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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 computationMon, 28 Nov 2011 12:31:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/28/t1322501501x8xcbb40c6rtfa3.htm/, Retrieved Fri, 19 Apr 2024 21:05:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147907, Retrieved Fri, 19 Apr 2024 21:05:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [WS8 Exponential S...] [2011-11-28 17:31:17] [2a6d487209befbc7c5ce02a41ecac161] [Current]
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Dataseries X:
2564
2820
3508
3088
3299
2939
3320
3418
3604
3495
4163
4882
2211
3260
2992
2425
2707
3244
3965
3315
3333
3583
4021
4904
2252
2952
3573
3048
3059
2731
3563
3092
3478
3478
4308
5029
2075
3264
3308
3688
3136
2824
3644
4694
2914
3686
4358
5587
2265
3685
3754
3708
3210
3517
3905
3670
4221
4404
5086
5725




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147907&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147907&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.182050486447323
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.182050486447323 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147907&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]0.182050486447323[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147907&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
alpha0.182050486447323
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
228202564256
335082610.60492453051897.395075469485
430882773.97613455517314.023865444834
532992831.14433201547467.855667984533
629392916.3176839591922.6823160408112
733202920.44701062817399.552989371829
834182993.18582670479424.814173295206
936043070.5234536029533.476546397096
1034953167.64311838273327.356881617267
1141633227.23859792304935.761402076965
1248823397.594416369781484.40558363022
1322113667.83117495478-1456.83117495478
1432603402.61435088264-142.614350882638
1529923376.65133893008-384.651338930084
1624253306.62537556525-881.625375565248
1727073146.12504707929-439.125047079291
1832443066.1821186473177.817881352697
1939653098.55395044659866.446049553407
2033153256.2908752481558.7091247518479
2133333266.9788999681266.0211000318773
2235833278.99807334471304.001926655287
2340213334.34177197323686.658228026768
2449043459.348236408561444.65176359144
2522523722.34779271737-1470.34779271737
2629523454.67026180642-502.670261806422
2735733363.15889612196209.84110387804
2830483401.3605711596-353.3605711596
2930593337.03110728869-278.031107288691
3027313286.4154089593-555.415408959297
3135633185.30176357792377.698236422082
3230923254.06191124885-162.061911248854
3334783224.55846147142253.441538528582
3434783270.6976168465207.302383153496
3543083308.43711654129999.562883458713
3650293490.408025709631538.59197429037
3720753770.50944307314-1695.50944307314
3832643461.84112418565-197.841124185647
3933083425.82405128836-117.824051288365
4036883404.37412543612283.625874563876
4131363456.00835386952-320.008353869525
4228243397.75067738037-573.750677380371
4336443293.29908746379350.700912536207
4446943357.144359188531336.85564081147
4529143600.51957890811-686.519578908105
4636863475.53835561227210.461644387727
4743583513.85300035156844.146999648437
4855873667.530372270611919.46962772939
4922654016.97075171961-1751.97075171961
5036853698.02362412757-13.0236241275697
5137543695.6526670198458.3473329801614
5237083706.274827371781.72517262821884
5332103706.58889588795-496.588895887954
5435173616.18464582721-99.184645827213
5539053598.12803280626306.871967193737
5636703653.9942237109316.0057762890697
5742213656.90808307032564.091916929678
5844043759.60129094837644.398709051627
5950863876.914389397251209.08561060275
6057254097.029012963941627.97098703606

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2820 & 2564 & 256 \tabularnewline
3 & 3508 & 2610.60492453051 & 897.395075469485 \tabularnewline
4 & 3088 & 2773.97613455517 & 314.023865444834 \tabularnewline
5 & 3299 & 2831.14433201547 & 467.855667984533 \tabularnewline
6 & 2939 & 2916.31768395919 & 22.6823160408112 \tabularnewline
7 & 3320 & 2920.44701062817 & 399.552989371829 \tabularnewline
8 & 3418 & 2993.18582670479 & 424.814173295206 \tabularnewline
9 & 3604 & 3070.5234536029 & 533.476546397096 \tabularnewline
10 & 3495 & 3167.64311838273 & 327.356881617267 \tabularnewline
11 & 4163 & 3227.23859792304 & 935.761402076965 \tabularnewline
12 & 4882 & 3397.59441636978 & 1484.40558363022 \tabularnewline
13 & 2211 & 3667.83117495478 & -1456.83117495478 \tabularnewline
14 & 3260 & 3402.61435088264 & -142.614350882638 \tabularnewline
15 & 2992 & 3376.65133893008 & -384.651338930084 \tabularnewline
16 & 2425 & 3306.62537556525 & -881.625375565248 \tabularnewline
17 & 2707 & 3146.12504707929 & -439.125047079291 \tabularnewline
18 & 3244 & 3066.1821186473 & 177.817881352697 \tabularnewline
19 & 3965 & 3098.55395044659 & 866.446049553407 \tabularnewline
20 & 3315 & 3256.29087524815 & 58.7091247518479 \tabularnewline
21 & 3333 & 3266.97889996812 & 66.0211000318773 \tabularnewline
22 & 3583 & 3278.99807334471 & 304.001926655287 \tabularnewline
23 & 4021 & 3334.34177197323 & 686.658228026768 \tabularnewline
24 & 4904 & 3459.34823640856 & 1444.65176359144 \tabularnewline
25 & 2252 & 3722.34779271737 & -1470.34779271737 \tabularnewline
26 & 2952 & 3454.67026180642 & -502.670261806422 \tabularnewline
27 & 3573 & 3363.15889612196 & 209.84110387804 \tabularnewline
28 & 3048 & 3401.3605711596 & -353.3605711596 \tabularnewline
29 & 3059 & 3337.03110728869 & -278.031107288691 \tabularnewline
30 & 2731 & 3286.4154089593 & -555.415408959297 \tabularnewline
31 & 3563 & 3185.30176357792 & 377.698236422082 \tabularnewline
32 & 3092 & 3254.06191124885 & -162.061911248854 \tabularnewline
33 & 3478 & 3224.55846147142 & 253.441538528582 \tabularnewline
34 & 3478 & 3270.6976168465 & 207.302383153496 \tabularnewline
35 & 4308 & 3308.43711654129 & 999.562883458713 \tabularnewline
36 & 5029 & 3490.40802570963 & 1538.59197429037 \tabularnewline
37 & 2075 & 3770.50944307314 & -1695.50944307314 \tabularnewline
38 & 3264 & 3461.84112418565 & -197.841124185647 \tabularnewline
39 & 3308 & 3425.82405128836 & -117.824051288365 \tabularnewline
40 & 3688 & 3404.37412543612 & 283.625874563876 \tabularnewline
41 & 3136 & 3456.00835386952 & -320.008353869525 \tabularnewline
42 & 2824 & 3397.75067738037 & -573.750677380371 \tabularnewline
43 & 3644 & 3293.29908746379 & 350.700912536207 \tabularnewline
44 & 4694 & 3357.14435918853 & 1336.85564081147 \tabularnewline
45 & 2914 & 3600.51957890811 & -686.519578908105 \tabularnewline
46 & 3686 & 3475.53835561227 & 210.461644387727 \tabularnewline
47 & 4358 & 3513.85300035156 & 844.146999648437 \tabularnewline
48 & 5587 & 3667.53037227061 & 1919.46962772939 \tabularnewline
49 & 2265 & 4016.97075171961 & -1751.97075171961 \tabularnewline
50 & 3685 & 3698.02362412757 & -13.0236241275697 \tabularnewline
51 & 3754 & 3695.65266701984 & 58.3473329801614 \tabularnewline
52 & 3708 & 3706.27482737178 & 1.72517262821884 \tabularnewline
53 & 3210 & 3706.58889588795 & -496.588895887954 \tabularnewline
54 & 3517 & 3616.18464582721 & -99.184645827213 \tabularnewline
55 & 3905 & 3598.12803280626 & 306.871967193737 \tabularnewline
56 & 3670 & 3653.99422371093 & 16.0057762890697 \tabularnewline
57 & 4221 & 3656.90808307032 & 564.091916929678 \tabularnewline
58 & 4404 & 3759.60129094837 & 644.398709051627 \tabularnewline
59 & 5086 & 3876.91438939725 & 1209.08561060275 \tabularnewline
60 & 5725 & 4097.02901296394 & 1627.97098703606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147907&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]2[/C][C]2820[/C][C]2564[/C][C]256[/C][/ROW]
[ROW][C]3[/C][C]3508[/C][C]2610.60492453051[/C][C]897.395075469485[/C][/ROW]
[ROW][C]4[/C][C]3088[/C][C]2773.97613455517[/C][C]314.023865444834[/C][/ROW]
[ROW][C]5[/C][C]3299[/C][C]2831.14433201547[/C][C]467.855667984533[/C][/ROW]
[ROW][C]6[/C][C]2939[/C][C]2916.31768395919[/C][C]22.6823160408112[/C][/ROW]
[ROW][C]7[/C][C]3320[/C][C]2920.44701062817[/C][C]399.552989371829[/C][/ROW]
[ROW][C]8[/C][C]3418[/C][C]2993.18582670479[/C][C]424.814173295206[/C][/ROW]
[ROW][C]9[/C][C]3604[/C][C]3070.5234536029[/C][C]533.476546397096[/C][/ROW]
[ROW][C]10[/C][C]3495[/C][C]3167.64311838273[/C][C]327.356881617267[/C][/ROW]
[ROW][C]11[/C][C]4163[/C][C]3227.23859792304[/C][C]935.761402076965[/C][/ROW]
[ROW][C]12[/C][C]4882[/C][C]3397.59441636978[/C][C]1484.40558363022[/C][/ROW]
[ROW][C]13[/C][C]2211[/C][C]3667.83117495478[/C][C]-1456.83117495478[/C][/ROW]
[ROW][C]14[/C][C]3260[/C][C]3402.61435088264[/C][C]-142.614350882638[/C][/ROW]
[ROW][C]15[/C][C]2992[/C][C]3376.65133893008[/C][C]-384.651338930084[/C][/ROW]
[ROW][C]16[/C][C]2425[/C][C]3306.62537556525[/C][C]-881.625375565248[/C][/ROW]
[ROW][C]17[/C][C]2707[/C][C]3146.12504707929[/C][C]-439.125047079291[/C][/ROW]
[ROW][C]18[/C][C]3244[/C][C]3066.1821186473[/C][C]177.817881352697[/C][/ROW]
[ROW][C]19[/C][C]3965[/C][C]3098.55395044659[/C][C]866.446049553407[/C][/ROW]
[ROW][C]20[/C][C]3315[/C][C]3256.29087524815[/C][C]58.7091247518479[/C][/ROW]
[ROW][C]21[/C][C]3333[/C][C]3266.97889996812[/C][C]66.0211000318773[/C][/ROW]
[ROW][C]22[/C][C]3583[/C][C]3278.99807334471[/C][C]304.001926655287[/C][/ROW]
[ROW][C]23[/C][C]4021[/C][C]3334.34177197323[/C][C]686.658228026768[/C][/ROW]
[ROW][C]24[/C][C]4904[/C][C]3459.34823640856[/C][C]1444.65176359144[/C][/ROW]
[ROW][C]25[/C][C]2252[/C][C]3722.34779271737[/C][C]-1470.34779271737[/C][/ROW]
[ROW][C]26[/C][C]2952[/C][C]3454.67026180642[/C][C]-502.670261806422[/C][/ROW]
[ROW][C]27[/C][C]3573[/C][C]3363.15889612196[/C][C]209.84110387804[/C][/ROW]
[ROW][C]28[/C][C]3048[/C][C]3401.3605711596[/C][C]-353.3605711596[/C][/ROW]
[ROW][C]29[/C][C]3059[/C][C]3337.03110728869[/C][C]-278.031107288691[/C][/ROW]
[ROW][C]30[/C][C]2731[/C][C]3286.4154089593[/C][C]-555.415408959297[/C][/ROW]
[ROW][C]31[/C][C]3563[/C][C]3185.30176357792[/C][C]377.698236422082[/C][/ROW]
[ROW][C]32[/C][C]3092[/C][C]3254.06191124885[/C][C]-162.061911248854[/C][/ROW]
[ROW][C]33[/C][C]3478[/C][C]3224.55846147142[/C][C]253.441538528582[/C][/ROW]
[ROW][C]34[/C][C]3478[/C][C]3270.6976168465[/C][C]207.302383153496[/C][/ROW]
[ROW][C]35[/C][C]4308[/C][C]3308.43711654129[/C][C]999.562883458713[/C][/ROW]
[ROW][C]36[/C][C]5029[/C][C]3490.40802570963[/C][C]1538.59197429037[/C][/ROW]
[ROW][C]37[/C][C]2075[/C][C]3770.50944307314[/C][C]-1695.50944307314[/C][/ROW]
[ROW][C]38[/C][C]3264[/C][C]3461.84112418565[/C][C]-197.841124185647[/C][/ROW]
[ROW][C]39[/C][C]3308[/C][C]3425.82405128836[/C][C]-117.824051288365[/C][/ROW]
[ROW][C]40[/C][C]3688[/C][C]3404.37412543612[/C][C]283.625874563876[/C][/ROW]
[ROW][C]41[/C][C]3136[/C][C]3456.00835386952[/C][C]-320.008353869525[/C][/ROW]
[ROW][C]42[/C][C]2824[/C][C]3397.75067738037[/C][C]-573.750677380371[/C][/ROW]
[ROW][C]43[/C][C]3644[/C][C]3293.29908746379[/C][C]350.700912536207[/C][/ROW]
[ROW][C]44[/C][C]4694[/C][C]3357.14435918853[/C][C]1336.85564081147[/C][/ROW]
[ROW][C]45[/C][C]2914[/C][C]3600.51957890811[/C][C]-686.519578908105[/C][/ROW]
[ROW][C]46[/C][C]3686[/C][C]3475.53835561227[/C][C]210.461644387727[/C][/ROW]
[ROW][C]47[/C][C]4358[/C][C]3513.85300035156[/C][C]844.146999648437[/C][/ROW]
[ROW][C]48[/C][C]5587[/C][C]3667.53037227061[/C][C]1919.46962772939[/C][/ROW]
[ROW][C]49[/C][C]2265[/C][C]4016.97075171961[/C][C]-1751.97075171961[/C][/ROW]
[ROW][C]50[/C][C]3685[/C][C]3698.02362412757[/C][C]-13.0236241275697[/C][/ROW]
[ROW][C]51[/C][C]3754[/C][C]3695.65266701984[/C][C]58.3473329801614[/C][/ROW]
[ROW][C]52[/C][C]3708[/C][C]3706.27482737178[/C][C]1.72517262821884[/C][/ROW]
[ROW][C]53[/C][C]3210[/C][C]3706.58889588795[/C][C]-496.588895887954[/C][/ROW]
[ROW][C]54[/C][C]3517[/C][C]3616.18464582721[/C][C]-99.184645827213[/C][/ROW]
[ROW][C]55[/C][C]3905[/C][C]3598.12803280626[/C][C]306.871967193737[/C][/ROW]
[ROW][C]56[/C][C]3670[/C][C]3653.99422371093[/C][C]16.0057762890697[/C][/ROW]
[ROW][C]57[/C][C]4221[/C][C]3656.90808307032[/C][C]564.091916929678[/C][/ROW]
[ROW][C]58[/C][C]4404[/C][C]3759.60129094837[/C][C]644.398709051627[/C][/ROW]
[ROW][C]59[/C][C]5086[/C][C]3876.91438939725[/C][C]1209.08561060275[/C][/ROW]
[ROW][C]60[/C][C]5725[/C][C]4097.02901296394[/C][C]1627.97098703606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147907&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147907&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
228202564256
335082610.60492453051897.395075469485
430882773.97613455517314.023865444834
532992831.14433201547467.855667984533
629392916.3176839591922.6823160408112
733202920.44701062817399.552989371829
834182993.18582670479424.814173295206
936043070.5234536029533.476546397096
1034953167.64311838273327.356881617267
1141633227.23859792304935.761402076965
1248823397.594416369781484.40558363022
1322113667.83117495478-1456.83117495478
1432603402.61435088264-142.614350882638
1529923376.65133893008-384.651338930084
1624253306.62537556525-881.625375565248
1727073146.12504707929-439.125047079291
1832443066.1821186473177.817881352697
1939653098.55395044659866.446049553407
2033153256.2908752481558.7091247518479
2133333266.9788999681266.0211000318773
2235833278.99807334471304.001926655287
2340213334.34177197323686.658228026768
2449043459.348236408561444.65176359144
2522523722.34779271737-1470.34779271737
2629523454.67026180642-502.670261806422
2735733363.15889612196209.84110387804
2830483401.3605711596-353.3605711596
2930593337.03110728869-278.031107288691
3027313286.4154089593-555.415408959297
3135633185.30176357792377.698236422082
3230923254.06191124885-162.061911248854
3334783224.55846147142253.441538528582
3434783270.6976168465207.302383153496
3543083308.43711654129999.562883458713
3650293490.408025709631538.59197429037
3720753770.50944307314-1695.50944307314
3832643461.84112418565-197.841124185647
3933083425.82405128836-117.824051288365
4036883404.37412543612283.625874563876
4131363456.00835386952-320.008353869525
4228243397.75067738037-573.750677380371
4336443293.29908746379350.700912536207
4446943357.144359188531336.85564081147
4529143600.51957890811-686.519578908105
4636863475.53835561227210.461644387727
4743583513.85300035156844.146999648437
4855873667.530372270611919.46962772939
4922654016.97075171961-1751.97075171961
5036853698.02362412757-13.0236241275697
5137543695.6526670198458.3473329801614
5237083706.274827371781.72517262821884
5332103706.58889588795-496.588895887954
5435173616.18464582721-99.184645827213
5539053598.12803280626306.871967193737
5636703653.9942237109316.0057762890697
5742213656.90808307032564.091916929678
5844043759.60129094837644.398709051627
5950863876.914389397251209.08561060275
6057254097.029012963941627.97098703606







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
614393.401923075982867.952802749785918.85104340218
624393.401923075982842.880342775435943.92350337653
634393.401923075982818.206911894365968.5969342576
644393.401923075982793.914043933035992.88980221893
654393.401923075982769.984654534426016.81919161755
664393.401923075982746.402900589116040.40094556285
674393.401923075982723.154057534336063.64978861763
684393.401923075982700.224411820836086.57943433113
694393.401923075982677.601166317226109.20267983474
704393.401923075982655.272356798586131.53148935339
714393.401923075982633.226777972116153.57706817985
724393.401923075982611.45391774166175.34992841036

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 4393.40192307598 & 2867.95280274978 & 5918.85104340218 \tabularnewline
62 & 4393.40192307598 & 2842.88034277543 & 5943.92350337653 \tabularnewline
63 & 4393.40192307598 & 2818.20691189436 & 5968.5969342576 \tabularnewline
64 & 4393.40192307598 & 2793.91404393303 & 5992.88980221893 \tabularnewline
65 & 4393.40192307598 & 2769.98465453442 & 6016.81919161755 \tabularnewline
66 & 4393.40192307598 & 2746.40290058911 & 6040.40094556285 \tabularnewline
67 & 4393.40192307598 & 2723.15405753433 & 6063.64978861763 \tabularnewline
68 & 4393.40192307598 & 2700.22441182083 & 6086.57943433113 \tabularnewline
69 & 4393.40192307598 & 2677.60116631722 & 6109.20267983474 \tabularnewline
70 & 4393.40192307598 & 2655.27235679858 & 6131.53148935339 \tabularnewline
71 & 4393.40192307598 & 2633.22677797211 & 6153.57706817985 \tabularnewline
72 & 4393.40192307598 & 2611.4539177416 & 6175.34992841036 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147907&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]61[/C][C]4393.40192307598[/C][C]2867.95280274978[/C][C]5918.85104340218[/C][/ROW]
[ROW][C]62[/C][C]4393.40192307598[/C][C]2842.88034277543[/C][C]5943.92350337653[/C][/ROW]
[ROW][C]63[/C][C]4393.40192307598[/C][C]2818.20691189436[/C][C]5968.5969342576[/C][/ROW]
[ROW][C]64[/C][C]4393.40192307598[/C][C]2793.91404393303[/C][C]5992.88980221893[/C][/ROW]
[ROW][C]65[/C][C]4393.40192307598[/C][C]2769.98465453442[/C][C]6016.81919161755[/C][/ROW]
[ROW][C]66[/C][C]4393.40192307598[/C][C]2746.40290058911[/C][C]6040.40094556285[/C][/ROW]
[ROW][C]67[/C][C]4393.40192307598[/C][C]2723.15405753433[/C][C]6063.64978861763[/C][/ROW]
[ROW][C]68[/C][C]4393.40192307598[/C][C]2700.22441182083[/C][C]6086.57943433113[/C][/ROW]
[ROW][C]69[/C][C]4393.40192307598[/C][C]2677.60116631722[/C][C]6109.20267983474[/C][/ROW]
[ROW][C]70[/C][C]4393.40192307598[/C][C]2655.27235679858[/C][C]6131.53148935339[/C][/ROW]
[ROW][C]71[/C][C]4393.40192307598[/C][C]2633.22677797211[/C][C]6153.57706817985[/C][/ROW]
[ROW][C]72[/C][C]4393.40192307598[/C][C]2611.4539177416[/C][C]6175.34992841036[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147907&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147907&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
614393.401923075982867.952802749785918.85104340218
624393.401923075982842.880342775435943.92350337653
634393.401923075982818.206911894365968.5969342576
644393.401923075982793.914043933035992.88980221893
654393.401923075982769.984654534426016.81919161755
664393.401923075982746.402900589116040.40094556285
674393.401923075982723.154057534336063.64978861763
684393.401923075982700.224411820836086.57943433113
694393.401923075982677.601166317226109.20267983474
704393.401923075982655.272356798586131.53148935339
714393.401923075982633.226777972116153.57706817985
724393.401923075982611.45391774166175.34992841036



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')