Free Statistics

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 computationThu, 22 Dec 2016 20:58:45 +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/22/t1482436733jc43ub661yd16jp.htm/, Retrieved Fri, 01 Nov 2024 03:43:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302665, Retrieved Fri, 01 Nov 2024 03:43:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-22 19:58:45] [037fdaa34a77b5f63489b3bcd360a80c] [Current]
Feedback Forum

Post a new message
Dataseries X:
3455
3585
3675
3680
3735
3860
3765
3905
4110
4170
4110
4025
4145
4285
4370
4355
4385
4525
4375
4525
4610
4595
4500
4370
4390
4530
4590
4580
4595
4685
4490
4635
4710
4655
4665
4550
4590
4675
4645
4665
4635
4720
4565
4720
4830
4830
4765
4705
4675
4900
4945
4905
4955
5120
4860
5040
5140
5240
5145
5070
5085
5215
5255
5275
5315
5450
5205
5370
5500
5490
5440
5360
5380
5460
5450
5520
5475
5600
5250
5465
5515
5425
5325
5275
5160
5360
5435
5285
5415
5575
5265
5480
5565
5500
5280
5135
5050
5100
5070
5115
5140
5330
5080
5285
5405
5385
5255
5100
5040
5235
5310
5265
5380
5465
5225
5445




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302665&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302665&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302665&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.852434355089833
beta0.0639027324935784
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.852434355089833 \tabularnewline
beta & 0.0639027324935784 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302665&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]0.852434355089833[/C][/ROW]
[ROW][C]beta[/C][C]0.0639027324935784[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302665&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302665&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
alpha0.852434355089833
beta0.0639027324935784
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1341453812.12740384616332.872596153844
1442854252.6971401773332.302859822672
1543704388.39387044698-18.3938704469801
1643554387.99799896256-32.997998962559
1743854422.93890375039-37.9389037503915
1845254564.93470336079-39.9347033607901
1943754370.97052299794.02947700209916
2045254519.494084271955.50591572804842
2146104734.36780241771-124.367802417712
2245954687.79969511515-92.7996951151545
2345004544.9612599231-44.9612599230968
2443704415.86944752762-45.8694475276152
2543904539.29204968813-149.292049688129
2645304494.8219777790535.1780222209527
2745904595.97278561315-5.97278561315306
2845804575.170904302874.82909569712501
2945954614.84926566816-19.8492656681565
3046854746.17762689915-61.1776268991462
3144904513.64253212093-23.6425321209272
3246354610.3377004014824.6622995985163
3347104794.96188941442-84.9618894144214
3446554761.37546812408-106.375468124081
3546654588.0167395088176.9832604911908
3645504543.37613056926.62386943080128
3745904679.77920105585-89.7792010558542
3846754699.99819207583-24.9981920758255
3946454727.2391310705-82.2391310705034
4046654622.32358458842.6764154120046
4146354671.98867714488-36.9886771448828
4247204763.0405896749-43.0405896748989
4345654532.9254164748332.0745835251701
4447204668.6993714332451.3006285667643
4548304845.76075917989-15.7607591798915
4648304857.67997144763-27.6799714476319
4747654772.42432882147-7.42432882146932
4847054634.8141291285970.185870871409
4946754804.00122474526-129.001224745258
5049004791.03630258705108.963697412953
5149454922.0122888412222.9877111587803
5249054928.94909702264-23.9490970226361
5349554910.1553353411444.8446646588591
5451205074.6202958687745.3797041312318
5548604940.32709665712-80.3270966571217
5650404986.3653167299853.6346832700165
5751405158.88973378938-18.8897337893832
5852405169.5817479144270.418252085582
5951455179.48004493041-34.4800449304148
6050705037.3280263556332.6719736443683
6150855150.16912862873-65.1691286287287
6252155235.23475743353-20.2347574335263
6352555244.8550598488710.1449401511336
6452755234.6830252121640.3169747878401
6553155285.0892619005429.9107380994647
6654505440.355284843449.64471515655805
6752055258.55606131997-53.5560613199741
6853705350.146996698219.8530033018042
6955005484.2964598661215.7035401338799
7054905540.66397814786-50.6639781478598
7154405428.2807576010711.7192423989291
7253605334.3490582282625.6509417717425
7353805425.31387908436-45.3138790843595
7454605533.56381962515-73.5638196251475
7554505498.93085455277-48.9308545527747
7655205436.3581673432483.6418326567609
7754755518.0256568994-43.0256568993991
7856005600.01982505736-0.0198250573621408
7952505392.02169950023-142.02169950023
8054655405.5809105259759.419089474035
8155155561.5475943939-46.5475943938991
8254255540.36759021831-115.367590218308
8353255363.82086451859-38.8208645185878
8452755207.8962729949367.1037270050738
8551605305.0163464202-145.016346420201
8653605299.9681207061160.0318792938888
8754355365.9894044306669.0105955693443
8852855413.07955224655-128.079552246551
8954155273.60593222603141.394067773971
9055755507.2271095430867.772890456924
9152655327.8312070815-62.8312070814964
9254805434.702570476545.2974295234953
9355655558.30689275436.69310724570278
9455005570.5682678198-70.5682678198
9552805444.15868201936-164.158682019361
9651355190.84813852058-55.848138520575
9750505138.98611853307-88.986118533071
9851005202.13812201139-102.138122011388
9950705112.59127190826-42.5912719082608
10051155010.73133997446104.268660025545
10151405097.0079652564642.9920347435354
10253305218.44726820544111.552731794563
10350805042.0462986301837.9537013698246
10452855241.2244670920743.7755329079291
10554055348.1901132324956.8098867675117
10653855384.856946372020.143053627980407
10752555301.85055817049-46.8505581704912
10851005167.84768439394-67.8476843939352
10950405103.54044161014-63.5404416101373
11052355190.5021595757644.4978404242429
11153105246.7873239014263.2126760985821
11252655274.60065198516-9.60065198515895
11353805266.37690836797113.623091632029
11454655473.59730100601-8.59730100600609
11552255192.8262552353432.1737447646619
11654455396.5322694509848.4677305490231

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4145 & 3812.12740384616 & 332.872596153844 \tabularnewline
14 & 4285 & 4252.69714017733 & 32.302859822672 \tabularnewline
15 & 4370 & 4388.39387044698 & -18.3938704469801 \tabularnewline
16 & 4355 & 4387.99799896256 & -32.997998962559 \tabularnewline
17 & 4385 & 4422.93890375039 & -37.9389037503915 \tabularnewline
18 & 4525 & 4564.93470336079 & -39.9347033607901 \tabularnewline
19 & 4375 & 4370.9705229979 & 4.02947700209916 \tabularnewline
20 & 4525 & 4519.49408427195 & 5.50591572804842 \tabularnewline
21 & 4610 & 4734.36780241771 & -124.367802417712 \tabularnewline
22 & 4595 & 4687.79969511515 & -92.7996951151545 \tabularnewline
23 & 4500 & 4544.9612599231 & -44.9612599230968 \tabularnewline
24 & 4370 & 4415.86944752762 & -45.8694475276152 \tabularnewline
25 & 4390 & 4539.29204968813 & -149.292049688129 \tabularnewline
26 & 4530 & 4494.82197777905 & 35.1780222209527 \tabularnewline
27 & 4590 & 4595.97278561315 & -5.97278561315306 \tabularnewline
28 & 4580 & 4575.17090430287 & 4.82909569712501 \tabularnewline
29 & 4595 & 4614.84926566816 & -19.8492656681565 \tabularnewline
30 & 4685 & 4746.17762689915 & -61.1776268991462 \tabularnewline
31 & 4490 & 4513.64253212093 & -23.6425321209272 \tabularnewline
32 & 4635 & 4610.33770040148 & 24.6622995985163 \tabularnewline
33 & 4710 & 4794.96188941442 & -84.9618894144214 \tabularnewline
34 & 4655 & 4761.37546812408 & -106.375468124081 \tabularnewline
35 & 4665 & 4588.01673950881 & 76.9832604911908 \tabularnewline
36 & 4550 & 4543.3761305692 & 6.62386943080128 \tabularnewline
37 & 4590 & 4679.77920105585 & -89.7792010558542 \tabularnewline
38 & 4675 & 4699.99819207583 & -24.9981920758255 \tabularnewline
39 & 4645 & 4727.2391310705 & -82.2391310705034 \tabularnewline
40 & 4665 & 4622.323584588 & 42.6764154120046 \tabularnewline
41 & 4635 & 4671.98867714488 & -36.9886771448828 \tabularnewline
42 & 4720 & 4763.0405896749 & -43.0405896748989 \tabularnewline
43 & 4565 & 4532.92541647483 & 32.0745835251701 \tabularnewline
44 & 4720 & 4668.69937143324 & 51.3006285667643 \tabularnewline
45 & 4830 & 4845.76075917989 & -15.7607591798915 \tabularnewline
46 & 4830 & 4857.67997144763 & -27.6799714476319 \tabularnewline
47 & 4765 & 4772.42432882147 & -7.42432882146932 \tabularnewline
48 & 4705 & 4634.81412912859 & 70.185870871409 \tabularnewline
49 & 4675 & 4804.00122474526 & -129.001224745258 \tabularnewline
50 & 4900 & 4791.03630258705 & 108.963697412953 \tabularnewline
51 & 4945 & 4922.01228884122 & 22.9877111587803 \tabularnewline
52 & 4905 & 4928.94909702264 & -23.9490970226361 \tabularnewline
53 & 4955 & 4910.15533534114 & 44.8446646588591 \tabularnewline
54 & 5120 & 5074.62029586877 & 45.3797041312318 \tabularnewline
55 & 4860 & 4940.32709665712 & -80.3270966571217 \tabularnewline
56 & 5040 & 4986.36531672998 & 53.6346832700165 \tabularnewline
57 & 5140 & 5158.88973378938 & -18.8897337893832 \tabularnewline
58 & 5240 & 5169.58174791442 & 70.418252085582 \tabularnewline
59 & 5145 & 5179.48004493041 & -34.4800449304148 \tabularnewline
60 & 5070 & 5037.32802635563 & 32.6719736443683 \tabularnewline
61 & 5085 & 5150.16912862873 & -65.1691286287287 \tabularnewline
62 & 5215 & 5235.23475743353 & -20.2347574335263 \tabularnewline
63 & 5255 & 5244.85505984887 & 10.1449401511336 \tabularnewline
64 & 5275 & 5234.68302521216 & 40.3169747878401 \tabularnewline
65 & 5315 & 5285.08926190054 & 29.9107380994647 \tabularnewline
66 & 5450 & 5440.35528484344 & 9.64471515655805 \tabularnewline
67 & 5205 & 5258.55606131997 & -53.5560613199741 \tabularnewline
68 & 5370 & 5350.1469966982 & 19.8530033018042 \tabularnewline
69 & 5500 & 5484.29645986612 & 15.7035401338799 \tabularnewline
70 & 5490 & 5540.66397814786 & -50.6639781478598 \tabularnewline
71 & 5440 & 5428.28075760107 & 11.7192423989291 \tabularnewline
72 & 5360 & 5334.34905822826 & 25.6509417717425 \tabularnewline
73 & 5380 & 5425.31387908436 & -45.3138790843595 \tabularnewline
74 & 5460 & 5533.56381962515 & -73.5638196251475 \tabularnewline
75 & 5450 & 5498.93085455277 & -48.9308545527747 \tabularnewline
76 & 5520 & 5436.35816734324 & 83.6418326567609 \tabularnewline
77 & 5475 & 5518.0256568994 & -43.0256568993991 \tabularnewline
78 & 5600 & 5600.01982505736 & -0.0198250573621408 \tabularnewline
79 & 5250 & 5392.02169950023 & -142.02169950023 \tabularnewline
80 & 5465 & 5405.58091052597 & 59.419089474035 \tabularnewline
81 & 5515 & 5561.5475943939 & -46.5475943938991 \tabularnewline
82 & 5425 & 5540.36759021831 & -115.367590218308 \tabularnewline
83 & 5325 & 5363.82086451859 & -38.8208645185878 \tabularnewline
84 & 5275 & 5207.89627299493 & 67.1037270050738 \tabularnewline
85 & 5160 & 5305.0163464202 & -145.016346420201 \tabularnewline
86 & 5360 & 5299.96812070611 & 60.0318792938888 \tabularnewline
87 & 5435 & 5365.98940443066 & 69.0105955693443 \tabularnewline
88 & 5285 & 5413.07955224655 & -128.079552246551 \tabularnewline
89 & 5415 & 5273.60593222603 & 141.394067773971 \tabularnewline
90 & 5575 & 5507.22710954308 & 67.772890456924 \tabularnewline
91 & 5265 & 5327.8312070815 & -62.8312070814964 \tabularnewline
92 & 5480 & 5434.7025704765 & 45.2974295234953 \tabularnewline
93 & 5565 & 5558.3068927543 & 6.69310724570278 \tabularnewline
94 & 5500 & 5570.5682678198 & -70.5682678198 \tabularnewline
95 & 5280 & 5444.15868201936 & -164.158682019361 \tabularnewline
96 & 5135 & 5190.84813852058 & -55.848138520575 \tabularnewline
97 & 5050 & 5138.98611853307 & -88.986118533071 \tabularnewline
98 & 5100 & 5202.13812201139 & -102.138122011388 \tabularnewline
99 & 5070 & 5112.59127190826 & -42.5912719082608 \tabularnewline
100 & 5115 & 5010.73133997446 & 104.268660025545 \tabularnewline
101 & 5140 & 5097.00796525646 & 42.9920347435354 \tabularnewline
102 & 5330 & 5218.44726820544 & 111.552731794563 \tabularnewline
103 & 5080 & 5042.04629863018 & 37.9537013698246 \tabularnewline
104 & 5285 & 5241.22446709207 & 43.7755329079291 \tabularnewline
105 & 5405 & 5348.19011323249 & 56.8098867675117 \tabularnewline
106 & 5385 & 5384.85694637202 & 0.143053627980407 \tabularnewline
107 & 5255 & 5301.85055817049 & -46.8505581704912 \tabularnewline
108 & 5100 & 5167.84768439394 & -67.8476843939352 \tabularnewline
109 & 5040 & 5103.54044161014 & -63.5404416101373 \tabularnewline
110 & 5235 & 5190.50215957576 & 44.4978404242429 \tabularnewline
111 & 5310 & 5246.78732390142 & 63.2126760985821 \tabularnewline
112 & 5265 & 5274.60065198516 & -9.60065198515895 \tabularnewline
113 & 5380 & 5266.37690836797 & 113.623091632029 \tabularnewline
114 & 5465 & 5473.59730100601 & -8.59730100600609 \tabularnewline
115 & 5225 & 5192.82625523534 & 32.1737447646619 \tabularnewline
116 & 5445 & 5396.53226945098 & 48.4677305490231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302665&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]4145[/C][C]3812.12740384616[/C][C]332.872596153844[/C][/ROW]
[ROW][C]14[/C][C]4285[/C][C]4252.69714017733[/C][C]32.302859822672[/C][/ROW]
[ROW][C]15[/C][C]4370[/C][C]4388.39387044698[/C][C]-18.3938704469801[/C][/ROW]
[ROW][C]16[/C][C]4355[/C][C]4387.99799896256[/C][C]-32.997998962559[/C][/ROW]
[ROW][C]17[/C][C]4385[/C][C]4422.93890375039[/C][C]-37.9389037503915[/C][/ROW]
[ROW][C]18[/C][C]4525[/C][C]4564.93470336079[/C][C]-39.9347033607901[/C][/ROW]
[ROW][C]19[/C][C]4375[/C][C]4370.9705229979[/C][C]4.02947700209916[/C][/ROW]
[ROW][C]20[/C][C]4525[/C][C]4519.49408427195[/C][C]5.50591572804842[/C][/ROW]
[ROW][C]21[/C][C]4610[/C][C]4734.36780241771[/C][C]-124.367802417712[/C][/ROW]
[ROW][C]22[/C][C]4595[/C][C]4687.79969511515[/C][C]-92.7996951151545[/C][/ROW]
[ROW][C]23[/C][C]4500[/C][C]4544.9612599231[/C][C]-44.9612599230968[/C][/ROW]
[ROW][C]24[/C][C]4370[/C][C]4415.86944752762[/C][C]-45.8694475276152[/C][/ROW]
[ROW][C]25[/C][C]4390[/C][C]4539.29204968813[/C][C]-149.292049688129[/C][/ROW]
[ROW][C]26[/C][C]4530[/C][C]4494.82197777905[/C][C]35.1780222209527[/C][/ROW]
[ROW][C]27[/C][C]4590[/C][C]4595.97278561315[/C][C]-5.97278561315306[/C][/ROW]
[ROW][C]28[/C][C]4580[/C][C]4575.17090430287[/C][C]4.82909569712501[/C][/ROW]
[ROW][C]29[/C][C]4595[/C][C]4614.84926566816[/C][C]-19.8492656681565[/C][/ROW]
[ROW][C]30[/C][C]4685[/C][C]4746.17762689915[/C][C]-61.1776268991462[/C][/ROW]
[ROW][C]31[/C][C]4490[/C][C]4513.64253212093[/C][C]-23.6425321209272[/C][/ROW]
[ROW][C]32[/C][C]4635[/C][C]4610.33770040148[/C][C]24.6622995985163[/C][/ROW]
[ROW][C]33[/C][C]4710[/C][C]4794.96188941442[/C][C]-84.9618894144214[/C][/ROW]
[ROW][C]34[/C][C]4655[/C][C]4761.37546812408[/C][C]-106.375468124081[/C][/ROW]
[ROW][C]35[/C][C]4665[/C][C]4588.01673950881[/C][C]76.9832604911908[/C][/ROW]
[ROW][C]36[/C][C]4550[/C][C]4543.3761305692[/C][C]6.62386943080128[/C][/ROW]
[ROW][C]37[/C][C]4590[/C][C]4679.77920105585[/C][C]-89.7792010558542[/C][/ROW]
[ROW][C]38[/C][C]4675[/C][C]4699.99819207583[/C][C]-24.9981920758255[/C][/ROW]
[ROW][C]39[/C][C]4645[/C][C]4727.2391310705[/C][C]-82.2391310705034[/C][/ROW]
[ROW][C]40[/C][C]4665[/C][C]4622.323584588[/C][C]42.6764154120046[/C][/ROW]
[ROW][C]41[/C][C]4635[/C][C]4671.98867714488[/C][C]-36.9886771448828[/C][/ROW]
[ROW][C]42[/C][C]4720[/C][C]4763.0405896749[/C][C]-43.0405896748989[/C][/ROW]
[ROW][C]43[/C][C]4565[/C][C]4532.92541647483[/C][C]32.0745835251701[/C][/ROW]
[ROW][C]44[/C][C]4720[/C][C]4668.69937143324[/C][C]51.3006285667643[/C][/ROW]
[ROW][C]45[/C][C]4830[/C][C]4845.76075917989[/C][C]-15.7607591798915[/C][/ROW]
[ROW][C]46[/C][C]4830[/C][C]4857.67997144763[/C][C]-27.6799714476319[/C][/ROW]
[ROW][C]47[/C][C]4765[/C][C]4772.42432882147[/C][C]-7.42432882146932[/C][/ROW]
[ROW][C]48[/C][C]4705[/C][C]4634.81412912859[/C][C]70.185870871409[/C][/ROW]
[ROW][C]49[/C][C]4675[/C][C]4804.00122474526[/C][C]-129.001224745258[/C][/ROW]
[ROW][C]50[/C][C]4900[/C][C]4791.03630258705[/C][C]108.963697412953[/C][/ROW]
[ROW][C]51[/C][C]4945[/C][C]4922.01228884122[/C][C]22.9877111587803[/C][/ROW]
[ROW][C]52[/C][C]4905[/C][C]4928.94909702264[/C][C]-23.9490970226361[/C][/ROW]
[ROW][C]53[/C][C]4955[/C][C]4910.15533534114[/C][C]44.8446646588591[/C][/ROW]
[ROW][C]54[/C][C]5120[/C][C]5074.62029586877[/C][C]45.3797041312318[/C][/ROW]
[ROW][C]55[/C][C]4860[/C][C]4940.32709665712[/C][C]-80.3270966571217[/C][/ROW]
[ROW][C]56[/C][C]5040[/C][C]4986.36531672998[/C][C]53.6346832700165[/C][/ROW]
[ROW][C]57[/C][C]5140[/C][C]5158.88973378938[/C][C]-18.8897337893832[/C][/ROW]
[ROW][C]58[/C][C]5240[/C][C]5169.58174791442[/C][C]70.418252085582[/C][/ROW]
[ROW][C]59[/C][C]5145[/C][C]5179.48004493041[/C][C]-34.4800449304148[/C][/ROW]
[ROW][C]60[/C][C]5070[/C][C]5037.32802635563[/C][C]32.6719736443683[/C][/ROW]
[ROW][C]61[/C][C]5085[/C][C]5150.16912862873[/C][C]-65.1691286287287[/C][/ROW]
[ROW][C]62[/C][C]5215[/C][C]5235.23475743353[/C][C]-20.2347574335263[/C][/ROW]
[ROW][C]63[/C][C]5255[/C][C]5244.85505984887[/C][C]10.1449401511336[/C][/ROW]
[ROW][C]64[/C][C]5275[/C][C]5234.68302521216[/C][C]40.3169747878401[/C][/ROW]
[ROW][C]65[/C][C]5315[/C][C]5285.08926190054[/C][C]29.9107380994647[/C][/ROW]
[ROW][C]66[/C][C]5450[/C][C]5440.35528484344[/C][C]9.64471515655805[/C][/ROW]
[ROW][C]67[/C][C]5205[/C][C]5258.55606131997[/C][C]-53.5560613199741[/C][/ROW]
[ROW][C]68[/C][C]5370[/C][C]5350.1469966982[/C][C]19.8530033018042[/C][/ROW]
[ROW][C]69[/C][C]5500[/C][C]5484.29645986612[/C][C]15.7035401338799[/C][/ROW]
[ROW][C]70[/C][C]5490[/C][C]5540.66397814786[/C][C]-50.6639781478598[/C][/ROW]
[ROW][C]71[/C][C]5440[/C][C]5428.28075760107[/C][C]11.7192423989291[/C][/ROW]
[ROW][C]72[/C][C]5360[/C][C]5334.34905822826[/C][C]25.6509417717425[/C][/ROW]
[ROW][C]73[/C][C]5380[/C][C]5425.31387908436[/C][C]-45.3138790843595[/C][/ROW]
[ROW][C]74[/C][C]5460[/C][C]5533.56381962515[/C][C]-73.5638196251475[/C][/ROW]
[ROW][C]75[/C][C]5450[/C][C]5498.93085455277[/C][C]-48.9308545527747[/C][/ROW]
[ROW][C]76[/C][C]5520[/C][C]5436.35816734324[/C][C]83.6418326567609[/C][/ROW]
[ROW][C]77[/C][C]5475[/C][C]5518.0256568994[/C][C]-43.0256568993991[/C][/ROW]
[ROW][C]78[/C][C]5600[/C][C]5600.01982505736[/C][C]-0.0198250573621408[/C][/ROW]
[ROW][C]79[/C][C]5250[/C][C]5392.02169950023[/C][C]-142.02169950023[/C][/ROW]
[ROW][C]80[/C][C]5465[/C][C]5405.58091052597[/C][C]59.419089474035[/C][/ROW]
[ROW][C]81[/C][C]5515[/C][C]5561.5475943939[/C][C]-46.5475943938991[/C][/ROW]
[ROW][C]82[/C][C]5425[/C][C]5540.36759021831[/C][C]-115.367590218308[/C][/ROW]
[ROW][C]83[/C][C]5325[/C][C]5363.82086451859[/C][C]-38.8208645185878[/C][/ROW]
[ROW][C]84[/C][C]5275[/C][C]5207.89627299493[/C][C]67.1037270050738[/C][/ROW]
[ROW][C]85[/C][C]5160[/C][C]5305.0163464202[/C][C]-145.016346420201[/C][/ROW]
[ROW][C]86[/C][C]5360[/C][C]5299.96812070611[/C][C]60.0318792938888[/C][/ROW]
[ROW][C]87[/C][C]5435[/C][C]5365.98940443066[/C][C]69.0105955693443[/C][/ROW]
[ROW][C]88[/C][C]5285[/C][C]5413.07955224655[/C][C]-128.079552246551[/C][/ROW]
[ROW][C]89[/C][C]5415[/C][C]5273.60593222603[/C][C]141.394067773971[/C][/ROW]
[ROW][C]90[/C][C]5575[/C][C]5507.22710954308[/C][C]67.772890456924[/C][/ROW]
[ROW][C]91[/C][C]5265[/C][C]5327.8312070815[/C][C]-62.8312070814964[/C][/ROW]
[ROW][C]92[/C][C]5480[/C][C]5434.7025704765[/C][C]45.2974295234953[/C][/ROW]
[ROW][C]93[/C][C]5565[/C][C]5558.3068927543[/C][C]6.69310724570278[/C][/ROW]
[ROW][C]94[/C][C]5500[/C][C]5570.5682678198[/C][C]-70.5682678198[/C][/ROW]
[ROW][C]95[/C][C]5280[/C][C]5444.15868201936[/C][C]-164.158682019361[/C][/ROW]
[ROW][C]96[/C][C]5135[/C][C]5190.84813852058[/C][C]-55.848138520575[/C][/ROW]
[ROW][C]97[/C][C]5050[/C][C]5138.98611853307[/C][C]-88.986118533071[/C][/ROW]
[ROW][C]98[/C][C]5100[/C][C]5202.13812201139[/C][C]-102.138122011388[/C][/ROW]
[ROW][C]99[/C][C]5070[/C][C]5112.59127190826[/C][C]-42.5912719082608[/C][/ROW]
[ROW][C]100[/C][C]5115[/C][C]5010.73133997446[/C][C]104.268660025545[/C][/ROW]
[ROW][C]101[/C][C]5140[/C][C]5097.00796525646[/C][C]42.9920347435354[/C][/ROW]
[ROW][C]102[/C][C]5330[/C][C]5218.44726820544[/C][C]111.552731794563[/C][/ROW]
[ROW][C]103[/C][C]5080[/C][C]5042.04629863018[/C][C]37.9537013698246[/C][/ROW]
[ROW][C]104[/C][C]5285[/C][C]5241.22446709207[/C][C]43.7755329079291[/C][/ROW]
[ROW][C]105[/C][C]5405[/C][C]5348.19011323249[/C][C]56.8098867675117[/C][/ROW]
[ROW][C]106[/C][C]5385[/C][C]5384.85694637202[/C][C]0.143053627980407[/C][/ROW]
[ROW][C]107[/C][C]5255[/C][C]5301.85055817049[/C][C]-46.8505581704912[/C][/ROW]
[ROW][C]108[/C][C]5100[/C][C]5167.84768439394[/C][C]-67.8476843939352[/C][/ROW]
[ROW][C]109[/C][C]5040[/C][C]5103.54044161014[/C][C]-63.5404416101373[/C][/ROW]
[ROW][C]110[/C][C]5235[/C][C]5190.50215957576[/C][C]44.4978404242429[/C][/ROW]
[ROW][C]111[/C][C]5310[/C][C]5246.78732390142[/C][C]63.2126760985821[/C][/ROW]
[ROW][C]112[/C][C]5265[/C][C]5274.60065198516[/C][C]-9.60065198515895[/C][/ROW]
[ROW][C]113[/C][C]5380[/C][C]5266.37690836797[/C][C]113.623091632029[/C][/ROW]
[ROW][C]114[/C][C]5465[/C][C]5473.59730100601[/C][C]-8.59730100600609[/C][/ROW]
[ROW][C]115[/C][C]5225[/C][C]5192.82625523534[/C][C]32.1737447646619[/C][/ROW]
[ROW][C]116[/C][C]5445[/C][C]5396.53226945098[/C][C]48.4677305490231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302665&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302665&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
1341453812.12740384616332.872596153844
1442854252.6971401773332.302859822672
1543704388.39387044698-18.3938704469801
1643554387.99799896256-32.997998962559
1743854422.93890375039-37.9389037503915
1845254564.93470336079-39.9347033607901
1943754370.97052299794.02947700209916
2045254519.494084271955.50591572804842
2146104734.36780241771-124.367802417712
2245954687.79969511515-92.7996951151545
2345004544.9612599231-44.9612599230968
2443704415.86944752762-45.8694475276152
2543904539.29204968813-149.292049688129
2645304494.8219777790535.1780222209527
2745904595.97278561315-5.97278561315306
2845804575.170904302874.82909569712501
2945954614.84926566816-19.8492656681565
3046854746.17762689915-61.1776268991462
3144904513.64253212093-23.6425321209272
3246354610.3377004014824.6622995985163
3347104794.96188941442-84.9618894144214
3446554761.37546812408-106.375468124081
3546654588.0167395088176.9832604911908
3645504543.37613056926.62386943080128
3745904679.77920105585-89.7792010558542
3846754699.99819207583-24.9981920758255
3946454727.2391310705-82.2391310705034
4046654622.32358458842.6764154120046
4146354671.98867714488-36.9886771448828
4247204763.0405896749-43.0405896748989
4345654532.9254164748332.0745835251701
4447204668.6993714332451.3006285667643
4548304845.76075917989-15.7607591798915
4648304857.67997144763-27.6799714476319
4747654772.42432882147-7.42432882146932
4847054634.8141291285970.185870871409
4946754804.00122474526-129.001224745258
5049004791.03630258705108.963697412953
5149454922.0122888412222.9877111587803
5249054928.94909702264-23.9490970226361
5349554910.1553353411444.8446646588591
5451205074.6202958687745.3797041312318
5548604940.32709665712-80.3270966571217
5650404986.3653167299853.6346832700165
5751405158.88973378938-18.8897337893832
5852405169.5817479144270.418252085582
5951455179.48004493041-34.4800449304148
6050705037.3280263556332.6719736443683
6150855150.16912862873-65.1691286287287
6252155235.23475743353-20.2347574335263
6352555244.8550598488710.1449401511336
6452755234.6830252121640.3169747878401
6553155285.0892619005429.9107380994647
6654505440.355284843449.64471515655805
6752055258.55606131997-53.5560613199741
6853705350.146996698219.8530033018042
6955005484.2964598661215.7035401338799
7054905540.66397814786-50.6639781478598
7154405428.2807576010711.7192423989291
7253605334.3490582282625.6509417717425
7353805425.31387908436-45.3138790843595
7454605533.56381962515-73.5638196251475
7554505498.93085455277-48.9308545527747
7655205436.3581673432483.6418326567609
7754755518.0256568994-43.0256568993991
7856005600.01982505736-0.0198250573621408
7952505392.02169950023-142.02169950023
8054655405.5809105259759.419089474035
8155155561.5475943939-46.5475943938991
8254255540.36759021831-115.367590218308
8353255363.82086451859-38.8208645185878
8452755207.8962729949367.1037270050738
8551605305.0163464202-145.016346420201
8653605299.9681207061160.0318792938888
8754355365.9894044306669.0105955693443
8852855413.07955224655-128.079552246551
8954155273.60593222603141.394067773971
9055755507.2271095430867.772890456924
9152655327.8312070815-62.8312070814964
9254805434.702570476545.2974295234953
9355655558.30689275436.69310724570278
9455005570.5682678198-70.5682678198
9552805444.15868201936-164.158682019361
9651355190.84813852058-55.848138520575
9750505138.98611853307-88.986118533071
9851005202.13812201139-102.138122011388
9950705112.59127190826-42.5912719082608
10051155010.73133997446104.268660025545
10151405097.0079652564642.9920347435354
10253305218.44726820544111.552731794563
10350805042.0462986301837.9537013698246
10452855241.2244670920743.7755329079291
10554055348.1901132324956.8098867675117
10653855384.856946372020.143053627980407
10752555301.85055817049-46.8505581704912
10851005167.84768439394-67.8476843939352
10950405103.54044161014-63.5404416101373
11052355190.5021595757644.4978404242429
11153105246.7873239014263.2126760985821
11252655274.60065198516-9.60065198515895
11353805266.37690836797113.623091632029
11454655473.59730100601-8.59730100600609
11552255192.8262552353432.1737447646619
11654455396.5322694509848.4677305490231







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1175518.272503444695375.28568769665661.25931919277
1185503.907335763615310.876154408455696.93851711877
1195419.593344705545182.617447279285656.5692421318
1205330.730110445365052.780150029355608.68007086137
1215336.891093540325019.592835368545654.1893517121
1225509.417764505125153.686233076755865.1492959335
1235543.567340866585149.895233654895937.23944807828
1245516.34212278715084.95142361545947.73282195879
1255544.599727492855075.529499788016013.66995519768
1265640.852816221815134.013698139176147.69193430446
1275377.819584628174833.029433568455922.60973568789
1285559.14420308614976.152381704076142.13602446814

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 5518.27250344469 & 5375.2856876966 & 5661.25931919277 \tabularnewline
118 & 5503.90733576361 & 5310.87615440845 & 5696.93851711877 \tabularnewline
119 & 5419.59334470554 & 5182.61744727928 & 5656.5692421318 \tabularnewline
120 & 5330.73011044536 & 5052.78015002935 & 5608.68007086137 \tabularnewline
121 & 5336.89109354032 & 5019.59283536854 & 5654.1893517121 \tabularnewline
122 & 5509.41776450512 & 5153.68623307675 & 5865.1492959335 \tabularnewline
123 & 5543.56734086658 & 5149.89523365489 & 5937.23944807828 \tabularnewline
124 & 5516.3421227871 & 5084.9514236154 & 5947.73282195879 \tabularnewline
125 & 5544.59972749285 & 5075.52949978801 & 6013.66995519768 \tabularnewline
126 & 5640.85281622181 & 5134.01369813917 & 6147.69193430446 \tabularnewline
127 & 5377.81958462817 & 4833.02943356845 & 5922.60973568789 \tabularnewline
128 & 5559.1442030861 & 4976.15238170407 & 6142.13602446814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302665&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]5518.27250344469[/C][C]5375.2856876966[/C][C]5661.25931919277[/C][/ROW]
[ROW][C]118[/C][C]5503.90733576361[/C][C]5310.87615440845[/C][C]5696.93851711877[/C][/ROW]
[ROW][C]119[/C][C]5419.59334470554[/C][C]5182.61744727928[/C][C]5656.5692421318[/C][/ROW]
[ROW][C]120[/C][C]5330.73011044536[/C][C]5052.78015002935[/C][C]5608.68007086137[/C][/ROW]
[ROW][C]121[/C][C]5336.89109354032[/C][C]5019.59283536854[/C][C]5654.1893517121[/C][/ROW]
[ROW][C]122[/C][C]5509.41776450512[/C][C]5153.68623307675[/C][C]5865.1492959335[/C][/ROW]
[ROW][C]123[/C][C]5543.56734086658[/C][C]5149.89523365489[/C][C]5937.23944807828[/C][/ROW]
[ROW][C]124[/C][C]5516.3421227871[/C][C]5084.9514236154[/C][C]5947.73282195879[/C][/ROW]
[ROW][C]125[/C][C]5544.59972749285[/C][C]5075.52949978801[/C][C]6013.66995519768[/C][/ROW]
[ROW][C]126[/C][C]5640.85281622181[/C][C]5134.01369813917[/C][C]6147.69193430446[/C][/ROW]
[ROW][C]127[/C][C]5377.81958462817[/C][C]4833.02943356845[/C][C]5922.60973568789[/C][/ROW]
[ROW][C]128[/C][C]5559.1442030861[/C][C]4976.15238170407[/C][C]6142.13602446814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302665&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302665&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
1175518.272503444695375.28568769665661.25931919277
1185503.907335763615310.876154408455696.93851711877
1195419.593344705545182.617447279285656.5692421318
1205330.730110445365052.780150029355608.68007086137
1215336.891093540325019.592835368545654.1893517121
1225509.417764505125153.686233076755865.1492959335
1235543.567340866585149.895233654895937.23944807828
1245516.34212278715084.95142361545947.73282195879
1255544.599727492855075.529499788016013.66995519768
1265640.852816221815134.013698139176147.69193430446
1275377.819584628174833.029433568455922.60973568789
1285559.14420308614976.152381704076142.13602446814



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):
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')