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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 31 Dec 2014 13:14:12 +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/2014/Dec/31/t14200316708jelmpa5avcy1z6.htm/, Retrieved Thu, 16 May 2024 20:28:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271812, Retrieved Thu, 16 May 2024 20:28:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-31 13:14:12] [517bf63cbd197750110a40d4d2cd39d6] [Current]
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Dataseries X:
2745
1395
1550
1378
1318
1395
1483
1049
783
1208
857
48
2681
1249
1705
1472
1413
1651
1525
1095
900
1255
984
101
2655
1309
1844
1825
1629
1718
1595
1539
1513
1475
1184
211
3387
1546
1955
1899
2415
3439
1148
1127
1186
1009
817
236
2762
1035
1500
1519
1539
1452
1409
1288
987
1542
1248
1400
4190
2185
1097
1215
1236
1374
1548
1178
902




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271812&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271812&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271812&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.42211942844619
beta0
gamma0.0129449424738222

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.42211942844619 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.0129449424738222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271812&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]0.42211942844619[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.0129449424738222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271812&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271812&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
alpha0.42211942844619
beta0
gamma0.0129449424738222







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1326812622.1714743589758.8285256410254
1412491218.8896274893930.1103725106143
1517051688.3602902343616.6397097656427
1614721463.103057853968.89694214603628
1714131408.160786164724.8392138352765
1816511648.255668520162.74433147984428
1915251557.92459366638-32.9245936663835
2010951126.32863918326-31.3286391832628
21900854.28136809438445.7186319056165
2212551295.75724704088-40.75724704088
23984927.229977392156.7700226079004
24101135.12086306538-34.1208630653803
2526552749.29334783883-94.2933478388318
2613091281.1609533537727.8390466462326
2718441749.5720762690294.4279237309756
2818251557.09283952194267.907160478061
2916291611.4534587895417.5465412104629
3017181856.89667987228-138.896679872284
3115951706.50935620355-111.509356203547
3215391241.75318541985297.24681458015
3315131108.98035926077404.019640739235
3414751701.05516114815-226.055161148145
3511841255.03960739697-71.03960739697
36211408.299643947913-197.299643947913
3733872953.14106686045433.858933139548
3815461708.86563870096-162.865638700961
3919552097.27473563734-142.274735637345
4018991806.1764417198692.8235582801376
4124151784.75801554891630.241984451087
4234392287.661592972861151.33840702714
4311482682.11244120307-1534.11244120307
4411271619.90562325626-492.905623256256
4511861154.3928297395231.6071702604786
4610091584.55173550091-575.551735500909
47817992.166501659016-175.166501659016
48236100.528048405573135.471951594427
4927622790.56029129493-28.5602912949316
5010351346.62484822995-311.624848229953
5115001672.39382560659-172.393825606593
5215191370.34036217402148.659637825982
5315391376.51165879502162.488341204975
5414521685.8654656036-233.865465603601
5514091475.50598062981-66.5059806298148
5612881040.59324674929247.406753250709
57987891.50437701015395.495622989847
5815421344.08990833806197.910091661944
5912481081.19307299742166.80692700258
601400336.2320195616441063.76798043836
6141903416.88898693442773.111013065582
6221852309.23707523741-124.237075237409
6310972715.14760811742-1618.14760811742
6412151805.21506675017-590.215066750174
6512361499.59644280595-263.596442805952
6613741626.12660764094-252.126607640944
6715481409.3106943381138.6893056619
6811781063.3631426785114.636857321502
69902857.09312928173144.9068707182694

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2681 & 2622.17147435897 & 58.8285256410254 \tabularnewline
14 & 1249 & 1218.88962748939 & 30.1103725106143 \tabularnewline
15 & 1705 & 1688.36029023436 & 16.6397097656427 \tabularnewline
16 & 1472 & 1463.10305785396 & 8.89694214603628 \tabularnewline
17 & 1413 & 1408.16078616472 & 4.8392138352765 \tabularnewline
18 & 1651 & 1648.25566852016 & 2.74433147984428 \tabularnewline
19 & 1525 & 1557.92459366638 & -32.9245936663835 \tabularnewline
20 & 1095 & 1126.32863918326 & -31.3286391832628 \tabularnewline
21 & 900 & 854.281368094384 & 45.7186319056165 \tabularnewline
22 & 1255 & 1295.75724704088 & -40.75724704088 \tabularnewline
23 & 984 & 927.2299773921 & 56.7700226079004 \tabularnewline
24 & 101 & 135.12086306538 & -34.1208630653803 \tabularnewline
25 & 2655 & 2749.29334783883 & -94.2933478388318 \tabularnewline
26 & 1309 & 1281.16095335377 & 27.8390466462326 \tabularnewline
27 & 1844 & 1749.57207626902 & 94.4279237309756 \tabularnewline
28 & 1825 & 1557.09283952194 & 267.907160478061 \tabularnewline
29 & 1629 & 1611.45345878954 & 17.5465412104629 \tabularnewline
30 & 1718 & 1856.89667987228 & -138.896679872284 \tabularnewline
31 & 1595 & 1706.50935620355 & -111.509356203547 \tabularnewline
32 & 1539 & 1241.75318541985 & 297.24681458015 \tabularnewline
33 & 1513 & 1108.98035926077 & 404.019640739235 \tabularnewline
34 & 1475 & 1701.05516114815 & -226.055161148145 \tabularnewline
35 & 1184 & 1255.03960739697 & -71.03960739697 \tabularnewline
36 & 211 & 408.299643947913 & -197.299643947913 \tabularnewline
37 & 3387 & 2953.14106686045 & 433.858933139548 \tabularnewline
38 & 1546 & 1708.86563870096 & -162.865638700961 \tabularnewline
39 & 1955 & 2097.27473563734 & -142.274735637345 \tabularnewline
40 & 1899 & 1806.17644171986 & 92.8235582801376 \tabularnewline
41 & 2415 & 1784.75801554891 & 630.241984451087 \tabularnewline
42 & 3439 & 2287.66159297286 & 1151.33840702714 \tabularnewline
43 & 1148 & 2682.11244120307 & -1534.11244120307 \tabularnewline
44 & 1127 & 1619.90562325626 & -492.905623256256 \tabularnewline
45 & 1186 & 1154.39282973952 & 31.6071702604786 \tabularnewline
46 & 1009 & 1584.55173550091 & -575.551735500909 \tabularnewline
47 & 817 & 992.166501659016 & -175.166501659016 \tabularnewline
48 & 236 & 100.528048405573 & 135.471951594427 \tabularnewline
49 & 2762 & 2790.56029129493 & -28.5602912949316 \tabularnewline
50 & 1035 & 1346.62484822995 & -311.624848229953 \tabularnewline
51 & 1500 & 1672.39382560659 & -172.393825606593 \tabularnewline
52 & 1519 & 1370.34036217402 & 148.659637825982 \tabularnewline
53 & 1539 & 1376.51165879502 & 162.488341204975 \tabularnewline
54 & 1452 & 1685.8654656036 & -233.865465603601 \tabularnewline
55 & 1409 & 1475.50598062981 & -66.5059806298148 \tabularnewline
56 & 1288 & 1040.59324674929 & 247.406753250709 \tabularnewline
57 & 987 & 891.504377010153 & 95.495622989847 \tabularnewline
58 & 1542 & 1344.08990833806 & 197.910091661944 \tabularnewline
59 & 1248 & 1081.19307299742 & 166.80692700258 \tabularnewline
60 & 1400 & 336.232019561644 & 1063.76798043836 \tabularnewline
61 & 4190 & 3416.88898693442 & 773.111013065582 \tabularnewline
62 & 2185 & 2309.23707523741 & -124.237075237409 \tabularnewline
63 & 1097 & 2715.14760811742 & -1618.14760811742 \tabularnewline
64 & 1215 & 1805.21506675017 & -590.215066750174 \tabularnewline
65 & 1236 & 1499.59644280595 & -263.596442805952 \tabularnewline
66 & 1374 & 1626.12660764094 & -252.126607640944 \tabularnewline
67 & 1548 & 1409.3106943381 & 138.6893056619 \tabularnewline
68 & 1178 & 1063.3631426785 & 114.636857321502 \tabularnewline
69 & 902 & 857.093129281731 & 44.9068707182694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271812&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]2681[/C][C]2622.17147435897[/C][C]58.8285256410254[/C][/ROW]
[ROW][C]14[/C][C]1249[/C][C]1218.88962748939[/C][C]30.1103725106143[/C][/ROW]
[ROW][C]15[/C][C]1705[/C][C]1688.36029023436[/C][C]16.6397097656427[/C][/ROW]
[ROW][C]16[/C][C]1472[/C][C]1463.10305785396[/C][C]8.89694214603628[/C][/ROW]
[ROW][C]17[/C][C]1413[/C][C]1408.16078616472[/C][C]4.8392138352765[/C][/ROW]
[ROW][C]18[/C][C]1651[/C][C]1648.25566852016[/C][C]2.74433147984428[/C][/ROW]
[ROW][C]19[/C][C]1525[/C][C]1557.92459366638[/C][C]-32.9245936663835[/C][/ROW]
[ROW][C]20[/C][C]1095[/C][C]1126.32863918326[/C][C]-31.3286391832628[/C][/ROW]
[ROW][C]21[/C][C]900[/C][C]854.281368094384[/C][C]45.7186319056165[/C][/ROW]
[ROW][C]22[/C][C]1255[/C][C]1295.75724704088[/C][C]-40.75724704088[/C][/ROW]
[ROW][C]23[/C][C]984[/C][C]927.2299773921[/C][C]56.7700226079004[/C][/ROW]
[ROW][C]24[/C][C]101[/C][C]135.12086306538[/C][C]-34.1208630653803[/C][/ROW]
[ROW][C]25[/C][C]2655[/C][C]2749.29334783883[/C][C]-94.2933478388318[/C][/ROW]
[ROW][C]26[/C][C]1309[/C][C]1281.16095335377[/C][C]27.8390466462326[/C][/ROW]
[ROW][C]27[/C][C]1844[/C][C]1749.57207626902[/C][C]94.4279237309756[/C][/ROW]
[ROW][C]28[/C][C]1825[/C][C]1557.09283952194[/C][C]267.907160478061[/C][/ROW]
[ROW][C]29[/C][C]1629[/C][C]1611.45345878954[/C][C]17.5465412104629[/C][/ROW]
[ROW][C]30[/C][C]1718[/C][C]1856.89667987228[/C][C]-138.896679872284[/C][/ROW]
[ROW][C]31[/C][C]1595[/C][C]1706.50935620355[/C][C]-111.509356203547[/C][/ROW]
[ROW][C]32[/C][C]1539[/C][C]1241.75318541985[/C][C]297.24681458015[/C][/ROW]
[ROW][C]33[/C][C]1513[/C][C]1108.98035926077[/C][C]404.019640739235[/C][/ROW]
[ROW][C]34[/C][C]1475[/C][C]1701.05516114815[/C][C]-226.055161148145[/C][/ROW]
[ROW][C]35[/C][C]1184[/C][C]1255.03960739697[/C][C]-71.03960739697[/C][/ROW]
[ROW][C]36[/C][C]211[/C][C]408.299643947913[/C][C]-197.299643947913[/C][/ROW]
[ROW][C]37[/C][C]3387[/C][C]2953.14106686045[/C][C]433.858933139548[/C][/ROW]
[ROW][C]38[/C][C]1546[/C][C]1708.86563870096[/C][C]-162.865638700961[/C][/ROW]
[ROW][C]39[/C][C]1955[/C][C]2097.27473563734[/C][C]-142.274735637345[/C][/ROW]
[ROW][C]40[/C][C]1899[/C][C]1806.17644171986[/C][C]92.8235582801376[/C][/ROW]
[ROW][C]41[/C][C]2415[/C][C]1784.75801554891[/C][C]630.241984451087[/C][/ROW]
[ROW][C]42[/C][C]3439[/C][C]2287.66159297286[/C][C]1151.33840702714[/C][/ROW]
[ROW][C]43[/C][C]1148[/C][C]2682.11244120307[/C][C]-1534.11244120307[/C][/ROW]
[ROW][C]44[/C][C]1127[/C][C]1619.90562325626[/C][C]-492.905623256256[/C][/ROW]
[ROW][C]45[/C][C]1186[/C][C]1154.39282973952[/C][C]31.6071702604786[/C][/ROW]
[ROW][C]46[/C][C]1009[/C][C]1584.55173550091[/C][C]-575.551735500909[/C][/ROW]
[ROW][C]47[/C][C]817[/C][C]992.166501659016[/C][C]-175.166501659016[/C][/ROW]
[ROW][C]48[/C][C]236[/C][C]100.528048405573[/C][C]135.471951594427[/C][/ROW]
[ROW][C]49[/C][C]2762[/C][C]2790.56029129493[/C][C]-28.5602912949316[/C][/ROW]
[ROW][C]50[/C][C]1035[/C][C]1346.62484822995[/C][C]-311.624848229953[/C][/ROW]
[ROW][C]51[/C][C]1500[/C][C]1672.39382560659[/C][C]-172.393825606593[/C][/ROW]
[ROW][C]52[/C][C]1519[/C][C]1370.34036217402[/C][C]148.659637825982[/C][/ROW]
[ROW][C]53[/C][C]1539[/C][C]1376.51165879502[/C][C]162.488341204975[/C][/ROW]
[ROW][C]54[/C][C]1452[/C][C]1685.8654656036[/C][C]-233.865465603601[/C][/ROW]
[ROW][C]55[/C][C]1409[/C][C]1475.50598062981[/C][C]-66.5059806298148[/C][/ROW]
[ROW][C]56[/C][C]1288[/C][C]1040.59324674929[/C][C]247.406753250709[/C][/ROW]
[ROW][C]57[/C][C]987[/C][C]891.504377010153[/C][C]95.495622989847[/C][/ROW]
[ROW][C]58[/C][C]1542[/C][C]1344.08990833806[/C][C]197.910091661944[/C][/ROW]
[ROW][C]59[/C][C]1248[/C][C]1081.19307299742[/C][C]166.80692700258[/C][/ROW]
[ROW][C]60[/C][C]1400[/C][C]336.232019561644[/C][C]1063.76798043836[/C][/ROW]
[ROW][C]61[/C][C]4190[/C][C]3416.88898693442[/C][C]773.111013065582[/C][/ROW]
[ROW][C]62[/C][C]2185[/C][C]2309.23707523741[/C][C]-124.237075237409[/C][/ROW]
[ROW][C]63[/C][C]1097[/C][C]2715.14760811742[/C][C]-1618.14760811742[/C][/ROW]
[ROW][C]64[/C][C]1215[/C][C]1805.21506675017[/C][C]-590.215066750174[/C][/ROW]
[ROW][C]65[/C][C]1236[/C][C]1499.59644280595[/C][C]-263.596442805952[/C][/ROW]
[ROW][C]66[/C][C]1374[/C][C]1626.12660764094[/C][C]-252.126607640944[/C][/ROW]
[ROW][C]67[/C][C]1548[/C][C]1409.3106943381[/C][C]138.6893056619[/C][/ROW]
[ROW][C]68[/C][C]1178[/C][C]1063.3631426785[/C][C]114.636857321502[/C][/ROW]
[ROW][C]69[/C][C]902[/C][C]857.093129281731[/C][C]44.9068707182694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271812&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271812&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
1326812622.1714743589758.8285256410254
1412491218.8896274893930.1103725106143
1517051688.3602902343616.6397097656427
1614721463.103057853968.89694214603628
1714131408.160786164724.8392138352765
1816511648.255668520162.74433147984428
1915251557.92459366638-32.9245936663835
2010951126.32863918326-31.3286391832628
21900854.28136809438445.7186319056165
2212551295.75724704088-40.75724704088
23984927.229977392156.7700226079004
24101135.12086306538-34.1208630653803
2526552749.29334783883-94.2933478388318
2613091281.1609533537727.8390466462326
2718441749.5720762690294.4279237309756
2818251557.09283952194267.907160478061
2916291611.4534587895417.5465412104629
3017181856.89667987228-138.896679872284
3115951706.50935620355-111.509356203547
3215391241.75318541985297.24681458015
3315131108.98035926077404.019640739235
3414751701.05516114815-226.055161148145
3511841255.03960739697-71.03960739697
36211408.299643947913-197.299643947913
3733872953.14106686045433.858933139548
3815461708.86563870096-162.865638700961
3919552097.27473563734-142.274735637345
4018991806.1764417198692.8235582801376
4124151784.75801554891630.241984451087
4234392287.661592972861151.33840702714
4311482682.11244120307-1534.11244120307
4411271619.90562325626-492.905623256256
4511861154.3928297395231.6071702604786
4610091584.55173550091-575.551735500909
47817992.166501659016-175.166501659016
48236100.528048405573135.471951594427
4927622790.56029129493-28.5602912949316
5010351346.62484822995-311.624848229953
5115001672.39382560659-172.393825606593
5215191370.34036217402148.659637825982
5315391376.51165879502162.488341204975
5414521685.8654656036-233.865465603601
5514091475.50598062981-66.5059806298148
5612881040.59324674929247.406753250709
57987891.50437701015395.495622989847
5815421344.08990833806197.910091661944
5912481081.19307299742166.80692700258
601400336.2320195616441063.76798043836
6141903416.88898693442773.111013065582
6221852309.23707523741-124.237075237409
6310972715.14760811742-1618.14760811742
6412151805.21506675017-590.215066750174
6512361499.59644280595-263.596442805952
6613741626.12660764094-252.126607640944
6715481409.3106943381138.6893056619
6811781063.3631426785114.636857321502
69902857.09312928173144.9068707182694







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
701289.09029023911433.5756240450782144.60495643314
71942.41908883225313.8073507443361871.03082692017
72133.755425152103-862.6050398184041130.11589012261
732763.200963173451703.413912772373822.98801357453
741322.49114280799202.8648621949442442.11742342104
751769.66916580081593.2434672201552946.09486438147
761550.47775169719319.8714619673842781.08404142701
771496.44368771348213.9436852323332778.94369019463
781734.32883392787401.9547601761573066.70290767958
791626.86400967929246.4165863967833007.3114329618
801222.19308009729-204.7089853889522649.09514558353
81967.010997726735-504.8802756119162438.90227106539

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
70 & 1289.09029023911 & 433.575624045078 & 2144.60495643314 \tabularnewline
71 & 942.419088832253 & 13.807350744336 & 1871.03082692017 \tabularnewline
72 & 133.755425152103 & -862.605039818404 & 1130.11589012261 \tabularnewline
73 & 2763.20096317345 & 1703.41391277237 & 3822.98801357453 \tabularnewline
74 & 1322.49114280799 & 202.864862194944 & 2442.11742342104 \tabularnewline
75 & 1769.66916580081 & 593.243467220155 & 2946.09486438147 \tabularnewline
76 & 1550.47775169719 & 319.871461967384 & 2781.08404142701 \tabularnewline
77 & 1496.44368771348 & 213.943685232333 & 2778.94369019463 \tabularnewline
78 & 1734.32883392787 & 401.954760176157 & 3066.70290767958 \tabularnewline
79 & 1626.86400967929 & 246.416586396783 & 3007.3114329618 \tabularnewline
80 & 1222.19308009729 & -204.708985388952 & 2649.09514558353 \tabularnewline
81 & 967.010997726735 & -504.880275611916 & 2438.90227106539 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271812&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]70[/C][C]1289.09029023911[/C][C]433.575624045078[/C][C]2144.60495643314[/C][/ROW]
[ROW][C]71[/C][C]942.419088832253[/C][C]13.807350744336[/C][C]1871.03082692017[/C][/ROW]
[ROW][C]72[/C][C]133.755425152103[/C][C]-862.605039818404[/C][C]1130.11589012261[/C][/ROW]
[ROW][C]73[/C][C]2763.20096317345[/C][C]1703.41391277237[/C][C]3822.98801357453[/C][/ROW]
[ROW][C]74[/C][C]1322.49114280799[/C][C]202.864862194944[/C][C]2442.11742342104[/C][/ROW]
[ROW][C]75[/C][C]1769.66916580081[/C][C]593.243467220155[/C][C]2946.09486438147[/C][/ROW]
[ROW][C]76[/C][C]1550.47775169719[/C][C]319.871461967384[/C][C]2781.08404142701[/C][/ROW]
[ROW][C]77[/C][C]1496.44368771348[/C][C]213.943685232333[/C][C]2778.94369019463[/C][/ROW]
[ROW][C]78[/C][C]1734.32883392787[/C][C]401.954760176157[/C][C]3066.70290767958[/C][/ROW]
[ROW][C]79[/C][C]1626.86400967929[/C][C]246.416586396783[/C][C]3007.3114329618[/C][/ROW]
[ROW][C]80[/C][C]1222.19308009729[/C][C]-204.708985388952[/C][C]2649.09514558353[/C][/ROW]
[ROW][C]81[/C][C]967.010997726735[/C][C]-504.880275611916[/C][C]2438.90227106539[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271812&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271812&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
701289.09029023911433.5756240450782144.60495643314
71942.41908883225313.8073507443361871.03082692017
72133.755425152103-862.6050398184041130.11589012261
732763.200963173451703.413912772373822.98801357453
741322.49114280799202.8648621949442442.11742342104
751769.66916580081593.2434672201552946.09486438147
761550.47775169719319.8714619673842781.08404142701
771496.44368771348213.9436852323332778.94369019463
781734.32883392787401.9547601761573066.70290767958
791626.86400967929246.4165863967833007.3114329618
801222.19308009729-204.7089853889522649.09514558353
81967.010997726735-504.8802756119162438.90227106539



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')