Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 04 Dec 2016 11:18:15 +0000
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/Dec/04/t1480850338t2vfz78krpoiu4n.htm/, Retrieved Tue, 21 May 2024 10:41:55 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 21 May 2024 10:41:55 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
98,98
98,97
98,91
98,98
98,95
98,96
98,96
99,04
99,33
100,04
100,14
100,21
100,21
100,27
100,44
100,57
100,51
100,47
100,47
100,49
101
101,61
101,65
101,74
101,74
101,73
101,77
101,82
101,97
102,09
102,09
102,08
102,42
102,78
103,04
103,08
99,16
99,19
99,23
99,31
99,46
99,49
99,95
100,14
100,43
101,1
101,26
101,28
101,04
101,12
101,07
100,97
101,01
100,99
101,19
101,25
101,33
101,79
102,06
102,09
102,27
102,26
102,46
102,46
102,51
102,56
102,59
102,26
102,33
102,84
102,93
102,95




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

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

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







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13100.2199.45277363957090.757226360429129
14100.27100.273653880283-0.00365388028328084
15100.44100.4369814955060.00301850449415042
16100.57100.5619765280160.00802347198379039
17100.51100.5086525504780.00134744952174515
18100.47100.47031727598-0.0003172759801231
19100.47100.4628741380920.00712586190819309
20100.49100.571098793087-0.081098793086781
21101100.7915702301250.208429769875494
22101.61101.716718009189-0.106718009189336
23101.65101.705224351002-0.0552243510022095
24101.74101.7181873949930.0218126050068577
25101.74101.7392291803440.000770819656395361
26101.73101.802685634596-0.0726856345963682
27101.77101.89756188697-0.127561886969971
28101.82101.891908488114-0.0719084881139764
29101.97101.7563130809040.213686919096389
30102.09101.9279008946320.162099105368426
31102.09102.0807195506350.00928044936502204
32102.08102.190689758366-0.110689758365623
33102.42102.3843373209190.0356626790810282
34102.78103.145003107941-0.365003107941035
35103.04102.8748540284330.165145971567483
36103.08103.107378912001-0.0273789120006569
3799.16103.077544340488-3.91754434048833
3899.1999.2243183626174-0.0343183626174408
3999.2399.3565521648337-0.12655216483374
4099.3199.3520384289799-0.0420384289798648
4199.4699.25101073580950.208989264190478
4299.4999.42205508448420.0679449155157954
4399.9599.4841775305040.465822469496047
44100.14100.0512300881820.0887699118175505
45100.43100.440961122088-0.0109611220879913
46101.1101.143392300535-0.0433923005355012
47101.26101.1953857736610.0646142263392306
48101.28101.328414235545-0.0484142355449819
49101.04101.279807558204-0.239807558204376
50101.12101.1031286228190.0168713771808626
51101.07101.287319394646-0.217319394645926
52100.97101.191944298589-0.221944298588824
53101.01100.9079039202140.102096079785625
54100.99100.9694897481210.0205102518789602
55101.19100.9821825421180.207817457882001
56101.25101.290916999877-0.040916999877382
57101.33101.552892864718-0.222892864718105
58101.79102.048643419463-0.258643419462615
59102.06101.8851673782990.174832621700816
60102.09102.127948921592-0.0379489215924735
61102.27102.0887891102320.18121088976784
62102.26102.332350229228-0.072350229227709
63102.46102.4277725770220.0322274229779822
64102.46102.581873189217-0.121873189217325
65102.51102.3951152724810.114884727518628
66102.56102.4670071645440.0929928354562435
67102.59102.5500944542740.0399055457259578
68102.26102.690563513081-0.430563513081324
69102.33102.564650576481-0.234650576480604
70102.84103.054477996048-0.214477996048302
71102.93102.934835037532-0.00483503753150671
72102.95102.997442892669-0.0474428926691388

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 100.21 & 99.4527736395709 & 0.757226360429129 \tabularnewline
14 & 100.27 & 100.273653880283 & -0.00365388028328084 \tabularnewline
15 & 100.44 & 100.436981495506 & 0.00301850449415042 \tabularnewline
16 & 100.57 & 100.561976528016 & 0.00802347198379039 \tabularnewline
17 & 100.51 & 100.508652550478 & 0.00134744952174515 \tabularnewline
18 & 100.47 & 100.47031727598 & -0.0003172759801231 \tabularnewline
19 & 100.47 & 100.462874138092 & 0.00712586190819309 \tabularnewline
20 & 100.49 & 100.571098793087 & -0.081098793086781 \tabularnewline
21 & 101 & 100.791570230125 & 0.208429769875494 \tabularnewline
22 & 101.61 & 101.716718009189 & -0.106718009189336 \tabularnewline
23 & 101.65 & 101.705224351002 & -0.0552243510022095 \tabularnewline
24 & 101.74 & 101.718187394993 & 0.0218126050068577 \tabularnewline
25 & 101.74 & 101.739229180344 & 0.000770819656395361 \tabularnewline
26 & 101.73 & 101.802685634596 & -0.0726856345963682 \tabularnewline
27 & 101.77 & 101.89756188697 & -0.127561886969971 \tabularnewline
28 & 101.82 & 101.891908488114 & -0.0719084881139764 \tabularnewline
29 & 101.97 & 101.756313080904 & 0.213686919096389 \tabularnewline
30 & 102.09 & 101.927900894632 & 0.162099105368426 \tabularnewline
31 & 102.09 & 102.080719550635 & 0.00928044936502204 \tabularnewline
32 & 102.08 & 102.190689758366 & -0.110689758365623 \tabularnewline
33 & 102.42 & 102.384337320919 & 0.0356626790810282 \tabularnewline
34 & 102.78 & 103.145003107941 & -0.365003107941035 \tabularnewline
35 & 103.04 & 102.874854028433 & 0.165145971567483 \tabularnewline
36 & 103.08 & 103.107378912001 & -0.0273789120006569 \tabularnewline
37 & 99.16 & 103.077544340488 & -3.91754434048833 \tabularnewline
38 & 99.19 & 99.2243183626174 & -0.0343183626174408 \tabularnewline
39 & 99.23 & 99.3565521648337 & -0.12655216483374 \tabularnewline
40 & 99.31 & 99.3520384289799 & -0.0420384289798648 \tabularnewline
41 & 99.46 & 99.2510107358095 & 0.208989264190478 \tabularnewline
42 & 99.49 & 99.4220550844842 & 0.0679449155157954 \tabularnewline
43 & 99.95 & 99.484177530504 & 0.465822469496047 \tabularnewline
44 & 100.14 & 100.051230088182 & 0.0887699118175505 \tabularnewline
45 & 100.43 & 100.440961122088 & -0.0109611220879913 \tabularnewline
46 & 101.1 & 101.143392300535 & -0.0433923005355012 \tabularnewline
47 & 101.26 & 101.195385773661 & 0.0646142263392306 \tabularnewline
48 & 101.28 & 101.328414235545 & -0.0484142355449819 \tabularnewline
49 & 101.04 & 101.279807558204 & -0.239807558204376 \tabularnewline
50 & 101.12 & 101.103128622819 & 0.0168713771808626 \tabularnewline
51 & 101.07 & 101.287319394646 & -0.217319394645926 \tabularnewline
52 & 100.97 & 101.191944298589 & -0.221944298588824 \tabularnewline
53 & 101.01 & 100.907903920214 & 0.102096079785625 \tabularnewline
54 & 100.99 & 100.969489748121 & 0.0205102518789602 \tabularnewline
55 & 101.19 & 100.982182542118 & 0.207817457882001 \tabularnewline
56 & 101.25 & 101.290916999877 & -0.040916999877382 \tabularnewline
57 & 101.33 & 101.552892864718 & -0.222892864718105 \tabularnewline
58 & 101.79 & 102.048643419463 & -0.258643419462615 \tabularnewline
59 & 102.06 & 101.885167378299 & 0.174832621700816 \tabularnewline
60 & 102.09 & 102.127948921592 & -0.0379489215924735 \tabularnewline
61 & 102.27 & 102.088789110232 & 0.18121088976784 \tabularnewline
62 & 102.26 & 102.332350229228 & -0.072350229227709 \tabularnewline
63 & 102.46 & 102.427772577022 & 0.0322274229779822 \tabularnewline
64 & 102.46 & 102.581873189217 & -0.121873189217325 \tabularnewline
65 & 102.51 & 102.395115272481 & 0.114884727518628 \tabularnewline
66 & 102.56 & 102.467007164544 & 0.0929928354562435 \tabularnewline
67 & 102.59 & 102.550094454274 & 0.0399055457259578 \tabularnewline
68 & 102.26 & 102.690563513081 & -0.430563513081324 \tabularnewline
69 & 102.33 & 102.564650576481 & -0.234650576480604 \tabularnewline
70 & 102.84 & 103.054477996048 & -0.214477996048302 \tabularnewline
71 & 102.93 & 102.934835037532 & -0.00483503753150671 \tabularnewline
72 & 102.95 & 102.997442892669 & -0.0474428926691388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100.21[/C][C]99.4527736395709[/C][C]0.757226360429129[/C][/ROW]
[ROW][C]14[/C][C]100.27[/C][C]100.273653880283[/C][C]-0.00365388028328084[/C][/ROW]
[ROW][C]15[/C][C]100.44[/C][C]100.436981495506[/C][C]0.00301850449415042[/C][/ROW]
[ROW][C]16[/C][C]100.57[/C][C]100.561976528016[/C][C]0.00802347198379039[/C][/ROW]
[ROW][C]17[/C][C]100.51[/C][C]100.508652550478[/C][C]0.00134744952174515[/C][/ROW]
[ROW][C]18[/C][C]100.47[/C][C]100.47031727598[/C][C]-0.0003172759801231[/C][/ROW]
[ROW][C]19[/C][C]100.47[/C][C]100.462874138092[/C][C]0.00712586190819309[/C][/ROW]
[ROW][C]20[/C][C]100.49[/C][C]100.571098793087[/C][C]-0.081098793086781[/C][/ROW]
[ROW][C]21[/C][C]101[/C][C]100.791570230125[/C][C]0.208429769875494[/C][/ROW]
[ROW][C]22[/C][C]101.61[/C][C]101.716718009189[/C][C]-0.106718009189336[/C][/ROW]
[ROW][C]23[/C][C]101.65[/C][C]101.705224351002[/C][C]-0.0552243510022095[/C][/ROW]
[ROW][C]24[/C][C]101.74[/C][C]101.718187394993[/C][C]0.0218126050068577[/C][/ROW]
[ROW][C]25[/C][C]101.74[/C][C]101.739229180344[/C][C]0.000770819656395361[/C][/ROW]
[ROW][C]26[/C][C]101.73[/C][C]101.802685634596[/C][C]-0.0726856345963682[/C][/ROW]
[ROW][C]27[/C][C]101.77[/C][C]101.89756188697[/C][C]-0.127561886969971[/C][/ROW]
[ROW][C]28[/C][C]101.82[/C][C]101.891908488114[/C][C]-0.0719084881139764[/C][/ROW]
[ROW][C]29[/C][C]101.97[/C][C]101.756313080904[/C][C]0.213686919096389[/C][/ROW]
[ROW][C]30[/C][C]102.09[/C][C]101.927900894632[/C][C]0.162099105368426[/C][/ROW]
[ROW][C]31[/C][C]102.09[/C][C]102.080719550635[/C][C]0.00928044936502204[/C][/ROW]
[ROW][C]32[/C][C]102.08[/C][C]102.190689758366[/C][C]-0.110689758365623[/C][/ROW]
[ROW][C]33[/C][C]102.42[/C][C]102.384337320919[/C][C]0.0356626790810282[/C][/ROW]
[ROW][C]34[/C][C]102.78[/C][C]103.145003107941[/C][C]-0.365003107941035[/C][/ROW]
[ROW][C]35[/C][C]103.04[/C][C]102.874854028433[/C][C]0.165145971567483[/C][/ROW]
[ROW][C]36[/C][C]103.08[/C][C]103.107378912001[/C][C]-0.0273789120006569[/C][/ROW]
[ROW][C]37[/C][C]99.16[/C][C]103.077544340488[/C][C]-3.91754434048833[/C][/ROW]
[ROW][C]38[/C][C]99.19[/C][C]99.2243183626174[/C][C]-0.0343183626174408[/C][/ROW]
[ROW][C]39[/C][C]99.23[/C][C]99.3565521648337[/C][C]-0.12655216483374[/C][/ROW]
[ROW][C]40[/C][C]99.31[/C][C]99.3520384289799[/C][C]-0.0420384289798648[/C][/ROW]
[ROW][C]41[/C][C]99.46[/C][C]99.2510107358095[/C][C]0.208989264190478[/C][/ROW]
[ROW][C]42[/C][C]99.49[/C][C]99.4220550844842[/C][C]0.0679449155157954[/C][/ROW]
[ROW][C]43[/C][C]99.95[/C][C]99.484177530504[/C][C]0.465822469496047[/C][/ROW]
[ROW][C]44[/C][C]100.14[/C][C]100.051230088182[/C][C]0.0887699118175505[/C][/ROW]
[ROW][C]45[/C][C]100.43[/C][C]100.440961122088[/C][C]-0.0109611220879913[/C][/ROW]
[ROW][C]46[/C][C]101.1[/C][C]101.143392300535[/C][C]-0.0433923005355012[/C][/ROW]
[ROW][C]47[/C][C]101.26[/C][C]101.195385773661[/C][C]0.0646142263392306[/C][/ROW]
[ROW][C]48[/C][C]101.28[/C][C]101.328414235545[/C][C]-0.0484142355449819[/C][/ROW]
[ROW][C]49[/C][C]101.04[/C][C]101.279807558204[/C][C]-0.239807558204376[/C][/ROW]
[ROW][C]50[/C][C]101.12[/C][C]101.103128622819[/C][C]0.0168713771808626[/C][/ROW]
[ROW][C]51[/C][C]101.07[/C][C]101.287319394646[/C][C]-0.217319394645926[/C][/ROW]
[ROW][C]52[/C][C]100.97[/C][C]101.191944298589[/C][C]-0.221944298588824[/C][/ROW]
[ROW][C]53[/C][C]101.01[/C][C]100.907903920214[/C][C]0.102096079785625[/C][/ROW]
[ROW][C]54[/C][C]100.99[/C][C]100.969489748121[/C][C]0.0205102518789602[/C][/ROW]
[ROW][C]55[/C][C]101.19[/C][C]100.982182542118[/C][C]0.207817457882001[/C][/ROW]
[ROW][C]56[/C][C]101.25[/C][C]101.290916999877[/C][C]-0.040916999877382[/C][/ROW]
[ROW][C]57[/C][C]101.33[/C][C]101.552892864718[/C][C]-0.222892864718105[/C][/ROW]
[ROW][C]58[/C][C]101.79[/C][C]102.048643419463[/C][C]-0.258643419462615[/C][/ROW]
[ROW][C]59[/C][C]102.06[/C][C]101.885167378299[/C][C]0.174832621700816[/C][/ROW]
[ROW][C]60[/C][C]102.09[/C][C]102.127948921592[/C][C]-0.0379489215924735[/C][/ROW]
[ROW][C]61[/C][C]102.27[/C][C]102.088789110232[/C][C]0.18121088976784[/C][/ROW]
[ROW][C]62[/C][C]102.26[/C][C]102.332350229228[/C][C]-0.072350229227709[/C][/ROW]
[ROW][C]63[/C][C]102.46[/C][C]102.427772577022[/C][C]0.0322274229779822[/C][/ROW]
[ROW][C]64[/C][C]102.46[/C][C]102.581873189217[/C][C]-0.121873189217325[/C][/ROW]
[ROW][C]65[/C][C]102.51[/C][C]102.395115272481[/C][C]0.114884727518628[/C][/ROW]
[ROW][C]66[/C][C]102.56[/C][C]102.467007164544[/C][C]0.0929928354562435[/C][/ROW]
[ROW][C]67[/C][C]102.59[/C][C]102.550094454274[/C][C]0.0399055457259578[/C][/ROW]
[ROW][C]68[/C][C]102.26[/C][C]102.690563513081[/C][C]-0.430563513081324[/C][/ROW]
[ROW][C]69[/C][C]102.33[/C][C]102.564650576481[/C][C]-0.234650576480604[/C][/ROW]
[ROW][C]70[/C][C]102.84[/C][C]103.054477996048[/C][C]-0.214477996048302[/C][/ROW]
[ROW][C]71[/C][C]102.93[/C][C]102.934835037532[/C][C]-0.00483503753150671[/C][/ROW]
[ROW][C]72[/C][C]102.95[/C][C]102.997442892669[/C][C]-0.0474428926691388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
13100.2199.45277363957090.757226360429129
14100.27100.273653880283-0.00365388028328084
15100.44100.4369814955060.00301850449415042
16100.57100.5619765280160.00802347198379039
17100.51100.5086525504780.00134744952174515
18100.47100.47031727598-0.0003172759801231
19100.47100.4628741380920.00712586190819309
20100.49100.571098793087-0.081098793086781
21101100.7915702301250.208429769875494
22101.61101.716718009189-0.106718009189336
23101.65101.705224351002-0.0552243510022095
24101.74101.7181873949930.0218126050068577
25101.74101.7392291803440.000770819656395361
26101.73101.802685634596-0.0726856345963682
27101.77101.89756188697-0.127561886969971
28101.82101.891908488114-0.0719084881139764
29101.97101.7563130809040.213686919096389
30102.09101.9279008946320.162099105368426
31102.09102.0807195506350.00928044936502204
32102.08102.190689758366-0.110689758365623
33102.42102.3843373209190.0356626790810282
34102.78103.145003107941-0.365003107941035
35103.04102.8748540284330.165145971567483
36103.08103.107378912001-0.0273789120006569
3799.16103.077544340488-3.91754434048833
3899.1999.2243183626174-0.0343183626174408
3999.2399.3565521648337-0.12655216483374
4099.3199.3520384289799-0.0420384289798648
4199.4699.25101073580950.208989264190478
4299.4999.42205508448420.0679449155157954
4399.9599.4841775305040.465822469496047
44100.14100.0512300881820.0887699118175505
45100.43100.440961122088-0.0109611220879913
46101.1101.143392300535-0.0433923005355012
47101.26101.1953857736610.0646142263392306
48101.28101.328414235545-0.0484142355449819
49101.04101.279807558204-0.239807558204376
50101.12101.1031286228190.0168713771808626
51101.07101.287319394646-0.217319394645926
52100.97101.191944298589-0.221944298588824
53101.01100.9079039202140.102096079785625
54100.99100.9694897481210.0205102518789602
55101.19100.9821825421180.207817457882001
56101.25101.290916999877-0.040916999877382
57101.33101.552892864718-0.222892864718105
58101.79102.048643419463-0.258643419462615
59102.06101.8851673782990.174832621700816
60102.09102.127948921592-0.0379489215924735
61102.27102.0887891102320.18121088976784
62102.26102.332350229228-0.072350229227709
63102.46102.4277725770220.0322274229779822
64102.46102.581873189217-0.121873189217325
65102.51102.3951152724810.114884727518628
66102.56102.4670071645440.0929928354562435
67102.59102.5500944542740.0399055457259578
68102.26102.690563513081-0.430563513081324
69102.33102.564650576481-0.234650576480604
70102.84103.054477996048-0.214477996048302
71102.93102.934835037532-0.00483503753150671
72102.95102.997442892669-0.0474428926691388







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.947707795101101.895661068474103.999754521729
74103.009629143512101.522281095806104.496977191219
75103.177699719408101.355402897367104.999996541449
76103.299536192672101.195438223222105.403634162121
77103.233080209649100.884149750397105.582010668901
78103.188890636157100.618671136555105.75911013576
79103.178148670755100.404113641507105.952183700003
80103.278563681844100.312389853033106.244737510654
81103.584986873537100.432901965489106.737071781584
82104.316787186613100.976320106866107.657254266359
83104.411154798823100.909946444743107.912363152903
84104.47773618995.4642198598098113.49125251819

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.947707795101 & 101.895661068474 & 103.999754521729 \tabularnewline
74 & 103.009629143512 & 101.522281095806 & 104.496977191219 \tabularnewline
75 & 103.177699719408 & 101.355402897367 & 104.999996541449 \tabularnewline
76 & 103.299536192672 & 101.195438223222 & 105.403634162121 \tabularnewline
77 & 103.233080209649 & 100.884149750397 & 105.582010668901 \tabularnewline
78 & 103.188890636157 & 100.618671136555 & 105.75911013576 \tabularnewline
79 & 103.178148670755 & 100.404113641507 & 105.952183700003 \tabularnewline
80 & 103.278563681844 & 100.312389853033 & 106.244737510654 \tabularnewline
81 & 103.584986873537 & 100.432901965489 & 106.737071781584 \tabularnewline
82 & 104.316787186613 & 100.976320106866 & 107.657254266359 \tabularnewline
83 & 104.411154798823 & 100.909946444743 & 107.912363152903 \tabularnewline
84 & 104.477736189 & 95.4642198598098 & 113.49125251819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]102.947707795101[/C][C]101.895661068474[/C][C]103.999754521729[/C][/ROW]
[ROW][C]74[/C][C]103.009629143512[/C][C]101.522281095806[/C][C]104.496977191219[/C][/ROW]
[ROW][C]75[/C][C]103.177699719408[/C][C]101.355402897367[/C][C]104.999996541449[/C][/ROW]
[ROW][C]76[/C][C]103.299536192672[/C][C]101.195438223222[/C][C]105.403634162121[/C][/ROW]
[ROW][C]77[/C][C]103.233080209649[/C][C]100.884149750397[/C][C]105.582010668901[/C][/ROW]
[ROW][C]78[/C][C]103.188890636157[/C][C]100.618671136555[/C][C]105.75911013576[/C][/ROW]
[ROW][C]79[/C][C]103.178148670755[/C][C]100.404113641507[/C][C]105.952183700003[/C][/ROW]
[ROW][C]80[/C][C]103.278563681844[/C][C]100.312389853033[/C][C]106.244737510654[/C][/ROW]
[ROW][C]81[/C][C]103.584986873537[/C][C]100.432901965489[/C][C]106.737071781584[/C][/ROW]
[ROW][C]82[/C][C]104.316787186613[/C][C]100.976320106866[/C][C]107.657254266359[/C][/ROW]
[ROW][C]83[/C][C]104.411154798823[/C][C]100.909946444743[/C][C]107.912363152903[/C][/ROW]
[ROW][C]84[/C][C]104.477736189[/C][C]95.4642198598098[/C][C]113.49125251819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73102.947707795101101.895661068474103.999754521729
74103.009629143512101.522281095806104.496977191219
75103.177699719408101.355402897367104.999996541449
76103.299536192672101.195438223222105.403634162121
77103.233080209649100.884149750397105.582010668901
78103.188890636157100.618671136555105.75911013576
79103.178148670755100.404113641507105.952183700003
80103.278563681844100.312389853033106.244737510654
81103.584986873537100.432901965489106.737071781584
82104.316787186613100.976320106866107.657254266359
83104.411154798823100.909946444743107.912363152903
84104.47773618995.4642198598098113.49125251819



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):
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')