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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 25 Nov 2014 17:44:26 +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/Nov/25/t1416937515psjaa1wvu33ipc9.htm/, Retrieved Thu, 23 May 2024 09:13:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=258802, Retrieved Thu, 23 May 2024 09:13:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Notched Boxplots] [Boxplot levendgeb...] [2014-10-05 11:36:47] [8ce78276f6c66aaddbb0f99a7ed09e17]
- RMPD    [Exponential Smoothing] [Exponential smoot...] [2014-11-25 17:44:26] [8bdab0fd537d5455eaa21dec7dfb1324] [Current]
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Dataseries X:
15071
14236
14771
14804
15597
15418
16903
16350
16393
15685
14556
14850
15391
13704
15409
15098
15254
15522
16669
16238
16246
15424
14952
15008
14929
13905
14994
14753
15031
15386
16160
16116
16219
16064
15436
15404
15112
14119
14775
14289
15121
15371
15782
16104
15674
15105
14223
14385
14558
13804
14672
14244
15089
14580
15218
15696
15129
15110
14204
13655
14534
12746
14074
13699
14184
14110
15820
15362
14993
14437
13694
13688




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258802&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258802&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258802&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.358694899866019
beta0.000922395392208858
gamma0.570991114069437

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.358694899866019 \tabularnewline
beta & 0.000922395392208858 \tabularnewline
gamma & 0.570991114069437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258802&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]0.358694899866019[/C][/ROW]
[ROW][C]beta[/C][C]0.000922395392208858[/C][/ROW]
[ROW][C]gamma[/C][C]0.570991114069437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258802&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258802&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
alpha0.358694899866019
beta0.000922395392208858
gamma0.570991114069437







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131539115364.764155982926.2358440170847
141370413699.81097646814.18902353190242
151540915415.3261008611-6.32610086112072
161509815117.2757440519-19.2757440518562
171525415258.9490387308-4.94903873078692
181552215500.301278775321.6987212247095
191666916890.8024469489-221.80244694887
201623816265.2209360905-27.2209360905435
211624616292.1758145066-46.1758145066124
221542415526.8997303788-102.899730378815
231495214361.1180216744590.881978325564
241500814875.3044385078132.695561492161
251492915477.2509898267-548.250989826653
261390513598.0839699914306.916030008564
271499415418.3602153549-424.360215354884
281475314965.5078603435-212.507860343461
291503115042.9385945929-11.9385945928716
301538615291.361936010794.6380639893396
311616016618.7054233525-458.705423352516
321611615979.1658929628136.834107037237
331621916057.845976366161.154023634024
341606415346.055894569717.944105431048
351543614728.9158978842707.084102115847
361540415117.2039569923286.796043007713
371511215525.3268859811-413.326885981111
381411914007.9957360323111.004263967701
391477515490.4508698047-715.450869804712
401428915010.8952836634-721.895283663443
411512114979.0206778244141.979322175635
421537115321.695679578549.304320421521
431578216430.1560358101-648.156035810054
441610415940.6741317026163.325868297394
451567416037.7091142023-363.70911420232
461510515341.3117518282-236.311751828229
471422314377.3659403341-154.36594033415
481438514301.927972676683.0720273234147
491455814379.7106458461178.289354153918
501380413265.889473805538.110526195009
511467214598.356742850773.643257149286
521424414399.1886979424-155.188697942425
531508914886.8128515019202.187148498075
541458015217.059141115-637.059141115007
551521815823.6123757379-605.612375737879
561569615646.236435868549.7635641315246
571512915509.2079338775-380.207933877506
581511014853.1975228071256.802477192876
591420414095.9539883418108.04601165818
601365514201.4914308962-546.4914308962
611453414088.0159023132445.984097686751
621274613201.7595457703-455.759545770339
631407414007.108394350766.8916056492963
641369913721.1788627672-22.178862767214
651418414386.8745571813-202.874557181349
661411014263.87634034-153.87634034001
671582015054.7836673126765.216332687392
681536215609.079511742-247.079511741962
691499315208.0072204379-215.00722043785
701443714844.4473453293-407.447345329278
711369413794.1831645045-100.183164504468
721368813584.9967142394103.0032857606

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15391 & 15364.7641559829 & 26.2358440170847 \tabularnewline
14 & 13704 & 13699.8109764681 & 4.18902353190242 \tabularnewline
15 & 15409 & 15415.3261008611 & -6.32610086112072 \tabularnewline
16 & 15098 & 15117.2757440519 & -19.2757440518562 \tabularnewline
17 & 15254 & 15258.9490387308 & -4.94903873078692 \tabularnewline
18 & 15522 & 15500.3012787753 & 21.6987212247095 \tabularnewline
19 & 16669 & 16890.8024469489 & -221.80244694887 \tabularnewline
20 & 16238 & 16265.2209360905 & -27.2209360905435 \tabularnewline
21 & 16246 & 16292.1758145066 & -46.1758145066124 \tabularnewline
22 & 15424 & 15526.8997303788 & -102.899730378815 \tabularnewline
23 & 14952 & 14361.1180216744 & 590.881978325564 \tabularnewline
24 & 15008 & 14875.3044385078 & 132.695561492161 \tabularnewline
25 & 14929 & 15477.2509898267 & -548.250989826653 \tabularnewline
26 & 13905 & 13598.0839699914 & 306.916030008564 \tabularnewline
27 & 14994 & 15418.3602153549 & -424.360215354884 \tabularnewline
28 & 14753 & 14965.5078603435 & -212.507860343461 \tabularnewline
29 & 15031 & 15042.9385945929 & -11.9385945928716 \tabularnewline
30 & 15386 & 15291.3619360107 & 94.6380639893396 \tabularnewline
31 & 16160 & 16618.7054233525 & -458.705423352516 \tabularnewline
32 & 16116 & 15979.1658929628 & 136.834107037237 \tabularnewline
33 & 16219 & 16057.845976366 & 161.154023634024 \tabularnewline
34 & 16064 & 15346.055894569 & 717.944105431048 \tabularnewline
35 & 15436 & 14728.9158978842 & 707.084102115847 \tabularnewline
36 & 15404 & 15117.2039569923 & 286.796043007713 \tabularnewline
37 & 15112 & 15525.3268859811 & -413.326885981111 \tabularnewline
38 & 14119 & 14007.9957360323 & 111.004263967701 \tabularnewline
39 & 14775 & 15490.4508698047 & -715.450869804712 \tabularnewline
40 & 14289 & 15010.8952836634 & -721.895283663443 \tabularnewline
41 & 15121 & 14979.0206778244 & 141.979322175635 \tabularnewline
42 & 15371 & 15321.6956795785 & 49.304320421521 \tabularnewline
43 & 15782 & 16430.1560358101 & -648.156035810054 \tabularnewline
44 & 16104 & 15940.6741317026 & 163.325868297394 \tabularnewline
45 & 15674 & 16037.7091142023 & -363.70911420232 \tabularnewline
46 & 15105 & 15341.3117518282 & -236.311751828229 \tabularnewline
47 & 14223 & 14377.3659403341 & -154.36594033415 \tabularnewline
48 & 14385 & 14301.9279726766 & 83.0720273234147 \tabularnewline
49 & 14558 & 14379.7106458461 & 178.289354153918 \tabularnewline
50 & 13804 & 13265.889473805 & 538.110526195009 \tabularnewline
51 & 14672 & 14598.3567428507 & 73.643257149286 \tabularnewline
52 & 14244 & 14399.1886979424 & -155.188697942425 \tabularnewline
53 & 15089 & 14886.8128515019 & 202.187148498075 \tabularnewline
54 & 14580 & 15217.059141115 & -637.059141115007 \tabularnewline
55 & 15218 & 15823.6123757379 & -605.612375737879 \tabularnewline
56 & 15696 & 15646.2364358685 & 49.7635641315246 \tabularnewline
57 & 15129 & 15509.2079338775 & -380.207933877506 \tabularnewline
58 & 15110 & 14853.1975228071 & 256.802477192876 \tabularnewline
59 & 14204 & 14095.9539883418 & 108.04601165818 \tabularnewline
60 & 13655 & 14201.4914308962 & -546.4914308962 \tabularnewline
61 & 14534 & 14088.0159023132 & 445.984097686751 \tabularnewline
62 & 12746 & 13201.7595457703 & -455.759545770339 \tabularnewline
63 & 14074 & 14007.1083943507 & 66.8916056492963 \tabularnewline
64 & 13699 & 13721.1788627672 & -22.178862767214 \tabularnewline
65 & 14184 & 14386.8745571813 & -202.874557181349 \tabularnewline
66 & 14110 & 14263.87634034 & -153.87634034001 \tabularnewline
67 & 15820 & 15054.7836673126 & 765.216332687392 \tabularnewline
68 & 15362 & 15609.079511742 & -247.079511741962 \tabularnewline
69 & 14993 & 15208.0072204379 & -215.00722043785 \tabularnewline
70 & 14437 & 14844.4473453293 & -407.447345329278 \tabularnewline
71 & 13694 & 13794.1831645045 & -100.183164504468 \tabularnewline
72 & 13688 & 13584.9967142394 & 103.0032857606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258802&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]15391[/C][C]15364.7641559829[/C][C]26.2358440170847[/C][/ROW]
[ROW][C]14[/C][C]13704[/C][C]13699.8109764681[/C][C]4.18902353190242[/C][/ROW]
[ROW][C]15[/C][C]15409[/C][C]15415.3261008611[/C][C]-6.32610086112072[/C][/ROW]
[ROW][C]16[/C][C]15098[/C][C]15117.2757440519[/C][C]-19.2757440518562[/C][/ROW]
[ROW][C]17[/C][C]15254[/C][C]15258.9490387308[/C][C]-4.94903873078692[/C][/ROW]
[ROW][C]18[/C][C]15522[/C][C]15500.3012787753[/C][C]21.6987212247095[/C][/ROW]
[ROW][C]19[/C][C]16669[/C][C]16890.8024469489[/C][C]-221.80244694887[/C][/ROW]
[ROW][C]20[/C][C]16238[/C][C]16265.2209360905[/C][C]-27.2209360905435[/C][/ROW]
[ROW][C]21[/C][C]16246[/C][C]16292.1758145066[/C][C]-46.1758145066124[/C][/ROW]
[ROW][C]22[/C][C]15424[/C][C]15526.8997303788[/C][C]-102.899730378815[/C][/ROW]
[ROW][C]23[/C][C]14952[/C][C]14361.1180216744[/C][C]590.881978325564[/C][/ROW]
[ROW][C]24[/C][C]15008[/C][C]14875.3044385078[/C][C]132.695561492161[/C][/ROW]
[ROW][C]25[/C][C]14929[/C][C]15477.2509898267[/C][C]-548.250989826653[/C][/ROW]
[ROW][C]26[/C][C]13905[/C][C]13598.0839699914[/C][C]306.916030008564[/C][/ROW]
[ROW][C]27[/C][C]14994[/C][C]15418.3602153549[/C][C]-424.360215354884[/C][/ROW]
[ROW][C]28[/C][C]14753[/C][C]14965.5078603435[/C][C]-212.507860343461[/C][/ROW]
[ROW][C]29[/C][C]15031[/C][C]15042.9385945929[/C][C]-11.9385945928716[/C][/ROW]
[ROW][C]30[/C][C]15386[/C][C]15291.3619360107[/C][C]94.6380639893396[/C][/ROW]
[ROW][C]31[/C][C]16160[/C][C]16618.7054233525[/C][C]-458.705423352516[/C][/ROW]
[ROW][C]32[/C][C]16116[/C][C]15979.1658929628[/C][C]136.834107037237[/C][/ROW]
[ROW][C]33[/C][C]16219[/C][C]16057.845976366[/C][C]161.154023634024[/C][/ROW]
[ROW][C]34[/C][C]16064[/C][C]15346.055894569[/C][C]717.944105431048[/C][/ROW]
[ROW][C]35[/C][C]15436[/C][C]14728.9158978842[/C][C]707.084102115847[/C][/ROW]
[ROW][C]36[/C][C]15404[/C][C]15117.2039569923[/C][C]286.796043007713[/C][/ROW]
[ROW][C]37[/C][C]15112[/C][C]15525.3268859811[/C][C]-413.326885981111[/C][/ROW]
[ROW][C]38[/C][C]14119[/C][C]14007.9957360323[/C][C]111.004263967701[/C][/ROW]
[ROW][C]39[/C][C]14775[/C][C]15490.4508698047[/C][C]-715.450869804712[/C][/ROW]
[ROW][C]40[/C][C]14289[/C][C]15010.8952836634[/C][C]-721.895283663443[/C][/ROW]
[ROW][C]41[/C][C]15121[/C][C]14979.0206778244[/C][C]141.979322175635[/C][/ROW]
[ROW][C]42[/C][C]15371[/C][C]15321.6956795785[/C][C]49.304320421521[/C][/ROW]
[ROW][C]43[/C][C]15782[/C][C]16430.1560358101[/C][C]-648.156035810054[/C][/ROW]
[ROW][C]44[/C][C]16104[/C][C]15940.6741317026[/C][C]163.325868297394[/C][/ROW]
[ROW][C]45[/C][C]15674[/C][C]16037.7091142023[/C][C]-363.70911420232[/C][/ROW]
[ROW][C]46[/C][C]15105[/C][C]15341.3117518282[/C][C]-236.311751828229[/C][/ROW]
[ROW][C]47[/C][C]14223[/C][C]14377.3659403341[/C][C]-154.36594033415[/C][/ROW]
[ROW][C]48[/C][C]14385[/C][C]14301.9279726766[/C][C]83.0720273234147[/C][/ROW]
[ROW][C]49[/C][C]14558[/C][C]14379.7106458461[/C][C]178.289354153918[/C][/ROW]
[ROW][C]50[/C][C]13804[/C][C]13265.889473805[/C][C]538.110526195009[/C][/ROW]
[ROW][C]51[/C][C]14672[/C][C]14598.3567428507[/C][C]73.643257149286[/C][/ROW]
[ROW][C]52[/C][C]14244[/C][C]14399.1886979424[/C][C]-155.188697942425[/C][/ROW]
[ROW][C]53[/C][C]15089[/C][C]14886.8128515019[/C][C]202.187148498075[/C][/ROW]
[ROW][C]54[/C][C]14580[/C][C]15217.059141115[/C][C]-637.059141115007[/C][/ROW]
[ROW][C]55[/C][C]15218[/C][C]15823.6123757379[/C][C]-605.612375737879[/C][/ROW]
[ROW][C]56[/C][C]15696[/C][C]15646.2364358685[/C][C]49.7635641315246[/C][/ROW]
[ROW][C]57[/C][C]15129[/C][C]15509.2079338775[/C][C]-380.207933877506[/C][/ROW]
[ROW][C]58[/C][C]15110[/C][C]14853.1975228071[/C][C]256.802477192876[/C][/ROW]
[ROW][C]59[/C][C]14204[/C][C]14095.9539883418[/C][C]108.04601165818[/C][/ROW]
[ROW][C]60[/C][C]13655[/C][C]14201.4914308962[/C][C]-546.4914308962[/C][/ROW]
[ROW][C]61[/C][C]14534[/C][C]14088.0159023132[/C][C]445.984097686751[/C][/ROW]
[ROW][C]62[/C][C]12746[/C][C]13201.7595457703[/C][C]-455.759545770339[/C][/ROW]
[ROW][C]63[/C][C]14074[/C][C]14007.1083943507[/C][C]66.8916056492963[/C][/ROW]
[ROW][C]64[/C][C]13699[/C][C]13721.1788627672[/C][C]-22.178862767214[/C][/ROW]
[ROW][C]65[/C][C]14184[/C][C]14386.8745571813[/C][C]-202.874557181349[/C][/ROW]
[ROW][C]66[/C][C]14110[/C][C]14263.87634034[/C][C]-153.87634034001[/C][/ROW]
[ROW][C]67[/C][C]15820[/C][C]15054.7836673126[/C][C]765.216332687392[/C][/ROW]
[ROW][C]68[/C][C]15362[/C][C]15609.079511742[/C][C]-247.079511741962[/C][/ROW]
[ROW][C]69[/C][C]14993[/C][C]15208.0072204379[/C][C]-215.00722043785[/C][/ROW]
[ROW][C]70[/C][C]14437[/C][C]14844.4473453293[/C][C]-407.447345329278[/C][/ROW]
[ROW][C]71[/C][C]13694[/C][C]13794.1831645045[/C][C]-100.183164504468[/C][/ROW]
[ROW][C]72[/C][C]13688[/C][C]13584.9967142394[/C][C]103.0032857606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258802&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258802&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
131539115364.764155982926.2358440170847
141370413699.81097646814.18902353190242
151540915415.3261008611-6.32610086112072
161509815117.2757440519-19.2757440518562
171525415258.9490387308-4.94903873078692
181552215500.301278775321.6987212247095
191666916890.8024469489-221.80244694887
201623816265.2209360905-27.2209360905435
211624616292.1758145066-46.1758145066124
221542415526.8997303788-102.899730378815
231495214361.1180216744590.881978325564
241500814875.3044385078132.695561492161
251492915477.2509898267-548.250989826653
261390513598.0839699914306.916030008564
271499415418.3602153549-424.360215354884
281475314965.5078603435-212.507860343461
291503115042.9385945929-11.9385945928716
301538615291.361936010794.6380639893396
311616016618.7054233525-458.705423352516
321611615979.1658929628136.834107037237
331621916057.845976366161.154023634024
341606415346.055894569717.944105431048
351543614728.9158978842707.084102115847
361540415117.2039569923286.796043007713
371511215525.3268859811-413.326885981111
381411914007.9957360323111.004263967701
391477515490.4508698047-715.450869804712
401428915010.8952836634-721.895283663443
411512114979.0206778244141.979322175635
421537115321.695679578549.304320421521
431578216430.1560358101-648.156035810054
441610415940.6741317026163.325868297394
451567416037.7091142023-363.70911420232
461510515341.3117518282-236.311751828229
471422314377.3659403341-154.36594033415
481438514301.927972676683.0720273234147
491455814379.7106458461178.289354153918
501380413265.889473805538.110526195009
511467214598.356742850773.643257149286
521424414399.1886979424-155.188697942425
531508914886.8128515019202.187148498075
541458015217.059141115-637.059141115007
551521815823.6123757379-605.612375737879
561569615646.236435868549.7635641315246
571512915509.2079338775-380.207933877506
581511014853.1975228071256.802477192876
591420414095.9539883418108.04601165818
601365514201.4914308962-546.4914308962
611453414088.0159023132445.984097686751
621274613201.7595457703-455.759545770339
631407414007.108394350766.8916056492963
641369913721.1788627672-22.178862767214
651418414386.8745571813-202.874557181349
661411014263.87634034-153.87634034001
671582015054.7836673126765.216332687392
681536215609.079511742-247.079511741962
691499315208.0072204379-215.00722043785
701443714844.4473453293-407.447345329278
711369413794.1831645045-100.183164504468
721368813584.9967142394103.0032857606







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7314067.775778184613382.30957774214753.2419786272
7412691.059537874811962.753878823613419.3651969259
7513851.134333652413082.300130007314619.9685372976
7613508.436389984712701.036418542414315.8363614269
7714115.768852442213271.496811304814960.0408935795
7814083.398355131313203.734878426614963.061831836
7915266.019667187814352.273271758516179.7660626172
8015174.867556172614228.205361378816121.5297509664
8114873.96063028413895.431916963415852.4893436045
8214516.921242888413507.475863854815526.3666219219
8313725.321128134512685.824131842514764.8181244264
8413626.506663069512557.750076280214695.2632498588

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 14067.7757781846 & 13382.309577742 & 14753.2419786272 \tabularnewline
74 & 12691.0595378748 & 11962.7538788236 & 13419.3651969259 \tabularnewline
75 & 13851.1343336524 & 13082.3001300073 & 14619.9685372976 \tabularnewline
76 & 13508.4363899847 & 12701.0364185424 & 14315.8363614269 \tabularnewline
77 & 14115.7688524422 & 13271.4968113048 & 14960.0408935795 \tabularnewline
78 & 14083.3983551313 & 13203.7348784266 & 14963.061831836 \tabularnewline
79 & 15266.0196671878 & 14352.2732717585 & 16179.7660626172 \tabularnewline
80 & 15174.8675561726 & 14228.2053613788 & 16121.5297509664 \tabularnewline
81 & 14873.960630284 & 13895.4319169634 & 15852.4893436045 \tabularnewline
82 & 14516.9212428884 & 13507.4758638548 & 15526.3666219219 \tabularnewline
83 & 13725.3211281345 & 12685.8241318425 & 14764.8181244264 \tabularnewline
84 & 13626.5066630695 & 12557.7500762802 & 14695.2632498588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258802&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]73[/C][C]14067.7757781846[/C][C]13382.309577742[/C][C]14753.2419786272[/C][/ROW]
[ROW][C]74[/C][C]12691.0595378748[/C][C]11962.7538788236[/C][C]13419.3651969259[/C][/ROW]
[ROW][C]75[/C][C]13851.1343336524[/C][C]13082.3001300073[/C][C]14619.9685372976[/C][/ROW]
[ROW][C]76[/C][C]13508.4363899847[/C][C]12701.0364185424[/C][C]14315.8363614269[/C][/ROW]
[ROW][C]77[/C][C]14115.7688524422[/C][C]13271.4968113048[/C][C]14960.0408935795[/C][/ROW]
[ROW][C]78[/C][C]14083.3983551313[/C][C]13203.7348784266[/C][C]14963.061831836[/C][/ROW]
[ROW][C]79[/C][C]15266.0196671878[/C][C]14352.2732717585[/C][C]16179.7660626172[/C][/ROW]
[ROW][C]80[/C][C]15174.8675561726[/C][C]14228.2053613788[/C][C]16121.5297509664[/C][/ROW]
[ROW][C]81[/C][C]14873.960630284[/C][C]13895.4319169634[/C][C]15852.4893436045[/C][/ROW]
[ROW][C]82[/C][C]14516.9212428884[/C][C]13507.4758638548[/C][C]15526.3666219219[/C][/ROW]
[ROW][C]83[/C][C]13725.3211281345[/C][C]12685.8241318425[/C][C]14764.8181244264[/C][/ROW]
[ROW][C]84[/C][C]13626.5066630695[/C][C]12557.7500762802[/C][C]14695.2632498588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258802&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258802&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
7314067.775778184613382.30957774214753.2419786272
7412691.059537874811962.753878823613419.3651969259
7513851.134333652413082.300130007314619.9685372976
7613508.436389984712701.036418542414315.8363614269
7714115.768852442213271.496811304814960.0408935795
7814083.398355131313203.734878426614963.061831836
7915266.019667187814352.273271758516179.7660626172
8015174.867556172614228.205361378816121.5297509664
8114873.96063028413895.431916963415852.4893436045
8214516.921242888413507.475863854815526.3666219219
8313725.321128134512685.824131842514764.8181244264
8413626.506663069512557.750076280214695.2632498588



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')