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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 22 Dec 2012 04:38:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/22/t13561691254kalz1f2lpdgep8.htm/, Retrieved Sat, 27 Apr 2024 05:20:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204478, Retrieved Sat, 27 Apr 2024 05:20:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2012-12-22 09:38:06] [abfcbcdb56ba76a2d4388c2da0a635eb] [Current]
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Dataseries X:
9,24
9,29
9,39
9,42
9,42
9,43
9,5
9,53
9,58
9,58
9,6
9,61
9,65
9,71
9,78
9,79
9,84
9,87
9,9
9,95
9,96
9,98
10,01
10
10,03
10,05
10,06
10,09
10,24
10,23
10,27
10,28
10,29
10,44
10,51
10,52
10,57
10,62
10,71
10,73
10,74
10,75
10,79
10,81
10,87
10,92
10,95
10,94
10,97
10,99
11,04
11,09
11,12
11,11
11,14
11,2
11,25
11,3
11,31
11,31
11,33
11,41
11,46
11,48
11,58
11,63
11,69
11,74
11,68
11,69
11,71
11,75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204478&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204478&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204478&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0395252367775957
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0395252367775957 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204478&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0395252367775957[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204478&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204478&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
alpha1
beta0.0395252367775957
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
39.399.340.0500000000000025
49.429.44197626183888-0.0219762618388799
59.429.47110764488621-0.0511076448862102
69.439.46908760312094-0.0390876031209384
79.59.477542656352510.0224573436474866
89.539.54843028817758-0.0184302881775782
99.589.577701826673480.0022981733265226
109.589.62779266251836-0.0477926625183649
119.69.62590364621609-0.0259036462160953
129.619.644879798466-0.034879798466001
139.659.65350116617288-0.00350116617287632
149.719.69336278175090.0166372182491035
159.789.754020371741510.0259796282584848
169.799.82504722269982-0.0350472226998235
179.849.833661972924220.00633802707578468
189.879.88391248494509-0.0139124849450898
199.99.91336259068347-0.0133625906834691
209.959.942834431122740.00716556887725517
219.969.99311765192926-0.0331176519292615
229.9810.0018086688952-0.0218086688952415
2310.0110.0209466760934-0.0109466760933525
241010.0505140061288-0.0505140061288358
2510.0310.038517428076-0.00851742807600964
2610.0510.0681807747146-0.0181807747145672
2710.0610.0874621752892-0.0274621752891751
2810.0910.0963767263084-0.00637672630844222
2910.2410.12612468469120.113875315308766
3010.2310.2806256334919-0.0506256334919364
3110.2710.26862464334120.00137535665884592
3210.2810.3086790046387-0.0286790046387466
3310.2910.3175454601899-0.0275454601898559
3410.4410.32645671935370.113543280646297
3510.5110.48094454440580.0290554555942482
3610.5210.5520929681678-0.0320929681677971
3710.5710.56082448600210.00917551399793304
3810.6210.61118715036540.00881284963460693
3910.7110.66153548033390.0484645196661155
4010.7310.753451051949-0.023451051949003
4110.7410.772524143568-0.0325241435680343
4210.7510.7812386190925-0.0312386190925196
4310.7910.7900039052763-3.90527628191251e-06
4410.8110.8300037509193-0.0200037509193098
4510.8710.84921309792780.0207869020722118
4610.9210.91003470515410.00996529484593722
4710.9510.9604285857924-0.0104285857924076
4810.9410.9900163934697-0.050016393469706
4910.9710.9780394836751-0.00803948367505392
5010.9911.0077217211792-0.01772172117923
5111.0411.02702126595350.0129787340464844
5211.0911.07753425348980.0124657465102267
5311.1211.1280269650722-0.00802696507220091
5411.1111.1577096973771-0.0477096973771154
5511.1411.1458239602917-0.00582396029169807
5611.211.17559376688220.0244062331178121
5711.2511.2365584290250.0134415709749849
5811.311.28708971030050.0129102896995352
5911.3111.3375999925577-0.0275999925577075
6011.3111.3465090963168-0.036509096316804
6111.3311.3450660656403-0.0150660656403474
6211.4111.36447057582860.045529424171395
6311.4611.44627013709930.0137298629006732
6411.4811.4968128131814-0.0168128131813994
6511.5811.51614828275950.0638517172404924
6611.6311.61867203700210.0113279629979068
6711.6911.66911977742180.0208802225782048
6811.7411.72994507316320.0100549268368351
6911.6811.7803424965272-0.100342496527174
7011.6911.7163764355931-0.0263764355930824
7111.7111.7253339007309-0.0153339007309157
7211.7511.74472782467380.00527217532619595

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9.39 & 9.34 & 0.0500000000000025 \tabularnewline
4 & 9.42 & 9.44197626183888 & -0.0219762618388799 \tabularnewline
5 & 9.42 & 9.47110764488621 & -0.0511076448862102 \tabularnewline
6 & 9.43 & 9.46908760312094 & -0.0390876031209384 \tabularnewline
7 & 9.5 & 9.47754265635251 & 0.0224573436474866 \tabularnewline
8 & 9.53 & 9.54843028817758 & -0.0184302881775782 \tabularnewline
9 & 9.58 & 9.57770182667348 & 0.0022981733265226 \tabularnewline
10 & 9.58 & 9.62779266251836 & -0.0477926625183649 \tabularnewline
11 & 9.6 & 9.62590364621609 & -0.0259036462160953 \tabularnewline
12 & 9.61 & 9.644879798466 & -0.034879798466001 \tabularnewline
13 & 9.65 & 9.65350116617288 & -0.00350116617287632 \tabularnewline
14 & 9.71 & 9.6933627817509 & 0.0166372182491035 \tabularnewline
15 & 9.78 & 9.75402037174151 & 0.0259796282584848 \tabularnewline
16 & 9.79 & 9.82504722269982 & -0.0350472226998235 \tabularnewline
17 & 9.84 & 9.83366197292422 & 0.00633802707578468 \tabularnewline
18 & 9.87 & 9.88391248494509 & -0.0139124849450898 \tabularnewline
19 & 9.9 & 9.91336259068347 & -0.0133625906834691 \tabularnewline
20 & 9.95 & 9.94283443112274 & 0.00716556887725517 \tabularnewline
21 & 9.96 & 9.99311765192926 & -0.0331176519292615 \tabularnewline
22 & 9.98 & 10.0018086688952 & -0.0218086688952415 \tabularnewline
23 & 10.01 & 10.0209466760934 & -0.0109466760933525 \tabularnewline
24 & 10 & 10.0505140061288 & -0.0505140061288358 \tabularnewline
25 & 10.03 & 10.038517428076 & -0.00851742807600964 \tabularnewline
26 & 10.05 & 10.0681807747146 & -0.0181807747145672 \tabularnewline
27 & 10.06 & 10.0874621752892 & -0.0274621752891751 \tabularnewline
28 & 10.09 & 10.0963767263084 & -0.00637672630844222 \tabularnewline
29 & 10.24 & 10.1261246846912 & 0.113875315308766 \tabularnewline
30 & 10.23 & 10.2806256334919 & -0.0506256334919364 \tabularnewline
31 & 10.27 & 10.2686246433412 & 0.00137535665884592 \tabularnewline
32 & 10.28 & 10.3086790046387 & -0.0286790046387466 \tabularnewline
33 & 10.29 & 10.3175454601899 & -0.0275454601898559 \tabularnewline
34 & 10.44 & 10.3264567193537 & 0.113543280646297 \tabularnewline
35 & 10.51 & 10.4809445444058 & 0.0290554555942482 \tabularnewline
36 & 10.52 & 10.5520929681678 & -0.0320929681677971 \tabularnewline
37 & 10.57 & 10.5608244860021 & 0.00917551399793304 \tabularnewline
38 & 10.62 & 10.6111871503654 & 0.00881284963460693 \tabularnewline
39 & 10.71 & 10.6615354803339 & 0.0484645196661155 \tabularnewline
40 & 10.73 & 10.753451051949 & -0.023451051949003 \tabularnewline
41 & 10.74 & 10.772524143568 & -0.0325241435680343 \tabularnewline
42 & 10.75 & 10.7812386190925 & -0.0312386190925196 \tabularnewline
43 & 10.79 & 10.7900039052763 & -3.90527628191251e-06 \tabularnewline
44 & 10.81 & 10.8300037509193 & -0.0200037509193098 \tabularnewline
45 & 10.87 & 10.8492130979278 & 0.0207869020722118 \tabularnewline
46 & 10.92 & 10.9100347051541 & 0.00996529484593722 \tabularnewline
47 & 10.95 & 10.9604285857924 & -0.0104285857924076 \tabularnewline
48 & 10.94 & 10.9900163934697 & -0.050016393469706 \tabularnewline
49 & 10.97 & 10.9780394836751 & -0.00803948367505392 \tabularnewline
50 & 10.99 & 11.0077217211792 & -0.01772172117923 \tabularnewline
51 & 11.04 & 11.0270212659535 & 0.0129787340464844 \tabularnewline
52 & 11.09 & 11.0775342534898 & 0.0124657465102267 \tabularnewline
53 & 11.12 & 11.1280269650722 & -0.00802696507220091 \tabularnewline
54 & 11.11 & 11.1577096973771 & -0.0477096973771154 \tabularnewline
55 & 11.14 & 11.1458239602917 & -0.00582396029169807 \tabularnewline
56 & 11.2 & 11.1755937668822 & 0.0244062331178121 \tabularnewline
57 & 11.25 & 11.236558429025 & 0.0134415709749849 \tabularnewline
58 & 11.3 & 11.2870897103005 & 0.0129102896995352 \tabularnewline
59 & 11.31 & 11.3375999925577 & -0.0275999925577075 \tabularnewline
60 & 11.31 & 11.3465090963168 & -0.036509096316804 \tabularnewline
61 & 11.33 & 11.3450660656403 & -0.0150660656403474 \tabularnewline
62 & 11.41 & 11.3644705758286 & 0.045529424171395 \tabularnewline
63 & 11.46 & 11.4462701370993 & 0.0137298629006732 \tabularnewline
64 & 11.48 & 11.4968128131814 & -0.0168128131813994 \tabularnewline
65 & 11.58 & 11.5161482827595 & 0.0638517172404924 \tabularnewline
66 & 11.63 & 11.6186720370021 & 0.0113279629979068 \tabularnewline
67 & 11.69 & 11.6691197774218 & 0.0208802225782048 \tabularnewline
68 & 11.74 & 11.7299450731632 & 0.0100549268368351 \tabularnewline
69 & 11.68 & 11.7803424965272 & -0.100342496527174 \tabularnewline
70 & 11.69 & 11.7163764355931 & -0.0263764355930824 \tabularnewline
71 & 11.71 & 11.7253339007309 & -0.0153339007309157 \tabularnewline
72 & 11.75 & 11.7447278246738 & 0.00527217532619595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204478&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]9.39[/C][C]9.34[/C][C]0.0500000000000025[/C][/ROW]
[ROW][C]4[/C][C]9.42[/C][C]9.44197626183888[/C][C]-0.0219762618388799[/C][/ROW]
[ROW][C]5[/C][C]9.42[/C][C]9.47110764488621[/C][C]-0.0511076448862102[/C][/ROW]
[ROW][C]6[/C][C]9.43[/C][C]9.46908760312094[/C][C]-0.0390876031209384[/C][/ROW]
[ROW][C]7[/C][C]9.5[/C][C]9.47754265635251[/C][C]0.0224573436474866[/C][/ROW]
[ROW][C]8[/C][C]9.53[/C][C]9.54843028817758[/C][C]-0.0184302881775782[/C][/ROW]
[ROW][C]9[/C][C]9.58[/C][C]9.57770182667348[/C][C]0.0022981733265226[/C][/ROW]
[ROW][C]10[/C][C]9.58[/C][C]9.62779266251836[/C][C]-0.0477926625183649[/C][/ROW]
[ROW][C]11[/C][C]9.6[/C][C]9.62590364621609[/C][C]-0.0259036462160953[/C][/ROW]
[ROW][C]12[/C][C]9.61[/C][C]9.644879798466[/C][C]-0.034879798466001[/C][/ROW]
[ROW][C]13[/C][C]9.65[/C][C]9.65350116617288[/C][C]-0.00350116617287632[/C][/ROW]
[ROW][C]14[/C][C]9.71[/C][C]9.6933627817509[/C][C]0.0166372182491035[/C][/ROW]
[ROW][C]15[/C][C]9.78[/C][C]9.75402037174151[/C][C]0.0259796282584848[/C][/ROW]
[ROW][C]16[/C][C]9.79[/C][C]9.82504722269982[/C][C]-0.0350472226998235[/C][/ROW]
[ROW][C]17[/C][C]9.84[/C][C]9.83366197292422[/C][C]0.00633802707578468[/C][/ROW]
[ROW][C]18[/C][C]9.87[/C][C]9.88391248494509[/C][C]-0.0139124849450898[/C][/ROW]
[ROW][C]19[/C][C]9.9[/C][C]9.91336259068347[/C][C]-0.0133625906834691[/C][/ROW]
[ROW][C]20[/C][C]9.95[/C][C]9.94283443112274[/C][C]0.00716556887725517[/C][/ROW]
[ROW][C]21[/C][C]9.96[/C][C]9.99311765192926[/C][C]-0.0331176519292615[/C][/ROW]
[ROW][C]22[/C][C]9.98[/C][C]10.0018086688952[/C][C]-0.0218086688952415[/C][/ROW]
[ROW][C]23[/C][C]10.01[/C][C]10.0209466760934[/C][C]-0.0109466760933525[/C][/ROW]
[ROW][C]24[/C][C]10[/C][C]10.0505140061288[/C][C]-0.0505140061288358[/C][/ROW]
[ROW][C]25[/C][C]10.03[/C][C]10.038517428076[/C][C]-0.00851742807600964[/C][/ROW]
[ROW][C]26[/C][C]10.05[/C][C]10.0681807747146[/C][C]-0.0181807747145672[/C][/ROW]
[ROW][C]27[/C][C]10.06[/C][C]10.0874621752892[/C][C]-0.0274621752891751[/C][/ROW]
[ROW][C]28[/C][C]10.09[/C][C]10.0963767263084[/C][C]-0.00637672630844222[/C][/ROW]
[ROW][C]29[/C][C]10.24[/C][C]10.1261246846912[/C][C]0.113875315308766[/C][/ROW]
[ROW][C]30[/C][C]10.23[/C][C]10.2806256334919[/C][C]-0.0506256334919364[/C][/ROW]
[ROW][C]31[/C][C]10.27[/C][C]10.2686246433412[/C][C]0.00137535665884592[/C][/ROW]
[ROW][C]32[/C][C]10.28[/C][C]10.3086790046387[/C][C]-0.0286790046387466[/C][/ROW]
[ROW][C]33[/C][C]10.29[/C][C]10.3175454601899[/C][C]-0.0275454601898559[/C][/ROW]
[ROW][C]34[/C][C]10.44[/C][C]10.3264567193537[/C][C]0.113543280646297[/C][/ROW]
[ROW][C]35[/C][C]10.51[/C][C]10.4809445444058[/C][C]0.0290554555942482[/C][/ROW]
[ROW][C]36[/C][C]10.52[/C][C]10.5520929681678[/C][C]-0.0320929681677971[/C][/ROW]
[ROW][C]37[/C][C]10.57[/C][C]10.5608244860021[/C][C]0.00917551399793304[/C][/ROW]
[ROW][C]38[/C][C]10.62[/C][C]10.6111871503654[/C][C]0.00881284963460693[/C][/ROW]
[ROW][C]39[/C][C]10.71[/C][C]10.6615354803339[/C][C]0.0484645196661155[/C][/ROW]
[ROW][C]40[/C][C]10.73[/C][C]10.753451051949[/C][C]-0.023451051949003[/C][/ROW]
[ROW][C]41[/C][C]10.74[/C][C]10.772524143568[/C][C]-0.0325241435680343[/C][/ROW]
[ROW][C]42[/C][C]10.75[/C][C]10.7812386190925[/C][C]-0.0312386190925196[/C][/ROW]
[ROW][C]43[/C][C]10.79[/C][C]10.7900039052763[/C][C]-3.90527628191251e-06[/C][/ROW]
[ROW][C]44[/C][C]10.81[/C][C]10.8300037509193[/C][C]-0.0200037509193098[/C][/ROW]
[ROW][C]45[/C][C]10.87[/C][C]10.8492130979278[/C][C]0.0207869020722118[/C][/ROW]
[ROW][C]46[/C][C]10.92[/C][C]10.9100347051541[/C][C]0.00996529484593722[/C][/ROW]
[ROW][C]47[/C][C]10.95[/C][C]10.9604285857924[/C][C]-0.0104285857924076[/C][/ROW]
[ROW][C]48[/C][C]10.94[/C][C]10.9900163934697[/C][C]-0.050016393469706[/C][/ROW]
[ROW][C]49[/C][C]10.97[/C][C]10.9780394836751[/C][C]-0.00803948367505392[/C][/ROW]
[ROW][C]50[/C][C]10.99[/C][C]11.0077217211792[/C][C]-0.01772172117923[/C][/ROW]
[ROW][C]51[/C][C]11.04[/C][C]11.0270212659535[/C][C]0.0129787340464844[/C][/ROW]
[ROW][C]52[/C][C]11.09[/C][C]11.0775342534898[/C][C]0.0124657465102267[/C][/ROW]
[ROW][C]53[/C][C]11.12[/C][C]11.1280269650722[/C][C]-0.00802696507220091[/C][/ROW]
[ROW][C]54[/C][C]11.11[/C][C]11.1577096973771[/C][C]-0.0477096973771154[/C][/ROW]
[ROW][C]55[/C][C]11.14[/C][C]11.1458239602917[/C][C]-0.00582396029169807[/C][/ROW]
[ROW][C]56[/C][C]11.2[/C][C]11.1755937668822[/C][C]0.0244062331178121[/C][/ROW]
[ROW][C]57[/C][C]11.25[/C][C]11.236558429025[/C][C]0.0134415709749849[/C][/ROW]
[ROW][C]58[/C][C]11.3[/C][C]11.2870897103005[/C][C]0.0129102896995352[/C][/ROW]
[ROW][C]59[/C][C]11.31[/C][C]11.3375999925577[/C][C]-0.0275999925577075[/C][/ROW]
[ROW][C]60[/C][C]11.31[/C][C]11.3465090963168[/C][C]-0.036509096316804[/C][/ROW]
[ROW][C]61[/C][C]11.33[/C][C]11.3450660656403[/C][C]-0.0150660656403474[/C][/ROW]
[ROW][C]62[/C][C]11.41[/C][C]11.3644705758286[/C][C]0.045529424171395[/C][/ROW]
[ROW][C]63[/C][C]11.46[/C][C]11.4462701370993[/C][C]0.0137298629006732[/C][/ROW]
[ROW][C]64[/C][C]11.48[/C][C]11.4968128131814[/C][C]-0.0168128131813994[/C][/ROW]
[ROW][C]65[/C][C]11.58[/C][C]11.5161482827595[/C][C]0.0638517172404924[/C][/ROW]
[ROW][C]66[/C][C]11.63[/C][C]11.6186720370021[/C][C]0.0113279629979068[/C][/ROW]
[ROW][C]67[/C][C]11.69[/C][C]11.6691197774218[/C][C]0.0208802225782048[/C][/ROW]
[ROW][C]68[/C][C]11.74[/C][C]11.7299450731632[/C][C]0.0100549268368351[/C][/ROW]
[ROW][C]69[/C][C]11.68[/C][C]11.7803424965272[/C][C]-0.100342496527174[/C][/ROW]
[ROW][C]70[/C][C]11.69[/C][C]11.7163764355931[/C][C]-0.0263764355930824[/C][/ROW]
[ROW][C]71[/C][C]11.71[/C][C]11.7253339007309[/C][C]-0.0153339007309157[/C][/ROW]
[ROW][C]72[/C][C]11.75[/C][C]11.7447278246738[/C][C]0.00527217532619595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204478&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204478&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
39.399.340.0500000000000025
49.429.44197626183888-0.0219762618388799
59.429.47110764488621-0.0511076448862102
69.439.46908760312094-0.0390876031209384
79.59.477542656352510.0224573436474866
89.539.54843028817758-0.0184302881775782
99.589.577701826673480.0022981733265226
109.589.62779266251836-0.0477926625183649
119.69.62590364621609-0.0259036462160953
129.619.644879798466-0.034879798466001
139.659.65350116617288-0.00350116617287632
149.719.69336278175090.0166372182491035
159.789.754020371741510.0259796282584848
169.799.82504722269982-0.0350472226998235
179.849.833661972924220.00633802707578468
189.879.88391248494509-0.0139124849450898
199.99.91336259068347-0.0133625906834691
209.959.942834431122740.00716556887725517
219.969.99311765192926-0.0331176519292615
229.9810.0018086688952-0.0218086688952415
2310.0110.0209466760934-0.0109466760933525
241010.0505140061288-0.0505140061288358
2510.0310.038517428076-0.00851742807600964
2610.0510.0681807747146-0.0181807747145672
2710.0610.0874621752892-0.0274621752891751
2810.0910.0963767263084-0.00637672630844222
2910.2410.12612468469120.113875315308766
3010.2310.2806256334919-0.0506256334919364
3110.2710.26862464334120.00137535665884592
3210.2810.3086790046387-0.0286790046387466
3310.2910.3175454601899-0.0275454601898559
3410.4410.32645671935370.113543280646297
3510.5110.48094454440580.0290554555942482
3610.5210.5520929681678-0.0320929681677971
3710.5710.56082448600210.00917551399793304
3810.6210.61118715036540.00881284963460693
3910.7110.66153548033390.0484645196661155
4010.7310.753451051949-0.023451051949003
4110.7410.772524143568-0.0325241435680343
4210.7510.7812386190925-0.0312386190925196
4310.7910.7900039052763-3.90527628191251e-06
4410.8110.8300037509193-0.0200037509193098
4510.8710.84921309792780.0207869020722118
4610.9210.91003470515410.00996529484593722
4710.9510.9604285857924-0.0104285857924076
4810.9410.9900163934697-0.050016393469706
4910.9710.9780394836751-0.00803948367505392
5010.9911.0077217211792-0.01772172117923
5111.0411.02702126595350.0129787340464844
5211.0911.07753425348980.0124657465102267
5311.1211.1280269650722-0.00802696507220091
5411.1111.1577096973771-0.0477096973771154
5511.1411.1458239602917-0.00582396029169807
5611.211.17559376688220.0244062331178121
5711.2511.2365584290250.0134415709749849
5811.311.28708971030050.0129102896995352
5911.3111.3375999925577-0.0275999925577075
6011.3111.3465090963168-0.036509096316804
6111.3311.3450660656403-0.0150660656403474
6211.4111.36447057582860.045529424171395
6311.4611.44627013709930.0137298629006732
6411.4811.4968128131814-0.0168128131813994
6511.5811.51614828275950.0638517172404924
6611.6311.61867203700210.0113279629979068
6711.6911.66911977742180.0208802225782048
6811.7411.72994507316320.0100549268368351
6911.6811.7803424965272-0.100342496527174
7011.6911.7163764355931-0.0263764355930824
7111.7111.7253339007309-0.0153339007309157
7211.7511.74472782467380.00527217532619595







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7311.784936208651911.716820721117411.8530516961865
7411.819872417303811.721620395977211.9181244386304
7511.854808625955711.7321068863211.9775103655914
7611.889744834607611.745311500372912.0341781688423
7711.924681043259511.76010956993612.089252516583
7811.959617251911411.775936662184912.143297841638
7911.994553460563311.792464736432112.1966421846945
8012.029489669215211.809484790361612.2494945480689
8112.064425877867111.826854964897712.3019967908365
8212.09936208651911.844474415021112.354249758017
8312.134298295170911.862268880128212.4063277102136
8412.169234503822811.880182141540212.4582868661055

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 11.7849362086519 & 11.7168207211174 & 11.8530516961865 \tabularnewline
74 & 11.8198724173038 & 11.7216203959772 & 11.9181244386304 \tabularnewline
75 & 11.8548086259557 & 11.73210688632 & 11.9775103655914 \tabularnewline
76 & 11.8897448346076 & 11.7453115003729 & 12.0341781688423 \tabularnewline
77 & 11.9246810432595 & 11.760109569936 & 12.089252516583 \tabularnewline
78 & 11.9596172519114 & 11.7759366621849 & 12.143297841638 \tabularnewline
79 & 11.9945534605633 & 11.7924647364321 & 12.1966421846945 \tabularnewline
80 & 12.0294896692152 & 11.8094847903616 & 12.2494945480689 \tabularnewline
81 & 12.0644258778671 & 11.8268549648977 & 12.3019967908365 \tabularnewline
82 & 12.099362086519 & 11.8444744150211 & 12.354249758017 \tabularnewline
83 & 12.1342982951709 & 11.8622688801282 & 12.4063277102136 \tabularnewline
84 & 12.1692345038228 & 11.8801821415402 & 12.4582868661055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204478&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]11.7849362086519[/C][C]11.7168207211174[/C][C]11.8530516961865[/C][/ROW]
[ROW][C]74[/C][C]11.8198724173038[/C][C]11.7216203959772[/C][C]11.9181244386304[/C][/ROW]
[ROW][C]75[/C][C]11.8548086259557[/C][C]11.73210688632[/C][C]11.9775103655914[/C][/ROW]
[ROW][C]76[/C][C]11.8897448346076[/C][C]11.7453115003729[/C][C]12.0341781688423[/C][/ROW]
[ROW][C]77[/C][C]11.9246810432595[/C][C]11.760109569936[/C][C]12.089252516583[/C][/ROW]
[ROW][C]78[/C][C]11.9596172519114[/C][C]11.7759366621849[/C][C]12.143297841638[/C][/ROW]
[ROW][C]79[/C][C]11.9945534605633[/C][C]11.7924647364321[/C][C]12.1966421846945[/C][/ROW]
[ROW][C]80[/C][C]12.0294896692152[/C][C]11.8094847903616[/C][C]12.2494945480689[/C][/ROW]
[ROW][C]81[/C][C]12.0644258778671[/C][C]11.8268549648977[/C][C]12.3019967908365[/C][/ROW]
[ROW][C]82[/C][C]12.099362086519[/C][C]11.8444744150211[/C][C]12.354249758017[/C][/ROW]
[ROW][C]83[/C][C]12.1342982951709[/C][C]11.8622688801282[/C][C]12.4063277102136[/C][/ROW]
[ROW][C]84[/C][C]12.1692345038228[/C][C]11.8801821415402[/C][C]12.4582868661055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204478&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204478&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
7311.784936208651911.716820721117411.8530516961865
7411.819872417303811.721620395977211.9181244386304
7511.854808625955711.7321068863211.9775103655914
7611.889744834607611.745311500372912.0341781688423
7711.924681043259511.76010956993612.089252516583
7811.959617251911411.775936662184912.143297841638
7911.994553460563311.792464736432112.1966421846945
8012.029489669215211.809484790361612.2494945480689
8112.064425877867111.826854964897712.3019967908365
8212.09936208651911.844474415021112.354249758017
8312.134298295170911.862268880128212.4063277102136
8412.169234503822811.880182141540212.4582868661055



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=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')