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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 computationSat, 10 Nov 2012 09:57:27 -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/t1352559475sdniytaqo4roqgy.htm/, Retrieved Sat, 10 Dec 2022 06:40:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187363, Retrieved Sat, 10 Dec 2022 06:40:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
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] [c63d55528b56cf8bb48e0b5d1a959d8e] [Current]
-             [Exponential Smoothing] [Triple smoothing] [2012-11-10 14:59:32] [86dcce9422b96d4554cb918e531c1d5d]
-   P           [Exponential Smoothing] [Triple Smoothing ...] [2012-11-11 17:39:21] [74be16979710d4c4e7c6647856088456]
-  M              [Exponential Smoothing] [Triple Smoothing ...] [2012-11-11 17:40:47] [74be16979710d4c4e7c6647856088456]
-   P         [Exponential Smoothing] [Double Smoothing ...] [2012-11-11 17:31:29] [74be16979710d4c4e7c6647856088456]
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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 time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187363&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187363&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187363&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.23686471684421
beta0.331698570367038
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.23686471684421 \tabularnewline
beta & 0.331698570367038 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187363&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]0.23686471684421[/C][/ROW]
[ROW][C]beta[/C][C]0.331698570367038[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187363&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187363&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
alpha0.23686471684421
beta0.331698570367038
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
327951526473814777
4264417283557.144645609-19140.1446456088
5283706292838.717516783-9132.71751678298
6281288303773.160281193-22485.1602811932
7271146309778.273414608-38632.2734146079
8283944308923.456765479-24979.4567654789
9269155309339.932501821-40184.9325018207
10270899302997.530296393-32098.5302963932
11276507296048.604147738-19541.6041477385
12319957290538.63209904329418.3679009569
13250746298936.883115533-48190.883115533
14247772285165.99459897-37393.9945989696
15280449271014.5483249149434.45167508634
16274925268696.3517729816228.64822701865
17296013266108.183985329904.8160146998
18287881271477.61722937816403.382770622
19279098274937.8131699144160.18683008617
20294763275824.88423139618938.1157686035
21261924281700.249216468-19776.2492164684
22291596276851.77292433414744.227075666
23287537281338.3993063736198.60069362691
24326201284287.87804018341913.1219598172
25255598298989.883827985-43391.8838279846
26253086290076.943586409-36990.9435864086
27285261279773.8673301055487.13266989455
28284747279963.4599056744783.54009432637
29300402280362.22791047220039.7720895278
30288854285949.1375469952904.86245300493
31295433287705.619991057727.38000894967
32307256291211.50907166616044.4909283336
33273189297948.0068317-24759.0068317
34287540293074.337725904-5534.3377259039
35290705292319.49430483-1614.49430483032
36337006292366.27640102844639.7235989721
37268335306876.290597652-38541.2905976519
38259060298655.557327004-39595.5573270036
39293703287074.1740738496628.82592615089
40294262286962.5277980767299.47220192384
41312404287583.2366166624820.7633833401
42301014294304.2311017996709.76889820135
43309942297262.54103544212679.4589645575
44317079302631.05569157314447.9443084265
45293912309553.603707832-15641.6037078321
46304060308120.074814132-4060.07481413212
47301299309110.810791421-7811.81079142075
48357634308599.13697620849034.8630237915
49281493325404.990274379-43911.990274379
50282478316744.949935482-34266.9499354819
51319111307677.20431596111433.795684039
52315223310332.6797585384890.32024146238
53328445311822.45789792616622.5421020737
54321081317397.1801470543683.81985294586
55328040320196.6048229787843.39517702215
56326362324597.5235549491764.47644505074
57313566327697.191757479-14131.1917574789
58319768325921.481947837-6153.48194783728
59324315325551.945263853-1236.94526385277
60387243326249.77871987660993.2212801243
61293308346479.839329963-53171.8393299626
62295109335490.636705062-40381.6367050619
63339190324358.28997183114831.710028169
64335678327469.3301438118208.66985618934
65345401329656.54199253315744.4580074673
66351002334865.7218315416136.2781684598
67351889341435.5001098110453.4998901895
68355773347480.5360376438292.4639623572
69333363353665.21852325-20302.2185232503
70336214351481.731269075-15267.7312690752
71343910349291.186066799-5381.18606679927
72405788349019.62724674456768.3727532565

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 279515 & 264738 & 14777 \tabularnewline
4 & 264417 & 283557.144645609 & -19140.1446456088 \tabularnewline
5 & 283706 & 292838.717516783 & -9132.71751678298 \tabularnewline
6 & 281288 & 303773.160281193 & -22485.1602811932 \tabularnewline
7 & 271146 & 309778.273414608 & -38632.2734146079 \tabularnewline
8 & 283944 & 308923.456765479 & -24979.4567654789 \tabularnewline
9 & 269155 & 309339.932501821 & -40184.9325018207 \tabularnewline
10 & 270899 & 302997.530296393 & -32098.5302963932 \tabularnewline
11 & 276507 & 296048.604147738 & -19541.6041477385 \tabularnewline
12 & 319957 & 290538.632099043 & 29418.3679009569 \tabularnewline
13 & 250746 & 298936.883115533 & -48190.883115533 \tabularnewline
14 & 247772 & 285165.99459897 & -37393.9945989696 \tabularnewline
15 & 280449 & 271014.548324914 & 9434.45167508634 \tabularnewline
16 & 274925 & 268696.351772981 & 6228.64822701865 \tabularnewline
17 & 296013 & 266108.1839853 & 29904.8160146998 \tabularnewline
18 & 287881 & 271477.617229378 & 16403.382770622 \tabularnewline
19 & 279098 & 274937.813169914 & 4160.18683008617 \tabularnewline
20 & 294763 & 275824.884231396 & 18938.1157686035 \tabularnewline
21 & 261924 & 281700.249216468 & -19776.2492164684 \tabularnewline
22 & 291596 & 276851.772924334 & 14744.227075666 \tabularnewline
23 & 287537 & 281338.399306373 & 6198.60069362691 \tabularnewline
24 & 326201 & 284287.878040183 & 41913.1219598172 \tabularnewline
25 & 255598 & 298989.883827985 & -43391.8838279846 \tabularnewline
26 & 253086 & 290076.943586409 & -36990.9435864086 \tabularnewline
27 & 285261 & 279773.867330105 & 5487.13266989455 \tabularnewline
28 & 284747 & 279963.459905674 & 4783.54009432637 \tabularnewline
29 & 300402 & 280362.227910472 & 20039.7720895278 \tabularnewline
30 & 288854 & 285949.137546995 & 2904.86245300493 \tabularnewline
31 & 295433 & 287705.61999105 & 7727.38000894967 \tabularnewline
32 & 307256 & 291211.509071666 & 16044.4909283336 \tabularnewline
33 & 273189 & 297948.0068317 & -24759.0068317 \tabularnewline
34 & 287540 & 293074.337725904 & -5534.3377259039 \tabularnewline
35 & 290705 & 292319.49430483 & -1614.49430483032 \tabularnewline
36 & 337006 & 292366.276401028 & 44639.7235989721 \tabularnewline
37 & 268335 & 306876.290597652 & -38541.2905976519 \tabularnewline
38 & 259060 & 298655.557327004 & -39595.5573270036 \tabularnewline
39 & 293703 & 287074.174073849 & 6628.82592615089 \tabularnewline
40 & 294262 & 286962.527798076 & 7299.47220192384 \tabularnewline
41 & 312404 & 287583.23661666 & 24820.7633833401 \tabularnewline
42 & 301014 & 294304.231101799 & 6709.76889820135 \tabularnewline
43 & 309942 & 297262.541035442 & 12679.4589645575 \tabularnewline
44 & 317079 & 302631.055691573 & 14447.9443084265 \tabularnewline
45 & 293912 & 309553.603707832 & -15641.6037078321 \tabularnewline
46 & 304060 & 308120.074814132 & -4060.07481413212 \tabularnewline
47 & 301299 & 309110.810791421 & -7811.81079142075 \tabularnewline
48 & 357634 & 308599.136976208 & 49034.8630237915 \tabularnewline
49 & 281493 & 325404.990274379 & -43911.990274379 \tabularnewline
50 & 282478 & 316744.949935482 & -34266.9499354819 \tabularnewline
51 & 319111 & 307677.204315961 & 11433.795684039 \tabularnewline
52 & 315223 & 310332.679758538 & 4890.32024146238 \tabularnewline
53 & 328445 & 311822.457897926 & 16622.5421020737 \tabularnewline
54 & 321081 & 317397.180147054 & 3683.81985294586 \tabularnewline
55 & 328040 & 320196.604822978 & 7843.39517702215 \tabularnewline
56 & 326362 & 324597.523554949 & 1764.47644505074 \tabularnewline
57 & 313566 & 327697.191757479 & -14131.1917574789 \tabularnewline
58 & 319768 & 325921.481947837 & -6153.48194783728 \tabularnewline
59 & 324315 & 325551.945263853 & -1236.94526385277 \tabularnewline
60 & 387243 & 326249.778719876 & 60993.2212801243 \tabularnewline
61 & 293308 & 346479.839329963 & -53171.8393299626 \tabularnewline
62 & 295109 & 335490.636705062 & -40381.6367050619 \tabularnewline
63 & 339190 & 324358.289971831 & 14831.710028169 \tabularnewline
64 & 335678 & 327469.330143811 & 8208.66985618934 \tabularnewline
65 & 345401 & 329656.541992533 & 15744.4580074673 \tabularnewline
66 & 351002 & 334865.72183154 & 16136.2781684598 \tabularnewline
67 & 351889 & 341435.50010981 & 10453.4998901895 \tabularnewline
68 & 355773 & 347480.536037643 & 8292.4639623572 \tabularnewline
69 & 333363 & 353665.21852325 & -20302.2185232503 \tabularnewline
70 & 336214 & 351481.731269075 & -15267.7312690752 \tabularnewline
71 & 343910 & 349291.186066799 & -5381.18606679927 \tabularnewline
72 & 405788 & 349019.627246744 & 56768.3727532565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187363&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]3[/C][C]279515[/C][C]264738[/C][C]14777[/C][/ROW]
[ROW][C]4[/C][C]264417[/C][C]283557.144645609[/C][C]-19140.1446456088[/C][/ROW]
[ROW][C]5[/C][C]283706[/C][C]292838.717516783[/C][C]-9132.71751678298[/C][/ROW]
[ROW][C]6[/C][C]281288[/C][C]303773.160281193[/C][C]-22485.1602811932[/C][/ROW]
[ROW][C]7[/C][C]271146[/C][C]309778.273414608[/C][C]-38632.2734146079[/C][/ROW]
[ROW][C]8[/C][C]283944[/C][C]308923.456765479[/C][C]-24979.4567654789[/C][/ROW]
[ROW][C]9[/C][C]269155[/C][C]309339.932501821[/C][C]-40184.9325018207[/C][/ROW]
[ROW][C]10[/C][C]270899[/C][C]302997.530296393[/C][C]-32098.5302963932[/C][/ROW]
[ROW][C]11[/C][C]276507[/C][C]296048.604147738[/C][C]-19541.6041477385[/C][/ROW]
[ROW][C]12[/C][C]319957[/C][C]290538.632099043[/C][C]29418.3679009569[/C][/ROW]
[ROW][C]13[/C][C]250746[/C][C]298936.883115533[/C][C]-48190.883115533[/C][/ROW]
[ROW][C]14[/C][C]247772[/C][C]285165.99459897[/C][C]-37393.9945989696[/C][/ROW]
[ROW][C]15[/C][C]280449[/C][C]271014.548324914[/C][C]9434.45167508634[/C][/ROW]
[ROW][C]16[/C][C]274925[/C][C]268696.351772981[/C][C]6228.64822701865[/C][/ROW]
[ROW][C]17[/C][C]296013[/C][C]266108.1839853[/C][C]29904.8160146998[/C][/ROW]
[ROW][C]18[/C][C]287881[/C][C]271477.617229378[/C][C]16403.382770622[/C][/ROW]
[ROW][C]19[/C][C]279098[/C][C]274937.813169914[/C][C]4160.18683008617[/C][/ROW]
[ROW][C]20[/C][C]294763[/C][C]275824.884231396[/C][C]18938.1157686035[/C][/ROW]
[ROW][C]21[/C][C]261924[/C][C]281700.249216468[/C][C]-19776.2492164684[/C][/ROW]
[ROW][C]22[/C][C]291596[/C][C]276851.772924334[/C][C]14744.227075666[/C][/ROW]
[ROW][C]23[/C][C]287537[/C][C]281338.399306373[/C][C]6198.60069362691[/C][/ROW]
[ROW][C]24[/C][C]326201[/C][C]284287.878040183[/C][C]41913.1219598172[/C][/ROW]
[ROW][C]25[/C][C]255598[/C][C]298989.883827985[/C][C]-43391.8838279846[/C][/ROW]
[ROW][C]26[/C][C]253086[/C][C]290076.943586409[/C][C]-36990.9435864086[/C][/ROW]
[ROW][C]27[/C][C]285261[/C][C]279773.867330105[/C][C]5487.13266989455[/C][/ROW]
[ROW][C]28[/C][C]284747[/C][C]279963.459905674[/C][C]4783.54009432637[/C][/ROW]
[ROW][C]29[/C][C]300402[/C][C]280362.227910472[/C][C]20039.7720895278[/C][/ROW]
[ROW][C]30[/C][C]288854[/C][C]285949.137546995[/C][C]2904.86245300493[/C][/ROW]
[ROW][C]31[/C][C]295433[/C][C]287705.61999105[/C][C]7727.38000894967[/C][/ROW]
[ROW][C]32[/C][C]307256[/C][C]291211.509071666[/C][C]16044.4909283336[/C][/ROW]
[ROW][C]33[/C][C]273189[/C][C]297948.0068317[/C][C]-24759.0068317[/C][/ROW]
[ROW][C]34[/C][C]287540[/C][C]293074.337725904[/C][C]-5534.3377259039[/C][/ROW]
[ROW][C]35[/C][C]290705[/C][C]292319.49430483[/C][C]-1614.49430483032[/C][/ROW]
[ROW][C]36[/C][C]337006[/C][C]292366.276401028[/C][C]44639.7235989721[/C][/ROW]
[ROW][C]37[/C][C]268335[/C][C]306876.290597652[/C][C]-38541.2905976519[/C][/ROW]
[ROW][C]38[/C][C]259060[/C][C]298655.557327004[/C][C]-39595.5573270036[/C][/ROW]
[ROW][C]39[/C][C]293703[/C][C]287074.174073849[/C][C]6628.82592615089[/C][/ROW]
[ROW][C]40[/C][C]294262[/C][C]286962.527798076[/C][C]7299.47220192384[/C][/ROW]
[ROW][C]41[/C][C]312404[/C][C]287583.23661666[/C][C]24820.7633833401[/C][/ROW]
[ROW][C]42[/C][C]301014[/C][C]294304.231101799[/C][C]6709.76889820135[/C][/ROW]
[ROW][C]43[/C][C]309942[/C][C]297262.541035442[/C][C]12679.4589645575[/C][/ROW]
[ROW][C]44[/C][C]317079[/C][C]302631.055691573[/C][C]14447.9443084265[/C][/ROW]
[ROW][C]45[/C][C]293912[/C][C]309553.603707832[/C][C]-15641.6037078321[/C][/ROW]
[ROW][C]46[/C][C]304060[/C][C]308120.074814132[/C][C]-4060.07481413212[/C][/ROW]
[ROW][C]47[/C][C]301299[/C][C]309110.810791421[/C][C]-7811.81079142075[/C][/ROW]
[ROW][C]48[/C][C]357634[/C][C]308599.136976208[/C][C]49034.8630237915[/C][/ROW]
[ROW][C]49[/C][C]281493[/C][C]325404.990274379[/C][C]-43911.990274379[/C][/ROW]
[ROW][C]50[/C][C]282478[/C][C]316744.949935482[/C][C]-34266.9499354819[/C][/ROW]
[ROW][C]51[/C][C]319111[/C][C]307677.204315961[/C][C]11433.795684039[/C][/ROW]
[ROW][C]52[/C][C]315223[/C][C]310332.679758538[/C][C]4890.32024146238[/C][/ROW]
[ROW][C]53[/C][C]328445[/C][C]311822.457897926[/C][C]16622.5421020737[/C][/ROW]
[ROW][C]54[/C][C]321081[/C][C]317397.180147054[/C][C]3683.81985294586[/C][/ROW]
[ROW][C]55[/C][C]328040[/C][C]320196.604822978[/C][C]7843.39517702215[/C][/ROW]
[ROW][C]56[/C][C]326362[/C][C]324597.523554949[/C][C]1764.47644505074[/C][/ROW]
[ROW][C]57[/C][C]313566[/C][C]327697.191757479[/C][C]-14131.1917574789[/C][/ROW]
[ROW][C]58[/C][C]319768[/C][C]325921.481947837[/C][C]-6153.48194783728[/C][/ROW]
[ROW][C]59[/C][C]324315[/C][C]325551.945263853[/C][C]-1236.94526385277[/C][/ROW]
[ROW][C]60[/C][C]387243[/C][C]326249.778719876[/C][C]60993.2212801243[/C][/ROW]
[ROW][C]61[/C][C]293308[/C][C]346479.839329963[/C][C]-53171.8393299626[/C][/ROW]
[ROW][C]62[/C][C]295109[/C][C]335490.636705062[/C][C]-40381.6367050619[/C][/ROW]
[ROW][C]63[/C][C]339190[/C][C]324358.289971831[/C][C]14831.710028169[/C][/ROW]
[ROW][C]64[/C][C]335678[/C][C]327469.330143811[/C][C]8208.66985618934[/C][/ROW]
[ROW][C]65[/C][C]345401[/C][C]329656.541992533[/C][C]15744.4580074673[/C][/ROW]
[ROW][C]66[/C][C]351002[/C][C]334865.72183154[/C][C]16136.2781684598[/C][/ROW]
[ROW][C]67[/C][C]351889[/C][C]341435.50010981[/C][C]10453.4998901895[/C][/ROW]
[ROW][C]68[/C][C]355773[/C][C]347480.536037643[/C][C]8292.4639623572[/C][/ROW]
[ROW][C]69[/C][C]333363[/C][C]353665.21852325[/C][C]-20302.2185232503[/C][/ROW]
[ROW][C]70[/C][C]336214[/C][C]351481.731269075[/C][C]-15267.7312690752[/C][/ROW]
[ROW][C]71[/C][C]343910[/C][C]349291.186066799[/C][C]-5381.18606679927[/C][/ROW]
[ROW][C]72[/C][C]405788[/C][C]349019.627246744[/C][C]56768.3727532565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187363&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187363&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
327951526473814777
4264417283557.144645609-19140.1446456088
5283706292838.717516783-9132.71751678298
6281288303773.160281193-22485.1602811932
7271146309778.273414608-38632.2734146079
8283944308923.456765479-24979.4567654789
9269155309339.932501821-40184.9325018207
10270899302997.530296393-32098.5302963932
11276507296048.604147738-19541.6041477385
12319957290538.63209904329418.3679009569
13250746298936.883115533-48190.883115533
14247772285165.99459897-37393.9945989696
15280449271014.5483249149434.45167508634
16274925268696.3517729816228.64822701865
17296013266108.183985329904.8160146998
18287881271477.61722937816403.382770622
19279098274937.8131699144160.18683008617
20294763275824.88423139618938.1157686035
21261924281700.249216468-19776.2492164684
22291596276851.77292433414744.227075666
23287537281338.3993063736198.60069362691
24326201284287.87804018341913.1219598172
25255598298989.883827985-43391.8838279846
26253086290076.943586409-36990.9435864086
27285261279773.8673301055487.13266989455
28284747279963.4599056744783.54009432637
29300402280362.22791047220039.7720895278
30288854285949.1375469952904.86245300493
31295433287705.619991057727.38000894967
32307256291211.50907166616044.4909283336
33273189297948.0068317-24759.0068317
34287540293074.337725904-5534.3377259039
35290705292319.49430483-1614.49430483032
36337006292366.27640102844639.7235989721
37268335306876.290597652-38541.2905976519
38259060298655.557327004-39595.5573270036
39293703287074.1740738496628.82592615089
40294262286962.5277980767299.47220192384
41312404287583.2366166624820.7633833401
42301014294304.2311017996709.76889820135
43309942297262.54103544212679.4589645575
44317079302631.05569157314447.9443084265
45293912309553.603707832-15641.6037078321
46304060308120.074814132-4060.07481413212
47301299309110.810791421-7811.81079142075
48357634308599.13697620849034.8630237915
49281493325404.990274379-43911.990274379
50282478316744.949935482-34266.9499354819
51319111307677.20431596111433.795684039
52315223310332.6797585384890.32024146238
53328445311822.45789792616622.5421020737
54321081317397.1801470543683.81985294586
55328040320196.6048229787843.39517702215
56326362324597.5235549491764.47644505074
57313566327697.191757479-14131.1917574789
58319768325921.481947837-6153.48194783728
59324315325551.945263853-1236.94526385277
60387243326249.77871987660993.2212801243
61293308346479.839329963-53171.8393299626
62295109335490.636705062-40381.6367050619
63339190324358.28997183114831.710028169
64335678327469.3301438118208.66985618934
65345401329656.54199253315744.4580074673
66351002334865.7218315416136.2781684598
67351889341435.5001098110453.4998901895
68355773347480.5360376438292.4639623572
69333363353665.21852325-20302.2185232503
70336214351481.731269075-15267.7312690752
71343910349291.186066799-5381.18606679927
72405788349019.62724674456768.3727532565







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73367929.265874365317722.828688937418135.703059792
74373392.479964079320747.55066839426037.409259769
75378855.694053794322617.006047813435094.382059775
76384318.908143509323280.309899035445357.506387982
77389782.122233223322764.440102795456799.804363651
78395245.336322938321144.813027708469345.859618168
79400708.550412652318517.408702223482899.692123082
80406171.764502367314979.779197821497363.749806913
81411634.978592082310621.164816306512648.792367858
82417098.192681796305518.890204007528677.495159585
83422561.406771511299738.165957603545384.647585419
84428024.620861225293333.367997985562715.873724466

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 367929.265874365 & 317722.828688937 & 418135.703059792 \tabularnewline
74 & 373392.479964079 & 320747.55066839 & 426037.409259769 \tabularnewline
75 & 378855.694053794 & 322617.006047813 & 435094.382059775 \tabularnewline
76 & 384318.908143509 & 323280.309899035 & 445357.506387982 \tabularnewline
77 & 389782.122233223 & 322764.440102795 & 456799.804363651 \tabularnewline
78 & 395245.336322938 & 321144.813027708 & 469345.859618168 \tabularnewline
79 & 400708.550412652 & 318517.408702223 & 482899.692123082 \tabularnewline
80 & 406171.764502367 & 314979.779197821 & 497363.749806913 \tabularnewline
81 & 411634.978592082 & 310621.164816306 & 512648.792367858 \tabularnewline
82 & 417098.192681796 & 305518.890204007 & 528677.495159585 \tabularnewline
83 & 422561.406771511 & 299738.165957603 & 545384.647585419 \tabularnewline
84 & 428024.620861225 & 293333.367997985 & 562715.873724466 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187363&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]367929.265874365[/C][C]317722.828688937[/C][C]418135.703059792[/C][/ROW]
[ROW][C]74[/C][C]373392.479964079[/C][C]320747.55066839[/C][C]426037.409259769[/C][/ROW]
[ROW][C]75[/C][C]378855.694053794[/C][C]322617.006047813[/C][C]435094.382059775[/C][/ROW]
[ROW][C]76[/C][C]384318.908143509[/C][C]323280.309899035[/C][C]445357.506387982[/C][/ROW]
[ROW][C]77[/C][C]389782.122233223[/C][C]322764.440102795[/C][C]456799.804363651[/C][/ROW]
[ROW][C]78[/C][C]395245.336322938[/C][C]321144.813027708[/C][C]469345.859618168[/C][/ROW]
[ROW][C]79[/C][C]400708.550412652[/C][C]318517.408702223[/C][C]482899.692123082[/C][/ROW]
[ROW][C]80[/C][C]406171.764502367[/C][C]314979.779197821[/C][C]497363.749806913[/C][/ROW]
[ROW][C]81[/C][C]411634.978592082[/C][C]310621.164816306[/C][C]512648.792367858[/C][/ROW]
[ROW][C]82[/C][C]417098.192681796[/C][C]305518.890204007[/C][C]528677.495159585[/C][/ROW]
[ROW][C]83[/C][C]422561.406771511[/C][C]299738.165957603[/C][C]545384.647585419[/C][/ROW]
[ROW][C]84[/C][C]428024.620861225[/C][C]293333.367997985[/C][C]562715.873724466[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187363&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187363&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
73367929.265874365317722.828688937418135.703059792
74373392.479964079320747.55066839426037.409259769
75378855.694053794322617.006047813435094.382059775
76384318.908143509323280.309899035445357.506387982
77389782.122233223322764.440102795456799.804363651
78395245.336322938321144.813027708469345.859618168
79400708.550412652318517.408702223482899.692123082
80406171.764502367314979.779197821497363.749806913
81411634.978592082310621.164816306512648.792367858
82417098.192681796305518.890204007528677.495159585
83422561.406771511299738.165957603545384.647585419
84428024.620861225293333.367997985562715.873724466



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')