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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 21:23:42 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/16/t1502911452ejkgkos99rzfdjk.htm/, Retrieved Sat, 11 May 2024 14:48:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307498, Retrieved Sat, 11 May 2024 14:48:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-16 19:23:42] [888a13d027786d499af5f5e6685ea85b] [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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307498&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307498&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307498&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00926118605789056
beta1
gamma0.929768627341417

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605789056 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627341417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307498&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]0.00926118605789056[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627341417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307498&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307498&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
alpha0.00926118605789056
beta1
gamma0.929768627341417







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1360006205.18162393163-205.18162393163
1445004700.18653484721-200.186534847211
1553005543.38374146667-243.383741466673
1640004233.92686860526-233.926868605263
1756005747.39113734886-147.391137348855
1846004660.291812854-60.2918128539986
1961005827.60742437886272.392575621137
2055006000.52676624757-500.526766247567
2158006694.98582010764-894.985820107643
2265005765.00308507851734.996914921488
2364005452.75619994403947.24380005597
2476006876.24757377749723.75242622251
2555005607.03395789381-107.033957893806
2646004110.24094600834489.759053991664
2751004929.11798264565170.882017354354
2837003645.1271294220754.8728705779286
2953005256.5718785668243.4281214331795
3041004268.83199001853-168.831990018531
3158005757.9520170059242.047982994075
3255005230.97888275975269.021117240254
3349005590.55424857492-690.554248574922
3470006187.17793731835812.822062681651
3563006095.12717189315204.872828106847
3672007322.95971563047-122.959715630466
3754005289.86481161122110.135188388784
3850004356.08054953953643.919450460473
3945004895.33383949175-395.333839491751
4037003506.67722339615193.322776603851
4149005117.5847782431-217.584778243098
4244003938.20825618063461.791743819371
4360005639.56840383107360.431596168932
4458005339.71662835183460.28337164817
4550004834.0088881837165.991111816303
4667006848.2107211232-148.210721123196
4762006203.14073057076-3.1407305707562
4880007141.03314152938858.966858470617
4964005354.814897766051045.18510223395
5039004953.11520142451-1053.11520142451
5139004535.3443622865-635.344362286495
5239003700.49662341783199.50337658217
5346004946.79391724402-346.793917244025
5446004404.68038953226195.319610467738
5562006020.38273996376179.617260036244
5657005819.33985079785-119.339850797845
5751005040.3106762442759.6893237557288
5864006766.25025213129-366.250252131291
5959006252.92572917827-352.925729178269
6085007978.60888934565521.391110654349
6167006354.56732743804345.432672561961
6239004000.80735739303-100.807357393028
6341003972.79450960532127.205490394684
6434003917.20316145675-517.203161456755
6547004650.1670122805549.832987719451
6654004611.30225617758788.697743822418
6768006223.73442870585576.265571294149
6867005760.35049302491939.64950697509
6954005175.22266024484224.777339755162
7063006531.04217828023-231.042178280232
7156006053.20464127835-453.204641278354
7280008604.37504314325-604.375043143245
7361006818.42823010608-718.428230106078
7449004044.51169654625855.488303453745
7544004245.00110582863154.998894171374
7633003605.93245466229-305.93245466229
7749004875.0067462484724.9932537515297
7859005528.11699585006371.88300414994
7969006948.73917201934-48.7391720193355
8065006816.24640648108-316.246406481082
8148005551.29176568289-751.291765682886
8269006459.46483202994440.535167970055
8354005770.69464089165-370.694640891651
8483008171.63596240868128.364037591316
8569006282.45880898719617.541191012812
8650004978.1578123116421.8421876883558
8746004525.3620663208374.6379336791679
8831003459.91112805986-359.91112805986
8949005031.77291517981-131.772915179815
9047005999.97228840127-1299.97228840127
9171006999.1690537507100.830946249302
9271006604.54766683011495.452333169893
9354004936.78473241503463.215267584968
9470006955.7339746202544.266025379753
9552005514.02086261866-314.020862618661
9681008373.72146662001-273.721466620007
9769006926.22870739702-26.228707397021
9851005056.0695413624343.930458637572
9939004641.15286609427-741.152866094269
10027003149.34455057978-449.344550579779
10153004911.18722813339388.812771866611
10251004793.59088061308306.409119386918
10367007098.38164133215-398.381641332146
10477007058.3783266092641.621673390798
10557005359.36014629878340.639853701223
10664006987.20708993033-587.207089930328
10748005199.71009786026-399.710097860258
10883008085.04873512229214.951264877708

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6000 & 6205.18162393163 & -205.18162393163 \tabularnewline
14 & 4500 & 4700.18653484721 & -200.186534847211 \tabularnewline
15 & 5300 & 5543.38374146667 & -243.383741466673 \tabularnewline
16 & 4000 & 4233.92686860526 & -233.926868605263 \tabularnewline
17 & 5600 & 5747.39113734886 & -147.391137348855 \tabularnewline
18 & 4600 & 4660.291812854 & -60.2918128539986 \tabularnewline
19 & 6100 & 5827.60742437886 & 272.392575621137 \tabularnewline
20 & 5500 & 6000.52676624757 & -500.526766247567 \tabularnewline
21 & 5800 & 6694.98582010764 & -894.985820107643 \tabularnewline
22 & 6500 & 5765.00308507851 & 734.996914921488 \tabularnewline
23 & 6400 & 5452.75619994403 & 947.24380005597 \tabularnewline
24 & 7600 & 6876.24757377749 & 723.75242622251 \tabularnewline
25 & 5500 & 5607.03395789381 & -107.033957893806 \tabularnewline
26 & 4600 & 4110.24094600834 & 489.759053991664 \tabularnewline
27 & 5100 & 4929.11798264565 & 170.882017354354 \tabularnewline
28 & 3700 & 3645.12712942207 & 54.8728705779286 \tabularnewline
29 & 5300 & 5256.57187856682 & 43.4281214331795 \tabularnewline
30 & 4100 & 4268.83199001853 & -168.831990018531 \tabularnewline
31 & 5800 & 5757.95201700592 & 42.047982994075 \tabularnewline
32 & 5500 & 5230.97888275975 & 269.021117240254 \tabularnewline
33 & 4900 & 5590.55424857492 & -690.554248574922 \tabularnewline
34 & 7000 & 6187.17793731835 & 812.822062681651 \tabularnewline
35 & 6300 & 6095.12717189315 & 204.872828106847 \tabularnewline
36 & 7200 & 7322.95971563047 & -122.959715630466 \tabularnewline
37 & 5400 & 5289.86481161122 & 110.135188388784 \tabularnewline
38 & 5000 & 4356.08054953953 & 643.919450460473 \tabularnewline
39 & 4500 & 4895.33383949175 & -395.333839491751 \tabularnewline
40 & 3700 & 3506.67722339615 & 193.322776603851 \tabularnewline
41 & 4900 & 5117.5847782431 & -217.584778243098 \tabularnewline
42 & 4400 & 3938.20825618063 & 461.791743819371 \tabularnewline
43 & 6000 & 5639.56840383107 & 360.431596168932 \tabularnewline
44 & 5800 & 5339.71662835183 & 460.28337164817 \tabularnewline
45 & 5000 & 4834.0088881837 & 165.991111816303 \tabularnewline
46 & 6700 & 6848.2107211232 & -148.210721123196 \tabularnewline
47 & 6200 & 6203.14073057076 & -3.1407305707562 \tabularnewline
48 & 8000 & 7141.03314152938 & 858.966858470617 \tabularnewline
49 & 6400 & 5354.81489776605 & 1045.18510223395 \tabularnewline
50 & 3900 & 4953.11520142451 & -1053.11520142451 \tabularnewline
51 & 3900 & 4535.3443622865 & -635.344362286495 \tabularnewline
52 & 3900 & 3700.49662341783 & 199.50337658217 \tabularnewline
53 & 4600 & 4946.79391724402 & -346.793917244025 \tabularnewline
54 & 4600 & 4404.68038953226 & 195.319610467738 \tabularnewline
55 & 6200 & 6020.38273996376 & 179.617260036244 \tabularnewline
56 & 5700 & 5819.33985079785 & -119.339850797845 \tabularnewline
57 & 5100 & 5040.31067624427 & 59.6893237557288 \tabularnewline
58 & 6400 & 6766.25025213129 & -366.250252131291 \tabularnewline
59 & 5900 & 6252.92572917827 & -352.925729178269 \tabularnewline
60 & 8500 & 7978.60888934565 & 521.391110654349 \tabularnewline
61 & 6700 & 6354.56732743804 & 345.432672561961 \tabularnewline
62 & 3900 & 4000.80735739303 & -100.807357393028 \tabularnewline
63 & 4100 & 3972.79450960532 & 127.205490394684 \tabularnewline
64 & 3400 & 3917.20316145675 & -517.203161456755 \tabularnewline
65 & 4700 & 4650.16701228055 & 49.832987719451 \tabularnewline
66 & 5400 & 4611.30225617758 & 788.697743822418 \tabularnewline
67 & 6800 & 6223.73442870585 & 576.265571294149 \tabularnewline
68 & 6700 & 5760.35049302491 & 939.64950697509 \tabularnewline
69 & 5400 & 5175.22266024484 & 224.777339755162 \tabularnewline
70 & 6300 & 6531.04217828023 & -231.042178280232 \tabularnewline
71 & 5600 & 6053.20464127835 & -453.204641278354 \tabularnewline
72 & 8000 & 8604.37504314325 & -604.375043143245 \tabularnewline
73 & 6100 & 6818.42823010608 & -718.428230106078 \tabularnewline
74 & 4900 & 4044.51169654625 & 855.488303453745 \tabularnewline
75 & 4400 & 4245.00110582863 & 154.998894171374 \tabularnewline
76 & 3300 & 3605.93245466229 & -305.93245466229 \tabularnewline
77 & 4900 & 4875.00674624847 & 24.9932537515297 \tabularnewline
78 & 5900 & 5528.11699585006 & 371.88300414994 \tabularnewline
79 & 6900 & 6948.73917201934 & -48.7391720193355 \tabularnewline
80 & 6500 & 6816.24640648108 & -316.246406481082 \tabularnewline
81 & 4800 & 5551.29176568289 & -751.291765682886 \tabularnewline
82 & 6900 & 6459.46483202994 & 440.535167970055 \tabularnewline
83 & 5400 & 5770.69464089165 & -370.694640891651 \tabularnewline
84 & 8300 & 8171.63596240868 & 128.364037591316 \tabularnewline
85 & 6900 & 6282.45880898719 & 617.541191012812 \tabularnewline
86 & 5000 & 4978.15781231164 & 21.8421876883558 \tabularnewline
87 & 4600 & 4525.36206632083 & 74.6379336791679 \tabularnewline
88 & 3100 & 3459.91112805986 & -359.91112805986 \tabularnewline
89 & 4900 & 5031.77291517981 & -131.772915179815 \tabularnewline
90 & 4700 & 5999.97228840127 & -1299.97228840127 \tabularnewline
91 & 7100 & 6999.1690537507 & 100.830946249302 \tabularnewline
92 & 7100 & 6604.54766683011 & 495.452333169893 \tabularnewline
93 & 5400 & 4936.78473241503 & 463.215267584968 \tabularnewline
94 & 7000 & 6955.73397462025 & 44.266025379753 \tabularnewline
95 & 5200 & 5514.02086261866 & -314.020862618661 \tabularnewline
96 & 8100 & 8373.72146662001 & -273.721466620007 \tabularnewline
97 & 6900 & 6926.22870739702 & -26.228707397021 \tabularnewline
98 & 5100 & 5056.06954136243 & 43.930458637572 \tabularnewline
99 & 3900 & 4641.15286609427 & -741.152866094269 \tabularnewline
100 & 2700 & 3149.34455057978 & -449.344550579779 \tabularnewline
101 & 5300 & 4911.18722813339 & 388.812771866611 \tabularnewline
102 & 5100 & 4793.59088061308 & 306.409119386918 \tabularnewline
103 & 6700 & 7098.38164133215 & -398.381641332146 \tabularnewline
104 & 7700 & 7058.3783266092 & 641.621673390798 \tabularnewline
105 & 5700 & 5359.36014629878 & 340.639853701223 \tabularnewline
106 & 6400 & 6987.20708993033 & -587.207089930328 \tabularnewline
107 & 4800 & 5199.71009786026 & -399.710097860258 \tabularnewline
108 & 8300 & 8085.04873512229 & 214.951264877708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307498&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]6205.18162393163[/C][C]-205.18162393163[/C][/ROW]
[ROW][C]14[/C][C]4500[/C][C]4700.18653484721[/C][C]-200.186534847211[/C][/ROW]
[ROW][C]15[/C][C]5300[/C][C]5543.38374146667[/C][C]-243.383741466673[/C][/ROW]
[ROW][C]16[/C][C]4000[/C][C]4233.92686860526[/C][C]-233.926868605263[/C][/ROW]
[ROW][C]17[/C][C]5600[/C][C]5747.39113734886[/C][C]-147.391137348855[/C][/ROW]
[ROW][C]18[/C][C]4600[/C][C]4660.291812854[/C][C]-60.2918128539986[/C][/ROW]
[ROW][C]19[/C][C]6100[/C][C]5827.60742437886[/C][C]272.392575621137[/C][/ROW]
[ROW][C]20[/C][C]5500[/C][C]6000.52676624757[/C][C]-500.526766247567[/C][/ROW]
[ROW][C]21[/C][C]5800[/C][C]6694.98582010764[/C][C]-894.985820107643[/C][/ROW]
[ROW][C]22[/C][C]6500[/C][C]5765.00308507851[/C][C]734.996914921488[/C][/ROW]
[ROW][C]23[/C][C]6400[/C][C]5452.75619994403[/C][C]947.24380005597[/C][/ROW]
[ROW][C]24[/C][C]7600[/C][C]6876.24757377749[/C][C]723.75242622251[/C][/ROW]
[ROW][C]25[/C][C]5500[/C][C]5607.03395789381[/C][C]-107.033957893806[/C][/ROW]
[ROW][C]26[/C][C]4600[/C][C]4110.24094600834[/C][C]489.759053991664[/C][/ROW]
[ROW][C]27[/C][C]5100[/C][C]4929.11798264565[/C][C]170.882017354354[/C][/ROW]
[ROW][C]28[/C][C]3700[/C][C]3645.12712942207[/C][C]54.8728705779286[/C][/ROW]
[ROW][C]29[/C][C]5300[/C][C]5256.57187856682[/C][C]43.4281214331795[/C][/ROW]
[ROW][C]30[/C][C]4100[/C][C]4268.83199001853[/C][C]-168.831990018531[/C][/ROW]
[ROW][C]31[/C][C]5800[/C][C]5757.95201700592[/C][C]42.047982994075[/C][/ROW]
[ROW][C]32[/C][C]5500[/C][C]5230.97888275975[/C][C]269.021117240254[/C][/ROW]
[ROW][C]33[/C][C]4900[/C][C]5590.55424857492[/C][C]-690.554248574922[/C][/ROW]
[ROW][C]34[/C][C]7000[/C][C]6187.17793731835[/C][C]812.822062681651[/C][/ROW]
[ROW][C]35[/C][C]6300[/C][C]6095.12717189315[/C][C]204.872828106847[/C][/ROW]
[ROW][C]36[/C][C]7200[/C][C]7322.95971563047[/C][C]-122.959715630466[/C][/ROW]
[ROW][C]37[/C][C]5400[/C][C]5289.86481161122[/C][C]110.135188388784[/C][/ROW]
[ROW][C]38[/C][C]5000[/C][C]4356.08054953953[/C][C]643.919450460473[/C][/ROW]
[ROW][C]39[/C][C]4500[/C][C]4895.33383949175[/C][C]-395.333839491751[/C][/ROW]
[ROW][C]40[/C][C]3700[/C][C]3506.67722339615[/C][C]193.322776603851[/C][/ROW]
[ROW][C]41[/C][C]4900[/C][C]5117.5847782431[/C][C]-217.584778243098[/C][/ROW]
[ROW][C]42[/C][C]4400[/C][C]3938.20825618063[/C][C]461.791743819371[/C][/ROW]
[ROW][C]43[/C][C]6000[/C][C]5639.56840383107[/C][C]360.431596168932[/C][/ROW]
[ROW][C]44[/C][C]5800[/C][C]5339.71662835183[/C][C]460.28337164817[/C][/ROW]
[ROW][C]45[/C][C]5000[/C][C]4834.0088881837[/C][C]165.991111816303[/C][/ROW]
[ROW][C]46[/C][C]6700[/C][C]6848.2107211232[/C][C]-148.210721123196[/C][/ROW]
[ROW][C]47[/C][C]6200[/C][C]6203.14073057076[/C][C]-3.1407305707562[/C][/ROW]
[ROW][C]48[/C][C]8000[/C][C]7141.03314152938[/C][C]858.966858470617[/C][/ROW]
[ROW][C]49[/C][C]6400[/C][C]5354.81489776605[/C][C]1045.18510223395[/C][/ROW]
[ROW][C]50[/C][C]3900[/C][C]4953.11520142451[/C][C]-1053.11520142451[/C][/ROW]
[ROW][C]51[/C][C]3900[/C][C]4535.3443622865[/C][C]-635.344362286495[/C][/ROW]
[ROW][C]52[/C][C]3900[/C][C]3700.49662341783[/C][C]199.50337658217[/C][/ROW]
[ROW][C]53[/C][C]4600[/C][C]4946.79391724402[/C][C]-346.793917244025[/C][/ROW]
[ROW][C]54[/C][C]4600[/C][C]4404.68038953226[/C][C]195.319610467738[/C][/ROW]
[ROW][C]55[/C][C]6200[/C][C]6020.38273996376[/C][C]179.617260036244[/C][/ROW]
[ROW][C]56[/C][C]5700[/C][C]5819.33985079785[/C][C]-119.339850797845[/C][/ROW]
[ROW][C]57[/C][C]5100[/C][C]5040.31067624427[/C][C]59.6893237557288[/C][/ROW]
[ROW][C]58[/C][C]6400[/C][C]6766.25025213129[/C][C]-366.250252131291[/C][/ROW]
[ROW][C]59[/C][C]5900[/C][C]6252.92572917827[/C][C]-352.925729178269[/C][/ROW]
[ROW][C]60[/C][C]8500[/C][C]7978.60888934565[/C][C]521.391110654349[/C][/ROW]
[ROW][C]61[/C][C]6700[/C][C]6354.56732743804[/C][C]345.432672561961[/C][/ROW]
[ROW][C]62[/C][C]3900[/C][C]4000.80735739303[/C][C]-100.807357393028[/C][/ROW]
[ROW][C]63[/C][C]4100[/C][C]3972.79450960532[/C][C]127.205490394684[/C][/ROW]
[ROW][C]64[/C][C]3400[/C][C]3917.20316145675[/C][C]-517.203161456755[/C][/ROW]
[ROW][C]65[/C][C]4700[/C][C]4650.16701228055[/C][C]49.832987719451[/C][/ROW]
[ROW][C]66[/C][C]5400[/C][C]4611.30225617758[/C][C]788.697743822418[/C][/ROW]
[ROW][C]67[/C][C]6800[/C][C]6223.73442870585[/C][C]576.265571294149[/C][/ROW]
[ROW][C]68[/C][C]6700[/C][C]5760.35049302491[/C][C]939.64950697509[/C][/ROW]
[ROW][C]69[/C][C]5400[/C][C]5175.22266024484[/C][C]224.777339755162[/C][/ROW]
[ROW][C]70[/C][C]6300[/C][C]6531.04217828023[/C][C]-231.042178280232[/C][/ROW]
[ROW][C]71[/C][C]5600[/C][C]6053.20464127835[/C][C]-453.204641278354[/C][/ROW]
[ROW][C]72[/C][C]8000[/C][C]8604.37504314325[/C][C]-604.375043143245[/C][/ROW]
[ROW][C]73[/C][C]6100[/C][C]6818.42823010608[/C][C]-718.428230106078[/C][/ROW]
[ROW][C]74[/C][C]4900[/C][C]4044.51169654625[/C][C]855.488303453745[/C][/ROW]
[ROW][C]75[/C][C]4400[/C][C]4245.00110582863[/C][C]154.998894171374[/C][/ROW]
[ROW][C]76[/C][C]3300[/C][C]3605.93245466229[/C][C]-305.93245466229[/C][/ROW]
[ROW][C]77[/C][C]4900[/C][C]4875.00674624847[/C][C]24.9932537515297[/C][/ROW]
[ROW][C]78[/C][C]5900[/C][C]5528.11699585006[/C][C]371.88300414994[/C][/ROW]
[ROW][C]79[/C][C]6900[/C][C]6948.73917201934[/C][C]-48.7391720193355[/C][/ROW]
[ROW][C]80[/C][C]6500[/C][C]6816.24640648108[/C][C]-316.246406481082[/C][/ROW]
[ROW][C]81[/C][C]4800[/C][C]5551.29176568289[/C][C]-751.291765682886[/C][/ROW]
[ROW][C]82[/C][C]6900[/C][C]6459.46483202994[/C][C]440.535167970055[/C][/ROW]
[ROW][C]83[/C][C]5400[/C][C]5770.69464089165[/C][C]-370.694640891651[/C][/ROW]
[ROW][C]84[/C][C]8300[/C][C]8171.63596240868[/C][C]128.364037591316[/C][/ROW]
[ROW][C]85[/C][C]6900[/C][C]6282.45880898719[/C][C]617.541191012812[/C][/ROW]
[ROW][C]86[/C][C]5000[/C][C]4978.15781231164[/C][C]21.8421876883558[/C][/ROW]
[ROW][C]87[/C][C]4600[/C][C]4525.36206632083[/C][C]74.6379336791679[/C][/ROW]
[ROW][C]88[/C][C]3100[/C][C]3459.91112805986[/C][C]-359.91112805986[/C][/ROW]
[ROW][C]89[/C][C]4900[/C][C]5031.77291517981[/C][C]-131.772915179815[/C][/ROW]
[ROW][C]90[/C][C]4700[/C][C]5999.97228840127[/C][C]-1299.97228840127[/C][/ROW]
[ROW][C]91[/C][C]7100[/C][C]6999.1690537507[/C][C]100.830946249302[/C][/ROW]
[ROW][C]92[/C][C]7100[/C][C]6604.54766683011[/C][C]495.452333169893[/C][/ROW]
[ROW][C]93[/C][C]5400[/C][C]4936.78473241503[/C][C]463.215267584968[/C][/ROW]
[ROW][C]94[/C][C]7000[/C][C]6955.73397462025[/C][C]44.266025379753[/C][/ROW]
[ROW][C]95[/C][C]5200[/C][C]5514.02086261866[/C][C]-314.020862618661[/C][/ROW]
[ROW][C]96[/C][C]8100[/C][C]8373.72146662001[/C][C]-273.721466620007[/C][/ROW]
[ROW][C]97[/C][C]6900[/C][C]6926.22870739702[/C][C]-26.228707397021[/C][/ROW]
[ROW][C]98[/C][C]5100[/C][C]5056.06954136243[/C][C]43.930458637572[/C][/ROW]
[ROW][C]99[/C][C]3900[/C][C]4641.15286609427[/C][C]-741.152866094269[/C][/ROW]
[ROW][C]100[/C][C]2700[/C][C]3149.34455057978[/C][C]-449.344550579779[/C][/ROW]
[ROW][C]101[/C][C]5300[/C][C]4911.18722813339[/C][C]388.812771866611[/C][/ROW]
[ROW][C]102[/C][C]5100[/C][C]4793.59088061308[/C][C]306.409119386918[/C][/ROW]
[ROW][C]103[/C][C]6700[/C][C]7098.38164133215[/C][C]-398.381641332146[/C][/ROW]
[ROW][C]104[/C][C]7700[/C][C]7058.3783266092[/C][C]641.621673390798[/C][/ROW]
[ROW][C]105[/C][C]5700[/C][C]5359.36014629878[/C][C]340.639853701223[/C][/ROW]
[ROW][C]106[/C][C]6400[/C][C]6987.20708993033[/C][C]-587.207089930328[/C][/ROW]
[ROW][C]107[/C][C]4800[/C][C]5199.71009786026[/C][C]-399.710097860258[/C][/ROW]
[ROW][C]108[/C][C]8300[/C][C]8085.04873512229[/C][C]214.951264877708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307498&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307498&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
1360006205.18162393163-205.18162393163
1445004700.18653484721-200.186534847211
1553005543.38374146667-243.383741466673
1640004233.92686860526-233.926868605263
1756005747.39113734886-147.391137348855
1846004660.291812854-60.2918128539986
1961005827.60742437886272.392575621137
2055006000.52676624757-500.526766247567
2158006694.98582010764-894.985820107643
2265005765.00308507851734.996914921488
2364005452.75619994403947.24380005597
2476006876.24757377749723.75242622251
2555005607.03395789381-107.033957893806
2646004110.24094600834489.759053991664
2751004929.11798264565170.882017354354
2837003645.1271294220754.8728705779286
2953005256.5718785668243.4281214331795
3041004268.83199001853-168.831990018531
3158005757.9520170059242.047982994075
3255005230.97888275975269.021117240254
3349005590.55424857492-690.554248574922
3470006187.17793731835812.822062681651
3563006095.12717189315204.872828106847
3672007322.95971563047-122.959715630466
3754005289.86481161122110.135188388784
3850004356.08054953953643.919450460473
3945004895.33383949175-395.333839491751
4037003506.67722339615193.322776603851
4149005117.5847782431-217.584778243098
4244003938.20825618063461.791743819371
4360005639.56840383107360.431596168932
4458005339.71662835183460.28337164817
4550004834.0088881837165.991111816303
4667006848.2107211232-148.210721123196
4762006203.14073057076-3.1407305707562
4880007141.03314152938858.966858470617
4964005354.814897766051045.18510223395
5039004953.11520142451-1053.11520142451
5139004535.3443622865-635.344362286495
5239003700.49662341783199.50337658217
5346004946.79391724402-346.793917244025
5446004404.68038953226195.319610467738
5562006020.38273996376179.617260036244
5657005819.33985079785-119.339850797845
5751005040.3106762442759.6893237557288
5864006766.25025213129-366.250252131291
5959006252.92572917827-352.925729178269
6085007978.60888934565521.391110654349
6167006354.56732743804345.432672561961
6239004000.80735739303-100.807357393028
6341003972.79450960532127.205490394684
6434003917.20316145675-517.203161456755
6547004650.1670122805549.832987719451
6654004611.30225617758788.697743822418
6768006223.73442870585576.265571294149
6867005760.35049302491939.64950697509
6954005175.22266024484224.777339755162
7063006531.04217828023-231.042178280232
7156006053.20464127835-453.204641278354
7280008604.37504314325-604.375043143245
7361006818.42823010608-718.428230106078
7449004044.51169654625855.488303453745
7544004245.00110582863154.998894171374
7633003605.93245466229-305.93245466229
7749004875.0067462484724.9932537515297
7859005528.11699585006371.88300414994
7969006948.73917201934-48.7391720193355
8065006816.24640648108-316.246406481082
8148005551.29176568289-751.291765682886
8269006459.46483202994440.535167970055
8354005770.69464089165-370.694640891651
8483008171.63596240868128.364037591316
8569006282.45880898719617.541191012812
8650004978.1578123116421.8421876883558
8746004525.3620663208374.6379336791679
8831003459.91112805986-359.91112805986
8949005031.77291517981-131.772915179815
9047005999.97228840127-1299.97228840127
9171006999.1690537507100.830946249302
9271006604.54766683011495.452333169893
9354004936.78473241503463.215267584968
9470006955.7339746202544.266025379753
9552005514.02086261866-314.020862618661
9681008373.72146662001-273.721466620007
9769006926.22870739702-26.228707397021
9851005056.0695413624343.930458637572
9939004641.15286609427-741.152866094269
10027003149.34455057978-449.344550579779
10153004911.18722813339388.812771866611
10251004793.59088061308306.409119386918
10367007098.38164133215-398.381641332146
10477007058.3783266092641.621673390798
10557005359.36014629878340.639853701223
10664006987.20708993033-587.207089930328
10748005199.71009786026-399.710097860258
10883008085.04873512229214.951264877708







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1096863.896767829875947.270110227297780.52342543246
1105052.686288051234135.90240658915969.47016951335
1113907.848345156092990.710808555834824.98588175636
1122692.240725765551774.47480541033610.00664612081
1135235.016757740584316.269848182636153.76366729853
1145039.008582118994118.850885443025959.16627879497
1156689.996177297925767.921711056017612.07064353982
1167613.637170954516689.065153536398538.20918837263
1175627.430450910484699.707110153926555.15379166705
1186390.27983385155458.680674335147321.87899336785
1194779.224319269283842.956871146515715.49176739205
1208236.45559965837294.662657375719178.24854194088

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 6863.89676782987 & 5947.27011022729 & 7780.52342543246 \tabularnewline
110 & 5052.68628805123 & 4135.9024065891 & 5969.47016951335 \tabularnewline
111 & 3907.84834515609 & 2990.71080855583 & 4824.98588175636 \tabularnewline
112 & 2692.24072576555 & 1774.4748054103 & 3610.00664612081 \tabularnewline
113 & 5235.01675774058 & 4316.26984818263 & 6153.76366729853 \tabularnewline
114 & 5039.00858211899 & 4118.85088544302 & 5959.16627879497 \tabularnewline
115 & 6689.99617729792 & 5767.92171105601 & 7612.07064353982 \tabularnewline
116 & 7613.63717095451 & 6689.06515353639 & 8538.20918837263 \tabularnewline
117 & 5627.43045091048 & 4699.70711015392 & 6555.15379166705 \tabularnewline
118 & 6390.2798338515 & 5458.68067433514 & 7321.87899336785 \tabularnewline
119 & 4779.22431926928 & 3842.95687114651 & 5715.49176739205 \tabularnewline
120 & 8236.4555996583 & 7294.66265737571 & 9178.24854194088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307498&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]6863.89676782987[/C][C]5947.27011022729[/C][C]7780.52342543246[/C][/ROW]
[ROW][C]110[/C][C]5052.68628805123[/C][C]4135.9024065891[/C][C]5969.47016951335[/C][/ROW]
[ROW][C]111[/C][C]3907.84834515609[/C][C]2990.71080855583[/C][C]4824.98588175636[/C][/ROW]
[ROW][C]112[/C][C]2692.24072576555[/C][C]1774.4748054103[/C][C]3610.00664612081[/C][/ROW]
[ROW][C]113[/C][C]5235.01675774058[/C][C]4316.26984818263[/C][C]6153.76366729853[/C][/ROW]
[ROW][C]114[/C][C]5039.00858211899[/C][C]4118.85088544302[/C][C]5959.16627879497[/C][/ROW]
[ROW][C]115[/C][C]6689.99617729792[/C][C]5767.92171105601[/C][C]7612.07064353982[/C][/ROW]
[ROW][C]116[/C][C]7613.63717095451[/C][C]6689.06515353639[/C][C]8538.20918837263[/C][/ROW]
[ROW][C]117[/C][C]5627.43045091048[/C][C]4699.70711015392[/C][C]6555.15379166705[/C][/ROW]
[ROW][C]118[/C][C]6390.2798338515[/C][C]5458.68067433514[/C][C]7321.87899336785[/C][/ROW]
[ROW][C]119[/C][C]4779.22431926928[/C][C]3842.95687114651[/C][C]5715.49176739205[/C][/ROW]
[ROW][C]120[/C][C]8236.4555996583[/C][C]7294.66265737571[/C][C]9178.24854194088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307498&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307498&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
1096863.896767829875947.270110227297780.52342543246
1105052.686288051234135.90240658915969.47016951335
1113907.848345156092990.710808555834824.98588175636
1122692.240725765551774.47480541033610.00664612081
1135235.016757740584316.269848182636153.76366729853
1145039.008582118994118.850885443025959.16627879497
1156689.996177297925767.921711056017612.07064353982
1167613.637170954516689.065153536398538.20918837263
1175627.430450910484699.707110153926555.15379166705
1186390.27983385155458.680674335147321.87899336785
1194779.224319269283842.956871146515715.49176739205
1208236.45559965837294.662657375719178.24854194088



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')