Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Aug 2010 19:54:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/16/t1281988470340uuhfym87m2a1.htm/, Retrieved Thu, 16 May 2024 12:34:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79043, Retrieved Thu, 16 May 2024 12:34:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDe Cock Nicola
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2010-08-16 19:54:13] [c2fbba04702f7f714f5f9c5d7ee07bac] [Current]
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Dataseries X:
76
75
74
72
70
69
70
72
73
73
74
76
74
67
66
58
55
58
64
68
66
76
75
88
85
83
77
66
65
65
63
62
57
68
69
79
74
76
82
75
75
76
78
77
67
74
68
87
76
88
95
96
96
105
108
113
101
107
102
116
105
121
134
140
131
141
131
128
123
129
125
144
135
141
156
159
146
154
145
133
126
127
122
148




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79043&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79043&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.796773318034331
beta0.0131562838165992
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.796773318034331 \tabularnewline
beta & 0.0131562838165992 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79043&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]0.796773318034331[/C][/ROW]
[ROW][C]beta[/C][C]0.0131562838165992[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79043&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
alpha0.796773318034331
beta0.0131562838165992
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137479.5803952991453-5.58039529914534
146767.9006174409027-0.900617440902664
156665.98178759041250.0182124095874769
165857.50358109490570.496418905094266
175554.07826719105170.921732808948285
185856.62649419171571.3735058082843
196463.75741307628990.242586923710114
206865.73978890461672.26021109538333
216668.6034466731327-2.60344667313272
227666.81458087626729.18541912373277
237575.806722316124-0.806722316123938
248877.70393553876110.296064461239
258583.04639707800771.95360292199234
268378.55576092748444.44423907251557
277781.3735259620734-4.37352596207342
286669.7384721854195-3.73847218541947
296563.22614097581541.77385902418457
306566.7548600002482-1.75486000024823
316371.3402825192019-8.3402825192019
326266.9810564008034-4.98105640080344
335763.0976976245827-6.09769762458272
346860.89494644776197.10505355223808
356966.15145923255842.84854076744156
367973.20840851527285.79159148472721
377473.21013436443270.789865635567338
387668.2299471187477.77005288125302
398271.872009825274910.1279901747251
407572.03883339179232.96116660820775
417572.17347420968932.8265257903107
427676.0234606411593-0.0234606411592608
437880.8678924035702-2.86789240357020
447781.8267798371326-4.82677983713259
456778.116205179314-11.116205179314
467474.822177474344-0.822177474343988
476873.0385343936094-5.03853439360944
488774.467789471059712.5322105289403
497678.9528460323263-2.95284603232629
508872.498962485911115.5010375140889
519582.950940075624912.0490599243751
529683.382945579741212.6170544202588
539691.47601073115064.52398926884938
5410596.40932444392628.5906755560738
55108107.9395309530190.060469046980586
56113111.2645825296361.73541747036437
57101112.004223348916-11.0042233489161
58107111.392425529664-4.39242552966425
59102106.370787093354-4.37078709335414
60116112.3734885652283.62651143477159
61105106.992949350156-1.99294935015591
62121105.44147388585315.5585261141473
63134115.62559203019118.3744079698090
64140121.66707278578818.3329272142123
65131133.183758226321-2.18375822632143
66141134.0427545345586.95724546544227
67131142.964577073295-11.9645770732949
68128137.349388612978-9.34938861297812
69123126.852321104405-3.85232110440545
70129133.542036585655-4.54203658565527
71125128.663395936463-3.66339593646279
72144137.1202139106216.87978608937868
73135133.4890971238421.51090287615850
74141138.6323794999732.36762050002744
75156139.07637742114816.9236225788518
76159144.13605220726514.8639477927345
77146148.865416773383-2.86541677338283
78154151.17804332842.82195667159999
79145153.055272142834-8.0552721428335
80133151.223082462648-18.2230824626477
81126134.816516929158-8.8165169291583
82127137.402361160027-10.4023611600268
83122127.963138298558-5.96313829855828
84148136.63633641666311.3636635833369

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 74 & 79.5803952991453 & -5.58039529914534 \tabularnewline
14 & 67 & 67.9006174409027 & -0.900617440902664 \tabularnewline
15 & 66 & 65.9817875904125 & 0.0182124095874769 \tabularnewline
16 & 58 & 57.5035810949057 & 0.496418905094266 \tabularnewline
17 & 55 & 54.0782671910517 & 0.921732808948285 \tabularnewline
18 & 58 & 56.6264941917157 & 1.3735058082843 \tabularnewline
19 & 64 & 63.7574130762899 & 0.242586923710114 \tabularnewline
20 & 68 & 65.7397889046167 & 2.26021109538333 \tabularnewline
21 & 66 & 68.6034466731327 & -2.60344667313272 \tabularnewline
22 & 76 & 66.8145808762672 & 9.18541912373277 \tabularnewline
23 & 75 & 75.806722316124 & -0.806722316123938 \tabularnewline
24 & 88 & 77.703935538761 & 10.296064461239 \tabularnewline
25 & 85 & 83.0463970780077 & 1.95360292199234 \tabularnewline
26 & 83 & 78.5557609274844 & 4.44423907251557 \tabularnewline
27 & 77 & 81.3735259620734 & -4.37352596207342 \tabularnewline
28 & 66 & 69.7384721854195 & -3.73847218541947 \tabularnewline
29 & 65 & 63.2261409758154 & 1.77385902418457 \tabularnewline
30 & 65 & 66.7548600002482 & -1.75486000024823 \tabularnewline
31 & 63 & 71.3402825192019 & -8.3402825192019 \tabularnewline
32 & 62 & 66.9810564008034 & -4.98105640080344 \tabularnewline
33 & 57 & 63.0976976245827 & -6.09769762458272 \tabularnewline
34 & 68 & 60.8949464477619 & 7.10505355223808 \tabularnewline
35 & 69 & 66.1514592325584 & 2.84854076744156 \tabularnewline
36 & 79 & 73.2084085152728 & 5.79159148472721 \tabularnewline
37 & 74 & 73.2101343644327 & 0.789865635567338 \tabularnewline
38 & 76 & 68.229947118747 & 7.77005288125302 \tabularnewline
39 & 82 & 71.8720098252749 & 10.1279901747251 \tabularnewline
40 & 75 & 72.0388333917923 & 2.96116660820775 \tabularnewline
41 & 75 & 72.1734742096893 & 2.8265257903107 \tabularnewline
42 & 76 & 76.0234606411593 & -0.0234606411592608 \tabularnewline
43 & 78 & 80.8678924035702 & -2.86789240357020 \tabularnewline
44 & 77 & 81.8267798371326 & -4.82677983713259 \tabularnewline
45 & 67 & 78.116205179314 & -11.116205179314 \tabularnewline
46 & 74 & 74.822177474344 & -0.822177474343988 \tabularnewline
47 & 68 & 73.0385343936094 & -5.03853439360944 \tabularnewline
48 & 87 & 74.4677894710597 & 12.5322105289403 \tabularnewline
49 & 76 & 78.9528460323263 & -2.95284603232629 \tabularnewline
50 & 88 & 72.4989624859111 & 15.5010375140889 \tabularnewline
51 & 95 & 82.9509400756249 & 12.0490599243751 \tabularnewline
52 & 96 & 83.3829455797412 & 12.6170544202588 \tabularnewline
53 & 96 & 91.4760107311506 & 4.52398926884938 \tabularnewline
54 & 105 & 96.4093244439262 & 8.5906755560738 \tabularnewline
55 & 108 & 107.939530953019 & 0.060469046980586 \tabularnewline
56 & 113 & 111.264582529636 & 1.73541747036437 \tabularnewline
57 & 101 & 112.004223348916 & -11.0042233489161 \tabularnewline
58 & 107 & 111.392425529664 & -4.39242552966425 \tabularnewline
59 & 102 & 106.370787093354 & -4.37078709335414 \tabularnewline
60 & 116 & 112.373488565228 & 3.62651143477159 \tabularnewline
61 & 105 & 106.992949350156 & -1.99294935015591 \tabularnewline
62 & 121 & 105.441473885853 & 15.5585261141473 \tabularnewline
63 & 134 & 115.625592030191 & 18.3744079698090 \tabularnewline
64 & 140 & 121.667072785788 & 18.3329272142123 \tabularnewline
65 & 131 & 133.183758226321 & -2.18375822632143 \tabularnewline
66 & 141 & 134.042754534558 & 6.95724546544227 \tabularnewline
67 & 131 & 142.964577073295 & -11.9645770732949 \tabularnewline
68 & 128 & 137.349388612978 & -9.34938861297812 \tabularnewline
69 & 123 & 126.852321104405 & -3.85232110440545 \tabularnewline
70 & 129 & 133.542036585655 & -4.54203658565527 \tabularnewline
71 & 125 & 128.663395936463 & -3.66339593646279 \tabularnewline
72 & 144 & 137.120213910621 & 6.87978608937868 \tabularnewline
73 & 135 & 133.489097123842 & 1.51090287615850 \tabularnewline
74 & 141 & 138.632379499973 & 2.36762050002744 \tabularnewline
75 & 156 & 139.076377421148 & 16.9236225788518 \tabularnewline
76 & 159 & 144.136052207265 & 14.8639477927345 \tabularnewline
77 & 146 & 148.865416773383 & -2.86541677338283 \tabularnewline
78 & 154 & 151.1780433284 & 2.82195667159999 \tabularnewline
79 & 145 & 153.055272142834 & -8.0552721428335 \tabularnewline
80 & 133 & 151.223082462648 & -18.2230824626477 \tabularnewline
81 & 126 & 134.816516929158 & -8.8165169291583 \tabularnewline
82 & 127 & 137.402361160027 & -10.4023611600268 \tabularnewline
83 & 122 & 127.963138298558 & -5.96313829855828 \tabularnewline
84 & 148 & 136.636336416663 & 11.3636635833369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79043&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]74[/C][C]79.5803952991453[/C][C]-5.58039529914534[/C][/ROW]
[ROW][C]14[/C][C]67[/C][C]67.9006174409027[/C][C]-0.900617440902664[/C][/ROW]
[ROW][C]15[/C][C]66[/C][C]65.9817875904125[/C][C]0.0182124095874769[/C][/ROW]
[ROW][C]16[/C][C]58[/C][C]57.5035810949057[/C][C]0.496418905094266[/C][/ROW]
[ROW][C]17[/C][C]55[/C][C]54.0782671910517[/C][C]0.921732808948285[/C][/ROW]
[ROW][C]18[/C][C]58[/C][C]56.6264941917157[/C][C]1.3735058082843[/C][/ROW]
[ROW][C]19[/C][C]64[/C][C]63.7574130762899[/C][C]0.242586923710114[/C][/ROW]
[ROW][C]20[/C][C]68[/C][C]65.7397889046167[/C][C]2.26021109538333[/C][/ROW]
[ROW][C]21[/C][C]66[/C][C]68.6034466731327[/C][C]-2.60344667313272[/C][/ROW]
[ROW][C]22[/C][C]76[/C][C]66.8145808762672[/C][C]9.18541912373277[/C][/ROW]
[ROW][C]23[/C][C]75[/C][C]75.806722316124[/C][C]-0.806722316123938[/C][/ROW]
[ROW][C]24[/C][C]88[/C][C]77.703935538761[/C][C]10.296064461239[/C][/ROW]
[ROW][C]25[/C][C]85[/C][C]83.0463970780077[/C][C]1.95360292199234[/C][/ROW]
[ROW][C]26[/C][C]83[/C][C]78.5557609274844[/C][C]4.44423907251557[/C][/ROW]
[ROW][C]27[/C][C]77[/C][C]81.3735259620734[/C][C]-4.37352596207342[/C][/ROW]
[ROW][C]28[/C][C]66[/C][C]69.7384721854195[/C][C]-3.73847218541947[/C][/ROW]
[ROW][C]29[/C][C]65[/C][C]63.2261409758154[/C][C]1.77385902418457[/C][/ROW]
[ROW][C]30[/C][C]65[/C][C]66.7548600002482[/C][C]-1.75486000024823[/C][/ROW]
[ROW][C]31[/C][C]63[/C][C]71.3402825192019[/C][C]-8.3402825192019[/C][/ROW]
[ROW][C]32[/C][C]62[/C][C]66.9810564008034[/C][C]-4.98105640080344[/C][/ROW]
[ROW][C]33[/C][C]57[/C][C]63.0976976245827[/C][C]-6.09769762458272[/C][/ROW]
[ROW][C]34[/C][C]68[/C][C]60.8949464477619[/C][C]7.10505355223808[/C][/ROW]
[ROW][C]35[/C][C]69[/C][C]66.1514592325584[/C][C]2.84854076744156[/C][/ROW]
[ROW][C]36[/C][C]79[/C][C]73.2084085152728[/C][C]5.79159148472721[/C][/ROW]
[ROW][C]37[/C][C]74[/C][C]73.2101343644327[/C][C]0.789865635567338[/C][/ROW]
[ROW][C]38[/C][C]76[/C][C]68.229947118747[/C][C]7.77005288125302[/C][/ROW]
[ROW][C]39[/C][C]82[/C][C]71.8720098252749[/C][C]10.1279901747251[/C][/ROW]
[ROW][C]40[/C][C]75[/C][C]72.0388333917923[/C][C]2.96116660820775[/C][/ROW]
[ROW][C]41[/C][C]75[/C][C]72.1734742096893[/C][C]2.8265257903107[/C][/ROW]
[ROW][C]42[/C][C]76[/C][C]76.0234606411593[/C][C]-0.0234606411592608[/C][/ROW]
[ROW][C]43[/C][C]78[/C][C]80.8678924035702[/C][C]-2.86789240357020[/C][/ROW]
[ROW][C]44[/C][C]77[/C][C]81.8267798371326[/C][C]-4.82677983713259[/C][/ROW]
[ROW][C]45[/C][C]67[/C][C]78.116205179314[/C][C]-11.116205179314[/C][/ROW]
[ROW][C]46[/C][C]74[/C][C]74.822177474344[/C][C]-0.822177474343988[/C][/ROW]
[ROW][C]47[/C][C]68[/C][C]73.0385343936094[/C][C]-5.03853439360944[/C][/ROW]
[ROW][C]48[/C][C]87[/C][C]74.4677894710597[/C][C]12.5322105289403[/C][/ROW]
[ROW][C]49[/C][C]76[/C][C]78.9528460323263[/C][C]-2.95284603232629[/C][/ROW]
[ROW][C]50[/C][C]88[/C][C]72.4989624859111[/C][C]15.5010375140889[/C][/ROW]
[ROW][C]51[/C][C]95[/C][C]82.9509400756249[/C][C]12.0490599243751[/C][/ROW]
[ROW][C]52[/C][C]96[/C][C]83.3829455797412[/C][C]12.6170544202588[/C][/ROW]
[ROW][C]53[/C][C]96[/C][C]91.4760107311506[/C][C]4.52398926884938[/C][/ROW]
[ROW][C]54[/C][C]105[/C][C]96.4093244439262[/C][C]8.5906755560738[/C][/ROW]
[ROW][C]55[/C][C]108[/C][C]107.939530953019[/C][C]0.060469046980586[/C][/ROW]
[ROW][C]56[/C][C]113[/C][C]111.264582529636[/C][C]1.73541747036437[/C][/ROW]
[ROW][C]57[/C][C]101[/C][C]112.004223348916[/C][C]-11.0042233489161[/C][/ROW]
[ROW][C]58[/C][C]107[/C][C]111.392425529664[/C][C]-4.39242552966425[/C][/ROW]
[ROW][C]59[/C][C]102[/C][C]106.370787093354[/C][C]-4.37078709335414[/C][/ROW]
[ROW][C]60[/C][C]116[/C][C]112.373488565228[/C][C]3.62651143477159[/C][/ROW]
[ROW][C]61[/C][C]105[/C][C]106.992949350156[/C][C]-1.99294935015591[/C][/ROW]
[ROW][C]62[/C][C]121[/C][C]105.441473885853[/C][C]15.5585261141473[/C][/ROW]
[ROW][C]63[/C][C]134[/C][C]115.625592030191[/C][C]18.3744079698090[/C][/ROW]
[ROW][C]64[/C][C]140[/C][C]121.667072785788[/C][C]18.3329272142123[/C][/ROW]
[ROW][C]65[/C][C]131[/C][C]133.183758226321[/C][C]-2.18375822632143[/C][/ROW]
[ROW][C]66[/C][C]141[/C][C]134.042754534558[/C][C]6.95724546544227[/C][/ROW]
[ROW][C]67[/C][C]131[/C][C]142.964577073295[/C][C]-11.9645770732949[/C][/ROW]
[ROW][C]68[/C][C]128[/C][C]137.349388612978[/C][C]-9.34938861297812[/C][/ROW]
[ROW][C]69[/C][C]123[/C][C]126.852321104405[/C][C]-3.85232110440545[/C][/ROW]
[ROW][C]70[/C][C]129[/C][C]133.542036585655[/C][C]-4.54203658565527[/C][/ROW]
[ROW][C]71[/C][C]125[/C][C]128.663395936463[/C][C]-3.66339593646279[/C][/ROW]
[ROW][C]72[/C][C]144[/C][C]137.120213910621[/C][C]6.87978608937868[/C][/ROW]
[ROW][C]73[/C][C]135[/C][C]133.489097123842[/C][C]1.51090287615850[/C][/ROW]
[ROW][C]74[/C][C]141[/C][C]138.632379499973[/C][C]2.36762050002744[/C][/ROW]
[ROW][C]75[/C][C]156[/C][C]139.076377421148[/C][C]16.9236225788518[/C][/ROW]
[ROW][C]76[/C][C]159[/C][C]144.136052207265[/C][C]14.8639477927345[/C][/ROW]
[ROW][C]77[/C][C]146[/C][C]148.865416773383[/C][C]-2.86541677338283[/C][/ROW]
[ROW][C]78[/C][C]154[/C][C]151.1780433284[/C][C]2.82195667159999[/C][/ROW]
[ROW][C]79[/C][C]145[/C][C]153.055272142834[/C][C]-8.0552721428335[/C][/ROW]
[ROW][C]80[/C][C]133[/C][C]151.223082462648[/C][C]-18.2230824626477[/C][/ROW]
[ROW][C]81[/C][C]126[/C][C]134.816516929158[/C][C]-8.8165169291583[/C][/ROW]
[ROW][C]82[/C][C]127[/C][C]137.402361160027[/C][C]-10.4023611600268[/C][/ROW]
[ROW][C]83[/C][C]122[/C][C]127.963138298558[/C][C]-5.96313829855828[/C][/ROW]
[ROW][C]84[/C][C]148[/C][C]136.636336416663[/C][C]11.3636635833369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79043&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79043&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
137479.5803952991453-5.58039529914534
146767.9006174409027-0.900617440902664
156665.98178759041250.0182124095874769
165857.50358109490570.496418905094266
175554.07826719105170.921732808948285
185856.62649419171571.3735058082843
196463.75741307628990.242586923710114
206865.73978890461672.26021109538333
216668.6034466731327-2.60344667313272
227666.81458087626729.18541912373277
237575.806722316124-0.806722316123938
248877.70393553876110.296064461239
258583.04639707800771.95360292199234
268378.55576092748444.44423907251557
277781.3735259620734-4.37352596207342
286669.7384721854195-3.73847218541947
296563.22614097581541.77385902418457
306566.7548600002482-1.75486000024823
316371.3402825192019-8.3402825192019
326266.9810564008034-4.98105640080344
335763.0976976245827-6.09769762458272
346860.89494644776197.10505355223808
356966.15145923255842.84854076744156
367973.20840851527285.79159148472721
377473.21013436443270.789865635567338
387668.2299471187477.77005288125302
398271.872009825274910.1279901747251
407572.03883339179232.96116660820775
417572.17347420968932.8265257903107
427676.0234606411593-0.0234606411592608
437880.8678924035702-2.86789240357020
447781.8267798371326-4.82677983713259
456778.116205179314-11.116205179314
467474.822177474344-0.822177474343988
476873.0385343936094-5.03853439360944
488774.467789471059712.5322105289403
497678.9528460323263-2.95284603232629
508872.498962485911115.5010375140889
519582.950940075624912.0490599243751
529683.382945579741212.6170544202588
539691.47601073115064.52398926884938
5410596.40932444392628.5906755560738
55108107.9395309530190.060469046980586
56113111.2645825296361.73541747036437
57101112.004223348916-11.0042233489161
58107111.392425529664-4.39242552966425
59102106.370787093354-4.37078709335414
60116112.3734885652283.62651143477159
61105106.992949350156-1.99294935015591
62121105.44147388585315.5585261141473
63134115.62559203019118.3744079698090
64140121.66707278578818.3329272142123
65131133.183758226321-2.18375822632143
66141134.0427545345586.95724546544227
67131142.964577073295-11.9645770732949
68128137.349388612978-9.34938861297812
69123126.852321104405-3.85232110440545
70129133.542036585655-4.54203658565527
71125128.663395936463-3.66339593646279
72144137.1202139106216.87978608937868
73135133.4890971238421.51090287615850
74141138.6323794999732.36762050002744
75156139.07637742114816.9236225788518
76159144.13605220726514.8639477927345
77146148.865416773383-2.86541677338283
78154151.17804332842.82195667159999
79145153.055272142834-8.0552721428335
80133151.223082462648-18.2230824626477
81126134.816516929158-8.8165169291583
82127137.402361160027-10.4023611600268
83122127.963138298558-5.96313829855828
84148136.63633641666311.3636635833369







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85135.439853439265120.095201830217150.784505048313
86139.490658625666119.770171825321159.211145426010
87140.918810976790117.544729318343164.292892635238
88131.810654082974105.205008806137158.416299359810
89120.67296936009091.1181499950518150.227788725129
90126.03377417538793.733922765828158.333625584945
91123.03168330915488.141981861168157.921384757140
92125.21547241029387.8581211625884162.572823657998
93125.09538592522785.3691550088904164.821616841564
94134.33127761784492.3176107314006176.344944504287
95134.13915852213389.906277246782178.372039797484
96151.204015049935104.809792228174197.598237871695

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 135.439853439265 & 120.095201830217 & 150.784505048313 \tabularnewline
86 & 139.490658625666 & 119.770171825321 & 159.211145426010 \tabularnewline
87 & 140.918810976790 & 117.544729318343 & 164.292892635238 \tabularnewline
88 & 131.810654082974 & 105.205008806137 & 158.416299359810 \tabularnewline
89 & 120.672969360090 & 91.1181499950518 & 150.227788725129 \tabularnewline
90 & 126.033774175387 & 93.733922765828 & 158.333625584945 \tabularnewline
91 & 123.031683309154 & 88.141981861168 & 157.921384757140 \tabularnewline
92 & 125.215472410293 & 87.8581211625884 & 162.572823657998 \tabularnewline
93 & 125.095385925227 & 85.3691550088904 & 164.821616841564 \tabularnewline
94 & 134.331277617844 & 92.3176107314006 & 176.344944504287 \tabularnewline
95 & 134.139158522133 & 89.906277246782 & 178.372039797484 \tabularnewline
96 & 151.204015049935 & 104.809792228174 & 197.598237871695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79043&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]135.439853439265[/C][C]120.095201830217[/C][C]150.784505048313[/C][/ROW]
[ROW][C]86[/C][C]139.490658625666[/C][C]119.770171825321[/C][C]159.211145426010[/C][/ROW]
[ROW][C]87[/C][C]140.918810976790[/C][C]117.544729318343[/C][C]164.292892635238[/C][/ROW]
[ROW][C]88[/C][C]131.810654082974[/C][C]105.205008806137[/C][C]158.416299359810[/C][/ROW]
[ROW][C]89[/C][C]120.672969360090[/C][C]91.1181499950518[/C][C]150.227788725129[/C][/ROW]
[ROW][C]90[/C][C]126.033774175387[/C][C]93.733922765828[/C][C]158.333625584945[/C][/ROW]
[ROW][C]91[/C][C]123.031683309154[/C][C]88.141981861168[/C][C]157.921384757140[/C][/ROW]
[ROW][C]92[/C][C]125.215472410293[/C][C]87.8581211625884[/C][C]162.572823657998[/C][/ROW]
[ROW][C]93[/C][C]125.095385925227[/C][C]85.3691550088904[/C][C]164.821616841564[/C][/ROW]
[ROW][C]94[/C][C]134.331277617844[/C][C]92.3176107314006[/C][C]176.344944504287[/C][/ROW]
[ROW][C]95[/C][C]134.139158522133[/C][C]89.906277246782[/C][C]178.372039797484[/C][/ROW]
[ROW][C]96[/C][C]151.204015049935[/C][C]104.809792228174[/C][C]197.598237871695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79043&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79043&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
85135.439853439265120.095201830217150.784505048313
86139.490658625666119.770171825321159.211145426010
87140.918810976790117.544729318343164.292892635238
88131.810654082974105.205008806137158.416299359810
89120.67296936009091.1181499950518150.227788725129
90126.03377417538793.733922765828158.333625584945
91123.03168330915488.141981861168157.921384757140
92125.21547241029387.8581211625884162.572823657998
93125.09538592522785.3691550088904164.821616841564
94134.33127761784492.3176107314006176.344944504287
95134.13915852213389.906277246782178.372039797484
96151.204015049935104.809792228174197.598237871695



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')