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 computationFri, 16 Dec 2016 15:58:25 +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/t1481900311msm8imosin4gfab.htm/, Retrieved Thu, 02 May 2024 23:27:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300336, Retrieved Thu, 02 May 2024 23:27:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-16 14:58:25] [1a4fa2544711480e714211476e711237] [Current]
Feedback Forum

Post a new message
Dataseries X:
1100
680
860
440
1480
1620
1240
1440
1540
860
1180
1180
1480
940
1300
860
1220
2180
940
920
2060
1160
980
1020
740
720
1340
1140
1200
1900
1020
2140
2020
1340
1400
2320
1280
1160
2120
1540
2400
1420
1480
3380
1880
2200
1980
1340
1960
1340
3300
1780
2040
4460
800
1420
1960
1940
1880
940
1880
720
1660
4260
2540
2320
2860
5880
3140
4440
3600
2920
2260
3740
3380
4560
3320
4760
4000
4840
6160
3440
3280
2000
3600
4320
3480
5620
4200
8540
3800
5380
5140
2720
3120
3440
5020
5800
2260
5800
5660
4880
3440
5900
5960
5520
5920
3840




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=300336&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=300336&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300336&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
alpha0.289888508389799
beta0.114439504399955
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.289888508389799 \tabularnewline
beta & 0.114439504399955 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300336&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]0.289888508389799[/C][/ROW]
[ROW][C]beta[/C][C]0.114439504399955[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300336&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300336&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
alpha0.289888508389799
beta0.114439504399955
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3860260600
444033.8379233727017406.162076627298
51480-235.041235811511715.04123581151
61620-67.59539413995371687.59539413995
71240147.8796796775811092.12032032242
81440226.9641335297691213.03586647023
91540381.3427122968271158.65728770317
10860558.39567069122301.60432930878
111180497.004457674087682.995542325913
121180568.832344838505611.167655161495
131480640.113454849628839.886545150372
14940805.560524564263134.439475435737
151300770.966584384892529.033415615108
16860868.311416332082-8.31141633208244
171220809.610427734754410.389572265246
182180885.900593990051294.09940600995
199401261.29944178067-321.299441780672
209201157.75371542899-237.753715428989
2120601070.53952754675989.460472453253
2211601371.90568166053-211.905681660533
239801317.97968649759-337.979686497589
2410201216.29391235579-196.293912355791
257401149.16922482925-409.169224829248
267201006.76036534666-286.760365346658
271340890.323239254839449.676760745161
2811401002.28866355835137.711336441648
2912001028.38742823311171.612571766892
3019001070.00696655833829.993033441665
3110201330.01820246002-310.018202460022
3221401249.26852163573890.731478364267
3320201546.15212184431473.84787815569
3413401737.9057169078-397.905716907796
3514001663.74756092984-263.747560929836
3623201619.73056719729700.269432802707
3712801878.40224825391-598.402248253908
3811601740.75211939255-580.752119392554
3921201588.95228433238531.04771566762
4015401777.06779226851-237.067792268509
4124001734.65078910614665.349210893856
4214201975.90686356064-555.906863560644
4314801844.69279434208-364.692794342082
4433801756.810913397671623.18908660233
4518802299.04195227264-419.041952272642
4622002235.35209160691-35.3520916069101
4719802281.7167173983-301.716717398302
4813402240.85593838189-900.855938381889
4919601996.42596127182-36.4259612718167
5013402001.37588059706-661.375880597057
5133001803.219055395841496.78094460416
5217802280.34234778239-500.342347782395
5320402161.92384196877-121.923841968773
5444602149.159725809962310.84027419004
558002918.28739699496-2118.28739699496
5614202333.18831106783-913.188311067827
5719602067.13885588712-107.138855887117
5819402031.19957585138-91.199575851382
5918801996.85539161351-116.855391613514
609401951.19723897621-1011.19723897621
6118801612.73349997212267.266500027882
627201653.74819251688-933.748192516883
6316601315.62571370853344.374286291474
6442601359.440766503382900.55923349662
6525402240.4896351849299.510364815095
6623202377.46049274576-57.4604927457635
6728602409.04336642007450.956633579929
6858802602.970872268253277.02912773175
6931403724.85876717843-584.85876717843
7044403707.82722814022732.172771859783
7136004096.87760748362-496.877607483615
7229204113.15664143392-1193.15664143392
7322603888.00977448011-1628.00977448011
7437403482.79525006083257.204749939174
7533803632.61544182593-252.615441825932
7645603626.26417785471933.735822145295
7733203994.79891541621-674.798915416205
7847603874.65166750184885.348332498164
7940004236.14434102874-236.144341028737
8048404264.69515924031575.304840759692
8161604547.561334302591612.43866569741
8234405184.57285141535-1744.57285141535
8332804790.54963104114-1510.54963104114
8420004414.25502628703-2414.25502628703
8536003695.8944329449-95.8944329448973
8643203646.41866513728673.581334862719
8734803842.35093674628-362.350936746283
8856203725.957464727631894.04253527237
8942004326.50081830395-126.500818303949
9085404337.115246628354202.88475337165
9138005742.19822976156-1942.19822976156
9253805301.460434747178.5395652529041
9351405449.11683127422-309.116831274218
9427205474.14123595769-2754.14123595769
9531204699.01336135548-1579.01336135548
9634404212.15826330172-772.158263301721
9750203933.585069509741086.41493049026
9858004229.832372986031570.16762701397
9922604718.40385971581-2458.40385971581
10058003957.581963497321842.41803650268
10156604504.640572158391155.35942784161
10248804890.85748479038-10.8574847903792
10334404938.64132238991-1498.64132238991
10459004505.416750372561394.58324962744
10559604957.169611044361002.83038895564
10655205328.6264138066191.373586193397
10759205471.19997517339448.800024826613
10838405703.28730779671-1863.28730779671

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 860 & 260 & 600 \tabularnewline
4 & 440 & 33.8379233727017 & 406.162076627298 \tabularnewline
5 & 1480 & -235.04123581151 & 1715.04123581151 \tabularnewline
6 & 1620 & -67.5953941399537 & 1687.59539413995 \tabularnewline
7 & 1240 & 147.879679677581 & 1092.12032032242 \tabularnewline
8 & 1440 & 226.964133529769 & 1213.03586647023 \tabularnewline
9 & 1540 & 381.342712296827 & 1158.65728770317 \tabularnewline
10 & 860 & 558.39567069122 & 301.60432930878 \tabularnewline
11 & 1180 & 497.004457674087 & 682.995542325913 \tabularnewline
12 & 1180 & 568.832344838505 & 611.167655161495 \tabularnewline
13 & 1480 & 640.113454849628 & 839.886545150372 \tabularnewline
14 & 940 & 805.560524564263 & 134.439475435737 \tabularnewline
15 & 1300 & 770.966584384892 & 529.033415615108 \tabularnewline
16 & 860 & 868.311416332082 & -8.31141633208244 \tabularnewline
17 & 1220 & 809.610427734754 & 410.389572265246 \tabularnewline
18 & 2180 & 885.90059399005 & 1294.09940600995 \tabularnewline
19 & 940 & 1261.29944178067 & -321.299441780672 \tabularnewline
20 & 920 & 1157.75371542899 & -237.753715428989 \tabularnewline
21 & 2060 & 1070.53952754675 & 989.460472453253 \tabularnewline
22 & 1160 & 1371.90568166053 & -211.905681660533 \tabularnewline
23 & 980 & 1317.97968649759 & -337.979686497589 \tabularnewline
24 & 1020 & 1216.29391235579 & -196.293912355791 \tabularnewline
25 & 740 & 1149.16922482925 & -409.169224829248 \tabularnewline
26 & 720 & 1006.76036534666 & -286.760365346658 \tabularnewline
27 & 1340 & 890.323239254839 & 449.676760745161 \tabularnewline
28 & 1140 & 1002.28866355835 & 137.711336441648 \tabularnewline
29 & 1200 & 1028.38742823311 & 171.612571766892 \tabularnewline
30 & 1900 & 1070.00696655833 & 829.993033441665 \tabularnewline
31 & 1020 & 1330.01820246002 & -310.018202460022 \tabularnewline
32 & 2140 & 1249.26852163573 & 890.731478364267 \tabularnewline
33 & 2020 & 1546.15212184431 & 473.84787815569 \tabularnewline
34 & 1340 & 1737.9057169078 & -397.905716907796 \tabularnewline
35 & 1400 & 1663.74756092984 & -263.747560929836 \tabularnewline
36 & 2320 & 1619.73056719729 & 700.269432802707 \tabularnewline
37 & 1280 & 1878.40224825391 & -598.402248253908 \tabularnewline
38 & 1160 & 1740.75211939255 & -580.752119392554 \tabularnewline
39 & 2120 & 1588.95228433238 & 531.04771566762 \tabularnewline
40 & 1540 & 1777.06779226851 & -237.067792268509 \tabularnewline
41 & 2400 & 1734.65078910614 & 665.349210893856 \tabularnewline
42 & 1420 & 1975.90686356064 & -555.906863560644 \tabularnewline
43 & 1480 & 1844.69279434208 & -364.692794342082 \tabularnewline
44 & 3380 & 1756.81091339767 & 1623.18908660233 \tabularnewline
45 & 1880 & 2299.04195227264 & -419.041952272642 \tabularnewline
46 & 2200 & 2235.35209160691 & -35.3520916069101 \tabularnewline
47 & 1980 & 2281.7167173983 & -301.716717398302 \tabularnewline
48 & 1340 & 2240.85593838189 & -900.855938381889 \tabularnewline
49 & 1960 & 1996.42596127182 & -36.4259612718167 \tabularnewline
50 & 1340 & 2001.37588059706 & -661.375880597057 \tabularnewline
51 & 3300 & 1803.21905539584 & 1496.78094460416 \tabularnewline
52 & 1780 & 2280.34234778239 & -500.342347782395 \tabularnewline
53 & 2040 & 2161.92384196877 & -121.923841968773 \tabularnewline
54 & 4460 & 2149.15972580996 & 2310.84027419004 \tabularnewline
55 & 800 & 2918.28739699496 & -2118.28739699496 \tabularnewline
56 & 1420 & 2333.18831106783 & -913.188311067827 \tabularnewline
57 & 1960 & 2067.13885588712 & -107.138855887117 \tabularnewline
58 & 1940 & 2031.19957585138 & -91.199575851382 \tabularnewline
59 & 1880 & 1996.85539161351 & -116.855391613514 \tabularnewline
60 & 940 & 1951.19723897621 & -1011.19723897621 \tabularnewline
61 & 1880 & 1612.73349997212 & 267.266500027882 \tabularnewline
62 & 720 & 1653.74819251688 & -933.748192516883 \tabularnewline
63 & 1660 & 1315.62571370853 & 344.374286291474 \tabularnewline
64 & 4260 & 1359.44076650338 & 2900.55923349662 \tabularnewline
65 & 2540 & 2240.4896351849 & 299.510364815095 \tabularnewline
66 & 2320 & 2377.46049274576 & -57.4604927457635 \tabularnewline
67 & 2860 & 2409.04336642007 & 450.956633579929 \tabularnewline
68 & 5880 & 2602.97087226825 & 3277.02912773175 \tabularnewline
69 & 3140 & 3724.85876717843 & -584.85876717843 \tabularnewline
70 & 4440 & 3707.82722814022 & 732.172771859783 \tabularnewline
71 & 3600 & 4096.87760748362 & -496.877607483615 \tabularnewline
72 & 2920 & 4113.15664143392 & -1193.15664143392 \tabularnewline
73 & 2260 & 3888.00977448011 & -1628.00977448011 \tabularnewline
74 & 3740 & 3482.79525006083 & 257.204749939174 \tabularnewline
75 & 3380 & 3632.61544182593 & -252.615441825932 \tabularnewline
76 & 4560 & 3626.26417785471 & 933.735822145295 \tabularnewline
77 & 3320 & 3994.79891541621 & -674.798915416205 \tabularnewline
78 & 4760 & 3874.65166750184 & 885.348332498164 \tabularnewline
79 & 4000 & 4236.14434102874 & -236.144341028737 \tabularnewline
80 & 4840 & 4264.69515924031 & 575.304840759692 \tabularnewline
81 & 6160 & 4547.56133430259 & 1612.43866569741 \tabularnewline
82 & 3440 & 5184.57285141535 & -1744.57285141535 \tabularnewline
83 & 3280 & 4790.54963104114 & -1510.54963104114 \tabularnewline
84 & 2000 & 4414.25502628703 & -2414.25502628703 \tabularnewline
85 & 3600 & 3695.8944329449 & -95.8944329448973 \tabularnewline
86 & 4320 & 3646.41866513728 & 673.581334862719 \tabularnewline
87 & 3480 & 3842.35093674628 & -362.350936746283 \tabularnewline
88 & 5620 & 3725.95746472763 & 1894.04253527237 \tabularnewline
89 & 4200 & 4326.50081830395 & -126.500818303949 \tabularnewline
90 & 8540 & 4337.11524662835 & 4202.88475337165 \tabularnewline
91 & 3800 & 5742.19822976156 & -1942.19822976156 \tabularnewline
92 & 5380 & 5301.4604347471 & 78.5395652529041 \tabularnewline
93 & 5140 & 5449.11683127422 & -309.116831274218 \tabularnewline
94 & 2720 & 5474.14123595769 & -2754.14123595769 \tabularnewline
95 & 3120 & 4699.01336135548 & -1579.01336135548 \tabularnewline
96 & 3440 & 4212.15826330172 & -772.158263301721 \tabularnewline
97 & 5020 & 3933.58506950974 & 1086.41493049026 \tabularnewline
98 & 5800 & 4229.83237298603 & 1570.16762701397 \tabularnewline
99 & 2260 & 4718.40385971581 & -2458.40385971581 \tabularnewline
100 & 5800 & 3957.58196349732 & 1842.41803650268 \tabularnewline
101 & 5660 & 4504.64057215839 & 1155.35942784161 \tabularnewline
102 & 4880 & 4890.85748479038 & -10.8574847903792 \tabularnewline
103 & 3440 & 4938.64132238991 & -1498.64132238991 \tabularnewline
104 & 5900 & 4505.41675037256 & 1394.58324962744 \tabularnewline
105 & 5960 & 4957.16961104436 & 1002.83038895564 \tabularnewline
106 & 5520 & 5328.6264138066 & 191.373586193397 \tabularnewline
107 & 5920 & 5471.19997517339 & 448.800024826613 \tabularnewline
108 & 3840 & 5703.28730779671 & -1863.28730779671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300336&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]860[/C][C]260[/C][C]600[/C][/ROW]
[ROW][C]4[/C][C]440[/C][C]33.8379233727017[/C][C]406.162076627298[/C][/ROW]
[ROW][C]5[/C][C]1480[/C][C]-235.04123581151[/C][C]1715.04123581151[/C][/ROW]
[ROW][C]6[/C][C]1620[/C][C]-67.5953941399537[/C][C]1687.59539413995[/C][/ROW]
[ROW][C]7[/C][C]1240[/C][C]147.879679677581[/C][C]1092.12032032242[/C][/ROW]
[ROW][C]8[/C][C]1440[/C][C]226.964133529769[/C][C]1213.03586647023[/C][/ROW]
[ROW][C]9[/C][C]1540[/C][C]381.342712296827[/C][C]1158.65728770317[/C][/ROW]
[ROW][C]10[/C][C]860[/C][C]558.39567069122[/C][C]301.60432930878[/C][/ROW]
[ROW][C]11[/C][C]1180[/C][C]497.004457674087[/C][C]682.995542325913[/C][/ROW]
[ROW][C]12[/C][C]1180[/C][C]568.832344838505[/C][C]611.167655161495[/C][/ROW]
[ROW][C]13[/C][C]1480[/C][C]640.113454849628[/C][C]839.886545150372[/C][/ROW]
[ROW][C]14[/C][C]940[/C][C]805.560524564263[/C][C]134.439475435737[/C][/ROW]
[ROW][C]15[/C][C]1300[/C][C]770.966584384892[/C][C]529.033415615108[/C][/ROW]
[ROW][C]16[/C][C]860[/C][C]868.311416332082[/C][C]-8.31141633208244[/C][/ROW]
[ROW][C]17[/C][C]1220[/C][C]809.610427734754[/C][C]410.389572265246[/C][/ROW]
[ROW][C]18[/C][C]2180[/C][C]885.90059399005[/C][C]1294.09940600995[/C][/ROW]
[ROW][C]19[/C][C]940[/C][C]1261.29944178067[/C][C]-321.299441780672[/C][/ROW]
[ROW][C]20[/C][C]920[/C][C]1157.75371542899[/C][C]-237.753715428989[/C][/ROW]
[ROW][C]21[/C][C]2060[/C][C]1070.53952754675[/C][C]989.460472453253[/C][/ROW]
[ROW][C]22[/C][C]1160[/C][C]1371.90568166053[/C][C]-211.905681660533[/C][/ROW]
[ROW][C]23[/C][C]980[/C][C]1317.97968649759[/C][C]-337.979686497589[/C][/ROW]
[ROW][C]24[/C][C]1020[/C][C]1216.29391235579[/C][C]-196.293912355791[/C][/ROW]
[ROW][C]25[/C][C]740[/C][C]1149.16922482925[/C][C]-409.169224829248[/C][/ROW]
[ROW][C]26[/C][C]720[/C][C]1006.76036534666[/C][C]-286.760365346658[/C][/ROW]
[ROW][C]27[/C][C]1340[/C][C]890.323239254839[/C][C]449.676760745161[/C][/ROW]
[ROW][C]28[/C][C]1140[/C][C]1002.28866355835[/C][C]137.711336441648[/C][/ROW]
[ROW][C]29[/C][C]1200[/C][C]1028.38742823311[/C][C]171.612571766892[/C][/ROW]
[ROW][C]30[/C][C]1900[/C][C]1070.00696655833[/C][C]829.993033441665[/C][/ROW]
[ROW][C]31[/C][C]1020[/C][C]1330.01820246002[/C][C]-310.018202460022[/C][/ROW]
[ROW][C]32[/C][C]2140[/C][C]1249.26852163573[/C][C]890.731478364267[/C][/ROW]
[ROW][C]33[/C][C]2020[/C][C]1546.15212184431[/C][C]473.84787815569[/C][/ROW]
[ROW][C]34[/C][C]1340[/C][C]1737.9057169078[/C][C]-397.905716907796[/C][/ROW]
[ROW][C]35[/C][C]1400[/C][C]1663.74756092984[/C][C]-263.747560929836[/C][/ROW]
[ROW][C]36[/C][C]2320[/C][C]1619.73056719729[/C][C]700.269432802707[/C][/ROW]
[ROW][C]37[/C][C]1280[/C][C]1878.40224825391[/C][C]-598.402248253908[/C][/ROW]
[ROW][C]38[/C][C]1160[/C][C]1740.75211939255[/C][C]-580.752119392554[/C][/ROW]
[ROW][C]39[/C][C]2120[/C][C]1588.95228433238[/C][C]531.04771566762[/C][/ROW]
[ROW][C]40[/C][C]1540[/C][C]1777.06779226851[/C][C]-237.067792268509[/C][/ROW]
[ROW][C]41[/C][C]2400[/C][C]1734.65078910614[/C][C]665.349210893856[/C][/ROW]
[ROW][C]42[/C][C]1420[/C][C]1975.90686356064[/C][C]-555.906863560644[/C][/ROW]
[ROW][C]43[/C][C]1480[/C][C]1844.69279434208[/C][C]-364.692794342082[/C][/ROW]
[ROW][C]44[/C][C]3380[/C][C]1756.81091339767[/C][C]1623.18908660233[/C][/ROW]
[ROW][C]45[/C][C]1880[/C][C]2299.04195227264[/C][C]-419.041952272642[/C][/ROW]
[ROW][C]46[/C][C]2200[/C][C]2235.35209160691[/C][C]-35.3520916069101[/C][/ROW]
[ROW][C]47[/C][C]1980[/C][C]2281.7167173983[/C][C]-301.716717398302[/C][/ROW]
[ROW][C]48[/C][C]1340[/C][C]2240.85593838189[/C][C]-900.855938381889[/C][/ROW]
[ROW][C]49[/C][C]1960[/C][C]1996.42596127182[/C][C]-36.4259612718167[/C][/ROW]
[ROW][C]50[/C][C]1340[/C][C]2001.37588059706[/C][C]-661.375880597057[/C][/ROW]
[ROW][C]51[/C][C]3300[/C][C]1803.21905539584[/C][C]1496.78094460416[/C][/ROW]
[ROW][C]52[/C][C]1780[/C][C]2280.34234778239[/C][C]-500.342347782395[/C][/ROW]
[ROW][C]53[/C][C]2040[/C][C]2161.92384196877[/C][C]-121.923841968773[/C][/ROW]
[ROW][C]54[/C][C]4460[/C][C]2149.15972580996[/C][C]2310.84027419004[/C][/ROW]
[ROW][C]55[/C][C]800[/C][C]2918.28739699496[/C][C]-2118.28739699496[/C][/ROW]
[ROW][C]56[/C][C]1420[/C][C]2333.18831106783[/C][C]-913.188311067827[/C][/ROW]
[ROW][C]57[/C][C]1960[/C][C]2067.13885588712[/C][C]-107.138855887117[/C][/ROW]
[ROW][C]58[/C][C]1940[/C][C]2031.19957585138[/C][C]-91.199575851382[/C][/ROW]
[ROW][C]59[/C][C]1880[/C][C]1996.85539161351[/C][C]-116.855391613514[/C][/ROW]
[ROW][C]60[/C][C]940[/C][C]1951.19723897621[/C][C]-1011.19723897621[/C][/ROW]
[ROW][C]61[/C][C]1880[/C][C]1612.73349997212[/C][C]267.266500027882[/C][/ROW]
[ROW][C]62[/C][C]720[/C][C]1653.74819251688[/C][C]-933.748192516883[/C][/ROW]
[ROW][C]63[/C][C]1660[/C][C]1315.62571370853[/C][C]344.374286291474[/C][/ROW]
[ROW][C]64[/C][C]4260[/C][C]1359.44076650338[/C][C]2900.55923349662[/C][/ROW]
[ROW][C]65[/C][C]2540[/C][C]2240.4896351849[/C][C]299.510364815095[/C][/ROW]
[ROW][C]66[/C][C]2320[/C][C]2377.46049274576[/C][C]-57.4604927457635[/C][/ROW]
[ROW][C]67[/C][C]2860[/C][C]2409.04336642007[/C][C]450.956633579929[/C][/ROW]
[ROW][C]68[/C][C]5880[/C][C]2602.97087226825[/C][C]3277.02912773175[/C][/ROW]
[ROW][C]69[/C][C]3140[/C][C]3724.85876717843[/C][C]-584.85876717843[/C][/ROW]
[ROW][C]70[/C][C]4440[/C][C]3707.82722814022[/C][C]732.172771859783[/C][/ROW]
[ROW][C]71[/C][C]3600[/C][C]4096.87760748362[/C][C]-496.877607483615[/C][/ROW]
[ROW][C]72[/C][C]2920[/C][C]4113.15664143392[/C][C]-1193.15664143392[/C][/ROW]
[ROW][C]73[/C][C]2260[/C][C]3888.00977448011[/C][C]-1628.00977448011[/C][/ROW]
[ROW][C]74[/C][C]3740[/C][C]3482.79525006083[/C][C]257.204749939174[/C][/ROW]
[ROW][C]75[/C][C]3380[/C][C]3632.61544182593[/C][C]-252.615441825932[/C][/ROW]
[ROW][C]76[/C][C]4560[/C][C]3626.26417785471[/C][C]933.735822145295[/C][/ROW]
[ROW][C]77[/C][C]3320[/C][C]3994.79891541621[/C][C]-674.798915416205[/C][/ROW]
[ROW][C]78[/C][C]4760[/C][C]3874.65166750184[/C][C]885.348332498164[/C][/ROW]
[ROW][C]79[/C][C]4000[/C][C]4236.14434102874[/C][C]-236.144341028737[/C][/ROW]
[ROW][C]80[/C][C]4840[/C][C]4264.69515924031[/C][C]575.304840759692[/C][/ROW]
[ROW][C]81[/C][C]6160[/C][C]4547.56133430259[/C][C]1612.43866569741[/C][/ROW]
[ROW][C]82[/C][C]3440[/C][C]5184.57285141535[/C][C]-1744.57285141535[/C][/ROW]
[ROW][C]83[/C][C]3280[/C][C]4790.54963104114[/C][C]-1510.54963104114[/C][/ROW]
[ROW][C]84[/C][C]2000[/C][C]4414.25502628703[/C][C]-2414.25502628703[/C][/ROW]
[ROW][C]85[/C][C]3600[/C][C]3695.8944329449[/C][C]-95.8944329448973[/C][/ROW]
[ROW][C]86[/C][C]4320[/C][C]3646.41866513728[/C][C]673.581334862719[/C][/ROW]
[ROW][C]87[/C][C]3480[/C][C]3842.35093674628[/C][C]-362.350936746283[/C][/ROW]
[ROW][C]88[/C][C]5620[/C][C]3725.95746472763[/C][C]1894.04253527237[/C][/ROW]
[ROW][C]89[/C][C]4200[/C][C]4326.50081830395[/C][C]-126.500818303949[/C][/ROW]
[ROW][C]90[/C][C]8540[/C][C]4337.11524662835[/C][C]4202.88475337165[/C][/ROW]
[ROW][C]91[/C][C]3800[/C][C]5742.19822976156[/C][C]-1942.19822976156[/C][/ROW]
[ROW][C]92[/C][C]5380[/C][C]5301.4604347471[/C][C]78.5395652529041[/C][/ROW]
[ROW][C]93[/C][C]5140[/C][C]5449.11683127422[/C][C]-309.116831274218[/C][/ROW]
[ROW][C]94[/C][C]2720[/C][C]5474.14123595769[/C][C]-2754.14123595769[/C][/ROW]
[ROW][C]95[/C][C]3120[/C][C]4699.01336135548[/C][C]-1579.01336135548[/C][/ROW]
[ROW][C]96[/C][C]3440[/C][C]4212.15826330172[/C][C]-772.158263301721[/C][/ROW]
[ROW][C]97[/C][C]5020[/C][C]3933.58506950974[/C][C]1086.41493049026[/C][/ROW]
[ROW][C]98[/C][C]5800[/C][C]4229.83237298603[/C][C]1570.16762701397[/C][/ROW]
[ROW][C]99[/C][C]2260[/C][C]4718.40385971581[/C][C]-2458.40385971581[/C][/ROW]
[ROW][C]100[/C][C]5800[/C][C]3957.58196349732[/C][C]1842.41803650268[/C][/ROW]
[ROW][C]101[/C][C]5660[/C][C]4504.64057215839[/C][C]1155.35942784161[/C][/ROW]
[ROW][C]102[/C][C]4880[/C][C]4890.85748479038[/C][C]-10.8574847903792[/C][/ROW]
[ROW][C]103[/C][C]3440[/C][C]4938.64132238991[/C][C]-1498.64132238991[/C][/ROW]
[ROW][C]104[/C][C]5900[/C][C]4505.41675037256[/C][C]1394.58324962744[/C][/ROW]
[ROW][C]105[/C][C]5960[/C][C]4957.16961104436[/C][C]1002.83038895564[/C][/ROW]
[ROW][C]106[/C][C]5520[/C][C]5328.6264138066[/C][C]191.373586193397[/C][/ROW]
[ROW][C]107[/C][C]5920[/C][C]5471.19997517339[/C][C]448.800024826613[/C][/ROW]
[ROW][C]108[/C][C]3840[/C][C]5703.28730779671[/C][C]-1863.28730779671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300336&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300336&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
3860260600
444033.8379233727017406.162076627298
51480-235.041235811511715.04123581151
61620-67.59539413995371687.59539413995
71240147.8796796775811092.12032032242
81440226.9641335297691213.03586647023
91540381.3427122968271158.65728770317
10860558.39567069122301.60432930878
111180497.004457674087682.995542325913
121180568.832344838505611.167655161495
131480640.113454849628839.886545150372
14940805.560524564263134.439475435737
151300770.966584384892529.033415615108
16860868.311416332082-8.31141633208244
171220809.610427734754410.389572265246
182180885.900593990051294.09940600995
199401261.29944178067-321.299441780672
209201157.75371542899-237.753715428989
2120601070.53952754675989.460472453253
2211601371.90568166053-211.905681660533
239801317.97968649759-337.979686497589
2410201216.29391235579-196.293912355791
257401149.16922482925-409.169224829248
267201006.76036534666-286.760365346658
271340890.323239254839449.676760745161
2811401002.28866355835137.711336441648
2912001028.38742823311171.612571766892
3019001070.00696655833829.993033441665
3110201330.01820246002-310.018202460022
3221401249.26852163573890.731478364267
3320201546.15212184431473.84787815569
3413401737.9057169078-397.905716907796
3514001663.74756092984-263.747560929836
3623201619.73056719729700.269432802707
3712801878.40224825391-598.402248253908
3811601740.75211939255-580.752119392554
3921201588.95228433238531.04771566762
4015401777.06779226851-237.067792268509
4124001734.65078910614665.349210893856
4214201975.90686356064-555.906863560644
4314801844.69279434208-364.692794342082
4433801756.810913397671623.18908660233
4518802299.04195227264-419.041952272642
4622002235.35209160691-35.3520916069101
4719802281.7167173983-301.716717398302
4813402240.85593838189-900.855938381889
4919601996.42596127182-36.4259612718167
5013402001.37588059706-661.375880597057
5133001803.219055395841496.78094460416
5217802280.34234778239-500.342347782395
5320402161.92384196877-121.923841968773
5444602149.159725809962310.84027419004
558002918.28739699496-2118.28739699496
5614202333.18831106783-913.188311067827
5719602067.13885588712-107.138855887117
5819402031.19957585138-91.199575851382
5918801996.85539161351-116.855391613514
609401951.19723897621-1011.19723897621
6118801612.73349997212267.266500027882
627201653.74819251688-933.748192516883
6316601315.62571370853344.374286291474
6442601359.440766503382900.55923349662
6525402240.4896351849299.510364815095
6623202377.46049274576-57.4604927457635
6728602409.04336642007450.956633579929
6858802602.970872268253277.02912773175
6931403724.85876717843-584.85876717843
7044403707.82722814022732.172771859783
7136004096.87760748362-496.877607483615
7229204113.15664143392-1193.15664143392
7322603888.00977448011-1628.00977448011
7437403482.79525006083257.204749939174
7533803632.61544182593-252.615441825932
7645603626.26417785471933.735822145295
7733203994.79891541621-674.798915416205
7847603874.65166750184885.348332498164
7940004236.14434102874-236.144341028737
8048404264.69515924031575.304840759692
8161604547.561334302591612.43866569741
8234405184.57285141535-1744.57285141535
8332804790.54963104114-1510.54963104114
8420004414.25502628703-2414.25502628703
8536003695.8944329449-95.8944329448973
8643203646.41866513728673.581334862719
8734803842.35093674628-362.350936746283
8856203725.957464727631894.04253527237
8942004326.50081830395-126.500818303949
9085404337.115246628354202.88475337165
9138005742.19822976156-1942.19822976156
9253805301.460434747178.5395652529041
9351405449.11683127422-309.116831274218
9427205474.14123595769-2754.14123595769
9531204699.01336135548-1579.01336135548
9634404212.15826330172-772.158263301721
9750203933.585069509741086.41493049026
9858004229.832372986031570.16762701397
9922604718.40385971581-2458.40385971581
10058003957.581963497321842.41803650268
10156604504.640572158391155.35942784161
10248804890.85748479038-10.8574847903792
10334404938.64132238991-1498.64132238991
10459004505.416750372561394.58324962744
10559604957.169611044361002.83038895564
10655205328.6264138066191.373586193397
10759205471.19997517339448.800024826613
10838405703.28730779671-1863.28730779671







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1095203.313100007692950.170464023197456.4557359922
1105243.484470577512875.679360044547611.28958111049
1115283.655841147332783.50468943237783.80699286236
1125323.827211717152674.187560164717973.46686326958
1135363.998582286962548.473964821028179.52319975291
1145404.169952856782407.222193556448401.11771215713
1155444.34132342662251.330892899538637.35175395367
1165484.512693996422081.688512656068887.33687533677
1175524.684064566241899.141264367199150.22686476528
1185564.855435136051704.475337858579425.23553241353
1195605.026805705871498.40916677519711.64444463665
1205645.198176275691281.5922440266610008.8041085247

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 5203.31310000769 & 2950.17046402319 & 7456.4557359922 \tabularnewline
110 & 5243.48447057751 & 2875.67936004454 & 7611.28958111049 \tabularnewline
111 & 5283.65584114733 & 2783.5046894323 & 7783.80699286236 \tabularnewline
112 & 5323.82721171715 & 2674.18756016471 & 7973.46686326958 \tabularnewline
113 & 5363.99858228696 & 2548.47396482102 & 8179.52319975291 \tabularnewline
114 & 5404.16995285678 & 2407.22219355644 & 8401.11771215713 \tabularnewline
115 & 5444.3413234266 & 2251.33089289953 & 8637.35175395367 \tabularnewline
116 & 5484.51269399642 & 2081.68851265606 & 8887.33687533677 \tabularnewline
117 & 5524.68406456624 & 1899.14126436719 & 9150.22686476528 \tabularnewline
118 & 5564.85543513605 & 1704.47533785857 & 9425.23553241353 \tabularnewline
119 & 5605.02680570587 & 1498.4091667751 & 9711.64444463665 \tabularnewline
120 & 5645.19817627569 & 1281.59224402666 & 10008.8041085247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300336&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]109[/C][C]5203.31310000769[/C][C]2950.17046402319[/C][C]7456.4557359922[/C][/ROW]
[ROW][C]110[/C][C]5243.48447057751[/C][C]2875.67936004454[/C][C]7611.28958111049[/C][/ROW]
[ROW][C]111[/C][C]5283.65584114733[/C][C]2783.5046894323[/C][C]7783.80699286236[/C][/ROW]
[ROW][C]112[/C][C]5323.82721171715[/C][C]2674.18756016471[/C][C]7973.46686326958[/C][/ROW]
[ROW][C]113[/C][C]5363.99858228696[/C][C]2548.47396482102[/C][C]8179.52319975291[/C][/ROW]
[ROW][C]114[/C][C]5404.16995285678[/C][C]2407.22219355644[/C][C]8401.11771215713[/C][/ROW]
[ROW][C]115[/C][C]5444.3413234266[/C][C]2251.33089289953[/C][C]8637.35175395367[/C][/ROW]
[ROW][C]116[/C][C]5484.51269399642[/C][C]2081.68851265606[/C][C]8887.33687533677[/C][/ROW]
[ROW][C]117[/C][C]5524.68406456624[/C][C]1899.14126436719[/C][C]9150.22686476528[/C][/ROW]
[ROW][C]118[/C][C]5564.85543513605[/C][C]1704.47533785857[/C][C]9425.23553241353[/C][/ROW]
[ROW][C]119[/C][C]5605.02680570587[/C][C]1498.4091667751[/C][C]9711.64444463665[/C][/ROW]
[ROW][C]120[/C][C]5645.19817627569[/C][C]1281.59224402666[/C][C]10008.8041085247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300336&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300336&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
1095203.313100007692950.170464023197456.4557359922
1105243.484470577512875.679360044547611.28958111049
1115283.655841147332783.50468943237783.80699286236
1125323.827211717152674.187560164717973.46686326958
1135363.998582286962548.473964821028179.52319975291
1145404.169952856782407.222193556448401.11771215713
1155444.34132342662251.330892899538637.35175395367
1165484.512693996422081.688512656068887.33687533677
1175524.684064566241899.141264367199150.22686476528
1185564.855435136051704.475337858579425.23553241353
1195605.026805705871498.40916677519711.64444463665
1205645.198176275691281.5922440266610008.8041085247



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')