Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 21 May 2015 20:21:29 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/21/t1432236108pqi7l562ogxc8p7.htm/, Retrieved Sat, 04 May 2024 07:04:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279202, Retrieved Sat, 04 May 2024 07:04:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-05-21 19:21:29] [d95fe07e11cd60b998b93c9c7758de3b] [Current]
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Dataseries X:
81
85
90
84
94
131
130
99
101
82
90
85
105
110
115
110
114
149
147
113
113
107
109
103
113
112
114
106
107
134
135
105
105
90
92
83
95
98
95
81
83
106
114
80
82
76
78
70
82
86
87
74
79
110
117
82
71
67
66
57
71
77
76
69
74
101
105
73
68
65
70
65
80
92
93
90
96
125
134
100
97
97
101
90
108
113
112
103
103
125
128
91
84
83
83
69
77
83
78
70
75
101
117
80
87
81
78
73
93
105
102
97
100
127
138
107
107
106
109
107
129
138
137
134
134
166
180
131
135
127
121
116




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279202&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279202&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.770741148761065
beta0.0585705005606894
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.770741148761065 \tabularnewline
beta & 0.0585705005606894 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279202&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]0.770741148761065[/C][/ROW]
[ROW][C]beta[/C][C]0.0585705005606894[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279202&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
alpha0.770741148761065
beta0.0585705005606894
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310594.03392094017110.966079059829
14110108.3182345730051.68176542699501
15115115.730998407884-0.730998407883959
16110110.792813301557-0.792813301556762
17114114.47952851743-0.479528517429543
18149149.677724664825-0.677724664825234
19147150.734235234803-3.73423523480318
20113116.724727228373-3.72472722837328
21113115.512736542272-2.51273654227222
2210794.079778584141912.9202214158581
23109112.333223318007-3.33322331800667
24103105.242332036471-2.24233203647086
25113126.530081331336-13.5300813313364
26112119.031198335241-7.0311983352411
27114118.007561590335-4.00756159033543
28106109.214096493775-3.21409649377546
29107109.681422874454-2.68142287445424
30134141.612661213598-7.61266121359756
31135134.7859079936470.21409200635253
32105102.1624654616692.83753453833091
33105104.9231251274970.0768748725027422
349087.77811708368572.22188291631433
359292.3306018384982-0.330601838498211
368386.2105331869937-3.21053318699366
3795102.527008588922-7.5270085889223
389899.7786371160825-1.77863711608254
3995102.367445586005-7.36744558600456
408189.8854989775212-8.88549897752119
418384.5669502850118-1.56695028501183
42106114.74012681742-8.74012681742046
43114107.3013434254136.69865657458659
448079.03260128939960.967398710600392
458278.3898739145643.61012608543604
467663.290259790142212.7097402098578
477874.64484788318573.35515211681425
487070.175536465331-0.175536465330978
498287.4488712146224-5.44887121462236
508687.3211361703799-1.32113617037992
518788.7029938618332-1.70299386183324
527480.2162729482496-6.21627294824955
537978.73077155661380.269228443386169
54110108.8554653348051.14453466519494
55117113.201708246243.79829175376017
568281.87969693041910.120303069580856
577181.6478094782192-10.6478094782192
586757.45940591255089.54059408744922
596663.89793787930462.10206212069536
605757.2679662872678-0.267966287267825
617172.8715198287016-1.87151982870157
627776.21922470384350.780775296156534
637679.0003619541563-3.00036195415635
646968.28722435233750.712775647662482
657473.75010782498480.249892175015219
66101104.180720544003-3.18072054400349
67105105.726605411826-0.726605411826355
687369.79448896725493.20551103274514
696869.3317185050545-1.3317185050545
706557.23243863317117.7675613668289
717060.79949138066419.20050861933593
726559.61809696186855.38190303813147
738079.98452111647490.0154788835251196
749286.255772569155.74422743085002
759393.080747931379-0.0807479313789941
769086.68610639569913.31389360430093
779695.38203959058990.617960409410074
78125126.660836117881-1.66083611788069
79134131.3603945546782.63960544532154
80100100.495796146172-0.495796146172268
819797.5445572387112-0.544557238711207
829789.57808131029037.42191868970966
8310194.6316615370946.368338462906
849091.688508788666-1.68850878866603
85108106.3525588080161.64744119198363
86113116.246051687889-3.24605168788926
87112115.45163101907-3.45163101906996
88103107.73020123681-4.73020123681012
89103109.738059304727-6.73805930472724
90125134.622670238537-9.62267023853738
91128133.610046908453-5.6100469084526
929194.7342889786789-3.73428897867889
938488.1956427571477-4.19564275714772
948377.99650154620565.00349845379445
958379.59038062730363.40961937269644
966971.0319706673773-2.03197066737725
977784.6928446337869-7.69284463378686
988384.3406207468441-1.34062074684408
997883.1287819331841-5.12878193318409
1007071.906986981472-1.90698698147199
1017573.84334830545631.15665169454373
102101102.720658896686-1.7206588966858
103117107.6443319895029.35566801049808
1048080.3348548875545-0.334854887554471
1058776.065536992228510.9344630077715
1068180.07480320089630.92519679910373
1077878.4138787403425-0.413878740342483
1087365.74232801009857.25767198990154
1099385.7659851103987.23401488960202
11010599.54932703929195.45067296070809
111102104.184442965447-2.18444296544705
1129797.5846063252588-0.58460632525879
113100102.916253048904-2.91625304890422
114127129.484603472557-2.48460347255701
115138137.8141765451520.185823454848219
116107102.2568907910734.74310920892685
117107105.7555986577761.24440134222391
118106100.834826242855.16517375715003
119109103.1594390687255.84056093127538
12010798.37416302021268.62583697978737
121129120.81560998838.18439001169966
122138136.334213114161.66578688583974
123137137.542498641071-0.542498641071433
124134133.8898295059440.110170494055581
125134140.568659502041-6.56865950204144
126166165.6022708341180.397729165881628
127180178.0770729159721.9229270840284
128131146.293337675131-15.2933376751311
129135134.0324176685240.967582331476279
130127130.270060836469-3.2700608364691
131121126.34024013312-5.34024013312019
132116113.1633887082552.83661129174496

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 105 & 94.033920940171 & 10.966079059829 \tabularnewline
14 & 110 & 108.318234573005 & 1.68176542699501 \tabularnewline
15 & 115 & 115.730998407884 & -0.730998407883959 \tabularnewline
16 & 110 & 110.792813301557 & -0.792813301556762 \tabularnewline
17 & 114 & 114.47952851743 & -0.479528517429543 \tabularnewline
18 & 149 & 149.677724664825 & -0.677724664825234 \tabularnewline
19 & 147 & 150.734235234803 & -3.73423523480318 \tabularnewline
20 & 113 & 116.724727228373 & -3.72472722837328 \tabularnewline
21 & 113 & 115.512736542272 & -2.51273654227222 \tabularnewline
22 & 107 & 94.0797785841419 & 12.9202214158581 \tabularnewline
23 & 109 & 112.333223318007 & -3.33322331800667 \tabularnewline
24 & 103 & 105.242332036471 & -2.24233203647086 \tabularnewline
25 & 113 & 126.530081331336 & -13.5300813313364 \tabularnewline
26 & 112 & 119.031198335241 & -7.0311983352411 \tabularnewline
27 & 114 & 118.007561590335 & -4.00756159033543 \tabularnewline
28 & 106 & 109.214096493775 & -3.21409649377546 \tabularnewline
29 & 107 & 109.681422874454 & -2.68142287445424 \tabularnewline
30 & 134 & 141.612661213598 & -7.61266121359756 \tabularnewline
31 & 135 & 134.785907993647 & 0.21409200635253 \tabularnewline
32 & 105 & 102.162465461669 & 2.83753453833091 \tabularnewline
33 & 105 & 104.923125127497 & 0.0768748725027422 \tabularnewline
34 & 90 & 87.7781170836857 & 2.22188291631433 \tabularnewline
35 & 92 & 92.3306018384982 & -0.330601838498211 \tabularnewline
36 & 83 & 86.2105331869937 & -3.21053318699366 \tabularnewline
37 & 95 & 102.527008588922 & -7.5270085889223 \tabularnewline
38 & 98 & 99.7786371160825 & -1.77863711608254 \tabularnewline
39 & 95 & 102.367445586005 & -7.36744558600456 \tabularnewline
40 & 81 & 89.8854989775212 & -8.88549897752119 \tabularnewline
41 & 83 & 84.5669502850118 & -1.56695028501183 \tabularnewline
42 & 106 & 114.74012681742 & -8.74012681742046 \tabularnewline
43 & 114 & 107.301343425413 & 6.69865657458659 \tabularnewline
44 & 80 & 79.0326012893996 & 0.967398710600392 \tabularnewline
45 & 82 & 78.389873914564 & 3.61012608543604 \tabularnewline
46 & 76 & 63.2902597901422 & 12.7097402098578 \tabularnewline
47 & 78 & 74.6448478831857 & 3.35515211681425 \tabularnewline
48 & 70 & 70.175536465331 & -0.175536465330978 \tabularnewline
49 & 82 & 87.4488712146224 & -5.44887121462236 \tabularnewline
50 & 86 & 87.3211361703799 & -1.32113617037992 \tabularnewline
51 & 87 & 88.7029938618332 & -1.70299386183324 \tabularnewline
52 & 74 & 80.2162729482496 & -6.21627294824955 \tabularnewline
53 & 79 & 78.7307715566138 & 0.269228443386169 \tabularnewline
54 & 110 & 108.855465334805 & 1.14453466519494 \tabularnewline
55 & 117 & 113.20170824624 & 3.79829175376017 \tabularnewline
56 & 82 & 81.8796969304191 & 0.120303069580856 \tabularnewline
57 & 71 & 81.6478094782192 & -10.6478094782192 \tabularnewline
58 & 67 & 57.4594059125508 & 9.54059408744922 \tabularnewline
59 & 66 & 63.8979378793046 & 2.10206212069536 \tabularnewline
60 & 57 & 57.2679662872678 & -0.267966287267825 \tabularnewline
61 & 71 & 72.8715198287016 & -1.87151982870157 \tabularnewline
62 & 77 & 76.2192247038435 & 0.780775296156534 \tabularnewline
63 & 76 & 79.0003619541563 & -3.00036195415635 \tabularnewline
64 & 69 & 68.2872243523375 & 0.712775647662482 \tabularnewline
65 & 74 & 73.7501078249848 & 0.249892175015219 \tabularnewline
66 & 101 & 104.180720544003 & -3.18072054400349 \tabularnewline
67 & 105 & 105.726605411826 & -0.726605411826355 \tabularnewline
68 & 73 & 69.7944889672549 & 3.20551103274514 \tabularnewline
69 & 68 & 69.3317185050545 & -1.3317185050545 \tabularnewline
70 & 65 & 57.2324386331711 & 7.7675613668289 \tabularnewline
71 & 70 & 60.7994913806641 & 9.20050861933593 \tabularnewline
72 & 65 & 59.6180969618685 & 5.38190303813147 \tabularnewline
73 & 80 & 79.9845211164749 & 0.0154788835251196 \tabularnewline
74 & 92 & 86.25577256915 & 5.74422743085002 \tabularnewline
75 & 93 & 93.080747931379 & -0.0807479313789941 \tabularnewline
76 & 90 & 86.6861063956991 & 3.31389360430093 \tabularnewline
77 & 96 & 95.3820395905899 & 0.617960409410074 \tabularnewline
78 & 125 & 126.660836117881 & -1.66083611788069 \tabularnewline
79 & 134 & 131.360394554678 & 2.63960544532154 \tabularnewline
80 & 100 & 100.495796146172 & -0.495796146172268 \tabularnewline
81 & 97 & 97.5445572387112 & -0.544557238711207 \tabularnewline
82 & 97 & 89.5780813102903 & 7.42191868970966 \tabularnewline
83 & 101 & 94.631661537094 & 6.368338462906 \tabularnewline
84 & 90 & 91.688508788666 & -1.68850878866603 \tabularnewline
85 & 108 & 106.352558808016 & 1.64744119198363 \tabularnewline
86 & 113 & 116.246051687889 & -3.24605168788926 \tabularnewline
87 & 112 & 115.45163101907 & -3.45163101906996 \tabularnewline
88 & 103 & 107.73020123681 & -4.73020123681012 \tabularnewline
89 & 103 & 109.738059304727 & -6.73805930472724 \tabularnewline
90 & 125 & 134.622670238537 & -9.62267023853738 \tabularnewline
91 & 128 & 133.610046908453 & -5.6100469084526 \tabularnewline
92 & 91 & 94.7342889786789 & -3.73428897867889 \tabularnewline
93 & 84 & 88.1956427571477 & -4.19564275714772 \tabularnewline
94 & 83 & 77.9965015462056 & 5.00349845379445 \tabularnewline
95 & 83 & 79.5903806273036 & 3.40961937269644 \tabularnewline
96 & 69 & 71.0319706673773 & -2.03197066737725 \tabularnewline
97 & 77 & 84.6928446337869 & -7.69284463378686 \tabularnewline
98 & 83 & 84.3406207468441 & -1.34062074684408 \tabularnewline
99 & 78 & 83.1287819331841 & -5.12878193318409 \tabularnewline
100 & 70 & 71.906986981472 & -1.90698698147199 \tabularnewline
101 & 75 & 73.8433483054563 & 1.15665169454373 \tabularnewline
102 & 101 & 102.720658896686 & -1.7206588966858 \tabularnewline
103 & 117 & 107.644331989502 & 9.35566801049808 \tabularnewline
104 & 80 & 80.3348548875545 & -0.334854887554471 \tabularnewline
105 & 87 & 76.0655369922285 & 10.9344630077715 \tabularnewline
106 & 81 & 80.0748032008963 & 0.92519679910373 \tabularnewline
107 & 78 & 78.4138787403425 & -0.413878740342483 \tabularnewline
108 & 73 & 65.7423280100985 & 7.25767198990154 \tabularnewline
109 & 93 & 85.765985110398 & 7.23401488960202 \tabularnewline
110 & 105 & 99.5493270392919 & 5.45067296070809 \tabularnewline
111 & 102 & 104.184442965447 & -2.18444296544705 \tabularnewline
112 & 97 & 97.5846063252588 & -0.58460632525879 \tabularnewline
113 & 100 & 102.916253048904 & -2.91625304890422 \tabularnewline
114 & 127 & 129.484603472557 & -2.48460347255701 \tabularnewline
115 & 138 & 137.814176545152 & 0.185823454848219 \tabularnewline
116 & 107 & 102.256890791073 & 4.74310920892685 \tabularnewline
117 & 107 & 105.755598657776 & 1.24440134222391 \tabularnewline
118 & 106 & 100.83482624285 & 5.16517375715003 \tabularnewline
119 & 109 & 103.159439068725 & 5.84056093127538 \tabularnewline
120 & 107 & 98.3741630202126 & 8.62583697978737 \tabularnewline
121 & 129 & 120.8156099883 & 8.18439001169966 \tabularnewline
122 & 138 & 136.33421311416 & 1.66578688583974 \tabularnewline
123 & 137 & 137.542498641071 & -0.542498641071433 \tabularnewline
124 & 134 & 133.889829505944 & 0.110170494055581 \tabularnewline
125 & 134 & 140.568659502041 & -6.56865950204144 \tabularnewline
126 & 166 & 165.602270834118 & 0.397729165881628 \tabularnewline
127 & 180 & 178.077072915972 & 1.9229270840284 \tabularnewline
128 & 131 & 146.293337675131 & -15.2933376751311 \tabularnewline
129 & 135 & 134.032417668524 & 0.967582331476279 \tabularnewline
130 & 127 & 130.270060836469 & -3.2700608364691 \tabularnewline
131 & 121 & 126.34024013312 & -5.34024013312019 \tabularnewline
132 & 116 & 113.163388708255 & 2.83661129174496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279202&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]105[/C][C]94.033920940171[/C][C]10.966079059829[/C][/ROW]
[ROW][C]14[/C][C]110[/C][C]108.318234573005[/C][C]1.68176542699501[/C][/ROW]
[ROW][C]15[/C][C]115[/C][C]115.730998407884[/C][C]-0.730998407883959[/C][/ROW]
[ROW][C]16[/C][C]110[/C][C]110.792813301557[/C][C]-0.792813301556762[/C][/ROW]
[ROW][C]17[/C][C]114[/C][C]114.47952851743[/C][C]-0.479528517429543[/C][/ROW]
[ROW][C]18[/C][C]149[/C][C]149.677724664825[/C][C]-0.677724664825234[/C][/ROW]
[ROW][C]19[/C][C]147[/C][C]150.734235234803[/C][C]-3.73423523480318[/C][/ROW]
[ROW][C]20[/C][C]113[/C][C]116.724727228373[/C][C]-3.72472722837328[/C][/ROW]
[ROW][C]21[/C][C]113[/C][C]115.512736542272[/C][C]-2.51273654227222[/C][/ROW]
[ROW][C]22[/C][C]107[/C][C]94.0797785841419[/C][C]12.9202214158581[/C][/ROW]
[ROW][C]23[/C][C]109[/C][C]112.333223318007[/C][C]-3.33322331800667[/C][/ROW]
[ROW][C]24[/C][C]103[/C][C]105.242332036471[/C][C]-2.24233203647086[/C][/ROW]
[ROW][C]25[/C][C]113[/C][C]126.530081331336[/C][C]-13.5300813313364[/C][/ROW]
[ROW][C]26[/C][C]112[/C][C]119.031198335241[/C][C]-7.0311983352411[/C][/ROW]
[ROW][C]27[/C][C]114[/C][C]118.007561590335[/C][C]-4.00756159033543[/C][/ROW]
[ROW][C]28[/C][C]106[/C][C]109.214096493775[/C][C]-3.21409649377546[/C][/ROW]
[ROW][C]29[/C][C]107[/C][C]109.681422874454[/C][C]-2.68142287445424[/C][/ROW]
[ROW][C]30[/C][C]134[/C][C]141.612661213598[/C][C]-7.61266121359756[/C][/ROW]
[ROW][C]31[/C][C]135[/C][C]134.785907993647[/C][C]0.21409200635253[/C][/ROW]
[ROW][C]32[/C][C]105[/C][C]102.162465461669[/C][C]2.83753453833091[/C][/ROW]
[ROW][C]33[/C][C]105[/C][C]104.923125127497[/C][C]0.0768748725027422[/C][/ROW]
[ROW][C]34[/C][C]90[/C][C]87.7781170836857[/C][C]2.22188291631433[/C][/ROW]
[ROW][C]35[/C][C]92[/C][C]92.3306018384982[/C][C]-0.330601838498211[/C][/ROW]
[ROW][C]36[/C][C]83[/C][C]86.2105331869937[/C][C]-3.21053318699366[/C][/ROW]
[ROW][C]37[/C][C]95[/C][C]102.527008588922[/C][C]-7.5270085889223[/C][/ROW]
[ROW][C]38[/C][C]98[/C][C]99.7786371160825[/C][C]-1.77863711608254[/C][/ROW]
[ROW][C]39[/C][C]95[/C][C]102.367445586005[/C][C]-7.36744558600456[/C][/ROW]
[ROW][C]40[/C][C]81[/C][C]89.8854989775212[/C][C]-8.88549897752119[/C][/ROW]
[ROW][C]41[/C][C]83[/C][C]84.5669502850118[/C][C]-1.56695028501183[/C][/ROW]
[ROW][C]42[/C][C]106[/C][C]114.74012681742[/C][C]-8.74012681742046[/C][/ROW]
[ROW][C]43[/C][C]114[/C][C]107.301343425413[/C][C]6.69865657458659[/C][/ROW]
[ROW][C]44[/C][C]80[/C][C]79.0326012893996[/C][C]0.967398710600392[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]78.389873914564[/C][C]3.61012608543604[/C][/ROW]
[ROW][C]46[/C][C]76[/C][C]63.2902597901422[/C][C]12.7097402098578[/C][/ROW]
[ROW][C]47[/C][C]78[/C][C]74.6448478831857[/C][C]3.35515211681425[/C][/ROW]
[ROW][C]48[/C][C]70[/C][C]70.175536465331[/C][C]-0.175536465330978[/C][/ROW]
[ROW][C]49[/C][C]82[/C][C]87.4488712146224[/C][C]-5.44887121462236[/C][/ROW]
[ROW][C]50[/C][C]86[/C][C]87.3211361703799[/C][C]-1.32113617037992[/C][/ROW]
[ROW][C]51[/C][C]87[/C][C]88.7029938618332[/C][C]-1.70299386183324[/C][/ROW]
[ROW][C]52[/C][C]74[/C][C]80.2162729482496[/C][C]-6.21627294824955[/C][/ROW]
[ROW][C]53[/C][C]79[/C][C]78.7307715566138[/C][C]0.269228443386169[/C][/ROW]
[ROW][C]54[/C][C]110[/C][C]108.855465334805[/C][C]1.14453466519494[/C][/ROW]
[ROW][C]55[/C][C]117[/C][C]113.20170824624[/C][C]3.79829175376017[/C][/ROW]
[ROW][C]56[/C][C]82[/C][C]81.8796969304191[/C][C]0.120303069580856[/C][/ROW]
[ROW][C]57[/C][C]71[/C][C]81.6478094782192[/C][C]-10.6478094782192[/C][/ROW]
[ROW][C]58[/C][C]67[/C][C]57.4594059125508[/C][C]9.54059408744922[/C][/ROW]
[ROW][C]59[/C][C]66[/C][C]63.8979378793046[/C][C]2.10206212069536[/C][/ROW]
[ROW][C]60[/C][C]57[/C][C]57.2679662872678[/C][C]-0.267966287267825[/C][/ROW]
[ROW][C]61[/C][C]71[/C][C]72.8715198287016[/C][C]-1.87151982870157[/C][/ROW]
[ROW][C]62[/C][C]77[/C][C]76.2192247038435[/C][C]0.780775296156534[/C][/ROW]
[ROW][C]63[/C][C]76[/C][C]79.0003619541563[/C][C]-3.00036195415635[/C][/ROW]
[ROW][C]64[/C][C]69[/C][C]68.2872243523375[/C][C]0.712775647662482[/C][/ROW]
[ROW][C]65[/C][C]74[/C][C]73.7501078249848[/C][C]0.249892175015219[/C][/ROW]
[ROW][C]66[/C][C]101[/C][C]104.180720544003[/C][C]-3.18072054400349[/C][/ROW]
[ROW][C]67[/C][C]105[/C][C]105.726605411826[/C][C]-0.726605411826355[/C][/ROW]
[ROW][C]68[/C][C]73[/C][C]69.7944889672549[/C][C]3.20551103274514[/C][/ROW]
[ROW][C]69[/C][C]68[/C][C]69.3317185050545[/C][C]-1.3317185050545[/C][/ROW]
[ROW][C]70[/C][C]65[/C][C]57.2324386331711[/C][C]7.7675613668289[/C][/ROW]
[ROW][C]71[/C][C]70[/C][C]60.7994913806641[/C][C]9.20050861933593[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]59.6180969618685[/C][C]5.38190303813147[/C][/ROW]
[ROW][C]73[/C][C]80[/C][C]79.9845211164749[/C][C]0.0154788835251196[/C][/ROW]
[ROW][C]74[/C][C]92[/C][C]86.25577256915[/C][C]5.74422743085002[/C][/ROW]
[ROW][C]75[/C][C]93[/C][C]93.080747931379[/C][C]-0.0807479313789941[/C][/ROW]
[ROW][C]76[/C][C]90[/C][C]86.6861063956991[/C][C]3.31389360430093[/C][/ROW]
[ROW][C]77[/C][C]96[/C][C]95.3820395905899[/C][C]0.617960409410074[/C][/ROW]
[ROW][C]78[/C][C]125[/C][C]126.660836117881[/C][C]-1.66083611788069[/C][/ROW]
[ROW][C]79[/C][C]134[/C][C]131.360394554678[/C][C]2.63960544532154[/C][/ROW]
[ROW][C]80[/C][C]100[/C][C]100.495796146172[/C][C]-0.495796146172268[/C][/ROW]
[ROW][C]81[/C][C]97[/C][C]97.5445572387112[/C][C]-0.544557238711207[/C][/ROW]
[ROW][C]82[/C][C]97[/C][C]89.5780813102903[/C][C]7.42191868970966[/C][/ROW]
[ROW][C]83[/C][C]101[/C][C]94.631661537094[/C][C]6.368338462906[/C][/ROW]
[ROW][C]84[/C][C]90[/C][C]91.688508788666[/C][C]-1.68850878866603[/C][/ROW]
[ROW][C]85[/C][C]108[/C][C]106.352558808016[/C][C]1.64744119198363[/C][/ROW]
[ROW][C]86[/C][C]113[/C][C]116.246051687889[/C][C]-3.24605168788926[/C][/ROW]
[ROW][C]87[/C][C]112[/C][C]115.45163101907[/C][C]-3.45163101906996[/C][/ROW]
[ROW][C]88[/C][C]103[/C][C]107.73020123681[/C][C]-4.73020123681012[/C][/ROW]
[ROW][C]89[/C][C]103[/C][C]109.738059304727[/C][C]-6.73805930472724[/C][/ROW]
[ROW][C]90[/C][C]125[/C][C]134.622670238537[/C][C]-9.62267023853738[/C][/ROW]
[ROW][C]91[/C][C]128[/C][C]133.610046908453[/C][C]-5.6100469084526[/C][/ROW]
[ROW][C]92[/C][C]91[/C][C]94.7342889786789[/C][C]-3.73428897867889[/C][/ROW]
[ROW][C]93[/C][C]84[/C][C]88.1956427571477[/C][C]-4.19564275714772[/C][/ROW]
[ROW][C]94[/C][C]83[/C][C]77.9965015462056[/C][C]5.00349845379445[/C][/ROW]
[ROW][C]95[/C][C]83[/C][C]79.5903806273036[/C][C]3.40961937269644[/C][/ROW]
[ROW][C]96[/C][C]69[/C][C]71.0319706673773[/C][C]-2.03197066737725[/C][/ROW]
[ROW][C]97[/C][C]77[/C][C]84.6928446337869[/C][C]-7.69284463378686[/C][/ROW]
[ROW][C]98[/C][C]83[/C][C]84.3406207468441[/C][C]-1.34062074684408[/C][/ROW]
[ROW][C]99[/C][C]78[/C][C]83.1287819331841[/C][C]-5.12878193318409[/C][/ROW]
[ROW][C]100[/C][C]70[/C][C]71.906986981472[/C][C]-1.90698698147199[/C][/ROW]
[ROW][C]101[/C][C]75[/C][C]73.8433483054563[/C][C]1.15665169454373[/C][/ROW]
[ROW][C]102[/C][C]101[/C][C]102.720658896686[/C][C]-1.7206588966858[/C][/ROW]
[ROW][C]103[/C][C]117[/C][C]107.644331989502[/C][C]9.35566801049808[/C][/ROW]
[ROW][C]104[/C][C]80[/C][C]80.3348548875545[/C][C]-0.334854887554471[/C][/ROW]
[ROW][C]105[/C][C]87[/C][C]76.0655369922285[/C][C]10.9344630077715[/C][/ROW]
[ROW][C]106[/C][C]81[/C][C]80.0748032008963[/C][C]0.92519679910373[/C][/ROW]
[ROW][C]107[/C][C]78[/C][C]78.4138787403425[/C][C]-0.413878740342483[/C][/ROW]
[ROW][C]108[/C][C]73[/C][C]65.7423280100985[/C][C]7.25767198990154[/C][/ROW]
[ROW][C]109[/C][C]93[/C][C]85.765985110398[/C][C]7.23401488960202[/C][/ROW]
[ROW][C]110[/C][C]105[/C][C]99.5493270392919[/C][C]5.45067296070809[/C][/ROW]
[ROW][C]111[/C][C]102[/C][C]104.184442965447[/C][C]-2.18444296544705[/C][/ROW]
[ROW][C]112[/C][C]97[/C][C]97.5846063252588[/C][C]-0.58460632525879[/C][/ROW]
[ROW][C]113[/C][C]100[/C][C]102.916253048904[/C][C]-2.91625304890422[/C][/ROW]
[ROW][C]114[/C][C]127[/C][C]129.484603472557[/C][C]-2.48460347255701[/C][/ROW]
[ROW][C]115[/C][C]138[/C][C]137.814176545152[/C][C]0.185823454848219[/C][/ROW]
[ROW][C]116[/C][C]107[/C][C]102.256890791073[/C][C]4.74310920892685[/C][/ROW]
[ROW][C]117[/C][C]107[/C][C]105.755598657776[/C][C]1.24440134222391[/C][/ROW]
[ROW][C]118[/C][C]106[/C][C]100.83482624285[/C][C]5.16517375715003[/C][/ROW]
[ROW][C]119[/C][C]109[/C][C]103.159439068725[/C][C]5.84056093127538[/C][/ROW]
[ROW][C]120[/C][C]107[/C][C]98.3741630202126[/C][C]8.62583697978737[/C][/ROW]
[ROW][C]121[/C][C]129[/C][C]120.8156099883[/C][C]8.18439001169966[/C][/ROW]
[ROW][C]122[/C][C]138[/C][C]136.33421311416[/C][C]1.66578688583974[/C][/ROW]
[ROW][C]123[/C][C]137[/C][C]137.542498641071[/C][C]-0.542498641071433[/C][/ROW]
[ROW][C]124[/C][C]134[/C][C]133.889829505944[/C][C]0.110170494055581[/C][/ROW]
[ROW][C]125[/C][C]134[/C][C]140.568659502041[/C][C]-6.56865950204144[/C][/ROW]
[ROW][C]126[/C][C]166[/C][C]165.602270834118[/C][C]0.397729165881628[/C][/ROW]
[ROW][C]127[/C][C]180[/C][C]178.077072915972[/C][C]1.9229270840284[/C][/ROW]
[ROW][C]128[/C][C]131[/C][C]146.293337675131[/C][C]-15.2933376751311[/C][/ROW]
[ROW][C]129[/C][C]135[/C][C]134.032417668524[/C][C]0.967582331476279[/C][/ROW]
[ROW][C]130[/C][C]127[/C][C]130.270060836469[/C][C]-3.2700608364691[/C][/ROW]
[ROW][C]131[/C][C]121[/C][C]126.34024013312[/C][C]-5.34024013312019[/C][/ROW]
[ROW][C]132[/C][C]116[/C][C]113.163388708255[/C][C]2.83661129174496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279202&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279202&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
1310594.03392094017110.966079059829
14110108.3182345730051.68176542699501
15115115.730998407884-0.730998407883959
16110110.792813301557-0.792813301556762
17114114.47952851743-0.479528517429543
18149149.677724664825-0.677724664825234
19147150.734235234803-3.73423523480318
20113116.724727228373-3.72472722837328
21113115.512736542272-2.51273654227222
2210794.079778584141912.9202214158581
23109112.333223318007-3.33322331800667
24103105.242332036471-2.24233203647086
25113126.530081331336-13.5300813313364
26112119.031198335241-7.0311983352411
27114118.007561590335-4.00756159033543
28106109.214096493775-3.21409649377546
29107109.681422874454-2.68142287445424
30134141.612661213598-7.61266121359756
31135134.7859079936470.21409200635253
32105102.1624654616692.83753453833091
33105104.9231251274970.0768748725027422
349087.77811708368572.22188291631433
359292.3306018384982-0.330601838498211
368386.2105331869937-3.21053318699366
3795102.527008588922-7.5270085889223
389899.7786371160825-1.77863711608254
3995102.367445586005-7.36744558600456
408189.8854989775212-8.88549897752119
418384.5669502850118-1.56695028501183
42106114.74012681742-8.74012681742046
43114107.3013434254136.69865657458659
448079.03260128939960.967398710600392
458278.3898739145643.61012608543604
467663.290259790142212.7097402098578
477874.64484788318573.35515211681425
487070.175536465331-0.175536465330978
498287.4488712146224-5.44887121462236
508687.3211361703799-1.32113617037992
518788.7029938618332-1.70299386183324
527480.2162729482496-6.21627294824955
537978.73077155661380.269228443386169
54110108.8554653348051.14453466519494
55117113.201708246243.79829175376017
568281.87969693041910.120303069580856
577181.6478094782192-10.6478094782192
586757.45940591255089.54059408744922
596663.89793787930462.10206212069536
605757.2679662872678-0.267966287267825
617172.8715198287016-1.87151982870157
627776.21922470384350.780775296156534
637679.0003619541563-3.00036195415635
646968.28722435233750.712775647662482
657473.75010782498480.249892175015219
66101104.180720544003-3.18072054400349
67105105.726605411826-0.726605411826355
687369.79448896725493.20551103274514
696869.3317185050545-1.3317185050545
706557.23243863317117.7675613668289
717060.79949138066419.20050861933593
726559.61809696186855.38190303813147
738079.98452111647490.0154788835251196
749286.255772569155.74422743085002
759393.080747931379-0.0807479313789941
769086.68610639569913.31389360430093
779695.38203959058990.617960409410074
78125126.660836117881-1.66083611788069
79134131.3603945546782.63960544532154
80100100.495796146172-0.495796146172268
819797.5445572387112-0.544557238711207
829789.57808131029037.42191868970966
8310194.6316615370946.368338462906
849091.688508788666-1.68850878866603
85108106.3525588080161.64744119198363
86113116.246051687889-3.24605168788926
87112115.45163101907-3.45163101906996
88103107.73020123681-4.73020123681012
89103109.738059304727-6.73805930472724
90125134.622670238537-9.62267023853738
91128133.610046908453-5.6100469084526
929194.7342889786789-3.73428897867889
938488.1956427571477-4.19564275714772
948377.99650154620565.00349845379445
958379.59038062730363.40961937269644
966971.0319706673773-2.03197066737725
977784.6928446337869-7.69284463378686
988384.3406207468441-1.34062074684408
997883.1287819331841-5.12878193318409
1007071.906986981472-1.90698698147199
1017573.84334830545631.15665169454373
102101102.720658896686-1.7206588966858
103117107.6443319895029.35566801049808
1048080.3348548875545-0.334854887554471
1058776.065536992228510.9344630077715
1068180.07480320089630.92519679910373
1077878.4138787403425-0.413878740342483
1087365.74232801009857.25767198990154
1099385.7659851103987.23401488960202
11010599.54932703929195.45067296070809
111102104.184442965447-2.18444296544705
1129797.5846063252588-0.58460632525879
113100102.916253048904-2.91625304890422
114127129.484603472557-2.48460347255701
115138137.8141765451520.185823454848219
116107102.2568907910734.74310920892685
117107105.7555986577761.24440134222391
118106100.834826242855.16517375715003
119109103.1594390687255.84056093127538
12010798.37416302021268.62583697978737
121129120.81560998838.18439001169966
122138136.334213114161.66578688583974
123137137.542498641071-0.542498641071433
124134133.8898295059440.110170494055581
125134140.568659502041-6.56865950204144
126166165.6022708341180.397729165881628
127180178.0770729159721.9229270840284
128131146.293337675131-15.2933376751311
129135134.0324176685240.967582331476279
130127130.270060836469-3.2700608364691
131121126.34024013312-5.34024013312019
132116113.1633887082552.83661129174496







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133130.367673238281120.270348870116140.464997606445
134137.040354963137124.008677382391150.072032543884
135135.339855102666119.674243919662151.005466285669
136131.160806133856113.018817173548149.302795094164
137135.124432875619114.59637076056155.652494990677
138166.015304204459143.154078721935188.876529686983
139177.712688171396152.548225191635202.877151151157
140139.592549705541112.139670471751167.045428939331
141142.629833550333112.892948733777172.36671836689
142136.889564084461104.865651726684168.913476442237
143134.892486346429100.573074127164169.211898565693
144127.83424557889391.2067812896567164.461709868129

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 130.367673238281 & 120.270348870116 & 140.464997606445 \tabularnewline
134 & 137.040354963137 & 124.008677382391 & 150.072032543884 \tabularnewline
135 & 135.339855102666 & 119.674243919662 & 151.005466285669 \tabularnewline
136 & 131.160806133856 & 113.018817173548 & 149.302795094164 \tabularnewline
137 & 135.124432875619 & 114.59637076056 & 155.652494990677 \tabularnewline
138 & 166.015304204459 & 143.154078721935 & 188.876529686983 \tabularnewline
139 & 177.712688171396 & 152.548225191635 & 202.877151151157 \tabularnewline
140 & 139.592549705541 & 112.139670471751 & 167.045428939331 \tabularnewline
141 & 142.629833550333 & 112.892948733777 & 172.36671836689 \tabularnewline
142 & 136.889564084461 & 104.865651726684 & 168.913476442237 \tabularnewline
143 & 134.892486346429 & 100.573074127164 & 169.211898565693 \tabularnewline
144 & 127.834245578893 & 91.2067812896567 & 164.461709868129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279202&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]133[/C][C]130.367673238281[/C][C]120.270348870116[/C][C]140.464997606445[/C][/ROW]
[ROW][C]134[/C][C]137.040354963137[/C][C]124.008677382391[/C][C]150.072032543884[/C][/ROW]
[ROW][C]135[/C][C]135.339855102666[/C][C]119.674243919662[/C][C]151.005466285669[/C][/ROW]
[ROW][C]136[/C][C]131.160806133856[/C][C]113.018817173548[/C][C]149.302795094164[/C][/ROW]
[ROW][C]137[/C][C]135.124432875619[/C][C]114.59637076056[/C][C]155.652494990677[/C][/ROW]
[ROW][C]138[/C][C]166.015304204459[/C][C]143.154078721935[/C][C]188.876529686983[/C][/ROW]
[ROW][C]139[/C][C]177.712688171396[/C][C]152.548225191635[/C][C]202.877151151157[/C][/ROW]
[ROW][C]140[/C][C]139.592549705541[/C][C]112.139670471751[/C][C]167.045428939331[/C][/ROW]
[ROW][C]141[/C][C]142.629833550333[/C][C]112.892948733777[/C][C]172.36671836689[/C][/ROW]
[ROW][C]142[/C][C]136.889564084461[/C][C]104.865651726684[/C][C]168.913476442237[/C][/ROW]
[ROW][C]143[/C][C]134.892486346429[/C][C]100.573074127164[/C][C]169.211898565693[/C][/ROW]
[ROW][C]144[/C][C]127.834245578893[/C][C]91.2067812896567[/C][C]164.461709868129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279202&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279202&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
133130.367673238281120.270348870116140.464997606445
134137.040354963137124.008677382391150.072032543884
135135.339855102666119.674243919662151.005466285669
136131.160806133856113.018817173548149.302795094164
137135.124432875619114.59637076056155.652494990677
138166.015304204459143.154078721935188.876529686983
139177.712688171396152.548225191635202.877151151157
140139.592549705541112.139670471751167.045428939331
141142.629833550333112.892948733777172.36671836689
142136.889564084461104.865651726684168.913476442237
143134.892486346429100.573074127164169.211898565693
144127.83424557889391.2067812896567164.461709868129



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')