Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 14:43:11 +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/2016/Nov/26/t14801714342pf2wx5ylr1rfla.htm/, Retrieved Sat, 04 May 2024 04:56:49 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 04:56:49 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
98,36
95,05
93,72
91,33
91,33
90,4
90,59
91,84
91,28
91,11
90,62
91,13
90,97
90,27
91,07
90,46
92,41
94,64
95,56
96,21
96,7
96,12
96,23
96,43
96,36
96,06
96,14
96,19
95,87
95,58
95,29
96,06
94,83
94,88
97,41
97,87
97,89
98,87
98,72
98,17
98,03
98,65
99,28
100,09
101,29
101,95
103,29
103,78
105,79
106,14
106,5
106,89
106,59
106,01
105,91
105,65
104,72
103,42
102,47
99,32
97,71
98,44
96,4
97,44
98,21
97,42
97,44
96,66
94,78
113,29
114,16
115,05




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.806965010206489
beta0.306603902148388
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.806965010206489 \tabularnewline
beta & 0.306603902148388 \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]0.806965010206489[/C][/ROW]
[ROW][C]beta[/C][C]0.306603902148388[/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
alpha0.806965010206489
beta0.306603902148388
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
393.7291.741.98
491.3390.51767958984140.81232041015862
591.3388.55406580326162.77593419673836
690.488.86183744702821.5381625529718
790.5988.55134074142032.03865925857971
891.8489.14912962746232.69087037253767
991.2890.93900149867060.340998501329352
1091.1190.91697837031640.193021629683571
1190.6290.8233002296688-0.203300229668841
1291.1390.35950395326480.770496046735161
1390.9790.87216226837780.0978377316221781
1490.2790.8662157360125-0.59621573601251
1591.0790.1526774648150.917322535185022
1690.4690.8874742967743-0.427474296774307
1792.4190.43130203847371.97869796152627
1894.6492.40639332222012.23360667777992
1995.5695.13982290491170.420177095088263
2096.2196.5138379033515-0.303837903351521
2196.797.2284229761229-0.528422976122869
2296.1297.631034069282-1.511034069282
2396.2396.8668544258751-0.636854425875143
2496.4396.6505375234877-0.220537523487735
2596.3696.7156087045386-0.355608704538582
2696.0696.5836979532921-0.523697953292128
2796.1496.1865724342718-0.0465724342717522
2896.1996.1629476271120.0270523728879652
2995.8796.2054287240089-0.33542872400885
3095.5895.8724089465017-0.292408946501723
3195.2995.5017572058704-0.211757205870413
3296.0695.14379592207190.916204077928057
3394.8395.9227458767063-1.09274587670629
3494.8894.81017783274770.0698221672523118
3597.4194.65303682658652.75696317341347
3697.8797.34644861647540.523551383524648
3797.8998.3671115998895-0.477111599889454
3898.8798.46222827455910.407771725440867
3998.7299.3723051488877-0.652305148887734
4098.1799.2655446370778-1.09554463707778
4198.0398.5300472237779-0.500047223777855
4298.6598.15137439212420.498625607875823
4399.2898.7019648525680.578035147432004
44100.0999.45965269199280.630347308007245
45101.29100.4155142763250.874485723675036
46101.95101.7847510716070.1652489283926
47103.29102.6225442511350.667455748865081
48103.78104.030741743651-0.250741743651233
49105.79104.63594781081.15405218920046
50106.14106.660307429554-0.520307429554165
51106.5107.204783674741-0.70478367474098
52106.89107.426017439921-0.536017439921324
53106.59107.650818955674-1.06081895567395
54106.01107.189657647739-1.17965764773922
55105.91106.340728404962-0.430728404962082
56105.65105.989588628234-0.339588628233855
57104.72105.627974912249-0.907974912249429
58103.42104.583043452068-1.16304345206771
59102.47103.044521997944-0.574521997943663
6099.32101.838769324573-2.51876932457294
6197.7198.4408866544551-0.730886654455148
6298.4496.3049277733052.13507222669502
6396.497.0099540560544-0.609954056054434
6497.4495.34892618508942.09107381491062
6598.2196.38490389733551.82509610266447
6697.4297.6578096632664-0.237809663266361
6797.4497.20718411778570.232815882214325
6896.6697.1939399049478-0.533939904947786
6994.7896.4298439255035-1.64984392550352
70113.2994.35705033776518.932949662235
71114.16113.5782152850290.581784714971306
72115.05118.134576595235-3.08457659523529

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 93.72 & 91.74 & 1.98 \tabularnewline
4 & 91.33 & 90.5176795898414 & 0.81232041015862 \tabularnewline
5 & 91.33 & 88.5540658032616 & 2.77593419673836 \tabularnewline
6 & 90.4 & 88.8618374470282 & 1.5381625529718 \tabularnewline
7 & 90.59 & 88.5513407414203 & 2.03865925857971 \tabularnewline
8 & 91.84 & 89.1491296274623 & 2.69087037253767 \tabularnewline
9 & 91.28 & 90.9390014986706 & 0.340998501329352 \tabularnewline
10 & 91.11 & 90.9169783703164 & 0.193021629683571 \tabularnewline
11 & 90.62 & 90.8233002296688 & -0.203300229668841 \tabularnewline
12 & 91.13 & 90.3595039532648 & 0.770496046735161 \tabularnewline
13 & 90.97 & 90.8721622683778 & 0.0978377316221781 \tabularnewline
14 & 90.27 & 90.8662157360125 & -0.59621573601251 \tabularnewline
15 & 91.07 & 90.152677464815 & 0.917322535185022 \tabularnewline
16 & 90.46 & 90.8874742967743 & -0.427474296774307 \tabularnewline
17 & 92.41 & 90.4313020384737 & 1.97869796152627 \tabularnewline
18 & 94.64 & 92.4063933222201 & 2.23360667777992 \tabularnewline
19 & 95.56 & 95.1398229049117 & 0.420177095088263 \tabularnewline
20 & 96.21 & 96.5138379033515 & -0.303837903351521 \tabularnewline
21 & 96.7 & 97.2284229761229 & -0.528422976122869 \tabularnewline
22 & 96.12 & 97.631034069282 & -1.511034069282 \tabularnewline
23 & 96.23 & 96.8668544258751 & -0.636854425875143 \tabularnewline
24 & 96.43 & 96.6505375234877 & -0.220537523487735 \tabularnewline
25 & 96.36 & 96.7156087045386 & -0.355608704538582 \tabularnewline
26 & 96.06 & 96.5836979532921 & -0.523697953292128 \tabularnewline
27 & 96.14 & 96.1865724342718 & -0.0465724342717522 \tabularnewline
28 & 96.19 & 96.162947627112 & 0.0270523728879652 \tabularnewline
29 & 95.87 & 96.2054287240089 & -0.33542872400885 \tabularnewline
30 & 95.58 & 95.8724089465017 & -0.292408946501723 \tabularnewline
31 & 95.29 & 95.5017572058704 & -0.211757205870413 \tabularnewline
32 & 96.06 & 95.1437959220719 & 0.916204077928057 \tabularnewline
33 & 94.83 & 95.9227458767063 & -1.09274587670629 \tabularnewline
34 & 94.88 & 94.8101778327477 & 0.0698221672523118 \tabularnewline
35 & 97.41 & 94.6530368265865 & 2.75696317341347 \tabularnewline
36 & 97.87 & 97.3464486164754 & 0.523551383524648 \tabularnewline
37 & 97.89 & 98.3671115998895 & -0.477111599889454 \tabularnewline
38 & 98.87 & 98.4622282745591 & 0.407771725440867 \tabularnewline
39 & 98.72 & 99.3723051488877 & -0.652305148887734 \tabularnewline
40 & 98.17 & 99.2655446370778 & -1.09554463707778 \tabularnewline
41 & 98.03 & 98.5300472237779 & -0.500047223777855 \tabularnewline
42 & 98.65 & 98.1513743921242 & 0.498625607875823 \tabularnewline
43 & 99.28 & 98.701964852568 & 0.578035147432004 \tabularnewline
44 & 100.09 & 99.4596526919928 & 0.630347308007245 \tabularnewline
45 & 101.29 & 100.415514276325 & 0.874485723675036 \tabularnewline
46 & 101.95 & 101.784751071607 & 0.1652489283926 \tabularnewline
47 & 103.29 & 102.622544251135 & 0.667455748865081 \tabularnewline
48 & 103.78 & 104.030741743651 & -0.250741743651233 \tabularnewline
49 & 105.79 & 104.6359478108 & 1.15405218920046 \tabularnewline
50 & 106.14 & 106.660307429554 & -0.520307429554165 \tabularnewline
51 & 106.5 & 107.204783674741 & -0.70478367474098 \tabularnewline
52 & 106.89 & 107.426017439921 & -0.536017439921324 \tabularnewline
53 & 106.59 & 107.650818955674 & -1.06081895567395 \tabularnewline
54 & 106.01 & 107.189657647739 & -1.17965764773922 \tabularnewline
55 & 105.91 & 106.340728404962 & -0.430728404962082 \tabularnewline
56 & 105.65 & 105.989588628234 & -0.339588628233855 \tabularnewline
57 & 104.72 & 105.627974912249 & -0.907974912249429 \tabularnewline
58 & 103.42 & 104.583043452068 & -1.16304345206771 \tabularnewline
59 & 102.47 & 103.044521997944 & -0.574521997943663 \tabularnewline
60 & 99.32 & 101.838769324573 & -2.51876932457294 \tabularnewline
61 & 97.71 & 98.4408866544551 & -0.730886654455148 \tabularnewline
62 & 98.44 & 96.304927773305 & 2.13507222669502 \tabularnewline
63 & 96.4 & 97.0099540560544 & -0.609954056054434 \tabularnewline
64 & 97.44 & 95.3489261850894 & 2.09107381491062 \tabularnewline
65 & 98.21 & 96.3849038973355 & 1.82509610266447 \tabularnewline
66 & 97.42 & 97.6578096632664 & -0.237809663266361 \tabularnewline
67 & 97.44 & 97.2071841177857 & 0.232815882214325 \tabularnewline
68 & 96.66 & 97.1939399049478 & -0.533939904947786 \tabularnewline
69 & 94.78 & 96.4298439255035 & -1.64984392550352 \tabularnewline
70 & 113.29 & 94.357050337765 & 18.932949662235 \tabularnewline
71 & 114.16 & 113.578215285029 & 0.581784714971306 \tabularnewline
72 & 115.05 & 118.134576595235 & -3.08457659523529 \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]93.72[/C][C]91.74[/C][C]1.98[/C][/ROW]
[ROW][C]4[/C][C]91.33[/C][C]90.5176795898414[/C][C]0.81232041015862[/C][/ROW]
[ROW][C]5[/C][C]91.33[/C][C]88.5540658032616[/C][C]2.77593419673836[/C][/ROW]
[ROW][C]6[/C][C]90.4[/C][C]88.8618374470282[/C][C]1.5381625529718[/C][/ROW]
[ROW][C]7[/C][C]90.59[/C][C]88.5513407414203[/C][C]2.03865925857971[/C][/ROW]
[ROW][C]8[/C][C]91.84[/C][C]89.1491296274623[/C][C]2.69087037253767[/C][/ROW]
[ROW][C]9[/C][C]91.28[/C][C]90.9390014986706[/C][C]0.340998501329352[/C][/ROW]
[ROW][C]10[/C][C]91.11[/C][C]90.9169783703164[/C][C]0.193021629683571[/C][/ROW]
[ROW][C]11[/C][C]90.62[/C][C]90.8233002296688[/C][C]-0.203300229668841[/C][/ROW]
[ROW][C]12[/C][C]91.13[/C][C]90.3595039532648[/C][C]0.770496046735161[/C][/ROW]
[ROW][C]13[/C][C]90.97[/C][C]90.8721622683778[/C][C]0.0978377316221781[/C][/ROW]
[ROW][C]14[/C][C]90.27[/C][C]90.8662157360125[/C][C]-0.59621573601251[/C][/ROW]
[ROW][C]15[/C][C]91.07[/C][C]90.152677464815[/C][C]0.917322535185022[/C][/ROW]
[ROW][C]16[/C][C]90.46[/C][C]90.8874742967743[/C][C]-0.427474296774307[/C][/ROW]
[ROW][C]17[/C][C]92.41[/C][C]90.4313020384737[/C][C]1.97869796152627[/C][/ROW]
[ROW][C]18[/C][C]94.64[/C][C]92.4063933222201[/C][C]2.23360667777992[/C][/ROW]
[ROW][C]19[/C][C]95.56[/C][C]95.1398229049117[/C][C]0.420177095088263[/C][/ROW]
[ROW][C]20[/C][C]96.21[/C][C]96.5138379033515[/C][C]-0.303837903351521[/C][/ROW]
[ROW][C]21[/C][C]96.7[/C][C]97.2284229761229[/C][C]-0.528422976122869[/C][/ROW]
[ROW][C]22[/C][C]96.12[/C][C]97.631034069282[/C][C]-1.511034069282[/C][/ROW]
[ROW][C]23[/C][C]96.23[/C][C]96.8668544258751[/C][C]-0.636854425875143[/C][/ROW]
[ROW][C]24[/C][C]96.43[/C][C]96.6505375234877[/C][C]-0.220537523487735[/C][/ROW]
[ROW][C]25[/C][C]96.36[/C][C]96.7156087045386[/C][C]-0.355608704538582[/C][/ROW]
[ROW][C]26[/C][C]96.06[/C][C]96.5836979532921[/C][C]-0.523697953292128[/C][/ROW]
[ROW][C]27[/C][C]96.14[/C][C]96.1865724342718[/C][C]-0.0465724342717522[/C][/ROW]
[ROW][C]28[/C][C]96.19[/C][C]96.162947627112[/C][C]0.0270523728879652[/C][/ROW]
[ROW][C]29[/C][C]95.87[/C][C]96.2054287240089[/C][C]-0.33542872400885[/C][/ROW]
[ROW][C]30[/C][C]95.58[/C][C]95.8724089465017[/C][C]-0.292408946501723[/C][/ROW]
[ROW][C]31[/C][C]95.29[/C][C]95.5017572058704[/C][C]-0.211757205870413[/C][/ROW]
[ROW][C]32[/C][C]96.06[/C][C]95.1437959220719[/C][C]0.916204077928057[/C][/ROW]
[ROW][C]33[/C][C]94.83[/C][C]95.9227458767063[/C][C]-1.09274587670629[/C][/ROW]
[ROW][C]34[/C][C]94.88[/C][C]94.8101778327477[/C][C]0.0698221672523118[/C][/ROW]
[ROW][C]35[/C][C]97.41[/C][C]94.6530368265865[/C][C]2.75696317341347[/C][/ROW]
[ROW][C]36[/C][C]97.87[/C][C]97.3464486164754[/C][C]0.523551383524648[/C][/ROW]
[ROW][C]37[/C][C]97.89[/C][C]98.3671115998895[/C][C]-0.477111599889454[/C][/ROW]
[ROW][C]38[/C][C]98.87[/C][C]98.4622282745591[/C][C]0.407771725440867[/C][/ROW]
[ROW][C]39[/C][C]98.72[/C][C]99.3723051488877[/C][C]-0.652305148887734[/C][/ROW]
[ROW][C]40[/C][C]98.17[/C][C]99.2655446370778[/C][C]-1.09554463707778[/C][/ROW]
[ROW][C]41[/C][C]98.03[/C][C]98.5300472237779[/C][C]-0.500047223777855[/C][/ROW]
[ROW][C]42[/C][C]98.65[/C][C]98.1513743921242[/C][C]0.498625607875823[/C][/ROW]
[ROW][C]43[/C][C]99.28[/C][C]98.701964852568[/C][C]0.578035147432004[/C][/ROW]
[ROW][C]44[/C][C]100.09[/C][C]99.4596526919928[/C][C]0.630347308007245[/C][/ROW]
[ROW][C]45[/C][C]101.29[/C][C]100.415514276325[/C][C]0.874485723675036[/C][/ROW]
[ROW][C]46[/C][C]101.95[/C][C]101.784751071607[/C][C]0.1652489283926[/C][/ROW]
[ROW][C]47[/C][C]103.29[/C][C]102.622544251135[/C][C]0.667455748865081[/C][/ROW]
[ROW][C]48[/C][C]103.78[/C][C]104.030741743651[/C][C]-0.250741743651233[/C][/ROW]
[ROW][C]49[/C][C]105.79[/C][C]104.6359478108[/C][C]1.15405218920046[/C][/ROW]
[ROW][C]50[/C][C]106.14[/C][C]106.660307429554[/C][C]-0.520307429554165[/C][/ROW]
[ROW][C]51[/C][C]106.5[/C][C]107.204783674741[/C][C]-0.70478367474098[/C][/ROW]
[ROW][C]52[/C][C]106.89[/C][C]107.426017439921[/C][C]-0.536017439921324[/C][/ROW]
[ROW][C]53[/C][C]106.59[/C][C]107.650818955674[/C][C]-1.06081895567395[/C][/ROW]
[ROW][C]54[/C][C]106.01[/C][C]107.189657647739[/C][C]-1.17965764773922[/C][/ROW]
[ROW][C]55[/C][C]105.91[/C][C]106.340728404962[/C][C]-0.430728404962082[/C][/ROW]
[ROW][C]56[/C][C]105.65[/C][C]105.989588628234[/C][C]-0.339588628233855[/C][/ROW]
[ROW][C]57[/C][C]104.72[/C][C]105.627974912249[/C][C]-0.907974912249429[/C][/ROW]
[ROW][C]58[/C][C]103.42[/C][C]104.583043452068[/C][C]-1.16304345206771[/C][/ROW]
[ROW][C]59[/C][C]102.47[/C][C]103.044521997944[/C][C]-0.574521997943663[/C][/ROW]
[ROW][C]60[/C][C]99.32[/C][C]101.838769324573[/C][C]-2.51876932457294[/C][/ROW]
[ROW][C]61[/C][C]97.71[/C][C]98.4408866544551[/C][C]-0.730886654455148[/C][/ROW]
[ROW][C]62[/C][C]98.44[/C][C]96.304927773305[/C][C]2.13507222669502[/C][/ROW]
[ROW][C]63[/C][C]96.4[/C][C]97.0099540560544[/C][C]-0.609954056054434[/C][/ROW]
[ROW][C]64[/C][C]97.44[/C][C]95.3489261850894[/C][C]2.09107381491062[/C][/ROW]
[ROW][C]65[/C][C]98.21[/C][C]96.3849038973355[/C][C]1.82509610266447[/C][/ROW]
[ROW][C]66[/C][C]97.42[/C][C]97.6578096632664[/C][C]-0.237809663266361[/C][/ROW]
[ROW][C]67[/C][C]97.44[/C][C]97.2071841177857[/C][C]0.232815882214325[/C][/ROW]
[ROW][C]68[/C][C]96.66[/C][C]97.1939399049478[/C][C]-0.533939904947786[/C][/ROW]
[ROW][C]69[/C][C]94.78[/C][C]96.4298439255035[/C][C]-1.64984392550352[/C][/ROW]
[ROW][C]70[/C][C]113.29[/C][C]94.357050337765[/C][C]18.932949662235[/C][/ROW]
[ROW][C]71[/C][C]114.16[/C][C]113.578215285029[/C][C]0.581784714971306[/C][/ROW]
[ROW][C]72[/C][C]115.05[/C][C]118.134576595235[/C][C]-3.08457659523529[/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
393.7291.741.98
491.3390.51767958984140.81232041015862
591.3388.55406580326162.77593419673836
690.488.86183744702821.5381625529718
790.5988.55134074142032.03865925857971
891.8489.14912962746232.69087037253767
991.2890.93900149867060.340998501329352
1091.1190.91697837031640.193021629683571
1190.6290.8233002296688-0.203300229668841
1291.1390.35950395326480.770496046735161
1390.9790.87216226837780.0978377316221781
1490.2790.8662157360125-0.59621573601251
1591.0790.1526774648150.917322535185022
1690.4690.8874742967743-0.427474296774307
1792.4190.43130203847371.97869796152627
1894.6492.40639332222012.23360667777992
1995.5695.13982290491170.420177095088263
2096.2196.5138379033515-0.303837903351521
2196.797.2284229761229-0.528422976122869
2296.1297.631034069282-1.511034069282
2396.2396.8668544258751-0.636854425875143
2496.4396.6505375234877-0.220537523487735
2596.3696.7156087045386-0.355608704538582
2696.0696.5836979532921-0.523697953292128
2796.1496.1865724342718-0.0465724342717522
2896.1996.1629476271120.0270523728879652
2995.8796.2054287240089-0.33542872400885
3095.5895.8724089465017-0.292408946501723
3195.2995.5017572058704-0.211757205870413
3296.0695.14379592207190.916204077928057
3394.8395.9227458767063-1.09274587670629
3494.8894.81017783274770.0698221672523118
3597.4194.65303682658652.75696317341347
3697.8797.34644861647540.523551383524648
3797.8998.3671115998895-0.477111599889454
3898.8798.46222827455910.407771725440867
3998.7299.3723051488877-0.652305148887734
4098.1799.2655446370778-1.09554463707778
4198.0398.5300472237779-0.500047223777855
4298.6598.15137439212420.498625607875823
4399.2898.7019648525680.578035147432004
44100.0999.45965269199280.630347308007245
45101.29100.4155142763250.874485723675036
46101.95101.7847510716070.1652489283926
47103.29102.6225442511350.667455748865081
48103.78104.030741743651-0.250741743651233
49105.79104.63594781081.15405218920046
50106.14106.660307429554-0.520307429554165
51106.5107.204783674741-0.70478367474098
52106.89107.426017439921-0.536017439921324
53106.59107.650818955674-1.06081895567395
54106.01107.189657647739-1.17965764773922
55105.91106.340728404962-0.430728404962082
56105.65105.989588628234-0.339588628233855
57104.72105.627974912249-0.907974912249429
58103.42104.583043452068-1.16304345206771
59102.47103.044521997944-0.574521997943663
6099.32101.838769324573-2.51876932457294
6197.7198.4408866544551-0.730886654455148
6298.4496.3049277733052.13507222669502
6396.497.0099540560544-0.609954056054434
6497.4495.34892618508942.09107381491062
6598.2196.38490389733551.82509610266447
6697.4297.6578096632664-0.237809663266361
6797.4497.20718411778570.232815882214325
6896.6697.1939399049478-0.533939904947786
6994.7896.4298439255035-1.64984392550352
70113.2994.35705033776518.932949662235
71114.16113.5782152850290.581784714971306
72115.05118.134576595235-3.08457659523529







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73118.969130925687113.997826929901123.940434921473
74122.292830639795115.068643535488129.517017744101
75125.616530353903115.917499764671135.315560943134
76128.94023006801116.555296680245141.325163455776
77132.263929782118116.994326391521147.533533172716
78135.587629496226117.24588478986153.929374202593
79138.911329210334117.319924092464160.502734328205
80142.235028924442117.22514922821167.244908620675
81145.55872863855116.969197553133174.148259723968
82148.882428352658116.558812261655181.206044443661
83152.206128066766115.99998967276188.412266460772
84155.529827780874115.298099571057195.761555990692

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 118.969130925687 & 113.997826929901 & 123.940434921473 \tabularnewline
74 & 122.292830639795 & 115.068643535488 & 129.517017744101 \tabularnewline
75 & 125.616530353903 & 115.917499764671 & 135.315560943134 \tabularnewline
76 & 128.94023006801 & 116.555296680245 & 141.325163455776 \tabularnewline
77 & 132.263929782118 & 116.994326391521 & 147.533533172716 \tabularnewline
78 & 135.587629496226 & 117.24588478986 & 153.929374202593 \tabularnewline
79 & 138.911329210334 & 117.319924092464 & 160.502734328205 \tabularnewline
80 & 142.235028924442 & 117.22514922821 & 167.244908620675 \tabularnewline
81 & 145.55872863855 & 116.969197553133 & 174.148259723968 \tabularnewline
82 & 148.882428352658 & 116.558812261655 & 181.206044443661 \tabularnewline
83 & 152.206128066766 & 115.99998967276 & 188.412266460772 \tabularnewline
84 & 155.529827780874 & 115.298099571057 & 195.761555990692 \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]118.969130925687[/C][C]113.997826929901[/C][C]123.940434921473[/C][/ROW]
[ROW][C]74[/C][C]122.292830639795[/C][C]115.068643535488[/C][C]129.517017744101[/C][/ROW]
[ROW][C]75[/C][C]125.616530353903[/C][C]115.917499764671[/C][C]135.315560943134[/C][/ROW]
[ROW][C]76[/C][C]128.94023006801[/C][C]116.555296680245[/C][C]141.325163455776[/C][/ROW]
[ROW][C]77[/C][C]132.263929782118[/C][C]116.994326391521[/C][C]147.533533172716[/C][/ROW]
[ROW][C]78[/C][C]135.587629496226[/C][C]117.24588478986[/C][C]153.929374202593[/C][/ROW]
[ROW][C]79[/C][C]138.911329210334[/C][C]117.319924092464[/C][C]160.502734328205[/C][/ROW]
[ROW][C]80[/C][C]142.235028924442[/C][C]117.22514922821[/C][C]167.244908620675[/C][/ROW]
[ROW][C]81[/C][C]145.55872863855[/C][C]116.969197553133[/C][C]174.148259723968[/C][/ROW]
[ROW][C]82[/C][C]148.882428352658[/C][C]116.558812261655[/C][C]181.206044443661[/C][/ROW]
[ROW][C]83[/C][C]152.206128066766[/C][C]115.99998967276[/C][C]188.412266460772[/C][/ROW]
[ROW][C]84[/C][C]155.529827780874[/C][C]115.298099571057[/C][C]195.761555990692[/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
73118.969130925687113.997826929901123.940434921473
74122.292830639795115.068643535488129.517017744101
75125.616530353903115.917499764671135.315560943134
76128.94023006801116.555296680245141.325163455776
77132.263929782118116.994326391521147.533533172716
78135.587629496226117.24588478986153.929374202593
79138.911329210334117.319924092464160.502734328205
80142.235028924442117.22514922821167.244908620675
81145.55872863855116.969197553133174.148259723968
82148.882428352658116.558812261655181.206044443661
83152.206128066766115.99998967276188.412266460772
84155.529827780874115.298099571057195.761555990692



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')