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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 Nov 2012 07:56:26 -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/2012/Nov/22/t13535890170rl10zpji1wo0em.htm/, Retrieved Thu, 02 May 2024 13:28:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191639, Retrieved Thu, 02 May 2024 13:28:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:53:26] [64c86865dff7d646747b84f713e71815]
- R P   [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:55:09] [64c86865dff7d646747b84f713e71815]
-   P       [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:56:26] [46cc0db4bd6f6541b375e62191991224] [Current]
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Dataseries X:
3.06
3.07
3.08
3.07
3.08
3.06
3.07
3.04
3.05
3.06
3.05
3.06
3.07
3.07
3.1
3.1
3.1
3.1
3.09
3.08
3.1
3.08
3.08
3.09
3.11
3.19
3.24
3.25
3.22
3.21
3.21
3.19
3.21
3.21
3.19
3.18
3.16
3.15
3.15
3.14
3.14
3.12
3.12
3.12
3.12
3.13
3.14
3.14
3.16
3.19
3.18
3.18
3.19
3.18
3.17
3.17
3.16
3.15
3.14
3.15
3.15
3.16
3.18
3.18
3.19
3.18
3.19
3.2
3.2
3.18
3.2
3.21
3.24
3.29
3.28
3.27
3.29
3.27
3.27
3.25
3.25
3.23
3.23
3.25




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=191639&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=191639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191639&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
alpha0.842164161589222
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.842164161589222 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191639&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]0.842164161589222[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191639&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
alpha0.842164161589222
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133.073.057604166666670.0123958333333332
143.073.067910917495460.00208908250454254
153.13.098287692153810.00171230784618892
163.13.099180494031240.000819505968763234
173.13.10015474349743-0.000154743497428278
183.13.099891848312080.000108151687920444
193.093.09651702069675-0.00651702069675242
203.083.062979377001370.0170206229986301
213.13.088847626607830.0111523733921715
223.083.10852384670447-0.0285238467044682
233.083.074786176168390.00521382383160862
243.093.089044495986640.000955504013363306
253.113.101673118212340.00832688178766317
263.193.106926369215770.0830736307842321
273.243.205445959533670.0345540404663254
283.253.233855975495420.016144024504583
293.223.24758221378477-0.0275822137847679
303.213.22426238036236-0.014262380362362
313.213.207739516033370.00226048396663359
323.193.185309055920540.00469094407945514
333.213.199867471720730.010132528279267
343.213.21242248534899-0.0024224853489887
353.193.20599145943027-0.0159914594302748
363.183.20171933417028-0.0217193341702799
373.163.19641548789913-0.0364154878991299
383.153.17578603444412-0.0257860344441219
393.153.17496978584693-0.0249697858469342
403.143.15034520822251-0.0103452082225099
413.143.134861596560160.00513840343984207
423.123.14120024138511-0.0212002413851149
433.123.12144245928898-0.00144245928898457
443.123.096277126783510.023722873216486
453.123.12772242823328-0.00772242823327529
463.133.123259006277660.00674099372234016
473.143.12240346362780.0175965363722024
483.143.14551388078036-0.00551388078035808
493.163.15153810683130.00846189316870216
503.193.170380484075520.0196195159244796
513.183.20793199601769-0.0279319960176916
523.183.18312103361912-0.0031210336191152
533.193.176165231733160.01383476826684
543.183.18567046126297-0.005670461262969
553.173.18210978952535-0.012109789525351
563.173.151932805149860.0180671948501376
573.163.17365190145161-0.0136519014516066
583.153.16647773598506-0.0164777359850627
593.143.14778160497354-0.00778160497354374
603.153.145871808929670.00412819107032592
613.153.16222212033542-0.0122221203354176
623.163.16540623543097-0.00540623543097185
633.183.174376623709650.00562337629035348
643.183.18174085234965-0.00174085234964627
653.193.178623622871930.011376377128069
663.183.18297985923327-0.0029798592332666
673.193.180668759323070.00933124067693214
683.23.173311651801110.026688348198892
693.23.197284764326320.00271523567367948
703.183.20344839721171-0.0234483972117103
713.23.180254386261660.0197456137383374
723.213.203406819929050.00659318007094711
733.243.219252391620830.0207476083791716
743.293.251278221565530.0387217784344664
753.283.29915250965717-0.0191525096571739
763.273.2844890358789-0.0144890358789009
773.293.272706112019730.0172938879802733
783.273.27977993534409-0.00977993534408972
793.273.27368518781336-0.00368518781336169
803.253.2581056843231-0.00810568432310221
813.253.248992693306390.00100730669361138
823.233.24958841068189-0.0195884106818882
833.233.2364627049841-0.00646270498409907
843.253.235467506492910.0145324935070894

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.07 & 3.05760416666667 & 0.0123958333333332 \tabularnewline
14 & 3.07 & 3.06791091749546 & 0.00208908250454254 \tabularnewline
15 & 3.1 & 3.09828769215381 & 0.00171230784618892 \tabularnewline
16 & 3.1 & 3.09918049403124 & 0.000819505968763234 \tabularnewline
17 & 3.1 & 3.10015474349743 & -0.000154743497428278 \tabularnewline
18 & 3.1 & 3.09989184831208 & 0.000108151687920444 \tabularnewline
19 & 3.09 & 3.09651702069675 & -0.00651702069675242 \tabularnewline
20 & 3.08 & 3.06297937700137 & 0.0170206229986301 \tabularnewline
21 & 3.1 & 3.08884762660783 & 0.0111523733921715 \tabularnewline
22 & 3.08 & 3.10852384670447 & -0.0285238467044682 \tabularnewline
23 & 3.08 & 3.07478617616839 & 0.00521382383160862 \tabularnewline
24 & 3.09 & 3.08904449598664 & 0.000955504013363306 \tabularnewline
25 & 3.11 & 3.10167311821234 & 0.00832688178766317 \tabularnewline
26 & 3.19 & 3.10692636921577 & 0.0830736307842321 \tabularnewline
27 & 3.24 & 3.20544595953367 & 0.0345540404663254 \tabularnewline
28 & 3.25 & 3.23385597549542 & 0.016144024504583 \tabularnewline
29 & 3.22 & 3.24758221378477 & -0.0275822137847679 \tabularnewline
30 & 3.21 & 3.22426238036236 & -0.014262380362362 \tabularnewline
31 & 3.21 & 3.20773951603337 & 0.00226048396663359 \tabularnewline
32 & 3.19 & 3.18530905592054 & 0.00469094407945514 \tabularnewline
33 & 3.21 & 3.19986747172073 & 0.010132528279267 \tabularnewline
34 & 3.21 & 3.21242248534899 & -0.0024224853489887 \tabularnewline
35 & 3.19 & 3.20599145943027 & -0.0159914594302748 \tabularnewline
36 & 3.18 & 3.20171933417028 & -0.0217193341702799 \tabularnewline
37 & 3.16 & 3.19641548789913 & -0.0364154878991299 \tabularnewline
38 & 3.15 & 3.17578603444412 & -0.0257860344441219 \tabularnewline
39 & 3.15 & 3.17496978584693 & -0.0249697858469342 \tabularnewline
40 & 3.14 & 3.15034520822251 & -0.0103452082225099 \tabularnewline
41 & 3.14 & 3.13486159656016 & 0.00513840343984207 \tabularnewline
42 & 3.12 & 3.14120024138511 & -0.0212002413851149 \tabularnewline
43 & 3.12 & 3.12144245928898 & -0.00144245928898457 \tabularnewline
44 & 3.12 & 3.09627712678351 & 0.023722873216486 \tabularnewline
45 & 3.12 & 3.12772242823328 & -0.00772242823327529 \tabularnewline
46 & 3.13 & 3.12325900627766 & 0.00674099372234016 \tabularnewline
47 & 3.14 & 3.1224034636278 & 0.0175965363722024 \tabularnewline
48 & 3.14 & 3.14551388078036 & -0.00551388078035808 \tabularnewline
49 & 3.16 & 3.1515381068313 & 0.00846189316870216 \tabularnewline
50 & 3.19 & 3.17038048407552 & 0.0196195159244796 \tabularnewline
51 & 3.18 & 3.20793199601769 & -0.0279319960176916 \tabularnewline
52 & 3.18 & 3.18312103361912 & -0.0031210336191152 \tabularnewline
53 & 3.19 & 3.17616523173316 & 0.01383476826684 \tabularnewline
54 & 3.18 & 3.18567046126297 & -0.005670461262969 \tabularnewline
55 & 3.17 & 3.18210978952535 & -0.012109789525351 \tabularnewline
56 & 3.17 & 3.15193280514986 & 0.0180671948501376 \tabularnewline
57 & 3.16 & 3.17365190145161 & -0.0136519014516066 \tabularnewline
58 & 3.15 & 3.16647773598506 & -0.0164777359850627 \tabularnewline
59 & 3.14 & 3.14778160497354 & -0.00778160497354374 \tabularnewline
60 & 3.15 & 3.14587180892967 & 0.00412819107032592 \tabularnewline
61 & 3.15 & 3.16222212033542 & -0.0122221203354176 \tabularnewline
62 & 3.16 & 3.16540623543097 & -0.00540623543097185 \tabularnewline
63 & 3.18 & 3.17437662370965 & 0.00562337629035348 \tabularnewline
64 & 3.18 & 3.18174085234965 & -0.00174085234964627 \tabularnewline
65 & 3.19 & 3.17862362287193 & 0.011376377128069 \tabularnewline
66 & 3.18 & 3.18297985923327 & -0.0029798592332666 \tabularnewline
67 & 3.19 & 3.18066875932307 & 0.00933124067693214 \tabularnewline
68 & 3.2 & 3.17331165180111 & 0.026688348198892 \tabularnewline
69 & 3.2 & 3.19728476432632 & 0.00271523567367948 \tabularnewline
70 & 3.18 & 3.20344839721171 & -0.0234483972117103 \tabularnewline
71 & 3.2 & 3.18025438626166 & 0.0197456137383374 \tabularnewline
72 & 3.21 & 3.20340681992905 & 0.00659318007094711 \tabularnewline
73 & 3.24 & 3.21925239162083 & 0.0207476083791716 \tabularnewline
74 & 3.29 & 3.25127822156553 & 0.0387217784344664 \tabularnewline
75 & 3.28 & 3.29915250965717 & -0.0191525096571739 \tabularnewline
76 & 3.27 & 3.2844890358789 & -0.0144890358789009 \tabularnewline
77 & 3.29 & 3.27270611201973 & 0.0172938879802733 \tabularnewline
78 & 3.27 & 3.27977993534409 & -0.00977993534408972 \tabularnewline
79 & 3.27 & 3.27368518781336 & -0.00368518781336169 \tabularnewline
80 & 3.25 & 3.2581056843231 & -0.00810568432310221 \tabularnewline
81 & 3.25 & 3.24899269330639 & 0.00100730669361138 \tabularnewline
82 & 3.23 & 3.24958841068189 & -0.0195884106818882 \tabularnewline
83 & 3.23 & 3.2364627049841 & -0.00646270498409907 \tabularnewline
84 & 3.25 & 3.23546750649291 & 0.0145324935070894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191639&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]3.07[/C][C]3.05760416666667[/C][C]0.0123958333333332[/C][/ROW]
[ROW][C]14[/C][C]3.07[/C][C]3.06791091749546[/C][C]0.00208908250454254[/C][/ROW]
[ROW][C]15[/C][C]3.1[/C][C]3.09828769215381[/C][C]0.00171230784618892[/C][/ROW]
[ROW][C]16[/C][C]3.1[/C][C]3.09918049403124[/C][C]0.000819505968763234[/C][/ROW]
[ROW][C]17[/C][C]3.1[/C][C]3.10015474349743[/C][C]-0.000154743497428278[/C][/ROW]
[ROW][C]18[/C][C]3.1[/C][C]3.09989184831208[/C][C]0.000108151687920444[/C][/ROW]
[ROW][C]19[/C][C]3.09[/C][C]3.09651702069675[/C][C]-0.00651702069675242[/C][/ROW]
[ROW][C]20[/C][C]3.08[/C][C]3.06297937700137[/C][C]0.0170206229986301[/C][/ROW]
[ROW][C]21[/C][C]3.1[/C][C]3.08884762660783[/C][C]0.0111523733921715[/C][/ROW]
[ROW][C]22[/C][C]3.08[/C][C]3.10852384670447[/C][C]-0.0285238467044682[/C][/ROW]
[ROW][C]23[/C][C]3.08[/C][C]3.07478617616839[/C][C]0.00521382383160862[/C][/ROW]
[ROW][C]24[/C][C]3.09[/C][C]3.08904449598664[/C][C]0.000955504013363306[/C][/ROW]
[ROW][C]25[/C][C]3.11[/C][C]3.10167311821234[/C][C]0.00832688178766317[/C][/ROW]
[ROW][C]26[/C][C]3.19[/C][C]3.10692636921577[/C][C]0.0830736307842321[/C][/ROW]
[ROW][C]27[/C][C]3.24[/C][C]3.20544595953367[/C][C]0.0345540404663254[/C][/ROW]
[ROW][C]28[/C][C]3.25[/C][C]3.23385597549542[/C][C]0.016144024504583[/C][/ROW]
[ROW][C]29[/C][C]3.22[/C][C]3.24758221378477[/C][C]-0.0275822137847679[/C][/ROW]
[ROW][C]30[/C][C]3.21[/C][C]3.22426238036236[/C][C]-0.014262380362362[/C][/ROW]
[ROW][C]31[/C][C]3.21[/C][C]3.20773951603337[/C][C]0.00226048396663359[/C][/ROW]
[ROW][C]32[/C][C]3.19[/C][C]3.18530905592054[/C][C]0.00469094407945514[/C][/ROW]
[ROW][C]33[/C][C]3.21[/C][C]3.19986747172073[/C][C]0.010132528279267[/C][/ROW]
[ROW][C]34[/C][C]3.21[/C][C]3.21242248534899[/C][C]-0.0024224853489887[/C][/ROW]
[ROW][C]35[/C][C]3.19[/C][C]3.20599145943027[/C][C]-0.0159914594302748[/C][/ROW]
[ROW][C]36[/C][C]3.18[/C][C]3.20171933417028[/C][C]-0.0217193341702799[/C][/ROW]
[ROW][C]37[/C][C]3.16[/C][C]3.19641548789913[/C][C]-0.0364154878991299[/C][/ROW]
[ROW][C]38[/C][C]3.15[/C][C]3.17578603444412[/C][C]-0.0257860344441219[/C][/ROW]
[ROW][C]39[/C][C]3.15[/C][C]3.17496978584693[/C][C]-0.0249697858469342[/C][/ROW]
[ROW][C]40[/C][C]3.14[/C][C]3.15034520822251[/C][C]-0.0103452082225099[/C][/ROW]
[ROW][C]41[/C][C]3.14[/C][C]3.13486159656016[/C][C]0.00513840343984207[/C][/ROW]
[ROW][C]42[/C][C]3.12[/C][C]3.14120024138511[/C][C]-0.0212002413851149[/C][/ROW]
[ROW][C]43[/C][C]3.12[/C][C]3.12144245928898[/C][C]-0.00144245928898457[/C][/ROW]
[ROW][C]44[/C][C]3.12[/C][C]3.09627712678351[/C][C]0.023722873216486[/C][/ROW]
[ROW][C]45[/C][C]3.12[/C][C]3.12772242823328[/C][C]-0.00772242823327529[/C][/ROW]
[ROW][C]46[/C][C]3.13[/C][C]3.12325900627766[/C][C]0.00674099372234016[/C][/ROW]
[ROW][C]47[/C][C]3.14[/C][C]3.1224034636278[/C][C]0.0175965363722024[/C][/ROW]
[ROW][C]48[/C][C]3.14[/C][C]3.14551388078036[/C][C]-0.00551388078035808[/C][/ROW]
[ROW][C]49[/C][C]3.16[/C][C]3.1515381068313[/C][C]0.00846189316870216[/C][/ROW]
[ROW][C]50[/C][C]3.19[/C][C]3.17038048407552[/C][C]0.0196195159244796[/C][/ROW]
[ROW][C]51[/C][C]3.18[/C][C]3.20793199601769[/C][C]-0.0279319960176916[/C][/ROW]
[ROW][C]52[/C][C]3.18[/C][C]3.18312103361912[/C][C]-0.0031210336191152[/C][/ROW]
[ROW][C]53[/C][C]3.19[/C][C]3.17616523173316[/C][C]0.01383476826684[/C][/ROW]
[ROW][C]54[/C][C]3.18[/C][C]3.18567046126297[/C][C]-0.005670461262969[/C][/ROW]
[ROW][C]55[/C][C]3.17[/C][C]3.18210978952535[/C][C]-0.012109789525351[/C][/ROW]
[ROW][C]56[/C][C]3.17[/C][C]3.15193280514986[/C][C]0.0180671948501376[/C][/ROW]
[ROW][C]57[/C][C]3.16[/C][C]3.17365190145161[/C][C]-0.0136519014516066[/C][/ROW]
[ROW][C]58[/C][C]3.15[/C][C]3.16647773598506[/C][C]-0.0164777359850627[/C][/ROW]
[ROW][C]59[/C][C]3.14[/C][C]3.14778160497354[/C][C]-0.00778160497354374[/C][/ROW]
[ROW][C]60[/C][C]3.15[/C][C]3.14587180892967[/C][C]0.00412819107032592[/C][/ROW]
[ROW][C]61[/C][C]3.15[/C][C]3.16222212033542[/C][C]-0.0122221203354176[/C][/ROW]
[ROW][C]62[/C][C]3.16[/C][C]3.16540623543097[/C][C]-0.00540623543097185[/C][/ROW]
[ROW][C]63[/C][C]3.18[/C][C]3.17437662370965[/C][C]0.00562337629035348[/C][/ROW]
[ROW][C]64[/C][C]3.18[/C][C]3.18174085234965[/C][C]-0.00174085234964627[/C][/ROW]
[ROW][C]65[/C][C]3.19[/C][C]3.17862362287193[/C][C]0.011376377128069[/C][/ROW]
[ROW][C]66[/C][C]3.18[/C][C]3.18297985923327[/C][C]-0.0029798592332666[/C][/ROW]
[ROW][C]67[/C][C]3.19[/C][C]3.18066875932307[/C][C]0.00933124067693214[/C][/ROW]
[ROW][C]68[/C][C]3.2[/C][C]3.17331165180111[/C][C]0.026688348198892[/C][/ROW]
[ROW][C]69[/C][C]3.2[/C][C]3.19728476432632[/C][C]0.00271523567367948[/C][/ROW]
[ROW][C]70[/C][C]3.18[/C][C]3.20344839721171[/C][C]-0.0234483972117103[/C][/ROW]
[ROW][C]71[/C][C]3.2[/C][C]3.18025438626166[/C][C]0.0197456137383374[/C][/ROW]
[ROW][C]72[/C][C]3.21[/C][C]3.20340681992905[/C][C]0.00659318007094711[/C][/ROW]
[ROW][C]73[/C][C]3.24[/C][C]3.21925239162083[/C][C]0.0207476083791716[/C][/ROW]
[ROW][C]74[/C][C]3.29[/C][C]3.25127822156553[/C][C]0.0387217784344664[/C][/ROW]
[ROW][C]75[/C][C]3.28[/C][C]3.29915250965717[/C][C]-0.0191525096571739[/C][/ROW]
[ROW][C]76[/C][C]3.27[/C][C]3.2844890358789[/C][C]-0.0144890358789009[/C][/ROW]
[ROW][C]77[/C][C]3.29[/C][C]3.27270611201973[/C][C]0.0172938879802733[/C][/ROW]
[ROW][C]78[/C][C]3.27[/C][C]3.27977993534409[/C][C]-0.00977993534408972[/C][/ROW]
[ROW][C]79[/C][C]3.27[/C][C]3.27368518781336[/C][C]-0.00368518781336169[/C][/ROW]
[ROW][C]80[/C][C]3.25[/C][C]3.2581056843231[/C][C]-0.00810568432310221[/C][/ROW]
[ROW][C]81[/C][C]3.25[/C][C]3.24899269330639[/C][C]0.00100730669361138[/C][/ROW]
[ROW][C]82[/C][C]3.23[/C][C]3.24958841068189[/C][C]-0.0195884106818882[/C][/ROW]
[ROW][C]83[/C][C]3.23[/C][C]3.2364627049841[/C][C]-0.00646270498409907[/C][/ROW]
[ROW][C]84[/C][C]3.25[/C][C]3.23546750649291[/C][C]0.0145324935070894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191639&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191639&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
133.073.057604166666670.0123958333333332
143.073.067910917495460.00208908250454254
153.13.098287692153810.00171230784618892
163.13.099180494031240.000819505968763234
173.13.10015474349743-0.000154743497428278
183.13.099891848312080.000108151687920444
193.093.09651702069675-0.00651702069675242
203.083.062979377001370.0170206229986301
213.13.088847626607830.0111523733921715
223.083.10852384670447-0.0285238467044682
233.083.074786176168390.00521382383160862
243.093.089044495986640.000955504013363306
253.113.101673118212340.00832688178766317
263.193.106926369215770.0830736307842321
273.243.205445959533670.0345540404663254
283.253.233855975495420.016144024504583
293.223.24758221378477-0.0275822137847679
303.213.22426238036236-0.014262380362362
313.213.207739516033370.00226048396663359
323.193.185309055920540.00469094407945514
333.213.199867471720730.010132528279267
343.213.21242248534899-0.0024224853489887
353.193.20599145943027-0.0159914594302748
363.183.20171933417028-0.0217193341702799
373.163.19641548789913-0.0364154878991299
383.153.17578603444412-0.0257860344441219
393.153.17496978584693-0.0249697858469342
403.143.15034520822251-0.0103452082225099
413.143.134861596560160.00513840343984207
423.123.14120024138511-0.0212002413851149
433.123.12144245928898-0.00144245928898457
443.123.096277126783510.023722873216486
453.123.12772242823328-0.00772242823327529
463.133.123259006277660.00674099372234016
473.143.12240346362780.0175965363722024
483.143.14551388078036-0.00551388078035808
493.163.15153810683130.00846189316870216
503.193.170380484075520.0196195159244796
513.183.20793199601769-0.0279319960176916
523.183.18312103361912-0.0031210336191152
533.193.176165231733160.01383476826684
543.183.18567046126297-0.005670461262969
553.173.18210978952535-0.012109789525351
563.173.151932805149860.0180671948501376
573.163.17365190145161-0.0136519014516066
583.153.16647773598506-0.0164777359850627
593.143.14778160497354-0.00778160497354374
603.153.145871808929670.00412819107032592
613.153.16222212033542-0.0122221203354176
623.163.16540623543097-0.00540623543097185
633.183.174376623709650.00562337629035348
643.183.18174085234965-0.00174085234964627
653.193.178623622871930.011376377128069
663.183.18297985923327-0.0029798592332666
673.193.180668759323070.00933124067693214
683.23.173311651801110.026688348198892
693.23.197284764326320.00271523567367948
703.183.20344839721171-0.0234483972117103
713.23.180254386261660.0197456137383374
723.213.203406819929050.00659318007094711
733.243.219252391620830.0207476083791716
743.293.251278221565530.0387217784344664
753.283.29915250965717-0.0191525096571739
763.273.2844890358789-0.0144890358789009
773.293.272706112019730.0172938879802733
783.273.27977993534409-0.00977993534408972
793.273.27368518781336-0.00368518781336169
803.253.2581056843231-0.00810568432310221
813.253.248992693306390.00100730669361138
823.233.24958841068189-0.0195884106818882
833.233.2364627049841-0.00646270498409907
843.253.235467506492910.0145324935070894







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853.260233359487483.224094874294573.2963718446804
863.277623265416983.230376560139983.32486997069397
873.283752822654743.227552180247163.33995346506232
883.285954969407933.222042738539993.34986720027587
893.291390676736413.220602017319733.36217933615308
903.279626987785863.202573140707973.35668083486375
913.2827305208913.199883937394783.36557710438721
923.269556837733073.181296895264883.35781678020126
933.268708520135983.175348579626253.36206846064571
943.265205177594763.167009762531363.36340059265816
953.270647836119293.16784413683293.37345153540568
963.278409090909093.171194998391093.3856231834271

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3.26023335948748 & 3.22409487429457 & 3.2963718446804 \tabularnewline
86 & 3.27762326541698 & 3.23037656013998 & 3.32486997069397 \tabularnewline
87 & 3.28375282265474 & 3.22755218024716 & 3.33995346506232 \tabularnewline
88 & 3.28595496940793 & 3.22204273853999 & 3.34986720027587 \tabularnewline
89 & 3.29139067673641 & 3.22060201731973 & 3.36217933615308 \tabularnewline
90 & 3.27962698778586 & 3.20257314070797 & 3.35668083486375 \tabularnewline
91 & 3.282730520891 & 3.19988393739478 & 3.36557710438721 \tabularnewline
92 & 3.26955683773307 & 3.18129689526488 & 3.35781678020126 \tabularnewline
93 & 3.26870852013598 & 3.17534857962625 & 3.36206846064571 \tabularnewline
94 & 3.26520517759476 & 3.16700976253136 & 3.36340059265816 \tabularnewline
95 & 3.27064783611929 & 3.1678441368329 & 3.37345153540568 \tabularnewline
96 & 3.27840909090909 & 3.17119499839109 & 3.3856231834271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191639&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]85[/C][C]3.26023335948748[/C][C]3.22409487429457[/C][C]3.2963718446804[/C][/ROW]
[ROW][C]86[/C][C]3.27762326541698[/C][C]3.23037656013998[/C][C]3.32486997069397[/C][/ROW]
[ROW][C]87[/C][C]3.28375282265474[/C][C]3.22755218024716[/C][C]3.33995346506232[/C][/ROW]
[ROW][C]88[/C][C]3.28595496940793[/C][C]3.22204273853999[/C][C]3.34986720027587[/C][/ROW]
[ROW][C]89[/C][C]3.29139067673641[/C][C]3.22060201731973[/C][C]3.36217933615308[/C][/ROW]
[ROW][C]90[/C][C]3.27962698778586[/C][C]3.20257314070797[/C][C]3.35668083486375[/C][/ROW]
[ROW][C]91[/C][C]3.282730520891[/C][C]3.19988393739478[/C][C]3.36557710438721[/C][/ROW]
[ROW][C]92[/C][C]3.26955683773307[/C][C]3.18129689526488[/C][C]3.35781678020126[/C][/ROW]
[ROW][C]93[/C][C]3.26870852013598[/C][C]3.17534857962625[/C][C]3.36206846064571[/C][/ROW]
[ROW][C]94[/C][C]3.26520517759476[/C][C]3.16700976253136[/C][C]3.36340059265816[/C][/ROW]
[ROW][C]95[/C][C]3.27064783611929[/C][C]3.1678441368329[/C][C]3.37345153540568[/C][/ROW]
[ROW][C]96[/C][C]3.27840909090909[/C][C]3.17119499839109[/C][C]3.3856231834271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191639&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191639&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
853.260233359487483.224094874294573.2963718446804
863.277623265416983.230376560139983.32486997069397
873.283752822654743.227552180247163.33995346506232
883.285954969407933.222042738539993.34986720027587
893.291390676736413.220602017319733.36217933615308
903.279626987785863.202573140707973.35668083486375
913.2827305208913.199883937394783.36557710438721
923.269556837733073.181296895264883.35781678020126
933.268708520135983.175348579626253.36206846064571
943.265205177594763.167009762531363.36340059265816
953.270647836119293.16784413683293.37345153540568
963.278409090909093.171194998391093.3856231834271



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')