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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 16:10:31 +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/2016/Apr/25/t14615970553lqwq3rjxss3k88.htm/, Retrieved Sun, 05 May 2024 22:37:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294735, Retrieved Sun, 05 May 2024 22:37:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 15:10:31] [c9bda892eb41b28d549a884a1978c032] [Current]
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Dataseries X:
94.65
94.16
93.91
93.21
92.81
93.55
93.03
93.25
94.24
93.23
93.52
92.05
93.42
95.15
95.12
95.46
94.92
95.63
94.96
95.1
95.22
93.77
95.01
94.87
95.01
96.68
94.94
93.9
94.83
96.27
96.51
96.69
97.47
96.41
98.68
99.3
99.22
99.7
98
98.51
98.6
98.14
99.14
98.25
99.72
99.23
101.32
101.07
101.66
103.09
102.3
100.01
98.78
99.46
99.73
99.52
98.97
97.97
99.37
99.14
99.89
100.29
99.57
101.11
101.44
100.81
101.26
99.86
100.57
100.35
101.15
101.33
102.09
101.79
102.83
102.5
102.22
102.43
102.89
102.12
103.25
103.36
103.5
103.68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294735&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294735&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.772125155625731
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.772125155625731 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294735&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]0.772125155625731[/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=294735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294735&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
alpha0.772125155625731
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
294.1694.65-0.490000000000009
393.9194.2716586737434-0.361658673743392
493.2193.9924129139959-0.782412913995884
592.8193.3882922210132-0.578292221013228
693.5592.94177824986620.608221750133751
793.0393.4114015633432-0.381401563343218
893.2593.11691182189090.133088178109062
994.2493.21967255212531.02032744787465
1093.2394.0074930416048-0.777493041604757
1193.5293.40717110585780.112828894142226
1292.0593.4942891333064-1.44428913330641
1393.4292.37911716148361.04088283851637
1495.1593.18280898516121.96719101483878
1595.1294.70172665363920.418273346360849
1695.4695.02468602629210.435313973707864
1794.9295.3608028959874-0.44080289598736
1895.6395.02044789132280.60955210867715
1994.9695.4910984080972-0.531098408097193
2095.195.08102396709260.0189760329074318
2195.2295.09567583945440.124324160545626
2293.7795.1916696512637-1.42166965126371
2395.0194.09396275053330.916037249466669
2494.8794.80125815433680.0687418456632543
2595.0194.85433546261750.155664537382521
2696.6894.97452796776941.70547203223065
2794.9496.2913658260708-1.35136582607079
2893.995.2479422773086-1.34794227730858
2994.8394.20716213666720.622837863332805
3096.2794.68807091882261.58192908117736
3196.5195.90951815681560.600481843184426
3296.6996.37316529343480.316834706565231
3397.4796.61780134054910.85219865945092
3496.4197.2758053631017-0.865805363101671
3598.6896.60729526237522.07270473762482
3699.398.20768273047991.09231726952005
3799.2299.05108837220080.168911627799218
3899.799.18150928910230.518490710897751
399899.5818490099447-1.58184900994468
4098.5198.36046359696470.14953640303527
4198.698.47592441543010.124075584569937
4298.1498.5717262954755-0.431726295475471
4399.1498.23837956239380.90162043760624
4498.2598.9345433830958-0.684543383095814
4599.7298.40599021689041.31400978310961
4699.2399.4205702251676-0.190570225167619
47101.3299.27342616040242.04657383959756
48101.07100.8536373048010.21636269519874
49101.66101.0206963845030.639303615496814
50103.09101.5143187881111.57568121188925
51102.3102.730941889057-0.43094188905728
52100.01102.398200815903-2.38820081590328
5398.78100.554210889258-1.77421088925847
5499.4699.18429803027690.275701969723087
5599.7399.39717445655570.332825543444343
5699.5299.6541574310838-0.134157431083835
5798.9799.5505711037299-0.580571103729881
5897.9799.1022975499106-1.13229754991065
5999.3798.22802212797131.14197787202875
6099.1499.10977197013260.0302280298674162
6199.8999.13311179239820.756888207601776
62100.2999.7175242174840.57247578251598
6399.57100.159547170151-0.58954717015115
64101.1199.70434296964951.40565703035053
65101.44100.7896861229650.650313877034719
66100.81101.291809826476-0.48180982647628
67101.26100.9197923392260.340207660773729
6899.86101.182475232246-1.32247523224625
69100.57100.1613588377370.408641162263052
70100.35100.476880958744-0.12688095874438
71101.15100.3789129787280.771087021272081
72101.33100.9742886650290.355711334971389
73102.09101.2489423349010.841057665098759
74101.79101.898344115456-0.108344115455836
75102.83101.8146888984481.01531110155163
76102.5102.598636140742-0.0986361407424567
77102.22102.522476695221-0.302476695221372
78102.43102.288926829850.141073170149596
79102.89102.3978529733070.492147026693218
80102.12102.777852072883-0.657852072883031
81103.25102.269907938730.980092061270483
82103.36103.0266616740660.333338325934463
83103.5103.2840405808540.215959419146287
84103.68103.4507882809710.229211719029124

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 94.16 & 94.65 & -0.490000000000009 \tabularnewline
3 & 93.91 & 94.2716586737434 & -0.361658673743392 \tabularnewline
4 & 93.21 & 93.9924129139959 & -0.782412913995884 \tabularnewline
5 & 92.81 & 93.3882922210132 & -0.578292221013228 \tabularnewline
6 & 93.55 & 92.9417782498662 & 0.608221750133751 \tabularnewline
7 & 93.03 & 93.4114015633432 & -0.381401563343218 \tabularnewline
8 & 93.25 & 93.1169118218909 & 0.133088178109062 \tabularnewline
9 & 94.24 & 93.2196725521253 & 1.02032744787465 \tabularnewline
10 & 93.23 & 94.0074930416048 & -0.777493041604757 \tabularnewline
11 & 93.52 & 93.4071711058578 & 0.112828894142226 \tabularnewline
12 & 92.05 & 93.4942891333064 & -1.44428913330641 \tabularnewline
13 & 93.42 & 92.3791171614836 & 1.04088283851637 \tabularnewline
14 & 95.15 & 93.1828089851612 & 1.96719101483878 \tabularnewline
15 & 95.12 & 94.7017266536392 & 0.418273346360849 \tabularnewline
16 & 95.46 & 95.0246860262921 & 0.435313973707864 \tabularnewline
17 & 94.92 & 95.3608028959874 & -0.44080289598736 \tabularnewline
18 & 95.63 & 95.0204478913228 & 0.60955210867715 \tabularnewline
19 & 94.96 & 95.4910984080972 & -0.531098408097193 \tabularnewline
20 & 95.1 & 95.0810239670926 & 0.0189760329074318 \tabularnewline
21 & 95.22 & 95.0956758394544 & 0.124324160545626 \tabularnewline
22 & 93.77 & 95.1916696512637 & -1.42166965126371 \tabularnewline
23 & 95.01 & 94.0939627505333 & 0.916037249466669 \tabularnewline
24 & 94.87 & 94.8012581543368 & 0.0687418456632543 \tabularnewline
25 & 95.01 & 94.8543354626175 & 0.155664537382521 \tabularnewline
26 & 96.68 & 94.9745279677694 & 1.70547203223065 \tabularnewline
27 & 94.94 & 96.2913658260708 & -1.35136582607079 \tabularnewline
28 & 93.9 & 95.2479422773086 & -1.34794227730858 \tabularnewline
29 & 94.83 & 94.2071621366672 & 0.622837863332805 \tabularnewline
30 & 96.27 & 94.6880709188226 & 1.58192908117736 \tabularnewline
31 & 96.51 & 95.9095181568156 & 0.600481843184426 \tabularnewline
32 & 96.69 & 96.3731652934348 & 0.316834706565231 \tabularnewline
33 & 97.47 & 96.6178013405491 & 0.85219865945092 \tabularnewline
34 & 96.41 & 97.2758053631017 & -0.865805363101671 \tabularnewline
35 & 98.68 & 96.6072952623752 & 2.07270473762482 \tabularnewline
36 & 99.3 & 98.2076827304799 & 1.09231726952005 \tabularnewline
37 & 99.22 & 99.0510883722008 & 0.168911627799218 \tabularnewline
38 & 99.7 & 99.1815092891023 & 0.518490710897751 \tabularnewline
39 & 98 & 99.5818490099447 & -1.58184900994468 \tabularnewline
40 & 98.51 & 98.3604635969647 & 0.14953640303527 \tabularnewline
41 & 98.6 & 98.4759244154301 & 0.124075584569937 \tabularnewline
42 & 98.14 & 98.5717262954755 & -0.431726295475471 \tabularnewline
43 & 99.14 & 98.2383795623938 & 0.90162043760624 \tabularnewline
44 & 98.25 & 98.9345433830958 & -0.684543383095814 \tabularnewline
45 & 99.72 & 98.4059902168904 & 1.31400978310961 \tabularnewline
46 & 99.23 & 99.4205702251676 & -0.190570225167619 \tabularnewline
47 & 101.32 & 99.2734261604024 & 2.04657383959756 \tabularnewline
48 & 101.07 & 100.853637304801 & 0.21636269519874 \tabularnewline
49 & 101.66 & 101.020696384503 & 0.639303615496814 \tabularnewline
50 & 103.09 & 101.514318788111 & 1.57568121188925 \tabularnewline
51 & 102.3 & 102.730941889057 & -0.43094188905728 \tabularnewline
52 & 100.01 & 102.398200815903 & -2.38820081590328 \tabularnewline
53 & 98.78 & 100.554210889258 & -1.77421088925847 \tabularnewline
54 & 99.46 & 99.1842980302769 & 0.275701969723087 \tabularnewline
55 & 99.73 & 99.3971744565557 & 0.332825543444343 \tabularnewline
56 & 99.52 & 99.6541574310838 & -0.134157431083835 \tabularnewline
57 & 98.97 & 99.5505711037299 & -0.580571103729881 \tabularnewline
58 & 97.97 & 99.1022975499106 & -1.13229754991065 \tabularnewline
59 & 99.37 & 98.2280221279713 & 1.14197787202875 \tabularnewline
60 & 99.14 & 99.1097719701326 & 0.0302280298674162 \tabularnewline
61 & 99.89 & 99.1331117923982 & 0.756888207601776 \tabularnewline
62 & 100.29 & 99.717524217484 & 0.57247578251598 \tabularnewline
63 & 99.57 & 100.159547170151 & -0.58954717015115 \tabularnewline
64 & 101.11 & 99.7043429696495 & 1.40565703035053 \tabularnewline
65 & 101.44 & 100.789686122965 & 0.650313877034719 \tabularnewline
66 & 100.81 & 101.291809826476 & -0.48180982647628 \tabularnewline
67 & 101.26 & 100.919792339226 & 0.340207660773729 \tabularnewline
68 & 99.86 & 101.182475232246 & -1.32247523224625 \tabularnewline
69 & 100.57 & 100.161358837737 & 0.408641162263052 \tabularnewline
70 & 100.35 & 100.476880958744 & -0.12688095874438 \tabularnewline
71 & 101.15 & 100.378912978728 & 0.771087021272081 \tabularnewline
72 & 101.33 & 100.974288665029 & 0.355711334971389 \tabularnewline
73 & 102.09 & 101.248942334901 & 0.841057665098759 \tabularnewline
74 & 101.79 & 101.898344115456 & -0.108344115455836 \tabularnewline
75 & 102.83 & 101.814688898448 & 1.01531110155163 \tabularnewline
76 & 102.5 & 102.598636140742 & -0.0986361407424567 \tabularnewline
77 & 102.22 & 102.522476695221 & -0.302476695221372 \tabularnewline
78 & 102.43 & 102.28892682985 & 0.141073170149596 \tabularnewline
79 & 102.89 & 102.397852973307 & 0.492147026693218 \tabularnewline
80 & 102.12 & 102.777852072883 & -0.657852072883031 \tabularnewline
81 & 103.25 & 102.26990793873 & 0.980092061270483 \tabularnewline
82 & 103.36 & 103.026661674066 & 0.333338325934463 \tabularnewline
83 & 103.5 & 103.284040580854 & 0.215959419146287 \tabularnewline
84 & 103.68 & 103.450788280971 & 0.229211719029124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294735&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]94.16[/C][C]94.65[/C][C]-0.490000000000009[/C][/ROW]
[ROW][C]3[/C][C]93.91[/C][C]94.2716586737434[/C][C]-0.361658673743392[/C][/ROW]
[ROW][C]4[/C][C]93.21[/C][C]93.9924129139959[/C][C]-0.782412913995884[/C][/ROW]
[ROW][C]5[/C][C]92.81[/C][C]93.3882922210132[/C][C]-0.578292221013228[/C][/ROW]
[ROW][C]6[/C][C]93.55[/C][C]92.9417782498662[/C][C]0.608221750133751[/C][/ROW]
[ROW][C]7[/C][C]93.03[/C][C]93.4114015633432[/C][C]-0.381401563343218[/C][/ROW]
[ROW][C]8[/C][C]93.25[/C][C]93.1169118218909[/C][C]0.133088178109062[/C][/ROW]
[ROW][C]9[/C][C]94.24[/C][C]93.2196725521253[/C][C]1.02032744787465[/C][/ROW]
[ROW][C]10[/C][C]93.23[/C][C]94.0074930416048[/C][C]-0.777493041604757[/C][/ROW]
[ROW][C]11[/C][C]93.52[/C][C]93.4071711058578[/C][C]0.112828894142226[/C][/ROW]
[ROW][C]12[/C][C]92.05[/C][C]93.4942891333064[/C][C]-1.44428913330641[/C][/ROW]
[ROW][C]13[/C][C]93.42[/C][C]92.3791171614836[/C][C]1.04088283851637[/C][/ROW]
[ROW][C]14[/C][C]95.15[/C][C]93.1828089851612[/C][C]1.96719101483878[/C][/ROW]
[ROW][C]15[/C][C]95.12[/C][C]94.7017266536392[/C][C]0.418273346360849[/C][/ROW]
[ROW][C]16[/C][C]95.46[/C][C]95.0246860262921[/C][C]0.435313973707864[/C][/ROW]
[ROW][C]17[/C][C]94.92[/C][C]95.3608028959874[/C][C]-0.44080289598736[/C][/ROW]
[ROW][C]18[/C][C]95.63[/C][C]95.0204478913228[/C][C]0.60955210867715[/C][/ROW]
[ROW][C]19[/C][C]94.96[/C][C]95.4910984080972[/C][C]-0.531098408097193[/C][/ROW]
[ROW][C]20[/C][C]95.1[/C][C]95.0810239670926[/C][C]0.0189760329074318[/C][/ROW]
[ROW][C]21[/C][C]95.22[/C][C]95.0956758394544[/C][C]0.124324160545626[/C][/ROW]
[ROW][C]22[/C][C]93.77[/C][C]95.1916696512637[/C][C]-1.42166965126371[/C][/ROW]
[ROW][C]23[/C][C]95.01[/C][C]94.0939627505333[/C][C]0.916037249466669[/C][/ROW]
[ROW][C]24[/C][C]94.87[/C][C]94.8012581543368[/C][C]0.0687418456632543[/C][/ROW]
[ROW][C]25[/C][C]95.01[/C][C]94.8543354626175[/C][C]0.155664537382521[/C][/ROW]
[ROW][C]26[/C][C]96.68[/C][C]94.9745279677694[/C][C]1.70547203223065[/C][/ROW]
[ROW][C]27[/C][C]94.94[/C][C]96.2913658260708[/C][C]-1.35136582607079[/C][/ROW]
[ROW][C]28[/C][C]93.9[/C][C]95.2479422773086[/C][C]-1.34794227730858[/C][/ROW]
[ROW][C]29[/C][C]94.83[/C][C]94.2071621366672[/C][C]0.622837863332805[/C][/ROW]
[ROW][C]30[/C][C]96.27[/C][C]94.6880709188226[/C][C]1.58192908117736[/C][/ROW]
[ROW][C]31[/C][C]96.51[/C][C]95.9095181568156[/C][C]0.600481843184426[/C][/ROW]
[ROW][C]32[/C][C]96.69[/C][C]96.3731652934348[/C][C]0.316834706565231[/C][/ROW]
[ROW][C]33[/C][C]97.47[/C][C]96.6178013405491[/C][C]0.85219865945092[/C][/ROW]
[ROW][C]34[/C][C]96.41[/C][C]97.2758053631017[/C][C]-0.865805363101671[/C][/ROW]
[ROW][C]35[/C][C]98.68[/C][C]96.6072952623752[/C][C]2.07270473762482[/C][/ROW]
[ROW][C]36[/C][C]99.3[/C][C]98.2076827304799[/C][C]1.09231726952005[/C][/ROW]
[ROW][C]37[/C][C]99.22[/C][C]99.0510883722008[/C][C]0.168911627799218[/C][/ROW]
[ROW][C]38[/C][C]99.7[/C][C]99.1815092891023[/C][C]0.518490710897751[/C][/ROW]
[ROW][C]39[/C][C]98[/C][C]99.5818490099447[/C][C]-1.58184900994468[/C][/ROW]
[ROW][C]40[/C][C]98.51[/C][C]98.3604635969647[/C][C]0.14953640303527[/C][/ROW]
[ROW][C]41[/C][C]98.6[/C][C]98.4759244154301[/C][C]0.124075584569937[/C][/ROW]
[ROW][C]42[/C][C]98.14[/C][C]98.5717262954755[/C][C]-0.431726295475471[/C][/ROW]
[ROW][C]43[/C][C]99.14[/C][C]98.2383795623938[/C][C]0.90162043760624[/C][/ROW]
[ROW][C]44[/C][C]98.25[/C][C]98.9345433830958[/C][C]-0.684543383095814[/C][/ROW]
[ROW][C]45[/C][C]99.72[/C][C]98.4059902168904[/C][C]1.31400978310961[/C][/ROW]
[ROW][C]46[/C][C]99.23[/C][C]99.4205702251676[/C][C]-0.190570225167619[/C][/ROW]
[ROW][C]47[/C][C]101.32[/C][C]99.2734261604024[/C][C]2.04657383959756[/C][/ROW]
[ROW][C]48[/C][C]101.07[/C][C]100.853637304801[/C][C]0.21636269519874[/C][/ROW]
[ROW][C]49[/C][C]101.66[/C][C]101.020696384503[/C][C]0.639303615496814[/C][/ROW]
[ROW][C]50[/C][C]103.09[/C][C]101.514318788111[/C][C]1.57568121188925[/C][/ROW]
[ROW][C]51[/C][C]102.3[/C][C]102.730941889057[/C][C]-0.43094188905728[/C][/ROW]
[ROW][C]52[/C][C]100.01[/C][C]102.398200815903[/C][C]-2.38820081590328[/C][/ROW]
[ROW][C]53[/C][C]98.78[/C][C]100.554210889258[/C][C]-1.77421088925847[/C][/ROW]
[ROW][C]54[/C][C]99.46[/C][C]99.1842980302769[/C][C]0.275701969723087[/C][/ROW]
[ROW][C]55[/C][C]99.73[/C][C]99.3971744565557[/C][C]0.332825543444343[/C][/ROW]
[ROW][C]56[/C][C]99.52[/C][C]99.6541574310838[/C][C]-0.134157431083835[/C][/ROW]
[ROW][C]57[/C][C]98.97[/C][C]99.5505711037299[/C][C]-0.580571103729881[/C][/ROW]
[ROW][C]58[/C][C]97.97[/C][C]99.1022975499106[/C][C]-1.13229754991065[/C][/ROW]
[ROW][C]59[/C][C]99.37[/C][C]98.2280221279713[/C][C]1.14197787202875[/C][/ROW]
[ROW][C]60[/C][C]99.14[/C][C]99.1097719701326[/C][C]0.0302280298674162[/C][/ROW]
[ROW][C]61[/C][C]99.89[/C][C]99.1331117923982[/C][C]0.756888207601776[/C][/ROW]
[ROW][C]62[/C][C]100.29[/C][C]99.717524217484[/C][C]0.57247578251598[/C][/ROW]
[ROW][C]63[/C][C]99.57[/C][C]100.159547170151[/C][C]-0.58954717015115[/C][/ROW]
[ROW][C]64[/C][C]101.11[/C][C]99.7043429696495[/C][C]1.40565703035053[/C][/ROW]
[ROW][C]65[/C][C]101.44[/C][C]100.789686122965[/C][C]0.650313877034719[/C][/ROW]
[ROW][C]66[/C][C]100.81[/C][C]101.291809826476[/C][C]-0.48180982647628[/C][/ROW]
[ROW][C]67[/C][C]101.26[/C][C]100.919792339226[/C][C]0.340207660773729[/C][/ROW]
[ROW][C]68[/C][C]99.86[/C][C]101.182475232246[/C][C]-1.32247523224625[/C][/ROW]
[ROW][C]69[/C][C]100.57[/C][C]100.161358837737[/C][C]0.408641162263052[/C][/ROW]
[ROW][C]70[/C][C]100.35[/C][C]100.476880958744[/C][C]-0.12688095874438[/C][/ROW]
[ROW][C]71[/C][C]101.15[/C][C]100.378912978728[/C][C]0.771087021272081[/C][/ROW]
[ROW][C]72[/C][C]101.33[/C][C]100.974288665029[/C][C]0.355711334971389[/C][/ROW]
[ROW][C]73[/C][C]102.09[/C][C]101.248942334901[/C][C]0.841057665098759[/C][/ROW]
[ROW][C]74[/C][C]101.79[/C][C]101.898344115456[/C][C]-0.108344115455836[/C][/ROW]
[ROW][C]75[/C][C]102.83[/C][C]101.814688898448[/C][C]1.01531110155163[/C][/ROW]
[ROW][C]76[/C][C]102.5[/C][C]102.598636140742[/C][C]-0.0986361407424567[/C][/ROW]
[ROW][C]77[/C][C]102.22[/C][C]102.522476695221[/C][C]-0.302476695221372[/C][/ROW]
[ROW][C]78[/C][C]102.43[/C][C]102.28892682985[/C][C]0.141073170149596[/C][/ROW]
[ROW][C]79[/C][C]102.89[/C][C]102.397852973307[/C][C]0.492147026693218[/C][/ROW]
[ROW][C]80[/C][C]102.12[/C][C]102.777852072883[/C][C]-0.657852072883031[/C][/ROW]
[ROW][C]81[/C][C]103.25[/C][C]102.26990793873[/C][C]0.980092061270483[/C][/ROW]
[ROW][C]82[/C][C]103.36[/C][C]103.026661674066[/C][C]0.333338325934463[/C][/ROW]
[ROW][C]83[/C][C]103.5[/C][C]103.284040580854[/C][C]0.215959419146287[/C][/ROW]
[ROW][C]84[/C][C]103.68[/C][C]103.450788280971[/C][C]0.229211719029124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294735&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294735&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
294.1694.65-0.490000000000009
393.9194.2716586737434-0.361658673743392
493.2193.9924129139959-0.782412913995884
592.8193.3882922210132-0.578292221013228
693.5592.94177824986620.608221750133751
793.0393.4114015633432-0.381401563343218
893.2593.11691182189090.133088178109062
994.2493.21967255212531.02032744787465
1093.2394.0074930416048-0.777493041604757
1193.5293.40717110585780.112828894142226
1292.0593.4942891333064-1.44428913330641
1393.4292.37911716148361.04088283851637
1495.1593.18280898516121.96719101483878
1595.1294.70172665363920.418273346360849
1695.4695.02468602629210.435313973707864
1794.9295.3608028959874-0.44080289598736
1895.6395.02044789132280.60955210867715
1994.9695.4910984080972-0.531098408097193
2095.195.08102396709260.0189760329074318
2195.2295.09567583945440.124324160545626
2293.7795.1916696512637-1.42166965126371
2395.0194.09396275053330.916037249466669
2494.8794.80125815433680.0687418456632543
2595.0194.85433546261750.155664537382521
2696.6894.97452796776941.70547203223065
2794.9496.2913658260708-1.35136582607079
2893.995.2479422773086-1.34794227730858
2994.8394.20716213666720.622837863332805
3096.2794.68807091882261.58192908117736
3196.5195.90951815681560.600481843184426
3296.6996.37316529343480.316834706565231
3397.4796.61780134054910.85219865945092
3496.4197.2758053631017-0.865805363101671
3598.6896.60729526237522.07270473762482
3699.398.20768273047991.09231726952005
3799.2299.05108837220080.168911627799218
3899.799.18150928910230.518490710897751
399899.5818490099447-1.58184900994468
4098.5198.36046359696470.14953640303527
4198.698.47592441543010.124075584569937
4298.1498.5717262954755-0.431726295475471
4399.1498.23837956239380.90162043760624
4498.2598.9345433830958-0.684543383095814
4599.7298.40599021689041.31400978310961
4699.2399.4205702251676-0.190570225167619
47101.3299.27342616040242.04657383959756
48101.07100.8536373048010.21636269519874
49101.66101.0206963845030.639303615496814
50103.09101.5143187881111.57568121188925
51102.3102.730941889057-0.43094188905728
52100.01102.398200815903-2.38820081590328
5398.78100.554210889258-1.77421088925847
5499.4699.18429803027690.275701969723087
5599.7399.39717445655570.332825543444343
5699.5299.6541574310838-0.134157431083835
5798.9799.5505711037299-0.580571103729881
5897.9799.1022975499106-1.13229754991065
5999.3798.22802212797131.14197787202875
6099.1499.10977197013260.0302280298674162
6199.8999.13311179239820.756888207601776
62100.2999.7175242174840.57247578251598
6399.57100.159547170151-0.58954717015115
64101.1199.70434296964951.40565703035053
65101.44100.7896861229650.650313877034719
66100.81101.291809826476-0.48180982647628
67101.26100.9197923392260.340207660773729
6899.86101.182475232246-1.32247523224625
69100.57100.1613588377370.408641162263052
70100.35100.476880958744-0.12688095874438
71101.15100.3789129787280.771087021272081
72101.33100.9742886650290.355711334971389
73102.09101.2489423349010.841057665098759
74101.79101.898344115456-0.108344115455836
75102.83101.8146888984481.01531110155163
76102.5102.598636140742-0.0986361407424567
77102.22102.522476695221-0.302476695221372
78102.43102.288926829850.141073170149596
79102.89102.3978529733070.492147026693218
80102.12102.777852072883-0.657852072883031
81103.25102.269907938730.980092061270483
82103.36103.0266616740660.333338325934463
83103.5103.2840405808540.215959419146287
84103.68103.4507882809710.229211719029124







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85103.627768415197101.874310728523105.381226101872
86103.627768415197101.412451572735105.84308525766
87103.627768415197101.031493474819106.224043355576
88103.627768415197100.699687402046106.555849428349
89103.627768415197100.401830834723106.853705995672
90103.627768415197100.129241850105107.12629498029
91103.62776841519799.876408264506107.379128565889
92103.62776841519799.6395710988984107.615965731497
93103.62776841519799.4160309248884107.839505905507
94103.62776841519799.2037716316527108.051765198742
95103.62776841519799.0012403006872108.254296529708
96103.62776841519798.8072106416723108.448326188723

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 103.627768415197 & 101.874310728523 & 105.381226101872 \tabularnewline
86 & 103.627768415197 & 101.412451572735 & 105.84308525766 \tabularnewline
87 & 103.627768415197 & 101.031493474819 & 106.224043355576 \tabularnewline
88 & 103.627768415197 & 100.699687402046 & 106.555849428349 \tabularnewline
89 & 103.627768415197 & 100.401830834723 & 106.853705995672 \tabularnewline
90 & 103.627768415197 & 100.129241850105 & 107.12629498029 \tabularnewline
91 & 103.627768415197 & 99.876408264506 & 107.379128565889 \tabularnewline
92 & 103.627768415197 & 99.6395710988984 & 107.615965731497 \tabularnewline
93 & 103.627768415197 & 99.4160309248884 & 107.839505905507 \tabularnewline
94 & 103.627768415197 & 99.2037716316527 & 108.051765198742 \tabularnewline
95 & 103.627768415197 & 99.0012403006872 & 108.254296529708 \tabularnewline
96 & 103.627768415197 & 98.8072106416723 & 108.448326188723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294735&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]85[/C][C]103.627768415197[/C][C]101.874310728523[/C][C]105.381226101872[/C][/ROW]
[ROW][C]86[/C][C]103.627768415197[/C][C]101.412451572735[/C][C]105.84308525766[/C][/ROW]
[ROW][C]87[/C][C]103.627768415197[/C][C]101.031493474819[/C][C]106.224043355576[/C][/ROW]
[ROW][C]88[/C][C]103.627768415197[/C][C]100.699687402046[/C][C]106.555849428349[/C][/ROW]
[ROW][C]89[/C][C]103.627768415197[/C][C]100.401830834723[/C][C]106.853705995672[/C][/ROW]
[ROW][C]90[/C][C]103.627768415197[/C][C]100.129241850105[/C][C]107.12629498029[/C][/ROW]
[ROW][C]91[/C][C]103.627768415197[/C][C]99.876408264506[/C][C]107.379128565889[/C][/ROW]
[ROW][C]92[/C][C]103.627768415197[/C][C]99.6395710988984[/C][C]107.615965731497[/C][/ROW]
[ROW][C]93[/C][C]103.627768415197[/C][C]99.4160309248884[/C][C]107.839505905507[/C][/ROW]
[ROW][C]94[/C][C]103.627768415197[/C][C]99.2037716316527[/C][C]108.051765198742[/C][/ROW]
[ROW][C]95[/C][C]103.627768415197[/C][C]99.0012403006872[/C][C]108.254296529708[/C][/ROW]
[ROW][C]96[/C][C]103.627768415197[/C][C]98.8072106416723[/C][C]108.448326188723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294735&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294735&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
85103.627768415197101.874310728523105.381226101872
86103.627768415197101.412451572735105.84308525766
87103.627768415197101.031493474819106.224043355576
88103.627768415197100.699687402046106.555849428349
89103.627768415197100.401830834723106.853705995672
90103.627768415197100.129241850105107.12629498029
91103.62776841519799.876408264506107.379128565889
92103.62776841519799.6395710988984107.615965731497
93103.62776841519799.4160309248884107.839505905507
94103.62776841519799.2037716316527108.051765198742
95103.62776841519799.0012403006872108.254296529708
96103.62776841519798.8072106416723108.448326188723



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')