Free Statistics

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 computationSat, 10 Nov 2012 09:59:32 -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/10/t1352559596l1fscajlqonht4x.htm/, Retrieved Thu, 18 Apr 2024 22:19:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187364, Retrieved Thu, 18 Apr 2024 22:19:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D  [Exponential Smoothing] [Single smoothing] [2012-11-10 14:54:36] [86dcce9422b96d4554cb918e531c1d5d]
- R       [Exponential Smoothing] [double smoothing] [2012-11-10 14:57:27] [86dcce9422b96d4554cb918e531c1d5d]
-             [Exponential Smoothing] [Triple smoothing] [2012-11-10 14:59:32] [c63d55528b56cf8bb48e0b5d1a959d8e] [Current]
-   P           [Exponential Smoothing] [Triple Smoothing ...] [2012-11-11 17:39:21] [74be16979710d4c4e7c6647856088456]
-  M              [Exponential Smoothing] [Triple Smoothing ...] [2012-11-11 17:40:47] [74be16979710d4c4e7c6647856088456]
Feedback Forum

Post a new message
Dataseries X:
236422
250580
279515
264417
283706
281288
271146
283944
269155
270899
276507
319957
250746
247772
280449
274925
296013
287881
279098
294763
261924
291596
287537
326201
255598
253086
285261
284747
300402
288854
295433
307256
273189
287540
290705
337006
268335
259060
293703
294262
312404
301014
309942
317079
293912
304060
301299
357634
281493
282478
319111
315223
328445
321081
328040
326362
313566
319768
324315
387243
293308
295109
339190
335678
345401
351002
351889
355773
333363
336214
343910
405788




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187364&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187364&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187364&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.123317799752845
beta0.175163040458387
gamma0.643865065278512

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.123317799752845 \tabularnewline
beta & 0.175163040458387 \tabularnewline
gamma & 0.643865065278512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187364&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]0.123317799752845[/C][/ROW]
[ROW][C]beta[/C][C]0.175163040458387[/C][/ROW]
[ROW][C]gamma[/C][C]0.643865065278512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187364&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187364&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
alpha0.123317799752845
beta0.175163040458387
gamma0.643865065278512







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13250746247057.4703525643688.52964743599
14247772244458.4438205163313.55617948377
15280449278168.3765871492280.62341285148
16274925273187.6101338451737.38986615522
17296013294028.5071881381984.49281186151
18287881286324.9512423971556.04875760345
19279098277476.0056265821621.99437341793
20294763290966.311859863796.68814013957
21261924277777.724410534-15853.7244105337
22291596277801.60611409213794.3938859085
23287537285169.7223829872367.27761701291
24326201329184.931718819-2983.93171881913
25255598262078.290993578-6480.29099357792
26253086258167.719188918-5081.71918891778
27285261290232.077361665-4971.07736166503
28284747283866.535544667880.464455333189
29300402304538.85397798-4136.85397797974
30288854295503.97438145-6649.97438145045
31295433285168.43708592110264.5629140793
32307256300626.8832177076629.11678229278
33273189276431.614942403-3242.61494240334
34287540294754.407567488-7214.40756748809
35290705292636.162053943-1931.1620539435
36337006332562.4823231494443.51767685113
37268335264020.399649184314.60035082028
38259060262085.846338908-3025.84633890755
39293703294365.963359734-662.96335973352
40294262291827.5175360352434.48246396502
41312404309885.7791548172518.2208451826
42301014300423.180505666590.819494334166
43309942300854.7937296459087.2062703548
44317079314417.1035685442661.89643145638
45293912284375.7991177489536.20088225242
46304060302523.9809073881536.01909261203
47301299305147.513485255-3848.51348525478
48357634349074.7452119248559.25478807616
49281493281695.410901786-202.410901785654
50282478275690.80749686787.19250320044
51319111311357.1837726277753.81622737291
52315223312629.2571371252593.74286287534
53328445331782.046487432-3337.04648743192
54321081321410.581175337-329.581175337429
55328040327405.867321257634.132678742521
56326362336997.568841192-10635.5688411918
57313566309608.1888540053957.81114599505
58319768322843.569777831-3075.56977783085
59324315322050.3541444812264.64585551928
60387243374058.57050890813184.4294910918
61293308302727.227519033-9419.22751903284
62295109299755.602411173-4646.60241117253
63339190334534.8244083554655.17559164495
64335678332422.3771793493255.62282065087
65345401348233.639914435-2832.63991443528
66351002339557.45655554511444.543444455
67351889347738.4848132214150.51518677932
68355773351668.2229293544104.77707064583
69333363334918.201497101-1555.20149710146
70336214343968.705806762-7754.70580676233
71343910345976.835379331-2066.83537933056
72405788403885.1769446021902.82305539818

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 250746 & 247057.470352564 & 3688.52964743599 \tabularnewline
14 & 247772 & 244458.443820516 & 3313.55617948377 \tabularnewline
15 & 280449 & 278168.376587149 & 2280.62341285148 \tabularnewline
16 & 274925 & 273187.610133845 & 1737.38986615522 \tabularnewline
17 & 296013 & 294028.507188138 & 1984.49281186151 \tabularnewline
18 & 287881 & 286324.951242397 & 1556.04875760345 \tabularnewline
19 & 279098 & 277476.005626582 & 1621.99437341793 \tabularnewline
20 & 294763 & 290966.31185986 & 3796.68814013957 \tabularnewline
21 & 261924 & 277777.724410534 & -15853.7244105337 \tabularnewline
22 & 291596 & 277801.606114092 & 13794.3938859085 \tabularnewline
23 & 287537 & 285169.722382987 & 2367.27761701291 \tabularnewline
24 & 326201 & 329184.931718819 & -2983.93171881913 \tabularnewline
25 & 255598 & 262078.290993578 & -6480.29099357792 \tabularnewline
26 & 253086 & 258167.719188918 & -5081.71918891778 \tabularnewline
27 & 285261 & 290232.077361665 & -4971.07736166503 \tabularnewline
28 & 284747 & 283866.535544667 & 880.464455333189 \tabularnewline
29 & 300402 & 304538.85397798 & -4136.85397797974 \tabularnewline
30 & 288854 & 295503.97438145 & -6649.97438145045 \tabularnewline
31 & 295433 & 285168.437085921 & 10264.5629140793 \tabularnewline
32 & 307256 & 300626.883217707 & 6629.11678229278 \tabularnewline
33 & 273189 & 276431.614942403 & -3242.61494240334 \tabularnewline
34 & 287540 & 294754.407567488 & -7214.40756748809 \tabularnewline
35 & 290705 & 292636.162053943 & -1931.1620539435 \tabularnewline
36 & 337006 & 332562.482323149 & 4443.51767685113 \tabularnewline
37 & 268335 & 264020.39964918 & 4314.60035082028 \tabularnewline
38 & 259060 & 262085.846338908 & -3025.84633890755 \tabularnewline
39 & 293703 & 294365.963359734 & -662.96335973352 \tabularnewline
40 & 294262 & 291827.517536035 & 2434.48246396502 \tabularnewline
41 & 312404 & 309885.779154817 & 2518.2208451826 \tabularnewline
42 & 301014 & 300423.180505666 & 590.819494334166 \tabularnewline
43 & 309942 & 300854.793729645 & 9087.2062703548 \tabularnewline
44 & 317079 & 314417.103568544 & 2661.89643145638 \tabularnewline
45 & 293912 & 284375.799117748 & 9536.20088225242 \tabularnewline
46 & 304060 & 302523.980907388 & 1536.01909261203 \tabularnewline
47 & 301299 & 305147.513485255 & -3848.51348525478 \tabularnewline
48 & 357634 & 349074.745211924 & 8559.25478807616 \tabularnewline
49 & 281493 & 281695.410901786 & -202.410901785654 \tabularnewline
50 & 282478 & 275690.8074968 & 6787.19250320044 \tabularnewline
51 & 319111 & 311357.183772627 & 7753.81622737291 \tabularnewline
52 & 315223 & 312629.257137125 & 2593.74286287534 \tabularnewline
53 & 328445 & 331782.046487432 & -3337.04648743192 \tabularnewline
54 & 321081 & 321410.581175337 & -329.581175337429 \tabularnewline
55 & 328040 & 327405.867321257 & 634.132678742521 \tabularnewline
56 & 326362 & 336997.568841192 & -10635.5688411918 \tabularnewline
57 & 313566 & 309608.188854005 & 3957.81114599505 \tabularnewline
58 & 319768 & 322843.569777831 & -3075.56977783085 \tabularnewline
59 & 324315 & 322050.354144481 & 2264.64585551928 \tabularnewline
60 & 387243 & 374058.570508908 & 13184.4294910918 \tabularnewline
61 & 293308 & 302727.227519033 & -9419.22751903284 \tabularnewline
62 & 295109 & 299755.602411173 & -4646.60241117253 \tabularnewline
63 & 339190 & 334534.824408355 & 4655.17559164495 \tabularnewline
64 & 335678 & 332422.377179349 & 3255.62282065087 \tabularnewline
65 & 345401 & 348233.639914435 & -2832.63991443528 \tabularnewline
66 & 351002 & 339557.456555545 & 11444.543444455 \tabularnewline
67 & 351889 & 347738.484813221 & 4150.51518677932 \tabularnewline
68 & 355773 & 351668.222929354 & 4104.77707064583 \tabularnewline
69 & 333363 & 334918.201497101 & -1555.20149710146 \tabularnewline
70 & 336214 & 343968.705806762 & -7754.70580676233 \tabularnewline
71 & 343910 & 345976.835379331 & -2066.83537933056 \tabularnewline
72 & 405788 & 403885.176944602 & 1902.82305539818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187364&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]250746[/C][C]247057.470352564[/C][C]3688.52964743599[/C][/ROW]
[ROW][C]14[/C][C]247772[/C][C]244458.443820516[/C][C]3313.55617948377[/C][/ROW]
[ROW][C]15[/C][C]280449[/C][C]278168.376587149[/C][C]2280.62341285148[/C][/ROW]
[ROW][C]16[/C][C]274925[/C][C]273187.610133845[/C][C]1737.38986615522[/C][/ROW]
[ROW][C]17[/C][C]296013[/C][C]294028.507188138[/C][C]1984.49281186151[/C][/ROW]
[ROW][C]18[/C][C]287881[/C][C]286324.951242397[/C][C]1556.04875760345[/C][/ROW]
[ROW][C]19[/C][C]279098[/C][C]277476.005626582[/C][C]1621.99437341793[/C][/ROW]
[ROW][C]20[/C][C]294763[/C][C]290966.31185986[/C][C]3796.68814013957[/C][/ROW]
[ROW][C]21[/C][C]261924[/C][C]277777.724410534[/C][C]-15853.7244105337[/C][/ROW]
[ROW][C]22[/C][C]291596[/C][C]277801.606114092[/C][C]13794.3938859085[/C][/ROW]
[ROW][C]23[/C][C]287537[/C][C]285169.722382987[/C][C]2367.27761701291[/C][/ROW]
[ROW][C]24[/C][C]326201[/C][C]329184.931718819[/C][C]-2983.93171881913[/C][/ROW]
[ROW][C]25[/C][C]255598[/C][C]262078.290993578[/C][C]-6480.29099357792[/C][/ROW]
[ROW][C]26[/C][C]253086[/C][C]258167.719188918[/C][C]-5081.71918891778[/C][/ROW]
[ROW][C]27[/C][C]285261[/C][C]290232.077361665[/C][C]-4971.07736166503[/C][/ROW]
[ROW][C]28[/C][C]284747[/C][C]283866.535544667[/C][C]880.464455333189[/C][/ROW]
[ROW][C]29[/C][C]300402[/C][C]304538.85397798[/C][C]-4136.85397797974[/C][/ROW]
[ROW][C]30[/C][C]288854[/C][C]295503.97438145[/C][C]-6649.97438145045[/C][/ROW]
[ROW][C]31[/C][C]295433[/C][C]285168.437085921[/C][C]10264.5629140793[/C][/ROW]
[ROW][C]32[/C][C]307256[/C][C]300626.883217707[/C][C]6629.11678229278[/C][/ROW]
[ROW][C]33[/C][C]273189[/C][C]276431.614942403[/C][C]-3242.61494240334[/C][/ROW]
[ROW][C]34[/C][C]287540[/C][C]294754.407567488[/C][C]-7214.40756748809[/C][/ROW]
[ROW][C]35[/C][C]290705[/C][C]292636.162053943[/C][C]-1931.1620539435[/C][/ROW]
[ROW][C]36[/C][C]337006[/C][C]332562.482323149[/C][C]4443.51767685113[/C][/ROW]
[ROW][C]37[/C][C]268335[/C][C]264020.39964918[/C][C]4314.60035082028[/C][/ROW]
[ROW][C]38[/C][C]259060[/C][C]262085.846338908[/C][C]-3025.84633890755[/C][/ROW]
[ROW][C]39[/C][C]293703[/C][C]294365.963359734[/C][C]-662.96335973352[/C][/ROW]
[ROW][C]40[/C][C]294262[/C][C]291827.517536035[/C][C]2434.48246396502[/C][/ROW]
[ROW][C]41[/C][C]312404[/C][C]309885.779154817[/C][C]2518.2208451826[/C][/ROW]
[ROW][C]42[/C][C]301014[/C][C]300423.180505666[/C][C]590.819494334166[/C][/ROW]
[ROW][C]43[/C][C]309942[/C][C]300854.793729645[/C][C]9087.2062703548[/C][/ROW]
[ROW][C]44[/C][C]317079[/C][C]314417.103568544[/C][C]2661.89643145638[/C][/ROW]
[ROW][C]45[/C][C]293912[/C][C]284375.799117748[/C][C]9536.20088225242[/C][/ROW]
[ROW][C]46[/C][C]304060[/C][C]302523.980907388[/C][C]1536.01909261203[/C][/ROW]
[ROW][C]47[/C][C]301299[/C][C]305147.513485255[/C][C]-3848.51348525478[/C][/ROW]
[ROW][C]48[/C][C]357634[/C][C]349074.745211924[/C][C]8559.25478807616[/C][/ROW]
[ROW][C]49[/C][C]281493[/C][C]281695.410901786[/C][C]-202.410901785654[/C][/ROW]
[ROW][C]50[/C][C]282478[/C][C]275690.8074968[/C][C]6787.19250320044[/C][/ROW]
[ROW][C]51[/C][C]319111[/C][C]311357.183772627[/C][C]7753.81622737291[/C][/ROW]
[ROW][C]52[/C][C]315223[/C][C]312629.257137125[/C][C]2593.74286287534[/C][/ROW]
[ROW][C]53[/C][C]328445[/C][C]331782.046487432[/C][C]-3337.04648743192[/C][/ROW]
[ROW][C]54[/C][C]321081[/C][C]321410.581175337[/C][C]-329.581175337429[/C][/ROW]
[ROW][C]55[/C][C]328040[/C][C]327405.867321257[/C][C]634.132678742521[/C][/ROW]
[ROW][C]56[/C][C]326362[/C][C]336997.568841192[/C][C]-10635.5688411918[/C][/ROW]
[ROW][C]57[/C][C]313566[/C][C]309608.188854005[/C][C]3957.81114599505[/C][/ROW]
[ROW][C]58[/C][C]319768[/C][C]322843.569777831[/C][C]-3075.56977783085[/C][/ROW]
[ROW][C]59[/C][C]324315[/C][C]322050.354144481[/C][C]2264.64585551928[/C][/ROW]
[ROW][C]60[/C][C]387243[/C][C]374058.570508908[/C][C]13184.4294910918[/C][/ROW]
[ROW][C]61[/C][C]293308[/C][C]302727.227519033[/C][C]-9419.22751903284[/C][/ROW]
[ROW][C]62[/C][C]295109[/C][C]299755.602411173[/C][C]-4646.60241117253[/C][/ROW]
[ROW][C]63[/C][C]339190[/C][C]334534.824408355[/C][C]4655.17559164495[/C][/ROW]
[ROW][C]64[/C][C]335678[/C][C]332422.377179349[/C][C]3255.62282065087[/C][/ROW]
[ROW][C]65[/C][C]345401[/C][C]348233.639914435[/C][C]-2832.63991443528[/C][/ROW]
[ROW][C]66[/C][C]351002[/C][C]339557.456555545[/C][C]11444.543444455[/C][/ROW]
[ROW][C]67[/C][C]351889[/C][C]347738.484813221[/C][C]4150.51518677932[/C][/ROW]
[ROW][C]68[/C][C]355773[/C][C]351668.222929354[/C][C]4104.77707064583[/C][/ROW]
[ROW][C]69[/C][C]333363[/C][C]334918.201497101[/C][C]-1555.20149710146[/C][/ROW]
[ROW][C]70[/C][C]336214[/C][C]343968.705806762[/C][C]-7754.70580676233[/C][/ROW]
[ROW][C]71[/C][C]343910[/C][C]345976.835379331[/C][C]-2066.83537933056[/C][/ROW]
[ROW][C]72[/C][C]405788[/C][C]403885.176944602[/C][C]1902.82305539818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187364&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187364&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
13250746247057.4703525643688.52964743599
14247772244458.4438205163313.55617948377
15280449278168.3765871492280.62341285148
16274925273187.6101338451737.38986615522
17296013294028.5071881381984.49281186151
18287881286324.9512423971556.04875760345
19279098277476.0056265821621.99437341793
20294763290966.311859863796.68814013957
21261924277777.724410534-15853.7244105337
22291596277801.60611409213794.3938859085
23287537285169.7223829872367.27761701291
24326201329184.931718819-2983.93171881913
25255598262078.290993578-6480.29099357792
26253086258167.719188918-5081.71918891778
27285261290232.077361665-4971.07736166503
28284747283866.535544667880.464455333189
29300402304538.85397798-4136.85397797974
30288854295503.97438145-6649.97438145045
31295433285168.43708592110264.5629140793
32307256300626.8832177076629.11678229278
33273189276431.614942403-3242.61494240334
34287540294754.407567488-7214.40756748809
35290705292636.162053943-1931.1620539435
36337006332562.4823231494443.51767685113
37268335264020.399649184314.60035082028
38259060262085.846338908-3025.84633890755
39293703294365.963359734-662.96335973352
40294262291827.5175360352434.48246396502
41312404309885.7791548172518.2208451826
42301014300423.180505666590.819494334166
43309942300854.7937296459087.2062703548
44317079314417.1035685442661.89643145638
45293912284375.7991177489536.20088225242
46304060302523.9809073881536.01909261203
47301299305147.513485255-3848.51348525478
48357634349074.7452119248559.25478807616
49281493281695.410901786-202.410901785654
50282478275690.80749686787.19250320044
51319111311357.1837726277753.81622737291
52315223312629.2571371252593.74286287534
53328445331782.046487432-3337.04648743192
54321081321410.581175337-329.581175337429
55328040327405.867321257634.132678742521
56326362336997.568841192-10635.5688411918
57313566309608.1888540053957.81114599505
58319768322843.569777831-3075.56977783085
59324315322050.3541444812264.64585551928
60387243374058.57050890813184.4294910918
61293308302727.227519033-9419.22751903284
62295109299755.602411173-4646.60241117253
63339190334534.8244083554655.17559164495
64335678332422.3771793493255.62282065087
65345401348233.639914435-2832.63991443528
66351002339557.45655554511444.543444455
67351889347738.4848132214150.51518677932
68355773351668.2229293544104.77707064583
69333363334918.201497101-1555.20149710146
70336214343968.705806762-7754.70580676233
71343910345976.835379331-2066.83537933056
72405788403885.1769446021902.82305539818







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73318430.3838425307039.402823894329821.364861105
74319544.506260067308034.53359573331054.478924403
75360477.844595925348812.623319676372143.065872173
76357231.356634847345370.948413045369091.764856649
77369364.231739578357265.626754832381462.836724325
78369317.221365542356935.002253341381699.440477744
79371943.38650947359230.413197296384656.359821644
80375219.497308251362127.578120879388311.416495624
81354563.780266432341044.297753709368083.262779155
82360135.615122776346140.081792575374131.148452977
83366307.099188983351787.627094074380826.571283891
84426752.15411058411661.831313591441842.47690757

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 318430.3838425 & 307039.402823894 & 329821.364861105 \tabularnewline
74 & 319544.506260067 & 308034.53359573 & 331054.478924403 \tabularnewline
75 & 360477.844595925 & 348812.623319676 & 372143.065872173 \tabularnewline
76 & 357231.356634847 & 345370.948413045 & 369091.764856649 \tabularnewline
77 & 369364.231739578 & 357265.626754832 & 381462.836724325 \tabularnewline
78 & 369317.221365542 & 356935.002253341 & 381699.440477744 \tabularnewline
79 & 371943.38650947 & 359230.413197296 & 384656.359821644 \tabularnewline
80 & 375219.497308251 & 362127.578120879 & 388311.416495624 \tabularnewline
81 & 354563.780266432 & 341044.297753709 & 368083.262779155 \tabularnewline
82 & 360135.615122776 & 346140.081792575 & 374131.148452977 \tabularnewline
83 & 366307.099188983 & 351787.627094074 & 380826.571283891 \tabularnewline
84 & 426752.15411058 & 411661.831313591 & 441842.47690757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187364&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]318430.3838425[/C][C]307039.402823894[/C][C]329821.364861105[/C][/ROW]
[ROW][C]74[/C][C]319544.506260067[/C][C]308034.53359573[/C][C]331054.478924403[/C][/ROW]
[ROW][C]75[/C][C]360477.844595925[/C][C]348812.623319676[/C][C]372143.065872173[/C][/ROW]
[ROW][C]76[/C][C]357231.356634847[/C][C]345370.948413045[/C][C]369091.764856649[/C][/ROW]
[ROW][C]77[/C][C]369364.231739578[/C][C]357265.626754832[/C][C]381462.836724325[/C][/ROW]
[ROW][C]78[/C][C]369317.221365542[/C][C]356935.002253341[/C][C]381699.440477744[/C][/ROW]
[ROW][C]79[/C][C]371943.38650947[/C][C]359230.413197296[/C][C]384656.359821644[/C][/ROW]
[ROW][C]80[/C][C]375219.497308251[/C][C]362127.578120879[/C][C]388311.416495624[/C][/ROW]
[ROW][C]81[/C][C]354563.780266432[/C][C]341044.297753709[/C][C]368083.262779155[/C][/ROW]
[ROW][C]82[/C][C]360135.615122776[/C][C]346140.081792575[/C][C]374131.148452977[/C][/ROW]
[ROW][C]83[/C][C]366307.099188983[/C][C]351787.627094074[/C][C]380826.571283891[/C][/ROW]
[ROW][C]84[/C][C]426752.15411058[/C][C]411661.831313591[/C][C]441842.47690757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187364&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187364&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
73318430.3838425307039.402823894329821.364861105
74319544.506260067308034.53359573331054.478924403
75360477.844595925348812.623319676372143.065872173
76357231.356634847345370.948413045369091.764856649
77369364.231739578357265.626754832381462.836724325
78369317.221365542356935.002253341381699.440477744
79371943.38650947359230.413197296384656.359821644
80375219.497308251362127.578120879388311.416495624
81354563.780266432341044.297753709368083.262779155
82360135.615122776346140.081792575374131.148452977
83366307.099188983351787.627094074380826.571283891
84426752.15411058411661.831313591441842.47690757



Parameters (Session):
par1 = 12 ; par2 = Single ; 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')