabularnewline
40 & 9112 & 8689.61676050825 & 422.383239491748 \tabularnewline
41 & 8472 & 8861.103686033 & -389.103686032995 \tabularnewline
42 & 8230 & 8329.26089772807 & -99.260897728067 \tabularnewline
43 & 8384 & 8365.90658871498 & 18.0934112850191 \tabularnewline
44 & 8625 & 8383.68597391713 & 241.314026082870 \tabularnewline
45 & 8221 & 7896.00965962521 & 324.990340374787 \tabularnewline
46 & 8649 & 8510.66861110863 & 138.331388891374 \tabularnewline
47 & 8625 & 8601.93898023799 & 23.0610197620117 \tabularnewline
48 & 10443 & 9387.21859523958 & 1055.78140476042 \tabularnewline
49 & 10357 & 10451.2545903467 & -94.2545903467144 \tabularnewline
50 & 8586 & 8892.3825826454 & -306.382582645396 \tabularnewline
51 & 8892 & 9386.19159501558 & -494.191595015576 \tabularnewline
52 & 8329 & 8893.78995931962 & -564.789959319616 \tabularnewline
53 & 8101 & 8758.82950000134 & -657.829500001344 \tabularnewline
54 & 7922 & 8298.01841584362 & -376.018415843619 \tabularnewline
55 & 8120 & 8353.0375376632 & -233.037537663193 \tabularnewline
56 & 7838 & 8422.78977342329 & -584.78977342329 \tabularnewline
57 & 7735 & 7909.32979364573 & -174.329793645733 \tabularnewline
58 & 8406 & 8436.66298295507 & -30.6629829550675 \tabularnewline
59 & 8209 & 8482.623936501 & -273.623936501006 \tabularnewline
60 & 9451 & 9561.85696016096 & -110.856960160962 \tabularnewline
61 & 10041 & 10205.9677681594 & -164.967768159438 \tabularnewline
62 & 9411 & 8578.57390800513 & 832.42609199487 \tabularnewline
63 & 10405 & 9086.01450733354 & 1318.98549266646 \tabularnewline
64 & 8467 & 8684.39395953467 & -217.393959534669 \tabularnewline
65 & 8464 & 8542.78142865477 & -78.781428654771 \tabularnewline
66 & 8102 & 8203.00123047686 & -101.001230476862 \tabularnewline
67 & 7627 & 8318.266257289 & -691.266257289006 \tabularnewline
68 & 7513 & 8253.30868108957 & -740.308681089573 \tabularnewline
69 & 7510 & 7854.35672547885 & -344.356725478853 \tabularnewline
70 & 8291 & 8414.62083907508 & -123.620839075076 \tabularnewline
71 & 8064 & 8381.3602080626 & -317.360208062602 \tabularnewline
72 & 9383 & 9507.11022847005 & -124.110228470046 \tabularnewline
73 & 9706 & 10134.0379869939 & -428.037986993937 \tabularnewline
74 & 8579 & 8791.99337919066 & -212.993379190664 \tabularnewline
75 & 9474 & 9381.92171962309 & 92.0782803769125 \tabularnewline
76 & 8318 & 8439.81620253703 & -121.816202537029 \tabularnewline
77 & 8213 & 8346.03167141113 & -133.031671411134 \tabularnewline
78 & 8059 & 7996.17712591597 & 62.8228740840332 \tabularnewline
79 & 9111 & 7943.07358653374 & 1167.92641346626 \tabularnewline
80 & 7708 & 7978.26144211615 & -270.261442116152 \tabularnewline
81 & 7680 & 7728.11644621713 & -48.1164462171328 \tabularnewline
82 & 8014 & 8373.45253564256 & -359.452535642564 \tabularnewline
83 & 8007 & 8267.01962824298 & -260.019628242977 \tabularnewline
84 & 8718 & 9454.75568599356 & -736.755685993556 \tabularnewline
85 & 9486 & 9951.88661121125 & -465.886611211248 \tabularnewline
86 & 9113 & 8672.53218116372 & 440.467818836281 \tabularnewline
87 & 9025 & 9395.12740395928 & -370.127403959275 \tabularnewline
88 & 8476 & 8359.7551637003 & 116.244836299706 \tabularnewline
89 & 7952 & 8277.30117263641 & -325.301172636413 \tabularnewline
90 & 7759 & 7974.78391873713 & -215.783918737132 \tabularnewline
91 & 7835 & 8238.64088847943 & -403.640888479433 \tabularnewline
92 & 7600 & 7741.72305384134 & -141.723053841341 \tabularnewline
93 & 7651 & 7566.70513958672 & 84.294860413278 \tabularnewline
94 & 8319 & 8126.07985893804 & 192.920141061962 \tabularnewline
95 & 8812 & 8083.87589607805 & 728.124103921947 \tabularnewline
96 & 8630 & 9188.55280672682 & -558.552806726819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104977&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]10102[/C][C]10040.4337606838[/C][C]61.5662393162402[/C][/ROW]
[ROW][C]14[/C][C]8463[/C][C]8403.52843507176[/C][C]59.4715649282425[/C][/ROW]
[ROW][C]15[/C][C]9114[/C][C]9059.07690397433[/C][C]54.9230960256718[/C][/ROW]
[ROW][C]16[/C][C]8563[/C][C]8529.76075320513[/C][C]33.2392467948721[/C][/ROW]
[ROW][C]17[/C][C]8872[/C][C]8874.1452968581[/C][C]-2.14529685809612[/C][/ROW]
[ROW][C]18[/C][C]8301[/C][C]8294.42492348267[/C][C]6.57507651732703[/C][/ROW]
[ROW][C]19[/C][C]8301[/C][C]8164.41050195957[/C][C]136.589498040431[/C][/ROW]
[ROW][C]20[/C][C]8278[/C][C]8300.72809680264[/C][C]-22.7280968026425[/C][/ROW]
[ROW][C]21[/C][C]7736[/C][C]7797.19317558775[/C][C]-61.1931755877531[/C][/ROW]
[ROW][C]22[/C][C]7973[/C][C]8408.77949760859[/C][C]-435.77949760859[/C][/ROW]
[ROW][C]23[/C][C]8268[/C][C]8611.7423251823[/C][C]-343.742325182295[/C][/ROW]
[ROW][C]24[/C][C]9476[/C][C]8799.14691404673[/C][C]676.853085953275[/C][/ROW]
[ROW][C]25[/C][C]11100[/C][C]10093.6184900840[/C][C]1006.38150991604[/C][/ROW]
[ROW][C]26[/C][C]8962[/C][C]8514.50897235092[/C][C]447.491027649075[/C][/ROW]
[ROW][C]27[/C][C]9173[/C][C]9192.6778494662[/C][C]-19.6778494661939[/C][/ROW]
[ROW][C]28[/C][C]8738[/C][C]8652.19089891796[/C][C]85.8091010820353[/C][/ROW]
[ROW][C]29[/C][C]8459[/C][C]8989.12596304143[/C][C]-530.125963041428[/C][/ROW]
[ROW][C]30[/C][C]8078[/C][C]8379.39131259644[/C][C]-301.391312596435[/C][/ROW]
[ROW][C]31[/C][C]8411[/C][C]8269.64879929562[/C][C]141.351200704379[/C][/ROW]
[ROW][C]32[/C][C]8291[/C][C]8358.08224692338[/C][C]-67.082246923379[/C][/ROW]
[ROW][C]33[/C][C]7810[/C][C]7840.17230073919[/C][C]-30.1723007391902[/C][/ROW]
[ROW][C]34[/C][C]8616[/C][C]8340.39980801158[/C][C]275.600191988422[/C][/ROW]
[ROW][C]35[/C][C]8312[/C][C]8615.1883734454[/C][C]-303.188373445406[/C][/ROW]
[ROW][C]36[/C][C]9692[/C][C]9113.73522726881[/C][C]578.264772731187[/C][/ROW]
[ROW][C]37[/C][C]9911[/C][C]10501.7613282095[/C][C]-590.761328209517[/C][/ROW]
[ROW][C]38[/C][C]8915[/C][C]8654.86941101666[/C][C]260.130588983337[/C][/ROW]
[ROW][C]39[/C][C]9452[/C][C]9180.17680584806[/C][C]271.823194151941[/C][/ROW]
[ROW][C]40[/C][C]9112[/C][C]8689.61676050825[/C][C]422.383239491748[/C][/ROW]
[ROW][C]41[/C][C]8472[/C][C]8861.103686033[/C][C]-389.103686032995[/C][/ROW]
[ROW][C]42[/C][C]8230[/C][C]8329.26089772807[/C][C]-99.260897728067[/C][/ROW]
[ROW][C]43[/C][C]8384[/C][C]8365.90658871498[/C][C]18.0934112850191[/C][/ROW]
[ROW][C]44[/C][C]8625[/C][C]8383.68597391713[/C][C]241.314026082870[/C][/ROW]
[ROW][C]45[/C][C]8221[/C][C]7896.00965962521[/C][C]324.990340374787[/C][/ROW]
[ROW][C]46[/C][C]8649[/C][C]8510.66861110863[/C][C]138.331388891374[/C][/ROW]
[ROW][C]47[/C][C]8625[/C][C]8601.93898023799[/C][C]23.0610197620117[/C][/ROW]
[ROW][C]48[/C][C]10443[/C][C]9387.21859523958[/C][C]1055.78140476042[/C][/ROW]
[ROW][C]49[/C][C]10357[/C][C]10451.2545903467[/C][C]-94.2545903467144[/C][/ROW]
[ROW][C]50[/C][C]8586[/C][C]8892.3825826454[/C][C]-306.382582645396[/C][/ROW]
[ROW][C]51[/C][C]8892[/C][C]9386.19159501558[/C][C]-494.191595015576[/C][/ROW]
[ROW][C]52[/C][C]8329[/C][C]8893.78995931962[/C][C]-564.789959319616[/C][/ROW]
[ROW][C]53[/C][C]8101[/C][C]8758.82950000134[/C][C]-657.829500001344[/C][/ROW]
[ROW][C]54[/C][C]7922[/C][C]8298.01841584362[/C][C]-376.018415843619[/C][/ROW]
[ROW][C]55[/C][C]8120[/C][C]8353.0375376632[/C][C]-233.037537663193[/C][/ROW]
[ROW][C]56[/C][C]7838[/C][C]8422.78977342329[/C][C]-584.78977342329[/C][/ROW]
[ROW][C]57[/C][C]7735[/C][C]7909.32979364573[/C][C]-174.329793645733[/C][/ROW]
[ROW][C]58[/C][C]8406[/C][C]8436.66298295507[/C][C]-30.6629829550675[/C][/ROW]
[ROW][C]59[/C][C]8209[/C][C]8482.623936501[/C][C]-273.623936501006[/C][/ROW]
[ROW][C]60[/C][C]9451[/C][C]9561.85696016096[/C][C]-110.856960160962[/C][/ROW]
[ROW][C]61[/C][C]10041[/C][C]10205.9677681594[/C][C]-164.967768159438[/C][/ROW]
[ROW][C]62[/C][C]9411[/C][C]8578.57390800513[/C][C]832.42609199487[/C][/ROW]
[ROW][C]63[/C][C]10405[/C][C]9086.01450733354[/C][C]1318.98549266646[/C][/ROW]
[ROW][C]64[/C][C]8467[/C][C]8684.39395953467[/C][C]-217.393959534669[/C][/ROW]
[ROW][C]65[/C][C]8464[/C][C]8542.78142865477[/C][C]-78.781428654771[/C][/ROW]
[ROW][C]66[/C][C]8102[/C][C]8203.00123047686[/C][C]-101.001230476862[/C][/ROW]
[ROW][C]67[/C][C]7627[/C][C]8318.266257289[/C][C]-691.266257289006[/C][/ROW]
[ROW][C]68[/C][C]7513[/C][C]8253.30868108957[/C][C]-740.308681089573[/C][/ROW]
[ROW][C]69[/C][C]7510[/C][C]7854.35672547885[/C][C]-344.356725478853[/C][/ROW]
[ROW][C]70[/C][C]8291[/C][C]8414.62083907508[/C][C]-123.620839075076[/C][/ROW]
[ROW][C]71[/C][C]8064[/C][C]8381.3602080626[/C][C]-317.360208062602[/C][/ROW]
[ROW][C]72[/C][C]9383[/C][C]9507.11022847005[/C][C]-124.110228470046[/C][/ROW]
[ROW][C]73[/C][C]9706[/C][C]10134.0379869939[/C][C]-428.037986993937[/C][/ROW]
[ROW][C]74[/C][C]8579[/C][C]8791.99337919066[/C][C]-212.993379190664[/C][/ROW]
[ROW][C]75[/C][C]9474[/C][C]9381.92171962309[/C][C]92.0782803769125[/C][/ROW]
[ROW][C]76[/C][C]8318[/C][C]8439.81620253703[/C][C]-121.816202537029[/C][/ROW]
[ROW][C]77[/C][C]8213[/C][C]8346.03167141113[/C][C]-133.031671411134[/C][/ROW]
[ROW][C]78[/C][C]8059[/C][C]7996.17712591597[/C][C]62.8228740840332[/C][/ROW]
[ROW][C]79[/C][C]9111[/C][C]7943.07358653374[/C][C]1167.92641346626[/C][/ROW]
[ROW][C]80[/C][C]7708[/C][C]7978.26144211615[/C][C]-270.261442116152[/C][/ROW]
[ROW][C]81[/C][C]7680[/C][C]7728.11644621713[/C][C]-48.1164462171328[/C][/ROW]
[ROW][C]82[/C][C]8014[/C][C]8373.45253564256[/C][C]-359.452535642564[/C][/ROW]
[ROW][C]83[/C][C]8007[/C][C]8267.01962824298[/C][C]-260.019628242977[/C][/ROW]
[ROW][C]84[/C][C]8718[/C][C]9454.75568599356[/C][C]-736.755685993556[/C][/ROW]
[ROW][C]85[/C][C]9486[/C][C]9951.88661121125[/C][C]-465.886611211248[/C][/ROW]
[ROW][C]86[/C][C]9113[/C][C]8672.53218116372[/C][C]440.467818836281[/C][/ROW]
[ROW][C]87[/C][C]9025[/C][C]9395.12740395928[/C][C]-370.127403959275[/C][/ROW]
[ROW][C]88[/C][C]8476[/C][C]8359.7551637003[/C][C]116.244836299706[/C][/ROW]
[ROW][C]89[/C][C]7952[/C][C]8277.30117263641[/C][C]-325.301172636413[/C][/ROW]
[ROW][C]90[/C][C]7759[/C][C]7974.78391873713[/C][C]-215.783918737132[/C][/ROW]
[ROW][C]91[/C][C]7835[/C][C]8238.64088847943[/C][C]-403.640888479433[/C][/ROW]
[ROW][C]92[/C][C]7600[/C][C]7741.72305384134[/C][C]-141.723053841341[/C][/ROW]
[ROW][C]93[/C][C]7651[/C][C]7566.70513958672[/C][C]84.294860413278[/C][/ROW]
[ROW][C]94[/C][C]8319[/C][C]8126.07985893804[/C][C]192.920141061962[/C][/ROW]
[ROW][C]95[/C][C]8812[/C][C]8083.87589607805[/C][C]728.124103921947[/C][/ROW]
[ROW][C]96[/C][C]8630[/C][C]9188.55280672682[/C][C]-558.552806726819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104977&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104977&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
131010210040.433760683861.5662393162402
1484638403.5284350717659.4715649282425
1591149059.0769039743354.9230960256718
1685638529.7607532051333.2392467948721
1788728874.1452968581-2.14529685809612
1883018294.424923482676.57507651732703
1983018164.41050195957136.589498040431
2082788300.72809680264-22.7280968026425
2177367797.19317558775-61.1931755877531
2279738408.77949760859-435.77949760859
2382688611.7423251823-343.742325182295
2494768799.14691404673676.853085953275
251110010093.61849008401006.38150991604
2689628514.50897235092447.491027649075
2791739192.6778494662-19.6778494661939
2887388652.1908989179685.8091010820353
2984598989.12596304143-530.125963041428
3080788379.39131259644-301.391312596435
3184118269.64879929562141.351200704379
3282918358.08224692338-67.082246923379
3378107840.17230073919-30.1723007391902
3486168340.39980801158275.600191988422
3583128615.1883734454-303.188373445406
3696929113.73522726881578.264772731187
37991110501.7613282095-590.761328209517
3889158654.86941101666260.130588983337
3994529180.17680584806271.823194151941
4091128689.61676050825422.383239491748
4184728861.103686033-389.103686032995
4282308329.26089772807-99.260897728067
4383848365.9065887149818.0934112850191
4486258383.68597391713241.314026082870
4582217896.00965962521324.990340374787
4686498510.66861110863138.331388891374
4786258601.9389802379923.0610197620117
48104439387.218595239581055.78140476042
491035710451.2545903467-94.2545903467144
5085868892.3825826454-306.382582645396
5188929386.19159501558-494.191595015576
5283298893.78995931962-564.789959319616
5381018758.82950000134-657.829500001344
5479228298.01841584362-376.018415843619
5581208353.0375376632-233.037537663193
5678388422.78977342329-584.78977342329
5777357909.32979364573-174.329793645733
5884068436.66298295507-30.6629829550675
5982098482.623936501-273.623936501006
6094519561.85696016096-110.856960160962
611004110205.9677681594-164.967768159438
6294118578.57390800513832.42609199487
63104059086.014507333541318.98549266646
6484678684.39395953467-217.393959534669
6584648542.78142865477-78.781428654771
6681028203.00123047686-101.001230476862
6776278318.266257289-691.266257289006
6875138253.30868108957-740.308681089573
6975107854.35672547885-344.356725478853
7082918414.62083907508-123.620839075076
7180648381.3602080626-317.360208062602
7293839507.11022847005-124.110228470046
73970610134.0379869939-428.037986993937
7485798791.99337919066-212.993379190664
7594749381.9217196230992.0782803769125
7683188439.81620253703-121.816202537029
7782138346.03167141113-133.031671411134
7880597996.1771259159762.8228740840332
7991117943.073586533741167.92641346626
8077087978.26144211615-270.261442116152
8176807728.11644621713-48.1164462171328
8280148373.45253564256-359.452535642564
8380078267.01962824298-260.019628242977
8487189454.75568599356-736.755685993556
8594869951.88661121125-465.886611211248
8691138672.53218116372440.467818836281
8790259395.12740395928-370.127403959275
8884768359.7551637003116.244836299706
8979528277.30117263641-325.301172636413
9077597974.78391873713-215.783918737132
9178358238.64088847943-403.640888479433
9276007741.72305384134-141.723053841341
9376517566.7051395867284.294860413278
9483198126.07985893804192.920141061962
9588128083.87589607805728.124103921947
9686309188.55280672682-558.552806726819







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
979778.616625284388954.414385688410602.8188648804
988802.160700299867976.383912443339627.93748815638
999252.38753968218425.0392001235610079.7358792406
1008386.986668442967558.069756697349215.90358018858
1018163.817637894167333.335116593728994.3001591946
1027914.536344737877082.491159791078746.58152968467
1038134.928717188237301.323797936448968.53363644002
1047742.178399454426907.016658826658577.3401400822
1057644.274127039496807.558461705068480.98979237392
1068231.284837855327393.018128374589069.55154733605
1078338.999280263667499.184391236759178.81416929058
1089009.548542370788168.188322584449850.90876215713

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 9778.61662528438 & 8954.4143856884 & 10602.8188648804 \tabularnewline
98 & 8802.16070029986 & 7976.38391244333 & 9627.93748815638 \tabularnewline
99 & 9252.3875396821 & 8425.03920012356 & 10079.7358792406 \tabularnewline
100 & 8386.98666844296 & 7558.06975669734 & 9215.90358018858 \tabularnewline
101 & 8163.81763789416 & 7333.33511659372 & 8994.3001591946 \tabularnewline
102 & 7914.53634473787 & 7082.49115979107 & 8746.58152968467 \tabularnewline
103 & 8134.92871718823 & 7301.32379793644 & 8968.53363644002 \tabularnewline
104 & 7742.17839945442 & 6907.01665882665 & 8577.3401400822 \tabularnewline
105 & 7644.27412703949 & 6807.55846170506 & 8480.98979237392 \tabularnewline
106 & 8231.28483785532 & 7393.01812837458 & 9069.55154733605 \tabularnewline
107 & 8338.99928026366 & 7499.18439123675 & 9178.81416929058 \tabularnewline
108 & 9009.54854237078 & 8168.18832258444 & 9850.90876215713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104977&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]97[/C][C]9778.61662528438[/C][C]8954.4143856884[/C][C]10602.8188648804[/C][/ROW]
[ROW][C]98[/C][C]8802.16070029986[/C][C]7976.38391244333[/C][C]9627.93748815638[/C][/ROW]
[ROW][C]99[/C][C]9252.3875396821[/C][C]8425.03920012356[/C][C]10079.7358792406[/C][/ROW]
[ROW][C]100[/C][C]8386.98666844296[/C][C]7558.06975669734[/C][C]9215.90358018858[/C][/ROW]
[ROW][C]101[/C][C]8163.81763789416[/C][C]7333.33511659372[/C][C]8994.3001591946[/C][/ROW]
[ROW][C]102[/C][C]7914.53634473787[/C][C]7082.49115979107[/C][C]8746.58152968467[/C][/ROW]
[ROW][C]103[/C][C]8134.92871718823[/C][C]7301.32379793644[/C][C]8968.53363644002[/C][/ROW]
[ROW][C]104[/C][C]7742.17839945442[/C][C]6907.01665882665[/C][C]8577.3401400822[/C][/ROW]
[ROW][C]105[/C][C]7644.27412703949[/C][C]6807.55846170506[/C][C]8480.98979237392[/C][/ROW]
[ROW][C]106[/C][C]8231.28483785532[/C][C]7393.01812837458[/C][C]9069.55154733605[/C][/ROW]
[ROW][C]107[/C][C]8338.99928026366[/C][C]7499.18439123675[/C][C]9178.81416929058[/C][/ROW]
[ROW][C]108[/C][C]9009.54854237078[/C][C]8168.18832258444[/C][C]9850.90876215713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104977&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104977&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
979778.616625284388954.414385688410602.8188648804
988802.160700299867976.383912443339627.93748815638
999252.38753968218425.0392001235610079.7358792406
1008386.986668442967558.069756697349215.90358018858
1018163.817637894167333.335116593728994.3001591946
1027914.536344737877082.491159791078746.58152968467
1038134.928717188237301.323797936448968.53363644002
1047742.178399454426907.016658826658577.3401400822
1057644.274127039496807.558461705068480.98979237392
1068231.284837855327393.018128374589069.55154733605
1078338.999280263667499.184391236759178.81416929058
1089009.548542370788168.188322584449850.90876215713



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')