Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Aug 2010 13:53:17 +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/2010/Aug/15/t12818803802ilui3t81ghh44g.htm/, Retrieved Sat, 27 Apr 2024 22:57:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78869, Retrieved Sat, 27 Apr 2024 22:57:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVanhille Olivier
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks B - sta...] [2010-08-15 13:53:17] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [Current]
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Dataseries X:
31
30
29
27
25
24
25
27
28
28
29
31
31
27
25
16
20
21
25
24
28
27
23
36
37
30
27
22
22
25
33
35
35
29
25
34
31
29
21
19
18
25
23
22
20
15
17
25
26
26
23
24
24
42
40
45
47
40
39
49
55
54
48
44
48
62
57
60
56
57
54
62
65
68
69
67
72
82
72
77
79
78
76
79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78869&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78869&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.520658832476764
beta0.0678765650221037
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.520658832476764 \tabularnewline
beta & 0.0678765650221037 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78869&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]0.520658832476764[/C][/ROW]
[ROW][C]beta[/C][C]0.0678765650221037[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78869&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
alpha0.520658832476764
beta0.0678765650221037
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133133.4532585470086-2.45325854700856
142727.9437063932416-0.94370639324157
152525.1867648143935-0.186764814393538
161615.73399785280390.266002147196119
172019.77636866650640.223631333493604
182120.55458199235830.445418007641692
192521.63067848553883.36932151446123
202425.2648714500173-1.26487145001733
212825.60819635146242.39180364853759
222727.2732623898038-0.273262389803808
232328.5827476842846-5.58274768428455
243627.59717195164678.40282804835326
253730.80598902473756.19401097526254
263030.9832039372554-0.983203937255428
272729.0280343300294-2.02803433002937
282219.22805598650242.77194401349764
292225.0378508230883-3.03785082308835
302524.59198695420730.408013045792671
313327.41656444674425.58343555325582
323530.42685284841664.57314715158338
333536.2135641724594-1.21356417245944
342935.2475476858378-6.24754768583777
352531.2138392076751-6.21383920767509
363436.893664703057-2.89366470305702
373133.0529844221021-2.05298442210209
382925.09543887771093.90456112228908
392124.9564784361844-3.95647843618443
401916.15729495307582.84270504692423
411818.9255881332679-0.92558813326794
422521.01241521648473.98758478351532
432328.0892037074704-5.08920370747038
442224.5889209187551-2.58892091875512
452023.1502235058480-3.15022350584795
461517.9718243487926-2.97182434879256
471714.9845254806892.01547451931101
482526.156057971405-1.15605797140502
492623.30000439298392.69999560701610
502620.51776330912975.48223669087033
512317.33279619388005.66720380611997
522417.04418496759086.95581503240918
532420.53385518510023.46614481489981
544227.80371709043114.1962829095690
554036.74701110080243.25298889919762
564539.98560564456665.0143943554334
574743.70224386144863.29775613855138
584043.6600891697479-3.66008916974786
593944.3742660117102-5.37426601171016
604951.5860705744416-2.58607057444163
615551.19134795642313.80865204357686
625451.71667626581592.28332373418412
634848.238472867004-0.238472867003964
644446.567637215551-2.56763721555102
654844.16446531554833.83553468445174
666257.52147468337464.47852531662537
675756.56755475209050.432445247909548
686059.49023667149960.509763328500441
695660.1877617203684-4.18776172036841
705752.7976002848954.20239971510503
715456.946216368561-2.94621636856097
726267.0069523359703-5.00695233597027
736568.579723856218-3.57972385621802
746864.4286610041043.57133899589599
756960.3593770076448.64062299235602
766762.45595246972364.54404753027639
777267.33707245909544.66292754090462
788281.97455012879230.0254498712076980
797277.1467373538709-5.14673735387086
807777.3885519880269-0.388551988026904
817975.52181882477053.47818117522954
827876.57084128713031.42915871286971
837676.17700439504-0.177004395040044
847987.1177103046551-8.11771030465512

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31 & 33.4532585470086 & -2.45325854700856 \tabularnewline
14 & 27 & 27.9437063932416 & -0.94370639324157 \tabularnewline
15 & 25 & 25.1867648143935 & -0.186764814393538 \tabularnewline
16 & 16 & 15.7339978528039 & 0.266002147196119 \tabularnewline
17 & 20 & 19.7763686665064 & 0.223631333493604 \tabularnewline
18 & 21 & 20.5545819923583 & 0.445418007641692 \tabularnewline
19 & 25 & 21.6306784855388 & 3.36932151446123 \tabularnewline
20 & 24 & 25.2648714500173 & -1.26487145001733 \tabularnewline
21 & 28 & 25.6081963514624 & 2.39180364853759 \tabularnewline
22 & 27 & 27.2732623898038 & -0.273262389803808 \tabularnewline
23 & 23 & 28.5827476842846 & -5.58274768428455 \tabularnewline
24 & 36 & 27.5971719516467 & 8.40282804835326 \tabularnewline
25 & 37 & 30.8059890247375 & 6.19401097526254 \tabularnewline
26 & 30 & 30.9832039372554 & -0.983203937255428 \tabularnewline
27 & 27 & 29.0280343300294 & -2.02803433002937 \tabularnewline
28 & 22 & 19.2280559865024 & 2.77194401349764 \tabularnewline
29 & 22 & 25.0378508230883 & -3.03785082308835 \tabularnewline
30 & 25 & 24.5919869542073 & 0.408013045792671 \tabularnewline
31 & 33 & 27.4165644467442 & 5.58343555325582 \tabularnewline
32 & 35 & 30.4268528484166 & 4.57314715158338 \tabularnewline
33 & 35 & 36.2135641724594 & -1.21356417245944 \tabularnewline
34 & 29 & 35.2475476858378 & -6.24754768583777 \tabularnewline
35 & 25 & 31.2138392076751 & -6.21383920767509 \tabularnewline
36 & 34 & 36.893664703057 & -2.89366470305702 \tabularnewline
37 & 31 & 33.0529844221021 & -2.05298442210209 \tabularnewline
38 & 29 & 25.0954388777109 & 3.90456112228908 \tabularnewline
39 & 21 & 24.9564784361844 & -3.95647843618443 \tabularnewline
40 & 19 & 16.1572949530758 & 2.84270504692423 \tabularnewline
41 & 18 & 18.9255881332679 & -0.92558813326794 \tabularnewline
42 & 25 & 21.0124152164847 & 3.98758478351532 \tabularnewline
43 & 23 & 28.0892037074704 & -5.08920370747038 \tabularnewline
44 & 22 & 24.5889209187551 & -2.58892091875512 \tabularnewline
45 & 20 & 23.1502235058480 & -3.15022350584795 \tabularnewline
46 & 15 & 17.9718243487926 & -2.97182434879256 \tabularnewline
47 & 17 & 14.984525480689 & 2.01547451931101 \tabularnewline
48 & 25 & 26.156057971405 & -1.15605797140502 \tabularnewline
49 & 26 & 23.3000043929839 & 2.69999560701610 \tabularnewline
50 & 26 & 20.5177633091297 & 5.48223669087033 \tabularnewline
51 & 23 & 17.3327961938800 & 5.66720380611997 \tabularnewline
52 & 24 & 17.0441849675908 & 6.95581503240918 \tabularnewline
53 & 24 & 20.5338551851002 & 3.46614481489981 \tabularnewline
54 & 42 & 27.803717090431 & 14.1962829095690 \tabularnewline
55 & 40 & 36.7470111008024 & 3.25298889919762 \tabularnewline
56 & 45 & 39.9856056445666 & 5.0143943554334 \tabularnewline
57 & 47 & 43.7022438614486 & 3.29775613855138 \tabularnewline
58 & 40 & 43.6600891697479 & -3.66008916974786 \tabularnewline
59 & 39 & 44.3742660117102 & -5.37426601171016 \tabularnewline
60 & 49 & 51.5860705744416 & -2.58607057444163 \tabularnewline
61 & 55 & 51.1913479564231 & 3.80865204357686 \tabularnewline
62 & 54 & 51.7166762658159 & 2.28332373418412 \tabularnewline
63 & 48 & 48.238472867004 & -0.238472867003964 \tabularnewline
64 & 44 & 46.567637215551 & -2.56763721555102 \tabularnewline
65 & 48 & 44.1644653155483 & 3.83553468445174 \tabularnewline
66 & 62 & 57.5214746833746 & 4.47852531662537 \tabularnewline
67 & 57 & 56.5675547520905 & 0.432445247909548 \tabularnewline
68 & 60 & 59.4902366714996 & 0.509763328500441 \tabularnewline
69 & 56 & 60.1877617203684 & -4.18776172036841 \tabularnewline
70 & 57 & 52.797600284895 & 4.20239971510503 \tabularnewline
71 & 54 & 56.946216368561 & -2.94621636856097 \tabularnewline
72 & 62 & 67.0069523359703 & -5.00695233597027 \tabularnewline
73 & 65 & 68.579723856218 & -3.57972385621802 \tabularnewline
74 & 68 & 64.428661004104 & 3.57133899589599 \tabularnewline
75 & 69 & 60.359377007644 & 8.64062299235602 \tabularnewline
76 & 67 & 62.4559524697236 & 4.54404753027639 \tabularnewline
77 & 72 & 67.3370724590954 & 4.66292754090462 \tabularnewline
78 & 82 & 81.9745501287923 & 0.0254498712076980 \tabularnewline
79 & 72 & 77.1467373538709 & -5.14673735387086 \tabularnewline
80 & 77 & 77.3885519880269 & -0.388551988026904 \tabularnewline
81 & 79 & 75.5218188247705 & 3.47818117522954 \tabularnewline
82 & 78 & 76.5708412871303 & 1.42915871286971 \tabularnewline
83 & 76 & 76.17700439504 & -0.177004395040044 \tabularnewline
84 & 79 & 87.1177103046551 & -8.11771030465512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78869&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]31[/C][C]33.4532585470086[/C][C]-2.45325854700856[/C][/ROW]
[ROW][C]14[/C][C]27[/C][C]27.9437063932416[/C][C]-0.94370639324157[/C][/ROW]
[ROW][C]15[/C][C]25[/C][C]25.1867648143935[/C][C]-0.186764814393538[/C][/ROW]
[ROW][C]16[/C][C]16[/C][C]15.7339978528039[/C][C]0.266002147196119[/C][/ROW]
[ROW][C]17[/C][C]20[/C][C]19.7763686665064[/C][C]0.223631333493604[/C][/ROW]
[ROW][C]18[/C][C]21[/C][C]20.5545819923583[/C][C]0.445418007641692[/C][/ROW]
[ROW][C]19[/C][C]25[/C][C]21.6306784855388[/C][C]3.36932151446123[/C][/ROW]
[ROW][C]20[/C][C]24[/C][C]25.2648714500173[/C][C]-1.26487145001733[/C][/ROW]
[ROW][C]21[/C][C]28[/C][C]25.6081963514624[/C][C]2.39180364853759[/C][/ROW]
[ROW][C]22[/C][C]27[/C][C]27.2732623898038[/C][C]-0.273262389803808[/C][/ROW]
[ROW][C]23[/C][C]23[/C][C]28.5827476842846[/C][C]-5.58274768428455[/C][/ROW]
[ROW][C]24[/C][C]36[/C][C]27.5971719516467[/C][C]8.40282804835326[/C][/ROW]
[ROW][C]25[/C][C]37[/C][C]30.8059890247375[/C][C]6.19401097526254[/C][/ROW]
[ROW][C]26[/C][C]30[/C][C]30.9832039372554[/C][C]-0.983203937255428[/C][/ROW]
[ROW][C]27[/C][C]27[/C][C]29.0280343300294[/C][C]-2.02803433002937[/C][/ROW]
[ROW][C]28[/C][C]22[/C][C]19.2280559865024[/C][C]2.77194401349764[/C][/ROW]
[ROW][C]29[/C][C]22[/C][C]25.0378508230883[/C][C]-3.03785082308835[/C][/ROW]
[ROW][C]30[/C][C]25[/C][C]24.5919869542073[/C][C]0.408013045792671[/C][/ROW]
[ROW][C]31[/C][C]33[/C][C]27.4165644467442[/C][C]5.58343555325582[/C][/ROW]
[ROW][C]32[/C][C]35[/C][C]30.4268528484166[/C][C]4.57314715158338[/C][/ROW]
[ROW][C]33[/C][C]35[/C][C]36.2135641724594[/C][C]-1.21356417245944[/C][/ROW]
[ROW][C]34[/C][C]29[/C][C]35.2475476858378[/C][C]-6.24754768583777[/C][/ROW]
[ROW][C]35[/C][C]25[/C][C]31.2138392076751[/C][C]-6.21383920767509[/C][/ROW]
[ROW][C]36[/C][C]34[/C][C]36.893664703057[/C][C]-2.89366470305702[/C][/ROW]
[ROW][C]37[/C][C]31[/C][C]33.0529844221021[/C][C]-2.05298442210209[/C][/ROW]
[ROW][C]38[/C][C]29[/C][C]25.0954388777109[/C][C]3.90456112228908[/C][/ROW]
[ROW][C]39[/C][C]21[/C][C]24.9564784361844[/C][C]-3.95647843618443[/C][/ROW]
[ROW][C]40[/C][C]19[/C][C]16.1572949530758[/C][C]2.84270504692423[/C][/ROW]
[ROW][C]41[/C][C]18[/C][C]18.9255881332679[/C][C]-0.92558813326794[/C][/ROW]
[ROW][C]42[/C][C]25[/C][C]21.0124152164847[/C][C]3.98758478351532[/C][/ROW]
[ROW][C]43[/C][C]23[/C][C]28.0892037074704[/C][C]-5.08920370747038[/C][/ROW]
[ROW][C]44[/C][C]22[/C][C]24.5889209187551[/C][C]-2.58892091875512[/C][/ROW]
[ROW][C]45[/C][C]20[/C][C]23.1502235058480[/C][C]-3.15022350584795[/C][/ROW]
[ROW][C]46[/C][C]15[/C][C]17.9718243487926[/C][C]-2.97182434879256[/C][/ROW]
[ROW][C]47[/C][C]17[/C][C]14.984525480689[/C][C]2.01547451931101[/C][/ROW]
[ROW][C]48[/C][C]25[/C][C]26.156057971405[/C][C]-1.15605797140502[/C][/ROW]
[ROW][C]49[/C][C]26[/C][C]23.3000043929839[/C][C]2.69999560701610[/C][/ROW]
[ROW][C]50[/C][C]26[/C][C]20.5177633091297[/C][C]5.48223669087033[/C][/ROW]
[ROW][C]51[/C][C]23[/C][C]17.3327961938800[/C][C]5.66720380611997[/C][/ROW]
[ROW][C]52[/C][C]24[/C][C]17.0441849675908[/C][C]6.95581503240918[/C][/ROW]
[ROW][C]53[/C][C]24[/C][C]20.5338551851002[/C][C]3.46614481489981[/C][/ROW]
[ROW][C]54[/C][C]42[/C][C]27.803717090431[/C][C]14.1962829095690[/C][/ROW]
[ROW][C]55[/C][C]40[/C][C]36.7470111008024[/C][C]3.25298889919762[/C][/ROW]
[ROW][C]56[/C][C]45[/C][C]39.9856056445666[/C][C]5.0143943554334[/C][/ROW]
[ROW][C]57[/C][C]47[/C][C]43.7022438614486[/C][C]3.29775613855138[/C][/ROW]
[ROW][C]58[/C][C]40[/C][C]43.6600891697479[/C][C]-3.66008916974786[/C][/ROW]
[ROW][C]59[/C][C]39[/C][C]44.3742660117102[/C][C]-5.37426601171016[/C][/ROW]
[ROW][C]60[/C][C]49[/C][C]51.5860705744416[/C][C]-2.58607057444163[/C][/ROW]
[ROW][C]61[/C][C]55[/C][C]51.1913479564231[/C][C]3.80865204357686[/C][/ROW]
[ROW][C]62[/C][C]54[/C][C]51.7166762658159[/C][C]2.28332373418412[/C][/ROW]
[ROW][C]63[/C][C]48[/C][C]48.238472867004[/C][C]-0.238472867003964[/C][/ROW]
[ROW][C]64[/C][C]44[/C][C]46.567637215551[/C][C]-2.56763721555102[/C][/ROW]
[ROW][C]65[/C][C]48[/C][C]44.1644653155483[/C][C]3.83553468445174[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]57.5214746833746[/C][C]4.47852531662537[/C][/ROW]
[ROW][C]67[/C][C]57[/C][C]56.5675547520905[/C][C]0.432445247909548[/C][/ROW]
[ROW][C]68[/C][C]60[/C][C]59.4902366714996[/C][C]0.509763328500441[/C][/ROW]
[ROW][C]69[/C][C]56[/C][C]60.1877617203684[/C][C]-4.18776172036841[/C][/ROW]
[ROW][C]70[/C][C]57[/C][C]52.797600284895[/C][C]4.20239971510503[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]56.946216368561[/C][C]-2.94621636856097[/C][/ROW]
[ROW][C]72[/C][C]62[/C][C]67.0069523359703[/C][C]-5.00695233597027[/C][/ROW]
[ROW][C]73[/C][C]65[/C][C]68.579723856218[/C][C]-3.57972385621802[/C][/ROW]
[ROW][C]74[/C][C]68[/C][C]64.428661004104[/C][C]3.57133899589599[/C][/ROW]
[ROW][C]75[/C][C]69[/C][C]60.359377007644[/C][C]8.64062299235602[/C][/ROW]
[ROW][C]76[/C][C]67[/C][C]62.4559524697236[/C][C]4.54404753027639[/C][/ROW]
[ROW][C]77[/C][C]72[/C][C]67.3370724590954[/C][C]4.66292754090462[/C][/ROW]
[ROW][C]78[/C][C]82[/C][C]81.9745501287923[/C][C]0.0254498712076980[/C][/ROW]
[ROW][C]79[/C][C]72[/C][C]77.1467373538709[/C][C]-5.14673735387086[/C][/ROW]
[ROW][C]80[/C][C]77[/C][C]77.3885519880269[/C][C]-0.388551988026904[/C][/ROW]
[ROW][C]81[/C][C]79[/C][C]75.5218188247705[/C][C]3.47818117522954[/C][/ROW]
[ROW][C]82[/C][C]78[/C][C]76.5708412871303[/C][C]1.42915871286971[/C][/ROW]
[ROW][C]83[/C][C]76[/C][C]76.17700439504[/C][C]-0.177004395040044[/C][/ROW]
[ROW][C]84[/C][C]79[/C][C]87.1177103046551[/C][C]-8.11771030465512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78869&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78869&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
133133.4532585470086-2.45325854700856
142727.9437063932416-0.94370639324157
152525.1867648143935-0.186764814393538
161615.73399785280390.266002147196119
172019.77636866650640.223631333493604
182120.55458199235830.445418007641692
192521.63067848553883.36932151446123
202425.2648714500173-1.26487145001733
212825.60819635146242.39180364853759
222727.2732623898038-0.273262389803808
232328.5827476842846-5.58274768428455
243627.59717195164678.40282804835326
253730.80598902473756.19401097526254
263030.9832039372554-0.983203937255428
272729.0280343300294-2.02803433002937
282219.22805598650242.77194401349764
292225.0378508230883-3.03785082308835
302524.59198695420730.408013045792671
313327.41656444674425.58343555325582
323530.42685284841664.57314715158338
333536.2135641724594-1.21356417245944
342935.2475476858378-6.24754768583777
352531.2138392076751-6.21383920767509
363436.893664703057-2.89366470305702
373133.0529844221021-2.05298442210209
382925.09543887771093.90456112228908
392124.9564784361844-3.95647843618443
401916.15729495307582.84270504692423
411818.9255881332679-0.92558813326794
422521.01241521648473.98758478351532
432328.0892037074704-5.08920370747038
442224.5889209187551-2.58892091875512
452023.1502235058480-3.15022350584795
461517.9718243487926-2.97182434879256
471714.9845254806892.01547451931101
482526.156057971405-1.15605797140502
492623.30000439298392.69999560701610
502620.51776330912975.48223669087033
512317.33279619388005.66720380611997
522417.04418496759086.95581503240918
532420.53385518510023.46614481489981
544227.80371709043114.1962829095690
554036.74701110080243.25298889919762
564539.98560564456665.0143943554334
574743.70224386144863.29775613855138
584043.6600891697479-3.66008916974786
593944.3742660117102-5.37426601171016
604951.5860705744416-2.58607057444163
615551.19134795642313.80865204357686
625451.71667626581592.28332373418412
634848.238472867004-0.238472867003964
644446.567637215551-2.56763721555102
654844.16446531554833.83553468445174
666257.52147468337464.47852531662537
675756.56755475209050.432445247909548
686059.49023667149960.509763328500441
695660.1877617203684-4.18776172036841
705752.7976002848954.20239971510503
715456.946216368561-2.94621636856097
726267.0069523359703-5.00695233597027
736568.579723856218-3.57972385621802
746864.4286610041043.57133899589599
756960.3593770076448.64062299235602
766762.45595246972364.54404753027639
777267.33707245909544.66292754090462
788281.97455012879230.0254498712076980
797277.1467373538709-5.14673735387086
807777.3885519880269-0.388551988026904
817975.52181882477053.47818117522954
827876.57084128713031.42915871286971
837676.17700439504-0.177004395040044
847987.1177103046551-8.11771030465512







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8588.070982587434479.931872290917596.2100928839512
8689.65405775368980.341495271030698.9666202363473
8786.471552408868675.988775925140296.954328892597
8882.11660103844870.458773669128493.7744284077678
8984.539164678351271.696333892290797.3819954644116
9094.211481682307880.1703219083364108.252641456279
9186.575844236209371.3207464430091101.830942029410
9291.644703994618275.1584885600217108.130919429215
9391.714046613139673.9784464277361109.449646798543
9489.727310097691670.7233071895518108.731313005831
9587.526329359982167.2343947243924107.818263995572
9694.466002719895472.8662702628792116.065735176912

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 88.0709825874344 & 79.9318722909175 & 96.2100928839512 \tabularnewline
86 & 89.654057753689 & 80.3414952710306 & 98.9666202363473 \tabularnewline
87 & 86.4715524088686 & 75.9887759251402 & 96.954328892597 \tabularnewline
88 & 82.116601038448 & 70.4587736691284 & 93.7744284077678 \tabularnewline
89 & 84.5391646783512 & 71.6963338922907 & 97.3819954644116 \tabularnewline
90 & 94.2114816823078 & 80.1703219083364 & 108.252641456279 \tabularnewline
91 & 86.5758442362093 & 71.3207464430091 & 101.830942029410 \tabularnewline
92 & 91.6447039946182 & 75.1584885600217 & 108.130919429215 \tabularnewline
93 & 91.7140466131396 & 73.9784464277361 & 109.449646798543 \tabularnewline
94 & 89.7273100976916 & 70.7233071895518 & 108.731313005831 \tabularnewline
95 & 87.5263293599821 & 67.2343947243924 & 107.818263995572 \tabularnewline
96 & 94.4660027198954 & 72.8662702628792 & 116.065735176912 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78869&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]88.0709825874344[/C][C]79.9318722909175[/C][C]96.2100928839512[/C][/ROW]
[ROW][C]86[/C][C]89.654057753689[/C][C]80.3414952710306[/C][C]98.9666202363473[/C][/ROW]
[ROW][C]87[/C][C]86.4715524088686[/C][C]75.9887759251402[/C][C]96.954328892597[/C][/ROW]
[ROW][C]88[/C][C]82.116601038448[/C][C]70.4587736691284[/C][C]93.7744284077678[/C][/ROW]
[ROW][C]89[/C][C]84.5391646783512[/C][C]71.6963338922907[/C][C]97.3819954644116[/C][/ROW]
[ROW][C]90[/C][C]94.2114816823078[/C][C]80.1703219083364[/C][C]108.252641456279[/C][/ROW]
[ROW][C]91[/C][C]86.5758442362093[/C][C]71.3207464430091[/C][C]101.830942029410[/C][/ROW]
[ROW][C]92[/C][C]91.6447039946182[/C][C]75.1584885600217[/C][C]108.130919429215[/C][/ROW]
[ROW][C]93[/C][C]91.7140466131396[/C][C]73.9784464277361[/C][C]109.449646798543[/C][/ROW]
[ROW][C]94[/C][C]89.7273100976916[/C][C]70.7233071895518[/C][C]108.731313005831[/C][/ROW]
[ROW][C]95[/C][C]87.5263293599821[/C][C]67.2343947243924[/C][C]107.818263995572[/C][/ROW]
[ROW][C]96[/C][C]94.4660027198954[/C][C]72.8662702628792[/C][C]116.065735176912[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78869&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78869&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
8588.070982587434479.931872290917596.2100928839512
8689.65405775368980.341495271030698.9666202363473
8786.471552408868675.988775925140296.954328892597
8882.11660103844870.458773669128493.7744284077678
8984.539164678351271.696333892290797.3819954644116
9094.211481682307880.1703219083364108.252641456279
9186.575844236209371.3207464430091101.830942029410
9291.644703994618275.1584885600217108.130919429215
9391.714046613139673.9784464277361109.449646798543
9489.727310097691670.7233071895518108.731313005831
9587.526329359982167.2343947243924107.818263995572
9694.466002719895472.8662702628792116.065735176912



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')