Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 15:49:06 -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/May/26/t1211838859n08x3a5gr4i9vib.htm/, Retrieved Tue, 14 May 2024 13:36:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13305, Retrieved Tue, 14 May 2024 13:36:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [jasper ledeganck ...] [2008-05-26 21:49:06] [f4cdd97ad79577515d23a9f09979a316] [Current]
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Dataseries X:
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
42553




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13305&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13305&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13305&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.448709214642811
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.448709214642811 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13305&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]0.448709214642811[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13305&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13305&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
alpha0.448709214642811
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33502235338-316
43477735196.2078881729-419.207888172874
52688735008.1054458987-8121.10544589875
62397031364.0905992381-7394.09059923806
72278028046.2940134562-5266.29401345616
81735125683.2593626001-8332.25936260011
92138221944.4978078076-562.497807807606
102456121692.09985822802868.90014177205
111740922979.4017877311-5570.40178773114
121151420479.9111763134-8965.91117631339
133151416456.824213832615057.1757861674
142707123213.11773558253857.88226441747
152946224944.18505663374517.81494336628
162610526971.3702517732-866.370251773158
172239726582.6219365101-4185.62193651013
182384324704.4948045869-861.49480458695
192170524317.9341474019-2612.93414740188
201808923145.4865182078-5056.4865182078
212076420876.5944237708-112.594423770817
222531620826.07226830754489.92773169255
231770422840.7442145982-5136.7442145982
241554820535.8397522448-4987.83975224484
252802918297.75009425099731.24990574914
262938322664.25159695256718.74840304751
273643825679.015916266610758.9840837334
283203430506.67121483311527.32878516690
292267931191.9977145267-8512.9977145267
302431927372.1371957854-3053.13719578538
311800426002.1664024678-7998.16640246777
321753722413.3154374339-4876.31543743394
332036620225.2677671523140.732232847658
342278220288.41561682832493.58438317166
351916921407.3099070469-2238.30990704687
361380720402.9596265286-6595.95962652865
372974317443.291762693312299.7082373067
382559122962.28418619092628.71581380910
392909624141.81319452434954.18680547568
402648226364.8024652031117.197534796913
412240526417.3900789999-4012.39007899988
422704424616.99367781122427.00632218876
431797025706.0137785737-7736.0137785737
441873022234.7931115239-3504.79311152393
451968420662.1601469665-978.160146966493
461978520223.2506756263-438.250675626263
471847920026.6035591493-1547.60355914932
481069819332.179581545-8634.17958154501
493195615457.943642425016498.0563575750
502950622860.77355376536645.22644623471
513450625842.54789357898663.4521064211
522716529729.9186843467-2564.91868434672
532673628579.0160358708-1843.01603587083
542369127752.0377578411-4061.03775784112
551815725929.8126948854-7772.81269488543
561732822442.0800149977-5114.08001499772
571820520147.3451878476-1942.34518784760
582099519275.79700404331719.20299595674
591738220047.2192301706-2665.21923017058
60936718851.3108025498-9484.31080254982
613112414595.613150909416528.3868490906
622655122012.05263327744538.94736672261
633065124048.72014150456602.27985849545
642585927011.2239516621-1152.22395166209
652510026494.2104472192-1394.21044721916
662577825868.6153724006-90.6153724006472
672041825827.9554198162-5409.95541981619
681868823400.4585721378-4712.45857213785
692042421285.9349871971-861.934987197092
702477620899.17681601873876.82318398128
711981422638.743102212-2824.74310221200
721273821371.2548432508-8633.25484325076
734255317497.433842724525055.5661572755

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 35022 & 35338 & -316 \tabularnewline
4 & 34777 & 35196.2078881729 & -419.207888172874 \tabularnewline
5 & 26887 & 35008.1054458987 & -8121.10544589875 \tabularnewline
6 & 23970 & 31364.0905992381 & -7394.09059923806 \tabularnewline
7 & 22780 & 28046.2940134562 & -5266.29401345616 \tabularnewline
8 & 17351 & 25683.2593626001 & -8332.25936260011 \tabularnewline
9 & 21382 & 21944.4978078076 & -562.497807807606 \tabularnewline
10 & 24561 & 21692.0998582280 & 2868.90014177205 \tabularnewline
11 & 17409 & 22979.4017877311 & -5570.40178773114 \tabularnewline
12 & 11514 & 20479.9111763134 & -8965.91117631339 \tabularnewline
13 & 31514 & 16456.8242138326 & 15057.1757861674 \tabularnewline
14 & 27071 & 23213.1177355825 & 3857.88226441747 \tabularnewline
15 & 29462 & 24944.1850566337 & 4517.81494336628 \tabularnewline
16 & 26105 & 26971.3702517732 & -866.370251773158 \tabularnewline
17 & 22397 & 26582.6219365101 & -4185.62193651013 \tabularnewline
18 & 23843 & 24704.4948045869 & -861.49480458695 \tabularnewline
19 & 21705 & 24317.9341474019 & -2612.93414740188 \tabularnewline
20 & 18089 & 23145.4865182078 & -5056.4865182078 \tabularnewline
21 & 20764 & 20876.5944237708 & -112.594423770817 \tabularnewline
22 & 25316 & 20826.0722683075 & 4489.92773169255 \tabularnewline
23 & 17704 & 22840.7442145982 & -5136.7442145982 \tabularnewline
24 & 15548 & 20535.8397522448 & -4987.83975224484 \tabularnewline
25 & 28029 & 18297.7500942509 & 9731.24990574914 \tabularnewline
26 & 29383 & 22664.2515969525 & 6718.74840304751 \tabularnewline
27 & 36438 & 25679.0159162666 & 10758.9840837334 \tabularnewline
28 & 32034 & 30506.6712148331 & 1527.32878516690 \tabularnewline
29 & 22679 & 31191.9977145267 & -8512.9977145267 \tabularnewline
30 & 24319 & 27372.1371957854 & -3053.13719578538 \tabularnewline
31 & 18004 & 26002.1664024678 & -7998.16640246777 \tabularnewline
32 & 17537 & 22413.3154374339 & -4876.31543743394 \tabularnewline
33 & 20366 & 20225.2677671523 & 140.732232847658 \tabularnewline
34 & 22782 & 20288.4156168283 & 2493.58438317166 \tabularnewline
35 & 19169 & 21407.3099070469 & -2238.30990704687 \tabularnewline
36 & 13807 & 20402.9596265286 & -6595.95962652865 \tabularnewline
37 & 29743 & 17443.2917626933 & 12299.7082373067 \tabularnewline
38 & 25591 & 22962.2841861909 & 2628.71581380910 \tabularnewline
39 & 29096 & 24141.8131945243 & 4954.18680547568 \tabularnewline
40 & 26482 & 26364.8024652031 & 117.197534796913 \tabularnewline
41 & 22405 & 26417.3900789999 & -4012.39007899988 \tabularnewline
42 & 27044 & 24616.9936778112 & 2427.00632218876 \tabularnewline
43 & 17970 & 25706.0137785737 & -7736.0137785737 \tabularnewline
44 & 18730 & 22234.7931115239 & -3504.79311152393 \tabularnewline
45 & 19684 & 20662.1601469665 & -978.160146966493 \tabularnewline
46 & 19785 & 20223.2506756263 & -438.250675626263 \tabularnewline
47 & 18479 & 20026.6035591493 & -1547.60355914932 \tabularnewline
48 & 10698 & 19332.179581545 & -8634.17958154501 \tabularnewline
49 & 31956 & 15457.9436424250 & 16498.0563575750 \tabularnewline
50 & 29506 & 22860.7735537653 & 6645.22644623471 \tabularnewline
51 & 34506 & 25842.5478935789 & 8663.4521064211 \tabularnewline
52 & 27165 & 29729.9186843467 & -2564.91868434672 \tabularnewline
53 & 26736 & 28579.0160358708 & -1843.01603587083 \tabularnewline
54 & 23691 & 27752.0377578411 & -4061.03775784112 \tabularnewline
55 & 18157 & 25929.8126948854 & -7772.81269488543 \tabularnewline
56 & 17328 & 22442.0800149977 & -5114.08001499772 \tabularnewline
57 & 18205 & 20147.3451878476 & -1942.34518784760 \tabularnewline
58 & 20995 & 19275.7970040433 & 1719.20299595674 \tabularnewline
59 & 17382 & 20047.2192301706 & -2665.21923017058 \tabularnewline
60 & 9367 & 18851.3108025498 & -9484.31080254982 \tabularnewline
61 & 31124 & 14595.6131509094 & 16528.3868490906 \tabularnewline
62 & 26551 & 22012.0526332774 & 4538.94736672261 \tabularnewline
63 & 30651 & 24048.7201415045 & 6602.27985849545 \tabularnewline
64 & 25859 & 27011.2239516621 & -1152.22395166209 \tabularnewline
65 & 25100 & 26494.2104472192 & -1394.21044721916 \tabularnewline
66 & 25778 & 25868.6153724006 & -90.6153724006472 \tabularnewline
67 & 20418 & 25827.9554198162 & -5409.95541981619 \tabularnewline
68 & 18688 & 23400.4585721378 & -4712.45857213785 \tabularnewline
69 & 20424 & 21285.9349871971 & -861.934987197092 \tabularnewline
70 & 24776 & 20899.1768160187 & 3876.82318398128 \tabularnewline
71 & 19814 & 22638.743102212 & -2824.74310221200 \tabularnewline
72 & 12738 & 21371.2548432508 & -8633.25484325076 \tabularnewline
73 & 42553 & 17497.4338427245 & 25055.5661572755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13305&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]35022[/C][C]35338[/C][C]-316[/C][/ROW]
[ROW][C]4[/C][C]34777[/C][C]35196.2078881729[/C][C]-419.207888172874[/C][/ROW]
[ROW][C]5[/C][C]26887[/C][C]35008.1054458987[/C][C]-8121.10544589875[/C][/ROW]
[ROW][C]6[/C][C]23970[/C][C]31364.0905992381[/C][C]-7394.09059923806[/C][/ROW]
[ROW][C]7[/C][C]22780[/C][C]28046.2940134562[/C][C]-5266.29401345616[/C][/ROW]
[ROW][C]8[/C][C]17351[/C][C]25683.2593626001[/C][C]-8332.25936260011[/C][/ROW]
[ROW][C]9[/C][C]21382[/C][C]21944.4978078076[/C][C]-562.497807807606[/C][/ROW]
[ROW][C]10[/C][C]24561[/C][C]21692.0998582280[/C][C]2868.90014177205[/C][/ROW]
[ROW][C]11[/C][C]17409[/C][C]22979.4017877311[/C][C]-5570.40178773114[/C][/ROW]
[ROW][C]12[/C][C]11514[/C][C]20479.9111763134[/C][C]-8965.91117631339[/C][/ROW]
[ROW][C]13[/C][C]31514[/C][C]16456.8242138326[/C][C]15057.1757861674[/C][/ROW]
[ROW][C]14[/C][C]27071[/C][C]23213.1177355825[/C][C]3857.88226441747[/C][/ROW]
[ROW][C]15[/C][C]29462[/C][C]24944.1850566337[/C][C]4517.81494336628[/C][/ROW]
[ROW][C]16[/C][C]26105[/C][C]26971.3702517732[/C][C]-866.370251773158[/C][/ROW]
[ROW][C]17[/C][C]22397[/C][C]26582.6219365101[/C][C]-4185.62193651013[/C][/ROW]
[ROW][C]18[/C][C]23843[/C][C]24704.4948045869[/C][C]-861.49480458695[/C][/ROW]
[ROW][C]19[/C][C]21705[/C][C]24317.9341474019[/C][C]-2612.93414740188[/C][/ROW]
[ROW][C]20[/C][C]18089[/C][C]23145.4865182078[/C][C]-5056.4865182078[/C][/ROW]
[ROW][C]21[/C][C]20764[/C][C]20876.5944237708[/C][C]-112.594423770817[/C][/ROW]
[ROW][C]22[/C][C]25316[/C][C]20826.0722683075[/C][C]4489.92773169255[/C][/ROW]
[ROW][C]23[/C][C]17704[/C][C]22840.7442145982[/C][C]-5136.7442145982[/C][/ROW]
[ROW][C]24[/C][C]15548[/C][C]20535.8397522448[/C][C]-4987.83975224484[/C][/ROW]
[ROW][C]25[/C][C]28029[/C][C]18297.7500942509[/C][C]9731.24990574914[/C][/ROW]
[ROW][C]26[/C][C]29383[/C][C]22664.2515969525[/C][C]6718.74840304751[/C][/ROW]
[ROW][C]27[/C][C]36438[/C][C]25679.0159162666[/C][C]10758.9840837334[/C][/ROW]
[ROW][C]28[/C][C]32034[/C][C]30506.6712148331[/C][C]1527.32878516690[/C][/ROW]
[ROW][C]29[/C][C]22679[/C][C]31191.9977145267[/C][C]-8512.9977145267[/C][/ROW]
[ROW][C]30[/C][C]24319[/C][C]27372.1371957854[/C][C]-3053.13719578538[/C][/ROW]
[ROW][C]31[/C][C]18004[/C][C]26002.1664024678[/C][C]-7998.16640246777[/C][/ROW]
[ROW][C]32[/C][C]17537[/C][C]22413.3154374339[/C][C]-4876.31543743394[/C][/ROW]
[ROW][C]33[/C][C]20366[/C][C]20225.2677671523[/C][C]140.732232847658[/C][/ROW]
[ROW][C]34[/C][C]22782[/C][C]20288.4156168283[/C][C]2493.58438317166[/C][/ROW]
[ROW][C]35[/C][C]19169[/C][C]21407.3099070469[/C][C]-2238.30990704687[/C][/ROW]
[ROW][C]36[/C][C]13807[/C][C]20402.9596265286[/C][C]-6595.95962652865[/C][/ROW]
[ROW][C]37[/C][C]29743[/C][C]17443.2917626933[/C][C]12299.7082373067[/C][/ROW]
[ROW][C]38[/C][C]25591[/C][C]22962.2841861909[/C][C]2628.71581380910[/C][/ROW]
[ROW][C]39[/C][C]29096[/C][C]24141.8131945243[/C][C]4954.18680547568[/C][/ROW]
[ROW][C]40[/C][C]26482[/C][C]26364.8024652031[/C][C]117.197534796913[/C][/ROW]
[ROW][C]41[/C][C]22405[/C][C]26417.3900789999[/C][C]-4012.39007899988[/C][/ROW]
[ROW][C]42[/C][C]27044[/C][C]24616.9936778112[/C][C]2427.00632218876[/C][/ROW]
[ROW][C]43[/C][C]17970[/C][C]25706.0137785737[/C][C]-7736.0137785737[/C][/ROW]
[ROW][C]44[/C][C]18730[/C][C]22234.7931115239[/C][C]-3504.79311152393[/C][/ROW]
[ROW][C]45[/C][C]19684[/C][C]20662.1601469665[/C][C]-978.160146966493[/C][/ROW]
[ROW][C]46[/C][C]19785[/C][C]20223.2506756263[/C][C]-438.250675626263[/C][/ROW]
[ROW][C]47[/C][C]18479[/C][C]20026.6035591493[/C][C]-1547.60355914932[/C][/ROW]
[ROW][C]48[/C][C]10698[/C][C]19332.179581545[/C][C]-8634.17958154501[/C][/ROW]
[ROW][C]49[/C][C]31956[/C][C]15457.9436424250[/C][C]16498.0563575750[/C][/ROW]
[ROW][C]50[/C][C]29506[/C][C]22860.7735537653[/C][C]6645.22644623471[/C][/ROW]
[ROW][C]51[/C][C]34506[/C][C]25842.5478935789[/C][C]8663.4521064211[/C][/ROW]
[ROW][C]52[/C][C]27165[/C][C]29729.9186843467[/C][C]-2564.91868434672[/C][/ROW]
[ROW][C]53[/C][C]26736[/C][C]28579.0160358708[/C][C]-1843.01603587083[/C][/ROW]
[ROW][C]54[/C][C]23691[/C][C]27752.0377578411[/C][C]-4061.03775784112[/C][/ROW]
[ROW][C]55[/C][C]18157[/C][C]25929.8126948854[/C][C]-7772.81269488543[/C][/ROW]
[ROW][C]56[/C][C]17328[/C][C]22442.0800149977[/C][C]-5114.08001499772[/C][/ROW]
[ROW][C]57[/C][C]18205[/C][C]20147.3451878476[/C][C]-1942.34518784760[/C][/ROW]
[ROW][C]58[/C][C]20995[/C][C]19275.7970040433[/C][C]1719.20299595674[/C][/ROW]
[ROW][C]59[/C][C]17382[/C][C]20047.2192301706[/C][C]-2665.21923017058[/C][/ROW]
[ROW][C]60[/C][C]9367[/C][C]18851.3108025498[/C][C]-9484.31080254982[/C][/ROW]
[ROW][C]61[/C][C]31124[/C][C]14595.6131509094[/C][C]16528.3868490906[/C][/ROW]
[ROW][C]62[/C][C]26551[/C][C]22012.0526332774[/C][C]4538.94736672261[/C][/ROW]
[ROW][C]63[/C][C]30651[/C][C]24048.7201415045[/C][C]6602.27985849545[/C][/ROW]
[ROW][C]64[/C][C]25859[/C][C]27011.2239516621[/C][C]-1152.22395166209[/C][/ROW]
[ROW][C]65[/C][C]25100[/C][C]26494.2104472192[/C][C]-1394.21044721916[/C][/ROW]
[ROW][C]66[/C][C]25778[/C][C]25868.6153724006[/C][C]-90.6153724006472[/C][/ROW]
[ROW][C]67[/C][C]20418[/C][C]25827.9554198162[/C][C]-5409.95541981619[/C][/ROW]
[ROW][C]68[/C][C]18688[/C][C]23400.4585721378[/C][C]-4712.45857213785[/C][/ROW]
[ROW][C]69[/C][C]20424[/C][C]21285.9349871971[/C][C]-861.934987197092[/C][/ROW]
[ROW][C]70[/C][C]24776[/C][C]20899.1768160187[/C][C]3876.82318398128[/C][/ROW]
[ROW][C]71[/C][C]19814[/C][C]22638.743102212[/C][C]-2824.74310221200[/C][/ROW]
[ROW][C]72[/C][C]12738[/C][C]21371.2548432508[/C][C]-8633.25484325076[/C][/ROW]
[ROW][C]73[/C][C]42553[/C][C]17497.4338427245[/C][C]25055.5661572755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13305&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13305&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
33502235338-316
43477735196.2078881729-419.207888172874
52688735008.1054458987-8121.10544589875
62397031364.0905992381-7394.09059923806
72278028046.2940134562-5266.29401345616
81735125683.2593626001-8332.25936260011
92138221944.4978078076-562.497807807606
102456121692.09985822802868.90014177205
111740922979.4017877311-5570.40178773114
121151420479.9111763134-8965.91117631339
133151416456.824213832615057.1757861674
142707123213.11773558253857.88226441747
152946224944.18505663374517.81494336628
162610526971.3702517732-866.370251773158
172239726582.6219365101-4185.62193651013
182384324704.4948045869-861.49480458695
192170524317.9341474019-2612.93414740188
201808923145.4865182078-5056.4865182078
212076420876.5944237708-112.594423770817
222531620826.07226830754489.92773169255
231770422840.7442145982-5136.7442145982
241554820535.8397522448-4987.83975224484
252802918297.75009425099731.24990574914
262938322664.25159695256718.74840304751
273643825679.015916266610758.9840837334
283203430506.67121483311527.32878516690
292267931191.9977145267-8512.9977145267
302431927372.1371957854-3053.13719578538
311800426002.1664024678-7998.16640246777
321753722413.3154374339-4876.31543743394
332036620225.2677671523140.732232847658
342278220288.41561682832493.58438317166
351916921407.3099070469-2238.30990704687
361380720402.9596265286-6595.95962652865
372974317443.291762693312299.7082373067
382559122962.28418619092628.71581380910
392909624141.81319452434954.18680547568
402648226364.8024652031117.197534796913
412240526417.3900789999-4012.39007899988
422704424616.99367781122427.00632218876
431797025706.0137785737-7736.0137785737
441873022234.7931115239-3504.79311152393
451968420662.1601469665-978.160146966493
461978520223.2506756263-438.250675626263
471847920026.6035591493-1547.60355914932
481069819332.179581545-8634.17958154501
493195615457.943642425016498.0563575750
502950622860.77355376536645.22644623471
513450625842.54789357898663.4521064211
522716529729.9186843467-2564.91868434672
532673628579.0160358708-1843.01603587083
542369127752.0377578411-4061.03775784112
551815725929.8126948854-7772.81269488543
561732822442.0800149977-5114.08001499772
571820520147.3451878476-1942.34518784760
582099519275.79700404331719.20299595674
591738220047.2192301706-2665.21923017058
60936718851.3108025498-9484.31080254982
613112414595.613150909416528.3868490906
622655122012.05263327744538.94736672261
633065124048.72014150456602.27985849545
642585927011.2239516621-1152.22395166209
652510026494.2104472192-1394.21044721916
662577825868.6153724006-90.6153724006472
672041825827.9554198162-5409.95541981619
681868823400.4585721378-4712.45857213785
692042421285.9349871971-861.934987197092
702477620899.17681601873876.82318398128
711981422638.743102212-2824.74310221200
721273821371.2548432508-8633.25484325076
734255317497.433842724525055.5661572755







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7428740.097255586615316.652037596042163.5424735771
7528740.097255586614027.242209981443452.9523011918
7628740.097255586612842.068268772344638.1262424008
7728740.097255586611739.316457688445740.8780534847
7828740.097255586610703.862343311346776.3321678619
7928740.09725558669724.7089639062147755.4855472669
8028740.09725558668793.563372328348686.6311388448
8128740.09725558667903.9883091309949576.2062020421
8228740.09725558667050.8681752074750429.3263359657
8328740.09725558666230.057713778651250.1367973945
8428740.09725558665438.1423537686952042.0521574044
8528740.09725558664672.2696776984852807.9248334746

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 28740.0972555866 & 15316.6520375960 & 42163.5424735771 \tabularnewline
75 & 28740.0972555866 & 14027.2422099814 & 43452.9523011918 \tabularnewline
76 & 28740.0972555866 & 12842.0682687723 & 44638.1262424008 \tabularnewline
77 & 28740.0972555866 & 11739.3164576884 & 45740.8780534847 \tabularnewline
78 & 28740.0972555866 & 10703.8623433113 & 46776.3321678619 \tabularnewline
79 & 28740.0972555866 & 9724.70896390621 & 47755.4855472669 \tabularnewline
80 & 28740.0972555866 & 8793.5633723283 & 48686.6311388448 \tabularnewline
81 & 28740.0972555866 & 7903.98830913099 & 49576.2062020421 \tabularnewline
82 & 28740.0972555866 & 7050.86817520747 & 50429.3263359657 \tabularnewline
83 & 28740.0972555866 & 6230.0577137786 & 51250.1367973945 \tabularnewline
84 & 28740.0972555866 & 5438.14235376869 & 52042.0521574044 \tabularnewline
85 & 28740.0972555866 & 4672.26967769848 & 52807.9248334746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13305&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]74[/C][C]28740.0972555866[/C][C]15316.6520375960[/C][C]42163.5424735771[/C][/ROW]
[ROW][C]75[/C][C]28740.0972555866[/C][C]14027.2422099814[/C][C]43452.9523011918[/C][/ROW]
[ROW][C]76[/C][C]28740.0972555866[/C][C]12842.0682687723[/C][C]44638.1262424008[/C][/ROW]
[ROW][C]77[/C][C]28740.0972555866[/C][C]11739.3164576884[/C][C]45740.8780534847[/C][/ROW]
[ROW][C]78[/C][C]28740.0972555866[/C][C]10703.8623433113[/C][C]46776.3321678619[/C][/ROW]
[ROW][C]79[/C][C]28740.0972555866[/C][C]9724.70896390621[/C][C]47755.4855472669[/C][/ROW]
[ROW][C]80[/C][C]28740.0972555866[/C][C]8793.5633723283[/C][C]48686.6311388448[/C][/ROW]
[ROW][C]81[/C][C]28740.0972555866[/C][C]7903.98830913099[/C][C]49576.2062020421[/C][/ROW]
[ROW][C]82[/C][C]28740.0972555866[/C][C]7050.86817520747[/C][C]50429.3263359657[/C][/ROW]
[ROW][C]83[/C][C]28740.0972555866[/C][C]6230.0577137786[/C][C]51250.1367973945[/C][/ROW]
[ROW][C]84[/C][C]28740.0972555866[/C][C]5438.14235376869[/C][C]52042.0521574044[/C][/ROW]
[ROW][C]85[/C][C]28740.0972555866[/C][C]4672.26967769848[/C][C]52807.9248334746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13305&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13305&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
7428740.097255586615316.652037596042163.5424735771
7528740.097255586614027.242209981443452.9523011918
7628740.097255586612842.068268772344638.1262424008
7728740.097255586611739.316457688445740.8780534847
7828740.097255586610703.862343311346776.3321678619
7928740.09725558669724.7089639062147755.4855472669
8028740.09725558668793.563372328348686.6311388448
8128740.09725558667903.9883091309949576.2062020421
8228740.09725558667050.8681752074750429.3263359657
8328740.09725558666230.057713778651250.1367973945
8428740.09725558665438.1423537686952042.0521574044
8528740.09725558664672.2696776984852807.9248334746



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')