Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 24 Jul 2010 09:49:04 +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/Jul/24/t1279964958afz9h6cwly5yqfd.htm/, Retrieved Wed, 01 May 2024 23:06:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78086, Retrieved Wed, 01 May 2024 23:06:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsFebiri Lordina
Estimated Impact199
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Triple exponentia...] [2010-07-24 09:49:04] [ee335b92128d1ec04d3c346475765c6a] [Current]
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Dataseries X:
297
296
295
293
291
290
291
293
294
294
295
297
302
297
301
298
295
287
290
288
288
287
274
282
296
292
298
296
292
296
293
295
294
291
279
284
299
296
299
299
291
298
288
284
277
270
251
257
269
271
268
268
258
261
255
251
239
229
210
218
226
227
222
215
203
205
194
190
182
179
158
163
165
169
163
154
142
146
133
131
128
120
88
95




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78086&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78086&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78086&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.509341826247958
beta0.078544945072969
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.509341826247958 \tabularnewline
beta & 0.078544945072969 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78086&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]0.509341826247958[/C][/ROW]
[ROW][C]beta[/C][C]0.078544945072969[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78086&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78086&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
alpha0.509341826247958
beta0.078544945072969
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13302300.9997329059831.00026709401698
14297296.6262964501440.373703549856259
15301301.157008776380-0.157008776379655
16298298.494459121936-0.494459121936472
17295296.265250448955-1.2652504489551
18287288.926160952036-1.92616095203596
19290289.0067169959160.99328300408439
20288291.030672126812-3.03067212681174
21288289.842146182603-1.84214618260268
22287288.018622230618-1.01862223061840
23274287.657135574702-13.6571355747016
24282281.6452883352650.35471166473485
25296286.483574191769.51642580824029
26292285.6541361244406.34586387555964
27298292.7190358318555.28096416814458
28296292.6309679261273.36903207387326
29292292.116232999024-0.116232999024191
30296285.20890400887010.7910959911295
31293293.878908422203-0.878908422202755
32295293.579560817561.42043918244013
33294296.024073310026-2.0240733100257
34291295.28741810765-4.28741810764978
35279287.704498014518-8.7044980145182
36284291.933090849267-7.93309084926716
37299297.5565857064521.4434142935483
38296291.2478559006574.7521440993433
39299297.1030398252771.89696017472301
40299294.3424049122624.65759508773829
41291292.814618647480-1.81461864747968
42298290.3667583519137.63324164808733
43288291.548775999850-3.54877599984974
44284290.757359124645-6.75735912464529
45277286.758948099093-9.7589480990934
46270280.075075289218-10.0750752892178
47251266.248446905583-15.2484469055829
48257266.132095343942-9.1320953439423
49269274.307243558909-5.30724355890897
50271264.4752059432336.524794056767
51268268.194901603801-0.194901603800758
52268264.0021808820033.99781911799749
53258257.2151622069550.784837793044858
54261259.0834417803051.91655821969528
55255249.9949202646355.00507973536531
56251250.4559850103270.544014989673258
57239247.465778122548-8.46577812254827
58229240.099258407255-11.0992584072547
59210221.985437880254-11.9854378802537
60218225.435476083455-7.43547608345511
61226235.322718477454-9.3227184774538
62227228.061513740369-1.06151374036861
63222223.1272086282-1.12720862820001
64215218.986616247199-3.98661624719853
65203204.706686619467-1.70668661946675
66205203.911911474981.08808852501997
67194193.9343750716960.065624928304402
68190187.5106531131972.48934688680305
69182178.9883239883193.01167601168112
70179174.5325502127224.46744978727796
71158162.892396424216-4.8923964242164
72163171.451161439866-8.4511614398663
73165179.117916333114-14.1179163331138
74169172.498741064334-3.49874106433359
75163165.224312807779-2.22431280777860
76154158.011529067990-4.01152906799032
77142143.726181146087-1.72618114608693
78146143.1805807298592.81941927014068
79133132.5402922153150.459707784685293
80131126.4793667424144.52063325758616
81128118.3020604969149.69793950308576
82120117.2877785628442.71222143715582
838899.4125193325367-11.4125193325367
8495101.894721206481-6.89472120648109

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 302 & 300.999732905983 & 1.00026709401698 \tabularnewline
14 & 297 & 296.626296450144 & 0.373703549856259 \tabularnewline
15 & 301 & 301.157008776380 & -0.157008776379655 \tabularnewline
16 & 298 & 298.494459121936 & -0.494459121936472 \tabularnewline
17 & 295 & 296.265250448955 & -1.2652504489551 \tabularnewline
18 & 287 & 288.926160952036 & -1.92616095203596 \tabularnewline
19 & 290 & 289.006716995916 & 0.99328300408439 \tabularnewline
20 & 288 & 291.030672126812 & -3.03067212681174 \tabularnewline
21 & 288 & 289.842146182603 & -1.84214618260268 \tabularnewline
22 & 287 & 288.018622230618 & -1.01862223061840 \tabularnewline
23 & 274 & 287.657135574702 & -13.6571355747016 \tabularnewline
24 & 282 & 281.645288335265 & 0.35471166473485 \tabularnewline
25 & 296 & 286.48357419176 & 9.51642580824029 \tabularnewline
26 & 292 & 285.654136124440 & 6.34586387555964 \tabularnewline
27 & 298 & 292.719035831855 & 5.28096416814458 \tabularnewline
28 & 296 & 292.630967926127 & 3.36903207387326 \tabularnewline
29 & 292 & 292.116232999024 & -0.116232999024191 \tabularnewline
30 & 296 & 285.208904008870 & 10.7910959911295 \tabularnewline
31 & 293 & 293.878908422203 & -0.878908422202755 \tabularnewline
32 & 295 & 293.57956081756 & 1.42043918244013 \tabularnewline
33 & 294 & 296.024073310026 & -2.0240733100257 \tabularnewline
34 & 291 & 295.28741810765 & -4.28741810764978 \tabularnewline
35 & 279 & 287.704498014518 & -8.7044980145182 \tabularnewline
36 & 284 & 291.933090849267 & -7.93309084926716 \tabularnewline
37 & 299 & 297.556585706452 & 1.4434142935483 \tabularnewline
38 & 296 & 291.247855900657 & 4.7521440993433 \tabularnewline
39 & 299 & 297.103039825277 & 1.89696017472301 \tabularnewline
40 & 299 & 294.342404912262 & 4.65759508773829 \tabularnewline
41 & 291 & 292.814618647480 & -1.81461864747968 \tabularnewline
42 & 298 & 290.366758351913 & 7.63324164808733 \tabularnewline
43 & 288 & 291.548775999850 & -3.54877599984974 \tabularnewline
44 & 284 & 290.757359124645 & -6.75735912464529 \tabularnewline
45 & 277 & 286.758948099093 & -9.7589480990934 \tabularnewline
46 & 270 & 280.075075289218 & -10.0750752892178 \tabularnewline
47 & 251 & 266.248446905583 & -15.2484469055829 \tabularnewline
48 & 257 & 266.132095343942 & -9.1320953439423 \tabularnewline
49 & 269 & 274.307243558909 & -5.30724355890897 \tabularnewline
50 & 271 & 264.475205943233 & 6.524794056767 \tabularnewline
51 & 268 & 268.194901603801 & -0.194901603800758 \tabularnewline
52 & 268 & 264.002180882003 & 3.99781911799749 \tabularnewline
53 & 258 & 257.215162206955 & 0.784837793044858 \tabularnewline
54 & 261 & 259.083441780305 & 1.91655821969528 \tabularnewline
55 & 255 & 249.994920264635 & 5.00507973536531 \tabularnewline
56 & 251 & 250.455985010327 & 0.544014989673258 \tabularnewline
57 & 239 & 247.465778122548 & -8.46577812254827 \tabularnewline
58 & 229 & 240.099258407255 & -11.0992584072547 \tabularnewline
59 & 210 & 221.985437880254 & -11.9854378802537 \tabularnewline
60 & 218 & 225.435476083455 & -7.43547608345511 \tabularnewline
61 & 226 & 235.322718477454 & -9.3227184774538 \tabularnewline
62 & 227 & 228.061513740369 & -1.06151374036861 \tabularnewline
63 & 222 & 223.1272086282 & -1.12720862820001 \tabularnewline
64 & 215 & 218.986616247199 & -3.98661624719853 \tabularnewline
65 & 203 & 204.706686619467 & -1.70668661946675 \tabularnewline
66 & 205 & 203.91191147498 & 1.08808852501997 \tabularnewline
67 & 194 & 193.934375071696 & 0.065624928304402 \tabularnewline
68 & 190 & 187.510653113197 & 2.48934688680305 \tabularnewline
69 & 182 & 178.988323988319 & 3.01167601168112 \tabularnewline
70 & 179 & 174.532550212722 & 4.46744978727796 \tabularnewline
71 & 158 & 162.892396424216 & -4.8923964242164 \tabularnewline
72 & 163 & 171.451161439866 & -8.4511614398663 \tabularnewline
73 & 165 & 179.117916333114 & -14.1179163331138 \tabularnewline
74 & 169 & 172.498741064334 & -3.49874106433359 \tabularnewline
75 & 163 & 165.224312807779 & -2.22431280777860 \tabularnewline
76 & 154 & 158.011529067990 & -4.01152906799032 \tabularnewline
77 & 142 & 143.726181146087 & -1.72618114608693 \tabularnewline
78 & 146 & 143.180580729859 & 2.81941927014068 \tabularnewline
79 & 133 & 132.540292215315 & 0.459707784685293 \tabularnewline
80 & 131 & 126.479366742414 & 4.52063325758616 \tabularnewline
81 & 128 & 118.302060496914 & 9.69793950308576 \tabularnewline
82 & 120 & 117.287778562844 & 2.71222143715582 \tabularnewline
83 & 88 & 99.4125193325367 & -11.4125193325367 \tabularnewline
84 & 95 & 101.894721206481 & -6.89472120648109 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78086&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]302[/C][C]300.999732905983[/C][C]1.00026709401698[/C][/ROW]
[ROW][C]14[/C][C]297[/C][C]296.626296450144[/C][C]0.373703549856259[/C][/ROW]
[ROW][C]15[/C][C]301[/C][C]301.157008776380[/C][C]-0.157008776379655[/C][/ROW]
[ROW][C]16[/C][C]298[/C][C]298.494459121936[/C][C]-0.494459121936472[/C][/ROW]
[ROW][C]17[/C][C]295[/C][C]296.265250448955[/C][C]-1.2652504489551[/C][/ROW]
[ROW][C]18[/C][C]287[/C][C]288.926160952036[/C][C]-1.92616095203596[/C][/ROW]
[ROW][C]19[/C][C]290[/C][C]289.006716995916[/C][C]0.99328300408439[/C][/ROW]
[ROW][C]20[/C][C]288[/C][C]291.030672126812[/C][C]-3.03067212681174[/C][/ROW]
[ROW][C]21[/C][C]288[/C][C]289.842146182603[/C][C]-1.84214618260268[/C][/ROW]
[ROW][C]22[/C][C]287[/C][C]288.018622230618[/C][C]-1.01862223061840[/C][/ROW]
[ROW][C]23[/C][C]274[/C][C]287.657135574702[/C][C]-13.6571355747016[/C][/ROW]
[ROW][C]24[/C][C]282[/C][C]281.645288335265[/C][C]0.35471166473485[/C][/ROW]
[ROW][C]25[/C][C]296[/C][C]286.48357419176[/C][C]9.51642580824029[/C][/ROW]
[ROW][C]26[/C][C]292[/C][C]285.654136124440[/C][C]6.34586387555964[/C][/ROW]
[ROW][C]27[/C][C]298[/C][C]292.719035831855[/C][C]5.28096416814458[/C][/ROW]
[ROW][C]28[/C][C]296[/C][C]292.630967926127[/C][C]3.36903207387326[/C][/ROW]
[ROW][C]29[/C][C]292[/C][C]292.116232999024[/C][C]-0.116232999024191[/C][/ROW]
[ROW][C]30[/C][C]296[/C][C]285.208904008870[/C][C]10.7910959911295[/C][/ROW]
[ROW][C]31[/C][C]293[/C][C]293.878908422203[/C][C]-0.878908422202755[/C][/ROW]
[ROW][C]32[/C][C]295[/C][C]293.57956081756[/C][C]1.42043918244013[/C][/ROW]
[ROW][C]33[/C][C]294[/C][C]296.024073310026[/C][C]-2.0240733100257[/C][/ROW]
[ROW][C]34[/C][C]291[/C][C]295.28741810765[/C][C]-4.28741810764978[/C][/ROW]
[ROW][C]35[/C][C]279[/C][C]287.704498014518[/C][C]-8.7044980145182[/C][/ROW]
[ROW][C]36[/C][C]284[/C][C]291.933090849267[/C][C]-7.93309084926716[/C][/ROW]
[ROW][C]37[/C][C]299[/C][C]297.556585706452[/C][C]1.4434142935483[/C][/ROW]
[ROW][C]38[/C][C]296[/C][C]291.247855900657[/C][C]4.7521440993433[/C][/ROW]
[ROW][C]39[/C][C]299[/C][C]297.103039825277[/C][C]1.89696017472301[/C][/ROW]
[ROW][C]40[/C][C]299[/C][C]294.342404912262[/C][C]4.65759508773829[/C][/ROW]
[ROW][C]41[/C][C]291[/C][C]292.814618647480[/C][C]-1.81461864747968[/C][/ROW]
[ROW][C]42[/C][C]298[/C][C]290.366758351913[/C][C]7.63324164808733[/C][/ROW]
[ROW][C]43[/C][C]288[/C][C]291.548775999850[/C][C]-3.54877599984974[/C][/ROW]
[ROW][C]44[/C][C]284[/C][C]290.757359124645[/C][C]-6.75735912464529[/C][/ROW]
[ROW][C]45[/C][C]277[/C][C]286.758948099093[/C][C]-9.7589480990934[/C][/ROW]
[ROW][C]46[/C][C]270[/C][C]280.075075289218[/C][C]-10.0750752892178[/C][/ROW]
[ROW][C]47[/C][C]251[/C][C]266.248446905583[/C][C]-15.2484469055829[/C][/ROW]
[ROW][C]48[/C][C]257[/C][C]266.132095343942[/C][C]-9.1320953439423[/C][/ROW]
[ROW][C]49[/C][C]269[/C][C]274.307243558909[/C][C]-5.30724355890897[/C][/ROW]
[ROW][C]50[/C][C]271[/C][C]264.475205943233[/C][C]6.524794056767[/C][/ROW]
[ROW][C]51[/C][C]268[/C][C]268.194901603801[/C][C]-0.194901603800758[/C][/ROW]
[ROW][C]52[/C][C]268[/C][C]264.002180882003[/C][C]3.99781911799749[/C][/ROW]
[ROW][C]53[/C][C]258[/C][C]257.215162206955[/C][C]0.784837793044858[/C][/ROW]
[ROW][C]54[/C][C]261[/C][C]259.083441780305[/C][C]1.91655821969528[/C][/ROW]
[ROW][C]55[/C][C]255[/C][C]249.994920264635[/C][C]5.00507973536531[/C][/ROW]
[ROW][C]56[/C][C]251[/C][C]250.455985010327[/C][C]0.544014989673258[/C][/ROW]
[ROW][C]57[/C][C]239[/C][C]247.465778122548[/C][C]-8.46577812254827[/C][/ROW]
[ROW][C]58[/C][C]229[/C][C]240.099258407255[/C][C]-11.0992584072547[/C][/ROW]
[ROW][C]59[/C][C]210[/C][C]221.985437880254[/C][C]-11.9854378802537[/C][/ROW]
[ROW][C]60[/C][C]218[/C][C]225.435476083455[/C][C]-7.43547608345511[/C][/ROW]
[ROW][C]61[/C][C]226[/C][C]235.322718477454[/C][C]-9.3227184774538[/C][/ROW]
[ROW][C]62[/C][C]227[/C][C]228.061513740369[/C][C]-1.06151374036861[/C][/ROW]
[ROW][C]63[/C][C]222[/C][C]223.1272086282[/C][C]-1.12720862820001[/C][/ROW]
[ROW][C]64[/C][C]215[/C][C]218.986616247199[/C][C]-3.98661624719853[/C][/ROW]
[ROW][C]65[/C][C]203[/C][C]204.706686619467[/C][C]-1.70668661946675[/C][/ROW]
[ROW][C]66[/C][C]205[/C][C]203.91191147498[/C][C]1.08808852501997[/C][/ROW]
[ROW][C]67[/C][C]194[/C][C]193.934375071696[/C][C]0.065624928304402[/C][/ROW]
[ROW][C]68[/C][C]190[/C][C]187.510653113197[/C][C]2.48934688680305[/C][/ROW]
[ROW][C]69[/C][C]182[/C][C]178.988323988319[/C][C]3.01167601168112[/C][/ROW]
[ROW][C]70[/C][C]179[/C][C]174.532550212722[/C][C]4.46744978727796[/C][/ROW]
[ROW][C]71[/C][C]158[/C][C]162.892396424216[/C][C]-4.8923964242164[/C][/ROW]
[ROW][C]72[/C][C]163[/C][C]171.451161439866[/C][C]-8.4511614398663[/C][/ROW]
[ROW][C]73[/C][C]165[/C][C]179.117916333114[/C][C]-14.1179163331138[/C][/ROW]
[ROW][C]74[/C][C]169[/C][C]172.498741064334[/C][C]-3.49874106433359[/C][/ROW]
[ROW][C]75[/C][C]163[/C][C]165.224312807779[/C][C]-2.22431280777860[/C][/ROW]
[ROW][C]76[/C][C]154[/C][C]158.011529067990[/C][C]-4.01152906799032[/C][/ROW]
[ROW][C]77[/C][C]142[/C][C]143.726181146087[/C][C]-1.72618114608693[/C][/ROW]
[ROW][C]78[/C][C]146[/C][C]143.180580729859[/C][C]2.81941927014068[/C][/ROW]
[ROW][C]79[/C][C]133[/C][C]132.540292215315[/C][C]0.459707784685293[/C][/ROW]
[ROW][C]80[/C][C]131[/C][C]126.479366742414[/C][C]4.52063325758616[/C][/ROW]
[ROW][C]81[/C][C]128[/C][C]118.302060496914[/C][C]9.69793950308576[/C][/ROW]
[ROW][C]82[/C][C]120[/C][C]117.287778562844[/C][C]2.71222143715582[/C][/ROW]
[ROW][C]83[/C][C]88[/C][C]99.4125193325367[/C][C]-11.4125193325367[/C][/ROW]
[ROW][C]84[/C][C]95[/C][C]101.894721206481[/C][C]-6.89472120648109[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78086&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78086&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
13302300.9997329059831.00026709401698
14297296.6262964501440.373703549856259
15301301.157008776380-0.157008776379655
16298298.494459121936-0.494459121936472
17295296.265250448955-1.2652504489551
18287288.926160952036-1.92616095203596
19290289.0067169959160.99328300408439
20288291.030672126812-3.03067212681174
21288289.842146182603-1.84214618260268
22287288.018622230618-1.01862223061840
23274287.657135574702-13.6571355747016
24282281.6452883352650.35471166473485
25296286.483574191769.51642580824029
26292285.6541361244406.34586387555964
27298292.7190358318555.28096416814458
28296292.6309679261273.36903207387326
29292292.116232999024-0.116232999024191
30296285.20890400887010.7910959911295
31293293.878908422203-0.878908422202755
32295293.579560817561.42043918244013
33294296.024073310026-2.0240733100257
34291295.28741810765-4.28741810764978
35279287.704498014518-8.7044980145182
36284291.933090849267-7.93309084926716
37299297.5565857064521.4434142935483
38296291.2478559006574.7521440993433
39299297.1030398252771.89696017472301
40299294.3424049122624.65759508773829
41291292.814618647480-1.81461864747968
42298290.3667583519137.63324164808733
43288291.548775999850-3.54877599984974
44284290.757359124645-6.75735912464529
45277286.758948099093-9.7589480990934
46270280.075075289218-10.0750752892178
47251266.248446905583-15.2484469055829
48257266.132095343942-9.1320953439423
49269274.307243558909-5.30724355890897
50271264.4752059432336.524794056767
51268268.194901603801-0.194901603800758
52268264.0021808820033.99781911799749
53258257.2151622069550.784837793044858
54261259.0834417803051.91655821969528
55255249.9949202646355.00507973536531
56251250.4559850103270.544014989673258
57239247.465778122548-8.46577812254827
58229240.099258407255-11.0992584072547
59210221.985437880254-11.9854378802537
60218225.435476083455-7.43547608345511
61226235.322718477454-9.3227184774538
62227228.061513740369-1.06151374036861
63222223.1272086282-1.12720862820001
64215218.986616247199-3.98661624719853
65203204.706686619467-1.70668661946675
66205203.911911474981.08808852501997
67194193.9343750716960.065624928304402
68190187.5106531131972.48934688680305
69182178.9883239883193.01167601168112
70179174.5325502127224.46744978727796
71158162.892396424216-4.8923964242164
72163171.451161439866-8.4511614398663
73165179.117916333114-14.1179163331138
74169172.498741064334-3.49874106433359
75163165.224312807779-2.22431280777860
76154158.011529067990-4.01152906799032
77142143.726181146087-1.72618114608693
78146143.1805807298592.81941927014068
79133132.5402922153150.459707784685293
80131126.4793667424144.52063325758616
81128118.3020604969149.69793950308576
82120117.2877785628442.71222143715582
838899.4125193325367-11.4125193325367
8495101.894721206481-6.89472120648109







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85106.62660921416595.0943192121202118.158899216209
86112.02628153614898.868432478417125.184130593879
87106.91680566743392.107253891232121.726357443633
8899.806620152955783.3141697280492116.299070577862
8988.692897491885470.4833122189284106.902482764842
9091.332968406063671.3701840169507111.295752795176
9178.062144753811756.309031697370699.8152578102527
9273.70453073151550.123389762038197.285671700992
9365.529044616382340.081936366852690.976152865912
9455.523698941378228.172666665829982.8747312169264
9528.6041687821459-0.68860962168086857.8969471859727
9638.84010689974537.5679990260330270.1122147734576

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 106.626609214165 & 95.0943192121202 & 118.158899216209 \tabularnewline
86 & 112.026281536148 & 98.868432478417 & 125.184130593879 \tabularnewline
87 & 106.916805667433 & 92.107253891232 & 121.726357443633 \tabularnewline
88 & 99.8066201529557 & 83.3141697280492 & 116.299070577862 \tabularnewline
89 & 88.6928974918854 & 70.4833122189284 & 106.902482764842 \tabularnewline
90 & 91.3329684060636 & 71.3701840169507 & 111.295752795176 \tabularnewline
91 & 78.0621447538117 & 56.3090316973706 & 99.8152578102527 \tabularnewline
92 & 73.704530731515 & 50.1233897620381 & 97.285671700992 \tabularnewline
93 & 65.5290446163823 & 40.0819363668526 & 90.976152865912 \tabularnewline
94 & 55.5236989413782 & 28.1726666658299 & 82.8747312169264 \tabularnewline
95 & 28.6041687821459 & -0.688609621680868 & 57.8969471859727 \tabularnewline
96 & 38.8401068997453 & 7.56799902603302 & 70.1122147734576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78086&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]106.626609214165[/C][C]95.0943192121202[/C][C]118.158899216209[/C][/ROW]
[ROW][C]86[/C][C]112.026281536148[/C][C]98.868432478417[/C][C]125.184130593879[/C][/ROW]
[ROW][C]87[/C][C]106.916805667433[/C][C]92.107253891232[/C][C]121.726357443633[/C][/ROW]
[ROW][C]88[/C][C]99.8066201529557[/C][C]83.3141697280492[/C][C]116.299070577862[/C][/ROW]
[ROW][C]89[/C][C]88.6928974918854[/C][C]70.4833122189284[/C][C]106.902482764842[/C][/ROW]
[ROW][C]90[/C][C]91.3329684060636[/C][C]71.3701840169507[/C][C]111.295752795176[/C][/ROW]
[ROW][C]91[/C][C]78.0621447538117[/C][C]56.3090316973706[/C][C]99.8152578102527[/C][/ROW]
[ROW][C]92[/C][C]73.704530731515[/C][C]50.1233897620381[/C][C]97.285671700992[/C][/ROW]
[ROW][C]93[/C][C]65.5290446163823[/C][C]40.0819363668526[/C][C]90.976152865912[/C][/ROW]
[ROW][C]94[/C][C]55.5236989413782[/C][C]28.1726666658299[/C][C]82.8747312169264[/C][/ROW]
[ROW][C]95[/C][C]28.6041687821459[/C][C]-0.688609621680868[/C][C]57.8969471859727[/C][/ROW]
[ROW][C]96[/C][C]38.8401068997453[/C][C]7.56799902603302[/C][C]70.1122147734576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78086&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78086&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
85106.62660921416595.0943192121202118.158899216209
86112.02628153614898.868432478417125.184130593879
87106.91680566743392.107253891232121.726357443633
8899.806620152955783.3141697280492116.299070577862
8988.692897491885470.4833122189284106.902482764842
9091.332968406063671.3701840169507111.295752795176
9178.062144753811756.309031697370699.8152578102527
9273.70453073151550.123389762038197.285671700992
9365.529044616382340.081936366852690.976152865912
9455.523698941378228.172666665829982.8747312169264
9528.6041687821459-0.68860962168086857.8969471859727
9638.84010689974537.5679990260330270.1122147734576



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')