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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 27 Nov 2010 13:02:33 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/27/t1290862881mc63hzbml9zrxhb.htm/, Retrieved Mon, 29 Apr 2024 16:25:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102370, Retrieved Mon, 29 Apr 2024 16:25:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact231

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Workshop 8 Regres...] [2010-11-27 09:22:21] [87d60b8864dc39f7ed759c345edfb471]
- RMP   [Spectral Analysis] [Workshop 8 Regres...] [2010-11-27 12:28:23] [87d60b8864dc39f7ed759c345edfb471]
- RMP       [Exponential Smoothing] [Workshop 8 Regres...] [2010-11-27 13:02:33] [c52f616cc59ab01e55ce1a10b5754887] [Current]
-   P         [Exponential Smoothing] [Workshop 8 Regres...] [2010-11-27 13:15:31] [87d60b8864dc39f7ed759c345edfb471]
-   P           [Exponential Smoothing] [Workshop 8 Regres...] [2010-11-27 13:17:03] [87d60b8864dc39f7ed759c345edfb471]
- R  D          [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:11:22] [033eb2749a430605d9b2be7c4aac4a0c]
-   P             [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:21:35] [033eb2749a430605d9b2be7c4aac4a0c]
-   P               [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:23:28] [033eb2749a430605d9b2be7c4aac4a0c]
- RMP             [Multiple Regression] [ws 8 - werklooshe...] [2010-11-29 10:16:03] [033eb2749a430605d9b2be7c4aac4a0c]
- R  D              [Multiple Regression] [ws 8 multiple regr] [2010-11-30 16:05:15] [4eaa304e6a28c475ba490fccf4c01ad3]
- R  D            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:56:04] [48146708a479232c43a8f6e52fbf83b4]
- R PD            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:57:52] [48146708a479232c43a8f6e52fbf83b4]
- R PD            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:59:42] [48146708a479232c43a8f6e52fbf83b4]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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25
17
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102370&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102370&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.098155242834915
beta0.0343410839300175
gamma0.291862308416832

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.098155242834915 \tabularnewline
beta & 0.0343410839300175 \tabularnewline
gamma & 0.291862308416832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102370&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]0.098155242834915[/C][/ROW]
[ROW][C]beta[/C][C]0.0343410839300175[/C][/ROW]
[ROW][C]gamma[/C][C]0.291862308416832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102370&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.098155242834915
beta0.0343410839300175
gamma0.291862308416832






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132323.9407051282051-0.940705128205131
141818.4734042273127-0.47340422731267
151514.67537562900660.324624370993439
161210.87343861823431.12656138176569
172119.61234662797671.38765337202334
181514.04822629500890.951773704991053
192021.5695302857669-1.56953028576691
203118.00473123184212.995268768158
212721.95501413134935.04498586865068
223422.100273839195511.8997261608045
232129.7501400020546-8.75014000205462
243136.1352856044103-5.13528560441032
251928.7353310927983-9.73533109279827
261622.5549834855285-6.55498348552847
272018.37676073373011.6232392662699
282114.92444038538496.07555961461514
292224.245592945388-2.24559294538802
301718.2256250315818-1.22562503158176
312424.8777271260046-0.877727126004594
322525.2249952297038-0.224995229703811
332625.75094477994750.249055220052501
342527.1794943734804-2.17949437348036
351727.9143781778676-10.9143781778676
363234.9335903984696-2.93359039846963
373326.44138243111706.55861756888296
381322.6548450980675-9.65484509806753
393220.271892752503511.7281072474965
402518.96430579826406.03569420173602
412926.07213541486732.92786458513271
422220.82671629395751.17328370604254
431827.8122182439617-9.81221824396166
441727.430574310146-10.430574310146
452027.0214157974156-7.02141579741562
461527.0144401806347-12.0144401806347
472024.3690123524528-4.36901235245283
483334.0375962623899-1.03759626238988
492928.14261841147010.857381588529947
502319.42228068985923.57771931014081
512623.90450479883612.0954952011639
521820.0586595880739-2.05865958807387
532025.4322347737117-5.43223477371167
541118.7544917138134-7.75449171381337
552821.79214377139456.20785622860549
562622.6941950387913.30580496120899
572224.4509772793287-2.45097727932865
581723.5140868067799-6.51408680677995
591223.3751842851588-11.3751842851588
601433.163585956078-19.163585956078
611725.8577677766990-8.85776777669897
622116.73665706921084.26334293078918
631920.7351344812155-1.73513448121549
641815.24604563191872.75395436808126
651020.0464388758477-10.0464388758477
662912.131391094419516.8686089055805
673121.17087568698999.8291243130101
681921.5865716512114-2.58657165121142
69921.1519161460759-12.1519161460759
702018.06285726704951.93714273295050
712817.371961888000410.6280381119996
721927.2422284888402-8.24222848884021
733023.73000624094746.26999375905261
742919.60738988685919.3926101131409
752622.60769383976263.39230616023736
762318.89801503815524.10198496184484
771320.5605510453933-7.56055104539328
782120.0813916657840.918608334216017
791925.7560969619197-6.75609696191973
802821.27366188079346.72633811920658
812319.26455804777123.73544195222881
821821.5261016266073-3.52610162660731
832122.6508449980264-1.65084499802639
842026.3718732685513-6.37187326855135
852326.892293994386-3.89229399438598
862122.5890896770853-1.58908967708532
872122.890074592955-1.89007459295501
881518.7888538806877-3.78885388068774
892816.520669792417511.4793302075825
901920.1199466417961-1.11994664179613
912623.54532637082492.45467362917508
921023.5176592493214-13.5176592493214
931618.6679263427215-2.66792634272150
942218.30169066257133.69830933742869
951920.5655827255514-1.56558272555139
963122.98906442946358.01093557053652
973125.55910296538545.4408970346146
982922.79490547403916.20509452596095
991923.8246475836695-4.82464758366946
1002218.96864592880863.03135407119143
1012321.44474661233481.5552533876652
1021520.7761976475165-5.77619764751653
1032024.6923253165335-4.69232531653347
1041819.7417940100302-1.74179401003025
1052318.92622527063174.07377472936827
1062520.94262734257434.05737265742570
1072121.9026599410408-0.902659941040831
1082426.9605532153950-2.96055321539497
1092527.7888928073504-2.78889280735043
1101724.4019871167118-7.40198711671178
1111321.1310096444457-8.13100964444574
1122817.945214558607310.0547854413927
1132120.67277489485180.327225105148205
1142517.90040909917987.0995909008202
115923.3555197336149-14.3555197336149
1161618.1904114571158-2.19041145711583
1171918.81733198158930.182668018410684
1181720.3901497325718-3.39014973257184
1192519.23117817309495.76882182690513
1202024.3422946477942-4.34229464779417
1212925.01558468742873.98441531257131
1221421.0375047068512-7.03750470685117
1232217.56986566603594.43013433396406
1241520.4055699810182-5.40556998101823
1251919.0048598459936-0.00485984599361799
1262017.93104294875192.06895705124815
1271517.1766773394644-2.17667733946443
1282016.38167392627843.61832607372156
1291818.195616076569-0.195616076569014
1303318.781845417454014.2181545825460
1312221.81230818769010.187691812309911
1321623.7457153533617-7.7457153533617
1331726.2966806952366-9.29668069523663
1341618.0891232220929-2.08912322209294
1352118.11758315059942.88241684940057
1362618.19919456952167.80080543047845
1371819.5475436969447-1.54754369694466
1381818.8942020398857-0.894202039885734
1391716.74752532346290.252474676537052
1402217.74052387705034.25947612294967
1413018.639913656683711.3600863433163
1423024.21966081458245.78033918541763
1432422.76579650521211.23420349478794
1442122.7541739536077-1.7541739536077
1452125.5456373902177-4.54563739021775
1462919.77820137382079.22179862617935
1473122.34024341838748.65975658161259
1482024.4177706252788-4.41777062527876
1491622.1992440725596-6.19924407255963
1502221.33866546720800.661334532791972
1512019.72912092631150.270879073688477
1522821.86131503287216.13868496712787
1533824.903165098947713.0968349010523
1542229.2795896433223-7.27958964332232
1552025.3980709242075-5.39807092420746
1561723.9773706994309-6.97737069943092
1572825.53228931651032.46771068348967
1582224.1115721224774-2.11157212247739
1593125.40957800659395.59042199340615

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 23 & 23.9407051282051 & -0.940705128205131 \tabularnewline
14 & 18 & 18.4734042273127 & -0.47340422731267 \tabularnewline
15 & 15 & 14.6753756290066 & 0.324624370993439 \tabularnewline
16 & 12 & 10.8734386182343 & 1.12656138176569 \tabularnewline
17 & 21 & 19.6123466279767 & 1.38765337202334 \tabularnewline
18 & 15 & 14.0482262950089 & 0.951773704991053 \tabularnewline
19 & 20 & 21.5695302857669 & -1.56953028576691 \tabularnewline
20 & 31 & 18.004731231842 & 12.995268768158 \tabularnewline
21 & 27 & 21.9550141313493 & 5.04498586865068 \tabularnewline
22 & 34 & 22.1002738391955 & 11.8997261608045 \tabularnewline
23 & 21 & 29.7501400020546 & -8.75014000205462 \tabularnewline
24 & 31 & 36.1352856044103 & -5.13528560441032 \tabularnewline
25 & 19 & 28.7353310927983 & -9.73533109279827 \tabularnewline
26 & 16 & 22.5549834855285 & -6.55498348552847 \tabularnewline
27 & 20 & 18.3767607337301 & 1.6232392662699 \tabularnewline
28 & 21 & 14.9244403853849 & 6.07555961461514 \tabularnewline
29 & 22 & 24.245592945388 & -2.24559294538802 \tabularnewline
30 & 17 & 18.2256250315818 & -1.22562503158176 \tabularnewline
31 & 24 & 24.8777271260046 & -0.877727126004594 \tabularnewline
32 & 25 & 25.2249952297038 & -0.224995229703811 \tabularnewline
33 & 26 & 25.7509447799475 & 0.249055220052501 \tabularnewline
34 & 25 & 27.1794943734804 & -2.17949437348036 \tabularnewline
35 & 17 & 27.9143781778676 & -10.9143781778676 \tabularnewline
36 & 32 & 34.9335903984696 & -2.93359039846963 \tabularnewline
37 & 33 & 26.4413824311170 & 6.55861756888296 \tabularnewline
38 & 13 & 22.6548450980675 & -9.65484509806753 \tabularnewline
39 & 32 & 20.2718927525035 & 11.7281072474965 \tabularnewline
40 & 25 & 18.9643057982640 & 6.03569420173602 \tabularnewline
41 & 29 & 26.0721354148673 & 2.92786458513271 \tabularnewline
42 & 22 & 20.8267162939575 & 1.17328370604254 \tabularnewline
43 & 18 & 27.8122182439617 & -9.81221824396166 \tabularnewline
44 & 17 & 27.430574310146 & -10.430574310146 \tabularnewline
45 & 20 & 27.0214157974156 & -7.02141579741562 \tabularnewline
46 & 15 & 27.0144401806347 & -12.0144401806347 \tabularnewline
47 & 20 & 24.3690123524528 & -4.36901235245283 \tabularnewline
48 & 33 & 34.0375962623899 & -1.03759626238988 \tabularnewline
49 & 29 & 28.1426184114701 & 0.857381588529947 \tabularnewline
50 & 23 & 19.4222806898592 & 3.57771931014081 \tabularnewline
51 & 26 & 23.9045047988361 & 2.0954952011639 \tabularnewline
52 & 18 & 20.0586595880739 & -2.05865958807387 \tabularnewline
53 & 20 & 25.4322347737117 & -5.43223477371167 \tabularnewline
54 & 11 & 18.7544917138134 & -7.75449171381337 \tabularnewline
55 & 28 & 21.7921437713945 & 6.20785622860549 \tabularnewline
56 & 26 & 22.694195038791 & 3.30580496120899 \tabularnewline
57 & 22 & 24.4509772793287 & -2.45097727932865 \tabularnewline
58 & 17 & 23.5140868067799 & -6.51408680677995 \tabularnewline
59 & 12 & 23.3751842851588 & -11.3751842851588 \tabularnewline
60 & 14 & 33.163585956078 & -19.163585956078 \tabularnewline
61 & 17 & 25.8577677766990 & -8.85776777669897 \tabularnewline
62 & 21 & 16.7366570692108 & 4.26334293078918 \tabularnewline
63 & 19 & 20.7351344812155 & -1.73513448121549 \tabularnewline
64 & 18 & 15.2460456319187 & 2.75395436808126 \tabularnewline
65 & 10 & 20.0464388758477 & -10.0464388758477 \tabularnewline
66 & 29 & 12.1313910944195 & 16.8686089055805 \tabularnewline
67 & 31 & 21.1708756869899 & 9.8291243130101 \tabularnewline
68 & 19 & 21.5865716512114 & -2.58657165121142 \tabularnewline
69 & 9 & 21.1519161460759 & -12.1519161460759 \tabularnewline
70 & 20 & 18.0628572670495 & 1.93714273295050 \tabularnewline
71 & 28 & 17.3719618880004 & 10.6280381119996 \tabularnewline
72 & 19 & 27.2422284888402 & -8.24222848884021 \tabularnewline
73 & 30 & 23.7300062409474 & 6.26999375905261 \tabularnewline
74 & 29 & 19.6073898868591 & 9.3926101131409 \tabularnewline
75 & 26 & 22.6076938397626 & 3.39230616023736 \tabularnewline
76 & 23 & 18.8980150381552 & 4.10198496184484 \tabularnewline
77 & 13 & 20.5605510453933 & -7.56055104539328 \tabularnewline
78 & 21 & 20.081391665784 & 0.918608334216017 \tabularnewline
79 & 19 & 25.7560969619197 & -6.75609696191973 \tabularnewline
80 & 28 & 21.2736618807934 & 6.72633811920658 \tabularnewline
81 & 23 & 19.2645580477712 & 3.73544195222881 \tabularnewline
82 & 18 & 21.5261016266073 & -3.52610162660731 \tabularnewline
83 & 21 & 22.6508449980264 & -1.65084499802639 \tabularnewline
84 & 20 & 26.3718732685513 & -6.37187326855135 \tabularnewline
85 & 23 & 26.892293994386 & -3.89229399438598 \tabularnewline
86 & 21 & 22.5890896770853 & -1.58908967708532 \tabularnewline
87 & 21 & 22.890074592955 & -1.89007459295501 \tabularnewline
88 & 15 & 18.7888538806877 & -3.78885388068774 \tabularnewline
89 & 28 & 16.5206697924175 & 11.4793302075825 \tabularnewline
90 & 19 & 20.1199466417961 & -1.11994664179613 \tabularnewline
91 & 26 & 23.5453263708249 & 2.45467362917508 \tabularnewline
92 & 10 & 23.5176592493214 & -13.5176592493214 \tabularnewline
93 & 16 & 18.6679263427215 & -2.66792634272150 \tabularnewline
94 & 22 & 18.3016906625713 & 3.69830933742869 \tabularnewline
95 & 19 & 20.5655827255514 & -1.56558272555139 \tabularnewline
96 & 31 & 22.9890644294635 & 8.01093557053652 \tabularnewline
97 & 31 & 25.5591029653854 & 5.4408970346146 \tabularnewline
98 & 29 & 22.7949054740391 & 6.20509452596095 \tabularnewline
99 & 19 & 23.8246475836695 & -4.82464758366946 \tabularnewline
100 & 22 & 18.9686459288086 & 3.03135407119143 \tabularnewline
101 & 23 & 21.4447466123348 & 1.5552533876652 \tabularnewline
102 & 15 & 20.7761976475165 & -5.77619764751653 \tabularnewline
103 & 20 & 24.6923253165335 & -4.69232531653347 \tabularnewline
104 & 18 & 19.7417940100302 & -1.74179401003025 \tabularnewline
105 & 23 & 18.9262252706317 & 4.07377472936827 \tabularnewline
106 & 25 & 20.9426273425743 & 4.05737265742570 \tabularnewline
107 & 21 & 21.9026599410408 & -0.902659941040831 \tabularnewline
108 & 24 & 26.9605532153950 & -2.96055321539497 \tabularnewline
109 & 25 & 27.7888928073504 & -2.78889280735043 \tabularnewline
110 & 17 & 24.4019871167118 & -7.40198711671178 \tabularnewline
111 & 13 & 21.1310096444457 & -8.13100964444574 \tabularnewline
112 & 28 & 17.9452145586073 & 10.0547854413927 \tabularnewline
113 & 21 & 20.6727748948518 & 0.327225105148205 \tabularnewline
114 & 25 & 17.9004090991798 & 7.0995909008202 \tabularnewline
115 & 9 & 23.3555197336149 & -14.3555197336149 \tabularnewline
116 & 16 & 18.1904114571158 & -2.19041145711583 \tabularnewline
117 & 19 & 18.8173319815893 & 0.182668018410684 \tabularnewline
118 & 17 & 20.3901497325718 & -3.39014973257184 \tabularnewline
119 & 25 & 19.2311781730949 & 5.76882182690513 \tabularnewline
120 & 20 & 24.3422946477942 & -4.34229464779417 \tabularnewline
121 & 29 & 25.0155846874287 & 3.98441531257131 \tabularnewline
122 & 14 & 21.0375047068512 & -7.03750470685117 \tabularnewline
123 & 22 & 17.5698656660359 & 4.43013433396406 \tabularnewline
124 & 15 & 20.4055699810182 & -5.40556998101823 \tabularnewline
125 & 19 & 19.0048598459936 & -0.00485984599361799 \tabularnewline
126 & 20 & 17.9310429487519 & 2.06895705124815 \tabularnewline
127 & 15 & 17.1766773394644 & -2.17667733946443 \tabularnewline
128 & 20 & 16.3816739262784 & 3.61832607372156 \tabularnewline
129 & 18 & 18.195616076569 & -0.195616076569014 \tabularnewline
130 & 33 & 18.7818454174540 & 14.2181545825460 \tabularnewline
131 & 22 & 21.8123081876901 & 0.187691812309911 \tabularnewline
132 & 16 & 23.7457153533617 & -7.7457153533617 \tabularnewline
133 & 17 & 26.2966806952366 & -9.29668069523663 \tabularnewline
134 & 16 & 18.0891232220929 & -2.08912322209294 \tabularnewline
135 & 21 & 18.1175831505994 & 2.88241684940057 \tabularnewline
136 & 26 & 18.1991945695216 & 7.80080543047845 \tabularnewline
137 & 18 & 19.5475436969447 & -1.54754369694466 \tabularnewline
138 & 18 & 18.8942020398857 & -0.894202039885734 \tabularnewline
139 & 17 & 16.7475253234629 & 0.252474676537052 \tabularnewline
140 & 22 & 17.7405238770503 & 4.25947612294967 \tabularnewline
141 & 30 & 18.6399136566837 & 11.3600863433163 \tabularnewline
142 & 30 & 24.2196608145824 & 5.78033918541763 \tabularnewline
143 & 24 & 22.7657965052121 & 1.23420349478794 \tabularnewline
144 & 21 & 22.7541739536077 & -1.7541739536077 \tabularnewline
145 & 21 & 25.5456373902177 & -4.54563739021775 \tabularnewline
146 & 29 & 19.7782013738207 & 9.22179862617935 \tabularnewline
147 & 31 & 22.3402434183874 & 8.65975658161259 \tabularnewline
148 & 20 & 24.4177706252788 & -4.41777062527876 \tabularnewline
149 & 16 & 22.1992440725596 & -6.19924407255963 \tabularnewline
150 & 22 & 21.3386654672080 & 0.661334532791972 \tabularnewline
151 & 20 & 19.7291209263115 & 0.270879073688477 \tabularnewline
152 & 28 & 21.8613150328721 & 6.13868496712787 \tabularnewline
153 & 38 & 24.9031650989477 & 13.0968349010523 \tabularnewline
154 & 22 & 29.2795896433223 & -7.27958964332232 \tabularnewline
155 & 20 & 25.3980709242075 & -5.39807092420746 \tabularnewline
156 & 17 & 23.9773706994309 & -6.97737069943092 \tabularnewline
157 & 28 & 25.5322893165103 & 2.46771068348967 \tabularnewline
158 & 22 & 24.1115721224774 & -2.11157212247739 \tabularnewline
159 & 31 & 25.4095780065939 & 5.59042199340615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102370&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]23[/C][C]23.9407051282051[/C][C]-0.940705128205131[/C][/ROW]
[ROW][C]14[/C][C]18[/C][C]18.4734042273127[/C][C]-0.47340422731267[/C][/ROW]
[ROW][C]15[/C][C]15[/C][C]14.6753756290066[/C][C]0.324624370993439[/C][/ROW]
[ROW][C]16[/C][C]12[/C][C]10.8734386182343[/C][C]1.12656138176569[/C][/ROW]
[ROW][C]17[/C][C]21[/C][C]19.6123466279767[/C][C]1.38765337202334[/C][/ROW]
[ROW][C]18[/C][C]15[/C][C]14.0482262950089[/C][C]0.951773704991053[/C][/ROW]
[ROW][C]19[/C][C]20[/C][C]21.5695302857669[/C][C]-1.56953028576691[/C][/ROW]
[ROW][C]20[/C][C]31[/C][C]18.004731231842[/C][C]12.995268768158[/C][/ROW]
[ROW][C]21[/C][C]27[/C][C]21.9550141313493[/C][C]5.04498586865068[/C][/ROW]
[ROW][C]22[/C][C]34[/C][C]22.1002738391955[/C][C]11.8997261608045[/C][/ROW]
[ROW][C]23[/C][C]21[/C][C]29.7501400020546[/C][C]-8.75014000205462[/C][/ROW]
[ROW][C]24[/C][C]31[/C][C]36.1352856044103[/C][C]-5.13528560441032[/C][/ROW]
[ROW][C]25[/C][C]19[/C][C]28.7353310927983[/C][C]-9.73533109279827[/C][/ROW]
[ROW][C]26[/C][C]16[/C][C]22.5549834855285[/C][C]-6.55498348552847[/C][/ROW]
[ROW][C]27[/C][C]20[/C][C]18.3767607337301[/C][C]1.6232392662699[/C][/ROW]
[ROW][C]28[/C][C]21[/C][C]14.9244403853849[/C][C]6.07555961461514[/C][/ROW]
[ROW][C]29[/C][C]22[/C][C]24.245592945388[/C][C]-2.24559294538802[/C][/ROW]
[ROW][C]30[/C][C]17[/C][C]18.2256250315818[/C][C]-1.22562503158176[/C][/ROW]
[ROW][C]31[/C][C]24[/C][C]24.8777271260046[/C][C]-0.877727126004594[/C][/ROW]
[ROW][C]32[/C][C]25[/C][C]25.2249952297038[/C][C]-0.224995229703811[/C][/ROW]
[ROW][C]33[/C][C]26[/C][C]25.7509447799475[/C][C]0.249055220052501[/C][/ROW]
[ROW][C]34[/C][C]25[/C][C]27.1794943734804[/C][C]-2.17949437348036[/C][/ROW]
[ROW][C]35[/C][C]17[/C][C]27.9143781778676[/C][C]-10.9143781778676[/C][/ROW]
[ROW][C]36[/C][C]32[/C][C]34.9335903984696[/C][C]-2.93359039846963[/C][/ROW]
[ROW][C]37[/C][C]33[/C][C]26.4413824311170[/C][C]6.55861756888296[/C][/ROW]
[ROW][C]38[/C][C]13[/C][C]22.6548450980675[/C][C]-9.65484509806753[/C][/ROW]
[ROW][C]39[/C][C]32[/C][C]20.2718927525035[/C][C]11.7281072474965[/C][/ROW]
[ROW][C]40[/C][C]25[/C][C]18.9643057982640[/C][C]6.03569420173602[/C][/ROW]
[ROW][C]41[/C][C]29[/C][C]26.0721354148673[/C][C]2.92786458513271[/C][/ROW]
[ROW][C]42[/C][C]22[/C][C]20.8267162939575[/C][C]1.17328370604254[/C][/ROW]
[ROW][C]43[/C][C]18[/C][C]27.8122182439617[/C][C]-9.81221824396166[/C][/ROW]
[ROW][C]44[/C][C]17[/C][C]27.430574310146[/C][C]-10.430574310146[/C][/ROW]
[ROW][C]45[/C][C]20[/C][C]27.0214157974156[/C][C]-7.02141579741562[/C][/ROW]
[ROW][C]46[/C][C]15[/C][C]27.0144401806347[/C][C]-12.0144401806347[/C][/ROW]
[ROW][C]47[/C][C]20[/C][C]24.3690123524528[/C][C]-4.36901235245283[/C][/ROW]
[ROW][C]48[/C][C]33[/C][C]34.0375962623899[/C][C]-1.03759626238988[/C][/ROW]
[ROW][C]49[/C][C]29[/C][C]28.1426184114701[/C][C]0.857381588529947[/C][/ROW]
[ROW][C]50[/C][C]23[/C][C]19.4222806898592[/C][C]3.57771931014081[/C][/ROW]
[ROW][C]51[/C][C]26[/C][C]23.9045047988361[/C][C]2.0954952011639[/C][/ROW]
[ROW][C]52[/C][C]18[/C][C]20.0586595880739[/C][C]-2.05865958807387[/C][/ROW]
[ROW][C]53[/C][C]20[/C][C]25.4322347737117[/C][C]-5.43223477371167[/C][/ROW]
[ROW][C]54[/C][C]11[/C][C]18.7544917138134[/C][C]-7.75449171381337[/C][/ROW]
[ROW][C]55[/C][C]28[/C][C]21.7921437713945[/C][C]6.20785622860549[/C][/ROW]
[ROW][C]56[/C][C]26[/C][C]22.694195038791[/C][C]3.30580496120899[/C][/ROW]
[ROW][C]57[/C][C]22[/C][C]24.4509772793287[/C][C]-2.45097727932865[/C][/ROW]
[ROW][C]58[/C][C]17[/C][C]23.5140868067799[/C][C]-6.51408680677995[/C][/ROW]
[ROW][C]59[/C][C]12[/C][C]23.3751842851588[/C][C]-11.3751842851588[/C][/ROW]
[ROW][C]60[/C][C]14[/C][C]33.163585956078[/C][C]-19.163585956078[/C][/ROW]
[ROW][C]61[/C][C]17[/C][C]25.8577677766990[/C][C]-8.85776777669897[/C][/ROW]
[ROW][C]62[/C][C]21[/C][C]16.7366570692108[/C][C]4.26334293078918[/C][/ROW]
[ROW][C]63[/C][C]19[/C][C]20.7351344812155[/C][C]-1.73513448121549[/C][/ROW]
[ROW][C]64[/C][C]18[/C][C]15.2460456319187[/C][C]2.75395436808126[/C][/ROW]
[ROW][C]65[/C][C]10[/C][C]20.0464388758477[/C][C]-10.0464388758477[/C][/ROW]
[ROW][C]66[/C][C]29[/C][C]12.1313910944195[/C][C]16.8686089055805[/C][/ROW]
[ROW][C]67[/C][C]31[/C][C]21.1708756869899[/C][C]9.8291243130101[/C][/ROW]
[ROW][C]68[/C][C]19[/C][C]21.5865716512114[/C][C]-2.58657165121142[/C][/ROW]
[ROW][C]69[/C][C]9[/C][C]21.1519161460759[/C][C]-12.1519161460759[/C][/ROW]
[ROW][C]70[/C][C]20[/C][C]18.0628572670495[/C][C]1.93714273295050[/C][/ROW]
[ROW][C]71[/C][C]28[/C][C]17.3719618880004[/C][C]10.6280381119996[/C][/ROW]
[ROW][C]72[/C][C]19[/C][C]27.2422284888402[/C][C]-8.24222848884021[/C][/ROW]
[ROW][C]73[/C][C]30[/C][C]23.7300062409474[/C][C]6.26999375905261[/C][/ROW]
[ROW][C]74[/C][C]29[/C][C]19.6073898868591[/C][C]9.3926101131409[/C][/ROW]
[ROW][C]75[/C][C]26[/C][C]22.6076938397626[/C][C]3.39230616023736[/C][/ROW]
[ROW][C]76[/C][C]23[/C][C]18.8980150381552[/C][C]4.10198496184484[/C][/ROW]
[ROW][C]77[/C][C]13[/C][C]20.5605510453933[/C][C]-7.56055104539328[/C][/ROW]
[ROW][C]78[/C][C]21[/C][C]20.081391665784[/C][C]0.918608334216017[/C][/ROW]
[ROW][C]79[/C][C]19[/C][C]25.7560969619197[/C][C]-6.75609696191973[/C][/ROW]
[ROW][C]80[/C][C]28[/C][C]21.2736618807934[/C][C]6.72633811920658[/C][/ROW]
[ROW][C]81[/C][C]23[/C][C]19.2645580477712[/C][C]3.73544195222881[/C][/ROW]
[ROW][C]82[/C][C]18[/C][C]21.5261016266073[/C][C]-3.52610162660731[/C][/ROW]
[ROW][C]83[/C][C]21[/C][C]22.6508449980264[/C][C]-1.65084499802639[/C][/ROW]
[ROW][C]84[/C][C]20[/C][C]26.3718732685513[/C][C]-6.37187326855135[/C][/ROW]
[ROW][C]85[/C][C]23[/C][C]26.892293994386[/C][C]-3.89229399438598[/C][/ROW]
[ROW][C]86[/C][C]21[/C][C]22.5890896770853[/C][C]-1.58908967708532[/C][/ROW]
[ROW][C]87[/C][C]21[/C][C]22.890074592955[/C][C]-1.89007459295501[/C][/ROW]
[ROW][C]88[/C][C]15[/C][C]18.7888538806877[/C][C]-3.78885388068774[/C][/ROW]
[ROW][C]89[/C][C]28[/C][C]16.5206697924175[/C][C]11.4793302075825[/C][/ROW]
[ROW][C]90[/C][C]19[/C][C]20.1199466417961[/C][C]-1.11994664179613[/C][/ROW]
[ROW][C]91[/C][C]26[/C][C]23.5453263708249[/C][C]2.45467362917508[/C][/ROW]
[ROW][C]92[/C][C]10[/C][C]23.5176592493214[/C][C]-13.5176592493214[/C][/ROW]
[ROW][C]93[/C][C]16[/C][C]18.6679263427215[/C][C]-2.66792634272150[/C][/ROW]
[ROW][C]94[/C][C]22[/C][C]18.3016906625713[/C][C]3.69830933742869[/C][/ROW]
[ROW][C]95[/C][C]19[/C][C]20.5655827255514[/C][C]-1.56558272555139[/C][/ROW]
[ROW][C]96[/C][C]31[/C][C]22.9890644294635[/C][C]8.01093557053652[/C][/ROW]
[ROW][C]97[/C][C]31[/C][C]25.5591029653854[/C][C]5.4408970346146[/C][/ROW]
[ROW][C]98[/C][C]29[/C][C]22.7949054740391[/C][C]6.20509452596095[/C][/ROW]
[ROW][C]99[/C][C]19[/C][C]23.8246475836695[/C][C]-4.82464758366946[/C][/ROW]
[ROW][C]100[/C][C]22[/C][C]18.9686459288086[/C][C]3.03135407119143[/C][/ROW]
[ROW][C]101[/C][C]23[/C][C]21.4447466123348[/C][C]1.5552533876652[/C][/ROW]
[ROW][C]102[/C][C]15[/C][C]20.7761976475165[/C][C]-5.77619764751653[/C][/ROW]
[ROW][C]103[/C][C]20[/C][C]24.6923253165335[/C][C]-4.69232531653347[/C][/ROW]
[ROW][C]104[/C][C]18[/C][C]19.7417940100302[/C][C]-1.74179401003025[/C][/ROW]
[ROW][C]105[/C][C]23[/C][C]18.9262252706317[/C][C]4.07377472936827[/C][/ROW]
[ROW][C]106[/C][C]25[/C][C]20.9426273425743[/C][C]4.05737265742570[/C][/ROW]
[ROW][C]107[/C][C]21[/C][C]21.9026599410408[/C][C]-0.902659941040831[/C][/ROW]
[ROW][C]108[/C][C]24[/C][C]26.9605532153950[/C][C]-2.96055321539497[/C][/ROW]
[ROW][C]109[/C][C]25[/C][C]27.7888928073504[/C][C]-2.78889280735043[/C][/ROW]
[ROW][C]110[/C][C]17[/C][C]24.4019871167118[/C][C]-7.40198711671178[/C][/ROW]
[ROW][C]111[/C][C]13[/C][C]21.1310096444457[/C][C]-8.13100964444574[/C][/ROW]
[ROW][C]112[/C][C]28[/C][C]17.9452145586073[/C][C]10.0547854413927[/C][/ROW]
[ROW][C]113[/C][C]21[/C][C]20.6727748948518[/C][C]0.327225105148205[/C][/ROW]
[ROW][C]114[/C][C]25[/C][C]17.9004090991798[/C][C]7.0995909008202[/C][/ROW]
[ROW][C]115[/C][C]9[/C][C]23.3555197336149[/C][C]-14.3555197336149[/C][/ROW]
[ROW][C]116[/C][C]16[/C][C]18.1904114571158[/C][C]-2.19041145711583[/C][/ROW]
[ROW][C]117[/C][C]19[/C][C]18.8173319815893[/C][C]0.182668018410684[/C][/ROW]
[ROW][C]118[/C][C]17[/C][C]20.3901497325718[/C][C]-3.39014973257184[/C][/ROW]
[ROW][C]119[/C][C]25[/C][C]19.2311781730949[/C][C]5.76882182690513[/C][/ROW]
[ROW][C]120[/C][C]20[/C][C]24.3422946477942[/C][C]-4.34229464779417[/C][/ROW]
[ROW][C]121[/C][C]29[/C][C]25.0155846874287[/C][C]3.98441531257131[/C][/ROW]
[ROW][C]122[/C][C]14[/C][C]21.0375047068512[/C][C]-7.03750470685117[/C][/ROW]
[ROW][C]123[/C][C]22[/C][C]17.5698656660359[/C][C]4.43013433396406[/C][/ROW]
[ROW][C]124[/C][C]15[/C][C]20.4055699810182[/C][C]-5.40556998101823[/C][/ROW]
[ROW][C]125[/C][C]19[/C][C]19.0048598459936[/C][C]-0.00485984599361799[/C][/ROW]
[ROW][C]126[/C][C]20[/C][C]17.9310429487519[/C][C]2.06895705124815[/C][/ROW]
[ROW][C]127[/C][C]15[/C][C]17.1766773394644[/C][C]-2.17667733946443[/C][/ROW]
[ROW][C]128[/C][C]20[/C][C]16.3816739262784[/C][C]3.61832607372156[/C][/ROW]
[ROW][C]129[/C][C]18[/C][C]18.195616076569[/C][C]-0.195616076569014[/C][/ROW]
[ROW][C]130[/C][C]33[/C][C]18.7818454174540[/C][C]14.2181545825460[/C][/ROW]
[ROW][C]131[/C][C]22[/C][C]21.8123081876901[/C][C]0.187691812309911[/C][/ROW]
[ROW][C]132[/C][C]16[/C][C]23.7457153533617[/C][C]-7.7457153533617[/C][/ROW]
[ROW][C]133[/C][C]17[/C][C]26.2966806952366[/C][C]-9.29668069523663[/C][/ROW]
[ROW][C]134[/C][C]16[/C][C]18.0891232220929[/C][C]-2.08912322209294[/C][/ROW]
[ROW][C]135[/C][C]21[/C][C]18.1175831505994[/C][C]2.88241684940057[/C][/ROW]
[ROW][C]136[/C][C]26[/C][C]18.1991945695216[/C][C]7.80080543047845[/C][/ROW]
[ROW][C]137[/C][C]18[/C][C]19.5475436969447[/C][C]-1.54754369694466[/C][/ROW]
[ROW][C]138[/C][C]18[/C][C]18.8942020398857[/C][C]-0.894202039885734[/C][/ROW]
[ROW][C]139[/C][C]17[/C][C]16.7475253234629[/C][C]0.252474676537052[/C][/ROW]
[ROW][C]140[/C][C]22[/C][C]17.7405238770503[/C][C]4.25947612294967[/C][/ROW]
[ROW][C]141[/C][C]30[/C][C]18.6399136566837[/C][C]11.3600863433163[/C][/ROW]
[ROW][C]142[/C][C]30[/C][C]24.2196608145824[/C][C]5.78033918541763[/C][/ROW]
[ROW][C]143[/C][C]24[/C][C]22.7657965052121[/C][C]1.23420349478794[/C][/ROW]
[ROW][C]144[/C][C]21[/C][C]22.7541739536077[/C][C]-1.7541739536077[/C][/ROW]
[ROW][C]145[/C][C]21[/C][C]25.5456373902177[/C][C]-4.54563739021775[/C][/ROW]
[ROW][C]146[/C][C]29[/C][C]19.7782013738207[/C][C]9.22179862617935[/C][/ROW]
[ROW][C]147[/C][C]31[/C][C]22.3402434183874[/C][C]8.65975658161259[/C][/ROW]
[ROW][C]148[/C][C]20[/C][C]24.4177706252788[/C][C]-4.41777062527876[/C][/ROW]
[ROW][C]149[/C][C]16[/C][C]22.1992440725596[/C][C]-6.19924407255963[/C][/ROW]
[ROW][C]150[/C][C]22[/C][C]21.3386654672080[/C][C]0.661334532791972[/C][/ROW]
[ROW][C]151[/C][C]20[/C][C]19.7291209263115[/C][C]0.270879073688477[/C][/ROW]
[ROW][C]152[/C][C]28[/C][C]21.8613150328721[/C][C]6.13868496712787[/C][/ROW]
[ROW][C]153[/C][C]38[/C][C]24.9031650989477[/C][C]13.0968349010523[/C][/ROW]
[ROW][C]154[/C][C]22[/C][C]29.2795896433223[/C][C]-7.27958964332232[/C][/ROW]
[ROW][C]155[/C][C]20[/C][C]25.3980709242075[/C][C]-5.39807092420746[/C][/ROW]
[ROW][C]156[/C][C]17[/C][C]23.9773706994309[/C][C]-6.97737069943092[/C][/ROW]
[ROW][C]157[/C][C]28[/C][C]25.5322893165103[/C][C]2.46771068348967[/C][/ROW]
[ROW][C]158[/C][C]22[/C][C]24.1115721224774[/C][C]-2.11157212247739[/C][/ROW]
[ROW][C]159[/C][C]31[/C][C]25.4095780065939[/C][C]5.59042199340615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102370&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102370&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132323.9407051282051-0.940705128205131
141818.4734042273127-0.47340422731267
151514.67537562900660.324624370993439
161210.87343861823431.12656138176569
172119.61234662797671.38765337202334
181514.04822629500890.951773704991053
192021.5695302857669-1.56953028576691
203118.00473123184212.995268768158
212721.95501413134935.04498586865068
223422.100273839195511.8997261608045
232129.7501400020546-8.75014000205462
243136.1352856044103-5.13528560441032
251928.7353310927983-9.73533109279827
261622.5549834855285-6.55498348552847
272018.37676073373011.6232392662699
282114.92444038538496.07555961461514
292224.245592945388-2.24559294538802
301718.2256250315818-1.22562503158176
312424.8777271260046-0.877727126004594
322525.2249952297038-0.224995229703811
332625.75094477994750.249055220052501
342527.1794943734804-2.17949437348036
351727.9143781778676-10.9143781778676
363234.9335903984696-2.93359039846963
373326.44138243111706.55861756888296
381322.6548450980675-9.65484509806753
393220.271892752503511.7281072474965
402518.96430579826406.03569420173602
412926.07213541486732.92786458513271
422220.82671629395751.17328370604254
431827.8122182439617-9.81221824396166
441727.430574310146-10.430574310146
452027.0214157974156-7.02141579741562
461527.0144401806347-12.0144401806347
472024.3690123524528-4.36901235245283
483334.0375962623899-1.03759626238988
492928.14261841147010.857381588529947
502319.42228068985923.57771931014081
512623.90450479883612.0954952011639
521820.0586595880739-2.05865958807387
532025.4322347737117-5.43223477371167
541118.7544917138134-7.75449171381337
552821.79214377139456.20785622860549
562622.6941950387913.30580496120899
572224.4509772793287-2.45097727932865
581723.5140868067799-6.51408680677995
591223.3751842851588-11.3751842851588
601433.163585956078-19.163585956078
611725.8577677766990-8.85776777669897
622116.73665706921084.26334293078918
631920.7351344812155-1.73513448121549
641815.24604563191872.75395436808126
651020.0464388758477-10.0464388758477
662912.131391094419516.8686089055805
673121.17087568698999.8291243130101
681921.5865716512114-2.58657165121142
69921.1519161460759-12.1519161460759
702018.06285726704951.93714273295050
712817.371961888000410.6280381119996
721927.2422284888402-8.24222848884021
733023.73000624094746.26999375905261
742919.60738988685919.3926101131409
752622.60769383976263.39230616023736
762318.89801503815524.10198496184484
771320.5605510453933-7.56055104539328
782120.0813916657840.918608334216017
791925.7560969619197-6.75609696191973
802821.27366188079346.72633811920658
812319.26455804777123.73544195222881
821821.5261016266073-3.52610162660731
832122.6508449980264-1.65084499802639
842026.3718732685513-6.37187326855135
852326.892293994386-3.89229399438598
862122.5890896770853-1.58908967708532
872122.890074592955-1.89007459295501
881518.7888538806877-3.78885388068774
892816.520669792417511.4793302075825
901920.1199466417961-1.11994664179613
912623.54532637082492.45467362917508
921023.5176592493214-13.5176592493214
931618.6679263427215-2.66792634272150
942218.30169066257133.69830933742869
951920.5655827255514-1.56558272555139
963122.98906442946358.01093557053652
973125.55910296538545.4408970346146
982922.79490547403916.20509452596095
991923.8246475836695-4.82464758366946
1002218.96864592880863.03135407119143
1012321.44474661233481.5552533876652
1021520.7761976475165-5.77619764751653
1032024.6923253165335-4.69232531653347
1041819.7417940100302-1.74179401003025
1052318.92622527063174.07377472936827
1062520.94262734257434.05737265742570
1072121.9026599410408-0.902659941040831
1082426.9605532153950-2.96055321539497
1092527.7888928073504-2.78889280735043
1101724.4019871167118-7.40198711671178
1111321.1310096444457-8.13100964444574
1122817.945214558607310.0547854413927
1132120.67277489485180.327225105148205
1142517.90040909917987.0995909008202
115923.3555197336149-14.3555197336149
1161618.1904114571158-2.19041145711583
1171918.81733198158930.182668018410684
1181720.3901497325718-3.39014973257184
1192519.23117817309495.76882182690513
1202024.3422946477942-4.34229464779417
1212925.01558468742873.98441531257131
1221421.0375047068512-7.03750470685117
1232217.56986566603594.43013433396406
1241520.4055699810182-5.40556998101823
1251919.0048598459936-0.00485984599361799
1262017.93104294875192.06895705124815
1271517.1766773394644-2.17667733946443
1282016.38167392627843.61832607372156
1291818.195616076569-0.195616076569014
1303318.781845417454014.2181545825460
1312221.81230818769010.187691812309911
1321623.7457153533617-7.7457153533617
1331726.2966806952366-9.29668069523663
1341618.0891232220929-2.08912322209294
1352118.11758315059942.88241684940057
1362618.19919456952167.80080543047845
1371819.5475436969447-1.54754369694466
1381818.8942020398857-0.894202039885734
1391716.74752532346290.252474676537052
1402217.74052387705034.25947612294967
1413018.639913656683711.3600863433163
1423024.21966081458245.78033918541763
1432422.76579650521211.23420349478794
1442122.7541739536077-1.7541739536077
1452125.5456373902177-4.54563739021775
1462919.77820137382079.22179862617935
1473122.34024341838748.65975658161259
1482024.4177706252788-4.41777062527876
1491622.1992440725596-6.19924407255963
1502221.33866546720800.661334532791972
1512019.72912092631150.270879073688477
1522821.86131503287216.13868496712787
1533824.903165098947713.0968349010523
1542229.2795896433223-7.27958964332232
1552025.3980709242075-5.39807092420746
1561723.9773706994309-6.97737069943092
1572825.53228931651032.46771068348967
1582224.1115721224774-2.11157212247739
1593125.40957800659395.59042199340615






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
16023.729624469392011.097121554813836.3621273839703
16121.47669209550358.7792511462249334.1741330447821
16223.052178122410410.285780061279635.8185761835411
16321.29449000394978.455039292490734.1339407154087
16424.963217802541912.046548018448037.8798875866358
16529.231947983733316.233827466753142.2300685007136
16626.913271339817113.829408880263439.9971337993708
16724.219855306317011.045905850222437.3938047624115
16822.90983484389529.6414051889485636.1782644988419
16927.655745693848514.288400150667441.0230912370295
17024.799202516971311.328468510985738.2699365229570
17128.350590705698514.771964295910541.9292171154866

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
160 & 23.7296244693920 & 11.0971215548138 & 36.3621273839703 \tabularnewline
161 & 21.4766920955035 & 8.77925114622493 & 34.1741330447821 \tabularnewline
162 & 23.0521781224104 & 10.2857800612796 & 35.8185761835411 \tabularnewline
163 & 21.2944900039497 & 8.4550392924907 & 34.1339407154087 \tabularnewline
164 & 24.9632178025419 & 12.0465480184480 & 37.8798875866358 \tabularnewline
165 & 29.2319479837333 & 16.2338274667531 & 42.2300685007136 \tabularnewline
166 & 26.9132713398171 & 13.8294088802634 & 39.9971337993708 \tabularnewline
167 & 24.2198553063170 & 11.0459058502224 & 37.3938047624115 \tabularnewline
168 & 22.9098348438952 & 9.64140518894856 & 36.1782644988419 \tabularnewline
169 & 27.6557456938485 & 14.2884001506674 & 41.0230912370295 \tabularnewline
170 & 24.7992025169713 & 11.3284685109857 & 38.2699365229570 \tabularnewline
171 & 28.3505907056985 & 14.7719642959105 & 41.9292171154866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102370&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]160[/C][C]23.7296244693920[/C][C]11.0971215548138[/C][C]36.3621273839703[/C][/ROW]
[ROW][C]161[/C][C]21.4766920955035[/C][C]8.77925114622493[/C][C]34.1741330447821[/C][/ROW]
[ROW][C]162[/C][C]23.0521781224104[/C][C]10.2857800612796[/C][C]35.8185761835411[/C][/ROW]
[ROW][C]163[/C][C]21.2944900039497[/C][C]8.4550392924907[/C][C]34.1339407154087[/C][/ROW]
[ROW][C]164[/C][C]24.9632178025419[/C][C]12.0465480184480[/C][C]37.8798875866358[/C][/ROW]
[ROW][C]165[/C][C]29.2319479837333[/C][C]16.2338274667531[/C][C]42.2300685007136[/C][/ROW]
[ROW][C]166[/C][C]26.9132713398171[/C][C]13.8294088802634[/C][C]39.9971337993708[/C][/ROW]
[ROW][C]167[/C][C]24.2198553063170[/C][C]11.0459058502224[/C][C]37.3938047624115[/C][/ROW]
[ROW][C]168[/C][C]22.9098348438952[/C][C]9.64140518894856[/C][C]36.1782644988419[/C][/ROW]
[ROW][C]169[/C][C]27.6557456938485[/C][C]14.2884001506674[/C][C]41.0230912370295[/C][/ROW]
[ROW][C]170[/C][C]24.7992025169713[/C][C]11.3284685109857[/C][C]38.2699365229570[/C][/ROW]
[ROW][C]171[/C][C]28.3505907056985[/C][C]14.7719642959105[/C][C]41.9292171154866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102370&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102370&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
16023.729624469392011.097121554813836.3621273839703
16121.47669209550358.7792511462249334.1741330447821
16223.052178122410410.285780061279635.8185761835411
16321.29449000394978.455039292490734.1339407154087
16424.963217802541912.046548018448037.8798875866358
16529.231947983733316.233827466753142.2300685007136
16626.913271339817113.829408880263439.9971337993708
16724.219855306317011.045905850222437.3938047624115
16822.90983484389529.6414051889485636.1782644988419
16927.655745693848514.288400150667441.0230912370295
17024.799202516971311.328468510985738.2699365229570
17128.350590705698514.771964295910541.9292171154866


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')