Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 May 2017 17:16:25 +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/May/15/t1494865069qf0dpv9owixqt5c.htm/, Retrieved Sun, 19 May 2024 06:53:43 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 May 2024 06:53:43 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92.49
92.46
92.55
92.24
92.41
92.83
92.85
93.04
93.04
92.83
92.96
92.83
93.01
93.21
93.58
94.07
94.57
95.03
95.21
95.89
96.43
96.35
96.71
96.32
97.23
97.88
98.2
98.56
99.31
99.69
99.77
101.06
101.77
101.91
102.52
102.09
102.22
102.74
103.56
104.4
104.76
104.86
104.84
104.96
104.83
104.58
104.8
104.17
104.63
105.32
106.16
107.22
107.51
107.87
107.79
108.04
107.74
107.71
111.19
110.82
113.65
114.72
114.32
116.76
116.47
117.34
116.92
116.48
115.07
116.45
116.84
114.31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.799978409267924
beta0.248607805211648
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.799978409267924 \tabularnewline
beta & 0.248607805211648 \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]0.799978409267924[/C][/ROW]
[ROW][C]beta[/C][C]0.248607805211648[/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
alpha0.799978409267924
beta0.248607805211648
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
392.5592.430.120000000000005
492.2492.5198631142975-0.279863114297527
592.4192.23418494901030.175815050989669
692.8392.34800572897830.481994271021676
792.8592.80262271744880.04737728255121
893.0492.91897793432390.121022065676087
993.0493.1183163621571-0.0783163621570822
1092.8393.1426127248327-0.312612724832718
1192.9692.9173043632640.0426956367359566
1292.8392.9847263652413-0.154726365241331
1393.0192.86344291297860.146557087021449
1493.2193.01232711952640.19767288047359
1593.5893.24141621294630.338583787053707
1694.0793.65056882961370.419431170386247
1794.5794.20781444620970.362185553790326
1895.0394.79129658591330.2387034140867
1995.2195.3234692241516-0.113469224151629
2095.8995.55134449670420.338655503295755
2196.4396.20826189285310.221738107146919
2296.3596.8157473655278-0.465747365527804
2396.7196.7806310590728-0.070631059072781
2496.3297.0475520999918-0.727552099991797
2597.2396.64425429220340.585745707796619
2697.8897.40805999538360.471940004616428
2798.298.17468343496270.0253165650372864
2898.5698.5890527464513-0.0290527464512707
2999.3198.9541497469420.355850253058037
3099.6999.6979326469494-0.00793264694944185
3199.77100.149119429511-0.379119429511448
32101.06100.2279651957620.832034804238191
33101.77101.4411840104880.32881598951198
34101.91102.317233850512-0.407233850511943
35102.52102.523468685223-0.00346868522308341
36102.09103.052017079422-0.962017079422182
37102.22102.622420654017-0.402420654017007
38102.74102.5604555144290.179544485571157
39103.56102.9997578861270.560242113873031
40104.4103.8550315836110.544968416389494
41104.76104.806470449218-0.0464704492182904
42104.86105.275528908264-0.41552890826398
43104.84105.36670781481-0.526707814810166
44104.96105.264193884661-0.304193884660961
45104.83105.279187947972-0.449187947971524
46104.58105.088854998336-0.508854998335664
47104.8104.7495881685610.0504118314394049
48104.17104.86774867685-0.697748676850196
49104.63104.2486280633810.381371936618748
50105.32104.5686282267280.751371773272254
51106.16105.3340537477090.82594625229089
52107.22106.3234021564220.896597843577709
53107.51107.547586477784-0.0375864777842736
54107.87108.016968280132-0.1469682801321
55107.79108.369617821858-0.579617821857894
56108.04108.260882170951-0.220882170951313
57107.74108.395198055633-0.655198055632766
58107.71108.051764246152-0.341764246152238
59111.19107.8911003441443.29889965585571
60110.82111.298977014334-0.478977014333765
61113.65111.5893745470392.06062545296088
62114.72114.3212182180190.398781781980844
63114.32115.802932902987-1.48293290298706
64116.76115.4843894719751.27561052802497
65116.47117.626315766744-1.1563157667439
66117.34117.592784439514-0.252784439514116
67116.92118.231784675258-1.31178467525791
68116.48117.762718700944-1.28271870094368
69115.07117.061796658921-1.9917966589211
70116.45115.3974972946041.05250270539646
71116.84116.3778943537030.462105646296877
72114.31116.97789048862-2.66789048861959

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 92.55 & 92.43 & 0.120000000000005 \tabularnewline
4 & 92.24 & 92.5198631142975 & -0.279863114297527 \tabularnewline
5 & 92.41 & 92.2341849490103 & 0.175815050989669 \tabularnewline
6 & 92.83 & 92.3480057289783 & 0.481994271021676 \tabularnewline
7 & 92.85 & 92.8026227174488 & 0.04737728255121 \tabularnewline
8 & 93.04 & 92.9189779343239 & 0.121022065676087 \tabularnewline
9 & 93.04 & 93.1183163621571 & -0.0783163621570822 \tabularnewline
10 & 92.83 & 93.1426127248327 & -0.312612724832718 \tabularnewline
11 & 92.96 & 92.917304363264 & 0.0426956367359566 \tabularnewline
12 & 92.83 & 92.9847263652413 & -0.154726365241331 \tabularnewline
13 & 93.01 & 92.8634429129786 & 0.146557087021449 \tabularnewline
14 & 93.21 & 93.0123271195264 & 0.19767288047359 \tabularnewline
15 & 93.58 & 93.2414162129463 & 0.338583787053707 \tabularnewline
16 & 94.07 & 93.6505688296137 & 0.419431170386247 \tabularnewline
17 & 94.57 & 94.2078144462097 & 0.362185553790326 \tabularnewline
18 & 95.03 & 94.7912965859133 & 0.2387034140867 \tabularnewline
19 & 95.21 & 95.3234692241516 & -0.113469224151629 \tabularnewline
20 & 95.89 & 95.5513444967042 & 0.338655503295755 \tabularnewline
21 & 96.43 & 96.2082618928531 & 0.221738107146919 \tabularnewline
22 & 96.35 & 96.8157473655278 & -0.465747365527804 \tabularnewline
23 & 96.71 & 96.7806310590728 & -0.070631059072781 \tabularnewline
24 & 96.32 & 97.0475520999918 & -0.727552099991797 \tabularnewline
25 & 97.23 & 96.6442542922034 & 0.585745707796619 \tabularnewline
26 & 97.88 & 97.4080599953836 & 0.471940004616428 \tabularnewline
27 & 98.2 & 98.1746834349627 & 0.0253165650372864 \tabularnewline
28 & 98.56 & 98.5890527464513 & -0.0290527464512707 \tabularnewline
29 & 99.31 & 98.954149746942 & 0.355850253058037 \tabularnewline
30 & 99.69 & 99.6979326469494 & -0.00793264694944185 \tabularnewline
31 & 99.77 & 100.149119429511 & -0.379119429511448 \tabularnewline
32 & 101.06 & 100.227965195762 & 0.832034804238191 \tabularnewline
33 & 101.77 & 101.441184010488 & 0.32881598951198 \tabularnewline
34 & 101.91 & 102.317233850512 & -0.407233850511943 \tabularnewline
35 & 102.52 & 102.523468685223 & -0.00346868522308341 \tabularnewline
36 & 102.09 & 103.052017079422 & -0.962017079422182 \tabularnewline
37 & 102.22 & 102.622420654017 & -0.402420654017007 \tabularnewline
38 & 102.74 & 102.560455514429 & 0.179544485571157 \tabularnewline
39 & 103.56 & 102.999757886127 & 0.560242113873031 \tabularnewline
40 & 104.4 & 103.855031583611 & 0.544968416389494 \tabularnewline
41 & 104.76 & 104.806470449218 & -0.0464704492182904 \tabularnewline
42 & 104.86 & 105.275528908264 & -0.41552890826398 \tabularnewline
43 & 104.84 & 105.36670781481 & -0.526707814810166 \tabularnewline
44 & 104.96 & 105.264193884661 & -0.304193884660961 \tabularnewline
45 & 104.83 & 105.279187947972 & -0.449187947971524 \tabularnewline
46 & 104.58 & 105.088854998336 & -0.508854998335664 \tabularnewline
47 & 104.8 & 104.749588168561 & 0.0504118314394049 \tabularnewline
48 & 104.17 & 104.86774867685 & -0.697748676850196 \tabularnewline
49 & 104.63 & 104.248628063381 & 0.381371936618748 \tabularnewline
50 & 105.32 & 104.568628226728 & 0.751371773272254 \tabularnewline
51 & 106.16 & 105.334053747709 & 0.82594625229089 \tabularnewline
52 & 107.22 & 106.323402156422 & 0.896597843577709 \tabularnewline
53 & 107.51 & 107.547586477784 & -0.0375864777842736 \tabularnewline
54 & 107.87 & 108.016968280132 & -0.1469682801321 \tabularnewline
55 & 107.79 & 108.369617821858 & -0.579617821857894 \tabularnewline
56 & 108.04 & 108.260882170951 & -0.220882170951313 \tabularnewline
57 & 107.74 & 108.395198055633 & -0.655198055632766 \tabularnewline
58 & 107.71 & 108.051764246152 & -0.341764246152238 \tabularnewline
59 & 111.19 & 107.891100344144 & 3.29889965585571 \tabularnewline
60 & 110.82 & 111.298977014334 & -0.478977014333765 \tabularnewline
61 & 113.65 & 111.589374547039 & 2.06062545296088 \tabularnewline
62 & 114.72 & 114.321218218019 & 0.398781781980844 \tabularnewline
63 & 114.32 & 115.802932902987 & -1.48293290298706 \tabularnewline
64 & 116.76 & 115.484389471975 & 1.27561052802497 \tabularnewline
65 & 116.47 & 117.626315766744 & -1.1563157667439 \tabularnewline
66 & 117.34 & 117.592784439514 & -0.252784439514116 \tabularnewline
67 & 116.92 & 118.231784675258 & -1.31178467525791 \tabularnewline
68 & 116.48 & 117.762718700944 & -1.28271870094368 \tabularnewline
69 & 115.07 & 117.061796658921 & -1.9917966589211 \tabularnewline
70 & 116.45 & 115.397497294604 & 1.05250270539646 \tabularnewline
71 & 116.84 & 116.377894353703 & 0.462105646296877 \tabularnewline
72 & 114.31 & 116.97789048862 & -2.66789048861959 \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]3[/C][C]92.55[/C][C]92.43[/C][C]0.120000000000005[/C][/ROW]
[ROW][C]4[/C][C]92.24[/C][C]92.5198631142975[/C][C]-0.279863114297527[/C][/ROW]
[ROW][C]5[/C][C]92.41[/C][C]92.2341849490103[/C][C]0.175815050989669[/C][/ROW]
[ROW][C]6[/C][C]92.83[/C][C]92.3480057289783[/C][C]0.481994271021676[/C][/ROW]
[ROW][C]7[/C][C]92.85[/C][C]92.8026227174488[/C][C]0.04737728255121[/C][/ROW]
[ROW][C]8[/C][C]93.04[/C][C]92.9189779343239[/C][C]0.121022065676087[/C][/ROW]
[ROW][C]9[/C][C]93.04[/C][C]93.1183163621571[/C][C]-0.0783163621570822[/C][/ROW]
[ROW][C]10[/C][C]92.83[/C][C]93.1426127248327[/C][C]-0.312612724832718[/C][/ROW]
[ROW][C]11[/C][C]92.96[/C][C]92.917304363264[/C][C]0.0426956367359566[/C][/ROW]
[ROW][C]12[/C][C]92.83[/C][C]92.9847263652413[/C][C]-0.154726365241331[/C][/ROW]
[ROW][C]13[/C][C]93.01[/C][C]92.8634429129786[/C][C]0.146557087021449[/C][/ROW]
[ROW][C]14[/C][C]93.21[/C][C]93.0123271195264[/C][C]0.19767288047359[/C][/ROW]
[ROW][C]15[/C][C]93.58[/C][C]93.2414162129463[/C][C]0.338583787053707[/C][/ROW]
[ROW][C]16[/C][C]94.07[/C][C]93.6505688296137[/C][C]0.419431170386247[/C][/ROW]
[ROW][C]17[/C][C]94.57[/C][C]94.2078144462097[/C][C]0.362185553790326[/C][/ROW]
[ROW][C]18[/C][C]95.03[/C][C]94.7912965859133[/C][C]0.2387034140867[/C][/ROW]
[ROW][C]19[/C][C]95.21[/C][C]95.3234692241516[/C][C]-0.113469224151629[/C][/ROW]
[ROW][C]20[/C][C]95.89[/C][C]95.5513444967042[/C][C]0.338655503295755[/C][/ROW]
[ROW][C]21[/C][C]96.43[/C][C]96.2082618928531[/C][C]0.221738107146919[/C][/ROW]
[ROW][C]22[/C][C]96.35[/C][C]96.8157473655278[/C][C]-0.465747365527804[/C][/ROW]
[ROW][C]23[/C][C]96.71[/C][C]96.7806310590728[/C][C]-0.070631059072781[/C][/ROW]
[ROW][C]24[/C][C]96.32[/C][C]97.0475520999918[/C][C]-0.727552099991797[/C][/ROW]
[ROW][C]25[/C][C]97.23[/C][C]96.6442542922034[/C][C]0.585745707796619[/C][/ROW]
[ROW][C]26[/C][C]97.88[/C][C]97.4080599953836[/C][C]0.471940004616428[/C][/ROW]
[ROW][C]27[/C][C]98.2[/C][C]98.1746834349627[/C][C]0.0253165650372864[/C][/ROW]
[ROW][C]28[/C][C]98.56[/C][C]98.5890527464513[/C][C]-0.0290527464512707[/C][/ROW]
[ROW][C]29[/C][C]99.31[/C][C]98.954149746942[/C][C]0.355850253058037[/C][/ROW]
[ROW][C]30[/C][C]99.69[/C][C]99.6979326469494[/C][C]-0.00793264694944185[/C][/ROW]
[ROW][C]31[/C][C]99.77[/C][C]100.149119429511[/C][C]-0.379119429511448[/C][/ROW]
[ROW][C]32[/C][C]101.06[/C][C]100.227965195762[/C][C]0.832034804238191[/C][/ROW]
[ROW][C]33[/C][C]101.77[/C][C]101.441184010488[/C][C]0.32881598951198[/C][/ROW]
[ROW][C]34[/C][C]101.91[/C][C]102.317233850512[/C][C]-0.407233850511943[/C][/ROW]
[ROW][C]35[/C][C]102.52[/C][C]102.523468685223[/C][C]-0.00346868522308341[/C][/ROW]
[ROW][C]36[/C][C]102.09[/C][C]103.052017079422[/C][C]-0.962017079422182[/C][/ROW]
[ROW][C]37[/C][C]102.22[/C][C]102.622420654017[/C][C]-0.402420654017007[/C][/ROW]
[ROW][C]38[/C][C]102.74[/C][C]102.560455514429[/C][C]0.179544485571157[/C][/ROW]
[ROW][C]39[/C][C]103.56[/C][C]102.999757886127[/C][C]0.560242113873031[/C][/ROW]
[ROW][C]40[/C][C]104.4[/C][C]103.855031583611[/C][C]0.544968416389494[/C][/ROW]
[ROW][C]41[/C][C]104.76[/C][C]104.806470449218[/C][C]-0.0464704492182904[/C][/ROW]
[ROW][C]42[/C][C]104.86[/C][C]105.275528908264[/C][C]-0.41552890826398[/C][/ROW]
[ROW][C]43[/C][C]104.84[/C][C]105.36670781481[/C][C]-0.526707814810166[/C][/ROW]
[ROW][C]44[/C][C]104.96[/C][C]105.264193884661[/C][C]-0.304193884660961[/C][/ROW]
[ROW][C]45[/C][C]104.83[/C][C]105.279187947972[/C][C]-0.449187947971524[/C][/ROW]
[ROW][C]46[/C][C]104.58[/C][C]105.088854998336[/C][C]-0.508854998335664[/C][/ROW]
[ROW][C]47[/C][C]104.8[/C][C]104.749588168561[/C][C]0.0504118314394049[/C][/ROW]
[ROW][C]48[/C][C]104.17[/C][C]104.86774867685[/C][C]-0.697748676850196[/C][/ROW]
[ROW][C]49[/C][C]104.63[/C][C]104.248628063381[/C][C]0.381371936618748[/C][/ROW]
[ROW][C]50[/C][C]105.32[/C][C]104.568628226728[/C][C]0.751371773272254[/C][/ROW]
[ROW][C]51[/C][C]106.16[/C][C]105.334053747709[/C][C]0.82594625229089[/C][/ROW]
[ROW][C]52[/C][C]107.22[/C][C]106.323402156422[/C][C]0.896597843577709[/C][/ROW]
[ROW][C]53[/C][C]107.51[/C][C]107.547586477784[/C][C]-0.0375864777842736[/C][/ROW]
[ROW][C]54[/C][C]107.87[/C][C]108.016968280132[/C][C]-0.1469682801321[/C][/ROW]
[ROW][C]55[/C][C]107.79[/C][C]108.369617821858[/C][C]-0.579617821857894[/C][/ROW]
[ROW][C]56[/C][C]108.04[/C][C]108.260882170951[/C][C]-0.220882170951313[/C][/ROW]
[ROW][C]57[/C][C]107.74[/C][C]108.395198055633[/C][C]-0.655198055632766[/C][/ROW]
[ROW][C]58[/C][C]107.71[/C][C]108.051764246152[/C][C]-0.341764246152238[/C][/ROW]
[ROW][C]59[/C][C]111.19[/C][C]107.891100344144[/C][C]3.29889965585571[/C][/ROW]
[ROW][C]60[/C][C]110.82[/C][C]111.298977014334[/C][C]-0.478977014333765[/C][/ROW]
[ROW][C]61[/C][C]113.65[/C][C]111.589374547039[/C][C]2.06062545296088[/C][/ROW]
[ROW][C]62[/C][C]114.72[/C][C]114.321218218019[/C][C]0.398781781980844[/C][/ROW]
[ROW][C]63[/C][C]114.32[/C][C]115.802932902987[/C][C]-1.48293290298706[/C][/ROW]
[ROW][C]64[/C][C]116.76[/C][C]115.484389471975[/C][C]1.27561052802497[/C][/ROW]
[ROW][C]65[/C][C]116.47[/C][C]117.626315766744[/C][C]-1.1563157667439[/C][/ROW]
[ROW][C]66[/C][C]117.34[/C][C]117.592784439514[/C][C]-0.252784439514116[/C][/ROW]
[ROW][C]67[/C][C]116.92[/C][C]118.231784675258[/C][C]-1.31178467525791[/C][/ROW]
[ROW][C]68[/C][C]116.48[/C][C]117.762718700944[/C][C]-1.28271870094368[/C][/ROW]
[ROW][C]69[/C][C]115.07[/C][C]117.061796658921[/C][C]-1.9917966589211[/C][/ROW]
[ROW][C]70[/C][C]116.45[/C][C]115.397497294604[/C][C]1.05250270539646[/C][/ROW]
[ROW][C]71[/C][C]116.84[/C][C]116.377894353703[/C][C]0.462105646296877[/C][/ROW]
[ROW][C]72[/C][C]114.31[/C][C]116.97789048862[/C][C]-2.66789048861959[/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
392.5592.430.120000000000005
492.2492.5198631142975-0.279863114297527
592.4192.23418494901030.175815050989669
692.8392.34800572897830.481994271021676
792.8592.80262271744880.04737728255121
893.0492.91897793432390.121022065676087
993.0493.1183163621571-0.0783163621570822
1092.8393.1426127248327-0.312612724832718
1192.9692.9173043632640.0426956367359566
1292.8392.9847263652413-0.154726365241331
1393.0192.86344291297860.146557087021449
1493.2193.01232711952640.19767288047359
1593.5893.24141621294630.338583787053707
1694.0793.65056882961370.419431170386247
1794.5794.20781444620970.362185553790326
1895.0394.79129658591330.2387034140867
1995.2195.3234692241516-0.113469224151629
2095.8995.55134449670420.338655503295755
2196.4396.20826189285310.221738107146919
2296.3596.8157473655278-0.465747365527804
2396.7196.7806310590728-0.070631059072781
2496.3297.0475520999918-0.727552099991797
2597.2396.64425429220340.585745707796619
2697.8897.40805999538360.471940004616428
2798.298.17468343496270.0253165650372864
2898.5698.5890527464513-0.0290527464512707
2999.3198.9541497469420.355850253058037
3099.6999.6979326469494-0.00793264694944185
3199.77100.149119429511-0.379119429511448
32101.06100.2279651957620.832034804238191
33101.77101.4411840104880.32881598951198
34101.91102.317233850512-0.407233850511943
35102.52102.523468685223-0.00346868522308341
36102.09103.052017079422-0.962017079422182
37102.22102.622420654017-0.402420654017007
38102.74102.5604555144290.179544485571157
39103.56102.9997578861270.560242113873031
40104.4103.8550315836110.544968416389494
41104.76104.806470449218-0.0464704492182904
42104.86105.275528908264-0.41552890826398
43104.84105.36670781481-0.526707814810166
44104.96105.264193884661-0.304193884660961
45104.83105.279187947972-0.449187947971524
46104.58105.088854998336-0.508854998335664
47104.8104.7495881685610.0504118314394049
48104.17104.86774867685-0.697748676850196
49104.63104.2486280633810.381371936618748
50105.32104.5686282267280.751371773272254
51106.16105.3340537477090.82594625229089
52107.22106.3234021564220.896597843577709
53107.51107.547586477784-0.0375864777842736
54107.87108.016968280132-0.1469682801321
55107.79108.369617821858-0.579617821857894
56108.04108.260882170951-0.220882170951313
57107.74108.395198055633-0.655198055632766
58107.71108.051764246152-0.341764246152238
59111.19107.8911003441443.29889965585571
60110.82111.298977014334-0.478977014333765
61113.65111.5893745470392.06062545296088
62114.72114.3212182180190.398781781980844
63114.32115.802932902987-1.48293290298706
64116.76115.4843894719751.27561052802497
65116.47117.626315766744-1.1563157667439
66117.34117.592784439514-0.252784439514116
67116.92118.231784675258-1.31178467525791
68116.48117.762718700944-1.28271870094368
69115.07117.061796658921-1.9917966589211
70116.45115.3974972946041.05250270539646
71116.84116.3778943537030.462105646296877
72114.31116.97789048862-2.66789048861959







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73114.543364895609112.931974178613116.154755612604
74114.243094091785111.965542873261116.520645310308
75113.942823287961110.957484909037116.928161666884
76113.642552484136109.903969157999117.381135810274
77113.342281680312108.804999686098117.879563674527
78113.042010876488107.661730098038118.422291654939
79112.741740072664106.475649300986119.007830844343
80112.44146926884105.248295212868119.634643324812
81112.141198465016103.981148969494120.301247960539
82111.840927661192102.675598094769121.006257227615
83111.540656857368101.332927625681121.748386089056
84111.24038605354499.9543227017409122.526449405347

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 114.543364895609 & 112.931974178613 & 116.154755612604 \tabularnewline
74 & 114.243094091785 & 111.965542873261 & 116.520645310308 \tabularnewline
75 & 113.942823287961 & 110.957484909037 & 116.928161666884 \tabularnewline
76 & 113.642552484136 & 109.903969157999 & 117.381135810274 \tabularnewline
77 & 113.342281680312 & 108.804999686098 & 117.879563674527 \tabularnewline
78 & 113.042010876488 & 107.661730098038 & 118.422291654939 \tabularnewline
79 & 112.741740072664 & 106.475649300986 & 119.007830844343 \tabularnewline
80 & 112.44146926884 & 105.248295212868 & 119.634643324812 \tabularnewline
81 & 112.141198465016 & 103.981148969494 & 120.301247960539 \tabularnewline
82 & 111.840927661192 & 102.675598094769 & 121.006257227615 \tabularnewline
83 & 111.540656857368 & 101.332927625681 & 121.748386089056 \tabularnewline
84 & 111.240386053544 & 99.9543227017409 & 122.526449405347 \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]114.543364895609[/C][C]112.931974178613[/C][C]116.154755612604[/C][/ROW]
[ROW][C]74[/C][C]114.243094091785[/C][C]111.965542873261[/C][C]116.520645310308[/C][/ROW]
[ROW][C]75[/C][C]113.942823287961[/C][C]110.957484909037[/C][C]116.928161666884[/C][/ROW]
[ROW][C]76[/C][C]113.642552484136[/C][C]109.903969157999[/C][C]117.381135810274[/C][/ROW]
[ROW][C]77[/C][C]113.342281680312[/C][C]108.804999686098[/C][C]117.879563674527[/C][/ROW]
[ROW][C]78[/C][C]113.042010876488[/C][C]107.661730098038[/C][C]118.422291654939[/C][/ROW]
[ROW][C]79[/C][C]112.741740072664[/C][C]106.475649300986[/C][C]119.007830844343[/C][/ROW]
[ROW][C]80[/C][C]112.44146926884[/C][C]105.248295212868[/C][C]119.634643324812[/C][/ROW]
[ROW][C]81[/C][C]112.141198465016[/C][C]103.981148969494[/C][C]120.301247960539[/C][/ROW]
[ROW][C]82[/C][C]111.840927661192[/C][C]102.675598094769[/C][C]121.006257227615[/C][/ROW]
[ROW][C]83[/C][C]111.540656857368[/C][C]101.332927625681[/C][C]121.748386089056[/C][/ROW]
[ROW][C]84[/C][C]111.240386053544[/C][C]99.9543227017409[/C][C]122.526449405347[/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
73114.543364895609112.931974178613116.154755612604
74114.243094091785111.965542873261116.520645310308
75113.942823287961110.957484909037116.928161666884
76113.642552484136109.903969157999117.381135810274
77113.342281680312108.804999686098117.879563674527
78113.042010876488107.661730098038118.422291654939
79112.741740072664106.475649300986119.007830844343
80112.44146926884105.248295212868119.634643324812
81112.141198465016103.981148969494120.301247960539
82111.840927661192102.675598094769121.006257227615
83111.540656857368101.332927625681121.748386089056
84111.24038605354499.9543227017409122.526449405347



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