Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 10 Jan 2017 10:13:35 +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/2017/Jan/10/t14840433062zndep1wl797ru9.htm/, Retrieved Wed, 15 May 2024 05:43:41 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 05:43:41 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92,64
91,48
92,65
93,91
90,49
94,56
95,11
93,07
93,26
92,92
90,9
91,77
86,16
92,79
97,45
97,74
99,92
99,46
98,52
97,92
97,85
104,94
104,55
105,35
95,75
105,99
106,11
107,33
106,11
108,17
104,62
106,71
97,86
104,41
96,09
102,41
96,3
103,04
105,11
99,4
104,45
104,31
104,06
101,16
100,82
102,6
92,78
99,68
95,14
101,28
100,03
101,17
98,93
97,77
100,24
98,05
95,82
99,19
97,42
98,02
97,34
101,23
100,16
100,72
99,8
100,39
101,82
102,95
98,8
100,24
98,4
98,15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.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]'Gwilym Jenkins' @ jenkins.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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.419816745481579
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.419816745481579 \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]0.419816745481579[/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
alpha0.419816745481579
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
291.4892.64-1.16
392.6592.15301257524140.496987424758643
493.9192.36165621844881.54834378155118
590.4993.0116768657063-2.52167686570628
694.5691.95303469078932.60696530921074
795.1193.04748238248552.0625176175145
893.0793.9133618161688-0.843361816168851
993.2693.5593044032414-0.299304403241393
1092.9293.4336514027643-0.513651402764296
1190.993.2180119425437-2.31801194254373
1291.7792.2448717128376-0.474871712837597
1386.1692.0455126158328-5.88551261583285
1492.7989.57467586396313.21532413603688
1597.4590.92452277842256.52547722157752
1697.7493.66402738829934.07597261170066
1799.9295.37518894481564.54481105518444
1899.4697.28317673083182.1768232691682
1998.5298.19704359118260.322956408817433
2097.9298.3326260996647-0.412626099664706
2197.8598.1593987534027-0.309398753402718
22104.9498.02950797569316.91049202430688
23104.55100.9306482470143.61935175298596
24105.35102.4501127207062.89988727929435
2595.75103.667533960562-7.91753396056242
26105.99100.3436206209995.64637937900078
27106.11102.7140652356463.39593476435438
28107.33104.1397355162853.19026448371538
29106.11105.4790619690630.63093803093652
30108.17105.7439403198122.4260596801882
31104.62106.762440799092-2.14244079909248
32106.71105.8630082754310.846991724569463
3397.86106.218589584689-8.35858958468911
34104.41102.7095137084291.70048629157129
3596.09103.423406329092-7.33340632909218
36102.41100.3447195507192.06528044928132
3796.3101.211758867443-4.91175886744269
38103.0499.14972024512263.8902797548774
39105.11100.7829248308284.32707516917189
4099.4102.599503445804-3.199503445804
41104.45101.2562983220293.19370167797054
42104.31102.5970677665141.7129322334859
43104.06103.3161854020070.743814597993364
44101.16103.628451225778-2.4684512257779
45100.82102.592154065792-1.77215406579181
46102.6101.8481741133990.751825886600869
4792.78102.163803210281-9.3838032102807
4899.6898.22432548630111.45567451369894
4995.1498.8354420231226-3.69544202312262
50101.2897.28403357985943.99596642014058
51100.0398.96160719741651.06839280258349
52101.1799.4101363866931.75986361330696
5398.93100.148956601323-1.21895660132301
5497.7799.6372182080723-1.86721820807232
55100.2498.85332873685541.38667126314455
5698.0599.4354765536016-1.38547655360162
5795.8298.8538302959275-3.03383029592754
5899.1997.58017753474781.60982246525219
5997.4298.2560079629131-0.836007962913115
6098.0297.90503782072620.114962179273746
6197.3497.9533008686824-0.613300868682416
62101.2397.69582689399113.53417310600886
63100.1699.17953194532430.980468054675697
64100.7299.59114885308691.12885114691309
6599.8100.065059467717-0.265059467717109
66100.3999.9537830646210.436216935378965
67101.82100.1369142387561.68308576124423
68102.95100.8435018254082.1064981745923
6998.8101.727845033428-2.92784503342791
70100.24100.49868666022-0.258686660219794
7198.4100.390085668427-1.99008566842681
7298.1599.5546143798783-1.40461437987832

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 91.48 & 92.64 & -1.16 \tabularnewline
3 & 92.65 & 92.1530125752414 & 0.496987424758643 \tabularnewline
4 & 93.91 & 92.3616562184488 & 1.54834378155118 \tabularnewline
5 & 90.49 & 93.0116768657063 & -2.52167686570628 \tabularnewline
6 & 94.56 & 91.9530346907893 & 2.60696530921074 \tabularnewline
7 & 95.11 & 93.0474823824855 & 2.0625176175145 \tabularnewline
8 & 93.07 & 93.9133618161688 & -0.843361816168851 \tabularnewline
9 & 93.26 & 93.5593044032414 & -0.299304403241393 \tabularnewline
10 & 92.92 & 93.4336514027643 & -0.513651402764296 \tabularnewline
11 & 90.9 & 93.2180119425437 & -2.31801194254373 \tabularnewline
12 & 91.77 & 92.2448717128376 & -0.474871712837597 \tabularnewline
13 & 86.16 & 92.0455126158328 & -5.88551261583285 \tabularnewline
14 & 92.79 & 89.5746758639631 & 3.21532413603688 \tabularnewline
15 & 97.45 & 90.9245227784225 & 6.52547722157752 \tabularnewline
16 & 97.74 & 93.6640273882993 & 4.07597261170066 \tabularnewline
17 & 99.92 & 95.3751889448156 & 4.54481105518444 \tabularnewline
18 & 99.46 & 97.2831767308318 & 2.1768232691682 \tabularnewline
19 & 98.52 & 98.1970435911826 & 0.322956408817433 \tabularnewline
20 & 97.92 & 98.3326260996647 & -0.412626099664706 \tabularnewline
21 & 97.85 & 98.1593987534027 & -0.309398753402718 \tabularnewline
22 & 104.94 & 98.0295079756931 & 6.91049202430688 \tabularnewline
23 & 104.55 & 100.930648247014 & 3.61935175298596 \tabularnewline
24 & 105.35 & 102.450112720706 & 2.89988727929435 \tabularnewline
25 & 95.75 & 103.667533960562 & -7.91753396056242 \tabularnewline
26 & 105.99 & 100.343620620999 & 5.64637937900078 \tabularnewline
27 & 106.11 & 102.714065235646 & 3.39593476435438 \tabularnewline
28 & 107.33 & 104.139735516285 & 3.19026448371538 \tabularnewline
29 & 106.11 & 105.479061969063 & 0.63093803093652 \tabularnewline
30 & 108.17 & 105.743940319812 & 2.4260596801882 \tabularnewline
31 & 104.62 & 106.762440799092 & -2.14244079909248 \tabularnewline
32 & 106.71 & 105.863008275431 & 0.846991724569463 \tabularnewline
33 & 97.86 & 106.218589584689 & -8.35858958468911 \tabularnewline
34 & 104.41 & 102.709513708429 & 1.70048629157129 \tabularnewline
35 & 96.09 & 103.423406329092 & -7.33340632909218 \tabularnewline
36 & 102.41 & 100.344719550719 & 2.06528044928132 \tabularnewline
37 & 96.3 & 101.211758867443 & -4.91175886744269 \tabularnewline
38 & 103.04 & 99.1497202451226 & 3.8902797548774 \tabularnewline
39 & 105.11 & 100.782924830828 & 4.32707516917189 \tabularnewline
40 & 99.4 & 102.599503445804 & -3.199503445804 \tabularnewline
41 & 104.45 & 101.256298322029 & 3.19370167797054 \tabularnewline
42 & 104.31 & 102.597067766514 & 1.7129322334859 \tabularnewline
43 & 104.06 & 103.316185402007 & 0.743814597993364 \tabularnewline
44 & 101.16 & 103.628451225778 & -2.4684512257779 \tabularnewline
45 & 100.82 & 102.592154065792 & -1.77215406579181 \tabularnewline
46 & 102.6 & 101.848174113399 & 0.751825886600869 \tabularnewline
47 & 92.78 & 102.163803210281 & -9.3838032102807 \tabularnewline
48 & 99.68 & 98.2243254863011 & 1.45567451369894 \tabularnewline
49 & 95.14 & 98.8354420231226 & -3.69544202312262 \tabularnewline
50 & 101.28 & 97.2840335798594 & 3.99596642014058 \tabularnewline
51 & 100.03 & 98.9616071974165 & 1.06839280258349 \tabularnewline
52 & 101.17 & 99.410136386693 & 1.75986361330696 \tabularnewline
53 & 98.93 & 100.148956601323 & -1.21895660132301 \tabularnewline
54 & 97.77 & 99.6372182080723 & -1.86721820807232 \tabularnewline
55 & 100.24 & 98.8533287368554 & 1.38667126314455 \tabularnewline
56 & 98.05 & 99.4354765536016 & -1.38547655360162 \tabularnewline
57 & 95.82 & 98.8538302959275 & -3.03383029592754 \tabularnewline
58 & 99.19 & 97.5801775347478 & 1.60982246525219 \tabularnewline
59 & 97.42 & 98.2560079629131 & -0.836007962913115 \tabularnewline
60 & 98.02 & 97.9050378207262 & 0.114962179273746 \tabularnewline
61 & 97.34 & 97.9533008686824 & -0.613300868682416 \tabularnewline
62 & 101.23 & 97.6958268939911 & 3.53417310600886 \tabularnewline
63 & 100.16 & 99.1795319453243 & 0.980468054675697 \tabularnewline
64 & 100.72 & 99.5911488530869 & 1.12885114691309 \tabularnewline
65 & 99.8 & 100.065059467717 & -0.265059467717109 \tabularnewline
66 & 100.39 & 99.953783064621 & 0.436216935378965 \tabularnewline
67 & 101.82 & 100.136914238756 & 1.68308576124423 \tabularnewline
68 & 102.95 & 100.843501825408 & 2.1064981745923 \tabularnewline
69 & 98.8 & 101.727845033428 & -2.92784503342791 \tabularnewline
70 & 100.24 & 100.49868666022 & -0.258686660219794 \tabularnewline
71 & 98.4 & 100.390085668427 & -1.99008566842681 \tabularnewline
72 & 98.15 & 99.5546143798783 & -1.40461437987832 \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]91.48[/C][C]92.64[/C][C]-1.16[/C][/ROW]
[ROW][C]3[/C][C]92.65[/C][C]92.1530125752414[/C][C]0.496987424758643[/C][/ROW]
[ROW][C]4[/C][C]93.91[/C][C]92.3616562184488[/C][C]1.54834378155118[/C][/ROW]
[ROW][C]5[/C][C]90.49[/C][C]93.0116768657063[/C][C]-2.52167686570628[/C][/ROW]
[ROW][C]6[/C][C]94.56[/C][C]91.9530346907893[/C][C]2.60696530921074[/C][/ROW]
[ROW][C]7[/C][C]95.11[/C][C]93.0474823824855[/C][C]2.0625176175145[/C][/ROW]
[ROW][C]8[/C][C]93.07[/C][C]93.9133618161688[/C][C]-0.843361816168851[/C][/ROW]
[ROW][C]9[/C][C]93.26[/C][C]93.5593044032414[/C][C]-0.299304403241393[/C][/ROW]
[ROW][C]10[/C][C]92.92[/C][C]93.4336514027643[/C][C]-0.513651402764296[/C][/ROW]
[ROW][C]11[/C][C]90.9[/C][C]93.2180119425437[/C][C]-2.31801194254373[/C][/ROW]
[ROW][C]12[/C][C]91.77[/C][C]92.2448717128376[/C][C]-0.474871712837597[/C][/ROW]
[ROW][C]13[/C][C]86.16[/C][C]92.0455126158328[/C][C]-5.88551261583285[/C][/ROW]
[ROW][C]14[/C][C]92.79[/C][C]89.5746758639631[/C][C]3.21532413603688[/C][/ROW]
[ROW][C]15[/C][C]97.45[/C][C]90.9245227784225[/C][C]6.52547722157752[/C][/ROW]
[ROW][C]16[/C][C]97.74[/C][C]93.6640273882993[/C][C]4.07597261170066[/C][/ROW]
[ROW][C]17[/C][C]99.92[/C][C]95.3751889448156[/C][C]4.54481105518444[/C][/ROW]
[ROW][C]18[/C][C]99.46[/C][C]97.2831767308318[/C][C]2.1768232691682[/C][/ROW]
[ROW][C]19[/C][C]98.52[/C][C]98.1970435911826[/C][C]0.322956408817433[/C][/ROW]
[ROW][C]20[/C][C]97.92[/C][C]98.3326260996647[/C][C]-0.412626099664706[/C][/ROW]
[ROW][C]21[/C][C]97.85[/C][C]98.1593987534027[/C][C]-0.309398753402718[/C][/ROW]
[ROW][C]22[/C][C]104.94[/C][C]98.0295079756931[/C][C]6.91049202430688[/C][/ROW]
[ROW][C]23[/C][C]104.55[/C][C]100.930648247014[/C][C]3.61935175298596[/C][/ROW]
[ROW][C]24[/C][C]105.35[/C][C]102.450112720706[/C][C]2.89988727929435[/C][/ROW]
[ROW][C]25[/C][C]95.75[/C][C]103.667533960562[/C][C]-7.91753396056242[/C][/ROW]
[ROW][C]26[/C][C]105.99[/C][C]100.343620620999[/C][C]5.64637937900078[/C][/ROW]
[ROW][C]27[/C][C]106.11[/C][C]102.714065235646[/C][C]3.39593476435438[/C][/ROW]
[ROW][C]28[/C][C]107.33[/C][C]104.139735516285[/C][C]3.19026448371538[/C][/ROW]
[ROW][C]29[/C][C]106.11[/C][C]105.479061969063[/C][C]0.63093803093652[/C][/ROW]
[ROW][C]30[/C][C]108.17[/C][C]105.743940319812[/C][C]2.4260596801882[/C][/ROW]
[ROW][C]31[/C][C]104.62[/C][C]106.762440799092[/C][C]-2.14244079909248[/C][/ROW]
[ROW][C]32[/C][C]106.71[/C][C]105.863008275431[/C][C]0.846991724569463[/C][/ROW]
[ROW][C]33[/C][C]97.86[/C][C]106.218589584689[/C][C]-8.35858958468911[/C][/ROW]
[ROW][C]34[/C][C]104.41[/C][C]102.709513708429[/C][C]1.70048629157129[/C][/ROW]
[ROW][C]35[/C][C]96.09[/C][C]103.423406329092[/C][C]-7.33340632909218[/C][/ROW]
[ROW][C]36[/C][C]102.41[/C][C]100.344719550719[/C][C]2.06528044928132[/C][/ROW]
[ROW][C]37[/C][C]96.3[/C][C]101.211758867443[/C][C]-4.91175886744269[/C][/ROW]
[ROW][C]38[/C][C]103.04[/C][C]99.1497202451226[/C][C]3.8902797548774[/C][/ROW]
[ROW][C]39[/C][C]105.11[/C][C]100.782924830828[/C][C]4.32707516917189[/C][/ROW]
[ROW][C]40[/C][C]99.4[/C][C]102.599503445804[/C][C]-3.199503445804[/C][/ROW]
[ROW][C]41[/C][C]104.45[/C][C]101.256298322029[/C][C]3.19370167797054[/C][/ROW]
[ROW][C]42[/C][C]104.31[/C][C]102.597067766514[/C][C]1.7129322334859[/C][/ROW]
[ROW][C]43[/C][C]104.06[/C][C]103.316185402007[/C][C]0.743814597993364[/C][/ROW]
[ROW][C]44[/C][C]101.16[/C][C]103.628451225778[/C][C]-2.4684512257779[/C][/ROW]
[ROW][C]45[/C][C]100.82[/C][C]102.592154065792[/C][C]-1.77215406579181[/C][/ROW]
[ROW][C]46[/C][C]102.6[/C][C]101.848174113399[/C][C]0.751825886600869[/C][/ROW]
[ROW][C]47[/C][C]92.78[/C][C]102.163803210281[/C][C]-9.3838032102807[/C][/ROW]
[ROW][C]48[/C][C]99.68[/C][C]98.2243254863011[/C][C]1.45567451369894[/C][/ROW]
[ROW][C]49[/C][C]95.14[/C][C]98.8354420231226[/C][C]-3.69544202312262[/C][/ROW]
[ROW][C]50[/C][C]101.28[/C][C]97.2840335798594[/C][C]3.99596642014058[/C][/ROW]
[ROW][C]51[/C][C]100.03[/C][C]98.9616071974165[/C][C]1.06839280258349[/C][/ROW]
[ROW][C]52[/C][C]101.17[/C][C]99.410136386693[/C][C]1.75986361330696[/C][/ROW]
[ROW][C]53[/C][C]98.93[/C][C]100.148956601323[/C][C]-1.21895660132301[/C][/ROW]
[ROW][C]54[/C][C]97.77[/C][C]99.6372182080723[/C][C]-1.86721820807232[/C][/ROW]
[ROW][C]55[/C][C]100.24[/C][C]98.8533287368554[/C][C]1.38667126314455[/C][/ROW]
[ROW][C]56[/C][C]98.05[/C][C]99.4354765536016[/C][C]-1.38547655360162[/C][/ROW]
[ROW][C]57[/C][C]95.82[/C][C]98.8538302959275[/C][C]-3.03383029592754[/C][/ROW]
[ROW][C]58[/C][C]99.19[/C][C]97.5801775347478[/C][C]1.60982246525219[/C][/ROW]
[ROW][C]59[/C][C]97.42[/C][C]98.2560079629131[/C][C]-0.836007962913115[/C][/ROW]
[ROW][C]60[/C][C]98.02[/C][C]97.9050378207262[/C][C]0.114962179273746[/C][/ROW]
[ROW][C]61[/C][C]97.34[/C][C]97.9533008686824[/C][C]-0.613300868682416[/C][/ROW]
[ROW][C]62[/C][C]101.23[/C][C]97.6958268939911[/C][C]3.53417310600886[/C][/ROW]
[ROW][C]63[/C][C]100.16[/C][C]99.1795319453243[/C][C]0.980468054675697[/C][/ROW]
[ROW][C]64[/C][C]100.72[/C][C]99.5911488530869[/C][C]1.12885114691309[/C][/ROW]
[ROW][C]65[/C][C]99.8[/C][C]100.065059467717[/C][C]-0.265059467717109[/C][/ROW]
[ROW][C]66[/C][C]100.39[/C][C]99.953783064621[/C][C]0.436216935378965[/C][/ROW]
[ROW][C]67[/C][C]101.82[/C][C]100.136914238756[/C][C]1.68308576124423[/C][/ROW]
[ROW][C]68[/C][C]102.95[/C][C]100.843501825408[/C][C]2.1064981745923[/C][/ROW]
[ROW][C]69[/C][C]98.8[/C][C]101.727845033428[/C][C]-2.92784503342791[/C][/ROW]
[ROW][C]70[/C][C]100.24[/C][C]100.49868666022[/C][C]-0.258686660219794[/C][/ROW]
[ROW][C]71[/C][C]98.4[/C][C]100.390085668427[/C][C]-1.99008566842681[/C][/ROW]
[ROW][C]72[/C][C]98.15[/C][C]99.5546143798783[/C][C]-1.40461437987832[/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
291.4892.64-1.16
392.6592.15301257524140.496987424758643
493.9192.36165621844881.54834378155118
590.4993.0116768657063-2.52167686570628
694.5691.95303469078932.60696530921074
795.1193.04748238248552.0625176175145
893.0793.9133618161688-0.843361816168851
993.2693.5593044032414-0.299304403241393
1092.9293.4336514027643-0.513651402764296
1190.993.2180119425437-2.31801194254373
1291.7792.2448717128376-0.474871712837597
1386.1692.0455126158328-5.88551261583285
1492.7989.57467586396313.21532413603688
1597.4590.92452277842256.52547722157752
1697.7493.66402738829934.07597261170066
1799.9295.37518894481564.54481105518444
1899.4697.28317673083182.1768232691682
1998.5298.19704359118260.322956408817433
2097.9298.3326260996647-0.412626099664706
2197.8598.1593987534027-0.309398753402718
22104.9498.02950797569316.91049202430688
23104.55100.9306482470143.61935175298596
24105.35102.4501127207062.89988727929435
2595.75103.667533960562-7.91753396056242
26105.99100.3436206209995.64637937900078
27106.11102.7140652356463.39593476435438
28107.33104.1397355162853.19026448371538
29106.11105.4790619690630.63093803093652
30108.17105.7439403198122.4260596801882
31104.62106.762440799092-2.14244079909248
32106.71105.8630082754310.846991724569463
3397.86106.218589584689-8.35858958468911
34104.41102.7095137084291.70048629157129
3596.09103.423406329092-7.33340632909218
36102.41100.3447195507192.06528044928132
3796.3101.211758867443-4.91175886744269
38103.0499.14972024512263.8902797548774
39105.11100.7829248308284.32707516917189
4099.4102.599503445804-3.199503445804
41104.45101.2562983220293.19370167797054
42104.31102.5970677665141.7129322334859
43104.06103.3161854020070.743814597993364
44101.16103.628451225778-2.4684512257779
45100.82102.592154065792-1.77215406579181
46102.6101.8481741133990.751825886600869
4792.78102.163803210281-9.3838032102807
4899.6898.22432548630111.45567451369894
4995.1498.8354420231226-3.69544202312262
50101.2897.28403357985943.99596642014058
51100.0398.96160719741651.06839280258349
52101.1799.4101363866931.75986361330696
5398.93100.148956601323-1.21895660132301
5497.7799.6372182080723-1.86721820807232
55100.2498.85332873685541.38667126314455
5698.0599.4354765536016-1.38547655360162
5795.8298.8538302959275-3.03383029592754
5899.1997.58017753474781.60982246525219
5997.4298.2560079629131-0.836007962913115
6098.0297.90503782072620.114962179273746
6197.3497.9533008686824-0.613300868682416
62101.2397.69582689399113.53417310600886
63100.1699.17953194532430.980468054675697
64100.7299.59114885308691.12885114691309
6599.8100.065059467717-0.265059467717109
66100.3999.9537830646210.436216935378965
67101.82100.1369142387561.68308576124423
68102.95100.8435018254082.1064981745923
6998.8101.727845033428-2.92784503342791
70100.24100.49868666022-0.258686660219794
7198.4100.390085668427-1.99008566842681
7298.1599.5546143798783-1.40461437987832







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7398.964933742261292.5195320919149105.410335392607
7498.964933742261291.97458111625105.955286368272
7598.964933742261291.4691444417488106.460723042774
7698.964933742261290.9957001128982106.934167371624
7798.964933742261290.548847238365107.381020246157
7898.964933742261290.1245525602782107.805314924244
7998.964933742261289.7197097404074108.210157744115
8098.964933742261289.3318659938154108.598001490707
8198.964933742261288.9590443940902108.970823090432
8298.964933742261288.5996238554543109.330243629068
8398.964933742261288.25225543797109.677612046552
8498.964933742261287.915802380343110.014065104179

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 98.9649337422612 & 92.5195320919149 & 105.410335392607 \tabularnewline
74 & 98.9649337422612 & 91.97458111625 & 105.955286368272 \tabularnewline
75 & 98.9649337422612 & 91.4691444417488 & 106.460723042774 \tabularnewline
76 & 98.9649337422612 & 90.9957001128982 & 106.934167371624 \tabularnewline
77 & 98.9649337422612 & 90.548847238365 & 107.381020246157 \tabularnewline
78 & 98.9649337422612 & 90.1245525602782 & 107.805314924244 \tabularnewline
79 & 98.9649337422612 & 89.7197097404074 & 108.210157744115 \tabularnewline
80 & 98.9649337422612 & 89.3318659938154 & 108.598001490707 \tabularnewline
81 & 98.9649337422612 & 88.9590443940902 & 108.970823090432 \tabularnewline
82 & 98.9649337422612 & 88.5996238554543 & 109.330243629068 \tabularnewline
83 & 98.9649337422612 & 88.25225543797 & 109.677612046552 \tabularnewline
84 & 98.9649337422612 & 87.915802380343 & 110.014065104179 \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]98.9649337422612[/C][C]92.5195320919149[/C][C]105.410335392607[/C][/ROW]
[ROW][C]74[/C][C]98.9649337422612[/C][C]91.97458111625[/C][C]105.955286368272[/C][/ROW]
[ROW][C]75[/C][C]98.9649337422612[/C][C]91.4691444417488[/C][C]106.460723042774[/C][/ROW]
[ROW][C]76[/C][C]98.9649337422612[/C][C]90.9957001128982[/C][C]106.934167371624[/C][/ROW]
[ROW][C]77[/C][C]98.9649337422612[/C][C]90.548847238365[/C][C]107.381020246157[/C][/ROW]
[ROW][C]78[/C][C]98.9649337422612[/C][C]90.1245525602782[/C][C]107.805314924244[/C][/ROW]
[ROW][C]79[/C][C]98.9649337422612[/C][C]89.7197097404074[/C][C]108.210157744115[/C][/ROW]
[ROW][C]80[/C][C]98.9649337422612[/C][C]89.3318659938154[/C][C]108.598001490707[/C][/ROW]
[ROW][C]81[/C][C]98.9649337422612[/C][C]88.9590443940902[/C][C]108.970823090432[/C][/ROW]
[ROW][C]82[/C][C]98.9649337422612[/C][C]88.5996238554543[/C][C]109.330243629068[/C][/ROW]
[ROW][C]83[/C][C]98.9649337422612[/C][C]88.25225543797[/C][C]109.677612046552[/C][/ROW]
[ROW][C]84[/C][C]98.9649337422612[/C][C]87.915802380343[/C][C]110.014065104179[/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
7398.964933742261292.5195320919149105.410335392607
7498.964933742261291.97458111625105.955286368272
7598.964933742261291.4691444417488106.460723042774
7698.964933742261290.9957001128982106.934167371624
7798.964933742261290.548847238365107.381020246157
7898.964933742261290.1245525602782107.805314924244
7998.964933742261289.7197097404074108.210157744115
8098.964933742261289.3318659938154108.598001490707
8198.964933742261288.9590443940902108.970823090432
8298.964933742261288.5996238554543109.330243629068
8398.964933742261288.25225543797109.677612046552
8498.964933742261287.915802380343110.014065104179



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')