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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 01 Jun 2008 13:15:45 -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/Jun/01/t1212347820cglus0onknj8e1j.htm/, Retrieved Sat, 18 May 2024 17:20:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13741, Retrieved Sat, 18 May 2024 17:20:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2008-06-01 19:15:45] [0344071b671470f3024f96efc0c7614f] [Current]
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Dataseries X:
12.23
12.25
12.33
12.37
12.38
12.41
12.41
12.41
12.43
12.44
12.46
12.46
12.46
12.47
12.55
12.58
12.6
12.62
12.62
12.66
12.7
12.76
12.79
12.81
12.86
13.03
13.09
13.15
13.17
13.18
13.18
13.19
13.19
13.19
13.25
13.24
13.3
13.35
13.35
13.35
13.36
13.37
13.38
13.39
13.4
13.4
13.44
13.44
13.44
13.47
13.52
13.58
13.65
13.66
13.68
13.68
13.77
13.78
13.79
13.79
13.82
13.86
13.94
14
14.02
14.03
14.07
14.1
14.1
14.16
14.17
14.17




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=13741&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=13741&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13741&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
alpha0.851663547967142
beta0.000749903072261239
gamma0.086671636330431

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.851663547967142 \tabularnewline
beta & 0.000749903072261239 \tabularnewline
gamma & 0.086671636330431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13741&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]0.851663547967142[/C][/ROW]
[ROW][C]beta[/C][C]0.000749903072261239[/C][/ROW]
[ROW][C]gamma[/C][C]0.086671636330431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13741&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13741&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
alpha0.851663547967142
beta0.000749903072261239
gamma0.086671636330431







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1312.4612.30156527777780.158434722222218
1412.4712.46040062911270.0095993708872566
1512.5512.5599844678501-0.00998446785011176
1612.5812.5899664216077-0.00996642160766292
1712.612.6074573794863-0.00745737948631842
1812.6212.6258304343119-0.00583043431194064
1912.6212.6226687086755-0.00266870867547553
2012.6612.65344800510110.00655199489886016
2112.712.68625108984490.0137489101551065
2212.7612.74477563925280.0152243607472329
2312.7912.77331649941480.0166835005851702
2412.8112.79352737762470.0164726223753302
2512.8612.8714394383643-0.0114394383642846
2613.0312.88370540472010.146294595279945
2713.0913.0995628612762-0.00956286127619954
2813.1513.13001144214170.0199885578582677
2913.1713.1731726811148-0.00317268111482605
3013.1813.1953449701131-0.0153449701130537
3113.1813.1842438293142-0.00424382931419842
3213.1913.2139223127206-0.0239223127205879
3313.1913.2209667184886-0.0309667184885694
3413.1913.2415016582464-0.0515016582464494
3513.2513.21326463634030.0367353636596892
3613.2413.2505945271423-0.0105945271423096
3713.313.30512262619-0.00512262619001014
3813.3513.32482733915400.0251726608460299
3913.3513.4354795421219-0.0854795421218633
4013.3513.4015577716172-0.051557771617194
4113.3613.3833473304182-0.0233473304182468
4213.3713.3880277219281-0.0180277219280764
4313.3813.37462939805350.0053706019465185
4413.3913.4120941811757-0.0220941811757420
4513.413.4204571773973-0.0204571773973008
4613.413.4495376178412-0.0495376178411657
4713.4413.42396789313220.0160321068677813
4813.4413.4429040233725-0.00290402337246576
4913.4413.5039040539385-0.0639040539385398
5013.4713.4737505791643-0.00375057916429888
5113.5213.5581431519462-0.0381431519462136
5213.5813.56479825496910.0152017450309465
5313.6513.60367586501070.0463241349892645
5413.6613.6676745076739-0.00767450767387956
5513.6813.66331428509660.0166857149033515
5613.6813.7099896854053-0.0299896854052601
5713.7713.71157142279590.0584285772040527
5813.7813.8074345000235-0.0274345000235154
5913.7913.8015187024960-0.0115187024959535
6013.7913.7967162695329-0.00671626953291415
6113.8213.8536517739228-0.0336517739228146
6213.8613.85002222694830.00997777305167347
6313.9413.9456591311541-0.00565913115410943
641413.98068083356520.0193191664347605
6514.0214.0234831689078-0.00348316890775102
6614.0314.0443546398909-0.0143546398909251
6714.0714.03460024500260.0353997549973695
6814.114.09660744193010.00339255806985683
6914.114.1277715103394-0.0277715103394236
7014.1614.14907729425790.0109227057421055
7114.1714.1760181336931-0.00601813369305049
7214.1714.1759501710322-0.0059501710322305

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 12.46 & 12.3015652777778 & 0.158434722222218 \tabularnewline
14 & 12.47 & 12.4604006291127 & 0.0095993708872566 \tabularnewline
15 & 12.55 & 12.5599844678501 & -0.00998446785011176 \tabularnewline
16 & 12.58 & 12.5899664216077 & -0.00996642160766292 \tabularnewline
17 & 12.6 & 12.6074573794863 & -0.00745737948631842 \tabularnewline
18 & 12.62 & 12.6258304343119 & -0.00583043431194064 \tabularnewline
19 & 12.62 & 12.6226687086755 & -0.00266870867547553 \tabularnewline
20 & 12.66 & 12.6534480051011 & 0.00655199489886016 \tabularnewline
21 & 12.7 & 12.6862510898449 & 0.0137489101551065 \tabularnewline
22 & 12.76 & 12.7447756392528 & 0.0152243607472329 \tabularnewline
23 & 12.79 & 12.7733164994148 & 0.0166835005851702 \tabularnewline
24 & 12.81 & 12.7935273776247 & 0.0164726223753302 \tabularnewline
25 & 12.86 & 12.8714394383643 & -0.0114394383642846 \tabularnewline
26 & 13.03 & 12.8837054047201 & 0.146294595279945 \tabularnewline
27 & 13.09 & 13.0995628612762 & -0.00956286127619954 \tabularnewline
28 & 13.15 & 13.1300114421417 & 0.0199885578582677 \tabularnewline
29 & 13.17 & 13.1731726811148 & -0.00317268111482605 \tabularnewline
30 & 13.18 & 13.1953449701131 & -0.0153449701130537 \tabularnewline
31 & 13.18 & 13.1842438293142 & -0.00424382931419842 \tabularnewline
32 & 13.19 & 13.2139223127206 & -0.0239223127205879 \tabularnewline
33 & 13.19 & 13.2209667184886 & -0.0309667184885694 \tabularnewline
34 & 13.19 & 13.2415016582464 & -0.0515016582464494 \tabularnewline
35 & 13.25 & 13.2132646363403 & 0.0367353636596892 \tabularnewline
36 & 13.24 & 13.2505945271423 & -0.0105945271423096 \tabularnewline
37 & 13.3 & 13.30512262619 & -0.00512262619001014 \tabularnewline
38 & 13.35 & 13.3248273391540 & 0.0251726608460299 \tabularnewline
39 & 13.35 & 13.4354795421219 & -0.0854795421218633 \tabularnewline
40 & 13.35 & 13.4015577716172 & -0.051557771617194 \tabularnewline
41 & 13.36 & 13.3833473304182 & -0.0233473304182468 \tabularnewline
42 & 13.37 & 13.3880277219281 & -0.0180277219280764 \tabularnewline
43 & 13.38 & 13.3746293980535 & 0.0053706019465185 \tabularnewline
44 & 13.39 & 13.4120941811757 & -0.0220941811757420 \tabularnewline
45 & 13.4 & 13.4204571773973 & -0.0204571773973008 \tabularnewline
46 & 13.4 & 13.4495376178412 & -0.0495376178411657 \tabularnewline
47 & 13.44 & 13.4239678931322 & 0.0160321068677813 \tabularnewline
48 & 13.44 & 13.4429040233725 & -0.00290402337246576 \tabularnewline
49 & 13.44 & 13.5039040539385 & -0.0639040539385398 \tabularnewline
50 & 13.47 & 13.4737505791643 & -0.00375057916429888 \tabularnewline
51 & 13.52 & 13.5581431519462 & -0.0381431519462136 \tabularnewline
52 & 13.58 & 13.5647982549691 & 0.0152017450309465 \tabularnewline
53 & 13.65 & 13.6036758650107 & 0.0463241349892645 \tabularnewline
54 & 13.66 & 13.6676745076739 & -0.00767450767387956 \tabularnewline
55 & 13.68 & 13.6633142850966 & 0.0166857149033515 \tabularnewline
56 & 13.68 & 13.7099896854053 & -0.0299896854052601 \tabularnewline
57 & 13.77 & 13.7115714227959 & 0.0584285772040527 \tabularnewline
58 & 13.78 & 13.8074345000235 & -0.0274345000235154 \tabularnewline
59 & 13.79 & 13.8015187024960 & -0.0115187024959535 \tabularnewline
60 & 13.79 & 13.7967162695329 & -0.00671626953291415 \tabularnewline
61 & 13.82 & 13.8536517739228 & -0.0336517739228146 \tabularnewline
62 & 13.86 & 13.8500222269483 & 0.00997777305167347 \tabularnewline
63 & 13.94 & 13.9456591311541 & -0.00565913115410943 \tabularnewline
64 & 14 & 13.9806808335652 & 0.0193191664347605 \tabularnewline
65 & 14.02 & 14.0234831689078 & -0.00348316890775102 \tabularnewline
66 & 14.03 & 14.0443546398909 & -0.0143546398909251 \tabularnewline
67 & 14.07 & 14.0346002450026 & 0.0353997549973695 \tabularnewline
68 & 14.1 & 14.0966074419301 & 0.00339255806985683 \tabularnewline
69 & 14.1 & 14.1277715103394 & -0.0277715103394236 \tabularnewline
70 & 14.16 & 14.1490772942579 & 0.0109227057421055 \tabularnewline
71 & 14.17 & 14.1760181336931 & -0.00601813369305049 \tabularnewline
72 & 14.17 & 14.1759501710322 & -0.0059501710322305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13741&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]13[/C][C]12.46[/C][C]12.3015652777778[/C][C]0.158434722222218[/C][/ROW]
[ROW][C]14[/C][C]12.47[/C][C]12.4604006291127[/C][C]0.0095993708872566[/C][/ROW]
[ROW][C]15[/C][C]12.55[/C][C]12.5599844678501[/C][C]-0.00998446785011176[/C][/ROW]
[ROW][C]16[/C][C]12.58[/C][C]12.5899664216077[/C][C]-0.00996642160766292[/C][/ROW]
[ROW][C]17[/C][C]12.6[/C][C]12.6074573794863[/C][C]-0.00745737948631842[/C][/ROW]
[ROW][C]18[/C][C]12.62[/C][C]12.6258304343119[/C][C]-0.00583043431194064[/C][/ROW]
[ROW][C]19[/C][C]12.62[/C][C]12.6226687086755[/C][C]-0.00266870867547553[/C][/ROW]
[ROW][C]20[/C][C]12.66[/C][C]12.6534480051011[/C][C]0.00655199489886016[/C][/ROW]
[ROW][C]21[/C][C]12.7[/C][C]12.6862510898449[/C][C]0.0137489101551065[/C][/ROW]
[ROW][C]22[/C][C]12.76[/C][C]12.7447756392528[/C][C]0.0152243607472329[/C][/ROW]
[ROW][C]23[/C][C]12.79[/C][C]12.7733164994148[/C][C]0.0166835005851702[/C][/ROW]
[ROW][C]24[/C][C]12.81[/C][C]12.7935273776247[/C][C]0.0164726223753302[/C][/ROW]
[ROW][C]25[/C][C]12.86[/C][C]12.8714394383643[/C][C]-0.0114394383642846[/C][/ROW]
[ROW][C]26[/C][C]13.03[/C][C]12.8837054047201[/C][C]0.146294595279945[/C][/ROW]
[ROW][C]27[/C][C]13.09[/C][C]13.0995628612762[/C][C]-0.00956286127619954[/C][/ROW]
[ROW][C]28[/C][C]13.15[/C][C]13.1300114421417[/C][C]0.0199885578582677[/C][/ROW]
[ROW][C]29[/C][C]13.17[/C][C]13.1731726811148[/C][C]-0.00317268111482605[/C][/ROW]
[ROW][C]30[/C][C]13.18[/C][C]13.1953449701131[/C][C]-0.0153449701130537[/C][/ROW]
[ROW][C]31[/C][C]13.18[/C][C]13.1842438293142[/C][C]-0.00424382931419842[/C][/ROW]
[ROW][C]32[/C][C]13.19[/C][C]13.2139223127206[/C][C]-0.0239223127205879[/C][/ROW]
[ROW][C]33[/C][C]13.19[/C][C]13.2209667184886[/C][C]-0.0309667184885694[/C][/ROW]
[ROW][C]34[/C][C]13.19[/C][C]13.2415016582464[/C][C]-0.0515016582464494[/C][/ROW]
[ROW][C]35[/C][C]13.25[/C][C]13.2132646363403[/C][C]0.0367353636596892[/C][/ROW]
[ROW][C]36[/C][C]13.24[/C][C]13.2505945271423[/C][C]-0.0105945271423096[/C][/ROW]
[ROW][C]37[/C][C]13.3[/C][C]13.30512262619[/C][C]-0.00512262619001014[/C][/ROW]
[ROW][C]38[/C][C]13.35[/C][C]13.3248273391540[/C][C]0.0251726608460299[/C][/ROW]
[ROW][C]39[/C][C]13.35[/C][C]13.4354795421219[/C][C]-0.0854795421218633[/C][/ROW]
[ROW][C]40[/C][C]13.35[/C][C]13.4015577716172[/C][C]-0.051557771617194[/C][/ROW]
[ROW][C]41[/C][C]13.36[/C][C]13.3833473304182[/C][C]-0.0233473304182468[/C][/ROW]
[ROW][C]42[/C][C]13.37[/C][C]13.3880277219281[/C][C]-0.0180277219280764[/C][/ROW]
[ROW][C]43[/C][C]13.38[/C][C]13.3746293980535[/C][C]0.0053706019465185[/C][/ROW]
[ROW][C]44[/C][C]13.39[/C][C]13.4120941811757[/C][C]-0.0220941811757420[/C][/ROW]
[ROW][C]45[/C][C]13.4[/C][C]13.4204571773973[/C][C]-0.0204571773973008[/C][/ROW]
[ROW][C]46[/C][C]13.4[/C][C]13.4495376178412[/C][C]-0.0495376178411657[/C][/ROW]
[ROW][C]47[/C][C]13.44[/C][C]13.4239678931322[/C][C]0.0160321068677813[/C][/ROW]
[ROW][C]48[/C][C]13.44[/C][C]13.4429040233725[/C][C]-0.00290402337246576[/C][/ROW]
[ROW][C]49[/C][C]13.44[/C][C]13.5039040539385[/C][C]-0.0639040539385398[/C][/ROW]
[ROW][C]50[/C][C]13.47[/C][C]13.4737505791643[/C][C]-0.00375057916429888[/C][/ROW]
[ROW][C]51[/C][C]13.52[/C][C]13.5581431519462[/C][C]-0.0381431519462136[/C][/ROW]
[ROW][C]52[/C][C]13.58[/C][C]13.5647982549691[/C][C]0.0152017450309465[/C][/ROW]
[ROW][C]53[/C][C]13.65[/C][C]13.6036758650107[/C][C]0.0463241349892645[/C][/ROW]
[ROW][C]54[/C][C]13.66[/C][C]13.6676745076739[/C][C]-0.00767450767387956[/C][/ROW]
[ROW][C]55[/C][C]13.68[/C][C]13.6633142850966[/C][C]0.0166857149033515[/C][/ROW]
[ROW][C]56[/C][C]13.68[/C][C]13.7099896854053[/C][C]-0.0299896854052601[/C][/ROW]
[ROW][C]57[/C][C]13.77[/C][C]13.7115714227959[/C][C]0.0584285772040527[/C][/ROW]
[ROW][C]58[/C][C]13.78[/C][C]13.8074345000235[/C][C]-0.0274345000235154[/C][/ROW]
[ROW][C]59[/C][C]13.79[/C][C]13.8015187024960[/C][C]-0.0115187024959535[/C][/ROW]
[ROW][C]60[/C][C]13.79[/C][C]13.7967162695329[/C][C]-0.00671626953291415[/C][/ROW]
[ROW][C]61[/C][C]13.82[/C][C]13.8536517739228[/C][C]-0.0336517739228146[/C][/ROW]
[ROW][C]62[/C][C]13.86[/C][C]13.8500222269483[/C][C]0.00997777305167347[/C][/ROW]
[ROW][C]63[/C][C]13.94[/C][C]13.9456591311541[/C][C]-0.00565913115410943[/C][/ROW]
[ROW][C]64[/C][C]14[/C][C]13.9806808335652[/C][C]0.0193191664347605[/C][/ROW]
[ROW][C]65[/C][C]14.02[/C][C]14.0234831689078[/C][C]-0.00348316890775102[/C][/ROW]
[ROW][C]66[/C][C]14.03[/C][C]14.0443546398909[/C][C]-0.0143546398909251[/C][/ROW]
[ROW][C]67[/C][C]14.07[/C][C]14.0346002450026[/C][C]0.0353997549973695[/C][/ROW]
[ROW][C]68[/C][C]14.1[/C][C]14.0966074419301[/C][C]0.00339255806985683[/C][/ROW]
[ROW][C]69[/C][C]14.1[/C][C]14.1277715103394[/C][C]-0.0277715103394236[/C][/ROW]
[ROW][C]70[/C][C]14.16[/C][C]14.1490772942579[/C][C]0.0109227057421055[/C][/ROW]
[ROW][C]71[/C][C]14.17[/C][C]14.1760181336931[/C][C]-0.00601813369305049[/C][/ROW]
[ROW][C]72[/C][C]14.17[/C][C]14.1759501710322[/C][C]-0.0059501710322305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13741&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13741&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
1312.4612.30156527777780.158434722222218
1412.4712.46040062911270.0095993708872566
1512.5512.5599844678501-0.00998446785011176
1612.5812.5899664216077-0.00996642160766292
1712.612.6074573794863-0.00745737948631842
1812.6212.6258304343119-0.00583043431194064
1912.6212.6226687086755-0.00266870867547553
2012.6612.65344800510110.00655199489886016
2112.712.68625108984490.0137489101551065
2212.7612.74477563925280.0152243607472329
2312.7912.77331649941480.0166835005851702
2412.8112.79352737762470.0164726223753302
2512.8612.8714394383643-0.0114394383642846
2613.0312.88370540472010.146294595279945
2713.0913.0995628612762-0.00956286127619954
2813.1513.13001144214170.0199885578582677
2913.1713.1731726811148-0.00317268111482605
3013.1813.1953449701131-0.0153449701130537
3113.1813.1842438293142-0.00424382931419842
3213.1913.2139223127206-0.0239223127205879
3313.1913.2209667184886-0.0309667184885694
3413.1913.2415016582464-0.0515016582464494
3513.2513.21326463634030.0367353636596892
3613.2413.2505945271423-0.0105945271423096
3713.313.30512262619-0.00512262619001014
3813.3513.32482733915400.0251726608460299
3913.3513.4354795421219-0.0854795421218633
4013.3513.4015577716172-0.051557771617194
4113.3613.3833473304182-0.0233473304182468
4213.3713.3880277219281-0.0180277219280764
4313.3813.37462939805350.0053706019465185
4413.3913.4120941811757-0.0220941811757420
4513.413.4204571773973-0.0204571773973008
4613.413.4495376178412-0.0495376178411657
4713.4413.42396789313220.0160321068677813
4813.4413.4429040233725-0.00290402337246576
4913.4413.5039040539385-0.0639040539385398
5013.4713.4737505791643-0.00375057916429888
5113.5213.5581431519462-0.0381431519462136
5213.5813.56479825496910.0152017450309465
5313.6513.60367586501070.0463241349892645
5413.6613.6676745076739-0.00767450767387956
5513.6813.66331428509660.0166857149033515
5613.6813.7099896854053-0.0299896854052601
5713.7713.71157142279590.0584285772040527
5813.7813.8074345000235-0.0274345000235154
5913.7913.8015187024960-0.0115187024959535
6013.7913.7967162695329-0.00671626953291415
6113.8213.8536517739228-0.0336517739228146
6213.8613.85002222694830.00997777305167347
6313.9413.9456591311541-0.00565913115410943
641413.98068083356520.0193191664347605
6514.0214.0234831689078-0.00348316890775102
6614.0314.0443546398909-0.0143546398909251
6714.0714.03460024500260.0353997549973695
6814.114.09660744193010.00339255806985683
6914.114.1277715103394-0.0277715103394236
7014.1614.14907729425790.0109227057421055
7114.1714.1760181336931-0.00601813369305049
7214.1714.1759501710322-0.0059501710322305







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7314.233180418437514.157865424514814.3084954123602
7414.258781861729914.159823030641814.3577406928181
7514.345723726109714.227742669036814.4637047831826
7614.385893556201214.251534367196114.5202527452063
7714.411944280481114.262976363116514.5609121978458
7814.435639672709514.273353873401514.5979254720176
7914.438756642688814.264148174804814.6133651105727
8014.470187418359714.284053718480914.6563211182385
8114.498043101434514.301041586704714.6950446161644
8214.543497675221214.336182337124814.7508130133177
8314.560910599622114.343756468483514.7780647307608
8414.565965135654014.339385341288214.7925449300199

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 14.2331804184375 & 14.1578654245148 & 14.3084954123602 \tabularnewline
74 & 14.2587818617299 & 14.1598230306418 & 14.3577406928181 \tabularnewline
75 & 14.3457237261097 & 14.2277426690368 & 14.4637047831826 \tabularnewline
76 & 14.3858935562012 & 14.2515343671961 & 14.5202527452063 \tabularnewline
77 & 14.4119442804811 & 14.2629763631165 & 14.5609121978458 \tabularnewline
78 & 14.4356396727095 & 14.2733538734015 & 14.5979254720176 \tabularnewline
79 & 14.4387566426888 & 14.2641481748048 & 14.6133651105727 \tabularnewline
80 & 14.4701874183597 & 14.2840537184809 & 14.6563211182385 \tabularnewline
81 & 14.4980431014345 & 14.3010415867047 & 14.6950446161644 \tabularnewline
82 & 14.5434976752212 & 14.3361823371248 & 14.7508130133177 \tabularnewline
83 & 14.5609105996221 & 14.3437564684835 & 14.7780647307608 \tabularnewline
84 & 14.5659651356540 & 14.3393853412882 & 14.7925449300199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13741&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]14.2331804184375[/C][C]14.1578654245148[/C][C]14.3084954123602[/C][/ROW]
[ROW][C]74[/C][C]14.2587818617299[/C][C]14.1598230306418[/C][C]14.3577406928181[/C][/ROW]
[ROW][C]75[/C][C]14.3457237261097[/C][C]14.2277426690368[/C][C]14.4637047831826[/C][/ROW]
[ROW][C]76[/C][C]14.3858935562012[/C][C]14.2515343671961[/C][C]14.5202527452063[/C][/ROW]
[ROW][C]77[/C][C]14.4119442804811[/C][C]14.2629763631165[/C][C]14.5609121978458[/C][/ROW]
[ROW][C]78[/C][C]14.4356396727095[/C][C]14.2733538734015[/C][C]14.5979254720176[/C][/ROW]
[ROW][C]79[/C][C]14.4387566426888[/C][C]14.2641481748048[/C][C]14.6133651105727[/C][/ROW]
[ROW][C]80[/C][C]14.4701874183597[/C][C]14.2840537184809[/C][C]14.6563211182385[/C][/ROW]
[ROW][C]81[/C][C]14.4980431014345[/C][C]14.3010415867047[/C][C]14.6950446161644[/C][/ROW]
[ROW][C]82[/C][C]14.5434976752212[/C][C]14.3361823371248[/C][C]14.7508130133177[/C][/ROW]
[ROW][C]83[/C][C]14.5609105996221[/C][C]14.3437564684835[/C][C]14.7780647307608[/C][/ROW]
[ROW][C]84[/C][C]14.5659651356540[/C][C]14.3393853412882[/C][C]14.7925449300199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13741&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13741&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
7314.233180418437514.157865424514814.3084954123602
7414.258781861729914.159823030641814.3577406928181
7514.345723726109714.227742669036814.4637047831826
7614.385893556201214.251534367196114.5202527452063
7714.411944280481114.262976363116514.5609121978458
7814.435639672709514.273353873401514.5979254720176
7914.438756642688814.264148174804814.6133651105727
8014.470187418359714.284053718480914.6563211182385
8114.498043101434514.301041586704714.6950446161644
8214.543497675221214.336182337124814.7508130133177
8314.560910599622114.343756468483514.7780647307608
8414.565965135654014.339385341288214.7925449300199



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')