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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 18 Dec 2016 14:12:12 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/18/t1482066748z1qydjb8hvtdkty.htm/, Retrieved Mon, 07 Apr 2025 08:43:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301058, Retrieved Mon, 07 Apr 2025 08:43:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
-    D    [Exponential Smoothing] [] [2016-12-18 13:12:12] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3425
3440
3500
3545
3580
3620
3645
3655
3670
3675
3665
3665
3740
3800
3820
3860
3845
3865
3900
4050
4165
4100
4075
4110
4170
4235
4320
4370
4460
4575
4510
4510
4525
4570
4670
4735
4730
4680
4725
4750
4750
4740
4780
4835
4865
4885
4915
4925
4970
5015
5030
5030
5010
4985
4955
5000
5005
4990
5015
5030
5125
5055
5055
5000
4980
4950
4985
4930
4945
4930
4920
4920
4965
4970
4955
5050
5065
5065
5065
5085
5065
4920
4880
4955
5005
5010
5025
5005
4975
4970
4980
4900
4885
4895
4845
4875
4825
4765
4730
4630
4540
4555
4520
4520
4505
4485
4455
4410
4345
4350
4315
4245
4215
4175
4110
4085

Tables (Output of Computation)





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=301058&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=301058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301058&T=0

As an alternative you can also use a QR Code:  
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
alpha0.866614635189143
beta0.080946438363641
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.866614635189143 \tabularnewline
beta & 0.080946438363641 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301058&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]0.866614635189143[/C][/ROW]
[ROW][C]beta[/C][C]0.080946438363641[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301058&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.866614635189143
beta0.080946438363641
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1337403596.55048076923143.449519230769
1438003792.218890783837.78110921617463
1538203820.86091104197-0.860911041970212
1638603860.70323770118-0.703237701175567
1738453849.17454137136-4.17454137136065
1838653868.51138770492-3.51138770491798
1939004005.88494441569-105.884944415689
2040503926.9039833436123.096016656402
2141654059.78804877344105.211951226557
2241004176.42907326572-76.4290732657237
2340754117.58754305085-42.5875430508504
2441104098.0027556278711.9972443721299
2541704221.11427607781-51.1142760778112
2642354227.466548268737.53345173127309
2743204252.1157279168167.8842720831899
2843704353.7516008625716.2483991374284
2944604359.83649978991100.163500210087
3045754480.3880024386794.6119975613256
3145104706.73020762404-196.730207624044
3245104590.78000408904-80.7800040890434
3345254541.51076269211-16.5107626921063
3445704516.8121851868353.1878148131664
3546704572.280392438797.7196075613001
3647354688.8789853405746.1210146594331
3747304842.8486106741-112.848610674098
3846804808.89722833788-128.897228337879
3947254719.166448893585.83355110641787
4047504751.5909190518-1.59091905179775
4147504743.607763110196.39223688980564
4247404765.77594551252-25.7759455125215
4347804824.10299097968-44.1029909796835
4448354841.77011009909-6.77011009908983
4548654856.285532276728.71446772327727
4648854855.5878428721529.412157127852
4749154887.567323329427.4326766705981
4849254922.61686902492.38313097509763
4949705000.65533077564-30.6553307756367
5050155024.73595164228-9.735951642283
5150305053.54503561652-23.5450356165202
5250305054.76023052194-24.7602305219389
5350105021.37868740357-11.3786874035677
5449855016.22458393962-31.224583939621
5549555059.37200336775-104.372003367748
5650005017.54774451006-17.547744510056
5750055011.79145306319-6.79145306319424
5849904986.332070106153.6679298938534
5950154979.8464469550235.1535530449837
6050305002.8966431285127.1033568714884
6151255084.3361441864540.6638558135483
6250555164.40132784838-109.401327848384
6350555089.39351821964-34.3935182196437
6450005064.68066565827-64.680665658273
6549804979.323493459480.676506540521586
6649504963.65021182746-13.6502118274602
6749854995.18464168559-10.1846416855942
6849305036.08639584236-106.086395842358
6949454938.345796270336.65420372967401
7049304910.186800250219.8131997497976
7149204907.2782614237412.7217385762615
7249204893.6269987680226.3730012319847
7349654960.003159288264.99684071174033
7449704970.40109207801-0.40109207801288
7549554988.7645294024-33.7645294024005
7650504949.50613205781100.493867942189
7750655016.5454339739648.4545660260374
7850655044.2540597409320.7459402590684
7950655112.35953942879-47.3595394287941
8050855111.94588178733-26.9458817873265
8150655107.07200210279-42.0720021027882
8249205044.2677140922-124.267714092195
8348804911.26979809082-31.2697980908206
8449554853.94887463082101.05112536918
8550054980.0627167570224.9372832429781
8650105006.291926355793.70807364420671
8750255023.325090667351.67490933265071
8850055034.73204722985-29.7320472298452
8949754974.884030567710.115969432286875
9049704946.5245205785623.475479421435
9149804997.62138469852-17.6213846985247
9249005017.49844320626-117.498443206257
9348854917.57689336244-32.5768933624413
9448954838.147684294756.852315705295
9548454873.33123721961-28.3312372196078
9648754835.228365878639.7716341214045
9748254892.80709147542-67.8070914754207
9847654824.04810348065-59.0481034806508
9947304770.23944644677-40.2394464467661
10046304722.00810949607-92.0081094960688
10145404588.6779370129-48.6779370129043
10245554494.2317712146660.7682287853386
10345204547.86446117379-27.8644611737918
10445204520.52314013793-0.523140137925111
10545054516.48769371923-11.4876937192257
10644854451.9289373369833.0710626630234
10744554438.1385251287616.8614748712444
10844104434.45194210554-24.4519421055356
10943454403.68660204497-58.6866020449661
11043504326.3021340352423.6978659647639
11143154334.81797173494-19.817971734944
11242454286.91838221204-41.918382212044
11342154195.8294546267219.1705453732793
11441754172.592964858242.40703514175948
11541104157.54535720203-47.5453572020324
11640854109.13328390184-24.1332839018442

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3740 & 3596.55048076923 & 143.449519230769 \tabularnewline
14 & 3800 & 3792.21889078383 & 7.78110921617463 \tabularnewline
15 & 3820 & 3820.86091104197 & -0.860911041970212 \tabularnewline
16 & 3860 & 3860.70323770118 & -0.703237701175567 \tabularnewline
17 & 3845 & 3849.17454137136 & -4.17454137136065 \tabularnewline
18 & 3865 & 3868.51138770492 & -3.51138770491798 \tabularnewline
19 & 3900 & 4005.88494441569 & -105.884944415689 \tabularnewline
20 & 4050 & 3926.9039833436 & 123.096016656402 \tabularnewline
21 & 4165 & 4059.78804877344 & 105.211951226557 \tabularnewline
22 & 4100 & 4176.42907326572 & -76.4290732657237 \tabularnewline
23 & 4075 & 4117.58754305085 & -42.5875430508504 \tabularnewline
24 & 4110 & 4098.00275562787 & 11.9972443721299 \tabularnewline
25 & 4170 & 4221.11427607781 & -51.1142760778112 \tabularnewline
26 & 4235 & 4227.46654826873 & 7.53345173127309 \tabularnewline
27 & 4320 & 4252.11572791681 & 67.8842720831899 \tabularnewline
28 & 4370 & 4353.75160086257 & 16.2483991374284 \tabularnewline
29 & 4460 & 4359.83649978991 & 100.163500210087 \tabularnewline
30 & 4575 & 4480.38800243867 & 94.6119975613256 \tabularnewline
31 & 4510 & 4706.73020762404 & -196.730207624044 \tabularnewline
32 & 4510 & 4590.78000408904 & -80.7800040890434 \tabularnewline
33 & 4525 & 4541.51076269211 & -16.5107626921063 \tabularnewline
34 & 4570 & 4516.81218518683 & 53.1878148131664 \tabularnewline
35 & 4670 & 4572.2803924387 & 97.7196075613001 \tabularnewline
36 & 4735 & 4688.87898534057 & 46.1210146594331 \tabularnewline
37 & 4730 & 4842.8486106741 & -112.848610674098 \tabularnewline
38 & 4680 & 4808.89722833788 & -128.897228337879 \tabularnewline
39 & 4725 & 4719.16644889358 & 5.83355110641787 \tabularnewline
40 & 4750 & 4751.5909190518 & -1.59091905179775 \tabularnewline
41 & 4750 & 4743.60776311019 & 6.39223688980564 \tabularnewline
42 & 4740 & 4765.77594551252 & -25.7759455125215 \tabularnewline
43 & 4780 & 4824.10299097968 & -44.1029909796835 \tabularnewline
44 & 4835 & 4841.77011009909 & -6.77011009908983 \tabularnewline
45 & 4865 & 4856.28553227672 & 8.71446772327727 \tabularnewline
46 & 4885 & 4855.58784287215 & 29.412157127852 \tabularnewline
47 & 4915 & 4887.5673233294 & 27.4326766705981 \tabularnewline
48 & 4925 & 4922.6168690249 & 2.38313097509763 \tabularnewline
49 & 4970 & 5000.65533077564 & -30.6553307756367 \tabularnewline
50 & 5015 & 5024.73595164228 & -9.735951642283 \tabularnewline
51 & 5030 & 5053.54503561652 & -23.5450356165202 \tabularnewline
52 & 5030 & 5054.76023052194 & -24.7602305219389 \tabularnewline
53 & 5010 & 5021.37868740357 & -11.3786874035677 \tabularnewline
54 & 4985 & 5016.22458393962 & -31.224583939621 \tabularnewline
55 & 4955 & 5059.37200336775 & -104.372003367748 \tabularnewline
56 & 5000 & 5017.54774451006 & -17.547744510056 \tabularnewline
57 & 5005 & 5011.79145306319 & -6.79145306319424 \tabularnewline
58 & 4990 & 4986.33207010615 & 3.6679298938534 \tabularnewline
59 & 5015 & 4979.84644695502 & 35.1535530449837 \tabularnewline
60 & 5030 & 5002.89664312851 & 27.1033568714884 \tabularnewline
61 & 5125 & 5084.33614418645 & 40.6638558135483 \tabularnewline
62 & 5055 & 5164.40132784838 & -109.401327848384 \tabularnewline
63 & 5055 & 5089.39351821964 & -34.3935182196437 \tabularnewline
64 & 5000 & 5064.68066565827 & -64.680665658273 \tabularnewline
65 & 4980 & 4979.32349345948 & 0.676506540521586 \tabularnewline
66 & 4950 & 4963.65021182746 & -13.6502118274602 \tabularnewline
67 & 4985 & 4995.18464168559 & -10.1846416855942 \tabularnewline
68 & 4930 & 5036.08639584236 & -106.086395842358 \tabularnewline
69 & 4945 & 4938.34579627033 & 6.65420372967401 \tabularnewline
70 & 4930 & 4910.1868002502 & 19.8131997497976 \tabularnewline
71 & 4920 & 4907.27826142374 & 12.7217385762615 \tabularnewline
72 & 4920 & 4893.62699876802 & 26.3730012319847 \tabularnewline
73 & 4965 & 4960.00315928826 & 4.99684071174033 \tabularnewline
74 & 4970 & 4970.40109207801 & -0.40109207801288 \tabularnewline
75 & 4955 & 4988.7645294024 & -33.7645294024005 \tabularnewline
76 & 5050 & 4949.50613205781 & 100.493867942189 \tabularnewline
77 & 5065 & 5016.54543397396 & 48.4545660260374 \tabularnewline
78 & 5065 & 5044.25405974093 & 20.7459402590684 \tabularnewline
79 & 5065 & 5112.35953942879 & -47.3595394287941 \tabularnewline
80 & 5085 & 5111.94588178733 & -26.9458817873265 \tabularnewline
81 & 5065 & 5107.07200210279 & -42.0720021027882 \tabularnewline
82 & 4920 & 5044.2677140922 & -124.267714092195 \tabularnewline
83 & 4880 & 4911.26979809082 & -31.2697980908206 \tabularnewline
84 & 4955 & 4853.94887463082 & 101.05112536918 \tabularnewline
85 & 5005 & 4980.06271675702 & 24.9372832429781 \tabularnewline
86 & 5010 & 5006.29192635579 & 3.70807364420671 \tabularnewline
87 & 5025 & 5023.32509066735 & 1.67490933265071 \tabularnewline
88 & 5005 & 5034.73204722985 & -29.7320472298452 \tabularnewline
89 & 4975 & 4974.88403056771 & 0.115969432286875 \tabularnewline
90 & 4970 & 4946.52452057856 & 23.475479421435 \tabularnewline
91 & 4980 & 4997.62138469852 & -17.6213846985247 \tabularnewline
92 & 4900 & 5017.49844320626 & -117.498443206257 \tabularnewline
93 & 4885 & 4917.57689336244 & -32.5768933624413 \tabularnewline
94 & 4895 & 4838.1476842947 & 56.852315705295 \tabularnewline
95 & 4845 & 4873.33123721961 & -28.3312372196078 \tabularnewline
96 & 4875 & 4835.2283658786 & 39.7716341214045 \tabularnewline
97 & 4825 & 4892.80709147542 & -67.8070914754207 \tabularnewline
98 & 4765 & 4824.04810348065 & -59.0481034806508 \tabularnewline
99 & 4730 & 4770.23944644677 & -40.2394464467661 \tabularnewline
100 & 4630 & 4722.00810949607 & -92.0081094960688 \tabularnewline
101 & 4540 & 4588.6779370129 & -48.6779370129043 \tabularnewline
102 & 4555 & 4494.23177121466 & 60.7682287853386 \tabularnewline
103 & 4520 & 4547.86446117379 & -27.8644611737918 \tabularnewline
104 & 4520 & 4520.52314013793 & -0.523140137925111 \tabularnewline
105 & 4505 & 4516.48769371923 & -11.4876937192257 \tabularnewline
106 & 4485 & 4451.92893733698 & 33.0710626630234 \tabularnewline
107 & 4455 & 4438.13852512876 & 16.8614748712444 \tabularnewline
108 & 4410 & 4434.45194210554 & -24.4519421055356 \tabularnewline
109 & 4345 & 4403.68660204497 & -58.6866020449661 \tabularnewline
110 & 4350 & 4326.30213403524 & 23.6978659647639 \tabularnewline
111 & 4315 & 4334.81797173494 & -19.817971734944 \tabularnewline
112 & 4245 & 4286.91838221204 & -41.918382212044 \tabularnewline
113 & 4215 & 4195.82945462672 & 19.1705453732793 \tabularnewline
114 & 4175 & 4172.59296485824 & 2.40703514175948 \tabularnewline
115 & 4110 & 4157.54535720203 & -47.5453572020324 \tabularnewline
116 & 4085 & 4109.13328390184 & -24.1332839018442 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301058&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]3740[/C][C]3596.55048076923[/C][C]143.449519230769[/C][/ROW]
[ROW][C]14[/C][C]3800[/C][C]3792.21889078383[/C][C]7.78110921617463[/C][/ROW]
[ROW][C]15[/C][C]3820[/C][C]3820.86091104197[/C][C]-0.860911041970212[/C][/ROW]
[ROW][C]16[/C][C]3860[/C][C]3860.70323770118[/C][C]-0.703237701175567[/C][/ROW]
[ROW][C]17[/C][C]3845[/C][C]3849.17454137136[/C][C]-4.17454137136065[/C][/ROW]
[ROW][C]18[/C][C]3865[/C][C]3868.51138770492[/C][C]-3.51138770491798[/C][/ROW]
[ROW][C]19[/C][C]3900[/C][C]4005.88494441569[/C][C]-105.884944415689[/C][/ROW]
[ROW][C]20[/C][C]4050[/C][C]3926.9039833436[/C][C]123.096016656402[/C][/ROW]
[ROW][C]21[/C][C]4165[/C][C]4059.78804877344[/C][C]105.211951226557[/C][/ROW]
[ROW][C]22[/C][C]4100[/C][C]4176.42907326572[/C][C]-76.4290732657237[/C][/ROW]
[ROW][C]23[/C][C]4075[/C][C]4117.58754305085[/C][C]-42.5875430508504[/C][/ROW]
[ROW][C]24[/C][C]4110[/C][C]4098.00275562787[/C][C]11.9972443721299[/C][/ROW]
[ROW][C]25[/C][C]4170[/C][C]4221.11427607781[/C][C]-51.1142760778112[/C][/ROW]
[ROW][C]26[/C][C]4235[/C][C]4227.46654826873[/C][C]7.53345173127309[/C][/ROW]
[ROW][C]27[/C][C]4320[/C][C]4252.11572791681[/C][C]67.8842720831899[/C][/ROW]
[ROW][C]28[/C][C]4370[/C][C]4353.75160086257[/C][C]16.2483991374284[/C][/ROW]
[ROW][C]29[/C][C]4460[/C][C]4359.83649978991[/C][C]100.163500210087[/C][/ROW]
[ROW][C]30[/C][C]4575[/C][C]4480.38800243867[/C][C]94.6119975613256[/C][/ROW]
[ROW][C]31[/C][C]4510[/C][C]4706.73020762404[/C][C]-196.730207624044[/C][/ROW]
[ROW][C]32[/C][C]4510[/C][C]4590.78000408904[/C][C]-80.7800040890434[/C][/ROW]
[ROW][C]33[/C][C]4525[/C][C]4541.51076269211[/C][C]-16.5107626921063[/C][/ROW]
[ROW][C]34[/C][C]4570[/C][C]4516.81218518683[/C][C]53.1878148131664[/C][/ROW]
[ROW][C]35[/C][C]4670[/C][C]4572.2803924387[/C][C]97.7196075613001[/C][/ROW]
[ROW][C]36[/C][C]4735[/C][C]4688.87898534057[/C][C]46.1210146594331[/C][/ROW]
[ROW][C]37[/C][C]4730[/C][C]4842.8486106741[/C][C]-112.848610674098[/C][/ROW]
[ROW][C]38[/C][C]4680[/C][C]4808.89722833788[/C][C]-128.897228337879[/C][/ROW]
[ROW][C]39[/C][C]4725[/C][C]4719.16644889358[/C][C]5.83355110641787[/C][/ROW]
[ROW][C]40[/C][C]4750[/C][C]4751.5909190518[/C][C]-1.59091905179775[/C][/ROW]
[ROW][C]41[/C][C]4750[/C][C]4743.60776311019[/C][C]6.39223688980564[/C][/ROW]
[ROW][C]42[/C][C]4740[/C][C]4765.77594551252[/C][C]-25.7759455125215[/C][/ROW]
[ROW][C]43[/C][C]4780[/C][C]4824.10299097968[/C][C]-44.1029909796835[/C][/ROW]
[ROW][C]44[/C][C]4835[/C][C]4841.77011009909[/C][C]-6.77011009908983[/C][/ROW]
[ROW][C]45[/C][C]4865[/C][C]4856.28553227672[/C][C]8.71446772327727[/C][/ROW]
[ROW][C]46[/C][C]4885[/C][C]4855.58784287215[/C][C]29.412157127852[/C][/ROW]
[ROW][C]47[/C][C]4915[/C][C]4887.5673233294[/C][C]27.4326766705981[/C][/ROW]
[ROW][C]48[/C][C]4925[/C][C]4922.6168690249[/C][C]2.38313097509763[/C][/ROW]
[ROW][C]49[/C][C]4970[/C][C]5000.65533077564[/C][C]-30.6553307756367[/C][/ROW]
[ROW][C]50[/C][C]5015[/C][C]5024.73595164228[/C][C]-9.735951642283[/C][/ROW]
[ROW][C]51[/C][C]5030[/C][C]5053.54503561652[/C][C]-23.5450356165202[/C][/ROW]
[ROW][C]52[/C][C]5030[/C][C]5054.76023052194[/C][C]-24.7602305219389[/C][/ROW]
[ROW][C]53[/C][C]5010[/C][C]5021.37868740357[/C][C]-11.3786874035677[/C][/ROW]
[ROW][C]54[/C][C]4985[/C][C]5016.22458393962[/C][C]-31.224583939621[/C][/ROW]
[ROW][C]55[/C][C]4955[/C][C]5059.37200336775[/C][C]-104.372003367748[/C][/ROW]
[ROW][C]56[/C][C]5000[/C][C]5017.54774451006[/C][C]-17.547744510056[/C][/ROW]
[ROW][C]57[/C][C]5005[/C][C]5011.79145306319[/C][C]-6.79145306319424[/C][/ROW]
[ROW][C]58[/C][C]4990[/C][C]4986.33207010615[/C][C]3.6679298938534[/C][/ROW]
[ROW][C]59[/C][C]5015[/C][C]4979.84644695502[/C][C]35.1535530449837[/C][/ROW]
[ROW][C]60[/C][C]5030[/C][C]5002.89664312851[/C][C]27.1033568714884[/C][/ROW]
[ROW][C]61[/C][C]5125[/C][C]5084.33614418645[/C][C]40.6638558135483[/C][/ROW]
[ROW][C]62[/C][C]5055[/C][C]5164.40132784838[/C][C]-109.401327848384[/C][/ROW]
[ROW][C]63[/C][C]5055[/C][C]5089.39351821964[/C][C]-34.3935182196437[/C][/ROW]
[ROW][C]64[/C][C]5000[/C][C]5064.68066565827[/C][C]-64.680665658273[/C][/ROW]
[ROW][C]65[/C][C]4980[/C][C]4979.32349345948[/C][C]0.676506540521586[/C][/ROW]
[ROW][C]66[/C][C]4950[/C][C]4963.65021182746[/C][C]-13.6502118274602[/C][/ROW]
[ROW][C]67[/C][C]4985[/C][C]4995.18464168559[/C][C]-10.1846416855942[/C][/ROW]
[ROW][C]68[/C][C]4930[/C][C]5036.08639584236[/C][C]-106.086395842358[/C][/ROW]
[ROW][C]69[/C][C]4945[/C][C]4938.34579627033[/C][C]6.65420372967401[/C][/ROW]
[ROW][C]70[/C][C]4930[/C][C]4910.1868002502[/C][C]19.8131997497976[/C][/ROW]
[ROW][C]71[/C][C]4920[/C][C]4907.27826142374[/C][C]12.7217385762615[/C][/ROW]
[ROW][C]72[/C][C]4920[/C][C]4893.62699876802[/C][C]26.3730012319847[/C][/ROW]
[ROW][C]73[/C][C]4965[/C][C]4960.00315928826[/C][C]4.99684071174033[/C][/ROW]
[ROW][C]74[/C][C]4970[/C][C]4970.40109207801[/C][C]-0.40109207801288[/C][/ROW]
[ROW][C]75[/C][C]4955[/C][C]4988.7645294024[/C][C]-33.7645294024005[/C][/ROW]
[ROW][C]76[/C][C]5050[/C][C]4949.50613205781[/C][C]100.493867942189[/C][/ROW]
[ROW][C]77[/C][C]5065[/C][C]5016.54543397396[/C][C]48.4545660260374[/C][/ROW]
[ROW][C]78[/C][C]5065[/C][C]5044.25405974093[/C][C]20.7459402590684[/C][/ROW]
[ROW][C]79[/C][C]5065[/C][C]5112.35953942879[/C][C]-47.3595394287941[/C][/ROW]
[ROW][C]80[/C][C]5085[/C][C]5111.94588178733[/C][C]-26.9458817873265[/C][/ROW]
[ROW][C]81[/C][C]5065[/C][C]5107.07200210279[/C][C]-42.0720021027882[/C][/ROW]
[ROW][C]82[/C][C]4920[/C][C]5044.2677140922[/C][C]-124.267714092195[/C][/ROW]
[ROW][C]83[/C][C]4880[/C][C]4911.26979809082[/C][C]-31.2697980908206[/C][/ROW]
[ROW][C]84[/C][C]4955[/C][C]4853.94887463082[/C][C]101.05112536918[/C][/ROW]
[ROW][C]85[/C][C]5005[/C][C]4980.06271675702[/C][C]24.9372832429781[/C][/ROW]
[ROW][C]86[/C][C]5010[/C][C]5006.29192635579[/C][C]3.70807364420671[/C][/ROW]
[ROW][C]87[/C][C]5025[/C][C]5023.32509066735[/C][C]1.67490933265071[/C][/ROW]
[ROW][C]88[/C][C]5005[/C][C]5034.73204722985[/C][C]-29.7320472298452[/C][/ROW]
[ROW][C]89[/C][C]4975[/C][C]4974.88403056771[/C][C]0.115969432286875[/C][/ROW]
[ROW][C]90[/C][C]4970[/C][C]4946.52452057856[/C][C]23.475479421435[/C][/ROW]
[ROW][C]91[/C][C]4980[/C][C]4997.62138469852[/C][C]-17.6213846985247[/C][/ROW]
[ROW][C]92[/C][C]4900[/C][C]5017.49844320626[/C][C]-117.498443206257[/C][/ROW]
[ROW][C]93[/C][C]4885[/C][C]4917.57689336244[/C][C]-32.5768933624413[/C][/ROW]
[ROW][C]94[/C][C]4895[/C][C]4838.1476842947[/C][C]56.852315705295[/C][/ROW]
[ROW][C]95[/C][C]4845[/C][C]4873.33123721961[/C][C]-28.3312372196078[/C][/ROW]
[ROW][C]96[/C][C]4875[/C][C]4835.2283658786[/C][C]39.7716341214045[/C][/ROW]
[ROW][C]97[/C][C]4825[/C][C]4892.80709147542[/C][C]-67.8070914754207[/C][/ROW]
[ROW][C]98[/C][C]4765[/C][C]4824.04810348065[/C][C]-59.0481034806508[/C][/ROW]
[ROW][C]99[/C][C]4730[/C][C]4770.23944644677[/C][C]-40.2394464467661[/C][/ROW]
[ROW][C]100[/C][C]4630[/C][C]4722.00810949607[/C][C]-92.0081094960688[/C][/ROW]
[ROW][C]101[/C][C]4540[/C][C]4588.6779370129[/C][C]-48.6779370129043[/C][/ROW]
[ROW][C]102[/C][C]4555[/C][C]4494.23177121466[/C][C]60.7682287853386[/C][/ROW]
[ROW][C]103[/C][C]4520[/C][C]4547.86446117379[/C][C]-27.8644611737918[/C][/ROW]
[ROW][C]104[/C][C]4520[/C][C]4520.52314013793[/C][C]-0.523140137925111[/C][/ROW]
[ROW][C]105[/C][C]4505[/C][C]4516.48769371923[/C][C]-11.4876937192257[/C][/ROW]
[ROW][C]106[/C][C]4485[/C][C]4451.92893733698[/C][C]33.0710626630234[/C][/ROW]
[ROW][C]107[/C][C]4455[/C][C]4438.13852512876[/C][C]16.8614748712444[/C][/ROW]
[ROW][C]108[/C][C]4410[/C][C]4434.45194210554[/C][C]-24.4519421055356[/C][/ROW]
[ROW][C]109[/C][C]4345[/C][C]4403.68660204497[/C][C]-58.6866020449661[/C][/ROW]
[ROW][C]110[/C][C]4350[/C][C]4326.30213403524[/C][C]23.6978659647639[/C][/ROW]
[ROW][C]111[/C][C]4315[/C][C]4334.81797173494[/C][C]-19.817971734944[/C][/ROW]
[ROW][C]112[/C][C]4245[/C][C]4286.91838221204[/C][C]-41.918382212044[/C][/ROW]
[ROW][C]113[/C][C]4215[/C][C]4195.82945462672[/C][C]19.1705453732793[/C][/ROW]
[ROW][C]114[/C][C]4175[/C][C]4172.59296485824[/C][C]2.40703514175948[/C][/ROW]
[ROW][C]115[/C][C]4110[/C][C]4157.54535720203[/C][C]-47.5453572020324[/C][/ROW]
[ROW][C]116[/C][C]4085[/C][C]4109.13328390184[/C][C]-24.1332839018442[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301058&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301058&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1337403596.55048076923143.449519230769
1438003792.218890783837.78110921617463
1538203820.86091104197-0.860911041970212
1638603860.70323770118-0.703237701175567
1738453849.17454137136-4.17454137136065
1838653868.51138770492-3.51138770491798
1939004005.88494441569-105.884944415689
2040503926.9039833436123.096016656402
2141654059.78804877344105.211951226557
2241004176.42907326572-76.4290732657237
2340754117.58754305085-42.5875430508504
2441104098.0027556278711.9972443721299
2541704221.11427607781-51.1142760778112
2642354227.466548268737.53345173127309
2743204252.1157279168167.8842720831899
2843704353.7516008625716.2483991374284
2944604359.83649978991100.163500210087
3045754480.3880024386794.6119975613256
3145104706.73020762404-196.730207624044
3245104590.78000408904-80.7800040890434
3345254541.51076269211-16.5107626921063
3445704516.8121851868353.1878148131664
3546704572.280392438797.7196075613001
3647354688.8789853405746.1210146594331
3747304842.8486106741-112.848610674098
3846804808.89722833788-128.897228337879
3947254719.166448893585.83355110641787
4047504751.5909190518-1.59091905179775
4147504743.607763110196.39223688980564
4247404765.77594551252-25.7759455125215
4347804824.10299097968-44.1029909796835
4448354841.77011009909-6.77011009908983
4548654856.285532276728.71446772327727
4648854855.5878428721529.412157127852
4749154887.567323329427.4326766705981
4849254922.61686902492.38313097509763
4949705000.65533077564-30.6553307756367
5050155024.73595164228-9.735951642283
5150305053.54503561652-23.5450356165202
5250305054.76023052194-24.7602305219389
5350105021.37868740357-11.3786874035677
5449855016.22458393962-31.224583939621
5549555059.37200336775-104.372003367748
5650005017.54774451006-17.547744510056
5750055011.79145306319-6.79145306319424
5849904986.332070106153.6679298938534
5950154979.8464469550235.1535530449837
6050305002.8966431285127.1033568714884
6151255084.3361441864540.6638558135483
6250555164.40132784838-109.401327848384
6350555089.39351821964-34.3935182196437
6450005064.68066565827-64.680665658273
6549804979.323493459480.676506540521586
6649504963.65021182746-13.6502118274602
6749854995.18464168559-10.1846416855942
6849305036.08639584236-106.086395842358
6949454938.345796270336.65420372967401
7049304910.186800250219.8131997497976
7149204907.2782614237412.7217385762615
7249204893.6269987680226.3730012319847
7349654960.003159288264.99684071174033
7449704970.40109207801-0.40109207801288
7549554988.7645294024-33.7645294024005
7650504949.50613205781100.493867942189
7750655016.5454339739648.4545660260374
7850655044.2540597409320.7459402590684
7950655112.35953942879-47.3595394287941
8050855111.94588178733-26.9458817873265
8150655107.07200210279-42.0720021027882
8249205044.2677140922-124.267714092195
8348804911.26979809082-31.2697980908206
8449554853.94887463082101.05112536918
8550054980.0627167570224.9372832429781
8650105006.291926355793.70807364420671
8750255023.325090667351.67490933265071
8850055034.73204722985-29.7320472298452
8949754974.884030567710.115969432286875
9049704946.5245205785623.475479421435
9149804997.62138469852-17.6213846985247
9249005017.49844320626-117.498443206257
9348854917.57689336244-32.5768933624413
9448954838.147684294756.852315705295
9548454873.33123721961-28.3312372196078
9648754835.228365878639.7716341214045
9748254892.80709147542-67.8070914754207
9847654824.04810348065-59.0481034806508
9947304770.23944644677-40.2394464467661
10046304722.00810949607-92.0081094960688
10145404588.6779370129-48.6779370129043
10245554494.2317712146660.7682287853386
10345204547.86446117379-27.8644611737918
10445204520.52314013793-0.523140137925111
10545054516.48769371923-11.4876937192257
10644854451.9289373369833.0710626630234
10744554438.1385251287616.8614748712444
10844104434.45194210554-24.4519421055356
10943454403.68660204497-58.6866020449661
11043504326.3021340352423.6978659647639
11143154334.81797173494-19.817971734944
11242454286.91838221204-41.918382212044
11342154195.8294546267219.1705453732793
11441754172.592964858242.40703514175948
11541104157.54535720203-47.5453572020324
11640854109.13328390184-24.1332839018442






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174073.856261898563962.607066169644185.10545762749
1184016.684080969043864.247235759174169.12092617891
1193961.239451900323772.069972522854150.4089312778
1203925.414812805023701.489622772464149.34000283757
1213900.973719332753643.231610012964158.71582865253
1223879.253868223443588.096846645754170.41088980113
1233853.583088603223529.1011224594178.06505474745
1243813.455066341423455.542776719154171.36735596369
1253763.327033412313371.750476308784154.90359051584
1263716.38170214193290.819330551584141.94407373223
1273687.556993145023227.626117997684147.48786829236
1283681.778315552383187.052896553854176.5037345509

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4073.85626189856 & 3962.60706616964 & 4185.10545762749 \tabularnewline
118 & 4016.68408096904 & 3864.24723575917 & 4169.12092617891 \tabularnewline
119 & 3961.23945190032 & 3772.06997252285 & 4150.4089312778 \tabularnewline
120 & 3925.41481280502 & 3701.48962277246 & 4149.34000283757 \tabularnewline
121 & 3900.97371933275 & 3643.23161001296 & 4158.71582865253 \tabularnewline
122 & 3879.25386822344 & 3588.09684664575 & 4170.41088980113 \tabularnewline
123 & 3853.58308860322 & 3529.101122459 & 4178.06505474745 \tabularnewline
124 & 3813.45506634142 & 3455.54277671915 & 4171.36735596369 \tabularnewline
125 & 3763.32703341231 & 3371.75047630878 & 4154.90359051584 \tabularnewline
126 & 3716.3817021419 & 3290.81933055158 & 4141.94407373223 \tabularnewline
127 & 3687.55699314502 & 3227.62611799768 & 4147.48786829236 \tabularnewline
128 & 3681.77831555238 & 3187.05289655385 & 4176.5037345509 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301058&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]117[/C][C]4073.85626189856[/C][C]3962.60706616964[/C][C]4185.10545762749[/C][/ROW]
[ROW][C]118[/C][C]4016.68408096904[/C][C]3864.24723575917[/C][C]4169.12092617891[/C][/ROW]
[ROW][C]119[/C][C]3961.23945190032[/C][C]3772.06997252285[/C][C]4150.4089312778[/C][/ROW]
[ROW][C]120[/C][C]3925.41481280502[/C][C]3701.48962277246[/C][C]4149.34000283757[/C][/ROW]
[ROW][C]121[/C][C]3900.97371933275[/C][C]3643.23161001296[/C][C]4158.71582865253[/C][/ROW]
[ROW][C]122[/C][C]3879.25386822344[/C][C]3588.09684664575[/C][C]4170.41088980113[/C][/ROW]
[ROW][C]123[/C][C]3853.58308860322[/C][C]3529.101122459[/C][C]4178.06505474745[/C][/ROW]
[ROW][C]124[/C][C]3813.45506634142[/C][C]3455.54277671915[/C][C]4171.36735596369[/C][/ROW]
[ROW][C]125[/C][C]3763.32703341231[/C][C]3371.75047630878[/C][C]4154.90359051584[/C][/ROW]
[ROW][C]126[/C][C]3716.3817021419[/C][C]3290.81933055158[/C][C]4141.94407373223[/C][/ROW]
[ROW][C]127[/C][C]3687.55699314502[/C][C]3227.62611799768[/C][C]4147.48786829236[/C][/ROW]
[ROW][C]128[/C][C]3681.77831555238[/C][C]3187.05289655385[/C][C]4176.5037345509[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301058&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301058&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174073.856261898563962.607066169644185.10545762749
1184016.684080969043864.247235759174169.12092617891
1193961.239451900323772.069972522854150.4089312778
1203925.414812805023701.489622772464149.34000283757
1213900.973719332753643.231610012964158.71582865253
1223879.253868223443588.096846645754170.41088980113
1233853.583088603223529.1011224594178.06505474745
1243813.455066341423455.542776719154171.36735596369
1253763.327033412313371.750476308784154.90359051584
1263716.38170214193290.819330551584141.94407373223
1273687.556993145023227.626117997684147.48786829236
1283681.778315552383187.052896553854176.5037345509


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
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')