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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 computationMon, 19 Dec 2016 11:55:58 +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/19/t14821460849cczc0y1ex07xgh.htm/, Retrieved Fri, 01 Nov 2024 03:31:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301297, Retrieved Fri, 01 Nov 2024 03:31:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-19 10:55:58] [3373ac80755a3c11b71e203db9ac7f73] [Current]
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Dataseries X:
4150
4300
4300
4450
4500
4400
3950
2150
4350
4550
4600
4250
4350
4400
4300
4350
4350
4400
3850
2300
4300
4350
4350
4200
4150
4450
4300
4350
4300
4350
3900
2250
4300
4450
4400
4250
4250
4300
4450
3900
4350
4500
3800
2450
4400
4500
4500
4400
4450
4600
4700
4700
2950
3750
4050
2550
4600
5000
5100
4900
4950
5000
4950
5100
5250
5200
4300
2650
4950
5200
5350
5150
5350
5550
5400
5450
5450
5200
4400
2650
5100
5200
5300
4900
5200
5300
5250
5150
5050
4900
4150
2800
5100
5250
5200
5000
5150
5250
5250
5350
5450
5300
4300
3000
5300
5400
5550
5350
5500
5750
5750
5700
5800
5800
4600
3150
5500
5750
5950
5600
6100
6250
6150
6050
6300
5950




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=301297&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=301297&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301297&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
alpha0.614111436553776
beta0.00318603526061203
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.614111436553776 \tabularnewline
beta & 0.00318603526061203 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301297&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]0.614111436553776[/C][/ROW]
[ROW][C]beta[/C][C]0.00318603526061203[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301297&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301297&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
alpha0.614111436553776
beta0.00318603526061203
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1343504374.45245726496-24.4524572649598
1444004403.1745023124-3.17450231239945
1543004292.874038339427.12596166057847
1643504353.49648294638-3.49648294638155
1743504365.92205501836-15.9220550183636
1844004414.43578838981-14.435788389811
1938503907.5840103108-57.5840103108003
2023002055.37174792048244.628252079522
2143004397.56346037862-97.5634603786193
2243504537.75377127292-187.753771272924
2343504478.4398253772-128.439825377198
2442004051.13328245424148.866717545761
2541504242.33179538318-92.3317953831793
2644504228.9768884347221.0231115653
2743004256.405929762543.5940702374983
2843504339.5423962835210.4576037164779
2943004360.68317422584-60.6831742258391
3043504381.7668553015-31.7668553015001
3139003864.2962241159435.703775884057
3222502069.57993649142180.420063508576
3343004372.42191589855-72.4219158985534
3444504528.18237812197-78.1823781219673
3544004536.50230448275-136.502304482752
3642504104.57355264654145.426447353464
3742504293.98167685176-43.981676851763
3843004310.73605210668-10.7360521066839
3944504195.80260644735254.197393552648
4039004408.64851073823-508.648510738226
4143504110.36014235468239.639857645317
4245004315.82309355385184.176906446145
4338003931.33596909544-131.335969095436
4424502034.08180996583415.918190034175
4544004482.04979949224-82.0497994922353
4645004632.38274789275-132.38274789275
4745004607.79663951671-107.796639516714
4844004193.93156198467206.068438015326
4944504421.1344742933728.8655257066312
5046004483.32152929289116.678470707115
5147004447.58047560415252.419524395848
5247004660.2767678962839.7232321037209
5329504700.76488962147-1750.76488962147
5437503682.0182660043667.9817339956417
5540503224.06775589214825.932244107858
5625501914.44932546234635.550674537656
5746004497.49223536159102.507764638412
5850004761.72129616409238.278703835915
5951004966.04505499037133.954945009629
6049004702.39782740933197.602172590667
6149504926.1403814527723.8596185472297
6250004986.9823293110113.0176706889906
6349504889.1082497847660.8917502152399
6451004985.3366629661114.6633370339
6552505073.14450397894176.855496021059
6652005243.24129313834-43.2412931383442
6743004721.83952184699-421.839521846992
6826502648.360885383591.6391146164051
6949504843.28186310191106.718136898091
7052005111.2752061246488.7247938753571
7153505224.64222863377125.357771366227
7251504956.58458750329193.415412496706
7353505178.61702166398171.382978336022
7455505331.20441065761218.795589342389
7554005361.2531841991438.7468158008624
7654505445.391091376294.60890862370888
7754505466.9068703709-16.9068703708954
7852005518.92648376244-318.926483762441
7944004828.59839310677-428.598393106771
8026502751.330941314-101.330941313998
8151004883.17724564915216.822754350846
8252005219.16293762176-19.1629376217643
8353005266.4396234572133.5603765427923
8449004941.99329641218-41.9932964121763
8552005018.98309812562181.016901874381
8653005177.03018724988122.969812750122
8752505147.58716211212102.412837887881
8851505270.30357592494-120.303575924944
8950505214.34524258671-164.345242586714
9049005174.76886333833-274.76886333833
9141504510.59246826826-360.59246826826
9228002474.25528762379325.744712376215
9351004868.37629809286231.623701907144
9452505213.4830434088936.5169565911092
9552005295.09395344972-95.0939534497174
9650004891.52837279942108.471627200576
9751505061.1036434731388.8963565268677
9852505162.5814494471487.4185505528558
9952505111.2394259862138.760574013796
10053505256.2819559015393.7180440984666
10154505332.18005331334117.819946686659
10253005466.85992897994-166.85992897994
10343004870.13816232786-570.138162327862
10430002705.89309914412294.106900855877
10553005081.29959046324218.700409536763
10654005419.1593314046-19.1593314045958
10755505467.1591983602782.8408016397279
10853505173.79393159471176.206068405292
10955005386.02677098448113.973229015519
11057505504.01470979494245.98529020506
11157505551.47072188064198.529278119362
11257005734.75522609674-34.7552260967359
11358005733.04238023266.9576197680017
11458005837.67356424317-37.6735642431677
11546005321.72583016456-721.725830164562
11631503065.5316615597584.4683384402497
11755005312.92915443143187.070845568574
11857505632.03537288728117.964627112719
11959505765.18347956402184.816520435981
12056005535.581040254464.4189597455952
12161005680.08378955107419.916210448925
12262505987.4730661172262.526933882796
12361506046.63810974947103.361890250534
12460506172.84364899954-122.843648999539
12563006118.22675940604181.77324059396
12659506294.784239492-344.784239491999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4350 & 4374.45245726496 & -24.4524572649598 \tabularnewline
14 & 4400 & 4403.1745023124 & -3.17450231239945 \tabularnewline
15 & 4300 & 4292.87403833942 & 7.12596166057847 \tabularnewline
16 & 4350 & 4353.49648294638 & -3.49648294638155 \tabularnewline
17 & 4350 & 4365.92205501836 & -15.9220550183636 \tabularnewline
18 & 4400 & 4414.43578838981 & -14.435788389811 \tabularnewline
19 & 3850 & 3907.5840103108 & -57.5840103108003 \tabularnewline
20 & 2300 & 2055.37174792048 & 244.628252079522 \tabularnewline
21 & 4300 & 4397.56346037862 & -97.5634603786193 \tabularnewline
22 & 4350 & 4537.75377127292 & -187.753771272924 \tabularnewline
23 & 4350 & 4478.4398253772 & -128.439825377198 \tabularnewline
24 & 4200 & 4051.13328245424 & 148.866717545761 \tabularnewline
25 & 4150 & 4242.33179538318 & -92.3317953831793 \tabularnewline
26 & 4450 & 4228.9768884347 & 221.0231115653 \tabularnewline
27 & 4300 & 4256.4059297625 & 43.5940702374983 \tabularnewline
28 & 4350 & 4339.54239628352 & 10.4576037164779 \tabularnewline
29 & 4300 & 4360.68317422584 & -60.6831742258391 \tabularnewline
30 & 4350 & 4381.7668553015 & -31.7668553015001 \tabularnewline
31 & 3900 & 3864.29622411594 & 35.703775884057 \tabularnewline
32 & 2250 & 2069.57993649142 & 180.420063508576 \tabularnewline
33 & 4300 & 4372.42191589855 & -72.4219158985534 \tabularnewline
34 & 4450 & 4528.18237812197 & -78.1823781219673 \tabularnewline
35 & 4400 & 4536.50230448275 & -136.502304482752 \tabularnewline
36 & 4250 & 4104.57355264654 & 145.426447353464 \tabularnewline
37 & 4250 & 4293.98167685176 & -43.981676851763 \tabularnewline
38 & 4300 & 4310.73605210668 & -10.7360521066839 \tabularnewline
39 & 4450 & 4195.80260644735 & 254.197393552648 \tabularnewline
40 & 3900 & 4408.64851073823 & -508.648510738226 \tabularnewline
41 & 4350 & 4110.36014235468 & 239.639857645317 \tabularnewline
42 & 4500 & 4315.82309355385 & 184.176906446145 \tabularnewline
43 & 3800 & 3931.33596909544 & -131.335969095436 \tabularnewline
44 & 2450 & 2034.08180996583 & 415.918190034175 \tabularnewline
45 & 4400 & 4482.04979949224 & -82.0497994922353 \tabularnewline
46 & 4500 & 4632.38274789275 & -132.38274789275 \tabularnewline
47 & 4500 & 4607.79663951671 & -107.796639516714 \tabularnewline
48 & 4400 & 4193.93156198467 & 206.068438015326 \tabularnewline
49 & 4450 & 4421.13447429337 & 28.8655257066312 \tabularnewline
50 & 4600 & 4483.32152929289 & 116.678470707115 \tabularnewline
51 & 4700 & 4447.58047560415 & 252.419524395848 \tabularnewline
52 & 4700 & 4660.27676789628 & 39.7232321037209 \tabularnewline
53 & 2950 & 4700.76488962147 & -1750.76488962147 \tabularnewline
54 & 3750 & 3682.01826600436 & 67.9817339956417 \tabularnewline
55 & 4050 & 3224.06775589214 & 825.932244107858 \tabularnewline
56 & 2550 & 1914.44932546234 & 635.550674537656 \tabularnewline
57 & 4600 & 4497.49223536159 & 102.507764638412 \tabularnewline
58 & 5000 & 4761.72129616409 & 238.278703835915 \tabularnewline
59 & 5100 & 4966.04505499037 & 133.954945009629 \tabularnewline
60 & 4900 & 4702.39782740933 & 197.602172590667 \tabularnewline
61 & 4950 & 4926.14038145277 & 23.8596185472297 \tabularnewline
62 & 5000 & 4986.98232931101 & 13.0176706889906 \tabularnewline
63 & 4950 & 4889.10824978476 & 60.8917502152399 \tabularnewline
64 & 5100 & 4985.3366629661 & 114.6633370339 \tabularnewline
65 & 5250 & 5073.14450397894 & 176.855496021059 \tabularnewline
66 & 5200 & 5243.24129313834 & -43.2412931383442 \tabularnewline
67 & 4300 & 4721.83952184699 & -421.839521846992 \tabularnewline
68 & 2650 & 2648.36088538359 & 1.6391146164051 \tabularnewline
69 & 4950 & 4843.28186310191 & 106.718136898091 \tabularnewline
70 & 5200 & 5111.27520612464 & 88.7247938753571 \tabularnewline
71 & 5350 & 5224.64222863377 & 125.357771366227 \tabularnewline
72 & 5150 & 4956.58458750329 & 193.415412496706 \tabularnewline
73 & 5350 & 5178.61702166398 & 171.382978336022 \tabularnewline
74 & 5550 & 5331.20441065761 & 218.795589342389 \tabularnewline
75 & 5400 & 5361.25318419914 & 38.7468158008624 \tabularnewline
76 & 5450 & 5445.39109137629 & 4.60890862370888 \tabularnewline
77 & 5450 & 5466.9068703709 & -16.9068703708954 \tabularnewline
78 & 5200 & 5518.92648376244 & -318.926483762441 \tabularnewline
79 & 4400 & 4828.59839310677 & -428.598393106771 \tabularnewline
80 & 2650 & 2751.330941314 & -101.330941313998 \tabularnewline
81 & 5100 & 4883.17724564915 & 216.822754350846 \tabularnewline
82 & 5200 & 5219.16293762176 & -19.1629376217643 \tabularnewline
83 & 5300 & 5266.43962345721 & 33.5603765427923 \tabularnewline
84 & 4900 & 4941.99329641218 & -41.9932964121763 \tabularnewline
85 & 5200 & 5018.98309812562 & 181.016901874381 \tabularnewline
86 & 5300 & 5177.03018724988 & 122.969812750122 \tabularnewline
87 & 5250 & 5147.58716211212 & 102.412837887881 \tabularnewline
88 & 5150 & 5270.30357592494 & -120.303575924944 \tabularnewline
89 & 5050 & 5214.34524258671 & -164.345242586714 \tabularnewline
90 & 4900 & 5174.76886333833 & -274.76886333833 \tabularnewline
91 & 4150 & 4510.59246826826 & -360.59246826826 \tabularnewline
92 & 2800 & 2474.25528762379 & 325.744712376215 \tabularnewline
93 & 5100 & 4868.37629809286 & 231.623701907144 \tabularnewline
94 & 5250 & 5213.48304340889 & 36.5169565911092 \tabularnewline
95 & 5200 & 5295.09395344972 & -95.0939534497174 \tabularnewline
96 & 5000 & 4891.52837279942 & 108.471627200576 \tabularnewline
97 & 5150 & 5061.10364347313 & 88.8963565268677 \tabularnewline
98 & 5250 & 5162.58144944714 & 87.4185505528558 \tabularnewline
99 & 5250 & 5111.2394259862 & 138.760574013796 \tabularnewline
100 & 5350 & 5256.28195590153 & 93.7180440984666 \tabularnewline
101 & 5450 & 5332.18005331334 & 117.819946686659 \tabularnewline
102 & 5300 & 5466.85992897994 & -166.85992897994 \tabularnewline
103 & 4300 & 4870.13816232786 & -570.138162327862 \tabularnewline
104 & 3000 & 2705.89309914412 & 294.106900855877 \tabularnewline
105 & 5300 & 5081.29959046324 & 218.700409536763 \tabularnewline
106 & 5400 & 5419.1593314046 & -19.1593314045958 \tabularnewline
107 & 5550 & 5467.15919836027 & 82.8408016397279 \tabularnewline
108 & 5350 & 5173.79393159471 & 176.206068405292 \tabularnewline
109 & 5500 & 5386.02677098448 & 113.973229015519 \tabularnewline
110 & 5750 & 5504.01470979494 & 245.98529020506 \tabularnewline
111 & 5750 & 5551.47072188064 & 198.529278119362 \tabularnewline
112 & 5700 & 5734.75522609674 & -34.7552260967359 \tabularnewline
113 & 5800 & 5733.042380232 & 66.9576197680017 \tabularnewline
114 & 5800 & 5837.67356424317 & -37.6735642431677 \tabularnewline
115 & 4600 & 5321.72583016456 & -721.725830164562 \tabularnewline
116 & 3150 & 3065.53166155975 & 84.4683384402497 \tabularnewline
117 & 5500 & 5312.92915443143 & 187.070845568574 \tabularnewline
118 & 5750 & 5632.03537288728 & 117.964627112719 \tabularnewline
119 & 5950 & 5765.18347956402 & 184.816520435981 \tabularnewline
120 & 5600 & 5535.5810402544 & 64.4189597455952 \tabularnewline
121 & 6100 & 5680.08378955107 & 419.916210448925 \tabularnewline
122 & 6250 & 5987.4730661172 & 262.526933882796 \tabularnewline
123 & 6150 & 6046.63810974947 & 103.361890250534 \tabularnewline
124 & 6050 & 6172.84364899954 & -122.843648999539 \tabularnewline
125 & 6300 & 6118.22675940604 & 181.77324059396 \tabularnewline
126 & 5950 & 6294.784239492 & -344.784239491999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301297&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]4350[/C][C]4374.45245726496[/C][C]-24.4524572649598[/C][/ROW]
[ROW][C]14[/C][C]4400[/C][C]4403.1745023124[/C][C]-3.17450231239945[/C][/ROW]
[ROW][C]15[/C][C]4300[/C][C]4292.87403833942[/C][C]7.12596166057847[/C][/ROW]
[ROW][C]16[/C][C]4350[/C][C]4353.49648294638[/C][C]-3.49648294638155[/C][/ROW]
[ROW][C]17[/C][C]4350[/C][C]4365.92205501836[/C][C]-15.9220550183636[/C][/ROW]
[ROW][C]18[/C][C]4400[/C][C]4414.43578838981[/C][C]-14.435788389811[/C][/ROW]
[ROW][C]19[/C][C]3850[/C][C]3907.5840103108[/C][C]-57.5840103108003[/C][/ROW]
[ROW][C]20[/C][C]2300[/C][C]2055.37174792048[/C][C]244.628252079522[/C][/ROW]
[ROW][C]21[/C][C]4300[/C][C]4397.56346037862[/C][C]-97.5634603786193[/C][/ROW]
[ROW][C]22[/C][C]4350[/C][C]4537.75377127292[/C][C]-187.753771272924[/C][/ROW]
[ROW][C]23[/C][C]4350[/C][C]4478.4398253772[/C][C]-128.439825377198[/C][/ROW]
[ROW][C]24[/C][C]4200[/C][C]4051.13328245424[/C][C]148.866717545761[/C][/ROW]
[ROW][C]25[/C][C]4150[/C][C]4242.33179538318[/C][C]-92.3317953831793[/C][/ROW]
[ROW][C]26[/C][C]4450[/C][C]4228.9768884347[/C][C]221.0231115653[/C][/ROW]
[ROW][C]27[/C][C]4300[/C][C]4256.4059297625[/C][C]43.5940702374983[/C][/ROW]
[ROW][C]28[/C][C]4350[/C][C]4339.54239628352[/C][C]10.4576037164779[/C][/ROW]
[ROW][C]29[/C][C]4300[/C][C]4360.68317422584[/C][C]-60.6831742258391[/C][/ROW]
[ROW][C]30[/C][C]4350[/C][C]4381.7668553015[/C][C]-31.7668553015001[/C][/ROW]
[ROW][C]31[/C][C]3900[/C][C]3864.29622411594[/C][C]35.703775884057[/C][/ROW]
[ROW][C]32[/C][C]2250[/C][C]2069.57993649142[/C][C]180.420063508576[/C][/ROW]
[ROW][C]33[/C][C]4300[/C][C]4372.42191589855[/C][C]-72.4219158985534[/C][/ROW]
[ROW][C]34[/C][C]4450[/C][C]4528.18237812197[/C][C]-78.1823781219673[/C][/ROW]
[ROW][C]35[/C][C]4400[/C][C]4536.50230448275[/C][C]-136.502304482752[/C][/ROW]
[ROW][C]36[/C][C]4250[/C][C]4104.57355264654[/C][C]145.426447353464[/C][/ROW]
[ROW][C]37[/C][C]4250[/C][C]4293.98167685176[/C][C]-43.981676851763[/C][/ROW]
[ROW][C]38[/C][C]4300[/C][C]4310.73605210668[/C][C]-10.7360521066839[/C][/ROW]
[ROW][C]39[/C][C]4450[/C][C]4195.80260644735[/C][C]254.197393552648[/C][/ROW]
[ROW][C]40[/C][C]3900[/C][C]4408.64851073823[/C][C]-508.648510738226[/C][/ROW]
[ROW][C]41[/C][C]4350[/C][C]4110.36014235468[/C][C]239.639857645317[/C][/ROW]
[ROW][C]42[/C][C]4500[/C][C]4315.82309355385[/C][C]184.176906446145[/C][/ROW]
[ROW][C]43[/C][C]3800[/C][C]3931.33596909544[/C][C]-131.335969095436[/C][/ROW]
[ROW][C]44[/C][C]2450[/C][C]2034.08180996583[/C][C]415.918190034175[/C][/ROW]
[ROW][C]45[/C][C]4400[/C][C]4482.04979949224[/C][C]-82.0497994922353[/C][/ROW]
[ROW][C]46[/C][C]4500[/C][C]4632.38274789275[/C][C]-132.38274789275[/C][/ROW]
[ROW][C]47[/C][C]4500[/C][C]4607.79663951671[/C][C]-107.796639516714[/C][/ROW]
[ROW][C]48[/C][C]4400[/C][C]4193.93156198467[/C][C]206.068438015326[/C][/ROW]
[ROW][C]49[/C][C]4450[/C][C]4421.13447429337[/C][C]28.8655257066312[/C][/ROW]
[ROW][C]50[/C][C]4600[/C][C]4483.32152929289[/C][C]116.678470707115[/C][/ROW]
[ROW][C]51[/C][C]4700[/C][C]4447.58047560415[/C][C]252.419524395848[/C][/ROW]
[ROW][C]52[/C][C]4700[/C][C]4660.27676789628[/C][C]39.7232321037209[/C][/ROW]
[ROW][C]53[/C][C]2950[/C][C]4700.76488962147[/C][C]-1750.76488962147[/C][/ROW]
[ROW][C]54[/C][C]3750[/C][C]3682.01826600436[/C][C]67.9817339956417[/C][/ROW]
[ROW][C]55[/C][C]4050[/C][C]3224.06775589214[/C][C]825.932244107858[/C][/ROW]
[ROW][C]56[/C][C]2550[/C][C]1914.44932546234[/C][C]635.550674537656[/C][/ROW]
[ROW][C]57[/C][C]4600[/C][C]4497.49223536159[/C][C]102.507764638412[/C][/ROW]
[ROW][C]58[/C][C]5000[/C][C]4761.72129616409[/C][C]238.278703835915[/C][/ROW]
[ROW][C]59[/C][C]5100[/C][C]4966.04505499037[/C][C]133.954945009629[/C][/ROW]
[ROW][C]60[/C][C]4900[/C][C]4702.39782740933[/C][C]197.602172590667[/C][/ROW]
[ROW][C]61[/C][C]4950[/C][C]4926.14038145277[/C][C]23.8596185472297[/C][/ROW]
[ROW][C]62[/C][C]5000[/C][C]4986.98232931101[/C][C]13.0176706889906[/C][/ROW]
[ROW][C]63[/C][C]4950[/C][C]4889.10824978476[/C][C]60.8917502152399[/C][/ROW]
[ROW][C]64[/C][C]5100[/C][C]4985.3366629661[/C][C]114.6633370339[/C][/ROW]
[ROW][C]65[/C][C]5250[/C][C]5073.14450397894[/C][C]176.855496021059[/C][/ROW]
[ROW][C]66[/C][C]5200[/C][C]5243.24129313834[/C][C]-43.2412931383442[/C][/ROW]
[ROW][C]67[/C][C]4300[/C][C]4721.83952184699[/C][C]-421.839521846992[/C][/ROW]
[ROW][C]68[/C][C]2650[/C][C]2648.36088538359[/C][C]1.6391146164051[/C][/ROW]
[ROW][C]69[/C][C]4950[/C][C]4843.28186310191[/C][C]106.718136898091[/C][/ROW]
[ROW][C]70[/C][C]5200[/C][C]5111.27520612464[/C][C]88.7247938753571[/C][/ROW]
[ROW][C]71[/C][C]5350[/C][C]5224.64222863377[/C][C]125.357771366227[/C][/ROW]
[ROW][C]72[/C][C]5150[/C][C]4956.58458750329[/C][C]193.415412496706[/C][/ROW]
[ROW][C]73[/C][C]5350[/C][C]5178.61702166398[/C][C]171.382978336022[/C][/ROW]
[ROW][C]74[/C][C]5550[/C][C]5331.20441065761[/C][C]218.795589342389[/C][/ROW]
[ROW][C]75[/C][C]5400[/C][C]5361.25318419914[/C][C]38.7468158008624[/C][/ROW]
[ROW][C]76[/C][C]5450[/C][C]5445.39109137629[/C][C]4.60890862370888[/C][/ROW]
[ROW][C]77[/C][C]5450[/C][C]5466.9068703709[/C][C]-16.9068703708954[/C][/ROW]
[ROW][C]78[/C][C]5200[/C][C]5518.92648376244[/C][C]-318.926483762441[/C][/ROW]
[ROW][C]79[/C][C]4400[/C][C]4828.59839310677[/C][C]-428.598393106771[/C][/ROW]
[ROW][C]80[/C][C]2650[/C][C]2751.330941314[/C][C]-101.330941313998[/C][/ROW]
[ROW][C]81[/C][C]5100[/C][C]4883.17724564915[/C][C]216.822754350846[/C][/ROW]
[ROW][C]82[/C][C]5200[/C][C]5219.16293762176[/C][C]-19.1629376217643[/C][/ROW]
[ROW][C]83[/C][C]5300[/C][C]5266.43962345721[/C][C]33.5603765427923[/C][/ROW]
[ROW][C]84[/C][C]4900[/C][C]4941.99329641218[/C][C]-41.9932964121763[/C][/ROW]
[ROW][C]85[/C][C]5200[/C][C]5018.98309812562[/C][C]181.016901874381[/C][/ROW]
[ROW][C]86[/C][C]5300[/C][C]5177.03018724988[/C][C]122.969812750122[/C][/ROW]
[ROW][C]87[/C][C]5250[/C][C]5147.58716211212[/C][C]102.412837887881[/C][/ROW]
[ROW][C]88[/C][C]5150[/C][C]5270.30357592494[/C][C]-120.303575924944[/C][/ROW]
[ROW][C]89[/C][C]5050[/C][C]5214.34524258671[/C][C]-164.345242586714[/C][/ROW]
[ROW][C]90[/C][C]4900[/C][C]5174.76886333833[/C][C]-274.76886333833[/C][/ROW]
[ROW][C]91[/C][C]4150[/C][C]4510.59246826826[/C][C]-360.59246826826[/C][/ROW]
[ROW][C]92[/C][C]2800[/C][C]2474.25528762379[/C][C]325.744712376215[/C][/ROW]
[ROW][C]93[/C][C]5100[/C][C]4868.37629809286[/C][C]231.623701907144[/C][/ROW]
[ROW][C]94[/C][C]5250[/C][C]5213.48304340889[/C][C]36.5169565911092[/C][/ROW]
[ROW][C]95[/C][C]5200[/C][C]5295.09395344972[/C][C]-95.0939534497174[/C][/ROW]
[ROW][C]96[/C][C]5000[/C][C]4891.52837279942[/C][C]108.471627200576[/C][/ROW]
[ROW][C]97[/C][C]5150[/C][C]5061.10364347313[/C][C]88.8963565268677[/C][/ROW]
[ROW][C]98[/C][C]5250[/C][C]5162.58144944714[/C][C]87.4185505528558[/C][/ROW]
[ROW][C]99[/C][C]5250[/C][C]5111.2394259862[/C][C]138.760574013796[/C][/ROW]
[ROW][C]100[/C][C]5350[/C][C]5256.28195590153[/C][C]93.7180440984666[/C][/ROW]
[ROW][C]101[/C][C]5450[/C][C]5332.18005331334[/C][C]117.819946686659[/C][/ROW]
[ROW][C]102[/C][C]5300[/C][C]5466.85992897994[/C][C]-166.85992897994[/C][/ROW]
[ROW][C]103[/C][C]4300[/C][C]4870.13816232786[/C][C]-570.138162327862[/C][/ROW]
[ROW][C]104[/C][C]3000[/C][C]2705.89309914412[/C][C]294.106900855877[/C][/ROW]
[ROW][C]105[/C][C]5300[/C][C]5081.29959046324[/C][C]218.700409536763[/C][/ROW]
[ROW][C]106[/C][C]5400[/C][C]5419.1593314046[/C][C]-19.1593314045958[/C][/ROW]
[ROW][C]107[/C][C]5550[/C][C]5467.15919836027[/C][C]82.8408016397279[/C][/ROW]
[ROW][C]108[/C][C]5350[/C][C]5173.79393159471[/C][C]176.206068405292[/C][/ROW]
[ROW][C]109[/C][C]5500[/C][C]5386.02677098448[/C][C]113.973229015519[/C][/ROW]
[ROW][C]110[/C][C]5750[/C][C]5504.01470979494[/C][C]245.98529020506[/C][/ROW]
[ROW][C]111[/C][C]5750[/C][C]5551.47072188064[/C][C]198.529278119362[/C][/ROW]
[ROW][C]112[/C][C]5700[/C][C]5734.75522609674[/C][C]-34.7552260967359[/C][/ROW]
[ROW][C]113[/C][C]5800[/C][C]5733.042380232[/C][C]66.9576197680017[/C][/ROW]
[ROW][C]114[/C][C]5800[/C][C]5837.67356424317[/C][C]-37.6735642431677[/C][/ROW]
[ROW][C]115[/C][C]4600[/C][C]5321.72583016456[/C][C]-721.725830164562[/C][/ROW]
[ROW][C]116[/C][C]3150[/C][C]3065.53166155975[/C][C]84.4683384402497[/C][/ROW]
[ROW][C]117[/C][C]5500[/C][C]5312.92915443143[/C][C]187.070845568574[/C][/ROW]
[ROW][C]118[/C][C]5750[/C][C]5632.03537288728[/C][C]117.964627112719[/C][/ROW]
[ROW][C]119[/C][C]5950[/C][C]5765.18347956402[/C][C]184.816520435981[/C][/ROW]
[ROW][C]120[/C][C]5600[/C][C]5535.5810402544[/C][C]64.4189597455952[/C][/ROW]
[ROW][C]121[/C][C]6100[/C][C]5680.08378955107[/C][C]419.916210448925[/C][/ROW]
[ROW][C]122[/C][C]6250[/C][C]5987.4730661172[/C][C]262.526933882796[/C][/ROW]
[ROW][C]123[/C][C]6150[/C][C]6046.63810974947[/C][C]103.361890250534[/C][/ROW]
[ROW][C]124[/C][C]6050[/C][C]6172.84364899954[/C][C]-122.843648999539[/C][/ROW]
[ROW][C]125[/C][C]6300[/C][C]6118.22675940604[/C][C]181.77324059396[/C][/ROW]
[ROW][C]126[/C][C]5950[/C][C]6294.784239492[/C][C]-344.784239491999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301297&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301297&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
1343504374.45245726496-24.4524572649598
1444004403.1745023124-3.17450231239945
1543004292.874038339427.12596166057847
1643504353.49648294638-3.49648294638155
1743504365.92205501836-15.9220550183636
1844004414.43578838981-14.435788389811
1938503907.5840103108-57.5840103108003
2023002055.37174792048244.628252079522
2143004397.56346037862-97.5634603786193
2243504537.75377127292-187.753771272924
2343504478.4398253772-128.439825377198
2442004051.13328245424148.866717545761
2541504242.33179538318-92.3317953831793
2644504228.9768884347221.0231115653
2743004256.405929762543.5940702374983
2843504339.5423962835210.4576037164779
2943004360.68317422584-60.6831742258391
3043504381.7668553015-31.7668553015001
3139003864.2962241159435.703775884057
3222502069.57993649142180.420063508576
3343004372.42191589855-72.4219158985534
3444504528.18237812197-78.1823781219673
3544004536.50230448275-136.502304482752
3642504104.57355264654145.426447353464
3742504293.98167685176-43.981676851763
3843004310.73605210668-10.7360521066839
3944504195.80260644735254.197393552648
4039004408.64851073823-508.648510738226
4143504110.36014235468239.639857645317
4245004315.82309355385184.176906446145
4338003931.33596909544-131.335969095436
4424502034.08180996583415.918190034175
4544004482.04979949224-82.0497994922353
4645004632.38274789275-132.38274789275
4745004607.79663951671-107.796639516714
4844004193.93156198467206.068438015326
4944504421.1344742933728.8655257066312
5046004483.32152929289116.678470707115
5147004447.58047560415252.419524395848
5247004660.2767678962839.7232321037209
5329504700.76488962147-1750.76488962147
5437503682.0182660043667.9817339956417
5540503224.06775589214825.932244107858
5625501914.44932546234635.550674537656
5746004497.49223536159102.507764638412
5850004761.72129616409238.278703835915
5951004966.04505499037133.954945009629
6049004702.39782740933197.602172590667
6149504926.1403814527723.8596185472297
6250004986.9823293110113.0176706889906
6349504889.1082497847660.8917502152399
6451004985.3366629661114.6633370339
6552505073.14450397894176.855496021059
6652005243.24129313834-43.2412931383442
6743004721.83952184699-421.839521846992
6826502648.360885383591.6391146164051
6949504843.28186310191106.718136898091
7052005111.2752061246488.7247938753571
7153505224.64222863377125.357771366227
7251504956.58458750329193.415412496706
7353505178.61702166398171.382978336022
7455505331.20441065761218.795589342389
7554005361.2531841991438.7468158008624
7654505445.391091376294.60890862370888
7754505466.9068703709-16.9068703708954
7852005518.92648376244-318.926483762441
7944004828.59839310677-428.598393106771
8026502751.330941314-101.330941313998
8151004883.17724564915216.822754350846
8252005219.16293762176-19.1629376217643
8353005266.4396234572133.5603765427923
8449004941.99329641218-41.9932964121763
8552005018.98309812562181.016901874381
8653005177.03018724988122.969812750122
8752505147.58716211212102.412837887881
8851505270.30357592494-120.303575924944
8950505214.34524258671-164.345242586714
9049005174.76886333833-274.76886333833
9141504510.59246826826-360.59246826826
9228002474.25528762379325.744712376215
9351004868.37629809286231.623701907144
9452505213.4830434088936.5169565911092
9552005295.09395344972-95.0939534497174
9650004891.52837279942108.471627200576
9751505061.1036434731388.8963565268677
9852505162.5814494471487.4185505528558
9952505111.2394259862138.760574013796
10053505256.2819559015393.7180440984666
10154505332.18005331334117.819946686659
10253005466.85992897994-166.85992897994
10343004870.13816232786-570.138162327862
10430002705.89309914412294.106900855877
10553005081.29959046324218.700409536763
10654005419.1593314046-19.1593314045958
10755505467.1591983602782.8408016397279
10853505173.79393159471176.206068405292
10955005386.02677098448113.973229015519
11057505504.01470979494245.98529020506
11157505551.47072188064198.529278119362
11257005734.75522609674-34.7552260967359
11358005733.04238023266.9576197680017
11458005837.67356424317-37.6735642431677
11546005321.72583016456-721.725830164562
11631503065.5316615597584.4683384402497
11755005312.92915443143187.070845568574
11857505632.03537288728117.964627112719
11959505765.18347956402184.816520435981
12056005535.581040254464.4189597455952
12161005680.08378955107419.916210448925
12262505987.4730661172262.526933882796
12361506046.63810974947103.361890250534
12460506172.84364899954-122.843648999539
12563006118.22675940604181.77324059396
12659506294.784239492-344.784239491999







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1275591.052150868755062.52108502456119.583216713
1283780.306006861033159.52612095164401.08589277047
1295977.893196186655276.419922937346679.36646943596
1306183.81371884565409.579590597076958.04784709413
1316245.984241504555404.859398025957087.10908498315
1325903.988097496835000.536691619516807.43950337416
1336009.908620155785047.806263064086972.01097724749
1346059.579142814735041.864718568827077.29356706065
1355957.166332140354886.404130269997027.9285340107
1366019.33685479934897.726309551187140.94740004742
1376039.840710791584869.293678471667210.3877431115
1386104.094566783874886.291524120557321.89760944719

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 5591.05215086875 & 5062.5210850245 & 6119.583216713 \tabularnewline
128 & 3780.30600686103 & 3159.5261209516 & 4401.08589277047 \tabularnewline
129 & 5977.89319618665 & 5276.41992293734 & 6679.36646943596 \tabularnewline
130 & 6183.8137188456 & 5409.57959059707 & 6958.04784709413 \tabularnewline
131 & 6245.98424150455 & 5404.85939802595 & 7087.10908498315 \tabularnewline
132 & 5903.98809749683 & 5000.53669161951 & 6807.43950337416 \tabularnewline
133 & 6009.90862015578 & 5047.80626306408 & 6972.01097724749 \tabularnewline
134 & 6059.57914281473 & 5041.86471856882 & 7077.29356706065 \tabularnewline
135 & 5957.16633214035 & 4886.40413026999 & 7027.9285340107 \tabularnewline
136 & 6019.3368547993 & 4897.72630955118 & 7140.94740004742 \tabularnewline
137 & 6039.84071079158 & 4869.29367847166 & 7210.3877431115 \tabularnewline
138 & 6104.09456678387 & 4886.29152412055 & 7321.89760944719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301297&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]5591.05215086875[/C][C]5062.5210850245[/C][C]6119.583216713[/C][/ROW]
[ROW][C]128[/C][C]3780.30600686103[/C][C]3159.5261209516[/C][C]4401.08589277047[/C][/ROW]
[ROW][C]129[/C][C]5977.89319618665[/C][C]5276.41992293734[/C][C]6679.36646943596[/C][/ROW]
[ROW][C]130[/C][C]6183.8137188456[/C][C]5409.57959059707[/C][C]6958.04784709413[/C][/ROW]
[ROW][C]131[/C][C]6245.98424150455[/C][C]5404.85939802595[/C][C]7087.10908498315[/C][/ROW]
[ROW][C]132[/C][C]5903.98809749683[/C][C]5000.53669161951[/C][C]6807.43950337416[/C][/ROW]
[ROW][C]133[/C][C]6009.90862015578[/C][C]5047.80626306408[/C][C]6972.01097724749[/C][/ROW]
[ROW][C]134[/C][C]6059.57914281473[/C][C]5041.86471856882[/C][C]7077.29356706065[/C][/ROW]
[ROW][C]135[/C][C]5957.16633214035[/C][C]4886.40413026999[/C][C]7027.9285340107[/C][/ROW]
[ROW][C]136[/C][C]6019.3368547993[/C][C]4897.72630955118[/C][C]7140.94740004742[/C][/ROW]
[ROW][C]137[/C][C]6039.84071079158[/C][C]4869.29367847166[/C][C]7210.3877431115[/C][/ROW]
[ROW][C]138[/C][C]6104.09456678387[/C][C]4886.29152412055[/C][C]7321.89760944719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301297&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301297&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
1275591.052150868755062.52108502456119.583216713
1283780.306006861033159.52612095164401.08589277047
1295977.893196186655276.419922937346679.36646943596
1306183.81371884565409.579590597076958.04784709413
1316245.984241504555404.859398025957087.10908498315
1325903.988097496835000.536691619516807.43950337416
1336009.908620155785047.806263064086972.01097724749
1346059.579142814735041.864718568827077.29356706065
1355957.166332140354886.404130269997027.9285340107
1366019.33685479934897.726309551187140.94740004742
1376039.840710791584869.293678471667210.3877431115
1386104.094566783874886.291524120557321.89760944719



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 18 ;
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')