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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 May 2012 03:00:28 -0400
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/May/29/t1338274856macnyo6afi9jygi.htm/, Retrieved Mon, 29 Apr 2024 19:34:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167927, Retrieved Mon, 29 Apr 2024 19:34:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-29 07:00:28] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
4.143
4.429
5.219
4.929
5.761
5.592
4.163
4.962
5.208
4.755
4.491
5.732
5.731
5.040
6.102
4.904
5.369
5.578
4.619
4.731
5.011
5.227
4.146
4.625
4.736
4.219
5.116
4.205
4.121
5.103
4.300
4.578
3.809
5.657
4.249
3.830
4.736
4.840
4.412
4.570
4.105
4.801
3.953
3.828
4.444
4.027
4.118
4.791
3.232
3.554
3.950
3.948
3.683
4.311
3.865
4.140
4.095
3.814
3.377
3.443
3.494
4.015
5.401
5.122
5.507
6.425
4.948
2.977
2.937
2.972
2.732
3.172
3.102
3.360
3.705
3.171
3.980
3.342
2.766
4.022
4.459




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167927&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167927&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.502173580585683
beta0
gamma0.460355021913269

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.502173580585683 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.460355021913269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167927&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]0.502173580585683[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.460355021913269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167927&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
alpha0.502173580585683
beta0
gamma0.460355021913269







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135.7315.653620459401710.077379540598292
145.044.999936316638420.0400636833615753
156.1026.10772146956729-0.00572146956728847
164.9044.903222861645530.0007771383544668
175.3695.37115434959934-0.00215434959933614
185.5785.6474053884176-0.0694053884176009
194.6194.326926398941060.292073601058942
204.7315.18880594124978-0.457805941249776
215.0115.15049078878937-0.139490788789375
225.2274.599525096194690.627474903805312
234.1464.67583431163666-0.529834311636655
244.6255.67551508118199-1.05051508118199
254.7365.15412399364491-0.418123993644909
264.2194.24305913470588-0.024059134705877
275.1165.30815060343058-0.19215060343058
284.2054.011521540598460.193478459401539
294.1214.57555071162724-0.454550711627235
305.1034.609207865407180.49379213459282
314.33.654394424048280.645605575951721
324.5784.52195332099590.0560466790040977
333.8094.81463185612865-1.00563185612865
345.6574.004483816322941.65251618367706
354.2494.33031315219543-0.0813131521954347
363.835.43590139774348-1.60590139774348
374.7364.78053939911884-0.044539399118837
384.844.147389413368780.692610586631225
394.4125.53385080174391-1.12185080174391
404.573.858728131622560.711271868377445
414.1054.53426616135713-0.429266161357133
424.8014.797958814534050.00304118546594534
433.9533.631495344563910.321504655436085
443.8284.20118604600287-0.373186046002873
454.4444.035003059497530.408996940502472
464.0274.54443033451501-0.517430334515008
474.1183.383216238835060.734783761164937
484.7914.549226397442680.241773602557318
493.2325.17954605995058-1.94754605995058
503.5543.75969414828533-0.205694148285334
513.954.2792180094321-0.329218009432098
523.9483.422243943309250.525756056690747
533.6833.7432358725223-0.0602358725223016
544.3114.291320641416110.0196793585838897
553.8653.206196890747880.658803109252117
564.143.786062908456790.353937091543206
574.0954.16428021745313-0.0692802174531257
583.8144.22121361579276-0.407213615792755
593.3773.40232597923408-0.0253259792340756
603.4434.07364257188563-0.630642571885633
613.4943.76411640398627-0.270116403986272
624.0153.58581755665750.429182443342503
635.4014.39585085443961.0051491455604
645.1224.40490101975670.717098980243296
655.5074.687684500807710.819315499192291
666.4255.695771455650320.729228544349678
674.9485.11343695512092-0.165436955120921
682.9775.2095231419599-2.2325231419599
692.9374.19189682684665-1.25489682684665
702.9723.57599836123697-0.603998361236967
712.7322.7458104461771-0.0138104461771045
723.1723.28418525978407-0.112185259784069
733.1023.31763892340619-0.215638923406194
743.363.326960364124380.0330396358756215
753.7054.0700594686932-0.365059468693201
763.1713.32501262635083-0.154012626350832
773.983.193772536974840.786227463025161
783.3424.1645977058806-0.822597705880599
792.7662.597940402082440.168059597917562
804.0222.387771358826221.63422864117378
814.4593.535974992533940.923025007466056

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.731 & 5.65362045940171 & 0.077379540598292 \tabularnewline
14 & 5.04 & 4.99993631663842 & 0.0400636833615753 \tabularnewline
15 & 6.102 & 6.10772146956729 & -0.00572146956728847 \tabularnewline
16 & 4.904 & 4.90322286164553 & 0.0007771383544668 \tabularnewline
17 & 5.369 & 5.37115434959934 & -0.00215434959933614 \tabularnewline
18 & 5.578 & 5.6474053884176 & -0.0694053884176009 \tabularnewline
19 & 4.619 & 4.32692639894106 & 0.292073601058942 \tabularnewline
20 & 4.731 & 5.18880594124978 & -0.457805941249776 \tabularnewline
21 & 5.011 & 5.15049078878937 & -0.139490788789375 \tabularnewline
22 & 5.227 & 4.59952509619469 & 0.627474903805312 \tabularnewline
23 & 4.146 & 4.67583431163666 & -0.529834311636655 \tabularnewline
24 & 4.625 & 5.67551508118199 & -1.05051508118199 \tabularnewline
25 & 4.736 & 5.15412399364491 & -0.418123993644909 \tabularnewline
26 & 4.219 & 4.24305913470588 & -0.024059134705877 \tabularnewline
27 & 5.116 & 5.30815060343058 & -0.19215060343058 \tabularnewline
28 & 4.205 & 4.01152154059846 & 0.193478459401539 \tabularnewline
29 & 4.121 & 4.57555071162724 & -0.454550711627235 \tabularnewline
30 & 5.103 & 4.60920786540718 & 0.49379213459282 \tabularnewline
31 & 4.3 & 3.65439442404828 & 0.645605575951721 \tabularnewline
32 & 4.578 & 4.5219533209959 & 0.0560466790040977 \tabularnewline
33 & 3.809 & 4.81463185612865 & -1.00563185612865 \tabularnewline
34 & 5.657 & 4.00448381632294 & 1.65251618367706 \tabularnewline
35 & 4.249 & 4.33031315219543 & -0.0813131521954347 \tabularnewline
36 & 3.83 & 5.43590139774348 & -1.60590139774348 \tabularnewline
37 & 4.736 & 4.78053939911884 & -0.044539399118837 \tabularnewline
38 & 4.84 & 4.14738941336878 & 0.692610586631225 \tabularnewline
39 & 4.412 & 5.53385080174391 & -1.12185080174391 \tabularnewline
40 & 4.57 & 3.85872813162256 & 0.711271868377445 \tabularnewline
41 & 4.105 & 4.53426616135713 & -0.429266161357133 \tabularnewline
42 & 4.801 & 4.79795881453405 & 0.00304118546594534 \tabularnewline
43 & 3.953 & 3.63149534456391 & 0.321504655436085 \tabularnewline
44 & 3.828 & 4.20118604600287 & -0.373186046002873 \tabularnewline
45 & 4.444 & 4.03500305949753 & 0.408996940502472 \tabularnewline
46 & 4.027 & 4.54443033451501 & -0.517430334515008 \tabularnewline
47 & 4.118 & 3.38321623883506 & 0.734783761164937 \tabularnewline
48 & 4.791 & 4.54922639744268 & 0.241773602557318 \tabularnewline
49 & 3.232 & 5.17954605995058 & -1.94754605995058 \tabularnewline
50 & 3.554 & 3.75969414828533 & -0.205694148285334 \tabularnewline
51 & 3.95 & 4.2792180094321 & -0.329218009432098 \tabularnewline
52 & 3.948 & 3.42224394330925 & 0.525756056690747 \tabularnewline
53 & 3.683 & 3.7432358725223 & -0.0602358725223016 \tabularnewline
54 & 4.311 & 4.29132064141611 & 0.0196793585838897 \tabularnewline
55 & 3.865 & 3.20619689074788 & 0.658803109252117 \tabularnewline
56 & 4.14 & 3.78606290845679 & 0.353937091543206 \tabularnewline
57 & 4.095 & 4.16428021745313 & -0.0692802174531257 \tabularnewline
58 & 3.814 & 4.22121361579276 & -0.407213615792755 \tabularnewline
59 & 3.377 & 3.40232597923408 & -0.0253259792340756 \tabularnewline
60 & 3.443 & 4.07364257188563 & -0.630642571885633 \tabularnewline
61 & 3.494 & 3.76411640398627 & -0.270116403986272 \tabularnewline
62 & 4.015 & 3.5858175566575 & 0.429182443342503 \tabularnewline
63 & 5.401 & 4.3958508544396 & 1.0051491455604 \tabularnewline
64 & 5.122 & 4.4049010197567 & 0.717098980243296 \tabularnewline
65 & 5.507 & 4.68768450080771 & 0.819315499192291 \tabularnewline
66 & 6.425 & 5.69577145565032 & 0.729228544349678 \tabularnewline
67 & 4.948 & 5.11343695512092 & -0.165436955120921 \tabularnewline
68 & 2.977 & 5.2095231419599 & -2.2325231419599 \tabularnewline
69 & 2.937 & 4.19189682684665 & -1.25489682684665 \tabularnewline
70 & 2.972 & 3.57599836123697 & -0.603998361236967 \tabularnewline
71 & 2.732 & 2.7458104461771 & -0.0138104461771045 \tabularnewline
72 & 3.172 & 3.28418525978407 & -0.112185259784069 \tabularnewline
73 & 3.102 & 3.31763892340619 & -0.215638923406194 \tabularnewline
74 & 3.36 & 3.32696036412438 & 0.0330396358756215 \tabularnewline
75 & 3.705 & 4.0700594686932 & -0.365059468693201 \tabularnewline
76 & 3.171 & 3.32501262635083 & -0.154012626350832 \tabularnewline
77 & 3.98 & 3.19377253697484 & 0.786227463025161 \tabularnewline
78 & 3.342 & 4.1645977058806 & -0.822597705880599 \tabularnewline
79 & 2.766 & 2.59794040208244 & 0.168059597917562 \tabularnewline
80 & 4.022 & 2.38777135882622 & 1.63422864117378 \tabularnewline
81 & 4.459 & 3.53597499253394 & 0.923025007466056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167927&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]5.731[/C][C]5.65362045940171[/C][C]0.077379540598292[/C][/ROW]
[ROW][C]14[/C][C]5.04[/C][C]4.99993631663842[/C][C]0.0400636833615753[/C][/ROW]
[ROW][C]15[/C][C]6.102[/C][C]6.10772146956729[/C][C]-0.00572146956728847[/C][/ROW]
[ROW][C]16[/C][C]4.904[/C][C]4.90322286164553[/C][C]0.0007771383544668[/C][/ROW]
[ROW][C]17[/C][C]5.369[/C][C]5.37115434959934[/C][C]-0.00215434959933614[/C][/ROW]
[ROW][C]18[/C][C]5.578[/C][C]5.6474053884176[/C][C]-0.0694053884176009[/C][/ROW]
[ROW][C]19[/C][C]4.619[/C][C]4.32692639894106[/C][C]0.292073601058942[/C][/ROW]
[ROW][C]20[/C][C]4.731[/C][C]5.18880594124978[/C][C]-0.457805941249776[/C][/ROW]
[ROW][C]21[/C][C]5.011[/C][C]5.15049078878937[/C][C]-0.139490788789375[/C][/ROW]
[ROW][C]22[/C][C]5.227[/C][C]4.59952509619469[/C][C]0.627474903805312[/C][/ROW]
[ROW][C]23[/C][C]4.146[/C][C]4.67583431163666[/C][C]-0.529834311636655[/C][/ROW]
[ROW][C]24[/C][C]4.625[/C][C]5.67551508118199[/C][C]-1.05051508118199[/C][/ROW]
[ROW][C]25[/C][C]4.736[/C][C]5.15412399364491[/C][C]-0.418123993644909[/C][/ROW]
[ROW][C]26[/C][C]4.219[/C][C]4.24305913470588[/C][C]-0.024059134705877[/C][/ROW]
[ROW][C]27[/C][C]5.116[/C][C]5.30815060343058[/C][C]-0.19215060343058[/C][/ROW]
[ROW][C]28[/C][C]4.205[/C][C]4.01152154059846[/C][C]0.193478459401539[/C][/ROW]
[ROW][C]29[/C][C]4.121[/C][C]4.57555071162724[/C][C]-0.454550711627235[/C][/ROW]
[ROW][C]30[/C][C]5.103[/C][C]4.60920786540718[/C][C]0.49379213459282[/C][/ROW]
[ROW][C]31[/C][C]4.3[/C][C]3.65439442404828[/C][C]0.645605575951721[/C][/ROW]
[ROW][C]32[/C][C]4.578[/C][C]4.5219533209959[/C][C]0.0560466790040977[/C][/ROW]
[ROW][C]33[/C][C]3.809[/C][C]4.81463185612865[/C][C]-1.00563185612865[/C][/ROW]
[ROW][C]34[/C][C]5.657[/C][C]4.00448381632294[/C][C]1.65251618367706[/C][/ROW]
[ROW][C]35[/C][C]4.249[/C][C]4.33031315219543[/C][C]-0.0813131521954347[/C][/ROW]
[ROW][C]36[/C][C]3.83[/C][C]5.43590139774348[/C][C]-1.60590139774348[/C][/ROW]
[ROW][C]37[/C][C]4.736[/C][C]4.78053939911884[/C][C]-0.044539399118837[/C][/ROW]
[ROW][C]38[/C][C]4.84[/C][C]4.14738941336878[/C][C]0.692610586631225[/C][/ROW]
[ROW][C]39[/C][C]4.412[/C][C]5.53385080174391[/C][C]-1.12185080174391[/C][/ROW]
[ROW][C]40[/C][C]4.57[/C][C]3.85872813162256[/C][C]0.711271868377445[/C][/ROW]
[ROW][C]41[/C][C]4.105[/C][C]4.53426616135713[/C][C]-0.429266161357133[/C][/ROW]
[ROW][C]42[/C][C]4.801[/C][C]4.79795881453405[/C][C]0.00304118546594534[/C][/ROW]
[ROW][C]43[/C][C]3.953[/C][C]3.63149534456391[/C][C]0.321504655436085[/C][/ROW]
[ROW][C]44[/C][C]3.828[/C][C]4.20118604600287[/C][C]-0.373186046002873[/C][/ROW]
[ROW][C]45[/C][C]4.444[/C][C]4.03500305949753[/C][C]0.408996940502472[/C][/ROW]
[ROW][C]46[/C][C]4.027[/C][C]4.54443033451501[/C][C]-0.517430334515008[/C][/ROW]
[ROW][C]47[/C][C]4.118[/C][C]3.38321623883506[/C][C]0.734783761164937[/C][/ROW]
[ROW][C]48[/C][C]4.791[/C][C]4.54922639744268[/C][C]0.241773602557318[/C][/ROW]
[ROW][C]49[/C][C]3.232[/C][C]5.17954605995058[/C][C]-1.94754605995058[/C][/ROW]
[ROW][C]50[/C][C]3.554[/C][C]3.75969414828533[/C][C]-0.205694148285334[/C][/ROW]
[ROW][C]51[/C][C]3.95[/C][C]4.2792180094321[/C][C]-0.329218009432098[/C][/ROW]
[ROW][C]52[/C][C]3.948[/C][C]3.42224394330925[/C][C]0.525756056690747[/C][/ROW]
[ROW][C]53[/C][C]3.683[/C][C]3.7432358725223[/C][C]-0.0602358725223016[/C][/ROW]
[ROW][C]54[/C][C]4.311[/C][C]4.29132064141611[/C][C]0.0196793585838897[/C][/ROW]
[ROW][C]55[/C][C]3.865[/C][C]3.20619689074788[/C][C]0.658803109252117[/C][/ROW]
[ROW][C]56[/C][C]4.14[/C][C]3.78606290845679[/C][C]0.353937091543206[/C][/ROW]
[ROW][C]57[/C][C]4.095[/C][C]4.16428021745313[/C][C]-0.0692802174531257[/C][/ROW]
[ROW][C]58[/C][C]3.814[/C][C]4.22121361579276[/C][C]-0.407213615792755[/C][/ROW]
[ROW][C]59[/C][C]3.377[/C][C]3.40232597923408[/C][C]-0.0253259792340756[/C][/ROW]
[ROW][C]60[/C][C]3.443[/C][C]4.07364257188563[/C][C]-0.630642571885633[/C][/ROW]
[ROW][C]61[/C][C]3.494[/C][C]3.76411640398627[/C][C]-0.270116403986272[/C][/ROW]
[ROW][C]62[/C][C]4.015[/C][C]3.5858175566575[/C][C]0.429182443342503[/C][/ROW]
[ROW][C]63[/C][C]5.401[/C][C]4.3958508544396[/C][C]1.0051491455604[/C][/ROW]
[ROW][C]64[/C][C]5.122[/C][C]4.4049010197567[/C][C]0.717098980243296[/C][/ROW]
[ROW][C]65[/C][C]5.507[/C][C]4.68768450080771[/C][C]0.819315499192291[/C][/ROW]
[ROW][C]66[/C][C]6.425[/C][C]5.69577145565032[/C][C]0.729228544349678[/C][/ROW]
[ROW][C]67[/C][C]4.948[/C][C]5.11343695512092[/C][C]-0.165436955120921[/C][/ROW]
[ROW][C]68[/C][C]2.977[/C][C]5.2095231419599[/C][C]-2.2325231419599[/C][/ROW]
[ROW][C]69[/C][C]2.937[/C][C]4.19189682684665[/C][C]-1.25489682684665[/C][/ROW]
[ROW][C]70[/C][C]2.972[/C][C]3.57599836123697[/C][C]-0.603998361236967[/C][/ROW]
[ROW][C]71[/C][C]2.732[/C][C]2.7458104461771[/C][C]-0.0138104461771045[/C][/ROW]
[ROW][C]72[/C][C]3.172[/C][C]3.28418525978407[/C][C]-0.112185259784069[/C][/ROW]
[ROW][C]73[/C][C]3.102[/C][C]3.31763892340619[/C][C]-0.215638923406194[/C][/ROW]
[ROW][C]74[/C][C]3.36[/C][C]3.32696036412438[/C][C]0.0330396358756215[/C][/ROW]
[ROW][C]75[/C][C]3.705[/C][C]4.0700594686932[/C][C]-0.365059468693201[/C][/ROW]
[ROW][C]76[/C][C]3.171[/C][C]3.32501262635083[/C][C]-0.154012626350832[/C][/ROW]
[ROW][C]77[/C][C]3.98[/C][C]3.19377253697484[/C][C]0.786227463025161[/C][/ROW]
[ROW][C]78[/C][C]3.342[/C][C]4.1645977058806[/C][C]-0.822597705880599[/C][/ROW]
[ROW][C]79[/C][C]2.766[/C][C]2.59794040208244[/C][C]0.168059597917562[/C][/ROW]
[ROW][C]80[/C][C]4.022[/C][C]2.38777135882622[/C][C]1.63422864117378[/C][/ROW]
[ROW][C]81[/C][C]4.459[/C][C]3.53597499253394[/C][C]0.923025007466056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167927&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
135.7315.653620459401710.077379540598292
145.044.999936316638420.0400636833615753
156.1026.10772146956729-0.00572146956728847
164.9044.903222861645530.0007771383544668
175.3695.37115434959934-0.00215434959933614
185.5785.6474053884176-0.0694053884176009
194.6194.326926398941060.292073601058942
204.7315.18880594124978-0.457805941249776
215.0115.15049078878937-0.139490788789375
225.2274.599525096194690.627474903805312
234.1464.67583431163666-0.529834311636655
244.6255.67551508118199-1.05051508118199
254.7365.15412399364491-0.418123993644909
264.2194.24305913470588-0.024059134705877
275.1165.30815060343058-0.19215060343058
284.2054.011521540598460.193478459401539
294.1214.57555071162724-0.454550711627235
305.1034.609207865407180.49379213459282
314.33.654394424048280.645605575951721
324.5784.52195332099590.0560466790040977
333.8094.81463185612865-1.00563185612865
345.6574.004483816322941.65251618367706
354.2494.33031315219543-0.0813131521954347
363.835.43590139774348-1.60590139774348
374.7364.78053939911884-0.044539399118837
384.844.147389413368780.692610586631225
394.4125.53385080174391-1.12185080174391
404.573.858728131622560.711271868377445
414.1054.53426616135713-0.429266161357133
424.8014.797958814534050.00304118546594534
433.9533.631495344563910.321504655436085
443.8284.20118604600287-0.373186046002873
454.4444.035003059497530.408996940502472
464.0274.54443033451501-0.517430334515008
474.1183.383216238835060.734783761164937
484.7914.549226397442680.241773602557318
493.2325.17954605995058-1.94754605995058
503.5543.75969414828533-0.205694148285334
513.954.2792180094321-0.329218009432098
523.9483.422243943309250.525756056690747
533.6833.7432358725223-0.0602358725223016
544.3114.291320641416110.0196793585838897
553.8653.206196890747880.658803109252117
564.143.786062908456790.353937091543206
574.0954.16428021745313-0.0692802174531257
583.8144.22121361579276-0.407213615792755
593.3773.40232597923408-0.0253259792340756
603.4434.07364257188563-0.630642571885633
613.4943.76411640398627-0.270116403986272
624.0153.58581755665750.429182443342503
635.4014.39585085443961.0051491455604
645.1224.40490101975670.717098980243296
655.5074.687684500807710.819315499192291
666.4255.695771455650320.729228544349678
674.9485.11343695512092-0.165436955120921
682.9775.2095231419599-2.2325231419599
692.9374.19189682684665-1.25489682684665
702.9723.57599836123697-0.603998361236967
712.7322.7458104461771-0.0138104461771045
723.1723.28418525978407-0.112185259784069
733.1023.31763892340619-0.215638923406194
743.363.326960364124380.0330396358756215
753.7054.0700594686932-0.365059468693201
763.1713.32501262635083-0.154012626350832
773.983.193772536974840.786227463025161
783.3424.1645977058806-0.822597705880599
792.7662.597940402082440.168059597917562
804.0222.387771358826221.63422864117378
814.4593.535974992533940.923025007466056







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
824.162942220195022.786732406046575.53915203434346
833.771323757063732.231334333708485.31131318041898
844.294088577821922.606136743339215.98204041230464
854.360169525921212.536219042212546.18412000962989
864.534770516297512.58428100376266.48526002883241
875.170042873037383.100737842357717.23934790371704
884.656686310655932.47502701519216.83834560611975
894.818268594932362.529764443096227.1067727467685
905.025565551243282.634987122398337.41614398008823
914.099030844926751.610561597387956.58750009246555
924.140478776432891.557826425179656.72313112768612
934.305024523399071.631504907065316.97854413973282

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
82 & 4.16294222019502 & 2.78673240604657 & 5.53915203434346 \tabularnewline
83 & 3.77132375706373 & 2.23133433370848 & 5.31131318041898 \tabularnewline
84 & 4.29408857782192 & 2.60613674333921 & 5.98204041230464 \tabularnewline
85 & 4.36016952592121 & 2.53621904221254 & 6.18412000962989 \tabularnewline
86 & 4.53477051629751 & 2.5842810037626 & 6.48526002883241 \tabularnewline
87 & 5.17004287303738 & 3.10073784235771 & 7.23934790371704 \tabularnewline
88 & 4.65668631065593 & 2.4750270151921 & 6.83834560611975 \tabularnewline
89 & 4.81826859493236 & 2.52976444309622 & 7.1067727467685 \tabularnewline
90 & 5.02556555124328 & 2.63498712239833 & 7.41614398008823 \tabularnewline
91 & 4.09903084492675 & 1.61056159738795 & 6.58750009246555 \tabularnewline
92 & 4.14047877643289 & 1.55782642517965 & 6.72313112768612 \tabularnewline
93 & 4.30502452339907 & 1.63150490706531 & 6.97854413973282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167927&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]82[/C][C]4.16294222019502[/C][C]2.78673240604657[/C][C]5.53915203434346[/C][/ROW]
[ROW][C]83[/C][C]3.77132375706373[/C][C]2.23133433370848[/C][C]5.31131318041898[/C][/ROW]
[ROW][C]84[/C][C]4.29408857782192[/C][C]2.60613674333921[/C][C]5.98204041230464[/C][/ROW]
[ROW][C]85[/C][C]4.36016952592121[/C][C]2.53621904221254[/C][C]6.18412000962989[/C][/ROW]
[ROW][C]86[/C][C]4.53477051629751[/C][C]2.5842810037626[/C][C]6.48526002883241[/C][/ROW]
[ROW][C]87[/C][C]5.17004287303738[/C][C]3.10073784235771[/C][C]7.23934790371704[/C][/ROW]
[ROW][C]88[/C][C]4.65668631065593[/C][C]2.4750270151921[/C][C]6.83834560611975[/C][/ROW]
[ROW][C]89[/C][C]4.81826859493236[/C][C]2.52976444309622[/C][C]7.1067727467685[/C][/ROW]
[ROW][C]90[/C][C]5.02556555124328[/C][C]2.63498712239833[/C][C]7.41614398008823[/C][/ROW]
[ROW][C]91[/C][C]4.09903084492675[/C][C]1.61056159738795[/C][C]6.58750009246555[/C][/ROW]
[ROW][C]92[/C][C]4.14047877643289[/C][C]1.55782642517965[/C][C]6.72313112768612[/C][/ROW]
[ROW][C]93[/C][C]4.30502452339907[/C][C]1.63150490706531[/C][C]6.97854413973282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167927&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167927&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
824.162942220195022.786732406046575.53915203434346
833.771323757063732.231334333708485.31131318041898
844.294088577821922.606136743339215.98204041230464
854.360169525921212.536219042212546.18412000962989
864.534770516297512.58428100376266.48526002883241
875.170042873037383.100737842357717.23934790371704
884.656686310655932.47502701519216.83834560611975
894.818268594932362.529764443096227.1067727467685
905.025565551243282.634987122398337.41614398008823
914.099030844926751.610561597387956.58750009246555
924.140478776432891.557826425179656.72313112768612
934.305024523399071.631504907065316.97854413973282



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')