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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 18:25:26 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t1461605255s0bfvolr0rhr9ex.htm/, Retrieved Mon, 06 May 2024 06:41:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294758, Retrieved Mon, 06 May 2024 06:41:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 17:25:26] [ed8c98a61958118f8b1101b2c94f1953] [Current]
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Dataseries X:
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
101.27
101.27
101.27
101.25
101.25
101.25
101.25
101.25
101.25
101.25
101.25
101.25
102.55
102.55
102.55
102.55
102.55
102.55
102.55
102.55
102.55
102.55
102.55
102.55
132.09
132.09
132.09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294758&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294758&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294758&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.706748241973233
beta0.203355669298036
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.706748241973233 \tabularnewline
beta & 0.203355669298036 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294758&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]0.706748241973233[/C][/ROW]
[ROW][C]beta[/C][C]0.203355669298036[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294758&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294758&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
alpha0.706748241973233
beta0.203355669298036
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1396.1996.3995664885791-0.209566488579142
1496.1996.265671176967-0.0756711769670488
1596.1996.2155156482693-0.0255156482693337
1696.1996.05480474092480.135195259075218
1796.1995.88557003696060.304429963039382
1896.1995.88037973899390.309620261006117
1996.1996.9192924556451-0.72929245564508
2096.1996.4069050632822-0.216905063282169
2196.1996.2253987064323-0.035398706432261
2299.1395.68954553292113.44045446707888
2399.1398.58356706749580.54643293250416
2499.1399.5113550577278-0.381355057727816
2599.1399.6652608443926-0.535260844392567
2699.1399.7377333537362-0.607733353736236
2799.1399.6464814061752-0.516481406175174
2899.1399.4318467567871-0.3018467567871
2999.1399.1815957424704-0.0515957424703828
3099.1399.05168143414830.0783185658517027
3199.1399.7350486651617-0.605048665161704
3299.1399.5848369017226-0.454836901722643
3399.1399.3752859618611-0.245285961861143
3499.5899.7568959502212-0.176895950221208
3599.5898.77389069959520.806109300404842
3699.5899.18345110533480.396548894665216
3799.5899.52425921506280.0557407849371714
3899.5899.7604158183271-0.180415818327148
3999.5899.8266627111476-0.246662711147621
4099.5899.7330305705469-0.153030570546917
4199.5899.54971882892540.0302811710746198
4299.5899.41581105103320.164188948966839
4399.5899.8728630330065-0.29286303300654
4499.5899.94592129115-0.365921291150002
4599.5899.8317843148101-0.251784314810052
46101.27100.2011529770861.06884702291366
47101.27100.5256731325340.744326867466256
48101.27100.9037572264950.366242773504538
49101.25101.253709379299-0.00370937929893955
50101.25101.503001083006-0.253001083005842
51101.25101.613760445375-0.363760445374993
52101.25101.562794970142-0.312794970141653
53101.25101.393407355824-0.143407355824053
54101.25101.2223276050250.0276723949753404
55101.25101.480542834237-0.230542834236502
56101.25101.618531899168-0.368531899168048
57101.25101.577709835864-0.327709835863601
58102.55102.3235106900360.226489309963824
59102.55101.8556151102430.694384889757217
60102.55101.982106130730.567893869269781
61102.55102.2919742140030.258025785997006
62102.55102.618617165575-0.0686171655748637
63102.55102.820430429184-0.270430429184273
64102.55102.857264511518-0.307264511518284
65102.55102.748242981525-0.198242981525127
66102.55102.586178653078-0.0361786530778971
67102.55102.714224534421-0.164224534420924
68102.55102.86039208372-0.310392083719819
69102.55102.883186794728-0.333186794727581
70132.09103.8107650376428.2792349623604
71132.09127.220621272644.8693787273601
72132.09134.715898230531-2.62589823053105

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 96.19 & 96.3995664885791 & -0.209566488579142 \tabularnewline
14 & 96.19 & 96.265671176967 & -0.0756711769670488 \tabularnewline
15 & 96.19 & 96.2155156482693 & -0.0255156482693337 \tabularnewline
16 & 96.19 & 96.0548047409248 & 0.135195259075218 \tabularnewline
17 & 96.19 & 95.8855700369606 & 0.304429963039382 \tabularnewline
18 & 96.19 & 95.8803797389939 & 0.309620261006117 \tabularnewline
19 & 96.19 & 96.9192924556451 & -0.72929245564508 \tabularnewline
20 & 96.19 & 96.4069050632822 & -0.216905063282169 \tabularnewline
21 & 96.19 & 96.2253987064323 & -0.035398706432261 \tabularnewline
22 & 99.13 & 95.6895455329211 & 3.44045446707888 \tabularnewline
23 & 99.13 & 98.5835670674958 & 0.54643293250416 \tabularnewline
24 & 99.13 & 99.5113550577278 & -0.381355057727816 \tabularnewline
25 & 99.13 & 99.6652608443926 & -0.535260844392567 \tabularnewline
26 & 99.13 & 99.7377333537362 & -0.607733353736236 \tabularnewline
27 & 99.13 & 99.6464814061752 & -0.516481406175174 \tabularnewline
28 & 99.13 & 99.4318467567871 & -0.3018467567871 \tabularnewline
29 & 99.13 & 99.1815957424704 & -0.0515957424703828 \tabularnewline
30 & 99.13 & 99.0516814341483 & 0.0783185658517027 \tabularnewline
31 & 99.13 & 99.7350486651617 & -0.605048665161704 \tabularnewline
32 & 99.13 & 99.5848369017226 & -0.454836901722643 \tabularnewline
33 & 99.13 & 99.3752859618611 & -0.245285961861143 \tabularnewline
34 & 99.58 & 99.7568959502212 & -0.176895950221208 \tabularnewline
35 & 99.58 & 98.7738906995952 & 0.806109300404842 \tabularnewline
36 & 99.58 & 99.1834511053348 & 0.396548894665216 \tabularnewline
37 & 99.58 & 99.5242592150628 & 0.0557407849371714 \tabularnewline
38 & 99.58 & 99.7604158183271 & -0.180415818327148 \tabularnewline
39 & 99.58 & 99.8266627111476 & -0.246662711147621 \tabularnewline
40 & 99.58 & 99.7330305705469 & -0.153030570546917 \tabularnewline
41 & 99.58 & 99.5497188289254 & 0.0302811710746198 \tabularnewline
42 & 99.58 & 99.4158110510332 & 0.164188948966839 \tabularnewline
43 & 99.58 & 99.8728630330065 & -0.29286303300654 \tabularnewline
44 & 99.58 & 99.94592129115 & -0.365921291150002 \tabularnewline
45 & 99.58 & 99.8317843148101 & -0.251784314810052 \tabularnewline
46 & 101.27 & 100.201152977086 & 1.06884702291366 \tabularnewline
47 & 101.27 & 100.525673132534 & 0.744326867466256 \tabularnewline
48 & 101.27 & 100.903757226495 & 0.366242773504538 \tabularnewline
49 & 101.25 & 101.253709379299 & -0.00370937929893955 \tabularnewline
50 & 101.25 & 101.503001083006 & -0.253001083005842 \tabularnewline
51 & 101.25 & 101.613760445375 & -0.363760445374993 \tabularnewline
52 & 101.25 & 101.562794970142 & -0.312794970141653 \tabularnewline
53 & 101.25 & 101.393407355824 & -0.143407355824053 \tabularnewline
54 & 101.25 & 101.222327605025 & 0.0276723949753404 \tabularnewline
55 & 101.25 & 101.480542834237 & -0.230542834236502 \tabularnewline
56 & 101.25 & 101.618531899168 & -0.368531899168048 \tabularnewline
57 & 101.25 & 101.577709835864 & -0.327709835863601 \tabularnewline
58 & 102.55 & 102.323510690036 & 0.226489309963824 \tabularnewline
59 & 102.55 & 101.855615110243 & 0.694384889757217 \tabularnewline
60 & 102.55 & 101.98210613073 & 0.567893869269781 \tabularnewline
61 & 102.55 & 102.291974214003 & 0.258025785997006 \tabularnewline
62 & 102.55 & 102.618617165575 & -0.0686171655748637 \tabularnewline
63 & 102.55 & 102.820430429184 & -0.270430429184273 \tabularnewline
64 & 102.55 & 102.857264511518 & -0.307264511518284 \tabularnewline
65 & 102.55 & 102.748242981525 & -0.198242981525127 \tabularnewline
66 & 102.55 & 102.586178653078 & -0.0361786530778971 \tabularnewline
67 & 102.55 & 102.714224534421 & -0.164224534420924 \tabularnewline
68 & 102.55 & 102.86039208372 & -0.310392083719819 \tabularnewline
69 & 102.55 & 102.883186794728 & -0.333186794727581 \tabularnewline
70 & 132.09 & 103.81076503764 & 28.2792349623604 \tabularnewline
71 & 132.09 & 127.22062127264 & 4.8693787273601 \tabularnewline
72 & 132.09 & 134.715898230531 & -2.62589823053105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294758&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]96.19[/C][C]96.3995664885791[/C][C]-0.209566488579142[/C][/ROW]
[ROW][C]14[/C][C]96.19[/C][C]96.265671176967[/C][C]-0.0756711769670488[/C][/ROW]
[ROW][C]15[/C][C]96.19[/C][C]96.2155156482693[/C][C]-0.0255156482693337[/C][/ROW]
[ROW][C]16[/C][C]96.19[/C][C]96.0548047409248[/C][C]0.135195259075218[/C][/ROW]
[ROW][C]17[/C][C]96.19[/C][C]95.8855700369606[/C][C]0.304429963039382[/C][/ROW]
[ROW][C]18[/C][C]96.19[/C][C]95.8803797389939[/C][C]0.309620261006117[/C][/ROW]
[ROW][C]19[/C][C]96.19[/C][C]96.9192924556451[/C][C]-0.72929245564508[/C][/ROW]
[ROW][C]20[/C][C]96.19[/C][C]96.4069050632822[/C][C]-0.216905063282169[/C][/ROW]
[ROW][C]21[/C][C]96.19[/C][C]96.2253987064323[/C][C]-0.035398706432261[/C][/ROW]
[ROW][C]22[/C][C]99.13[/C][C]95.6895455329211[/C][C]3.44045446707888[/C][/ROW]
[ROW][C]23[/C][C]99.13[/C][C]98.5835670674958[/C][C]0.54643293250416[/C][/ROW]
[ROW][C]24[/C][C]99.13[/C][C]99.5113550577278[/C][C]-0.381355057727816[/C][/ROW]
[ROW][C]25[/C][C]99.13[/C][C]99.6652608443926[/C][C]-0.535260844392567[/C][/ROW]
[ROW][C]26[/C][C]99.13[/C][C]99.7377333537362[/C][C]-0.607733353736236[/C][/ROW]
[ROW][C]27[/C][C]99.13[/C][C]99.6464814061752[/C][C]-0.516481406175174[/C][/ROW]
[ROW][C]28[/C][C]99.13[/C][C]99.4318467567871[/C][C]-0.3018467567871[/C][/ROW]
[ROW][C]29[/C][C]99.13[/C][C]99.1815957424704[/C][C]-0.0515957424703828[/C][/ROW]
[ROW][C]30[/C][C]99.13[/C][C]99.0516814341483[/C][C]0.0783185658517027[/C][/ROW]
[ROW][C]31[/C][C]99.13[/C][C]99.7350486651617[/C][C]-0.605048665161704[/C][/ROW]
[ROW][C]32[/C][C]99.13[/C][C]99.5848369017226[/C][C]-0.454836901722643[/C][/ROW]
[ROW][C]33[/C][C]99.13[/C][C]99.3752859618611[/C][C]-0.245285961861143[/C][/ROW]
[ROW][C]34[/C][C]99.58[/C][C]99.7568959502212[/C][C]-0.176895950221208[/C][/ROW]
[ROW][C]35[/C][C]99.58[/C][C]98.7738906995952[/C][C]0.806109300404842[/C][/ROW]
[ROW][C]36[/C][C]99.58[/C][C]99.1834511053348[/C][C]0.396548894665216[/C][/ROW]
[ROW][C]37[/C][C]99.58[/C][C]99.5242592150628[/C][C]0.0557407849371714[/C][/ROW]
[ROW][C]38[/C][C]99.58[/C][C]99.7604158183271[/C][C]-0.180415818327148[/C][/ROW]
[ROW][C]39[/C][C]99.58[/C][C]99.8266627111476[/C][C]-0.246662711147621[/C][/ROW]
[ROW][C]40[/C][C]99.58[/C][C]99.7330305705469[/C][C]-0.153030570546917[/C][/ROW]
[ROW][C]41[/C][C]99.58[/C][C]99.5497188289254[/C][C]0.0302811710746198[/C][/ROW]
[ROW][C]42[/C][C]99.58[/C][C]99.4158110510332[/C][C]0.164188948966839[/C][/ROW]
[ROW][C]43[/C][C]99.58[/C][C]99.8728630330065[/C][C]-0.29286303300654[/C][/ROW]
[ROW][C]44[/C][C]99.58[/C][C]99.94592129115[/C][C]-0.365921291150002[/C][/ROW]
[ROW][C]45[/C][C]99.58[/C][C]99.8317843148101[/C][C]-0.251784314810052[/C][/ROW]
[ROW][C]46[/C][C]101.27[/C][C]100.201152977086[/C][C]1.06884702291366[/C][/ROW]
[ROW][C]47[/C][C]101.27[/C][C]100.525673132534[/C][C]0.744326867466256[/C][/ROW]
[ROW][C]48[/C][C]101.27[/C][C]100.903757226495[/C][C]0.366242773504538[/C][/ROW]
[ROW][C]49[/C][C]101.25[/C][C]101.253709379299[/C][C]-0.00370937929893955[/C][/ROW]
[ROW][C]50[/C][C]101.25[/C][C]101.503001083006[/C][C]-0.253001083005842[/C][/ROW]
[ROW][C]51[/C][C]101.25[/C][C]101.613760445375[/C][C]-0.363760445374993[/C][/ROW]
[ROW][C]52[/C][C]101.25[/C][C]101.562794970142[/C][C]-0.312794970141653[/C][/ROW]
[ROW][C]53[/C][C]101.25[/C][C]101.393407355824[/C][C]-0.143407355824053[/C][/ROW]
[ROW][C]54[/C][C]101.25[/C][C]101.222327605025[/C][C]0.0276723949753404[/C][/ROW]
[ROW][C]55[/C][C]101.25[/C][C]101.480542834237[/C][C]-0.230542834236502[/C][/ROW]
[ROW][C]56[/C][C]101.25[/C][C]101.618531899168[/C][C]-0.368531899168048[/C][/ROW]
[ROW][C]57[/C][C]101.25[/C][C]101.577709835864[/C][C]-0.327709835863601[/C][/ROW]
[ROW][C]58[/C][C]102.55[/C][C]102.323510690036[/C][C]0.226489309963824[/C][/ROW]
[ROW][C]59[/C][C]102.55[/C][C]101.855615110243[/C][C]0.694384889757217[/C][/ROW]
[ROW][C]60[/C][C]102.55[/C][C]101.98210613073[/C][C]0.567893869269781[/C][/ROW]
[ROW][C]61[/C][C]102.55[/C][C]102.291974214003[/C][C]0.258025785997006[/C][/ROW]
[ROW][C]62[/C][C]102.55[/C][C]102.618617165575[/C][C]-0.0686171655748637[/C][/ROW]
[ROW][C]63[/C][C]102.55[/C][C]102.820430429184[/C][C]-0.270430429184273[/C][/ROW]
[ROW][C]64[/C][C]102.55[/C][C]102.857264511518[/C][C]-0.307264511518284[/C][/ROW]
[ROW][C]65[/C][C]102.55[/C][C]102.748242981525[/C][C]-0.198242981525127[/C][/ROW]
[ROW][C]66[/C][C]102.55[/C][C]102.586178653078[/C][C]-0.0361786530778971[/C][/ROW]
[ROW][C]67[/C][C]102.55[/C][C]102.714224534421[/C][C]-0.164224534420924[/C][/ROW]
[ROW][C]68[/C][C]102.55[/C][C]102.86039208372[/C][C]-0.310392083719819[/C][/ROW]
[ROW][C]69[/C][C]102.55[/C][C]102.883186794728[/C][C]-0.333186794727581[/C][/ROW]
[ROW][C]70[/C][C]132.09[/C][C]103.81076503764[/C][C]28.2792349623604[/C][/ROW]
[ROW][C]71[/C][C]132.09[/C][C]127.22062127264[/C][C]4.8693787273601[/C][/ROW]
[ROW][C]72[/C][C]132.09[/C][C]134.715898230531[/C][C]-2.62589823053105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294758&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294758&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
1396.1996.3995664885791-0.209566488579142
1496.1996.265671176967-0.0756711769670488
1596.1996.2155156482693-0.0255156482693337
1696.1996.05480474092480.135195259075218
1796.1995.88557003696060.304429963039382
1896.1995.88037973899390.309620261006117
1996.1996.9192924556451-0.72929245564508
2096.1996.4069050632822-0.216905063282169
2196.1996.2253987064323-0.035398706432261
2299.1395.68954553292113.44045446707888
2399.1398.58356706749580.54643293250416
2499.1399.5113550577278-0.381355057727816
2599.1399.6652608443926-0.535260844392567
2699.1399.7377333537362-0.607733353736236
2799.1399.6464814061752-0.516481406175174
2899.1399.4318467567871-0.3018467567871
2999.1399.1815957424704-0.0515957424703828
3099.1399.05168143414830.0783185658517027
3199.1399.7350486651617-0.605048665161704
3299.1399.5848369017226-0.454836901722643
3399.1399.3752859618611-0.245285961861143
3499.5899.7568959502212-0.176895950221208
3599.5898.77389069959520.806109300404842
3699.5899.18345110533480.396548894665216
3799.5899.52425921506280.0557407849371714
3899.5899.7604158183271-0.180415818327148
3999.5899.8266627111476-0.246662711147621
4099.5899.7330305705469-0.153030570546917
4199.5899.54971882892540.0302811710746198
4299.5899.41581105103320.164188948966839
4399.5899.8728630330065-0.29286303300654
4499.5899.94592129115-0.365921291150002
4599.5899.8317843148101-0.251784314810052
46101.27100.2011529770861.06884702291366
47101.27100.5256731325340.744326867466256
48101.27100.9037572264950.366242773504538
49101.25101.253709379299-0.00370937929893955
50101.25101.503001083006-0.253001083005842
51101.25101.613760445375-0.363760445374993
52101.25101.562794970142-0.312794970141653
53101.25101.393407355824-0.143407355824053
54101.25101.2223276050250.0276723949753404
55101.25101.480542834237-0.230542834236502
56101.25101.618531899168-0.368531899168048
57101.25101.577709835864-0.327709835863601
58102.55102.3235106900360.226489309963824
59102.55101.8556151102430.694384889757217
60102.55101.982106130730.567893869269781
61102.55102.2919742140030.258025785997006
62102.55102.618617165575-0.0686171655748637
63102.55102.820430429184-0.270430429184273
64102.55102.857264511518-0.307264511518284
65102.55102.748242981525-0.198242981525127
66102.55102.586178653078-0.0361786530778971
67102.55102.714224534421-0.164224534420924
68102.55102.86039208372-0.310392083719819
69102.55102.883186794728-0.333186794727581
70132.09103.8107650376428.2792349623604
71132.09127.220621272644.8693787273601
72132.09134.715898230531-2.62589823053105







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73136.68920020591129.316807958484144.061592453335
74140.755863563179131.084861485362150.426865640996
75145.023543910874132.892860515144157.154227306604
76149.383343146865134.632734562803164.133951730927
77153.697216841451136.180333806875171.214099876027
78157.879228132489137.467080833051178.291375431927
79162.205852173738138.744668815375185.667035532101
80166.739424668575140.065122028717193.413727308433
81171.386316951722141.346176333228201.426457570215
82189.806825171216153.766647923219225.847002419212
83183.351989223303145.734616229185220.969362217421
84183.722498013495143.896538297097223.548457729893

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 136.68920020591 & 129.316807958484 & 144.061592453335 \tabularnewline
74 & 140.755863563179 & 131.084861485362 & 150.426865640996 \tabularnewline
75 & 145.023543910874 & 132.892860515144 & 157.154227306604 \tabularnewline
76 & 149.383343146865 & 134.632734562803 & 164.133951730927 \tabularnewline
77 & 153.697216841451 & 136.180333806875 & 171.214099876027 \tabularnewline
78 & 157.879228132489 & 137.467080833051 & 178.291375431927 \tabularnewline
79 & 162.205852173738 & 138.744668815375 & 185.667035532101 \tabularnewline
80 & 166.739424668575 & 140.065122028717 & 193.413727308433 \tabularnewline
81 & 171.386316951722 & 141.346176333228 & 201.426457570215 \tabularnewline
82 & 189.806825171216 & 153.766647923219 & 225.847002419212 \tabularnewline
83 & 183.351989223303 & 145.734616229185 & 220.969362217421 \tabularnewline
84 & 183.722498013495 & 143.896538297097 & 223.548457729893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294758&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]136.68920020591[/C][C]129.316807958484[/C][C]144.061592453335[/C][/ROW]
[ROW][C]74[/C][C]140.755863563179[/C][C]131.084861485362[/C][C]150.426865640996[/C][/ROW]
[ROW][C]75[/C][C]145.023543910874[/C][C]132.892860515144[/C][C]157.154227306604[/C][/ROW]
[ROW][C]76[/C][C]149.383343146865[/C][C]134.632734562803[/C][C]164.133951730927[/C][/ROW]
[ROW][C]77[/C][C]153.697216841451[/C][C]136.180333806875[/C][C]171.214099876027[/C][/ROW]
[ROW][C]78[/C][C]157.879228132489[/C][C]137.467080833051[/C][C]178.291375431927[/C][/ROW]
[ROW][C]79[/C][C]162.205852173738[/C][C]138.744668815375[/C][C]185.667035532101[/C][/ROW]
[ROW][C]80[/C][C]166.739424668575[/C][C]140.065122028717[/C][C]193.413727308433[/C][/ROW]
[ROW][C]81[/C][C]171.386316951722[/C][C]141.346176333228[/C][C]201.426457570215[/C][/ROW]
[ROW][C]82[/C][C]189.806825171216[/C][C]153.766647923219[/C][C]225.847002419212[/C][/ROW]
[ROW][C]83[/C][C]183.351989223303[/C][C]145.734616229185[/C][C]220.969362217421[/C][/ROW]
[ROW][C]84[/C][C]183.722498013495[/C][C]143.896538297097[/C][C]223.548457729893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294758&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294758&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
73136.68920020591129.316807958484144.061592453335
74140.755863563179131.084861485362150.426865640996
75145.023543910874132.892860515144157.154227306604
76149.383343146865134.632734562803164.133951730927
77153.697216841451136.180333806875171.214099876027
78157.879228132489137.467080833051178.291375431927
79162.205852173738138.744668815375185.667035532101
80166.739424668575140.065122028717193.413727308433
81171.386316951722141.346176333228201.426457570215
82189.806825171216153.766647923219225.847002419212
83183.351989223303145.734616229185220.969362217421
84183.722498013495143.896538297097223.548457729893



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')