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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Dec 2014 07:51:58 +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/2014/Dec/15/t14186302607xf2gbbmj6g8wfy.htm/, Retrieved Thu, 16 May 2024 12:15:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267951, Retrieved Thu, 16 May 2024 12:15:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-15 07:51:58] [6baf0af87d9d8aa2cb91b54f39a0a5b0] [Current]
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Dataseries X:
26
57
37
67
43
52
52
43
84
67
49
70
52
58
68
62
43
56
56
74
65
63
58
57
63
53
57
51
64
53
29
54
58
43
51
53
54
56
61
47
39
48
50
35
30
68
49
61
67
47
56
50
43
67
62
57
41
54
45
48
61
56
41
43
53
44
66
58
46
37
51
51
56
66
37
59
42
38
66
34
53
49
55
49
59
40
58
60
63
56
54
52
34
69
32
48
67
58
57
42
64
58
66
26
61
52
51
55
50
60
56
63
61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267951&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267951&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267951&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0751894870985707
beta0.0576383147895329
gamma0.399978729626341

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0751894870985707 \tabularnewline
beta & 0.0576383147895329 \tabularnewline
gamma & 0.399978729626341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267951&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]0.0751894870985707[/C][/ROW]
[ROW][C]beta[/C][C]0.0576383147895329[/C][/ROW]
[ROW][C]gamma[/C][C]0.399978729626341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267951&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267951&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
alpha0.0751894870985707
beta0.0576383147895329
gamma0.399978729626341







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135249.406252.59374999999996
145854.58410442288033.41589557711967
156864.7969126756453.203087324355
166260.46593484324321.53406515675683
174341.84944574784331.15055425215665
185655.58410693087050.415893069129496
195656.9736650451272-0.973665045127156
207447.254523332457326.7454766675427
216589.5271457564225-24.5271457564225
226370.0883103684856-7.08831036848564
235852.22163944928495.77836055071515
245773.9724491491129-16.9724491491129
256355.73185523437967.26814476562042
265361.5650732862287-8.56507328622865
275770.7461797381422-13.7461797381422
285164.3978215274539-13.3978215274539
296444.326442553783319.6735574462167
305359.0720526939575-6.07205269395747
312959.3216325681728-30.3216325681728
325457.3839312673838-3.38393126738382
335878.0292516018358-20.0292516018358
344365.0028959496959-22.0028959496959
355150.33318924274590.666810757254083
365362.820828403076-9.82082840307605
375453.65245237300930.347547626990661
385652.64632826797813.35367173202189
396160.39653081702290.603469182977122
404754.9076096123528-7.90760961235283
413947.1577183244986-8.1577183244986
424849.8421045741218-1.84210457412176
435041.01284764578328.98715235421685
443551.7386329126661-16.7386329126661
453064.9082654149171-34.9082654149171
466849.654246550197818.3457534498022
474946.19996637994182.8000336200582
486154.77382613281536.22617386718475
496750.448138731251616.5518612687484
504751.7174081333827-4.71740813338266
515657.7534800653948-1.75348006539483
525048.83888201450091.16111798549906
534341.61747696131931.38252303868067
546747.335838285720219.6641617142798
556244.20309654203817.796903457962
565746.187056335001710.8129436649983
574154.9385096697663-13.9385096697663
585461.2822390167214-7.28223901672143
594550.3616445085226-5.36164450852257
604859.7648791601554-11.7648791601554
616158.00370523432082.9962947656792
625650.42512524198295.57487475801705
634158.4150296112176-17.4150296112176
644349.4166873011356-6.41668730113555
655341.69028561526811.309714384732
664454.9434267446694-10.9434267446694
676648.711860146848217.2881398531518
685847.965214313374410.0347856866256
694647.3901575988935-1.39015759889349
703757.0816318502843-20.0816318502843
715145.79568028122425.20431971877581
725153.5571556644053-2.55715566440527
735657.9208121294615-1.92081212946152
746650.877317307644715.1226826923553
753751.0733963244623-14.0733963244623
765946.401478080719512.5985219192805
774246.751136290257-4.75113629025695
783850.5847677640692-12.5847677640692
796654.685296100617311.3147038993827
803450.7930964737692-16.7930964737692
815343.84509457209469.1549054279054
824947.33145360971981.66854639028021
835547.04460372233057.95539627766953
844952.1641776093165-3.16417760931651
855956.73719945950882.26280054049116
864056.3504859560358-16.3504859560358
875843.281704903544414.7182950964556
886050.66681330439659.33318669560345
896344.3652147445918.63478525541
905647.172855009698.82714499031002
915461.9299810077928-7.92998100779285
925246.31630205937575.68369794062427
933450.8767336495194-16.8767336495194
946949.743864442960519.2561355570395
953253.2884871528397-21.2884871528397
964852.152847150575-4.15284715057496
976758.7115100823288.288489917672
985851.97135492074626.02864507925382
995752.25334772381774.74665227618235
1004257.0291178335373-15.0291178335373
1016452.363252763872511.6367472361275
1025851.01331466292776.98668533707232
1036659.4220355092876.57796449071304
1042649.9863525276051-23.9863525276051
1056143.893507795571917.1064922044281
1065258.7516138967462-6.75161389674623
1075145.30045706444445.69954293555559
1085552.60691430586172.39308569413826
1095064.3625684677832-14.3625684677832
1106055.08789884614974.91210115385031
1115654.81141931504121.18858068495875
1126351.988787845338811.0112121546612
1136159.24183471400161.75816528599839

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 52 & 49.40625 & 2.59374999999996 \tabularnewline
14 & 58 & 54.5841044228803 & 3.41589557711967 \tabularnewline
15 & 68 & 64.796912675645 & 3.203087324355 \tabularnewline
16 & 62 & 60.4659348432432 & 1.53406515675683 \tabularnewline
17 & 43 & 41.8494457478433 & 1.15055425215665 \tabularnewline
18 & 56 & 55.5841069308705 & 0.415893069129496 \tabularnewline
19 & 56 & 56.9736650451272 & -0.973665045127156 \tabularnewline
20 & 74 & 47.2545233324573 & 26.7454766675427 \tabularnewline
21 & 65 & 89.5271457564225 & -24.5271457564225 \tabularnewline
22 & 63 & 70.0883103684856 & -7.08831036848564 \tabularnewline
23 & 58 & 52.2216394492849 & 5.77836055071515 \tabularnewline
24 & 57 & 73.9724491491129 & -16.9724491491129 \tabularnewline
25 & 63 & 55.7318552343796 & 7.26814476562042 \tabularnewline
26 & 53 & 61.5650732862287 & -8.56507328622865 \tabularnewline
27 & 57 & 70.7461797381422 & -13.7461797381422 \tabularnewline
28 & 51 & 64.3978215274539 & -13.3978215274539 \tabularnewline
29 & 64 & 44.3264425537833 & 19.6735574462167 \tabularnewline
30 & 53 & 59.0720526939575 & -6.07205269395747 \tabularnewline
31 & 29 & 59.3216325681728 & -30.3216325681728 \tabularnewline
32 & 54 & 57.3839312673838 & -3.38393126738382 \tabularnewline
33 & 58 & 78.0292516018358 & -20.0292516018358 \tabularnewline
34 & 43 & 65.0028959496959 & -22.0028959496959 \tabularnewline
35 & 51 & 50.3331892427459 & 0.666810757254083 \tabularnewline
36 & 53 & 62.820828403076 & -9.82082840307605 \tabularnewline
37 & 54 & 53.6524523730093 & 0.347547626990661 \tabularnewline
38 & 56 & 52.6463282679781 & 3.35367173202189 \tabularnewline
39 & 61 & 60.3965308170229 & 0.603469182977122 \tabularnewline
40 & 47 & 54.9076096123528 & -7.90760961235283 \tabularnewline
41 & 39 & 47.1577183244986 & -8.1577183244986 \tabularnewline
42 & 48 & 49.8421045741218 & -1.84210457412176 \tabularnewline
43 & 50 & 41.0128476457832 & 8.98715235421685 \tabularnewline
44 & 35 & 51.7386329126661 & -16.7386329126661 \tabularnewline
45 & 30 & 64.9082654149171 & -34.9082654149171 \tabularnewline
46 & 68 & 49.6542465501978 & 18.3457534498022 \tabularnewline
47 & 49 & 46.1999663799418 & 2.8000336200582 \tabularnewline
48 & 61 & 54.7738261328153 & 6.22617386718475 \tabularnewline
49 & 67 & 50.4481387312516 & 16.5518612687484 \tabularnewline
50 & 47 & 51.7174081333827 & -4.71740813338266 \tabularnewline
51 & 56 & 57.7534800653948 & -1.75348006539483 \tabularnewline
52 & 50 & 48.8388820145009 & 1.16111798549906 \tabularnewline
53 & 43 & 41.6174769613193 & 1.38252303868067 \tabularnewline
54 & 67 & 47.3358382857202 & 19.6641617142798 \tabularnewline
55 & 62 & 44.203096542038 & 17.796903457962 \tabularnewline
56 & 57 & 46.1870563350017 & 10.8129436649983 \tabularnewline
57 & 41 & 54.9385096697663 & -13.9385096697663 \tabularnewline
58 & 54 & 61.2822390167214 & -7.28223901672143 \tabularnewline
59 & 45 & 50.3616445085226 & -5.36164450852257 \tabularnewline
60 & 48 & 59.7648791601554 & -11.7648791601554 \tabularnewline
61 & 61 & 58.0037052343208 & 2.9962947656792 \tabularnewline
62 & 56 & 50.4251252419829 & 5.57487475801705 \tabularnewline
63 & 41 & 58.4150296112176 & -17.4150296112176 \tabularnewline
64 & 43 & 49.4166873011356 & -6.41668730113555 \tabularnewline
65 & 53 & 41.690285615268 & 11.309714384732 \tabularnewline
66 & 44 & 54.9434267446694 & -10.9434267446694 \tabularnewline
67 & 66 & 48.7118601468482 & 17.2881398531518 \tabularnewline
68 & 58 & 47.9652143133744 & 10.0347856866256 \tabularnewline
69 & 46 & 47.3901575988935 & -1.39015759889349 \tabularnewline
70 & 37 & 57.0816318502843 & -20.0816318502843 \tabularnewline
71 & 51 & 45.7956802812242 & 5.20431971877581 \tabularnewline
72 & 51 & 53.5571556644053 & -2.55715566440527 \tabularnewline
73 & 56 & 57.9208121294615 & -1.92081212946152 \tabularnewline
74 & 66 & 50.8773173076447 & 15.1226826923553 \tabularnewline
75 & 37 & 51.0733963244623 & -14.0733963244623 \tabularnewline
76 & 59 & 46.4014780807195 & 12.5985219192805 \tabularnewline
77 & 42 & 46.751136290257 & -4.75113629025695 \tabularnewline
78 & 38 & 50.5847677640692 & -12.5847677640692 \tabularnewline
79 & 66 & 54.6852961006173 & 11.3147038993827 \tabularnewline
80 & 34 & 50.7930964737692 & -16.7930964737692 \tabularnewline
81 & 53 & 43.8450945720946 & 9.1549054279054 \tabularnewline
82 & 49 & 47.3314536097198 & 1.66854639028021 \tabularnewline
83 & 55 & 47.0446037223305 & 7.95539627766953 \tabularnewline
84 & 49 & 52.1641776093165 & -3.16417760931651 \tabularnewline
85 & 59 & 56.7371994595088 & 2.26280054049116 \tabularnewline
86 & 40 & 56.3504859560358 & -16.3504859560358 \tabularnewline
87 & 58 & 43.2817049035444 & 14.7182950964556 \tabularnewline
88 & 60 & 50.6668133043965 & 9.33318669560345 \tabularnewline
89 & 63 & 44.36521474459 & 18.63478525541 \tabularnewline
90 & 56 & 47.17285500969 & 8.82714499031002 \tabularnewline
91 & 54 & 61.9299810077928 & -7.92998100779285 \tabularnewline
92 & 52 & 46.3163020593757 & 5.68369794062427 \tabularnewline
93 & 34 & 50.8767336495194 & -16.8767336495194 \tabularnewline
94 & 69 & 49.7438644429605 & 19.2561355570395 \tabularnewline
95 & 32 & 53.2884871528397 & -21.2884871528397 \tabularnewline
96 & 48 & 52.152847150575 & -4.15284715057496 \tabularnewline
97 & 67 & 58.711510082328 & 8.288489917672 \tabularnewline
98 & 58 & 51.9713549207462 & 6.02864507925382 \tabularnewline
99 & 57 & 52.2533477238177 & 4.74665227618235 \tabularnewline
100 & 42 & 57.0291178335373 & -15.0291178335373 \tabularnewline
101 & 64 & 52.3632527638725 & 11.6367472361275 \tabularnewline
102 & 58 & 51.0133146629277 & 6.98668533707232 \tabularnewline
103 & 66 & 59.422035509287 & 6.57796449071304 \tabularnewline
104 & 26 & 49.9863525276051 & -23.9863525276051 \tabularnewline
105 & 61 & 43.8935077955719 & 17.1064922044281 \tabularnewline
106 & 52 & 58.7516138967462 & -6.75161389674623 \tabularnewline
107 & 51 & 45.3004570644444 & 5.69954293555559 \tabularnewline
108 & 55 & 52.6069143058617 & 2.39308569413826 \tabularnewline
109 & 50 & 64.3625684677832 & -14.3625684677832 \tabularnewline
110 & 60 & 55.0878988461497 & 4.91210115385031 \tabularnewline
111 & 56 & 54.8114193150412 & 1.18858068495875 \tabularnewline
112 & 63 & 51.9887878453388 & 11.0112121546612 \tabularnewline
113 & 61 & 59.2418347140016 & 1.75816528599839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267951&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]52[/C][C]49.40625[/C][C]2.59374999999996[/C][/ROW]
[ROW][C]14[/C][C]58[/C][C]54.5841044228803[/C][C]3.41589557711967[/C][/ROW]
[ROW][C]15[/C][C]68[/C][C]64.796912675645[/C][C]3.203087324355[/C][/ROW]
[ROW][C]16[/C][C]62[/C][C]60.4659348432432[/C][C]1.53406515675683[/C][/ROW]
[ROW][C]17[/C][C]43[/C][C]41.8494457478433[/C][C]1.15055425215665[/C][/ROW]
[ROW][C]18[/C][C]56[/C][C]55.5841069308705[/C][C]0.415893069129496[/C][/ROW]
[ROW][C]19[/C][C]56[/C][C]56.9736650451272[/C][C]-0.973665045127156[/C][/ROW]
[ROW][C]20[/C][C]74[/C][C]47.2545233324573[/C][C]26.7454766675427[/C][/ROW]
[ROW][C]21[/C][C]65[/C][C]89.5271457564225[/C][C]-24.5271457564225[/C][/ROW]
[ROW][C]22[/C][C]63[/C][C]70.0883103684856[/C][C]-7.08831036848564[/C][/ROW]
[ROW][C]23[/C][C]58[/C][C]52.2216394492849[/C][C]5.77836055071515[/C][/ROW]
[ROW][C]24[/C][C]57[/C][C]73.9724491491129[/C][C]-16.9724491491129[/C][/ROW]
[ROW][C]25[/C][C]63[/C][C]55.7318552343796[/C][C]7.26814476562042[/C][/ROW]
[ROW][C]26[/C][C]53[/C][C]61.5650732862287[/C][C]-8.56507328622865[/C][/ROW]
[ROW][C]27[/C][C]57[/C][C]70.7461797381422[/C][C]-13.7461797381422[/C][/ROW]
[ROW][C]28[/C][C]51[/C][C]64.3978215274539[/C][C]-13.3978215274539[/C][/ROW]
[ROW][C]29[/C][C]64[/C][C]44.3264425537833[/C][C]19.6735574462167[/C][/ROW]
[ROW][C]30[/C][C]53[/C][C]59.0720526939575[/C][C]-6.07205269395747[/C][/ROW]
[ROW][C]31[/C][C]29[/C][C]59.3216325681728[/C][C]-30.3216325681728[/C][/ROW]
[ROW][C]32[/C][C]54[/C][C]57.3839312673838[/C][C]-3.38393126738382[/C][/ROW]
[ROW][C]33[/C][C]58[/C][C]78.0292516018358[/C][C]-20.0292516018358[/C][/ROW]
[ROW][C]34[/C][C]43[/C][C]65.0028959496959[/C][C]-22.0028959496959[/C][/ROW]
[ROW][C]35[/C][C]51[/C][C]50.3331892427459[/C][C]0.666810757254083[/C][/ROW]
[ROW][C]36[/C][C]53[/C][C]62.820828403076[/C][C]-9.82082840307605[/C][/ROW]
[ROW][C]37[/C][C]54[/C][C]53.6524523730093[/C][C]0.347547626990661[/C][/ROW]
[ROW][C]38[/C][C]56[/C][C]52.6463282679781[/C][C]3.35367173202189[/C][/ROW]
[ROW][C]39[/C][C]61[/C][C]60.3965308170229[/C][C]0.603469182977122[/C][/ROW]
[ROW][C]40[/C][C]47[/C][C]54.9076096123528[/C][C]-7.90760961235283[/C][/ROW]
[ROW][C]41[/C][C]39[/C][C]47.1577183244986[/C][C]-8.1577183244986[/C][/ROW]
[ROW][C]42[/C][C]48[/C][C]49.8421045741218[/C][C]-1.84210457412176[/C][/ROW]
[ROW][C]43[/C][C]50[/C][C]41.0128476457832[/C][C]8.98715235421685[/C][/ROW]
[ROW][C]44[/C][C]35[/C][C]51.7386329126661[/C][C]-16.7386329126661[/C][/ROW]
[ROW][C]45[/C][C]30[/C][C]64.9082654149171[/C][C]-34.9082654149171[/C][/ROW]
[ROW][C]46[/C][C]68[/C][C]49.6542465501978[/C][C]18.3457534498022[/C][/ROW]
[ROW][C]47[/C][C]49[/C][C]46.1999663799418[/C][C]2.8000336200582[/C][/ROW]
[ROW][C]48[/C][C]61[/C][C]54.7738261328153[/C][C]6.22617386718475[/C][/ROW]
[ROW][C]49[/C][C]67[/C][C]50.4481387312516[/C][C]16.5518612687484[/C][/ROW]
[ROW][C]50[/C][C]47[/C][C]51.7174081333827[/C][C]-4.71740813338266[/C][/ROW]
[ROW][C]51[/C][C]56[/C][C]57.7534800653948[/C][C]-1.75348006539483[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]48.8388820145009[/C][C]1.16111798549906[/C][/ROW]
[ROW][C]53[/C][C]43[/C][C]41.6174769613193[/C][C]1.38252303868067[/C][/ROW]
[ROW][C]54[/C][C]67[/C][C]47.3358382857202[/C][C]19.6641617142798[/C][/ROW]
[ROW][C]55[/C][C]62[/C][C]44.203096542038[/C][C]17.796903457962[/C][/ROW]
[ROW][C]56[/C][C]57[/C][C]46.1870563350017[/C][C]10.8129436649983[/C][/ROW]
[ROW][C]57[/C][C]41[/C][C]54.9385096697663[/C][C]-13.9385096697663[/C][/ROW]
[ROW][C]58[/C][C]54[/C][C]61.2822390167214[/C][C]-7.28223901672143[/C][/ROW]
[ROW][C]59[/C][C]45[/C][C]50.3616445085226[/C][C]-5.36164450852257[/C][/ROW]
[ROW][C]60[/C][C]48[/C][C]59.7648791601554[/C][C]-11.7648791601554[/C][/ROW]
[ROW][C]61[/C][C]61[/C][C]58.0037052343208[/C][C]2.9962947656792[/C][/ROW]
[ROW][C]62[/C][C]56[/C][C]50.4251252419829[/C][C]5.57487475801705[/C][/ROW]
[ROW][C]63[/C][C]41[/C][C]58.4150296112176[/C][C]-17.4150296112176[/C][/ROW]
[ROW][C]64[/C][C]43[/C][C]49.4166873011356[/C][C]-6.41668730113555[/C][/ROW]
[ROW][C]65[/C][C]53[/C][C]41.690285615268[/C][C]11.309714384732[/C][/ROW]
[ROW][C]66[/C][C]44[/C][C]54.9434267446694[/C][C]-10.9434267446694[/C][/ROW]
[ROW][C]67[/C][C]66[/C][C]48.7118601468482[/C][C]17.2881398531518[/C][/ROW]
[ROW][C]68[/C][C]58[/C][C]47.9652143133744[/C][C]10.0347856866256[/C][/ROW]
[ROW][C]69[/C][C]46[/C][C]47.3901575988935[/C][C]-1.39015759889349[/C][/ROW]
[ROW][C]70[/C][C]37[/C][C]57.0816318502843[/C][C]-20.0816318502843[/C][/ROW]
[ROW][C]71[/C][C]51[/C][C]45.7956802812242[/C][C]5.20431971877581[/C][/ROW]
[ROW][C]72[/C][C]51[/C][C]53.5571556644053[/C][C]-2.55715566440527[/C][/ROW]
[ROW][C]73[/C][C]56[/C][C]57.9208121294615[/C][C]-1.92081212946152[/C][/ROW]
[ROW][C]74[/C][C]66[/C][C]50.8773173076447[/C][C]15.1226826923553[/C][/ROW]
[ROW][C]75[/C][C]37[/C][C]51.0733963244623[/C][C]-14.0733963244623[/C][/ROW]
[ROW][C]76[/C][C]59[/C][C]46.4014780807195[/C][C]12.5985219192805[/C][/ROW]
[ROW][C]77[/C][C]42[/C][C]46.751136290257[/C][C]-4.75113629025695[/C][/ROW]
[ROW][C]78[/C][C]38[/C][C]50.5847677640692[/C][C]-12.5847677640692[/C][/ROW]
[ROW][C]79[/C][C]66[/C][C]54.6852961006173[/C][C]11.3147038993827[/C][/ROW]
[ROW][C]80[/C][C]34[/C][C]50.7930964737692[/C][C]-16.7930964737692[/C][/ROW]
[ROW][C]81[/C][C]53[/C][C]43.8450945720946[/C][C]9.1549054279054[/C][/ROW]
[ROW][C]82[/C][C]49[/C][C]47.3314536097198[/C][C]1.66854639028021[/C][/ROW]
[ROW][C]83[/C][C]55[/C][C]47.0446037223305[/C][C]7.95539627766953[/C][/ROW]
[ROW][C]84[/C][C]49[/C][C]52.1641776093165[/C][C]-3.16417760931651[/C][/ROW]
[ROW][C]85[/C][C]59[/C][C]56.7371994595088[/C][C]2.26280054049116[/C][/ROW]
[ROW][C]86[/C][C]40[/C][C]56.3504859560358[/C][C]-16.3504859560358[/C][/ROW]
[ROW][C]87[/C][C]58[/C][C]43.2817049035444[/C][C]14.7182950964556[/C][/ROW]
[ROW][C]88[/C][C]60[/C][C]50.6668133043965[/C][C]9.33318669560345[/C][/ROW]
[ROW][C]89[/C][C]63[/C][C]44.36521474459[/C][C]18.63478525541[/C][/ROW]
[ROW][C]90[/C][C]56[/C][C]47.17285500969[/C][C]8.82714499031002[/C][/ROW]
[ROW][C]91[/C][C]54[/C][C]61.9299810077928[/C][C]-7.92998100779285[/C][/ROW]
[ROW][C]92[/C][C]52[/C][C]46.3163020593757[/C][C]5.68369794062427[/C][/ROW]
[ROW][C]93[/C][C]34[/C][C]50.8767336495194[/C][C]-16.8767336495194[/C][/ROW]
[ROW][C]94[/C][C]69[/C][C]49.7438644429605[/C][C]19.2561355570395[/C][/ROW]
[ROW][C]95[/C][C]32[/C][C]53.2884871528397[/C][C]-21.2884871528397[/C][/ROW]
[ROW][C]96[/C][C]48[/C][C]52.152847150575[/C][C]-4.15284715057496[/C][/ROW]
[ROW][C]97[/C][C]67[/C][C]58.711510082328[/C][C]8.288489917672[/C][/ROW]
[ROW][C]98[/C][C]58[/C][C]51.9713549207462[/C][C]6.02864507925382[/C][/ROW]
[ROW][C]99[/C][C]57[/C][C]52.2533477238177[/C][C]4.74665227618235[/C][/ROW]
[ROW][C]100[/C][C]42[/C][C]57.0291178335373[/C][C]-15.0291178335373[/C][/ROW]
[ROW][C]101[/C][C]64[/C][C]52.3632527638725[/C][C]11.6367472361275[/C][/ROW]
[ROW][C]102[/C][C]58[/C][C]51.0133146629277[/C][C]6.98668533707232[/C][/ROW]
[ROW][C]103[/C][C]66[/C][C]59.422035509287[/C][C]6.57796449071304[/C][/ROW]
[ROW][C]104[/C][C]26[/C][C]49.9863525276051[/C][C]-23.9863525276051[/C][/ROW]
[ROW][C]105[/C][C]61[/C][C]43.8935077955719[/C][C]17.1064922044281[/C][/ROW]
[ROW][C]106[/C][C]52[/C][C]58.7516138967462[/C][C]-6.75161389674623[/C][/ROW]
[ROW][C]107[/C][C]51[/C][C]45.3004570644444[/C][C]5.69954293555559[/C][/ROW]
[ROW][C]108[/C][C]55[/C][C]52.6069143058617[/C][C]2.39308569413826[/C][/ROW]
[ROW][C]109[/C][C]50[/C][C]64.3625684677832[/C][C]-14.3625684677832[/C][/ROW]
[ROW][C]110[/C][C]60[/C][C]55.0878988461497[/C][C]4.91210115385031[/C][/ROW]
[ROW][C]111[/C][C]56[/C][C]54.8114193150412[/C][C]1.18858068495875[/C][/ROW]
[ROW][C]112[/C][C]63[/C][C]51.9887878453388[/C][C]11.0112121546612[/C][/ROW]
[ROW][C]113[/C][C]61[/C][C]59.2418347140016[/C][C]1.75816528599839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267951&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267951&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
135249.406252.59374999999996
145854.58410442288033.41589557711967
156864.7969126756453.203087324355
166260.46593484324321.53406515675683
174341.84944574784331.15055425215665
185655.58410693087050.415893069129496
195656.9736650451272-0.973665045127156
207447.254523332457326.7454766675427
216589.5271457564225-24.5271457564225
226370.0883103684856-7.08831036848564
235852.22163944928495.77836055071515
245773.9724491491129-16.9724491491129
256355.73185523437967.26814476562042
265361.5650732862287-8.56507328622865
275770.7461797381422-13.7461797381422
285164.3978215274539-13.3978215274539
296444.326442553783319.6735574462167
305359.0720526939575-6.07205269395747
312959.3216325681728-30.3216325681728
325457.3839312673838-3.38393126738382
335878.0292516018358-20.0292516018358
344365.0028959496959-22.0028959496959
355150.33318924274590.666810757254083
365362.820828403076-9.82082840307605
375453.65245237300930.347547626990661
385652.64632826797813.35367173202189
396160.39653081702290.603469182977122
404754.9076096123528-7.90760961235283
413947.1577183244986-8.1577183244986
424849.8421045741218-1.84210457412176
435041.01284764578328.98715235421685
443551.7386329126661-16.7386329126661
453064.9082654149171-34.9082654149171
466849.654246550197818.3457534498022
474946.19996637994182.8000336200582
486154.77382613281536.22617386718475
496750.448138731251616.5518612687484
504751.7174081333827-4.71740813338266
515657.7534800653948-1.75348006539483
525048.83888201450091.16111798549906
534341.61747696131931.38252303868067
546747.335838285720219.6641617142798
556244.20309654203817.796903457962
565746.187056335001710.8129436649983
574154.9385096697663-13.9385096697663
585461.2822390167214-7.28223901672143
594550.3616445085226-5.36164450852257
604859.7648791601554-11.7648791601554
616158.00370523432082.9962947656792
625650.42512524198295.57487475801705
634158.4150296112176-17.4150296112176
644349.4166873011356-6.41668730113555
655341.69028561526811.309714384732
664454.9434267446694-10.9434267446694
676648.711860146848217.2881398531518
685847.965214313374410.0347856866256
694647.3901575988935-1.39015759889349
703757.0816318502843-20.0816318502843
715145.79568028122425.20431971877581
725153.5571556644053-2.55715566440527
735657.9208121294615-1.92081212946152
746650.877317307644715.1226826923553
753751.0733963244623-14.0733963244623
765946.401478080719512.5985219192805
774246.751136290257-4.75113629025695
783850.5847677640692-12.5847677640692
796654.685296100617311.3147038993827
803450.7930964737692-16.7930964737692
815343.84509457209469.1549054279054
824947.33145360971981.66854639028021
835547.04460372233057.95539627766953
844952.1641776093165-3.16417760931651
855956.73719945950882.26280054049116
864056.3504859560358-16.3504859560358
875843.281704903544414.7182950964556
886050.66681330439659.33318669560345
896344.3652147445918.63478525541
905647.172855009698.82714499031002
915461.9299810077928-7.92998100779285
925246.31630205937575.68369794062427
933450.8767336495194-16.8767336495194
946949.743864442960519.2561355570395
953253.2884871528397-21.2884871528397
964852.152847150575-4.15284715057496
976758.7115100823288.288489917672
985851.97135492074626.02864507925382
995752.25334772381774.74665227618235
1004257.0291178335373-15.0291178335373
1016452.363252763872511.6367472361275
1025851.01331466292776.98668533707232
1036659.4220355092876.57796449071304
1042649.9863525276051-23.9863525276051
1056143.893507795571917.1064922044281
1065258.7516138967462-6.75161389674623
1075145.30045706444445.69954293555559
1085552.60691430586172.39308569413826
1095064.3625684677832-14.3625684677832
1106055.08789884614974.91210115385031
1115654.81141931504121.18858068495875
1126351.988787845338811.0112121546612
1136159.24183471400161.75816528599839







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
11455.483368858187631.424257488471379.5424802279038
11563.239614594532839.10454878052187.3746804085446
11641.998988709517617.779743962303766.2182334567316
11753.009577368616828.697567454552277.3215872826814
11857.781579699125933.367870948100182.1952884501517
11949.498418958554624.973745541660574.0230923754488
12055.183162650767830.537942768148979.8283825333867
12160.580424023147735.804776930150785.3560711161446
12259.597235218969434.680999006964184.5134714309748
12357.634561150975532.567311188631282.7018111133197
12458.411336694858233.182404626532783.6402687631837
12561.421331706862236.01982489726786.8228385164573

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
114 & 55.4833688581876 & 31.4242574884713 & 79.5424802279038 \tabularnewline
115 & 63.2396145945328 & 39.104548780521 & 87.3746804085446 \tabularnewline
116 & 41.9989887095176 & 17.7797439623037 & 66.2182334567316 \tabularnewline
117 & 53.0095773686168 & 28.6975674545522 & 77.3215872826814 \tabularnewline
118 & 57.7815796991259 & 33.3678709481001 & 82.1952884501517 \tabularnewline
119 & 49.4984189585546 & 24.9737455416605 & 74.0230923754488 \tabularnewline
120 & 55.1831626507678 & 30.5379427681489 & 79.8283825333867 \tabularnewline
121 & 60.5804240231477 & 35.8047769301507 & 85.3560711161446 \tabularnewline
122 & 59.5972352189694 & 34.6809990069641 & 84.5134714309748 \tabularnewline
123 & 57.6345611509755 & 32.5673111886312 & 82.7018111133197 \tabularnewline
124 & 58.4113366948582 & 33.1824046265327 & 83.6402687631837 \tabularnewline
125 & 61.4213317068622 & 36.019824897267 & 86.8228385164573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267951&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]114[/C][C]55.4833688581876[/C][C]31.4242574884713[/C][C]79.5424802279038[/C][/ROW]
[ROW][C]115[/C][C]63.2396145945328[/C][C]39.104548780521[/C][C]87.3746804085446[/C][/ROW]
[ROW][C]116[/C][C]41.9989887095176[/C][C]17.7797439623037[/C][C]66.2182334567316[/C][/ROW]
[ROW][C]117[/C][C]53.0095773686168[/C][C]28.6975674545522[/C][C]77.3215872826814[/C][/ROW]
[ROW][C]118[/C][C]57.7815796991259[/C][C]33.3678709481001[/C][C]82.1952884501517[/C][/ROW]
[ROW][C]119[/C][C]49.4984189585546[/C][C]24.9737455416605[/C][C]74.0230923754488[/C][/ROW]
[ROW][C]120[/C][C]55.1831626507678[/C][C]30.5379427681489[/C][C]79.8283825333867[/C][/ROW]
[ROW][C]121[/C][C]60.5804240231477[/C][C]35.8047769301507[/C][C]85.3560711161446[/C][/ROW]
[ROW][C]122[/C][C]59.5972352189694[/C][C]34.6809990069641[/C][C]84.5134714309748[/C][/ROW]
[ROW][C]123[/C][C]57.6345611509755[/C][C]32.5673111886312[/C][C]82.7018111133197[/C][/ROW]
[ROW][C]124[/C][C]58.4113366948582[/C][C]33.1824046265327[/C][C]83.6402687631837[/C][/ROW]
[ROW][C]125[/C][C]61.4213317068622[/C][C]36.019824897267[/C][C]86.8228385164573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267951&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267951&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
11455.483368858187631.424257488471379.5424802279038
11563.239614594532839.10454878052187.3746804085446
11641.998988709517617.779743962303766.2182334567316
11753.009577368616828.697567454552277.3215872826814
11857.781579699125933.367870948100182.1952884501517
11949.498418958554624.973745541660574.0230923754488
12055.183162650767830.537942768148979.8283825333867
12160.580424023147735.804776930150785.3560711161446
12259.597235218969434.680999006964184.5134714309748
12357.634561150975532.567311188631282.7018111133197
12458.411336694858233.182404626532783.6402687631837
12561.421331706862236.01982489726786.8228385164573



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')