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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 14:04:37 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/26/t1369591503uht12bs5y5vnih3.htm/, Retrieved Mon, 29 Apr 2024 07:59:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210648, Retrieved Mon, 29 Apr 2024 07:59:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Classical Deompos...] [2013-05-02 20:21:47] [6a6c2f75bf2bd9708d5f14e301096fe2]
- RMPD    [Exponential Smoothing] [] [2013-05-26 18:04:37] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
67,66
68
68,02
68,11
68,41
68,4
68,4
68,55
68,54
68,99
68,97
68,98
68,98
68,94
69,21
69,21
69,67
69,66
69,66
69,66
69,77
70,32
70,34
70,38
70,38
70,29
70,42
70,29
70,59
70,64
70,64
70,68
70,78
70,9
71,04
71,15
71,15
71,15
71,07
71,17
71,24
71,23
71,23
71,23
71,24
71,28
71,52
71,52
71,52
71,6
71,61
71,78
71,66
71,86
71,86
71,82
71,8
72,22
72,51
72,56
72,56
72,78
72,88
73,05
73,02
73,08
73,08
73,24
73,82
74
74,37
74,38




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210648&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210648&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210648&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.919827232958154
beta0.180193143589243
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.919827232958154 \tabularnewline
beta & 0.180193143589243 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210648&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]0.919827232958154[/C][/ROW]
[ROW][C]beta[/C][C]0.180193143589243[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210648&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210648&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
alpha0.919827232958154
beta0.180193143589243
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
368.0268.34-0.320000000000007
468.1168.3326163860404-0.222616386040357
568.4168.37791097191070.0320890280893309
668.468.6628091801202-0.262809180120243
768.468.6328922677518-0.232892267751794
868.5568.5918926537204-0.0418926537203674
968.5468.7196361228882-0.179636122888212
1068.9968.69090532841330.299094671586687
1168.9769.152098069081-0.18209806908105
1268.9869.1404944939268-0.160494493926777
1368.9869.1221610651545-0.142161065154511
1468.9469.0971285158305-0.15712851583055
1569.2169.03228498668540.177715013314611
1669.2169.3048953066633-0.094895306663318
1769.6769.31102265963730.358977340362657
1869.6669.7941336931627-0.13413369316271
1969.6669.8014355708682-0.141435570868182
2069.6669.7785785231812-0.118578523181242
2169.7769.75709202803570.0129079719643386
2270.3269.85868984384950.461310156150532
2370.3470.4492007717778-0.109200771777765
2470.3870.4968405591532-0.116840559153189
2570.3870.5180871412208-0.13808714122078
2670.2970.4969030697658-0.206903069765801
2770.4270.3781267609690.0418732390310339
2870.2970.4951220212716-0.205122021271578
2970.5970.35092604519370.239073954806301
3070.6470.6549393104366-0.0149393104365885
3170.6470.7228281174528-0.0828281174528485
3270.6870.7145424753683-0.0345424753682977
3370.7870.74494598534480.0350540146551879
3470.970.84517632452990.0548236754701463
3571.0470.97267817177110.0673218282289412
3671.1571.12283452176820.0271654782318365
3771.1571.2405565520475-0.090556552047488
3871.1571.2349852159091-0.0849852159091427
3971.0771.2204525392305-0.150452539230457
4071.1771.12076424477110.0492357552289349
4171.2471.21291533874940.0270846612506261
4271.2371.2891804426957-0.0591804426956912
4371.2371.2762875999427-0.0462875999427297
4471.2371.2675819345722-0.0375819345722164
4571.2471.260654900892-0.0206549008920263
4671.2871.26587433498030.0141256650196908
4771.5271.3054271611660.214572838833959
4871.5271.5649214666446-0.0449214666446238
4971.5271.57828026455-0.0582802645500351
5071.671.56969152293860.0303084770613822
5171.6171.6476126442268-0.0376126442267974
5271.7871.65682390204290.123176097957057
5371.6671.8343490382655-0.17434903826549
5471.8671.70930469825310.150695301746936
5571.8671.908222222076-0.0482222220760207
5671.8271.9161773229172-0.0961773229172564
5771.871.8640809555579-0.0640809555578841
5872.2271.83088650298680.389113497013199
5972.5172.27904687355470.230953126445286
6072.5672.6200067144828-0.0600067144828245
6172.5672.6833878634857-0.123387863485704
6272.7872.66801819157890.111981808421092
6372.8872.8877085533073-0.00770855330733866
6473.0572.99602679459690.0539732054030679
6573.0273.1700274704888-0.15002747048878
6673.0873.1315162319145-0.0515162319145475
6773.0873.175079675075-0.0950796750750271
6873.2473.16281314772220.0771868522778192
6973.8273.32179551884930.498204481150722
707473.95061704982810.049382950171875
7174.3774.17478536802120.195214631978843
7274.3874.5654497924105-0.185449792410466

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 68.02 & 68.34 & -0.320000000000007 \tabularnewline
4 & 68.11 & 68.3326163860404 & -0.222616386040357 \tabularnewline
5 & 68.41 & 68.3779109719107 & 0.0320890280893309 \tabularnewline
6 & 68.4 & 68.6628091801202 & -0.262809180120243 \tabularnewline
7 & 68.4 & 68.6328922677518 & -0.232892267751794 \tabularnewline
8 & 68.55 & 68.5918926537204 & -0.0418926537203674 \tabularnewline
9 & 68.54 & 68.7196361228882 & -0.179636122888212 \tabularnewline
10 & 68.99 & 68.6909053284133 & 0.299094671586687 \tabularnewline
11 & 68.97 & 69.152098069081 & -0.18209806908105 \tabularnewline
12 & 68.98 & 69.1404944939268 & -0.160494493926777 \tabularnewline
13 & 68.98 & 69.1221610651545 & -0.142161065154511 \tabularnewline
14 & 68.94 & 69.0971285158305 & -0.15712851583055 \tabularnewline
15 & 69.21 & 69.0322849866854 & 0.177715013314611 \tabularnewline
16 & 69.21 & 69.3048953066633 & -0.094895306663318 \tabularnewline
17 & 69.67 & 69.3110226596373 & 0.358977340362657 \tabularnewline
18 & 69.66 & 69.7941336931627 & -0.13413369316271 \tabularnewline
19 & 69.66 & 69.8014355708682 & -0.141435570868182 \tabularnewline
20 & 69.66 & 69.7785785231812 & -0.118578523181242 \tabularnewline
21 & 69.77 & 69.7570920280357 & 0.0129079719643386 \tabularnewline
22 & 70.32 & 69.8586898438495 & 0.461310156150532 \tabularnewline
23 & 70.34 & 70.4492007717778 & -0.109200771777765 \tabularnewline
24 & 70.38 & 70.4968405591532 & -0.116840559153189 \tabularnewline
25 & 70.38 & 70.5180871412208 & -0.13808714122078 \tabularnewline
26 & 70.29 & 70.4969030697658 & -0.206903069765801 \tabularnewline
27 & 70.42 & 70.378126760969 & 0.0418732390310339 \tabularnewline
28 & 70.29 & 70.4951220212716 & -0.205122021271578 \tabularnewline
29 & 70.59 & 70.3509260451937 & 0.239073954806301 \tabularnewline
30 & 70.64 & 70.6549393104366 & -0.0149393104365885 \tabularnewline
31 & 70.64 & 70.7228281174528 & -0.0828281174528485 \tabularnewline
32 & 70.68 & 70.7145424753683 & -0.0345424753682977 \tabularnewline
33 & 70.78 & 70.7449459853448 & 0.0350540146551879 \tabularnewline
34 & 70.9 & 70.8451763245299 & 0.0548236754701463 \tabularnewline
35 & 71.04 & 70.9726781717711 & 0.0673218282289412 \tabularnewline
36 & 71.15 & 71.1228345217682 & 0.0271654782318365 \tabularnewline
37 & 71.15 & 71.2405565520475 & -0.090556552047488 \tabularnewline
38 & 71.15 & 71.2349852159091 & -0.0849852159091427 \tabularnewline
39 & 71.07 & 71.2204525392305 & -0.150452539230457 \tabularnewline
40 & 71.17 & 71.1207642447711 & 0.0492357552289349 \tabularnewline
41 & 71.24 & 71.2129153387494 & 0.0270846612506261 \tabularnewline
42 & 71.23 & 71.2891804426957 & -0.0591804426956912 \tabularnewline
43 & 71.23 & 71.2762875999427 & -0.0462875999427297 \tabularnewline
44 & 71.23 & 71.2675819345722 & -0.0375819345722164 \tabularnewline
45 & 71.24 & 71.260654900892 & -0.0206549008920263 \tabularnewline
46 & 71.28 & 71.2658743349803 & 0.0141256650196908 \tabularnewline
47 & 71.52 & 71.305427161166 & 0.214572838833959 \tabularnewline
48 & 71.52 & 71.5649214666446 & -0.0449214666446238 \tabularnewline
49 & 71.52 & 71.57828026455 & -0.0582802645500351 \tabularnewline
50 & 71.6 & 71.5696915229386 & 0.0303084770613822 \tabularnewline
51 & 71.61 & 71.6476126442268 & -0.0376126442267974 \tabularnewline
52 & 71.78 & 71.6568239020429 & 0.123176097957057 \tabularnewline
53 & 71.66 & 71.8343490382655 & -0.17434903826549 \tabularnewline
54 & 71.86 & 71.7093046982531 & 0.150695301746936 \tabularnewline
55 & 71.86 & 71.908222222076 & -0.0482222220760207 \tabularnewline
56 & 71.82 & 71.9161773229172 & -0.0961773229172564 \tabularnewline
57 & 71.8 & 71.8640809555579 & -0.0640809555578841 \tabularnewline
58 & 72.22 & 71.8308865029868 & 0.389113497013199 \tabularnewline
59 & 72.51 & 72.2790468735547 & 0.230953126445286 \tabularnewline
60 & 72.56 & 72.6200067144828 & -0.0600067144828245 \tabularnewline
61 & 72.56 & 72.6833878634857 & -0.123387863485704 \tabularnewline
62 & 72.78 & 72.6680181915789 & 0.111981808421092 \tabularnewline
63 & 72.88 & 72.8877085533073 & -0.00770855330733866 \tabularnewline
64 & 73.05 & 72.9960267945969 & 0.0539732054030679 \tabularnewline
65 & 73.02 & 73.1700274704888 & -0.15002747048878 \tabularnewline
66 & 73.08 & 73.1315162319145 & -0.0515162319145475 \tabularnewline
67 & 73.08 & 73.175079675075 & -0.0950796750750271 \tabularnewline
68 & 73.24 & 73.1628131477222 & 0.0771868522778192 \tabularnewline
69 & 73.82 & 73.3217955188493 & 0.498204481150722 \tabularnewline
70 & 74 & 73.9506170498281 & 0.049382950171875 \tabularnewline
71 & 74.37 & 74.1747853680212 & 0.195214631978843 \tabularnewline
72 & 74.38 & 74.5654497924105 & -0.185449792410466 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210648&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]68.02[/C][C]68.34[/C][C]-0.320000000000007[/C][/ROW]
[ROW][C]4[/C][C]68.11[/C][C]68.3326163860404[/C][C]-0.222616386040357[/C][/ROW]
[ROW][C]5[/C][C]68.41[/C][C]68.3779109719107[/C][C]0.0320890280893309[/C][/ROW]
[ROW][C]6[/C][C]68.4[/C][C]68.6628091801202[/C][C]-0.262809180120243[/C][/ROW]
[ROW][C]7[/C][C]68.4[/C][C]68.6328922677518[/C][C]-0.232892267751794[/C][/ROW]
[ROW][C]8[/C][C]68.55[/C][C]68.5918926537204[/C][C]-0.0418926537203674[/C][/ROW]
[ROW][C]9[/C][C]68.54[/C][C]68.7196361228882[/C][C]-0.179636122888212[/C][/ROW]
[ROW][C]10[/C][C]68.99[/C][C]68.6909053284133[/C][C]0.299094671586687[/C][/ROW]
[ROW][C]11[/C][C]68.97[/C][C]69.152098069081[/C][C]-0.18209806908105[/C][/ROW]
[ROW][C]12[/C][C]68.98[/C][C]69.1404944939268[/C][C]-0.160494493926777[/C][/ROW]
[ROW][C]13[/C][C]68.98[/C][C]69.1221610651545[/C][C]-0.142161065154511[/C][/ROW]
[ROW][C]14[/C][C]68.94[/C][C]69.0971285158305[/C][C]-0.15712851583055[/C][/ROW]
[ROW][C]15[/C][C]69.21[/C][C]69.0322849866854[/C][C]0.177715013314611[/C][/ROW]
[ROW][C]16[/C][C]69.21[/C][C]69.3048953066633[/C][C]-0.094895306663318[/C][/ROW]
[ROW][C]17[/C][C]69.67[/C][C]69.3110226596373[/C][C]0.358977340362657[/C][/ROW]
[ROW][C]18[/C][C]69.66[/C][C]69.7941336931627[/C][C]-0.13413369316271[/C][/ROW]
[ROW][C]19[/C][C]69.66[/C][C]69.8014355708682[/C][C]-0.141435570868182[/C][/ROW]
[ROW][C]20[/C][C]69.66[/C][C]69.7785785231812[/C][C]-0.118578523181242[/C][/ROW]
[ROW][C]21[/C][C]69.77[/C][C]69.7570920280357[/C][C]0.0129079719643386[/C][/ROW]
[ROW][C]22[/C][C]70.32[/C][C]69.8586898438495[/C][C]0.461310156150532[/C][/ROW]
[ROW][C]23[/C][C]70.34[/C][C]70.4492007717778[/C][C]-0.109200771777765[/C][/ROW]
[ROW][C]24[/C][C]70.38[/C][C]70.4968405591532[/C][C]-0.116840559153189[/C][/ROW]
[ROW][C]25[/C][C]70.38[/C][C]70.5180871412208[/C][C]-0.13808714122078[/C][/ROW]
[ROW][C]26[/C][C]70.29[/C][C]70.4969030697658[/C][C]-0.206903069765801[/C][/ROW]
[ROW][C]27[/C][C]70.42[/C][C]70.378126760969[/C][C]0.0418732390310339[/C][/ROW]
[ROW][C]28[/C][C]70.29[/C][C]70.4951220212716[/C][C]-0.205122021271578[/C][/ROW]
[ROW][C]29[/C][C]70.59[/C][C]70.3509260451937[/C][C]0.239073954806301[/C][/ROW]
[ROW][C]30[/C][C]70.64[/C][C]70.6549393104366[/C][C]-0.0149393104365885[/C][/ROW]
[ROW][C]31[/C][C]70.64[/C][C]70.7228281174528[/C][C]-0.0828281174528485[/C][/ROW]
[ROW][C]32[/C][C]70.68[/C][C]70.7145424753683[/C][C]-0.0345424753682977[/C][/ROW]
[ROW][C]33[/C][C]70.78[/C][C]70.7449459853448[/C][C]0.0350540146551879[/C][/ROW]
[ROW][C]34[/C][C]70.9[/C][C]70.8451763245299[/C][C]0.0548236754701463[/C][/ROW]
[ROW][C]35[/C][C]71.04[/C][C]70.9726781717711[/C][C]0.0673218282289412[/C][/ROW]
[ROW][C]36[/C][C]71.15[/C][C]71.1228345217682[/C][C]0.0271654782318365[/C][/ROW]
[ROW][C]37[/C][C]71.15[/C][C]71.2405565520475[/C][C]-0.090556552047488[/C][/ROW]
[ROW][C]38[/C][C]71.15[/C][C]71.2349852159091[/C][C]-0.0849852159091427[/C][/ROW]
[ROW][C]39[/C][C]71.07[/C][C]71.2204525392305[/C][C]-0.150452539230457[/C][/ROW]
[ROW][C]40[/C][C]71.17[/C][C]71.1207642447711[/C][C]0.0492357552289349[/C][/ROW]
[ROW][C]41[/C][C]71.24[/C][C]71.2129153387494[/C][C]0.0270846612506261[/C][/ROW]
[ROW][C]42[/C][C]71.23[/C][C]71.2891804426957[/C][C]-0.0591804426956912[/C][/ROW]
[ROW][C]43[/C][C]71.23[/C][C]71.2762875999427[/C][C]-0.0462875999427297[/C][/ROW]
[ROW][C]44[/C][C]71.23[/C][C]71.2675819345722[/C][C]-0.0375819345722164[/C][/ROW]
[ROW][C]45[/C][C]71.24[/C][C]71.260654900892[/C][C]-0.0206549008920263[/C][/ROW]
[ROW][C]46[/C][C]71.28[/C][C]71.2658743349803[/C][C]0.0141256650196908[/C][/ROW]
[ROW][C]47[/C][C]71.52[/C][C]71.305427161166[/C][C]0.214572838833959[/C][/ROW]
[ROW][C]48[/C][C]71.52[/C][C]71.5649214666446[/C][C]-0.0449214666446238[/C][/ROW]
[ROW][C]49[/C][C]71.52[/C][C]71.57828026455[/C][C]-0.0582802645500351[/C][/ROW]
[ROW][C]50[/C][C]71.6[/C][C]71.5696915229386[/C][C]0.0303084770613822[/C][/ROW]
[ROW][C]51[/C][C]71.61[/C][C]71.6476126442268[/C][C]-0.0376126442267974[/C][/ROW]
[ROW][C]52[/C][C]71.78[/C][C]71.6568239020429[/C][C]0.123176097957057[/C][/ROW]
[ROW][C]53[/C][C]71.66[/C][C]71.8343490382655[/C][C]-0.17434903826549[/C][/ROW]
[ROW][C]54[/C][C]71.86[/C][C]71.7093046982531[/C][C]0.150695301746936[/C][/ROW]
[ROW][C]55[/C][C]71.86[/C][C]71.908222222076[/C][C]-0.0482222220760207[/C][/ROW]
[ROW][C]56[/C][C]71.82[/C][C]71.9161773229172[/C][C]-0.0961773229172564[/C][/ROW]
[ROW][C]57[/C][C]71.8[/C][C]71.8640809555579[/C][C]-0.0640809555578841[/C][/ROW]
[ROW][C]58[/C][C]72.22[/C][C]71.8308865029868[/C][C]0.389113497013199[/C][/ROW]
[ROW][C]59[/C][C]72.51[/C][C]72.2790468735547[/C][C]0.230953126445286[/C][/ROW]
[ROW][C]60[/C][C]72.56[/C][C]72.6200067144828[/C][C]-0.0600067144828245[/C][/ROW]
[ROW][C]61[/C][C]72.56[/C][C]72.6833878634857[/C][C]-0.123387863485704[/C][/ROW]
[ROW][C]62[/C][C]72.78[/C][C]72.6680181915789[/C][C]0.111981808421092[/C][/ROW]
[ROW][C]63[/C][C]72.88[/C][C]72.8877085533073[/C][C]-0.00770855330733866[/C][/ROW]
[ROW][C]64[/C][C]73.05[/C][C]72.9960267945969[/C][C]0.0539732054030679[/C][/ROW]
[ROW][C]65[/C][C]73.02[/C][C]73.1700274704888[/C][C]-0.15002747048878[/C][/ROW]
[ROW][C]66[/C][C]73.08[/C][C]73.1315162319145[/C][C]-0.0515162319145475[/C][/ROW]
[ROW][C]67[/C][C]73.08[/C][C]73.175079675075[/C][C]-0.0950796750750271[/C][/ROW]
[ROW][C]68[/C][C]73.24[/C][C]73.1628131477222[/C][C]0.0771868522778192[/C][/ROW]
[ROW][C]69[/C][C]73.82[/C][C]73.3217955188493[/C][C]0.498204481150722[/C][/ROW]
[ROW][C]70[/C][C]74[/C][C]73.9506170498281[/C][C]0.049382950171875[/C][/ROW]
[ROW][C]71[/C][C]74.37[/C][C]74.1747853680212[/C][C]0.195214631978843[/C][/ROW]
[ROW][C]72[/C][C]74.38[/C][C]74.5654497924105[/C][C]-0.185449792410466[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210648&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210648&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
368.0268.34-0.320000000000007
468.1168.3326163860404-0.222616386040357
568.4168.37791097191070.0320890280893309
668.468.6628091801202-0.262809180120243
768.468.6328922677518-0.232892267751794
868.5568.5918926537204-0.0418926537203674
968.5468.7196361228882-0.179636122888212
1068.9968.69090532841330.299094671586687
1168.9769.152098069081-0.18209806908105
1268.9869.1404944939268-0.160494493926777
1368.9869.1221610651545-0.142161065154511
1468.9469.0971285158305-0.15712851583055
1569.2169.03228498668540.177715013314611
1669.2169.3048953066633-0.094895306663318
1769.6769.31102265963730.358977340362657
1869.6669.7941336931627-0.13413369316271
1969.6669.8014355708682-0.141435570868182
2069.6669.7785785231812-0.118578523181242
2169.7769.75709202803570.0129079719643386
2270.3269.85868984384950.461310156150532
2370.3470.4492007717778-0.109200771777765
2470.3870.4968405591532-0.116840559153189
2570.3870.5180871412208-0.13808714122078
2670.2970.4969030697658-0.206903069765801
2770.4270.3781267609690.0418732390310339
2870.2970.4951220212716-0.205122021271578
2970.5970.35092604519370.239073954806301
3070.6470.6549393104366-0.0149393104365885
3170.6470.7228281174528-0.0828281174528485
3270.6870.7145424753683-0.0345424753682977
3370.7870.74494598534480.0350540146551879
3470.970.84517632452990.0548236754701463
3571.0470.97267817177110.0673218282289412
3671.1571.12283452176820.0271654782318365
3771.1571.2405565520475-0.090556552047488
3871.1571.2349852159091-0.0849852159091427
3971.0771.2204525392305-0.150452539230457
4071.1771.12076424477110.0492357552289349
4171.2471.21291533874940.0270846612506261
4271.2371.2891804426957-0.0591804426956912
4371.2371.2762875999427-0.0462875999427297
4471.2371.2675819345722-0.0375819345722164
4571.2471.260654900892-0.0206549008920263
4671.2871.26587433498030.0141256650196908
4771.5271.3054271611660.214572838833959
4871.5271.5649214666446-0.0449214666446238
4971.5271.57828026455-0.0582802645500351
5071.671.56969152293860.0303084770613822
5171.6171.6476126442268-0.0376126442267974
5271.7871.65682390204290.123176097957057
5371.6671.8343490382655-0.17434903826549
5471.8671.70930469825310.150695301746936
5571.8671.908222222076-0.0482222220760207
5671.8271.9161773229172-0.0961773229172564
5771.871.8640809555579-0.0640809555578841
5872.2271.83088650298680.389113497013199
5972.5172.27904687355470.230953126445286
6072.5672.6200067144828-0.0600067144828245
6172.5672.6833878634857-0.123387863485704
6272.7872.66801819157890.111981808421092
6372.8872.8877085533073-0.00770855330733866
6473.0572.99602679459690.0539732054030679
6573.0273.1700274704888-0.15002747048878
6673.0873.1315162319145-0.0515162319145475
6773.0873.175079675075-0.0950796750750271
6873.2473.16281314772220.0771868522778192
6973.8273.32179551884930.498204481150722
707473.95061704982810.049382950171875
7174.3774.17478536802120.195214631978843
7274.3874.5654497924105-0.185449792410466







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7374.575231047359974.248278909326874.902183185393
7474.75559407171574.273024405167875.2381637382622
7574.9359570960774.303300646126175.5686135460139
7675.116320120425174.33215612419775.9004841166531
7775.296683144780174.357149312654376.2362169769059
7875.477046169135174.377246414404876.5768459238655
7975.657409193490274.39198690032876.9228314866524
8075.837772217845274.401179223656377.2743652120342
8176.018135242200374.40476906431977.6315014200816
8276.198498266555374.402775590407777.994220942703
8376.378861290910474.395258175689378.3624644061315
8476.559224315265474.382298050587178.7361505799438

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 74.5752310473599 & 74.2482789093268 & 74.902183185393 \tabularnewline
74 & 74.755594071715 & 74.2730244051678 & 75.2381637382622 \tabularnewline
75 & 74.93595709607 & 74.3033006461261 & 75.5686135460139 \tabularnewline
76 & 75.1163201204251 & 74.332156124197 & 75.9004841166531 \tabularnewline
77 & 75.2966831447801 & 74.3571493126543 & 76.2362169769059 \tabularnewline
78 & 75.4770461691351 & 74.3772464144048 & 76.5768459238655 \tabularnewline
79 & 75.6574091934902 & 74.391986900328 & 76.9228314866524 \tabularnewline
80 & 75.8377722178452 & 74.4011792236563 & 77.2743652120342 \tabularnewline
81 & 76.0181352422003 & 74.404769064319 & 77.6315014200816 \tabularnewline
82 & 76.1984982665553 & 74.4027755904077 & 77.994220942703 \tabularnewline
83 & 76.3788612909104 & 74.3952581756893 & 78.3624644061315 \tabularnewline
84 & 76.5592243152654 & 74.3822980505871 & 78.7361505799438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210648&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]73[/C][C]74.5752310473599[/C][C]74.2482789093268[/C][C]74.902183185393[/C][/ROW]
[ROW][C]74[/C][C]74.755594071715[/C][C]74.2730244051678[/C][C]75.2381637382622[/C][/ROW]
[ROW][C]75[/C][C]74.93595709607[/C][C]74.3033006461261[/C][C]75.5686135460139[/C][/ROW]
[ROW][C]76[/C][C]75.1163201204251[/C][C]74.332156124197[/C][C]75.9004841166531[/C][/ROW]
[ROW][C]77[/C][C]75.2966831447801[/C][C]74.3571493126543[/C][C]76.2362169769059[/C][/ROW]
[ROW][C]78[/C][C]75.4770461691351[/C][C]74.3772464144048[/C][C]76.5768459238655[/C][/ROW]
[ROW][C]79[/C][C]75.6574091934902[/C][C]74.391986900328[/C][C]76.9228314866524[/C][/ROW]
[ROW][C]80[/C][C]75.8377722178452[/C][C]74.4011792236563[/C][C]77.2743652120342[/C][/ROW]
[ROW][C]81[/C][C]76.0181352422003[/C][C]74.404769064319[/C][C]77.6315014200816[/C][/ROW]
[ROW][C]82[/C][C]76.1984982665553[/C][C]74.4027755904077[/C][C]77.994220942703[/C][/ROW]
[ROW][C]83[/C][C]76.3788612909104[/C][C]74.3952581756893[/C][C]78.3624644061315[/C][/ROW]
[ROW][C]84[/C][C]76.5592243152654[/C][C]74.3822980505871[/C][C]78.7361505799438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210648&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210648&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
7374.575231047359974.248278909326874.902183185393
7474.75559407171574.273024405167875.2381637382622
7574.9359570960774.303300646126175.5686135460139
7675.116320120425174.33215612419775.9004841166531
7775.296683144780174.357149312654376.2362169769059
7875.477046169135174.377246414404876.5768459238655
7975.657409193490274.39198690032876.9228314866524
8075.837772217845274.401179223656377.2743652120342
8176.018135242200374.40476906431977.6315014200816
8276.198498266555374.402775590407777.994220942703
8376.378861290910474.395258175689378.3624644061315
8476.559224315265474.382298050587178.7361505799438



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')