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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 27 May 2015 07:56:14 +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/2015/May/27/t1432709802p167umdgfu90rw4.htm/, Retrieved Sat, 04 May 2024 13:11:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279459, Retrieved Sat, 04 May 2024 13:11:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2015-04-02 21:48:37] [693750cd301bd4fecbcaa8326eb70b61]
- R PD    [Exponential Smoothing] [] [2015-05-27 06:56:14] [567f06ca3de45fa0ce67a0a89b883c29] [Current]
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Dataseries X:
94.67
94.6
93.9
93.41
93.37
93.35
93.08
93.05
92.61
92.37
92.24
91.95
92.63
92.7
92.47
92.58
92.55
92.56
89.92
89.96
90.03
90.31
90.8
90.36
90.31
93.8
93.95
93.99
94.44
94.15
91.91
91.86
93.12
93.47
93.57
94.57
95.85
96.62
95.69
95.39
95.14
95.07
94.21
95.4
95.1
94.89
95.43
94.88
96.03
96.37
96.04
95.72
95.74
95.78
93.66
95.29
94.33
95.66
95.2
94.61
96.21
96.27
95.12
95.55
93.51
92.86
92.45
93.34
92.01
91.77
92.19
91.97




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=279459&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=279459&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279459&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
alpha0.874098986481221
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.874098986481221 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279459&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]0.874098986481221[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279459&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279459&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
alpha0.874098986481221
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
393.994.53-0.629999999999981
493.4193.9093176385168-0.499317638516828
593.3793.4028645967571-0.0328645967570509
693.3593.30413768604060.0458623139594039
793.0893.2742258881902-0.194225888190189
893.0593.03445323617470.0155467638252702
992.6192.9780426466775-0.368042646677452
1092.3792.5863369422348-0.216336942234804
1192.2492.3272370402889-0.087237040288926
1291.9592.1809832317887-0.230983231788741
1392.6391.9090810229880.720918977011948
1492.792.46923557012930.230764429870746
1592.4792.6009465243952-0.130946524395185
1692.5892.41648630013810.163513699861895
1792.5592.48941345946320.0605865405368178
1892.5692.47237209314080.087627906859197
1989.9292.4789675577139-2.5589675577139
2089.9690.1721766090779-0.212176609077858
2190.0389.91671325012790.113286749872131
2290.3189.94573708337280.364262916627155
2390.890.19413892960930.60586107039066
2490.3690.6537214771862-0.293721477186239
2590.3190.32697983167-0.0169798316699712
2693.890.24213777801663.55786222198337
2793.9593.28206154029210.667938459707898
2893.9993.79590587095460.194094129045396
2994.4493.89556335243510.544436647564879
3094.1594.3014548742748-0.151454874274805
3191.9194.0990683221736-2.18906832217355
3291.8692.1156059204235-0.255605920423491
3393.1291.82218104444271.29781895555729
3493.4792.88660327813140.583396721868553
3593.5793.32654976143320.243450238566794
3694.5793.4693493682231.10065063177696
3795.8594.36142696992921.48857303007081
3896.6295.59258714681741.02741285318265
3995.6996.4206476804821-0.730647680482079
4095.3995.7119892834978-0.321989283497828
4195.1495.3605387771346-0.22053877713455
4295.0795.0977660555614-0.027766055561429
4394.2195.0034957745366-0.793495774536595
4495.494.2399019222371.160098077763
4595.195.1839424762285-0.083942476228458
4694.8995.0405684428344-0.150568442834413
4795.4394.83895671955680.591043280443216
4894.8895.2855870519587-0.405587051958747
4996.0394.86106382091171.16893617908831
5096.3795.8128297503140.557170249685996
5196.0496.229851700862-0.189851700862022
5295.7295.9939025215568-0.273902521556792
5395.7495.68448460506930.0555153949306515
5495.7895.66301055551230.116989444487686
5593.6695.695270910368-2.035270910368
5695.2993.84624267040061.44375732959941
5794.3395.0382294889283-0.708229488928268
5895.6694.34916681045991.31083318954005
5995.295.4249647728828-0.224964772882842
6094.6195.158323292912-0.548323292911959
6196.2194.60903445831361.60096554168643
6296.2795.9384368156930.331563184306972
6395.1296.1582558590502-1.03825585905022
6495.5595.18071746494620.36928253505377
6593.5195.4335069545619-1.92350695456193
6692.8693.6821714750898-0.822171475089775
6792.4592.893512222-0.44351222200001
6893.3492.43583863825780.90416136174224
6992.0193.1561651681721-1.14616516817213
7091.7792.0843033563328-0.3143033563328
7192.1991.73957111111460.450428888885355
7291.9792.0632905463712-0.0932905463711933

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 93.9 & 94.53 & -0.629999999999981 \tabularnewline
4 & 93.41 & 93.9093176385168 & -0.499317638516828 \tabularnewline
5 & 93.37 & 93.4028645967571 & -0.0328645967570509 \tabularnewline
6 & 93.35 & 93.3041376860406 & 0.0458623139594039 \tabularnewline
7 & 93.08 & 93.2742258881902 & -0.194225888190189 \tabularnewline
8 & 93.05 & 93.0344532361747 & 0.0155467638252702 \tabularnewline
9 & 92.61 & 92.9780426466775 & -0.368042646677452 \tabularnewline
10 & 92.37 & 92.5863369422348 & -0.216336942234804 \tabularnewline
11 & 92.24 & 92.3272370402889 & -0.087237040288926 \tabularnewline
12 & 91.95 & 92.1809832317887 & -0.230983231788741 \tabularnewline
13 & 92.63 & 91.909081022988 & 0.720918977011948 \tabularnewline
14 & 92.7 & 92.4692355701293 & 0.230764429870746 \tabularnewline
15 & 92.47 & 92.6009465243952 & -0.130946524395185 \tabularnewline
16 & 92.58 & 92.4164863001381 & 0.163513699861895 \tabularnewline
17 & 92.55 & 92.4894134594632 & 0.0605865405368178 \tabularnewline
18 & 92.56 & 92.4723720931408 & 0.087627906859197 \tabularnewline
19 & 89.92 & 92.4789675577139 & -2.5589675577139 \tabularnewline
20 & 89.96 & 90.1721766090779 & -0.212176609077858 \tabularnewline
21 & 90.03 & 89.9167132501279 & 0.113286749872131 \tabularnewline
22 & 90.31 & 89.9457370833728 & 0.364262916627155 \tabularnewline
23 & 90.8 & 90.1941389296093 & 0.60586107039066 \tabularnewline
24 & 90.36 & 90.6537214771862 & -0.293721477186239 \tabularnewline
25 & 90.31 & 90.32697983167 & -0.0169798316699712 \tabularnewline
26 & 93.8 & 90.2421377780166 & 3.55786222198337 \tabularnewline
27 & 93.95 & 93.2820615402921 & 0.667938459707898 \tabularnewline
28 & 93.99 & 93.7959058709546 & 0.194094129045396 \tabularnewline
29 & 94.44 & 93.8955633524351 & 0.544436647564879 \tabularnewline
30 & 94.15 & 94.3014548742748 & -0.151454874274805 \tabularnewline
31 & 91.91 & 94.0990683221736 & -2.18906832217355 \tabularnewline
32 & 91.86 & 92.1156059204235 & -0.255605920423491 \tabularnewline
33 & 93.12 & 91.8221810444427 & 1.29781895555729 \tabularnewline
34 & 93.47 & 92.8866032781314 & 0.583396721868553 \tabularnewline
35 & 93.57 & 93.3265497614332 & 0.243450238566794 \tabularnewline
36 & 94.57 & 93.469349368223 & 1.10065063177696 \tabularnewline
37 & 95.85 & 94.3614269699292 & 1.48857303007081 \tabularnewline
38 & 96.62 & 95.5925871468174 & 1.02741285318265 \tabularnewline
39 & 95.69 & 96.4206476804821 & -0.730647680482079 \tabularnewline
40 & 95.39 & 95.7119892834978 & -0.321989283497828 \tabularnewline
41 & 95.14 & 95.3605387771346 & -0.22053877713455 \tabularnewline
42 & 95.07 & 95.0977660555614 & -0.027766055561429 \tabularnewline
43 & 94.21 & 95.0034957745366 & -0.793495774536595 \tabularnewline
44 & 95.4 & 94.239901922237 & 1.160098077763 \tabularnewline
45 & 95.1 & 95.1839424762285 & -0.083942476228458 \tabularnewline
46 & 94.89 & 95.0405684428344 & -0.150568442834413 \tabularnewline
47 & 95.43 & 94.8389567195568 & 0.591043280443216 \tabularnewline
48 & 94.88 & 95.2855870519587 & -0.405587051958747 \tabularnewline
49 & 96.03 & 94.8610638209117 & 1.16893617908831 \tabularnewline
50 & 96.37 & 95.812829750314 & 0.557170249685996 \tabularnewline
51 & 96.04 & 96.229851700862 & -0.189851700862022 \tabularnewline
52 & 95.72 & 95.9939025215568 & -0.273902521556792 \tabularnewline
53 & 95.74 & 95.6844846050693 & 0.0555153949306515 \tabularnewline
54 & 95.78 & 95.6630105555123 & 0.116989444487686 \tabularnewline
55 & 93.66 & 95.695270910368 & -2.035270910368 \tabularnewline
56 & 95.29 & 93.8462426704006 & 1.44375732959941 \tabularnewline
57 & 94.33 & 95.0382294889283 & -0.708229488928268 \tabularnewline
58 & 95.66 & 94.3491668104599 & 1.31083318954005 \tabularnewline
59 & 95.2 & 95.4249647728828 & -0.224964772882842 \tabularnewline
60 & 94.61 & 95.158323292912 & -0.548323292911959 \tabularnewline
61 & 96.21 & 94.6090344583136 & 1.60096554168643 \tabularnewline
62 & 96.27 & 95.938436815693 & 0.331563184306972 \tabularnewline
63 & 95.12 & 96.1582558590502 & -1.03825585905022 \tabularnewline
64 & 95.55 & 95.1807174649462 & 0.36928253505377 \tabularnewline
65 & 93.51 & 95.4335069545619 & -1.92350695456193 \tabularnewline
66 & 92.86 & 93.6821714750898 & -0.822171475089775 \tabularnewline
67 & 92.45 & 92.893512222 & -0.44351222200001 \tabularnewline
68 & 93.34 & 92.4358386382578 & 0.90416136174224 \tabularnewline
69 & 92.01 & 93.1561651681721 & -1.14616516817213 \tabularnewline
70 & 91.77 & 92.0843033563328 & -0.3143033563328 \tabularnewline
71 & 92.19 & 91.7395711111146 & 0.450428888885355 \tabularnewline
72 & 91.97 & 92.0632905463712 & -0.0932905463711933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279459&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]93.9[/C][C]94.53[/C][C]-0.629999999999981[/C][/ROW]
[ROW][C]4[/C][C]93.41[/C][C]93.9093176385168[/C][C]-0.499317638516828[/C][/ROW]
[ROW][C]5[/C][C]93.37[/C][C]93.4028645967571[/C][C]-0.0328645967570509[/C][/ROW]
[ROW][C]6[/C][C]93.35[/C][C]93.3041376860406[/C][C]0.0458623139594039[/C][/ROW]
[ROW][C]7[/C][C]93.08[/C][C]93.2742258881902[/C][C]-0.194225888190189[/C][/ROW]
[ROW][C]8[/C][C]93.05[/C][C]93.0344532361747[/C][C]0.0155467638252702[/C][/ROW]
[ROW][C]9[/C][C]92.61[/C][C]92.9780426466775[/C][C]-0.368042646677452[/C][/ROW]
[ROW][C]10[/C][C]92.37[/C][C]92.5863369422348[/C][C]-0.216336942234804[/C][/ROW]
[ROW][C]11[/C][C]92.24[/C][C]92.3272370402889[/C][C]-0.087237040288926[/C][/ROW]
[ROW][C]12[/C][C]91.95[/C][C]92.1809832317887[/C][C]-0.230983231788741[/C][/ROW]
[ROW][C]13[/C][C]92.63[/C][C]91.909081022988[/C][C]0.720918977011948[/C][/ROW]
[ROW][C]14[/C][C]92.7[/C][C]92.4692355701293[/C][C]0.230764429870746[/C][/ROW]
[ROW][C]15[/C][C]92.47[/C][C]92.6009465243952[/C][C]-0.130946524395185[/C][/ROW]
[ROW][C]16[/C][C]92.58[/C][C]92.4164863001381[/C][C]0.163513699861895[/C][/ROW]
[ROW][C]17[/C][C]92.55[/C][C]92.4894134594632[/C][C]0.0605865405368178[/C][/ROW]
[ROW][C]18[/C][C]92.56[/C][C]92.4723720931408[/C][C]0.087627906859197[/C][/ROW]
[ROW][C]19[/C][C]89.92[/C][C]92.4789675577139[/C][C]-2.5589675577139[/C][/ROW]
[ROW][C]20[/C][C]89.96[/C][C]90.1721766090779[/C][C]-0.212176609077858[/C][/ROW]
[ROW][C]21[/C][C]90.03[/C][C]89.9167132501279[/C][C]0.113286749872131[/C][/ROW]
[ROW][C]22[/C][C]90.31[/C][C]89.9457370833728[/C][C]0.364262916627155[/C][/ROW]
[ROW][C]23[/C][C]90.8[/C][C]90.1941389296093[/C][C]0.60586107039066[/C][/ROW]
[ROW][C]24[/C][C]90.36[/C][C]90.6537214771862[/C][C]-0.293721477186239[/C][/ROW]
[ROW][C]25[/C][C]90.31[/C][C]90.32697983167[/C][C]-0.0169798316699712[/C][/ROW]
[ROW][C]26[/C][C]93.8[/C][C]90.2421377780166[/C][C]3.55786222198337[/C][/ROW]
[ROW][C]27[/C][C]93.95[/C][C]93.2820615402921[/C][C]0.667938459707898[/C][/ROW]
[ROW][C]28[/C][C]93.99[/C][C]93.7959058709546[/C][C]0.194094129045396[/C][/ROW]
[ROW][C]29[/C][C]94.44[/C][C]93.8955633524351[/C][C]0.544436647564879[/C][/ROW]
[ROW][C]30[/C][C]94.15[/C][C]94.3014548742748[/C][C]-0.151454874274805[/C][/ROW]
[ROW][C]31[/C][C]91.91[/C][C]94.0990683221736[/C][C]-2.18906832217355[/C][/ROW]
[ROW][C]32[/C][C]91.86[/C][C]92.1156059204235[/C][C]-0.255605920423491[/C][/ROW]
[ROW][C]33[/C][C]93.12[/C][C]91.8221810444427[/C][C]1.29781895555729[/C][/ROW]
[ROW][C]34[/C][C]93.47[/C][C]92.8866032781314[/C][C]0.583396721868553[/C][/ROW]
[ROW][C]35[/C][C]93.57[/C][C]93.3265497614332[/C][C]0.243450238566794[/C][/ROW]
[ROW][C]36[/C][C]94.57[/C][C]93.469349368223[/C][C]1.10065063177696[/C][/ROW]
[ROW][C]37[/C][C]95.85[/C][C]94.3614269699292[/C][C]1.48857303007081[/C][/ROW]
[ROW][C]38[/C][C]96.62[/C][C]95.5925871468174[/C][C]1.02741285318265[/C][/ROW]
[ROW][C]39[/C][C]95.69[/C][C]96.4206476804821[/C][C]-0.730647680482079[/C][/ROW]
[ROW][C]40[/C][C]95.39[/C][C]95.7119892834978[/C][C]-0.321989283497828[/C][/ROW]
[ROW][C]41[/C][C]95.14[/C][C]95.3605387771346[/C][C]-0.22053877713455[/C][/ROW]
[ROW][C]42[/C][C]95.07[/C][C]95.0977660555614[/C][C]-0.027766055561429[/C][/ROW]
[ROW][C]43[/C][C]94.21[/C][C]95.0034957745366[/C][C]-0.793495774536595[/C][/ROW]
[ROW][C]44[/C][C]95.4[/C][C]94.239901922237[/C][C]1.160098077763[/C][/ROW]
[ROW][C]45[/C][C]95.1[/C][C]95.1839424762285[/C][C]-0.083942476228458[/C][/ROW]
[ROW][C]46[/C][C]94.89[/C][C]95.0405684428344[/C][C]-0.150568442834413[/C][/ROW]
[ROW][C]47[/C][C]95.43[/C][C]94.8389567195568[/C][C]0.591043280443216[/C][/ROW]
[ROW][C]48[/C][C]94.88[/C][C]95.2855870519587[/C][C]-0.405587051958747[/C][/ROW]
[ROW][C]49[/C][C]96.03[/C][C]94.8610638209117[/C][C]1.16893617908831[/C][/ROW]
[ROW][C]50[/C][C]96.37[/C][C]95.812829750314[/C][C]0.557170249685996[/C][/ROW]
[ROW][C]51[/C][C]96.04[/C][C]96.229851700862[/C][C]-0.189851700862022[/C][/ROW]
[ROW][C]52[/C][C]95.72[/C][C]95.9939025215568[/C][C]-0.273902521556792[/C][/ROW]
[ROW][C]53[/C][C]95.74[/C][C]95.6844846050693[/C][C]0.0555153949306515[/C][/ROW]
[ROW][C]54[/C][C]95.78[/C][C]95.6630105555123[/C][C]0.116989444487686[/C][/ROW]
[ROW][C]55[/C][C]93.66[/C][C]95.695270910368[/C][C]-2.035270910368[/C][/ROW]
[ROW][C]56[/C][C]95.29[/C][C]93.8462426704006[/C][C]1.44375732959941[/C][/ROW]
[ROW][C]57[/C][C]94.33[/C][C]95.0382294889283[/C][C]-0.708229488928268[/C][/ROW]
[ROW][C]58[/C][C]95.66[/C][C]94.3491668104599[/C][C]1.31083318954005[/C][/ROW]
[ROW][C]59[/C][C]95.2[/C][C]95.4249647728828[/C][C]-0.224964772882842[/C][/ROW]
[ROW][C]60[/C][C]94.61[/C][C]95.158323292912[/C][C]-0.548323292911959[/C][/ROW]
[ROW][C]61[/C][C]96.21[/C][C]94.6090344583136[/C][C]1.60096554168643[/C][/ROW]
[ROW][C]62[/C][C]96.27[/C][C]95.938436815693[/C][C]0.331563184306972[/C][/ROW]
[ROW][C]63[/C][C]95.12[/C][C]96.1582558590502[/C][C]-1.03825585905022[/C][/ROW]
[ROW][C]64[/C][C]95.55[/C][C]95.1807174649462[/C][C]0.36928253505377[/C][/ROW]
[ROW][C]65[/C][C]93.51[/C][C]95.4335069545619[/C][C]-1.92350695456193[/C][/ROW]
[ROW][C]66[/C][C]92.86[/C][C]93.6821714750898[/C][C]-0.822171475089775[/C][/ROW]
[ROW][C]67[/C][C]92.45[/C][C]92.893512222[/C][C]-0.44351222200001[/C][/ROW]
[ROW][C]68[/C][C]93.34[/C][C]92.4358386382578[/C][C]0.90416136174224[/C][/ROW]
[ROW][C]69[/C][C]92.01[/C][C]93.1561651681721[/C][C]-1.14616516817213[/C][/ROW]
[ROW][C]70[/C][C]91.77[/C][C]92.0843033563328[/C][C]-0.3143033563328[/C][/ROW]
[ROW][C]71[/C][C]92.19[/C][C]91.7395711111146[/C][C]0.450428888885355[/C][/ROW]
[ROW][C]72[/C][C]91.97[/C][C]92.0632905463712[/C][C]-0.0932905463711933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279459&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279459&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
393.994.53-0.629999999999981
493.4193.9093176385168-0.499317638516828
593.3793.4028645967571-0.0328645967570509
693.3593.30413768604060.0458623139594039
793.0893.2742258881902-0.194225888190189
893.0593.03445323617470.0155467638252702
992.6192.9780426466775-0.368042646677452
1092.3792.5863369422348-0.216336942234804
1192.2492.3272370402889-0.087237040288926
1291.9592.1809832317887-0.230983231788741
1392.6391.9090810229880.720918977011948
1492.792.46923557012930.230764429870746
1592.4792.6009465243952-0.130946524395185
1692.5892.41648630013810.163513699861895
1792.5592.48941345946320.0605865405368178
1892.5692.47237209314080.087627906859197
1989.9292.4789675577139-2.5589675577139
2089.9690.1721766090779-0.212176609077858
2190.0389.91671325012790.113286749872131
2290.3189.94573708337280.364262916627155
2390.890.19413892960930.60586107039066
2490.3690.6537214771862-0.293721477186239
2590.3190.32697983167-0.0169798316699712
2693.890.24213777801663.55786222198337
2793.9593.28206154029210.667938459707898
2893.9993.79590587095460.194094129045396
2994.4493.89556335243510.544436647564879
3094.1594.3014548742748-0.151454874274805
3191.9194.0990683221736-2.18906832217355
3291.8692.1156059204235-0.255605920423491
3393.1291.82218104444271.29781895555729
3493.4792.88660327813140.583396721868553
3593.5793.32654976143320.243450238566794
3694.5793.4693493682231.10065063177696
3795.8594.36142696992921.48857303007081
3896.6295.59258714681741.02741285318265
3995.6996.4206476804821-0.730647680482079
4095.3995.7119892834978-0.321989283497828
4195.1495.3605387771346-0.22053877713455
4295.0795.0977660555614-0.027766055561429
4394.2195.0034957745366-0.793495774536595
4495.494.2399019222371.160098077763
4595.195.1839424762285-0.083942476228458
4694.8995.0405684428344-0.150568442834413
4795.4394.83895671955680.591043280443216
4894.8895.2855870519587-0.405587051958747
4996.0394.86106382091171.16893617908831
5096.3795.8128297503140.557170249685996
5196.0496.229851700862-0.189851700862022
5295.7295.9939025215568-0.273902521556792
5395.7495.68448460506930.0555153949306515
5495.7895.66301055551230.116989444487686
5593.6695.695270910368-2.035270910368
5695.2993.84624267040061.44375732959941
5794.3395.0382294889283-0.708229488928268
5895.6694.34916681045991.31083318954005
5995.295.4249647728828-0.224964772882842
6094.6195.158323292912-0.548323292911959
6196.2194.60903445831361.60096554168643
6296.2795.9384368156930.331563184306972
6395.1296.1582558590502-1.03825585905022
6495.5595.18071746494620.36928253505377
6593.5195.4335069545619-1.92350695456193
6692.8693.6821714750898-0.822171475089775
6792.4592.893512222-0.44351222200001
6893.3492.43583863825780.90416136174224
6992.0193.1561651681721-1.14616516817213
7091.7792.0843033563328-0.3143033563328
7192.1991.73957111111460.450428888885355
7291.9792.0632905463712-0.0932905463711933







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7391.911745374339890.110925339436293.7125654092435
7491.841745374339889.449941083782494.2335496648973
7591.771745374339888.908442608206394.6350481404734
7691.701745374339888.434287999443194.9692027492365
7791.631745374339888.004893755788995.2585969928907
7891.561745374339887.608034759081795.5154559895979
7991.491745374339887.236207500530895.7472832481488
8091.421745374339886.884413827974595.9590769207051
8191.351745374339886.549126034035996.1543647146436
8291.281745374339886.227744237212996.3357465114666
8391.211745374339885.918286915043296.5052038336363
8491.141745374339885.619202714792796.6642880338868

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 91.9117453743398 & 90.1109253394362 & 93.7125654092435 \tabularnewline
74 & 91.8417453743398 & 89.4499410837824 & 94.2335496648973 \tabularnewline
75 & 91.7717453743398 & 88.9084426082063 & 94.6350481404734 \tabularnewline
76 & 91.7017453743398 & 88.4342879994431 & 94.9692027492365 \tabularnewline
77 & 91.6317453743398 & 88.0048937557889 & 95.2585969928907 \tabularnewline
78 & 91.5617453743398 & 87.6080347590817 & 95.5154559895979 \tabularnewline
79 & 91.4917453743398 & 87.2362075005308 & 95.7472832481488 \tabularnewline
80 & 91.4217453743398 & 86.8844138279745 & 95.9590769207051 \tabularnewline
81 & 91.3517453743398 & 86.5491260340359 & 96.1543647146436 \tabularnewline
82 & 91.2817453743398 & 86.2277442372129 & 96.3357465114666 \tabularnewline
83 & 91.2117453743398 & 85.9182869150432 & 96.5052038336363 \tabularnewline
84 & 91.1417453743398 & 85.6192027147927 & 96.6642880338868 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279459&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]91.9117453743398[/C][C]90.1109253394362[/C][C]93.7125654092435[/C][/ROW]
[ROW][C]74[/C][C]91.8417453743398[/C][C]89.4499410837824[/C][C]94.2335496648973[/C][/ROW]
[ROW][C]75[/C][C]91.7717453743398[/C][C]88.9084426082063[/C][C]94.6350481404734[/C][/ROW]
[ROW][C]76[/C][C]91.7017453743398[/C][C]88.4342879994431[/C][C]94.9692027492365[/C][/ROW]
[ROW][C]77[/C][C]91.6317453743398[/C][C]88.0048937557889[/C][C]95.2585969928907[/C][/ROW]
[ROW][C]78[/C][C]91.5617453743398[/C][C]87.6080347590817[/C][C]95.5154559895979[/C][/ROW]
[ROW][C]79[/C][C]91.4917453743398[/C][C]87.2362075005308[/C][C]95.7472832481488[/C][/ROW]
[ROW][C]80[/C][C]91.4217453743398[/C][C]86.8844138279745[/C][C]95.9590769207051[/C][/ROW]
[ROW][C]81[/C][C]91.3517453743398[/C][C]86.5491260340359[/C][C]96.1543647146436[/C][/ROW]
[ROW][C]82[/C][C]91.2817453743398[/C][C]86.2277442372129[/C][C]96.3357465114666[/C][/ROW]
[ROW][C]83[/C][C]91.2117453743398[/C][C]85.9182869150432[/C][C]96.5052038336363[/C][/ROW]
[ROW][C]84[/C][C]91.1417453743398[/C][C]85.6192027147927[/C][C]96.6642880338868[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279459&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279459&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
7391.911745374339890.110925339436293.7125654092435
7491.841745374339889.449941083782494.2335496648973
7591.771745374339888.908442608206394.6350481404734
7691.701745374339888.434287999443194.9692027492365
7791.631745374339888.004893755788995.2585969928907
7891.561745374339887.608034759081795.5154559895979
7991.491745374339887.236207500530895.7472832481488
8091.421745374339886.884413827974595.9590769207051
8191.351745374339886.549126034035996.1543647146436
8291.281745374339886.227744237212996.3357465114666
8391.211745374339885.918286915043296.5052038336363
8491.141745374339885.619202714792796.6642880338868



Parameters (Session):
par1 = 0,1 ; par2 = 0,9 ;
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')