Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Aug 2010 19:20:39 +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/17/t1282072938cwhd9h1fsydtiy0.htm/, Retrieved Sat, 27 Apr 2024 08:36:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79154, Retrieved Sat, 27 Apr 2024 08:36:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSchrauwen Nathalie
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS A - STA...] [2010-08-17 19:20:39] [dd2ef098fd65ce7e9f689caa343b799f] [Current]
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Dataseries X:
125
124
123
121
141
140
125
115
116
116
117
119
114
110
108
111
124
125
118
108
107
103
113
116
113
105
102
107
119
116
113
102
96
95
101
110
103
88
79
96
118
116
114
102
98
98
101
117
109
98
93
98
114
115
112
112
103
107
104
117
123
113
97
90
109
104
92
102
90
97
99
108
106
86
72
71
96
88
83
90
85
100
108
118
124
99
92
86
112
104
93
104
96
109
113
123
127
96
100
95
133
130
117
129
122
134
141
152
161
122
126
119
160
162
145
161
151
166
169
185




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79154&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79154&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.852574377903842
beta0.0116103049718575
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.852574377903842 \tabularnewline
beta & 0.0116103049718575 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79154&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]0.852574377903842[/C][/ROW]
[ROW][C]beta[/C][C]0.0116103049718575[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79154&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
alpha0.852574377903842
beta0.0116103049718575
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31231230
4121122-1
5141120.13752697355820.8624730264425
6140137.1209485752102.87905142479033
7125138.800664410429-13.8006644104294
8115126.123073967225-11.1230739672251
9116115.6182251305460.381774869454063
10116114.925894688931.07410531107014
11117114.8344596338462.16554036615371
12119115.6949900648543.30500993514612
13114117.559718186550-3.5597181865503
14110113.536518601187-3.53651860118705
15108109.498091633199-1.49809163319894
16111107.182746186793.81725381321003
17124109.43691373157714.5630862684230
18125120.9968575695354.00314243046468
19118123.593289559116-5.59328955911619
20108117.952683507563-9.952683507563
21107108.496851756317-1.49685175631714
22103106.235428690599-3.23542869059904
23113102.45971310521710.5402868947825
24116110.5331542606915.46684573930912
25113114.335223863793-1.33522386379326
26105112.324806294824-7.32480629482389
27102105.135318527689-3.13531852768861
28107101.4866452711925.51335472880787
29119105.26618399677613.7338160032239
30116116.190223597188-0.190223597188449
31113115.241100840838-2.24110084083844
32102112.521268824763-10.5212688247633
3396102.637831398577-6.63783139857702
349595.9996076600766-0.999607660076649
3510194.15849425300726.84150574699275
3611099.070234891908210.9297651080918
37103107.575710615723-4.57571061572277
3888102.816321669003-14.8163216690034
397989.179388563341-10.1793885633410
409679.395023625893516.6049763741065
4111892.610688787659725.3893112123403
42116113.5669726277622.43302737223837
43114114.975400736747-0.97540073674736
44102113.468235222007-11.4682352220072
4598102.901627843727-4.90162784372738
469897.8850221746310.114977825369081
4710197.14658408813633.85341591186366
4811799.633586137351717.3664138626483
49109113.813328035276-4.81332803527634
5098109.035544839988-11.0355448399877
519398.8436220434358-5.84362204343577
529893.02035563447824.97964436552184
5311496.47402060044717.5259793995531
54115110.79785286344.20214713660005
55112113.803722701084-1.80372270108359
56112111.6712873810530.328712618946582
57103111.360165588103-8.36016558810333
58107103.5583745222143.44162547778619
59104105.852555573482-1.85255557348248
60117103.61471571193513.3852842880648
61123114.5007639157038.49923608429749
62113121.305223562580-8.30522356258025
6397113.70042099093-16.7004209909300
649098.7727765965878-8.77277659658776
6510990.51720005775718.482799942243
66104105.681984471569-1.68198447156894
6792103.638140985079-11.6381409850785
6810292.99073168551489.0092683144852
6990100.035954105488-10.0359541054881
709790.74436548627216.25563451372788
719995.40449022658723.59550977341283
7210897.832251458845810.1677485411542
73106105.9639820391850.0360179608146325
7486105.458015252038-19.4580152520378
757288.139327171366-16.139327171366
767173.4903099892101-2.49030998921013
779670.453444436794225.5465555632058
788891.5729684659963-3.57296846599631
798387.8305648520608-4.83056485206085
809082.96815071790867.03184928209143
818588.2889327392391-3.28893273923912
8210084.777924459999615.2220755400004
8310897.19960552460510.8003944753951
84118105.95838391525612.0416160847441
85124115.8945917727998.10540822720124
8699122.555122252200-23.5551222522002
8792101.989531777561-9.98953177756073
888692.8907332986035-6.8907332986035
8911286.365682057996125.6343179420039
90104107.824401248976-3.82440124897619
9193104.129514848028-11.1295148480281
9210494.0963086089659.903691391035
9396102.093508254810-6.09350825480951
9410996.391587867812812.6084121321872
95113106.7592518606946.24074813930596
96123111.75978365859311.2402163414069
97127121.1339968998105.86600310018953
9896125.984359133190-29.9843591331898
9910099.9728164551020.0271835448979232
1009599.5486151860766-4.54861518607657
10113395.178180017512737.8218199824873
102130127.3060771574012.69392284259881
103117129.511495441588-12.5114954415883
104129118.62931679529810.3706832047024
105122127.358553121602-5.35855312160182
106134122.62440313807811.3755968619217
107141132.2699637017608.73003629823953
108152139.74640267470012.2535973252996
109161150.34823355155010.6517664484504
110122159.689822557451-37.689822557451
111126127.443533082782-1.44353308278231
112119126.085612281661-7.08561228166147
113160119.84726133181540.1527386681853
114162154.2805759041787.71942409582229
115145161.138489347694-16.1384893476941
116161147.49600784502313.5039921549769
117151159.259617841229-8.25961784122887
118166152.38637252990413.6136274700962
119169164.2964522462824.70354775371754
120185168.65658505749516.3434149425053

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 123 & 123 & 0 \tabularnewline
4 & 121 & 122 & -1 \tabularnewline
5 & 141 & 120.137526973558 & 20.8624730264425 \tabularnewline
6 & 140 & 137.120948575210 & 2.87905142479033 \tabularnewline
7 & 125 & 138.800664410429 & -13.8006644104294 \tabularnewline
8 & 115 & 126.123073967225 & -11.1230739672251 \tabularnewline
9 & 116 & 115.618225130546 & 0.381774869454063 \tabularnewline
10 & 116 & 114.92589468893 & 1.07410531107014 \tabularnewline
11 & 117 & 114.834459633846 & 2.16554036615371 \tabularnewline
12 & 119 & 115.694990064854 & 3.30500993514612 \tabularnewline
13 & 114 & 117.559718186550 & -3.5597181865503 \tabularnewline
14 & 110 & 113.536518601187 & -3.53651860118705 \tabularnewline
15 & 108 & 109.498091633199 & -1.49809163319894 \tabularnewline
16 & 111 & 107.18274618679 & 3.81725381321003 \tabularnewline
17 & 124 & 109.436913731577 & 14.5630862684230 \tabularnewline
18 & 125 & 120.996857569535 & 4.00314243046468 \tabularnewline
19 & 118 & 123.593289559116 & -5.59328955911619 \tabularnewline
20 & 108 & 117.952683507563 & -9.952683507563 \tabularnewline
21 & 107 & 108.496851756317 & -1.49685175631714 \tabularnewline
22 & 103 & 106.235428690599 & -3.23542869059904 \tabularnewline
23 & 113 & 102.459713105217 & 10.5402868947825 \tabularnewline
24 & 116 & 110.533154260691 & 5.46684573930912 \tabularnewline
25 & 113 & 114.335223863793 & -1.33522386379326 \tabularnewline
26 & 105 & 112.324806294824 & -7.32480629482389 \tabularnewline
27 & 102 & 105.135318527689 & -3.13531852768861 \tabularnewline
28 & 107 & 101.486645271192 & 5.51335472880787 \tabularnewline
29 & 119 & 105.266183996776 & 13.7338160032239 \tabularnewline
30 & 116 & 116.190223597188 & -0.190223597188449 \tabularnewline
31 & 113 & 115.241100840838 & -2.24110084083844 \tabularnewline
32 & 102 & 112.521268824763 & -10.5212688247633 \tabularnewline
33 & 96 & 102.637831398577 & -6.63783139857702 \tabularnewline
34 & 95 & 95.9996076600766 & -0.999607660076649 \tabularnewline
35 & 101 & 94.1584942530072 & 6.84150574699275 \tabularnewline
36 & 110 & 99.0702348919082 & 10.9297651080918 \tabularnewline
37 & 103 & 107.575710615723 & -4.57571061572277 \tabularnewline
38 & 88 & 102.816321669003 & -14.8163216690034 \tabularnewline
39 & 79 & 89.179388563341 & -10.1793885633410 \tabularnewline
40 & 96 & 79.3950236258935 & 16.6049763741065 \tabularnewline
41 & 118 & 92.6106887876597 & 25.3893112123403 \tabularnewline
42 & 116 & 113.566972627762 & 2.43302737223837 \tabularnewline
43 & 114 & 114.975400736747 & -0.97540073674736 \tabularnewline
44 & 102 & 113.468235222007 & -11.4682352220072 \tabularnewline
45 & 98 & 102.901627843727 & -4.90162784372738 \tabularnewline
46 & 98 & 97.885022174631 & 0.114977825369081 \tabularnewline
47 & 101 & 97.1465840881363 & 3.85341591186366 \tabularnewline
48 & 117 & 99.6335861373517 & 17.3664138626483 \tabularnewline
49 & 109 & 113.813328035276 & -4.81332803527634 \tabularnewline
50 & 98 & 109.035544839988 & -11.0355448399877 \tabularnewline
51 & 93 & 98.8436220434358 & -5.84362204343577 \tabularnewline
52 & 98 & 93.0203556344782 & 4.97964436552184 \tabularnewline
53 & 114 & 96.474020600447 & 17.5259793995531 \tabularnewline
54 & 115 & 110.7978528634 & 4.20214713660005 \tabularnewline
55 & 112 & 113.803722701084 & -1.80372270108359 \tabularnewline
56 & 112 & 111.671287381053 & 0.328712618946582 \tabularnewline
57 & 103 & 111.360165588103 & -8.36016558810333 \tabularnewline
58 & 107 & 103.558374522214 & 3.44162547778619 \tabularnewline
59 & 104 & 105.852555573482 & -1.85255557348248 \tabularnewline
60 & 117 & 103.614715711935 & 13.3852842880648 \tabularnewline
61 & 123 & 114.500763915703 & 8.49923608429749 \tabularnewline
62 & 113 & 121.305223562580 & -8.30522356258025 \tabularnewline
63 & 97 & 113.70042099093 & -16.7004209909300 \tabularnewline
64 & 90 & 98.7727765965878 & -8.77277659658776 \tabularnewline
65 & 109 & 90.517200057757 & 18.482799942243 \tabularnewline
66 & 104 & 105.681984471569 & -1.68198447156894 \tabularnewline
67 & 92 & 103.638140985079 & -11.6381409850785 \tabularnewline
68 & 102 & 92.9907316855148 & 9.0092683144852 \tabularnewline
69 & 90 & 100.035954105488 & -10.0359541054881 \tabularnewline
70 & 97 & 90.7443654862721 & 6.25563451372788 \tabularnewline
71 & 99 & 95.4044902265872 & 3.59550977341283 \tabularnewline
72 & 108 & 97.8322514588458 & 10.1677485411542 \tabularnewline
73 & 106 & 105.963982039185 & 0.0360179608146325 \tabularnewline
74 & 86 & 105.458015252038 & -19.4580152520378 \tabularnewline
75 & 72 & 88.139327171366 & -16.139327171366 \tabularnewline
76 & 71 & 73.4903099892101 & -2.49030998921013 \tabularnewline
77 & 96 & 70.4534444367942 & 25.5465555632058 \tabularnewline
78 & 88 & 91.5729684659963 & -3.57296846599631 \tabularnewline
79 & 83 & 87.8305648520608 & -4.83056485206085 \tabularnewline
80 & 90 & 82.9681507179086 & 7.03184928209143 \tabularnewline
81 & 85 & 88.2889327392391 & -3.28893273923912 \tabularnewline
82 & 100 & 84.7779244599996 & 15.2220755400004 \tabularnewline
83 & 108 & 97.199605524605 & 10.8003944753951 \tabularnewline
84 & 118 & 105.958383915256 & 12.0416160847441 \tabularnewline
85 & 124 & 115.894591772799 & 8.10540822720124 \tabularnewline
86 & 99 & 122.555122252200 & -23.5551222522002 \tabularnewline
87 & 92 & 101.989531777561 & -9.98953177756073 \tabularnewline
88 & 86 & 92.8907332986035 & -6.8907332986035 \tabularnewline
89 & 112 & 86.3656820579961 & 25.6343179420039 \tabularnewline
90 & 104 & 107.824401248976 & -3.82440124897619 \tabularnewline
91 & 93 & 104.129514848028 & -11.1295148480281 \tabularnewline
92 & 104 & 94.096308608965 & 9.903691391035 \tabularnewline
93 & 96 & 102.093508254810 & -6.09350825480951 \tabularnewline
94 & 109 & 96.3915878678128 & 12.6084121321872 \tabularnewline
95 & 113 & 106.759251860694 & 6.24074813930596 \tabularnewline
96 & 123 & 111.759783658593 & 11.2402163414069 \tabularnewline
97 & 127 & 121.133996899810 & 5.86600310018953 \tabularnewline
98 & 96 & 125.984359133190 & -29.9843591331898 \tabularnewline
99 & 100 & 99.972816455102 & 0.0271835448979232 \tabularnewline
100 & 95 & 99.5486151860766 & -4.54861518607657 \tabularnewline
101 & 133 & 95.1781800175127 & 37.8218199824873 \tabularnewline
102 & 130 & 127.306077157401 & 2.69392284259881 \tabularnewline
103 & 117 & 129.511495441588 & -12.5114954415883 \tabularnewline
104 & 129 & 118.629316795298 & 10.3706832047024 \tabularnewline
105 & 122 & 127.358553121602 & -5.35855312160182 \tabularnewline
106 & 134 & 122.624403138078 & 11.3755968619217 \tabularnewline
107 & 141 & 132.269963701760 & 8.73003629823953 \tabularnewline
108 & 152 & 139.746402674700 & 12.2535973252996 \tabularnewline
109 & 161 & 150.348233551550 & 10.6517664484504 \tabularnewline
110 & 122 & 159.689822557451 & -37.689822557451 \tabularnewline
111 & 126 & 127.443533082782 & -1.44353308278231 \tabularnewline
112 & 119 & 126.085612281661 & -7.08561228166147 \tabularnewline
113 & 160 & 119.847261331815 & 40.1527386681853 \tabularnewline
114 & 162 & 154.280575904178 & 7.71942409582229 \tabularnewline
115 & 145 & 161.138489347694 & -16.1384893476941 \tabularnewline
116 & 161 & 147.496007845023 & 13.5039921549769 \tabularnewline
117 & 151 & 159.259617841229 & -8.25961784122887 \tabularnewline
118 & 166 & 152.386372529904 & 13.6136274700962 \tabularnewline
119 & 169 & 164.296452246282 & 4.70354775371754 \tabularnewline
120 & 185 & 168.656585057495 & 16.3434149425053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79154&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]3[/C][C]123[/C][C]123[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]121[/C][C]122[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]141[/C][C]120.137526973558[/C][C]20.8624730264425[/C][/ROW]
[ROW][C]6[/C][C]140[/C][C]137.120948575210[/C][C]2.87905142479033[/C][/ROW]
[ROW][C]7[/C][C]125[/C][C]138.800664410429[/C][C]-13.8006644104294[/C][/ROW]
[ROW][C]8[/C][C]115[/C][C]126.123073967225[/C][C]-11.1230739672251[/C][/ROW]
[ROW][C]9[/C][C]116[/C][C]115.618225130546[/C][C]0.381774869454063[/C][/ROW]
[ROW][C]10[/C][C]116[/C][C]114.92589468893[/C][C]1.07410531107014[/C][/ROW]
[ROW][C]11[/C][C]117[/C][C]114.834459633846[/C][C]2.16554036615371[/C][/ROW]
[ROW][C]12[/C][C]119[/C][C]115.694990064854[/C][C]3.30500993514612[/C][/ROW]
[ROW][C]13[/C][C]114[/C][C]117.559718186550[/C][C]-3.5597181865503[/C][/ROW]
[ROW][C]14[/C][C]110[/C][C]113.536518601187[/C][C]-3.53651860118705[/C][/ROW]
[ROW][C]15[/C][C]108[/C][C]109.498091633199[/C][C]-1.49809163319894[/C][/ROW]
[ROW][C]16[/C][C]111[/C][C]107.18274618679[/C][C]3.81725381321003[/C][/ROW]
[ROW][C]17[/C][C]124[/C][C]109.436913731577[/C][C]14.5630862684230[/C][/ROW]
[ROW][C]18[/C][C]125[/C][C]120.996857569535[/C][C]4.00314243046468[/C][/ROW]
[ROW][C]19[/C][C]118[/C][C]123.593289559116[/C][C]-5.59328955911619[/C][/ROW]
[ROW][C]20[/C][C]108[/C][C]117.952683507563[/C][C]-9.952683507563[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]108.496851756317[/C][C]-1.49685175631714[/C][/ROW]
[ROW][C]22[/C][C]103[/C][C]106.235428690599[/C][C]-3.23542869059904[/C][/ROW]
[ROW][C]23[/C][C]113[/C][C]102.459713105217[/C][C]10.5402868947825[/C][/ROW]
[ROW][C]24[/C][C]116[/C][C]110.533154260691[/C][C]5.46684573930912[/C][/ROW]
[ROW][C]25[/C][C]113[/C][C]114.335223863793[/C][C]-1.33522386379326[/C][/ROW]
[ROW][C]26[/C][C]105[/C][C]112.324806294824[/C][C]-7.32480629482389[/C][/ROW]
[ROW][C]27[/C][C]102[/C][C]105.135318527689[/C][C]-3.13531852768861[/C][/ROW]
[ROW][C]28[/C][C]107[/C][C]101.486645271192[/C][C]5.51335472880787[/C][/ROW]
[ROW][C]29[/C][C]119[/C][C]105.266183996776[/C][C]13.7338160032239[/C][/ROW]
[ROW][C]30[/C][C]116[/C][C]116.190223597188[/C][C]-0.190223597188449[/C][/ROW]
[ROW][C]31[/C][C]113[/C][C]115.241100840838[/C][C]-2.24110084083844[/C][/ROW]
[ROW][C]32[/C][C]102[/C][C]112.521268824763[/C][C]-10.5212688247633[/C][/ROW]
[ROW][C]33[/C][C]96[/C][C]102.637831398577[/C][C]-6.63783139857702[/C][/ROW]
[ROW][C]34[/C][C]95[/C][C]95.9996076600766[/C][C]-0.999607660076649[/C][/ROW]
[ROW][C]35[/C][C]101[/C][C]94.1584942530072[/C][C]6.84150574699275[/C][/ROW]
[ROW][C]36[/C][C]110[/C][C]99.0702348919082[/C][C]10.9297651080918[/C][/ROW]
[ROW][C]37[/C][C]103[/C][C]107.575710615723[/C][C]-4.57571061572277[/C][/ROW]
[ROW][C]38[/C][C]88[/C][C]102.816321669003[/C][C]-14.8163216690034[/C][/ROW]
[ROW][C]39[/C][C]79[/C][C]89.179388563341[/C][C]-10.1793885633410[/C][/ROW]
[ROW][C]40[/C][C]96[/C][C]79.3950236258935[/C][C]16.6049763741065[/C][/ROW]
[ROW][C]41[/C][C]118[/C][C]92.6106887876597[/C][C]25.3893112123403[/C][/ROW]
[ROW][C]42[/C][C]116[/C][C]113.566972627762[/C][C]2.43302737223837[/C][/ROW]
[ROW][C]43[/C][C]114[/C][C]114.975400736747[/C][C]-0.97540073674736[/C][/ROW]
[ROW][C]44[/C][C]102[/C][C]113.468235222007[/C][C]-11.4682352220072[/C][/ROW]
[ROW][C]45[/C][C]98[/C][C]102.901627843727[/C][C]-4.90162784372738[/C][/ROW]
[ROW][C]46[/C][C]98[/C][C]97.885022174631[/C][C]0.114977825369081[/C][/ROW]
[ROW][C]47[/C][C]101[/C][C]97.1465840881363[/C][C]3.85341591186366[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]99.6335861373517[/C][C]17.3664138626483[/C][/ROW]
[ROW][C]49[/C][C]109[/C][C]113.813328035276[/C][C]-4.81332803527634[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]109.035544839988[/C][C]-11.0355448399877[/C][/ROW]
[ROW][C]51[/C][C]93[/C][C]98.8436220434358[/C][C]-5.84362204343577[/C][/ROW]
[ROW][C]52[/C][C]98[/C][C]93.0203556344782[/C][C]4.97964436552184[/C][/ROW]
[ROW][C]53[/C][C]114[/C][C]96.474020600447[/C][C]17.5259793995531[/C][/ROW]
[ROW][C]54[/C][C]115[/C][C]110.7978528634[/C][C]4.20214713660005[/C][/ROW]
[ROW][C]55[/C][C]112[/C][C]113.803722701084[/C][C]-1.80372270108359[/C][/ROW]
[ROW][C]56[/C][C]112[/C][C]111.671287381053[/C][C]0.328712618946582[/C][/ROW]
[ROW][C]57[/C][C]103[/C][C]111.360165588103[/C][C]-8.36016558810333[/C][/ROW]
[ROW][C]58[/C][C]107[/C][C]103.558374522214[/C][C]3.44162547778619[/C][/ROW]
[ROW][C]59[/C][C]104[/C][C]105.852555573482[/C][C]-1.85255557348248[/C][/ROW]
[ROW][C]60[/C][C]117[/C][C]103.614715711935[/C][C]13.3852842880648[/C][/ROW]
[ROW][C]61[/C][C]123[/C][C]114.500763915703[/C][C]8.49923608429749[/C][/ROW]
[ROW][C]62[/C][C]113[/C][C]121.305223562580[/C][C]-8.30522356258025[/C][/ROW]
[ROW][C]63[/C][C]97[/C][C]113.70042099093[/C][C]-16.7004209909300[/C][/ROW]
[ROW][C]64[/C][C]90[/C][C]98.7727765965878[/C][C]-8.77277659658776[/C][/ROW]
[ROW][C]65[/C][C]109[/C][C]90.517200057757[/C][C]18.482799942243[/C][/ROW]
[ROW][C]66[/C][C]104[/C][C]105.681984471569[/C][C]-1.68198447156894[/C][/ROW]
[ROW][C]67[/C][C]92[/C][C]103.638140985079[/C][C]-11.6381409850785[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]92.9907316855148[/C][C]9.0092683144852[/C][/ROW]
[ROW][C]69[/C][C]90[/C][C]100.035954105488[/C][C]-10.0359541054881[/C][/ROW]
[ROW][C]70[/C][C]97[/C][C]90.7443654862721[/C][C]6.25563451372788[/C][/ROW]
[ROW][C]71[/C][C]99[/C][C]95.4044902265872[/C][C]3.59550977341283[/C][/ROW]
[ROW][C]72[/C][C]108[/C][C]97.8322514588458[/C][C]10.1677485411542[/C][/ROW]
[ROW][C]73[/C][C]106[/C][C]105.963982039185[/C][C]0.0360179608146325[/C][/ROW]
[ROW][C]74[/C][C]86[/C][C]105.458015252038[/C][C]-19.4580152520378[/C][/ROW]
[ROW][C]75[/C][C]72[/C][C]88.139327171366[/C][C]-16.139327171366[/C][/ROW]
[ROW][C]76[/C][C]71[/C][C]73.4903099892101[/C][C]-2.49030998921013[/C][/ROW]
[ROW][C]77[/C][C]96[/C][C]70.4534444367942[/C][C]25.5465555632058[/C][/ROW]
[ROW][C]78[/C][C]88[/C][C]91.5729684659963[/C][C]-3.57296846599631[/C][/ROW]
[ROW][C]79[/C][C]83[/C][C]87.8305648520608[/C][C]-4.83056485206085[/C][/ROW]
[ROW][C]80[/C][C]90[/C][C]82.9681507179086[/C][C]7.03184928209143[/C][/ROW]
[ROW][C]81[/C][C]85[/C][C]88.2889327392391[/C][C]-3.28893273923912[/C][/ROW]
[ROW][C]82[/C][C]100[/C][C]84.7779244599996[/C][C]15.2220755400004[/C][/ROW]
[ROW][C]83[/C][C]108[/C][C]97.199605524605[/C][C]10.8003944753951[/C][/ROW]
[ROW][C]84[/C][C]118[/C][C]105.958383915256[/C][C]12.0416160847441[/C][/ROW]
[ROW][C]85[/C][C]124[/C][C]115.894591772799[/C][C]8.10540822720124[/C][/ROW]
[ROW][C]86[/C][C]99[/C][C]122.555122252200[/C][C]-23.5551222522002[/C][/ROW]
[ROW][C]87[/C][C]92[/C][C]101.989531777561[/C][C]-9.98953177756073[/C][/ROW]
[ROW][C]88[/C][C]86[/C][C]92.8907332986035[/C][C]-6.8907332986035[/C][/ROW]
[ROW][C]89[/C][C]112[/C][C]86.3656820579961[/C][C]25.6343179420039[/C][/ROW]
[ROW][C]90[/C][C]104[/C][C]107.824401248976[/C][C]-3.82440124897619[/C][/ROW]
[ROW][C]91[/C][C]93[/C][C]104.129514848028[/C][C]-11.1295148480281[/C][/ROW]
[ROW][C]92[/C][C]104[/C][C]94.096308608965[/C][C]9.903691391035[/C][/ROW]
[ROW][C]93[/C][C]96[/C][C]102.093508254810[/C][C]-6.09350825480951[/C][/ROW]
[ROW][C]94[/C][C]109[/C][C]96.3915878678128[/C][C]12.6084121321872[/C][/ROW]
[ROW][C]95[/C][C]113[/C][C]106.759251860694[/C][C]6.24074813930596[/C][/ROW]
[ROW][C]96[/C][C]123[/C][C]111.759783658593[/C][C]11.2402163414069[/C][/ROW]
[ROW][C]97[/C][C]127[/C][C]121.133996899810[/C][C]5.86600310018953[/C][/ROW]
[ROW][C]98[/C][C]96[/C][C]125.984359133190[/C][C]-29.9843591331898[/C][/ROW]
[ROW][C]99[/C][C]100[/C][C]99.972816455102[/C][C]0.0271835448979232[/C][/ROW]
[ROW][C]100[/C][C]95[/C][C]99.5486151860766[/C][C]-4.54861518607657[/C][/ROW]
[ROW][C]101[/C][C]133[/C][C]95.1781800175127[/C][C]37.8218199824873[/C][/ROW]
[ROW][C]102[/C][C]130[/C][C]127.306077157401[/C][C]2.69392284259881[/C][/ROW]
[ROW][C]103[/C][C]117[/C][C]129.511495441588[/C][C]-12.5114954415883[/C][/ROW]
[ROW][C]104[/C][C]129[/C][C]118.629316795298[/C][C]10.3706832047024[/C][/ROW]
[ROW][C]105[/C][C]122[/C][C]127.358553121602[/C][C]-5.35855312160182[/C][/ROW]
[ROW][C]106[/C][C]134[/C][C]122.624403138078[/C][C]11.3755968619217[/C][/ROW]
[ROW][C]107[/C][C]141[/C][C]132.269963701760[/C][C]8.73003629823953[/C][/ROW]
[ROW][C]108[/C][C]152[/C][C]139.746402674700[/C][C]12.2535973252996[/C][/ROW]
[ROW][C]109[/C][C]161[/C][C]150.348233551550[/C][C]10.6517664484504[/C][/ROW]
[ROW][C]110[/C][C]122[/C][C]159.689822557451[/C][C]-37.689822557451[/C][/ROW]
[ROW][C]111[/C][C]126[/C][C]127.443533082782[/C][C]-1.44353308278231[/C][/ROW]
[ROW][C]112[/C][C]119[/C][C]126.085612281661[/C][C]-7.08561228166147[/C][/ROW]
[ROW][C]113[/C][C]160[/C][C]119.847261331815[/C][C]40.1527386681853[/C][/ROW]
[ROW][C]114[/C][C]162[/C][C]154.280575904178[/C][C]7.71942409582229[/C][/ROW]
[ROW][C]115[/C][C]145[/C][C]161.138489347694[/C][C]-16.1384893476941[/C][/ROW]
[ROW][C]116[/C][C]161[/C][C]147.496007845023[/C][C]13.5039921549769[/C][/ROW]
[ROW][C]117[/C][C]151[/C][C]159.259617841229[/C][C]-8.25961784122887[/C][/ROW]
[ROW][C]118[/C][C]166[/C][C]152.386372529904[/C][C]13.6136274700962[/C][/ROW]
[ROW][C]119[/C][C]169[/C][C]164.296452246282[/C][C]4.70354775371754[/C][/ROW]
[ROW][C]120[/C][C]185[/C][C]168.656585057495[/C][C]16.3434149425053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79154&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79154&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
31231230
4121122-1
5141120.13752697355820.8624730264425
6140137.1209485752102.87905142479033
7125138.800664410429-13.8006644104294
8115126.123073967225-11.1230739672251
9116115.6182251305460.381774869454063
10116114.925894688931.07410531107014
11117114.8344596338462.16554036615371
12119115.6949900648543.30500993514612
13114117.559718186550-3.5597181865503
14110113.536518601187-3.53651860118705
15108109.498091633199-1.49809163319894
16111107.182746186793.81725381321003
17124109.43691373157714.5630862684230
18125120.9968575695354.00314243046468
19118123.593289559116-5.59328955911619
20108117.952683507563-9.952683507563
21107108.496851756317-1.49685175631714
22103106.235428690599-3.23542869059904
23113102.45971310521710.5402868947825
24116110.5331542606915.46684573930912
25113114.335223863793-1.33522386379326
26105112.324806294824-7.32480629482389
27102105.135318527689-3.13531852768861
28107101.4866452711925.51335472880787
29119105.26618399677613.7338160032239
30116116.190223597188-0.190223597188449
31113115.241100840838-2.24110084083844
32102112.521268824763-10.5212688247633
3396102.637831398577-6.63783139857702
349595.9996076600766-0.999607660076649
3510194.15849425300726.84150574699275
3611099.070234891908210.9297651080918
37103107.575710615723-4.57571061572277
3888102.816321669003-14.8163216690034
397989.179388563341-10.1793885633410
409679.395023625893516.6049763741065
4111892.610688787659725.3893112123403
42116113.5669726277622.43302737223837
43114114.975400736747-0.97540073674736
44102113.468235222007-11.4682352220072
4598102.901627843727-4.90162784372738
469897.8850221746310.114977825369081
4710197.14658408813633.85341591186366
4811799.633586137351717.3664138626483
49109113.813328035276-4.81332803527634
5098109.035544839988-11.0355448399877
519398.8436220434358-5.84362204343577
529893.02035563447824.97964436552184
5311496.47402060044717.5259793995531
54115110.79785286344.20214713660005
55112113.803722701084-1.80372270108359
56112111.6712873810530.328712618946582
57103111.360165588103-8.36016558810333
58107103.5583745222143.44162547778619
59104105.852555573482-1.85255557348248
60117103.61471571193513.3852842880648
61123114.5007639157038.49923608429749
62113121.305223562580-8.30522356258025
6397113.70042099093-16.7004209909300
649098.7727765965878-8.77277659658776
6510990.51720005775718.482799942243
66104105.681984471569-1.68198447156894
6792103.638140985079-11.6381409850785
6810292.99073168551489.0092683144852
6990100.035954105488-10.0359541054881
709790.74436548627216.25563451372788
719995.40449022658723.59550977341283
7210897.832251458845810.1677485411542
73106105.9639820391850.0360179608146325
7486105.458015252038-19.4580152520378
757288.139327171366-16.139327171366
767173.4903099892101-2.49030998921013
779670.453444436794225.5465555632058
788891.5729684659963-3.57296846599631
798387.8305648520608-4.83056485206085
809082.96815071790867.03184928209143
818588.2889327392391-3.28893273923912
8210084.777924459999615.2220755400004
8310897.19960552460510.8003944753951
84118105.95838391525612.0416160847441
85124115.8945917727998.10540822720124
8699122.555122252200-23.5551222522002
8792101.989531777561-9.98953177756073
888692.8907332986035-6.8907332986035
8911286.365682057996125.6343179420039
90104107.824401248976-3.82440124897619
9193104.129514848028-11.1295148480281
9210494.0963086089659.903691391035
9396102.093508254810-6.09350825480951
9410996.391587867812812.6084121321872
95113106.7592518606946.24074813930596
96123111.75978365859311.2402163414069
97127121.1339968998105.86600310018953
9896125.984359133190-29.9843591331898
9910099.9728164551020.0271835448979232
1009599.5486151860766-4.54861518607657
10113395.178180017512737.8218199824873
102130127.3060771574012.69392284259881
103117129.511495441588-12.5114954415883
104129118.62931679529810.3706832047024
105122127.358553121602-5.35855312160182
106134122.62440313807811.3755968619217
107141132.2699637017608.73003629823953
108152139.74640267470012.2535973252996
109161150.34823355155010.6517664484504
110122159.689822557451-37.689822557451
111126127.443533082782-1.44353308278231
112119126.085612281661-7.08561228166147
113160119.84726133181540.1527386681853
114162154.2805759041787.71942409582229
115145161.138489347694-16.1384893476941
116161147.49600784502313.5039921549769
117151159.259617841229-8.25961784122887
118166152.38637252990413.6136274700962
119169164.2964522462824.70354775371754
120185168.65658505749516.3434149425053







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121183.102348116508159.621775068916206.582921164100
122183.614134348091152.606797653314214.621471042868
123184.125920579674146.963567960784221.288273198564
124184.637706811257142.091238989816227.184174632697
125185.149493042840137.725370612698232.573615472981
126185.661279274422133.722036996830237.600521552014
127186.173065506005129.992797902333242.353333109678
128186.684851737588126.478804110677246.890899364499
129187.196637969171123.138617077901251.254658860441
130187.708424200754119.941794355282255.475054046225
131188.220210432336116.865221435005259.575199429668
132188.731996663919113.890877706956263.573115620882

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 183.102348116508 & 159.621775068916 & 206.582921164100 \tabularnewline
122 & 183.614134348091 & 152.606797653314 & 214.621471042868 \tabularnewline
123 & 184.125920579674 & 146.963567960784 & 221.288273198564 \tabularnewline
124 & 184.637706811257 & 142.091238989816 & 227.184174632697 \tabularnewline
125 & 185.149493042840 & 137.725370612698 & 232.573615472981 \tabularnewline
126 & 185.661279274422 & 133.722036996830 & 237.600521552014 \tabularnewline
127 & 186.173065506005 & 129.992797902333 & 242.353333109678 \tabularnewline
128 & 186.684851737588 & 126.478804110677 & 246.890899364499 \tabularnewline
129 & 187.196637969171 & 123.138617077901 & 251.254658860441 \tabularnewline
130 & 187.708424200754 & 119.941794355282 & 255.475054046225 \tabularnewline
131 & 188.220210432336 & 116.865221435005 & 259.575199429668 \tabularnewline
132 & 188.731996663919 & 113.890877706956 & 263.573115620882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79154&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]183.102348116508[/C][C]159.621775068916[/C][C]206.582921164100[/C][/ROW]
[ROW][C]122[/C][C]183.614134348091[/C][C]152.606797653314[/C][C]214.621471042868[/C][/ROW]
[ROW][C]123[/C][C]184.125920579674[/C][C]146.963567960784[/C][C]221.288273198564[/C][/ROW]
[ROW][C]124[/C][C]184.637706811257[/C][C]142.091238989816[/C][C]227.184174632697[/C][/ROW]
[ROW][C]125[/C][C]185.149493042840[/C][C]137.725370612698[/C][C]232.573615472981[/C][/ROW]
[ROW][C]126[/C][C]185.661279274422[/C][C]133.722036996830[/C][C]237.600521552014[/C][/ROW]
[ROW][C]127[/C][C]186.173065506005[/C][C]129.992797902333[/C][C]242.353333109678[/C][/ROW]
[ROW][C]128[/C][C]186.684851737588[/C][C]126.478804110677[/C][C]246.890899364499[/C][/ROW]
[ROW][C]129[/C][C]187.196637969171[/C][C]123.138617077901[/C][C]251.254658860441[/C][/ROW]
[ROW][C]130[/C][C]187.708424200754[/C][C]119.941794355282[/C][C]255.475054046225[/C][/ROW]
[ROW][C]131[/C][C]188.220210432336[/C][C]116.865221435005[/C][C]259.575199429668[/C][/ROW]
[ROW][C]132[/C][C]188.731996663919[/C][C]113.890877706956[/C][C]263.573115620882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79154&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79154&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
121183.102348116508159.621775068916206.582921164100
122183.614134348091152.606797653314214.621471042868
123184.125920579674146.963567960784221.288273198564
124184.637706811257142.091238989816227.184174632697
125185.149493042840137.725370612698232.573615472981
126185.661279274422133.722036996830237.600521552014
127186.173065506005129.992797902333242.353333109678
128186.684851737588126.478804110677246.890899364499
129187.196637969171123.138617077901251.254658860441
130187.708424200754119.941794355282255.475054046225
131188.220210432336116.865221435005259.575199429668
132188.731996663919113.890877706956263.573115620882



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')