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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 computationFri, 16 Dec 2016 13:34:28 +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/t1481891696ld8wv9t6lysbbrn.htm/, Retrieved Thu, 02 May 2024 15:56:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300215, Retrieved Thu, 02 May 2024 15:56:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
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 12:34:28] [b7b12d6257d20c3ae3b596da588d7d29] [Current]
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Dataseries X:
3655
3390
4000
3810
3790
3790
3350
3900
3725
3945
3840
3625
4000
3915
4200
3900
4140
3945
3735
3970
3745
4140
3840
3570
4085
3865
4280
4280
4240
4065
4060
4265
4085
4450
4195
4160
4580
4130
4645
4375
4480
4485
4465
4515
4465
4790
4270
4495
4490
4275
4695
4630
4560
4665
4725
4840
4745
4940
4635
4910
4690
4585
5065
4705
4580
4660
4510
4885
4765
4700
4590
4655
4845
4495
5020
4535
4700
4435
4285
4780
4450
4875
4670
4325
5000
4675
4950
4790
4785
4520
4735
5055
4640
5045
4710
4650
4915
4260
4505
4575
4785
4610
5220
5285
4870
5440
4615
4645
4845
4780
5005
4905
4630
4785
5160




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=300215&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=300215&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300215&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
alpha0.407811145095738
beta0
gamma0.716527328566045

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.407811145095738 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.716527328566045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300215&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]0.407811145095738[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.716527328566045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300215&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300215&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
alpha0.407811145095738
beta0
gamma0.716527328566045







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1340003877.7938034188122.206196581197
1439153839.8438477223775.1561522776278
1542004167.9146929150332.0853070849698
1639003888.212434076111.7875659239035
1741404141.06586350474-1.0658635047439
1839453964.09418782635-19.0941878263548
1937353555.39536056221179.604639437789
2039704158.56146290717-188.561462907172
2137453892.62699213607-147.626992136067
2241404056.5110547640183.4889452359866
2338403983.39677246153-143.396772461532
2435703705.04763248562-135.047632485624
2540854070.4995035221514.5004964778536
2638653968.66171174353-103.66171174353
2742804205.5328396264774.4671603735324
2842803934.50164556414345.498354435861
2942404317.99209306119-77.9920930611934
3040654101.99927408976-36.9992740897569
3140603770.31033977336289.689660226639
3242654262.150284698752.84971530125404
3340854091.64471979408-6.64471979407699
3444504411.0899229183238.910077081684
3541954223.52384746207-28.5238474620719
3641603995.56386945576164.436130544238
3745804546.6047438712733.3952561287306
3841304402.33391676217-272.333916762168
3946454646.00219320426-1.00219320425913
4043754459.19757590383-84.1975759038287
4144804487.75797982692-7.75797982691529
4244854317.80146737455167.198532625447
4344654208.00715912099256.992840879014
4445154564.80119520958-49.8011952095785
4544654368.7953282637196.2046717362946
4647904749.5134480717840.4865519282221
4742704533.9767476031-263.9767476031
4844954291.87313381664203.126866183365
4944904803.08932336059-313.089323360595
5042754387.79137390236-112.791373902364
5146954811.65421822845-116.654218228453
5246304542.383993129787.6160068703002
5345604673.44670203772-113.446702037723
5446654534.62661032942130.373389670578
5547254447.91607417949277.083925820514
5648404682.72478717701157.275212822994
5747454633.12012351156111.879876488437
5849404996.58848188099-56.5884818809873
5946354612.2737862335322.7262137664684
6049104685.29200644001224.70799355999
6146904986.26862573613-296.26862573613
6245854662.82066964428-77.8206696442776
6350655099.30587675255-34.3058767525472
6447054950.2940625012-245.294062501197
6545804860.2775070521-280.277507052105
6646604756.8795726811-96.8795726811049
6745104639.74488680956-129.744886809557
6848854657.80710289004227.192897109961
6947654617.4535237815147.546476218497
7047004923.98270974075-223.982709740746
7145904505.0575542052884.942445794718
7246554689.15305468852-34.1530546885233
7348454663.50271579827181.497284201729
7444954627.58474964003-132.584749640027
7550205060.20072965969-40.2007296596948
7645354819.25852758876-284.258527588765
7747004698.507671376731.49232862326971
7844354787.8379358312-352.837935831205
7942854552.37518318705-267.375183187048
8047804665.76589186729114.234108132715
8144504545.55093033033-95.5509303303306
8248754595.29520679807279.704793201926
8346704512.86239558968157.137604410322
8443254675.86534337406-350.865343374065
8550004612.56084695604387.439153043956
8646754527.35713915664147.642860843363
8749505113.45340289576-163.453402895761
8847904718.6889046645471.311095335458
8947854864.19296345979-79.1929634597873
9045204770.26962654314-250.269626543144
9147354612.898885878122.101114122004
9250555047.0466323577.95336764300464
9346404794.47331808647-154.473318086466
9450454979.4167084416765.5832915583314
9547104757.65511441318-47.6551144131763
9646504621.5857531332328.4142468667669
9749155026.23269416989-111.232694169888
9842604635.91480695175-375.914806951751
9945054876.49420813855-371.494208138551
10045754496.5035049818978.4964950181102
10147854581.07604314295203.923956857049
10246104530.0197778615379.9802221384707
10352204665.33277198247554.66722801753
10452855227.4506861909257.5493138090833
10548704926.18234173366-56.1823417336564
10654405244.5841978904195.415802109599
10746155027.72048506042-412.720485060417
10846454775.05111014957-130.051110149569
10948455055.81919253599-210.819192535994
11047804512.57904010204267.420959897962
11150055017.39368331907-12.3936833190737
11249054974.78800575664-69.7880057566354
11346305052.10978952619-422.109789526193
11447854693.1582419414591.8417580585547
11551605034.7274547505125.272545249501

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4000 & 3877.7938034188 & 122.206196581197 \tabularnewline
14 & 3915 & 3839.84384772237 & 75.1561522776278 \tabularnewline
15 & 4200 & 4167.91469291503 & 32.0853070849698 \tabularnewline
16 & 3900 & 3888.2124340761 & 11.7875659239035 \tabularnewline
17 & 4140 & 4141.06586350474 & -1.0658635047439 \tabularnewline
18 & 3945 & 3964.09418782635 & -19.0941878263548 \tabularnewline
19 & 3735 & 3555.39536056221 & 179.604639437789 \tabularnewline
20 & 3970 & 4158.56146290717 & -188.561462907172 \tabularnewline
21 & 3745 & 3892.62699213607 & -147.626992136067 \tabularnewline
22 & 4140 & 4056.51105476401 & 83.4889452359866 \tabularnewline
23 & 3840 & 3983.39677246153 & -143.396772461532 \tabularnewline
24 & 3570 & 3705.04763248562 & -135.047632485624 \tabularnewline
25 & 4085 & 4070.49950352215 & 14.5004964778536 \tabularnewline
26 & 3865 & 3968.66171174353 & -103.66171174353 \tabularnewline
27 & 4280 & 4205.53283962647 & 74.4671603735324 \tabularnewline
28 & 4280 & 3934.50164556414 & 345.498354435861 \tabularnewline
29 & 4240 & 4317.99209306119 & -77.9920930611934 \tabularnewline
30 & 4065 & 4101.99927408976 & -36.9992740897569 \tabularnewline
31 & 4060 & 3770.31033977336 & 289.689660226639 \tabularnewline
32 & 4265 & 4262.15028469875 & 2.84971530125404 \tabularnewline
33 & 4085 & 4091.64471979408 & -6.64471979407699 \tabularnewline
34 & 4450 & 4411.08992291832 & 38.910077081684 \tabularnewline
35 & 4195 & 4223.52384746207 & -28.5238474620719 \tabularnewline
36 & 4160 & 3995.56386945576 & 164.436130544238 \tabularnewline
37 & 4580 & 4546.60474387127 & 33.3952561287306 \tabularnewline
38 & 4130 & 4402.33391676217 & -272.333916762168 \tabularnewline
39 & 4645 & 4646.00219320426 & -1.00219320425913 \tabularnewline
40 & 4375 & 4459.19757590383 & -84.1975759038287 \tabularnewline
41 & 4480 & 4487.75797982692 & -7.75797982691529 \tabularnewline
42 & 4485 & 4317.80146737455 & 167.198532625447 \tabularnewline
43 & 4465 & 4208.00715912099 & 256.992840879014 \tabularnewline
44 & 4515 & 4564.80119520958 & -49.8011952095785 \tabularnewline
45 & 4465 & 4368.79532826371 & 96.2046717362946 \tabularnewline
46 & 4790 & 4749.51344807178 & 40.4865519282221 \tabularnewline
47 & 4270 & 4533.9767476031 & -263.9767476031 \tabularnewline
48 & 4495 & 4291.87313381664 & 203.126866183365 \tabularnewline
49 & 4490 & 4803.08932336059 & -313.089323360595 \tabularnewline
50 & 4275 & 4387.79137390236 & -112.791373902364 \tabularnewline
51 & 4695 & 4811.65421822845 & -116.654218228453 \tabularnewline
52 & 4630 & 4542.3839931297 & 87.6160068703002 \tabularnewline
53 & 4560 & 4673.44670203772 & -113.446702037723 \tabularnewline
54 & 4665 & 4534.62661032942 & 130.373389670578 \tabularnewline
55 & 4725 & 4447.91607417949 & 277.083925820514 \tabularnewline
56 & 4840 & 4682.72478717701 & 157.275212822994 \tabularnewline
57 & 4745 & 4633.12012351156 & 111.879876488437 \tabularnewline
58 & 4940 & 4996.58848188099 & -56.5884818809873 \tabularnewline
59 & 4635 & 4612.27378623353 & 22.7262137664684 \tabularnewline
60 & 4910 & 4685.29200644001 & 224.70799355999 \tabularnewline
61 & 4690 & 4986.26862573613 & -296.26862573613 \tabularnewline
62 & 4585 & 4662.82066964428 & -77.8206696442776 \tabularnewline
63 & 5065 & 5099.30587675255 & -34.3058767525472 \tabularnewline
64 & 4705 & 4950.2940625012 & -245.294062501197 \tabularnewline
65 & 4580 & 4860.2775070521 & -280.277507052105 \tabularnewline
66 & 4660 & 4756.8795726811 & -96.8795726811049 \tabularnewline
67 & 4510 & 4639.74488680956 & -129.744886809557 \tabularnewline
68 & 4885 & 4657.80710289004 & 227.192897109961 \tabularnewline
69 & 4765 & 4617.4535237815 & 147.546476218497 \tabularnewline
70 & 4700 & 4923.98270974075 & -223.982709740746 \tabularnewline
71 & 4590 & 4505.05755420528 & 84.942445794718 \tabularnewline
72 & 4655 & 4689.15305468852 & -34.1530546885233 \tabularnewline
73 & 4845 & 4663.50271579827 & 181.497284201729 \tabularnewline
74 & 4495 & 4627.58474964003 & -132.584749640027 \tabularnewline
75 & 5020 & 5060.20072965969 & -40.2007296596948 \tabularnewline
76 & 4535 & 4819.25852758876 & -284.258527588765 \tabularnewline
77 & 4700 & 4698.50767137673 & 1.49232862326971 \tabularnewline
78 & 4435 & 4787.8379358312 & -352.837935831205 \tabularnewline
79 & 4285 & 4552.37518318705 & -267.375183187048 \tabularnewline
80 & 4780 & 4665.76589186729 & 114.234108132715 \tabularnewline
81 & 4450 & 4545.55093033033 & -95.5509303303306 \tabularnewline
82 & 4875 & 4595.29520679807 & 279.704793201926 \tabularnewline
83 & 4670 & 4512.86239558968 & 157.137604410322 \tabularnewline
84 & 4325 & 4675.86534337406 & -350.865343374065 \tabularnewline
85 & 5000 & 4612.56084695604 & 387.439153043956 \tabularnewline
86 & 4675 & 4527.35713915664 & 147.642860843363 \tabularnewline
87 & 4950 & 5113.45340289576 & -163.453402895761 \tabularnewline
88 & 4790 & 4718.68890466454 & 71.311095335458 \tabularnewline
89 & 4785 & 4864.19296345979 & -79.1929634597873 \tabularnewline
90 & 4520 & 4770.26962654314 & -250.269626543144 \tabularnewline
91 & 4735 & 4612.898885878 & 122.101114122004 \tabularnewline
92 & 5055 & 5047.046632357 & 7.95336764300464 \tabularnewline
93 & 4640 & 4794.47331808647 & -154.473318086466 \tabularnewline
94 & 5045 & 4979.41670844167 & 65.5832915583314 \tabularnewline
95 & 4710 & 4757.65511441318 & -47.6551144131763 \tabularnewline
96 & 4650 & 4621.58575313323 & 28.4142468667669 \tabularnewline
97 & 4915 & 5026.23269416989 & -111.232694169888 \tabularnewline
98 & 4260 & 4635.91480695175 & -375.914806951751 \tabularnewline
99 & 4505 & 4876.49420813855 & -371.494208138551 \tabularnewline
100 & 4575 & 4496.50350498189 & 78.4964950181102 \tabularnewline
101 & 4785 & 4581.07604314295 & 203.923956857049 \tabularnewline
102 & 4610 & 4530.01977786153 & 79.9802221384707 \tabularnewline
103 & 5220 & 4665.33277198247 & 554.66722801753 \tabularnewline
104 & 5285 & 5227.45068619092 & 57.5493138090833 \tabularnewline
105 & 4870 & 4926.18234173366 & -56.1823417336564 \tabularnewline
106 & 5440 & 5244.5841978904 & 195.415802109599 \tabularnewline
107 & 4615 & 5027.72048506042 & -412.720485060417 \tabularnewline
108 & 4645 & 4775.05111014957 & -130.051110149569 \tabularnewline
109 & 4845 & 5055.81919253599 & -210.819192535994 \tabularnewline
110 & 4780 & 4512.57904010204 & 267.420959897962 \tabularnewline
111 & 5005 & 5017.39368331907 & -12.3936833190737 \tabularnewline
112 & 4905 & 4974.78800575664 & -69.7880057566354 \tabularnewline
113 & 4630 & 5052.10978952619 & -422.109789526193 \tabularnewline
114 & 4785 & 4693.15824194145 & 91.8417580585547 \tabularnewline
115 & 5160 & 5034.7274547505 & 125.272545249501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300215&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]4000[/C][C]3877.7938034188[/C][C]122.206196581197[/C][/ROW]
[ROW][C]14[/C][C]3915[/C][C]3839.84384772237[/C][C]75.1561522776278[/C][/ROW]
[ROW][C]15[/C][C]4200[/C][C]4167.91469291503[/C][C]32.0853070849698[/C][/ROW]
[ROW][C]16[/C][C]3900[/C][C]3888.2124340761[/C][C]11.7875659239035[/C][/ROW]
[ROW][C]17[/C][C]4140[/C][C]4141.06586350474[/C][C]-1.0658635047439[/C][/ROW]
[ROW][C]18[/C][C]3945[/C][C]3964.09418782635[/C][C]-19.0941878263548[/C][/ROW]
[ROW][C]19[/C][C]3735[/C][C]3555.39536056221[/C][C]179.604639437789[/C][/ROW]
[ROW][C]20[/C][C]3970[/C][C]4158.56146290717[/C][C]-188.561462907172[/C][/ROW]
[ROW][C]21[/C][C]3745[/C][C]3892.62699213607[/C][C]-147.626992136067[/C][/ROW]
[ROW][C]22[/C][C]4140[/C][C]4056.51105476401[/C][C]83.4889452359866[/C][/ROW]
[ROW][C]23[/C][C]3840[/C][C]3983.39677246153[/C][C]-143.396772461532[/C][/ROW]
[ROW][C]24[/C][C]3570[/C][C]3705.04763248562[/C][C]-135.047632485624[/C][/ROW]
[ROW][C]25[/C][C]4085[/C][C]4070.49950352215[/C][C]14.5004964778536[/C][/ROW]
[ROW][C]26[/C][C]3865[/C][C]3968.66171174353[/C][C]-103.66171174353[/C][/ROW]
[ROW][C]27[/C][C]4280[/C][C]4205.53283962647[/C][C]74.4671603735324[/C][/ROW]
[ROW][C]28[/C][C]4280[/C][C]3934.50164556414[/C][C]345.498354435861[/C][/ROW]
[ROW][C]29[/C][C]4240[/C][C]4317.99209306119[/C][C]-77.9920930611934[/C][/ROW]
[ROW][C]30[/C][C]4065[/C][C]4101.99927408976[/C][C]-36.9992740897569[/C][/ROW]
[ROW][C]31[/C][C]4060[/C][C]3770.31033977336[/C][C]289.689660226639[/C][/ROW]
[ROW][C]32[/C][C]4265[/C][C]4262.15028469875[/C][C]2.84971530125404[/C][/ROW]
[ROW][C]33[/C][C]4085[/C][C]4091.64471979408[/C][C]-6.64471979407699[/C][/ROW]
[ROW][C]34[/C][C]4450[/C][C]4411.08992291832[/C][C]38.910077081684[/C][/ROW]
[ROW][C]35[/C][C]4195[/C][C]4223.52384746207[/C][C]-28.5238474620719[/C][/ROW]
[ROW][C]36[/C][C]4160[/C][C]3995.56386945576[/C][C]164.436130544238[/C][/ROW]
[ROW][C]37[/C][C]4580[/C][C]4546.60474387127[/C][C]33.3952561287306[/C][/ROW]
[ROW][C]38[/C][C]4130[/C][C]4402.33391676217[/C][C]-272.333916762168[/C][/ROW]
[ROW][C]39[/C][C]4645[/C][C]4646.00219320426[/C][C]-1.00219320425913[/C][/ROW]
[ROW][C]40[/C][C]4375[/C][C]4459.19757590383[/C][C]-84.1975759038287[/C][/ROW]
[ROW][C]41[/C][C]4480[/C][C]4487.75797982692[/C][C]-7.75797982691529[/C][/ROW]
[ROW][C]42[/C][C]4485[/C][C]4317.80146737455[/C][C]167.198532625447[/C][/ROW]
[ROW][C]43[/C][C]4465[/C][C]4208.00715912099[/C][C]256.992840879014[/C][/ROW]
[ROW][C]44[/C][C]4515[/C][C]4564.80119520958[/C][C]-49.8011952095785[/C][/ROW]
[ROW][C]45[/C][C]4465[/C][C]4368.79532826371[/C][C]96.2046717362946[/C][/ROW]
[ROW][C]46[/C][C]4790[/C][C]4749.51344807178[/C][C]40.4865519282221[/C][/ROW]
[ROW][C]47[/C][C]4270[/C][C]4533.9767476031[/C][C]-263.9767476031[/C][/ROW]
[ROW][C]48[/C][C]4495[/C][C]4291.87313381664[/C][C]203.126866183365[/C][/ROW]
[ROW][C]49[/C][C]4490[/C][C]4803.08932336059[/C][C]-313.089323360595[/C][/ROW]
[ROW][C]50[/C][C]4275[/C][C]4387.79137390236[/C][C]-112.791373902364[/C][/ROW]
[ROW][C]51[/C][C]4695[/C][C]4811.65421822845[/C][C]-116.654218228453[/C][/ROW]
[ROW][C]52[/C][C]4630[/C][C]4542.3839931297[/C][C]87.6160068703002[/C][/ROW]
[ROW][C]53[/C][C]4560[/C][C]4673.44670203772[/C][C]-113.446702037723[/C][/ROW]
[ROW][C]54[/C][C]4665[/C][C]4534.62661032942[/C][C]130.373389670578[/C][/ROW]
[ROW][C]55[/C][C]4725[/C][C]4447.91607417949[/C][C]277.083925820514[/C][/ROW]
[ROW][C]56[/C][C]4840[/C][C]4682.72478717701[/C][C]157.275212822994[/C][/ROW]
[ROW][C]57[/C][C]4745[/C][C]4633.12012351156[/C][C]111.879876488437[/C][/ROW]
[ROW][C]58[/C][C]4940[/C][C]4996.58848188099[/C][C]-56.5884818809873[/C][/ROW]
[ROW][C]59[/C][C]4635[/C][C]4612.27378623353[/C][C]22.7262137664684[/C][/ROW]
[ROW][C]60[/C][C]4910[/C][C]4685.29200644001[/C][C]224.70799355999[/C][/ROW]
[ROW][C]61[/C][C]4690[/C][C]4986.26862573613[/C][C]-296.26862573613[/C][/ROW]
[ROW][C]62[/C][C]4585[/C][C]4662.82066964428[/C][C]-77.8206696442776[/C][/ROW]
[ROW][C]63[/C][C]5065[/C][C]5099.30587675255[/C][C]-34.3058767525472[/C][/ROW]
[ROW][C]64[/C][C]4705[/C][C]4950.2940625012[/C][C]-245.294062501197[/C][/ROW]
[ROW][C]65[/C][C]4580[/C][C]4860.2775070521[/C][C]-280.277507052105[/C][/ROW]
[ROW][C]66[/C][C]4660[/C][C]4756.8795726811[/C][C]-96.8795726811049[/C][/ROW]
[ROW][C]67[/C][C]4510[/C][C]4639.74488680956[/C][C]-129.744886809557[/C][/ROW]
[ROW][C]68[/C][C]4885[/C][C]4657.80710289004[/C][C]227.192897109961[/C][/ROW]
[ROW][C]69[/C][C]4765[/C][C]4617.4535237815[/C][C]147.546476218497[/C][/ROW]
[ROW][C]70[/C][C]4700[/C][C]4923.98270974075[/C][C]-223.982709740746[/C][/ROW]
[ROW][C]71[/C][C]4590[/C][C]4505.05755420528[/C][C]84.942445794718[/C][/ROW]
[ROW][C]72[/C][C]4655[/C][C]4689.15305468852[/C][C]-34.1530546885233[/C][/ROW]
[ROW][C]73[/C][C]4845[/C][C]4663.50271579827[/C][C]181.497284201729[/C][/ROW]
[ROW][C]74[/C][C]4495[/C][C]4627.58474964003[/C][C]-132.584749640027[/C][/ROW]
[ROW][C]75[/C][C]5020[/C][C]5060.20072965969[/C][C]-40.2007296596948[/C][/ROW]
[ROW][C]76[/C][C]4535[/C][C]4819.25852758876[/C][C]-284.258527588765[/C][/ROW]
[ROW][C]77[/C][C]4700[/C][C]4698.50767137673[/C][C]1.49232862326971[/C][/ROW]
[ROW][C]78[/C][C]4435[/C][C]4787.8379358312[/C][C]-352.837935831205[/C][/ROW]
[ROW][C]79[/C][C]4285[/C][C]4552.37518318705[/C][C]-267.375183187048[/C][/ROW]
[ROW][C]80[/C][C]4780[/C][C]4665.76589186729[/C][C]114.234108132715[/C][/ROW]
[ROW][C]81[/C][C]4450[/C][C]4545.55093033033[/C][C]-95.5509303303306[/C][/ROW]
[ROW][C]82[/C][C]4875[/C][C]4595.29520679807[/C][C]279.704793201926[/C][/ROW]
[ROW][C]83[/C][C]4670[/C][C]4512.86239558968[/C][C]157.137604410322[/C][/ROW]
[ROW][C]84[/C][C]4325[/C][C]4675.86534337406[/C][C]-350.865343374065[/C][/ROW]
[ROW][C]85[/C][C]5000[/C][C]4612.56084695604[/C][C]387.439153043956[/C][/ROW]
[ROW][C]86[/C][C]4675[/C][C]4527.35713915664[/C][C]147.642860843363[/C][/ROW]
[ROW][C]87[/C][C]4950[/C][C]5113.45340289576[/C][C]-163.453402895761[/C][/ROW]
[ROW][C]88[/C][C]4790[/C][C]4718.68890466454[/C][C]71.311095335458[/C][/ROW]
[ROW][C]89[/C][C]4785[/C][C]4864.19296345979[/C][C]-79.1929634597873[/C][/ROW]
[ROW][C]90[/C][C]4520[/C][C]4770.26962654314[/C][C]-250.269626543144[/C][/ROW]
[ROW][C]91[/C][C]4735[/C][C]4612.898885878[/C][C]122.101114122004[/C][/ROW]
[ROW][C]92[/C][C]5055[/C][C]5047.046632357[/C][C]7.95336764300464[/C][/ROW]
[ROW][C]93[/C][C]4640[/C][C]4794.47331808647[/C][C]-154.473318086466[/C][/ROW]
[ROW][C]94[/C][C]5045[/C][C]4979.41670844167[/C][C]65.5832915583314[/C][/ROW]
[ROW][C]95[/C][C]4710[/C][C]4757.65511441318[/C][C]-47.6551144131763[/C][/ROW]
[ROW][C]96[/C][C]4650[/C][C]4621.58575313323[/C][C]28.4142468667669[/C][/ROW]
[ROW][C]97[/C][C]4915[/C][C]5026.23269416989[/C][C]-111.232694169888[/C][/ROW]
[ROW][C]98[/C][C]4260[/C][C]4635.91480695175[/C][C]-375.914806951751[/C][/ROW]
[ROW][C]99[/C][C]4505[/C][C]4876.49420813855[/C][C]-371.494208138551[/C][/ROW]
[ROW][C]100[/C][C]4575[/C][C]4496.50350498189[/C][C]78.4964950181102[/C][/ROW]
[ROW][C]101[/C][C]4785[/C][C]4581.07604314295[/C][C]203.923956857049[/C][/ROW]
[ROW][C]102[/C][C]4610[/C][C]4530.01977786153[/C][C]79.9802221384707[/C][/ROW]
[ROW][C]103[/C][C]5220[/C][C]4665.33277198247[/C][C]554.66722801753[/C][/ROW]
[ROW][C]104[/C][C]5285[/C][C]5227.45068619092[/C][C]57.5493138090833[/C][/ROW]
[ROW][C]105[/C][C]4870[/C][C]4926.18234173366[/C][C]-56.1823417336564[/C][/ROW]
[ROW][C]106[/C][C]5440[/C][C]5244.5841978904[/C][C]195.415802109599[/C][/ROW]
[ROW][C]107[/C][C]4615[/C][C]5027.72048506042[/C][C]-412.720485060417[/C][/ROW]
[ROW][C]108[/C][C]4645[/C][C]4775.05111014957[/C][C]-130.051110149569[/C][/ROW]
[ROW][C]109[/C][C]4845[/C][C]5055.81919253599[/C][C]-210.819192535994[/C][/ROW]
[ROW][C]110[/C][C]4780[/C][C]4512.57904010204[/C][C]267.420959897962[/C][/ROW]
[ROW][C]111[/C][C]5005[/C][C]5017.39368331907[/C][C]-12.3936833190737[/C][/ROW]
[ROW][C]112[/C][C]4905[/C][C]4974.78800575664[/C][C]-69.7880057566354[/C][/ROW]
[ROW][C]113[/C][C]4630[/C][C]5052.10978952619[/C][C]-422.109789526193[/C][/ROW]
[ROW][C]114[/C][C]4785[/C][C]4693.15824194145[/C][C]91.8417580585547[/C][/ROW]
[ROW][C]115[/C][C]5160[/C][C]5034.7274547505[/C][C]125.272545249501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300215&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300215&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
1340003877.7938034188122.206196581197
1439153839.8438477223775.1561522776278
1542004167.9146929150332.0853070849698
1639003888.212434076111.7875659239035
1741404141.06586350474-1.0658635047439
1839453964.09418782635-19.0941878263548
1937353555.39536056221179.604639437789
2039704158.56146290717-188.561462907172
2137453892.62699213607-147.626992136067
2241404056.5110547640183.4889452359866
2338403983.39677246153-143.396772461532
2435703705.04763248562-135.047632485624
2540854070.4995035221514.5004964778536
2638653968.66171174353-103.66171174353
2742804205.5328396264774.4671603735324
2842803934.50164556414345.498354435861
2942404317.99209306119-77.9920930611934
3040654101.99927408976-36.9992740897569
3140603770.31033977336289.689660226639
3242654262.150284698752.84971530125404
3340854091.64471979408-6.64471979407699
3444504411.0899229183238.910077081684
3541954223.52384746207-28.5238474620719
3641603995.56386945576164.436130544238
3745804546.6047438712733.3952561287306
3841304402.33391676217-272.333916762168
3946454646.00219320426-1.00219320425913
4043754459.19757590383-84.1975759038287
4144804487.75797982692-7.75797982691529
4244854317.80146737455167.198532625447
4344654208.00715912099256.992840879014
4445154564.80119520958-49.8011952095785
4544654368.7953282637196.2046717362946
4647904749.5134480717840.4865519282221
4742704533.9767476031-263.9767476031
4844954291.87313381664203.126866183365
4944904803.08932336059-313.089323360595
5042754387.79137390236-112.791373902364
5146954811.65421822845-116.654218228453
5246304542.383993129787.6160068703002
5345604673.44670203772-113.446702037723
5446654534.62661032942130.373389670578
5547254447.91607417949277.083925820514
5648404682.72478717701157.275212822994
5747454633.12012351156111.879876488437
5849404996.58848188099-56.5884818809873
5946354612.2737862335322.7262137664684
6049104685.29200644001224.70799355999
6146904986.26862573613-296.26862573613
6245854662.82066964428-77.8206696442776
6350655099.30587675255-34.3058767525472
6447054950.2940625012-245.294062501197
6545804860.2775070521-280.277507052105
6646604756.8795726811-96.8795726811049
6745104639.74488680956-129.744886809557
6848854657.80710289004227.192897109961
6947654617.4535237815147.546476218497
7047004923.98270974075-223.982709740746
7145904505.0575542052884.942445794718
7246554689.15305468852-34.1530546885233
7348454663.50271579827181.497284201729
7444954627.58474964003-132.584749640027
7550205060.20072965969-40.2007296596948
7645354819.25852758876-284.258527588765
7747004698.507671376731.49232862326971
7844354787.8379358312-352.837935831205
7942854552.37518318705-267.375183187048
8047804665.76589186729114.234108132715
8144504545.55093033033-95.5509303303306
8248754595.29520679807279.704793201926
8346704512.86239558968157.137604410322
8443254675.86534337406-350.865343374065
8550004612.56084695604387.439153043956
8646754527.35713915664147.642860843363
8749505113.45340289576-163.453402895761
8847904718.6889046645471.311095335458
8947854864.19296345979-79.1929634597873
9045204770.26962654314-250.269626543144
9147354612.898885878122.101114122004
9250555047.0466323577.95336764300464
9346404794.47331808647-154.473318086466
9450454979.4167084416765.5832915583314
9547104757.65511441318-47.6551144131763
9646504621.5857531332328.4142468667669
9749155026.23269416989-111.232694169888
9842604635.91480695175-375.914806951751
9945054876.49420813855-371.494208138551
10045754496.5035049818978.4964950181102
10147854581.07604314295203.923956857049
10246104530.0197778615379.9802221384707
10352204665.33277198247554.66722801753
10452855227.4506861909257.5493138090833
10548704926.18234173366-56.1823417336564
10654405244.5841978904195.415802109599
10746155027.72048506042-412.720485060417
10846454775.05111014957-130.051110149569
10948455055.81919253599-210.819192535994
11047804512.57904010204267.420959897962
11150055017.39368331907-12.3936833190737
11249054974.78800575664-69.7880057566354
11346305052.10978952619-422.109789526193
11447854693.1582419414591.8417580585547
11551605034.7274547505125.272545249501







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1165210.79660777264846.266283492835575.32693205237
1174837.800452740764444.122903378215231.47800210331
1185285.87209216054865.06136460635706.68281971469
1194731.271553086434284.974203803155177.5689023697
1204766.856319114364296.451196342665237.26144188607
1215066.389221462174573.052992220445559.72545070391
1224812.050106849674296.802311478325327.29790222103
1235089.076693186144552.811883425495625.34150294679
1245027.171767713134470.683131943975583.66040348229
1254983.45687552634407.454048022125559.45970303047
1265014.726067340354419.848842322115609.60329235858
1275333.02652247364719.855609596955946.19743535025
1285404.852551828544720.753279108386088.9518245487
1295031.856396796714331.791063782115731.92172981131
1305479.928036216444764.252742496296195.60332993659
1314925.327497142374194.375527725775656.27946655898
1324960.912263170314214.996425326255706.82810101436
1335260.445165518124499.859803642686021.03052739355

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
116 & 5210.7966077726 & 4846.26628349283 & 5575.32693205237 \tabularnewline
117 & 4837.80045274076 & 4444.12290337821 & 5231.47800210331 \tabularnewline
118 & 5285.8720921605 & 4865.0613646063 & 5706.68281971469 \tabularnewline
119 & 4731.27155308643 & 4284.97420380315 & 5177.5689023697 \tabularnewline
120 & 4766.85631911436 & 4296.45119634266 & 5237.26144188607 \tabularnewline
121 & 5066.38922146217 & 4573.05299222044 & 5559.72545070391 \tabularnewline
122 & 4812.05010684967 & 4296.80231147832 & 5327.29790222103 \tabularnewline
123 & 5089.07669318614 & 4552.81188342549 & 5625.34150294679 \tabularnewline
124 & 5027.17176771313 & 4470.68313194397 & 5583.66040348229 \tabularnewline
125 & 4983.4568755263 & 4407.45404802212 & 5559.45970303047 \tabularnewline
126 & 5014.72606734035 & 4419.84884232211 & 5609.60329235858 \tabularnewline
127 & 5333.0265224736 & 4719.85560959695 & 5946.19743535025 \tabularnewline
128 & 5404.85255182854 & 4720.75327910838 & 6088.9518245487 \tabularnewline
129 & 5031.85639679671 & 4331.79106378211 & 5731.92172981131 \tabularnewline
130 & 5479.92803621644 & 4764.25274249629 & 6195.60332993659 \tabularnewline
131 & 4925.32749714237 & 4194.37552772577 & 5656.27946655898 \tabularnewline
132 & 4960.91226317031 & 4214.99642532625 & 5706.82810101436 \tabularnewline
133 & 5260.44516551812 & 4499.85980364268 & 6021.03052739355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300215&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]116[/C][C]5210.7966077726[/C][C]4846.26628349283[/C][C]5575.32693205237[/C][/ROW]
[ROW][C]117[/C][C]4837.80045274076[/C][C]4444.12290337821[/C][C]5231.47800210331[/C][/ROW]
[ROW][C]118[/C][C]5285.8720921605[/C][C]4865.0613646063[/C][C]5706.68281971469[/C][/ROW]
[ROW][C]119[/C][C]4731.27155308643[/C][C]4284.97420380315[/C][C]5177.5689023697[/C][/ROW]
[ROW][C]120[/C][C]4766.85631911436[/C][C]4296.45119634266[/C][C]5237.26144188607[/C][/ROW]
[ROW][C]121[/C][C]5066.38922146217[/C][C]4573.05299222044[/C][C]5559.72545070391[/C][/ROW]
[ROW][C]122[/C][C]4812.05010684967[/C][C]4296.80231147832[/C][C]5327.29790222103[/C][/ROW]
[ROW][C]123[/C][C]5089.07669318614[/C][C]4552.81188342549[/C][C]5625.34150294679[/C][/ROW]
[ROW][C]124[/C][C]5027.17176771313[/C][C]4470.68313194397[/C][C]5583.66040348229[/C][/ROW]
[ROW][C]125[/C][C]4983.4568755263[/C][C]4407.45404802212[/C][C]5559.45970303047[/C][/ROW]
[ROW][C]126[/C][C]5014.72606734035[/C][C]4419.84884232211[/C][C]5609.60329235858[/C][/ROW]
[ROW][C]127[/C][C]5333.0265224736[/C][C]4719.85560959695[/C][C]5946.19743535025[/C][/ROW]
[ROW][C]128[/C][C]5404.85255182854[/C][C]4720.75327910838[/C][C]6088.9518245487[/C][/ROW]
[ROW][C]129[/C][C]5031.85639679671[/C][C]4331.79106378211[/C][C]5731.92172981131[/C][/ROW]
[ROW][C]130[/C][C]5479.92803621644[/C][C]4764.25274249629[/C][C]6195.60332993659[/C][/ROW]
[ROW][C]131[/C][C]4925.32749714237[/C][C]4194.37552772577[/C][C]5656.27946655898[/C][/ROW]
[ROW][C]132[/C][C]4960.91226317031[/C][C]4214.99642532625[/C][C]5706.82810101436[/C][/ROW]
[ROW][C]133[/C][C]5260.44516551812[/C][C]4499.85980364268[/C][C]6021.03052739355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300215&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300215&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
1165210.79660777264846.266283492835575.32693205237
1174837.800452740764444.122903378215231.47800210331
1185285.87209216054865.06136460635706.68281971469
1194731.271553086434284.974203803155177.5689023697
1204766.856319114364296.451196342665237.26144188607
1215066.389221462174573.052992220445559.72545070391
1224812.050106849674296.802311478325327.29790222103
1235089.076693186144552.811883425495625.34150294679
1245027.171767713134470.683131943975583.66040348229
1254983.45687552634407.454048022125559.45970303047
1265014.726067340354419.848842322115609.60329235858
1275333.02652247364719.855609596955946.19743535025
1285404.852551828544720.753279108386088.9518245487
1295031.856396796714331.791063782115731.92172981131
1305479.928036216444764.252742496296195.60332993659
1314925.327497142374194.375527725775656.27946655898
1324960.912263170314214.996425326255706.82810101436
1335260.445165518124499.859803642686021.03052739355



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
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')