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Author's title

Exponential Smoothing bij Time Series Analysis-Inschrijvingen nieuwe person...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 May 2011 10:00:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/17/t1305626298kbn2l00oje8u8st.htm/, Retrieved Thu, 09 May 2024 22:55:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121694, Retrieved Thu, 09 May 2024 22:55:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [frederic.ledent@s...] [2010-01-25 19:19:03] [ef87393097b01fda8ad7ae01bd2302b6]
- R  D  [Exponential Smoothing] [Exponential Smoot...] [2011-05-17 09:50:26] [64436569c304b71889fb9a9a76c05abb]
-    D      [Exponential Smoothing] [Exponential Smoot...] [2011-05-17 10:00:51] [ebb64913e7d7e5b0e5266ebfea2a3acd] [Current]
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Dataseries X:
26281
23899
25727
30733
28599
16723
43738
45272
46532
41032
37967
35366
33892
21560
26588
33527
24859
17952
45504
40129
40357
41913
33730
37842
33025
24050
30429
34507
25189
20253
48527
44446
46380
48950
38883
42928
37107
30186
32602
39892
32194
21629
59968
45694
55756
48554
41052
49822
39191
31994
35735
38930
33658
23849
58972
59249
63955
53785
52760
44795
37348
32370
32717
40974
33591
21124
58608
46865
51378
46235
47206
45382
41227
33795
31295
42625
33625
21538
56421
53152
53536
52408
41454
38271
35306
26414
31917
38030
27534
18387




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121694&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121694&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121694&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.299879412252782
beta0
gamma0.349182850776405

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.299879412252782 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.349182850776405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121694&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]0.299879412252782[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.349182850776405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121694&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121694&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
alpha0.299879412252782
beta0
gamma0.349182850776405







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133389233798.397696158493.6023038415951
142156021552.97200267857.02799732148924
152658826888.1310517072-300.131051707198
163352733929.5240389334-402.524038933356
172485925109.3522847842-250.35228478421
181795218072.0832006946-120.08320069464
194550442850.43657931222653.56342068777
204012944771.087406539-4642.08740653903
214035744549.5657657189-4192.56576571891
224191337901.57072517914011.42927482095
233373036129.7009680399-2399.70096803994
243784232996.45936977994845.54063022006
253302532829.7714509667195.228549033258
262405020941.17248184953108.82751815046
273042927209.38889904173219.6111009583
283450735671.1619825215-1164.16198252153
292518926248.5428154518-1059.5428154518
302025318736.4019317571516.59806824305
314852746355.33894095462171.66105904542
324444646275.7477951946-1829.74779519455
334638047090.2980031004-710.298003100448
344895043101.07933923085848.92066076915
353888339770.2737958123-887.273795812296
364292838731.22179160384196.7782083962
373710736906.5305457332200.4694542668
383018624327.45260788055858.54739211946
393260232244.5889745158357.41102548422
403989239535.1691910924356.830808907573
413219429409.90555661252784.0944433875
422162922508.9016903962-879.901690396178
435996853324.33102860096643.66897139913
444569453339.683081199-7645.683081199
455575652905.99930390982850.00069609021
464855451211.8180620544-2657.81806205442
474105243089.3371452171-2037.33714521712
484982242959.26218260196862.73781739811
493919140569.2102791524-1378.21027915242
503199427845.43807574484148.56192425518
513573534183.88932295511551.1106770449
523893042327.2384151215-3397.23841512149
533365831269.54841018782388.45158981219
542384923057.1729841271791.827015872852
555897258047.8843362817924.115663718301
565924952638.34746552536610.65253447473
576395559536.00617751684418.99382248316
585378556508.9716928303-2723.97169283033
595276047666.93184290675093.06815709334
604479552234.4682698308-7439.46826983076
613734843085.2062658501-5737.20626585011
623237029937.28734908572432.71265091434
633271735205.7453001402-2488.74530014017
644097440801.3467616453172.653238354709
653359132136.10371915691454.89628084312
662112423250.7063630654-2126.70636306539
675860856096.89418218232511.1058178177
684686552618.1462843655-5753.14628436547
695137854823.7040192324-3445.70401923241
704623548471.9813162077-2236.98131620768
714720642443.78266926974762.21733073031
724538243768.42814239321613.57185760684
734122738220.52776591553006.47223408447
743379529875.02246899073919.97753100931
753129534350.2593572568-3055.25935725682
764262540339.38980954762285.61019045239
773362532590.0778854171034.92211458299
782153822697.0158892503-1159.01588925028
795642157362.1369654417-941.136965441707
805315250821.46917539842330.53082460164
815353656187.9243639391-2651.9243639391
825240850134.65846141782273.3415385822
834145446861.8263071366-5407.82630713655
843827144359.0796649402-6088.07966494024
853530637091.4423342542-1785.44233425417
862641428241.0030737985-1827.00307379846
873191729045.73844148052871.26155851945
883803037403.5710188032626.428981196754
892753429681.4224998943-2147.4224998943
901838719621.4912786712-1234.49127867119

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 33892 & 33798.3976961584 & 93.6023038415951 \tabularnewline
14 & 21560 & 21552.9720026785 & 7.02799732148924 \tabularnewline
15 & 26588 & 26888.1310517072 & -300.131051707198 \tabularnewline
16 & 33527 & 33929.5240389334 & -402.524038933356 \tabularnewline
17 & 24859 & 25109.3522847842 & -250.35228478421 \tabularnewline
18 & 17952 & 18072.0832006946 & -120.08320069464 \tabularnewline
19 & 45504 & 42850.4365793122 & 2653.56342068777 \tabularnewline
20 & 40129 & 44771.087406539 & -4642.08740653903 \tabularnewline
21 & 40357 & 44549.5657657189 & -4192.56576571891 \tabularnewline
22 & 41913 & 37901.5707251791 & 4011.42927482095 \tabularnewline
23 & 33730 & 36129.7009680399 & -2399.70096803994 \tabularnewline
24 & 37842 & 32996.4593697799 & 4845.54063022006 \tabularnewline
25 & 33025 & 32829.7714509667 & 195.228549033258 \tabularnewline
26 & 24050 & 20941.1724818495 & 3108.82751815046 \tabularnewline
27 & 30429 & 27209.3888990417 & 3219.6111009583 \tabularnewline
28 & 34507 & 35671.1619825215 & -1164.16198252153 \tabularnewline
29 & 25189 & 26248.5428154518 & -1059.5428154518 \tabularnewline
30 & 20253 & 18736.401931757 & 1516.59806824305 \tabularnewline
31 & 48527 & 46355.3389409546 & 2171.66105904542 \tabularnewline
32 & 44446 & 46275.7477951946 & -1829.74779519455 \tabularnewline
33 & 46380 & 47090.2980031004 & -710.298003100448 \tabularnewline
34 & 48950 & 43101.0793392308 & 5848.92066076915 \tabularnewline
35 & 38883 & 39770.2737958123 & -887.273795812296 \tabularnewline
36 & 42928 & 38731.2217916038 & 4196.7782083962 \tabularnewline
37 & 37107 & 36906.5305457332 & 200.4694542668 \tabularnewline
38 & 30186 & 24327.4526078805 & 5858.54739211946 \tabularnewline
39 & 32602 & 32244.5889745158 & 357.41102548422 \tabularnewline
40 & 39892 & 39535.1691910924 & 356.830808907573 \tabularnewline
41 & 32194 & 29409.9055566125 & 2784.0944433875 \tabularnewline
42 & 21629 & 22508.9016903962 & -879.901690396178 \tabularnewline
43 & 59968 & 53324.3310286009 & 6643.66897139913 \tabularnewline
44 & 45694 & 53339.683081199 & -7645.683081199 \tabularnewline
45 & 55756 & 52905.9993039098 & 2850.00069609021 \tabularnewline
46 & 48554 & 51211.8180620544 & -2657.81806205442 \tabularnewline
47 & 41052 & 43089.3371452171 & -2037.33714521712 \tabularnewline
48 & 49822 & 42959.2621826019 & 6862.73781739811 \tabularnewline
49 & 39191 & 40569.2102791524 & -1378.21027915242 \tabularnewline
50 & 31994 & 27845.4380757448 & 4148.56192425518 \tabularnewline
51 & 35735 & 34183.8893229551 & 1551.1106770449 \tabularnewline
52 & 38930 & 42327.2384151215 & -3397.23841512149 \tabularnewline
53 & 33658 & 31269.5484101878 & 2388.45158981219 \tabularnewline
54 & 23849 & 23057.1729841271 & 791.827015872852 \tabularnewline
55 & 58972 & 58047.8843362817 & 924.115663718301 \tabularnewline
56 & 59249 & 52638.3474655253 & 6610.65253447473 \tabularnewline
57 & 63955 & 59536.0061775168 & 4418.99382248316 \tabularnewline
58 & 53785 & 56508.9716928303 & -2723.97169283033 \tabularnewline
59 & 52760 & 47666.9318429067 & 5093.06815709334 \tabularnewline
60 & 44795 & 52234.4682698308 & -7439.46826983076 \tabularnewline
61 & 37348 & 43085.2062658501 & -5737.20626585011 \tabularnewline
62 & 32370 & 29937.2873490857 & 2432.71265091434 \tabularnewline
63 & 32717 & 35205.7453001402 & -2488.74530014017 \tabularnewline
64 & 40974 & 40801.3467616453 & 172.653238354709 \tabularnewline
65 & 33591 & 32136.1037191569 & 1454.89628084312 \tabularnewline
66 & 21124 & 23250.7063630654 & -2126.70636306539 \tabularnewline
67 & 58608 & 56096.8941821823 & 2511.1058178177 \tabularnewline
68 & 46865 & 52618.1462843655 & -5753.14628436547 \tabularnewline
69 & 51378 & 54823.7040192324 & -3445.70401923241 \tabularnewline
70 & 46235 & 48471.9813162077 & -2236.98131620768 \tabularnewline
71 & 47206 & 42443.7826692697 & 4762.21733073031 \tabularnewline
72 & 45382 & 43768.4281423932 & 1613.57185760684 \tabularnewline
73 & 41227 & 38220.5277659155 & 3006.47223408447 \tabularnewline
74 & 33795 & 29875.0224689907 & 3919.97753100931 \tabularnewline
75 & 31295 & 34350.2593572568 & -3055.25935725682 \tabularnewline
76 & 42625 & 40339.3898095476 & 2285.61019045239 \tabularnewline
77 & 33625 & 32590.077885417 & 1034.92211458299 \tabularnewline
78 & 21538 & 22697.0158892503 & -1159.01588925028 \tabularnewline
79 & 56421 & 57362.1369654417 & -941.136965441707 \tabularnewline
80 & 53152 & 50821.4691753984 & 2330.53082460164 \tabularnewline
81 & 53536 & 56187.9243639391 & -2651.9243639391 \tabularnewline
82 & 52408 & 50134.6584614178 & 2273.3415385822 \tabularnewline
83 & 41454 & 46861.8263071366 & -5407.82630713655 \tabularnewline
84 & 38271 & 44359.0796649402 & -6088.07966494024 \tabularnewline
85 & 35306 & 37091.4423342542 & -1785.44233425417 \tabularnewline
86 & 26414 & 28241.0030737985 & -1827.00307379846 \tabularnewline
87 & 31917 & 29045.7384414805 & 2871.26155851945 \tabularnewline
88 & 38030 & 37403.5710188032 & 626.428981196754 \tabularnewline
89 & 27534 & 29681.4224998943 & -2147.4224998943 \tabularnewline
90 & 18387 & 19621.4912786712 & -1234.49127867119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121694&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]33892[/C][C]33798.3976961584[/C][C]93.6023038415951[/C][/ROW]
[ROW][C]14[/C][C]21560[/C][C]21552.9720026785[/C][C]7.02799732148924[/C][/ROW]
[ROW][C]15[/C][C]26588[/C][C]26888.1310517072[/C][C]-300.131051707198[/C][/ROW]
[ROW][C]16[/C][C]33527[/C][C]33929.5240389334[/C][C]-402.524038933356[/C][/ROW]
[ROW][C]17[/C][C]24859[/C][C]25109.3522847842[/C][C]-250.35228478421[/C][/ROW]
[ROW][C]18[/C][C]17952[/C][C]18072.0832006946[/C][C]-120.08320069464[/C][/ROW]
[ROW][C]19[/C][C]45504[/C][C]42850.4365793122[/C][C]2653.56342068777[/C][/ROW]
[ROW][C]20[/C][C]40129[/C][C]44771.087406539[/C][C]-4642.08740653903[/C][/ROW]
[ROW][C]21[/C][C]40357[/C][C]44549.5657657189[/C][C]-4192.56576571891[/C][/ROW]
[ROW][C]22[/C][C]41913[/C][C]37901.5707251791[/C][C]4011.42927482095[/C][/ROW]
[ROW][C]23[/C][C]33730[/C][C]36129.7009680399[/C][C]-2399.70096803994[/C][/ROW]
[ROW][C]24[/C][C]37842[/C][C]32996.4593697799[/C][C]4845.54063022006[/C][/ROW]
[ROW][C]25[/C][C]33025[/C][C]32829.7714509667[/C][C]195.228549033258[/C][/ROW]
[ROW][C]26[/C][C]24050[/C][C]20941.1724818495[/C][C]3108.82751815046[/C][/ROW]
[ROW][C]27[/C][C]30429[/C][C]27209.3888990417[/C][C]3219.6111009583[/C][/ROW]
[ROW][C]28[/C][C]34507[/C][C]35671.1619825215[/C][C]-1164.16198252153[/C][/ROW]
[ROW][C]29[/C][C]25189[/C][C]26248.5428154518[/C][C]-1059.5428154518[/C][/ROW]
[ROW][C]30[/C][C]20253[/C][C]18736.401931757[/C][C]1516.59806824305[/C][/ROW]
[ROW][C]31[/C][C]48527[/C][C]46355.3389409546[/C][C]2171.66105904542[/C][/ROW]
[ROW][C]32[/C][C]44446[/C][C]46275.7477951946[/C][C]-1829.74779519455[/C][/ROW]
[ROW][C]33[/C][C]46380[/C][C]47090.2980031004[/C][C]-710.298003100448[/C][/ROW]
[ROW][C]34[/C][C]48950[/C][C]43101.0793392308[/C][C]5848.92066076915[/C][/ROW]
[ROW][C]35[/C][C]38883[/C][C]39770.2737958123[/C][C]-887.273795812296[/C][/ROW]
[ROW][C]36[/C][C]42928[/C][C]38731.2217916038[/C][C]4196.7782083962[/C][/ROW]
[ROW][C]37[/C][C]37107[/C][C]36906.5305457332[/C][C]200.4694542668[/C][/ROW]
[ROW][C]38[/C][C]30186[/C][C]24327.4526078805[/C][C]5858.54739211946[/C][/ROW]
[ROW][C]39[/C][C]32602[/C][C]32244.5889745158[/C][C]357.41102548422[/C][/ROW]
[ROW][C]40[/C][C]39892[/C][C]39535.1691910924[/C][C]356.830808907573[/C][/ROW]
[ROW][C]41[/C][C]32194[/C][C]29409.9055566125[/C][C]2784.0944433875[/C][/ROW]
[ROW][C]42[/C][C]21629[/C][C]22508.9016903962[/C][C]-879.901690396178[/C][/ROW]
[ROW][C]43[/C][C]59968[/C][C]53324.3310286009[/C][C]6643.66897139913[/C][/ROW]
[ROW][C]44[/C][C]45694[/C][C]53339.683081199[/C][C]-7645.683081199[/C][/ROW]
[ROW][C]45[/C][C]55756[/C][C]52905.9993039098[/C][C]2850.00069609021[/C][/ROW]
[ROW][C]46[/C][C]48554[/C][C]51211.8180620544[/C][C]-2657.81806205442[/C][/ROW]
[ROW][C]47[/C][C]41052[/C][C]43089.3371452171[/C][C]-2037.33714521712[/C][/ROW]
[ROW][C]48[/C][C]49822[/C][C]42959.2621826019[/C][C]6862.73781739811[/C][/ROW]
[ROW][C]49[/C][C]39191[/C][C]40569.2102791524[/C][C]-1378.21027915242[/C][/ROW]
[ROW][C]50[/C][C]31994[/C][C]27845.4380757448[/C][C]4148.56192425518[/C][/ROW]
[ROW][C]51[/C][C]35735[/C][C]34183.8893229551[/C][C]1551.1106770449[/C][/ROW]
[ROW][C]52[/C][C]38930[/C][C]42327.2384151215[/C][C]-3397.23841512149[/C][/ROW]
[ROW][C]53[/C][C]33658[/C][C]31269.5484101878[/C][C]2388.45158981219[/C][/ROW]
[ROW][C]54[/C][C]23849[/C][C]23057.1729841271[/C][C]791.827015872852[/C][/ROW]
[ROW][C]55[/C][C]58972[/C][C]58047.8843362817[/C][C]924.115663718301[/C][/ROW]
[ROW][C]56[/C][C]59249[/C][C]52638.3474655253[/C][C]6610.65253447473[/C][/ROW]
[ROW][C]57[/C][C]63955[/C][C]59536.0061775168[/C][C]4418.99382248316[/C][/ROW]
[ROW][C]58[/C][C]53785[/C][C]56508.9716928303[/C][C]-2723.97169283033[/C][/ROW]
[ROW][C]59[/C][C]52760[/C][C]47666.9318429067[/C][C]5093.06815709334[/C][/ROW]
[ROW][C]60[/C][C]44795[/C][C]52234.4682698308[/C][C]-7439.46826983076[/C][/ROW]
[ROW][C]61[/C][C]37348[/C][C]43085.2062658501[/C][C]-5737.20626585011[/C][/ROW]
[ROW][C]62[/C][C]32370[/C][C]29937.2873490857[/C][C]2432.71265091434[/C][/ROW]
[ROW][C]63[/C][C]32717[/C][C]35205.7453001402[/C][C]-2488.74530014017[/C][/ROW]
[ROW][C]64[/C][C]40974[/C][C]40801.3467616453[/C][C]172.653238354709[/C][/ROW]
[ROW][C]65[/C][C]33591[/C][C]32136.1037191569[/C][C]1454.89628084312[/C][/ROW]
[ROW][C]66[/C][C]21124[/C][C]23250.7063630654[/C][C]-2126.70636306539[/C][/ROW]
[ROW][C]67[/C][C]58608[/C][C]56096.8941821823[/C][C]2511.1058178177[/C][/ROW]
[ROW][C]68[/C][C]46865[/C][C]52618.1462843655[/C][C]-5753.14628436547[/C][/ROW]
[ROW][C]69[/C][C]51378[/C][C]54823.7040192324[/C][C]-3445.70401923241[/C][/ROW]
[ROW][C]70[/C][C]46235[/C][C]48471.9813162077[/C][C]-2236.98131620768[/C][/ROW]
[ROW][C]71[/C][C]47206[/C][C]42443.7826692697[/C][C]4762.21733073031[/C][/ROW]
[ROW][C]72[/C][C]45382[/C][C]43768.4281423932[/C][C]1613.57185760684[/C][/ROW]
[ROW][C]73[/C][C]41227[/C][C]38220.5277659155[/C][C]3006.47223408447[/C][/ROW]
[ROW][C]74[/C][C]33795[/C][C]29875.0224689907[/C][C]3919.97753100931[/C][/ROW]
[ROW][C]75[/C][C]31295[/C][C]34350.2593572568[/C][C]-3055.25935725682[/C][/ROW]
[ROW][C]76[/C][C]42625[/C][C]40339.3898095476[/C][C]2285.61019045239[/C][/ROW]
[ROW][C]77[/C][C]33625[/C][C]32590.077885417[/C][C]1034.92211458299[/C][/ROW]
[ROW][C]78[/C][C]21538[/C][C]22697.0158892503[/C][C]-1159.01588925028[/C][/ROW]
[ROW][C]79[/C][C]56421[/C][C]57362.1369654417[/C][C]-941.136965441707[/C][/ROW]
[ROW][C]80[/C][C]53152[/C][C]50821.4691753984[/C][C]2330.53082460164[/C][/ROW]
[ROW][C]81[/C][C]53536[/C][C]56187.9243639391[/C][C]-2651.9243639391[/C][/ROW]
[ROW][C]82[/C][C]52408[/C][C]50134.6584614178[/C][C]2273.3415385822[/C][/ROW]
[ROW][C]83[/C][C]41454[/C][C]46861.8263071366[/C][C]-5407.82630713655[/C][/ROW]
[ROW][C]84[/C][C]38271[/C][C]44359.0796649402[/C][C]-6088.07966494024[/C][/ROW]
[ROW][C]85[/C][C]35306[/C][C]37091.4423342542[/C][C]-1785.44233425417[/C][/ROW]
[ROW][C]86[/C][C]26414[/C][C]28241.0030737985[/C][C]-1827.00307379846[/C][/ROW]
[ROW][C]87[/C][C]31917[/C][C]29045.7384414805[/C][C]2871.26155851945[/C][/ROW]
[ROW][C]88[/C][C]38030[/C][C]37403.5710188032[/C][C]626.428981196754[/C][/ROW]
[ROW][C]89[/C][C]27534[/C][C]29681.4224998943[/C][C]-2147.4224998943[/C][/ROW]
[ROW][C]90[/C][C]18387[/C][C]19621.4912786712[/C][C]-1234.49127867119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121694&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121694&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
133389233798.397696158493.6023038415951
142156021552.97200267857.02799732148924
152658826888.1310517072-300.131051707198
163352733929.5240389334-402.524038933356
172485925109.3522847842-250.35228478421
181795218072.0832006946-120.08320069464
194550442850.43657931222653.56342068777
204012944771.087406539-4642.08740653903
214035744549.5657657189-4192.56576571891
224191337901.57072517914011.42927482095
233373036129.7009680399-2399.70096803994
243784232996.45936977994845.54063022006
253302532829.7714509667195.228549033258
262405020941.17248184953108.82751815046
273042927209.38889904173219.6111009583
283450735671.1619825215-1164.16198252153
292518926248.5428154518-1059.5428154518
302025318736.4019317571516.59806824305
314852746355.33894095462171.66105904542
324444646275.7477951946-1829.74779519455
334638047090.2980031004-710.298003100448
344895043101.07933923085848.92066076915
353888339770.2737958123-887.273795812296
364292838731.22179160384196.7782083962
373710736906.5305457332200.4694542668
383018624327.45260788055858.54739211946
393260232244.5889745158357.41102548422
403989239535.1691910924356.830808907573
413219429409.90555661252784.0944433875
422162922508.9016903962-879.901690396178
435996853324.33102860096643.66897139913
444569453339.683081199-7645.683081199
455575652905.99930390982850.00069609021
464855451211.8180620544-2657.81806205442
474105243089.3371452171-2037.33714521712
484982242959.26218260196862.73781739811
493919140569.2102791524-1378.21027915242
503199427845.43807574484148.56192425518
513573534183.88932295511551.1106770449
523893042327.2384151215-3397.23841512149
533365831269.54841018782388.45158981219
542384923057.1729841271791.827015872852
555897258047.8843362817924.115663718301
565924952638.34746552536610.65253447473
576395559536.00617751684418.99382248316
585378556508.9716928303-2723.97169283033
595276047666.93184290675093.06815709334
604479552234.4682698308-7439.46826983076
613734843085.2062658501-5737.20626585011
623237029937.28734908572432.71265091434
633271735205.7453001402-2488.74530014017
644097440801.3467616453172.653238354709
653359132136.10371915691454.89628084312
662112423250.7063630654-2126.70636306539
675860856096.89418218232511.1058178177
684686552618.1462843655-5753.14628436547
695137854823.7040192324-3445.70401923241
704623548471.9813162077-2236.98131620768
714720642443.78266926974762.21733073031
724538243768.42814239321613.57185760684
734122738220.52776591553006.47223408447
743379529875.02246899073919.97753100931
753129534350.2593572568-3055.25935725682
764262540339.38980954762285.61019045239
773362532590.0778854171034.92211458299
782153822697.0158892503-1159.01588925028
795642157362.1369654417-941.136965441707
805315250821.46917539842330.53082460164
815353656187.9243639391-2651.9243639391
825240850134.65846141782273.3415385822
834145446861.8263071366-5407.82630713655
843827144359.0796649402-6088.07966494024
853530637091.4423342542-1785.44233425417
862641428241.0030737985-1827.00307379846
873191729045.73844148052871.26155851945
883803037403.5710188032626.428981196754
892753429681.4224998943-2147.4224998943
901838719621.4912786712-1234.49127867119







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9149828.014653611446267.777982466353388.2513247564
9245023.580622292241044.761594940249002.3996496443
9347981.526753192143435.521805660952527.5317007233
9444408.714352096439627.049820940349190.3788832525
9539313.138910273934442.021501763444184.2563187844
9638308.742746430633123.070704643643494.4147882176
9734199.857476295928990.188701417139409.5262511746
9826305.391323875121451.366067855731159.4165798945
9928698.285982998423194.120850344134202.4511156527
10035206.575118763228487.880163022641925.2700745039
10127180.610661996421313.386151472533047.8351725202
10218409.607112014914974.516388195121844.6978358347

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
91 & 49828.0146536114 & 46267.7779824663 & 53388.2513247564 \tabularnewline
92 & 45023.5806222922 & 41044.7615949402 & 49002.3996496443 \tabularnewline
93 & 47981.5267531921 & 43435.5218056609 & 52527.5317007233 \tabularnewline
94 & 44408.7143520964 & 39627.0498209403 & 49190.3788832525 \tabularnewline
95 & 39313.1389102739 & 34442.0215017634 & 44184.2563187844 \tabularnewline
96 & 38308.7427464306 & 33123.0707046436 & 43494.4147882176 \tabularnewline
97 & 34199.8574762959 & 28990.1887014171 & 39409.5262511746 \tabularnewline
98 & 26305.3913238751 & 21451.3660678557 & 31159.4165798945 \tabularnewline
99 & 28698.2859829984 & 23194.1208503441 & 34202.4511156527 \tabularnewline
100 & 35206.5751187632 & 28487.8801630226 & 41925.2700745039 \tabularnewline
101 & 27180.6106619964 & 21313.3861514725 & 33047.8351725202 \tabularnewline
102 & 18409.6071120149 & 14974.5163881951 & 21844.6978358347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121694&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]91[/C][C]49828.0146536114[/C][C]46267.7779824663[/C][C]53388.2513247564[/C][/ROW]
[ROW][C]92[/C][C]45023.5806222922[/C][C]41044.7615949402[/C][C]49002.3996496443[/C][/ROW]
[ROW][C]93[/C][C]47981.5267531921[/C][C]43435.5218056609[/C][C]52527.5317007233[/C][/ROW]
[ROW][C]94[/C][C]44408.7143520964[/C][C]39627.0498209403[/C][C]49190.3788832525[/C][/ROW]
[ROW][C]95[/C][C]39313.1389102739[/C][C]34442.0215017634[/C][C]44184.2563187844[/C][/ROW]
[ROW][C]96[/C][C]38308.7427464306[/C][C]33123.0707046436[/C][C]43494.4147882176[/C][/ROW]
[ROW][C]97[/C][C]34199.8574762959[/C][C]28990.1887014171[/C][C]39409.5262511746[/C][/ROW]
[ROW][C]98[/C][C]26305.3913238751[/C][C]21451.3660678557[/C][C]31159.4165798945[/C][/ROW]
[ROW][C]99[/C][C]28698.2859829984[/C][C]23194.1208503441[/C][C]34202.4511156527[/C][/ROW]
[ROW][C]100[/C][C]35206.5751187632[/C][C]28487.8801630226[/C][C]41925.2700745039[/C][/ROW]
[ROW][C]101[/C][C]27180.6106619964[/C][C]21313.3861514725[/C][C]33047.8351725202[/C][/ROW]
[ROW][C]102[/C][C]18409.6071120149[/C][C]14974.5163881951[/C][C]21844.6978358347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121694&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121694&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
9149828.014653611446267.777982466353388.2513247564
9245023.580622292241044.761594940249002.3996496443
9347981.526753192143435.521805660952527.5317007233
9444408.714352096439627.049820940349190.3788832525
9539313.138910273934442.021501763444184.2563187844
9638308.742746430633123.070704643643494.4147882176
9734199.857476295928990.188701417139409.5262511746
9826305.391323875121451.366067855731159.4165798945
9928698.285982998423194.120850344134202.4511156527
10035206.575118763228487.880163022641925.2700745039
10127180.610661996421313.386151472533047.8351725202
10218409.607112014914974.516388195121844.6978358347



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=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')