Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 08 Aug 2010 13:53:04 +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/08/t1281275568m51iu1mbxzk8how.htm/, Retrieved Fri, 03 May 2024 18:37:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78513, Retrieved Fri, 03 May 2024 18:37:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPhilippe De Vocht
Estimated Impact242
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Omzet product Y] [2010-08-08 13:53:04] [181f2439255053cc457d7672472fa443] [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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78513&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78513&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78513&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.520658832476646
beta0.067876565022126
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.520658832476646 \tabularnewline
beta & 0.067876565022126 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78513&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]0.520658832476646[/C][/ROW]
[ROW][C]beta[/C][C]0.067876565022126[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78513&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78513&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
alpha0.520658832476646
beta0.067876565022126
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133133.4532585470086-2.45325854700855
142727.9437063932419-0.94370639324185
152525.1867648143938-0.186764814393758
161615.7339978528040.266002147196016
172019.77636866650640.223631333493614
182120.55458199235820.445418007641752
192521.63067848553873.36932151446134
202425.2648714500169-1.26487145001688
212825.60819635146232.39180364853766
222727.2732623898035-0.273262389803502
232328.5827476842845-5.58274768428446
243627.59717195164748.40282804835264
253730.80598902473656.19401097526351
263030.9832039372543-0.983203937254345
272729.0280343300292-2.02803433002919
282219.22805598650272.77194401349728
292225.0378508230883-3.03785082308835
302524.59198695420780.408013045792174
313327.41656444674485.5834355532552
323530.4268528484164.57314715158404
333536.2135641724589-1.21356417245894
342935.2475476858376-6.2475476858376
352531.2138392076751-6.21383920767513
363436.8936647030592-2.89366470305916
373133.0529844221037-2.05298442210366
382925.09543887771113.90456112228889
392124.9564784361836-3.95647843618357
401916.15729495307622.8427050469238
411818.9255881332673-0.925588133267304
422521.01241521648473.98758478351532
432328.0892037074708-5.08920370747081
442224.588920918756-2.588920918756
452023.1502235058481-3.15022350584807
461517.9718243487919-2.97182434879194
471714.98452548068812.01547451931187
482526.156057971405-1.156057971405
492623.30000439298452.69999560701545
502620.51776330913025.48223669086979
512317.33279619387875.66720380612129
522417.04418496759016.95581503240989
532420.53385518509873.46614481490132
544227.803717090430514.1962829095695
554036.74701110080033.25298889919974
564539.98560564456575.01439435543433
574743.70224386144773.29775613855232
584043.6600891697468-3.66008916974681
593944.3742660117104-5.37426601171036
604951.5860705744426-2.58607057444264
615551.1913479564253.80865204357505
625451.71667626581762.28332373418243
634848.2384728670048-0.238472867004774
644446.5676372155521-2.56763721555208
654844.16446531554883.83553468445121
666257.52147468337594.47852531662414
675756.56755475208970.432445247910273
686059.49023667149910.509763328500867
695660.1877617203679-4.18776172036789
705752.7976002848944.20239971510598
715456.9462163685593-2.94621636855931
726267.0069523359699-5.00695233596994
736568.5797238562198-3.57972385621977
746864.42866100410633.57133899589368
756960.3593770076458.64062299235505
766762.45595246972324.54404753027679
777267.33707245909544.66292754090463
788281.97455012879290.0254498712070728
797277.1467373538709-5.14673735387088
807777.3885519880273-0.388551988027331
817975.52181882476993.47818117523011
827876.57084128712961.42915871287043
837676.1770043950383-0.177004395038267
847987.1177103046535-8.11771030465347

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31 & 33.4532585470086 & -2.45325854700855 \tabularnewline
14 & 27 & 27.9437063932419 & -0.94370639324185 \tabularnewline
15 & 25 & 25.1867648143938 & -0.186764814393758 \tabularnewline
16 & 16 & 15.733997852804 & 0.266002147196016 \tabularnewline
17 & 20 & 19.7763686665064 & 0.223631333493614 \tabularnewline
18 & 21 & 20.5545819923582 & 0.445418007641752 \tabularnewline
19 & 25 & 21.6306784855387 & 3.36932151446134 \tabularnewline
20 & 24 & 25.2648714500169 & -1.26487145001688 \tabularnewline
21 & 28 & 25.6081963514623 & 2.39180364853766 \tabularnewline
22 & 27 & 27.2732623898035 & -0.273262389803502 \tabularnewline
23 & 23 & 28.5827476842845 & -5.58274768428446 \tabularnewline
24 & 36 & 27.5971719516474 & 8.40282804835264 \tabularnewline
25 & 37 & 30.8059890247365 & 6.19401097526351 \tabularnewline
26 & 30 & 30.9832039372543 & -0.983203937254345 \tabularnewline
27 & 27 & 29.0280343300292 & -2.02803433002919 \tabularnewline
28 & 22 & 19.2280559865027 & 2.77194401349728 \tabularnewline
29 & 22 & 25.0378508230883 & -3.03785082308835 \tabularnewline
30 & 25 & 24.5919869542078 & 0.408013045792174 \tabularnewline
31 & 33 & 27.4165644467448 & 5.5834355532552 \tabularnewline
32 & 35 & 30.426852848416 & 4.57314715158404 \tabularnewline
33 & 35 & 36.2135641724589 & -1.21356417245894 \tabularnewline
34 & 29 & 35.2475476858376 & -6.2475476858376 \tabularnewline
35 & 25 & 31.2138392076751 & -6.21383920767513 \tabularnewline
36 & 34 & 36.8936647030592 & -2.89366470305916 \tabularnewline
37 & 31 & 33.0529844221037 & -2.05298442210366 \tabularnewline
38 & 29 & 25.0954388777111 & 3.90456112228889 \tabularnewline
39 & 21 & 24.9564784361836 & -3.95647843618357 \tabularnewline
40 & 19 & 16.1572949530762 & 2.8427050469238 \tabularnewline
41 & 18 & 18.9255881332673 & -0.925588133267304 \tabularnewline
42 & 25 & 21.0124152164847 & 3.98758478351532 \tabularnewline
43 & 23 & 28.0892037074708 & -5.08920370747081 \tabularnewline
44 & 22 & 24.588920918756 & -2.588920918756 \tabularnewline
45 & 20 & 23.1502235058481 & -3.15022350584807 \tabularnewline
46 & 15 & 17.9718243487919 & -2.97182434879194 \tabularnewline
47 & 17 & 14.9845254806881 & 2.01547451931187 \tabularnewline
48 & 25 & 26.156057971405 & -1.156057971405 \tabularnewline
49 & 26 & 23.3000043929845 & 2.69999560701545 \tabularnewline
50 & 26 & 20.5177633091302 & 5.48223669086979 \tabularnewline
51 & 23 & 17.3327961938787 & 5.66720380612129 \tabularnewline
52 & 24 & 17.0441849675901 & 6.95581503240989 \tabularnewline
53 & 24 & 20.5338551850987 & 3.46614481490132 \tabularnewline
54 & 42 & 27.8037170904305 & 14.1962829095695 \tabularnewline
55 & 40 & 36.7470111008003 & 3.25298889919974 \tabularnewline
56 & 45 & 39.9856056445657 & 5.01439435543433 \tabularnewline
57 & 47 & 43.7022438614477 & 3.29775613855232 \tabularnewline
58 & 40 & 43.6600891697468 & -3.66008916974681 \tabularnewline
59 & 39 & 44.3742660117104 & -5.37426601171036 \tabularnewline
60 & 49 & 51.5860705744426 & -2.58607057444264 \tabularnewline
61 & 55 & 51.191347956425 & 3.80865204357505 \tabularnewline
62 & 54 & 51.7166762658176 & 2.28332373418243 \tabularnewline
63 & 48 & 48.2384728670048 & -0.238472867004774 \tabularnewline
64 & 44 & 46.5676372155521 & -2.56763721555208 \tabularnewline
65 & 48 & 44.1644653155488 & 3.83553468445121 \tabularnewline
66 & 62 & 57.5214746833759 & 4.47852531662414 \tabularnewline
67 & 57 & 56.5675547520897 & 0.432445247910273 \tabularnewline
68 & 60 & 59.4902366714991 & 0.509763328500867 \tabularnewline
69 & 56 & 60.1877617203679 & -4.18776172036789 \tabularnewline
70 & 57 & 52.797600284894 & 4.20239971510598 \tabularnewline
71 & 54 & 56.9462163685593 & -2.94621636855931 \tabularnewline
72 & 62 & 67.0069523359699 & -5.00695233596994 \tabularnewline
73 & 65 & 68.5797238562198 & -3.57972385621977 \tabularnewline
74 & 68 & 64.4286610041063 & 3.57133899589368 \tabularnewline
75 & 69 & 60.359377007645 & 8.64062299235505 \tabularnewline
76 & 67 & 62.4559524697232 & 4.54404753027679 \tabularnewline
77 & 72 & 67.3370724590954 & 4.66292754090463 \tabularnewline
78 & 82 & 81.9745501287929 & 0.0254498712070728 \tabularnewline
79 & 72 & 77.1467373538709 & -5.14673735387088 \tabularnewline
80 & 77 & 77.3885519880273 & -0.388551988027331 \tabularnewline
81 & 79 & 75.5218188247699 & 3.47818117523011 \tabularnewline
82 & 78 & 76.5708412871296 & 1.42915871287043 \tabularnewline
83 & 76 & 76.1770043950383 & -0.177004395038267 \tabularnewline
84 & 79 & 87.1177103046535 & -8.11771030465347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78513&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]-2.45325854700855[/C][/ROW]
[ROW][C]14[/C][C]27[/C][C]27.9437063932419[/C][C]-0.94370639324185[/C][/ROW]
[ROW][C]15[/C][C]25[/C][C]25.1867648143938[/C][C]-0.186764814393758[/C][/ROW]
[ROW][C]16[/C][C]16[/C][C]15.733997852804[/C][C]0.266002147196016[/C][/ROW]
[ROW][C]17[/C][C]20[/C][C]19.7763686665064[/C][C]0.223631333493614[/C][/ROW]
[ROW][C]18[/C][C]21[/C][C]20.5545819923582[/C][C]0.445418007641752[/C][/ROW]
[ROW][C]19[/C][C]25[/C][C]21.6306784855387[/C][C]3.36932151446134[/C][/ROW]
[ROW][C]20[/C][C]24[/C][C]25.2648714500169[/C][C]-1.26487145001688[/C][/ROW]
[ROW][C]21[/C][C]28[/C][C]25.6081963514623[/C][C]2.39180364853766[/C][/ROW]
[ROW][C]22[/C][C]27[/C][C]27.2732623898035[/C][C]-0.273262389803502[/C][/ROW]
[ROW][C]23[/C][C]23[/C][C]28.5827476842845[/C][C]-5.58274768428446[/C][/ROW]
[ROW][C]24[/C][C]36[/C][C]27.5971719516474[/C][C]8.40282804835264[/C][/ROW]
[ROW][C]25[/C][C]37[/C][C]30.8059890247365[/C][C]6.19401097526351[/C][/ROW]
[ROW][C]26[/C][C]30[/C][C]30.9832039372543[/C][C]-0.983203937254345[/C][/ROW]
[ROW][C]27[/C][C]27[/C][C]29.0280343300292[/C][C]-2.02803433002919[/C][/ROW]
[ROW][C]28[/C][C]22[/C][C]19.2280559865027[/C][C]2.77194401349728[/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]24.5919869542078[/C][C]0.408013045792174[/C][/ROW]
[ROW][C]31[/C][C]33[/C][C]27.4165644467448[/C][C]5.5834355532552[/C][/ROW]
[ROW][C]32[/C][C]35[/C][C]30.426852848416[/C][C]4.57314715158404[/C][/ROW]
[ROW][C]33[/C][C]35[/C][C]36.2135641724589[/C][C]-1.21356417245894[/C][/ROW]
[ROW][C]34[/C][C]29[/C][C]35.2475476858376[/C][C]-6.2475476858376[/C][/ROW]
[ROW][C]35[/C][C]25[/C][C]31.2138392076751[/C][C]-6.21383920767513[/C][/ROW]
[ROW][C]36[/C][C]34[/C][C]36.8936647030592[/C][C]-2.89366470305916[/C][/ROW]
[ROW][C]37[/C][C]31[/C][C]33.0529844221037[/C][C]-2.05298442210366[/C][/ROW]
[ROW][C]38[/C][C]29[/C][C]25.0954388777111[/C][C]3.90456112228889[/C][/ROW]
[ROW][C]39[/C][C]21[/C][C]24.9564784361836[/C][C]-3.95647843618357[/C][/ROW]
[ROW][C]40[/C][C]19[/C][C]16.1572949530762[/C][C]2.8427050469238[/C][/ROW]
[ROW][C]41[/C][C]18[/C][C]18.9255881332673[/C][C]-0.925588133267304[/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]28.0892037074708[/C][C]-5.08920370747081[/C][/ROW]
[ROW][C]44[/C][C]22[/C][C]24.588920918756[/C][C]-2.588920918756[/C][/ROW]
[ROW][C]45[/C][C]20[/C][C]23.1502235058481[/C][C]-3.15022350584807[/C][/ROW]
[ROW][C]46[/C][C]15[/C][C]17.9718243487919[/C][C]-2.97182434879194[/C][/ROW]
[ROW][C]47[/C][C]17[/C][C]14.9845254806881[/C][C]2.01547451931187[/C][/ROW]
[ROW][C]48[/C][C]25[/C][C]26.156057971405[/C][C]-1.156057971405[/C][/ROW]
[ROW][C]49[/C][C]26[/C][C]23.3000043929845[/C][C]2.69999560701545[/C][/ROW]
[ROW][C]50[/C][C]26[/C][C]20.5177633091302[/C][C]5.48223669086979[/C][/ROW]
[ROW][C]51[/C][C]23[/C][C]17.3327961938787[/C][C]5.66720380612129[/C][/ROW]
[ROW][C]52[/C][C]24[/C][C]17.0441849675901[/C][C]6.95581503240989[/C][/ROW]
[ROW][C]53[/C][C]24[/C][C]20.5338551850987[/C][C]3.46614481490132[/C][/ROW]
[ROW][C]54[/C][C]42[/C][C]27.8037170904305[/C][C]14.1962829095695[/C][/ROW]
[ROW][C]55[/C][C]40[/C][C]36.7470111008003[/C][C]3.25298889919974[/C][/ROW]
[ROW][C]56[/C][C]45[/C][C]39.9856056445657[/C][C]5.01439435543433[/C][/ROW]
[ROW][C]57[/C][C]47[/C][C]43.7022438614477[/C][C]3.29775613855232[/C][/ROW]
[ROW][C]58[/C][C]40[/C][C]43.6600891697468[/C][C]-3.66008916974681[/C][/ROW]
[ROW][C]59[/C][C]39[/C][C]44.3742660117104[/C][C]-5.37426601171036[/C][/ROW]
[ROW][C]60[/C][C]49[/C][C]51.5860705744426[/C][C]-2.58607057444264[/C][/ROW]
[ROW][C]61[/C][C]55[/C][C]51.191347956425[/C][C]3.80865204357505[/C][/ROW]
[ROW][C]62[/C][C]54[/C][C]51.7166762658176[/C][C]2.28332373418243[/C][/ROW]
[ROW][C]63[/C][C]48[/C][C]48.2384728670048[/C][C]-0.238472867004774[/C][/ROW]
[ROW][C]64[/C][C]44[/C][C]46.5676372155521[/C][C]-2.56763721555208[/C][/ROW]
[ROW][C]65[/C][C]48[/C][C]44.1644653155488[/C][C]3.83553468445121[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]57.5214746833759[/C][C]4.47852531662414[/C][/ROW]
[ROW][C]67[/C][C]57[/C][C]56.5675547520897[/C][C]0.432445247910273[/C][/ROW]
[ROW][C]68[/C][C]60[/C][C]59.4902366714991[/C][C]0.509763328500867[/C][/ROW]
[ROW][C]69[/C][C]56[/C][C]60.1877617203679[/C][C]-4.18776172036789[/C][/ROW]
[ROW][C]70[/C][C]57[/C][C]52.797600284894[/C][C]4.20239971510598[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]56.9462163685593[/C][C]-2.94621636855931[/C][/ROW]
[ROW][C]72[/C][C]62[/C][C]67.0069523359699[/C][C]-5.00695233596994[/C][/ROW]
[ROW][C]73[/C][C]65[/C][C]68.5797238562198[/C][C]-3.57972385621977[/C][/ROW]
[ROW][C]74[/C][C]68[/C][C]64.4286610041063[/C][C]3.57133899589368[/C][/ROW]
[ROW][C]75[/C][C]69[/C][C]60.359377007645[/C][C]8.64062299235505[/C][/ROW]
[ROW][C]76[/C][C]67[/C][C]62.4559524697232[/C][C]4.54404753027679[/C][/ROW]
[ROW][C]77[/C][C]72[/C][C]67.3370724590954[/C][C]4.66292754090463[/C][/ROW]
[ROW][C]78[/C][C]82[/C][C]81.9745501287929[/C][C]0.0254498712070728[/C][/ROW]
[ROW][C]79[/C][C]72[/C][C]77.1467373538709[/C][C]-5.14673735387088[/C][/ROW]
[ROW][C]80[/C][C]77[/C][C]77.3885519880273[/C][C]-0.388551988027331[/C][/ROW]
[ROW][C]81[/C][C]79[/C][C]75.5218188247699[/C][C]3.47818117523011[/C][/ROW]
[ROW][C]82[/C][C]78[/C][C]76.5708412871296[/C][C]1.42915871287043[/C][/ROW]
[ROW][C]83[/C][C]76[/C][C]76.1770043950383[/C][C]-0.177004395038267[/C][/ROW]
[ROW][C]84[/C][C]79[/C][C]87.1177103046535[/C][C]-8.11771030465347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78513&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78513&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
133133.4532585470086-2.45325854700855
142727.9437063932419-0.94370639324185
152525.1867648143938-0.186764814393758
161615.7339978528040.266002147196016
172019.77636866650640.223631333493614
182120.55458199235820.445418007641752
192521.63067848553873.36932151446134
202425.2648714500169-1.26487145001688
212825.60819635146232.39180364853766
222727.2732623898035-0.273262389803502
232328.5827476842845-5.58274768428446
243627.59717195164748.40282804835264
253730.80598902473656.19401097526351
263030.9832039372543-0.983203937254345
272729.0280343300292-2.02803433002919
282219.22805598650272.77194401349728
292225.0378508230883-3.03785082308835
302524.59198695420780.408013045792174
313327.41656444674485.5834355532552
323530.4268528484164.57314715158404
333536.2135641724589-1.21356417245894
342935.2475476858376-6.2475476858376
352531.2138392076751-6.21383920767513
363436.8936647030592-2.89366470305916
373133.0529844221037-2.05298442210366
382925.09543887771113.90456112228889
392124.9564784361836-3.95647843618357
401916.15729495307622.8427050469238
411818.9255881332673-0.925588133267304
422521.01241521648473.98758478351532
432328.0892037074708-5.08920370747081
442224.588920918756-2.588920918756
452023.1502235058481-3.15022350584807
461517.9718243487919-2.97182434879194
471714.98452548068812.01547451931187
482526.156057971405-1.156057971405
492623.30000439298452.69999560701545
502620.51776330913025.48223669086979
512317.33279619387875.66720380612129
522417.04418496759016.95581503240989
532420.53385518509873.46614481490132
544227.803717090430514.1962829095695
554036.74701110080033.25298889919974
564539.98560564456575.01439435543433
574743.70224386144773.29775613855232
584043.6600891697468-3.66008916974681
593944.3742660117104-5.37426601171036
604951.5860705744426-2.58607057444264
615551.1913479564253.80865204357505
625451.71667626581762.28332373418243
634848.2384728670048-0.238472867004774
644446.5676372155521-2.56763721555208
654844.16446531554883.83553468445121
666257.52147468337594.47852531662414
675756.56755475208970.432445247910273
686059.49023667149910.509763328500867
695660.1877617203679-4.18776172036789
705752.7976002848944.20239971510598
715456.9462163685593-2.94621636855931
726267.0069523359699-5.00695233596994
736568.5797238562198-3.57972385621977
746864.42866100410633.57133899589368
756960.3593770076458.64062299235505
766762.45595246972324.54404753027679
777267.33707245909544.66292754090463
788281.97455012879290.0254498712070728
797277.1467373538709-5.14673735387088
807777.3885519880273-0.388551988027331
817975.52181882476993.47818117523011
827876.57084128712961.42915871287043
837676.1770043950383-0.177004395038267
847987.1177103046535-8.11771030465347







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8588.07098258743579.931872290918296.2100928839519
8689.654057753691380.341495271033498.9666202363492
8786.471552408872675.988775925145196.9543288926002
8882.116601038452670.45877366913493.7744284077712
8984.539164678356371.696333892297397.3819954644154
9094.211481682313480.1703219083436108.252641456283
9186.575844236214471.320746443016101.830942029413
9291.644703994623675.158488560029108.130919429218
9391.714046613145373.9784464277438109.449646798547
9489.727310097697170.7233071895595108.731313005835
9587.526329359986867.2343947243994107.818263995574
9694.466002719898372.8662702628845116.065735176912

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 88.070982587435 & 79.9318722909182 & 96.2100928839519 \tabularnewline
86 & 89.6540577536913 & 80.3414952710334 & 98.9666202363492 \tabularnewline
87 & 86.4715524088726 & 75.9887759251451 & 96.9543288926002 \tabularnewline
88 & 82.1166010384526 & 70.458773669134 & 93.7744284077712 \tabularnewline
89 & 84.5391646783563 & 71.6963338922973 & 97.3819954644154 \tabularnewline
90 & 94.2114816823134 & 80.1703219083436 & 108.252641456283 \tabularnewline
91 & 86.5758442362144 & 71.320746443016 & 101.830942029413 \tabularnewline
92 & 91.6447039946236 & 75.158488560029 & 108.130919429218 \tabularnewline
93 & 91.7140466131453 & 73.9784464277438 & 109.449646798547 \tabularnewline
94 & 89.7273100976971 & 70.7233071895595 & 108.731313005835 \tabularnewline
95 & 87.5263293599868 & 67.2343947243994 & 107.818263995574 \tabularnewline
96 & 94.4660027198983 & 72.8662702628845 & 116.065735176912 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78513&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]88.070982587435[/C][C]79.9318722909182[/C][C]96.2100928839519[/C][/ROW]
[ROW][C]86[/C][C]89.6540577536913[/C][C]80.3414952710334[/C][C]98.9666202363492[/C][/ROW]
[ROW][C]87[/C][C]86.4715524088726[/C][C]75.9887759251451[/C][C]96.9543288926002[/C][/ROW]
[ROW][C]88[/C][C]82.1166010384526[/C][C]70.458773669134[/C][C]93.7744284077712[/C][/ROW]
[ROW][C]89[/C][C]84.5391646783563[/C][C]71.6963338922973[/C][C]97.3819954644154[/C][/ROW]
[ROW][C]90[/C][C]94.2114816823134[/C][C]80.1703219083436[/C][C]108.252641456283[/C][/ROW]
[ROW][C]91[/C][C]86.5758442362144[/C][C]71.320746443016[/C][C]101.830942029413[/C][/ROW]
[ROW][C]92[/C][C]91.6447039946236[/C][C]75.158488560029[/C][C]108.130919429218[/C][/ROW]
[ROW][C]93[/C][C]91.7140466131453[/C][C]73.9784464277438[/C][C]109.449646798547[/C][/ROW]
[ROW][C]94[/C][C]89.7273100976971[/C][C]70.7233071895595[/C][C]108.731313005835[/C][/ROW]
[ROW][C]95[/C][C]87.5263293599868[/C][C]67.2343947243994[/C][C]107.818263995574[/C][/ROW]
[ROW][C]96[/C][C]94.4660027198983[/C][C]72.8662702628845[/C][C]116.065735176912[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78513&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78513&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
8588.07098258743579.931872290918296.2100928839519
8689.654057753691380.341495271033498.9666202363492
8786.471552408872675.988775925145196.9543288926002
8882.116601038452670.45877366913493.7744284077712
8984.539164678356371.696333892297397.3819954644154
9094.211481682313480.1703219083436108.252641456283
9186.575844236214471.320746443016101.830942029413
9291.644703994623675.158488560029108.130919429218
9391.714046613145373.9784464277438109.449646798547
9489.727310097697170.7233071895595108.731313005835
9587.526329359986867.2343947243994107.818263995574
9694.466002719898372.8662702628845116.065735176912



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')