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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Apr 2008 14:54:56 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/15/t1208292936pmnyvoth3vkfsku.htm/, Retrieved Thu, 16 May 2024 14:52:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10136, Retrieved Thu, 16 May 2024 14:52:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact269
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [test] [2008-04-15 20:54:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
13328
12873
14000
13477
14237
13674
13529
14058
12975
14326
14008
16193
14483
14011
15057
14884
15414
14440
14900
15074
14442
15307
14938
17193
15528
14765
15838
15723
16150
15486
15986
15983
15692
16490
15686
18897
16316
15636
17163
16534
16518
16375
16290
16352
15943
16362
16393
19051
16747
16320
17910
16961
17480
17049
16879
17473
16998
17307
17418
20169
17871
17226
19062
17804
19100
18522
18060
18869
18127
18871
18890
21263
19547
18450
20254
19240
20216
19420
19415
20018
18652
19978
19509
21971




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10136&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10136&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10136&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.440051506384153
beta0.000510357792766258
gamma0.969612467681559

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.440051506384153 \tabularnewline
beta & 0.000510357792766258 \tabularnewline
gamma & 0.969612467681559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10136&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]0.440051506384153[/C][/ROW]
[ROW][C]beta[/C][C]0.000510357792766258[/C][/ROW]
[ROW][C]gamma[/C][C]0.969612467681559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10136&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10136&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
alpha0.440051506384153
beta0.000510357792766258
gamma0.969612467681559







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131448313950.0064127244532.993587275634
141401113710.3180276635300.681972336470
151505714858.4539887859198.546011214061
161488414757.8307940628126.169205937182
171541415346.879194847267.1208051528447
181444014409.496592875230.503407124801
191490014882.374378915617.6256210843821
201507415074.1789431872-0.178943187207551
211444214462.2002026382-20.2002026381779
221530715336.5931238976-29.5931238976373
231493814973.0809767451-35.0809767451283
241719317227.6015232389-34.6015232389
251552815796.1793597404-268.179359740365
261476515019.3832309765-254.383230976508
271583815923.2660255566-85.2660255565697
281572315640.763094344082.2369056560492
291615016200.2974877907-50.2974877906745
301548615138.1294300757347.870569924311
311598615765.315618536220.684381463989
321598316042.5739394619-59.5739394618704
331569215349.5587830130342.44121698697
341649016436.547282224253.4527177757809
351568616073.7925925929-387.79259259293
361889718313.7834502122583.216549787812
371631616895.902837954-579.902837953989
381563615936.0503022292-300.050302229214
391716316983.0463333612179.953666638754
401653416889.6413325144-355.641332514424
411651817207.8578450821-689.85784508209
421637516035.9966343456339.003365654389
431629016603.8926137903-313.892613790318
441635216491.7088311061-139.708831106091
451594315964.7551711965-21.7551711965316
461636216746.0563229807-384.05632298073
471639315944.7054354088448.294564591182
481905119156.3562268122-105.356226812200
491674716770.4584969018-23.4584969017887
501632016188.8764249222131.123575077825
511791017737.8757527059172.124247294105
521696117327.2676307851-366.267630785063
531748017460.009975119119.9900248809172
541704917134.9256386614-85.9256386614434
551687917158.8465352252-279.846535225188
561747317157.4450247844315.554975215622
571699816867.0219923134130.978007686619
581730717547.9730593580-240.973059358035
591741817241.1132802829176.886719717128
602016920181.7132615435-12.7132615435003
611787117740.7680291173130.231970882684
621722617274.8412128557-48.8412128556665
631906218848.1932548181213.806745181941
641780418111.7650355630-307.765035563043
651910018504.8029249481595.197075051859
661852218340.3783130132181.621686986797
671806018365.5852249806-305.585224980576
681886918703.5773108708165.422689129176
691812718200.9628220797-73.9628220796694
701887118612.3533893378258.646610662221
711889018747.3054779328142.694522067235
722126321783.5634715530-520.56347155304
731954719028.8903805260518.109619474024
741845018582.0878468771-132.087846877093
752025420385.1178385465-131.117838546452
761924019132.7870737037107.212926296310
772021620265.7094088722-49.7094088722079
781942019548.113819717-128.113819717008
791941519150.0971746056264.902825394409
802001820037.3628166549-19.3628166549206
811865219274.9496496976-622.949649697624
821997819650.4021559322327.597844067837
831950919746.2597465845-237.259746584492
842197122352.5260978327-381.526097832706

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14483 & 13950.0064127244 & 532.993587275634 \tabularnewline
14 & 14011 & 13710.3180276635 & 300.681972336470 \tabularnewline
15 & 15057 & 14858.4539887859 & 198.546011214061 \tabularnewline
16 & 14884 & 14757.8307940628 & 126.169205937182 \tabularnewline
17 & 15414 & 15346.8791948472 & 67.1208051528447 \tabularnewline
18 & 14440 & 14409.4965928752 & 30.503407124801 \tabularnewline
19 & 14900 & 14882.3743789156 & 17.6256210843821 \tabularnewline
20 & 15074 & 15074.1789431872 & -0.178943187207551 \tabularnewline
21 & 14442 & 14462.2002026382 & -20.2002026381779 \tabularnewline
22 & 15307 & 15336.5931238976 & -29.5931238976373 \tabularnewline
23 & 14938 & 14973.0809767451 & -35.0809767451283 \tabularnewline
24 & 17193 & 17227.6015232389 & -34.6015232389 \tabularnewline
25 & 15528 & 15796.1793597404 & -268.179359740365 \tabularnewline
26 & 14765 & 15019.3832309765 & -254.383230976508 \tabularnewline
27 & 15838 & 15923.2660255566 & -85.2660255565697 \tabularnewline
28 & 15723 & 15640.7630943440 & 82.2369056560492 \tabularnewline
29 & 16150 & 16200.2974877907 & -50.2974877906745 \tabularnewline
30 & 15486 & 15138.1294300757 & 347.870569924311 \tabularnewline
31 & 15986 & 15765.315618536 & 220.684381463989 \tabularnewline
32 & 15983 & 16042.5739394619 & -59.5739394618704 \tabularnewline
33 & 15692 & 15349.5587830130 & 342.44121698697 \tabularnewline
34 & 16490 & 16436.5472822242 & 53.4527177757809 \tabularnewline
35 & 15686 & 16073.7925925929 & -387.79259259293 \tabularnewline
36 & 18897 & 18313.7834502122 & 583.216549787812 \tabularnewline
37 & 16316 & 16895.902837954 & -579.902837953989 \tabularnewline
38 & 15636 & 15936.0503022292 & -300.050302229214 \tabularnewline
39 & 17163 & 16983.0463333612 & 179.953666638754 \tabularnewline
40 & 16534 & 16889.6413325144 & -355.641332514424 \tabularnewline
41 & 16518 & 17207.8578450821 & -689.85784508209 \tabularnewline
42 & 16375 & 16035.9966343456 & 339.003365654389 \tabularnewline
43 & 16290 & 16603.8926137903 & -313.892613790318 \tabularnewline
44 & 16352 & 16491.7088311061 & -139.708831106091 \tabularnewline
45 & 15943 & 15964.7551711965 & -21.7551711965316 \tabularnewline
46 & 16362 & 16746.0563229807 & -384.05632298073 \tabularnewline
47 & 16393 & 15944.7054354088 & 448.294564591182 \tabularnewline
48 & 19051 & 19156.3562268122 & -105.356226812200 \tabularnewline
49 & 16747 & 16770.4584969018 & -23.4584969017887 \tabularnewline
50 & 16320 & 16188.8764249222 & 131.123575077825 \tabularnewline
51 & 17910 & 17737.8757527059 & 172.124247294105 \tabularnewline
52 & 16961 & 17327.2676307851 & -366.267630785063 \tabularnewline
53 & 17480 & 17460.0099751191 & 19.9900248809172 \tabularnewline
54 & 17049 & 17134.9256386614 & -85.9256386614434 \tabularnewline
55 & 16879 & 17158.8465352252 & -279.846535225188 \tabularnewline
56 & 17473 & 17157.4450247844 & 315.554975215622 \tabularnewline
57 & 16998 & 16867.0219923134 & 130.978007686619 \tabularnewline
58 & 17307 & 17547.9730593580 & -240.973059358035 \tabularnewline
59 & 17418 & 17241.1132802829 & 176.886719717128 \tabularnewline
60 & 20169 & 20181.7132615435 & -12.7132615435003 \tabularnewline
61 & 17871 & 17740.7680291173 & 130.231970882684 \tabularnewline
62 & 17226 & 17274.8412128557 & -48.8412128556665 \tabularnewline
63 & 19062 & 18848.1932548181 & 213.806745181941 \tabularnewline
64 & 17804 & 18111.7650355630 & -307.765035563043 \tabularnewline
65 & 19100 & 18504.8029249481 & 595.197075051859 \tabularnewline
66 & 18522 & 18340.3783130132 & 181.621686986797 \tabularnewline
67 & 18060 & 18365.5852249806 & -305.585224980576 \tabularnewline
68 & 18869 & 18703.5773108708 & 165.422689129176 \tabularnewline
69 & 18127 & 18200.9628220797 & -73.9628220796694 \tabularnewline
70 & 18871 & 18612.3533893378 & 258.646610662221 \tabularnewline
71 & 18890 & 18747.3054779328 & 142.694522067235 \tabularnewline
72 & 21263 & 21783.5634715530 & -520.56347155304 \tabularnewline
73 & 19547 & 19028.8903805260 & 518.109619474024 \tabularnewline
74 & 18450 & 18582.0878468771 & -132.087846877093 \tabularnewline
75 & 20254 & 20385.1178385465 & -131.117838546452 \tabularnewline
76 & 19240 & 19132.7870737037 & 107.212926296310 \tabularnewline
77 & 20216 & 20265.7094088722 & -49.7094088722079 \tabularnewline
78 & 19420 & 19548.113819717 & -128.113819717008 \tabularnewline
79 & 19415 & 19150.0971746056 & 264.902825394409 \tabularnewline
80 & 20018 & 20037.3628166549 & -19.3628166549206 \tabularnewline
81 & 18652 & 19274.9496496976 & -622.949649697624 \tabularnewline
82 & 19978 & 19650.4021559322 & 327.597844067837 \tabularnewline
83 & 19509 & 19746.2597465845 & -237.259746584492 \tabularnewline
84 & 21971 & 22352.5260978327 & -381.526097832706 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10136&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]14483[/C][C]13950.0064127244[/C][C]532.993587275634[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]13710.3180276635[/C][C]300.681972336470[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14858.4539887859[/C][C]198.546011214061[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14757.8307940628[/C][C]126.169205937182[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]15346.8791948472[/C][C]67.1208051528447[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14409.4965928752[/C][C]30.503407124801[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14882.3743789156[/C][C]17.6256210843821[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]15074.1789431872[/C][C]-0.178943187207551[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14462.2002026382[/C][C]-20.2002026381779[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]15336.5931238976[/C][C]-29.5931238976373[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14973.0809767451[/C][C]-35.0809767451283[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]17227.6015232389[/C][C]-34.6015232389[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15796.1793597404[/C][C]-268.179359740365[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15019.3832309765[/C][C]-254.383230976508[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15923.2660255566[/C][C]-85.2660255565697[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15640.7630943440[/C][C]82.2369056560492[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]16200.2974877907[/C][C]-50.2974877906745[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15138.1294300757[/C][C]347.870569924311[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15765.315618536[/C][C]220.684381463989[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]16042.5739394619[/C][C]-59.5739394618704[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15349.5587830130[/C][C]342.44121698697[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]16436.5472822242[/C][C]53.4527177757809[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]16073.7925925929[/C][C]-387.79259259293[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]18313.7834502122[/C][C]583.216549787812[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16895.902837954[/C][C]-579.902837953989[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]15936.0503022292[/C][C]-300.050302229214[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16983.0463333612[/C][C]179.953666638754[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16889.6413325144[/C][C]-355.641332514424[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]17207.8578450821[/C][C]-689.85784508209[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16035.9966343456[/C][C]339.003365654389[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16603.8926137903[/C][C]-313.892613790318[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16491.7088311061[/C][C]-139.708831106091[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]15964.7551711965[/C][C]-21.7551711965316[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16746.0563229807[/C][C]-384.05632298073[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]15944.7054354088[/C][C]448.294564591182[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]19156.3562268122[/C][C]-105.356226812200[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]16770.4584969018[/C][C]-23.4584969017887[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]16188.8764249222[/C][C]131.123575077825[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]17737.8757527059[/C][C]172.124247294105[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17327.2676307851[/C][C]-366.267630785063[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17460.0099751191[/C][C]19.9900248809172[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17134.9256386614[/C][C]-85.9256386614434[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17158.8465352252[/C][C]-279.846535225188[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17157.4450247844[/C][C]315.554975215622[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]16867.0219923134[/C][C]130.978007686619[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17547.9730593580[/C][C]-240.973059358035[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17241.1132802829[/C][C]176.886719717128[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]20181.7132615435[/C][C]-12.7132615435003[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]17740.7680291173[/C][C]130.231970882684[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]17274.8412128557[/C][C]-48.8412128556665[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]18848.1932548181[/C][C]213.806745181941[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18111.7650355630[/C][C]-307.765035563043[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18504.8029249481[/C][C]595.197075051859[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18340.3783130132[/C][C]181.621686986797[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18365.5852249806[/C][C]-305.585224980576[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18703.5773108708[/C][C]165.422689129176[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18200.9628220797[/C][C]-73.9628220796694[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18612.3533893378[/C][C]258.646610662221[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18747.3054779328[/C][C]142.694522067235[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]21783.5634715530[/C][C]-520.56347155304[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19028.8903805260[/C][C]518.109619474024[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]18582.0878468771[/C][C]-132.087846877093[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]20385.1178385465[/C][C]-131.117838546452[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19132.7870737037[/C][C]107.212926296310[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]20265.7094088722[/C][C]-49.7094088722079[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19548.113819717[/C][C]-128.113819717008[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19150.0971746056[/C][C]264.902825394409[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]20037.3628166549[/C][C]-19.3628166549206[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19274.9496496976[/C][C]-622.949649697624[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19650.4021559322[/C][C]327.597844067837[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19746.2597465845[/C][C]-237.259746584492[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]22352.5260978327[/C][C]-381.526097832706[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10136&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10136&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
131448313950.0064127244532.993587275634
141401113710.3180276635300.681972336470
151505714858.4539887859198.546011214061
161488414757.8307940628126.169205937182
171541415346.879194847267.1208051528447
181444014409.496592875230.503407124801
191490014882.374378915617.6256210843821
201507415074.1789431872-0.178943187207551
211444214462.2002026382-20.2002026381779
221530715336.5931238976-29.5931238976373
231493814973.0809767451-35.0809767451283
241719317227.6015232389-34.6015232389
251552815796.1793597404-268.179359740365
261476515019.3832309765-254.383230976508
271583815923.2660255566-85.2660255565697
281572315640.763094344082.2369056560492
291615016200.2974877907-50.2974877906745
301548615138.1294300757347.870569924311
311598615765.315618536220.684381463989
321598316042.5739394619-59.5739394618704
331569215349.5587830130342.44121698697
341649016436.547282224253.4527177757809
351568616073.7925925929-387.79259259293
361889718313.7834502122583.216549787812
371631616895.902837954-579.902837953989
381563615936.0503022292-300.050302229214
391716316983.0463333612179.953666638754
401653416889.6413325144-355.641332514424
411651817207.8578450821-689.85784508209
421637516035.9966343456339.003365654389
431629016603.8926137903-313.892613790318
441635216491.7088311061-139.708831106091
451594315964.7551711965-21.7551711965316
461636216746.0563229807-384.05632298073
471639315944.7054354088448.294564591182
481905119156.3562268122-105.356226812200
491674716770.4584969018-23.4584969017887
501632016188.8764249222131.123575077825
511791017737.8757527059172.124247294105
521696117327.2676307851-366.267630785063
531748017460.009975119119.9900248809172
541704917134.9256386614-85.9256386614434
551687917158.8465352252-279.846535225188
561747317157.4450247844315.554975215622
571699816867.0219923134130.978007686619
581730717547.9730593580-240.973059358035
591741817241.1132802829176.886719717128
602016920181.7132615435-12.7132615435003
611787117740.7680291173130.231970882684
621722617274.8412128557-48.8412128556665
631906218848.1932548181213.806745181941
641780418111.7650355630-307.765035563043
651910018504.8029249481595.197075051859
661852218340.3783130132181.621686986797
671806018365.5852249806-305.585224980576
681886918703.5773108708165.422689129176
691812718200.9628220797-73.9628220796694
701887118612.3533893378258.646610662221
711889018747.3054779328142.694522067235
722126321783.5634715530-520.56347155304
731954719028.8903805260518.109619474024
741845018582.0878468771-132.087846877093
752025420385.1178385465-131.117838546452
761924019132.7870737037107.212926296310
772021620265.7094088722-49.7094088722079
781942019548.113819717-128.113819717008
791941519150.0971746056264.902825394409
802001820037.3628166549-19.3628166549206
811865219274.9496496976-622.949649697624
821997819650.4021559322327.597844067837
831950919746.2597465845-237.259746584492
842197122352.5260978327-381.526097832706







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520131.543851706619588.764074226320674.3236291868
8619069.624411246318480.39259108119658.8562314116
8720990.227487978320335.357782440721645.0971935158
8819883.062559205619199.857931330020566.2671870813
8920913.994213540520173.362229941321654.6261971398
9020146.972887516119383.476170341420910.4696046907
9120009.788200345519213.063017878320806.5133828126
9220642.330661550219795.935049376921488.7262737234
9319519.289666735118669.910167721920368.6691657482
9420733.159856054519817.256158959321649.0635531497
9520360.655569500519426.686977069321294.6241619316
9623101.553534085122199.366344090024003.7407240801

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20131.5438517066 & 19588.7640742263 & 20674.3236291868 \tabularnewline
86 & 19069.6244112463 & 18480.392591081 & 19658.8562314116 \tabularnewline
87 & 20990.2274879783 & 20335.3577824407 & 21645.0971935158 \tabularnewline
88 & 19883.0625592056 & 19199.8579313300 & 20566.2671870813 \tabularnewline
89 & 20913.9942135405 & 20173.3622299413 & 21654.6261971398 \tabularnewline
90 & 20146.9728875161 & 19383.4761703414 & 20910.4696046907 \tabularnewline
91 & 20009.7882003455 & 19213.0630178783 & 20806.5133828126 \tabularnewline
92 & 20642.3306615502 & 19795.9350493769 & 21488.7262737234 \tabularnewline
93 & 19519.2896667351 & 18669.9101677219 & 20368.6691657482 \tabularnewline
94 & 20733.1598560545 & 19817.2561589593 & 21649.0635531497 \tabularnewline
95 & 20360.6555695005 & 19426.6869770693 & 21294.6241619316 \tabularnewline
96 & 23101.5535340851 & 22199.3663440900 & 24003.7407240801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10136&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]20131.5438517066[/C][C]19588.7640742263[/C][C]20674.3236291868[/C][/ROW]
[ROW][C]86[/C][C]19069.6244112463[/C][C]18480.392591081[/C][C]19658.8562314116[/C][/ROW]
[ROW][C]87[/C][C]20990.2274879783[/C][C]20335.3577824407[/C][C]21645.0971935158[/C][/ROW]
[ROW][C]88[/C][C]19883.0625592056[/C][C]19199.8579313300[/C][C]20566.2671870813[/C][/ROW]
[ROW][C]89[/C][C]20913.9942135405[/C][C]20173.3622299413[/C][C]21654.6261971398[/C][/ROW]
[ROW][C]90[/C][C]20146.9728875161[/C][C]19383.4761703414[/C][C]20910.4696046907[/C][/ROW]
[ROW][C]91[/C][C]20009.7882003455[/C][C]19213.0630178783[/C][C]20806.5133828126[/C][/ROW]
[ROW][C]92[/C][C]20642.3306615502[/C][C]19795.9350493769[/C][C]21488.7262737234[/C][/ROW]
[ROW][C]93[/C][C]19519.2896667351[/C][C]18669.9101677219[/C][C]20368.6691657482[/C][/ROW]
[ROW][C]94[/C][C]20733.1598560545[/C][C]19817.2561589593[/C][C]21649.0635531497[/C][/ROW]
[ROW][C]95[/C][C]20360.6555695005[/C][C]19426.6869770693[/C][C]21294.6241619316[/C][/ROW]
[ROW][C]96[/C][C]23101.5535340851[/C][C]22199.3663440900[/C][C]24003.7407240801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10136&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10136&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
8520131.543851706619588.764074226320674.3236291868
8619069.624411246318480.39259108119658.8562314116
8720990.227487978320335.357782440721645.0971935158
8819883.062559205619199.857931330020566.2671870813
8920913.994213540520173.362229941321654.6261971398
9020146.972887516119383.476170341420910.4696046907
9120009.788200345519213.063017878320806.5133828126
9220642.330661550219795.935049376921488.7262737234
9319519.289666735118669.910167721920368.6691657482
9420733.159856054519817.256158959321649.0635531497
9520360.655569500519426.686977069321294.6241619316
9623101.553534085122199.366344090024003.7407240801



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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()

bitmap(file='hist.png')
hist(myresid,main="Residual Histogram")
grid()
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')