Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Aug 2017 16:06:39 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/15/t1502806053wkqa0vqcwdgp2i4.htm/, Retrieved Mon, 20 May 2024 02:21:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307287, Retrieved Mon, 20 May 2024 02:21:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-15 14:06:39] [f8975010d6e80ebfdd11eb899305ce74] [Current]
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Dataseries X:
5204472
5185089
5165433
5124756
5527158
5505864
5204472
5004090
5023473
5023473
5045040
5083806
5144139
5144139
5105373
5004090
5527158
5606874
5486481
5204472
5325138
5144139
5225766
5264805
5305482
5204472
5225766
5083806
5527158
5667207
5546814
5325138
5566197
5305482
5546814
5527158
5587491
5365815
5606874
5587491
5949216
5867589
5546814
5385198
5606874
5305482
5527158
5566197
5647824
5467098
5566197
5626530
5848206
5667207
5426148
5165433
5406765
4743375
5064423
5245149
5426148
5165433
5165433
5165433
5305482
5105373
4842747
4622982
4782414
4159974
4541355
4763031
4803708
4582032
4601415
4541355
4743375
4601415
4321590
4119297
4461366
3718533
4200924
4420689
4420689
4159974
3918915
3899532
4119297
3918915
3537807
3275181
3557190
2894073
3496857
3817632
3918915
3697239
3417141
3617523
3697239
3636906
3033849
2754024
2954133
2351349
2973789
3195465
3376191
3074799
2792790
2954133
3033849
2874417
2271633
2009007
2250066
1586949
2310399
2754024




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=307287&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=307287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307287&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
alpha0.405343002238553
beta0.064519551098525
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238553 \tabularnewline
beta & 0.064519551098525 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307287&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]0.405343002238553[/C][/ROW]
[ROW][C]beta[/C][C]0.064519551098525[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307287&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
alpha0.405343002238553
beta0.064519551098525
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1351441395143915.29166667223.708333332092
1451441395132625.4458171711513.5541828265
1551053735086627.9687638218745.0312361801
1650040904984856.4506692819233.5493307197
1755271585513176.081298413981.9187015994
1856068745593866.7880092713007.2119907346
1954864815292882.70091867193598.299081326
2052044725190976.9111619313495.0888380697
2153251385236174.1014183488963.8985816557
2251441395298227.17826804-154088.178268036
2352257665276795.49802474-51029.4980247375
2452648055303765.88121366-38960.8812136631
2553054825344558.92216222-39076.9221622199
2652044725326390.02173263-121918.021732631
2752257665229455.25690839-3689.25690838974
2850838065117141.96336809-33335.9633680936
2955271585617916.46981793-90758.469817929
3056672075649719.0275563917487.9724436067
3155468145452205.3730692394608.6269307695
3253251385194750.77995289130387.220047108
3355661975326940.06240538239256.937594618
3453054825304043.927550831438.07244917192
3555468145409668.87287465137145.127125349
3655271585527743.03981404-585.039814042859
3755874915592677.90982905-5186.90982904658
3853658155548525.81423762-182710.814237619
3956068745505206.5573221101667.4426779
4055874915428676.46803946158814.531960544
4159492165988923.58781337-39707.587813369
4258675896122856.32832934-255267.328329337
4355468145870577.8725939-323763.872593902
4453851985463807.71250979-78609.7125097914
4556068745569548.6950973537325.3049026513
4653054825311626.31166764-6144.31166764442
4755271585482924.6197150844233.3802849213
4855661975467053.2530607799143.7469392316
4956478245557901.9170248689922.082975137
5054670985437449.0589656129648.9410343915
5155661975645582.91697707-79385.9169770712
5256265305521179.07877681105350.921223186
5358482065931836.36756141-83630.3675614074
5456672075908766.35313604-241559.353136041
5554261485610656.02293923-184508.02293923
5651654335399100.42231465-233667.422314652
5754067655499861.80085345-93096.8008534545
5847433755148743.73155647-405368.731556466
5950644235163255.43942995-98832.4394299518
6052451495093383.41958012151765.58041988
6154261485172791.68546274253356.314537255
6251654335059731.56249564105701.43750436
6351654335212831.0516778-47398.0516778044
6451654335191061.51385363-25628.5138536338
6553054825412635.90277702-107153.902777025
6651053735261889.75455217-156516.754552169
6748427475010173.44301393-167426.44301393
6846229824754752.11098042-131770.110980419
6947824144961516.38027387-179102.380273874
7041599744368700.82224418-208726.82224418
7145413554629205.55010031-87850.5501003079
7247630314697093.6796794865937.3203205168
7348037084784167.9254573419540.0745426593
7445820324464457.35292053117574.647079472
7546014154507567.7296150593847.2703849506
7645413554535930.175528035424.82447197475
7747433754702358.0715922941016.9284077119
7846014154566938.9093150134476.0906849923
7943215904375768.5797695-54178.5797695043
8041192974180032.37550539-60735.3755053859
8144613664381878.9634787179487.0365212895
8237185333877462.557448-158929.557447997
8342009244232532.62776909-31608.6277690884
8444206894418640.378473832048.62152616587
8544206894454527.80625749-33838.8062574873
8641599744172381.89459403-12407.8945940277
8739189154146200.20437838-227285.20437838
8838995323980919.4873577-81387.4873577016
8941192974120160.01550918-863.015509176534
9039189153949616.59036672-30701.5903667249
9135378073663344.29552571-125537.295525711
9232751813416954.55022684-141773.550226843
9335571903649388.02443185-92198.0244318536
9428940732909165.08719207-15092.0871920711
9534968573377573.57058314119283.429416863
9638176323628127.71067806189504.289321941
9739189153706829.54611926212085.453880745
9836972393531714.17467413165524.825325869
9934171413449134.18622091-31993.1862209062
10036175233454136.41931959163386.580680406
10136972393751243.90823499-54004.9082349851
10236369063550791.3399582886114.6600417229
10330338493267905.29026747-234056.290267467
10427540242977465.39029635-223441.390296348
10529541333213732.25113268-259599.251132676
10623513492454584.45530405-103235.455304047
10729737892967945.280874895843.71912511205
10831954653212081.31478647-16616.3147864742
10933761913213077.63498051163113.365019494
11030747992981559.403211793239.5967883016
11127927902741468.4292984651321.5707015442
11229541332887849.3487758166283.6512241941
11330338493005207.6725935228641.3274064846
11428744172912623.86707577-38206.867075773
11522716332376747.34316709-105114.343167089
11620090072136051.82713567-127044.827135668
11722500662383578.29455546-133512.294555465
11815869491765506.74412467-178557.744124671
11923103992308215.986068562183.0139314374
12027540242532431.5103156221592.489684396

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5144139 & 5143915.29166667 & 223.708333332092 \tabularnewline
14 & 5144139 & 5132625.44581717 & 11513.5541828265 \tabularnewline
15 & 5105373 & 5086627.96876382 & 18745.0312361801 \tabularnewline
16 & 5004090 & 4984856.45066928 & 19233.5493307197 \tabularnewline
17 & 5527158 & 5513176.0812984 & 13981.9187015994 \tabularnewline
18 & 5606874 & 5593866.78800927 & 13007.2119907346 \tabularnewline
19 & 5486481 & 5292882.70091867 & 193598.299081326 \tabularnewline
20 & 5204472 & 5190976.91116193 & 13495.0888380697 \tabularnewline
21 & 5325138 & 5236174.10141834 & 88963.8985816557 \tabularnewline
22 & 5144139 & 5298227.17826804 & -154088.178268036 \tabularnewline
23 & 5225766 & 5276795.49802474 & -51029.4980247375 \tabularnewline
24 & 5264805 & 5303765.88121366 & -38960.8812136631 \tabularnewline
25 & 5305482 & 5344558.92216222 & -39076.9221622199 \tabularnewline
26 & 5204472 & 5326390.02173263 & -121918.021732631 \tabularnewline
27 & 5225766 & 5229455.25690839 & -3689.25690838974 \tabularnewline
28 & 5083806 & 5117141.96336809 & -33335.9633680936 \tabularnewline
29 & 5527158 & 5617916.46981793 & -90758.469817929 \tabularnewline
30 & 5667207 & 5649719.02755639 & 17487.9724436067 \tabularnewline
31 & 5546814 & 5452205.37306923 & 94608.6269307695 \tabularnewline
32 & 5325138 & 5194750.77995289 & 130387.220047108 \tabularnewline
33 & 5566197 & 5326940.06240538 & 239256.937594618 \tabularnewline
34 & 5305482 & 5304043.92755083 & 1438.07244917192 \tabularnewline
35 & 5546814 & 5409668.87287465 & 137145.127125349 \tabularnewline
36 & 5527158 & 5527743.03981404 & -585.039814042859 \tabularnewline
37 & 5587491 & 5592677.90982905 & -5186.90982904658 \tabularnewline
38 & 5365815 & 5548525.81423762 & -182710.814237619 \tabularnewline
39 & 5606874 & 5505206.5573221 & 101667.4426779 \tabularnewline
40 & 5587491 & 5428676.46803946 & 158814.531960544 \tabularnewline
41 & 5949216 & 5988923.58781337 & -39707.587813369 \tabularnewline
42 & 5867589 & 6122856.32832934 & -255267.328329337 \tabularnewline
43 & 5546814 & 5870577.8725939 & -323763.872593902 \tabularnewline
44 & 5385198 & 5463807.71250979 & -78609.7125097914 \tabularnewline
45 & 5606874 & 5569548.69509735 & 37325.3049026513 \tabularnewline
46 & 5305482 & 5311626.31166764 & -6144.31166764442 \tabularnewline
47 & 5527158 & 5482924.61971508 & 44233.3802849213 \tabularnewline
48 & 5566197 & 5467053.25306077 & 99143.7469392316 \tabularnewline
49 & 5647824 & 5557901.91702486 & 89922.082975137 \tabularnewline
50 & 5467098 & 5437449.05896561 & 29648.9410343915 \tabularnewline
51 & 5566197 & 5645582.91697707 & -79385.9169770712 \tabularnewline
52 & 5626530 & 5521179.07877681 & 105350.921223186 \tabularnewline
53 & 5848206 & 5931836.36756141 & -83630.3675614074 \tabularnewline
54 & 5667207 & 5908766.35313604 & -241559.353136041 \tabularnewline
55 & 5426148 & 5610656.02293923 & -184508.02293923 \tabularnewline
56 & 5165433 & 5399100.42231465 & -233667.422314652 \tabularnewline
57 & 5406765 & 5499861.80085345 & -93096.8008534545 \tabularnewline
58 & 4743375 & 5148743.73155647 & -405368.731556466 \tabularnewline
59 & 5064423 & 5163255.43942995 & -98832.4394299518 \tabularnewline
60 & 5245149 & 5093383.41958012 & 151765.58041988 \tabularnewline
61 & 5426148 & 5172791.68546274 & 253356.314537255 \tabularnewline
62 & 5165433 & 5059731.56249564 & 105701.43750436 \tabularnewline
63 & 5165433 & 5212831.0516778 & -47398.0516778044 \tabularnewline
64 & 5165433 & 5191061.51385363 & -25628.5138536338 \tabularnewline
65 & 5305482 & 5412635.90277702 & -107153.902777025 \tabularnewline
66 & 5105373 & 5261889.75455217 & -156516.754552169 \tabularnewline
67 & 4842747 & 5010173.44301393 & -167426.44301393 \tabularnewline
68 & 4622982 & 4754752.11098042 & -131770.110980419 \tabularnewline
69 & 4782414 & 4961516.38027387 & -179102.380273874 \tabularnewline
70 & 4159974 & 4368700.82224418 & -208726.82224418 \tabularnewline
71 & 4541355 & 4629205.55010031 & -87850.5501003079 \tabularnewline
72 & 4763031 & 4697093.67967948 & 65937.3203205168 \tabularnewline
73 & 4803708 & 4784167.92545734 & 19540.0745426593 \tabularnewline
74 & 4582032 & 4464457.35292053 & 117574.647079472 \tabularnewline
75 & 4601415 & 4507567.72961505 & 93847.2703849506 \tabularnewline
76 & 4541355 & 4535930.17552803 & 5424.82447197475 \tabularnewline
77 & 4743375 & 4702358.07159229 & 41016.9284077119 \tabularnewline
78 & 4601415 & 4566938.90931501 & 34476.0906849923 \tabularnewline
79 & 4321590 & 4375768.5797695 & -54178.5797695043 \tabularnewline
80 & 4119297 & 4180032.37550539 & -60735.3755053859 \tabularnewline
81 & 4461366 & 4381878.96347871 & 79487.0365212895 \tabularnewline
82 & 3718533 & 3877462.557448 & -158929.557447997 \tabularnewline
83 & 4200924 & 4232532.62776909 & -31608.6277690884 \tabularnewline
84 & 4420689 & 4418640.37847383 & 2048.62152616587 \tabularnewline
85 & 4420689 & 4454527.80625749 & -33838.8062574873 \tabularnewline
86 & 4159974 & 4172381.89459403 & -12407.8945940277 \tabularnewline
87 & 3918915 & 4146200.20437838 & -227285.20437838 \tabularnewline
88 & 3899532 & 3980919.4873577 & -81387.4873577016 \tabularnewline
89 & 4119297 & 4120160.01550918 & -863.015509176534 \tabularnewline
90 & 3918915 & 3949616.59036672 & -30701.5903667249 \tabularnewline
91 & 3537807 & 3663344.29552571 & -125537.295525711 \tabularnewline
92 & 3275181 & 3416954.55022684 & -141773.550226843 \tabularnewline
93 & 3557190 & 3649388.02443185 & -92198.0244318536 \tabularnewline
94 & 2894073 & 2909165.08719207 & -15092.0871920711 \tabularnewline
95 & 3496857 & 3377573.57058314 & 119283.429416863 \tabularnewline
96 & 3817632 & 3628127.71067806 & 189504.289321941 \tabularnewline
97 & 3918915 & 3706829.54611926 & 212085.453880745 \tabularnewline
98 & 3697239 & 3531714.17467413 & 165524.825325869 \tabularnewline
99 & 3417141 & 3449134.18622091 & -31993.1862209062 \tabularnewline
100 & 3617523 & 3454136.41931959 & 163386.580680406 \tabularnewline
101 & 3697239 & 3751243.90823499 & -54004.9082349851 \tabularnewline
102 & 3636906 & 3550791.33995828 & 86114.6600417229 \tabularnewline
103 & 3033849 & 3267905.29026747 & -234056.290267467 \tabularnewline
104 & 2754024 & 2977465.39029635 & -223441.390296348 \tabularnewline
105 & 2954133 & 3213732.25113268 & -259599.251132676 \tabularnewline
106 & 2351349 & 2454584.45530405 & -103235.455304047 \tabularnewline
107 & 2973789 & 2967945.28087489 & 5843.71912511205 \tabularnewline
108 & 3195465 & 3212081.31478647 & -16616.3147864742 \tabularnewline
109 & 3376191 & 3213077.63498051 & 163113.365019494 \tabularnewline
110 & 3074799 & 2981559.4032117 & 93239.5967883016 \tabularnewline
111 & 2792790 & 2741468.42929846 & 51321.5707015442 \tabularnewline
112 & 2954133 & 2887849.34877581 & 66283.6512241941 \tabularnewline
113 & 3033849 & 3005207.67259352 & 28641.3274064846 \tabularnewline
114 & 2874417 & 2912623.86707577 & -38206.867075773 \tabularnewline
115 & 2271633 & 2376747.34316709 & -105114.343167089 \tabularnewline
116 & 2009007 & 2136051.82713567 & -127044.827135668 \tabularnewline
117 & 2250066 & 2383578.29455546 & -133512.294555465 \tabularnewline
118 & 1586949 & 1765506.74412467 & -178557.744124671 \tabularnewline
119 & 2310399 & 2308215.98606856 & 2183.0139314374 \tabularnewline
120 & 2754024 & 2532431.5103156 & 221592.489684396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307287&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]5144139[/C][C]5143915.29166667[/C][C]223.708333332092[/C][/ROW]
[ROW][C]14[/C][C]5144139[/C][C]5132625.44581717[/C][C]11513.5541828265[/C][/ROW]
[ROW][C]15[/C][C]5105373[/C][C]5086627.96876382[/C][C]18745.0312361801[/C][/ROW]
[ROW][C]16[/C][C]5004090[/C][C]4984856.45066928[/C][C]19233.5493307197[/C][/ROW]
[ROW][C]17[/C][C]5527158[/C][C]5513176.0812984[/C][C]13981.9187015994[/C][/ROW]
[ROW][C]18[/C][C]5606874[/C][C]5593866.78800927[/C][C]13007.2119907346[/C][/ROW]
[ROW][C]19[/C][C]5486481[/C][C]5292882.70091867[/C][C]193598.299081326[/C][/ROW]
[ROW][C]20[/C][C]5204472[/C][C]5190976.91116193[/C][C]13495.0888380697[/C][/ROW]
[ROW][C]21[/C][C]5325138[/C][C]5236174.10141834[/C][C]88963.8985816557[/C][/ROW]
[ROW][C]22[/C][C]5144139[/C][C]5298227.17826804[/C][C]-154088.178268036[/C][/ROW]
[ROW][C]23[/C][C]5225766[/C][C]5276795.49802474[/C][C]-51029.4980247375[/C][/ROW]
[ROW][C]24[/C][C]5264805[/C][C]5303765.88121366[/C][C]-38960.8812136631[/C][/ROW]
[ROW][C]25[/C][C]5305482[/C][C]5344558.92216222[/C][C]-39076.9221622199[/C][/ROW]
[ROW][C]26[/C][C]5204472[/C][C]5326390.02173263[/C][C]-121918.021732631[/C][/ROW]
[ROW][C]27[/C][C]5225766[/C][C]5229455.25690839[/C][C]-3689.25690838974[/C][/ROW]
[ROW][C]28[/C][C]5083806[/C][C]5117141.96336809[/C][C]-33335.9633680936[/C][/ROW]
[ROW][C]29[/C][C]5527158[/C][C]5617916.46981793[/C][C]-90758.469817929[/C][/ROW]
[ROW][C]30[/C][C]5667207[/C][C]5649719.02755639[/C][C]17487.9724436067[/C][/ROW]
[ROW][C]31[/C][C]5546814[/C][C]5452205.37306923[/C][C]94608.6269307695[/C][/ROW]
[ROW][C]32[/C][C]5325138[/C][C]5194750.77995289[/C][C]130387.220047108[/C][/ROW]
[ROW][C]33[/C][C]5566197[/C][C]5326940.06240538[/C][C]239256.937594618[/C][/ROW]
[ROW][C]34[/C][C]5305482[/C][C]5304043.92755083[/C][C]1438.07244917192[/C][/ROW]
[ROW][C]35[/C][C]5546814[/C][C]5409668.87287465[/C][C]137145.127125349[/C][/ROW]
[ROW][C]36[/C][C]5527158[/C][C]5527743.03981404[/C][C]-585.039814042859[/C][/ROW]
[ROW][C]37[/C][C]5587491[/C][C]5592677.90982905[/C][C]-5186.90982904658[/C][/ROW]
[ROW][C]38[/C][C]5365815[/C][C]5548525.81423762[/C][C]-182710.814237619[/C][/ROW]
[ROW][C]39[/C][C]5606874[/C][C]5505206.5573221[/C][C]101667.4426779[/C][/ROW]
[ROW][C]40[/C][C]5587491[/C][C]5428676.46803946[/C][C]158814.531960544[/C][/ROW]
[ROW][C]41[/C][C]5949216[/C][C]5988923.58781337[/C][C]-39707.587813369[/C][/ROW]
[ROW][C]42[/C][C]5867589[/C][C]6122856.32832934[/C][C]-255267.328329337[/C][/ROW]
[ROW][C]43[/C][C]5546814[/C][C]5870577.8725939[/C][C]-323763.872593902[/C][/ROW]
[ROW][C]44[/C][C]5385198[/C][C]5463807.71250979[/C][C]-78609.7125097914[/C][/ROW]
[ROW][C]45[/C][C]5606874[/C][C]5569548.69509735[/C][C]37325.3049026513[/C][/ROW]
[ROW][C]46[/C][C]5305482[/C][C]5311626.31166764[/C][C]-6144.31166764442[/C][/ROW]
[ROW][C]47[/C][C]5527158[/C][C]5482924.61971508[/C][C]44233.3802849213[/C][/ROW]
[ROW][C]48[/C][C]5566197[/C][C]5467053.25306077[/C][C]99143.7469392316[/C][/ROW]
[ROW][C]49[/C][C]5647824[/C][C]5557901.91702486[/C][C]89922.082975137[/C][/ROW]
[ROW][C]50[/C][C]5467098[/C][C]5437449.05896561[/C][C]29648.9410343915[/C][/ROW]
[ROW][C]51[/C][C]5566197[/C][C]5645582.91697707[/C][C]-79385.9169770712[/C][/ROW]
[ROW][C]52[/C][C]5626530[/C][C]5521179.07877681[/C][C]105350.921223186[/C][/ROW]
[ROW][C]53[/C][C]5848206[/C][C]5931836.36756141[/C][C]-83630.3675614074[/C][/ROW]
[ROW][C]54[/C][C]5667207[/C][C]5908766.35313604[/C][C]-241559.353136041[/C][/ROW]
[ROW][C]55[/C][C]5426148[/C][C]5610656.02293923[/C][C]-184508.02293923[/C][/ROW]
[ROW][C]56[/C][C]5165433[/C][C]5399100.42231465[/C][C]-233667.422314652[/C][/ROW]
[ROW][C]57[/C][C]5406765[/C][C]5499861.80085345[/C][C]-93096.8008534545[/C][/ROW]
[ROW][C]58[/C][C]4743375[/C][C]5148743.73155647[/C][C]-405368.731556466[/C][/ROW]
[ROW][C]59[/C][C]5064423[/C][C]5163255.43942995[/C][C]-98832.4394299518[/C][/ROW]
[ROW][C]60[/C][C]5245149[/C][C]5093383.41958012[/C][C]151765.58041988[/C][/ROW]
[ROW][C]61[/C][C]5426148[/C][C]5172791.68546274[/C][C]253356.314537255[/C][/ROW]
[ROW][C]62[/C][C]5165433[/C][C]5059731.56249564[/C][C]105701.43750436[/C][/ROW]
[ROW][C]63[/C][C]5165433[/C][C]5212831.0516778[/C][C]-47398.0516778044[/C][/ROW]
[ROW][C]64[/C][C]5165433[/C][C]5191061.51385363[/C][C]-25628.5138536338[/C][/ROW]
[ROW][C]65[/C][C]5305482[/C][C]5412635.90277702[/C][C]-107153.902777025[/C][/ROW]
[ROW][C]66[/C][C]5105373[/C][C]5261889.75455217[/C][C]-156516.754552169[/C][/ROW]
[ROW][C]67[/C][C]4842747[/C][C]5010173.44301393[/C][C]-167426.44301393[/C][/ROW]
[ROW][C]68[/C][C]4622982[/C][C]4754752.11098042[/C][C]-131770.110980419[/C][/ROW]
[ROW][C]69[/C][C]4782414[/C][C]4961516.38027387[/C][C]-179102.380273874[/C][/ROW]
[ROW][C]70[/C][C]4159974[/C][C]4368700.82224418[/C][C]-208726.82224418[/C][/ROW]
[ROW][C]71[/C][C]4541355[/C][C]4629205.55010031[/C][C]-87850.5501003079[/C][/ROW]
[ROW][C]72[/C][C]4763031[/C][C]4697093.67967948[/C][C]65937.3203205168[/C][/ROW]
[ROW][C]73[/C][C]4803708[/C][C]4784167.92545734[/C][C]19540.0745426593[/C][/ROW]
[ROW][C]74[/C][C]4582032[/C][C]4464457.35292053[/C][C]117574.647079472[/C][/ROW]
[ROW][C]75[/C][C]4601415[/C][C]4507567.72961505[/C][C]93847.2703849506[/C][/ROW]
[ROW][C]76[/C][C]4541355[/C][C]4535930.17552803[/C][C]5424.82447197475[/C][/ROW]
[ROW][C]77[/C][C]4743375[/C][C]4702358.07159229[/C][C]41016.9284077119[/C][/ROW]
[ROW][C]78[/C][C]4601415[/C][C]4566938.90931501[/C][C]34476.0906849923[/C][/ROW]
[ROW][C]79[/C][C]4321590[/C][C]4375768.5797695[/C][C]-54178.5797695043[/C][/ROW]
[ROW][C]80[/C][C]4119297[/C][C]4180032.37550539[/C][C]-60735.3755053859[/C][/ROW]
[ROW][C]81[/C][C]4461366[/C][C]4381878.96347871[/C][C]79487.0365212895[/C][/ROW]
[ROW][C]82[/C][C]3718533[/C][C]3877462.557448[/C][C]-158929.557447997[/C][/ROW]
[ROW][C]83[/C][C]4200924[/C][C]4232532.62776909[/C][C]-31608.6277690884[/C][/ROW]
[ROW][C]84[/C][C]4420689[/C][C]4418640.37847383[/C][C]2048.62152616587[/C][/ROW]
[ROW][C]85[/C][C]4420689[/C][C]4454527.80625749[/C][C]-33838.8062574873[/C][/ROW]
[ROW][C]86[/C][C]4159974[/C][C]4172381.89459403[/C][C]-12407.8945940277[/C][/ROW]
[ROW][C]87[/C][C]3918915[/C][C]4146200.20437838[/C][C]-227285.20437838[/C][/ROW]
[ROW][C]88[/C][C]3899532[/C][C]3980919.4873577[/C][C]-81387.4873577016[/C][/ROW]
[ROW][C]89[/C][C]4119297[/C][C]4120160.01550918[/C][C]-863.015509176534[/C][/ROW]
[ROW][C]90[/C][C]3918915[/C][C]3949616.59036672[/C][C]-30701.5903667249[/C][/ROW]
[ROW][C]91[/C][C]3537807[/C][C]3663344.29552571[/C][C]-125537.295525711[/C][/ROW]
[ROW][C]92[/C][C]3275181[/C][C]3416954.55022684[/C][C]-141773.550226843[/C][/ROW]
[ROW][C]93[/C][C]3557190[/C][C]3649388.02443185[/C][C]-92198.0244318536[/C][/ROW]
[ROW][C]94[/C][C]2894073[/C][C]2909165.08719207[/C][C]-15092.0871920711[/C][/ROW]
[ROW][C]95[/C][C]3496857[/C][C]3377573.57058314[/C][C]119283.429416863[/C][/ROW]
[ROW][C]96[/C][C]3817632[/C][C]3628127.71067806[/C][C]189504.289321941[/C][/ROW]
[ROW][C]97[/C][C]3918915[/C][C]3706829.54611926[/C][C]212085.453880745[/C][/ROW]
[ROW][C]98[/C][C]3697239[/C][C]3531714.17467413[/C][C]165524.825325869[/C][/ROW]
[ROW][C]99[/C][C]3417141[/C][C]3449134.18622091[/C][C]-31993.1862209062[/C][/ROW]
[ROW][C]100[/C][C]3617523[/C][C]3454136.41931959[/C][C]163386.580680406[/C][/ROW]
[ROW][C]101[/C][C]3697239[/C][C]3751243.90823499[/C][C]-54004.9082349851[/C][/ROW]
[ROW][C]102[/C][C]3636906[/C][C]3550791.33995828[/C][C]86114.6600417229[/C][/ROW]
[ROW][C]103[/C][C]3033849[/C][C]3267905.29026747[/C][C]-234056.290267467[/C][/ROW]
[ROW][C]104[/C][C]2754024[/C][C]2977465.39029635[/C][C]-223441.390296348[/C][/ROW]
[ROW][C]105[/C][C]2954133[/C][C]3213732.25113268[/C][C]-259599.251132676[/C][/ROW]
[ROW][C]106[/C][C]2351349[/C][C]2454584.45530405[/C][C]-103235.455304047[/C][/ROW]
[ROW][C]107[/C][C]2973789[/C][C]2967945.28087489[/C][C]5843.71912511205[/C][/ROW]
[ROW][C]108[/C][C]3195465[/C][C]3212081.31478647[/C][C]-16616.3147864742[/C][/ROW]
[ROW][C]109[/C][C]3376191[/C][C]3213077.63498051[/C][C]163113.365019494[/C][/ROW]
[ROW][C]110[/C][C]3074799[/C][C]2981559.4032117[/C][C]93239.5967883016[/C][/ROW]
[ROW][C]111[/C][C]2792790[/C][C]2741468.42929846[/C][C]51321.5707015442[/C][/ROW]
[ROW][C]112[/C][C]2954133[/C][C]2887849.34877581[/C][C]66283.6512241941[/C][/ROW]
[ROW][C]113[/C][C]3033849[/C][C]3005207.67259352[/C][C]28641.3274064846[/C][/ROW]
[ROW][C]114[/C][C]2874417[/C][C]2912623.86707577[/C][C]-38206.867075773[/C][/ROW]
[ROW][C]115[/C][C]2271633[/C][C]2376747.34316709[/C][C]-105114.343167089[/C][/ROW]
[ROW][C]116[/C][C]2009007[/C][C]2136051.82713567[/C][C]-127044.827135668[/C][/ROW]
[ROW][C]117[/C][C]2250066[/C][C]2383578.29455546[/C][C]-133512.294555465[/C][/ROW]
[ROW][C]118[/C][C]1586949[/C][C]1765506.74412467[/C][C]-178557.744124671[/C][/ROW]
[ROW][C]119[/C][C]2310399[/C][C]2308215.98606856[/C][C]2183.0139314374[/C][/ROW]
[ROW][C]120[/C][C]2754024[/C][C]2532431.5103156[/C][C]221592.489684396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307287&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
1351441395143915.29166667223.708333332092
1451441395132625.4458171711513.5541828265
1551053735086627.9687638218745.0312361801
1650040904984856.4506692819233.5493307197
1755271585513176.081298413981.9187015994
1856068745593866.7880092713007.2119907346
1954864815292882.70091867193598.299081326
2052044725190976.9111619313495.0888380697
2153251385236174.1014183488963.8985816557
2251441395298227.17826804-154088.178268036
2352257665276795.49802474-51029.4980247375
2452648055303765.88121366-38960.8812136631
2553054825344558.92216222-39076.9221622199
2652044725326390.02173263-121918.021732631
2752257665229455.25690839-3689.25690838974
2850838065117141.96336809-33335.9633680936
2955271585617916.46981793-90758.469817929
3056672075649719.0275563917487.9724436067
3155468145452205.3730692394608.6269307695
3253251385194750.77995289130387.220047108
3355661975326940.06240538239256.937594618
3453054825304043.927550831438.07244917192
3555468145409668.87287465137145.127125349
3655271585527743.03981404-585.039814042859
3755874915592677.90982905-5186.90982904658
3853658155548525.81423762-182710.814237619
3956068745505206.5573221101667.4426779
4055874915428676.46803946158814.531960544
4159492165988923.58781337-39707.587813369
4258675896122856.32832934-255267.328329337
4355468145870577.8725939-323763.872593902
4453851985463807.71250979-78609.7125097914
4556068745569548.6950973537325.3049026513
4653054825311626.31166764-6144.31166764442
4755271585482924.6197150844233.3802849213
4855661975467053.2530607799143.7469392316
4956478245557901.9170248689922.082975137
5054670985437449.0589656129648.9410343915
5155661975645582.91697707-79385.9169770712
5256265305521179.07877681105350.921223186
5358482065931836.36756141-83630.3675614074
5456672075908766.35313604-241559.353136041
5554261485610656.02293923-184508.02293923
5651654335399100.42231465-233667.422314652
5754067655499861.80085345-93096.8008534545
5847433755148743.73155647-405368.731556466
5950644235163255.43942995-98832.4394299518
6052451495093383.41958012151765.58041988
6154261485172791.68546274253356.314537255
6251654335059731.56249564105701.43750436
6351654335212831.0516778-47398.0516778044
6451654335191061.51385363-25628.5138536338
6553054825412635.90277702-107153.902777025
6651053735261889.75455217-156516.754552169
6748427475010173.44301393-167426.44301393
6846229824754752.11098042-131770.110980419
6947824144961516.38027387-179102.380273874
7041599744368700.82224418-208726.82224418
7145413554629205.55010031-87850.5501003079
7247630314697093.6796794865937.3203205168
7348037084784167.9254573419540.0745426593
7445820324464457.35292053117574.647079472
7546014154507567.7296150593847.2703849506
7645413554535930.175528035424.82447197475
7747433754702358.0715922941016.9284077119
7846014154566938.9093150134476.0906849923
7943215904375768.5797695-54178.5797695043
8041192974180032.37550539-60735.3755053859
8144613664381878.9634787179487.0365212895
8237185333877462.557448-158929.557447997
8342009244232532.62776909-31608.6277690884
8444206894418640.378473832048.62152616587
8544206894454527.80625749-33838.8062574873
8641599744172381.89459403-12407.8945940277
8739189154146200.20437838-227285.20437838
8838995323980919.4873577-81387.4873577016
8941192974120160.01550918-863.015509176534
9039189153949616.59036672-30701.5903667249
9135378073663344.29552571-125537.295525711
9232751813416954.55022684-141773.550226843
9335571903649388.02443185-92198.0244318536
9428940732909165.08719207-15092.0871920711
9534968573377573.57058314119283.429416863
9638176323628127.71067806189504.289321941
9739189153706829.54611926212085.453880745
9836972393531714.17467413165524.825325869
9934171413449134.18622091-31993.1862209062
10036175233454136.41931959163386.580680406
10136972393751243.90823499-54004.9082349851
10236369063550791.3399582886114.6600417229
10330338493267905.29026747-234056.290267467
10427540242977465.39029635-223441.390296348
10529541333213732.25113268-259599.251132676
10623513492454584.45530405-103235.455304047
10729737892967945.280874895843.71912511205
10831954653212081.31478647-16616.3147864742
10933761913213077.63498051163113.365019494
11030747992981559.403211793239.5967883016
11127927902741468.4292984651321.5707015442
11229541332887849.3487758166283.6512241941
11330338493005207.6725935228641.3274064846
11428744172912623.86707577-38206.867075773
11522716332376747.34316709-105114.343167089
11620090072136051.82713567-127044.827135668
11722500662383578.29455546-133512.294555465
11815869491765506.74412467-178557.744124671
11923103992308215.986068562183.0139314374
12027540242532431.5103156221592.489684396







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212738010.729502872488769.513756592987251.94524914
1222395707.996443432124253.712898362667162.27998849
1232087340.988844551792895.408975192381786.56871391
1242214919.016737691896739.076668042533098.95680734
1252274394.610771931931767.658217932617021.56332593
1262121069.608946441753309.58005142488829.63784147
1271552512.291297971158956.601135641946067.98146029
1281335751.34982435915758.3354510571755744.36419765
1291628619.497020661181566.292435722075672.70160561
1301039062.18874731564342.9408036831513781.43669093
1311767479.619047991264503.975179452270455.26291652
1322127078.862349551595270.677110552658887.04758856

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2738010.72950287 & 2488769.51375659 & 2987251.94524914 \tabularnewline
122 & 2395707.99644343 & 2124253.71289836 & 2667162.27998849 \tabularnewline
123 & 2087340.98884455 & 1792895.40897519 & 2381786.56871391 \tabularnewline
124 & 2214919.01673769 & 1896739.07666804 & 2533098.95680734 \tabularnewline
125 & 2274394.61077193 & 1931767.65821793 & 2617021.56332593 \tabularnewline
126 & 2121069.60894644 & 1753309.5800514 & 2488829.63784147 \tabularnewline
127 & 1552512.29129797 & 1158956.60113564 & 1946067.98146029 \tabularnewline
128 & 1335751.34982435 & 915758.335451057 & 1755744.36419765 \tabularnewline
129 & 1628619.49702066 & 1181566.29243572 & 2075672.70160561 \tabularnewline
130 & 1039062.18874731 & 564342.940803683 & 1513781.43669093 \tabularnewline
131 & 1767479.61904799 & 1264503.97517945 & 2270455.26291652 \tabularnewline
132 & 2127078.86234955 & 1595270.67711055 & 2658887.04758856 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307287&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]121[/C][C]2738010.72950287[/C][C]2488769.51375659[/C][C]2987251.94524914[/C][/ROW]
[ROW][C]122[/C][C]2395707.99644343[/C][C]2124253.71289836[/C][C]2667162.27998849[/C][/ROW]
[ROW][C]123[/C][C]2087340.98884455[/C][C]1792895.40897519[/C][C]2381786.56871391[/C][/ROW]
[ROW][C]124[/C][C]2214919.01673769[/C][C]1896739.07666804[/C][C]2533098.95680734[/C][/ROW]
[ROW][C]125[/C][C]2274394.61077193[/C][C]1931767.65821793[/C][C]2617021.56332593[/C][/ROW]
[ROW][C]126[/C][C]2121069.60894644[/C][C]1753309.5800514[/C][C]2488829.63784147[/C][/ROW]
[ROW][C]127[/C][C]1552512.29129797[/C][C]1158956.60113564[/C][C]1946067.98146029[/C][/ROW]
[ROW][C]128[/C][C]1335751.34982435[/C][C]915758.335451057[/C][C]1755744.36419765[/C][/ROW]
[ROW][C]129[/C][C]1628619.49702066[/C][C]1181566.29243572[/C][C]2075672.70160561[/C][/ROW]
[ROW][C]130[/C][C]1039062.18874731[/C][C]564342.940803683[/C][C]1513781.43669093[/C][/ROW]
[ROW][C]131[/C][C]1767479.61904799[/C][C]1264503.97517945[/C][C]2270455.26291652[/C][/ROW]
[ROW][C]132[/C][C]2127078.86234955[/C][C]1595270.67711055[/C][C]2658887.04758856[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307287&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307287&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
1212738010.729502872488769.513756592987251.94524914
1222395707.996443432124253.712898362667162.27998849
1232087340.988844551792895.408975192381786.56871391
1242214919.016737691896739.076668042533098.95680734
1252274394.610771931931767.658217932617021.56332593
1262121069.608946441753309.58005142488829.63784147
1271552512.291297971158956.601135641946067.98146029
1281335751.34982435915758.3354510571755744.36419765
1291628619.497020661181566.292435722075672.70160561
1301039062.18874731564342.9408036831513781.43669093
1311767479.619047991264503.975179452270455.26291652
1322127078.862349551595270.677110552658887.04758856



Parameters (Session):
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')