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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 19:09:53 +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/16/t15029035855njr039legucswl.htm/, Retrieved Sat, 11 May 2024 19:06:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307469, Retrieved Sat, 11 May 2024 19:06:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Omzet Mercedes A-...] [2017-08-09 17:08:27] [761e4adbe8124e6083bfb711aef3fb41]
- RMPD  [(Partial) Autocorrelation Function] [] [2017-08-10 00:37:55] [761e4adbe8124e6083bfb711aef3fb41]
- RMP     [Classical Decomposition] [] [2017-08-16 12:59:43] [761e4adbe8124e6083bfb711aef3fb41]
- RMPD        [Exponential Smoothing] [] [2017-08-16 17:09:53] [35d4184f59ec62fac19bf382c4afaa07] [Current]
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Dataseries X:
982800
946400
1001000
800800
1037400
1019200
1092000
1128400
1255800
1092000
1037400
1292200
1092000
819000
964600
728000
1019200
837200
1110200
1001000
1055600
1183000
1164800
1383200
1001000
837200
928200
673400
964600
746200
1055600
1001000
891800
1274000
1146600
1310400
982800
910000
819000
673400
891800
800800
1092000
1055600
910000
1219400
1128400
1456000
1164800
709800
709800
709800
837200
837200
1128400
1037400
928200
1164800
1073800
1547000
1219400
709800
746200
618800
855400
982800
1237600
1219400
982800
1146600
1019200
1456000
1110200
891800
800800
600600
891800
1073800
1255800
1183000
873600
1255800
982800
1510600
1255800
910000
837200
564200
891800
855400
1292200
1292200
982800
1274000
946400
1474200
1255800
928200
709800
491400
964600
928200
1219400
1401400
1037400
1164800
873600
1510600




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=307469&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=307469&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307469&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
alpha0.00926118605787297
beta1
gamma0.929768627343133

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605787297 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627343133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307469&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]0.00926118605787297[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627343133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307469&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307469&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
alpha0.00926118605787297
beta1
gamma0.929768627343133







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310920001129343.05555556-37343.0555555557
14819000855433.949342192-36433.9493421924
159646001008895.84094694-44295.8409469364
16728000770574.690086162-42574.6900861622
1710192001046025.1869975-26825.1869974993
18837200848173.109939438-10973.1099394384
1911102001060624.5512369749575.4487630331
2010010001092095.87145707-91095.8714570715
2110556001218487.41925961-162887.41925961
2211830001049230.56148432133769.438515684
231164800992401.628389841172398.371610159
2413832001251477.05842753131722.941572472
2510010001020480.18033663-19480.1803366283
26837200748063.85217347289136.1478265278
27928200897099.47284144331100.527158557
28673400663413.137554759986.86244525039
29964600956696.0818991167903.91810088418
30746200776927.422183349-30727.4221833491
3110556001047947.267095167652.73290484468
321001000952038.15666210548961.843337895
338918001017480.87324034-125680.873240338
3412740001126066.38459215147933.615407848
3511466001109313.1452848337286.8547151743
3613104001332778.66824494-22378.6682449421
37982800962755.39571317120044.6042868287
38910000792806.660016306117193.339983694
39819000890950.758787502-71950.7587875018
40673400638215.25465806235184.7453419378
41891800931400.429640199-39600.4296401989
42800800716753.90262476184046.0973752385
4310920001026401.4494972165598.5505027917
441055600971828.42636003383771.573639967
45910000879789.61764911330210.3823508872
4612194001246374.3512446-26974.3512445986
4711284001128971.61296387-571.612963865744
4814560001299668.03175823156331.968241773
491164800974576.311393348190223.688606652
50709800901466.966659358-191666.966659358
51709800825432.673935911-115632.673935911
52709800673490.38546199936309.6145380009
53837200900316.49293824-63116.4929382396
54837200801651.8308949135548.1691050897
5511284001095709.6586734232690.3413265818
5610374001059119.85284526-21719.8528452599
57928200917336.54307639810863.4569236021
5811648001231457.54588778-66657.5458877764
5910738001138032.48271037-64232.4827103659
6015470001452106.817861194893.182138901
6112194001156531.2535939862868.7464060208
62709800728146.939045149-18346.9390451491
63746200723048.60074789723151.3992521026
64618800712930.975385136-94130.9753851364
65855400846330.3962348939069.60376510653
66982800839257.010624342143542.989375658
6712376001132719.66602448104880.333975519
6812194001048383.78973046171016.210269541
69982800941890.5241645340909.4758354702
7011466001188649.67644683-42049.6764468309
7110192001101683.24471249-82483.2447124945
7214560001565996.2578522-109996.257852199
7311102001240953.93787939-130753.937879393
74891800736101.128771328155698.871228672
75800800772590.20126079728209.7987392035
76600600656279.706748341-55679.7067483413
77891800887251.2278171924548.77218280756
7810738001006117.2932449367682.7067550735
7912558001264670.52930767-8870.52930766717
8011830001240556.84597981-57556.8459798128
818736001010335.10135432-136735.101354324
8212558001175622.5994293480177.4005706583
839828001050266.4246421-67466.4246421019
8415106001487237.7451581823362.254841821
8512558001143407.50323543112392.49676457
86910000906024.7218409593975.27815904096
87837200823615.89607041913584.1039295814
88564200629703.825306763-65503.8253067634
89891800915782.670562711-23982.6705627111
908554001091994.95648914-236594.956489143
9112922001273848.7677826218351.2322173845
9212922001202027.67536390172.3246369986
93982800898494.82129931384305.1787006874
9412740001265943.583381038056.41661897232
959464001003551.79699648-57151.7969964843
9614742001524017.30692489-49817.306924887
9712558001260573.62474646-4773.62474645558
98928200920204.6565280117995.34347198938
99709800844689.82162921-134889.82162921
100491400573180.708205433-81780.7082054331
101964600893836.07552027670763.924479724
102928200872433.54027122755766.4597287728
10312194001291905.45872253-72505.4587225269
10414014001284624.85544307116775.144556926
1051037400975403.54662655261996.4533734475
10611648001271671.69036739-106871.690367387
107873600946347.237810505-72747.237810505
10815106001471478.8697922239121.1302077798

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1092000 & 1129343.05555556 & -37343.0555555557 \tabularnewline
14 & 819000 & 855433.949342192 & -36433.9493421924 \tabularnewline
15 & 964600 & 1008895.84094694 & -44295.8409469364 \tabularnewline
16 & 728000 & 770574.690086162 & -42574.6900861622 \tabularnewline
17 & 1019200 & 1046025.1869975 & -26825.1869974993 \tabularnewline
18 & 837200 & 848173.109939438 & -10973.1099394384 \tabularnewline
19 & 1110200 & 1060624.55123697 & 49575.4487630331 \tabularnewline
20 & 1001000 & 1092095.87145707 & -91095.8714570715 \tabularnewline
21 & 1055600 & 1218487.41925961 & -162887.41925961 \tabularnewline
22 & 1183000 & 1049230.56148432 & 133769.438515684 \tabularnewline
23 & 1164800 & 992401.628389841 & 172398.371610159 \tabularnewline
24 & 1383200 & 1251477.05842753 & 131722.941572472 \tabularnewline
25 & 1001000 & 1020480.18033663 & -19480.1803366283 \tabularnewline
26 & 837200 & 748063.852173472 & 89136.1478265278 \tabularnewline
27 & 928200 & 897099.472841443 & 31100.527158557 \tabularnewline
28 & 673400 & 663413.13755475 & 9986.86244525039 \tabularnewline
29 & 964600 & 956696.081899116 & 7903.91810088418 \tabularnewline
30 & 746200 & 776927.422183349 & -30727.4221833491 \tabularnewline
31 & 1055600 & 1047947.26709516 & 7652.73290484468 \tabularnewline
32 & 1001000 & 952038.156662105 & 48961.843337895 \tabularnewline
33 & 891800 & 1017480.87324034 & -125680.873240338 \tabularnewline
34 & 1274000 & 1126066.38459215 & 147933.615407848 \tabularnewline
35 & 1146600 & 1109313.14528483 & 37286.8547151743 \tabularnewline
36 & 1310400 & 1332778.66824494 & -22378.6682449421 \tabularnewline
37 & 982800 & 962755.395713171 & 20044.6042868287 \tabularnewline
38 & 910000 & 792806.660016306 & 117193.339983694 \tabularnewline
39 & 819000 & 890950.758787502 & -71950.7587875018 \tabularnewline
40 & 673400 & 638215.254658062 & 35184.7453419378 \tabularnewline
41 & 891800 & 931400.429640199 & -39600.4296401989 \tabularnewline
42 & 800800 & 716753.902624761 & 84046.0973752385 \tabularnewline
43 & 1092000 & 1026401.44949721 & 65598.5505027917 \tabularnewline
44 & 1055600 & 971828.426360033 & 83771.573639967 \tabularnewline
45 & 910000 & 879789.617649113 & 30210.3823508872 \tabularnewline
46 & 1219400 & 1246374.3512446 & -26974.3512445986 \tabularnewline
47 & 1128400 & 1128971.61296387 & -571.612963865744 \tabularnewline
48 & 1456000 & 1299668.03175823 & 156331.968241773 \tabularnewline
49 & 1164800 & 974576.311393348 & 190223.688606652 \tabularnewline
50 & 709800 & 901466.966659358 & -191666.966659358 \tabularnewline
51 & 709800 & 825432.673935911 & -115632.673935911 \tabularnewline
52 & 709800 & 673490.385461999 & 36309.6145380009 \tabularnewline
53 & 837200 & 900316.49293824 & -63116.4929382396 \tabularnewline
54 & 837200 & 801651.83089491 & 35548.1691050897 \tabularnewline
55 & 1128400 & 1095709.65867342 & 32690.3413265818 \tabularnewline
56 & 1037400 & 1059119.85284526 & -21719.8528452599 \tabularnewline
57 & 928200 & 917336.543076398 & 10863.4569236021 \tabularnewline
58 & 1164800 & 1231457.54588778 & -66657.5458877764 \tabularnewline
59 & 1073800 & 1138032.48271037 & -64232.4827103659 \tabularnewline
60 & 1547000 & 1452106.8178611 & 94893.182138901 \tabularnewline
61 & 1219400 & 1156531.25359398 & 62868.7464060208 \tabularnewline
62 & 709800 & 728146.939045149 & -18346.9390451491 \tabularnewline
63 & 746200 & 723048.600747897 & 23151.3992521026 \tabularnewline
64 & 618800 & 712930.975385136 & -94130.9753851364 \tabularnewline
65 & 855400 & 846330.396234893 & 9069.60376510653 \tabularnewline
66 & 982800 & 839257.010624342 & 143542.989375658 \tabularnewline
67 & 1237600 & 1132719.66602448 & 104880.333975519 \tabularnewline
68 & 1219400 & 1048383.78973046 & 171016.210269541 \tabularnewline
69 & 982800 & 941890.52416453 & 40909.4758354702 \tabularnewline
70 & 1146600 & 1188649.67644683 & -42049.6764468309 \tabularnewline
71 & 1019200 & 1101683.24471249 & -82483.2447124945 \tabularnewline
72 & 1456000 & 1565996.2578522 & -109996.257852199 \tabularnewline
73 & 1110200 & 1240953.93787939 & -130753.937879393 \tabularnewline
74 & 891800 & 736101.128771328 & 155698.871228672 \tabularnewline
75 & 800800 & 772590.201260797 & 28209.7987392035 \tabularnewline
76 & 600600 & 656279.706748341 & -55679.7067483413 \tabularnewline
77 & 891800 & 887251.227817192 & 4548.77218280756 \tabularnewline
78 & 1073800 & 1006117.29324493 & 67682.7067550735 \tabularnewline
79 & 1255800 & 1264670.52930767 & -8870.52930766717 \tabularnewline
80 & 1183000 & 1240556.84597981 & -57556.8459798128 \tabularnewline
81 & 873600 & 1010335.10135432 & -136735.101354324 \tabularnewline
82 & 1255800 & 1175622.59942934 & 80177.4005706583 \tabularnewline
83 & 982800 & 1050266.4246421 & -67466.4246421019 \tabularnewline
84 & 1510600 & 1487237.74515818 & 23362.254841821 \tabularnewline
85 & 1255800 & 1143407.50323543 & 112392.49676457 \tabularnewline
86 & 910000 & 906024.721840959 & 3975.27815904096 \tabularnewline
87 & 837200 & 823615.896070419 & 13584.1039295814 \tabularnewline
88 & 564200 & 629703.825306763 & -65503.8253067634 \tabularnewline
89 & 891800 & 915782.670562711 & -23982.6705627111 \tabularnewline
90 & 855400 & 1091994.95648914 & -236594.956489143 \tabularnewline
91 & 1292200 & 1273848.76778262 & 18351.2322173845 \tabularnewline
92 & 1292200 & 1202027.675363 & 90172.3246369986 \tabularnewline
93 & 982800 & 898494.821299313 & 84305.1787006874 \tabularnewline
94 & 1274000 & 1265943.58338103 & 8056.41661897232 \tabularnewline
95 & 946400 & 1003551.79699648 & -57151.7969964843 \tabularnewline
96 & 1474200 & 1524017.30692489 & -49817.306924887 \tabularnewline
97 & 1255800 & 1260573.62474646 & -4773.62474645558 \tabularnewline
98 & 928200 & 920204.656528011 & 7995.34347198938 \tabularnewline
99 & 709800 & 844689.82162921 & -134889.82162921 \tabularnewline
100 & 491400 & 573180.708205433 & -81780.7082054331 \tabularnewline
101 & 964600 & 893836.075520276 & 70763.924479724 \tabularnewline
102 & 928200 & 872433.540271227 & 55766.4597287728 \tabularnewline
103 & 1219400 & 1291905.45872253 & -72505.4587225269 \tabularnewline
104 & 1401400 & 1284624.85544307 & 116775.144556926 \tabularnewline
105 & 1037400 & 975403.546626552 & 61996.4533734475 \tabularnewline
106 & 1164800 & 1271671.69036739 & -106871.690367387 \tabularnewline
107 & 873600 & 946347.237810505 & -72747.237810505 \tabularnewline
108 & 1510600 & 1471478.86979222 & 39121.1302077798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307469&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]1092000[/C][C]1129343.05555556[/C][C]-37343.0555555557[/C][/ROW]
[ROW][C]14[/C][C]819000[/C][C]855433.949342192[/C][C]-36433.9493421924[/C][/ROW]
[ROW][C]15[/C][C]964600[/C][C]1008895.84094694[/C][C]-44295.8409469364[/C][/ROW]
[ROW][C]16[/C][C]728000[/C][C]770574.690086162[/C][C]-42574.6900861622[/C][/ROW]
[ROW][C]17[/C][C]1019200[/C][C]1046025.1869975[/C][C]-26825.1869974993[/C][/ROW]
[ROW][C]18[/C][C]837200[/C][C]848173.109939438[/C][C]-10973.1099394384[/C][/ROW]
[ROW][C]19[/C][C]1110200[/C][C]1060624.55123697[/C][C]49575.4487630331[/C][/ROW]
[ROW][C]20[/C][C]1001000[/C][C]1092095.87145707[/C][C]-91095.8714570715[/C][/ROW]
[ROW][C]21[/C][C]1055600[/C][C]1218487.41925961[/C][C]-162887.41925961[/C][/ROW]
[ROW][C]22[/C][C]1183000[/C][C]1049230.56148432[/C][C]133769.438515684[/C][/ROW]
[ROW][C]23[/C][C]1164800[/C][C]992401.628389841[/C][C]172398.371610159[/C][/ROW]
[ROW][C]24[/C][C]1383200[/C][C]1251477.05842753[/C][C]131722.941572472[/C][/ROW]
[ROW][C]25[/C][C]1001000[/C][C]1020480.18033663[/C][C]-19480.1803366283[/C][/ROW]
[ROW][C]26[/C][C]837200[/C][C]748063.852173472[/C][C]89136.1478265278[/C][/ROW]
[ROW][C]27[/C][C]928200[/C][C]897099.472841443[/C][C]31100.527158557[/C][/ROW]
[ROW][C]28[/C][C]673400[/C][C]663413.13755475[/C][C]9986.86244525039[/C][/ROW]
[ROW][C]29[/C][C]964600[/C][C]956696.081899116[/C][C]7903.91810088418[/C][/ROW]
[ROW][C]30[/C][C]746200[/C][C]776927.422183349[/C][C]-30727.4221833491[/C][/ROW]
[ROW][C]31[/C][C]1055600[/C][C]1047947.26709516[/C][C]7652.73290484468[/C][/ROW]
[ROW][C]32[/C][C]1001000[/C][C]952038.156662105[/C][C]48961.843337895[/C][/ROW]
[ROW][C]33[/C][C]891800[/C][C]1017480.87324034[/C][C]-125680.873240338[/C][/ROW]
[ROW][C]34[/C][C]1274000[/C][C]1126066.38459215[/C][C]147933.615407848[/C][/ROW]
[ROW][C]35[/C][C]1146600[/C][C]1109313.14528483[/C][C]37286.8547151743[/C][/ROW]
[ROW][C]36[/C][C]1310400[/C][C]1332778.66824494[/C][C]-22378.6682449421[/C][/ROW]
[ROW][C]37[/C][C]982800[/C][C]962755.395713171[/C][C]20044.6042868287[/C][/ROW]
[ROW][C]38[/C][C]910000[/C][C]792806.660016306[/C][C]117193.339983694[/C][/ROW]
[ROW][C]39[/C][C]819000[/C][C]890950.758787502[/C][C]-71950.7587875018[/C][/ROW]
[ROW][C]40[/C][C]673400[/C][C]638215.254658062[/C][C]35184.7453419378[/C][/ROW]
[ROW][C]41[/C][C]891800[/C][C]931400.429640199[/C][C]-39600.4296401989[/C][/ROW]
[ROW][C]42[/C][C]800800[/C][C]716753.902624761[/C][C]84046.0973752385[/C][/ROW]
[ROW][C]43[/C][C]1092000[/C][C]1026401.44949721[/C][C]65598.5505027917[/C][/ROW]
[ROW][C]44[/C][C]1055600[/C][C]971828.426360033[/C][C]83771.573639967[/C][/ROW]
[ROW][C]45[/C][C]910000[/C][C]879789.617649113[/C][C]30210.3823508872[/C][/ROW]
[ROW][C]46[/C][C]1219400[/C][C]1246374.3512446[/C][C]-26974.3512445986[/C][/ROW]
[ROW][C]47[/C][C]1128400[/C][C]1128971.61296387[/C][C]-571.612963865744[/C][/ROW]
[ROW][C]48[/C][C]1456000[/C][C]1299668.03175823[/C][C]156331.968241773[/C][/ROW]
[ROW][C]49[/C][C]1164800[/C][C]974576.311393348[/C][C]190223.688606652[/C][/ROW]
[ROW][C]50[/C][C]709800[/C][C]901466.966659358[/C][C]-191666.966659358[/C][/ROW]
[ROW][C]51[/C][C]709800[/C][C]825432.673935911[/C][C]-115632.673935911[/C][/ROW]
[ROW][C]52[/C][C]709800[/C][C]673490.385461999[/C][C]36309.6145380009[/C][/ROW]
[ROW][C]53[/C][C]837200[/C][C]900316.49293824[/C][C]-63116.4929382396[/C][/ROW]
[ROW][C]54[/C][C]837200[/C][C]801651.83089491[/C][C]35548.1691050897[/C][/ROW]
[ROW][C]55[/C][C]1128400[/C][C]1095709.65867342[/C][C]32690.3413265818[/C][/ROW]
[ROW][C]56[/C][C]1037400[/C][C]1059119.85284526[/C][C]-21719.8528452599[/C][/ROW]
[ROW][C]57[/C][C]928200[/C][C]917336.543076398[/C][C]10863.4569236021[/C][/ROW]
[ROW][C]58[/C][C]1164800[/C][C]1231457.54588778[/C][C]-66657.5458877764[/C][/ROW]
[ROW][C]59[/C][C]1073800[/C][C]1138032.48271037[/C][C]-64232.4827103659[/C][/ROW]
[ROW][C]60[/C][C]1547000[/C][C]1452106.8178611[/C][C]94893.182138901[/C][/ROW]
[ROW][C]61[/C][C]1219400[/C][C]1156531.25359398[/C][C]62868.7464060208[/C][/ROW]
[ROW][C]62[/C][C]709800[/C][C]728146.939045149[/C][C]-18346.9390451491[/C][/ROW]
[ROW][C]63[/C][C]746200[/C][C]723048.600747897[/C][C]23151.3992521026[/C][/ROW]
[ROW][C]64[/C][C]618800[/C][C]712930.975385136[/C][C]-94130.9753851364[/C][/ROW]
[ROW][C]65[/C][C]855400[/C][C]846330.396234893[/C][C]9069.60376510653[/C][/ROW]
[ROW][C]66[/C][C]982800[/C][C]839257.010624342[/C][C]143542.989375658[/C][/ROW]
[ROW][C]67[/C][C]1237600[/C][C]1132719.66602448[/C][C]104880.333975519[/C][/ROW]
[ROW][C]68[/C][C]1219400[/C][C]1048383.78973046[/C][C]171016.210269541[/C][/ROW]
[ROW][C]69[/C][C]982800[/C][C]941890.52416453[/C][C]40909.4758354702[/C][/ROW]
[ROW][C]70[/C][C]1146600[/C][C]1188649.67644683[/C][C]-42049.6764468309[/C][/ROW]
[ROW][C]71[/C][C]1019200[/C][C]1101683.24471249[/C][C]-82483.2447124945[/C][/ROW]
[ROW][C]72[/C][C]1456000[/C][C]1565996.2578522[/C][C]-109996.257852199[/C][/ROW]
[ROW][C]73[/C][C]1110200[/C][C]1240953.93787939[/C][C]-130753.937879393[/C][/ROW]
[ROW][C]74[/C][C]891800[/C][C]736101.128771328[/C][C]155698.871228672[/C][/ROW]
[ROW][C]75[/C][C]800800[/C][C]772590.201260797[/C][C]28209.7987392035[/C][/ROW]
[ROW][C]76[/C][C]600600[/C][C]656279.706748341[/C][C]-55679.7067483413[/C][/ROW]
[ROW][C]77[/C][C]891800[/C][C]887251.227817192[/C][C]4548.77218280756[/C][/ROW]
[ROW][C]78[/C][C]1073800[/C][C]1006117.29324493[/C][C]67682.7067550735[/C][/ROW]
[ROW][C]79[/C][C]1255800[/C][C]1264670.52930767[/C][C]-8870.52930766717[/C][/ROW]
[ROW][C]80[/C][C]1183000[/C][C]1240556.84597981[/C][C]-57556.8459798128[/C][/ROW]
[ROW][C]81[/C][C]873600[/C][C]1010335.10135432[/C][C]-136735.101354324[/C][/ROW]
[ROW][C]82[/C][C]1255800[/C][C]1175622.59942934[/C][C]80177.4005706583[/C][/ROW]
[ROW][C]83[/C][C]982800[/C][C]1050266.4246421[/C][C]-67466.4246421019[/C][/ROW]
[ROW][C]84[/C][C]1510600[/C][C]1487237.74515818[/C][C]23362.254841821[/C][/ROW]
[ROW][C]85[/C][C]1255800[/C][C]1143407.50323543[/C][C]112392.49676457[/C][/ROW]
[ROW][C]86[/C][C]910000[/C][C]906024.721840959[/C][C]3975.27815904096[/C][/ROW]
[ROW][C]87[/C][C]837200[/C][C]823615.896070419[/C][C]13584.1039295814[/C][/ROW]
[ROW][C]88[/C][C]564200[/C][C]629703.825306763[/C][C]-65503.8253067634[/C][/ROW]
[ROW][C]89[/C][C]891800[/C][C]915782.670562711[/C][C]-23982.6705627111[/C][/ROW]
[ROW][C]90[/C][C]855400[/C][C]1091994.95648914[/C][C]-236594.956489143[/C][/ROW]
[ROW][C]91[/C][C]1292200[/C][C]1273848.76778262[/C][C]18351.2322173845[/C][/ROW]
[ROW][C]92[/C][C]1292200[/C][C]1202027.675363[/C][C]90172.3246369986[/C][/ROW]
[ROW][C]93[/C][C]982800[/C][C]898494.821299313[/C][C]84305.1787006874[/C][/ROW]
[ROW][C]94[/C][C]1274000[/C][C]1265943.58338103[/C][C]8056.41661897232[/C][/ROW]
[ROW][C]95[/C][C]946400[/C][C]1003551.79699648[/C][C]-57151.7969964843[/C][/ROW]
[ROW][C]96[/C][C]1474200[/C][C]1524017.30692489[/C][C]-49817.306924887[/C][/ROW]
[ROW][C]97[/C][C]1255800[/C][C]1260573.62474646[/C][C]-4773.62474645558[/C][/ROW]
[ROW][C]98[/C][C]928200[/C][C]920204.656528011[/C][C]7995.34347198938[/C][/ROW]
[ROW][C]99[/C][C]709800[/C][C]844689.82162921[/C][C]-134889.82162921[/C][/ROW]
[ROW][C]100[/C][C]491400[/C][C]573180.708205433[/C][C]-81780.7082054331[/C][/ROW]
[ROW][C]101[/C][C]964600[/C][C]893836.075520276[/C][C]70763.924479724[/C][/ROW]
[ROW][C]102[/C][C]928200[/C][C]872433.540271227[/C][C]55766.4597287728[/C][/ROW]
[ROW][C]103[/C][C]1219400[/C][C]1291905.45872253[/C][C]-72505.4587225269[/C][/ROW]
[ROW][C]104[/C][C]1401400[/C][C]1284624.85544307[/C][C]116775.144556926[/C][/ROW]
[ROW][C]105[/C][C]1037400[/C][C]975403.546626552[/C][C]61996.4533734475[/C][/ROW]
[ROW][C]106[/C][C]1164800[/C][C]1271671.69036739[/C][C]-106871.690367387[/C][/ROW]
[ROW][C]107[/C][C]873600[/C][C]946347.237810505[/C][C]-72747.237810505[/C][/ROW]
[ROW][C]108[/C][C]1510600[/C][C]1471478.86979222[/C][C]39121.1302077798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307469&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307469&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
1310920001129343.05555556-37343.0555555557
14819000855433.949342192-36433.9493421924
159646001008895.84094694-44295.8409469364
16728000770574.690086162-42574.6900861622
1710192001046025.1869975-26825.1869974993
18837200848173.109939438-10973.1099394384
1911102001060624.5512369749575.4487630331
2010010001092095.87145707-91095.8714570715
2110556001218487.41925961-162887.41925961
2211830001049230.56148432133769.438515684
231164800992401.628389841172398.371610159
2413832001251477.05842753131722.941572472
2510010001020480.18033663-19480.1803366283
26837200748063.85217347289136.1478265278
27928200897099.47284144331100.527158557
28673400663413.137554759986.86244525039
29964600956696.0818991167903.91810088418
30746200776927.422183349-30727.4221833491
3110556001047947.267095167652.73290484468
321001000952038.15666210548961.843337895
338918001017480.87324034-125680.873240338
3412740001126066.38459215147933.615407848
3511466001109313.1452848337286.8547151743
3613104001332778.66824494-22378.6682449421
37982800962755.39571317120044.6042868287
38910000792806.660016306117193.339983694
39819000890950.758787502-71950.7587875018
40673400638215.25465806235184.7453419378
41891800931400.429640199-39600.4296401989
42800800716753.90262476184046.0973752385
4310920001026401.4494972165598.5505027917
441055600971828.42636003383771.573639967
45910000879789.61764911330210.3823508872
4612194001246374.3512446-26974.3512445986
4711284001128971.61296387-571.612963865744
4814560001299668.03175823156331.968241773
491164800974576.311393348190223.688606652
50709800901466.966659358-191666.966659358
51709800825432.673935911-115632.673935911
52709800673490.38546199936309.6145380009
53837200900316.49293824-63116.4929382396
54837200801651.8308949135548.1691050897
5511284001095709.6586734232690.3413265818
5610374001059119.85284526-21719.8528452599
57928200917336.54307639810863.4569236021
5811648001231457.54588778-66657.5458877764
5910738001138032.48271037-64232.4827103659
6015470001452106.817861194893.182138901
6112194001156531.2535939862868.7464060208
62709800728146.939045149-18346.9390451491
63746200723048.60074789723151.3992521026
64618800712930.975385136-94130.9753851364
65855400846330.3962348939069.60376510653
66982800839257.010624342143542.989375658
6712376001132719.66602448104880.333975519
6812194001048383.78973046171016.210269541
69982800941890.5241645340909.4758354702
7011466001188649.67644683-42049.6764468309
7110192001101683.24471249-82483.2447124945
7214560001565996.2578522-109996.257852199
7311102001240953.93787939-130753.937879393
74891800736101.128771328155698.871228672
75800800772590.20126079728209.7987392035
76600600656279.706748341-55679.7067483413
77891800887251.2278171924548.77218280756
7810738001006117.2932449367682.7067550735
7912558001264670.52930767-8870.52930766717
8011830001240556.84597981-57556.8459798128
818736001010335.10135432-136735.101354324
8212558001175622.5994293480177.4005706583
839828001050266.4246421-67466.4246421019
8415106001487237.7451581823362.254841821
8512558001143407.50323543112392.49676457
86910000906024.7218409593975.27815904096
87837200823615.89607041913584.1039295814
88564200629703.825306763-65503.8253067634
89891800915782.670562711-23982.6705627111
908554001091994.95648914-236594.956489143
9112922001273848.7677826218351.2322173845
9212922001202027.67536390172.3246369986
93982800898494.82129931384305.1787006874
9412740001265943.583381038056.41661897232
959464001003551.79699648-57151.7969964843
9614742001524017.30692489-49817.306924887
9712558001260573.62474646-4773.62474645558
98928200920204.6565280117995.34347198938
99709800844689.82162921-134889.82162921
100491400573180.708205433-81780.7082054331
101964600893836.07552027670763.924479724
102928200872433.54027122755766.4597287728
10312194001291905.45872253-72505.4587225269
10414014001284624.85544307116775.144556926
1051037400975403.54662655261996.4533734475
10611648001271671.69036739-106871.690367387
107873600946347.237810505-72747.237810505
10815106001471478.8697922239121.1302077798







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091249229.211745091082403.160061421416055.26342876
110919588.904425388752734.2379992821086443.57085149
111711228.398818231544309.367156985878147.430479477
112489987.812089231322954.414584576657021.209593885
113952773.049908949785561.1123694051119984.98744849
114917099.561945767749630.8611507441084568.26274079
1151217579.304268141049761.751412121385396.85712416
1161385681.965113971217409.857943881553954.07228406
1171024192.34206586855346.6940481791193037.99008355
1181163030.92976084993479.8827288711332581.9767928
119869818.826106921699418.1505485921040219.50166525
1201499034.919137911327628.60364251670441.23463333

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1249229.21174509 & 1082403.16006142 & 1416055.26342876 \tabularnewline
110 & 919588.904425388 & 752734.237999282 & 1086443.57085149 \tabularnewline
111 & 711228.398818231 & 544309.367156985 & 878147.430479477 \tabularnewline
112 & 489987.812089231 & 322954.414584576 & 657021.209593885 \tabularnewline
113 & 952773.049908949 & 785561.112369405 & 1119984.98744849 \tabularnewline
114 & 917099.561945767 & 749630.861150744 & 1084568.26274079 \tabularnewline
115 & 1217579.30426814 & 1049761.75141212 & 1385396.85712416 \tabularnewline
116 & 1385681.96511397 & 1217409.85794388 & 1553954.07228406 \tabularnewline
117 & 1024192.34206586 & 855346.694048179 & 1193037.99008355 \tabularnewline
118 & 1163030.92976084 & 993479.882728871 & 1332581.9767928 \tabularnewline
119 & 869818.826106921 & 699418.150548592 & 1040219.50166525 \tabularnewline
120 & 1499034.91913791 & 1327628.6036425 & 1670441.23463333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307469&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]1249229.21174509[/C][C]1082403.16006142[/C][C]1416055.26342876[/C][/ROW]
[ROW][C]110[/C][C]919588.904425388[/C][C]752734.237999282[/C][C]1086443.57085149[/C][/ROW]
[ROW][C]111[/C][C]711228.398818231[/C][C]544309.367156985[/C][C]878147.430479477[/C][/ROW]
[ROW][C]112[/C][C]489987.812089231[/C][C]322954.414584576[/C][C]657021.209593885[/C][/ROW]
[ROW][C]113[/C][C]952773.049908949[/C][C]785561.112369405[/C][C]1119984.98744849[/C][/ROW]
[ROW][C]114[/C][C]917099.561945767[/C][C]749630.861150744[/C][C]1084568.26274079[/C][/ROW]
[ROW][C]115[/C][C]1217579.30426814[/C][C]1049761.75141212[/C][C]1385396.85712416[/C][/ROW]
[ROW][C]116[/C][C]1385681.96511397[/C][C]1217409.85794388[/C][C]1553954.07228406[/C][/ROW]
[ROW][C]117[/C][C]1024192.34206586[/C][C]855346.694048179[/C][C]1193037.99008355[/C][/ROW]
[ROW][C]118[/C][C]1163030.92976084[/C][C]993479.882728871[/C][C]1332581.9767928[/C][/ROW]
[ROW][C]119[/C][C]869818.826106921[/C][C]699418.150548592[/C][C]1040219.50166525[/C][/ROW]
[ROW][C]120[/C][C]1499034.91913791[/C][C]1327628.6036425[/C][C]1670441.23463333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307469&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307469&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
1091249229.211745091082403.160061421416055.26342876
110919588.904425388752734.2379992821086443.57085149
111711228.398818231544309.367156985878147.430479477
112489987.812089231322954.414584576657021.209593885
113952773.049908949785561.1123694051119984.98744849
114917099.561945767749630.8611507441084568.26274079
1151217579.304268141049761.751412121385396.85712416
1161385681.965113971217409.857943881553954.07228406
1171024192.34206586855346.6940481791193037.99008355
1181163030.92976084993479.8827288711332581.9767928
119869818.826106921699418.1505485921040219.50166525
1201499034.919137911327628.60364251670441.23463333



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
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')