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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 11:09:10 +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/2014/Nov/28/t1417173138520qg7y6scze9nh.htm/, Retrieved Sun, 19 May 2024 13:53:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260832, Retrieved Sun, 19 May 2024 13:53:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2014-11-28 11:09:10] [be7d2a6a6c016378f31f309d9b06695b] [Current]
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Dataseries X:
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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260832&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260832&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260832&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0298471475566542
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0298471475566542 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260832&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0298471475566542[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260832&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260832&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
alpha1
beta0.0298471475566542
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37683-7
46981.7910699671034-12.7910699671034
57474.4092930143878-0.409293014387799
610179.397076785393521.6029232146065
7105107.041862422235-2.04186242223489
873110.980918653228-37.9809186532281
96877.8472965698479-9.84729656984788
106572.5533828560935-7.55338285609349
117069.32793592343580.672064076564226
126574.3479951190965-9.34799511909651
138069.06898412941810.931015870582
149284.39524377305137.60475622694865
159396.6222240542895-3.62222405428946
169097.5141109984578-7.51411099845782
179694.28983621872981.71016378127023
18125100.34087972945524.6591202705446
19134130.0768841307883.92311586921238
20100139.193977949018-39.1939779490179
2197104.024149505841-7.02414950584127
2297100.81449867908-3.81449867908043
23101100.7006467741510.299353225848748
2490104.709581614055-14.7095816140547
2510893.270542561123414.7294574388766
26113111.7101748507311.28982514926901
27112116.748672452284-4.7486724522835
28103115.606938124902-12.606938124902
29103106.23065698245-3.23065698245043
30125106.1342310867918.8657689132097
31128128.697320475313-0.697320475312608
3291131.676507448192-40.6765074481917
338493.4624297282961-9.46242972829614
348386.1800031919512-3.18000319195122
358385.0850891674504-2.08508916745042
366985.0228552034008-16.0228552034008
377770.54461867986596.45538132013407
388378.73729339866244.26270660133756
397884.8645230315833-6.86452303158329
407079.6596365997536-9.65963659975358
417571.37132400081713.62867599918293
4210176.479629628824.5203703712
43117103.21149274141313.788507258587
4480119.623040352146-39.623040352146
458781.44040562011235.55959437988773
468188.6063436539239-7.60634365392393
477882.3793159925186-4.37931599251864
487379.2486059018927-6.24860590189272
499374.062102839515518.9378971604845
5010594.627345050477310.3726549495227
51102106.93693921331-4.93693921330994
5297103.789585660132-6.78958566013205
5310098.58693589508551.41306410491447
54127101.62911182793225.3708881720681
55138129.3863604708478.61363952915298
56107140.643453040873-33.6434530408735
57107108.639291933647-1.63929193364716
58106108.590363745415-2.59036374541516
59109107.513048776481.48695122351965
60107110.557430029058-3.55743002905828
61129108.45125089005920.5487491099415
62138131.0645724368486.93542756315239
63137140.271575166694-3.27157516669351
64134139.173927979951-5.17392797995052
65134136.019500988085-2.01950098808544
66166135.95922464410330.0407753558968
67180168.85585609886711.144143901133
68131183.188477006277-52.1884770062767
69135132.6307998323132.3692001676867
70127136.701513699309-9.70151369930949
71121128.411951188403-7.41195118840329
72116122.1907255876-6.1907255876003

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 76 & 83 & -7 \tabularnewline
4 & 69 & 81.7910699671034 & -12.7910699671034 \tabularnewline
5 & 74 & 74.4092930143878 & -0.409293014387799 \tabularnewline
6 & 101 & 79.3970767853935 & 21.6029232146065 \tabularnewline
7 & 105 & 107.041862422235 & -2.04186242223489 \tabularnewline
8 & 73 & 110.980918653228 & -37.9809186532281 \tabularnewline
9 & 68 & 77.8472965698479 & -9.84729656984788 \tabularnewline
10 & 65 & 72.5533828560935 & -7.55338285609349 \tabularnewline
11 & 70 & 69.3279359234358 & 0.672064076564226 \tabularnewline
12 & 65 & 74.3479951190965 & -9.34799511909651 \tabularnewline
13 & 80 & 69.068984129418 & 10.931015870582 \tabularnewline
14 & 92 & 84.3952437730513 & 7.60475622694865 \tabularnewline
15 & 93 & 96.6222240542895 & -3.62222405428946 \tabularnewline
16 & 90 & 97.5141109984578 & -7.51411099845782 \tabularnewline
17 & 96 & 94.2898362187298 & 1.71016378127023 \tabularnewline
18 & 125 & 100.340879729455 & 24.6591202705446 \tabularnewline
19 & 134 & 130.076884130788 & 3.92311586921238 \tabularnewline
20 & 100 & 139.193977949018 & -39.1939779490179 \tabularnewline
21 & 97 & 104.024149505841 & -7.02414950584127 \tabularnewline
22 & 97 & 100.81449867908 & -3.81449867908043 \tabularnewline
23 & 101 & 100.700646774151 & 0.299353225848748 \tabularnewline
24 & 90 & 104.709581614055 & -14.7095816140547 \tabularnewline
25 & 108 & 93.2705425611234 & 14.7294574388766 \tabularnewline
26 & 113 & 111.710174850731 & 1.28982514926901 \tabularnewline
27 & 112 & 116.748672452284 & -4.7486724522835 \tabularnewline
28 & 103 & 115.606938124902 & -12.606938124902 \tabularnewline
29 & 103 & 106.23065698245 & -3.23065698245043 \tabularnewline
30 & 125 & 106.13423108679 & 18.8657689132097 \tabularnewline
31 & 128 & 128.697320475313 & -0.697320475312608 \tabularnewline
32 & 91 & 131.676507448192 & -40.6765074481917 \tabularnewline
33 & 84 & 93.4624297282961 & -9.46242972829614 \tabularnewline
34 & 83 & 86.1800031919512 & -3.18000319195122 \tabularnewline
35 & 83 & 85.0850891674504 & -2.08508916745042 \tabularnewline
36 & 69 & 85.0228552034008 & -16.0228552034008 \tabularnewline
37 & 77 & 70.5446186798659 & 6.45538132013407 \tabularnewline
38 & 83 & 78.7372933986624 & 4.26270660133756 \tabularnewline
39 & 78 & 84.8645230315833 & -6.86452303158329 \tabularnewline
40 & 70 & 79.6596365997536 & -9.65963659975358 \tabularnewline
41 & 75 & 71.3713240008171 & 3.62867599918293 \tabularnewline
42 & 101 & 76.4796296288 & 24.5203703712 \tabularnewline
43 & 117 & 103.211492741413 & 13.788507258587 \tabularnewline
44 & 80 & 119.623040352146 & -39.623040352146 \tabularnewline
45 & 87 & 81.4404056201123 & 5.55959437988773 \tabularnewline
46 & 81 & 88.6063436539239 & -7.60634365392393 \tabularnewline
47 & 78 & 82.3793159925186 & -4.37931599251864 \tabularnewline
48 & 73 & 79.2486059018927 & -6.24860590189272 \tabularnewline
49 & 93 & 74.0621028395155 & 18.9378971604845 \tabularnewline
50 & 105 & 94.6273450504773 & 10.3726549495227 \tabularnewline
51 & 102 & 106.93693921331 & -4.93693921330994 \tabularnewline
52 & 97 & 103.789585660132 & -6.78958566013205 \tabularnewline
53 & 100 & 98.5869358950855 & 1.41306410491447 \tabularnewline
54 & 127 & 101.629111827932 & 25.3708881720681 \tabularnewline
55 & 138 & 129.386360470847 & 8.61363952915298 \tabularnewline
56 & 107 & 140.643453040873 & -33.6434530408735 \tabularnewline
57 & 107 & 108.639291933647 & -1.63929193364716 \tabularnewline
58 & 106 & 108.590363745415 & -2.59036374541516 \tabularnewline
59 & 109 & 107.51304877648 & 1.48695122351965 \tabularnewline
60 & 107 & 110.557430029058 & -3.55743002905828 \tabularnewline
61 & 129 & 108.451250890059 & 20.5487491099415 \tabularnewline
62 & 138 & 131.064572436848 & 6.93542756315239 \tabularnewline
63 & 137 & 140.271575166694 & -3.27157516669351 \tabularnewline
64 & 134 & 139.173927979951 & -5.17392797995052 \tabularnewline
65 & 134 & 136.019500988085 & -2.01950098808544 \tabularnewline
66 & 166 & 135.959224644103 & 30.0407753558968 \tabularnewline
67 & 180 & 168.855856098867 & 11.144143901133 \tabularnewline
68 & 131 & 183.188477006277 & -52.1884770062767 \tabularnewline
69 & 135 & 132.630799832313 & 2.3692001676867 \tabularnewline
70 & 127 & 136.701513699309 & -9.70151369930949 \tabularnewline
71 & 121 & 128.411951188403 & -7.41195118840329 \tabularnewline
72 & 116 & 122.1907255876 & -6.1907255876003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260832&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]76[/C][C]83[/C][C]-7[/C][/ROW]
[ROW][C]4[/C][C]69[/C][C]81.7910699671034[/C][C]-12.7910699671034[/C][/ROW]
[ROW][C]5[/C][C]74[/C][C]74.4092930143878[/C][C]-0.409293014387799[/C][/ROW]
[ROW][C]6[/C][C]101[/C][C]79.3970767853935[/C][C]21.6029232146065[/C][/ROW]
[ROW][C]7[/C][C]105[/C][C]107.041862422235[/C][C]-2.04186242223489[/C][/ROW]
[ROW][C]8[/C][C]73[/C][C]110.980918653228[/C][C]-37.9809186532281[/C][/ROW]
[ROW][C]9[/C][C]68[/C][C]77.8472965698479[/C][C]-9.84729656984788[/C][/ROW]
[ROW][C]10[/C][C]65[/C][C]72.5533828560935[/C][C]-7.55338285609349[/C][/ROW]
[ROW][C]11[/C][C]70[/C][C]69.3279359234358[/C][C]0.672064076564226[/C][/ROW]
[ROW][C]12[/C][C]65[/C][C]74.3479951190965[/C][C]-9.34799511909651[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]69.068984129418[/C][C]10.931015870582[/C][/ROW]
[ROW][C]14[/C][C]92[/C][C]84.3952437730513[/C][C]7.60475622694865[/C][/ROW]
[ROW][C]15[/C][C]93[/C][C]96.6222240542895[/C][C]-3.62222405428946[/C][/ROW]
[ROW][C]16[/C][C]90[/C][C]97.5141109984578[/C][C]-7.51411099845782[/C][/ROW]
[ROW][C]17[/C][C]96[/C][C]94.2898362187298[/C][C]1.71016378127023[/C][/ROW]
[ROW][C]18[/C][C]125[/C][C]100.340879729455[/C][C]24.6591202705446[/C][/ROW]
[ROW][C]19[/C][C]134[/C][C]130.076884130788[/C][C]3.92311586921238[/C][/ROW]
[ROW][C]20[/C][C]100[/C][C]139.193977949018[/C][C]-39.1939779490179[/C][/ROW]
[ROW][C]21[/C][C]97[/C][C]104.024149505841[/C][C]-7.02414950584127[/C][/ROW]
[ROW][C]22[/C][C]97[/C][C]100.81449867908[/C][C]-3.81449867908043[/C][/ROW]
[ROW][C]23[/C][C]101[/C][C]100.700646774151[/C][C]0.299353225848748[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]104.709581614055[/C][C]-14.7095816140547[/C][/ROW]
[ROW][C]25[/C][C]108[/C][C]93.2705425611234[/C][C]14.7294574388766[/C][/ROW]
[ROW][C]26[/C][C]113[/C][C]111.710174850731[/C][C]1.28982514926901[/C][/ROW]
[ROW][C]27[/C][C]112[/C][C]116.748672452284[/C][C]-4.7486724522835[/C][/ROW]
[ROW][C]28[/C][C]103[/C][C]115.606938124902[/C][C]-12.606938124902[/C][/ROW]
[ROW][C]29[/C][C]103[/C][C]106.23065698245[/C][C]-3.23065698245043[/C][/ROW]
[ROW][C]30[/C][C]125[/C][C]106.13423108679[/C][C]18.8657689132097[/C][/ROW]
[ROW][C]31[/C][C]128[/C][C]128.697320475313[/C][C]-0.697320475312608[/C][/ROW]
[ROW][C]32[/C][C]91[/C][C]131.676507448192[/C][C]-40.6765074481917[/C][/ROW]
[ROW][C]33[/C][C]84[/C][C]93.4624297282961[/C][C]-9.46242972829614[/C][/ROW]
[ROW][C]34[/C][C]83[/C][C]86.1800031919512[/C][C]-3.18000319195122[/C][/ROW]
[ROW][C]35[/C][C]83[/C][C]85.0850891674504[/C][C]-2.08508916745042[/C][/ROW]
[ROW][C]36[/C][C]69[/C][C]85.0228552034008[/C][C]-16.0228552034008[/C][/ROW]
[ROW][C]37[/C][C]77[/C][C]70.5446186798659[/C][C]6.45538132013407[/C][/ROW]
[ROW][C]38[/C][C]83[/C][C]78.7372933986624[/C][C]4.26270660133756[/C][/ROW]
[ROW][C]39[/C][C]78[/C][C]84.8645230315833[/C][C]-6.86452303158329[/C][/ROW]
[ROW][C]40[/C][C]70[/C][C]79.6596365997536[/C][C]-9.65963659975358[/C][/ROW]
[ROW][C]41[/C][C]75[/C][C]71.3713240008171[/C][C]3.62867599918293[/C][/ROW]
[ROW][C]42[/C][C]101[/C][C]76.4796296288[/C][C]24.5203703712[/C][/ROW]
[ROW][C]43[/C][C]117[/C][C]103.211492741413[/C][C]13.788507258587[/C][/ROW]
[ROW][C]44[/C][C]80[/C][C]119.623040352146[/C][C]-39.623040352146[/C][/ROW]
[ROW][C]45[/C][C]87[/C][C]81.4404056201123[/C][C]5.55959437988773[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]88.6063436539239[/C][C]-7.60634365392393[/C][/ROW]
[ROW][C]47[/C][C]78[/C][C]82.3793159925186[/C][C]-4.37931599251864[/C][/ROW]
[ROW][C]48[/C][C]73[/C][C]79.2486059018927[/C][C]-6.24860590189272[/C][/ROW]
[ROW][C]49[/C][C]93[/C][C]74.0621028395155[/C][C]18.9378971604845[/C][/ROW]
[ROW][C]50[/C][C]105[/C][C]94.6273450504773[/C][C]10.3726549495227[/C][/ROW]
[ROW][C]51[/C][C]102[/C][C]106.93693921331[/C][C]-4.93693921330994[/C][/ROW]
[ROW][C]52[/C][C]97[/C][C]103.789585660132[/C][C]-6.78958566013205[/C][/ROW]
[ROW][C]53[/C][C]100[/C][C]98.5869358950855[/C][C]1.41306410491447[/C][/ROW]
[ROW][C]54[/C][C]127[/C][C]101.629111827932[/C][C]25.3708881720681[/C][/ROW]
[ROW][C]55[/C][C]138[/C][C]129.386360470847[/C][C]8.61363952915298[/C][/ROW]
[ROW][C]56[/C][C]107[/C][C]140.643453040873[/C][C]-33.6434530408735[/C][/ROW]
[ROW][C]57[/C][C]107[/C][C]108.639291933647[/C][C]-1.63929193364716[/C][/ROW]
[ROW][C]58[/C][C]106[/C][C]108.590363745415[/C][C]-2.59036374541516[/C][/ROW]
[ROW][C]59[/C][C]109[/C][C]107.51304877648[/C][C]1.48695122351965[/C][/ROW]
[ROW][C]60[/C][C]107[/C][C]110.557430029058[/C][C]-3.55743002905828[/C][/ROW]
[ROW][C]61[/C][C]129[/C][C]108.451250890059[/C][C]20.5487491099415[/C][/ROW]
[ROW][C]62[/C][C]138[/C][C]131.064572436848[/C][C]6.93542756315239[/C][/ROW]
[ROW][C]63[/C][C]137[/C][C]140.271575166694[/C][C]-3.27157516669351[/C][/ROW]
[ROW][C]64[/C][C]134[/C][C]139.173927979951[/C][C]-5.17392797995052[/C][/ROW]
[ROW][C]65[/C][C]134[/C][C]136.019500988085[/C][C]-2.01950098808544[/C][/ROW]
[ROW][C]66[/C][C]166[/C][C]135.959224644103[/C][C]30.0407753558968[/C][/ROW]
[ROW][C]67[/C][C]180[/C][C]168.855856098867[/C][C]11.144143901133[/C][/ROW]
[ROW][C]68[/C][C]131[/C][C]183.188477006277[/C][C]-52.1884770062767[/C][/ROW]
[ROW][C]69[/C][C]135[/C][C]132.630799832313[/C][C]2.3692001676867[/C][/ROW]
[ROW][C]70[/C][C]127[/C][C]136.701513699309[/C][C]-9.70151369930949[/C][/ROW]
[ROW][C]71[/C][C]121[/C][C]128.411951188403[/C][C]-7.41195118840329[/C][/ROW]
[ROW][C]72[/C][C]116[/C][C]122.1907255876[/C][C]-6.1907255876003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260832&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260832&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
37683-7
46981.7910699671034-12.7910699671034
57474.4092930143878-0.409293014387799
610179.397076785393521.6029232146065
7105107.041862422235-2.04186242223489
873110.980918653228-37.9809186532281
96877.8472965698479-9.84729656984788
106572.5533828560935-7.55338285609349
117069.32793592343580.672064076564226
126574.3479951190965-9.34799511909651
138069.06898412941810.931015870582
149284.39524377305137.60475622694865
159396.6222240542895-3.62222405428946
169097.5141109984578-7.51411099845782
179694.28983621872981.71016378127023
18125100.34087972945524.6591202705446
19134130.0768841307883.92311586921238
20100139.193977949018-39.1939779490179
2197104.024149505841-7.02414950584127
2297100.81449867908-3.81449867908043
23101100.7006467741510.299353225848748
2490104.709581614055-14.7095816140547
2510893.270542561123414.7294574388766
26113111.7101748507311.28982514926901
27112116.748672452284-4.7486724522835
28103115.606938124902-12.606938124902
29103106.23065698245-3.23065698245043
30125106.1342310867918.8657689132097
31128128.697320475313-0.697320475312608
3291131.676507448192-40.6765074481917
338493.4624297282961-9.46242972829614
348386.1800031919512-3.18000319195122
358385.0850891674504-2.08508916745042
366985.0228552034008-16.0228552034008
377770.54461867986596.45538132013407
388378.73729339866244.26270660133756
397884.8645230315833-6.86452303158329
407079.6596365997536-9.65963659975358
417571.37132400081713.62867599918293
4210176.479629628824.5203703712
43117103.21149274141313.788507258587
4480119.623040352146-39.623040352146
458781.44040562011235.55959437988773
468188.6063436539239-7.60634365392393
477882.3793159925186-4.37931599251864
487379.2486059018927-6.24860590189272
499374.062102839515518.9378971604845
5010594.627345050477310.3726549495227
51102106.93693921331-4.93693921330994
5297103.789585660132-6.78958566013205
5310098.58693589508551.41306410491447
54127101.62911182793225.3708881720681
55138129.3863604708478.61363952915298
56107140.643453040873-33.6434530408735
57107108.639291933647-1.63929193364716
58106108.590363745415-2.59036374541516
59109107.513048776481.48695122351965
60107110.557430029058-3.55743002905828
61129108.45125089005920.5487491099415
62138131.0645724368486.93542756315239
63137140.271575166694-3.27157516669351
64134139.173927979951-5.17392797995052
65134136.019500988085-2.01950098808544
66166135.95922464410330.0407753558968
67180168.85585609886711.144143901133
68131183.188477006277-52.1884770062767
69135132.6307998323132.3692001676867
70127136.701513699309-9.70151369930949
71121128.411951188403-7.41195118840329
72116122.1907255876-6.1907255876003







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73117.00595008750486.2145874619057147.797312713103
74118.01190017500973.811704606491162.212095743527
75119.01785026251364.0784556889259173.957244836101
76120.02380035001855.6511615658073184.396439134228
77121.02975043752248.010265501407194.049235373637
78122.03570052502740.8935290403929203.17787200966
79123.04165061253134.1476333165911211.935667908471
80124.04760070003627.6742777216662220.420923678405
81125.0535507875421.4062910353481228.700810539732
82126.05950087504415.2955772536926236.823424496396
83127.0654509625499.30644453111688244.824457393981
84128.0714010500533.41164747436034252.731154625746

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 117.005950087504 & 86.2145874619057 & 147.797312713103 \tabularnewline
74 & 118.011900175009 & 73.811704606491 & 162.212095743527 \tabularnewline
75 & 119.017850262513 & 64.0784556889259 & 173.957244836101 \tabularnewline
76 & 120.023800350018 & 55.6511615658073 & 184.396439134228 \tabularnewline
77 & 121.029750437522 & 48.010265501407 & 194.049235373637 \tabularnewline
78 & 122.035700525027 & 40.8935290403929 & 203.17787200966 \tabularnewline
79 & 123.041650612531 & 34.1476333165911 & 211.935667908471 \tabularnewline
80 & 124.047600700036 & 27.6742777216662 & 220.420923678405 \tabularnewline
81 & 125.05355078754 & 21.4062910353481 & 228.700810539732 \tabularnewline
82 & 126.059500875044 & 15.2955772536926 & 236.823424496396 \tabularnewline
83 & 127.065450962549 & 9.30644453111688 & 244.824457393981 \tabularnewline
84 & 128.071401050053 & 3.41164747436034 & 252.731154625746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260832&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]73[/C][C]117.005950087504[/C][C]86.2145874619057[/C][C]147.797312713103[/C][/ROW]
[ROW][C]74[/C][C]118.011900175009[/C][C]73.811704606491[/C][C]162.212095743527[/C][/ROW]
[ROW][C]75[/C][C]119.017850262513[/C][C]64.0784556889259[/C][C]173.957244836101[/C][/ROW]
[ROW][C]76[/C][C]120.023800350018[/C][C]55.6511615658073[/C][C]184.396439134228[/C][/ROW]
[ROW][C]77[/C][C]121.029750437522[/C][C]48.010265501407[/C][C]194.049235373637[/C][/ROW]
[ROW][C]78[/C][C]122.035700525027[/C][C]40.8935290403929[/C][C]203.17787200966[/C][/ROW]
[ROW][C]79[/C][C]123.041650612531[/C][C]34.1476333165911[/C][C]211.935667908471[/C][/ROW]
[ROW][C]80[/C][C]124.047600700036[/C][C]27.6742777216662[/C][C]220.420923678405[/C][/ROW]
[ROW][C]81[/C][C]125.05355078754[/C][C]21.4062910353481[/C][C]228.700810539732[/C][/ROW]
[ROW][C]82[/C][C]126.059500875044[/C][C]15.2955772536926[/C][C]236.823424496396[/C][/ROW]
[ROW][C]83[/C][C]127.065450962549[/C][C]9.30644453111688[/C][C]244.824457393981[/C][/ROW]
[ROW][C]84[/C][C]128.071401050053[/C][C]3.41164747436034[/C][C]252.731154625746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260832&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260832&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
73117.00595008750486.2145874619057147.797312713103
74118.01190017500973.811704606491162.212095743527
75119.01785026251364.0784556889259173.957244836101
76120.02380035001855.6511615658073184.396439134228
77121.02975043752248.010265501407194.049235373637
78122.03570052502740.8935290403929203.17787200966
79123.04165061253134.1476333165911211.935667908471
80124.04760070003627.6742777216662220.420923678405
81125.0535507875421.4062910353481228.700810539732
82126.05950087504415.2955772536926236.823424496396
83127.0654509625499.30644453111688244.824457393981
84128.0714010500533.41164747436034252.731154625746



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')