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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 16 Aug 2012 10:33:54 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/16/t1345127664nrpg37govfr7up8.htm/, Retrieved Fri, 03 May 2024 10:41:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169412, Retrieved Fri, 03 May 2024 10:41:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBelis Olivier
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2012-08-16 14:33:54] [084e0343a0486ff05530df6c705c8bb4] [Current]
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Dataseries X:
5400
5200
5500
4400
5700
5600
6000
6200
6900
6000
5700
7100
6000
4500
5300
4000
5600
4600
6100
5500
5800
6500
6400
7600
5500
4600
5100
3700
5300
4100
5800
5500
4900
7000
6300
7200
5400
5000
4500
3700
4900
4400
6000
5800
5000
6700
6200
8000
6400
3900
3900
3900
4600
4600
6200
5700
5100
6400
5900
8500
6700
3900
4100
3400
4700
5400
6800
6700
5400
6300
5600
8000
6100
4900
4400
3300
4900
5900
6900
6500
4800
6900
5400
8300
6900
5000
4600
3100
4900
4700
7100
7100
5400
7000
5200
8100
6900
5100
3900
2700
5300
5100
6700
7700
5700
6400
4800
8300




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169412&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169412&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00926118605787754
beta1
gamma0.929768627341831

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605787754 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627341831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169412&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]0.00926118605787754[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627341831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169412&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
alpha0.00926118605787754
beta1
gamma0.929768627341831







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1360006205.18162393162-205.181623931624
1445004700.18653484721-200.186534847209
1553005543.38374146668-243.383741466678
1640004233.92686860528-233.926868605279
1756005747.39113734889-147.391137348885
1846004660.29181285404-60.2918128540414
1961005827.60742437892272.392575621081
2055006000.52676624762-500.526766247624
2158006694.98582010772-894.985820107719
2265005765.00308507862734.996914921378
2364005452.75619994414947.243800055858
2476006876.24757377759723.752426222411
2555005607.0339578938-107.033957893802
2646004110.24094600832489.75905399168
2751004929.11798264558170.882017354417
2837003645.1271294219854.872870578019
2953005256.5718785667443.4281214332632
3041004268.83199001845-168.831990018452
3158005757.9520170059642.0479829940359
3255005230.97888275944269.021117240562
3349005590.55424857441-690.554248574411
3470006187.1779373185812.822062681497
3563006095.12717189337204.872828106634
3672007322.95971563057-122.959715630571
3754005289.86481161096110.135188389037
3850004356.08054953951643.919450460486
3945004895.33383949158-395.333839491585
4037003506.67722339594193.322776604065
4149005117.58477824287-217.584778242875
4244003938.20825618032461.791743819679
4360005639.56840383085360.431596169152
4458005339.71662835167460.283371648332
4550004834.0088881831165.991111816899
4667006848.21072112326-148.210721123255
4762006203.14073057057-3.14073057056976
4880007141.03314152905858.966858470947
4964005354.814897765771045.18510223423
5039004953.11520142444-1053.11520142444
5139004535.344362286-635.344362285998
5239003700.49662341759199.50337658241
5346004946.79391724362-346.793917243618
5446004404.68038953215195.319610467852
5562006020.38273996362179.61726003638
5657005819.33985079777-119.339850797771
5751005040.3106762440659.6893237559352
5864006766.25025213102-366.250252131017
5959006252.92572917807-352.925729178066
6085007978.60888934583521.391110654168
6167006354.56732743833345.43267256167
6239004000.80735739248-100.807357392485
6341003972.79450960493127.205490395069
6434003917.20316145674-517.203161456743
6547004650.1670122803249.832987719682
6654004611.30225617761788.697743822392
6768006223.73442870586576.265571294136
6867005760.35049302479939.649506975211
6954005175.22266024475224.777339755248
7063006531.04217827994-231.042178279936
7156006053.20464127805-453.204641278046
7280008604.37504314332-604.37504314332
7361006818.4282301061-718.428230106098
7449004044.51169654605855.488303453952
7544004245.00110582851154.998894171489
7633003605.93245466192-305.932454661922
7749004875.0067462483224.9932537516788
7859005528.11699585024371.883004149764
7969006948.73917201942-48.7391720194246
8065006816.24640648133-316.246406481328
8148005551.29176568286-751.291765682865
8269006459.46483202976440.535167970243
8354005770.69464089138-370.694640891383
8483008171.6359624084128.3640375916
8569006282.45880898686617.541191013141
8650004978.1578123119521.8421876880511
8746004525.3620663208674.6379336791388
8831003459.91112805968-359.911128059679
8949005031.7729151798-131.772915179796
9047005999.97228840143-1299.97228840143
9171006999.16905375072100.830946249278
9271006604.54766683006495.452333169943
9354004936.78473241479463.215267585211
9470006955.7339746204944.266025379512
9552005514.02086261856-314.02086261856
9681008373.72146662011-273.721466620114
9769006926.22870739734-26.2287073973403
9851005056.0695413625643.9304586374446
9939004641.15286609441-741.152866094406
10027003149.34455057975-449.344550579745
10153004911.18722813348388.812771866518
10251004793.5908806127306.409119387301
10367007098.38164133232-398.381641332322
10477007058.37832660954641.621673390458
10557005359.36014629908340.639853700925
10664006987.20708993047-587.207089930472
10748005199.71009786023-399.710097860232
10883008085.0487351223214.9512648777

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6000 & 6205.18162393162 & -205.181623931624 \tabularnewline
14 & 4500 & 4700.18653484721 & -200.186534847209 \tabularnewline
15 & 5300 & 5543.38374146668 & -243.383741466678 \tabularnewline
16 & 4000 & 4233.92686860528 & -233.926868605279 \tabularnewline
17 & 5600 & 5747.39113734889 & -147.391137348885 \tabularnewline
18 & 4600 & 4660.29181285404 & -60.2918128540414 \tabularnewline
19 & 6100 & 5827.60742437892 & 272.392575621081 \tabularnewline
20 & 5500 & 6000.52676624762 & -500.526766247624 \tabularnewline
21 & 5800 & 6694.98582010772 & -894.985820107719 \tabularnewline
22 & 6500 & 5765.00308507862 & 734.996914921378 \tabularnewline
23 & 6400 & 5452.75619994414 & 947.243800055858 \tabularnewline
24 & 7600 & 6876.24757377759 & 723.752426222411 \tabularnewline
25 & 5500 & 5607.0339578938 & -107.033957893802 \tabularnewline
26 & 4600 & 4110.24094600832 & 489.75905399168 \tabularnewline
27 & 5100 & 4929.11798264558 & 170.882017354417 \tabularnewline
28 & 3700 & 3645.12712942198 & 54.872870578019 \tabularnewline
29 & 5300 & 5256.57187856674 & 43.4281214332632 \tabularnewline
30 & 4100 & 4268.83199001845 & -168.831990018452 \tabularnewline
31 & 5800 & 5757.95201700596 & 42.0479829940359 \tabularnewline
32 & 5500 & 5230.97888275944 & 269.021117240562 \tabularnewline
33 & 4900 & 5590.55424857441 & -690.554248574411 \tabularnewline
34 & 7000 & 6187.1779373185 & 812.822062681497 \tabularnewline
35 & 6300 & 6095.12717189337 & 204.872828106634 \tabularnewline
36 & 7200 & 7322.95971563057 & -122.959715630571 \tabularnewline
37 & 5400 & 5289.86481161096 & 110.135188389037 \tabularnewline
38 & 5000 & 4356.08054953951 & 643.919450460486 \tabularnewline
39 & 4500 & 4895.33383949158 & -395.333839491585 \tabularnewline
40 & 3700 & 3506.67722339594 & 193.322776604065 \tabularnewline
41 & 4900 & 5117.58477824287 & -217.584778242875 \tabularnewline
42 & 4400 & 3938.20825618032 & 461.791743819679 \tabularnewline
43 & 6000 & 5639.56840383085 & 360.431596169152 \tabularnewline
44 & 5800 & 5339.71662835167 & 460.283371648332 \tabularnewline
45 & 5000 & 4834.0088881831 & 165.991111816899 \tabularnewline
46 & 6700 & 6848.21072112326 & -148.210721123255 \tabularnewline
47 & 6200 & 6203.14073057057 & -3.14073057056976 \tabularnewline
48 & 8000 & 7141.03314152905 & 858.966858470947 \tabularnewline
49 & 6400 & 5354.81489776577 & 1045.18510223423 \tabularnewline
50 & 3900 & 4953.11520142444 & -1053.11520142444 \tabularnewline
51 & 3900 & 4535.344362286 & -635.344362285998 \tabularnewline
52 & 3900 & 3700.49662341759 & 199.50337658241 \tabularnewline
53 & 4600 & 4946.79391724362 & -346.793917243618 \tabularnewline
54 & 4600 & 4404.68038953215 & 195.319610467852 \tabularnewline
55 & 6200 & 6020.38273996362 & 179.61726003638 \tabularnewline
56 & 5700 & 5819.33985079777 & -119.339850797771 \tabularnewline
57 & 5100 & 5040.31067624406 & 59.6893237559352 \tabularnewline
58 & 6400 & 6766.25025213102 & -366.250252131017 \tabularnewline
59 & 5900 & 6252.92572917807 & -352.925729178066 \tabularnewline
60 & 8500 & 7978.60888934583 & 521.391110654168 \tabularnewline
61 & 6700 & 6354.56732743833 & 345.43267256167 \tabularnewline
62 & 3900 & 4000.80735739248 & -100.807357392485 \tabularnewline
63 & 4100 & 3972.79450960493 & 127.205490395069 \tabularnewline
64 & 3400 & 3917.20316145674 & -517.203161456743 \tabularnewline
65 & 4700 & 4650.16701228032 & 49.832987719682 \tabularnewline
66 & 5400 & 4611.30225617761 & 788.697743822392 \tabularnewline
67 & 6800 & 6223.73442870586 & 576.265571294136 \tabularnewline
68 & 6700 & 5760.35049302479 & 939.649506975211 \tabularnewline
69 & 5400 & 5175.22266024475 & 224.777339755248 \tabularnewline
70 & 6300 & 6531.04217827994 & -231.042178279936 \tabularnewline
71 & 5600 & 6053.20464127805 & -453.204641278046 \tabularnewline
72 & 8000 & 8604.37504314332 & -604.37504314332 \tabularnewline
73 & 6100 & 6818.4282301061 & -718.428230106098 \tabularnewline
74 & 4900 & 4044.51169654605 & 855.488303453952 \tabularnewline
75 & 4400 & 4245.00110582851 & 154.998894171489 \tabularnewline
76 & 3300 & 3605.93245466192 & -305.932454661922 \tabularnewline
77 & 4900 & 4875.00674624832 & 24.9932537516788 \tabularnewline
78 & 5900 & 5528.11699585024 & 371.883004149764 \tabularnewline
79 & 6900 & 6948.73917201942 & -48.7391720194246 \tabularnewline
80 & 6500 & 6816.24640648133 & -316.246406481328 \tabularnewline
81 & 4800 & 5551.29176568286 & -751.291765682865 \tabularnewline
82 & 6900 & 6459.46483202976 & 440.535167970243 \tabularnewline
83 & 5400 & 5770.69464089138 & -370.694640891383 \tabularnewline
84 & 8300 & 8171.6359624084 & 128.3640375916 \tabularnewline
85 & 6900 & 6282.45880898686 & 617.541191013141 \tabularnewline
86 & 5000 & 4978.15781231195 & 21.8421876880511 \tabularnewline
87 & 4600 & 4525.36206632086 & 74.6379336791388 \tabularnewline
88 & 3100 & 3459.91112805968 & -359.911128059679 \tabularnewline
89 & 4900 & 5031.7729151798 & -131.772915179796 \tabularnewline
90 & 4700 & 5999.97228840143 & -1299.97228840143 \tabularnewline
91 & 7100 & 6999.16905375072 & 100.830946249278 \tabularnewline
92 & 7100 & 6604.54766683006 & 495.452333169943 \tabularnewline
93 & 5400 & 4936.78473241479 & 463.215267585211 \tabularnewline
94 & 7000 & 6955.73397462049 & 44.266025379512 \tabularnewline
95 & 5200 & 5514.02086261856 & -314.02086261856 \tabularnewline
96 & 8100 & 8373.72146662011 & -273.721466620114 \tabularnewline
97 & 6900 & 6926.22870739734 & -26.2287073973403 \tabularnewline
98 & 5100 & 5056.06954136256 & 43.9304586374446 \tabularnewline
99 & 3900 & 4641.15286609441 & -741.152866094406 \tabularnewline
100 & 2700 & 3149.34455057975 & -449.344550579745 \tabularnewline
101 & 5300 & 4911.18722813348 & 388.812771866518 \tabularnewline
102 & 5100 & 4793.5908806127 & 306.409119387301 \tabularnewline
103 & 6700 & 7098.38164133232 & -398.381641332322 \tabularnewline
104 & 7700 & 7058.37832660954 & 641.621673390458 \tabularnewline
105 & 5700 & 5359.36014629908 & 340.639853700925 \tabularnewline
106 & 6400 & 6987.20708993047 & -587.207089930472 \tabularnewline
107 & 4800 & 5199.71009786023 & -399.710097860232 \tabularnewline
108 & 8300 & 8085.0487351223 & 214.9512648777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169412&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]6000[/C][C]6205.18162393162[/C][C]-205.181623931624[/C][/ROW]
[ROW][C]14[/C][C]4500[/C][C]4700.18653484721[/C][C]-200.186534847209[/C][/ROW]
[ROW][C]15[/C][C]5300[/C][C]5543.38374146668[/C][C]-243.383741466678[/C][/ROW]
[ROW][C]16[/C][C]4000[/C][C]4233.92686860528[/C][C]-233.926868605279[/C][/ROW]
[ROW][C]17[/C][C]5600[/C][C]5747.39113734889[/C][C]-147.391137348885[/C][/ROW]
[ROW][C]18[/C][C]4600[/C][C]4660.29181285404[/C][C]-60.2918128540414[/C][/ROW]
[ROW][C]19[/C][C]6100[/C][C]5827.60742437892[/C][C]272.392575621081[/C][/ROW]
[ROW][C]20[/C][C]5500[/C][C]6000.52676624762[/C][C]-500.526766247624[/C][/ROW]
[ROW][C]21[/C][C]5800[/C][C]6694.98582010772[/C][C]-894.985820107719[/C][/ROW]
[ROW][C]22[/C][C]6500[/C][C]5765.00308507862[/C][C]734.996914921378[/C][/ROW]
[ROW][C]23[/C][C]6400[/C][C]5452.75619994414[/C][C]947.243800055858[/C][/ROW]
[ROW][C]24[/C][C]7600[/C][C]6876.24757377759[/C][C]723.752426222411[/C][/ROW]
[ROW][C]25[/C][C]5500[/C][C]5607.0339578938[/C][C]-107.033957893802[/C][/ROW]
[ROW][C]26[/C][C]4600[/C][C]4110.24094600832[/C][C]489.75905399168[/C][/ROW]
[ROW][C]27[/C][C]5100[/C][C]4929.11798264558[/C][C]170.882017354417[/C][/ROW]
[ROW][C]28[/C][C]3700[/C][C]3645.12712942198[/C][C]54.872870578019[/C][/ROW]
[ROW][C]29[/C][C]5300[/C][C]5256.57187856674[/C][C]43.4281214332632[/C][/ROW]
[ROW][C]30[/C][C]4100[/C][C]4268.83199001845[/C][C]-168.831990018452[/C][/ROW]
[ROW][C]31[/C][C]5800[/C][C]5757.95201700596[/C][C]42.0479829940359[/C][/ROW]
[ROW][C]32[/C][C]5500[/C][C]5230.97888275944[/C][C]269.021117240562[/C][/ROW]
[ROW][C]33[/C][C]4900[/C][C]5590.55424857441[/C][C]-690.554248574411[/C][/ROW]
[ROW][C]34[/C][C]7000[/C][C]6187.1779373185[/C][C]812.822062681497[/C][/ROW]
[ROW][C]35[/C][C]6300[/C][C]6095.12717189337[/C][C]204.872828106634[/C][/ROW]
[ROW][C]36[/C][C]7200[/C][C]7322.95971563057[/C][C]-122.959715630571[/C][/ROW]
[ROW][C]37[/C][C]5400[/C][C]5289.86481161096[/C][C]110.135188389037[/C][/ROW]
[ROW][C]38[/C][C]5000[/C][C]4356.08054953951[/C][C]643.919450460486[/C][/ROW]
[ROW][C]39[/C][C]4500[/C][C]4895.33383949158[/C][C]-395.333839491585[/C][/ROW]
[ROW][C]40[/C][C]3700[/C][C]3506.67722339594[/C][C]193.322776604065[/C][/ROW]
[ROW][C]41[/C][C]4900[/C][C]5117.58477824287[/C][C]-217.584778242875[/C][/ROW]
[ROW][C]42[/C][C]4400[/C][C]3938.20825618032[/C][C]461.791743819679[/C][/ROW]
[ROW][C]43[/C][C]6000[/C][C]5639.56840383085[/C][C]360.431596169152[/C][/ROW]
[ROW][C]44[/C][C]5800[/C][C]5339.71662835167[/C][C]460.283371648332[/C][/ROW]
[ROW][C]45[/C][C]5000[/C][C]4834.0088881831[/C][C]165.991111816899[/C][/ROW]
[ROW][C]46[/C][C]6700[/C][C]6848.21072112326[/C][C]-148.210721123255[/C][/ROW]
[ROW][C]47[/C][C]6200[/C][C]6203.14073057057[/C][C]-3.14073057056976[/C][/ROW]
[ROW][C]48[/C][C]8000[/C][C]7141.03314152905[/C][C]858.966858470947[/C][/ROW]
[ROW][C]49[/C][C]6400[/C][C]5354.81489776577[/C][C]1045.18510223423[/C][/ROW]
[ROW][C]50[/C][C]3900[/C][C]4953.11520142444[/C][C]-1053.11520142444[/C][/ROW]
[ROW][C]51[/C][C]3900[/C][C]4535.344362286[/C][C]-635.344362285998[/C][/ROW]
[ROW][C]52[/C][C]3900[/C][C]3700.49662341759[/C][C]199.50337658241[/C][/ROW]
[ROW][C]53[/C][C]4600[/C][C]4946.79391724362[/C][C]-346.793917243618[/C][/ROW]
[ROW][C]54[/C][C]4600[/C][C]4404.68038953215[/C][C]195.319610467852[/C][/ROW]
[ROW][C]55[/C][C]6200[/C][C]6020.38273996362[/C][C]179.61726003638[/C][/ROW]
[ROW][C]56[/C][C]5700[/C][C]5819.33985079777[/C][C]-119.339850797771[/C][/ROW]
[ROW][C]57[/C][C]5100[/C][C]5040.31067624406[/C][C]59.6893237559352[/C][/ROW]
[ROW][C]58[/C][C]6400[/C][C]6766.25025213102[/C][C]-366.250252131017[/C][/ROW]
[ROW][C]59[/C][C]5900[/C][C]6252.92572917807[/C][C]-352.925729178066[/C][/ROW]
[ROW][C]60[/C][C]8500[/C][C]7978.60888934583[/C][C]521.391110654168[/C][/ROW]
[ROW][C]61[/C][C]6700[/C][C]6354.56732743833[/C][C]345.43267256167[/C][/ROW]
[ROW][C]62[/C][C]3900[/C][C]4000.80735739248[/C][C]-100.807357392485[/C][/ROW]
[ROW][C]63[/C][C]4100[/C][C]3972.79450960493[/C][C]127.205490395069[/C][/ROW]
[ROW][C]64[/C][C]3400[/C][C]3917.20316145674[/C][C]-517.203161456743[/C][/ROW]
[ROW][C]65[/C][C]4700[/C][C]4650.16701228032[/C][C]49.832987719682[/C][/ROW]
[ROW][C]66[/C][C]5400[/C][C]4611.30225617761[/C][C]788.697743822392[/C][/ROW]
[ROW][C]67[/C][C]6800[/C][C]6223.73442870586[/C][C]576.265571294136[/C][/ROW]
[ROW][C]68[/C][C]6700[/C][C]5760.35049302479[/C][C]939.649506975211[/C][/ROW]
[ROW][C]69[/C][C]5400[/C][C]5175.22266024475[/C][C]224.777339755248[/C][/ROW]
[ROW][C]70[/C][C]6300[/C][C]6531.04217827994[/C][C]-231.042178279936[/C][/ROW]
[ROW][C]71[/C][C]5600[/C][C]6053.20464127805[/C][C]-453.204641278046[/C][/ROW]
[ROW][C]72[/C][C]8000[/C][C]8604.37504314332[/C][C]-604.37504314332[/C][/ROW]
[ROW][C]73[/C][C]6100[/C][C]6818.4282301061[/C][C]-718.428230106098[/C][/ROW]
[ROW][C]74[/C][C]4900[/C][C]4044.51169654605[/C][C]855.488303453952[/C][/ROW]
[ROW][C]75[/C][C]4400[/C][C]4245.00110582851[/C][C]154.998894171489[/C][/ROW]
[ROW][C]76[/C][C]3300[/C][C]3605.93245466192[/C][C]-305.932454661922[/C][/ROW]
[ROW][C]77[/C][C]4900[/C][C]4875.00674624832[/C][C]24.9932537516788[/C][/ROW]
[ROW][C]78[/C][C]5900[/C][C]5528.11699585024[/C][C]371.883004149764[/C][/ROW]
[ROW][C]79[/C][C]6900[/C][C]6948.73917201942[/C][C]-48.7391720194246[/C][/ROW]
[ROW][C]80[/C][C]6500[/C][C]6816.24640648133[/C][C]-316.246406481328[/C][/ROW]
[ROW][C]81[/C][C]4800[/C][C]5551.29176568286[/C][C]-751.291765682865[/C][/ROW]
[ROW][C]82[/C][C]6900[/C][C]6459.46483202976[/C][C]440.535167970243[/C][/ROW]
[ROW][C]83[/C][C]5400[/C][C]5770.69464089138[/C][C]-370.694640891383[/C][/ROW]
[ROW][C]84[/C][C]8300[/C][C]8171.6359624084[/C][C]128.3640375916[/C][/ROW]
[ROW][C]85[/C][C]6900[/C][C]6282.45880898686[/C][C]617.541191013141[/C][/ROW]
[ROW][C]86[/C][C]5000[/C][C]4978.15781231195[/C][C]21.8421876880511[/C][/ROW]
[ROW][C]87[/C][C]4600[/C][C]4525.36206632086[/C][C]74.6379336791388[/C][/ROW]
[ROW][C]88[/C][C]3100[/C][C]3459.91112805968[/C][C]-359.911128059679[/C][/ROW]
[ROW][C]89[/C][C]4900[/C][C]5031.7729151798[/C][C]-131.772915179796[/C][/ROW]
[ROW][C]90[/C][C]4700[/C][C]5999.97228840143[/C][C]-1299.97228840143[/C][/ROW]
[ROW][C]91[/C][C]7100[/C][C]6999.16905375072[/C][C]100.830946249278[/C][/ROW]
[ROW][C]92[/C][C]7100[/C][C]6604.54766683006[/C][C]495.452333169943[/C][/ROW]
[ROW][C]93[/C][C]5400[/C][C]4936.78473241479[/C][C]463.215267585211[/C][/ROW]
[ROW][C]94[/C][C]7000[/C][C]6955.73397462049[/C][C]44.266025379512[/C][/ROW]
[ROW][C]95[/C][C]5200[/C][C]5514.02086261856[/C][C]-314.02086261856[/C][/ROW]
[ROW][C]96[/C][C]8100[/C][C]8373.72146662011[/C][C]-273.721466620114[/C][/ROW]
[ROW][C]97[/C][C]6900[/C][C]6926.22870739734[/C][C]-26.2287073973403[/C][/ROW]
[ROW][C]98[/C][C]5100[/C][C]5056.06954136256[/C][C]43.9304586374446[/C][/ROW]
[ROW][C]99[/C][C]3900[/C][C]4641.15286609441[/C][C]-741.152866094406[/C][/ROW]
[ROW][C]100[/C][C]2700[/C][C]3149.34455057975[/C][C]-449.344550579745[/C][/ROW]
[ROW][C]101[/C][C]5300[/C][C]4911.18722813348[/C][C]388.812771866518[/C][/ROW]
[ROW][C]102[/C][C]5100[/C][C]4793.5908806127[/C][C]306.409119387301[/C][/ROW]
[ROW][C]103[/C][C]6700[/C][C]7098.38164133232[/C][C]-398.381641332322[/C][/ROW]
[ROW][C]104[/C][C]7700[/C][C]7058.37832660954[/C][C]641.621673390458[/C][/ROW]
[ROW][C]105[/C][C]5700[/C][C]5359.36014629908[/C][C]340.639853700925[/C][/ROW]
[ROW][C]106[/C][C]6400[/C][C]6987.20708993047[/C][C]-587.207089930472[/C][/ROW]
[ROW][C]107[/C][C]4800[/C][C]5199.71009786023[/C][C]-399.710097860232[/C][/ROW]
[ROW][C]108[/C][C]8300[/C][C]8085.0487351223[/C][C]214.9512648777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169412&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169412&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
1360006205.18162393162-205.181623931624
1445004700.18653484721-200.186534847209
1553005543.38374146668-243.383741466678
1640004233.92686860528-233.926868605279
1756005747.39113734889-147.391137348885
1846004660.29181285404-60.2918128540414
1961005827.60742437892272.392575621081
2055006000.52676624762-500.526766247624
2158006694.98582010772-894.985820107719
2265005765.00308507862734.996914921378
2364005452.75619994414947.243800055858
2476006876.24757377759723.752426222411
2555005607.0339578938-107.033957893802
2646004110.24094600832489.75905399168
2751004929.11798264558170.882017354417
2837003645.1271294219854.872870578019
2953005256.5718785667443.4281214332632
3041004268.83199001845-168.831990018452
3158005757.9520170059642.0479829940359
3255005230.97888275944269.021117240562
3349005590.55424857441-690.554248574411
3470006187.1779373185812.822062681497
3563006095.12717189337204.872828106634
3672007322.95971563057-122.959715630571
3754005289.86481161096110.135188389037
3850004356.08054953951643.919450460486
3945004895.33383949158-395.333839491585
4037003506.67722339594193.322776604065
4149005117.58477824287-217.584778242875
4244003938.20825618032461.791743819679
4360005639.56840383085360.431596169152
4458005339.71662835167460.283371648332
4550004834.0088881831165.991111816899
4667006848.21072112326-148.210721123255
4762006203.14073057057-3.14073057056976
4880007141.03314152905858.966858470947
4964005354.814897765771045.18510223423
5039004953.11520142444-1053.11520142444
5139004535.344362286-635.344362285998
5239003700.49662341759199.50337658241
5346004946.79391724362-346.793917243618
5446004404.68038953215195.319610467852
5562006020.38273996362179.61726003638
5657005819.33985079777-119.339850797771
5751005040.3106762440659.6893237559352
5864006766.25025213102-366.250252131017
5959006252.92572917807-352.925729178066
6085007978.60888934583521.391110654168
6167006354.56732743833345.43267256167
6239004000.80735739248-100.807357392485
6341003972.79450960493127.205490395069
6434003917.20316145674-517.203161456743
6547004650.1670122803249.832987719682
6654004611.30225617761788.697743822392
6768006223.73442870586576.265571294136
6867005760.35049302479939.649506975211
6954005175.22266024475224.777339755248
7063006531.04217827994-231.042178279936
7156006053.20464127805-453.204641278046
7280008604.37504314332-604.37504314332
7361006818.4282301061-718.428230106098
7449004044.51169654605855.488303453952
7544004245.00110582851154.998894171489
7633003605.93245466192-305.932454661922
7749004875.0067462483224.9932537516788
7859005528.11699585024371.883004149764
7969006948.73917201942-48.7391720194246
8065006816.24640648133-316.246406481328
8148005551.29176568286-751.291765682865
8269006459.46483202976440.535167970243
8354005770.69464089138-370.694640891383
8483008171.6359624084128.3640375916
8569006282.45880898686617.541191013141
8650004978.1578123119521.8421876880511
8746004525.3620663208674.6379336791388
8831003459.91112805968-359.911128059679
8949005031.7729151798-131.772915179796
9047005999.97228840143-1299.97228840143
9171006999.16905375072100.830946249278
9271006604.54766683006495.452333169943
9354004936.78473241479463.215267585211
9470006955.7339746204944.266025379512
9552005514.02086261856-314.02086261856
9681008373.72146662011-273.721466620114
9769006926.22870739734-26.2287073973403
9851005056.0695413625643.9304586374446
9939004641.15286609441-741.152866094406
10027003149.34455057975-449.344550579745
10153004911.18722813348388.812771866518
10251004793.5908806127306.409119387301
10367007098.38164133232-398.381641332322
10477007058.37832660954641.621673390458
10557005359.36014629908340.639853700925
10664006987.20708993047-587.207089930472
10748005199.71009786023-399.710097860232
10883008085.0487351223214.9512648777







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1096863.896767829995947.270110227417780.52342543257
1105052.686288051364135.902406589245969.47016951348
1113907.84834515592990.710808555644824.98588175616
1122692.240725765451774.47480541023610.0066461207
1135235.016757740824316.269848182886153.76366729877
1145039.008582119164118.85088544325959.16627879512
1156689.996177297825767.921711055947612.07064353971
1167613.637170954856689.065153536768538.20918837294
1175627.430450910714699.707110154186555.15379166724
1186390.279833851345458.680674335037321.87899336765
1194779.224319269183842.956871146475715.49176739189
1208236.455599658457294.662657375949178.24854194096

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 6863.89676782999 & 5947.27011022741 & 7780.52342543257 \tabularnewline
110 & 5052.68628805136 & 4135.90240658924 & 5969.47016951348 \tabularnewline
111 & 3907.8483451559 & 2990.71080855564 & 4824.98588175616 \tabularnewline
112 & 2692.24072576545 & 1774.4748054102 & 3610.0066461207 \tabularnewline
113 & 5235.01675774082 & 4316.26984818288 & 6153.76366729877 \tabularnewline
114 & 5039.00858211916 & 4118.8508854432 & 5959.16627879512 \tabularnewline
115 & 6689.99617729782 & 5767.92171105594 & 7612.07064353971 \tabularnewline
116 & 7613.63717095485 & 6689.06515353676 & 8538.20918837294 \tabularnewline
117 & 5627.43045091071 & 4699.70711015418 & 6555.15379166724 \tabularnewline
118 & 6390.27983385134 & 5458.68067433503 & 7321.87899336765 \tabularnewline
119 & 4779.22431926918 & 3842.95687114647 & 5715.49176739189 \tabularnewline
120 & 8236.45559965845 & 7294.66265737594 & 9178.24854194096 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169412&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]109[/C][C]6863.89676782999[/C][C]5947.27011022741[/C][C]7780.52342543257[/C][/ROW]
[ROW][C]110[/C][C]5052.68628805136[/C][C]4135.90240658924[/C][C]5969.47016951348[/C][/ROW]
[ROW][C]111[/C][C]3907.8483451559[/C][C]2990.71080855564[/C][C]4824.98588175616[/C][/ROW]
[ROW][C]112[/C][C]2692.24072576545[/C][C]1774.4748054102[/C][C]3610.0066461207[/C][/ROW]
[ROW][C]113[/C][C]5235.01675774082[/C][C]4316.26984818288[/C][C]6153.76366729877[/C][/ROW]
[ROW][C]114[/C][C]5039.00858211916[/C][C]4118.8508854432[/C][C]5959.16627879512[/C][/ROW]
[ROW][C]115[/C][C]6689.99617729782[/C][C]5767.92171105594[/C][C]7612.07064353971[/C][/ROW]
[ROW][C]116[/C][C]7613.63717095485[/C][C]6689.06515353676[/C][C]8538.20918837294[/C][/ROW]
[ROW][C]117[/C][C]5627.43045091071[/C][C]4699.70711015418[/C][C]6555.15379166724[/C][/ROW]
[ROW][C]118[/C][C]6390.27983385134[/C][C]5458.68067433503[/C][C]7321.87899336765[/C][/ROW]
[ROW][C]119[/C][C]4779.22431926918[/C][C]3842.95687114647[/C][C]5715.49176739189[/C][/ROW]
[ROW][C]120[/C][C]8236.45559965845[/C][C]7294.66265737594[/C][C]9178.24854194096[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169412&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169412&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
1096863.896767829995947.270110227417780.52342543257
1105052.686288051364135.902406589245969.47016951348
1113907.84834515592990.710808555644824.98588175616
1122692.240725765451774.47480541023610.0066461207
1135235.016757740824316.269848182886153.76366729877
1145039.008582119164118.85088544325959.16627879512
1156689.996177297825767.921711055947612.07064353971
1167613.637170954856689.065153536768538.20918837294
1175627.430450910714699.707110154186555.15379166724
1186390.279833851345458.680674335037321.87899336765
1194779.224319269183842.956871146475715.49176739189
1208236.455599658457294.662657375949178.24854194096



Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')