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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 19 Aug 2009 07:05:28 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Aug/19/t1250687174o5mb7o0zbun0udv.htm/, Retrieved Tue, 07 May 2024 05:48:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42935, Retrieved Tue, 07 May 2024 05:48:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Opgave 10 oefenin...] [2009-01-24 20:28:07] [74be16979710d4c4e7c6647856088456]
-    D    [Exponential Smoothing] [dennis volkaerts ...] [2009-08-19 13:05:28] [9e20205489828c19845a9d736cd20362] [Current]
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Dataseries X:
17.23
17.36
17.39
17.29
17.28
17.4
17.51
17.54
17.64
17.65
17.5
17.37
17.56
17.49
17.61
17.79
17.83
17.56
17.95
18.09
18.38
18.38
18.44
18.84
19.01
19.06
19.06
18.97
18.98
19.41
19.55
19.64
19.71
19.48
19.48
19.41
19.25
19.14
19.21
19.3
19.53
19.14
19.16
19.24
19.38
19.27
19.27
19.07
19.15
19.24
19.36
19.57
19.59
19.36
19.46
19.65
19.46
19.51
19.64
19.64
19.69
19.28
19.67
19.65
19.6
19.53
19.64
19.67
19.81
19.73
19.87
19.97
20.12
19.94
20.31
20.13
20.22
20.38
20.44
20.34
20.14
19.97
19.82
19.98
20.12




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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42935&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42935&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42935&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' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.930756132630198
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.930756132630198 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42935&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]0.930756132630198[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42935&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42935&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
alpha0.930756132630198
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
317.3917.360.0300000000000011
417.2917.3879226839789-0.0979226839789078
517.2817.2967805453419-0.0167805453419270
617.417.28116194985600.118838050143950
717.5117.39177119381730.118228806182657
817.5417.50181338022540.0381866197745993
917.6417.53735581076500.102644189234976
1017.6517.63289251937430.0171074806256648
1117.517.6488154118805-0.148815411880523
1217.3717.5103045546428-0.140304554642835
1317.5617.37971522997310.180284770026930
1417.4917.5475163852955-0.057516385295461
1517.6117.4939826569550.116017343045012
1617.7917.60196651048560.188033489514407
1717.8317.77697983399100.0530201660090164
1817.5617.8263286786569-0.266328678656947
1917.9517.57844162770170.371558372298303
2018.0917.92427186134840.165728138651563
2118.3818.07852434274780.301475657252233
2218.3818.3591246595740.0208753404259987
2318.4418.37855451069620.061445489303761
2418.8418.43574527668820.404254723311819
2519.0118.81200783955540.197992160444620
2619.0618.99629025710190.0637097428980837
2719.0619.05558849101260.00441150898739906
2818.9719.0596945300568-0.089694530056775
2918.9818.97621079614300.00378920385695380
3019.4118.97973762087070.430262379129307
3119.5519.38020696888540.169793031114647
3219.6419.53824287387320.101757126126820
3319.7119.63295394305450.0770460569454592
3419.4819.7046650330515-0.224665033051505
3519.4819.4955566757512-0.0155566757512489
3619.4119.4810772043924-0.0710772043924344
3719.2519.4149216605140-0.164921660513965
3819.1419.2614198135870-0.121419813587035
3919.2119.14840757746810.0615924225319127
4019.319.20573510246320.0942648975367852
4119.5319.29347273393730.236527266062666
4219.1419.5136219373594-0.373621937359417
4319.1619.1658710278770-0.00587102787696381
4419.2419.16040653267560.0795934673243615
4519.3819.23448864050510.145511359494911
4619.2719.3699242307223-0.0999242307223334
4719.2719.2769191401792-0.00691914017916773
4819.0719.2704791080249-0.200479108024879
4919.1519.08388194876650.0661180512335058
5019.2419.14542173042960.0945782695703627
5119.3619.23345103484580.126548965154196
5219.5719.35123726024110.218762739758922
5319.5919.55485202186270.0351479781373207
5419.3619.5875662180635-0.227566218063544
5519.4619.37575756502140.0842424349785631
5619.6519.45416672800540.195833271994562
5719.4619.6364397468874-0.176439746887411
5819.5119.47221737043220.0377826295677686
5919.6419.50738378460930.132616215390673
6019.6419.63081714037040.00918285962959686
6119.6919.63936414328570.0506358567142691
6219.2819.6864937774535-0.406493777453520
6319.6719.30814720121260.361852798787361
6419.6519.64494391279340.0050560872066221
6519.619.6496498969681-0.0496498969680523
6619.5319.6034379508806-0.0734379508805816
6719.6419.53508512773070.104914872269315
6819.6719.63273528849950.0372647115005371
6919.8119.66741964725930.142580352740715
7019.7319.8001271849653-0.0701271849652798
7119.8719.73485587749480.135144122505245
7219.9719.86064209830540.109357901694558
7320.1219.96242763595920.157572364040782
7419.9420.1090890801232-0.169089080123214
7520.3119.95170838183770.358291618162262
7620.1320.2851905027123-0.155190502712259
7720.2220.14074599058690.0792540094131375
7820.3820.21451214588370.165487854116328
7920.4420.36854098097830.071459019021745
8020.3420.4350519011645-0.095051901164485
8120.1420.3465817612375-0.20658176123748
8219.9720.1543045200761-0.18430452007615
8319.8219.9827619577438-0.162761957743808
8419.9819.83127026741490.148729732585139
8520.1219.96970137812290.150298621877074

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 17.39 & 17.36 & 0.0300000000000011 \tabularnewline
4 & 17.29 & 17.3879226839789 & -0.0979226839789078 \tabularnewline
5 & 17.28 & 17.2967805453419 & -0.0167805453419270 \tabularnewline
6 & 17.4 & 17.2811619498560 & 0.118838050143950 \tabularnewline
7 & 17.51 & 17.3917711938173 & 0.118228806182657 \tabularnewline
8 & 17.54 & 17.5018133802254 & 0.0381866197745993 \tabularnewline
9 & 17.64 & 17.5373558107650 & 0.102644189234976 \tabularnewline
10 & 17.65 & 17.6328925193743 & 0.0171074806256648 \tabularnewline
11 & 17.5 & 17.6488154118805 & -0.148815411880523 \tabularnewline
12 & 17.37 & 17.5103045546428 & -0.140304554642835 \tabularnewline
13 & 17.56 & 17.3797152299731 & 0.180284770026930 \tabularnewline
14 & 17.49 & 17.5475163852955 & -0.057516385295461 \tabularnewline
15 & 17.61 & 17.493982656955 & 0.116017343045012 \tabularnewline
16 & 17.79 & 17.6019665104856 & 0.188033489514407 \tabularnewline
17 & 17.83 & 17.7769798339910 & 0.0530201660090164 \tabularnewline
18 & 17.56 & 17.8263286786569 & -0.266328678656947 \tabularnewline
19 & 17.95 & 17.5784416277017 & 0.371558372298303 \tabularnewline
20 & 18.09 & 17.9242718613484 & 0.165728138651563 \tabularnewline
21 & 18.38 & 18.0785243427478 & 0.301475657252233 \tabularnewline
22 & 18.38 & 18.359124659574 & 0.0208753404259987 \tabularnewline
23 & 18.44 & 18.3785545106962 & 0.061445489303761 \tabularnewline
24 & 18.84 & 18.4357452766882 & 0.404254723311819 \tabularnewline
25 & 19.01 & 18.8120078395554 & 0.197992160444620 \tabularnewline
26 & 19.06 & 18.9962902571019 & 0.0637097428980837 \tabularnewline
27 & 19.06 & 19.0555884910126 & 0.00441150898739906 \tabularnewline
28 & 18.97 & 19.0596945300568 & -0.089694530056775 \tabularnewline
29 & 18.98 & 18.9762107961430 & 0.00378920385695380 \tabularnewline
30 & 19.41 & 18.9797376208707 & 0.430262379129307 \tabularnewline
31 & 19.55 & 19.3802069688854 & 0.169793031114647 \tabularnewline
32 & 19.64 & 19.5382428738732 & 0.101757126126820 \tabularnewline
33 & 19.71 & 19.6329539430545 & 0.0770460569454592 \tabularnewline
34 & 19.48 & 19.7046650330515 & -0.224665033051505 \tabularnewline
35 & 19.48 & 19.4955566757512 & -0.0155566757512489 \tabularnewline
36 & 19.41 & 19.4810772043924 & -0.0710772043924344 \tabularnewline
37 & 19.25 & 19.4149216605140 & -0.164921660513965 \tabularnewline
38 & 19.14 & 19.2614198135870 & -0.121419813587035 \tabularnewline
39 & 19.21 & 19.1484075774681 & 0.0615924225319127 \tabularnewline
40 & 19.3 & 19.2057351024632 & 0.0942648975367852 \tabularnewline
41 & 19.53 & 19.2934727339373 & 0.236527266062666 \tabularnewline
42 & 19.14 & 19.5136219373594 & -0.373621937359417 \tabularnewline
43 & 19.16 & 19.1658710278770 & -0.00587102787696381 \tabularnewline
44 & 19.24 & 19.1604065326756 & 0.0795934673243615 \tabularnewline
45 & 19.38 & 19.2344886405051 & 0.145511359494911 \tabularnewline
46 & 19.27 & 19.3699242307223 & -0.0999242307223334 \tabularnewline
47 & 19.27 & 19.2769191401792 & -0.00691914017916773 \tabularnewline
48 & 19.07 & 19.2704791080249 & -0.200479108024879 \tabularnewline
49 & 19.15 & 19.0838819487665 & 0.0661180512335058 \tabularnewline
50 & 19.24 & 19.1454217304296 & 0.0945782695703627 \tabularnewline
51 & 19.36 & 19.2334510348458 & 0.126548965154196 \tabularnewline
52 & 19.57 & 19.3512372602411 & 0.218762739758922 \tabularnewline
53 & 19.59 & 19.5548520218627 & 0.0351479781373207 \tabularnewline
54 & 19.36 & 19.5875662180635 & -0.227566218063544 \tabularnewline
55 & 19.46 & 19.3757575650214 & 0.0842424349785631 \tabularnewline
56 & 19.65 & 19.4541667280054 & 0.195833271994562 \tabularnewline
57 & 19.46 & 19.6364397468874 & -0.176439746887411 \tabularnewline
58 & 19.51 & 19.4722173704322 & 0.0377826295677686 \tabularnewline
59 & 19.64 & 19.5073837846093 & 0.132616215390673 \tabularnewline
60 & 19.64 & 19.6308171403704 & 0.00918285962959686 \tabularnewline
61 & 19.69 & 19.6393641432857 & 0.0506358567142691 \tabularnewline
62 & 19.28 & 19.6864937774535 & -0.406493777453520 \tabularnewline
63 & 19.67 & 19.3081472012126 & 0.361852798787361 \tabularnewline
64 & 19.65 & 19.6449439127934 & 0.0050560872066221 \tabularnewline
65 & 19.6 & 19.6496498969681 & -0.0496498969680523 \tabularnewline
66 & 19.53 & 19.6034379508806 & -0.0734379508805816 \tabularnewline
67 & 19.64 & 19.5350851277307 & 0.104914872269315 \tabularnewline
68 & 19.67 & 19.6327352884995 & 0.0372647115005371 \tabularnewline
69 & 19.81 & 19.6674196472593 & 0.142580352740715 \tabularnewline
70 & 19.73 & 19.8001271849653 & -0.0701271849652798 \tabularnewline
71 & 19.87 & 19.7348558774948 & 0.135144122505245 \tabularnewline
72 & 19.97 & 19.8606420983054 & 0.109357901694558 \tabularnewline
73 & 20.12 & 19.9624276359592 & 0.157572364040782 \tabularnewline
74 & 19.94 & 20.1090890801232 & -0.169089080123214 \tabularnewline
75 & 20.31 & 19.9517083818377 & 0.358291618162262 \tabularnewline
76 & 20.13 & 20.2851905027123 & -0.155190502712259 \tabularnewline
77 & 20.22 & 20.1407459905869 & 0.0792540094131375 \tabularnewline
78 & 20.38 & 20.2145121458837 & 0.165487854116328 \tabularnewline
79 & 20.44 & 20.3685409809783 & 0.071459019021745 \tabularnewline
80 & 20.34 & 20.4350519011645 & -0.095051901164485 \tabularnewline
81 & 20.14 & 20.3465817612375 & -0.20658176123748 \tabularnewline
82 & 19.97 & 20.1543045200761 & -0.18430452007615 \tabularnewline
83 & 19.82 & 19.9827619577438 & -0.162761957743808 \tabularnewline
84 & 19.98 & 19.8312702674149 & 0.148729732585139 \tabularnewline
85 & 20.12 & 19.9697013781229 & 0.150298621877074 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42935&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]17.39[/C][C]17.36[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]4[/C][C]17.29[/C][C]17.3879226839789[/C][C]-0.0979226839789078[/C][/ROW]
[ROW][C]5[/C][C]17.28[/C][C]17.2967805453419[/C][C]-0.0167805453419270[/C][/ROW]
[ROW][C]6[/C][C]17.4[/C][C]17.2811619498560[/C][C]0.118838050143950[/C][/ROW]
[ROW][C]7[/C][C]17.51[/C][C]17.3917711938173[/C][C]0.118228806182657[/C][/ROW]
[ROW][C]8[/C][C]17.54[/C][C]17.5018133802254[/C][C]0.0381866197745993[/C][/ROW]
[ROW][C]9[/C][C]17.64[/C][C]17.5373558107650[/C][C]0.102644189234976[/C][/ROW]
[ROW][C]10[/C][C]17.65[/C][C]17.6328925193743[/C][C]0.0171074806256648[/C][/ROW]
[ROW][C]11[/C][C]17.5[/C][C]17.6488154118805[/C][C]-0.148815411880523[/C][/ROW]
[ROW][C]12[/C][C]17.37[/C][C]17.5103045546428[/C][C]-0.140304554642835[/C][/ROW]
[ROW][C]13[/C][C]17.56[/C][C]17.3797152299731[/C][C]0.180284770026930[/C][/ROW]
[ROW][C]14[/C][C]17.49[/C][C]17.5475163852955[/C][C]-0.057516385295461[/C][/ROW]
[ROW][C]15[/C][C]17.61[/C][C]17.493982656955[/C][C]0.116017343045012[/C][/ROW]
[ROW][C]16[/C][C]17.79[/C][C]17.6019665104856[/C][C]0.188033489514407[/C][/ROW]
[ROW][C]17[/C][C]17.83[/C][C]17.7769798339910[/C][C]0.0530201660090164[/C][/ROW]
[ROW][C]18[/C][C]17.56[/C][C]17.8263286786569[/C][C]-0.266328678656947[/C][/ROW]
[ROW][C]19[/C][C]17.95[/C][C]17.5784416277017[/C][C]0.371558372298303[/C][/ROW]
[ROW][C]20[/C][C]18.09[/C][C]17.9242718613484[/C][C]0.165728138651563[/C][/ROW]
[ROW][C]21[/C][C]18.38[/C][C]18.0785243427478[/C][C]0.301475657252233[/C][/ROW]
[ROW][C]22[/C][C]18.38[/C][C]18.359124659574[/C][C]0.0208753404259987[/C][/ROW]
[ROW][C]23[/C][C]18.44[/C][C]18.3785545106962[/C][C]0.061445489303761[/C][/ROW]
[ROW][C]24[/C][C]18.84[/C][C]18.4357452766882[/C][C]0.404254723311819[/C][/ROW]
[ROW][C]25[/C][C]19.01[/C][C]18.8120078395554[/C][C]0.197992160444620[/C][/ROW]
[ROW][C]26[/C][C]19.06[/C][C]18.9962902571019[/C][C]0.0637097428980837[/C][/ROW]
[ROW][C]27[/C][C]19.06[/C][C]19.0555884910126[/C][C]0.00441150898739906[/C][/ROW]
[ROW][C]28[/C][C]18.97[/C][C]19.0596945300568[/C][C]-0.089694530056775[/C][/ROW]
[ROW][C]29[/C][C]18.98[/C][C]18.9762107961430[/C][C]0.00378920385695380[/C][/ROW]
[ROW][C]30[/C][C]19.41[/C][C]18.9797376208707[/C][C]0.430262379129307[/C][/ROW]
[ROW][C]31[/C][C]19.55[/C][C]19.3802069688854[/C][C]0.169793031114647[/C][/ROW]
[ROW][C]32[/C][C]19.64[/C][C]19.5382428738732[/C][C]0.101757126126820[/C][/ROW]
[ROW][C]33[/C][C]19.71[/C][C]19.6329539430545[/C][C]0.0770460569454592[/C][/ROW]
[ROW][C]34[/C][C]19.48[/C][C]19.7046650330515[/C][C]-0.224665033051505[/C][/ROW]
[ROW][C]35[/C][C]19.48[/C][C]19.4955566757512[/C][C]-0.0155566757512489[/C][/ROW]
[ROW][C]36[/C][C]19.41[/C][C]19.4810772043924[/C][C]-0.0710772043924344[/C][/ROW]
[ROW][C]37[/C][C]19.25[/C][C]19.4149216605140[/C][C]-0.164921660513965[/C][/ROW]
[ROW][C]38[/C][C]19.14[/C][C]19.2614198135870[/C][C]-0.121419813587035[/C][/ROW]
[ROW][C]39[/C][C]19.21[/C][C]19.1484075774681[/C][C]0.0615924225319127[/C][/ROW]
[ROW][C]40[/C][C]19.3[/C][C]19.2057351024632[/C][C]0.0942648975367852[/C][/ROW]
[ROW][C]41[/C][C]19.53[/C][C]19.2934727339373[/C][C]0.236527266062666[/C][/ROW]
[ROW][C]42[/C][C]19.14[/C][C]19.5136219373594[/C][C]-0.373621937359417[/C][/ROW]
[ROW][C]43[/C][C]19.16[/C][C]19.1658710278770[/C][C]-0.00587102787696381[/C][/ROW]
[ROW][C]44[/C][C]19.24[/C][C]19.1604065326756[/C][C]0.0795934673243615[/C][/ROW]
[ROW][C]45[/C][C]19.38[/C][C]19.2344886405051[/C][C]0.145511359494911[/C][/ROW]
[ROW][C]46[/C][C]19.27[/C][C]19.3699242307223[/C][C]-0.0999242307223334[/C][/ROW]
[ROW][C]47[/C][C]19.27[/C][C]19.2769191401792[/C][C]-0.00691914017916773[/C][/ROW]
[ROW][C]48[/C][C]19.07[/C][C]19.2704791080249[/C][C]-0.200479108024879[/C][/ROW]
[ROW][C]49[/C][C]19.15[/C][C]19.0838819487665[/C][C]0.0661180512335058[/C][/ROW]
[ROW][C]50[/C][C]19.24[/C][C]19.1454217304296[/C][C]0.0945782695703627[/C][/ROW]
[ROW][C]51[/C][C]19.36[/C][C]19.2334510348458[/C][C]0.126548965154196[/C][/ROW]
[ROW][C]52[/C][C]19.57[/C][C]19.3512372602411[/C][C]0.218762739758922[/C][/ROW]
[ROW][C]53[/C][C]19.59[/C][C]19.5548520218627[/C][C]0.0351479781373207[/C][/ROW]
[ROW][C]54[/C][C]19.36[/C][C]19.5875662180635[/C][C]-0.227566218063544[/C][/ROW]
[ROW][C]55[/C][C]19.46[/C][C]19.3757575650214[/C][C]0.0842424349785631[/C][/ROW]
[ROW][C]56[/C][C]19.65[/C][C]19.4541667280054[/C][C]0.195833271994562[/C][/ROW]
[ROW][C]57[/C][C]19.46[/C][C]19.6364397468874[/C][C]-0.176439746887411[/C][/ROW]
[ROW][C]58[/C][C]19.51[/C][C]19.4722173704322[/C][C]0.0377826295677686[/C][/ROW]
[ROW][C]59[/C][C]19.64[/C][C]19.5073837846093[/C][C]0.132616215390673[/C][/ROW]
[ROW][C]60[/C][C]19.64[/C][C]19.6308171403704[/C][C]0.00918285962959686[/C][/ROW]
[ROW][C]61[/C][C]19.69[/C][C]19.6393641432857[/C][C]0.0506358567142691[/C][/ROW]
[ROW][C]62[/C][C]19.28[/C][C]19.6864937774535[/C][C]-0.406493777453520[/C][/ROW]
[ROW][C]63[/C][C]19.67[/C][C]19.3081472012126[/C][C]0.361852798787361[/C][/ROW]
[ROW][C]64[/C][C]19.65[/C][C]19.6449439127934[/C][C]0.0050560872066221[/C][/ROW]
[ROW][C]65[/C][C]19.6[/C][C]19.6496498969681[/C][C]-0.0496498969680523[/C][/ROW]
[ROW][C]66[/C][C]19.53[/C][C]19.6034379508806[/C][C]-0.0734379508805816[/C][/ROW]
[ROW][C]67[/C][C]19.64[/C][C]19.5350851277307[/C][C]0.104914872269315[/C][/ROW]
[ROW][C]68[/C][C]19.67[/C][C]19.6327352884995[/C][C]0.0372647115005371[/C][/ROW]
[ROW][C]69[/C][C]19.81[/C][C]19.6674196472593[/C][C]0.142580352740715[/C][/ROW]
[ROW][C]70[/C][C]19.73[/C][C]19.8001271849653[/C][C]-0.0701271849652798[/C][/ROW]
[ROW][C]71[/C][C]19.87[/C][C]19.7348558774948[/C][C]0.135144122505245[/C][/ROW]
[ROW][C]72[/C][C]19.97[/C][C]19.8606420983054[/C][C]0.109357901694558[/C][/ROW]
[ROW][C]73[/C][C]20.12[/C][C]19.9624276359592[/C][C]0.157572364040782[/C][/ROW]
[ROW][C]74[/C][C]19.94[/C][C]20.1090890801232[/C][C]-0.169089080123214[/C][/ROW]
[ROW][C]75[/C][C]20.31[/C][C]19.9517083818377[/C][C]0.358291618162262[/C][/ROW]
[ROW][C]76[/C][C]20.13[/C][C]20.2851905027123[/C][C]-0.155190502712259[/C][/ROW]
[ROW][C]77[/C][C]20.22[/C][C]20.1407459905869[/C][C]0.0792540094131375[/C][/ROW]
[ROW][C]78[/C][C]20.38[/C][C]20.2145121458837[/C][C]0.165487854116328[/C][/ROW]
[ROW][C]79[/C][C]20.44[/C][C]20.3685409809783[/C][C]0.071459019021745[/C][/ROW]
[ROW][C]80[/C][C]20.34[/C][C]20.4350519011645[/C][C]-0.095051901164485[/C][/ROW]
[ROW][C]81[/C][C]20.14[/C][C]20.3465817612375[/C][C]-0.20658176123748[/C][/ROW]
[ROW][C]82[/C][C]19.97[/C][C]20.1543045200761[/C][C]-0.18430452007615[/C][/ROW]
[ROW][C]83[/C][C]19.82[/C][C]19.9827619577438[/C][C]-0.162761957743808[/C][/ROW]
[ROW][C]84[/C][C]19.98[/C][C]19.8312702674149[/C][C]0.148729732585139[/C][/ROW]
[ROW][C]85[/C][C]20.12[/C][C]19.9697013781229[/C][C]0.150298621877074[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42935&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42935&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
317.3917.360.0300000000000011
417.2917.3879226839789-0.0979226839789078
517.2817.2967805453419-0.0167805453419270
617.417.28116194985600.118838050143950
717.5117.39177119381730.118228806182657
817.5417.50181338022540.0381866197745993
917.6417.53735581076500.102644189234976
1017.6517.63289251937430.0171074806256648
1117.517.6488154118805-0.148815411880523
1217.3717.5103045546428-0.140304554642835
1317.5617.37971522997310.180284770026930
1417.4917.5475163852955-0.057516385295461
1517.6117.4939826569550.116017343045012
1617.7917.60196651048560.188033489514407
1717.8317.77697983399100.0530201660090164
1817.5617.8263286786569-0.266328678656947
1917.9517.57844162770170.371558372298303
2018.0917.92427186134840.165728138651563
2118.3818.07852434274780.301475657252233
2218.3818.3591246595740.0208753404259987
2318.4418.37855451069620.061445489303761
2418.8418.43574527668820.404254723311819
2519.0118.81200783955540.197992160444620
2619.0618.99629025710190.0637097428980837
2719.0619.05558849101260.00441150898739906
2818.9719.0596945300568-0.089694530056775
2918.9818.97621079614300.00378920385695380
3019.4118.97973762087070.430262379129307
3119.5519.38020696888540.169793031114647
3219.6419.53824287387320.101757126126820
3319.7119.63295394305450.0770460569454592
3419.4819.7046650330515-0.224665033051505
3519.4819.4955566757512-0.0155566757512489
3619.4119.4810772043924-0.0710772043924344
3719.2519.4149216605140-0.164921660513965
3819.1419.2614198135870-0.121419813587035
3919.2119.14840757746810.0615924225319127
4019.319.20573510246320.0942648975367852
4119.5319.29347273393730.236527266062666
4219.1419.5136219373594-0.373621937359417
4319.1619.1658710278770-0.00587102787696381
4419.2419.16040653267560.0795934673243615
4519.3819.23448864050510.145511359494911
4619.2719.3699242307223-0.0999242307223334
4719.2719.2769191401792-0.00691914017916773
4819.0719.2704791080249-0.200479108024879
4919.1519.08388194876650.0661180512335058
5019.2419.14542173042960.0945782695703627
5119.3619.23345103484580.126548965154196
5219.5719.35123726024110.218762739758922
5319.5919.55485202186270.0351479781373207
5419.3619.5875662180635-0.227566218063544
5519.4619.37575756502140.0842424349785631
5619.6519.45416672800540.195833271994562
5719.4619.6364397468874-0.176439746887411
5819.5119.47221737043220.0377826295677686
5919.6419.50738378460930.132616215390673
6019.6419.63081714037040.00918285962959686
6119.6919.63936414328570.0506358567142691
6219.2819.6864937774535-0.406493777453520
6319.6719.30814720121260.361852798787361
6419.6519.64494391279340.0050560872066221
6519.619.6496498969681-0.0496498969680523
6619.5319.6034379508806-0.0734379508805816
6719.6419.53508512773070.104914872269315
6819.6719.63273528849950.0372647115005371
6919.8119.66741964725930.142580352740715
7019.7319.8001271849653-0.0701271849652798
7119.8719.73485587749480.135144122505245
7219.9719.86064209830540.109357901694558
7320.1219.96242763595920.157572364040782
7419.9420.1090890801232-0.169089080123214
7520.3119.95170838183770.358291618162262
7620.1320.2851905027123-0.155190502712259
7720.2220.14074599058690.0792540094131375
7820.3820.21451214588370.165487854116328
7920.4420.36854098097830.071459019021745
8020.3420.4350519011645-0.095051901164485
8120.1420.3465817612375-0.20658176123748
8219.9720.1543045200761-0.18430452007615
8319.8219.9827619577438-0.162761957743808
8419.9819.83127026741490.148729732585139
8520.1219.96970137812290.150298621877074







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8620.109592742160919.785837136404620.4333483479172
8720.109592742160919.667300993961720.5518844903601
8820.109592742160919.574404654857420.6447808294643
8920.109592742160919.49540174006320.7237837442588
9020.109592742160919.425461990531920.7937234937899
9120.109592742160919.362037270245320.8571482140764
9220.109592742160919.303588100823520.9155973834982
9320.109592742160919.249099987906820.9700854964150
9420.109592742160919.197862475914221.0213230084076
9520.109592742160919.149355075405021.0698304089167
9620.109592742160919.103182947433521.1160025368882
9720.109592742160919.059038139491621.1601473448302

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 20.1095927421609 & 19.7858371364046 & 20.4333483479172 \tabularnewline
87 & 20.1095927421609 & 19.6673009939617 & 20.5518844903601 \tabularnewline
88 & 20.1095927421609 & 19.5744046548574 & 20.6447808294643 \tabularnewline
89 & 20.1095927421609 & 19.495401740063 & 20.7237837442588 \tabularnewline
90 & 20.1095927421609 & 19.4254619905319 & 20.7937234937899 \tabularnewline
91 & 20.1095927421609 & 19.3620372702453 & 20.8571482140764 \tabularnewline
92 & 20.1095927421609 & 19.3035881008235 & 20.9155973834982 \tabularnewline
93 & 20.1095927421609 & 19.2490999879068 & 20.9700854964150 \tabularnewline
94 & 20.1095927421609 & 19.1978624759142 & 21.0213230084076 \tabularnewline
95 & 20.1095927421609 & 19.1493550754050 & 21.0698304089167 \tabularnewline
96 & 20.1095927421609 & 19.1031829474335 & 21.1160025368882 \tabularnewline
97 & 20.1095927421609 & 19.0590381394916 & 21.1601473448302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42935&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]86[/C][C]20.1095927421609[/C][C]19.7858371364046[/C][C]20.4333483479172[/C][/ROW]
[ROW][C]87[/C][C]20.1095927421609[/C][C]19.6673009939617[/C][C]20.5518844903601[/C][/ROW]
[ROW][C]88[/C][C]20.1095927421609[/C][C]19.5744046548574[/C][C]20.6447808294643[/C][/ROW]
[ROW][C]89[/C][C]20.1095927421609[/C][C]19.495401740063[/C][C]20.7237837442588[/C][/ROW]
[ROW][C]90[/C][C]20.1095927421609[/C][C]19.4254619905319[/C][C]20.7937234937899[/C][/ROW]
[ROW][C]91[/C][C]20.1095927421609[/C][C]19.3620372702453[/C][C]20.8571482140764[/C][/ROW]
[ROW][C]92[/C][C]20.1095927421609[/C][C]19.3035881008235[/C][C]20.9155973834982[/C][/ROW]
[ROW][C]93[/C][C]20.1095927421609[/C][C]19.2490999879068[/C][C]20.9700854964150[/C][/ROW]
[ROW][C]94[/C][C]20.1095927421609[/C][C]19.1978624759142[/C][C]21.0213230084076[/C][/ROW]
[ROW][C]95[/C][C]20.1095927421609[/C][C]19.1493550754050[/C][C]21.0698304089167[/C][/ROW]
[ROW][C]96[/C][C]20.1095927421609[/C][C]19.1031829474335[/C][C]21.1160025368882[/C][/ROW]
[ROW][C]97[/C][C]20.1095927421609[/C][C]19.0590381394916[/C][C]21.1601473448302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42935&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42935&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
8620.109592742160919.785837136404620.4333483479172
8720.109592742160919.667300993961720.5518844903601
8820.109592742160919.574404654857420.6447808294643
8920.109592742160919.49540174006320.7237837442588
9020.109592742160919.425461990531920.7937234937899
9120.109592742160919.362037270245320.8571482140764
9220.109592742160919.303588100823520.9155973834982
9320.109592742160919.249099987906820.9700854964150
9420.109592742160919.197862475914221.0213230084076
9520.109592742160919.149355075405021.0698304089167
9620.109592742160919.103182947433521.1160025368882
9720.109592742160919.059038139491621.1601473448302



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')