Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 10 Aug 2010 16:31:59 +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/Aug/10/t1281457904741aenpfigeuxwn.htm/, Retrieved Sat, 04 May 2024 23:31:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78590, Retrieved Sat, 04 May 2024 23:31:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPlatini Olivier
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2010-08-10 16:31:59] [49dea061148f13f4e9d1975b9f021cec] [Current]
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Dataseries X:
94
93
92
90
110
109
94
84
85
85
86
88
93
94
90
91
104
103
88
79
82
88
93
89
94
96
94
92
113
122
107
98
103
110
113
110
123
124
118
117
139
146
134
121
123
122
127
122
139
136
127
123
140
146
138
120
122
115
115
102
119
114
108
102
121
109
102
95
98
92
94
90
113
111
103
90
108
99
95
91
85
72
90
90
114
115
104
93
101
90
79
75
71
61
84
87
107
99
93
74
87
71
67
61
63
52
80
84
102
93
87
72
83
72
66
64
64
47
77
79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78590&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78590&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78590&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.365777387991567
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.365777387991567 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78590&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]0.365777387991567[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78590&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78590&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
alpha0.365777387991567
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139394.5619658119659-1.56196581196586
149495.2432564147553-1.24325641475525
159090.9161237083847-0.916123708384688
169191.3753154155436-0.375315415543625
17104103.6156559007960.384344099204498
18103102.2171959924480.782804007551817
198891.9644837085955-3.96448370859551
207980.3086542572194-1.30865425721936
218280.66593383218531.33406616781467
228880.98986078141227.01013921858778
239384.55663357186698.4433664281331
248989.9393151340941-0.939315134094144
259493.89938990500040.100610094999595
269695.39094588674790.609054113252128
279491.94882144656892.05117855343114
289293.8363780725177-1.83637807251775
29113106.0240881170906.97591188290978
30122107.28938693928914.7106130607113
3110799.12031505605557.87968494394453
329893.48120176903774.51879823096229
3310397.64610474454885.35389525545118
34110103.0402881538366.9597118461641
35113107.4976008561625.50239914383845
36110105.8538342789324.1461657210683
37123112.33360704881010.6663929511903
38124118.0123541790975.98764582090315
39118117.4522248941070.547775105892953
40117116.3242942162780.675705783722094
41139135.0198212855083.9801787144915
42146140.0948710383335.9051289616668
43134124.3726231086939.62737689130746
44121117.2412256674233.75877433257693
45123121.6577665027231.34223349727658
46122126.603019945168-4.60301994516817
47127125.9066861462311.09331385376878
48122121.7900219642850.209978035714784
49139130.9653018287478.03469817125347
50136132.7140672905403.28593270946033
51127127.715623426682-0.715623426681802
52123126.206706662264-3.2067066622639
53140145.577906501360-5.57790650135954
54146148.377671783479-2.37767178347923
55138131.9864964365046.01350356349587
56120119.8112254052180.188774594782117
57122121.3893162207080.610683779292174
58115122.296371150803-7.29637115080284
59115124.227614083759-9.22761408375862
60102115.775556289368-13.7755562893678
61119124.797858381330-5.79785838133036
62114118.47521300308-4.47521300307987
63108108.100040147905-0.100040147904664
64102105.236388510888-3.23638851088785
65121123.092862845378-2.09286284537787
66109129.197039514833-20.1970395148332
67102111.609815529802-9.60981552980158
689590.02571282803144.9742871719686
699893.62182027923574.37817972076428
709290.89210700301221.10789299698779
719494.672601786576-0.672601786575981
729086.46536625957953.53463374042047
73113106.8789808513256.12101914867459
74111105.7548429703465.24515702965358
75103101.7099952322541.29000476774644
769097.365647542735-7.36564754273498
77108114.436982128694-6.43698212869378
7899107.47009997801-8.47009997800993
7995100.886982155598-5.88698215559765
809189.91417543068751.08582456931245
818591.709906363049-6.70990636304892
827282.8503321332926-10.8503321332926
839081.1275485113888.87245148861194
849079.080001544896610.9199984551034
85114103.83535966062810.1646403393723
86115103.63479541592511.3652045840753
8710499.32007568823464.67992431176539
889390.72607349803852.27392650196151
89101111.912326903993-10.9123269039928
9090102.019015518124-12.0190155181241
917995.776056371702-16.7760563717020
927585.2425842164814-10.2425842164814
937177.9504105386372-6.95041053863723
946166.3769136729022-5.37691367290218
958479.16481810358554.8351818964145
968776.939129796340410.0608702036596
97107100.9011730271486.0988269728521
989999.9748511803374-0.97485118033741
999386.90646217115736.09353782884267
1007477.3035896254469-3.30358962544692
1018788.0866936731075-1.08669367310749
1027181.0854898022608-10.0854898022608
1036772.5327477662147-5.53274776621473
1046170.2554994408607-9.25549944086075
1056365.4123500431171-2.41235004311707
1065256.4967203841547-4.49672038415467
1078076.08332154297553.91667845702447
1088476.8359151345727.16408486542801
10910297.22556238405584.77443761594418
1109391.32852222276891.67147777723112
1118783.71103264754853.28896735245145
1127267.12244091910984.87755908089021
1138382.30402971278860.695970287211424
1147270.2476440230511.75235597694895
1156668.912370241473-2.91237024147304
1166465.2325434717181-1.23254347171812
1176467.6640900377397-3.66409003773971
1184756.9686473910139-9.96864739101389
1197779.8897091709066-2.88970917090664
1207980.212258648891-1.21225864889095

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 93 & 94.5619658119659 & -1.56196581196586 \tabularnewline
14 & 94 & 95.2432564147553 & -1.24325641475525 \tabularnewline
15 & 90 & 90.9161237083847 & -0.916123708384688 \tabularnewline
16 & 91 & 91.3753154155436 & -0.375315415543625 \tabularnewline
17 & 104 & 103.615655900796 & 0.384344099204498 \tabularnewline
18 & 103 & 102.217195992448 & 0.782804007551817 \tabularnewline
19 & 88 & 91.9644837085955 & -3.96448370859551 \tabularnewline
20 & 79 & 80.3086542572194 & -1.30865425721936 \tabularnewline
21 & 82 & 80.6659338321853 & 1.33406616781467 \tabularnewline
22 & 88 & 80.9898607814122 & 7.01013921858778 \tabularnewline
23 & 93 & 84.5566335718669 & 8.4433664281331 \tabularnewline
24 & 89 & 89.9393151340941 & -0.939315134094144 \tabularnewline
25 & 94 & 93.8993899050004 & 0.100610094999595 \tabularnewline
26 & 96 & 95.3909458867479 & 0.609054113252128 \tabularnewline
27 & 94 & 91.9488214465689 & 2.05117855343114 \tabularnewline
28 & 92 & 93.8363780725177 & -1.83637807251775 \tabularnewline
29 & 113 & 106.024088117090 & 6.97591188290978 \tabularnewline
30 & 122 & 107.289386939289 & 14.7106130607113 \tabularnewline
31 & 107 & 99.1203150560555 & 7.87968494394453 \tabularnewline
32 & 98 & 93.4812017690377 & 4.51879823096229 \tabularnewline
33 & 103 & 97.6461047445488 & 5.35389525545118 \tabularnewline
34 & 110 & 103.040288153836 & 6.9597118461641 \tabularnewline
35 & 113 & 107.497600856162 & 5.50239914383845 \tabularnewline
36 & 110 & 105.853834278932 & 4.1461657210683 \tabularnewline
37 & 123 & 112.333607048810 & 10.6663929511903 \tabularnewline
38 & 124 & 118.012354179097 & 5.98764582090315 \tabularnewline
39 & 118 & 117.452224894107 & 0.547775105892953 \tabularnewline
40 & 117 & 116.324294216278 & 0.675705783722094 \tabularnewline
41 & 139 & 135.019821285508 & 3.9801787144915 \tabularnewline
42 & 146 & 140.094871038333 & 5.9051289616668 \tabularnewline
43 & 134 & 124.372623108693 & 9.62737689130746 \tabularnewline
44 & 121 & 117.241225667423 & 3.75877433257693 \tabularnewline
45 & 123 & 121.657766502723 & 1.34223349727658 \tabularnewline
46 & 122 & 126.603019945168 & -4.60301994516817 \tabularnewline
47 & 127 & 125.906686146231 & 1.09331385376878 \tabularnewline
48 & 122 & 121.790021964285 & 0.209978035714784 \tabularnewline
49 & 139 & 130.965301828747 & 8.03469817125347 \tabularnewline
50 & 136 & 132.714067290540 & 3.28593270946033 \tabularnewline
51 & 127 & 127.715623426682 & -0.715623426681802 \tabularnewline
52 & 123 & 126.206706662264 & -3.2067066622639 \tabularnewline
53 & 140 & 145.577906501360 & -5.57790650135954 \tabularnewline
54 & 146 & 148.377671783479 & -2.37767178347923 \tabularnewline
55 & 138 & 131.986496436504 & 6.01350356349587 \tabularnewline
56 & 120 & 119.811225405218 & 0.188774594782117 \tabularnewline
57 & 122 & 121.389316220708 & 0.610683779292174 \tabularnewline
58 & 115 & 122.296371150803 & -7.29637115080284 \tabularnewline
59 & 115 & 124.227614083759 & -9.22761408375862 \tabularnewline
60 & 102 & 115.775556289368 & -13.7755562893678 \tabularnewline
61 & 119 & 124.797858381330 & -5.79785838133036 \tabularnewline
62 & 114 & 118.47521300308 & -4.47521300307987 \tabularnewline
63 & 108 & 108.100040147905 & -0.100040147904664 \tabularnewline
64 & 102 & 105.236388510888 & -3.23638851088785 \tabularnewline
65 & 121 & 123.092862845378 & -2.09286284537787 \tabularnewline
66 & 109 & 129.197039514833 & -20.1970395148332 \tabularnewline
67 & 102 & 111.609815529802 & -9.60981552980158 \tabularnewline
68 & 95 & 90.0257128280314 & 4.9742871719686 \tabularnewline
69 & 98 & 93.6218202792357 & 4.37817972076428 \tabularnewline
70 & 92 & 90.8921070030122 & 1.10789299698779 \tabularnewline
71 & 94 & 94.672601786576 & -0.672601786575981 \tabularnewline
72 & 90 & 86.4653662595795 & 3.53463374042047 \tabularnewline
73 & 113 & 106.878980851325 & 6.12101914867459 \tabularnewline
74 & 111 & 105.754842970346 & 5.24515702965358 \tabularnewline
75 & 103 & 101.709995232254 & 1.29000476774644 \tabularnewline
76 & 90 & 97.365647542735 & -7.36564754273498 \tabularnewline
77 & 108 & 114.436982128694 & -6.43698212869378 \tabularnewline
78 & 99 & 107.47009997801 & -8.47009997800993 \tabularnewline
79 & 95 & 100.886982155598 & -5.88698215559765 \tabularnewline
80 & 91 & 89.9141754306875 & 1.08582456931245 \tabularnewline
81 & 85 & 91.709906363049 & -6.70990636304892 \tabularnewline
82 & 72 & 82.8503321332926 & -10.8503321332926 \tabularnewline
83 & 90 & 81.127548511388 & 8.87245148861194 \tabularnewline
84 & 90 & 79.0800015448966 & 10.9199984551034 \tabularnewline
85 & 114 & 103.835359660628 & 10.1646403393723 \tabularnewline
86 & 115 & 103.634795415925 & 11.3652045840753 \tabularnewline
87 & 104 & 99.3200756882346 & 4.67992431176539 \tabularnewline
88 & 93 & 90.7260734980385 & 2.27392650196151 \tabularnewline
89 & 101 & 111.912326903993 & -10.9123269039928 \tabularnewline
90 & 90 & 102.019015518124 & -12.0190155181241 \tabularnewline
91 & 79 & 95.776056371702 & -16.7760563717020 \tabularnewline
92 & 75 & 85.2425842164814 & -10.2425842164814 \tabularnewline
93 & 71 & 77.9504105386372 & -6.95041053863723 \tabularnewline
94 & 61 & 66.3769136729022 & -5.37691367290218 \tabularnewline
95 & 84 & 79.1648181035855 & 4.8351818964145 \tabularnewline
96 & 87 & 76.9391297963404 & 10.0608702036596 \tabularnewline
97 & 107 & 100.901173027148 & 6.0988269728521 \tabularnewline
98 & 99 & 99.9748511803374 & -0.97485118033741 \tabularnewline
99 & 93 & 86.9064621711573 & 6.09353782884267 \tabularnewline
100 & 74 & 77.3035896254469 & -3.30358962544692 \tabularnewline
101 & 87 & 88.0866936731075 & -1.08669367310749 \tabularnewline
102 & 71 & 81.0854898022608 & -10.0854898022608 \tabularnewline
103 & 67 & 72.5327477662147 & -5.53274776621473 \tabularnewline
104 & 61 & 70.2554994408607 & -9.25549944086075 \tabularnewline
105 & 63 & 65.4123500431171 & -2.41235004311707 \tabularnewline
106 & 52 & 56.4967203841547 & -4.49672038415467 \tabularnewline
107 & 80 & 76.0833215429755 & 3.91667845702447 \tabularnewline
108 & 84 & 76.835915134572 & 7.16408486542801 \tabularnewline
109 & 102 & 97.2255623840558 & 4.77443761594418 \tabularnewline
110 & 93 & 91.3285222227689 & 1.67147777723112 \tabularnewline
111 & 87 & 83.7110326475485 & 3.28896735245145 \tabularnewline
112 & 72 & 67.1224409191098 & 4.87755908089021 \tabularnewline
113 & 83 & 82.3040297127886 & 0.695970287211424 \tabularnewline
114 & 72 & 70.247644023051 & 1.75235597694895 \tabularnewline
115 & 66 & 68.912370241473 & -2.91237024147304 \tabularnewline
116 & 64 & 65.2325434717181 & -1.23254347171812 \tabularnewline
117 & 64 & 67.6640900377397 & -3.66409003773971 \tabularnewline
118 & 47 & 56.9686473910139 & -9.96864739101389 \tabularnewline
119 & 77 & 79.8897091709066 & -2.88970917090664 \tabularnewline
120 & 79 & 80.212258648891 & -1.21225864889095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78590&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]93[/C][C]94.5619658119659[/C][C]-1.56196581196586[/C][/ROW]
[ROW][C]14[/C][C]94[/C][C]95.2432564147553[/C][C]-1.24325641475525[/C][/ROW]
[ROW][C]15[/C][C]90[/C][C]90.9161237083847[/C][C]-0.916123708384688[/C][/ROW]
[ROW][C]16[/C][C]91[/C][C]91.3753154155436[/C][C]-0.375315415543625[/C][/ROW]
[ROW][C]17[/C][C]104[/C][C]103.615655900796[/C][C]0.384344099204498[/C][/ROW]
[ROW][C]18[/C][C]103[/C][C]102.217195992448[/C][C]0.782804007551817[/C][/ROW]
[ROW][C]19[/C][C]88[/C][C]91.9644837085955[/C][C]-3.96448370859551[/C][/ROW]
[ROW][C]20[/C][C]79[/C][C]80.3086542572194[/C][C]-1.30865425721936[/C][/ROW]
[ROW][C]21[/C][C]82[/C][C]80.6659338321853[/C][C]1.33406616781467[/C][/ROW]
[ROW][C]22[/C][C]88[/C][C]80.9898607814122[/C][C]7.01013921858778[/C][/ROW]
[ROW][C]23[/C][C]93[/C][C]84.5566335718669[/C][C]8.4433664281331[/C][/ROW]
[ROW][C]24[/C][C]89[/C][C]89.9393151340941[/C][C]-0.939315134094144[/C][/ROW]
[ROW][C]25[/C][C]94[/C][C]93.8993899050004[/C][C]0.100610094999595[/C][/ROW]
[ROW][C]26[/C][C]96[/C][C]95.3909458867479[/C][C]0.609054113252128[/C][/ROW]
[ROW][C]27[/C][C]94[/C][C]91.9488214465689[/C][C]2.05117855343114[/C][/ROW]
[ROW][C]28[/C][C]92[/C][C]93.8363780725177[/C][C]-1.83637807251775[/C][/ROW]
[ROW][C]29[/C][C]113[/C][C]106.024088117090[/C][C]6.97591188290978[/C][/ROW]
[ROW][C]30[/C][C]122[/C][C]107.289386939289[/C][C]14.7106130607113[/C][/ROW]
[ROW][C]31[/C][C]107[/C][C]99.1203150560555[/C][C]7.87968494394453[/C][/ROW]
[ROW][C]32[/C][C]98[/C][C]93.4812017690377[/C][C]4.51879823096229[/C][/ROW]
[ROW][C]33[/C][C]103[/C][C]97.6461047445488[/C][C]5.35389525545118[/C][/ROW]
[ROW][C]34[/C][C]110[/C][C]103.040288153836[/C][C]6.9597118461641[/C][/ROW]
[ROW][C]35[/C][C]113[/C][C]107.497600856162[/C][C]5.50239914383845[/C][/ROW]
[ROW][C]36[/C][C]110[/C][C]105.853834278932[/C][C]4.1461657210683[/C][/ROW]
[ROW][C]37[/C][C]123[/C][C]112.333607048810[/C][C]10.6663929511903[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]118.012354179097[/C][C]5.98764582090315[/C][/ROW]
[ROW][C]39[/C][C]118[/C][C]117.452224894107[/C][C]0.547775105892953[/C][/ROW]
[ROW][C]40[/C][C]117[/C][C]116.324294216278[/C][C]0.675705783722094[/C][/ROW]
[ROW][C]41[/C][C]139[/C][C]135.019821285508[/C][C]3.9801787144915[/C][/ROW]
[ROW][C]42[/C][C]146[/C][C]140.094871038333[/C][C]5.9051289616668[/C][/ROW]
[ROW][C]43[/C][C]134[/C][C]124.372623108693[/C][C]9.62737689130746[/C][/ROW]
[ROW][C]44[/C][C]121[/C][C]117.241225667423[/C][C]3.75877433257693[/C][/ROW]
[ROW][C]45[/C][C]123[/C][C]121.657766502723[/C][C]1.34223349727658[/C][/ROW]
[ROW][C]46[/C][C]122[/C][C]126.603019945168[/C][C]-4.60301994516817[/C][/ROW]
[ROW][C]47[/C][C]127[/C][C]125.906686146231[/C][C]1.09331385376878[/C][/ROW]
[ROW][C]48[/C][C]122[/C][C]121.790021964285[/C][C]0.209978035714784[/C][/ROW]
[ROW][C]49[/C][C]139[/C][C]130.965301828747[/C][C]8.03469817125347[/C][/ROW]
[ROW][C]50[/C][C]136[/C][C]132.714067290540[/C][C]3.28593270946033[/C][/ROW]
[ROW][C]51[/C][C]127[/C][C]127.715623426682[/C][C]-0.715623426681802[/C][/ROW]
[ROW][C]52[/C][C]123[/C][C]126.206706662264[/C][C]-3.2067066622639[/C][/ROW]
[ROW][C]53[/C][C]140[/C][C]145.577906501360[/C][C]-5.57790650135954[/C][/ROW]
[ROW][C]54[/C][C]146[/C][C]148.377671783479[/C][C]-2.37767178347923[/C][/ROW]
[ROW][C]55[/C][C]138[/C][C]131.986496436504[/C][C]6.01350356349587[/C][/ROW]
[ROW][C]56[/C][C]120[/C][C]119.811225405218[/C][C]0.188774594782117[/C][/ROW]
[ROW][C]57[/C][C]122[/C][C]121.389316220708[/C][C]0.610683779292174[/C][/ROW]
[ROW][C]58[/C][C]115[/C][C]122.296371150803[/C][C]-7.29637115080284[/C][/ROW]
[ROW][C]59[/C][C]115[/C][C]124.227614083759[/C][C]-9.22761408375862[/C][/ROW]
[ROW][C]60[/C][C]102[/C][C]115.775556289368[/C][C]-13.7755562893678[/C][/ROW]
[ROW][C]61[/C][C]119[/C][C]124.797858381330[/C][C]-5.79785838133036[/C][/ROW]
[ROW][C]62[/C][C]114[/C][C]118.47521300308[/C][C]-4.47521300307987[/C][/ROW]
[ROW][C]63[/C][C]108[/C][C]108.100040147905[/C][C]-0.100040147904664[/C][/ROW]
[ROW][C]64[/C][C]102[/C][C]105.236388510888[/C][C]-3.23638851088785[/C][/ROW]
[ROW][C]65[/C][C]121[/C][C]123.092862845378[/C][C]-2.09286284537787[/C][/ROW]
[ROW][C]66[/C][C]109[/C][C]129.197039514833[/C][C]-20.1970395148332[/C][/ROW]
[ROW][C]67[/C][C]102[/C][C]111.609815529802[/C][C]-9.60981552980158[/C][/ROW]
[ROW][C]68[/C][C]95[/C][C]90.0257128280314[/C][C]4.9742871719686[/C][/ROW]
[ROW][C]69[/C][C]98[/C][C]93.6218202792357[/C][C]4.37817972076428[/C][/ROW]
[ROW][C]70[/C][C]92[/C][C]90.8921070030122[/C][C]1.10789299698779[/C][/ROW]
[ROW][C]71[/C][C]94[/C][C]94.672601786576[/C][C]-0.672601786575981[/C][/ROW]
[ROW][C]72[/C][C]90[/C][C]86.4653662595795[/C][C]3.53463374042047[/C][/ROW]
[ROW][C]73[/C][C]113[/C][C]106.878980851325[/C][C]6.12101914867459[/C][/ROW]
[ROW][C]74[/C][C]111[/C][C]105.754842970346[/C][C]5.24515702965358[/C][/ROW]
[ROW][C]75[/C][C]103[/C][C]101.709995232254[/C][C]1.29000476774644[/C][/ROW]
[ROW][C]76[/C][C]90[/C][C]97.365647542735[/C][C]-7.36564754273498[/C][/ROW]
[ROW][C]77[/C][C]108[/C][C]114.436982128694[/C][C]-6.43698212869378[/C][/ROW]
[ROW][C]78[/C][C]99[/C][C]107.47009997801[/C][C]-8.47009997800993[/C][/ROW]
[ROW][C]79[/C][C]95[/C][C]100.886982155598[/C][C]-5.88698215559765[/C][/ROW]
[ROW][C]80[/C][C]91[/C][C]89.9141754306875[/C][C]1.08582456931245[/C][/ROW]
[ROW][C]81[/C][C]85[/C][C]91.709906363049[/C][C]-6.70990636304892[/C][/ROW]
[ROW][C]82[/C][C]72[/C][C]82.8503321332926[/C][C]-10.8503321332926[/C][/ROW]
[ROW][C]83[/C][C]90[/C][C]81.127548511388[/C][C]8.87245148861194[/C][/ROW]
[ROW][C]84[/C][C]90[/C][C]79.0800015448966[/C][C]10.9199984551034[/C][/ROW]
[ROW][C]85[/C][C]114[/C][C]103.835359660628[/C][C]10.1646403393723[/C][/ROW]
[ROW][C]86[/C][C]115[/C][C]103.634795415925[/C][C]11.3652045840753[/C][/ROW]
[ROW][C]87[/C][C]104[/C][C]99.3200756882346[/C][C]4.67992431176539[/C][/ROW]
[ROW][C]88[/C][C]93[/C][C]90.7260734980385[/C][C]2.27392650196151[/C][/ROW]
[ROW][C]89[/C][C]101[/C][C]111.912326903993[/C][C]-10.9123269039928[/C][/ROW]
[ROW][C]90[/C][C]90[/C][C]102.019015518124[/C][C]-12.0190155181241[/C][/ROW]
[ROW][C]91[/C][C]79[/C][C]95.776056371702[/C][C]-16.7760563717020[/C][/ROW]
[ROW][C]92[/C][C]75[/C][C]85.2425842164814[/C][C]-10.2425842164814[/C][/ROW]
[ROW][C]93[/C][C]71[/C][C]77.9504105386372[/C][C]-6.95041053863723[/C][/ROW]
[ROW][C]94[/C][C]61[/C][C]66.3769136729022[/C][C]-5.37691367290218[/C][/ROW]
[ROW][C]95[/C][C]84[/C][C]79.1648181035855[/C][C]4.8351818964145[/C][/ROW]
[ROW][C]96[/C][C]87[/C][C]76.9391297963404[/C][C]10.0608702036596[/C][/ROW]
[ROW][C]97[/C][C]107[/C][C]100.901173027148[/C][C]6.0988269728521[/C][/ROW]
[ROW][C]98[/C][C]99[/C][C]99.9748511803374[/C][C]-0.97485118033741[/C][/ROW]
[ROW][C]99[/C][C]93[/C][C]86.9064621711573[/C][C]6.09353782884267[/C][/ROW]
[ROW][C]100[/C][C]74[/C][C]77.3035896254469[/C][C]-3.30358962544692[/C][/ROW]
[ROW][C]101[/C][C]87[/C][C]88.0866936731075[/C][C]-1.08669367310749[/C][/ROW]
[ROW][C]102[/C][C]71[/C][C]81.0854898022608[/C][C]-10.0854898022608[/C][/ROW]
[ROW][C]103[/C][C]67[/C][C]72.5327477662147[/C][C]-5.53274776621473[/C][/ROW]
[ROW][C]104[/C][C]61[/C][C]70.2554994408607[/C][C]-9.25549944086075[/C][/ROW]
[ROW][C]105[/C][C]63[/C][C]65.4123500431171[/C][C]-2.41235004311707[/C][/ROW]
[ROW][C]106[/C][C]52[/C][C]56.4967203841547[/C][C]-4.49672038415467[/C][/ROW]
[ROW][C]107[/C][C]80[/C][C]76.0833215429755[/C][C]3.91667845702447[/C][/ROW]
[ROW][C]108[/C][C]84[/C][C]76.835915134572[/C][C]7.16408486542801[/C][/ROW]
[ROW][C]109[/C][C]102[/C][C]97.2255623840558[/C][C]4.77443761594418[/C][/ROW]
[ROW][C]110[/C][C]93[/C][C]91.3285222227689[/C][C]1.67147777723112[/C][/ROW]
[ROW][C]111[/C][C]87[/C][C]83.7110326475485[/C][C]3.28896735245145[/C][/ROW]
[ROW][C]112[/C][C]72[/C][C]67.1224409191098[/C][C]4.87755908089021[/C][/ROW]
[ROW][C]113[/C][C]83[/C][C]82.3040297127886[/C][C]0.695970287211424[/C][/ROW]
[ROW][C]114[/C][C]72[/C][C]70.247644023051[/C][C]1.75235597694895[/C][/ROW]
[ROW][C]115[/C][C]66[/C][C]68.912370241473[/C][C]-2.91237024147304[/C][/ROW]
[ROW][C]116[/C][C]64[/C][C]65.2325434717181[/C][C]-1.23254347171812[/C][/ROW]
[ROW][C]117[/C][C]64[/C][C]67.6640900377397[/C][C]-3.66409003773971[/C][/ROW]
[ROW][C]118[/C][C]47[/C][C]56.9686473910139[/C][C]-9.96864739101389[/C][/ROW]
[ROW][C]119[/C][C]77[/C][C]79.8897091709066[/C][C]-2.88970917090664[/C][/ROW]
[ROW][C]120[/C][C]79[/C][C]80.212258648891[/C][C]-1.21225864889095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78590&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78590&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
139394.5619658119659-1.56196581196586
149495.2432564147553-1.24325641475525
159090.9161237083847-0.916123708384688
169191.3753154155436-0.375315415543625
17104103.6156559007960.384344099204498
18103102.2171959924480.782804007551817
198891.9644837085955-3.96448370859551
207980.3086542572194-1.30865425721936
218280.66593383218531.33406616781467
228880.98986078141227.01013921858778
239384.55663357186698.4433664281331
248989.9393151340941-0.939315134094144
259493.89938990500040.100610094999595
269695.39094588674790.609054113252128
279491.94882144656892.05117855343114
289293.8363780725177-1.83637807251775
29113106.0240881170906.97591188290978
30122107.28938693928914.7106130607113
3110799.12031505605557.87968494394453
329893.48120176903774.51879823096229
3310397.64610474454885.35389525545118
34110103.0402881538366.9597118461641
35113107.4976008561625.50239914383845
36110105.8538342789324.1461657210683
37123112.33360704881010.6663929511903
38124118.0123541790975.98764582090315
39118117.4522248941070.547775105892953
40117116.3242942162780.675705783722094
41139135.0198212855083.9801787144915
42146140.0948710383335.9051289616668
43134124.3726231086939.62737689130746
44121117.2412256674233.75877433257693
45123121.6577665027231.34223349727658
46122126.603019945168-4.60301994516817
47127125.9066861462311.09331385376878
48122121.7900219642850.209978035714784
49139130.9653018287478.03469817125347
50136132.7140672905403.28593270946033
51127127.715623426682-0.715623426681802
52123126.206706662264-3.2067066622639
53140145.577906501360-5.57790650135954
54146148.377671783479-2.37767178347923
55138131.9864964365046.01350356349587
56120119.8112254052180.188774594782117
57122121.3893162207080.610683779292174
58115122.296371150803-7.29637115080284
59115124.227614083759-9.22761408375862
60102115.775556289368-13.7755562893678
61119124.797858381330-5.79785838133036
62114118.47521300308-4.47521300307987
63108108.100040147905-0.100040147904664
64102105.236388510888-3.23638851088785
65121123.092862845378-2.09286284537787
66109129.197039514833-20.1970395148332
67102111.609815529802-9.60981552980158
689590.02571282803144.9742871719686
699893.62182027923574.37817972076428
709290.89210700301221.10789299698779
719494.672601786576-0.672601786575981
729086.46536625957953.53463374042047
73113106.8789808513256.12101914867459
74111105.7548429703465.24515702965358
75103101.7099952322541.29000476774644
769097.365647542735-7.36564754273498
77108114.436982128694-6.43698212869378
7899107.47009997801-8.47009997800993
7995100.886982155598-5.88698215559765
809189.91417543068751.08582456931245
818591.709906363049-6.70990636304892
827282.8503321332926-10.8503321332926
839081.1275485113888.87245148861194
849079.080001544896610.9199984551034
85114103.83535966062810.1646403393723
86115103.63479541592511.3652045840753
8710499.32007568823464.67992431176539
889390.72607349803852.27392650196151
89101111.912326903993-10.9123269039928
9090102.019015518124-12.0190155181241
917995.776056371702-16.7760563717020
927585.2425842164814-10.2425842164814
937177.9504105386372-6.95041053863723
946166.3769136729022-5.37691367290218
958479.16481810358554.8351818964145
968776.939129796340410.0608702036596
97107100.9011730271486.0988269728521
989999.9748511803374-0.97485118033741
999386.90646217115736.09353782884267
1007477.3035896254469-3.30358962544692
1018788.0866936731075-1.08669367310749
1027181.0854898022608-10.0854898022608
1036772.5327477662147-5.53274776621473
1046170.2554994408607-9.25549944086075
1056365.4123500431171-2.41235004311707
1065256.4967203841547-4.49672038415467
1078076.08332154297553.91667845702447
1088476.8359151345727.16408486542801
10910297.22556238405584.77443761594418
1109391.32852222276891.67147777723112
1118783.71103264754853.28896735245145
1127267.12244091910984.87755908089021
1138382.30402971278860.695970287211424
1147270.2476440230511.75235597694895
1156668.912370241473-2.91237024147304
1166465.2325434717181-1.23254347171812
1176467.6640900377397-3.66409003773971
1184756.9686473910139-9.96864739101389
1197779.8897091709066-2.88970917090664
1207980.212258648891-1.21225864889095







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12196.022460526440783.440745007033108.604176045848
12286.411071750999173.014096173988399.80804732801
12379.208041863629965.04264939427993.3734343329808
12462.423941043247347.529722936530177.3181591499646
12573.169370849471457.580364395877888.758377303065
12661.528398657391645.274275752420677.7825215623626
12756.59367783718239.700605274453273.4867503999108
12855.044514368853137.535793975593672.5532347621126
12956.384755652223438.281311808328474.4881994961185
13043.031061456717524.351819817700661.7103030957343
13174.08805172930754.85023851136393.325864947251
13276.531468531468556.750850578325196.3120864846119

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 96.0224605264407 & 83.440745007033 & 108.604176045848 \tabularnewline
122 & 86.4110717509991 & 73.0140961739883 & 99.80804732801 \tabularnewline
123 & 79.2080418636299 & 65.042649394279 & 93.3734343329808 \tabularnewline
124 & 62.4239410432473 & 47.5297229365301 & 77.3181591499646 \tabularnewline
125 & 73.1693708494714 & 57.5803643958778 & 88.758377303065 \tabularnewline
126 & 61.5283986573916 & 45.2742757524206 & 77.7825215623626 \tabularnewline
127 & 56.593677837182 & 39.7006052744532 & 73.4867503999108 \tabularnewline
128 & 55.0445143688531 & 37.5357939755936 & 72.5532347621126 \tabularnewline
129 & 56.3847556522234 & 38.2813118083284 & 74.4881994961185 \tabularnewline
130 & 43.0310614567175 & 24.3518198177006 & 61.7103030957343 \tabularnewline
131 & 74.088051729307 & 54.850238511363 & 93.325864947251 \tabularnewline
132 & 76.5314685314685 & 56.7508505783251 & 96.3120864846119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78590&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]96.0224605264407[/C][C]83.440745007033[/C][C]108.604176045848[/C][/ROW]
[ROW][C]122[/C][C]86.4110717509991[/C][C]73.0140961739883[/C][C]99.80804732801[/C][/ROW]
[ROW][C]123[/C][C]79.2080418636299[/C][C]65.042649394279[/C][C]93.3734343329808[/C][/ROW]
[ROW][C]124[/C][C]62.4239410432473[/C][C]47.5297229365301[/C][C]77.3181591499646[/C][/ROW]
[ROW][C]125[/C][C]73.1693708494714[/C][C]57.5803643958778[/C][C]88.758377303065[/C][/ROW]
[ROW][C]126[/C][C]61.5283986573916[/C][C]45.2742757524206[/C][C]77.7825215623626[/C][/ROW]
[ROW][C]127[/C][C]56.593677837182[/C][C]39.7006052744532[/C][C]73.4867503999108[/C][/ROW]
[ROW][C]128[/C][C]55.0445143688531[/C][C]37.5357939755936[/C][C]72.5532347621126[/C][/ROW]
[ROW][C]129[/C][C]56.3847556522234[/C][C]38.2813118083284[/C][C]74.4881994961185[/C][/ROW]
[ROW][C]130[/C][C]43.0310614567175[/C][C]24.3518198177006[/C][C]61.7103030957343[/C][/ROW]
[ROW][C]131[/C][C]74.088051729307[/C][C]54.850238511363[/C][C]93.325864947251[/C][/ROW]
[ROW][C]132[/C][C]76.5314685314685[/C][C]56.7508505783251[/C][C]96.3120864846119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78590&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78590&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
12196.022460526440783.440745007033108.604176045848
12286.411071750999173.014096173988399.80804732801
12379.208041863629965.04264939427993.3734343329808
12462.423941043247347.529722936530177.3181591499646
12573.169370849471457.580364395877888.758377303065
12661.528398657391645.274275752420677.7825215623626
12756.59367783718239.700605274453273.4867503999108
12855.044514368853137.535793975593672.5532347621126
12956.384755652223438.281311808328474.4881994961185
13043.031061456717524.351819817700661.7103030957343
13174.08805172930754.85023851136393.325864947251
13276.531468531468556.750850578325196.3120864846119



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')