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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 computationThu, 13 Dec 2012 11:02:47 -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/2012/Dec/13/t1355414736k80necc8t67rrpi.htm/, Retrieved Mon, 29 Apr 2024 01:03:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=199301, Retrieved Mon, 29 Apr 2024 01:03:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Paper 4.2] [2012-12-13 16:02:47] [851af2766980873020febd248b5479af] [Current]
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Dataseries X:
3464
2582
3015
2629
1881
2654
2518
1612
1631
1980
2320
988
3395
3017
3631
2570
2403
2465
1711
1541
1751
2103
1410
823
3471
2207
2483
2334
2273
2247
1667
1692
1779
2000
1934
851
3314
3178
3360
2787
2474
2563
2528
1649
1902
2141
1471
1178
3038
2633
2636
2708
2252
2579
2321
1490
2076
2333
1566
961
3683
2904
3097
3269
2491
2692
2293
1994
2069
2540
2091
1109
4761
3051
3737
3505
2837
3419
2658
2133
2276
2403
1975
996
4505
3890
4352
3288
3314
2830
2414
2049
1981
2527
1813
926
4277
3301
3773
3175
3045
2933
2544
2324
2229
2844
2175
1055




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199301&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199301&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225106730423627
beta0
gamma0.506246088410288

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.225106730423627 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.506246088410288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199301&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]0.225106730423627[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.506246088410288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199301&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
alpha0.225106730423627
beta0
gamma0.506246088410288







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1333953322.8477564102672.1522435897436
1430172994.8370896798522.162910320149
1536313608.9484875810722.0515124189315
1625702539.9514757316330.0485242683653
1724032409.67131173945-6.6713117394529
1824652512.12526552186-47.1252655218586
1917112523.5977620356-812.597762035598
2015411416.59058096325124.409419036747
2117511416.9683561389334.031643861104
2221031815.11683830221287.88316169779
2314102197.79365319839-787.793653198393
24823671.745043967462151.254956032538
2534713179.76196144216291.238038557842
2622072881.45883178269-674.458831782686
2724833338.71228706355-855.712287063554
2823342075.26185750998258.73814249002
2922731982.05656295535290.943437044648
3022472135.63605227086111.363947729139
3116671882.50086800136-215.500868001362
3216921277.47965892926414.520341070744
3317791425.39536325048353.604636749515
3420001809.84642268535190.153577314651
3519341748.54995674439185.450043255606
36851809.961321454141.0386785459002
3733143348.08131269641-34.0813126964104
3831782597.71658195019580.283418049808
3933603266.317645197793.6823548022976
4027872653.76640581097133.233594189028
4124742544.94290102871-70.942901028709
4225632546.6126971401416.3873028598609
4325282143.87291532935384.127084670647
4416491920.98092678533-271.980926785332
4519021890.4641554541611.5358445458382
4621412133.793552959577.20644704042707
4714712029.46932289059-558.469322890594
481178866.768775610509311.231224389491
4930383436.24235496624-398.242354966245
5026332844.90962727128-211.909627271277
5126363144.29558539635-508.295585396354
5227082411.75048475661296.249515243387
5322522259.52724016738-7.52724016738239
5425792309.73080468162269.269195318383
5523212108.17585942458212.82414057542
5614901589.33998731918-99.3399873191802
5720761708.90570824612367.094291753881
5823332030.57534027441302.424659725591
5915661770.79964331526-204.799643315259
609611028.88446733194-67.8844673319363
6136833234.69951315476448.300486845236
6229042907.025125107-3.02512510700308
6330973137.16412506546-40.1641250654566
6432692825.61089866653443.389101333467
6524912587.34218835397-96.3421883539668
6626922726.13646682477-34.1364668247693
6722932434.1402214673-141.140221467298
6819941713.16675771056280.833242289436
6920692101.28798923081-32.2879892308051
7025402307.6849461217232.3150538783
7120911833.14976378642257.850236213583
7211091249.09019025448-140.090190254479
7347613641.143727249471119.85627275053
7430513287.59203754706-236.592037547056
7537373450.58441827148286.415581728524
7635053402.23797489871102.762025101288
7728372875.56241784436-38.5624178443595
7834193051.7657879291367.234212070903
7926582808.14463541701-150.144635417005
8021332250.67878943161-117.678789431611
8122762426.25899002115-150.258990021146
8224032709.90013170035-306.900131700351
8319752124.00109401622-149.001094016217
849961292.24981638112-296.24981638112
8545054143.41099385389361.589006146105
8638903087.05162570874802.948374291259
8743523689.22047574808662.779524251919
8832883653.55124370376-365.551243703757
8933142966.01552042769347.984479572307
9028303388.42181415194-558.421814151937
9124142733.46842625167-319.468426251671
9220492150.62257447973-101.622574479726
9319812317.03635818012-336.036358180122
9425272497.4095294626129.5904705373869
9518132049.19848138617-236.198481386168
969261140.05477156751-214.054771567514
9742774267.780018879849.21998112016445
9833013305.23941576388-4.23941576388142
9937733670.71848779137102.281512208629
10031753105.4769110967269.523088903281
10130452795.78991302151249.210086978491
10229332840.3903044478992.6096955521134
10325442425.72672390508118.273276094925
10423242026.87750291236297.122497087641
10522292191.0940794309137.9059205690901
10628442599.07471164084244.925288359157
10721752095.071513050179.9284869499029
10810551265.7767940274-210.776794027397

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3395 & 3322.84775641026 & 72.1522435897436 \tabularnewline
14 & 3017 & 2994.83708967985 & 22.162910320149 \tabularnewline
15 & 3631 & 3608.94848758107 & 22.0515124189315 \tabularnewline
16 & 2570 & 2539.95147573163 & 30.0485242683653 \tabularnewline
17 & 2403 & 2409.67131173945 & -6.6713117394529 \tabularnewline
18 & 2465 & 2512.12526552186 & -47.1252655218586 \tabularnewline
19 & 1711 & 2523.5977620356 & -812.597762035598 \tabularnewline
20 & 1541 & 1416.59058096325 & 124.409419036747 \tabularnewline
21 & 1751 & 1416.9683561389 & 334.031643861104 \tabularnewline
22 & 2103 & 1815.11683830221 & 287.88316169779 \tabularnewline
23 & 1410 & 2197.79365319839 & -787.793653198393 \tabularnewline
24 & 823 & 671.745043967462 & 151.254956032538 \tabularnewline
25 & 3471 & 3179.76196144216 & 291.238038557842 \tabularnewline
26 & 2207 & 2881.45883178269 & -674.458831782686 \tabularnewline
27 & 2483 & 3338.71228706355 & -855.712287063554 \tabularnewline
28 & 2334 & 2075.26185750998 & 258.73814249002 \tabularnewline
29 & 2273 & 1982.05656295535 & 290.943437044648 \tabularnewline
30 & 2247 & 2135.63605227086 & 111.363947729139 \tabularnewline
31 & 1667 & 1882.50086800136 & -215.500868001362 \tabularnewline
32 & 1692 & 1277.47965892926 & 414.520341070744 \tabularnewline
33 & 1779 & 1425.39536325048 & 353.604636749515 \tabularnewline
34 & 2000 & 1809.84642268535 & 190.153577314651 \tabularnewline
35 & 1934 & 1748.54995674439 & 185.450043255606 \tabularnewline
36 & 851 & 809.9613214541 & 41.0386785459002 \tabularnewline
37 & 3314 & 3348.08131269641 & -34.0813126964104 \tabularnewline
38 & 3178 & 2597.71658195019 & 580.283418049808 \tabularnewline
39 & 3360 & 3266.3176451977 & 93.6823548022976 \tabularnewline
40 & 2787 & 2653.76640581097 & 133.233594189028 \tabularnewline
41 & 2474 & 2544.94290102871 & -70.942901028709 \tabularnewline
42 & 2563 & 2546.61269714014 & 16.3873028598609 \tabularnewline
43 & 2528 & 2143.87291532935 & 384.127084670647 \tabularnewline
44 & 1649 & 1920.98092678533 & -271.980926785332 \tabularnewline
45 & 1902 & 1890.46415545416 & 11.5358445458382 \tabularnewline
46 & 2141 & 2133.79355295957 & 7.20644704042707 \tabularnewline
47 & 1471 & 2029.46932289059 & -558.469322890594 \tabularnewline
48 & 1178 & 866.768775610509 & 311.231224389491 \tabularnewline
49 & 3038 & 3436.24235496624 & -398.242354966245 \tabularnewline
50 & 2633 & 2844.90962727128 & -211.909627271277 \tabularnewline
51 & 2636 & 3144.29558539635 & -508.295585396354 \tabularnewline
52 & 2708 & 2411.75048475661 & 296.249515243387 \tabularnewline
53 & 2252 & 2259.52724016738 & -7.52724016738239 \tabularnewline
54 & 2579 & 2309.73080468162 & 269.269195318383 \tabularnewline
55 & 2321 & 2108.17585942458 & 212.82414057542 \tabularnewline
56 & 1490 & 1589.33998731918 & -99.3399873191802 \tabularnewline
57 & 2076 & 1708.90570824612 & 367.094291753881 \tabularnewline
58 & 2333 & 2030.57534027441 & 302.424659725591 \tabularnewline
59 & 1566 & 1770.79964331526 & -204.799643315259 \tabularnewline
60 & 961 & 1028.88446733194 & -67.8844673319363 \tabularnewline
61 & 3683 & 3234.69951315476 & 448.300486845236 \tabularnewline
62 & 2904 & 2907.025125107 & -3.02512510700308 \tabularnewline
63 & 3097 & 3137.16412506546 & -40.1641250654566 \tabularnewline
64 & 3269 & 2825.61089866653 & 443.389101333467 \tabularnewline
65 & 2491 & 2587.34218835397 & -96.3421883539668 \tabularnewline
66 & 2692 & 2726.13646682477 & -34.1364668247693 \tabularnewline
67 & 2293 & 2434.1402214673 & -141.140221467298 \tabularnewline
68 & 1994 & 1713.16675771056 & 280.833242289436 \tabularnewline
69 & 2069 & 2101.28798923081 & -32.2879892308051 \tabularnewline
70 & 2540 & 2307.6849461217 & 232.3150538783 \tabularnewline
71 & 2091 & 1833.14976378642 & 257.850236213583 \tabularnewline
72 & 1109 & 1249.09019025448 & -140.090190254479 \tabularnewline
73 & 4761 & 3641.14372724947 & 1119.85627275053 \tabularnewline
74 & 3051 & 3287.59203754706 & -236.592037547056 \tabularnewline
75 & 3737 & 3450.58441827148 & 286.415581728524 \tabularnewline
76 & 3505 & 3402.23797489871 & 102.762025101288 \tabularnewline
77 & 2837 & 2875.56241784436 & -38.5624178443595 \tabularnewline
78 & 3419 & 3051.7657879291 & 367.234212070903 \tabularnewline
79 & 2658 & 2808.14463541701 & -150.144635417005 \tabularnewline
80 & 2133 & 2250.67878943161 & -117.678789431611 \tabularnewline
81 & 2276 & 2426.25899002115 & -150.258990021146 \tabularnewline
82 & 2403 & 2709.90013170035 & -306.900131700351 \tabularnewline
83 & 1975 & 2124.00109401622 & -149.001094016217 \tabularnewline
84 & 996 & 1292.24981638112 & -296.24981638112 \tabularnewline
85 & 4505 & 4143.41099385389 & 361.589006146105 \tabularnewline
86 & 3890 & 3087.05162570874 & 802.948374291259 \tabularnewline
87 & 4352 & 3689.22047574808 & 662.779524251919 \tabularnewline
88 & 3288 & 3653.55124370376 & -365.551243703757 \tabularnewline
89 & 3314 & 2966.01552042769 & 347.984479572307 \tabularnewline
90 & 2830 & 3388.42181415194 & -558.421814151937 \tabularnewline
91 & 2414 & 2733.46842625167 & -319.468426251671 \tabularnewline
92 & 2049 & 2150.62257447973 & -101.622574479726 \tabularnewline
93 & 1981 & 2317.03635818012 & -336.036358180122 \tabularnewline
94 & 2527 & 2497.40952946261 & 29.5904705373869 \tabularnewline
95 & 1813 & 2049.19848138617 & -236.198481386168 \tabularnewline
96 & 926 & 1140.05477156751 & -214.054771567514 \tabularnewline
97 & 4277 & 4267.78001887984 & 9.21998112016445 \tabularnewline
98 & 3301 & 3305.23941576388 & -4.23941576388142 \tabularnewline
99 & 3773 & 3670.71848779137 & 102.281512208629 \tabularnewline
100 & 3175 & 3105.47691109672 & 69.523088903281 \tabularnewline
101 & 3045 & 2795.78991302151 & 249.210086978491 \tabularnewline
102 & 2933 & 2840.39030444789 & 92.6096955521134 \tabularnewline
103 & 2544 & 2425.72672390508 & 118.273276094925 \tabularnewline
104 & 2324 & 2026.87750291236 & 297.122497087641 \tabularnewline
105 & 2229 & 2191.09407943091 & 37.9059205690901 \tabularnewline
106 & 2844 & 2599.07471164084 & 244.925288359157 \tabularnewline
107 & 2175 & 2095.0715130501 & 79.9284869499029 \tabularnewline
108 & 1055 & 1265.7767940274 & -210.776794027397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199301&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]3395[/C][C]3322.84775641026[/C][C]72.1522435897436[/C][/ROW]
[ROW][C]14[/C][C]3017[/C][C]2994.83708967985[/C][C]22.162910320149[/C][/ROW]
[ROW][C]15[/C][C]3631[/C][C]3608.94848758107[/C][C]22.0515124189315[/C][/ROW]
[ROW][C]16[/C][C]2570[/C][C]2539.95147573163[/C][C]30.0485242683653[/C][/ROW]
[ROW][C]17[/C][C]2403[/C][C]2409.67131173945[/C][C]-6.6713117394529[/C][/ROW]
[ROW][C]18[/C][C]2465[/C][C]2512.12526552186[/C][C]-47.1252655218586[/C][/ROW]
[ROW][C]19[/C][C]1711[/C][C]2523.5977620356[/C][C]-812.597762035598[/C][/ROW]
[ROW][C]20[/C][C]1541[/C][C]1416.59058096325[/C][C]124.409419036747[/C][/ROW]
[ROW][C]21[/C][C]1751[/C][C]1416.9683561389[/C][C]334.031643861104[/C][/ROW]
[ROW][C]22[/C][C]2103[/C][C]1815.11683830221[/C][C]287.88316169779[/C][/ROW]
[ROW][C]23[/C][C]1410[/C][C]2197.79365319839[/C][C]-787.793653198393[/C][/ROW]
[ROW][C]24[/C][C]823[/C][C]671.745043967462[/C][C]151.254956032538[/C][/ROW]
[ROW][C]25[/C][C]3471[/C][C]3179.76196144216[/C][C]291.238038557842[/C][/ROW]
[ROW][C]26[/C][C]2207[/C][C]2881.45883178269[/C][C]-674.458831782686[/C][/ROW]
[ROW][C]27[/C][C]2483[/C][C]3338.71228706355[/C][C]-855.712287063554[/C][/ROW]
[ROW][C]28[/C][C]2334[/C][C]2075.26185750998[/C][C]258.73814249002[/C][/ROW]
[ROW][C]29[/C][C]2273[/C][C]1982.05656295535[/C][C]290.943437044648[/C][/ROW]
[ROW][C]30[/C][C]2247[/C][C]2135.63605227086[/C][C]111.363947729139[/C][/ROW]
[ROW][C]31[/C][C]1667[/C][C]1882.50086800136[/C][C]-215.500868001362[/C][/ROW]
[ROW][C]32[/C][C]1692[/C][C]1277.47965892926[/C][C]414.520341070744[/C][/ROW]
[ROW][C]33[/C][C]1779[/C][C]1425.39536325048[/C][C]353.604636749515[/C][/ROW]
[ROW][C]34[/C][C]2000[/C][C]1809.84642268535[/C][C]190.153577314651[/C][/ROW]
[ROW][C]35[/C][C]1934[/C][C]1748.54995674439[/C][C]185.450043255606[/C][/ROW]
[ROW][C]36[/C][C]851[/C][C]809.9613214541[/C][C]41.0386785459002[/C][/ROW]
[ROW][C]37[/C][C]3314[/C][C]3348.08131269641[/C][C]-34.0813126964104[/C][/ROW]
[ROW][C]38[/C][C]3178[/C][C]2597.71658195019[/C][C]580.283418049808[/C][/ROW]
[ROW][C]39[/C][C]3360[/C][C]3266.3176451977[/C][C]93.6823548022976[/C][/ROW]
[ROW][C]40[/C][C]2787[/C][C]2653.76640581097[/C][C]133.233594189028[/C][/ROW]
[ROW][C]41[/C][C]2474[/C][C]2544.94290102871[/C][C]-70.942901028709[/C][/ROW]
[ROW][C]42[/C][C]2563[/C][C]2546.61269714014[/C][C]16.3873028598609[/C][/ROW]
[ROW][C]43[/C][C]2528[/C][C]2143.87291532935[/C][C]384.127084670647[/C][/ROW]
[ROW][C]44[/C][C]1649[/C][C]1920.98092678533[/C][C]-271.980926785332[/C][/ROW]
[ROW][C]45[/C][C]1902[/C][C]1890.46415545416[/C][C]11.5358445458382[/C][/ROW]
[ROW][C]46[/C][C]2141[/C][C]2133.79355295957[/C][C]7.20644704042707[/C][/ROW]
[ROW][C]47[/C][C]1471[/C][C]2029.46932289059[/C][C]-558.469322890594[/C][/ROW]
[ROW][C]48[/C][C]1178[/C][C]866.768775610509[/C][C]311.231224389491[/C][/ROW]
[ROW][C]49[/C][C]3038[/C][C]3436.24235496624[/C][C]-398.242354966245[/C][/ROW]
[ROW][C]50[/C][C]2633[/C][C]2844.90962727128[/C][C]-211.909627271277[/C][/ROW]
[ROW][C]51[/C][C]2636[/C][C]3144.29558539635[/C][C]-508.295585396354[/C][/ROW]
[ROW][C]52[/C][C]2708[/C][C]2411.75048475661[/C][C]296.249515243387[/C][/ROW]
[ROW][C]53[/C][C]2252[/C][C]2259.52724016738[/C][C]-7.52724016738239[/C][/ROW]
[ROW][C]54[/C][C]2579[/C][C]2309.73080468162[/C][C]269.269195318383[/C][/ROW]
[ROW][C]55[/C][C]2321[/C][C]2108.17585942458[/C][C]212.82414057542[/C][/ROW]
[ROW][C]56[/C][C]1490[/C][C]1589.33998731918[/C][C]-99.3399873191802[/C][/ROW]
[ROW][C]57[/C][C]2076[/C][C]1708.90570824612[/C][C]367.094291753881[/C][/ROW]
[ROW][C]58[/C][C]2333[/C][C]2030.57534027441[/C][C]302.424659725591[/C][/ROW]
[ROW][C]59[/C][C]1566[/C][C]1770.79964331526[/C][C]-204.799643315259[/C][/ROW]
[ROW][C]60[/C][C]961[/C][C]1028.88446733194[/C][C]-67.8844673319363[/C][/ROW]
[ROW][C]61[/C][C]3683[/C][C]3234.69951315476[/C][C]448.300486845236[/C][/ROW]
[ROW][C]62[/C][C]2904[/C][C]2907.025125107[/C][C]-3.02512510700308[/C][/ROW]
[ROW][C]63[/C][C]3097[/C][C]3137.16412506546[/C][C]-40.1641250654566[/C][/ROW]
[ROW][C]64[/C][C]3269[/C][C]2825.61089866653[/C][C]443.389101333467[/C][/ROW]
[ROW][C]65[/C][C]2491[/C][C]2587.34218835397[/C][C]-96.3421883539668[/C][/ROW]
[ROW][C]66[/C][C]2692[/C][C]2726.13646682477[/C][C]-34.1364668247693[/C][/ROW]
[ROW][C]67[/C][C]2293[/C][C]2434.1402214673[/C][C]-141.140221467298[/C][/ROW]
[ROW][C]68[/C][C]1994[/C][C]1713.16675771056[/C][C]280.833242289436[/C][/ROW]
[ROW][C]69[/C][C]2069[/C][C]2101.28798923081[/C][C]-32.2879892308051[/C][/ROW]
[ROW][C]70[/C][C]2540[/C][C]2307.6849461217[/C][C]232.3150538783[/C][/ROW]
[ROW][C]71[/C][C]2091[/C][C]1833.14976378642[/C][C]257.850236213583[/C][/ROW]
[ROW][C]72[/C][C]1109[/C][C]1249.09019025448[/C][C]-140.090190254479[/C][/ROW]
[ROW][C]73[/C][C]4761[/C][C]3641.14372724947[/C][C]1119.85627275053[/C][/ROW]
[ROW][C]74[/C][C]3051[/C][C]3287.59203754706[/C][C]-236.592037547056[/C][/ROW]
[ROW][C]75[/C][C]3737[/C][C]3450.58441827148[/C][C]286.415581728524[/C][/ROW]
[ROW][C]76[/C][C]3505[/C][C]3402.23797489871[/C][C]102.762025101288[/C][/ROW]
[ROW][C]77[/C][C]2837[/C][C]2875.56241784436[/C][C]-38.5624178443595[/C][/ROW]
[ROW][C]78[/C][C]3419[/C][C]3051.7657879291[/C][C]367.234212070903[/C][/ROW]
[ROW][C]79[/C][C]2658[/C][C]2808.14463541701[/C][C]-150.144635417005[/C][/ROW]
[ROW][C]80[/C][C]2133[/C][C]2250.67878943161[/C][C]-117.678789431611[/C][/ROW]
[ROW][C]81[/C][C]2276[/C][C]2426.25899002115[/C][C]-150.258990021146[/C][/ROW]
[ROW][C]82[/C][C]2403[/C][C]2709.90013170035[/C][C]-306.900131700351[/C][/ROW]
[ROW][C]83[/C][C]1975[/C][C]2124.00109401622[/C][C]-149.001094016217[/C][/ROW]
[ROW][C]84[/C][C]996[/C][C]1292.24981638112[/C][C]-296.24981638112[/C][/ROW]
[ROW][C]85[/C][C]4505[/C][C]4143.41099385389[/C][C]361.589006146105[/C][/ROW]
[ROW][C]86[/C][C]3890[/C][C]3087.05162570874[/C][C]802.948374291259[/C][/ROW]
[ROW][C]87[/C][C]4352[/C][C]3689.22047574808[/C][C]662.779524251919[/C][/ROW]
[ROW][C]88[/C][C]3288[/C][C]3653.55124370376[/C][C]-365.551243703757[/C][/ROW]
[ROW][C]89[/C][C]3314[/C][C]2966.01552042769[/C][C]347.984479572307[/C][/ROW]
[ROW][C]90[/C][C]2830[/C][C]3388.42181415194[/C][C]-558.421814151937[/C][/ROW]
[ROW][C]91[/C][C]2414[/C][C]2733.46842625167[/C][C]-319.468426251671[/C][/ROW]
[ROW][C]92[/C][C]2049[/C][C]2150.62257447973[/C][C]-101.622574479726[/C][/ROW]
[ROW][C]93[/C][C]1981[/C][C]2317.03635818012[/C][C]-336.036358180122[/C][/ROW]
[ROW][C]94[/C][C]2527[/C][C]2497.40952946261[/C][C]29.5904705373869[/C][/ROW]
[ROW][C]95[/C][C]1813[/C][C]2049.19848138617[/C][C]-236.198481386168[/C][/ROW]
[ROW][C]96[/C][C]926[/C][C]1140.05477156751[/C][C]-214.054771567514[/C][/ROW]
[ROW][C]97[/C][C]4277[/C][C]4267.78001887984[/C][C]9.21998112016445[/C][/ROW]
[ROW][C]98[/C][C]3301[/C][C]3305.23941576388[/C][C]-4.23941576388142[/C][/ROW]
[ROW][C]99[/C][C]3773[/C][C]3670.71848779137[/C][C]102.281512208629[/C][/ROW]
[ROW][C]100[/C][C]3175[/C][C]3105.47691109672[/C][C]69.523088903281[/C][/ROW]
[ROW][C]101[/C][C]3045[/C][C]2795.78991302151[/C][C]249.210086978491[/C][/ROW]
[ROW][C]102[/C][C]2933[/C][C]2840.39030444789[/C][C]92.6096955521134[/C][/ROW]
[ROW][C]103[/C][C]2544[/C][C]2425.72672390508[/C][C]118.273276094925[/C][/ROW]
[ROW][C]104[/C][C]2324[/C][C]2026.87750291236[/C][C]297.122497087641[/C][/ROW]
[ROW][C]105[/C][C]2229[/C][C]2191.09407943091[/C][C]37.9059205690901[/C][/ROW]
[ROW][C]106[/C][C]2844[/C][C]2599.07471164084[/C][C]244.925288359157[/C][/ROW]
[ROW][C]107[/C][C]2175[/C][C]2095.0715130501[/C][C]79.9284869499029[/C][/ROW]
[ROW][C]108[/C][C]1055[/C][C]1265.7767940274[/C][C]-210.776794027397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199301&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
1333953322.8477564102672.1522435897436
1430172994.8370896798522.162910320149
1536313608.9484875810722.0515124189315
1625702539.9514757316330.0485242683653
1724032409.67131173945-6.6713117394529
1824652512.12526552186-47.1252655218586
1917112523.5977620356-812.597762035598
2015411416.59058096325124.409419036747
2117511416.9683561389334.031643861104
2221031815.11683830221287.88316169779
2314102197.79365319839-787.793653198393
24823671.745043967462151.254956032538
2534713179.76196144216291.238038557842
2622072881.45883178269-674.458831782686
2724833338.71228706355-855.712287063554
2823342075.26185750998258.73814249002
2922731982.05656295535290.943437044648
3022472135.63605227086111.363947729139
3116671882.50086800136-215.500868001362
3216921277.47965892926414.520341070744
3317791425.39536325048353.604636749515
3420001809.84642268535190.153577314651
3519341748.54995674439185.450043255606
36851809.961321454141.0386785459002
3733143348.08131269641-34.0813126964104
3831782597.71658195019580.283418049808
3933603266.317645197793.6823548022976
4027872653.76640581097133.233594189028
4124742544.94290102871-70.942901028709
4225632546.6126971401416.3873028598609
4325282143.87291532935384.127084670647
4416491920.98092678533-271.980926785332
4519021890.4641554541611.5358445458382
4621412133.793552959577.20644704042707
4714712029.46932289059-558.469322890594
481178866.768775610509311.231224389491
4930383436.24235496624-398.242354966245
5026332844.90962727128-211.909627271277
5126363144.29558539635-508.295585396354
5227082411.75048475661296.249515243387
5322522259.52724016738-7.52724016738239
5425792309.73080468162269.269195318383
5523212108.17585942458212.82414057542
5614901589.33998731918-99.3399873191802
5720761708.90570824612367.094291753881
5823332030.57534027441302.424659725591
5915661770.79964331526-204.799643315259
609611028.88446733194-67.8844673319363
6136833234.69951315476448.300486845236
6229042907.025125107-3.02512510700308
6330973137.16412506546-40.1641250654566
6432692825.61089866653443.389101333467
6524912587.34218835397-96.3421883539668
6626922726.13646682477-34.1364668247693
6722932434.1402214673-141.140221467298
6819941713.16675771056280.833242289436
6920692101.28798923081-32.2879892308051
7025402307.6849461217232.3150538783
7120911833.14976378642257.850236213583
7211091249.09019025448-140.090190254479
7347613641.143727249471119.85627275053
7430513287.59203754706-236.592037547056
7537373450.58441827148286.415581728524
7635053402.23797489871102.762025101288
7728372875.56241784436-38.5624178443595
7834193051.7657879291367.234212070903
7926582808.14463541701-150.144635417005
8021332250.67878943161-117.678789431611
8122762426.25899002115-150.258990021146
8224032709.90013170035-306.900131700351
8319752124.00109401622-149.001094016217
849961292.24981638112-296.24981638112
8545054143.41099385389361.589006146105
8638903087.05162570874802.948374291259
8743523689.22047574808662.779524251919
8832883653.55124370376-365.551243703757
8933142966.01552042769347.984479572307
9028303388.42181415194-558.421814151937
9124142733.46842625167-319.468426251671
9220492150.62257447973-101.622574479726
9319812317.03635818012-336.036358180122
9425272497.4095294626129.5904705373869
9518132049.19848138617-236.198481386168
969261140.05477156751-214.054771567514
9742774267.780018879849.21998112016445
9833013305.23941576388-4.23941576388142
9937733670.71848779137102.281512208629
10031753105.4769110967269.523088903281
10130452795.78991302151249.210086978491
10229332840.3903044478992.6096955521134
10325442425.72672390508118.273276094925
10423242026.87750291236297.122497087641
10522292191.0940794309137.9059205690901
10628442599.07471164084244.925288359157
10721752095.071513050179.9284869499029
10810551265.7767940274-210.776794027397







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1094481.827649092523843.196421831055120.45887635399
1103511.931623963982857.319650388864166.5435975391
1113920.15175890713249.939980838164590.36353697605
1123319.035232077772633.578582116044004.4918820395
1133064.186935881132363.817168907153764.5567028551
1142991.256210757112276.284321795313706.22809971891
1152565.813045421971836.531348462543295.0947423814
1162210.499882265721467.18380882562953.81595570585
1172206.144973000151449.054637208662963.23530879164
1182686.803669231581916.185237020613457.42210144255
1192062.940091246151279.026984085852846.85319840645
1201101.61312038974304.6270784215411898.59916235794

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 4481.82764909252 & 3843.19642183105 & 5120.45887635399 \tabularnewline
110 & 3511.93162396398 & 2857.31965038886 & 4166.5435975391 \tabularnewline
111 & 3920.1517589071 & 3249.93998083816 & 4590.36353697605 \tabularnewline
112 & 3319.03523207777 & 2633.57858211604 & 4004.4918820395 \tabularnewline
113 & 3064.18693588113 & 2363.81716890715 & 3764.5567028551 \tabularnewline
114 & 2991.25621075711 & 2276.28432179531 & 3706.22809971891 \tabularnewline
115 & 2565.81304542197 & 1836.53134846254 & 3295.0947423814 \tabularnewline
116 & 2210.49988226572 & 1467.1838088256 & 2953.81595570585 \tabularnewline
117 & 2206.14497300015 & 1449.05463720866 & 2963.23530879164 \tabularnewline
118 & 2686.80366923158 & 1916.18523702061 & 3457.42210144255 \tabularnewline
119 & 2062.94009124615 & 1279.02698408585 & 2846.85319840645 \tabularnewline
120 & 1101.61312038974 & 304.627078421541 & 1898.59916235794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199301&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]109[/C][C]4481.82764909252[/C][C]3843.19642183105[/C][C]5120.45887635399[/C][/ROW]
[ROW][C]110[/C][C]3511.93162396398[/C][C]2857.31965038886[/C][C]4166.5435975391[/C][/ROW]
[ROW][C]111[/C][C]3920.1517589071[/C][C]3249.93998083816[/C][C]4590.36353697605[/C][/ROW]
[ROW][C]112[/C][C]3319.03523207777[/C][C]2633.57858211604[/C][C]4004.4918820395[/C][/ROW]
[ROW][C]113[/C][C]3064.18693588113[/C][C]2363.81716890715[/C][C]3764.5567028551[/C][/ROW]
[ROW][C]114[/C][C]2991.25621075711[/C][C]2276.28432179531[/C][C]3706.22809971891[/C][/ROW]
[ROW][C]115[/C][C]2565.81304542197[/C][C]1836.53134846254[/C][C]3295.0947423814[/C][/ROW]
[ROW][C]116[/C][C]2210.49988226572[/C][C]1467.1838088256[/C][C]2953.81595570585[/C][/ROW]
[ROW][C]117[/C][C]2206.14497300015[/C][C]1449.05463720866[/C][C]2963.23530879164[/C][/ROW]
[ROW][C]118[/C][C]2686.80366923158[/C][C]1916.18523702061[/C][C]3457.42210144255[/C][/ROW]
[ROW][C]119[/C][C]2062.94009124615[/C][C]1279.02698408585[/C][C]2846.85319840645[/C][/ROW]
[ROW][C]120[/C][C]1101.61312038974[/C][C]304.627078421541[/C][C]1898.59916235794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199301&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199301&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
1094481.827649092523843.196421831055120.45887635399
1103511.931623963982857.319650388864166.5435975391
1113920.15175890713249.939980838164590.36353697605
1123319.035232077772633.578582116044004.4918820395
1133064.186935881132363.817168907153764.5567028551
1142991.256210757112276.284321795313706.22809971891
1152565.813045421971836.531348462543295.0947423814
1162210.499882265721467.18380882562953.81595570585
1172206.144973000151449.054637208662963.23530879164
1182686.803669231581916.185237020613457.42210144255
1192062.940091246151279.026984085852846.85319840645
1201101.61312038974304.6270784215411898.59916235794



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')