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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 11:27:29 +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/2014/Nov/28/t141717412044pdirpepgse5gt.htm/, Retrieved Sun, 19 May 2024 14:34:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260843, Retrieved Sun, 19 May 2024 14:34:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 11:27:29] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
37,3
39,5
40,6
41,4
41,3
43,5
44
44,9
46,4
47,4
48,7
49,7
51,1
53,2
56,2
58,1
60,6
64,1
67,4
68
70,9
72,8
74,9
76,1
77
78,1
80
79,7
82,7
84,3
83,5
85,9
87
88,6
90,6
91,3
91,6
93,2
95
95,2
97,4
98,6
99,6
100,6
101,3
102,8
103,2
103
105,4
104,7
105,2
105,2
102,8
100,3
99,8
99,4
100,6
100,2
100,4
98,8
96,9
96,3
96,1
93,5
92,1
91,7
87,9
86,4
84,9
81,7
82,6
83,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260843&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260843&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260843&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.910146248574539
beta0.296163152165104
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.910146248574539 \tabularnewline
beta & 0.296163152165104 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260843&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]0.910146248574539[/C][/ROW]
[ROW][C]beta[/C][C]0.296163152165104[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260843&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260843&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
alpha0.910146248574539
beta0.296163152165104
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
340.641.7-1.1
441.442.602332166468-1.20233216646802
541.343.0874363175986-1.78743631759861
643.542.55820347609460.941796523905417
74444.7668345979864-0.766834597986367
844.945.2136598817739-0.31365988177388
946.445.98839285342550.411607146574518
1047.447.5341743299489-0.134174329948856
1148.748.54704791334880.152952086651162
1249.749.8624770351875-0.162477035187507
1351.150.84702355073950.252976449260544
1453.252.27788374929820.92211625070177
1556.254.56631710641461.63368289358537
1658.157.94274230920260.157257690797366
1760.660.01779374314560.582206256854427
1864.162.63654525429621.4634547457038
1967.466.45183860608280.948161393917189
206870.0537182400932-2.05371824009323
2170.970.36986497538040.530135024619568
2272.873.1805949069517-0.3805949069517
2374.975.0598373724845-0.159837372484461
2476.177.0969170312883-0.996917031288305
257778.1034110166745-1.1034110166745
2678.178.715553495043-0.615553495042974
278079.6057941251140.394205874885955
2879.781.5213223537035-1.82132235370347
2982.780.92945519055961.77054480944037
3084.384.08396595966380.21603404033624
3183.585.8818769444247-2.38187694442468
3285.984.6732698176171.22673018238297
338787.0796902364357-0.0796902364357095
3488.688.27559636677340.324403633226609
3590.689.92673059405020.673269405949796
3691.392.0768646637057-0.776864663705709
3791.692.6977593955301-1.09775939553008
3893.292.73068998982460.469310010175434
399594.31638627448840.683613725511577
4095.296.2813995795702-1.08139957957019
4197.496.34849946271881.05150053728123
4298.698.6402842293064-0.0402842293063799
4399.699.9275265005411-0.327526500541083
44100.6100.865050944336-0.265050944336195
45101.3101.787992326896-0.48799232689629
46102.8102.3764852451940.423514754805566
47103.2103.908742071275-0.708742071275296
48103104.21943690645-1.21943690644956
49105.4103.7366233621641.66337663783561
50104.7106.325957887265-1.62595788726478
51105.2105.483237088217-0.283237088216978
52105.2105.786241525474-0.586241525473923
53102.8105.655445163039-2.85544516303943
54100.3102.689651290782-2.38965129078206
5599.899.50366320039710.296336799602912
5699.498.84219520657010.557804793429895
57100.698.56905860247352.03094139752648
58100.2100.1841356248890.0158643751105672
59100.499.96947412534470.430525874655302
6098.8100.24826425071-1.4482642507102
6196.998.4266983821612-1.52669838216124
6296.396.12222171376270.177778286237341
6396.195.41698854472990.683011455270105
6493.595.3556984039801-1.8556984039801
6592.192.4836041971358-0.383604197135853
6691.790.84792981531340.852070184686582
6787.990.5665768731602-2.66657687316021
6886.486.3639599634920.0360400365079698
6984.984.63083435155330.26916564844673
7081.783.1824412209347-1.48244122093473
7182.679.74023499649282.85976500350715
7283.181.02092623030032.07907376969966

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 40.6 & 41.7 & -1.1 \tabularnewline
4 & 41.4 & 42.602332166468 & -1.20233216646802 \tabularnewline
5 & 41.3 & 43.0874363175986 & -1.78743631759861 \tabularnewline
6 & 43.5 & 42.5582034760946 & 0.941796523905417 \tabularnewline
7 & 44 & 44.7668345979864 & -0.766834597986367 \tabularnewline
8 & 44.9 & 45.2136598817739 & -0.31365988177388 \tabularnewline
9 & 46.4 & 45.9883928534255 & 0.411607146574518 \tabularnewline
10 & 47.4 & 47.5341743299489 & -0.134174329948856 \tabularnewline
11 & 48.7 & 48.5470479133488 & 0.152952086651162 \tabularnewline
12 & 49.7 & 49.8624770351875 & -0.162477035187507 \tabularnewline
13 & 51.1 & 50.8470235507395 & 0.252976449260544 \tabularnewline
14 & 53.2 & 52.2778837492982 & 0.92211625070177 \tabularnewline
15 & 56.2 & 54.5663171064146 & 1.63368289358537 \tabularnewline
16 & 58.1 & 57.9427423092026 & 0.157257690797366 \tabularnewline
17 & 60.6 & 60.0177937431456 & 0.582206256854427 \tabularnewline
18 & 64.1 & 62.6365452542962 & 1.4634547457038 \tabularnewline
19 & 67.4 & 66.4518386060828 & 0.948161393917189 \tabularnewline
20 & 68 & 70.0537182400932 & -2.05371824009323 \tabularnewline
21 & 70.9 & 70.3698649753804 & 0.530135024619568 \tabularnewline
22 & 72.8 & 73.1805949069517 & -0.3805949069517 \tabularnewline
23 & 74.9 & 75.0598373724845 & -0.159837372484461 \tabularnewline
24 & 76.1 & 77.0969170312883 & -0.996917031288305 \tabularnewline
25 & 77 & 78.1034110166745 & -1.1034110166745 \tabularnewline
26 & 78.1 & 78.715553495043 & -0.615553495042974 \tabularnewline
27 & 80 & 79.605794125114 & 0.394205874885955 \tabularnewline
28 & 79.7 & 81.5213223537035 & -1.82132235370347 \tabularnewline
29 & 82.7 & 80.9294551905596 & 1.77054480944037 \tabularnewline
30 & 84.3 & 84.0839659596638 & 0.21603404033624 \tabularnewline
31 & 83.5 & 85.8818769444247 & -2.38187694442468 \tabularnewline
32 & 85.9 & 84.673269817617 & 1.22673018238297 \tabularnewline
33 & 87 & 87.0796902364357 & -0.0796902364357095 \tabularnewline
34 & 88.6 & 88.2755963667734 & 0.324403633226609 \tabularnewline
35 & 90.6 & 89.9267305940502 & 0.673269405949796 \tabularnewline
36 & 91.3 & 92.0768646637057 & -0.776864663705709 \tabularnewline
37 & 91.6 & 92.6977593955301 & -1.09775939553008 \tabularnewline
38 & 93.2 & 92.7306899898246 & 0.469310010175434 \tabularnewline
39 & 95 & 94.3163862744884 & 0.683613725511577 \tabularnewline
40 & 95.2 & 96.2813995795702 & -1.08139957957019 \tabularnewline
41 & 97.4 & 96.3484994627188 & 1.05150053728123 \tabularnewline
42 & 98.6 & 98.6402842293064 & -0.0402842293063799 \tabularnewline
43 & 99.6 & 99.9275265005411 & -0.327526500541083 \tabularnewline
44 & 100.6 & 100.865050944336 & -0.265050944336195 \tabularnewline
45 & 101.3 & 101.787992326896 & -0.48799232689629 \tabularnewline
46 & 102.8 & 102.376485245194 & 0.423514754805566 \tabularnewline
47 & 103.2 & 103.908742071275 & -0.708742071275296 \tabularnewline
48 & 103 & 104.21943690645 & -1.21943690644956 \tabularnewline
49 & 105.4 & 103.736623362164 & 1.66337663783561 \tabularnewline
50 & 104.7 & 106.325957887265 & -1.62595788726478 \tabularnewline
51 & 105.2 & 105.483237088217 & -0.283237088216978 \tabularnewline
52 & 105.2 & 105.786241525474 & -0.586241525473923 \tabularnewline
53 & 102.8 & 105.655445163039 & -2.85544516303943 \tabularnewline
54 & 100.3 & 102.689651290782 & -2.38965129078206 \tabularnewline
55 & 99.8 & 99.5036632003971 & 0.296336799602912 \tabularnewline
56 & 99.4 & 98.8421952065701 & 0.557804793429895 \tabularnewline
57 & 100.6 & 98.5690586024735 & 2.03094139752648 \tabularnewline
58 & 100.2 & 100.184135624889 & 0.0158643751105672 \tabularnewline
59 & 100.4 & 99.9694741253447 & 0.430525874655302 \tabularnewline
60 & 98.8 & 100.24826425071 & -1.4482642507102 \tabularnewline
61 & 96.9 & 98.4266983821612 & -1.52669838216124 \tabularnewline
62 & 96.3 & 96.1222217137627 & 0.177778286237341 \tabularnewline
63 & 96.1 & 95.4169885447299 & 0.683011455270105 \tabularnewline
64 & 93.5 & 95.3556984039801 & -1.8556984039801 \tabularnewline
65 & 92.1 & 92.4836041971358 & -0.383604197135853 \tabularnewline
66 & 91.7 & 90.8479298153134 & 0.852070184686582 \tabularnewline
67 & 87.9 & 90.5665768731602 & -2.66657687316021 \tabularnewline
68 & 86.4 & 86.363959963492 & 0.0360400365079698 \tabularnewline
69 & 84.9 & 84.6308343515533 & 0.26916564844673 \tabularnewline
70 & 81.7 & 83.1824412209347 & -1.48244122093473 \tabularnewline
71 & 82.6 & 79.7402349964928 & 2.85976500350715 \tabularnewline
72 & 83.1 & 81.0209262303003 & 2.07907376969966 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260843&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]40.6[/C][C]41.7[/C][C]-1.1[/C][/ROW]
[ROW][C]4[/C][C]41.4[/C][C]42.602332166468[/C][C]-1.20233216646802[/C][/ROW]
[ROW][C]5[/C][C]41.3[/C][C]43.0874363175986[/C][C]-1.78743631759861[/C][/ROW]
[ROW][C]6[/C][C]43.5[/C][C]42.5582034760946[/C][C]0.941796523905417[/C][/ROW]
[ROW][C]7[/C][C]44[/C][C]44.7668345979864[/C][C]-0.766834597986367[/C][/ROW]
[ROW][C]8[/C][C]44.9[/C][C]45.2136598817739[/C][C]-0.31365988177388[/C][/ROW]
[ROW][C]9[/C][C]46.4[/C][C]45.9883928534255[/C][C]0.411607146574518[/C][/ROW]
[ROW][C]10[/C][C]47.4[/C][C]47.5341743299489[/C][C]-0.134174329948856[/C][/ROW]
[ROW][C]11[/C][C]48.7[/C][C]48.5470479133488[/C][C]0.152952086651162[/C][/ROW]
[ROW][C]12[/C][C]49.7[/C][C]49.8624770351875[/C][C]-0.162477035187507[/C][/ROW]
[ROW][C]13[/C][C]51.1[/C][C]50.8470235507395[/C][C]0.252976449260544[/C][/ROW]
[ROW][C]14[/C][C]53.2[/C][C]52.2778837492982[/C][C]0.92211625070177[/C][/ROW]
[ROW][C]15[/C][C]56.2[/C][C]54.5663171064146[/C][C]1.63368289358537[/C][/ROW]
[ROW][C]16[/C][C]58.1[/C][C]57.9427423092026[/C][C]0.157257690797366[/C][/ROW]
[ROW][C]17[/C][C]60.6[/C][C]60.0177937431456[/C][C]0.582206256854427[/C][/ROW]
[ROW][C]18[/C][C]64.1[/C][C]62.6365452542962[/C][C]1.4634547457038[/C][/ROW]
[ROW][C]19[/C][C]67.4[/C][C]66.4518386060828[/C][C]0.948161393917189[/C][/ROW]
[ROW][C]20[/C][C]68[/C][C]70.0537182400932[/C][C]-2.05371824009323[/C][/ROW]
[ROW][C]21[/C][C]70.9[/C][C]70.3698649753804[/C][C]0.530135024619568[/C][/ROW]
[ROW][C]22[/C][C]72.8[/C][C]73.1805949069517[/C][C]-0.3805949069517[/C][/ROW]
[ROW][C]23[/C][C]74.9[/C][C]75.0598373724845[/C][C]-0.159837372484461[/C][/ROW]
[ROW][C]24[/C][C]76.1[/C][C]77.0969170312883[/C][C]-0.996917031288305[/C][/ROW]
[ROW][C]25[/C][C]77[/C][C]78.1034110166745[/C][C]-1.1034110166745[/C][/ROW]
[ROW][C]26[/C][C]78.1[/C][C]78.715553495043[/C][C]-0.615553495042974[/C][/ROW]
[ROW][C]27[/C][C]80[/C][C]79.605794125114[/C][C]0.394205874885955[/C][/ROW]
[ROW][C]28[/C][C]79.7[/C][C]81.5213223537035[/C][C]-1.82132235370347[/C][/ROW]
[ROW][C]29[/C][C]82.7[/C][C]80.9294551905596[/C][C]1.77054480944037[/C][/ROW]
[ROW][C]30[/C][C]84.3[/C][C]84.0839659596638[/C][C]0.21603404033624[/C][/ROW]
[ROW][C]31[/C][C]83.5[/C][C]85.8818769444247[/C][C]-2.38187694442468[/C][/ROW]
[ROW][C]32[/C][C]85.9[/C][C]84.673269817617[/C][C]1.22673018238297[/C][/ROW]
[ROW][C]33[/C][C]87[/C][C]87.0796902364357[/C][C]-0.0796902364357095[/C][/ROW]
[ROW][C]34[/C][C]88.6[/C][C]88.2755963667734[/C][C]0.324403633226609[/C][/ROW]
[ROW][C]35[/C][C]90.6[/C][C]89.9267305940502[/C][C]0.673269405949796[/C][/ROW]
[ROW][C]36[/C][C]91.3[/C][C]92.0768646637057[/C][C]-0.776864663705709[/C][/ROW]
[ROW][C]37[/C][C]91.6[/C][C]92.6977593955301[/C][C]-1.09775939553008[/C][/ROW]
[ROW][C]38[/C][C]93.2[/C][C]92.7306899898246[/C][C]0.469310010175434[/C][/ROW]
[ROW][C]39[/C][C]95[/C][C]94.3163862744884[/C][C]0.683613725511577[/C][/ROW]
[ROW][C]40[/C][C]95.2[/C][C]96.2813995795702[/C][C]-1.08139957957019[/C][/ROW]
[ROW][C]41[/C][C]97.4[/C][C]96.3484994627188[/C][C]1.05150053728123[/C][/ROW]
[ROW][C]42[/C][C]98.6[/C][C]98.6402842293064[/C][C]-0.0402842293063799[/C][/ROW]
[ROW][C]43[/C][C]99.6[/C][C]99.9275265005411[/C][C]-0.327526500541083[/C][/ROW]
[ROW][C]44[/C][C]100.6[/C][C]100.865050944336[/C][C]-0.265050944336195[/C][/ROW]
[ROW][C]45[/C][C]101.3[/C][C]101.787992326896[/C][C]-0.48799232689629[/C][/ROW]
[ROW][C]46[/C][C]102.8[/C][C]102.376485245194[/C][C]0.423514754805566[/C][/ROW]
[ROW][C]47[/C][C]103.2[/C][C]103.908742071275[/C][C]-0.708742071275296[/C][/ROW]
[ROW][C]48[/C][C]103[/C][C]104.21943690645[/C][C]-1.21943690644956[/C][/ROW]
[ROW][C]49[/C][C]105.4[/C][C]103.736623362164[/C][C]1.66337663783561[/C][/ROW]
[ROW][C]50[/C][C]104.7[/C][C]106.325957887265[/C][C]-1.62595788726478[/C][/ROW]
[ROW][C]51[/C][C]105.2[/C][C]105.483237088217[/C][C]-0.283237088216978[/C][/ROW]
[ROW][C]52[/C][C]105.2[/C][C]105.786241525474[/C][C]-0.586241525473923[/C][/ROW]
[ROW][C]53[/C][C]102.8[/C][C]105.655445163039[/C][C]-2.85544516303943[/C][/ROW]
[ROW][C]54[/C][C]100.3[/C][C]102.689651290782[/C][C]-2.38965129078206[/C][/ROW]
[ROW][C]55[/C][C]99.8[/C][C]99.5036632003971[/C][C]0.296336799602912[/C][/ROW]
[ROW][C]56[/C][C]99.4[/C][C]98.8421952065701[/C][C]0.557804793429895[/C][/ROW]
[ROW][C]57[/C][C]100.6[/C][C]98.5690586024735[/C][C]2.03094139752648[/C][/ROW]
[ROW][C]58[/C][C]100.2[/C][C]100.184135624889[/C][C]0.0158643751105672[/C][/ROW]
[ROW][C]59[/C][C]100.4[/C][C]99.9694741253447[/C][C]0.430525874655302[/C][/ROW]
[ROW][C]60[/C][C]98.8[/C][C]100.24826425071[/C][C]-1.4482642507102[/C][/ROW]
[ROW][C]61[/C][C]96.9[/C][C]98.4266983821612[/C][C]-1.52669838216124[/C][/ROW]
[ROW][C]62[/C][C]96.3[/C][C]96.1222217137627[/C][C]0.177778286237341[/C][/ROW]
[ROW][C]63[/C][C]96.1[/C][C]95.4169885447299[/C][C]0.683011455270105[/C][/ROW]
[ROW][C]64[/C][C]93.5[/C][C]95.3556984039801[/C][C]-1.8556984039801[/C][/ROW]
[ROW][C]65[/C][C]92.1[/C][C]92.4836041971358[/C][C]-0.383604197135853[/C][/ROW]
[ROW][C]66[/C][C]91.7[/C][C]90.8479298153134[/C][C]0.852070184686582[/C][/ROW]
[ROW][C]67[/C][C]87.9[/C][C]90.5665768731602[/C][C]-2.66657687316021[/C][/ROW]
[ROW][C]68[/C][C]86.4[/C][C]86.363959963492[/C][C]0.0360400365079698[/C][/ROW]
[ROW][C]69[/C][C]84.9[/C][C]84.6308343515533[/C][C]0.26916564844673[/C][/ROW]
[ROW][C]70[/C][C]81.7[/C][C]83.1824412209347[/C][C]-1.48244122093473[/C][/ROW]
[ROW][C]71[/C][C]82.6[/C][C]79.7402349964928[/C][C]2.85976500350715[/C][/ROW]
[ROW][C]72[/C][C]83.1[/C][C]81.0209262303003[/C][C]2.07907376969966[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260843&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260843&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
340.641.7-1.1
441.442.602332166468-1.20233216646802
541.343.0874363175986-1.78743631759861
643.542.55820347609460.941796523905417
74444.7668345979864-0.766834597986367
844.945.2136598817739-0.31365988177388
946.445.98839285342550.411607146574518
1047.447.5341743299489-0.134174329948856
1148.748.54704791334880.152952086651162
1249.749.8624770351875-0.162477035187507
1351.150.84702355073950.252976449260544
1453.252.27788374929820.92211625070177
1556.254.56631710641461.63368289358537
1658.157.94274230920260.157257690797366
1760.660.01779374314560.582206256854427
1864.162.63654525429621.4634547457038
1967.466.45183860608280.948161393917189
206870.0537182400932-2.05371824009323
2170.970.36986497538040.530135024619568
2272.873.1805949069517-0.3805949069517
2374.975.0598373724845-0.159837372484461
2476.177.0969170312883-0.996917031288305
257778.1034110166745-1.1034110166745
2678.178.715553495043-0.615553495042974
278079.6057941251140.394205874885955
2879.781.5213223537035-1.82132235370347
2982.780.92945519055961.77054480944037
3084.384.08396595966380.21603404033624
3183.585.8818769444247-2.38187694442468
3285.984.6732698176171.22673018238297
338787.0796902364357-0.0796902364357095
3488.688.27559636677340.324403633226609
3590.689.92673059405020.673269405949796
3691.392.0768646637057-0.776864663705709
3791.692.6977593955301-1.09775939553008
3893.292.73068998982460.469310010175434
399594.31638627448840.683613725511577
4095.296.2813995795702-1.08139957957019
4197.496.34849946271881.05150053728123
4298.698.6402842293064-0.0402842293063799
4399.699.9275265005411-0.327526500541083
44100.6100.865050944336-0.265050944336195
45101.3101.787992326896-0.48799232689629
46102.8102.3764852451940.423514754805566
47103.2103.908742071275-0.708742071275296
48103104.21943690645-1.21943690644956
49105.4103.7366233621641.66337663783561
50104.7106.325957887265-1.62595788726478
51105.2105.483237088217-0.283237088216978
52105.2105.786241525474-0.586241525473923
53102.8105.655445163039-2.85544516303943
54100.3102.689651290782-2.38965129078206
5599.899.50366320039710.296336799602912
5699.498.84219520657010.557804793429895
57100.698.56905860247352.03094139752648
58100.2100.1841356248890.0158643751105672
59100.499.96947412534470.430525874655302
6098.8100.24826425071-1.4482642507102
6196.998.4266983821612-1.52669838216124
6296.396.12222171376270.177778286237341
6396.195.41698854472990.683011455270105
6493.595.3556984039801-1.8556984039801
6592.192.4836041971358-0.383604197135853
6691.790.84792981531340.852070184686582
6787.990.5665768731602-2.66657687316021
6886.486.3639599634920.0360400365079698
6984.984.63083435155330.26916564844673
7081.783.1824412209347-1.48244122093473
7182.679.74023499649282.85976500350715
7283.181.02092623030032.07907376969966







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7382.151492305705979.821990758130784.480993853281
7481.389797189109577.787204071560984.9923903066582
7580.628102072513275.690870705016285.5653334400102
7679.866406955916873.509687914021486.2231259978123

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 82.1514923057059 & 79.8219907581307 & 84.480993853281 \tabularnewline
74 & 81.3897971891095 & 77.7872040715609 & 84.9923903066582 \tabularnewline
75 & 80.6281020725132 & 75.6908707050162 & 85.5653334400102 \tabularnewline
76 & 79.8664069559168 & 73.5096879140214 & 86.2231259978123 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260843&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]82.1514923057059[/C][C]79.8219907581307[/C][C]84.480993853281[/C][/ROW]
[ROW][C]74[/C][C]81.3897971891095[/C][C]77.7872040715609[/C][C]84.9923903066582[/C][/ROW]
[ROW][C]75[/C][C]80.6281020725132[/C][C]75.6908707050162[/C][C]85.5653334400102[/C][/ROW]
[ROW][C]76[/C][C]79.8664069559168[/C][C]73.5096879140214[/C][C]86.2231259978123[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260843&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260843&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
7382.151492305705979.821990758130784.480993853281
7481.389797189109577.787204071560984.9923903066582
7580.628102072513275.690870705016285.5653334400102
7679.866406955916873.509687914021486.2231259978123



Parameters (Session):
par1 = 4 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 4 ; 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')