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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 19:50:33 +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/26/t1461696648oogfatfkdh2sb5f.htm/, Retrieved Fri, 03 May 2024 20:21:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294966, Retrieved Fri, 03 May 2024 20:21:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 18:50:33] [9b4dafad127b39cd929ee42874de7246] [Current]
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Dataseries X:
113149
112534
108783
106640
102617
102191
117359
116083
108666
105017
100918
103907
105732
103409
100255
97036
94055
92523
106380
104846
101411
98072
95678
99148
106813
106782
103496
100854
99592
98923
110497
114783
113551
112376
111683
113467
117277
117442
115640
114872
111628
111098
124301
125847
125323
122394
121164
123963
130549
128563
125418
121982
117708
116905
128862
129655
128649
126084
123725
123974




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=294966&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=294966&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294966&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
alpha1
beta0.0103908931243082
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0103908931243082 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294966&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0103908931243082[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294966&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294966&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
alpha1
beta0.0103908931243082
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3108783111919-3136
4106640108135.414159162-1495.41415916217
5102617105976.875470458-3359.87547045774
6102191101918.963363533272.036636466772
7117359101495.79006714915863.2099328513
8116083116828.622986169-745.622986169372
9108666115544.875297409-6878.87529740906
10105017108056.397639378-3039.39763937824
11100918104375.815583345-3457.81558334519
12103907100240.8857911753666.11420882492
13105732103267.97999212464.02000789951
14103409105118.583360659-1709.58336065873
15100255102777.819262671-2522.81926267102
169703699597.6049173407-2561.60491734066
179405596351.9875544179-2296.98755441788
189252393347.119802232-824.119802232046
1910638091806.556461445414573.4435385546
20104846105814.987555708-968.987555707688
21101411104270.918909578-2859.91890957755
2298072100806.201797844-2734.20179784394
239567897438.7909991823-1760.79099918225
249914895026.49480809554121.50519190449
2510681398539.32092805598273.67907194413
26106782106290.291843037491.708156962733
27103496106264.401129945-2768.40112994461
28100854102949.634969678-2095.63496967815
2999592100285.859450681-693.859450680655
309892399016.6496312853-93.6496312853415
3111049798346.676527975512150.3234720245
32114783110046.9292405994736.0707594009
33113551114382.141245689-831.141245689199
34112376113141.504945834-765.504945834036
35111683111958.550665756-275.550665755756
36113467111262.6874482382204.31255176244
37117277113069.5922243754207.40777562451
38117442116923.310948902518.689051097623
39115640117093.700591397-1453.70059139709
40114872115276.595343917-404.595343917143
41111628114504.39123694-2876.3912369399
42111098111230.502963013-132.502963013161
43124301110699.12613888613601.8738611142
44125847124043.4617564671803.53824353301
45125323125608.202129601-285.202129601152
46122394125081.238624754-2687.23862475363
47121164122124.315815404-960.315815404305
48123963120884.3372764013078.66272359913
49130549123715.3273317286833.67266827243
50128563130372.33529407-1809.3352940701
51125418128367.534684403-2949.53468440338
52121982125191.886384731-3209.8863847313
53117708121722.532798366-4014.53279836639
54116905117406.818217115-501.818217114531
55128862116598.60387765312263.3961223473
56129655128683.031516101971.968483898978
57128649129486.131136737-837.131136737415
58126084128471.432596565-2387.43259656455
59123725125881.625039612-2156.62503961216
60123974123500.215779316473.784220683665

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 108783 & 111919 & -3136 \tabularnewline
4 & 106640 & 108135.414159162 & -1495.41415916217 \tabularnewline
5 & 102617 & 105976.875470458 & -3359.87547045774 \tabularnewline
6 & 102191 & 101918.963363533 & 272.036636466772 \tabularnewline
7 & 117359 & 101495.790067149 & 15863.2099328513 \tabularnewline
8 & 116083 & 116828.622986169 & -745.622986169372 \tabularnewline
9 & 108666 & 115544.875297409 & -6878.87529740906 \tabularnewline
10 & 105017 & 108056.397639378 & -3039.39763937824 \tabularnewline
11 & 100918 & 104375.815583345 & -3457.81558334519 \tabularnewline
12 & 103907 & 100240.885791175 & 3666.11420882492 \tabularnewline
13 & 105732 & 103267.9799921 & 2464.02000789951 \tabularnewline
14 & 103409 & 105118.583360659 & -1709.58336065873 \tabularnewline
15 & 100255 & 102777.819262671 & -2522.81926267102 \tabularnewline
16 & 97036 & 99597.6049173407 & -2561.60491734066 \tabularnewline
17 & 94055 & 96351.9875544179 & -2296.98755441788 \tabularnewline
18 & 92523 & 93347.119802232 & -824.119802232046 \tabularnewline
19 & 106380 & 91806.5564614454 & 14573.4435385546 \tabularnewline
20 & 104846 & 105814.987555708 & -968.987555707688 \tabularnewline
21 & 101411 & 104270.918909578 & -2859.91890957755 \tabularnewline
22 & 98072 & 100806.201797844 & -2734.20179784394 \tabularnewline
23 & 95678 & 97438.7909991823 & -1760.79099918225 \tabularnewline
24 & 99148 & 95026.4948080955 & 4121.50519190449 \tabularnewline
25 & 106813 & 98539.3209280559 & 8273.67907194413 \tabularnewline
26 & 106782 & 106290.291843037 & 491.708156962733 \tabularnewline
27 & 103496 & 106264.401129945 & -2768.40112994461 \tabularnewline
28 & 100854 & 102949.634969678 & -2095.63496967815 \tabularnewline
29 & 99592 & 100285.859450681 & -693.859450680655 \tabularnewline
30 & 98923 & 99016.6496312853 & -93.6496312853415 \tabularnewline
31 & 110497 & 98346.6765279755 & 12150.3234720245 \tabularnewline
32 & 114783 & 110046.929240599 & 4736.0707594009 \tabularnewline
33 & 113551 & 114382.141245689 & -831.141245689199 \tabularnewline
34 & 112376 & 113141.504945834 & -765.504945834036 \tabularnewline
35 & 111683 & 111958.550665756 & -275.550665755756 \tabularnewline
36 & 113467 & 111262.687448238 & 2204.31255176244 \tabularnewline
37 & 117277 & 113069.592224375 & 4207.40777562451 \tabularnewline
38 & 117442 & 116923.310948902 & 518.689051097623 \tabularnewline
39 & 115640 & 117093.700591397 & -1453.70059139709 \tabularnewline
40 & 114872 & 115276.595343917 & -404.595343917143 \tabularnewline
41 & 111628 & 114504.39123694 & -2876.3912369399 \tabularnewline
42 & 111098 & 111230.502963013 & -132.502963013161 \tabularnewline
43 & 124301 & 110699.126138886 & 13601.8738611142 \tabularnewline
44 & 125847 & 124043.461756467 & 1803.53824353301 \tabularnewline
45 & 125323 & 125608.202129601 & -285.202129601152 \tabularnewline
46 & 122394 & 125081.238624754 & -2687.23862475363 \tabularnewline
47 & 121164 & 122124.315815404 & -960.315815404305 \tabularnewline
48 & 123963 & 120884.337276401 & 3078.66272359913 \tabularnewline
49 & 130549 & 123715.327331728 & 6833.67266827243 \tabularnewline
50 & 128563 & 130372.33529407 & -1809.3352940701 \tabularnewline
51 & 125418 & 128367.534684403 & -2949.53468440338 \tabularnewline
52 & 121982 & 125191.886384731 & -3209.8863847313 \tabularnewline
53 & 117708 & 121722.532798366 & -4014.53279836639 \tabularnewline
54 & 116905 & 117406.818217115 & -501.818217114531 \tabularnewline
55 & 128862 & 116598.603877653 & 12263.3961223473 \tabularnewline
56 & 129655 & 128683.031516101 & 971.968483898978 \tabularnewline
57 & 128649 & 129486.131136737 & -837.131136737415 \tabularnewline
58 & 126084 & 128471.432596565 & -2387.43259656455 \tabularnewline
59 & 123725 & 125881.625039612 & -2156.62503961216 \tabularnewline
60 & 123974 & 123500.215779316 & 473.784220683665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294966&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]108783[/C][C]111919[/C][C]-3136[/C][/ROW]
[ROW][C]4[/C][C]106640[/C][C]108135.414159162[/C][C]-1495.41415916217[/C][/ROW]
[ROW][C]5[/C][C]102617[/C][C]105976.875470458[/C][C]-3359.87547045774[/C][/ROW]
[ROW][C]6[/C][C]102191[/C][C]101918.963363533[/C][C]272.036636466772[/C][/ROW]
[ROW][C]7[/C][C]117359[/C][C]101495.790067149[/C][C]15863.2099328513[/C][/ROW]
[ROW][C]8[/C][C]116083[/C][C]116828.622986169[/C][C]-745.622986169372[/C][/ROW]
[ROW][C]9[/C][C]108666[/C][C]115544.875297409[/C][C]-6878.87529740906[/C][/ROW]
[ROW][C]10[/C][C]105017[/C][C]108056.397639378[/C][C]-3039.39763937824[/C][/ROW]
[ROW][C]11[/C][C]100918[/C][C]104375.815583345[/C][C]-3457.81558334519[/C][/ROW]
[ROW][C]12[/C][C]103907[/C][C]100240.885791175[/C][C]3666.11420882492[/C][/ROW]
[ROW][C]13[/C][C]105732[/C][C]103267.9799921[/C][C]2464.02000789951[/C][/ROW]
[ROW][C]14[/C][C]103409[/C][C]105118.583360659[/C][C]-1709.58336065873[/C][/ROW]
[ROW][C]15[/C][C]100255[/C][C]102777.819262671[/C][C]-2522.81926267102[/C][/ROW]
[ROW][C]16[/C][C]97036[/C][C]99597.6049173407[/C][C]-2561.60491734066[/C][/ROW]
[ROW][C]17[/C][C]94055[/C][C]96351.9875544179[/C][C]-2296.98755441788[/C][/ROW]
[ROW][C]18[/C][C]92523[/C][C]93347.119802232[/C][C]-824.119802232046[/C][/ROW]
[ROW][C]19[/C][C]106380[/C][C]91806.5564614454[/C][C]14573.4435385546[/C][/ROW]
[ROW][C]20[/C][C]104846[/C][C]105814.987555708[/C][C]-968.987555707688[/C][/ROW]
[ROW][C]21[/C][C]101411[/C][C]104270.918909578[/C][C]-2859.91890957755[/C][/ROW]
[ROW][C]22[/C][C]98072[/C][C]100806.201797844[/C][C]-2734.20179784394[/C][/ROW]
[ROW][C]23[/C][C]95678[/C][C]97438.7909991823[/C][C]-1760.79099918225[/C][/ROW]
[ROW][C]24[/C][C]99148[/C][C]95026.4948080955[/C][C]4121.50519190449[/C][/ROW]
[ROW][C]25[/C][C]106813[/C][C]98539.3209280559[/C][C]8273.67907194413[/C][/ROW]
[ROW][C]26[/C][C]106782[/C][C]106290.291843037[/C][C]491.708156962733[/C][/ROW]
[ROW][C]27[/C][C]103496[/C][C]106264.401129945[/C][C]-2768.40112994461[/C][/ROW]
[ROW][C]28[/C][C]100854[/C][C]102949.634969678[/C][C]-2095.63496967815[/C][/ROW]
[ROW][C]29[/C][C]99592[/C][C]100285.859450681[/C][C]-693.859450680655[/C][/ROW]
[ROW][C]30[/C][C]98923[/C][C]99016.6496312853[/C][C]-93.6496312853415[/C][/ROW]
[ROW][C]31[/C][C]110497[/C][C]98346.6765279755[/C][C]12150.3234720245[/C][/ROW]
[ROW][C]32[/C][C]114783[/C][C]110046.929240599[/C][C]4736.0707594009[/C][/ROW]
[ROW][C]33[/C][C]113551[/C][C]114382.141245689[/C][C]-831.141245689199[/C][/ROW]
[ROW][C]34[/C][C]112376[/C][C]113141.504945834[/C][C]-765.504945834036[/C][/ROW]
[ROW][C]35[/C][C]111683[/C][C]111958.550665756[/C][C]-275.550665755756[/C][/ROW]
[ROW][C]36[/C][C]113467[/C][C]111262.687448238[/C][C]2204.31255176244[/C][/ROW]
[ROW][C]37[/C][C]117277[/C][C]113069.592224375[/C][C]4207.40777562451[/C][/ROW]
[ROW][C]38[/C][C]117442[/C][C]116923.310948902[/C][C]518.689051097623[/C][/ROW]
[ROW][C]39[/C][C]115640[/C][C]117093.700591397[/C][C]-1453.70059139709[/C][/ROW]
[ROW][C]40[/C][C]114872[/C][C]115276.595343917[/C][C]-404.595343917143[/C][/ROW]
[ROW][C]41[/C][C]111628[/C][C]114504.39123694[/C][C]-2876.3912369399[/C][/ROW]
[ROW][C]42[/C][C]111098[/C][C]111230.502963013[/C][C]-132.502963013161[/C][/ROW]
[ROW][C]43[/C][C]124301[/C][C]110699.126138886[/C][C]13601.8738611142[/C][/ROW]
[ROW][C]44[/C][C]125847[/C][C]124043.461756467[/C][C]1803.53824353301[/C][/ROW]
[ROW][C]45[/C][C]125323[/C][C]125608.202129601[/C][C]-285.202129601152[/C][/ROW]
[ROW][C]46[/C][C]122394[/C][C]125081.238624754[/C][C]-2687.23862475363[/C][/ROW]
[ROW][C]47[/C][C]121164[/C][C]122124.315815404[/C][C]-960.315815404305[/C][/ROW]
[ROW][C]48[/C][C]123963[/C][C]120884.337276401[/C][C]3078.66272359913[/C][/ROW]
[ROW][C]49[/C][C]130549[/C][C]123715.327331728[/C][C]6833.67266827243[/C][/ROW]
[ROW][C]50[/C][C]128563[/C][C]130372.33529407[/C][C]-1809.3352940701[/C][/ROW]
[ROW][C]51[/C][C]125418[/C][C]128367.534684403[/C][C]-2949.53468440338[/C][/ROW]
[ROW][C]52[/C][C]121982[/C][C]125191.886384731[/C][C]-3209.8863847313[/C][/ROW]
[ROW][C]53[/C][C]117708[/C][C]121722.532798366[/C][C]-4014.53279836639[/C][/ROW]
[ROW][C]54[/C][C]116905[/C][C]117406.818217115[/C][C]-501.818217114531[/C][/ROW]
[ROW][C]55[/C][C]128862[/C][C]116598.603877653[/C][C]12263.3961223473[/C][/ROW]
[ROW][C]56[/C][C]129655[/C][C]128683.031516101[/C][C]971.968483898978[/C][/ROW]
[ROW][C]57[/C][C]128649[/C][C]129486.131136737[/C][C]-837.131136737415[/C][/ROW]
[ROW][C]58[/C][C]126084[/C][C]128471.432596565[/C][C]-2387.43259656455[/C][/ROW]
[ROW][C]59[/C][C]123725[/C][C]125881.625039612[/C][C]-2156.62503961216[/C][/ROW]
[ROW][C]60[/C][C]123974[/C][C]123500.215779316[/C][C]473.784220683665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294966&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294966&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
3108783111919-3136
4106640108135.414159162-1495.41415916217
5102617105976.875470458-3359.87547045774
6102191101918.963363533272.036636466772
7117359101495.79006714915863.2099328513
8116083116828.622986169-745.622986169372
9108666115544.875297409-6878.87529740906
10105017108056.397639378-3039.39763937824
11100918104375.815583345-3457.81558334519
12103907100240.8857911753666.11420882492
13105732103267.97999212464.02000789951
14103409105118.583360659-1709.58336065873
15100255102777.819262671-2522.81926267102
169703699597.6049173407-2561.60491734066
179405596351.9875544179-2296.98755441788
189252393347.119802232-824.119802232046
1910638091806.556461445414573.4435385546
20104846105814.987555708-968.987555707688
21101411104270.918909578-2859.91890957755
2298072100806.201797844-2734.20179784394
239567897438.7909991823-1760.79099918225
249914895026.49480809554121.50519190449
2510681398539.32092805598273.67907194413
26106782106290.291843037491.708156962733
27103496106264.401129945-2768.40112994461
28100854102949.634969678-2095.63496967815
2999592100285.859450681-693.859450680655
309892399016.6496312853-93.6496312853415
3111049798346.676527975512150.3234720245
32114783110046.9292405994736.0707594009
33113551114382.141245689-831.141245689199
34112376113141.504945834-765.504945834036
35111683111958.550665756-275.550665755756
36113467111262.6874482382204.31255176244
37117277113069.5922243754207.40777562451
38117442116923.310948902518.689051097623
39115640117093.700591397-1453.70059139709
40114872115276.595343917-404.595343917143
41111628114504.39123694-2876.3912369399
42111098111230.502963013-132.502963013161
43124301110699.12613888613601.8738611142
44125847124043.4617564671803.53824353301
45125323125608.202129601-285.202129601152
46122394125081.238624754-2687.23862475363
47121164122124.315815404-960.315815404305
48123963120884.3372764013078.66272359913
49130549123715.3273317286833.67266827243
50128563130372.33529407-1809.3352940701
51125418128367.534684403-2949.53468440338
52121982125191.886384731-3209.8863847313
53117708121722.532798366-4014.53279836639
54116905117406.818217115-501.818217114531
55128862116598.60387765312263.3961223473
56129655128683.031516101971.968483898978
57128649129486.131136737-837.131136737415
58126084128471.432596565-2387.43259656455
59123725125881.625039612-2156.62503961216
60123974123500.215779316473.784220683665







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61123754.138820517114217.212456926133291.065184109
62123534.277641035109976.773658114137091.781623956
63123314.416461552106623.745718582140005.087204523
64123094.55528207103722.143667154142466.966896985
65122874.694102587101104.046879031144645.341326143
66122654.83292310598683.800892383146625.864953826
67122434.97174362296410.793360108148459.150127136
68122215.1105641494252.2213573183150177.999770961
69121995.24938465792185.4195647963151805.079204518
70121775.38820517490193.9720822636153356.804328085
71121555.52702569288265.5512880267154845.502763357
72121335.66584620986390.6302152375156280.701477181

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 123754.138820517 & 114217.212456926 & 133291.065184109 \tabularnewline
62 & 123534.277641035 & 109976.773658114 & 137091.781623956 \tabularnewline
63 & 123314.416461552 & 106623.745718582 & 140005.087204523 \tabularnewline
64 & 123094.55528207 & 103722.143667154 & 142466.966896985 \tabularnewline
65 & 122874.694102587 & 101104.046879031 & 144645.341326143 \tabularnewline
66 & 122654.832923105 & 98683.800892383 & 146625.864953826 \tabularnewline
67 & 122434.971743622 & 96410.793360108 & 148459.150127136 \tabularnewline
68 & 122215.11056414 & 94252.2213573183 & 150177.999770961 \tabularnewline
69 & 121995.249384657 & 92185.4195647963 & 151805.079204518 \tabularnewline
70 & 121775.388205174 & 90193.9720822636 & 153356.804328085 \tabularnewline
71 & 121555.527025692 & 88265.5512880267 & 154845.502763357 \tabularnewline
72 & 121335.665846209 & 86390.6302152375 & 156280.701477181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294966&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]61[/C][C]123754.138820517[/C][C]114217.212456926[/C][C]133291.065184109[/C][/ROW]
[ROW][C]62[/C][C]123534.277641035[/C][C]109976.773658114[/C][C]137091.781623956[/C][/ROW]
[ROW][C]63[/C][C]123314.416461552[/C][C]106623.745718582[/C][C]140005.087204523[/C][/ROW]
[ROW][C]64[/C][C]123094.55528207[/C][C]103722.143667154[/C][C]142466.966896985[/C][/ROW]
[ROW][C]65[/C][C]122874.694102587[/C][C]101104.046879031[/C][C]144645.341326143[/C][/ROW]
[ROW][C]66[/C][C]122654.832923105[/C][C]98683.800892383[/C][C]146625.864953826[/C][/ROW]
[ROW][C]67[/C][C]122434.971743622[/C][C]96410.793360108[/C][C]148459.150127136[/C][/ROW]
[ROW][C]68[/C][C]122215.11056414[/C][C]94252.2213573183[/C][C]150177.999770961[/C][/ROW]
[ROW][C]69[/C][C]121995.249384657[/C][C]92185.4195647963[/C][C]151805.079204518[/C][/ROW]
[ROW][C]70[/C][C]121775.388205174[/C][C]90193.9720822636[/C][C]153356.804328085[/C][/ROW]
[ROW][C]71[/C][C]121555.527025692[/C][C]88265.5512880267[/C][C]154845.502763357[/C][/ROW]
[ROW][C]72[/C][C]121335.665846209[/C][C]86390.6302152375[/C][C]156280.701477181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294966&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294966&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
61123754.138820517114217.212456926133291.065184109
62123534.277641035109976.773658114137091.781623956
63123314.416461552106623.745718582140005.087204523
64123094.55528207103722.143667154142466.966896985
65122874.694102587101104.046879031144645.341326143
66122654.83292310598683.800892383146625.864953826
67122434.97174362296410.793360108148459.150127136
68122215.1105641494252.2213573183150177.999770961
69121995.24938465792185.4195647963151805.079204518
70121775.38820517490193.9720822636153356.804328085
71121555.52702569288265.5512880267154845.502763357
72121335.66584620986390.6302152375156280.701477181



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