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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 01 Aug 2008 06:08:39 -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/2008/Aug/01/t12175925683qx747lw6fbw7qi.htm/, Retrieved Tue, 14 May 2024 09:22:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13894, Retrieved Tue, 14 May 2024 09:22:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact296
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Nietje van Santfo...] [2008-05-24 10:16:40] [f48bfde976615948c8f49c9cb95da62c]
-   PD  [Exponential Smoothing] [Single Exponentia...] [2008-07-16 11:00:01] [74be16979710d4c4e7c6647856088456]
-   PD      [Exponential Smoothing] [Double Ex Sm_Gem ...] [2008-08-01 12:08:39] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
11.73
11.74
11.65
11.38
11.53
11.75
11.82
11.83
11.63
11.55
11.4
11.4
11.63
11.46
11.35
11.7
11.52
11.64
11.9
11.73
11.7
11.54
11.97
11.64
11.98
11.79
11.66
11.96
11.83
12.36
12.53
12.55
12.53
12.24
12.34
12.05
12.22
12.23
11.92
12.13
12.1
12.15
12.23
12.08
12.02
11.93
12.16
11.87
11.93
11.79
11.43
11.63
11.93
11.89
11.83
11.59
12.04
11.81
11.9
11.72
11.91
11.94
11.91
11.84
12.01
11.89
11.8
11.7
11.5
11.76
11.61
11.27
11.64
11.39
11.54
11.62
11.59
11.44
11.31
11.56
11.4
11.51
11.5
11.24
11.8
11.87
11.86
12.11
11.92
12.61
13.34
13.31
13.47
13.3
13.18
13.24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13894&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]5 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=13894&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13894&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.776239907184881
beta0.000989663457731457
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.776239907184881 \tabularnewline
beta & 0.000989663457731457 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13894&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]0.776239907184881[/C][/ROW]
[ROW][C]beta[/C][C]0.000989663457731457[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13894&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13894&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
alpha0.776239907184881
beta0.000989663457731457
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
311.6511.75-0.0999999999999996
411.3811.6822991876545-0.302299187654453
511.5311.45733344150590.0726665584940971
611.7511.52348689497780.226513105022228
711.8211.70923618850010.110763811499872
811.8311.80522135172420.0247786482758396
911.6311.8344804351887-0.204480435188660
1011.5511.6856223837861-0.135622383786060
1111.411.5901105124913-0.190110512491268
1211.411.4521567352388-0.052156735238766
1311.6311.42124811758390.208751882416083
1411.4611.5930275476738-0.133027547673789
1511.3511.4994019507464-0.149401950746443
1611.711.39295111568830.307048884311650
1711.5211.641051514419-0.121051514419003
1811.6411.55675030563020.0832496943697905
1911.911.63109980195910.268900198040877
2011.7311.8497652015338-0.119765201533802
2111.711.7666410018402-0.0666410018401926
2211.5411.7247027312841-0.184702731284119
2311.9711.59097834317900.379021656820987
2411.6411.8951304923781-0.255130492378139
2511.9811.70683244074650.273167559253523
2611.7911.9288302714429-0.138830271442945
2711.6611.8309122926058-0.170912292605840
2811.9611.70795967103490.252040328965073
2911.8311.9135133746574-0.0835133746573735
3012.3611.85853274619120.501467253808833
3112.5312.25802266177410.271977338225943
3212.5512.47958228400150.0704177159985306
3312.5312.5447373798140-0.014737379814024
3412.2412.5437803704618-0.303780370461762
3512.3412.31822328785340.0217767121466093
3612.0512.3453933340569-0.295393334056911
3712.2212.12613640706810.0938635929318536
3812.2312.20910834849550.0208916515044830
3911.9212.2354526061888-0.31545260618881
4012.1312.00047069268340.129529307316576
4112.112.1110010049378-0.0110010049378069
4212.1512.11243762950020.0375623704998027
4312.2312.15159994012900.0784000598709564
4412.0812.2225223231666-0.142522323166606
4512.0212.1218464481325-0.101846448132452
4611.9312.0526665704609-0.122666570460916
4712.1611.96723104851030.192768951489729
4811.8712.1267972550864-0.256797255086408
4911.9311.9371949553668-0.00719495536682757
5011.7911.9413383943329-0.151338394332930
5111.4311.8334756829978-0.403475682997785
5211.6311.52958398952710.100416010472875
5311.9311.61691027864040.313089721359564
5411.8911.86956290997120.0204370900288087
5511.8311.8950625900254-0.065062590025434
5611.5911.8541440242298-0.26414402422977
5712.0411.65848758468790.381512415312088
5811.8111.9643085238942-0.154308523894214
5911.911.85408532466460.0459146753354425
6011.7211.8993186354218-0.17931863542184
6111.9111.76957910644860.140420893551402
6211.9411.88814203338400.0518579666159624
6311.9111.9379987202688-0.027998720268803
6411.8411.9258459508656-0.0858459508655827
6512.0111.86872390429680.141276095703203
6611.8911.9880115846716-0.0980115846715677
6711.811.9214793241477-0.121479324147691
6811.711.8366371453177-0.136637145317682
6911.511.7399238939114-0.239923893911355
7011.7611.56285103292420.197148967075755
7111.6111.7252030220270-0.115203022027035
7211.2711.6450064312637-0.375006431263721
7311.6411.36285198018610.277148019813861
7411.3911.5871387493014-0.197138749301406
7511.5411.44311375558480.0968862444151526
7611.6211.52739712529020.0926028747097813
7711.5911.6084267115281-0.0184267115281074
7811.4411.6032565463503-0.163256546350315
7911.3111.4855382672973-0.175538267297345
8011.5611.35815157496330.201848425036664
8111.411.5238625569038-0.123862556903790
8211.5111.43664852322220.0733514767778374
8311.511.5025762425390-0.00257624253904609
8411.2411.5095638569492-0.269563856949198
8511.811.30909794698920.490902053010766
8611.8711.69931314333820.170686856661758
8711.8611.84109564981460.0189043501854336
8812.1111.86507304018080.244926959819184
8911.9212.0646863569465-0.144686356946488
9012.6111.96175511845440.648244881545555
9113.3412.47482674319880.865173256801222
9213.3113.15695146999010.153048530009924
9313.4713.28641413932380.183585860676219
9413.313.4397221370248-0.139722137024782
9513.1813.3419582277792-0.161958227779209
9613.2413.22680935856450.0131906414354717

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 11.65 & 11.75 & -0.0999999999999996 \tabularnewline
4 & 11.38 & 11.6822991876545 & -0.302299187654453 \tabularnewline
5 & 11.53 & 11.4573334415059 & 0.0726665584940971 \tabularnewline
6 & 11.75 & 11.5234868949778 & 0.226513105022228 \tabularnewline
7 & 11.82 & 11.7092361885001 & 0.110763811499872 \tabularnewline
8 & 11.83 & 11.8052213517242 & 0.0247786482758396 \tabularnewline
9 & 11.63 & 11.8344804351887 & -0.204480435188660 \tabularnewline
10 & 11.55 & 11.6856223837861 & -0.135622383786060 \tabularnewline
11 & 11.4 & 11.5901105124913 & -0.190110512491268 \tabularnewline
12 & 11.4 & 11.4521567352388 & -0.052156735238766 \tabularnewline
13 & 11.63 & 11.4212481175839 & 0.208751882416083 \tabularnewline
14 & 11.46 & 11.5930275476738 & -0.133027547673789 \tabularnewline
15 & 11.35 & 11.4994019507464 & -0.149401950746443 \tabularnewline
16 & 11.7 & 11.3929511156883 & 0.307048884311650 \tabularnewline
17 & 11.52 & 11.641051514419 & -0.121051514419003 \tabularnewline
18 & 11.64 & 11.5567503056302 & 0.0832496943697905 \tabularnewline
19 & 11.9 & 11.6310998019591 & 0.268900198040877 \tabularnewline
20 & 11.73 & 11.8497652015338 & -0.119765201533802 \tabularnewline
21 & 11.7 & 11.7666410018402 & -0.0666410018401926 \tabularnewline
22 & 11.54 & 11.7247027312841 & -0.184702731284119 \tabularnewline
23 & 11.97 & 11.5909783431790 & 0.379021656820987 \tabularnewline
24 & 11.64 & 11.8951304923781 & -0.255130492378139 \tabularnewline
25 & 11.98 & 11.7068324407465 & 0.273167559253523 \tabularnewline
26 & 11.79 & 11.9288302714429 & -0.138830271442945 \tabularnewline
27 & 11.66 & 11.8309122926058 & -0.170912292605840 \tabularnewline
28 & 11.96 & 11.7079596710349 & 0.252040328965073 \tabularnewline
29 & 11.83 & 11.9135133746574 & -0.0835133746573735 \tabularnewline
30 & 12.36 & 11.8585327461912 & 0.501467253808833 \tabularnewline
31 & 12.53 & 12.2580226617741 & 0.271977338225943 \tabularnewline
32 & 12.55 & 12.4795822840015 & 0.0704177159985306 \tabularnewline
33 & 12.53 & 12.5447373798140 & -0.014737379814024 \tabularnewline
34 & 12.24 & 12.5437803704618 & -0.303780370461762 \tabularnewline
35 & 12.34 & 12.3182232878534 & 0.0217767121466093 \tabularnewline
36 & 12.05 & 12.3453933340569 & -0.295393334056911 \tabularnewline
37 & 12.22 & 12.1261364070681 & 0.0938635929318536 \tabularnewline
38 & 12.23 & 12.2091083484955 & 0.0208916515044830 \tabularnewline
39 & 11.92 & 12.2354526061888 & -0.31545260618881 \tabularnewline
40 & 12.13 & 12.0004706926834 & 0.129529307316576 \tabularnewline
41 & 12.1 & 12.1110010049378 & -0.0110010049378069 \tabularnewline
42 & 12.15 & 12.1124376295002 & 0.0375623704998027 \tabularnewline
43 & 12.23 & 12.1515999401290 & 0.0784000598709564 \tabularnewline
44 & 12.08 & 12.2225223231666 & -0.142522323166606 \tabularnewline
45 & 12.02 & 12.1218464481325 & -0.101846448132452 \tabularnewline
46 & 11.93 & 12.0526665704609 & -0.122666570460916 \tabularnewline
47 & 12.16 & 11.9672310485103 & 0.192768951489729 \tabularnewline
48 & 11.87 & 12.1267972550864 & -0.256797255086408 \tabularnewline
49 & 11.93 & 11.9371949553668 & -0.00719495536682757 \tabularnewline
50 & 11.79 & 11.9413383943329 & -0.151338394332930 \tabularnewline
51 & 11.43 & 11.8334756829978 & -0.403475682997785 \tabularnewline
52 & 11.63 & 11.5295839895271 & 0.100416010472875 \tabularnewline
53 & 11.93 & 11.6169102786404 & 0.313089721359564 \tabularnewline
54 & 11.89 & 11.8695629099712 & 0.0204370900288087 \tabularnewline
55 & 11.83 & 11.8950625900254 & -0.065062590025434 \tabularnewline
56 & 11.59 & 11.8541440242298 & -0.26414402422977 \tabularnewline
57 & 12.04 & 11.6584875846879 & 0.381512415312088 \tabularnewline
58 & 11.81 & 11.9643085238942 & -0.154308523894214 \tabularnewline
59 & 11.9 & 11.8540853246646 & 0.0459146753354425 \tabularnewline
60 & 11.72 & 11.8993186354218 & -0.17931863542184 \tabularnewline
61 & 11.91 & 11.7695791064486 & 0.140420893551402 \tabularnewline
62 & 11.94 & 11.8881420333840 & 0.0518579666159624 \tabularnewline
63 & 11.91 & 11.9379987202688 & -0.027998720268803 \tabularnewline
64 & 11.84 & 11.9258459508656 & -0.0858459508655827 \tabularnewline
65 & 12.01 & 11.8687239042968 & 0.141276095703203 \tabularnewline
66 & 11.89 & 11.9880115846716 & -0.0980115846715677 \tabularnewline
67 & 11.8 & 11.9214793241477 & -0.121479324147691 \tabularnewline
68 & 11.7 & 11.8366371453177 & -0.136637145317682 \tabularnewline
69 & 11.5 & 11.7399238939114 & -0.239923893911355 \tabularnewline
70 & 11.76 & 11.5628510329242 & 0.197148967075755 \tabularnewline
71 & 11.61 & 11.7252030220270 & -0.115203022027035 \tabularnewline
72 & 11.27 & 11.6450064312637 & -0.375006431263721 \tabularnewline
73 & 11.64 & 11.3628519801861 & 0.277148019813861 \tabularnewline
74 & 11.39 & 11.5871387493014 & -0.197138749301406 \tabularnewline
75 & 11.54 & 11.4431137555848 & 0.0968862444151526 \tabularnewline
76 & 11.62 & 11.5273971252902 & 0.0926028747097813 \tabularnewline
77 & 11.59 & 11.6084267115281 & -0.0184267115281074 \tabularnewline
78 & 11.44 & 11.6032565463503 & -0.163256546350315 \tabularnewline
79 & 11.31 & 11.4855382672973 & -0.175538267297345 \tabularnewline
80 & 11.56 & 11.3581515749633 & 0.201848425036664 \tabularnewline
81 & 11.4 & 11.5238625569038 & -0.123862556903790 \tabularnewline
82 & 11.51 & 11.4366485232222 & 0.0733514767778374 \tabularnewline
83 & 11.5 & 11.5025762425390 & -0.00257624253904609 \tabularnewline
84 & 11.24 & 11.5095638569492 & -0.269563856949198 \tabularnewline
85 & 11.8 & 11.3090979469892 & 0.490902053010766 \tabularnewline
86 & 11.87 & 11.6993131433382 & 0.170686856661758 \tabularnewline
87 & 11.86 & 11.8410956498146 & 0.0189043501854336 \tabularnewline
88 & 12.11 & 11.8650730401808 & 0.244926959819184 \tabularnewline
89 & 11.92 & 12.0646863569465 & -0.144686356946488 \tabularnewline
90 & 12.61 & 11.9617551184544 & 0.648244881545555 \tabularnewline
91 & 13.34 & 12.4748267431988 & 0.865173256801222 \tabularnewline
92 & 13.31 & 13.1569514699901 & 0.153048530009924 \tabularnewline
93 & 13.47 & 13.2864141393238 & 0.183585860676219 \tabularnewline
94 & 13.3 & 13.4397221370248 & -0.139722137024782 \tabularnewline
95 & 13.18 & 13.3419582277792 & -0.161958227779209 \tabularnewline
96 & 13.24 & 13.2268093585645 & 0.0131906414354717 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13894&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]11.65[/C][C]11.75[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]4[/C][C]11.38[/C][C]11.6822991876545[/C][C]-0.302299187654453[/C][/ROW]
[ROW][C]5[/C][C]11.53[/C][C]11.4573334415059[/C][C]0.0726665584940971[/C][/ROW]
[ROW][C]6[/C][C]11.75[/C][C]11.5234868949778[/C][C]0.226513105022228[/C][/ROW]
[ROW][C]7[/C][C]11.82[/C][C]11.7092361885001[/C][C]0.110763811499872[/C][/ROW]
[ROW][C]8[/C][C]11.83[/C][C]11.8052213517242[/C][C]0.0247786482758396[/C][/ROW]
[ROW][C]9[/C][C]11.63[/C][C]11.8344804351887[/C][C]-0.204480435188660[/C][/ROW]
[ROW][C]10[/C][C]11.55[/C][C]11.6856223837861[/C][C]-0.135622383786060[/C][/ROW]
[ROW][C]11[/C][C]11.4[/C][C]11.5901105124913[/C][C]-0.190110512491268[/C][/ROW]
[ROW][C]12[/C][C]11.4[/C][C]11.4521567352388[/C][C]-0.052156735238766[/C][/ROW]
[ROW][C]13[/C][C]11.63[/C][C]11.4212481175839[/C][C]0.208751882416083[/C][/ROW]
[ROW][C]14[/C][C]11.46[/C][C]11.5930275476738[/C][C]-0.133027547673789[/C][/ROW]
[ROW][C]15[/C][C]11.35[/C][C]11.4994019507464[/C][C]-0.149401950746443[/C][/ROW]
[ROW][C]16[/C][C]11.7[/C][C]11.3929511156883[/C][C]0.307048884311650[/C][/ROW]
[ROW][C]17[/C][C]11.52[/C][C]11.641051514419[/C][C]-0.121051514419003[/C][/ROW]
[ROW][C]18[/C][C]11.64[/C][C]11.5567503056302[/C][C]0.0832496943697905[/C][/ROW]
[ROW][C]19[/C][C]11.9[/C][C]11.6310998019591[/C][C]0.268900198040877[/C][/ROW]
[ROW][C]20[/C][C]11.73[/C][C]11.8497652015338[/C][C]-0.119765201533802[/C][/ROW]
[ROW][C]21[/C][C]11.7[/C][C]11.7666410018402[/C][C]-0.0666410018401926[/C][/ROW]
[ROW][C]22[/C][C]11.54[/C][C]11.7247027312841[/C][C]-0.184702731284119[/C][/ROW]
[ROW][C]23[/C][C]11.97[/C][C]11.5909783431790[/C][C]0.379021656820987[/C][/ROW]
[ROW][C]24[/C][C]11.64[/C][C]11.8951304923781[/C][C]-0.255130492378139[/C][/ROW]
[ROW][C]25[/C][C]11.98[/C][C]11.7068324407465[/C][C]0.273167559253523[/C][/ROW]
[ROW][C]26[/C][C]11.79[/C][C]11.9288302714429[/C][C]-0.138830271442945[/C][/ROW]
[ROW][C]27[/C][C]11.66[/C][C]11.8309122926058[/C][C]-0.170912292605840[/C][/ROW]
[ROW][C]28[/C][C]11.96[/C][C]11.7079596710349[/C][C]0.252040328965073[/C][/ROW]
[ROW][C]29[/C][C]11.83[/C][C]11.9135133746574[/C][C]-0.0835133746573735[/C][/ROW]
[ROW][C]30[/C][C]12.36[/C][C]11.8585327461912[/C][C]0.501467253808833[/C][/ROW]
[ROW][C]31[/C][C]12.53[/C][C]12.2580226617741[/C][C]0.271977338225943[/C][/ROW]
[ROW][C]32[/C][C]12.55[/C][C]12.4795822840015[/C][C]0.0704177159985306[/C][/ROW]
[ROW][C]33[/C][C]12.53[/C][C]12.5447373798140[/C][C]-0.014737379814024[/C][/ROW]
[ROW][C]34[/C][C]12.24[/C][C]12.5437803704618[/C][C]-0.303780370461762[/C][/ROW]
[ROW][C]35[/C][C]12.34[/C][C]12.3182232878534[/C][C]0.0217767121466093[/C][/ROW]
[ROW][C]36[/C][C]12.05[/C][C]12.3453933340569[/C][C]-0.295393334056911[/C][/ROW]
[ROW][C]37[/C][C]12.22[/C][C]12.1261364070681[/C][C]0.0938635929318536[/C][/ROW]
[ROW][C]38[/C][C]12.23[/C][C]12.2091083484955[/C][C]0.0208916515044830[/C][/ROW]
[ROW][C]39[/C][C]11.92[/C][C]12.2354526061888[/C][C]-0.31545260618881[/C][/ROW]
[ROW][C]40[/C][C]12.13[/C][C]12.0004706926834[/C][C]0.129529307316576[/C][/ROW]
[ROW][C]41[/C][C]12.1[/C][C]12.1110010049378[/C][C]-0.0110010049378069[/C][/ROW]
[ROW][C]42[/C][C]12.15[/C][C]12.1124376295002[/C][C]0.0375623704998027[/C][/ROW]
[ROW][C]43[/C][C]12.23[/C][C]12.1515999401290[/C][C]0.0784000598709564[/C][/ROW]
[ROW][C]44[/C][C]12.08[/C][C]12.2225223231666[/C][C]-0.142522323166606[/C][/ROW]
[ROW][C]45[/C][C]12.02[/C][C]12.1218464481325[/C][C]-0.101846448132452[/C][/ROW]
[ROW][C]46[/C][C]11.93[/C][C]12.0526665704609[/C][C]-0.122666570460916[/C][/ROW]
[ROW][C]47[/C][C]12.16[/C][C]11.9672310485103[/C][C]0.192768951489729[/C][/ROW]
[ROW][C]48[/C][C]11.87[/C][C]12.1267972550864[/C][C]-0.256797255086408[/C][/ROW]
[ROW][C]49[/C][C]11.93[/C][C]11.9371949553668[/C][C]-0.00719495536682757[/C][/ROW]
[ROW][C]50[/C][C]11.79[/C][C]11.9413383943329[/C][C]-0.151338394332930[/C][/ROW]
[ROW][C]51[/C][C]11.43[/C][C]11.8334756829978[/C][C]-0.403475682997785[/C][/ROW]
[ROW][C]52[/C][C]11.63[/C][C]11.5295839895271[/C][C]0.100416010472875[/C][/ROW]
[ROW][C]53[/C][C]11.93[/C][C]11.6169102786404[/C][C]0.313089721359564[/C][/ROW]
[ROW][C]54[/C][C]11.89[/C][C]11.8695629099712[/C][C]0.0204370900288087[/C][/ROW]
[ROW][C]55[/C][C]11.83[/C][C]11.8950625900254[/C][C]-0.065062590025434[/C][/ROW]
[ROW][C]56[/C][C]11.59[/C][C]11.8541440242298[/C][C]-0.26414402422977[/C][/ROW]
[ROW][C]57[/C][C]12.04[/C][C]11.6584875846879[/C][C]0.381512415312088[/C][/ROW]
[ROW][C]58[/C][C]11.81[/C][C]11.9643085238942[/C][C]-0.154308523894214[/C][/ROW]
[ROW][C]59[/C][C]11.9[/C][C]11.8540853246646[/C][C]0.0459146753354425[/C][/ROW]
[ROW][C]60[/C][C]11.72[/C][C]11.8993186354218[/C][C]-0.17931863542184[/C][/ROW]
[ROW][C]61[/C][C]11.91[/C][C]11.7695791064486[/C][C]0.140420893551402[/C][/ROW]
[ROW][C]62[/C][C]11.94[/C][C]11.8881420333840[/C][C]0.0518579666159624[/C][/ROW]
[ROW][C]63[/C][C]11.91[/C][C]11.9379987202688[/C][C]-0.027998720268803[/C][/ROW]
[ROW][C]64[/C][C]11.84[/C][C]11.9258459508656[/C][C]-0.0858459508655827[/C][/ROW]
[ROW][C]65[/C][C]12.01[/C][C]11.8687239042968[/C][C]0.141276095703203[/C][/ROW]
[ROW][C]66[/C][C]11.89[/C][C]11.9880115846716[/C][C]-0.0980115846715677[/C][/ROW]
[ROW][C]67[/C][C]11.8[/C][C]11.9214793241477[/C][C]-0.121479324147691[/C][/ROW]
[ROW][C]68[/C][C]11.7[/C][C]11.8366371453177[/C][C]-0.136637145317682[/C][/ROW]
[ROW][C]69[/C][C]11.5[/C][C]11.7399238939114[/C][C]-0.239923893911355[/C][/ROW]
[ROW][C]70[/C][C]11.76[/C][C]11.5628510329242[/C][C]0.197148967075755[/C][/ROW]
[ROW][C]71[/C][C]11.61[/C][C]11.7252030220270[/C][C]-0.115203022027035[/C][/ROW]
[ROW][C]72[/C][C]11.27[/C][C]11.6450064312637[/C][C]-0.375006431263721[/C][/ROW]
[ROW][C]73[/C][C]11.64[/C][C]11.3628519801861[/C][C]0.277148019813861[/C][/ROW]
[ROW][C]74[/C][C]11.39[/C][C]11.5871387493014[/C][C]-0.197138749301406[/C][/ROW]
[ROW][C]75[/C][C]11.54[/C][C]11.4431137555848[/C][C]0.0968862444151526[/C][/ROW]
[ROW][C]76[/C][C]11.62[/C][C]11.5273971252902[/C][C]0.0926028747097813[/C][/ROW]
[ROW][C]77[/C][C]11.59[/C][C]11.6084267115281[/C][C]-0.0184267115281074[/C][/ROW]
[ROW][C]78[/C][C]11.44[/C][C]11.6032565463503[/C][C]-0.163256546350315[/C][/ROW]
[ROW][C]79[/C][C]11.31[/C][C]11.4855382672973[/C][C]-0.175538267297345[/C][/ROW]
[ROW][C]80[/C][C]11.56[/C][C]11.3581515749633[/C][C]0.201848425036664[/C][/ROW]
[ROW][C]81[/C][C]11.4[/C][C]11.5238625569038[/C][C]-0.123862556903790[/C][/ROW]
[ROW][C]82[/C][C]11.51[/C][C]11.4366485232222[/C][C]0.0733514767778374[/C][/ROW]
[ROW][C]83[/C][C]11.5[/C][C]11.5025762425390[/C][C]-0.00257624253904609[/C][/ROW]
[ROW][C]84[/C][C]11.24[/C][C]11.5095638569492[/C][C]-0.269563856949198[/C][/ROW]
[ROW][C]85[/C][C]11.8[/C][C]11.3090979469892[/C][C]0.490902053010766[/C][/ROW]
[ROW][C]86[/C][C]11.87[/C][C]11.6993131433382[/C][C]0.170686856661758[/C][/ROW]
[ROW][C]87[/C][C]11.86[/C][C]11.8410956498146[/C][C]0.0189043501854336[/C][/ROW]
[ROW][C]88[/C][C]12.11[/C][C]11.8650730401808[/C][C]0.244926959819184[/C][/ROW]
[ROW][C]89[/C][C]11.92[/C][C]12.0646863569465[/C][C]-0.144686356946488[/C][/ROW]
[ROW][C]90[/C][C]12.61[/C][C]11.9617551184544[/C][C]0.648244881545555[/C][/ROW]
[ROW][C]91[/C][C]13.34[/C][C]12.4748267431988[/C][C]0.865173256801222[/C][/ROW]
[ROW][C]92[/C][C]13.31[/C][C]13.1569514699901[/C][C]0.153048530009924[/C][/ROW]
[ROW][C]93[/C][C]13.47[/C][C]13.2864141393238[/C][C]0.183585860676219[/C][/ROW]
[ROW][C]94[/C][C]13.3[/C][C]13.4397221370248[/C][C]-0.139722137024782[/C][/ROW]
[ROW][C]95[/C][C]13.18[/C][C]13.3419582277792[/C][C]-0.161958227779209[/C][/ROW]
[ROW][C]96[/C][C]13.24[/C][C]13.2268093585645[/C][C]0.0131906414354717[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13894&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13894&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
311.6511.75-0.0999999999999996
411.3811.6822991876545-0.302299187654453
511.5311.45733344150590.0726665584940971
611.7511.52348689497780.226513105022228
711.8211.70923618850010.110763811499872
811.8311.80522135172420.0247786482758396
911.6311.8344804351887-0.204480435188660
1011.5511.6856223837861-0.135622383786060
1111.411.5901105124913-0.190110512491268
1211.411.4521567352388-0.052156735238766
1311.6311.42124811758390.208751882416083
1411.4611.5930275476738-0.133027547673789
1511.3511.4994019507464-0.149401950746443
1611.711.39295111568830.307048884311650
1711.5211.641051514419-0.121051514419003
1811.6411.55675030563020.0832496943697905
1911.911.63109980195910.268900198040877
2011.7311.8497652015338-0.119765201533802
2111.711.7666410018402-0.0666410018401926
2211.5411.7247027312841-0.184702731284119
2311.9711.59097834317900.379021656820987
2411.6411.8951304923781-0.255130492378139
2511.9811.70683244074650.273167559253523
2611.7911.9288302714429-0.138830271442945
2711.6611.8309122926058-0.170912292605840
2811.9611.70795967103490.252040328965073
2911.8311.9135133746574-0.0835133746573735
3012.3611.85853274619120.501467253808833
3112.5312.25802266177410.271977338225943
3212.5512.47958228400150.0704177159985306
3312.5312.5447373798140-0.014737379814024
3412.2412.5437803704618-0.303780370461762
3512.3412.31822328785340.0217767121466093
3612.0512.3453933340569-0.295393334056911
3712.2212.12613640706810.0938635929318536
3812.2312.20910834849550.0208916515044830
3911.9212.2354526061888-0.31545260618881
4012.1312.00047069268340.129529307316576
4112.112.1110010049378-0.0110010049378069
4212.1512.11243762950020.0375623704998027
4312.2312.15159994012900.0784000598709564
4412.0812.2225223231666-0.142522323166606
4512.0212.1218464481325-0.101846448132452
4611.9312.0526665704609-0.122666570460916
4712.1611.96723104851030.192768951489729
4811.8712.1267972550864-0.256797255086408
4911.9311.9371949553668-0.00719495536682757
5011.7911.9413383943329-0.151338394332930
5111.4311.8334756829978-0.403475682997785
5211.6311.52958398952710.100416010472875
5311.9311.61691027864040.313089721359564
5411.8911.86956290997120.0204370900288087
5511.8311.8950625900254-0.065062590025434
5611.5911.8541440242298-0.26414402422977
5712.0411.65848758468790.381512415312088
5811.8111.9643085238942-0.154308523894214
5911.911.85408532466460.0459146753354425
6011.7211.8993186354218-0.17931863542184
6111.9111.76957910644860.140420893551402
6211.9411.88814203338400.0518579666159624
6311.9111.9379987202688-0.027998720268803
6411.8411.9258459508656-0.0858459508655827
6512.0111.86872390429680.141276095703203
6611.8911.9880115846716-0.0980115846715677
6711.811.9214793241477-0.121479324147691
6811.711.8366371453177-0.136637145317682
6911.511.7399238939114-0.239923893911355
7011.7611.56285103292420.197148967075755
7111.6111.7252030220270-0.115203022027035
7211.2711.6450064312637-0.375006431263721
7311.6411.36285198018610.277148019813861
7411.3911.5871387493014-0.197138749301406
7511.5411.44311375558480.0968862444151526
7611.6211.52739712529020.0926028747097813
7711.5911.6084267115281-0.0184267115281074
7811.4411.6032565463503-0.163256546350315
7911.3111.4855382672973-0.175538267297345
8011.5611.35815157496330.201848425036664
8111.411.5238625569038-0.123862556903790
8211.5111.43664852322220.0733514767778374
8311.511.5025762425390-0.00257624253904609
8411.2411.5095638569492-0.269563856949198
8511.811.30909794698920.490902053010766
8611.8711.69931314333820.170686856661758
8711.8611.84109564981460.0189043501854336
8812.1111.86507304018080.244926959819184
8911.9212.0646863569465-0.144686356946488
9012.6111.96175511845440.648244881545555
9113.3412.47482674319880.865173256801222
9213.3113.15695146999010.153048530009924
9313.4713.28641413932380.183585860676219
9413.313.4397221370248-0.139722137024782
9513.1813.3419582277792-0.161958227779209
9613.2413.22680935856450.0131906414354717







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9713.247628164598012.809454742261213.6858015869348
9813.258207868347812.703309775452713.8131059612430
9913.268787572097712.617590857599013.9199842865964
10013.279367275847512.544226488594314.0145080631007
10113.289946979597412.479369057098914.1005249020958
10213.300526683347212.420827210990314.1802261557042
10313.311106387097112.367212334055114.2550004401391
10413.321686090846912.317578895291614.3257932864022
10513.332265794596812.271248726555914.3932828626376
10613.342845498346612.22771587112514.4579751255682
10713.353425202096512.186590986245114.5202594179478
10813.364004905846312.147566888267414.5804429234253

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 13.2476281645980 & 12.8094547422612 & 13.6858015869348 \tabularnewline
98 & 13.2582078683478 & 12.7033097754527 & 13.8131059612430 \tabularnewline
99 & 13.2687875720977 & 12.6175908575990 & 13.9199842865964 \tabularnewline
100 & 13.2793672758475 & 12.5442264885943 & 14.0145080631007 \tabularnewline
101 & 13.2899469795974 & 12.4793690570989 & 14.1005249020958 \tabularnewline
102 & 13.3005266833472 & 12.4208272109903 & 14.1802261557042 \tabularnewline
103 & 13.3111063870971 & 12.3672123340551 & 14.2550004401391 \tabularnewline
104 & 13.3216860908469 & 12.3175788952916 & 14.3257932864022 \tabularnewline
105 & 13.3322657945968 & 12.2712487265559 & 14.3932828626376 \tabularnewline
106 & 13.3428454983466 & 12.227715871125 & 14.4579751255682 \tabularnewline
107 & 13.3534252020965 & 12.1865909862451 & 14.5202594179478 \tabularnewline
108 & 13.3640049058463 & 12.1475668882674 & 14.5804429234253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13894&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]97[/C][C]13.2476281645980[/C][C]12.8094547422612[/C][C]13.6858015869348[/C][/ROW]
[ROW][C]98[/C][C]13.2582078683478[/C][C]12.7033097754527[/C][C]13.8131059612430[/C][/ROW]
[ROW][C]99[/C][C]13.2687875720977[/C][C]12.6175908575990[/C][C]13.9199842865964[/C][/ROW]
[ROW][C]100[/C][C]13.2793672758475[/C][C]12.5442264885943[/C][C]14.0145080631007[/C][/ROW]
[ROW][C]101[/C][C]13.2899469795974[/C][C]12.4793690570989[/C][C]14.1005249020958[/C][/ROW]
[ROW][C]102[/C][C]13.3005266833472[/C][C]12.4208272109903[/C][C]14.1802261557042[/C][/ROW]
[ROW][C]103[/C][C]13.3111063870971[/C][C]12.3672123340551[/C][C]14.2550004401391[/C][/ROW]
[ROW][C]104[/C][C]13.3216860908469[/C][C]12.3175788952916[/C][C]14.3257932864022[/C][/ROW]
[ROW][C]105[/C][C]13.3322657945968[/C][C]12.2712487265559[/C][C]14.3932828626376[/C][/ROW]
[ROW][C]106[/C][C]13.3428454983466[/C][C]12.227715871125[/C][C]14.4579751255682[/C][/ROW]
[ROW][C]107[/C][C]13.3534252020965[/C][C]12.1865909862451[/C][C]14.5202594179478[/C][/ROW]
[ROW][C]108[/C][C]13.3640049058463[/C][C]12.1475668882674[/C][C]14.5804429234253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13894&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13894&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
9713.247628164598012.809454742261213.6858015869348
9813.258207868347812.703309775452713.8131059612430
9913.268787572097712.617590857599013.9199842865964
10013.279367275847512.544226488594314.0145080631007
10113.289946979597412.479369057098914.1005249020958
10213.300526683347212.420827210990314.1802261557042
10313.311106387097112.367212334055114.2550004401391
10413.321686090846912.317578895291614.3257932864022
10513.332265794596812.271248726555914.3932828626376
10613.342845498346612.22771587112514.4579751255682
10713.353425202096512.186590986245114.5202594179478
10813.364004905846312.147566888267414.5804429234253



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
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=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')