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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 computationThu, 19 Aug 2010 01:56:37 +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/19/t12821832871yjbeeh8t8kpnj7.htm/, Retrieved Fri, 03 May 2024 12:19:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79242, Retrieved Fri, 03 May 2024 12:19:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-08-19 01:56:37] [ea4db07d8da34007b79212461ea6aa7b] [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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79242&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79242&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.365777387991424
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.365777387991424 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79242&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]0.365777387991424[/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=79242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79242&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
alpha0.365777387991424
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139394.5619658119659-1.56196581196586
149495.2432564147555-1.24325641475546
159090.916123708385-0.916123708385001
169191.375315415544-0.375315415543952
17104103.6156559007960.384344099204228
18103102.2171959924480.782804007551704
198891.9644837085955-3.96448370859548
207980.3086542572199-1.30865425721991
218280.66593383218591.33406616781413
228880.98986078141247.01013921858764
239384.5566335718668.44336642813403
248989.9393151340924-0.939315134092354
259493.89938990499920.100610095000818
269695.3909458867470.609054113253023
279491.94882144656822.05117855343181
289293.836378072517-1.83637807251708
29113106.024088117096.97591188290978
30122107.28938693928814.7106130607122
3110799.12031505605227.87968494394775
329893.48120176903464.51879823096544
3310397.64610474454665.35389525545341
34110103.0402881538356.9597118461652
35113107.4976008561615.50239914383927
36110105.853834278934.14616572107037
37123112.33360704880710.6663929511926
38124118.0123541790945.98764582090638
39118117.4522248941040.547775105895795
40117116.3242942162760.675705783724482
41139135.0198212855083.98017871449213
42146140.0948710383345.90512896166598
43134124.3726231086929.62737689130783
44121117.2412256674213.75877433257907
45123121.6577665027211.34223349727851
46122126.603019945167-4.60301994516733
47127125.9066861462321.09331385376818
48122121.7900219642850.209978035714713
49139130.9653018287478.03469817125278
50136132.7140672905393.28593270946135
51127127.71562342668-0.715623426679713
52123126.206706662262-3.20670666226191
53140145.577906501359-5.57790650135905
54146148.377671783481-2.37767178348088
55138131.9864964365076.01350356349326
56120119.8112254052180.188774594781549
57122121.3893162207080.61068377929233
58115122.296371150802-7.29637115080169
59115124.227614083759-9.22761408375929
60102115.77555628937-13.7755562893696
61119124.797858381335-5.79785838133486
62114118.475213003084-4.47521300308364
63108108.100040147907-0.100040147906824
64102105.236388510888-3.23638851088805
65121123.092862845377-2.09286284537745
66109129.197039514834-20.1970395148335
67102111.609815529806-9.60981552980647
689590.0257128280364.97428717196391
699893.6218202792384.37817972076198
709290.89210700301161.10789299698841
719494.6726017865744-0.672601786574361
729086.46536625957733.53463374042272
73113106.8789808513246.12101914867569
74111105.7548429703465.24515702965442
75103101.7099952322531.29000476774694
769097.3656475427341-7.36564754273411
77108114.436982128694-6.43698212869384
7899107.470099978008-8.47009997800812
7995100.886982155598-5.88698215559813
809189.91417543069111.08582456930888
818591.7099063630525-6.7099063630525
827282.8503321332957-10.8503321332957
839081.1275485113918.87245148860907
849079.080001544896810.9199984551032
85114103.83535966062710.1646403393732
86115103.63479541592311.3652045840769
8710499.3200756882324.67992431176805
889390.72607349803482.27392650196524
89101111.912326903989-10.9123269039892
9090102.019015518122-12.0190155181215
917995.7760563717014-16.7760563717014
927585.2425842164849-10.2425842164849
937177.9504105386412-6.95041053864122
946166.3769136729053-5.37691367290529
958479.16481810359064.83518189640944
968776.939129796344610.0608702036554
97107100.901173027156.09882697284978
989999.974851180339-0.974851180339058
999386.90646217115826.0935378288418
1007477.3035896254456-3.30358962544555
1018788.0866936731042-1.08669367310422
1027181.0854898022562-10.0854898022562
1036772.5327477662106-5.53274776621065
1046170.2554994408588-9.25549944085876
1056365.4123500431176-2.4123500431176
1065256.4967203841557-4.49672038415572
1078076.08332154297943.91667845702062
1088476.83591513457687.16408486542316
10910297.22556238405964.77443761594043
1109391.3285222227711.67147777722896
1118783.71103264755093.28896735244912
1127267.12244091910984.87755908089017
1138382.30402971278660.695970287213441
1147270.24764402304661.75235597695344
1156668.9123702414677-2.91237024146766
1166465.2325434717131-1.23254347171307
1176467.6640900377365-3.66409003773653
1184756.9686473910121-9.96864739101214
1197779.889709170909-2.88970917090892
1207980.2122586488956-1.21225864889561

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 93 & 94.5619658119659 & -1.56196581196586 \tabularnewline
14 & 94 & 95.2432564147555 & -1.24325641475546 \tabularnewline
15 & 90 & 90.916123708385 & -0.916123708385001 \tabularnewline
16 & 91 & 91.375315415544 & -0.375315415543952 \tabularnewline
17 & 104 & 103.615655900796 & 0.384344099204228 \tabularnewline
18 & 103 & 102.217195992448 & 0.782804007551704 \tabularnewline
19 & 88 & 91.9644837085955 & -3.96448370859548 \tabularnewline
20 & 79 & 80.3086542572199 & -1.30865425721991 \tabularnewline
21 & 82 & 80.6659338321859 & 1.33406616781413 \tabularnewline
22 & 88 & 80.9898607814124 & 7.01013921858764 \tabularnewline
23 & 93 & 84.556633571866 & 8.44336642813403 \tabularnewline
24 & 89 & 89.9393151340924 & -0.939315134092354 \tabularnewline
25 & 94 & 93.8993899049992 & 0.100610095000818 \tabularnewline
26 & 96 & 95.390945886747 & 0.609054113253023 \tabularnewline
27 & 94 & 91.9488214465682 & 2.05117855343181 \tabularnewline
28 & 92 & 93.836378072517 & -1.83637807251708 \tabularnewline
29 & 113 & 106.02408811709 & 6.97591188290978 \tabularnewline
30 & 122 & 107.289386939288 & 14.7106130607122 \tabularnewline
31 & 107 & 99.1203150560522 & 7.87968494394775 \tabularnewline
32 & 98 & 93.4812017690346 & 4.51879823096544 \tabularnewline
33 & 103 & 97.6461047445466 & 5.35389525545341 \tabularnewline
34 & 110 & 103.040288153835 & 6.9597118461652 \tabularnewline
35 & 113 & 107.497600856161 & 5.50239914383927 \tabularnewline
36 & 110 & 105.85383427893 & 4.14616572107037 \tabularnewline
37 & 123 & 112.333607048807 & 10.6663929511926 \tabularnewline
38 & 124 & 118.012354179094 & 5.98764582090638 \tabularnewline
39 & 118 & 117.452224894104 & 0.547775105895795 \tabularnewline
40 & 117 & 116.324294216276 & 0.675705783724482 \tabularnewline
41 & 139 & 135.019821285508 & 3.98017871449213 \tabularnewline
42 & 146 & 140.094871038334 & 5.90512896166598 \tabularnewline
43 & 134 & 124.372623108692 & 9.62737689130783 \tabularnewline
44 & 121 & 117.241225667421 & 3.75877433257907 \tabularnewline
45 & 123 & 121.657766502721 & 1.34223349727851 \tabularnewline
46 & 122 & 126.603019945167 & -4.60301994516733 \tabularnewline
47 & 127 & 125.906686146232 & 1.09331385376818 \tabularnewline
48 & 122 & 121.790021964285 & 0.209978035714713 \tabularnewline
49 & 139 & 130.965301828747 & 8.03469817125278 \tabularnewline
50 & 136 & 132.714067290539 & 3.28593270946135 \tabularnewline
51 & 127 & 127.71562342668 & -0.715623426679713 \tabularnewline
52 & 123 & 126.206706662262 & -3.20670666226191 \tabularnewline
53 & 140 & 145.577906501359 & -5.57790650135905 \tabularnewline
54 & 146 & 148.377671783481 & -2.37767178348088 \tabularnewline
55 & 138 & 131.986496436507 & 6.01350356349326 \tabularnewline
56 & 120 & 119.811225405218 & 0.188774594781549 \tabularnewline
57 & 122 & 121.389316220708 & 0.61068377929233 \tabularnewline
58 & 115 & 122.296371150802 & -7.29637115080169 \tabularnewline
59 & 115 & 124.227614083759 & -9.22761408375929 \tabularnewline
60 & 102 & 115.77555628937 & -13.7755562893696 \tabularnewline
61 & 119 & 124.797858381335 & -5.79785838133486 \tabularnewline
62 & 114 & 118.475213003084 & -4.47521300308364 \tabularnewline
63 & 108 & 108.100040147907 & -0.100040147906824 \tabularnewline
64 & 102 & 105.236388510888 & -3.23638851088805 \tabularnewline
65 & 121 & 123.092862845377 & -2.09286284537745 \tabularnewline
66 & 109 & 129.197039514834 & -20.1970395148335 \tabularnewline
67 & 102 & 111.609815529806 & -9.60981552980647 \tabularnewline
68 & 95 & 90.025712828036 & 4.97428717196391 \tabularnewline
69 & 98 & 93.621820279238 & 4.37817972076198 \tabularnewline
70 & 92 & 90.8921070030116 & 1.10789299698841 \tabularnewline
71 & 94 & 94.6726017865744 & -0.672601786574361 \tabularnewline
72 & 90 & 86.4653662595773 & 3.53463374042272 \tabularnewline
73 & 113 & 106.878980851324 & 6.12101914867569 \tabularnewline
74 & 111 & 105.754842970346 & 5.24515702965442 \tabularnewline
75 & 103 & 101.709995232253 & 1.29000476774694 \tabularnewline
76 & 90 & 97.3656475427341 & -7.36564754273411 \tabularnewline
77 & 108 & 114.436982128694 & -6.43698212869384 \tabularnewline
78 & 99 & 107.470099978008 & -8.47009997800812 \tabularnewline
79 & 95 & 100.886982155598 & -5.88698215559813 \tabularnewline
80 & 91 & 89.9141754306911 & 1.08582456930888 \tabularnewline
81 & 85 & 91.7099063630525 & -6.7099063630525 \tabularnewline
82 & 72 & 82.8503321332957 & -10.8503321332957 \tabularnewline
83 & 90 & 81.127548511391 & 8.87245148860907 \tabularnewline
84 & 90 & 79.0800015448968 & 10.9199984551032 \tabularnewline
85 & 114 & 103.835359660627 & 10.1646403393732 \tabularnewline
86 & 115 & 103.634795415923 & 11.3652045840769 \tabularnewline
87 & 104 & 99.320075688232 & 4.67992431176805 \tabularnewline
88 & 93 & 90.7260734980348 & 2.27392650196524 \tabularnewline
89 & 101 & 111.912326903989 & -10.9123269039892 \tabularnewline
90 & 90 & 102.019015518122 & -12.0190155181215 \tabularnewline
91 & 79 & 95.7760563717014 & -16.7760563717014 \tabularnewline
92 & 75 & 85.2425842164849 & -10.2425842164849 \tabularnewline
93 & 71 & 77.9504105386412 & -6.95041053864122 \tabularnewline
94 & 61 & 66.3769136729053 & -5.37691367290529 \tabularnewline
95 & 84 & 79.1648181035906 & 4.83518189640944 \tabularnewline
96 & 87 & 76.9391297963446 & 10.0608702036554 \tabularnewline
97 & 107 & 100.90117302715 & 6.09882697284978 \tabularnewline
98 & 99 & 99.974851180339 & -0.974851180339058 \tabularnewline
99 & 93 & 86.9064621711582 & 6.0935378288418 \tabularnewline
100 & 74 & 77.3035896254456 & -3.30358962544555 \tabularnewline
101 & 87 & 88.0866936731042 & -1.08669367310422 \tabularnewline
102 & 71 & 81.0854898022562 & -10.0854898022562 \tabularnewline
103 & 67 & 72.5327477662106 & -5.53274776621065 \tabularnewline
104 & 61 & 70.2554994408588 & -9.25549944085876 \tabularnewline
105 & 63 & 65.4123500431176 & -2.4123500431176 \tabularnewline
106 & 52 & 56.4967203841557 & -4.49672038415572 \tabularnewline
107 & 80 & 76.0833215429794 & 3.91667845702062 \tabularnewline
108 & 84 & 76.8359151345768 & 7.16408486542316 \tabularnewline
109 & 102 & 97.2255623840596 & 4.77443761594043 \tabularnewline
110 & 93 & 91.328522222771 & 1.67147777722896 \tabularnewline
111 & 87 & 83.7110326475509 & 3.28896735244912 \tabularnewline
112 & 72 & 67.1224409191098 & 4.87755908089017 \tabularnewline
113 & 83 & 82.3040297127866 & 0.695970287213441 \tabularnewline
114 & 72 & 70.2476440230466 & 1.75235597695344 \tabularnewline
115 & 66 & 68.9123702414677 & -2.91237024146766 \tabularnewline
116 & 64 & 65.2325434717131 & -1.23254347171307 \tabularnewline
117 & 64 & 67.6640900377365 & -3.66409003773653 \tabularnewline
118 & 47 & 56.9686473910121 & -9.96864739101214 \tabularnewline
119 & 77 & 79.889709170909 & -2.88970917090892 \tabularnewline
120 & 79 & 80.2122586488956 & -1.21225864889561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79242&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]95.2432564147555[/C][C]-1.24325641475546[/C][/ROW]
[ROW][C]15[/C][C]90[/C][C]90.916123708385[/C][C]-0.916123708385001[/C][/ROW]
[ROW][C]16[/C][C]91[/C][C]91.375315415544[/C][C]-0.375315415543952[/C][/ROW]
[ROW][C]17[/C][C]104[/C][C]103.615655900796[/C][C]0.384344099204228[/C][/ROW]
[ROW][C]18[/C][C]103[/C][C]102.217195992448[/C][C]0.782804007551704[/C][/ROW]
[ROW][C]19[/C][C]88[/C][C]91.9644837085955[/C][C]-3.96448370859548[/C][/ROW]
[ROW][C]20[/C][C]79[/C][C]80.3086542572199[/C][C]-1.30865425721991[/C][/ROW]
[ROW][C]21[/C][C]82[/C][C]80.6659338321859[/C][C]1.33406616781413[/C][/ROW]
[ROW][C]22[/C][C]88[/C][C]80.9898607814124[/C][C]7.01013921858764[/C][/ROW]
[ROW][C]23[/C][C]93[/C][C]84.556633571866[/C][C]8.44336642813403[/C][/ROW]
[ROW][C]24[/C][C]89[/C][C]89.9393151340924[/C][C]-0.939315134092354[/C][/ROW]
[ROW][C]25[/C][C]94[/C][C]93.8993899049992[/C][C]0.100610095000818[/C][/ROW]
[ROW][C]26[/C][C]96[/C][C]95.390945886747[/C][C]0.609054113253023[/C][/ROW]
[ROW][C]27[/C][C]94[/C][C]91.9488214465682[/C][C]2.05117855343181[/C][/ROW]
[ROW][C]28[/C][C]92[/C][C]93.836378072517[/C][C]-1.83637807251708[/C][/ROW]
[ROW][C]29[/C][C]113[/C][C]106.02408811709[/C][C]6.97591188290978[/C][/ROW]
[ROW][C]30[/C][C]122[/C][C]107.289386939288[/C][C]14.7106130607122[/C][/ROW]
[ROW][C]31[/C][C]107[/C][C]99.1203150560522[/C][C]7.87968494394775[/C][/ROW]
[ROW][C]32[/C][C]98[/C][C]93.4812017690346[/C][C]4.51879823096544[/C][/ROW]
[ROW][C]33[/C][C]103[/C][C]97.6461047445466[/C][C]5.35389525545341[/C][/ROW]
[ROW][C]34[/C][C]110[/C][C]103.040288153835[/C][C]6.9597118461652[/C][/ROW]
[ROW][C]35[/C][C]113[/C][C]107.497600856161[/C][C]5.50239914383927[/C][/ROW]
[ROW][C]36[/C][C]110[/C][C]105.85383427893[/C][C]4.14616572107037[/C][/ROW]
[ROW][C]37[/C][C]123[/C][C]112.333607048807[/C][C]10.6663929511926[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]118.012354179094[/C][C]5.98764582090638[/C][/ROW]
[ROW][C]39[/C][C]118[/C][C]117.452224894104[/C][C]0.547775105895795[/C][/ROW]
[ROW][C]40[/C][C]117[/C][C]116.324294216276[/C][C]0.675705783724482[/C][/ROW]
[ROW][C]41[/C][C]139[/C][C]135.019821285508[/C][C]3.98017871449213[/C][/ROW]
[ROW][C]42[/C][C]146[/C][C]140.094871038334[/C][C]5.90512896166598[/C][/ROW]
[ROW][C]43[/C][C]134[/C][C]124.372623108692[/C][C]9.62737689130783[/C][/ROW]
[ROW][C]44[/C][C]121[/C][C]117.241225667421[/C][C]3.75877433257907[/C][/ROW]
[ROW][C]45[/C][C]123[/C][C]121.657766502721[/C][C]1.34223349727851[/C][/ROW]
[ROW][C]46[/C][C]122[/C][C]126.603019945167[/C][C]-4.60301994516733[/C][/ROW]
[ROW][C]47[/C][C]127[/C][C]125.906686146232[/C][C]1.09331385376818[/C][/ROW]
[ROW][C]48[/C][C]122[/C][C]121.790021964285[/C][C]0.209978035714713[/C][/ROW]
[ROW][C]49[/C][C]139[/C][C]130.965301828747[/C][C]8.03469817125278[/C][/ROW]
[ROW][C]50[/C][C]136[/C][C]132.714067290539[/C][C]3.28593270946135[/C][/ROW]
[ROW][C]51[/C][C]127[/C][C]127.71562342668[/C][C]-0.715623426679713[/C][/ROW]
[ROW][C]52[/C][C]123[/C][C]126.206706662262[/C][C]-3.20670666226191[/C][/ROW]
[ROW][C]53[/C][C]140[/C][C]145.577906501359[/C][C]-5.57790650135905[/C][/ROW]
[ROW][C]54[/C][C]146[/C][C]148.377671783481[/C][C]-2.37767178348088[/C][/ROW]
[ROW][C]55[/C][C]138[/C][C]131.986496436507[/C][C]6.01350356349326[/C][/ROW]
[ROW][C]56[/C][C]120[/C][C]119.811225405218[/C][C]0.188774594781549[/C][/ROW]
[ROW][C]57[/C][C]122[/C][C]121.389316220708[/C][C]0.61068377929233[/C][/ROW]
[ROW][C]58[/C][C]115[/C][C]122.296371150802[/C][C]-7.29637115080169[/C][/ROW]
[ROW][C]59[/C][C]115[/C][C]124.227614083759[/C][C]-9.22761408375929[/C][/ROW]
[ROW][C]60[/C][C]102[/C][C]115.77555628937[/C][C]-13.7755562893696[/C][/ROW]
[ROW][C]61[/C][C]119[/C][C]124.797858381335[/C][C]-5.79785838133486[/C][/ROW]
[ROW][C]62[/C][C]114[/C][C]118.475213003084[/C][C]-4.47521300308364[/C][/ROW]
[ROW][C]63[/C][C]108[/C][C]108.100040147907[/C][C]-0.100040147906824[/C][/ROW]
[ROW][C]64[/C][C]102[/C][C]105.236388510888[/C][C]-3.23638851088805[/C][/ROW]
[ROW][C]65[/C][C]121[/C][C]123.092862845377[/C][C]-2.09286284537745[/C][/ROW]
[ROW][C]66[/C][C]109[/C][C]129.197039514834[/C][C]-20.1970395148335[/C][/ROW]
[ROW][C]67[/C][C]102[/C][C]111.609815529806[/C][C]-9.60981552980647[/C][/ROW]
[ROW][C]68[/C][C]95[/C][C]90.025712828036[/C][C]4.97428717196391[/C][/ROW]
[ROW][C]69[/C][C]98[/C][C]93.621820279238[/C][C]4.37817972076198[/C][/ROW]
[ROW][C]70[/C][C]92[/C][C]90.8921070030116[/C][C]1.10789299698841[/C][/ROW]
[ROW][C]71[/C][C]94[/C][C]94.6726017865744[/C][C]-0.672601786574361[/C][/ROW]
[ROW][C]72[/C][C]90[/C][C]86.4653662595773[/C][C]3.53463374042272[/C][/ROW]
[ROW][C]73[/C][C]113[/C][C]106.878980851324[/C][C]6.12101914867569[/C][/ROW]
[ROW][C]74[/C][C]111[/C][C]105.754842970346[/C][C]5.24515702965442[/C][/ROW]
[ROW][C]75[/C][C]103[/C][C]101.709995232253[/C][C]1.29000476774694[/C][/ROW]
[ROW][C]76[/C][C]90[/C][C]97.3656475427341[/C][C]-7.36564754273411[/C][/ROW]
[ROW][C]77[/C][C]108[/C][C]114.436982128694[/C][C]-6.43698212869384[/C][/ROW]
[ROW][C]78[/C][C]99[/C][C]107.470099978008[/C][C]-8.47009997800812[/C][/ROW]
[ROW][C]79[/C][C]95[/C][C]100.886982155598[/C][C]-5.88698215559813[/C][/ROW]
[ROW][C]80[/C][C]91[/C][C]89.9141754306911[/C][C]1.08582456930888[/C][/ROW]
[ROW][C]81[/C][C]85[/C][C]91.7099063630525[/C][C]-6.7099063630525[/C][/ROW]
[ROW][C]82[/C][C]72[/C][C]82.8503321332957[/C][C]-10.8503321332957[/C][/ROW]
[ROW][C]83[/C][C]90[/C][C]81.127548511391[/C][C]8.87245148860907[/C][/ROW]
[ROW][C]84[/C][C]90[/C][C]79.0800015448968[/C][C]10.9199984551032[/C][/ROW]
[ROW][C]85[/C][C]114[/C][C]103.835359660627[/C][C]10.1646403393732[/C][/ROW]
[ROW][C]86[/C][C]115[/C][C]103.634795415923[/C][C]11.3652045840769[/C][/ROW]
[ROW][C]87[/C][C]104[/C][C]99.320075688232[/C][C]4.67992431176805[/C][/ROW]
[ROW][C]88[/C][C]93[/C][C]90.7260734980348[/C][C]2.27392650196524[/C][/ROW]
[ROW][C]89[/C][C]101[/C][C]111.912326903989[/C][C]-10.9123269039892[/C][/ROW]
[ROW][C]90[/C][C]90[/C][C]102.019015518122[/C][C]-12.0190155181215[/C][/ROW]
[ROW][C]91[/C][C]79[/C][C]95.7760563717014[/C][C]-16.7760563717014[/C][/ROW]
[ROW][C]92[/C][C]75[/C][C]85.2425842164849[/C][C]-10.2425842164849[/C][/ROW]
[ROW][C]93[/C][C]71[/C][C]77.9504105386412[/C][C]-6.95041053864122[/C][/ROW]
[ROW][C]94[/C][C]61[/C][C]66.3769136729053[/C][C]-5.37691367290529[/C][/ROW]
[ROW][C]95[/C][C]84[/C][C]79.1648181035906[/C][C]4.83518189640944[/C][/ROW]
[ROW][C]96[/C][C]87[/C][C]76.9391297963446[/C][C]10.0608702036554[/C][/ROW]
[ROW][C]97[/C][C]107[/C][C]100.90117302715[/C][C]6.09882697284978[/C][/ROW]
[ROW][C]98[/C][C]99[/C][C]99.974851180339[/C][C]-0.974851180339058[/C][/ROW]
[ROW][C]99[/C][C]93[/C][C]86.9064621711582[/C][C]6.0935378288418[/C][/ROW]
[ROW][C]100[/C][C]74[/C][C]77.3035896254456[/C][C]-3.30358962544555[/C][/ROW]
[ROW][C]101[/C][C]87[/C][C]88.0866936731042[/C][C]-1.08669367310422[/C][/ROW]
[ROW][C]102[/C][C]71[/C][C]81.0854898022562[/C][C]-10.0854898022562[/C][/ROW]
[ROW][C]103[/C][C]67[/C][C]72.5327477662106[/C][C]-5.53274776621065[/C][/ROW]
[ROW][C]104[/C][C]61[/C][C]70.2554994408588[/C][C]-9.25549944085876[/C][/ROW]
[ROW][C]105[/C][C]63[/C][C]65.4123500431176[/C][C]-2.4123500431176[/C][/ROW]
[ROW][C]106[/C][C]52[/C][C]56.4967203841557[/C][C]-4.49672038415572[/C][/ROW]
[ROW][C]107[/C][C]80[/C][C]76.0833215429794[/C][C]3.91667845702062[/C][/ROW]
[ROW][C]108[/C][C]84[/C][C]76.8359151345768[/C][C]7.16408486542316[/C][/ROW]
[ROW][C]109[/C][C]102[/C][C]97.2255623840596[/C][C]4.77443761594043[/C][/ROW]
[ROW][C]110[/C][C]93[/C][C]91.328522222771[/C][C]1.67147777722896[/C][/ROW]
[ROW][C]111[/C][C]87[/C][C]83.7110326475509[/C][C]3.28896735244912[/C][/ROW]
[ROW][C]112[/C][C]72[/C][C]67.1224409191098[/C][C]4.87755908089017[/C][/ROW]
[ROW][C]113[/C][C]83[/C][C]82.3040297127866[/C][C]0.695970287213441[/C][/ROW]
[ROW][C]114[/C][C]72[/C][C]70.2476440230466[/C][C]1.75235597695344[/C][/ROW]
[ROW][C]115[/C][C]66[/C][C]68.9123702414677[/C][C]-2.91237024146766[/C][/ROW]
[ROW][C]116[/C][C]64[/C][C]65.2325434717131[/C][C]-1.23254347171307[/C][/ROW]
[ROW][C]117[/C][C]64[/C][C]67.6640900377365[/C][C]-3.66409003773653[/C][/ROW]
[ROW][C]118[/C][C]47[/C][C]56.9686473910121[/C][C]-9.96864739101214[/C][/ROW]
[ROW][C]119[/C][C]77[/C][C]79.889709170909[/C][C]-2.88970917090892[/C][/ROW]
[ROW][C]120[/C][C]79[/C][C]80.2122586488956[/C][C]-1.21225864889561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79242&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79242&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
149495.2432564147555-1.24325641475546
159090.916123708385-0.916123708385001
169191.375315415544-0.375315415543952
17104103.6156559007960.384344099204228
18103102.2171959924480.782804007551704
198891.9644837085955-3.96448370859548
207980.3086542572199-1.30865425721991
218280.66593383218591.33406616781413
228880.98986078141247.01013921858764
239384.5566335718668.44336642813403
248989.9393151340924-0.939315134092354
259493.89938990499920.100610095000818
269695.3909458867470.609054113253023
279491.94882144656822.05117855343181
289293.836378072517-1.83637807251708
29113106.024088117096.97591188290978
30122107.28938693928814.7106130607122
3110799.12031505605227.87968494394775
329893.48120176903464.51879823096544
3310397.64610474454665.35389525545341
34110103.0402881538356.9597118461652
35113107.4976008561615.50239914383927
36110105.853834278934.14616572107037
37123112.33360704880710.6663929511926
38124118.0123541790945.98764582090638
39118117.4522248941040.547775105895795
40117116.3242942162760.675705783724482
41139135.0198212855083.98017871449213
42146140.0948710383345.90512896166598
43134124.3726231086929.62737689130783
44121117.2412256674213.75877433257907
45123121.6577665027211.34223349727851
46122126.603019945167-4.60301994516733
47127125.9066861462321.09331385376818
48122121.7900219642850.209978035714713
49139130.9653018287478.03469817125278
50136132.7140672905393.28593270946135
51127127.71562342668-0.715623426679713
52123126.206706662262-3.20670666226191
53140145.577906501359-5.57790650135905
54146148.377671783481-2.37767178348088
55138131.9864964365076.01350356349326
56120119.8112254052180.188774594781549
57122121.3893162207080.61068377929233
58115122.296371150802-7.29637115080169
59115124.227614083759-9.22761408375929
60102115.77555628937-13.7755562893696
61119124.797858381335-5.79785838133486
62114118.475213003084-4.47521300308364
63108108.100040147907-0.100040147906824
64102105.236388510888-3.23638851088805
65121123.092862845377-2.09286284537745
66109129.197039514834-20.1970395148335
67102111.609815529806-9.60981552980647
689590.0257128280364.97428717196391
699893.6218202792384.37817972076198
709290.89210700301161.10789299698841
719494.6726017865744-0.672601786574361
729086.46536625957733.53463374042272
73113106.8789808513246.12101914867569
74111105.7548429703465.24515702965442
75103101.7099952322531.29000476774694
769097.3656475427341-7.36564754273411
77108114.436982128694-6.43698212869384
7899107.470099978008-8.47009997800812
7995100.886982155598-5.88698215559813
809189.91417543069111.08582456930888
818591.7099063630525-6.7099063630525
827282.8503321332957-10.8503321332957
839081.1275485113918.87245148860907
849079.080001544896810.9199984551032
85114103.83535966062710.1646403393732
86115103.63479541592311.3652045840769
8710499.3200756882324.67992431176805
889390.72607349803482.27392650196524
89101111.912326903989-10.9123269039892
9090102.019015518122-12.0190155181215
917995.7760563717014-16.7760563717014
927585.2425842164849-10.2425842164849
937177.9504105386412-6.95041053864122
946166.3769136729053-5.37691367290529
958479.16481810359064.83518189640944
968776.939129796344610.0608702036554
97107100.901173027156.09882697284978
989999.974851180339-0.974851180339058
999386.90646217115826.0935378288418
1007477.3035896254456-3.30358962544555
1018788.0866936731042-1.08669367310422
1027181.0854898022562-10.0854898022562
1036772.5327477662106-5.53274776621065
1046170.2554994408588-9.25549944085876
1056365.4123500431176-2.4123500431176
1065256.4967203841557-4.49672038415572
1078076.08332154297943.91667845702062
1088476.83591513457687.16408486542316
10910297.22556238405964.77443761594043
1109391.3285222227711.67147777722896
1118783.71103264755093.28896735244912
1127267.12244091910984.87755908089017
1138382.30402971278660.695970287213441
1147270.24764402304661.75235597695344
1156668.9123702414677-2.91237024146766
1166465.2325434717131-1.23254347171307
1176467.6640900377365-3.66409003773653
1184756.9686473910121-9.96864739101214
1197779.889709170909-2.88970917090892
1207980.2122586488956-1.21225864889561







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12196.022460526445983.4407450070382108.604176045854
12286.411071751005373.014096173995199.8080473280155
12379.208041863637465.042649394287793.3734343329872
12462.423941043255647.5297229365477.3181591499711
12573.16937084947957.580364395887588.7583773030705
12661.528398657397845.274275752429477.7825215623662
12756.593677837185839.700605274459973.4867503999117
12855.044514368854937.535793975598772.5532347621111
12956.384755652223638.281311808332274.488199496115
13043.031061456715524.351819817702761.7103030957283
13174.088051729305454.850238511365893.3258649472451
13276.531468531468556.750850578329796.3120864846073

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 96.0224605264459 & 83.4407450070382 & 108.604176045854 \tabularnewline
122 & 86.4110717510053 & 73.0140961739951 & 99.8080473280155 \tabularnewline
123 & 79.2080418636374 & 65.0426493942877 & 93.3734343329872 \tabularnewline
124 & 62.4239410432556 & 47.52972293654 & 77.3181591499711 \tabularnewline
125 & 73.169370849479 & 57.5803643958875 & 88.7583773030705 \tabularnewline
126 & 61.5283986573978 & 45.2742757524294 & 77.7825215623662 \tabularnewline
127 & 56.5936778371858 & 39.7006052744599 & 73.4867503999117 \tabularnewline
128 & 55.0445143688549 & 37.5357939755987 & 72.5532347621111 \tabularnewline
129 & 56.3847556522236 & 38.2813118083322 & 74.488199496115 \tabularnewline
130 & 43.0310614567155 & 24.3518198177027 & 61.7103030957283 \tabularnewline
131 & 74.0880517293054 & 54.8502385113658 & 93.3258649472451 \tabularnewline
132 & 76.5314685314685 & 56.7508505783297 & 96.3120864846073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79242&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]96.0224605264459[/C][C]83.4407450070382[/C][C]108.604176045854[/C][/ROW]
[ROW][C]122[/C][C]86.4110717510053[/C][C]73.0140961739951[/C][C]99.8080473280155[/C][/ROW]
[ROW][C]123[/C][C]79.2080418636374[/C][C]65.0426493942877[/C][C]93.3734343329872[/C][/ROW]
[ROW][C]124[/C][C]62.4239410432556[/C][C]47.52972293654[/C][C]77.3181591499711[/C][/ROW]
[ROW][C]125[/C][C]73.169370849479[/C][C]57.5803643958875[/C][C]88.7583773030705[/C][/ROW]
[ROW][C]126[/C][C]61.5283986573978[/C][C]45.2742757524294[/C][C]77.7825215623662[/C][/ROW]
[ROW][C]127[/C][C]56.5936778371858[/C][C]39.7006052744599[/C][C]73.4867503999117[/C][/ROW]
[ROW][C]128[/C][C]55.0445143688549[/C][C]37.5357939755987[/C][C]72.5532347621111[/C][/ROW]
[ROW][C]129[/C][C]56.3847556522236[/C][C]38.2813118083322[/C][C]74.488199496115[/C][/ROW]
[ROW][C]130[/C][C]43.0310614567155[/C][C]24.3518198177027[/C][C]61.7103030957283[/C][/ROW]
[ROW][C]131[/C][C]74.0880517293054[/C][C]54.8502385113658[/C][C]93.3258649472451[/C][/ROW]
[ROW][C]132[/C][C]76.5314685314685[/C][C]56.7508505783297[/C][C]96.3120864846073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79242&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79242&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
12196.022460526445983.4407450070382108.604176045854
12286.411071751005373.014096173995199.8080473280155
12379.208041863637465.042649394287793.3734343329872
12462.423941043255647.5297229365477.3181591499711
12573.16937084947957.580364395887588.7583773030705
12661.528398657397845.274275752429477.7825215623662
12756.593677837185839.700605274459973.4867503999117
12855.044514368854937.535793975598772.5532347621111
12956.384755652223638.281311808332274.488199496115
13043.031061456715524.351819817702761.7103030957283
13174.088051729305454.850238511365893.3258649472451
13276.531468531468556.750850578329796.3120864846073



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')