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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 computationSun, 16 Jan 2011 14:33:13 +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/2011/Jan/16/t12951882871jkol4kv3wyjtl7.htm/, Retrieved Mon, 27 May 2024 06:16:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117414, Retrieved Mon, 27 May 2024 06:16:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2011-01-16 11:37:06] [e35ce2e7ec49602a729c3c8722e619b0]
- RMPD  [Variability] [] [2011-01-16 13:09:43] [e35ce2e7ec49602a729c3c8722e619b0]
- RM D      [Exponential Smoothing] [] [2011-01-16 14:33:13] [9ecedc6075144b73bec317d56fadfdf0] [Current]
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Dataseries X:
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18073
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
27390
26434
27525
30695
32436
30160
30236




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117414&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117414&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0233158672621605
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0233158672621605 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117414&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0233158672621605[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117414&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
alpha1
beta0.0233158672621605
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3108051073273
41087210885.7020583101-13.7020583101385
51062510952.3825829374-327.38258293736
61040710697.7493740896-290.74937408965
71046310472.9703002768-9.9703002768183
81055610528.73783407927.2621659209999
91064610622.373475120923.626524879106
101070210712.9243480388-10.9243480388413
111135310768.66963739584.330362609959
121134611433.2938065619-87.2938065619055
131145111424.258475755326.7415242447005
141196411529.881977585434.118022415023
151257412053.0038157717520.996184228283
161303112675.1512936473355.848706352725
171381213140.44821485671.551785149992
181454413937.1060271322606.893972867769
191493114683.2562864458247.743713554179
201488615076.0326459861-190.032645986086
211600515026.6018700368978.398129963203
221706416168.4140709646895.585929035435
231516817248.2954336078-2080.29543360781
241605015303.7915414117746.208458588264
251583916203.1900387821-364.190038782081
261513715983.6986321796-846.698632179638
271495415261.9571192607-307.957119260684
281564815071.7768319456576.223168054436
291530515779.2119748453-474.211974845302
301557915425.1553113857153.844688614317
311634815702.7423337244645.257666275596
321592816486.7870758212-558.787075821176
331617116053.7584705335117.241529466481
341593716299.4920584722-362.492058472171
351571316057.0402417532-344.040241753248
361559415825.0186451437-231.018645143688
371568315700.6322450784-17.6322450784319
381643815789.2211339927648.778866007349
391703216559.347975915472.652024085026
401769617164.3682677697531.631732230271
411774517840.7637226708-95.763722670763
421939417887.53090842441506.46909157556
432014819571.6555417982576.344458201835
442010820339.0935126829-231.093512682881
451858420293.705367016-1709.70536701602
461844118729.8421036213-288.842103621271
471839118580.1074994735-189.107499473514
481917818525.6982941175652.301705882488
491807319327.9072741067-1254.90727410675
501848318193.6480226774289.351977322644
511964418610.39451497271033.60548502735
521919519795.493923263-600.493923262991
531965019332.4928866565317.507113343541
542083019794.8958403661035.10415963403
552359520999.03019155452595.96980844549
562293723824.5574790248-887.557479024796
572181423145.8633066563-1331.86330665632
582192821991.809758587-63.8097585869764
592177722104.3219787257-327.321978725733
602138321945.6901829178-562.690182917773
612146721538.5705733031-71.5705733031427
622205221620.9018433161431.098156683871
632268022215.9532707143464.046729285667
642432022854.77292265781465.2270773422
652497724528.935962702448.064037297969
662520425196.38296432067.61703567938093
672739025423.56056211341966.43943788655
682643427655.4098030263-1221.40980302629
692752526670.9315741862854.06842581377
703069527781.84492023532913.1550797647
713243631019.76765738921416.23234261081
723016032793.7883427019-2633.78834270188
733023630456.3792833068-220.379283306815

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 10805 & 10732 & 73 \tabularnewline
4 & 10872 & 10885.7020583101 & -13.7020583101385 \tabularnewline
5 & 10625 & 10952.3825829374 & -327.38258293736 \tabularnewline
6 & 10407 & 10697.7493740896 & -290.74937408965 \tabularnewline
7 & 10463 & 10472.9703002768 & -9.9703002768183 \tabularnewline
8 & 10556 & 10528.737834079 & 27.2621659209999 \tabularnewline
9 & 10646 & 10622.3734751209 & 23.626524879106 \tabularnewline
10 & 10702 & 10712.9243480388 & -10.9243480388413 \tabularnewline
11 & 11353 & 10768.66963739 & 584.330362609959 \tabularnewline
12 & 11346 & 11433.2938065619 & -87.2938065619055 \tabularnewline
13 & 11451 & 11424.2584757553 & 26.7415242447005 \tabularnewline
14 & 11964 & 11529.881977585 & 434.118022415023 \tabularnewline
15 & 12574 & 12053.0038157717 & 520.996184228283 \tabularnewline
16 & 13031 & 12675.1512936473 & 355.848706352725 \tabularnewline
17 & 13812 & 13140.44821485 & 671.551785149992 \tabularnewline
18 & 14544 & 13937.1060271322 & 606.893972867769 \tabularnewline
19 & 14931 & 14683.2562864458 & 247.743713554179 \tabularnewline
20 & 14886 & 15076.0326459861 & -190.032645986086 \tabularnewline
21 & 16005 & 15026.6018700368 & 978.398129963203 \tabularnewline
22 & 17064 & 16168.4140709646 & 895.585929035435 \tabularnewline
23 & 15168 & 17248.2954336078 & -2080.29543360781 \tabularnewline
24 & 16050 & 15303.7915414117 & 746.208458588264 \tabularnewline
25 & 15839 & 16203.1900387821 & -364.190038782081 \tabularnewline
26 & 15137 & 15983.6986321796 & -846.698632179638 \tabularnewline
27 & 14954 & 15261.9571192607 & -307.957119260684 \tabularnewline
28 & 15648 & 15071.7768319456 & 576.223168054436 \tabularnewline
29 & 15305 & 15779.2119748453 & -474.211974845302 \tabularnewline
30 & 15579 & 15425.1553113857 & 153.844688614317 \tabularnewline
31 & 16348 & 15702.7423337244 & 645.257666275596 \tabularnewline
32 & 15928 & 16486.7870758212 & -558.787075821176 \tabularnewline
33 & 16171 & 16053.7584705335 & 117.241529466481 \tabularnewline
34 & 15937 & 16299.4920584722 & -362.492058472171 \tabularnewline
35 & 15713 & 16057.0402417532 & -344.040241753248 \tabularnewline
36 & 15594 & 15825.0186451437 & -231.018645143688 \tabularnewline
37 & 15683 & 15700.6322450784 & -17.6322450784319 \tabularnewline
38 & 16438 & 15789.2211339927 & 648.778866007349 \tabularnewline
39 & 17032 & 16559.347975915 & 472.652024085026 \tabularnewline
40 & 17696 & 17164.3682677697 & 531.631732230271 \tabularnewline
41 & 17745 & 17840.7637226708 & -95.763722670763 \tabularnewline
42 & 19394 & 17887.5309084244 & 1506.46909157556 \tabularnewline
43 & 20148 & 19571.6555417982 & 576.344458201835 \tabularnewline
44 & 20108 & 20339.0935126829 & -231.093512682881 \tabularnewline
45 & 18584 & 20293.705367016 & -1709.70536701602 \tabularnewline
46 & 18441 & 18729.8421036213 & -288.842103621271 \tabularnewline
47 & 18391 & 18580.1074994735 & -189.107499473514 \tabularnewline
48 & 19178 & 18525.6982941175 & 652.301705882488 \tabularnewline
49 & 18073 & 19327.9072741067 & -1254.90727410675 \tabularnewline
50 & 18483 & 18193.6480226774 & 289.351977322644 \tabularnewline
51 & 19644 & 18610.3945149727 & 1033.60548502735 \tabularnewline
52 & 19195 & 19795.493923263 & -600.493923262991 \tabularnewline
53 & 19650 & 19332.4928866565 & 317.507113343541 \tabularnewline
54 & 20830 & 19794.895840366 & 1035.10415963403 \tabularnewline
55 & 23595 & 20999.0301915545 & 2595.96980844549 \tabularnewline
56 & 22937 & 23824.5574790248 & -887.557479024796 \tabularnewline
57 & 21814 & 23145.8633066563 & -1331.86330665632 \tabularnewline
58 & 21928 & 21991.809758587 & -63.8097585869764 \tabularnewline
59 & 21777 & 22104.3219787257 & -327.321978725733 \tabularnewline
60 & 21383 & 21945.6901829178 & -562.690182917773 \tabularnewline
61 & 21467 & 21538.5705733031 & -71.5705733031427 \tabularnewline
62 & 22052 & 21620.9018433161 & 431.098156683871 \tabularnewline
63 & 22680 & 22215.9532707143 & 464.046729285667 \tabularnewline
64 & 24320 & 22854.7729226578 & 1465.2270773422 \tabularnewline
65 & 24977 & 24528.935962702 & 448.064037297969 \tabularnewline
66 & 25204 & 25196.3829643206 & 7.61703567938093 \tabularnewline
67 & 27390 & 25423.5605621134 & 1966.43943788655 \tabularnewline
68 & 26434 & 27655.4098030263 & -1221.40980302629 \tabularnewline
69 & 27525 & 26670.9315741862 & 854.06842581377 \tabularnewline
70 & 30695 & 27781.8449202353 & 2913.1550797647 \tabularnewline
71 & 32436 & 31019.7676573892 & 1416.23234261081 \tabularnewline
72 & 30160 & 32793.7883427019 & -2633.78834270188 \tabularnewline
73 & 30236 & 30456.3792833068 & -220.379283306815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117414&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]3[/C][C]10805[/C][C]10732[/C][C]73[/C][/ROW]
[ROW][C]4[/C][C]10872[/C][C]10885.7020583101[/C][C]-13.7020583101385[/C][/ROW]
[ROW][C]5[/C][C]10625[/C][C]10952.3825829374[/C][C]-327.38258293736[/C][/ROW]
[ROW][C]6[/C][C]10407[/C][C]10697.7493740896[/C][C]-290.74937408965[/C][/ROW]
[ROW][C]7[/C][C]10463[/C][C]10472.9703002768[/C][C]-9.9703002768183[/C][/ROW]
[ROW][C]8[/C][C]10556[/C][C]10528.737834079[/C][C]27.2621659209999[/C][/ROW]
[ROW][C]9[/C][C]10646[/C][C]10622.3734751209[/C][C]23.626524879106[/C][/ROW]
[ROW][C]10[/C][C]10702[/C][C]10712.9243480388[/C][C]-10.9243480388413[/C][/ROW]
[ROW][C]11[/C][C]11353[/C][C]10768.66963739[/C][C]584.330362609959[/C][/ROW]
[ROW][C]12[/C][C]11346[/C][C]11433.2938065619[/C][C]-87.2938065619055[/C][/ROW]
[ROW][C]13[/C][C]11451[/C][C]11424.2584757553[/C][C]26.7415242447005[/C][/ROW]
[ROW][C]14[/C][C]11964[/C][C]11529.881977585[/C][C]434.118022415023[/C][/ROW]
[ROW][C]15[/C][C]12574[/C][C]12053.0038157717[/C][C]520.996184228283[/C][/ROW]
[ROW][C]16[/C][C]13031[/C][C]12675.1512936473[/C][C]355.848706352725[/C][/ROW]
[ROW][C]17[/C][C]13812[/C][C]13140.44821485[/C][C]671.551785149992[/C][/ROW]
[ROW][C]18[/C][C]14544[/C][C]13937.1060271322[/C][C]606.893972867769[/C][/ROW]
[ROW][C]19[/C][C]14931[/C][C]14683.2562864458[/C][C]247.743713554179[/C][/ROW]
[ROW][C]20[/C][C]14886[/C][C]15076.0326459861[/C][C]-190.032645986086[/C][/ROW]
[ROW][C]21[/C][C]16005[/C][C]15026.6018700368[/C][C]978.398129963203[/C][/ROW]
[ROW][C]22[/C][C]17064[/C][C]16168.4140709646[/C][C]895.585929035435[/C][/ROW]
[ROW][C]23[/C][C]15168[/C][C]17248.2954336078[/C][C]-2080.29543360781[/C][/ROW]
[ROW][C]24[/C][C]16050[/C][C]15303.7915414117[/C][C]746.208458588264[/C][/ROW]
[ROW][C]25[/C][C]15839[/C][C]16203.1900387821[/C][C]-364.190038782081[/C][/ROW]
[ROW][C]26[/C][C]15137[/C][C]15983.6986321796[/C][C]-846.698632179638[/C][/ROW]
[ROW][C]27[/C][C]14954[/C][C]15261.9571192607[/C][C]-307.957119260684[/C][/ROW]
[ROW][C]28[/C][C]15648[/C][C]15071.7768319456[/C][C]576.223168054436[/C][/ROW]
[ROW][C]29[/C][C]15305[/C][C]15779.2119748453[/C][C]-474.211974845302[/C][/ROW]
[ROW][C]30[/C][C]15579[/C][C]15425.1553113857[/C][C]153.844688614317[/C][/ROW]
[ROW][C]31[/C][C]16348[/C][C]15702.7423337244[/C][C]645.257666275596[/C][/ROW]
[ROW][C]32[/C][C]15928[/C][C]16486.7870758212[/C][C]-558.787075821176[/C][/ROW]
[ROW][C]33[/C][C]16171[/C][C]16053.7584705335[/C][C]117.241529466481[/C][/ROW]
[ROW][C]34[/C][C]15937[/C][C]16299.4920584722[/C][C]-362.492058472171[/C][/ROW]
[ROW][C]35[/C][C]15713[/C][C]16057.0402417532[/C][C]-344.040241753248[/C][/ROW]
[ROW][C]36[/C][C]15594[/C][C]15825.0186451437[/C][C]-231.018645143688[/C][/ROW]
[ROW][C]37[/C][C]15683[/C][C]15700.6322450784[/C][C]-17.6322450784319[/C][/ROW]
[ROW][C]38[/C][C]16438[/C][C]15789.2211339927[/C][C]648.778866007349[/C][/ROW]
[ROW][C]39[/C][C]17032[/C][C]16559.347975915[/C][C]472.652024085026[/C][/ROW]
[ROW][C]40[/C][C]17696[/C][C]17164.3682677697[/C][C]531.631732230271[/C][/ROW]
[ROW][C]41[/C][C]17745[/C][C]17840.7637226708[/C][C]-95.763722670763[/C][/ROW]
[ROW][C]42[/C][C]19394[/C][C]17887.5309084244[/C][C]1506.46909157556[/C][/ROW]
[ROW][C]43[/C][C]20148[/C][C]19571.6555417982[/C][C]576.344458201835[/C][/ROW]
[ROW][C]44[/C][C]20108[/C][C]20339.0935126829[/C][C]-231.093512682881[/C][/ROW]
[ROW][C]45[/C][C]18584[/C][C]20293.705367016[/C][C]-1709.70536701602[/C][/ROW]
[ROW][C]46[/C][C]18441[/C][C]18729.8421036213[/C][C]-288.842103621271[/C][/ROW]
[ROW][C]47[/C][C]18391[/C][C]18580.1074994735[/C][C]-189.107499473514[/C][/ROW]
[ROW][C]48[/C][C]19178[/C][C]18525.6982941175[/C][C]652.301705882488[/C][/ROW]
[ROW][C]49[/C][C]18073[/C][C]19327.9072741067[/C][C]-1254.90727410675[/C][/ROW]
[ROW][C]50[/C][C]18483[/C][C]18193.6480226774[/C][C]289.351977322644[/C][/ROW]
[ROW][C]51[/C][C]19644[/C][C]18610.3945149727[/C][C]1033.60548502735[/C][/ROW]
[ROW][C]52[/C][C]19195[/C][C]19795.493923263[/C][C]-600.493923262991[/C][/ROW]
[ROW][C]53[/C][C]19650[/C][C]19332.4928866565[/C][C]317.507113343541[/C][/ROW]
[ROW][C]54[/C][C]20830[/C][C]19794.895840366[/C][C]1035.10415963403[/C][/ROW]
[ROW][C]55[/C][C]23595[/C][C]20999.0301915545[/C][C]2595.96980844549[/C][/ROW]
[ROW][C]56[/C][C]22937[/C][C]23824.5574790248[/C][C]-887.557479024796[/C][/ROW]
[ROW][C]57[/C][C]21814[/C][C]23145.8633066563[/C][C]-1331.86330665632[/C][/ROW]
[ROW][C]58[/C][C]21928[/C][C]21991.809758587[/C][C]-63.8097585869764[/C][/ROW]
[ROW][C]59[/C][C]21777[/C][C]22104.3219787257[/C][C]-327.321978725733[/C][/ROW]
[ROW][C]60[/C][C]21383[/C][C]21945.6901829178[/C][C]-562.690182917773[/C][/ROW]
[ROW][C]61[/C][C]21467[/C][C]21538.5705733031[/C][C]-71.5705733031427[/C][/ROW]
[ROW][C]62[/C][C]22052[/C][C]21620.9018433161[/C][C]431.098156683871[/C][/ROW]
[ROW][C]63[/C][C]22680[/C][C]22215.9532707143[/C][C]464.046729285667[/C][/ROW]
[ROW][C]64[/C][C]24320[/C][C]22854.7729226578[/C][C]1465.2270773422[/C][/ROW]
[ROW][C]65[/C][C]24977[/C][C]24528.935962702[/C][C]448.064037297969[/C][/ROW]
[ROW][C]66[/C][C]25204[/C][C]25196.3829643206[/C][C]7.61703567938093[/C][/ROW]
[ROW][C]67[/C][C]27390[/C][C]25423.5605621134[/C][C]1966.43943788655[/C][/ROW]
[ROW][C]68[/C][C]26434[/C][C]27655.4098030263[/C][C]-1221.40980302629[/C][/ROW]
[ROW][C]69[/C][C]27525[/C][C]26670.9315741862[/C][C]854.06842581377[/C][/ROW]
[ROW][C]70[/C][C]30695[/C][C]27781.8449202353[/C][C]2913.1550797647[/C][/ROW]
[ROW][C]71[/C][C]32436[/C][C]31019.7676573892[/C][C]1416.23234261081[/C][/ROW]
[ROW][C]72[/C][C]30160[/C][C]32793.7883427019[/C][C]-2633.78834270188[/C][/ROW]
[ROW][C]73[/C][C]30236[/C][C]30456.3792833068[/C][C]-220.379283306815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117414&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
3108051073273
41087210885.7020583101-13.7020583101385
51062510952.3825829374-327.38258293736
61040710697.7493740896-290.74937408965
71046310472.9703002768-9.9703002768183
81055610528.73783407927.2621659209999
91064610622.373475120923.626524879106
101070210712.9243480388-10.9243480388413
111135310768.66963739584.330362609959
121134611433.2938065619-87.2938065619055
131145111424.258475755326.7415242447005
141196411529.881977585434.118022415023
151257412053.0038157717520.996184228283
161303112675.1512936473355.848706352725
171381213140.44821485671.551785149992
181454413937.1060271322606.893972867769
191493114683.2562864458247.743713554179
201488615076.0326459861-190.032645986086
211600515026.6018700368978.398129963203
221706416168.4140709646895.585929035435
231516817248.2954336078-2080.29543360781
241605015303.7915414117746.208458588264
251583916203.1900387821-364.190038782081
261513715983.6986321796-846.698632179638
271495415261.9571192607-307.957119260684
281564815071.7768319456576.223168054436
291530515779.2119748453-474.211974845302
301557915425.1553113857153.844688614317
311634815702.7423337244645.257666275596
321592816486.7870758212-558.787075821176
331617116053.7584705335117.241529466481
341593716299.4920584722-362.492058472171
351571316057.0402417532-344.040241753248
361559415825.0186451437-231.018645143688
371568315700.6322450784-17.6322450784319
381643815789.2211339927648.778866007349
391703216559.347975915472.652024085026
401769617164.3682677697531.631732230271
411774517840.7637226708-95.763722670763
421939417887.53090842441506.46909157556
432014819571.6555417982576.344458201835
442010820339.0935126829-231.093512682881
451858420293.705367016-1709.70536701602
461844118729.8421036213-288.842103621271
471839118580.1074994735-189.107499473514
481917818525.6982941175652.301705882488
491807319327.9072741067-1254.90727410675
501848318193.6480226774289.351977322644
511964418610.39451497271033.60548502735
521919519795.493923263-600.493923262991
531965019332.4928866565317.507113343541
542083019794.8958403661035.10415963403
552359520999.03019155452595.96980844549
562293723824.5574790248-887.557479024796
572181423145.8633066563-1331.86330665632
582192821991.809758587-63.8097585869764
592177722104.3219787257-327.321978725733
602138321945.6901829178-562.690182917773
612146721538.5705733031-71.5705733031427
622205221620.9018433161431.098156683871
632268022215.9532707143464.046729285667
642432022854.77292265781465.2270773422
652497724528.935962702448.064037297969
662520425196.38296432067.61703567938093
672739025423.56056211341966.43943788655
682643427655.4098030263-1221.40980302629
692752526670.9315741862854.06842581377
703069527781.84492023532913.1550797647
713243631019.76765738921416.23234261081
723016032793.7883427019-2633.78834270188
733023630456.3792833068-220.379283306815







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7430527.240949189928751.394715553632303.0871828262
7530818.481898379828277.609345982733359.3544507769
7631109.722847569727961.606067732234257.8396274072
7731400.963796759627723.889354365335078.0382391539
7831692.204745949527534.059278646835850.3502132522
7931983.445695139427376.715847406236590.1755428727
8032274.686644329327242.82180546237306.5514831967
8132565.927593519227126.560521825238005.2946652133
8232857.168542709127023.941317966738690.3957674516
8333148.40949189926932.094690133439364.7242936647
8433439.65044108926848.881705073940030.419177104
8533730.891390278926772.661937328640689.1208432291

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 30527.2409491899 & 28751.3947155536 & 32303.0871828262 \tabularnewline
75 & 30818.4818983798 & 28277.6093459827 & 33359.3544507769 \tabularnewline
76 & 31109.7228475697 & 27961.6060677322 & 34257.8396274072 \tabularnewline
77 & 31400.9637967596 & 27723.8893543653 & 35078.0382391539 \tabularnewline
78 & 31692.2047459495 & 27534.0592786468 & 35850.3502132522 \tabularnewline
79 & 31983.4456951394 & 27376.7158474062 & 36590.1755428727 \tabularnewline
80 & 32274.6866443293 & 27242.821805462 & 37306.5514831967 \tabularnewline
81 & 32565.9275935192 & 27126.5605218252 & 38005.2946652133 \tabularnewline
82 & 32857.1685427091 & 27023.9413179667 & 38690.3957674516 \tabularnewline
83 & 33148.409491899 & 26932.0946901334 & 39364.7242936647 \tabularnewline
84 & 33439.650441089 & 26848.8817050739 & 40030.419177104 \tabularnewline
85 & 33730.8913902789 & 26772.6619373286 & 40689.1208432291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117414&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]74[/C][C]30527.2409491899[/C][C]28751.3947155536[/C][C]32303.0871828262[/C][/ROW]
[ROW][C]75[/C][C]30818.4818983798[/C][C]28277.6093459827[/C][C]33359.3544507769[/C][/ROW]
[ROW][C]76[/C][C]31109.7228475697[/C][C]27961.6060677322[/C][C]34257.8396274072[/C][/ROW]
[ROW][C]77[/C][C]31400.9637967596[/C][C]27723.8893543653[/C][C]35078.0382391539[/C][/ROW]
[ROW][C]78[/C][C]31692.2047459495[/C][C]27534.0592786468[/C][C]35850.3502132522[/C][/ROW]
[ROW][C]79[/C][C]31983.4456951394[/C][C]27376.7158474062[/C][C]36590.1755428727[/C][/ROW]
[ROW][C]80[/C][C]32274.6866443293[/C][C]27242.821805462[/C][C]37306.5514831967[/C][/ROW]
[ROW][C]81[/C][C]32565.9275935192[/C][C]27126.5605218252[/C][C]38005.2946652133[/C][/ROW]
[ROW][C]82[/C][C]32857.1685427091[/C][C]27023.9413179667[/C][C]38690.3957674516[/C][/ROW]
[ROW][C]83[/C][C]33148.409491899[/C][C]26932.0946901334[/C][C]39364.7242936647[/C][/ROW]
[ROW][C]84[/C][C]33439.650441089[/C][C]26848.8817050739[/C][C]40030.419177104[/C][/ROW]
[ROW][C]85[/C][C]33730.8913902789[/C][C]26772.6619373286[/C][C]40689.1208432291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117414&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117414&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
7430527.240949189928751.394715553632303.0871828262
7530818.481898379828277.609345982733359.3544507769
7631109.722847569727961.606067732234257.8396274072
7731400.963796759627723.889354365335078.0382391539
7831692.204745949527534.059278646835850.3502132522
7931983.445695139427376.715847406236590.1755428727
8032274.686644329327242.82180546237306.5514831967
8132565.927593519227126.560521825238005.2946652133
8232857.168542709127023.941317966738690.3957674516
8333148.40949189926932.094690133439364.7242936647
8433439.65044108926848.881705073940030.419177104
8533730.891390278926772.661937328640689.1208432291



Parameters (Session):
par1 = 200 ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')