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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 27 May 2013 05:01:33 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/27/t1369645373ve0quzpfr88fz53.htm/, Retrieved Thu, 02 May 2024 11:49:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210745, Retrieved Thu, 02 May 2024 11:49:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-27 09:01:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
13.29
13.34
13.41
13.45
13.52
13.52
13.53
13.55
13.52
13.51
13.55
13.56
13.62
13.69
13.67
13.66
13.69
13.69
13.7
13.73
13.79
13.8
13.84
13.84
13.88
13.97
14.06
14.11
14.13
14.15
14.2
14.28
14.3
14.33
14.4
14.4
14.42
14.51
14.64
14.68
14.72
14.73
14.76
14.78
14.83
14.84
14.85
14.87
14.87
14.96
15.08
15.08
15.12
15.12
15.1
15.16
15.22
15.28
15.29
15.32
15.4
15.44
15.48
15.52
15.6
15.61
15.66
15.69
15.75
15.82
15.81
15.82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210745&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210745&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210745&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0519842302842752
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0519842302842752 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210745&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]0.0519842302842752[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210745&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210745&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
beta0.0519842302842752
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
313.4113.390.0199999999999996
413.4513.4610396846057-0.0110396846056862
513.5213.50046579509890.019534204901122
613.5213.5714812657049-0.0514812657048793
713.5313.5688050517332-0.0388050517331511
813.5513.5767878009877-0.026787800987659
913.5213.5953952577723-0.0753952577723105
1013.5113.5614758933299-0.0514758933299309
1113.5513.5487999586370.00120004136302221
1213.5613.5888623418635-0.0288623418635456
1313.6213.59736195523760.0226380447624326
1413.6913.65853877656970.031461223430318
1513.6713.7301742640535-0.0601742640535097
1613.6613.7070461512538-0.047046151253765
1713.6913.694600493293-0.00460049329300105
1813.6913.7243613401902-0.0343613401902356
1913.713.7225750923689-0.0225750923689105
2013.7313.7314015435685-0.00140154356851596
2113.7913.76132868540490.0286713145951012
2213.813.8228191416254-0.0228191416253605
2313.8413.83163290611220.00836709388777912
2413.8413.8720678630477-0.0320678630476916
2513.8813.87040083987030.00959916012970474
2613.9713.9108998448210.0591001551789851
2714.0614.00397212089770.0560278791023254
2814.1114.09688468706730.0131153129327295
2914.1314.147566476515-0.0175664765150145
3014.1514.1666532967546-0.0166532967545763
3114.214.18578758794110.0142124120589049
3214.2814.23652640924250.0434735907575412
3314.314.3187863503957-0.0187863503956809
3414.3314.3378097564305-0.00780975643051285
3514.414.36740377225380.0325962277462359
3614.414.4390982620633-0.0390982620633231
3714.4214.4370657690045-0.0170657690045086
3814.5114.45617861813860.0538213818614004
3914.6414.54897648124750.0910235187525004
4014.6814.6837082688076-0.00370826880761754
4114.7214.723515497308-0.00351549730796386
4214.7314.7633327468863-0.0333327468863445
4314.7614.7715999696962-0.0115999696961975
4414.7814.8009969542002-0.0209969542002195
4514.8314.81990544369780.0100945563021941
4614.8414.8704302014372-0.0304302014372375
4714.8514.8788483108381-0.0288483108381268
4814.8714.8873486536042-0.0173486536042056
4914.8714.9064467972001-0.0364467972001226
5014.9614.90455213850130.0554478614986547
5115.0814.99743455290230.0825654470977355
5215.0815.1217266541177-0.041726654117717
5315.1215.11955752612110.000442473878930372
5415.1215.1595805277851-0.0395805277850858
5515.115.1575229645139-0.0575229645139324
5615.1615.134532677480.0254673225199937
5715.2215.19585657663860.0241434233613909
5815.2815.25711165391850.022888346081519
5915.2915.318301486972-0.0283014869720066
6015.3215.3268302559559-0.00683025595586528
6115.415.35647519035740.0435248096426442
6215.4415.43873779408490.00126220591510062
6315.4815.47880340888790.00119659111214609
6415.5215.51886561275580.001134387244214
6515.615.55892458300350.0410754169964793
6615.6115.6410598569397-0.031059856939688
6715.6615.64944523418390.0105547658160621
6815.6915.6999939155607-0.00999391556071849
6915.7515.72947438955280.0205256104472333
7015.8215.7905413976130.0294586023870185
7115.8115.8620727803833-0.0520727803833214
7215.8215.8493658169763-0.0293658169763322

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 13.41 & 13.39 & 0.0199999999999996 \tabularnewline
4 & 13.45 & 13.4610396846057 & -0.0110396846056862 \tabularnewline
5 & 13.52 & 13.5004657950989 & 0.019534204901122 \tabularnewline
6 & 13.52 & 13.5714812657049 & -0.0514812657048793 \tabularnewline
7 & 13.53 & 13.5688050517332 & -0.0388050517331511 \tabularnewline
8 & 13.55 & 13.5767878009877 & -0.026787800987659 \tabularnewline
9 & 13.52 & 13.5953952577723 & -0.0753952577723105 \tabularnewline
10 & 13.51 & 13.5614758933299 & -0.0514758933299309 \tabularnewline
11 & 13.55 & 13.548799958637 & 0.00120004136302221 \tabularnewline
12 & 13.56 & 13.5888623418635 & -0.0288623418635456 \tabularnewline
13 & 13.62 & 13.5973619552376 & 0.0226380447624326 \tabularnewline
14 & 13.69 & 13.6585387765697 & 0.031461223430318 \tabularnewline
15 & 13.67 & 13.7301742640535 & -0.0601742640535097 \tabularnewline
16 & 13.66 & 13.7070461512538 & -0.047046151253765 \tabularnewline
17 & 13.69 & 13.694600493293 & -0.00460049329300105 \tabularnewline
18 & 13.69 & 13.7243613401902 & -0.0343613401902356 \tabularnewline
19 & 13.7 & 13.7225750923689 & -0.0225750923689105 \tabularnewline
20 & 13.73 & 13.7314015435685 & -0.00140154356851596 \tabularnewline
21 & 13.79 & 13.7613286854049 & 0.0286713145951012 \tabularnewline
22 & 13.8 & 13.8228191416254 & -0.0228191416253605 \tabularnewline
23 & 13.84 & 13.8316329061122 & 0.00836709388777912 \tabularnewline
24 & 13.84 & 13.8720678630477 & -0.0320678630476916 \tabularnewline
25 & 13.88 & 13.8704008398703 & 0.00959916012970474 \tabularnewline
26 & 13.97 & 13.910899844821 & 0.0591001551789851 \tabularnewline
27 & 14.06 & 14.0039721208977 & 0.0560278791023254 \tabularnewline
28 & 14.11 & 14.0968846870673 & 0.0131153129327295 \tabularnewline
29 & 14.13 & 14.147566476515 & -0.0175664765150145 \tabularnewline
30 & 14.15 & 14.1666532967546 & -0.0166532967545763 \tabularnewline
31 & 14.2 & 14.1857875879411 & 0.0142124120589049 \tabularnewline
32 & 14.28 & 14.2365264092425 & 0.0434735907575412 \tabularnewline
33 & 14.3 & 14.3187863503957 & -0.0187863503956809 \tabularnewline
34 & 14.33 & 14.3378097564305 & -0.00780975643051285 \tabularnewline
35 & 14.4 & 14.3674037722538 & 0.0325962277462359 \tabularnewline
36 & 14.4 & 14.4390982620633 & -0.0390982620633231 \tabularnewline
37 & 14.42 & 14.4370657690045 & -0.0170657690045086 \tabularnewline
38 & 14.51 & 14.4561786181386 & 0.0538213818614004 \tabularnewline
39 & 14.64 & 14.5489764812475 & 0.0910235187525004 \tabularnewline
40 & 14.68 & 14.6837082688076 & -0.00370826880761754 \tabularnewline
41 & 14.72 & 14.723515497308 & -0.00351549730796386 \tabularnewline
42 & 14.73 & 14.7633327468863 & -0.0333327468863445 \tabularnewline
43 & 14.76 & 14.7715999696962 & -0.0115999696961975 \tabularnewline
44 & 14.78 & 14.8009969542002 & -0.0209969542002195 \tabularnewline
45 & 14.83 & 14.8199054436978 & 0.0100945563021941 \tabularnewline
46 & 14.84 & 14.8704302014372 & -0.0304302014372375 \tabularnewline
47 & 14.85 & 14.8788483108381 & -0.0288483108381268 \tabularnewline
48 & 14.87 & 14.8873486536042 & -0.0173486536042056 \tabularnewline
49 & 14.87 & 14.9064467972001 & -0.0364467972001226 \tabularnewline
50 & 14.96 & 14.9045521385013 & 0.0554478614986547 \tabularnewline
51 & 15.08 & 14.9974345529023 & 0.0825654470977355 \tabularnewline
52 & 15.08 & 15.1217266541177 & -0.041726654117717 \tabularnewline
53 & 15.12 & 15.1195575261211 & 0.000442473878930372 \tabularnewline
54 & 15.12 & 15.1595805277851 & -0.0395805277850858 \tabularnewline
55 & 15.1 & 15.1575229645139 & -0.0575229645139324 \tabularnewline
56 & 15.16 & 15.13453267748 & 0.0254673225199937 \tabularnewline
57 & 15.22 & 15.1958565766386 & 0.0241434233613909 \tabularnewline
58 & 15.28 & 15.2571116539185 & 0.022888346081519 \tabularnewline
59 & 15.29 & 15.318301486972 & -0.0283014869720066 \tabularnewline
60 & 15.32 & 15.3268302559559 & -0.00683025595586528 \tabularnewline
61 & 15.4 & 15.3564751903574 & 0.0435248096426442 \tabularnewline
62 & 15.44 & 15.4387377940849 & 0.00126220591510062 \tabularnewline
63 & 15.48 & 15.4788034088879 & 0.00119659111214609 \tabularnewline
64 & 15.52 & 15.5188656127558 & 0.001134387244214 \tabularnewline
65 & 15.6 & 15.5589245830035 & 0.0410754169964793 \tabularnewline
66 & 15.61 & 15.6410598569397 & -0.031059856939688 \tabularnewline
67 & 15.66 & 15.6494452341839 & 0.0105547658160621 \tabularnewline
68 & 15.69 & 15.6999939155607 & -0.00999391556071849 \tabularnewline
69 & 15.75 & 15.7294743895528 & 0.0205256104472333 \tabularnewline
70 & 15.82 & 15.790541397613 & 0.0294586023870185 \tabularnewline
71 & 15.81 & 15.8620727803833 & -0.0520727803833214 \tabularnewline
72 & 15.82 & 15.8493658169763 & -0.0293658169763322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210745&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]13.41[/C][C]13.39[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]4[/C][C]13.45[/C][C]13.4610396846057[/C][C]-0.0110396846056862[/C][/ROW]
[ROW][C]5[/C][C]13.52[/C][C]13.5004657950989[/C][C]0.019534204901122[/C][/ROW]
[ROW][C]6[/C][C]13.52[/C][C]13.5714812657049[/C][C]-0.0514812657048793[/C][/ROW]
[ROW][C]7[/C][C]13.53[/C][C]13.5688050517332[/C][C]-0.0388050517331511[/C][/ROW]
[ROW][C]8[/C][C]13.55[/C][C]13.5767878009877[/C][C]-0.026787800987659[/C][/ROW]
[ROW][C]9[/C][C]13.52[/C][C]13.5953952577723[/C][C]-0.0753952577723105[/C][/ROW]
[ROW][C]10[/C][C]13.51[/C][C]13.5614758933299[/C][C]-0.0514758933299309[/C][/ROW]
[ROW][C]11[/C][C]13.55[/C][C]13.548799958637[/C][C]0.00120004136302221[/C][/ROW]
[ROW][C]12[/C][C]13.56[/C][C]13.5888623418635[/C][C]-0.0288623418635456[/C][/ROW]
[ROW][C]13[/C][C]13.62[/C][C]13.5973619552376[/C][C]0.0226380447624326[/C][/ROW]
[ROW][C]14[/C][C]13.69[/C][C]13.6585387765697[/C][C]0.031461223430318[/C][/ROW]
[ROW][C]15[/C][C]13.67[/C][C]13.7301742640535[/C][C]-0.0601742640535097[/C][/ROW]
[ROW][C]16[/C][C]13.66[/C][C]13.7070461512538[/C][C]-0.047046151253765[/C][/ROW]
[ROW][C]17[/C][C]13.69[/C][C]13.694600493293[/C][C]-0.00460049329300105[/C][/ROW]
[ROW][C]18[/C][C]13.69[/C][C]13.7243613401902[/C][C]-0.0343613401902356[/C][/ROW]
[ROW][C]19[/C][C]13.7[/C][C]13.7225750923689[/C][C]-0.0225750923689105[/C][/ROW]
[ROW][C]20[/C][C]13.73[/C][C]13.7314015435685[/C][C]-0.00140154356851596[/C][/ROW]
[ROW][C]21[/C][C]13.79[/C][C]13.7613286854049[/C][C]0.0286713145951012[/C][/ROW]
[ROW][C]22[/C][C]13.8[/C][C]13.8228191416254[/C][C]-0.0228191416253605[/C][/ROW]
[ROW][C]23[/C][C]13.84[/C][C]13.8316329061122[/C][C]0.00836709388777912[/C][/ROW]
[ROW][C]24[/C][C]13.84[/C][C]13.8720678630477[/C][C]-0.0320678630476916[/C][/ROW]
[ROW][C]25[/C][C]13.88[/C][C]13.8704008398703[/C][C]0.00959916012970474[/C][/ROW]
[ROW][C]26[/C][C]13.97[/C][C]13.910899844821[/C][C]0.0591001551789851[/C][/ROW]
[ROW][C]27[/C][C]14.06[/C][C]14.0039721208977[/C][C]0.0560278791023254[/C][/ROW]
[ROW][C]28[/C][C]14.11[/C][C]14.0968846870673[/C][C]0.0131153129327295[/C][/ROW]
[ROW][C]29[/C][C]14.13[/C][C]14.147566476515[/C][C]-0.0175664765150145[/C][/ROW]
[ROW][C]30[/C][C]14.15[/C][C]14.1666532967546[/C][C]-0.0166532967545763[/C][/ROW]
[ROW][C]31[/C][C]14.2[/C][C]14.1857875879411[/C][C]0.0142124120589049[/C][/ROW]
[ROW][C]32[/C][C]14.28[/C][C]14.2365264092425[/C][C]0.0434735907575412[/C][/ROW]
[ROW][C]33[/C][C]14.3[/C][C]14.3187863503957[/C][C]-0.0187863503956809[/C][/ROW]
[ROW][C]34[/C][C]14.33[/C][C]14.3378097564305[/C][C]-0.00780975643051285[/C][/ROW]
[ROW][C]35[/C][C]14.4[/C][C]14.3674037722538[/C][C]0.0325962277462359[/C][/ROW]
[ROW][C]36[/C][C]14.4[/C][C]14.4390982620633[/C][C]-0.0390982620633231[/C][/ROW]
[ROW][C]37[/C][C]14.42[/C][C]14.4370657690045[/C][C]-0.0170657690045086[/C][/ROW]
[ROW][C]38[/C][C]14.51[/C][C]14.4561786181386[/C][C]0.0538213818614004[/C][/ROW]
[ROW][C]39[/C][C]14.64[/C][C]14.5489764812475[/C][C]0.0910235187525004[/C][/ROW]
[ROW][C]40[/C][C]14.68[/C][C]14.6837082688076[/C][C]-0.00370826880761754[/C][/ROW]
[ROW][C]41[/C][C]14.72[/C][C]14.723515497308[/C][C]-0.00351549730796386[/C][/ROW]
[ROW][C]42[/C][C]14.73[/C][C]14.7633327468863[/C][C]-0.0333327468863445[/C][/ROW]
[ROW][C]43[/C][C]14.76[/C][C]14.7715999696962[/C][C]-0.0115999696961975[/C][/ROW]
[ROW][C]44[/C][C]14.78[/C][C]14.8009969542002[/C][C]-0.0209969542002195[/C][/ROW]
[ROW][C]45[/C][C]14.83[/C][C]14.8199054436978[/C][C]0.0100945563021941[/C][/ROW]
[ROW][C]46[/C][C]14.84[/C][C]14.8704302014372[/C][C]-0.0304302014372375[/C][/ROW]
[ROW][C]47[/C][C]14.85[/C][C]14.8788483108381[/C][C]-0.0288483108381268[/C][/ROW]
[ROW][C]48[/C][C]14.87[/C][C]14.8873486536042[/C][C]-0.0173486536042056[/C][/ROW]
[ROW][C]49[/C][C]14.87[/C][C]14.9064467972001[/C][C]-0.0364467972001226[/C][/ROW]
[ROW][C]50[/C][C]14.96[/C][C]14.9045521385013[/C][C]0.0554478614986547[/C][/ROW]
[ROW][C]51[/C][C]15.08[/C][C]14.9974345529023[/C][C]0.0825654470977355[/C][/ROW]
[ROW][C]52[/C][C]15.08[/C][C]15.1217266541177[/C][C]-0.041726654117717[/C][/ROW]
[ROW][C]53[/C][C]15.12[/C][C]15.1195575261211[/C][C]0.000442473878930372[/C][/ROW]
[ROW][C]54[/C][C]15.12[/C][C]15.1595805277851[/C][C]-0.0395805277850858[/C][/ROW]
[ROW][C]55[/C][C]15.1[/C][C]15.1575229645139[/C][C]-0.0575229645139324[/C][/ROW]
[ROW][C]56[/C][C]15.16[/C][C]15.13453267748[/C][C]0.0254673225199937[/C][/ROW]
[ROW][C]57[/C][C]15.22[/C][C]15.1958565766386[/C][C]0.0241434233613909[/C][/ROW]
[ROW][C]58[/C][C]15.28[/C][C]15.2571116539185[/C][C]0.022888346081519[/C][/ROW]
[ROW][C]59[/C][C]15.29[/C][C]15.318301486972[/C][C]-0.0283014869720066[/C][/ROW]
[ROW][C]60[/C][C]15.32[/C][C]15.3268302559559[/C][C]-0.00683025595586528[/C][/ROW]
[ROW][C]61[/C][C]15.4[/C][C]15.3564751903574[/C][C]0.0435248096426442[/C][/ROW]
[ROW][C]62[/C][C]15.44[/C][C]15.4387377940849[/C][C]0.00126220591510062[/C][/ROW]
[ROW][C]63[/C][C]15.48[/C][C]15.4788034088879[/C][C]0.00119659111214609[/C][/ROW]
[ROW][C]64[/C][C]15.52[/C][C]15.5188656127558[/C][C]0.001134387244214[/C][/ROW]
[ROW][C]65[/C][C]15.6[/C][C]15.5589245830035[/C][C]0.0410754169964793[/C][/ROW]
[ROW][C]66[/C][C]15.61[/C][C]15.6410598569397[/C][C]-0.031059856939688[/C][/ROW]
[ROW][C]67[/C][C]15.66[/C][C]15.6494452341839[/C][C]0.0105547658160621[/C][/ROW]
[ROW][C]68[/C][C]15.69[/C][C]15.6999939155607[/C][C]-0.00999391556071849[/C][/ROW]
[ROW][C]69[/C][C]15.75[/C][C]15.7294743895528[/C][C]0.0205256104472333[/C][/ROW]
[ROW][C]70[/C][C]15.82[/C][C]15.790541397613[/C][C]0.0294586023870185[/C][/ROW]
[ROW][C]71[/C][C]15.81[/C][C]15.8620727803833[/C][C]-0.0520727803833214[/C][/ROW]
[ROW][C]72[/C][C]15.82[/C][C]15.8493658169763[/C][C]-0.0293658169763322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210745&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210745&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
313.4113.390.0199999999999996
413.4513.4610396846057-0.0110396846056862
513.5213.50046579509890.019534204901122
613.5213.5714812657049-0.0514812657048793
713.5313.5688050517332-0.0388050517331511
813.5513.5767878009877-0.026787800987659
913.5213.5953952577723-0.0753952577723105
1013.5113.5614758933299-0.0514758933299309
1113.5513.5487999586370.00120004136302221
1213.5613.5888623418635-0.0288623418635456
1313.6213.59736195523760.0226380447624326
1413.6913.65853877656970.031461223430318
1513.6713.7301742640535-0.0601742640535097
1613.6613.7070461512538-0.047046151253765
1713.6913.694600493293-0.00460049329300105
1813.6913.7243613401902-0.0343613401902356
1913.713.7225750923689-0.0225750923689105
2013.7313.7314015435685-0.00140154356851596
2113.7913.76132868540490.0286713145951012
2213.813.8228191416254-0.0228191416253605
2313.8413.83163290611220.00836709388777912
2413.8413.8720678630477-0.0320678630476916
2513.8813.87040083987030.00959916012970474
2613.9713.9108998448210.0591001551789851
2714.0614.00397212089770.0560278791023254
2814.1114.09688468706730.0131153129327295
2914.1314.147566476515-0.0175664765150145
3014.1514.1666532967546-0.0166532967545763
3114.214.18578758794110.0142124120589049
3214.2814.23652640924250.0434735907575412
3314.314.3187863503957-0.0187863503956809
3414.3314.3378097564305-0.00780975643051285
3514.414.36740377225380.0325962277462359
3614.414.4390982620633-0.0390982620633231
3714.4214.4370657690045-0.0170657690045086
3814.5114.45617861813860.0538213818614004
3914.6414.54897648124750.0910235187525004
4014.6814.6837082688076-0.00370826880761754
4114.7214.723515497308-0.00351549730796386
4214.7314.7633327468863-0.0333327468863445
4314.7614.7715999696962-0.0115999696961975
4414.7814.8009969542002-0.0209969542002195
4514.8314.81990544369780.0100945563021941
4614.8414.8704302014372-0.0304302014372375
4714.8514.8788483108381-0.0288483108381268
4814.8714.8873486536042-0.0173486536042056
4914.8714.9064467972001-0.0364467972001226
5014.9614.90455213850130.0554478614986547
5115.0814.99743455290230.0825654470977355
5215.0815.1217266541177-0.041726654117717
5315.1215.11955752612110.000442473878930372
5415.1215.1595805277851-0.0395805277850858
5515.115.1575229645139-0.0575229645139324
5615.1615.134532677480.0254673225199937
5715.2215.19585657663860.0241434233613909
5815.2815.25711165391850.022888346081519
5915.2915.318301486972-0.0283014869720066
6015.3215.3268302559559-0.00683025595586528
6115.415.35647519035740.0435248096426442
6215.4415.43873779408490.00126220591510062
6315.4815.47880340888790.00119659111214609
6415.5215.51886561275580.001134387244214
6515.615.55892458300350.0410754169964793
6615.6115.6410598569397-0.031059856939688
6715.6615.64944523418390.0105547658160621
6815.6915.6999939155607-0.00999391556071849
6915.7515.72947438955280.0205256104472333
7015.8215.7905413976130.0294586023870185
7115.8115.8620727803833-0.0520727803833214
7215.8215.8493658169763-0.0293658169763322







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7315.857839257584115.78959815726815.9260803579003
7415.895678515168315.796630823025715.9947262073109
7515.933517772752415.809075169117716.0579603763872
7615.971357030336615.824018761124716.1186952995485
7716.009196287920715.840366710524516.178025865317
7816.047035545504915.857573907045116.2364971839647
7916.08487480308915.875326256764616.2944233494135
8016.122714060673215.89342551403316.3520026073134
8116.160553318257315.911738498624116.4093681378906
8216.198392575841515.930171598337816.4666135533452
8316.236231833425615.948656727597116.5238069392541
8416.274071091009815.967143038223916.5809991437957

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 15.8578392575841 & 15.789598157268 & 15.9260803579003 \tabularnewline
74 & 15.8956785151683 & 15.7966308230257 & 15.9947262073109 \tabularnewline
75 & 15.9335177727524 & 15.8090751691177 & 16.0579603763872 \tabularnewline
76 & 15.9713570303366 & 15.8240187611247 & 16.1186952995485 \tabularnewline
77 & 16.0091962879207 & 15.8403667105245 & 16.178025865317 \tabularnewline
78 & 16.0470355455049 & 15.8575739070451 & 16.2364971839647 \tabularnewline
79 & 16.084874803089 & 15.8753262567646 & 16.2944233494135 \tabularnewline
80 & 16.1227140606732 & 15.893425514033 & 16.3520026073134 \tabularnewline
81 & 16.1605533182573 & 15.9117384986241 & 16.4093681378906 \tabularnewline
82 & 16.1983925758415 & 15.9301715983378 & 16.4666135533452 \tabularnewline
83 & 16.2362318334256 & 15.9486567275971 & 16.5238069392541 \tabularnewline
84 & 16.2740710910098 & 15.9671430382239 & 16.5809991437957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210745&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]15.8578392575841[/C][C]15.789598157268[/C][C]15.9260803579003[/C][/ROW]
[ROW][C]74[/C][C]15.8956785151683[/C][C]15.7966308230257[/C][C]15.9947262073109[/C][/ROW]
[ROW][C]75[/C][C]15.9335177727524[/C][C]15.8090751691177[/C][C]16.0579603763872[/C][/ROW]
[ROW][C]76[/C][C]15.9713570303366[/C][C]15.8240187611247[/C][C]16.1186952995485[/C][/ROW]
[ROW][C]77[/C][C]16.0091962879207[/C][C]15.8403667105245[/C][C]16.178025865317[/C][/ROW]
[ROW][C]78[/C][C]16.0470355455049[/C][C]15.8575739070451[/C][C]16.2364971839647[/C][/ROW]
[ROW][C]79[/C][C]16.084874803089[/C][C]15.8753262567646[/C][C]16.2944233494135[/C][/ROW]
[ROW][C]80[/C][C]16.1227140606732[/C][C]15.893425514033[/C][C]16.3520026073134[/C][/ROW]
[ROW][C]81[/C][C]16.1605533182573[/C][C]15.9117384986241[/C][C]16.4093681378906[/C][/ROW]
[ROW][C]82[/C][C]16.1983925758415[/C][C]15.9301715983378[/C][C]16.4666135533452[/C][/ROW]
[ROW][C]83[/C][C]16.2362318334256[/C][C]15.9486567275971[/C][C]16.5238069392541[/C][/ROW]
[ROW][C]84[/C][C]16.2740710910098[/C][C]15.9671430382239[/C][C]16.5809991437957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210745&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210745&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
7315.857839257584115.78959815726815.9260803579003
7415.895678515168315.796630823025715.9947262073109
7515.933517772752415.809075169117716.0579603763872
7615.971357030336615.824018761124716.1186952995485
7716.009196287920715.840366710524516.178025865317
7816.047035545504915.857573907045116.2364971839647
7916.08487480308915.875326256764616.2944233494135
8016.122714060673215.89342551403316.3520026073134
8116.160553318257315.911738498624116.4093681378906
8216.198392575841515.930171598337816.4666135533452
8316.236231833425615.948656727597116.5238069392541
8416.274071091009815.967143038223916.5809991437957



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')