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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 19:14:50 +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/07/t1481134528zprwwhejmlraus7.htm/, Retrieved Tue, 07 May 2024 07:46:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298276, Retrieved Tue, 07 May 2024 07:46:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-07 18:14:50] [153c3207812fd13fe5ceee3276565119] [Current]
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Dataseries X:
3780
3795
3840
3900
3940
3990
4050
4090
4145
4190
4175
4230
4220
4245
4295
4290
4325
4335
4360
4360
4320
4310
4345
4315
4315
4335
4365
4410
4435
4440
4390
4445
4470
4430
4450
4480
4565
4515
4490
4535
4545
4555
4575
4585
4600
4690
4720
4780
4775
4830
4865
4945
5005
5065
5105
5080
5045
5115
5095
5075
5080
5115
5115
5115
5065
5045
5080
5115
5080
5100
5085
5120
5195
5135
5200
5150
5105
5105
5030
5060
5075
5030
5090
5070
5160
5110
5145
5075
5125
5055
5050
5040
5020
5025
4960
4965
4875
4805
4735
4775
4815
4870
4860
4875
4900
4855
4880
4850
4880
4900
4910
4935
4965
4945
4965
4950




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298276&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298276&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.904018639282989
beta0.0996090127224506
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.904018639282989 \tabularnewline
beta & 0.0996090127224506 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298276&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]0.904018639282989[/C][/ROW]
[ROW][C]beta[/C][C]0.0996090127224506[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298276&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
alpha0.904018639282989
beta0.0996090127224506
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33840381030
439003854.8220113027445.1779886972604
539403917.4334130791522.5665869208519
639903961.6357713285128.3642286714862
740504013.6334593109236.3665406890846
840904076.1401354677913.8598645322108
941454119.5484155532925.4515844467114
1041904175.7277010651514.2722989348522
1141754223.08590184294-48.0859018429355
1242304209.7410680827820.2589319172166
1342204260.00552242927-40.0055224292655
1442454252.1873533087-7.18735330870095
1542954273.3902110848221.6097889151833
1642904322.57214919506-32.5721491950571
1743254319.839535286685.16046471331538
1843354351.68259927241-16.6825992724125
1943604362.27688483458-2.27688483457587
2043604385.68917491496-25.6891749149636
2143204385.62304916957-65.6230491695724
2243104343.5467059066-33.5467059066004
2343454327.447147502317.5528524977044
2443154359.12314871016-44.1231487101632
2543154331.06967610262-16.0696761026229
2643354326.93001694088.06998305920115
2743654345.3397487031319.6602512968657
2844104375.9976732409134.002326759085
2944354422.682956584312.3170434156955
3044404450.87346969046-10.8734696904639
3143904457.12018810101-67.1201881010093
3244454406.4747588457438.5252411542642
3344704454.803903277415.1960967226032
3444304483.41145056336-53.4114505633634
3544504445.18688042124.81311957879552
3644804460.0318206888119.9681793111895
3745654490.3753201145474.6246798854645
3845154576.84914815066-61.8491481506553
3944904534.37867477933-44.3786747793338
4045354503.7056061309831.2943938690169
4145454544.260412258970.739587741031755
4245554557.25970282338-2.25970282337948
4345754567.344096179867.65590382014307
4445854587.08178468314-2.08178468314327
4546004597.828959887442.17104011255651
4646904612.6162666741277.3837333258762
4747204702.3655317288417.6344682711615
4847804739.6883032163440.311696783664
4947754801.14171593003-26.1417159300281
5048304800.1659851055529.8340148944462
5148654852.4798637242712.5201362757261
5249454890.2690916446554.7309083553464
5350054971.1460752581633.8539247418403
5450655036.1983684499928.8016315500145
5551055099.276835383035.72316461696664
5650805142.00729988293-62.0072998829282
5750455117.92450362803-72.9245036280308
5851155077.4056165241837.5943834758173
5950955140.18317759171-45.1831775917135
6050755124.05960750363-49.0596075036274
6150805100.01393315778-20.0139331577784
6251155100.4238670696614.5761329303359
6351155133.41642296817-18.4164229681692
6451155134.92472387856-19.9247238785583
6550655133.27530306408-68.2753030640797
6650455081.76797536255-36.7679753625525
6750805055.4329616722924.5670383277147
6851155086.758166194628.2418338054049
6950805123.9485863885-43.9485863885011
7051005091.920021080888.07997891912237
7150855107.65383779366-22.653837793664
7251205093.5637694007826.4362305992199
7351955126.2325782157268.7674217842787
7451355203.36196947362-68.361969473619
7552005150.3679487857749.6320512142338
7651505208.51200912979-58.512009129794
7751055163.62291014982-58.6229101498157
7851055113.35465507549-8.35465507548997
7950305107.77751619589-77.7775161958853
8050605032.4370756595527.5629243404537
8150755054.8083541886820.1916458113246
8250305072.33408501443-42.3340850144286
8350905029.5232729425660.4767270574375
8450705085.10118406272-15.1011840627179
8551605070.9954172866889.0045827133181
8651105159.01792476766-49.0179247676606
8751455117.8515269455927.1484730544053
8850755147.98564911515-72.9856491151513
8951255081.0244171871343.9755828128746
9050555123.75825004904-68.7582500490353
9150505058.38702603748-8.38702603747515
9250405046.83727549852-6.83727549852483
9350205036.07284258571-16.072842585706
9450255015.511951056869.48804894313707
9549605018.91296557253-58.9129655725337
9649654955.173169487119.8268305128895
9748754954.46032072888-79.4603207288792
9848054865.87494792539-60.8749479253875
9947354788.60940664139-53.609406641388
10047754713.0846085875661.9153914124354
10148154747.571763462367.4282365377021
10248704793.1144381800676.8855618199404
10348604854.130133374155.8698666258515
10448754851.4748885533223.5251114466755
10549004866.8987128746633.1012871253433
10648554893.96029658323-38.9602965832264
10748804852.3685529107927.6314470892094
10848504873.4651544551-23.4651544551007
10948804846.2564760877233.7435239122806
11049004873.8040597716126.1959402283874
11149104896.8873897362813.1126102637245
11249354909.3239151773725.6760848226259
11349654935.4301462567629.569853743239
11449454967.71913515772-22.7191351577239
11549654950.6920815985214.3079184014769
11649504968.42657983321-18.4265798332117

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3840 & 3810 & 30 \tabularnewline
4 & 3900 & 3854.82201130274 & 45.1779886972604 \tabularnewline
5 & 3940 & 3917.43341307915 & 22.5665869208519 \tabularnewline
6 & 3990 & 3961.63577132851 & 28.3642286714862 \tabularnewline
7 & 4050 & 4013.63345931092 & 36.3665406890846 \tabularnewline
8 & 4090 & 4076.14013546779 & 13.8598645322108 \tabularnewline
9 & 4145 & 4119.54841555329 & 25.4515844467114 \tabularnewline
10 & 4190 & 4175.72770106515 & 14.2722989348522 \tabularnewline
11 & 4175 & 4223.08590184294 & -48.0859018429355 \tabularnewline
12 & 4230 & 4209.74106808278 & 20.2589319172166 \tabularnewline
13 & 4220 & 4260.00552242927 & -40.0055224292655 \tabularnewline
14 & 4245 & 4252.1873533087 & -7.18735330870095 \tabularnewline
15 & 4295 & 4273.39021108482 & 21.6097889151833 \tabularnewline
16 & 4290 & 4322.57214919506 & -32.5721491950571 \tabularnewline
17 & 4325 & 4319.83953528668 & 5.16046471331538 \tabularnewline
18 & 4335 & 4351.68259927241 & -16.6825992724125 \tabularnewline
19 & 4360 & 4362.27688483458 & -2.27688483457587 \tabularnewline
20 & 4360 & 4385.68917491496 & -25.6891749149636 \tabularnewline
21 & 4320 & 4385.62304916957 & -65.6230491695724 \tabularnewline
22 & 4310 & 4343.5467059066 & -33.5467059066004 \tabularnewline
23 & 4345 & 4327.4471475023 & 17.5528524977044 \tabularnewline
24 & 4315 & 4359.12314871016 & -44.1231487101632 \tabularnewline
25 & 4315 & 4331.06967610262 & -16.0696761026229 \tabularnewline
26 & 4335 & 4326.9300169408 & 8.06998305920115 \tabularnewline
27 & 4365 & 4345.33974870313 & 19.6602512968657 \tabularnewline
28 & 4410 & 4375.99767324091 & 34.002326759085 \tabularnewline
29 & 4435 & 4422.6829565843 & 12.3170434156955 \tabularnewline
30 & 4440 & 4450.87346969046 & -10.8734696904639 \tabularnewline
31 & 4390 & 4457.12018810101 & -67.1201881010093 \tabularnewline
32 & 4445 & 4406.47475884574 & 38.5252411542642 \tabularnewline
33 & 4470 & 4454.8039032774 & 15.1960967226032 \tabularnewline
34 & 4430 & 4483.41145056336 & -53.4114505633634 \tabularnewline
35 & 4450 & 4445.1868804212 & 4.81311957879552 \tabularnewline
36 & 4480 & 4460.03182068881 & 19.9681793111895 \tabularnewline
37 & 4565 & 4490.37532011454 & 74.6246798854645 \tabularnewline
38 & 4515 & 4576.84914815066 & -61.8491481506553 \tabularnewline
39 & 4490 & 4534.37867477933 & -44.3786747793338 \tabularnewline
40 & 4535 & 4503.70560613098 & 31.2943938690169 \tabularnewline
41 & 4545 & 4544.26041225897 & 0.739587741031755 \tabularnewline
42 & 4555 & 4557.25970282338 & -2.25970282337948 \tabularnewline
43 & 4575 & 4567.34409617986 & 7.65590382014307 \tabularnewline
44 & 4585 & 4587.08178468314 & -2.08178468314327 \tabularnewline
45 & 4600 & 4597.82895988744 & 2.17104011255651 \tabularnewline
46 & 4690 & 4612.61626667412 & 77.3837333258762 \tabularnewline
47 & 4720 & 4702.36553172884 & 17.6344682711615 \tabularnewline
48 & 4780 & 4739.68830321634 & 40.311696783664 \tabularnewline
49 & 4775 & 4801.14171593003 & -26.1417159300281 \tabularnewline
50 & 4830 & 4800.16598510555 & 29.8340148944462 \tabularnewline
51 & 4865 & 4852.47986372427 & 12.5201362757261 \tabularnewline
52 & 4945 & 4890.26909164465 & 54.7309083553464 \tabularnewline
53 & 5005 & 4971.14607525816 & 33.8539247418403 \tabularnewline
54 & 5065 & 5036.19836844999 & 28.8016315500145 \tabularnewline
55 & 5105 & 5099.27683538303 & 5.72316461696664 \tabularnewline
56 & 5080 & 5142.00729988293 & -62.0072998829282 \tabularnewline
57 & 5045 & 5117.92450362803 & -72.9245036280308 \tabularnewline
58 & 5115 & 5077.40561652418 & 37.5943834758173 \tabularnewline
59 & 5095 & 5140.18317759171 & -45.1831775917135 \tabularnewline
60 & 5075 & 5124.05960750363 & -49.0596075036274 \tabularnewline
61 & 5080 & 5100.01393315778 & -20.0139331577784 \tabularnewline
62 & 5115 & 5100.42386706966 & 14.5761329303359 \tabularnewline
63 & 5115 & 5133.41642296817 & -18.4164229681692 \tabularnewline
64 & 5115 & 5134.92472387856 & -19.9247238785583 \tabularnewline
65 & 5065 & 5133.27530306408 & -68.2753030640797 \tabularnewline
66 & 5045 & 5081.76797536255 & -36.7679753625525 \tabularnewline
67 & 5080 & 5055.43296167229 & 24.5670383277147 \tabularnewline
68 & 5115 & 5086.7581661946 & 28.2418338054049 \tabularnewline
69 & 5080 & 5123.9485863885 & -43.9485863885011 \tabularnewline
70 & 5100 & 5091.92002108088 & 8.07997891912237 \tabularnewline
71 & 5085 & 5107.65383779366 & -22.653837793664 \tabularnewline
72 & 5120 & 5093.56376940078 & 26.4362305992199 \tabularnewline
73 & 5195 & 5126.23257821572 & 68.7674217842787 \tabularnewline
74 & 5135 & 5203.36196947362 & -68.361969473619 \tabularnewline
75 & 5200 & 5150.36794878577 & 49.6320512142338 \tabularnewline
76 & 5150 & 5208.51200912979 & -58.512009129794 \tabularnewline
77 & 5105 & 5163.62291014982 & -58.6229101498157 \tabularnewline
78 & 5105 & 5113.35465507549 & -8.35465507548997 \tabularnewline
79 & 5030 & 5107.77751619589 & -77.7775161958853 \tabularnewline
80 & 5060 & 5032.43707565955 & 27.5629243404537 \tabularnewline
81 & 5075 & 5054.80835418868 & 20.1916458113246 \tabularnewline
82 & 5030 & 5072.33408501443 & -42.3340850144286 \tabularnewline
83 & 5090 & 5029.52327294256 & 60.4767270574375 \tabularnewline
84 & 5070 & 5085.10118406272 & -15.1011840627179 \tabularnewline
85 & 5160 & 5070.99541728668 & 89.0045827133181 \tabularnewline
86 & 5110 & 5159.01792476766 & -49.0179247676606 \tabularnewline
87 & 5145 & 5117.85152694559 & 27.1484730544053 \tabularnewline
88 & 5075 & 5147.98564911515 & -72.9856491151513 \tabularnewline
89 & 5125 & 5081.02441718713 & 43.9755828128746 \tabularnewline
90 & 5055 & 5123.75825004904 & -68.7582500490353 \tabularnewline
91 & 5050 & 5058.38702603748 & -8.38702603747515 \tabularnewline
92 & 5040 & 5046.83727549852 & -6.83727549852483 \tabularnewline
93 & 5020 & 5036.07284258571 & -16.072842585706 \tabularnewline
94 & 5025 & 5015.51195105686 & 9.48804894313707 \tabularnewline
95 & 4960 & 5018.91296557253 & -58.9129655725337 \tabularnewline
96 & 4965 & 4955.17316948711 & 9.8268305128895 \tabularnewline
97 & 4875 & 4954.46032072888 & -79.4603207288792 \tabularnewline
98 & 4805 & 4865.87494792539 & -60.8749479253875 \tabularnewline
99 & 4735 & 4788.60940664139 & -53.609406641388 \tabularnewline
100 & 4775 & 4713.08460858756 & 61.9153914124354 \tabularnewline
101 & 4815 & 4747.5717634623 & 67.4282365377021 \tabularnewline
102 & 4870 & 4793.11443818006 & 76.8855618199404 \tabularnewline
103 & 4860 & 4854.13013337415 & 5.8698666258515 \tabularnewline
104 & 4875 & 4851.47488855332 & 23.5251114466755 \tabularnewline
105 & 4900 & 4866.89871287466 & 33.1012871253433 \tabularnewline
106 & 4855 & 4893.96029658323 & -38.9602965832264 \tabularnewline
107 & 4880 & 4852.36855291079 & 27.6314470892094 \tabularnewline
108 & 4850 & 4873.4651544551 & -23.4651544551007 \tabularnewline
109 & 4880 & 4846.25647608772 & 33.7435239122806 \tabularnewline
110 & 4900 & 4873.80405977161 & 26.1959402283874 \tabularnewline
111 & 4910 & 4896.88738973628 & 13.1126102637245 \tabularnewline
112 & 4935 & 4909.32391517737 & 25.6760848226259 \tabularnewline
113 & 4965 & 4935.43014625676 & 29.569853743239 \tabularnewline
114 & 4945 & 4967.71913515772 & -22.7191351577239 \tabularnewline
115 & 4965 & 4950.69208159852 & 14.3079184014769 \tabularnewline
116 & 4950 & 4968.42657983321 & -18.4265798332117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298276&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]3840[/C][C]3810[/C][C]30[/C][/ROW]
[ROW][C]4[/C][C]3900[/C][C]3854.82201130274[/C][C]45.1779886972604[/C][/ROW]
[ROW][C]5[/C][C]3940[/C][C]3917.43341307915[/C][C]22.5665869208519[/C][/ROW]
[ROW][C]6[/C][C]3990[/C][C]3961.63577132851[/C][C]28.3642286714862[/C][/ROW]
[ROW][C]7[/C][C]4050[/C][C]4013.63345931092[/C][C]36.3665406890846[/C][/ROW]
[ROW][C]8[/C][C]4090[/C][C]4076.14013546779[/C][C]13.8598645322108[/C][/ROW]
[ROW][C]9[/C][C]4145[/C][C]4119.54841555329[/C][C]25.4515844467114[/C][/ROW]
[ROW][C]10[/C][C]4190[/C][C]4175.72770106515[/C][C]14.2722989348522[/C][/ROW]
[ROW][C]11[/C][C]4175[/C][C]4223.08590184294[/C][C]-48.0859018429355[/C][/ROW]
[ROW][C]12[/C][C]4230[/C][C]4209.74106808278[/C][C]20.2589319172166[/C][/ROW]
[ROW][C]13[/C][C]4220[/C][C]4260.00552242927[/C][C]-40.0055224292655[/C][/ROW]
[ROW][C]14[/C][C]4245[/C][C]4252.1873533087[/C][C]-7.18735330870095[/C][/ROW]
[ROW][C]15[/C][C]4295[/C][C]4273.39021108482[/C][C]21.6097889151833[/C][/ROW]
[ROW][C]16[/C][C]4290[/C][C]4322.57214919506[/C][C]-32.5721491950571[/C][/ROW]
[ROW][C]17[/C][C]4325[/C][C]4319.83953528668[/C][C]5.16046471331538[/C][/ROW]
[ROW][C]18[/C][C]4335[/C][C]4351.68259927241[/C][C]-16.6825992724125[/C][/ROW]
[ROW][C]19[/C][C]4360[/C][C]4362.27688483458[/C][C]-2.27688483457587[/C][/ROW]
[ROW][C]20[/C][C]4360[/C][C]4385.68917491496[/C][C]-25.6891749149636[/C][/ROW]
[ROW][C]21[/C][C]4320[/C][C]4385.62304916957[/C][C]-65.6230491695724[/C][/ROW]
[ROW][C]22[/C][C]4310[/C][C]4343.5467059066[/C][C]-33.5467059066004[/C][/ROW]
[ROW][C]23[/C][C]4345[/C][C]4327.4471475023[/C][C]17.5528524977044[/C][/ROW]
[ROW][C]24[/C][C]4315[/C][C]4359.12314871016[/C][C]-44.1231487101632[/C][/ROW]
[ROW][C]25[/C][C]4315[/C][C]4331.06967610262[/C][C]-16.0696761026229[/C][/ROW]
[ROW][C]26[/C][C]4335[/C][C]4326.9300169408[/C][C]8.06998305920115[/C][/ROW]
[ROW][C]27[/C][C]4365[/C][C]4345.33974870313[/C][C]19.6602512968657[/C][/ROW]
[ROW][C]28[/C][C]4410[/C][C]4375.99767324091[/C][C]34.002326759085[/C][/ROW]
[ROW][C]29[/C][C]4435[/C][C]4422.6829565843[/C][C]12.3170434156955[/C][/ROW]
[ROW][C]30[/C][C]4440[/C][C]4450.87346969046[/C][C]-10.8734696904639[/C][/ROW]
[ROW][C]31[/C][C]4390[/C][C]4457.12018810101[/C][C]-67.1201881010093[/C][/ROW]
[ROW][C]32[/C][C]4445[/C][C]4406.47475884574[/C][C]38.5252411542642[/C][/ROW]
[ROW][C]33[/C][C]4470[/C][C]4454.8039032774[/C][C]15.1960967226032[/C][/ROW]
[ROW][C]34[/C][C]4430[/C][C]4483.41145056336[/C][C]-53.4114505633634[/C][/ROW]
[ROW][C]35[/C][C]4450[/C][C]4445.1868804212[/C][C]4.81311957879552[/C][/ROW]
[ROW][C]36[/C][C]4480[/C][C]4460.03182068881[/C][C]19.9681793111895[/C][/ROW]
[ROW][C]37[/C][C]4565[/C][C]4490.37532011454[/C][C]74.6246798854645[/C][/ROW]
[ROW][C]38[/C][C]4515[/C][C]4576.84914815066[/C][C]-61.8491481506553[/C][/ROW]
[ROW][C]39[/C][C]4490[/C][C]4534.37867477933[/C][C]-44.3786747793338[/C][/ROW]
[ROW][C]40[/C][C]4535[/C][C]4503.70560613098[/C][C]31.2943938690169[/C][/ROW]
[ROW][C]41[/C][C]4545[/C][C]4544.26041225897[/C][C]0.739587741031755[/C][/ROW]
[ROW][C]42[/C][C]4555[/C][C]4557.25970282338[/C][C]-2.25970282337948[/C][/ROW]
[ROW][C]43[/C][C]4575[/C][C]4567.34409617986[/C][C]7.65590382014307[/C][/ROW]
[ROW][C]44[/C][C]4585[/C][C]4587.08178468314[/C][C]-2.08178468314327[/C][/ROW]
[ROW][C]45[/C][C]4600[/C][C]4597.82895988744[/C][C]2.17104011255651[/C][/ROW]
[ROW][C]46[/C][C]4690[/C][C]4612.61626667412[/C][C]77.3837333258762[/C][/ROW]
[ROW][C]47[/C][C]4720[/C][C]4702.36553172884[/C][C]17.6344682711615[/C][/ROW]
[ROW][C]48[/C][C]4780[/C][C]4739.68830321634[/C][C]40.311696783664[/C][/ROW]
[ROW][C]49[/C][C]4775[/C][C]4801.14171593003[/C][C]-26.1417159300281[/C][/ROW]
[ROW][C]50[/C][C]4830[/C][C]4800.16598510555[/C][C]29.8340148944462[/C][/ROW]
[ROW][C]51[/C][C]4865[/C][C]4852.47986372427[/C][C]12.5201362757261[/C][/ROW]
[ROW][C]52[/C][C]4945[/C][C]4890.26909164465[/C][C]54.7309083553464[/C][/ROW]
[ROW][C]53[/C][C]5005[/C][C]4971.14607525816[/C][C]33.8539247418403[/C][/ROW]
[ROW][C]54[/C][C]5065[/C][C]5036.19836844999[/C][C]28.8016315500145[/C][/ROW]
[ROW][C]55[/C][C]5105[/C][C]5099.27683538303[/C][C]5.72316461696664[/C][/ROW]
[ROW][C]56[/C][C]5080[/C][C]5142.00729988293[/C][C]-62.0072998829282[/C][/ROW]
[ROW][C]57[/C][C]5045[/C][C]5117.92450362803[/C][C]-72.9245036280308[/C][/ROW]
[ROW][C]58[/C][C]5115[/C][C]5077.40561652418[/C][C]37.5943834758173[/C][/ROW]
[ROW][C]59[/C][C]5095[/C][C]5140.18317759171[/C][C]-45.1831775917135[/C][/ROW]
[ROW][C]60[/C][C]5075[/C][C]5124.05960750363[/C][C]-49.0596075036274[/C][/ROW]
[ROW][C]61[/C][C]5080[/C][C]5100.01393315778[/C][C]-20.0139331577784[/C][/ROW]
[ROW][C]62[/C][C]5115[/C][C]5100.42386706966[/C][C]14.5761329303359[/C][/ROW]
[ROW][C]63[/C][C]5115[/C][C]5133.41642296817[/C][C]-18.4164229681692[/C][/ROW]
[ROW][C]64[/C][C]5115[/C][C]5134.92472387856[/C][C]-19.9247238785583[/C][/ROW]
[ROW][C]65[/C][C]5065[/C][C]5133.27530306408[/C][C]-68.2753030640797[/C][/ROW]
[ROW][C]66[/C][C]5045[/C][C]5081.76797536255[/C][C]-36.7679753625525[/C][/ROW]
[ROW][C]67[/C][C]5080[/C][C]5055.43296167229[/C][C]24.5670383277147[/C][/ROW]
[ROW][C]68[/C][C]5115[/C][C]5086.7581661946[/C][C]28.2418338054049[/C][/ROW]
[ROW][C]69[/C][C]5080[/C][C]5123.9485863885[/C][C]-43.9485863885011[/C][/ROW]
[ROW][C]70[/C][C]5100[/C][C]5091.92002108088[/C][C]8.07997891912237[/C][/ROW]
[ROW][C]71[/C][C]5085[/C][C]5107.65383779366[/C][C]-22.653837793664[/C][/ROW]
[ROW][C]72[/C][C]5120[/C][C]5093.56376940078[/C][C]26.4362305992199[/C][/ROW]
[ROW][C]73[/C][C]5195[/C][C]5126.23257821572[/C][C]68.7674217842787[/C][/ROW]
[ROW][C]74[/C][C]5135[/C][C]5203.36196947362[/C][C]-68.361969473619[/C][/ROW]
[ROW][C]75[/C][C]5200[/C][C]5150.36794878577[/C][C]49.6320512142338[/C][/ROW]
[ROW][C]76[/C][C]5150[/C][C]5208.51200912979[/C][C]-58.512009129794[/C][/ROW]
[ROW][C]77[/C][C]5105[/C][C]5163.62291014982[/C][C]-58.6229101498157[/C][/ROW]
[ROW][C]78[/C][C]5105[/C][C]5113.35465507549[/C][C]-8.35465507548997[/C][/ROW]
[ROW][C]79[/C][C]5030[/C][C]5107.77751619589[/C][C]-77.7775161958853[/C][/ROW]
[ROW][C]80[/C][C]5060[/C][C]5032.43707565955[/C][C]27.5629243404537[/C][/ROW]
[ROW][C]81[/C][C]5075[/C][C]5054.80835418868[/C][C]20.1916458113246[/C][/ROW]
[ROW][C]82[/C][C]5030[/C][C]5072.33408501443[/C][C]-42.3340850144286[/C][/ROW]
[ROW][C]83[/C][C]5090[/C][C]5029.52327294256[/C][C]60.4767270574375[/C][/ROW]
[ROW][C]84[/C][C]5070[/C][C]5085.10118406272[/C][C]-15.1011840627179[/C][/ROW]
[ROW][C]85[/C][C]5160[/C][C]5070.99541728668[/C][C]89.0045827133181[/C][/ROW]
[ROW][C]86[/C][C]5110[/C][C]5159.01792476766[/C][C]-49.0179247676606[/C][/ROW]
[ROW][C]87[/C][C]5145[/C][C]5117.85152694559[/C][C]27.1484730544053[/C][/ROW]
[ROW][C]88[/C][C]5075[/C][C]5147.98564911515[/C][C]-72.9856491151513[/C][/ROW]
[ROW][C]89[/C][C]5125[/C][C]5081.02441718713[/C][C]43.9755828128746[/C][/ROW]
[ROW][C]90[/C][C]5055[/C][C]5123.75825004904[/C][C]-68.7582500490353[/C][/ROW]
[ROW][C]91[/C][C]5050[/C][C]5058.38702603748[/C][C]-8.38702603747515[/C][/ROW]
[ROW][C]92[/C][C]5040[/C][C]5046.83727549852[/C][C]-6.83727549852483[/C][/ROW]
[ROW][C]93[/C][C]5020[/C][C]5036.07284258571[/C][C]-16.072842585706[/C][/ROW]
[ROW][C]94[/C][C]5025[/C][C]5015.51195105686[/C][C]9.48804894313707[/C][/ROW]
[ROW][C]95[/C][C]4960[/C][C]5018.91296557253[/C][C]-58.9129655725337[/C][/ROW]
[ROW][C]96[/C][C]4965[/C][C]4955.17316948711[/C][C]9.8268305128895[/C][/ROW]
[ROW][C]97[/C][C]4875[/C][C]4954.46032072888[/C][C]-79.4603207288792[/C][/ROW]
[ROW][C]98[/C][C]4805[/C][C]4865.87494792539[/C][C]-60.8749479253875[/C][/ROW]
[ROW][C]99[/C][C]4735[/C][C]4788.60940664139[/C][C]-53.609406641388[/C][/ROW]
[ROW][C]100[/C][C]4775[/C][C]4713.08460858756[/C][C]61.9153914124354[/C][/ROW]
[ROW][C]101[/C][C]4815[/C][C]4747.5717634623[/C][C]67.4282365377021[/C][/ROW]
[ROW][C]102[/C][C]4870[/C][C]4793.11443818006[/C][C]76.8855618199404[/C][/ROW]
[ROW][C]103[/C][C]4860[/C][C]4854.13013337415[/C][C]5.8698666258515[/C][/ROW]
[ROW][C]104[/C][C]4875[/C][C]4851.47488855332[/C][C]23.5251114466755[/C][/ROW]
[ROW][C]105[/C][C]4900[/C][C]4866.89871287466[/C][C]33.1012871253433[/C][/ROW]
[ROW][C]106[/C][C]4855[/C][C]4893.96029658323[/C][C]-38.9602965832264[/C][/ROW]
[ROW][C]107[/C][C]4880[/C][C]4852.36855291079[/C][C]27.6314470892094[/C][/ROW]
[ROW][C]108[/C][C]4850[/C][C]4873.4651544551[/C][C]-23.4651544551007[/C][/ROW]
[ROW][C]109[/C][C]4880[/C][C]4846.25647608772[/C][C]33.7435239122806[/C][/ROW]
[ROW][C]110[/C][C]4900[/C][C]4873.80405977161[/C][C]26.1959402283874[/C][/ROW]
[ROW][C]111[/C][C]4910[/C][C]4896.88738973628[/C][C]13.1126102637245[/C][/ROW]
[ROW][C]112[/C][C]4935[/C][C]4909.32391517737[/C][C]25.6760848226259[/C][/ROW]
[ROW][C]113[/C][C]4965[/C][C]4935.43014625676[/C][C]29.569853743239[/C][/ROW]
[ROW][C]114[/C][C]4945[/C][C]4967.71913515772[/C][C]-22.7191351577239[/C][/ROW]
[ROW][C]115[/C][C]4965[/C][C]4950.69208159852[/C][C]14.3079184014769[/C][/ROW]
[ROW][C]116[/C][C]4950[/C][C]4968.42657983321[/C][C]-18.4265798332117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298276&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298276&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
33840381030
439003854.8220113027445.1779886972604
539403917.4334130791522.5665869208519
639903961.6357713285128.3642286714862
740504013.6334593109236.3665406890846
840904076.1401354677913.8598645322108
941454119.5484155532925.4515844467114
1041904175.7277010651514.2722989348522
1141754223.08590184294-48.0859018429355
1242304209.7410680827820.2589319172166
1342204260.00552242927-40.0055224292655
1442454252.1873533087-7.18735330870095
1542954273.3902110848221.6097889151833
1642904322.57214919506-32.5721491950571
1743254319.839535286685.16046471331538
1843354351.68259927241-16.6825992724125
1943604362.27688483458-2.27688483457587
2043604385.68917491496-25.6891749149636
2143204385.62304916957-65.6230491695724
2243104343.5467059066-33.5467059066004
2343454327.447147502317.5528524977044
2443154359.12314871016-44.1231487101632
2543154331.06967610262-16.0696761026229
2643354326.93001694088.06998305920115
2743654345.3397487031319.6602512968657
2844104375.9976732409134.002326759085
2944354422.682956584312.3170434156955
3044404450.87346969046-10.8734696904639
3143904457.12018810101-67.1201881010093
3244454406.4747588457438.5252411542642
3344704454.803903277415.1960967226032
3444304483.41145056336-53.4114505633634
3544504445.18688042124.81311957879552
3644804460.0318206888119.9681793111895
3745654490.3753201145474.6246798854645
3845154576.84914815066-61.8491481506553
3944904534.37867477933-44.3786747793338
4045354503.7056061309831.2943938690169
4145454544.260412258970.739587741031755
4245554557.25970282338-2.25970282337948
4345754567.344096179867.65590382014307
4445854587.08178468314-2.08178468314327
4546004597.828959887442.17104011255651
4646904612.6162666741277.3837333258762
4747204702.3655317288417.6344682711615
4847804739.6883032163440.311696783664
4947754801.14171593003-26.1417159300281
5048304800.1659851055529.8340148944462
5148654852.4798637242712.5201362757261
5249454890.2690916446554.7309083553464
5350054971.1460752581633.8539247418403
5450655036.1983684499928.8016315500145
5551055099.276835383035.72316461696664
5650805142.00729988293-62.0072998829282
5750455117.92450362803-72.9245036280308
5851155077.4056165241837.5943834758173
5950955140.18317759171-45.1831775917135
6050755124.05960750363-49.0596075036274
6150805100.01393315778-20.0139331577784
6251155100.4238670696614.5761329303359
6351155133.41642296817-18.4164229681692
6451155134.92472387856-19.9247238785583
6550655133.27530306408-68.2753030640797
6650455081.76797536255-36.7679753625525
6750805055.4329616722924.5670383277147
6851155086.758166194628.2418338054049
6950805123.9485863885-43.9485863885011
7051005091.920021080888.07997891912237
7150855107.65383779366-22.653837793664
7251205093.5637694007826.4362305992199
7351955126.2325782157268.7674217842787
7451355203.36196947362-68.361969473619
7552005150.3679487857749.6320512142338
7651505208.51200912979-58.512009129794
7751055163.62291014982-58.6229101498157
7851055113.35465507549-8.35465507548997
7950305107.77751619589-77.7775161958853
8050605032.4370756595527.5629243404537
8150755054.8083541886820.1916458113246
8250305072.33408501443-42.3340850144286
8350905029.5232729425660.4767270574375
8450705085.10118406272-15.1011840627179
8551605070.9954172866889.0045827133181
8651105159.01792476766-49.0179247676606
8751455117.8515269455927.1484730544053
8850755147.98564911515-72.9856491151513
8951255081.0244171871343.9755828128746
9050555123.75825004904-68.7582500490353
9150505058.38702603748-8.38702603747515
9250405046.83727549852-6.83727549852483
9350205036.07284258571-16.072842585706
9450255015.511951056869.48804894313707
9549605018.91296557253-58.9129655725337
9649654955.173169487119.8268305128895
9748754954.46032072888-79.4603207288792
9848054865.87494792539-60.8749479253875
9947354788.60940664139-53.609406641388
10047754713.0846085875661.9153914124354
10148154747.571763462367.4282365377021
10248704793.1144381800676.8855618199404
10348604854.130133374155.8698666258515
10448754851.4748885533223.5251114466755
10549004866.8987128746633.1012871253433
10648554893.96029658323-38.9602965832264
10748804852.3685529107927.6314470892094
10848504873.4651544551-23.4651544551007
10948804846.2564760877233.7435239122806
11049004873.8040597716126.1959402283874
11149104896.8873897362813.1126102637245
11249354909.3239151773725.6760848226259
11349654935.4301462567629.569853743239
11449454967.71913515772-22.7191351577239
11549654950.6920815985214.3079184014769
11649504968.42657983321-18.4265798332117







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174954.909197408394876.295103827945033.52329098885
1184958.049786611044847.201983147235068.89759007485
1194961.190375813684821.366075344215101.01467628315
1204964.330965016334796.786342050975131.87558798168
1214967.471554218974772.667655004215162.27545343373
1224970.612143421614748.614087205245192.61019963798
1234973.752732624264724.4032575975223.10220765151
1244976.89332182694699.900800420845253.88584323296
1254980.033911029544675.021694573465285.04612748562
1264983.174500232194649.710599514115316.63840095026
1274986.315089434834623.93097531435348.69920355536
1284989.455678637474597.658667405985381.25268986896

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4954.90919740839 & 4876.29510382794 & 5033.52329098885 \tabularnewline
118 & 4958.04978661104 & 4847.20198314723 & 5068.89759007485 \tabularnewline
119 & 4961.19037581368 & 4821.36607534421 & 5101.01467628315 \tabularnewline
120 & 4964.33096501633 & 4796.78634205097 & 5131.87558798168 \tabularnewline
121 & 4967.47155421897 & 4772.66765500421 & 5162.27545343373 \tabularnewline
122 & 4970.61214342161 & 4748.61408720524 & 5192.61019963798 \tabularnewline
123 & 4973.75273262426 & 4724.403257597 & 5223.10220765151 \tabularnewline
124 & 4976.8933218269 & 4699.90080042084 & 5253.88584323296 \tabularnewline
125 & 4980.03391102954 & 4675.02169457346 & 5285.04612748562 \tabularnewline
126 & 4983.17450023219 & 4649.71059951411 & 5316.63840095026 \tabularnewline
127 & 4986.31508943483 & 4623.9309753143 & 5348.69920355536 \tabularnewline
128 & 4989.45567863747 & 4597.65866740598 & 5381.25268986896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298276&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]4954.90919740839[/C][C]4876.29510382794[/C][C]5033.52329098885[/C][/ROW]
[ROW][C]118[/C][C]4958.04978661104[/C][C]4847.20198314723[/C][C]5068.89759007485[/C][/ROW]
[ROW][C]119[/C][C]4961.19037581368[/C][C]4821.36607534421[/C][C]5101.01467628315[/C][/ROW]
[ROW][C]120[/C][C]4964.33096501633[/C][C]4796.78634205097[/C][C]5131.87558798168[/C][/ROW]
[ROW][C]121[/C][C]4967.47155421897[/C][C]4772.66765500421[/C][C]5162.27545343373[/C][/ROW]
[ROW][C]122[/C][C]4970.61214342161[/C][C]4748.61408720524[/C][C]5192.61019963798[/C][/ROW]
[ROW][C]123[/C][C]4973.75273262426[/C][C]4724.403257597[/C][C]5223.10220765151[/C][/ROW]
[ROW][C]124[/C][C]4976.8933218269[/C][C]4699.90080042084[/C][C]5253.88584323296[/C][/ROW]
[ROW][C]125[/C][C]4980.03391102954[/C][C]4675.02169457346[/C][C]5285.04612748562[/C][/ROW]
[ROW][C]126[/C][C]4983.17450023219[/C][C]4649.71059951411[/C][C]5316.63840095026[/C][/ROW]
[ROW][C]127[/C][C]4986.31508943483[/C][C]4623.9309753143[/C][C]5348.69920355536[/C][/ROW]
[ROW][C]128[/C][C]4989.45567863747[/C][C]4597.65866740598[/C][C]5381.25268986896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298276&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298276&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
1174954.909197408394876.295103827945033.52329098885
1184958.049786611044847.201983147235068.89759007485
1194961.190375813684821.366075344215101.01467628315
1204964.330965016334796.786342050975131.87558798168
1214967.471554218974772.667655004215162.27545343373
1224970.612143421614748.614087205245192.61019963798
1234973.752732624264724.4032575975223.10220765151
1244976.89332182694699.900800420845253.88584323296
1254980.033911029544675.021694573465285.04612748562
1264983.174500232194649.710599514115316.63840095026
1274986.315089434834623.93097531435348.69920355536
1284989.455678637474597.658667405985381.25268986896



Parameters (Session):
par1 = 121212 ; par2 = periodic18Double ; par3 = 0BFGSadditive ; par4 = 12 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')