Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 11 Jul 2010 16:01:25 +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/Jul/11/t1278864170rpzuyid9690txa8.htm/, Retrieved Fri, 03 May 2024 07:22:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77996, Retrieved Fri, 03 May 2024 07:22:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsFebiri Lordina
Estimated Impact211
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-07-11 16:01:25] [ee335b92128d1ec04d3c346475765c6a] [Current]
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Dataseries X:
213
212
211
209
229
228
213
203
204
204
205
207
205
208
201
201
220
218
203
185
179
182
182
185
183
192
177
172
188
182
162
150
141
135
139
148
142
156
143
134
146
142
117
106
104
99
105
106
96
104
96
85
91
98
73
70
62
60
70
82
72
73
68
53
61
73
46
50
52
45
58
73
58
49
44
35
46
61
29
33
37
31
44
57
42
34
27
22
30
47
12
13
18
11
26
41
21
24
30
34
48
64
35
44
55
53
73
94
73
78
87
87
91
104
73
84
103
111
131
155




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77996&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77996&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77996&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.575651073368057
beta0.0869583411263661
gamma0.402742687472037

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.575651073368057 \tabularnewline
beta & 0.0869583411263661 \tabularnewline
gamma & 0.402742687472037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77996&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]0.575651073368057[/C][/ROW]
[ROW][C]beta[/C][C]0.0869583411263661[/C][/ROW]
[ROW][C]gamma[/C][C]0.402742687472037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77996&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77996&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
alpha0.575651073368057
beta0.0869583411263661
gamma0.402742687472037







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13205209.192478598406-4.19247859840641
14208209.632082374054-1.63208237405388
15201202.032536769601-1.03253676960068
16201201.916846630005-0.916846630004585
17220220.811708811239-0.81170881123856
18218218.685886150255-0.685886150254959
19203198.7128043246874.28719567531294
20185190.858097501976-5.85809750197632
21179187.294217200712-8.29421720071221
22182181.1126393905930.88736060940741
23182181.1001593142460.899840685754185
24185182.0733153852592.92668461474102
25183180.2303837200942.76961627990596
26192184.1757681481987.82423185180241
27177182.689366602584-5.68936660258356
28172179.543655784908-7.54365578490805
29188191.372081448318-3.37208144831806
30182187.116246159165-5.11624615916494
31162167.284067282252-5.28406728225201
32150152.944275949712-2.94427594971205
33141149.328674507793-8.32867450779273
34135143.138082233170-8.1380822331703
35139135.9975135411483.00248645885151
36148136.34894926703611.6510507329643
37142138.8327556839373.16724431606301
38156141.65553644826914.3444635517309
39143142.3694242989340.630575701065709
40134141.842565480813-7.84256548081308
41146149.737292151698-3.73729215169757
42142144.542665587422-2.54266558742177
43117129.013747026312-12.0137470263116
44106112.682713645966-6.6827136459658
45104105.194591570029-1.19459157002912
4699102.169049253627-3.16904925362729
4710598.74467368911926.25532631088082
48106101.3664858832944.63351411670573
499698.7245163533632-2.72451635336317
5010497.43678118419356.56321881580647
519692.8892761714473.11072382855301
528591.4800289150223-6.48002891502232
539194.2741655201472-3.27416552014725
549888.58123072810749.41876927189264
557382.3381903051804-9.33819030518038
567070.1580679263133-0.158067926313279
576267.2101684585941-5.21016845859411
586061.102021148952-1.10202114895200
597058.944847066973711.0551529330263
608263.425236803629618.5747631963704
617269.43338694084862.56661305915139
627372.54491293119420.455087068805838
636866.45811673953941.54188326046064
645363.8455425495228-10.8455425495228
656161.7379184546695-0.737918454669504
667359.669320488325213.3306795116748
674656.7766086813169-10.7766086813169
685046.72327952102313.27672047897689
695245.90897015305456.09102984694554
704548.2520618502894-3.25206185028943
715847.261413023906910.7385869760931
727353.415358351795519.5846416482045
735859.525784897736-1.52578489773599
744960.572620874895-11.572620874895
754449.4320353622459-5.43203536224589
763541.9761871672008-6.97618716720078
774641.55403339166034.4459666083397
786144.442297426152916.5577025738471
792942.7666858290369-13.7666858290369
803333.7033191132543-0.703319113254338
813731.41063394446635.58936605553374
823132.475571950384-1.47557195038399
834433.516252886935910.4837471130641
845740.163547386507316.8364526134927
854243.5059419744658-1.50594197446578
863442.6721193844814-8.67211938448144
872735.1708476984624-8.17084769846244
882227.0296209699263-5.02962096992629
893027.35119595170692.64880404829310
904729.616491869505517.3835081304945
911227.7540167311256-15.7540167311256
921318.6342160669002-5.63421606690021
931813.77162706384914.22837293615093
941113.5886758044485-2.58867580444850
952611.970521855092514.0294781449075
964119.640674155944821.3593258440552
972125.9952352375190-4.99523523751904
982421.93054447887222.06945552112780
993021.43642811734178.56357188265828
1003424.64243802788539.3575619721147
1014838.78653675043519.21346324956492
1026452.08356299107811.916437008922
1033534.74715092569280.252849074307171
1044442.83445279487531.16554720512467
1055551.42613907297953.57386092702050
1065348.25970993854734.74029006145269
1077372.15261726656780.847382733432212
1089479.374921626744814.6250783732552
1097365.24231945913327.75768054086677
1107874.86832412574623.13167587425376
1118778.9483506744888.05164932551202
1128781.63280939374195.36719060625806
11391110.822142408706-19.8221424087059
114104118.864830003997-14.8648300039972
1157362.958471404143110.0415285958569
1168485.1059561337918-1.10595613379181
117103100.8858628473172.11413715268318
11811192.69672795288418.3032720471161
119131144.705635126675-13.7056351266745
120155153.5499400158221.4500599841777

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 205 & 209.192478598406 & -4.19247859840641 \tabularnewline
14 & 208 & 209.632082374054 & -1.63208237405388 \tabularnewline
15 & 201 & 202.032536769601 & -1.03253676960068 \tabularnewline
16 & 201 & 201.916846630005 & -0.916846630004585 \tabularnewline
17 & 220 & 220.811708811239 & -0.81170881123856 \tabularnewline
18 & 218 & 218.685886150255 & -0.685886150254959 \tabularnewline
19 & 203 & 198.712804324687 & 4.28719567531294 \tabularnewline
20 & 185 & 190.858097501976 & -5.85809750197632 \tabularnewline
21 & 179 & 187.294217200712 & -8.29421720071221 \tabularnewline
22 & 182 & 181.112639390593 & 0.88736060940741 \tabularnewline
23 & 182 & 181.100159314246 & 0.899840685754185 \tabularnewline
24 & 185 & 182.073315385259 & 2.92668461474102 \tabularnewline
25 & 183 & 180.230383720094 & 2.76961627990596 \tabularnewline
26 & 192 & 184.175768148198 & 7.82423185180241 \tabularnewline
27 & 177 & 182.689366602584 & -5.68936660258356 \tabularnewline
28 & 172 & 179.543655784908 & -7.54365578490805 \tabularnewline
29 & 188 & 191.372081448318 & -3.37208144831806 \tabularnewline
30 & 182 & 187.116246159165 & -5.11624615916494 \tabularnewline
31 & 162 & 167.284067282252 & -5.28406728225201 \tabularnewline
32 & 150 & 152.944275949712 & -2.94427594971205 \tabularnewline
33 & 141 & 149.328674507793 & -8.32867450779273 \tabularnewline
34 & 135 & 143.138082233170 & -8.1380822331703 \tabularnewline
35 & 139 & 135.997513541148 & 3.00248645885151 \tabularnewline
36 & 148 & 136.348949267036 & 11.6510507329643 \tabularnewline
37 & 142 & 138.832755683937 & 3.16724431606301 \tabularnewline
38 & 156 & 141.655536448269 & 14.3444635517309 \tabularnewline
39 & 143 & 142.369424298934 & 0.630575701065709 \tabularnewline
40 & 134 & 141.842565480813 & -7.84256548081308 \tabularnewline
41 & 146 & 149.737292151698 & -3.73729215169757 \tabularnewline
42 & 142 & 144.542665587422 & -2.54266558742177 \tabularnewline
43 & 117 & 129.013747026312 & -12.0137470263116 \tabularnewline
44 & 106 & 112.682713645966 & -6.6827136459658 \tabularnewline
45 & 104 & 105.194591570029 & -1.19459157002912 \tabularnewline
46 & 99 & 102.169049253627 & -3.16904925362729 \tabularnewline
47 & 105 & 98.7446736891192 & 6.25532631088082 \tabularnewline
48 & 106 & 101.366485883294 & 4.63351411670573 \tabularnewline
49 & 96 & 98.7245163533632 & -2.72451635336317 \tabularnewline
50 & 104 & 97.4367811841935 & 6.56321881580647 \tabularnewline
51 & 96 & 92.889276171447 & 3.11072382855301 \tabularnewline
52 & 85 & 91.4800289150223 & -6.48002891502232 \tabularnewline
53 & 91 & 94.2741655201472 & -3.27416552014725 \tabularnewline
54 & 98 & 88.5812307281074 & 9.41876927189264 \tabularnewline
55 & 73 & 82.3381903051804 & -9.33819030518038 \tabularnewline
56 & 70 & 70.1580679263133 & -0.158067926313279 \tabularnewline
57 & 62 & 67.2101684585941 & -5.21016845859411 \tabularnewline
58 & 60 & 61.102021148952 & -1.10202114895200 \tabularnewline
59 & 70 & 58.9448470669737 & 11.0551529330263 \tabularnewline
60 & 82 & 63.4252368036296 & 18.5747631963704 \tabularnewline
61 & 72 & 69.4333869408486 & 2.56661305915139 \tabularnewline
62 & 73 & 72.5449129311942 & 0.455087068805838 \tabularnewline
63 & 68 & 66.4581167395394 & 1.54188326046064 \tabularnewline
64 & 53 & 63.8455425495228 & -10.8455425495228 \tabularnewline
65 & 61 & 61.7379184546695 & -0.737918454669504 \tabularnewline
66 & 73 & 59.6693204883252 & 13.3306795116748 \tabularnewline
67 & 46 & 56.7766086813169 & -10.7766086813169 \tabularnewline
68 & 50 & 46.7232795210231 & 3.27672047897689 \tabularnewline
69 & 52 & 45.9089701530545 & 6.09102984694554 \tabularnewline
70 & 45 & 48.2520618502894 & -3.25206185028943 \tabularnewline
71 & 58 & 47.2614130239069 & 10.7385869760931 \tabularnewline
72 & 73 & 53.4153583517955 & 19.5846416482045 \tabularnewline
73 & 58 & 59.525784897736 & -1.52578489773599 \tabularnewline
74 & 49 & 60.572620874895 & -11.572620874895 \tabularnewline
75 & 44 & 49.4320353622459 & -5.43203536224589 \tabularnewline
76 & 35 & 41.9761871672008 & -6.97618716720078 \tabularnewline
77 & 46 & 41.5540333916603 & 4.4459666083397 \tabularnewline
78 & 61 & 44.4422974261529 & 16.5577025738471 \tabularnewline
79 & 29 & 42.7666858290369 & -13.7666858290369 \tabularnewline
80 & 33 & 33.7033191132543 & -0.703319113254338 \tabularnewline
81 & 37 & 31.4106339444663 & 5.58936605553374 \tabularnewline
82 & 31 & 32.475571950384 & -1.47557195038399 \tabularnewline
83 & 44 & 33.5162528869359 & 10.4837471130641 \tabularnewline
84 & 57 & 40.1635473865073 & 16.8364526134927 \tabularnewline
85 & 42 & 43.5059419744658 & -1.50594197446578 \tabularnewline
86 & 34 & 42.6721193844814 & -8.67211938448144 \tabularnewline
87 & 27 & 35.1708476984624 & -8.17084769846244 \tabularnewline
88 & 22 & 27.0296209699263 & -5.02962096992629 \tabularnewline
89 & 30 & 27.3511959517069 & 2.64880404829310 \tabularnewline
90 & 47 & 29.6164918695055 & 17.3835081304945 \tabularnewline
91 & 12 & 27.7540167311256 & -15.7540167311256 \tabularnewline
92 & 13 & 18.6342160669002 & -5.63421606690021 \tabularnewline
93 & 18 & 13.7716270638491 & 4.22837293615093 \tabularnewline
94 & 11 & 13.5886758044485 & -2.58867580444850 \tabularnewline
95 & 26 & 11.9705218550925 & 14.0294781449075 \tabularnewline
96 & 41 & 19.6406741559448 & 21.3593258440552 \tabularnewline
97 & 21 & 25.9952352375190 & -4.99523523751904 \tabularnewline
98 & 24 & 21.9305444788722 & 2.06945552112780 \tabularnewline
99 & 30 & 21.4364281173417 & 8.56357188265828 \tabularnewline
100 & 34 & 24.6424380278853 & 9.3575619721147 \tabularnewline
101 & 48 & 38.7865367504351 & 9.21346324956492 \tabularnewline
102 & 64 & 52.083562991078 & 11.916437008922 \tabularnewline
103 & 35 & 34.7471509256928 & 0.252849074307171 \tabularnewline
104 & 44 & 42.8344527948753 & 1.16554720512467 \tabularnewline
105 & 55 & 51.4261390729795 & 3.57386092702050 \tabularnewline
106 & 53 & 48.2597099385473 & 4.74029006145269 \tabularnewline
107 & 73 & 72.1526172665678 & 0.847382733432212 \tabularnewline
108 & 94 & 79.3749216267448 & 14.6250783732552 \tabularnewline
109 & 73 & 65.2423194591332 & 7.75768054086677 \tabularnewline
110 & 78 & 74.8683241257462 & 3.13167587425376 \tabularnewline
111 & 87 & 78.948350674488 & 8.05164932551202 \tabularnewline
112 & 87 & 81.6328093937419 & 5.36719060625806 \tabularnewline
113 & 91 & 110.822142408706 & -19.8221424087059 \tabularnewline
114 & 104 & 118.864830003997 & -14.8648300039972 \tabularnewline
115 & 73 & 62.9584714041431 & 10.0415285958569 \tabularnewline
116 & 84 & 85.1059561337918 & -1.10595613379181 \tabularnewline
117 & 103 & 100.885862847317 & 2.11413715268318 \tabularnewline
118 & 111 & 92.696727952884 & 18.3032720471161 \tabularnewline
119 & 131 & 144.705635126675 & -13.7056351266745 \tabularnewline
120 & 155 & 153.549940015822 & 1.4500599841777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77996&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]205[/C][C]209.192478598406[/C][C]-4.19247859840641[/C][/ROW]
[ROW][C]14[/C][C]208[/C][C]209.632082374054[/C][C]-1.63208237405388[/C][/ROW]
[ROW][C]15[/C][C]201[/C][C]202.032536769601[/C][C]-1.03253676960068[/C][/ROW]
[ROW][C]16[/C][C]201[/C][C]201.916846630005[/C][C]-0.916846630004585[/C][/ROW]
[ROW][C]17[/C][C]220[/C][C]220.811708811239[/C][C]-0.81170881123856[/C][/ROW]
[ROW][C]18[/C][C]218[/C][C]218.685886150255[/C][C]-0.685886150254959[/C][/ROW]
[ROW][C]19[/C][C]203[/C][C]198.712804324687[/C][C]4.28719567531294[/C][/ROW]
[ROW][C]20[/C][C]185[/C][C]190.858097501976[/C][C]-5.85809750197632[/C][/ROW]
[ROW][C]21[/C][C]179[/C][C]187.294217200712[/C][C]-8.29421720071221[/C][/ROW]
[ROW][C]22[/C][C]182[/C][C]181.112639390593[/C][C]0.88736060940741[/C][/ROW]
[ROW][C]23[/C][C]182[/C][C]181.100159314246[/C][C]0.899840685754185[/C][/ROW]
[ROW][C]24[/C][C]185[/C][C]182.073315385259[/C][C]2.92668461474102[/C][/ROW]
[ROW][C]25[/C][C]183[/C][C]180.230383720094[/C][C]2.76961627990596[/C][/ROW]
[ROW][C]26[/C][C]192[/C][C]184.175768148198[/C][C]7.82423185180241[/C][/ROW]
[ROW][C]27[/C][C]177[/C][C]182.689366602584[/C][C]-5.68936660258356[/C][/ROW]
[ROW][C]28[/C][C]172[/C][C]179.543655784908[/C][C]-7.54365578490805[/C][/ROW]
[ROW][C]29[/C][C]188[/C][C]191.372081448318[/C][C]-3.37208144831806[/C][/ROW]
[ROW][C]30[/C][C]182[/C][C]187.116246159165[/C][C]-5.11624615916494[/C][/ROW]
[ROW][C]31[/C][C]162[/C][C]167.284067282252[/C][C]-5.28406728225201[/C][/ROW]
[ROW][C]32[/C][C]150[/C][C]152.944275949712[/C][C]-2.94427594971205[/C][/ROW]
[ROW][C]33[/C][C]141[/C][C]149.328674507793[/C][C]-8.32867450779273[/C][/ROW]
[ROW][C]34[/C][C]135[/C][C]143.138082233170[/C][C]-8.1380822331703[/C][/ROW]
[ROW][C]35[/C][C]139[/C][C]135.997513541148[/C][C]3.00248645885151[/C][/ROW]
[ROW][C]36[/C][C]148[/C][C]136.348949267036[/C][C]11.6510507329643[/C][/ROW]
[ROW][C]37[/C][C]142[/C][C]138.832755683937[/C][C]3.16724431606301[/C][/ROW]
[ROW][C]38[/C][C]156[/C][C]141.655536448269[/C][C]14.3444635517309[/C][/ROW]
[ROW][C]39[/C][C]143[/C][C]142.369424298934[/C][C]0.630575701065709[/C][/ROW]
[ROW][C]40[/C][C]134[/C][C]141.842565480813[/C][C]-7.84256548081308[/C][/ROW]
[ROW][C]41[/C][C]146[/C][C]149.737292151698[/C][C]-3.73729215169757[/C][/ROW]
[ROW][C]42[/C][C]142[/C][C]144.542665587422[/C][C]-2.54266558742177[/C][/ROW]
[ROW][C]43[/C][C]117[/C][C]129.013747026312[/C][C]-12.0137470263116[/C][/ROW]
[ROW][C]44[/C][C]106[/C][C]112.682713645966[/C][C]-6.6827136459658[/C][/ROW]
[ROW][C]45[/C][C]104[/C][C]105.194591570029[/C][C]-1.19459157002912[/C][/ROW]
[ROW][C]46[/C][C]99[/C][C]102.169049253627[/C][C]-3.16904925362729[/C][/ROW]
[ROW][C]47[/C][C]105[/C][C]98.7446736891192[/C][C]6.25532631088082[/C][/ROW]
[ROW][C]48[/C][C]106[/C][C]101.366485883294[/C][C]4.63351411670573[/C][/ROW]
[ROW][C]49[/C][C]96[/C][C]98.7245163533632[/C][C]-2.72451635336317[/C][/ROW]
[ROW][C]50[/C][C]104[/C][C]97.4367811841935[/C][C]6.56321881580647[/C][/ROW]
[ROW][C]51[/C][C]96[/C][C]92.889276171447[/C][C]3.11072382855301[/C][/ROW]
[ROW][C]52[/C][C]85[/C][C]91.4800289150223[/C][C]-6.48002891502232[/C][/ROW]
[ROW][C]53[/C][C]91[/C][C]94.2741655201472[/C][C]-3.27416552014725[/C][/ROW]
[ROW][C]54[/C][C]98[/C][C]88.5812307281074[/C][C]9.41876927189264[/C][/ROW]
[ROW][C]55[/C][C]73[/C][C]82.3381903051804[/C][C]-9.33819030518038[/C][/ROW]
[ROW][C]56[/C][C]70[/C][C]70.1580679263133[/C][C]-0.158067926313279[/C][/ROW]
[ROW][C]57[/C][C]62[/C][C]67.2101684585941[/C][C]-5.21016845859411[/C][/ROW]
[ROW][C]58[/C][C]60[/C][C]61.102021148952[/C][C]-1.10202114895200[/C][/ROW]
[ROW][C]59[/C][C]70[/C][C]58.9448470669737[/C][C]11.0551529330263[/C][/ROW]
[ROW][C]60[/C][C]82[/C][C]63.4252368036296[/C][C]18.5747631963704[/C][/ROW]
[ROW][C]61[/C][C]72[/C][C]69.4333869408486[/C][C]2.56661305915139[/C][/ROW]
[ROW][C]62[/C][C]73[/C][C]72.5449129311942[/C][C]0.455087068805838[/C][/ROW]
[ROW][C]63[/C][C]68[/C][C]66.4581167395394[/C][C]1.54188326046064[/C][/ROW]
[ROW][C]64[/C][C]53[/C][C]63.8455425495228[/C][C]-10.8455425495228[/C][/ROW]
[ROW][C]65[/C][C]61[/C][C]61.7379184546695[/C][C]-0.737918454669504[/C][/ROW]
[ROW][C]66[/C][C]73[/C][C]59.6693204883252[/C][C]13.3306795116748[/C][/ROW]
[ROW][C]67[/C][C]46[/C][C]56.7766086813169[/C][C]-10.7766086813169[/C][/ROW]
[ROW][C]68[/C][C]50[/C][C]46.7232795210231[/C][C]3.27672047897689[/C][/ROW]
[ROW][C]69[/C][C]52[/C][C]45.9089701530545[/C][C]6.09102984694554[/C][/ROW]
[ROW][C]70[/C][C]45[/C][C]48.2520618502894[/C][C]-3.25206185028943[/C][/ROW]
[ROW][C]71[/C][C]58[/C][C]47.2614130239069[/C][C]10.7385869760931[/C][/ROW]
[ROW][C]72[/C][C]73[/C][C]53.4153583517955[/C][C]19.5846416482045[/C][/ROW]
[ROW][C]73[/C][C]58[/C][C]59.525784897736[/C][C]-1.52578489773599[/C][/ROW]
[ROW][C]74[/C][C]49[/C][C]60.572620874895[/C][C]-11.572620874895[/C][/ROW]
[ROW][C]75[/C][C]44[/C][C]49.4320353622459[/C][C]-5.43203536224589[/C][/ROW]
[ROW][C]76[/C][C]35[/C][C]41.9761871672008[/C][C]-6.97618716720078[/C][/ROW]
[ROW][C]77[/C][C]46[/C][C]41.5540333916603[/C][C]4.4459666083397[/C][/ROW]
[ROW][C]78[/C][C]61[/C][C]44.4422974261529[/C][C]16.5577025738471[/C][/ROW]
[ROW][C]79[/C][C]29[/C][C]42.7666858290369[/C][C]-13.7666858290369[/C][/ROW]
[ROW][C]80[/C][C]33[/C][C]33.7033191132543[/C][C]-0.703319113254338[/C][/ROW]
[ROW][C]81[/C][C]37[/C][C]31.4106339444663[/C][C]5.58936605553374[/C][/ROW]
[ROW][C]82[/C][C]31[/C][C]32.475571950384[/C][C]-1.47557195038399[/C][/ROW]
[ROW][C]83[/C][C]44[/C][C]33.5162528869359[/C][C]10.4837471130641[/C][/ROW]
[ROW][C]84[/C][C]57[/C][C]40.1635473865073[/C][C]16.8364526134927[/C][/ROW]
[ROW][C]85[/C][C]42[/C][C]43.5059419744658[/C][C]-1.50594197446578[/C][/ROW]
[ROW][C]86[/C][C]34[/C][C]42.6721193844814[/C][C]-8.67211938448144[/C][/ROW]
[ROW][C]87[/C][C]27[/C][C]35.1708476984624[/C][C]-8.17084769846244[/C][/ROW]
[ROW][C]88[/C][C]22[/C][C]27.0296209699263[/C][C]-5.02962096992629[/C][/ROW]
[ROW][C]89[/C][C]30[/C][C]27.3511959517069[/C][C]2.64880404829310[/C][/ROW]
[ROW][C]90[/C][C]47[/C][C]29.6164918695055[/C][C]17.3835081304945[/C][/ROW]
[ROW][C]91[/C][C]12[/C][C]27.7540167311256[/C][C]-15.7540167311256[/C][/ROW]
[ROW][C]92[/C][C]13[/C][C]18.6342160669002[/C][C]-5.63421606690021[/C][/ROW]
[ROW][C]93[/C][C]18[/C][C]13.7716270638491[/C][C]4.22837293615093[/C][/ROW]
[ROW][C]94[/C][C]11[/C][C]13.5886758044485[/C][C]-2.58867580444850[/C][/ROW]
[ROW][C]95[/C][C]26[/C][C]11.9705218550925[/C][C]14.0294781449075[/C][/ROW]
[ROW][C]96[/C][C]41[/C][C]19.6406741559448[/C][C]21.3593258440552[/C][/ROW]
[ROW][C]97[/C][C]21[/C][C]25.9952352375190[/C][C]-4.99523523751904[/C][/ROW]
[ROW][C]98[/C][C]24[/C][C]21.9305444788722[/C][C]2.06945552112780[/C][/ROW]
[ROW][C]99[/C][C]30[/C][C]21.4364281173417[/C][C]8.56357188265828[/C][/ROW]
[ROW][C]100[/C][C]34[/C][C]24.6424380278853[/C][C]9.3575619721147[/C][/ROW]
[ROW][C]101[/C][C]48[/C][C]38.7865367504351[/C][C]9.21346324956492[/C][/ROW]
[ROW][C]102[/C][C]64[/C][C]52.083562991078[/C][C]11.916437008922[/C][/ROW]
[ROW][C]103[/C][C]35[/C][C]34.7471509256928[/C][C]0.252849074307171[/C][/ROW]
[ROW][C]104[/C][C]44[/C][C]42.8344527948753[/C][C]1.16554720512467[/C][/ROW]
[ROW][C]105[/C][C]55[/C][C]51.4261390729795[/C][C]3.57386092702050[/C][/ROW]
[ROW][C]106[/C][C]53[/C][C]48.2597099385473[/C][C]4.74029006145269[/C][/ROW]
[ROW][C]107[/C][C]73[/C][C]72.1526172665678[/C][C]0.847382733432212[/C][/ROW]
[ROW][C]108[/C][C]94[/C][C]79.3749216267448[/C][C]14.6250783732552[/C][/ROW]
[ROW][C]109[/C][C]73[/C][C]65.2423194591332[/C][C]7.75768054086677[/C][/ROW]
[ROW][C]110[/C][C]78[/C][C]74.8683241257462[/C][C]3.13167587425376[/C][/ROW]
[ROW][C]111[/C][C]87[/C][C]78.948350674488[/C][C]8.05164932551202[/C][/ROW]
[ROW][C]112[/C][C]87[/C][C]81.6328093937419[/C][C]5.36719060625806[/C][/ROW]
[ROW][C]113[/C][C]91[/C][C]110.822142408706[/C][C]-19.8221424087059[/C][/ROW]
[ROW][C]114[/C][C]104[/C][C]118.864830003997[/C][C]-14.8648300039972[/C][/ROW]
[ROW][C]115[/C][C]73[/C][C]62.9584714041431[/C][C]10.0415285958569[/C][/ROW]
[ROW][C]116[/C][C]84[/C][C]85.1059561337918[/C][C]-1.10595613379181[/C][/ROW]
[ROW][C]117[/C][C]103[/C][C]100.885862847317[/C][C]2.11413715268318[/C][/ROW]
[ROW][C]118[/C][C]111[/C][C]92.696727952884[/C][C]18.3032720471161[/C][/ROW]
[ROW][C]119[/C][C]131[/C][C]144.705635126675[/C][C]-13.7056351266745[/C][/ROW]
[ROW][C]120[/C][C]155[/C][C]153.549940015822[/C][C]1.4500599841777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77996&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77996&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
13205209.192478598406-4.19247859840641
14208209.632082374054-1.63208237405388
15201202.032536769601-1.03253676960068
16201201.916846630005-0.916846630004585
17220220.811708811239-0.81170881123856
18218218.685886150255-0.685886150254959
19203198.7128043246874.28719567531294
20185190.858097501976-5.85809750197632
21179187.294217200712-8.29421720071221
22182181.1126393905930.88736060940741
23182181.1001593142460.899840685754185
24185182.0733153852592.92668461474102
25183180.2303837200942.76961627990596
26192184.1757681481987.82423185180241
27177182.689366602584-5.68936660258356
28172179.543655784908-7.54365578490805
29188191.372081448318-3.37208144831806
30182187.116246159165-5.11624615916494
31162167.284067282252-5.28406728225201
32150152.944275949712-2.94427594971205
33141149.328674507793-8.32867450779273
34135143.138082233170-8.1380822331703
35139135.9975135411483.00248645885151
36148136.34894926703611.6510507329643
37142138.8327556839373.16724431606301
38156141.65553644826914.3444635517309
39143142.3694242989340.630575701065709
40134141.842565480813-7.84256548081308
41146149.737292151698-3.73729215169757
42142144.542665587422-2.54266558742177
43117129.013747026312-12.0137470263116
44106112.682713645966-6.6827136459658
45104105.194591570029-1.19459157002912
4699102.169049253627-3.16904925362729
4710598.74467368911926.25532631088082
48106101.3664858832944.63351411670573
499698.7245163533632-2.72451635336317
5010497.43678118419356.56321881580647
519692.8892761714473.11072382855301
528591.4800289150223-6.48002891502232
539194.2741655201472-3.27416552014725
549888.58123072810749.41876927189264
557382.3381903051804-9.33819030518038
567070.1580679263133-0.158067926313279
576267.2101684585941-5.21016845859411
586061.102021148952-1.10202114895200
597058.944847066973711.0551529330263
608263.425236803629618.5747631963704
617269.43338694084862.56661305915139
627372.54491293119420.455087068805838
636866.45811673953941.54188326046064
645363.8455425495228-10.8455425495228
656161.7379184546695-0.737918454669504
667359.669320488325213.3306795116748
674656.7766086813169-10.7766086813169
685046.72327952102313.27672047897689
695245.90897015305456.09102984694554
704548.2520618502894-3.25206185028943
715847.261413023906910.7385869760931
727353.415358351795519.5846416482045
735859.525784897736-1.52578489773599
744960.572620874895-11.572620874895
754449.4320353622459-5.43203536224589
763541.9761871672008-6.97618716720078
774641.55403339166034.4459666083397
786144.442297426152916.5577025738471
792942.7666858290369-13.7666858290369
803333.7033191132543-0.703319113254338
813731.41063394446635.58936605553374
823132.475571950384-1.47557195038399
834433.516252886935910.4837471130641
845740.163547386507316.8364526134927
854243.5059419744658-1.50594197446578
863442.6721193844814-8.67211938448144
872735.1708476984624-8.17084769846244
882227.0296209699263-5.02962096992629
893027.35119595170692.64880404829310
904729.616491869505517.3835081304945
911227.7540167311256-15.7540167311256
921318.6342160669002-5.63421606690021
931813.77162706384914.22837293615093
941113.5886758044485-2.58867580444850
952611.970521855092514.0294781449075
964119.640674155944821.3593258440552
972125.9952352375190-4.99523523751904
982421.93054447887222.06945552112780
993021.43642811734178.56357188265828
1003424.64243802788539.3575619721147
1014838.78653675043519.21346324956492
1026452.08356299107811.916437008922
1033534.74715092569280.252849074307171
1044442.83445279487531.16554720512467
1055551.42613907297953.57386092702050
1065348.25970993854734.74029006145269
1077372.15261726656780.847382733432212
1089479.374921626744814.6250783732552
1097365.24231945913327.75768054086677
1107874.86832412574623.13167587425376
1118778.9483506744888.05164932551202
1128781.63280939374195.36719060625806
11391110.822142408706-19.8221424087059
114104118.864830003997-14.8648300039972
1157362.958471404143110.0415285958569
1168485.1059561337918-1.10595613379181
117103100.8858628473172.11413715268318
11811192.69672795288418.3032720471161
119131144.705635126675-13.7056351266745
120155153.5499400158221.4500599841777







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121113.160167846310100.882829002242125.437506690379
122119.191249417548103.011611990825135.370886844272
123122.860746197940103.174515090349142.546977305532
124118.07043928339296.0733979277513140.067480639033
125145.862307720869116.524862847368175.199752594370
126175.438910078245137.800668843947213.077151312543
127104.95780390651878.905076171792131.010531641243
128125.75566806475492.3688327937673159.142503335740
129150.286273132161108.078689547376192.493856716946
130139.29854958995497.5094619666208181.087637213287
131184.209649024615126.568799455319241.850498593910
132209.099935895541141.799453764276276.400418026806

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 113.160167846310 & 100.882829002242 & 125.437506690379 \tabularnewline
122 & 119.191249417548 & 103.011611990825 & 135.370886844272 \tabularnewline
123 & 122.860746197940 & 103.174515090349 & 142.546977305532 \tabularnewline
124 & 118.070439283392 & 96.0733979277513 & 140.067480639033 \tabularnewline
125 & 145.862307720869 & 116.524862847368 & 175.199752594370 \tabularnewline
126 & 175.438910078245 & 137.800668843947 & 213.077151312543 \tabularnewline
127 & 104.957803906518 & 78.905076171792 & 131.010531641243 \tabularnewline
128 & 125.755668064754 & 92.3688327937673 & 159.142503335740 \tabularnewline
129 & 150.286273132161 & 108.078689547376 & 192.493856716946 \tabularnewline
130 & 139.298549589954 & 97.5094619666208 & 181.087637213287 \tabularnewline
131 & 184.209649024615 & 126.568799455319 & 241.850498593910 \tabularnewline
132 & 209.099935895541 & 141.799453764276 & 276.400418026806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77996&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]113.160167846310[/C][C]100.882829002242[/C][C]125.437506690379[/C][/ROW]
[ROW][C]122[/C][C]119.191249417548[/C][C]103.011611990825[/C][C]135.370886844272[/C][/ROW]
[ROW][C]123[/C][C]122.860746197940[/C][C]103.174515090349[/C][C]142.546977305532[/C][/ROW]
[ROW][C]124[/C][C]118.070439283392[/C][C]96.0733979277513[/C][C]140.067480639033[/C][/ROW]
[ROW][C]125[/C][C]145.862307720869[/C][C]116.524862847368[/C][C]175.199752594370[/C][/ROW]
[ROW][C]126[/C][C]175.438910078245[/C][C]137.800668843947[/C][C]213.077151312543[/C][/ROW]
[ROW][C]127[/C][C]104.957803906518[/C][C]78.905076171792[/C][C]131.010531641243[/C][/ROW]
[ROW][C]128[/C][C]125.755668064754[/C][C]92.3688327937673[/C][C]159.142503335740[/C][/ROW]
[ROW][C]129[/C][C]150.286273132161[/C][C]108.078689547376[/C][C]192.493856716946[/C][/ROW]
[ROW][C]130[/C][C]139.298549589954[/C][C]97.5094619666208[/C][C]181.087637213287[/C][/ROW]
[ROW][C]131[/C][C]184.209649024615[/C][C]126.568799455319[/C][C]241.850498593910[/C][/ROW]
[ROW][C]132[/C][C]209.099935895541[/C][C]141.799453764276[/C][C]276.400418026806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77996&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77996&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
121113.160167846310100.882829002242125.437506690379
122119.191249417548103.011611990825135.370886844272
123122.860746197940103.174515090349142.546977305532
124118.07043928339296.0733979277513140.067480639033
125145.862307720869116.524862847368175.199752594370
126175.438910078245137.800668843947213.077151312543
127104.95780390651878.905076171792131.010531641243
128125.75566806475492.3688327937673159.142503335740
129150.286273132161108.078689547376192.493856716946
130139.29854958995497.5094619666208181.087637213287
131184.209649024615126.568799455319241.850498593910
132209.099935895541141.799453764276276.400418026806



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')