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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 11 Dec 2015 20:22:57 +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/2015/Dec/11/t1449865416mri9sj2hes5277k.htm/, Retrieved Thu, 16 May 2024 03:35:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286027, Retrieved Thu, 16 May 2024 03:35:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tripple] [2015-12-11 20:22:57] [42f75ab47e982481f307588c9de28675] [Current]
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Dataseries X:
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8
8
8.8
8.7
8.5
8.1
7.8
7.7
7.5
7.2
6.9
6.6
6.5
6.6
7.7
8
7.7
7.3
7
7
7.3
7.3
7.1
7.1
7
7
7.5
7.8
7.9
8.1
8.3
8.4
8.6
8.5
8.4
8.3
8
8
8.7
8.7
8.6
8.5
8.5
8.6
8.8
8.7
8.6
8.4
8.1
8.1
8.7
8.7
8.6
8.6
8.5
8.6
8.8
8.8
8.7
8.5
8.3
8.3
8.9
9
8.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286027&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286027&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286027&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.938003941477117
beta0.0190511611809337
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.938003941477117 \tabularnewline
beta & 0.0190511611809337 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286027&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]0.938003941477117[/C][/ROW]
[ROW][C]beta[/C][C]0.0190511611809337[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286027&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286027&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
alpha0.938003941477117
beta0.0190511611809337
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1388.32793803418804-0.327938034188035
147.97.90497175731061-0.00497175731060828
157.97.897360275485690.00263972451431016
1688.00110223232644-0.00110223232643669
1788.0013145219392-0.00131452193920367
187.97.91797085913358-0.0179708591335785
1987.822849012647890.177150987352108
207.77.77225126009819-0.0722512600981942
217.27.39058874843145-0.190588748431447
227.57.402852706431910.0971472935680859
237.37.39091690098008-0.0909169009800781
2477.30095144892693-0.300951448926925
2576.879930542423820.120069457576177
2676.892161389684480.107838610315518
277.26.987795982575420.212204017424579
287.37.288580636338540.0114193636614557
297.17.30145138370241-0.201451383702408
306.87.02669578236869-0.226695782368691
316.46.7415058467194-0.341505846719401
326.16.17329547834675-0.0732954783467523
336.55.767649862886550.732350137113452
347.76.664298445870021.03570155412998
357.97.538668834368660.361331165631345
367.57.88557207628031-0.385572076280313
376.97.43544568758262-0.535445687582619
386.66.84449574591924-0.244495745919239
396.96.622266595493420.277733404506581
407.76.979398257498410.720601742501591
4187.664288900844920.335711099155082
4287.921429077240020.0785709227599805
437.77.95051818318901-0.250518183189011
447.37.52096398337783-0.220963983377835
457.47.060794131064660.339205868935344
468.17.634495469961070.465504530038928
478.37.94903807573180.350961924268196
488.18.25655215162804-0.156552151628036
497.98.0326906628778-0.132690662877801
507.97.865496410751550.0345035892484544
518.37.970263760711180.329736239288819
528.68.437477547466840.162522452533159
538.78.598900170889430.101099829110574
548.58.63971411194058-0.139714111940583
558.38.45942973799955-0.159429737999551
5688.1345578295669-0.134557829566901
5787.809118423432280.190881576567718
588.88.267823256406950.53217674359305
598.78.655297153680210.044702846319792
608.58.65609594808124-0.156095948081235
618.18.44617066377972-0.346170663779723
627.88.09731077815307-0.297310778153073
637.77.9114227243601-0.211422724360104
647.57.85327464913215-0.353274649132148
657.27.51046624486727-0.310466244867275
666.97.12634200620343-0.22634200620343
676.66.83807192389334-0.238071923893338
686.56.414063843498190.0859361565018126
696.66.292653415621710.307346584378288
707.76.86087186707630.839128132923699
7187.49064118513820.509358814861799
727.77.90773907569657-0.207739075696574
737.37.62956428497662-0.329564284976617
7477.29158295953942-0.291582959539415
7577.10876729056802-0.108767290568024
767.37.132325563398160.167674436601842
777.37.284342207620910.015657792379093
787.17.22068563046015-0.120685630460152
797.17.042029180533890.0579708194661066
8076.932322631180390.0676773688196102
8176.823710723636840.176289276363163
827.57.315822022401830.184177977598173
837.87.312953872764490.487046127235505
847.97.666419159841460.233580840158544
858.17.804291950351790.295708049648205
868.38.075987332084440.224012667915565
878.48.418164072111-0.0181640721109968
888.68.575493731122060.0245062688779427
898.58.61288212525627-0.11288212525627
908.48.44699331560671-0.0469933156067146
918.38.37664490130972-0.0766449013097166
9288.16697280961752-0.166972809617516
9387.866501172768630.133498827231366
948.78.339708814658060.360291185341939
958.78.544704218586880.15529578141312
968.68.589236163947690.0107638360523126
978.58.53593925333094-0.0359392533309411
988.58.5001586528228-0.000158652822795702
998.68.62109717738795-0.0210971773879507
1008.88.782317920570640.017682079429358
1018.78.80866266600254-0.108662666002544
1028.68.65476698109196-0.0547669810919587
1038.48.57910004941468-0.17910004941468
1048.18.26970526353065-0.169705263530652
1058.17.987230415041780.112769584958217
1068.78.456615529107180.243384470892824
1078.78.538715287363070.161284712636929
1088.68.579483705784330.0205162942156658
1098.68.532192751865840.0678072481341569
1108.58.59755251146379-0.097552511463789
1118.68.62570414885385-0.0257041488538459
1128.88.78479241094230.0152075890577041
1138.88.80072369434251-0.000723694342507741
1148.78.7530858826074-0.0530858826074034
1158.58.67298708137609-0.172987081376089
1168.38.37171737605514-0.0717173760551386
1178.38.202227582074360.0977724179256452
1188.98.668934604726590.231065395273406
11998.737460719667440.262539280332557
1208.88.86936021979512-0.069360219795124

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8 & 8.32793803418804 & -0.327938034188035 \tabularnewline
14 & 7.9 & 7.90497175731061 & -0.00497175731060828 \tabularnewline
15 & 7.9 & 7.89736027548569 & 0.00263972451431016 \tabularnewline
16 & 8 & 8.00110223232644 & -0.00110223232643669 \tabularnewline
17 & 8 & 8.0013145219392 & -0.00131452193920367 \tabularnewline
18 & 7.9 & 7.91797085913358 & -0.0179708591335785 \tabularnewline
19 & 8 & 7.82284901264789 & 0.177150987352108 \tabularnewline
20 & 7.7 & 7.77225126009819 & -0.0722512600981942 \tabularnewline
21 & 7.2 & 7.39058874843145 & -0.190588748431447 \tabularnewline
22 & 7.5 & 7.40285270643191 & 0.0971472935680859 \tabularnewline
23 & 7.3 & 7.39091690098008 & -0.0909169009800781 \tabularnewline
24 & 7 & 7.30095144892693 & -0.300951448926925 \tabularnewline
25 & 7 & 6.87993054242382 & 0.120069457576177 \tabularnewline
26 & 7 & 6.89216138968448 & 0.107838610315518 \tabularnewline
27 & 7.2 & 6.98779598257542 & 0.212204017424579 \tabularnewline
28 & 7.3 & 7.28858063633854 & 0.0114193636614557 \tabularnewline
29 & 7.1 & 7.30145138370241 & -0.201451383702408 \tabularnewline
30 & 6.8 & 7.02669578236869 & -0.226695782368691 \tabularnewline
31 & 6.4 & 6.7415058467194 & -0.341505846719401 \tabularnewline
32 & 6.1 & 6.17329547834675 & -0.0732954783467523 \tabularnewline
33 & 6.5 & 5.76764986288655 & 0.732350137113452 \tabularnewline
34 & 7.7 & 6.66429844587002 & 1.03570155412998 \tabularnewline
35 & 7.9 & 7.53866883436866 & 0.361331165631345 \tabularnewline
36 & 7.5 & 7.88557207628031 & -0.385572076280313 \tabularnewline
37 & 6.9 & 7.43544568758262 & -0.535445687582619 \tabularnewline
38 & 6.6 & 6.84449574591924 & -0.244495745919239 \tabularnewline
39 & 6.9 & 6.62226659549342 & 0.277733404506581 \tabularnewline
40 & 7.7 & 6.97939825749841 & 0.720601742501591 \tabularnewline
41 & 8 & 7.66428890084492 & 0.335711099155082 \tabularnewline
42 & 8 & 7.92142907724002 & 0.0785709227599805 \tabularnewline
43 & 7.7 & 7.95051818318901 & -0.250518183189011 \tabularnewline
44 & 7.3 & 7.52096398337783 & -0.220963983377835 \tabularnewline
45 & 7.4 & 7.06079413106466 & 0.339205868935344 \tabularnewline
46 & 8.1 & 7.63449546996107 & 0.465504530038928 \tabularnewline
47 & 8.3 & 7.9490380757318 & 0.350961924268196 \tabularnewline
48 & 8.1 & 8.25655215162804 & -0.156552151628036 \tabularnewline
49 & 7.9 & 8.0326906628778 & -0.132690662877801 \tabularnewline
50 & 7.9 & 7.86549641075155 & 0.0345035892484544 \tabularnewline
51 & 8.3 & 7.97026376071118 & 0.329736239288819 \tabularnewline
52 & 8.6 & 8.43747754746684 & 0.162522452533159 \tabularnewline
53 & 8.7 & 8.59890017088943 & 0.101099829110574 \tabularnewline
54 & 8.5 & 8.63971411194058 & -0.139714111940583 \tabularnewline
55 & 8.3 & 8.45942973799955 & -0.159429737999551 \tabularnewline
56 & 8 & 8.1345578295669 & -0.134557829566901 \tabularnewline
57 & 8 & 7.80911842343228 & 0.190881576567718 \tabularnewline
58 & 8.8 & 8.26782325640695 & 0.53217674359305 \tabularnewline
59 & 8.7 & 8.65529715368021 & 0.044702846319792 \tabularnewline
60 & 8.5 & 8.65609594808124 & -0.156095948081235 \tabularnewline
61 & 8.1 & 8.44617066377972 & -0.346170663779723 \tabularnewline
62 & 7.8 & 8.09731077815307 & -0.297310778153073 \tabularnewline
63 & 7.7 & 7.9114227243601 & -0.211422724360104 \tabularnewline
64 & 7.5 & 7.85327464913215 & -0.353274649132148 \tabularnewline
65 & 7.2 & 7.51046624486727 & -0.310466244867275 \tabularnewline
66 & 6.9 & 7.12634200620343 & -0.22634200620343 \tabularnewline
67 & 6.6 & 6.83807192389334 & -0.238071923893338 \tabularnewline
68 & 6.5 & 6.41406384349819 & 0.0859361565018126 \tabularnewline
69 & 6.6 & 6.29265341562171 & 0.307346584378288 \tabularnewline
70 & 7.7 & 6.8608718670763 & 0.839128132923699 \tabularnewline
71 & 8 & 7.4906411851382 & 0.509358814861799 \tabularnewline
72 & 7.7 & 7.90773907569657 & -0.207739075696574 \tabularnewline
73 & 7.3 & 7.62956428497662 & -0.329564284976617 \tabularnewline
74 & 7 & 7.29158295953942 & -0.291582959539415 \tabularnewline
75 & 7 & 7.10876729056802 & -0.108767290568024 \tabularnewline
76 & 7.3 & 7.13232556339816 & 0.167674436601842 \tabularnewline
77 & 7.3 & 7.28434220762091 & 0.015657792379093 \tabularnewline
78 & 7.1 & 7.22068563046015 & -0.120685630460152 \tabularnewline
79 & 7.1 & 7.04202918053389 & 0.0579708194661066 \tabularnewline
80 & 7 & 6.93232263118039 & 0.0676773688196102 \tabularnewline
81 & 7 & 6.82371072363684 & 0.176289276363163 \tabularnewline
82 & 7.5 & 7.31582202240183 & 0.184177977598173 \tabularnewline
83 & 7.8 & 7.31295387276449 & 0.487046127235505 \tabularnewline
84 & 7.9 & 7.66641915984146 & 0.233580840158544 \tabularnewline
85 & 8.1 & 7.80429195035179 & 0.295708049648205 \tabularnewline
86 & 8.3 & 8.07598733208444 & 0.224012667915565 \tabularnewline
87 & 8.4 & 8.418164072111 & -0.0181640721109968 \tabularnewline
88 & 8.6 & 8.57549373112206 & 0.0245062688779427 \tabularnewline
89 & 8.5 & 8.61288212525627 & -0.11288212525627 \tabularnewline
90 & 8.4 & 8.44699331560671 & -0.0469933156067146 \tabularnewline
91 & 8.3 & 8.37664490130972 & -0.0766449013097166 \tabularnewline
92 & 8 & 8.16697280961752 & -0.166972809617516 \tabularnewline
93 & 8 & 7.86650117276863 & 0.133498827231366 \tabularnewline
94 & 8.7 & 8.33970881465806 & 0.360291185341939 \tabularnewline
95 & 8.7 & 8.54470421858688 & 0.15529578141312 \tabularnewline
96 & 8.6 & 8.58923616394769 & 0.0107638360523126 \tabularnewline
97 & 8.5 & 8.53593925333094 & -0.0359392533309411 \tabularnewline
98 & 8.5 & 8.5001586528228 & -0.000158652822795702 \tabularnewline
99 & 8.6 & 8.62109717738795 & -0.0210971773879507 \tabularnewline
100 & 8.8 & 8.78231792057064 & 0.017682079429358 \tabularnewline
101 & 8.7 & 8.80866266600254 & -0.108662666002544 \tabularnewline
102 & 8.6 & 8.65476698109196 & -0.0547669810919587 \tabularnewline
103 & 8.4 & 8.57910004941468 & -0.17910004941468 \tabularnewline
104 & 8.1 & 8.26970526353065 & -0.169705263530652 \tabularnewline
105 & 8.1 & 7.98723041504178 & 0.112769584958217 \tabularnewline
106 & 8.7 & 8.45661552910718 & 0.243384470892824 \tabularnewline
107 & 8.7 & 8.53871528736307 & 0.161284712636929 \tabularnewline
108 & 8.6 & 8.57948370578433 & 0.0205162942156658 \tabularnewline
109 & 8.6 & 8.53219275186584 & 0.0678072481341569 \tabularnewline
110 & 8.5 & 8.59755251146379 & -0.097552511463789 \tabularnewline
111 & 8.6 & 8.62570414885385 & -0.0257041488538459 \tabularnewline
112 & 8.8 & 8.7847924109423 & 0.0152075890577041 \tabularnewline
113 & 8.8 & 8.80072369434251 & -0.000723694342507741 \tabularnewline
114 & 8.7 & 8.7530858826074 & -0.0530858826074034 \tabularnewline
115 & 8.5 & 8.67298708137609 & -0.172987081376089 \tabularnewline
116 & 8.3 & 8.37171737605514 & -0.0717173760551386 \tabularnewline
117 & 8.3 & 8.20222758207436 & 0.0977724179256452 \tabularnewline
118 & 8.9 & 8.66893460472659 & 0.231065395273406 \tabularnewline
119 & 9 & 8.73746071966744 & 0.262539280332557 \tabularnewline
120 & 8.8 & 8.86936021979512 & -0.069360219795124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286027&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]8[/C][C]8.32793803418804[/C][C]-0.327938034188035[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.90497175731061[/C][C]-0.00497175731060828[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.89736027548569[/C][C]0.00263972451431016[/C][/ROW]
[ROW][C]16[/C][C]8[/C][C]8.00110223232644[/C][C]-0.00110223232643669[/C][/ROW]
[ROW][C]17[/C][C]8[/C][C]8.0013145219392[/C][C]-0.00131452193920367[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]7.91797085913358[/C][C]-0.0179708591335785[/C][/ROW]
[ROW][C]19[/C][C]8[/C][C]7.82284901264789[/C][C]0.177150987352108[/C][/ROW]
[ROW][C]20[/C][C]7.7[/C][C]7.77225126009819[/C][C]-0.0722512600981942[/C][/ROW]
[ROW][C]21[/C][C]7.2[/C][C]7.39058874843145[/C][C]-0.190588748431447[/C][/ROW]
[ROW][C]22[/C][C]7.5[/C][C]7.40285270643191[/C][C]0.0971472935680859[/C][/ROW]
[ROW][C]23[/C][C]7.3[/C][C]7.39091690098008[/C][C]-0.0909169009800781[/C][/ROW]
[ROW][C]24[/C][C]7[/C][C]7.30095144892693[/C][C]-0.300951448926925[/C][/ROW]
[ROW][C]25[/C][C]7[/C][C]6.87993054242382[/C][C]0.120069457576177[/C][/ROW]
[ROW][C]26[/C][C]7[/C][C]6.89216138968448[/C][C]0.107838610315518[/C][/ROW]
[ROW][C]27[/C][C]7.2[/C][C]6.98779598257542[/C][C]0.212204017424579[/C][/ROW]
[ROW][C]28[/C][C]7.3[/C][C]7.28858063633854[/C][C]0.0114193636614557[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.30145138370241[/C][C]-0.201451383702408[/C][/ROW]
[ROW][C]30[/C][C]6.8[/C][C]7.02669578236869[/C][C]-0.226695782368691[/C][/ROW]
[ROW][C]31[/C][C]6.4[/C][C]6.7415058467194[/C][C]-0.341505846719401[/C][/ROW]
[ROW][C]32[/C][C]6.1[/C][C]6.17329547834675[/C][C]-0.0732954783467523[/C][/ROW]
[ROW][C]33[/C][C]6.5[/C][C]5.76764986288655[/C][C]0.732350137113452[/C][/ROW]
[ROW][C]34[/C][C]7.7[/C][C]6.66429844587002[/C][C]1.03570155412998[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.53866883436866[/C][C]0.361331165631345[/C][/ROW]
[ROW][C]36[/C][C]7.5[/C][C]7.88557207628031[/C][C]-0.385572076280313[/C][/ROW]
[ROW][C]37[/C][C]6.9[/C][C]7.43544568758262[/C][C]-0.535445687582619[/C][/ROW]
[ROW][C]38[/C][C]6.6[/C][C]6.84449574591924[/C][C]-0.244495745919239[/C][/ROW]
[ROW][C]39[/C][C]6.9[/C][C]6.62226659549342[/C][C]0.277733404506581[/C][/ROW]
[ROW][C]40[/C][C]7.7[/C][C]6.97939825749841[/C][C]0.720601742501591[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]7.66428890084492[/C][C]0.335711099155082[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]7.92142907724002[/C][C]0.0785709227599805[/C][/ROW]
[ROW][C]43[/C][C]7.7[/C][C]7.95051818318901[/C][C]-0.250518183189011[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]7.52096398337783[/C][C]-0.220963983377835[/C][/ROW]
[ROW][C]45[/C][C]7.4[/C][C]7.06079413106466[/C][C]0.339205868935344[/C][/ROW]
[ROW][C]46[/C][C]8.1[/C][C]7.63449546996107[/C][C]0.465504530038928[/C][/ROW]
[ROW][C]47[/C][C]8.3[/C][C]7.9490380757318[/C][C]0.350961924268196[/C][/ROW]
[ROW][C]48[/C][C]8.1[/C][C]8.25655215162804[/C][C]-0.156552151628036[/C][/ROW]
[ROW][C]49[/C][C]7.9[/C][C]8.0326906628778[/C][C]-0.132690662877801[/C][/ROW]
[ROW][C]50[/C][C]7.9[/C][C]7.86549641075155[/C][C]0.0345035892484544[/C][/ROW]
[ROW][C]51[/C][C]8.3[/C][C]7.97026376071118[/C][C]0.329736239288819[/C][/ROW]
[ROW][C]52[/C][C]8.6[/C][C]8.43747754746684[/C][C]0.162522452533159[/C][/ROW]
[ROW][C]53[/C][C]8.7[/C][C]8.59890017088943[/C][C]0.101099829110574[/C][/ROW]
[ROW][C]54[/C][C]8.5[/C][C]8.63971411194058[/C][C]-0.139714111940583[/C][/ROW]
[ROW][C]55[/C][C]8.3[/C][C]8.45942973799955[/C][C]-0.159429737999551[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]8.1345578295669[/C][C]-0.134557829566901[/C][/ROW]
[ROW][C]57[/C][C]8[/C][C]7.80911842343228[/C][C]0.190881576567718[/C][/ROW]
[ROW][C]58[/C][C]8.8[/C][C]8.26782325640695[/C][C]0.53217674359305[/C][/ROW]
[ROW][C]59[/C][C]8.7[/C][C]8.65529715368021[/C][C]0.044702846319792[/C][/ROW]
[ROW][C]60[/C][C]8.5[/C][C]8.65609594808124[/C][C]-0.156095948081235[/C][/ROW]
[ROW][C]61[/C][C]8.1[/C][C]8.44617066377972[/C][C]-0.346170663779723[/C][/ROW]
[ROW][C]62[/C][C]7.8[/C][C]8.09731077815307[/C][C]-0.297310778153073[/C][/ROW]
[ROW][C]63[/C][C]7.7[/C][C]7.9114227243601[/C][C]-0.211422724360104[/C][/ROW]
[ROW][C]64[/C][C]7.5[/C][C]7.85327464913215[/C][C]-0.353274649132148[/C][/ROW]
[ROW][C]65[/C][C]7.2[/C][C]7.51046624486727[/C][C]-0.310466244867275[/C][/ROW]
[ROW][C]66[/C][C]6.9[/C][C]7.12634200620343[/C][C]-0.22634200620343[/C][/ROW]
[ROW][C]67[/C][C]6.6[/C][C]6.83807192389334[/C][C]-0.238071923893338[/C][/ROW]
[ROW][C]68[/C][C]6.5[/C][C]6.41406384349819[/C][C]0.0859361565018126[/C][/ROW]
[ROW][C]69[/C][C]6.6[/C][C]6.29265341562171[/C][C]0.307346584378288[/C][/ROW]
[ROW][C]70[/C][C]7.7[/C][C]6.8608718670763[/C][C]0.839128132923699[/C][/ROW]
[ROW][C]71[/C][C]8[/C][C]7.4906411851382[/C][C]0.509358814861799[/C][/ROW]
[ROW][C]72[/C][C]7.7[/C][C]7.90773907569657[/C][C]-0.207739075696574[/C][/ROW]
[ROW][C]73[/C][C]7.3[/C][C]7.62956428497662[/C][C]-0.329564284976617[/C][/ROW]
[ROW][C]74[/C][C]7[/C][C]7.29158295953942[/C][C]-0.291582959539415[/C][/ROW]
[ROW][C]75[/C][C]7[/C][C]7.10876729056802[/C][C]-0.108767290568024[/C][/ROW]
[ROW][C]76[/C][C]7.3[/C][C]7.13232556339816[/C][C]0.167674436601842[/C][/ROW]
[ROW][C]77[/C][C]7.3[/C][C]7.28434220762091[/C][C]0.015657792379093[/C][/ROW]
[ROW][C]78[/C][C]7.1[/C][C]7.22068563046015[/C][C]-0.120685630460152[/C][/ROW]
[ROW][C]79[/C][C]7.1[/C][C]7.04202918053389[/C][C]0.0579708194661066[/C][/ROW]
[ROW][C]80[/C][C]7[/C][C]6.93232263118039[/C][C]0.0676773688196102[/C][/ROW]
[ROW][C]81[/C][C]7[/C][C]6.82371072363684[/C][C]0.176289276363163[/C][/ROW]
[ROW][C]82[/C][C]7.5[/C][C]7.31582202240183[/C][C]0.184177977598173[/C][/ROW]
[ROW][C]83[/C][C]7.8[/C][C]7.31295387276449[/C][C]0.487046127235505[/C][/ROW]
[ROW][C]84[/C][C]7.9[/C][C]7.66641915984146[/C][C]0.233580840158544[/C][/ROW]
[ROW][C]85[/C][C]8.1[/C][C]7.80429195035179[/C][C]0.295708049648205[/C][/ROW]
[ROW][C]86[/C][C]8.3[/C][C]8.07598733208444[/C][C]0.224012667915565[/C][/ROW]
[ROW][C]87[/C][C]8.4[/C][C]8.418164072111[/C][C]-0.0181640721109968[/C][/ROW]
[ROW][C]88[/C][C]8.6[/C][C]8.57549373112206[/C][C]0.0245062688779427[/C][/ROW]
[ROW][C]89[/C][C]8.5[/C][C]8.61288212525627[/C][C]-0.11288212525627[/C][/ROW]
[ROW][C]90[/C][C]8.4[/C][C]8.44699331560671[/C][C]-0.0469933156067146[/C][/ROW]
[ROW][C]91[/C][C]8.3[/C][C]8.37664490130972[/C][C]-0.0766449013097166[/C][/ROW]
[ROW][C]92[/C][C]8[/C][C]8.16697280961752[/C][C]-0.166972809617516[/C][/ROW]
[ROW][C]93[/C][C]8[/C][C]7.86650117276863[/C][C]0.133498827231366[/C][/ROW]
[ROW][C]94[/C][C]8.7[/C][C]8.33970881465806[/C][C]0.360291185341939[/C][/ROW]
[ROW][C]95[/C][C]8.7[/C][C]8.54470421858688[/C][C]0.15529578141312[/C][/ROW]
[ROW][C]96[/C][C]8.6[/C][C]8.58923616394769[/C][C]0.0107638360523126[/C][/ROW]
[ROW][C]97[/C][C]8.5[/C][C]8.53593925333094[/C][C]-0.0359392533309411[/C][/ROW]
[ROW][C]98[/C][C]8.5[/C][C]8.5001586528228[/C][C]-0.000158652822795702[/C][/ROW]
[ROW][C]99[/C][C]8.6[/C][C]8.62109717738795[/C][C]-0.0210971773879507[/C][/ROW]
[ROW][C]100[/C][C]8.8[/C][C]8.78231792057064[/C][C]0.017682079429358[/C][/ROW]
[ROW][C]101[/C][C]8.7[/C][C]8.80866266600254[/C][C]-0.108662666002544[/C][/ROW]
[ROW][C]102[/C][C]8.6[/C][C]8.65476698109196[/C][C]-0.0547669810919587[/C][/ROW]
[ROW][C]103[/C][C]8.4[/C][C]8.57910004941468[/C][C]-0.17910004941468[/C][/ROW]
[ROW][C]104[/C][C]8.1[/C][C]8.26970526353065[/C][C]-0.169705263530652[/C][/ROW]
[ROW][C]105[/C][C]8.1[/C][C]7.98723041504178[/C][C]0.112769584958217[/C][/ROW]
[ROW][C]106[/C][C]8.7[/C][C]8.45661552910718[/C][C]0.243384470892824[/C][/ROW]
[ROW][C]107[/C][C]8.7[/C][C]8.53871528736307[/C][C]0.161284712636929[/C][/ROW]
[ROW][C]108[/C][C]8.6[/C][C]8.57948370578433[/C][C]0.0205162942156658[/C][/ROW]
[ROW][C]109[/C][C]8.6[/C][C]8.53219275186584[/C][C]0.0678072481341569[/C][/ROW]
[ROW][C]110[/C][C]8.5[/C][C]8.59755251146379[/C][C]-0.097552511463789[/C][/ROW]
[ROW][C]111[/C][C]8.6[/C][C]8.62570414885385[/C][C]-0.0257041488538459[/C][/ROW]
[ROW][C]112[/C][C]8.8[/C][C]8.7847924109423[/C][C]0.0152075890577041[/C][/ROW]
[ROW][C]113[/C][C]8.8[/C][C]8.80072369434251[/C][C]-0.000723694342507741[/C][/ROW]
[ROW][C]114[/C][C]8.7[/C][C]8.7530858826074[/C][C]-0.0530858826074034[/C][/ROW]
[ROW][C]115[/C][C]8.5[/C][C]8.67298708137609[/C][C]-0.172987081376089[/C][/ROW]
[ROW][C]116[/C][C]8.3[/C][C]8.37171737605514[/C][C]-0.0717173760551386[/C][/ROW]
[ROW][C]117[/C][C]8.3[/C][C]8.20222758207436[/C][C]0.0977724179256452[/C][/ROW]
[ROW][C]118[/C][C]8.9[/C][C]8.66893460472659[/C][C]0.231065395273406[/C][/ROW]
[ROW][C]119[/C][C]9[/C][C]8.73746071966744[/C][C]0.262539280332557[/C][/ROW]
[ROW][C]120[/C][C]8.8[/C][C]8.86936021979512[/C][C]-0.069360219795124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286027&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286027&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
1388.32793803418804-0.327938034188035
147.97.90497175731061-0.00497175731060828
157.97.897360275485690.00263972451431016
1688.00110223232644-0.00110223232643669
1788.0013145219392-0.00131452193920367
187.97.91797085913358-0.0179708591335785
1987.822849012647890.177150987352108
207.77.77225126009819-0.0722512600981942
217.27.39058874843145-0.190588748431447
227.57.402852706431910.0971472935680859
237.37.39091690098008-0.0909169009800781
2477.30095144892693-0.300951448926925
2576.879930542423820.120069457576177
2676.892161389684480.107838610315518
277.26.987795982575420.212204017424579
287.37.288580636338540.0114193636614557
297.17.30145138370241-0.201451383702408
306.87.02669578236869-0.226695782368691
316.46.7415058467194-0.341505846719401
326.16.17329547834675-0.0732954783467523
336.55.767649862886550.732350137113452
347.76.664298445870021.03570155412998
357.97.538668834368660.361331165631345
367.57.88557207628031-0.385572076280313
376.97.43544568758262-0.535445687582619
386.66.84449574591924-0.244495745919239
396.96.622266595493420.277733404506581
407.76.979398257498410.720601742501591
4187.664288900844920.335711099155082
4287.921429077240020.0785709227599805
437.77.95051818318901-0.250518183189011
447.37.52096398337783-0.220963983377835
457.47.060794131064660.339205868935344
468.17.634495469961070.465504530038928
478.37.94903807573180.350961924268196
488.18.25655215162804-0.156552151628036
497.98.0326906628778-0.132690662877801
507.97.865496410751550.0345035892484544
518.37.970263760711180.329736239288819
528.68.437477547466840.162522452533159
538.78.598900170889430.101099829110574
548.58.63971411194058-0.139714111940583
558.38.45942973799955-0.159429737999551
5688.1345578295669-0.134557829566901
5787.809118423432280.190881576567718
588.88.267823256406950.53217674359305
598.78.655297153680210.044702846319792
608.58.65609594808124-0.156095948081235
618.18.44617066377972-0.346170663779723
627.88.09731077815307-0.297310778153073
637.77.9114227243601-0.211422724360104
647.57.85327464913215-0.353274649132148
657.27.51046624486727-0.310466244867275
666.97.12634200620343-0.22634200620343
676.66.83807192389334-0.238071923893338
686.56.414063843498190.0859361565018126
696.66.292653415621710.307346584378288
707.76.86087186707630.839128132923699
7187.49064118513820.509358814861799
727.77.90773907569657-0.207739075696574
737.37.62956428497662-0.329564284976617
7477.29158295953942-0.291582959539415
7577.10876729056802-0.108767290568024
767.37.132325563398160.167674436601842
777.37.284342207620910.015657792379093
787.17.22068563046015-0.120685630460152
797.17.042029180533890.0579708194661066
8076.932322631180390.0676773688196102
8176.823710723636840.176289276363163
827.57.315822022401830.184177977598173
837.87.312953872764490.487046127235505
847.97.666419159841460.233580840158544
858.17.804291950351790.295708049648205
868.38.075987332084440.224012667915565
878.48.418164072111-0.0181640721109968
888.68.575493731122060.0245062688779427
898.58.61288212525627-0.11288212525627
908.48.44699331560671-0.0469933156067146
918.38.37664490130972-0.0766449013097166
9288.16697280961752-0.166972809617516
9387.866501172768630.133498827231366
948.78.339708814658060.360291185341939
958.78.544704218586880.15529578141312
968.68.589236163947690.0107638360523126
978.58.53593925333094-0.0359392533309411
988.58.5001586528228-0.000158652822795702
998.68.62109717738795-0.0210971773879507
1008.88.782317920570640.017682079429358
1018.78.80866266600254-0.108662666002544
1028.68.65476698109196-0.0547669810919587
1038.48.57910004941468-0.17910004941468
1048.18.26970526353065-0.169705263530652
1058.17.987230415041780.112769584958217
1068.78.456615529107180.243384470892824
1078.78.538715287363070.161284712636929
1088.68.579483705784330.0205162942156658
1098.68.532192751865840.0678072481341569
1108.58.59755251146379-0.097552511463789
1118.68.62570414885385-0.0257041488538459
1128.88.78479241094230.0152075890577041
1138.88.80072369434251-0.000723694342507741
1148.78.7530858826074-0.0530858826074034
1158.58.67298708137609-0.172987081376089
1168.38.37171737605514-0.0717173760551386
1178.38.202227582074360.0977724179256452
1188.98.668934604726590.231065395273406
11998.737460719667440.262539280332557
1208.88.86936021979512-0.069360219795124







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1218.74397148037468.221488528338369.26645443241083
1228.737539286885568.014755339360479.46032323441064
1238.865456315737.981568239903889.74934439155611
1249.055457307952948.0309148372144410.0799997786914
1259.060130146204117.9077940763470910.2124662160611
1269.013931855896537.7427096435973510.2851540681957
1278.981150010756237.5975879009793110.3647121205331
1288.856468073136017.3655732527641510.3473628935079
1298.774085634841587.1797989522583810.3683723174248
1309.164926659030847.4704159786344610.8594373394272
1319.022115901515197.229968871728610.8142629313018
1328.88593658947876.9982930931414810.7735800858159

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 8.7439714803746 & 8.22148852833836 & 9.26645443241083 \tabularnewline
122 & 8.73753928688556 & 8.01475533936047 & 9.46032323441064 \tabularnewline
123 & 8.86545631573 & 7.98156823990388 & 9.74934439155611 \tabularnewline
124 & 9.05545730795294 & 8.03091483721444 & 10.0799997786914 \tabularnewline
125 & 9.06013014620411 & 7.90779407634709 & 10.2124662160611 \tabularnewline
126 & 9.01393185589653 & 7.74270964359735 & 10.2851540681957 \tabularnewline
127 & 8.98115001075623 & 7.59758790097931 & 10.3647121205331 \tabularnewline
128 & 8.85646807313601 & 7.36557325276415 & 10.3473628935079 \tabularnewline
129 & 8.77408563484158 & 7.17979895225838 & 10.3683723174248 \tabularnewline
130 & 9.16492665903084 & 7.47041597863446 & 10.8594373394272 \tabularnewline
131 & 9.02211590151519 & 7.2299688717286 & 10.8142629313018 \tabularnewline
132 & 8.8859365894787 & 6.99829309314148 & 10.7735800858159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286027&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]121[/C][C]8.7439714803746[/C][C]8.22148852833836[/C][C]9.26645443241083[/C][/ROW]
[ROW][C]122[/C][C]8.73753928688556[/C][C]8.01475533936047[/C][C]9.46032323441064[/C][/ROW]
[ROW][C]123[/C][C]8.86545631573[/C][C]7.98156823990388[/C][C]9.74934439155611[/C][/ROW]
[ROW][C]124[/C][C]9.05545730795294[/C][C]8.03091483721444[/C][C]10.0799997786914[/C][/ROW]
[ROW][C]125[/C][C]9.06013014620411[/C][C]7.90779407634709[/C][C]10.2124662160611[/C][/ROW]
[ROW][C]126[/C][C]9.01393185589653[/C][C]7.74270964359735[/C][C]10.2851540681957[/C][/ROW]
[ROW][C]127[/C][C]8.98115001075623[/C][C]7.59758790097931[/C][C]10.3647121205331[/C][/ROW]
[ROW][C]128[/C][C]8.85646807313601[/C][C]7.36557325276415[/C][C]10.3473628935079[/C][/ROW]
[ROW][C]129[/C][C]8.77408563484158[/C][C]7.17979895225838[/C][C]10.3683723174248[/C][/ROW]
[ROW][C]130[/C][C]9.16492665903084[/C][C]7.47041597863446[/C][C]10.8594373394272[/C][/ROW]
[ROW][C]131[/C][C]9.02211590151519[/C][C]7.2299688717286[/C][C]10.8142629313018[/C][/ROW]
[ROW][C]132[/C][C]8.8859365894787[/C][C]6.99829309314148[/C][C]10.7735800858159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286027&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286027&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
1218.74397148037468.221488528338369.26645443241083
1228.737539286885568.014755339360479.46032323441064
1238.865456315737.981568239903889.74934439155611
1249.055457307952948.0309148372144410.0799997786914
1259.060130146204117.9077940763470910.2124662160611
1269.013931855896537.7427096435973510.2851540681957
1278.981150010756237.5975879009793110.3647121205331
1288.856468073136017.3655732527641510.3473628935079
1298.774085634841587.1797989522583810.3683723174248
1309.164926659030847.4704159786344610.8594373394272
1319.022115901515197.229968871728610.8142629313018
1328.88593658947876.9982930931414810.7735800858159



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')