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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 13 Jan 2013 14:57:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/13/t1358107065ig4tst5w4x115jf.htm/, Retrieved Sat, 04 May 2024 07:47:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205296, Retrieved Sat, 04 May 2024 07:47:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [triple model siga...] [2013-01-13 19:57:12] [4f05f4cbed182ac02528036e9f4f762f] [Current]
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Dataseries X:
4.69
4.69
4.69
4.69
4.69
4.69
4.69
4.73
4.78
4.79
4.79
4.8
4.8
4.81
5.16
5.26
5.29
5.29
5.29
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.35
5.44
5.47
5.47
5.48
5.48
5.48
5.48
5.48
5.48
5.48
5.5
5.55
5.55
5.57
5.58
5.58
5.58
5.59
5.59
5.59
5.61
5.61
5.61
5.63
5.69
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.71
5.74
5.77
5.79
5.79
5.8
5.8
5.8
5.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205296&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]2 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=205296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205296&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.613228226825395
beta0.0634702581194647
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.613228226825395 \tabularnewline
beta & 0.0634702581194647 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205296&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]0.613228226825395[/C][/ROW]
[ROW][C]beta[/C][C]0.0634702581194647[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205296&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
alpha0.613228226825395
beta0.0634702581194647
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134.84.542371794871790.257628205128206
144.814.715369455101150.0946305448988474
155.165.135428869279270.0245711307207346
165.265.26598222463006-0.00598222463005982
175.295.3079832280477-0.0179832280477044
185.295.31234160531072-0.0223416053107162
195.295.203157728150540.0868422718494593
205.35.34680853990729-0.0468085399072908
215.35.40167903088866-0.101679030888662
225.35.36019386176927-0.0601938617692719
235.35.32638905201122-0.0263890520112229
245.35.32103719761275-0.0210371976127464
255.35.40779176448748-0.107791764487478
265.35.285714325837510.014285674162493
275.35.61833346547379-0.318333465473786
285.355.50237089154342-0.152370891543423
295.445.419842902930710.020157097069287
305.475.417271115159250.0527288848407528
315.475.370640506797080.0993594932029165
325.485.445050746232320.0349492537676799
335.485.50679309935898-0.0267930993589767
345.485.50814811385239-0.0281481138523931
355.485.48918940837672-0.00918940837671833
365.485.479244248355520.000755751644483382
375.485.52944631019971-0.0494463101997056
385.485.476272626847130.00372737315287175
395.55.65926704466508-0.159267044665078
405.555.69672689380676-0.146726893806756
415.555.67629735917928-0.126297359179278
425.575.58272158789137-0.0127215878913667
435.585.497651032970380.0823489670296222
445.585.519716523272710.0602834767272897
455.585.557099038200630.0229009617993725
465.595.5743226529360.0156773470640017
475.595.577196293676010.012803706323993
485.595.573065094551810.0169349054481929
495.615.602882305750630.00711769424937447
505.615.596273292635070.0137267073649268
515.615.71405908235917-0.104059082359168
525.635.78407411734959-0.154074117349587
535.695.76060458699758-0.0706045869975815
545.75.74084072026975-0.0408407202697507
555.75.669934502992690.030065497007314
565.75.644006196749210.0559938032507876
575.75.656734911496410.0432650885035892
585.75.676880351051660.0231196489483363
595.75.676723903487330.0232760965126744
605.75.674537629864930.0254623701350676
615.75.70004413583662-4.41358366209954e-05
625.75.685577747997190.0144222520028077
635.75.75223920031602-0.0522392003160235
645.715.8307095203466-0.120709520346599
655.745.85730464397456-0.117304643974563
665.775.81591804256363-0.0459180425636347
675.795.764628407974810.0253715920251931
685.795.740972925319370.0490270746806294
695.85.739358102227120.0606418977728804
705.85.757895904574660.0421040954253415
715.85.765708773149520.0342912268504749
725.85.767818613676540.0321813863234555

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4.8 & 4.54237179487179 & 0.257628205128206 \tabularnewline
14 & 4.81 & 4.71536945510115 & 0.0946305448988474 \tabularnewline
15 & 5.16 & 5.13542886927927 & 0.0245711307207346 \tabularnewline
16 & 5.26 & 5.26598222463006 & -0.00598222463005982 \tabularnewline
17 & 5.29 & 5.3079832280477 & -0.0179832280477044 \tabularnewline
18 & 5.29 & 5.31234160531072 & -0.0223416053107162 \tabularnewline
19 & 5.29 & 5.20315772815054 & 0.0868422718494593 \tabularnewline
20 & 5.3 & 5.34680853990729 & -0.0468085399072908 \tabularnewline
21 & 5.3 & 5.40167903088866 & -0.101679030888662 \tabularnewline
22 & 5.3 & 5.36019386176927 & -0.0601938617692719 \tabularnewline
23 & 5.3 & 5.32638905201122 & -0.0263890520112229 \tabularnewline
24 & 5.3 & 5.32103719761275 & -0.0210371976127464 \tabularnewline
25 & 5.3 & 5.40779176448748 & -0.107791764487478 \tabularnewline
26 & 5.3 & 5.28571432583751 & 0.014285674162493 \tabularnewline
27 & 5.3 & 5.61833346547379 & -0.318333465473786 \tabularnewline
28 & 5.35 & 5.50237089154342 & -0.152370891543423 \tabularnewline
29 & 5.44 & 5.41984290293071 & 0.020157097069287 \tabularnewline
30 & 5.47 & 5.41727111515925 & 0.0527288848407528 \tabularnewline
31 & 5.47 & 5.37064050679708 & 0.0993594932029165 \tabularnewline
32 & 5.48 & 5.44505074623232 & 0.0349492537676799 \tabularnewline
33 & 5.48 & 5.50679309935898 & -0.0267930993589767 \tabularnewline
34 & 5.48 & 5.50814811385239 & -0.0281481138523931 \tabularnewline
35 & 5.48 & 5.48918940837672 & -0.00918940837671833 \tabularnewline
36 & 5.48 & 5.47924424835552 & 0.000755751644483382 \tabularnewline
37 & 5.48 & 5.52944631019971 & -0.0494463101997056 \tabularnewline
38 & 5.48 & 5.47627262684713 & 0.00372737315287175 \tabularnewline
39 & 5.5 & 5.65926704466508 & -0.159267044665078 \tabularnewline
40 & 5.55 & 5.69672689380676 & -0.146726893806756 \tabularnewline
41 & 5.55 & 5.67629735917928 & -0.126297359179278 \tabularnewline
42 & 5.57 & 5.58272158789137 & -0.0127215878913667 \tabularnewline
43 & 5.58 & 5.49765103297038 & 0.0823489670296222 \tabularnewline
44 & 5.58 & 5.51971652327271 & 0.0602834767272897 \tabularnewline
45 & 5.58 & 5.55709903820063 & 0.0229009617993725 \tabularnewline
46 & 5.59 & 5.574322652936 & 0.0156773470640017 \tabularnewline
47 & 5.59 & 5.57719629367601 & 0.012803706323993 \tabularnewline
48 & 5.59 & 5.57306509455181 & 0.0169349054481929 \tabularnewline
49 & 5.61 & 5.60288230575063 & 0.00711769424937447 \tabularnewline
50 & 5.61 & 5.59627329263507 & 0.0137267073649268 \tabularnewline
51 & 5.61 & 5.71405908235917 & -0.104059082359168 \tabularnewline
52 & 5.63 & 5.78407411734959 & -0.154074117349587 \tabularnewline
53 & 5.69 & 5.76060458699758 & -0.0706045869975815 \tabularnewline
54 & 5.7 & 5.74084072026975 & -0.0408407202697507 \tabularnewline
55 & 5.7 & 5.66993450299269 & 0.030065497007314 \tabularnewline
56 & 5.7 & 5.64400619674921 & 0.0559938032507876 \tabularnewline
57 & 5.7 & 5.65673491149641 & 0.0432650885035892 \tabularnewline
58 & 5.7 & 5.67688035105166 & 0.0231196489483363 \tabularnewline
59 & 5.7 & 5.67672390348733 & 0.0232760965126744 \tabularnewline
60 & 5.7 & 5.67453762986493 & 0.0254623701350676 \tabularnewline
61 & 5.7 & 5.70004413583662 & -4.41358366209954e-05 \tabularnewline
62 & 5.7 & 5.68557774799719 & 0.0144222520028077 \tabularnewline
63 & 5.7 & 5.75223920031602 & -0.0522392003160235 \tabularnewline
64 & 5.71 & 5.8307095203466 & -0.120709520346599 \tabularnewline
65 & 5.74 & 5.85730464397456 & -0.117304643974563 \tabularnewline
66 & 5.77 & 5.81591804256363 & -0.0459180425636347 \tabularnewline
67 & 5.79 & 5.76462840797481 & 0.0253715920251931 \tabularnewline
68 & 5.79 & 5.74097292531937 & 0.0490270746806294 \tabularnewline
69 & 5.8 & 5.73935810222712 & 0.0606418977728804 \tabularnewline
70 & 5.8 & 5.75789590457466 & 0.0421040954253415 \tabularnewline
71 & 5.8 & 5.76570877314952 & 0.0342912268504749 \tabularnewline
72 & 5.8 & 5.76781861367654 & 0.0321813863234555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205296&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]4.8[/C][C]4.54237179487179[/C][C]0.257628205128206[/C][/ROW]
[ROW][C]14[/C][C]4.81[/C][C]4.71536945510115[/C][C]0.0946305448988474[/C][/ROW]
[ROW][C]15[/C][C]5.16[/C][C]5.13542886927927[/C][C]0.0245711307207346[/C][/ROW]
[ROW][C]16[/C][C]5.26[/C][C]5.26598222463006[/C][C]-0.00598222463005982[/C][/ROW]
[ROW][C]17[/C][C]5.29[/C][C]5.3079832280477[/C][C]-0.0179832280477044[/C][/ROW]
[ROW][C]18[/C][C]5.29[/C][C]5.31234160531072[/C][C]-0.0223416053107162[/C][/ROW]
[ROW][C]19[/C][C]5.29[/C][C]5.20315772815054[/C][C]0.0868422718494593[/C][/ROW]
[ROW][C]20[/C][C]5.3[/C][C]5.34680853990729[/C][C]-0.0468085399072908[/C][/ROW]
[ROW][C]21[/C][C]5.3[/C][C]5.40167903088866[/C][C]-0.101679030888662[/C][/ROW]
[ROW][C]22[/C][C]5.3[/C][C]5.36019386176927[/C][C]-0.0601938617692719[/C][/ROW]
[ROW][C]23[/C][C]5.3[/C][C]5.32638905201122[/C][C]-0.0263890520112229[/C][/ROW]
[ROW][C]24[/C][C]5.3[/C][C]5.32103719761275[/C][C]-0.0210371976127464[/C][/ROW]
[ROW][C]25[/C][C]5.3[/C][C]5.40779176448748[/C][C]-0.107791764487478[/C][/ROW]
[ROW][C]26[/C][C]5.3[/C][C]5.28571432583751[/C][C]0.014285674162493[/C][/ROW]
[ROW][C]27[/C][C]5.3[/C][C]5.61833346547379[/C][C]-0.318333465473786[/C][/ROW]
[ROW][C]28[/C][C]5.35[/C][C]5.50237089154342[/C][C]-0.152370891543423[/C][/ROW]
[ROW][C]29[/C][C]5.44[/C][C]5.41984290293071[/C][C]0.020157097069287[/C][/ROW]
[ROW][C]30[/C][C]5.47[/C][C]5.41727111515925[/C][C]0.0527288848407528[/C][/ROW]
[ROW][C]31[/C][C]5.47[/C][C]5.37064050679708[/C][C]0.0993594932029165[/C][/ROW]
[ROW][C]32[/C][C]5.48[/C][C]5.44505074623232[/C][C]0.0349492537676799[/C][/ROW]
[ROW][C]33[/C][C]5.48[/C][C]5.50679309935898[/C][C]-0.0267930993589767[/C][/ROW]
[ROW][C]34[/C][C]5.48[/C][C]5.50814811385239[/C][C]-0.0281481138523931[/C][/ROW]
[ROW][C]35[/C][C]5.48[/C][C]5.48918940837672[/C][C]-0.00918940837671833[/C][/ROW]
[ROW][C]36[/C][C]5.48[/C][C]5.47924424835552[/C][C]0.000755751644483382[/C][/ROW]
[ROW][C]37[/C][C]5.48[/C][C]5.52944631019971[/C][C]-0.0494463101997056[/C][/ROW]
[ROW][C]38[/C][C]5.48[/C][C]5.47627262684713[/C][C]0.00372737315287175[/C][/ROW]
[ROW][C]39[/C][C]5.5[/C][C]5.65926704466508[/C][C]-0.159267044665078[/C][/ROW]
[ROW][C]40[/C][C]5.55[/C][C]5.69672689380676[/C][C]-0.146726893806756[/C][/ROW]
[ROW][C]41[/C][C]5.55[/C][C]5.67629735917928[/C][C]-0.126297359179278[/C][/ROW]
[ROW][C]42[/C][C]5.57[/C][C]5.58272158789137[/C][C]-0.0127215878913667[/C][/ROW]
[ROW][C]43[/C][C]5.58[/C][C]5.49765103297038[/C][C]0.0823489670296222[/C][/ROW]
[ROW][C]44[/C][C]5.58[/C][C]5.51971652327271[/C][C]0.0602834767272897[/C][/ROW]
[ROW][C]45[/C][C]5.58[/C][C]5.55709903820063[/C][C]0.0229009617993725[/C][/ROW]
[ROW][C]46[/C][C]5.59[/C][C]5.574322652936[/C][C]0.0156773470640017[/C][/ROW]
[ROW][C]47[/C][C]5.59[/C][C]5.57719629367601[/C][C]0.012803706323993[/C][/ROW]
[ROW][C]48[/C][C]5.59[/C][C]5.57306509455181[/C][C]0.0169349054481929[/C][/ROW]
[ROW][C]49[/C][C]5.61[/C][C]5.60288230575063[/C][C]0.00711769424937447[/C][/ROW]
[ROW][C]50[/C][C]5.61[/C][C]5.59627329263507[/C][C]0.0137267073649268[/C][/ROW]
[ROW][C]51[/C][C]5.61[/C][C]5.71405908235917[/C][C]-0.104059082359168[/C][/ROW]
[ROW][C]52[/C][C]5.63[/C][C]5.78407411734959[/C][C]-0.154074117349587[/C][/ROW]
[ROW][C]53[/C][C]5.69[/C][C]5.76060458699758[/C][C]-0.0706045869975815[/C][/ROW]
[ROW][C]54[/C][C]5.7[/C][C]5.74084072026975[/C][C]-0.0408407202697507[/C][/ROW]
[ROW][C]55[/C][C]5.7[/C][C]5.66993450299269[/C][C]0.030065497007314[/C][/ROW]
[ROW][C]56[/C][C]5.7[/C][C]5.64400619674921[/C][C]0.0559938032507876[/C][/ROW]
[ROW][C]57[/C][C]5.7[/C][C]5.65673491149641[/C][C]0.0432650885035892[/C][/ROW]
[ROW][C]58[/C][C]5.7[/C][C]5.67688035105166[/C][C]0.0231196489483363[/C][/ROW]
[ROW][C]59[/C][C]5.7[/C][C]5.67672390348733[/C][C]0.0232760965126744[/C][/ROW]
[ROW][C]60[/C][C]5.7[/C][C]5.67453762986493[/C][C]0.0254623701350676[/C][/ROW]
[ROW][C]61[/C][C]5.7[/C][C]5.70004413583662[/C][C]-4.41358366209954e-05[/C][/ROW]
[ROW][C]62[/C][C]5.7[/C][C]5.68557774799719[/C][C]0.0144222520028077[/C][/ROW]
[ROW][C]63[/C][C]5.7[/C][C]5.75223920031602[/C][C]-0.0522392003160235[/C][/ROW]
[ROW][C]64[/C][C]5.71[/C][C]5.8307095203466[/C][C]-0.120709520346599[/C][/ROW]
[ROW][C]65[/C][C]5.74[/C][C]5.85730464397456[/C][C]-0.117304643974563[/C][/ROW]
[ROW][C]66[/C][C]5.77[/C][C]5.81591804256363[/C][C]-0.0459180425636347[/C][/ROW]
[ROW][C]67[/C][C]5.79[/C][C]5.76462840797481[/C][C]0.0253715920251931[/C][/ROW]
[ROW][C]68[/C][C]5.79[/C][C]5.74097292531937[/C][C]0.0490270746806294[/C][/ROW]
[ROW][C]69[/C][C]5.8[/C][C]5.73935810222712[/C][C]0.0606418977728804[/C][/ROW]
[ROW][C]70[/C][C]5.8[/C][C]5.75789590457466[/C][C]0.0421040954253415[/C][/ROW]
[ROW][C]71[/C][C]5.8[/C][C]5.76570877314952[/C][C]0.0342912268504749[/C][/ROW]
[ROW][C]72[/C][C]5.8[/C][C]5.76781861367654[/C][C]0.0321813863234555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205296&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
134.84.542371794871790.257628205128206
144.814.715369455101150.0946305448988474
155.165.135428869279270.0245711307207346
165.265.26598222463006-0.00598222463005982
175.295.3079832280477-0.0179832280477044
185.295.31234160531072-0.0223416053107162
195.295.203157728150540.0868422718494593
205.35.34680853990729-0.0468085399072908
215.35.40167903088866-0.101679030888662
225.35.36019386176927-0.0601938617692719
235.35.32638905201122-0.0263890520112229
245.35.32103719761275-0.0210371976127464
255.35.40779176448748-0.107791764487478
265.35.285714325837510.014285674162493
275.35.61833346547379-0.318333465473786
285.355.50237089154342-0.152370891543423
295.445.419842902930710.020157097069287
305.475.417271115159250.0527288848407528
315.475.370640506797080.0993594932029165
325.485.445050746232320.0349492537676799
335.485.50679309935898-0.0267930993589767
345.485.50814811385239-0.0281481138523931
355.485.48918940837672-0.00918940837671833
365.485.479244248355520.000755751644483382
375.485.52944631019971-0.0494463101997056
385.485.476272626847130.00372737315287175
395.55.65926704466508-0.159267044665078
405.555.69672689380676-0.146726893806756
415.555.67629735917928-0.126297359179278
425.575.58272158789137-0.0127215878913667
435.585.497651032970380.0823489670296222
445.585.519716523272710.0602834767272897
455.585.557099038200630.0229009617993725
465.595.5743226529360.0156773470640017
475.595.577196293676010.012803706323993
485.595.573065094551810.0169349054481929
495.615.602882305750630.00711769424937447
505.615.596273292635070.0137267073649268
515.615.71405908235917-0.104059082359168
525.635.78407411734959-0.154074117349587
535.695.76060458699758-0.0706045869975815
545.75.74084072026975-0.0408407202697507
555.75.669934502992690.030065497007314
565.75.644006196749210.0559938032507876
575.75.656734911496410.0432650885035892
585.75.676880351051660.0231196489483363
595.75.676723903487330.0232760965126744
605.75.674537629864930.0254623701350676
615.75.70004413583662-4.41358366209954e-05
625.75.685577747997190.0144222520028077
635.75.75223920031602-0.0522392003160235
645.715.8307095203466-0.120709520346599
655.745.85730464397456-0.117304643974563
665.775.81591804256363-0.0459180425636347
675.795.764628407974810.0253715920251931
685.795.740972925319370.0490270746806294
695.85.739358102227120.0606418977728804
705.85.757895904574660.0421040954253415
715.85.765708773149520.0342912268504749
725.85.767818613676540.0321813863234555







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.784537465761985.620274750123515.94880018140044
745.772652303856325.576545762792545.9687588449201
755.801084486811435.574492436321486.02767653730139
765.88353784400475.627173774002036.13990191400738
775.98860146113525.702812616837596.27439030543281
786.054454501740775.739361039887286.36954796359426
796.068377936886015.72395063560236.41280523816972
806.046807655488355.672914832646116.42070047833059
816.026206616988595.622644141081116.42976909289607
826.004613193133985.571124549937666.43810183633029
835.986172075584035.522462263978286.44988188718978
845.967690097108925.473435527371786.46194466684605

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.78453746576198 & 5.62027475012351 & 5.94880018140044 \tabularnewline
74 & 5.77265230385632 & 5.57654576279254 & 5.9687588449201 \tabularnewline
75 & 5.80108448681143 & 5.57449243632148 & 6.02767653730139 \tabularnewline
76 & 5.8835378440047 & 5.62717377400203 & 6.13990191400738 \tabularnewline
77 & 5.9886014611352 & 5.70281261683759 & 6.27439030543281 \tabularnewline
78 & 6.05445450174077 & 5.73936103988728 & 6.36954796359426 \tabularnewline
79 & 6.06837793688601 & 5.7239506356023 & 6.41280523816972 \tabularnewline
80 & 6.04680765548835 & 5.67291483264611 & 6.42070047833059 \tabularnewline
81 & 6.02620661698859 & 5.62264414108111 & 6.42976909289607 \tabularnewline
82 & 6.00461319313398 & 5.57112454993766 & 6.43810183633029 \tabularnewline
83 & 5.98617207558403 & 5.52246226397828 & 6.44988188718978 \tabularnewline
84 & 5.96769009710892 & 5.47343552737178 & 6.46194466684605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205296&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]5.78453746576198[/C][C]5.62027475012351[/C][C]5.94880018140044[/C][/ROW]
[ROW][C]74[/C][C]5.77265230385632[/C][C]5.57654576279254[/C][C]5.9687588449201[/C][/ROW]
[ROW][C]75[/C][C]5.80108448681143[/C][C]5.57449243632148[/C][C]6.02767653730139[/C][/ROW]
[ROW][C]76[/C][C]5.8835378440047[/C][C]5.62717377400203[/C][C]6.13990191400738[/C][/ROW]
[ROW][C]77[/C][C]5.9886014611352[/C][C]5.70281261683759[/C][C]6.27439030543281[/C][/ROW]
[ROW][C]78[/C][C]6.05445450174077[/C][C]5.73936103988728[/C][C]6.36954796359426[/C][/ROW]
[ROW][C]79[/C][C]6.06837793688601[/C][C]5.7239506356023[/C][C]6.41280523816972[/C][/ROW]
[ROW][C]80[/C][C]6.04680765548835[/C][C]5.67291483264611[/C][C]6.42070047833059[/C][/ROW]
[ROW][C]81[/C][C]6.02620661698859[/C][C]5.62264414108111[/C][C]6.42976909289607[/C][/ROW]
[ROW][C]82[/C][C]6.00461319313398[/C][C]5.57112454993766[/C][C]6.43810183633029[/C][/ROW]
[ROW][C]83[/C][C]5.98617207558403[/C][C]5.52246226397828[/C][C]6.44988188718978[/C][/ROW]
[ROW][C]84[/C][C]5.96769009710892[/C][C]5.47343552737178[/C][C]6.46194466684605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205296&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205296&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
735.784537465761985.620274750123515.94880018140044
745.772652303856325.576545762792545.9687588449201
755.801084486811435.574492436321486.02767653730139
765.88353784400475.627173774002036.13990191400738
775.98860146113525.702812616837596.27439030543281
786.054454501740775.739361039887286.36954796359426
796.068377936886015.72395063560236.41280523816972
806.046807655488355.672914832646116.42070047833059
816.026206616988595.622644141081116.42976909289607
826.004613193133985.571124549937666.43810183633029
835.986172075584035.522462263978286.44988188718978
845.967690097108925.473435527371786.46194466684605



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')