Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Apr 2017 14:29:20 +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/2017/Apr/28/t1493386241j2tecyqun1uo843.htm/, Retrieved Fri, 10 May 2024 21:52:04 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 21:52:04 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
78,46
78,59
81,37
83,61
84,65
84,56
83,85
84,08
85,41
85,75
86,38
88,87
90,37
92,21
95,75
97,29
98,29
99,51
99,04
98,9
100,74
100,3
101,68
101,3
103,13
104,17
105,98
106,25
104,01
101,68
101,93
104,41
105,51
104,71
103,14
102,66
102,68
101,89
101,37
101,16
99,34
99,35
99,88
99,31
99,91
98,39
98,02
98,7
98,01
98,42
98,2
93,5
93,17
93,42
93,13
92,31
92,09
92,62
91,43
89,38
86,21
86,65
88,62
87,3
88,33
88,67
88,23
88,85
90,38
89,65
89,2
87,87





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99991957357055
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99991957357055 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \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]0.99991957357055[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/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
alpha0.99991957357055
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
278.5978.460.13000000000001
381.3778.58998954456422.78001045543583
483.6181.36977641368522.24022358631476
584.6583.60981982681581.04018017318423
684.5684.6499163420227-0.0899163420226898
783.8584.5600072316503-0.710007231650337
884.0883.85005710334650.229942896653483
985.4184.07998150651381.33001849348615
1085.7585.40989303136150.340106968638537
1186.3885.74997264641090.630027353589114
1288.8786.37994932914952.49005067085052
1390.3788.86979973411541.5002002658846
1492.2190.36987934424921.84012065575084
1595.7592.20985200566593.54014799433411
1697.2995.74971527853711.54028472146291
1798.2997.28987612039951.00012387960048
1899.5198.28991956360741.22008043639265
1999.0499.5099018732869-0.469901873286858
2098.999.0400377925299-0.140037792529853
21100.7498.90001126273971.83998873726034
22100.3100.739852016276-0.439852016275637
23101.68100.3000353757271.37996462427286
24101.3101.679889014373-0.379889014372509
25103.13101.3000305531171.82996944688298
26104.17103.1298528220911.04014717790862
27105.98104.1699163446761.81008365532362
28106.25105.9798544214350.270145578565391
29104.01106.249978273156-2.23997827315567
30101.68104.010180153455-2.33018015345455
31101.93101.680187408070.249812591930279
32104.41101.9299799084652.4800200915348
33105.51104.4098005408391.10019945916093
34104.71105.509911514886-0.799911514885821
35103.14104.710064334027-1.57006433402701
36102.66103.140126274668-0.480126274668393
37102.68102.6600386148420.0199613851580551
38101.89102.679998394577-0.789998394577069
39101.37101.89006353675-0.520063536750143
40101.16101.370041826853-0.210041826853356
4199.34101.160016892914-1.82001689291415
4299.3599.34014637746020.00985362253976518
4399.8899.34999920750830.530000792491677
4499.3199.8799573739286-0.569957373928645
4599.9199.31004583963650.599954160363467
4698.3999.909951747829-1.51995174782904
4798.0298.390122244292-0.37012224429202
4898.798.02002976761060.679970232389437
4998.0198.6999453124221-0.689945312422068
5098.4298.0100554898380.409944510162006
5198.298.4199670296268-0.219967029626773
5293.598.2000176911628-4.7000176911628
5393.1793.5003780056413-0.330378005641251
5493.4293.17002657112340.249973428876629
5593.1393.4199798955297-0.289979895529669
5692.3193.1300233220476-0.820023322047604
5792.0992.3100659515479-0.220065951547852
5892.6292.09001769911870.529982300881272
5991.4392.6199573754159-1.18995737541586
6089.3891.4300957040229-2.05009570402292
6186.2189.3801648818775-3.17016488187751
6286.6586.21025496504220.439745034957795
6388.6286.6499646328771.97003536712302
6487.388.6198415570895-1.31984155708955
6588.3387.30010615014391.02989384985612
6688.6788.32991716931490.340082830685063
6788.2388.6699726483522-0.43997264835221
6888.8588.23003538542920.619964614570819
6990.3888.84995013845971.53004986154033
7089.6590.3798769435528-0.729876943552753
7189.289.6500587013965-0.4500587013965
7287.8789.2000361966144-1.3300361966144

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 78.59 & 78.46 & 0.13000000000001 \tabularnewline
3 & 81.37 & 78.5899895445642 & 2.78001045543583 \tabularnewline
4 & 83.61 & 81.3697764136852 & 2.24022358631476 \tabularnewline
5 & 84.65 & 83.6098198268158 & 1.04018017318423 \tabularnewline
6 & 84.56 & 84.6499163420227 & -0.0899163420226898 \tabularnewline
7 & 83.85 & 84.5600072316503 & -0.710007231650337 \tabularnewline
8 & 84.08 & 83.8500571033465 & 0.229942896653483 \tabularnewline
9 & 85.41 & 84.0799815065138 & 1.33001849348615 \tabularnewline
10 & 85.75 & 85.4098930313615 & 0.340106968638537 \tabularnewline
11 & 86.38 & 85.7499726464109 & 0.630027353589114 \tabularnewline
12 & 88.87 & 86.3799493291495 & 2.49005067085052 \tabularnewline
13 & 90.37 & 88.8697997341154 & 1.5002002658846 \tabularnewline
14 & 92.21 & 90.3698793442492 & 1.84012065575084 \tabularnewline
15 & 95.75 & 92.2098520056659 & 3.54014799433411 \tabularnewline
16 & 97.29 & 95.7497152785371 & 1.54028472146291 \tabularnewline
17 & 98.29 & 97.2898761203995 & 1.00012387960048 \tabularnewline
18 & 99.51 & 98.2899195636074 & 1.22008043639265 \tabularnewline
19 & 99.04 & 99.5099018732869 & -0.469901873286858 \tabularnewline
20 & 98.9 & 99.0400377925299 & -0.140037792529853 \tabularnewline
21 & 100.74 & 98.9000112627397 & 1.83998873726034 \tabularnewline
22 & 100.3 & 100.739852016276 & -0.439852016275637 \tabularnewline
23 & 101.68 & 100.300035375727 & 1.37996462427286 \tabularnewline
24 & 101.3 & 101.679889014373 & -0.379889014372509 \tabularnewline
25 & 103.13 & 101.300030553117 & 1.82996944688298 \tabularnewline
26 & 104.17 & 103.129852822091 & 1.04014717790862 \tabularnewline
27 & 105.98 & 104.169916344676 & 1.81008365532362 \tabularnewline
28 & 106.25 & 105.979854421435 & 0.270145578565391 \tabularnewline
29 & 104.01 & 106.249978273156 & -2.23997827315567 \tabularnewline
30 & 101.68 & 104.010180153455 & -2.33018015345455 \tabularnewline
31 & 101.93 & 101.68018740807 & 0.249812591930279 \tabularnewline
32 & 104.41 & 101.929979908465 & 2.4800200915348 \tabularnewline
33 & 105.51 & 104.409800540839 & 1.10019945916093 \tabularnewline
34 & 104.71 & 105.509911514886 & -0.799911514885821 \tabularnewline
35 & 103.14 & 104.710064334027 & -1.57006433402701 \tabularnewline
36 & 102.66 & 103.140126274668 & -0.480126274668393 \tabularnewline
37 & 102.68 & 102.660038614842 & 0.0199613851580551 \tabularnewline
38 & 101.89 & 102.679998394577 & -0.789998394577069 \tabularnewline
39 & 101.37 & 101.89006353675 & -0.520063536750143 \tabularnewline
40 & 101.16 & 101.370041826853 & -0.210041826853356 \tabularnewline
41 & 99.34 & 101.160016892914 & -1.82001689291415 \tabularnewline
42 & 99.35 & 99.3401463774602 & 0.00985362253976518 \tabularnewline
43 & 99.88 & 99.3499992075083 & 0.530000792491677 \tabularnewline
44 & 99.31 & 99.8799573739286 & -0.569957373928645 \tabularnewline
45 & 99.91 & 99.3100458396365 & 0.599954160363467 \tabularnewline
46 & 98.39 & 99.909951747829 & -1.51995174782904 \tabularnewline
47 & 98.02 & 98.390122244292 & -0.37012224429202 \tabularnewline
48 & 98.7 & 98.0200297676106 & 0.679970232389437 \tabularnewline
49 & 98.01 & 98.6999453124221 & -0.689945312422068 \tabularnewline
50 & 98.42 & 98.010055489838 & 0.409944510162006 \tabularnewline
51 & 98.2 & 98.4199670296268 & -0.219967029626773 \tabularnewline
52 & 93.5 & 98.2000176911628 & -4.7000176911628 \tabularnewline
53 & 93.17 & 93.5003780056413 & -0.330378005641251 \tabularnewline
54 & 93.42 & 93.1700265711234 & 0.249973428876629 \tabularnewline
55 & 93.13 & 93.4199798955297 & -0.289979895529669 \tabularnewline
56 & 92.31 & 93.1300233220476 & -0.820023322047604 \tabularnewline
57 & 92.09 & 92.3100659515479 & -0.220065951547852 \tabularnewline
58 & 92.62 & 92.0900176991187 & 0.529982300881272 \tabularnewline
59 & 91.43 & 92.6199573754159 & -1.18995737541586 \tabularnewline
60 & 89.38 & 91.4300957040229 & -2.05009570402292 \tabularnewline
61 & 86.21 & 89.3801648818775 & -3.17016488187751 \tabularnewline
62 & 86.65 & 86.2102549650422 & 0.439745034957795 \tabularnewline
63 & 88.62 & 86.649964632877 & 1.97003536712302 \tabularnewline
64 & 87.3 & 88.6198415570895 & -1.31984155708955 \tabularnewline
65 & 88.33 & 87.3001061501439 & 1.02989384985612 \tabularnewline
66 & 88.67 & 88.3299171693149 & 0.340082830685063 \tabularnewline
67 & 88.23 & 88.6699726483522 & -0.43997264835221 \tabularnewline
68 & 88.85 & 88.2300353854292 & 0.619964614570819 \tabularnewline
69 & 90.38 & 88.8499501384597 & 1.53004986154033 \tabularnewline
70 & 89.65 & 90.3798769435528 & -0.729876943552753 \tabularnewline
71 & 89.2 & 89.6500587013965 & -0.4500587013965 \tabularnewline
72 & 87.87 & 89.2000361966144 & -1.3300361966144 \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]2[/C][C]78.59[/C][C]78.46[/C][C]0.13000000000001[/C][/ROW]
[ROW][C]3[/C][C]81.37[/C][C]78.5899895445642[/C][C]2.78001045543583[/C][/ROW]
[ROW][C]4[/C][C]83.61[/C][C]81.3697764136852[/C][C]2.24022358631476[/C][/ROW]
[ROW][C]5[/C][C]84.65[/C][C]83.6098198268158[/C][C]1.04018017318423[/C][/ROW]
[ROW][C]6[/C][C]84.56[/C][C]84.6499163420227[/C][C]-0.0899163420226898[/C][/ROW]
[ROW][C]7[/C][C]83.85[/C][C]84.5600072316503[/C][C]-0.710007231650337[/C][/ROW]
[ROW][C]8[/C][C]84.08[/C][C]83.8500571033465[/C][C]0.229942896653483[/C][/ROW]
[ROW][C]9[/C][C]85.41[/C][C]84.0799815065138[/C][C]1.33001849348615[/C][/ROW]
[ROW][C]10[/C][C]85.75[/C][C]85.4098930313615[/C][C]0.340106968638537[/C][/ROW]
[ROW][C]11[/C][C]86.38[/C][C]85.7499726464109[/C][C]0.630027353589114[/C][/ROW]
[ROW][C]12[/C][C]88.87[/C][C]86.3799493291495[/C][C]2.49005067085052[/C][/ROW]
[ROW][C]13[/C][C]90.37[/C][C]88.8697997341154[/C][C]1.5002002658846[/C][/ROW]
[ROW][C]14[/C][C]92.21[/C][C]90.3698793442492[/C][C]1.84012065575084[/C][/ROW]
[ROW][C]15[/C][C]95.75[/C][C]92.2098520056659[/C][C]3.54014799433411[/C][/ROW]
[ROW][C]16[/C][C]97.29[/C][C]95.7497152785371[/C][C]1.54028472146291[/C][/ROW]
[ROW][C]17[/C][C]98.29[/C][C]97.2898761203995[/C][C]1.00012387960048[/C][/ROW]
[ROW][C]18[/C][C]99.51[/C][C]98.2899195636074[/C][C]1.22008043639265[/C][/ROW]
[ROW][C]19[/C][C]99.04[/C][C]99.5099018732869[/C][C]-0.469901873286858[/C][/ROW]
[ROW][C]20[/C][C]98.9[/C][C]99.0400377925299[/C][C]-0.140037792529853[/C][/ROW]
[ROW][C]21[/C][C]100.74[/C][C]98.9000112627397[/C][C]1.83998873726034[/C][/ROW]
[ROW][C]22[/C][C]100.3[/C][C]100.739852016276[/C][C]-0.439852016275637[/C][/ROW]
[ROW][C]23[/C][C]101.68[/C][C]100.300035375727[/C][C]1.37996462427286[/C][/ROW]
[ROW][C]24[/C][C]101.3[/C][C]101.679889014373[/C][C]-0.379889014372509[/C][/ROW]
[ROW][C]25[/C][C]103.13[/C][C]101.300030553117[/C][C]1.82996944688298[/C][/ROW]
[ROW][C]26[/C][C]104.17[/C][C]103.129852822091[/C][C]1.04014717790862[/C][/ROW]
[ROW][C]27[/C][C]105.98[/C][C]104.169916344676[/C][C]1.81008365532362[/C][/ROW]
[ROW][C]28[/C][C]106.25[/C][C]105.979854421435[/C][C]0.270145578565391[/C][/ROW]
[ROW][C]29[/C][C]104.01[/C][C]106.249978273156[/C][C]-2.23997827315567[/C][/ROW]
[ROW][C]30[/C][C]101.68[/C][C]104.010180153455[/C][C]-2.33018015345455[/C][/ROW]
[ROW][C]31[/C][C]101.93[/C][C]101.68018740807[/C][C]0.249812591930279[/C][/ROW]
[ROW][C]32[/C][C]104.41[/C][C]101.929979908465[/C][C]2.4800200915348[/C][/ROW]
[ROW][C]33[/C][C]105.51[/C][C]104.409800540839[/C][C]1.10019945916093[/C][/ROW]
[ROW][C]34[/C][C]104.71[/C][C]105.509911514886[/C][C]-0.799911514885821[/C][/ROW]
[ROW][C]35[/C][C]103.14[/C][C]104.710064334027[/C][C]-1.57006433402701[/C][/ROW]
[ROW][C]36[/C][C]102.66[/C][C]103.140126274668[/C][C]-0.480126274668393[/C][/ROW]
[ROW][C]37[/C][C]102.68[/C][C]102.660038614842[/C][C]0.0199613851580551[/C][/ROW]
[ROW][C]38[/C][C]101.89[/C][C]102.679998394577[/C][C]-0.789998394577069[/C][/ROW]
[ROW][C]39[/C][C]101.37[/C][C]101.89006353675[/C][C]-0.520063536750143[/C][/ROW]
[ROW][C]40[/C][C]101.16[/C][C]101.370041826853[/C][C]-0.210041826853356[/C][/ROW]
[ROW][C]41[/C][C]99.34[/C][C]101.160016892914[/C][C]-1.82001689291415[/C][/ROW]
[ROW][C]42[/C][C]99.35[/C][C]99.3401463774602[/C][C]0.00985362253976518[/C][/ROW]
[ROW][C]43[/C][C]99.88[/C][C]99.3499992075083[/C][C]0.530000792491677[/C][/ROW]
[ROW][C]44[/C][C]99.31[/C][C]99.8799573739286[/C][C]-0.569957373928645[/C][/ROW]
[ROW][C]45[/C][C]99.91[/C][C]99.3100458396365[/C][C]0.599954160363467[/C][/ROW]
[ROW][C]46[/C][C]98.39[/C][C]99.909951747829[/C][C]-1.51995174782904[/C][/ROW]
[ROW][C]47[/C][C]98.02[/C][C]98.390122244292[/C][C]-0.37012224429202[/C][/ROW]
[ROW][C]48[/C][C]98.7[/C][C]98.0200297676106[/C][C]0.679970232389437[/C][/ROW]
[ROW][C]49[/C][C]98.01[/C][C]98.6999453124221[/C][C]-0.689945312422068[/C][/ROW]
[ROW][C]50[/C][C]98.42[/C][C]98.010055489838[/C][C]0.409944510162006[/C][/ROW]
[ROW][C]51[/C][C]98.2[/C][C]98.4199670296268[/C][C]-0.219967029626773[/C][/ROW]
[ROW][C]52[/C][C]93.5[/C][C]98.2000176911628[/C][C]-4.7000176911628[/C][/ROW]
[ROW][C]53[/C][C]93.17[/C][C]93.5003780056413[/C][C]-0.330378005641251[/C][/ROW]
[ROW][C]54[/C][C]93.42[/C][C]93.1700265711234[/C][C]0.249973428876629[/C][/ROW]
[ROW][C]55[/C][C]93.13[/C][C]93.4199798955297[/C][C]-0.289979895529669[/C][/ROW]
[ROW][C]56[/C][C]92.31[/C][C]93.1300233220476[/C][C]-0.820023322047604[/C][/ROW]
[ROW][C]57[/C][C]92.09[/C][C]92.3100659515479[/C][C]-0.220065951547852[/C][/ROW]
[ROW][C]58[/C][C]92.62[/C][C]92.0900176991187[/C][C]0.529982300881272[/C][/ROW]
[ROW][C]59[/C][C]91.43[/C][C]92.6199573754159[/C][C]-1.18995737541586[/C][/ROW]
[ROW][C]60[/C][C]89.38[/C][C]91.4300957040229[/C][C]-2.05009570402292[/C][/ROW]
[ROW][C]61[/C][C]86.21[/C][C]89.3801648818775[/C][C]-3.17016488187751[/C][/ROW]
[ROW][C]62[/C][C]86.65[/C][C]86.2102549650422[/C][C]0.439745034957795[/C][/ROW]
[ROW][C]63[/C][C]88.62[/C][C]86.649964632877[/C][C]1.97003536712302[/C][/ROW]
[ROW][C]64[/C][C]87.3[/C][C]88.6198415570895[/C][C]-1.31984155708955[/C][/ROW]
[ROW][C]65[/C][C]88.33[/C][C]87.3001061501439[/C][C]1.02989384985612[/C][/ROW]
[ROW][C]66[/C][C]88.67[/C][C]88.3299171693149[/C][C]0.340082830685063[/C][/ROW]
[ROW][C]67[/C][C]88.23[/C][C]88.6699726483522[/C][C]-0.43997264835221[/C][/ROW]
[ROW][C]68[/C][C]88.85[/C][C]88.2300353854292[/C][C]0.619964614570819[/C][/ROW]
[ROW][C]69[/C][C]90.38[/C][C]88.8499501384597[/C][C]1.53004986154033[/C][/ROW]
[ROW][C]70[/C][C]89.65[/C][C]90.3798769435528[/C][C]-0.729876943552753[/C][/ROW]
[ROW][C]71[/C][C]89.2[/C][C]89.6500587013965[/C][C]-0.4500587013965[/C][/ROW]
[ROW][C]72[/C][C]87.87[/C][C]89.2000361966144[/C][C]-1.3300361966144[/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
278.5978.460.13000000000001
381.3778.58998954456422.78001045543583
483.6181.36977641368522.24022358631476
584.6583.60981982681581.04018017318423
684.5684.6499163420227-0.0899163420226898
783.8584.5600072316503-0.710007231650337
884.0883.85005710334650.229942896653483
985.4184.07998150651381.33001849348615
1085.7585.40989303136150.340106968638537
1186.3885.74997264641090.630027353589114
1288.8786.37994932914952.49005067085052
1390.3788.86979973411541.5002002658846
1492.2190.36987934424921.84012065575084
1595.7592.20985200566593.54014799433411
1697.2995.74971527853711.54028472146291
1798.2997.28987612039951.00012387960048
1899.5198.28991956360741.22008043639265
1999.0499.5099018732869-0.469901873286858
2098.999.0400377925299-0.140037792529853
21100.7498.90001126273971.83998873726034
22100.3100.739852016276-0.439852016275637
23101.68100.3000353757271.37996462427286
24101.3101.679889014373-0.379889014372509
25103.13101.3000305531171.82996944688298
26104.17103.1298528220911.04014717790862
27105.98104.1699163446761.81008365532362
28106.25105.9798544214350.270145578565391
29104.01106.249978273156-2.23997827315567
30101.68104.010180153455-2.33018015345455
31101.93101.680187408070.249812591930279
32104.41101.9299799084652.4800200915348
33105.51104.4098005408391.10019945916093
34104.71105.509911514886-0.799911514885821
35103.14104.710064334027-1.57006433402701
36102.66103.140126274668-0.480126274668393
37102.68102.6600386148420.0199613851580551
38101.89102.679998394577-0.789998394577069
39101.37101.89006353675-0.520063536750143
40101.16101.370041826853-0.210041826853356
4199.34101.160016892914-1.82001689291415
4299.3599.34014637746020.00985362253976518
4399.8899.34999920750830.530000792491677
4499.3199.8799573739286-0.569957373928645
4599.9199.31004583963650.599954160363467
4698.3999.909951747829-1.51995174782904
4798.0298.390122244292-0.37012224429202
4898.798.02002976761060.679970232389437
4998.0198.6999453124221-0.689945312422068
5098.4298.0100554898380.409944510162006
5198.298.4199670296268-0.219967029626773
5293.598.2000176911628-4.7000176911628
5393.1793.5003780056413-0.330378005641251
5493.4293.17002657112340.249973428876629
5593.1393.4199798955297-0.289979895529669
5692.3193.1300233220476-0.820023322047604
5792.0992.3100659515479-0.220065951547852
5892.6292.09001769911870.529982300881272
5991.4392.6199573754159-1.18995737541586
6089.3891.4300957040229-2.05009570402292
6186.2189.3801648818775-3.17016488187751
6286.6586.21025496504220.439745034957795
6388.6286.6499646328771.97003536712302
6487.388.6198415570895-1.31984155708955
6588.3387.30010615014391.02989384985612
6688.6788.32991716931490.340082830685063
6788.2388.6699726483522-0.43997264835221
6888.8588.23003538542920.619964614570819
6990.3888.84995013845971.53004986154033
7089.6590.3798769435528-0.729876943552753
7189.289.6500587013965-0.4500587013965
7287.8789.2000361966144-1.3300361966144







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7387.870106970062385.100456056081390.6397578840434
7487.870106970062383.953386591555791.786827348569
7587.870106970062383.073188077533292.6670258625915
7687.870106970062382.331139268441793.409074671683
7787.870106970062381.677377722170994.0628362179538
7887.870106970062381.086330155058594.6538837850662
7987.870106970062380.542804586928695.1974093531961
8087.870106970062380.036902481989195.7033114581356
8187.870106970062379.561748233821896.1784657063028
8287.870106970062379.112335722298696.6278782178261
8387.870106970062378.684885711635897.0553282284889
8487.870106970062378.276462099402297.4637518407225

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 87.8701069700623 & 85.1004560560813 & 90.6397578840434 \tabularnewline
74 & 87.8701069700623 & 83.9533865915557 & 91.786827348569 \tabularnewline
75 & 87.8701069700623 & 83.0731880775332 & 92.6670258625915 \tabularnewline
76 & 87.8701069700623 & 82.3311392684417 & 93.409074671683 \tabularnewline
77 & 87.8701069700623 & 81.6773777221709 & 94.0628362179538 \tabularnewline
78 & 87.8701069700623 & 81.0863301550585 & 94.6538837850662 \tabularnewline
79 & 87.8701069700623 & 80.5428045869286 & 95.1974093531961 \tabularnewline
80 & 87.8701069700623 & 80.0369024819891 & 95.7033114581356 \tabularnewline
81 & 87.8701069700623 & 79.5617482338218 & 96.1784657063028 \tabularnewline
82 & 87.8701069700623 & 79.1123357222986 & 96.6278782178261 \tabularnewline
83 & 87.8701069700623 & 78.6848857116358 & 97.0553282284889 \tabularnewline
84 & 87.8701069700623 & 78.2764620994022 & 97.4637518407225 \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]87.8701069700623[/C][C]85.1004560560813[/C][C]90.6397578840434[/C][/ROW]
[ROW][C]74[/C][C]87.8701069700623[/C][C]83.9533865915557[/C][C]91.786827348569[/C][/ROW]
[ROW][C]75[/C][C]87.8701069700623[/C][C]83.0731880775332[/C][C]92.6670258625915[/C][/ROW]
[ROW][C]76[/C][C]87.8701069700623[/C][C]82.3311392684417[/C][C]93.409074671683[/C][/ROW]
[ROW][C]77[/C][C]87.8701069700623[/C][C]81.6773777221709[/C][C]94.0628362179538[/C][/ROW]
[ROW][C]78[/C][C]87.8701069700623[/C][C]81.0863301550585[/C][C]94.6538837850662[/C][/ROW]
[ROW][C]79[/C][C]87.8701069700623[/C][C]80.5428045869286[/C][C]95.1974093531961[/C][/ROW]
[ROW][C]80[/C][C]87.8701069700623[/C][C]80.0369024819891[/C][C]95.7033114581356[/C][/ROW]
[ROW][C]81[/C][C]87.8701069700623[/C][C]79.5617482338218[/C][C]96.1784657063028[/C][/ROW]
[ROW][C]82[/C][C]87.8701069700623[/C][C]79.1123357222986[/C][C]96.6278782178261[/C][/ROW]
[ROW][C]83[/C][C]87.8701069700623[/C][C]78.6848857116358[/C][C]97.0553282284889[/C][/ROW]
[ROW][C]84[/C][C]87.8701069700623[/C][C]78.2764620994022[/C][C]97.4637518407225[/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
7387.870106970062385.100456056081390.6397578840434
7487.870106970062383.953386591555791.786827348569
7587.870106970062383.073188077533292.6670258625915
7687.870106970062382.331139268441793.409074671683
7787.870106970062381.677377722170994.0628362179538
7887.870106970062381.086330155058594.6538837850662
7987.870106970062380.542804586928695.1974093531961
8087.870106970062380.036902481989195.7033114581356
8187.870106970062379.561748233821896.1784657063028
8287.870106970062379.112335722298696.6278782178261
8387.870106970062378.684885711635897.0553282284889
8487.870106970062378.276462099402297.4637518407225



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