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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Dec 2016 22:07:52 +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/16/t1481923397o182shzvcf00lu0.htm/, Retrieved Fri, 01 Nov 2024 03:28:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300564, Retrieved Fri, 01 Nov 2024 03:28:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-16 21:07:52] [8dbd6448339a84ba150e9d534057ba9c] [Current]
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Dataseries X:
4400
4300
4610
4100
4000
4130
4320
4560
4430
4580
4370
4480
4520
4320
4960
4450
4680
4570
4520
5450
5110
4820
4640
4510
4450
4650
4720
4380
4870
4350
4160
4770
4400
4700
4520
4290
4520
4500
4690
4380
4620
4230
4310
4900
4740
5080
5090
4500
4670
4710
4310
4390
4530
4490
4720
5150
5220
5490
5260
5050
4890
4960
5120
5060
5430
5360
5090
5390
5330
5560
5370
5040
4760
4630
4790
4550
5180
5020
5040
5590
5330
5550
5630
5540
4880
4550
4530
4580
5090
4720
4900
5840
5250
5530
5370
4730
5030
4980
5080
4750
4890
4640
4800
5600
5040
5720
5650
4900
5240
5120
4950
5320
5590
4850
5180
5700
5370
5820
5940
5270
5350
5320
5300
5440
5390
5400




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=300564&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=300564&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300564&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
alpha0.426929514032045
beta0.0117506737021564
gamma0.526968289263883

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.426929514032045 \tabularnewline
beta & 0.0117506737021564 \tabularnewline
gamma & 0.526968289263883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300564&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]0.426929514032045[/C][/ROW]
[ROW][C]beta[/C][C]0.0117506737021564[/C][/ROW]
[ROW][C]gamma[/C][C]0.526968289263883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300564&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300564&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
alpha0.426929514032045
beta0.0117506737021564
gamma0.526968289263883







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1345204323.12767094017196.872329059828
1443204199.13766657517120.862333424829
1549604863.3030829179496.6969170820603
1644504394.7200034725955.2799965274062
1746804665.8154752744214.1845247255796
1845704588.18723690969-18.1872369096882
1945204718.73063133238-198.730631332381
2054504905.78108161693544.218918383071
2151105033.1654769491976.8345230508103
2248205227.64513599114-407.645135991136
2346404839.49109244892-199.491092448916
2445104855.45336471864-345.453364718642
2544504816.82046533355-366.820465333554
2646504426.06736234982223.932637650183
2747205124.30414263978-404.304142639781
2843804424.17337525682-44.1733752568243
2948704634.75186402692235.248135973085
3043504637.18828733772-287.188287337718
3141604592.47742800425-432.477428004252
3247704897.03767603798-127.03767603798
3344004586.26980837208-186.269808372078
3447004510.36693549596189.633064504044
3545204431.3178610102888.6821389897232
3642904518.92517260533-228.925172605329
3745204516.868059999663.13194000033855
3845004457.5951278397442.4048721602649
3946904882.83552288487-192.835522884874
4043804377.028092288132.97190771187343
4146204687.63856357462-67.6385635746246
4242304396.99543415622-166.995434156216
4343104354.32784049097-44.3278404909743
4449004913.39283264734-13.3928326473379
4547404630.37840253275109.621597467248
4650804792.92621349291287.073786507093
4750904724.08713462561365.912865374388
4845004834.62483071547-334.624830715471
4946704857.47670013754-187.476700137537
5047104727.68748184526-17.6874818452625
5143105054.93110705131-744.931107051313
5243904368.4786250403621.5213749596405
5345304661.70678152354-131.706781523536
5444904309.40687311352180.593126886479
5547204449.62384196615270.376158033851
5651505151.41046368506-1.41046368505613
5752204909.74403930243310.255960697568
5854905211.62714190888278.372858091119
5952605162.9281197866797.0718802133306
6050504945.83173580634104.168264193663
6148905201.35331695667-311.353316956665
6249605070.22943229582-110.229432295822
6351205138.15690420177-18.1569042017745
6450604996.9057790544563.0942209455452
6554305265.2768372332164.723162766802
6653605138.99775857296221.002241427038
6750905328.93756363937-238.937563639372
6853905734.00862938298-344.008629382983
6953305441.28069487601-111.280694876006
7055605552.537876737087.46212326292061
7153705331.0378043691238.9621956308793
7250405088.59401404559-48.5940140455878
7347605149.96545094135-389.965450941351
7446305042.17468079747-412.174680797467
7547905003.64058130933-213.640581309327
7645504797.13083171282-247.130831712815
7751804955.85437311696224.145626883036
7850204864.34411363737155.655886362632
7950404879.5644957929160.435504207098
8055905417.48891586508172.511084134921
8153305412.23083667649-82.2308366764855
8255505568.56597783182-18.565977831825
8356305342.15244844923287.847551550765
8455405177.45865174938362.541348250623
8548805311.26229151305-431.262291513051
8645505178.92367596922-628.923675969218
8745305106.51093346252-576.510933462525
8845804731.84957850771-151.849578507706
8950905070.9324402760619.0675597239397
9047204867.51644518153-147.516445181534
9149004749.55743920903150.442560790968
9258405281.62258055466558.377419445342
9352505360.86880139881-110.868801398809
9455305520.75610985079.24389014930148
9553705395.44117218698-25.4411721869774
9647305114.67219675734-384.672196757345
9750304681.11927356993348.880726430073
9849804817.44042502411162.559574975887
9950805098.0194501595-18.0194501594988
10047505092.09593884795-342.095938847946
10148905402.67574051481-512.675740514807
10246404920.37199979269-280.371999792692
10348004833.44303347485-33.4430334748495
10456005407.04108870266192.958911297339
10550405123.18738047513-83.1873804751303
10657205326.31806831346393.681931686542
10756505351.73768503252298.262314967483
10849005099.38818995622-199.388189956216
10952404966.09869721707273.901302782931
11051205013.40024172448106.599758275519
11149505214.53302190028-264.533021900284
11253205003.23876140427316.761238595735
11355905544.6370633229845.362936677021
11448505374.57573775679-524.575737756792
11551805260.57979445729-80.5797944572923
11657005884.80915529043-184.809155290429
11753705356.7708087307313.2291912692717
11858205746.0471317306973.9528682693108
11959405605.51802348849334.481976511506
12052705217.8968278186652.1031721813442
12153505335.7172803680114.2827196319859
12253205221.1663481769198.8336518230863
12353005306.37595735747-6.37595735746891
12454405381.6074918905458.3925081094558
12553905730.21071691123-340.210716911234
12654005220.95626824738179.043731752619

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4520 & 4323.12767094017 & 196.872329059828 \tabularnewline
14 & 4320 & 4199.13766657517 & 120.862333424829 \tabularnewline
15 & 4960 & 4863.30308291794 & 96.6969170820603 \tabularnewline
16 & 4450 & 4394.72000347259 & 55.2799965274062 \tabularnewline
17 & 4680 & 4665.81547527442 & 14.1845247255796 \tabularnewline
18 & 4570 & 4588.18723690969 & -18.1872369096882 \tabularnewline
19 & 4520 & 4718.73063133238 & -198.730631332381 \tabularnewline
20 & 5450 & 4905.78108161693 & 544.218918383071 \tabularnewline
21 & 5110 & 5033.16547694919 & 76.8345230508103 \tabularnewline
22 & 4820 & 5227.64513599114 & -407.645135991136 \tabularnewline
23 & 4640 & 4839.49109244892 & -199.491092448916 \tabularnewline
24 & 4510 & 4855.45336471864 & -345.453364718642 \tabularnewline
25 & 4450 & 4816.82046533355 & -366.820465333554 \tabularnewline
26 & 4650 & 4426.06736234982 & 223.932637650183 \tabularnewline
27 & 4720 & 5124.30414263978 & -404.304142639781 \tabularnewline
28 & 4380 & 4424.17337525682 & -44.1733752568243 \tabularnewline
29 & 4870 & 4634.75186402692 & 235.248135973085 \tabularnewline
30 & 4350 & 4637.18828733772 & -287.188287337718 \tabularnewline
31 & 4160 & 4592.47742800425 & -432.477428004252 \tabularnewline
32 & 4770 & 4897.03767603798 & -127.03767603798 \tabularnewline
33 & 4400 & 4586.26980837208 & -186.269808372078 \tabularnewline
34 & 4700 & 4510.36693549596 & 189.633064504044 \tabularnewline
35 & 4520 & 4431.31786101028 & 88.6821389897232 \tabularnewline
36 & 4290 & 4518.92517260533 & -228.925172605329 \tabularnewline
37 & 4520 & 4516.86805999966 & 3.13194000033855 \tabularnewline
38 & 4500 & 4457.59512783974 & 42.4048721602649 \tabularnewline
39 & 4690 & 4882.83552288487 & -192.835522884874 \tabularnewline
40 & 4380 & 4377.02809228813 & 2.97190771187343 \tabularnewline
41 & 4620 & 4687.63856357462 & -67.6385635746246 \tabularnewline
42 & 4230 & 4396.99543415622 & -166.995434156216 \tabularnewline
43 & 4310 & 4354.32784049097 & -44.3278404909743 \tabularnewline
44 & 4900 & 4913.39283264734 & -13.3928326473379 \tabularnewline
45 & 4740 & 4630.37840253275 & 109.621597467248 \tabularnewline
46 & 5080 & 4792.92621349291 & 287.073786507093 \tabularnewline
47 & 5090 & 4724.08713462561 & 365.912865374388 \tabularnewline
48 & 4500 & 4834.62483071547 & -334.624830715471 \tabularnewline
49 & 4670 & 4857.47670013754 & -187.476700137537 \tabularnewline
50 & 4710 & 4727.68748184526 & -17.6874818452625 \tabularnewline
51 & 4310 & 5054.93110705131 & -744.931107051313 \tabularnewline
52 & 4390 & 4368.47862504036 & 21.5213749596405 \tabularnewline
53 & 4530 & 4661.70678152354 & -131.706781523536 \tabularnewline
54 & 4490 & 4309.40687311352 & 180.593126886479 \tabularnewline
55 & 4720 & 4449.62384196615 & 270.376158033851 \tabularnewline
56 & 5150 & 5151.41046368506 & -1.41046368505613 \tabularnewline
57 & 5220 & 4909.74403930243 & 310.255960697568 \tabularnewline
58 & 5490 & 5211.62714190888 & 278.372858091119 \tabularnewline
59 & 5260 & 5162.92811978667 & 97.0718802133306 \tabularnewline
60 & 5050 & 4945.83173580634 & 104.168264193663 \tabularnewline
61 & 4890 & 5201.35331695667 & -311.353316956665 \tabularnewline
62 & 4960 & 5070.22943229582 & -110.229432295822 \tabularnewline
63 & 5120 & 5138.15690420177 & -18.1569042017745 \tabularnewline
64 & 5060 & 4996.90577905445 & 63.0942209455452 \tabularnewline
65 & 5430 & 5265.2768372332 & 164.723162766802 \tabularnewline
66 & 5360 & 5138.99775857296 & 221.002241427038 \tabularnewline
67 & 5090 & 5328.93756363937 & -238.937563639372 \tabularnewline
68 & 5390 & 5734.00862938298 & -344.008629382983 \tabularnewline
69 & 5330 & 5441.28069487601 & -111.280694876006 \tabularnewline
70 & 5560 & 5552.53787673708 & 7.46212326292061 \tabularnewline
71 & 5370 & 5331.03780436912 & 38.9621956308793 \tabularnewline
72 & 5040 & 5088.59401404559 & -48.5940140455878 \tabularnewline
73 & 4760 & 5149.96545094135 & -389.965450941351 \tabularnewline
74 & 4630 & 5042.17468079747 & -412.174680797467 \tabularnewline
75 & 4790 & 5003.64058130933 & -213.640581309327 \tabularnewline
76 & 4550 & 4797.13083171282 & -247.130831712815 \tabularnewline
77 & 5180 & 4955.85437311696 & 224.145626883036 \tabularnewline
78 & 5020 & 4864.34411363737 & 155.655886362632 \tabularnewline
79 & 5040 & 4879.5644957929 & 160.435504207098 \tabularnewline
80 & 5590 & 5417.48891586508 & 172.511084134921 \tabularnewline
81 & 5330 & 5412.23083667649 & -82.2308366764855 \tabularnewline
82 & 5550 & 5568.56597783182 & -18.565977831825 \tabularnewline
83 & 5630 & 5342.15244844923 & 287.847551550765 \tabularnewline
84 & 5540 & 5177.45865174938 & 362.541348250623 \tabularnewline
85 & 4880 & 5311.26229151305 & -431.262291513051 \tabularnewline
86 & 4550 & 5178.92367596922 & -628.923675969218 \tabularnewline
87 & 4530 & 5106.51093346252 & -576.510933462525 \tabularnewline
88 & 4580 & 4731.84957850771 & -151.849578507706 \tabularnewline
89 & 5090 & 5070.93244027606 & 19.0675597239397 \tabularnewline
90 & 4720 & 4867.51644518153 & -147.516445181534 \tabularnewline
91 & 4900 & 4749.55743920903 & 150.442560790968 \tabularnewline
92 & 5840 & 5281.62258055466 & 558.377419445342 \tabularnewline
93 & 5250 & 5360.86880139881 & -110.868801398809 \tabularnewline
94 & 5530 & 5520.7561098507 & 9.24389014930148 \tabularnewline
95 & 5370 & 5395.44117218698 & -25.4411721869774 \tabularnewline
96 & 4730 & 5114.67219675734 & -384.672196757345 \tabularnewline
97 & 5030 & 4681.11927356993 & 348.880726430073 \tabularnewline
98 & 4980 & 4817.44042502411 & 162.559574975887 \tabularnewline
99 & 5080 & 5098.0194501595 & -18.0194501594988 \tabularnewline
100 & 4750 & 5092.09593884795 & -342.095938847946 \tabularnewline
101 & 4890 & 5402.67574051481 & -512.675740514807 \tabularnewline
102 & 4640 & 4920.37199979269 & -280.371999792692 \tabularnewline
103 & 4800 & 4833.44303347485 & -33.4430334748495 \tabularnewline
104 & 5600 & 5407.04108870266 & 192.958911297339 \tabularnewline
105 & 5040 & 5123.18738047513 & -83.1873804751303 \tabularnewline
106 & 5720 & 5326.31806831346 & 393.681931686542 \tabularnewline
107 & 5650 & 5351.73768503252 & 298.262314967483 \tabularnewline
108 & 4900 & 5099.38818995622 & -199.388189956216 \tabularnewline
109 & 5240 & 4966.09869721707 & 273.901302782931 \tabularnewline
110 & 5120 & 5013.40024172448 & 106.599758275519 \tabularnewline
111 & 4950 & 5214.53302190028 & -264.533021900284 \tabularnewline
112 & 5320 & 5003.23876140427 & 316.761238595735 \tabularnewline
113 & 5590 & 5544.63706332298 & 45.362936677021 \tabularnewline
114 & 4850 & 5374.57573775679 & -524.575737756792 \tabularnewline
115 & 5180 & 5260.57979445729 & -80.5797944572923 \tabularnewline
116 & 5700 & 5884.80915529043 & -184.809155290429 \tabularnewline
117 & 5370 & 5356.77080873073 & 13.2291912692717 \tabularnewline
118 & 5820 & 5746.04713173069 & 73.9528682693108 \tabularnewline
119 & 5940 & 5605.51802348849 & 334.481976511506 \tabularnewline
120 & 5270 & 5217.89682781866 & 52.1031721813442 \tabularnewline
121 & 5350 & 5335.71728036801 & 14.2827196319859 \tabularnewline
122 & 5320 & 5221.16634817691 & 98.8336518230863 \tabularnewline
123 & 5300 & 5306.37595735747 & -6.37595735746891 \tabularnewline
124 & 5440 & 5381.60749189054 & 58.3925081094558 \tabularnewline
125 & 5390 & 5730.21071691123 & -340.210716911234 \tabularnewline
126 & 5400 & 5220.95626824738 & 179.043731752619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300564&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]4520[/C][C]4323.12767094017[/C][C]196.872329059828[/C][/ROW]
[ROW][C]14[/C][C]4320[/C][C]4199.13766657517[/C][C]120.862333424829[/C][/ROW]
[ROW][C]15[/C][C]4960[/C][C]4863.30308291794[/C][C]96.6969170820603[/C][/ROW]
[ROW][C]16[/C][C]4450[/C][C]4394.72000347259[/C][C]55.2799965274062[/C][/ROW]
[ROW][C]17[/C][C]4680[/C][C]4665.81547527442[/C][C]14.1845247255796[/C][/ROW]
[ROW][C]18[/C][C]4570[/C][C]4588.18723690969[/C][C]-18.1872369096882[/C][/ROW]
[ROW][C]19[/C][C]4520[/C][C]4718.73063133238[/C][C]-198.730631332381[/C][/ROW]
[ROW][C]20[/C][C]5450[/C][C]4905.78108161693[/C][C]544.218918383071[/C][/ROW]
[ROW][C]21[/C][C]5110[/C][C]5033.16547694919[/C][C]76.8345230508103[/C][/ROW]
[ROW][C]22[/C][C]4820[/C][C]5227.64513599114[/C][C]-407.645135991136[/C][/ROW]
[ROW][C]23[/C][C]4640[/C][C]4839.49109244892[/C][C]-199.491092448916[/C][/ROW]
[ROW][C]24[/C][C]4510[/C][C]4855.45336471864[/C][C]-345.453364718642[/C][/ROW]
[ROW][C]25[/C][C]4450[/C][C]4816.82046533355[/C][C]-366.820465333554[/C][/ROW]
[ROW][C]26[/C][C]4650[/C][C]4426.06736234982[/C][C]223.932637650183[/C][/ROW]
[ROW][C]27[/C][C]4720[/C][C]5124.30414263978[/C][C]-404.304142639781[/C][/ROW]
[ROW][C]28[/C][C]4380[/C][C]4424.17337525682[/C][C]-44.1733752568243[/C][/ROW]
[ROW][C]29[/C][C]4870[/C][C]4634.75186402692[/C][C]235.248135973085[/C][/ROW]
[ROW][C]30[/C][C]4350[/C][C]4637.18828733772[/C][C]-287.188287337718[/C][/ROW]
[ROW][C]31[/C][C]4160[/C][C]4592.47742800425[/C][C]-432.477428004252[/C][/ROW]
[ROW][C]32[/C][C]4770[/C][C]4897.03767603798[/C][C]-127.03767603798[/C][/ROW]
[ROW][C]33[/C][C]4400[/C][C]4586.26980837208[/C][C]-186.269808372078[/C][/ROW]
[ROW][C]34[/C][C]4700[/C][C]4510.36693549596[/C][C]189.633064504044[/C][/ROW]
[ROW][C]35[/C][C]4520[/C][C]4431.31786101028[/C][C]88.6821389897232[/C][/ROW]
[ROW][C]36[/C][C]4290[/C][C]4518.92517260533[/C][C]-228.925172605329[/C][/ROW]
[ROW][C]37[/C][C]4520[/C][C]4516.86805999966[/C][C]3.13194000033855[/C][/ROW]
[ROW][C]38[/C][C]4500[/C][C]4457.59512783974[/C][C]42.4048721602649[/C][/ROW]
[ROW][C]39[/C][C]4690[/C][C]4882.83552288487[/C][C]-192.835522884874[/C][/ROW]
[ROW][C]40[/C][C]4380[/C][C]4377.02809228813[/C][C]2.97190771187343[/C][/ROW]
[ROW][C]41[/C][C]4620[/C][C]4687.63856357462[/C][C]-67.6385635746246[/C][/ROW]
[ROW][C]42[/C][C]4230[/C][C]4396.99543415622[/C][C]-166.995434156216[/C][/ROW]
[ROW][C]43[/C][C]4310[/C][C]4354.32784049097[/C][C]-44.3278404909743[/C][/ROW]
[ROW][C]44[/C][C]4900[/C][C]4913.39283264734[/C][C]-13.3928326473379[/C][/ROW]
[ROW][C]45[/C][C]4740[/C][C]4630.37840253275[/C][C]109.621597467248[/C][/ROW]
[ROW][C]46[/C][C]5080[/C][C]4792.92621349291[/C][C]287.073786507093[/C][/ROW]
[ROW][C]47[/C][C]5090[/C][C]4724.08713462561[/C][C]365.912865374388[/C][/ROW]
[ROW][C]48[/C][C]4500[/C][C]4834.62483071547[/C][C]-334.624830715471[/C][/ROW]
[ROW][C]49[/C][C]4670[/C][C]4857.47670013754[/C][C]-187.476700137537[/C][/ROW]
[ROW][C]50[/C][C]4710[/C][C]4727.68748184526[/C][C]-17.6874818452625[/C][/ROW]
[ROW][C]51[/C][C]4310[/C][C]5054.93110705131[/C][C]-744.931107051313[/C][/ROW]
[ROW][C]52[/C][C]4390[/C][C]4368.47862504036[/C][C]21.5213749596405[/C][/ROW]
[ROW][C]53[/C][C]4530[/C][C]4661.70678152354[/C][C]-131.706781523536[/C][/ROW]
[ROW][C]54[/C][C]4490[/C][C]4309.40687311352[/C][C]180.593126886479[/C][/ROW]
[ROW][C]55[/C][C]4720[/C][C]4449.62384196615[/C][C]270.376158033851[/C][/ROW]
[ROW][C]56[/C][C]5150[/C][C]5151.41046368506[/C][C]-1.41046368505613[/C][/ROW]
[ROW][C]57[/C][C]5220[/C][C]4909.74403930243[/C][C]310.255960697568[/C][/ROW]
[ROW][C]58[/C][C]5490[/C][C]5211.62714190888[/C][C]278.372858091119[/C][/ROW]
[ROW][C]59[/C][C]5260[/C][C]5162.92811978667[/C][C]97.0718802133306[/C][/ROW]
[ROW][C]60[/C][C]5050[/C][C]4945.83173580634[/C][C]104.168264193663[/C][/ROW]
[ROW][C]61[/C][C]4890[/C][C]5201.35331695667[/C][C]-311.353316956665[/C][/ROW]
[ROW][C]62[/C][C]4960[/C][C]5070.22943229582[/C][C]-110.229432295822[/C][/ROW]
[ROW][C]63[/C][C]5120[/C][C]5138.15690420177[/C][C]-18.1569042017745[/C][/ROW]
[ROW][C]64[/C][C]5060[/C][C]4996.90577905445[/C][C]63.0942209455452[/C][/ROW]
[ROW][C]65[/C][C]5430[/C][C]5265.2768372332[/C][C]164.723162766802[/C][/ROW]
[ROW][C]66[/C][C]5360[/C][C]5138.99775857296[/C][C]221.002241427038[/C][/ROW]
[ROW][C]67[/C][C]5090[/C][C]5328.93756363937[/C][C]-238.937563639372[/C][/ROW]
[ROW][C]68[/C][C]5390[/C][C]5734.00862938298[/C][C]-344.008629382983[/C][/ROW]
[ROW][C]69[/C][C]5330[/C][C]5441.28069487601[/C][C]-111.280694876006[/C][/ROW]
[ROW][C]70[/C][C]5560[/C][C]5552.53787673708[/C][C]7.46212326292061[/C][/ROW]
[ROW][C]71[/C][C]5370[/C][C]5331.03780436912[/C][C]38.9621956308793[/C][/ROW]
[ROW][C]72[/C][C]5040[/C][C]5088.59401404559[/C][C]-48.5940140455878[/C][/ROW]
[ROW][C]73[/C][C]4760[/C][C]5149.96545094135[/C][C]-389.965450941351[/C][/ROW]
[ROW][C]74[/C][C]4630[/C][C]5042.17468079747[/C][C]-412.174680797467[/C][/ROW]
[ROW][C]75[/C][C]4790[/C][C]5003.64058130933[/C][C]-213.640581309327[/C][/ROW]
[ROW][C]76[/C][C]4550[/C][C]4797.13083171282[/C][C]-247.130831712815[/C][/ROW]
[ROW][C]77[/C][C]5180[/C][C]4955.85437311696[/C][C]224.145626883036[/C][/ROW]
[ROW][C]78[/C][C]5020[/C][C]4864.34411363737[/C][C]155.655886362632[/C][/ROW]
[ROW][C]79[/C][C]5040[/C][C]4879.5644957929[/C][C]160.435504207098[/C][/ROW]
[ROW][C]80[/C][C]5590[/C][C]5417.48891586508[/C][C]172.511084134921[/C][/ROW]
[ROW][C]81[/C][C]5330[/C][C]5412.23083667649[/C][C]-82.2308366764855[/C][/ROW]
[ROW][C]82[/C][C]5550[/C][C]5568.56597783182[/C][C]-18.565977831825[/C][/ROW]
[ROW][C]83[/C][C]5630[/C][C]5342.15244844923[/C][C]287.847551550765[/C][/ROW]
[ROW][C]84[/C][C]5540[/C][C]5177.45865174938[/C][C]362.541348250623[/C][/ROW]
[ROW][C]85[/C][C]4880[/C][C]5311.26229151305[/C][C]-431.262291513051[/C][/ROW]
[ROW][C]86[/C][C]4550[/C][C]5178.92367596922[/C][C]-628.923675969218[/C][/ROW]
[ROW][C]87[/C][C]4530[/C][C]5106.51093346252[/C][C]-576.510933462525[/C][/ROW]
[ROW][C]88[/C][C]4580[/C][C]4731.84957850771[/C][C]-151.849578507706[/C][/ROW]
[ROW][C]89[/C][C]5090[/C][C]5070.93244027606[/C][C]19.0675597239397[/C][/ROW]
[ROW][C]90[/C][C]4720[/C][C]4867.51644518153[/C][C]-147.516445181534[/C][/ROW]
[ROW][C]91[/C][C]4900[/C][C]4749.55743920903[/C][C]150.442560790968[/C][/ROW]
[ROW][C]92[/C][C]5840[/C][C]5281.62258055466[/C][C]558.377419445342[/C][/ROW]
[ROW][C]93[/C][C]5250[/C][C]5360.86880139881[/C][C]-110.868801398809[/C][/ROW]
[ROW][C]94[/C][C]5530[/C][C]5520.7561098507[/C][C]9.24389014930148[/C][/ROW]
[ROW][C]95[/C][C]5370[/C][C]5395.44117218698[/C][C]-25.4411721869774[/C][/ROW]
[ROW][C]96[/C][C]4730[/C][C]5114.67219675734[/C][C]-384.672196757345[/C][/ROW]
[ROW][C]97[/C][C]5030[/C][C]4681.11927356993[/C][C]348.880726430073[/C][/ROW]
[ROW][C]98[/C][C]4980[/C][C]4817.44042502411[/C][C]162.559574975887[/C][/ROW]
[ROW][C]99[/C][C]5080[/C][C]5098.0194501595[/C][C]-18.0194501594988[/C][/ROW]
[ROW][C]100[/C][C]4750[/C][C]5092.09593884795[/C][C]-342.095938847946[/C][/ROW]
[ROW][C]101[/C][C]4890[/C][C]5402.67574051481[/C][C]-512.675740514807[/C][/ROW]
[ROW][C]102[/C][C]4640[/C][C]4920.37199979269[/C][C]-280.371999792692[/C][/ROW]
[ROW][C]103[/C][C]4800[/C][C]4833.44303347485[/C][C]-33.4430334748495[/C][/ROW]
[ROW][C]104[/C][C]5600[/C][C]5407.04108870266[/C][C]192.958911297339[/C][/ROW]
[ROW][C]105[/C][C]5040[/C][C]5123.18738047513[/C][C]-83.1873804751303[/C][/ROW]
[ROW][C]106[/C][C]5720[/C][C]5326.31806831346[/C][C]393.681931686542[/C][/ROW]
[ROW][C]107[/C][C]5650[/C][C]5351.73768503252[/C][C]298.262314967483[/C][/ROW]
[ROW][C]108[/C][C]4900[/C][C]5099.38818995622[/C][C]-199.388189956216[/C][/ROW]
[ROW][C]109[/C][C]5240[/C][C]4966.09869721707[/C][C]273.901302782931[/C][/ROW]
[ROW][C]110[/C][C]5120[/C][C]5013.40024172448[/C][C]106.599758275519[/C][/ROW]
[ROW][C]111[/C][C]4950[/C][C]5214.53302190028[/C][C]-264.533021900284[/C][/ROW]
[ROW][C]112[/C][C]5320[/C][C]5003.23876140427[/C][C]316.761238595735[/C][/ROW]
[ROW][C]113[/C][C]5590[/C][C]5544.63706332298[/C][C]45.362936677021[/C][/ROW]
[ROW][C]114[/C][C]4850[/C][C]5374.57573775679[/C][C]-524.575737756792[/C][/ROW]
[ROW][C]115[/C][C]5180[/C][C]5260.57979445729[/C][C]-80.5797944572923[/C][/ROW]
[ROW][C]116[/C][C]5700[/C][C]5884.80915529043[/C][C]-184.809155290429[/C][/ROW]
[ROW][C]117[/C][C]5370[/C][C]5356.77080873073[/C][C]13.2291912692717[/C][/ROW]
[ROW][C]118[/C][C]5820[/C][C]5746.04713173069[/C][C]73.9528682693108[/C][/ROW]
[ROW][C]119[/C][C]5940[/C][C]5605.51802348849[/C][C]334.481976511506[/C][/ROW]
[ROW][C]120[/C][C]5270[/C][C]5217.89682781866[/C][C]52.1031721813442[/C][/ROW]
[ROW][C]121[/C][C]5350[/C][C]5335.71728036801[/C][C]14.2827196319859[/C][/ROW]
[ROW][C]122[/C][C]5320[/C][C]5221.16634817691[/C][C]98.8336518230863[/C][/ROW]
[ROW][C]123[/C][C]5300[/C][C]5306.37595735747[/C][C]-6.37595735746891[/C][/ROW]
[ROW][C]124[/C][C]5440[/C][C]5381.60749189054[/C][C]58.3925081094558[/C][/ROW]
[ROW][C]125[/C][C]5390[/C][C]5730.21071691123[/C][C]-340.210716911234[/C][/ROW]
[ROW][C]126[/C][C]5400[/C][C]5220.95626824738[/C][C]179.043731752619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300564&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300564&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
1345204323.12767094017196.872329059828
1443204199.13766657517120.862333424829
1549604863.3030829179496.6969170820603
1644504394.7200034725955.2799965274062
1746804665.8154752744214.1845247255796
1845704588.18723690969-18.1872369096882
1945204718.73063133238-198.730631332381
2054504905.78108161693544.218918383071
2151105033.1654769491976.8345230508103
2248205227.64513599114-407.645135991136
2346404839.49109244892-199.491092448916
2445104855.45336471864-345.453364718642
2544504816.82046533355-366.820465333554
2646504426.06736234982223.932637650183
2747205124.30414263978-404.304142639781
2843804424.17337525682-44.1733752568243
2948704634.75186402692235.248135973085
3043504637.18828733772-287.188287337718
3141604592.47742800425-432.477428004252
3247704897.03767603798-127.03767603798
3344004586.26980837208-186.269808372078
3447004510.36693549596189.633064504044
3545204431.3178610102888.6821389897232
3642904518.92517260533-228.925172605329
3745204516.868059999663.13194000033855
3845004457.5951278397442.4048721602649
3946904882.83552288487-192.835522884874
4043804377.028092288132.97190771187343
4146204687.63856357462-67.6385635746246
4242304396.99543415622-166.995434156216
4343104354.32784049097-44.3278404909743
4449004913.39283264734-13.3928326473379
4547404630.37840253275109.621597467248
4650804792.92621349291287.073786507093
4750904724.08713462561365.912865374388
4845004834.62483071547-334.624830715471
4946704857.47670013754-187.476700137537
5047104727.68748184526-17.6874818452625
5143105054.93110705131-744.931107051313
5243904368.4786250403621.5213749596405
5345304661.70678152354-131.706781523536
5444904309.40687311352180.593126886479
5547204449.62384196615270.376158033851
5651505151.41046368506-1.41046368505613
5752204909.74403930243310.255960697568
5854905211.62714190888278.372858091119
5952605162.9281197866797.0718802133306
6050504945.83173580634104.168264193663
6148905201.35331695667-311.353316956665
6249605070.22943229582-110.229432295822
6351205138.15690420177-18.1569042017745
6450604996.9057790544563.0942209455452
6554305265.2768372332164.723162766802
6653605138.99775857296221.002241427038
6750905328.93756363937-238.937563639372
6853905734.00862938298-344.008629382983
6953305441.28069487601-111.280694876006
7055605552.537876737087.46212326292061
7153705331.0378043691238.9621956308793
7250405088.59401404559-48.5940140455878
7347605149.96545094135-389.965450941351
7446305042.17468079747-412.174680797467
7547905003.64058130933-213.640581309327
7645504797.13083171282-247.130831712815
7751804955.85437311696224.145626883036
7850204864.34411363737155.655886362632
7950404879.5644957929160.435504207098
8055905417.48891586508172.511084134921
8153305412.23083667649-82.2308366764855
8255505568.56597783182-18.565977831825
8356305342.15244844923287.847551550765
8455405177.45865174938362.541348250623
8548805311.26229151305-431.262291513051
8645505178.92367596922-628.923675969218
8745305106.51093346252-576.510933462525
8845804731.84957850771-151.849578507706
8950905070.9324402760619.0675597239397
9047204867.51644518153-147.516445181534
9149004749.55743920903150.442560790968
9258405281.62258055466558.377419445342
9352505360.86880139881-110.868801398809
9455305520.75610985079.24389014930148
9553705395.44117218698-25.4411721869774
9647305114.67219675734-384.672196757345
9750304681.11927356993348.880726430073
9849804817.44042502411162.559574975887
9950805098.0194501595-18.0194501594988
10047505092.09593884795-342.095938847946
10148905402.67574051481-512.675740514807
10246404920.37199979269-280.371999792692
10348004833.44303347485-33.4430334748495
10456005407.04108870266192.958911297339
10550405123.18738047513-83.1873804751303
10657205326.31806831346393.681931686542
10756505351.73768503252298.262314967483
10849005099.38818995622-199.388189956216
10952404966.09869721707273.901302782931
11051205013.40024172448106.599758275519
11149505214.53302190028-264.533021900284
11253205003.23876140427316.761238595735
11355905544.6370633229845.362936677021
11448505374.57573775679-524.575737756792
11551805260.57979445729-80.5797944572923
11657005884.80915529043-184.809155290429
11753705356.7708087307313.2291912692717
11858205746.0471317306973.9528682693108
11959405605.51802348849334.481976511506
12052705217.8968278186652.1031721813442
12153505335.7172803680114.2827196319859
12253205221.1663481769198.8336518230863
12353005306.37595735747-6.37595735746891
12454405381.6074918905458.3925081094558
12553905730.21071691123-340.210716911234
12654005220.95626824738179.043731752619







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1275542.503835457175048.65201514536036.35565576904
1286171.128381388465633.174902151356709.08186062557
1295784.192761105455204.570986266886363.81453594402
1306188.489374879585569.131429359626807.84732039955
1316097.024064358895439.502345796936754.54578292085
1325481.608355762594787.227109547556175.98960197764
1335565.782924819164835.640435338916295.92541429941
1345470.6160555584705.648535952946235.58357516306
1355481.310838683164682.324390402386280.29728696393
1365578.308295083544746.002794366716410.61379580037
1375780.799329654294915.786677645966645.81198166262
1385574.498724657414677.317056603756471.68039271107

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 5542.50383545717 & 5048.6520151453 & 6036.35565576904 \tabularnewline
128 & 6171.12838138846 & 5633.17490215135 & 6709.08186062557 \tabularnewline
129 & 5784.19276110545 & 5204.57098626688 & 6363.81453594402 \tabularnewline
130 & 6188.48937487958 & 5569.13142935962 & 6807.84732039955 \tabularnewline
131 & 6097.02406435889 & 5439.50234579693 & 6754.54578292085 \tabularnewline
132 & 5481.60835576259 & 4787.22710954755 & 6175.98960197764 \tabularnewline
133 & 5565.78292481916 & 4835.64043533891 & 6295.92541429941 \tabularnewline
134 & 5470.616055558 & 4705.64853595294 & 6235.58357516306 \tabularnewline
135 & 5481.31083868316 & 4682.32439040238 & 6280.29728696393 \tabularnewline
136 & 5578.30829508354 & 4746.00279436671 & 6410.61379580037 \tabularnewline
137 & 5780.79932965429 & 4915.78667764596 & 6645.81198166262 \tabularnewline
138 & 5574.49872465741 & 4677.31705660375 & 6471.68039271107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300564&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]127[/C][C]5542.50383545717[/C][C]5048.6520151453[/C][C]6036.35565576904[/C][/ROW]
[ROW][C]128[/C][C]6171.12838138846[/C][C]5633.17490215135[/C][C]6709.08186062557[/C][/ROW]
[ROW][C]129[/C][C]5784.19276110545[/C][C]5204.57098626688[/C][C]6363.81453594402[/C][/ROW]
[ROW][C]130[/C][C]6188.48937487958[/C][C]5569.13142935962[/C][C]6807.84732039955[/C][/ROW]
[ROW][C]131[/C][C]6097.02406435889[/C][C]5439.50234579693[/C][C]6754.54578292085[/C][/ROW]
[ROW][C]132[/C][C]5481.60835576259[/C][C]4787.22710954755[/C][C]6175.98960197764[/C][/ROW]
[ROW][C]133[/C][C]5565.78292481916[/C][C]4835.64043533891[/C][C]6295.92541429941[/C][/ROW]
[ROW][C]134[/C][C]5470.616055558[/C][C]4705.64853595294[/C][C]6235.58357516306[/C][/ROW]
[ROW][C]135[/C][C]5481.31083868316[/C][C]4682.32439040238[/C][C]6280.29728696393[/C][/ROW]
[ROW][C]136[/C][C]5578.30829508354[/C][C]4746.00279436671[/C][C]6410.61379580037[/C][/ROW]
[ROW][C]137[/C][C]5780.79932965429[/C][C]4915.78667764596[/C][C]6645.81198166262[/C][/ROW]
[ROW][C]138[/C][C]5574.49872465741[/C][C]4677.31705660375[/C][C]6471.68039271107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300564&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300564&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
1275542.503835457175048.65201514536036.35565576904
1286171.128381388465633.174902151356709.08186062557
1295784.192761105455204.570986266886363.81453594402
1306188.489374879585569.131429359626807.84732039955
1316097.024064358895439.502345796936754.54578292085
1325481.608355762594787.227109547556175.98960197764
1335565.782924819164835.640435338916295.92541429941
1345470.6160555584705.648535952946235.58357516306
1355481.310838683164682.324390402386280.29728696393
1365578.308295083544746.002794366716410.61379580037
1375780.799329654294915.786677645966645.81198166262
1385574.498724657414677.317056603756471.68039271107



Parameters (Session):
par1 = 12 ; par2 = Triple ; 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):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')