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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 25 Dec 2014 14:37:59 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/25/t1419518292glplqifo0jeqtgy.htm/, Retrieved Thu, 16 May 2024 23:29:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271492, Retrieved Thu, 16 May 2024 23:29:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-25 14:37:59] [0837030ca90013de3b1661dab7c6b0da] [Current]
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Dataseries X:
1196
1141
6081
-3508
1782
-891
-2043
35
5042
-1837
406
-3621
1987
1627
6692
-3999
679
-215
-2820
799
9957
5154
1302
6287
1891
2191
7336
-2351
881
388
-1936
1120
4438
-3495
1012
-3704
2879
1907
6451
-2814
1613
-40
-3086
292
5283
-1671
3529
-3191
2090
3278
5686
-1817
2322
-705
-1980
646
6077
2632
2356
-1717
1733
2232
6167
-4668
1694
589
-4163
174
5421
-38
3158
-4322
1920
2527
7755
-2567
-388
-2084
-2024
-131
5615
187
2054
-7172




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=271492&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=271492&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271492&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
alpha0.178460788013762
beta0.04662383379755
gamma0.264088569687817

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.178460788013762 \tabularnewline
beta & 0.04662383379755 \tabularnewline
gamma & 0.264088569687817 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271492&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]0.178460788013762[/C][/ROW]
[ROW][C]beta[/C][C]0.04662383379755[/C][/ROW]
[ROW][C]gamma[/C][C]0.264088569687817[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271492&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271492&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
alpha0.178460788013762
beta0.04662383379755
gamma0.264088569687817







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131987482.0366254024681504.96337459753
1416271186.74650365151440.253496348495
1566924582.85573613232109.1442638677
16-3999-2095.99537424398-1903.00462575602
17679382.126653220106296.873346779894
18-215-120.67837275-94.3216272499998
19-2820-7892.923395442055072.92339544205
20799115.966693778788683.033306221212
21995733065.8913226018-23108.8913226018
225154-11188.618479783616342.6184797836
2313022304.86128861206-1002.86128861206
246287-21312.010297659527599.0102976595
25189114012.9926914845-12121.9926914845
2621917810.87469044429-5619.87469044429
27733618436.6514841324-11100.6514841324
28-2351-6156.656561159033805.65656115903
29881748.79484084801132.20515915199
30388-197.418837892345585.418837892345
31-1936-3733.83754048761797.8375404876
321120104.3474298942681015.65257010573
33443819809.9148423209-15371.9148423209
34-3495-4465.38111762154970.381117621536
3510121831.48205881367-819.482058813666
36-3704-11652.76628436687948.76628436675
37287910432.0267138466-7553.02671384658
3819076133.08138880795-4226.08138880795
39645114692.8221896389-8241.8221896389
40-2814-4772.643029625271958.64302962527
411613716.068457887943896.931542112057
42-4077.1828594981641-117.182859498164
43-3086-5251.541308150372165.54130815037
44292286.1469758014735.85302419852695
4552838821.06319290197-3538.06319290197
46-1671-2468.65252522278797.65252522278
473529910.4474585958132618.55254140419
48-3191-8721.040994246725530.04099424672
4920907647.33681098472-5557.33681098472
5032784470.16662969113-1192.16662969113
51568611925.8831437952-6239.88314379524
52-1817-4010.729834849562193.72983484956
532322777.8380600948211544.16193990518
54-70541.1404744891508-746.140474489151
55-198014536.0424613853-16516.0424613853
56646-779.174971732421425.17497173242
576077-14967.380601305221044.3806013052
5826323557.33919236559-925.339192365595
592356-2086.546857838514442.54685783851
60-17175004.84028310779-6721.84028310779
611733-3731.168948528195464.16894852819
622232-2176.622934971174408.62293497117
636167-3715.702264216679882.70226421667
64-4668736.218418525446-5404.21841852545
65169477.98848918955411616.01151081045
6658930.7224398896798558.27756011032
67-4163-5103.68874435055940.688744350552
68174195.22121186337-21.2212118633699
6954217774.24236904773-2353.24236904773
70-38-3650.727923522033612.72792352203
713158493.678164449972664.32183555003
72-4322-8971.171753021164649.17175302116
7319207291.20468142658-5371.20468142658
7425272702.40356039531-175.403560395308
757755-2227.522563698659982.52256369865
76-2567-9863.933730082837296.93373008283
77-388851.11164623332-1239.11164623332
78-208446.76565947908-2130.76565947908
79-20246581.29596164068-8605.29596164068
80-131-206.48355982625375.483559826253
815615-7590.5552148916213205.5552148916
821872101.85806490179-1914.85806490179
832054-636.8022866298642690.80228662986
84-7172825.556557646843-7997.55655764684

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1987 & 482.036625402468 & 1504.96337459753 \tabularnewline
14 & 1627 & 1186.74650365151 & 440.253496348495 \tabularnewline
15 & 6692 & 4582.8557361323 & 2109.1442638677 \tabularnewline
16 & -3999 & -2095.99537424398 & -1903.00462575602 \tabularnewline
17 & 679 & 382.126653220106 & 296.873346779894 \tabularnewline
18 & -215 & -120.67837275 & -94.3216272499998 \tabularnewline
19 & -2820 & -7892.92339544205 & 5072.92339544205 \tabularnewline
20 & 799 & 115.966693778788 & 683.033306221212 \tabularnewline
21 & 9957 & 33065.8913226018 & -23108.8913226018 \tabularnewline
22 & 5154 & -11188.6184797836 & 16342.6184797836 \tabularnewline
23 & 1302 & 2304.86128861206 & -1002.86128861206 \tabularnewline
24 & 6287 & -21312.0102976595 & 27599.0102976595 \tabularnewline
25 & 1891 & 14012.9926914845 & -12121.9926914845 \tabularnewline
26 & 2191 & 7810.87469044429 & -5619.87469044429 \tabularnewline
27 & 7336 & 18436.6514841324 & -11100.6514841324 \tabularnewline
28 & -2351 & -6156.65656115903 & 3805.65656115903 \tabularnewline
29 & 881 & 748.79484084801 & 132.20515915199 \tabularnewline
30 & 388 & -197.418837892345 & 585.418837892345 \tabularnewline
31 & -1936 & -3733.8375404876 & 1797.8375404876 \tabularnewline
32 & 1120 & 104.347429894268 & 1015.65257010573 \tabularnewline
33 & 4438 & 19809.9148423209 & -15371.9148423209 \tabularnewline
34 & -3495 & -4465.38111762154 & 970.381117621536 \tabularnewline
35 & 1012 & 1831.48205881367 & -819.482058813666 \tabularnewline
36 & -3704 & -11652.7662843668 & 7948.76628436675 \tabularnewline
37 & 2879 & 10432.0267138466 & -7553.02671384658 \tabularnewline
38 & 1907 & 6133.08138880795 & -4226.08138880795 \tabularnewline
39 & 6451 & 14692.8221896389 & -8241.8221896389 \tabularnewline
40 & -2814 & -4772.64302962527 & 1958.64302962527 \tabularnewline
41 & 1613 & 716.068457887943 & 896.931542112057 \tabularnewline
42 & -40 & 77.1828594981641 & -117.182859498164 \tabularnewline
43 & -3086 & -5251.54130815037 & 2165.54130815037 \tabularnewline
44 & 292 & 286.146975801473 & 5.85302419852695 \tabularnewline
45 & 5283 & 8821.06319290197 & -3538.06319290197 \tabularnewline
46 & -1671 & -2468.65252522278 & 797.65252522278 \tabularnewline
47 & 3529 & 910.447458595813 & 2618.55254140419 \tabularnewline
48 & -3191 & -8721.04099424672 & 5530.04099424672 \tabularnewline
49 & 2090 & 7647.33681098472 & -5557.33681098472 \tabularnewline
50 & 3278 & 4470.16662969113 & -1192.16662969113 \tabularnewline
51 & 5686 & 11925.8831437952 & -6239.88314379524 \tabularnewline
52 & -1817 & -4010.72983484956 & 2193.72983484956 \tabularnewline
53 & 2322 & 777.838060094821 & 1544.16193990518 \tabularnewline
54 & -705 & 41.1404744891508 & -746.140474489151 \tabularnewline
55 & -1980 & 14536.0424613853 & -16516.0424613853 \tabularnewline
56 & 646 & -779.17497173242 & 1425.17497173242 \tabularnewline
57 & 6077 & -14967.3806013052 & 21044.3806013052 \tabularnewline
58 & 2632 & 3557.33919236559 & -925.339192365595 \tabularnewline
59 & 2356 & -2086.54685783851 & 4442.54685783851 \tabularnewline
60 & -1717 & 5004.84028310779 & -6721.84028310779 \tabularnewline
61 & 1733 & -3731.16894852819 & 5464.16894852819 \tabularnewline
62 & 2232 & -2176.62293497117 & 4408.62293497117 \tabularnewline
63 & 6167 & -3715.70226421667 & 9882.70226421667 \tabularnewline
64 & -4668 & 736.218418525446 & -5404.21841852545 \tabularnewline
65 & 1694 & 77.9884891895541 & 1616.01151081045 \tabularnewline
66 & 589 & 30.7224398896798 & 558.27756011032 \tabularnewline
67 & -4163 & -5103.68874435055 & 940.688744350552 \tabularnewline
68 & 174 & 195.22121186337 & -21.2212118633699 \tabularnewline
69 & 5421 & 7774.24236904773 & -2353.24236904773 \tabularnewline
70 & -38 & -3650.72792352203 & 3612.72792352203 \tabularnewline
71 & 3158 & 493.67816444997 & 2664.32183555003 \tabularnewline
72 & -4322 & -8971.17175302116 & 4649.17175302116 \tabularnewline
73 & 1920 & 7291.20468142658 & -5371.20468142658 \tabularnewline
74 & 2527 & 2702.40356039531 & -175.403560395308 \tabularnewline
75 & 7755 & -2227.52256369865 & 9982.52256369865 \tabularnewline
76 & -2567 & -9863.93373008283 & 7296.93373008283 \tabularnewline
77 & -388 & 851.11164623332 & -1239.11164623332 \tabularnewline
78 & -2084 & 46.76565947908 & -2130.76565947908 \tabularnewline
79 & -2024 & 6581.29596164068 & -8605.29596164068 \tabularnewline
80 & -131 & -206.483559826253 & 75.483559826253 \tabularnewline
81 & 5615 & -7590.55521489162 & 13205.5552148916 \tabularnewline
82 & 187 & 2101.85806490179 & -1914.85806490179 \tabularnewline
83 & 2054 & -636.802286629864 & 2690.80228662986 \tabularnewline
84 & -7172 & 825.556557646843 & -7997.55655764684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271492&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]13[/C][C]1987[/C][C]482.036625402468[/C][C]1504.96337459753[/C][/ROW]
[ROW][C]14[/C][C]1627[/C][C]1186.74650365151[/C][C]440.253496348495[/C][/ROW]
[ROW][C]15[/C][C]6692[/C][C]4582.8557361323[/C][C]2109.1442638677[/C][/ROW]
[ROW][C]16[/C][C]-3999[/C][C]-2095.99537424398[/C][C]-1903.00462575602[/C][/ROW]
[ROW][C]17[/C][C]679[/C][C]382.126653220106[/C][C]296.873346779894[/C][/ROW]
[ROW][C]18[/C][C]-215[/C][C]-120.67837275[/C][C]-94.3216272499998[/C][/ROW]
[ROW][C]19[/C][C]-2820[/C][C]-7892.92339544205[/C][C]5072.92339544205[/C][/ROW]
[ROW][C]20[/C][C]799[/C][C]115.966693778788[/C][C]683.033306221212[/C][/ROW]
[ROW][C]21[/C][C]9957[/C][C]33065.8913226018[/C][C]-23108.8913226018[/C][/ROW]
[ROW][C]22[/C][C]5154[/C][C]-11188.6184797836[/C][C]16342.6184797836[/C][/ROW]
[ROW][C]23[/C][C]1302[/C][C]2304.86128861206[/C][C]-1002.86128861206[/C][/ROW]
[ROW][C]24[/C][C]6287[/C][C]-21312.0102976595[/C][C]27599.0102976595[/C][/ROW]
[ROW][C]25[/C][C]1891[/C][C]14012.9926914845[/C][C]-12121.9926914845[/C][/ROW]
[ROW][C]26[/C][C]2191[/C][C]7810.87469044429[/C][C]-5619.87469044429[/C][/ROW]
[ROW][C]27[/C][C]7336[/C][C]18436.6514841324[/C][C]-11100.6514841324[/C][/ROW]
[ROW][C]28[/C][C]-2351[/C][C]-6156.65656115903[/C][C]3805.65656115903[/C][/ROW]
[ROW][C]29[/C][C]881[/C][C]748.79484084801[/C][C]132.20515915199[/C][/ROW]
[ROW][C]30[/C][C]388[/C][C]-197.418837892345[/C][C]585.418837892345[/C][/ROW]
[ROW][C]31[/C][C]-1936[/C][C]-3733.8375404876[/C][C]1797.8375404876[/C][/ROW]
[ROW][C]32[/C][C]1120[/C][C]104.347429894268[/C][C]1015.65257010573[/C][/ROW]
[ROW][C]33[/C][C]4438[/C][C]19809.9148423209[/C][C]-15371.9148423209[/C][/ROW]
[ROW][C]34[/C][C]-3495[/C][C]-4465.38111762154[/C][C]970.381117621536[/C][/ROW]
[ROW][C]35[/C][C]1012[/C][C]1831.48205881367[/C][C]-819.482058813666[/C][/ROW]
[ROW][C]36[/C][C]-3704[/C][C]-11652.7662843668[/C][C]7948.76628436675[/C][/ROW]
[ROW][C]37[/C][C]2879[/C][C]10432.0267138466[/C][C]-7553.02671384658[/C][/ROW]
[ROW][C]38[/C][C]1907[/C][C]6133.08138880795[/C][C]-4226.08138880795[/C][/ROW]
[ROW][C]39[/C][C]6451[/C][C]14692.8221896389[/C][C]-8241.8221896389[/C][/ROW]
[ROW][C]40[/C][C]-2814[/C][C]-4772.64302962527[/C][C]1958.64302962527[/C][/ROW]
[ROW][C]41[/C][C]1613[/C][C]716.068457887943[/C][C]896.931542112057[/C][/ROW]
[ROW][C]42[/C][C]-40[/C][C]77.1828594981641[/C][C]-117.182859498164[/C][/ROW]
[ROW][C]43[/C][C]-3086[/C][C]-5251.54130815037[/C][C]2165.54130815037[/C][/ROW]
[ROW][C]44[/C][C]292[/C][C]286.146975801473[/C][C]5.85302419852695[/C][/ROW]
[ROW][C]45[/C][C]5283[/C][C]8821.06319290197[/C][C]-3538.06319290197[/C][/ROW]
[ROW][C]46[/C][C]-1671[/C][C]-2468.65252522278[/C][C]797.65252522278[/C][/ROW]
[ROW][C]47[/C][C]3529[/C][C]910.447458595813[/C][C]2618.55254140419[/C][/ROW]
[ROW][C]48[/C][C]-3191[/C][C]-8721.04099424672[/C][C]5530.04099424672[/C][/ROW]
[ROW][C]49[/C][C]2090[/C][C]7647.33681098472[/C][C]-5557.33681098472[/C][/ROW]
[ROW][C]50[/C][C]3278[/C][C]4470.16662969113[/C][C]-1192.16662969113[/C][/ROW]
[ROW][C]51[/C][C]5686[/C][C]11925.8831437952[/C][C]-6239.88314379524[/C][/ROW]
[ROW][C]52[/C][C]-1817[/C][C]-4010.72983484956[/C][C]2193.72983484956[/C][/ROW]
[ROW][C]53[/C][C]2322[/C][C]777.838060094821[/C][C]1544.16193990518[/C][/ROW]
[ROW][C]54[/C][C]-705[/C][C]41.1404744891508[/C][C]-746.140474489151[/C][/ROW]
[ROW][C]55[/C][C]-1980[/C][C]14536.0424613853[/C][C]-16516.0424613853[/C][/ROW]
[ROW][C]56[/C][C]646[/C][C]-779.17497173242[/C][C]1425.17497173242[/C][/ROW]
[ROW][C]57[/C][C]6077[/C][C]-14967.3806013052[/C][C]21044.3806013052[/C][/ROW]
[ROW][C]58[/C][C]2632[/C][C]3557.33919236559[/C][C]-925.339192365595[/C][/ROW]
[ROW][C]59[/C][C]2356[/C][C]-2086.54685783851[/C][C]4442.54685783851[/C][/ROW]
[ROW][C]60[/C][C]-1717[/C][C]5004.84028310779[/C][C]-6721.84028310779[/C][/ROW]
[ROW][C]61[/C][C]1733[/C][C]-3731.16894852819[/C][C]5464.16894852819[/C][/ROW]
[ROW][C]62[/C][C]2232[/C][C]-2176.62293497117[/C][C]4408.62293497117[/C][/ROW]
[ROW][C]63[/C][C]6167[/C][C]-3715.70226421667[/C][C]9882.70226421667[/C][/ROW]
[ROW][C]64[/C][C]-4668[/C][C]736.218418525446[/C][C]-5404.21841852545[/C][/ROW]
[ROW][C]65[/C][C]1694[/C][C]77.9884891895541[/C][C]1616.01151081045[/C][/ROW]
[ROW][C]66[/C][C]589[/C][C]30.7224398896798[/C][C]558.27756011032[/C][/ROW]
[ROW][C]67[/C][C]-4163[/C][C]-5103.68874435055[/C][C]940.688744350552[/C][/ROW]
[ROW][C]68[/C][C]174[/C][C]195.22121186337[/C][C]-21.2212118633699[/C][/ROW]
[ROW][C]69[/C][C]5421[/C][C]7774.24236904773[/C][C]-2353.24236904773[/C][/ROW]
[ROW][C]70[/C][C]-38[/C][C]-3650.72792352203[/C][C]3612.72792352203[/C][/ROW]
[ROW][C]71[/C][C]3158[/C][C]493.67816444997[/C][C]2664.32183555003[/C][/ROW]
[ROW][C]72[/C][C]-4322[/C][C]-8971.17175302116[/C][C]4649.17175302116[/C][/ROW]
[ROW][C]73[/C][C]1920[/C][C]7291.20468142658[/C][C]-5371.20468142658[/C][/ROW]
[ROW][C]74[/C][C]2527[/C][C]2702.40356039531[/C][C]-175.403560395308[/C][/ROW]
[ROW][C]75[/C][C]7755[/C][C]-2227.52256369865[/C][C]9982.52256369865[/C][/ROW]
[ROW][C]76[/C][C]-2567[/C][C]-9863.93373008283[/C][C]7296.93373008283[/C][/ROW]
[ROW][C]77[/C][C]-388[/C][C]851.11164623332[/C][C]-1239.11164623332[/C][/ROW]
[ROW][C]78[/C][C]-2084[/C][C]46.76565947908[/C][C]-2130.76565947908[/C][/ROW]
[ROW][C]79[/C][C]-2024[/C][C]6581.29596164068[/C][C]-8605.29596164068[/C][/ROW]
[ROW][C]80[/C][C]-131[/C][C]-206.483559826253[/C][C]75.483559826253[/C][/ROW]
[ROW][C]81[/C][C]5615[/C][C]-7590.55521489162[/C][C]13205.5552148916[/C][/ROW]
[ROW][C]82[/C][C]187[/C][C]2101.85806490179[/C][C]-1914.85806490179[/C][/ROW]
[ROW][C]83[/C][C]2054[/C][C]-636.802286629864[/C][C]2690.80228662986[/C][/ROW]
[ROW][C]84[/C][C]-7172[/C][C]825.556557646843[/C][C]-7997.55655764684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271492&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271492&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
131987482.0366254024681504.96337459753
1416271186.74650365151440.253496348495
1566924582.85573613232109.1442638677
16-3999-2095.99537424398-1903.00462575602
17679382.126653220106296.873346779894
18-215-120.67837275-94.3216272499998
19-2820-7892.923395442055072.92339544205
20799115.966693778788683.033306221212
21995733065.8913226018-23108.8913226018
225154-11188.618479783616342.6184797836
2313022304.86128861206-1002.86128861206
246287-21312.010297659527599.0102976595
25189114012.9926914845-12121.9926914845
2621917810.87469044429-5619.87469044429
27733618436.6514841324-11100.6514841324
28-2351-6156.656561159033805.65656115903
29881748.79484084801132.20515915199
30388-197.418837892345585.418837892345
31-1936-3733.83754048761797.8375404876
321120104.3474298942681015.65257010573
33443819809.9148423209-15371.9148423209
34-3495-4465.38111762154970.381117621536
3510121831.48205881367-819.482058813666
36-3704-11652.76628436687948.76628436675
37287910432.0267138466-7553.02671384658
3819076133.08138880795-4226.08138880795
39645114692.8221896389-8241.8221896389
40-2814-4772.643029625271958.64302962527
411613716.068457887943896.931542112057
42-4077.1828594981641-117.182859498164
43-3086-5251.541308150372165.54130815037
44292286.1469758014735.85302419852695
4552838821.06319290197-3538.06319290197
46-1671-2468.65252522278797.65252522278
473529910.4474585958132618.55254140419
48-3191-8721.040994246725530.04099424672
4920907647.33681098472-5557.33681098472
5032784470.16662969113-1192.16662969113
51568611925.8831437952-6239.88314379524
52-1817-4010.729834849562193.72983484956
532322777.8380600948211544.16193990518
54-70541.1404744891508-746.140474489151
55-198014536.0424613853-16516.0424613853
56646-779.174971732421425.17497173242
576077-14967.380601305221044.3806013052
5826323557.33919236559-925.339192365595
592356-2086.546857838514442.54685783851
60-17175004.84028310779-6721.84028310779
611733-3731.168948528195464.16894852819
622232-2176.622934971174408.62293497117
636167-3715.702264216679882.70226421667
64-4668736.218418525446-5404.21841852545
65169477.98848918955411616.01151081045
6658930.7224398896798558.27756011032
67-4163-5103.68874435055940.688744350552
68174195.22121186337-21.2212118633699
6954217774.24236904773-2353.24236904773
70-38-3650.727923522033612.72792352203
713158493.678164449972664.32183555003
72-4322-8971.171753021164649.17175302116
7319207291.20468142658-5371.20468142658
7425272702.40356039531-175.403560395308
757755-2227.522563698659982.52256369865
76-2567-9863.933730082837296.93373008283
77-388851.11164623332-1239.11164623332
78-208446.76565947908-2130.76565947908
79-20246581.29596164068-8605.29596164068
80-131-206.48355982625375.483559826253
815615-7590.5552148916213205.5552148916
821872101.85806490179-1914.85806490179
832054-636.8022866298642690.80228662986
84-7172825.556557646843-7997.55655764684







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85487.145257726168-5347.036978703996321.32749415633
86244.420743531861-5748.766616872496237.60810393621
87776.933764888404-10621.464507189112175.3320369659
88-3733.41997777363-54542.86908931147076.0291337638
89271.164839567078-6689.277220728397231.60689986254
9089.6240506097161-5954.554668045186133.80276926461
91-443.294674197643-17235.964311259916349.3749628646
9225.0190528010914-5883.244499591465933.28260519365
93463.148204896047-53524.58444451654450.8808543081
94-298.589150742057-36659.558794896336062.3804934122
95-367.351052196933-46526.388273776445791.6861693825
96-2571.20649526307-335733.437213949330591.024223423

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 487.145257726168 & -5347.03697870399 & 6321.32749415633 \tabularnewline
86 & 244.420743531861 & -5748.76661687249 & 6237.60810393621 \tabularnewline
87 & 776.933764888404 & -10621.4645071891 & 12175.3320369659 \tabularnewline
88 & -3733.41997777363 & -54542.869089311 & 47076.0291337638 \tabularnewline
89 & 271.164839567078 & -6689.27722072839 & 7231.60689986254 \tabularnewline
90 & 89.6240506097161 & -5954.55466804518 & 6133.80276926461 \tabularnewline
91 & -443.294674197643 & -17235.9643112599 & 16349.3749628646 \tabularnewline
92 & 25.0190528010914 & -5883.24449959146 & 5933.28260519365 \tabularnewline
93 & 463.148204896047 & -53524.584444516 & 54450.8808543081 \tabularnewline
94 & -298.589150742057 & -36659.5587948963 & 36062.3804934122 \tabularnewline
95 & -367.351052196933 & -46526.3882737764 & 45791.6861693825 \tabularnewline
96 & -2571.20649526307 & -335733.437213949 & 330591.024223423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271492&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]487.145257726168[/C][C]-5347.03697870399[/C][C]6321.32749415633[/C][/ROW]
[ROW][C]86[/C][C]244.420743531861[/C][C]-5748.76661687249[/C][C]6237.60810393621[/C][/ROW]
[ROW][C]87[/C][C]776.933764888404[/C][C]-10621.4645071891[/C][C]12175.3320369659[/C][/ROW]
[ROW][C]88[/C][C]-3733.41997777363[/C][C]-54542.869089311[/C][C]47076.0291337638[/C][/ROW]
[ROW][C]89[/C][C]271.164839567078[/C][C]-6689.27722072839[/C][C]7231.60689986254[/C][/ROW]
[ROW][C]90[/C][C]89.6240506097161[/C][C]-5954.55466804518[/C][C]6133.80276926461[/C][/ROW]
[ROW][C]91[/C][C]-443.294674197643[/C][C]-17235.9643112599[/C][C]16349.3749628646[/C][/ROW]
[ROW][C]92[/C][C]25.0190528010914[/C][C]-5883.24449959146[/C][C]5933.28260519365[/C][/ROW]
[ROW][C]93[/C][C]463.148204896047[/C][C]-53524.584444516[/C][C]54450.8808543081[/C][/ROW]
[ROW][C]94[/C][C]-298.589150742057[/C][C]-36659.5587948963[/C][C]36062.3804934122[/C][/ROW]
[ROW][C]95[/C][C]-367.351052196933[/C][C]-46526.3882737764[/C][C]45791.6861693825[/C][/ROW]
[ROW][C]96[/C][C]-2571.20649526307[/C][C]-335733.437213949[/C][C]330591.024223423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271492&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271492&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
85487.145257726168-5347.036978703996321.32749415633
86244.420743531861-5748.766616872496237.60810393621
87776.933764888404-10621.464507189112175.3320369659
88-3733.41997777363-54542.86908931147076.0291337638
89271.164839567078-6689.277220728397231.60689986254
9089.6240506097161-5954.554668045186133.80276926461
91-443.294674197643-17235.964311259916349.3749628646
9225.0190528010914-5883.244499591465933.28260519365
93463.148204896047-53524.58444451654450.8808543081
94-298.589150742057-36659.558794896336062.3804934122
95-367.351052196933-46526.388273776445791.6861693825
96-2571.20649526307-335733.437213949330591.024223423



Parameters (Session):
par1 = 750 ; par2 = 5 ; par3 = 0 ; par4 = P1 P5 Q1 Q3 P95 P99 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')