Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 07 Aug 2010 13:19:56 +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/07/t12811871752a05h9uov3wav2u.htm/, Retrieved Mon, 06 May 2024 19:12:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78503, Retrieved Mon, 06 May 2024 19:12:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGosselin Claudia
Estimated Impact226
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdsreeks B - st...] [2010-08-07 13:19:56] [f0cd0ad4d4cb2a25864ed1f6cd7bfd87] [Current]
Feedback Forum

Post a new message
Dataseries X:
166
165
164
162
160
159
160
162
163
163
164
166
163
166
170
171
176
172
169
180
172
170
161
167
158
163
165
169
168
165
156
157
146
150
146
159
146
151
156
152
152
143
127
126
122
122
114
127
125
123
124
123
127
117
104
110
106
107
100
115
117
123
130
129
125
112
90
96
99
108
101
113
113
120
131
135
137
120
102
114
121
134
122
131




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78503&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78503&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78503&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.629181587767191
beta0.0412105272936492
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.629181587767191 \tabularnewline
beta & 0.0412105272936492 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78503&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]0.629181587767191[/C][/ROW]
[ROW][C]beta[/C][C]0.0412105272936492[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78503&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78503&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
alpha0.629181587767191
beta0.0412105272936492
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13163158.0734508547014.92654914529911
14166163.9668231213352.03317687866519
15170169.0924568813720.907543118627871
16171170.991727537660.00827246233981782
17176176.825408150483-0.825408150482559
18172173.363150342122-1.36315034212242
19169168.4438767187680.556123281231663
20180171.8299277221748.17007227782608
21172178.843376272332-6.84337627233197
22170174.899864839295-4.89986483929459
23161172.635460218965-11.6354602189646
24167166.6647815938350.335218406164785
25158165.353047197435-7.35304719743505
26163161.9052370040861.09476299591421
27165165.456529433316-0.456529433316348
28169165.5622128605823.43778713941796
29168172.731588624257-4.73158862425717
30165165.997998077423-0.99799807742258
31156161.415410331597-5.4154103315966
32157163.108076283288-6.10807628328797
33146154.440898210801-8.44089821080087
34150149.041707930130.958292069869628
35146146.946123303462-0.946123303461746
36159151.3977478057687.60225219423216
37146151.253594164881-5.2535941648807
38151151.760008587292-0.760008587291765
39156153.0216567557242.97834324427649
40152156.274237268001-4.27423726800109
41152154.903684124029-2.9036841240287
42143150.093746917097-7.09374691709718
43127139.268797712543-12.2687977125427
44126135.445913664715-9.4459136647145
45122122.780358420159-0.780358420159331
46122124.851842927184-2.85184292718409
47114118.719417983047-4.71941798304671
48127122.9356313322524.06436866774831
49125114.67536989148710.3246301085129
50123125.930594672566-2.93059467256623
51124126.437493018267-2.43749301826719
52123122.6774052639530.32259473604698
53127123.9107779223443.08922207765633
54117120.676561420825-3.67656142082477
55104109.530089069581-5.53008906958102
56110110.616031918222-0.616031918221893
57106106.570550405005-0.570550405004965
58107107.862465025745-0.862465025745081
59100102.197338571444-2.19733857144375
60115111.231132186093.76886781390998
61117105.07224976051711.9277502394833
62123112.42829645741410.5717035425861
63130121.9709928663288.02900713367222
64129126.4486600039082.55133999609151
65125130.796957775159-5.7969577751586
66112119.919157790429-7.91915779042853
6790105.762308221345-15.7623082213452
6896102.313548291892-6.31354829189227
699994.63342764582144.3665723541786
7010898.98472375693359.0152762430665
7110199.35689563379431.6431043662057
72113113.436383977466-0.436383977465894
73113107.9650403702155.03495962978531
74120110.6106425219629.38935747803775
75131118.56511245063412.4348875493656
76135123.9964607867811.0035392132201
77137130.9989826215136.00101737848746
78120127.495167577491-7.49516757749142
79102111.445560897239-9.44556089723908
80114116.3876032177-2.38760321769955
81121116.1524427485724.84755725142803
82134123.55710454899510.4428954510045
83122123.157701531511-1.15770153151095
84131135.695170433302-4.69517043330245

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 163 & 158.073450854701 & 4.92654914529911 \tabularnewline
14 & 166 & 163.966823121335 & 2.03317687866519 \tabularnewline
15 & 170 & 169.092456881372 & 0.907543118627871 \tabularnewline
16 & 171 & 170.99172753766 & 0.00827246233981782 \tabularnewline
17 & 176 & 176.825408150483 & -0.825408150482559 \tabularnewline
18 & 172 & 173.363150342122 & -1.36315034212242 \tabularnewline
19 & 169 & 168.443876718768 & 0.556123281231663 \tabularnewline
20 & 180 & 171.829927722174 & 8.17007227782608 \tabularnewline
21 & 172 & 178.843376272332 & -6.84337627233197 \tabularnewline
22 & 170 & 174.899864839295 & -4.89986483929459 \tabularnewline
23 & 161 & 172.635460218965 & -11.6354602189646 \tabularnewline
24 & 167 & 166.664781593835 & 0.335218406164785 \tabularnewline
25 & 158 & 165.353047197435 & -7.35304719743505 \tabularnewline
26 & 163 & 161.905237004086 & 1.09476299591421 \tabularnewline
27 & 165 & 165.456529433316 & -0.456529433316348 \tabularnewline
28 & 169 & 165.562212860582 & 3.43778713941796 \tabularnewline
29 & 168 & 172.731588624257 & -4.73158862425717 \tabularnewline
30 & 165 & 165.997998077423 & -0.99799807742258 \tabularnewline
31 & 156 & 161.415410331597 & -5.4154103315966 \tabularnewline
32 & 157 & 163.108076283288 & -6.10807628328797 \tabularnewline
33 & 146 & 154.440898210801 & -8.44089821080087 \tabularnewline
34 & 150 & 149.04170793013 & 0.958292069869628 \tabularnewline
35 & 146 & 146.946123303462 & -0.946123303461746 \tabularnewline
36 & 159 & 151.397747805768 & 7.60225219423216 \tabularnewline
37 & 146 & 151.253594164881 & -5.2535941648807 \tabularnewline
38 & 151 & 151.760008587292 & -0.760008587291765 \tabularnewline
39 & 156 & 153.021656755724 & 2.97834324427649 \tabularnewline
40 & 152 & 156.274237268001 & -4.27423726800109 \tabularnewline
41 & 152 & 154.903684124029 & -2.9036841240287 \tabularnewline
42 & 143 & 150.093746917097 & -7.09374691709718 \tabularnewline
43 & 127 & 139.268797712543 & -12.2687977125427 \tabularnewline
44 & 126 & 135.445913664715 & -9.4459136647145 \tabularnewline
45 & 122 & 122.780358420159 & -0.780358420159331 \tabularnewline
46 & 122 & 124.851842927184 & -2.85184292718409 \tabularnewline
47 & 114 & 118.719417983047 & -4.71941798304671 \tabularnewline
48 & 127 & 122.935631332252 & 4.06436866774831 \tabularnewline
49 & 125 & 114.675369891487 & 10.3246301085129 \tabularnewline
50 & 123 & 125.930594672566 & -2.93059467256623 \tabularnewline
51 & 124 & 126.437493018267 & -2.43749301826719 \tabularnewline
52 & 123 & 122.677405263953 & 0.32259473604698 \tabularnewline
53 & 127 & 123.910777922344 & 3.08922207765633 \tabularnewline
54 & 117 & 120.676561420825 & -3.67656142082477 \tabularnewline
55 & 104 & 109.530089069581 & -5.53008906958102 \tabularnewline
56 & 110 & 110.616031918222 & -0.616031918221893 \tabularnewline
57 & 106 & 106.570550405005 & -0.570550405004965 \tabularnewline
58 & 107 & 107.862465025745 & -0.862465025745081 \tabularnewline
59 & 100 & 102.197338571444 & -2.19733857144375 \tabularnewline
60 & 115 & 111.23113218609 & 3.76886781390998 \tabularnewline
61 & 117 & 105.072249760517 & 11.9277502394833 \tabularnewline
62 & 123 & 112.428296457414 & 10.5717035425861 \tabularnewline
63 & 130 & 121.970992866328 & 8.02900713367222 \tabularnewline
64 & 129 & 126.448660003908 & 2.55133999609151 \tabularnewline
65 & 125 & 130.796957775159 & -5.7969577751586 \tabularnewline
66 & 112 & 119.919157790429 & -7.91915779042853 \tabularnewline
67 & 90 & 105.762308221345 & -15.7623082213452 \tabularnewline
68 & 96 & 102.313548291892 & -6.31354829189227 \tabularnewline
69 & 99 & 94.6334276458214 & 4.3665723541786 \tabularnewline
70 & 108 & 98.9847237569335 & 9.0152762430665 \tabularnewline
71 & 101 & 99.3568956337943 & 1.6431043662057 \tabularnewline
72 & 113 & 113.436383977466 & -0.436383977465894 \tabularnewline
73 & 113 & 107.965040370215 & 5.03495962978531 \tabularnewline
74 & 120 & 110.610642521962 & 9.38935747803775 \tabularnewline
75 & 131 & 118.565112450634 & 12.4348875493656 \tabularnewline
76 & 135 & 123.99646078678 & 11.0035392132201 \tabularnewline
77 & 137 & 130.998982621513 & 6.00101737848746 \tabularnewline
78 & 120 & 127.495167577491 & -7.49516757749142 \tabularnewline
79 & 102 & 111.445560897239 & -9.44556089723908 \tabularnewline
80 & 114 & 116.3876032177 & -2.38760321769955 \tabularnewline
81 & 121 & 116.152442748572 & 4.84755725142803 \tabularnewline
82 & 134 & 123.557104548995 & 10.4428954510045 \tabularnewline
83 & 122 & 123.157701531511 & -1.15770153151095 \tabularnewline
84 & 131 & 135.695170433302 & -4.69517043330245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78503&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]163[/C][C]158.073450854701[/C][C]4.92654914529911[/C][/ROW]
[ROW][C]14[/C][C]166[/C][C]163.966823121335[/C][C]2.03317687866519[/C][/ROW]
[ROW][C]15[/C][C]170[/C][C]169.092456881372[/C][C]0.907543118627871[/C][/ROW]
[ROW][C]16[/C][C]171[/C][C]170.99172753766[/C][C]0.00827246233981782[/C][/ROW]
[ROW][C]17[/C][C]176[/C][C]176.825408150483[/C][C]-0.825408150482559[/C][/ROW]
[ROW][C]18[/C][C]172[/C][C]173.363150342122[/C][C]-1.36315034212242[/C][/ROW]
[ROW][C]19[/C][C]169[/C][C]168.443876718768[/C][C]0.556123281231663[/C][/ROW]
[ROW][C]20[/C][C]180[/C][C]171.829927722174[/C][C]8.17007227782608[/C][/ROW]
[ROW][C]21[/C][C]172[/C][C]178.843376272332[/C][C]-6.84337627233197[/C][/ROW]
[ROW][C]22[/C][C]170[/C][C]174.899864839295[/C][C]-4.89986483929459[/C][/ROW]
[ROW][C]23[/C][C]161[/C][C]172.635460218965[/C][C]-11.6354602189646[/C][/ROW]
[ROW][C]24[/C][C]167[/C][C]166.664781593835[/C][C]0.335218406164785[/C][/ROW]
[ROW][C]25[/C][C]158[/C][C]165.353047197435[/C][C]-7.35304719743505[/C][/ROW]
[ROW][C]26[/C][C]163[/C][C]161.905237004086[/C][C]1.09476299591421[/C][/ROW]
[ROW][C]27[/C][C]165[/C][C]165.456529433316[/C][C]-0.456529433316348[/C][/ROW]
[ROW][C]28[/C][C]169[/C][C]165.562212860582[/C][C]3.43778713941796[/C][/ROW]
[ROW][C]29[/C][C]168[/C][C]172.731588624257[/C][C]-4.73158862425717[/C][/ROW]
[ROW][C]30[/C][C]165[/C][C]165.997998077423[/C][C]-0.99799807742258[/C][/ROW]
[ROW][C]31[/C][C]156[/C][C]161.415410331597[/C][C]-5.4154103315966[/C][/ROW]
[ROW][C]32[/C][C]157[/C][C]163.108076283288[/C][C]-6.10807628328797[/C][/ROW]
[ROW][C]33[/C][C]146[/C][C]154.440898210801[/C][C]-8.44089821080087[/C][/ROW]
[ROW][C]34[/C][C]150[/C][C]149.04170793013[/C][C]0.958292069869628[/C][/ROW]
[ROW][C]35[/C][C]146[/C][C]146.946123303462[/C][C]-0.946123303461746[/C][/ROW]
[ROW][C]36[/C][C]159[/C][C]151.397747805768[/C][C]7.60225219423216[/C][/ROW]
[ROW][C]37[/C][C]146[/C][C]151.253594164881[/C][C]-5.2535941648807[/C][/ROW]
[ROW][C]38[/C][C]151[/C][C]151.760008587292[/C][C]-0.760008587291765[/C][/ROW]
[ROW][C]39[/C][C]156[/C][C]153.021656755724[/C][C]2.97834324427649[/C][/ROW]
[ROW][C]40[/C][C]152[/C][C]156.274237268001[/C][C]-4.27423726800109[/C][/ROW]
[ROW][C]41[/C][C]152[/C][C]154.903684124029[/C][C]-2.9036841240287[/C][/ROW]
[ROW][C]42[/C][C]143[/C][C]150.093746917097[/C][C]-7.09374691709718[/C][/ROW]
[ROW][C]43[/C][C]127[/C][C]139.268797712543[/C][C]-12.2687977125427[/C][/ROW]
[ROW][C]44[/C][C]126[/C][C]135.445913664715[/C][C]-9.4459136647145[/C][/ROW]
[ROW][C]45[/C][C]122[/C][C]122.780358420159[/C][C]-0.780358420159331[/C][/ROW]
[ROW][C]46[/C][C]122[/C][C]124.851842927184[/C][C]-2.85184292718409[/C][/ROW]
[ROW][C]47[/C][C]114[/C][C]118.719417983047[/C][C]-4.71941798304671[/C][/ROW]
[ROW][C]48[/C][C]127[/C][C]122.935631332252[/C][C]4.06436866774831[/C][/ROW]
[ROW][C]49[/C][C]125[/C][C]114.675369891487[/C][C]10.3246301085129[/C][/ROW]
[ROW][C]50[/C][C]123[/C][C]125.930594672566[/C][C]-2.93059467256623[/C][/ROW]
[ROW][C]51[/C][C]124[/C][C]126.437493018267[/C][C]-2.43749301826719[/C][/ROW]
[ROW][C]52[/C][C]123[/C][C]122.677405263953[/C][C]0.32259473604698[/C][/ROW]
[ROW][C]53[/C][C]127[/C][C]123.910777922344[/C][C]3.08922207765633[/C][/ROW]
[ROW][C]54[/C][C]117[/C][C]120.676561420825[/C][C]-3.67656142082477[/C][/ROW]
[ROW][C]55[/C][C]104[/C][C]109.530089069581[/C][C]-5.53008906958102[/C][/ROW]
[ROW][C]56[/C][C]110[/C][C]110.616031918222[/C][C]-0.616031918221893[/C][/ROW]
[ROW][C]57[/C][C]106[/C][C]106.570550405005[/C][C]-0.570550405004965[/C][/ROW]
[ROW][C]58[/C][C]107[/C][C]107.862465025745[/C][C]-0.862465025745081[/C][/ROW]
[ROW][C]59[/C][C]100[/C][C]102.197338571444[/C][C]-2.19733857144375[/C][/ROW]
[ROW][C]60[/C][C]115[/C][C]111.23113218609[/C][C]3.76886781390998[/C][/ROW]
[ROW][C]61[/C][C]117[/C][C]105.072249760517[/C][C]11.9277502394833[/C][/ROW]
[ROW][C]62[/C][C]123[/C][C]112.428296457414[/C][C]10.5717035425861[/C][/ROW]
[ROW][C]63[/C][C]130[/C][C]121.970992866328[/C][C]8.02900713367222[/C][/ROW]
[ROW][C]64[/C][C]129[/C][C]126.448660003908[/C][C]2.55133999609151[/C][/ROW]
[ROW][C]65[/C][C]125[/C][C]130.796957775159[/C][C]-5.7969577751586[/C][/ROW]
[ROW][C]66[/C][C]112[/C][C]119.919157790429[/C][C]-7.91915779042853[/C][/ROW]
[ROW][C]67[/C][C]90[/C][C]105.762308221345[/C][C]-15.7623082213452[/C][/ROW]
[ROW][C]68[/C][C]96[/C][C]102.313548291892[/C][C]-6.31354829189227[/C][/ROW]
[ROW][C]69[/C][C]99[/C][C]94.6334276458214[/C][C]4.3665723541786[/C][/ROW]
[ROW][C]70[/C][C]108[/C][C]98.9847237569335[/C][C]9.0152762430665[/C][/ROW]
[ROW][C]71[/C][C]101[/C][C]99.3568956337943[/C][C]1.6431043662057[/C][/ROW]
[ROW][C]72[/C][C]113[/C][C]113.436383977466[/C][C]-0.436383977465894[/C][/ROW]
[ROW][C]73[/C][C]113[/C][C]107.965040370215[/C][C]5.03495962978531[/C][/ROW]
[ROW][C]74[/C][C]120[/C][C]110.610642521962[/C][C]9.38935747803775[/C][/ROW]
[ROW][C]75[/C][C]131[/C][C]118.565112450634[/C][C]12.4348875493656[/C][/ROW]
[ROW][C]76[/C][C]135[/C][C]123.99646078678[/C][C]11.0035392132201[/C][/ROW]
[ROW][C]77[/C][C]137[/C][C]130.998982621513[/C][C]6.00101737848746[/C][/ROW]
[ROW][C]78[/C][C]120[/C][C]127.495167577491[/C][C]-7.49516757749142[/C][/ROW]
[ROW][C]79[/C][C]102[/C][C]111.445560897239[/C][C]-9.44556089723908[/C][/ROW]
[ROW][C]80[/C][C]114[/C][C]116.3876032177[/C][C]-2.38760321769955[/C][/ROW]
[ROW][C]81[/C][C]121[/C][C]116.152442748572[/C][C]4.84755725142803[/C][/ROW]
[ROW][C]82[/C][C]134[/C][C]123.557104548995[/C][C]10.4428954510045[/C][/ROW]
[ROW][C]83[/C][C]122[/C][C]123.157701531511[/C][C]-1.15770153151095[/C][/ROW]
[ROW][C]84[/C][C]131[/C][C]135.695170433302[/C][C]-4.69517043330245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78503&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78503&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
13163158.0734508547014.92654914529911
14166163.9668231213352.03317687866519
15170169.0924568813720.907543118627871
16171170.991727537660.00827246233981782
17176176.825408150483-0.825408150482559
18172173.363150342122-1.36315034212242
19169168.4438767187680.556123281231663
20180171.8299277221748.17007227782608
21172178.843376272332-6.84337627233197
22170174.899864839295-4.89986483929459
23161172.635460218965-11.6354602189646
24167166.6647815938350.335218406164785
25158165.353047197435-7.35304719743505
26163161.9052370040861.09476299591421
27165165.456529433316-0.456529433316348
28169165.5622128605823.43778713941796
29168172.731588624257-4.73158862425717
30165165.997998077423-0.99799807742258
31156161.415410331597-5.4154103315966
32157163.108076283288-6.10807628328797
33146154.440898210801-8.44089821080087
34150149.041707930130.958292069869628
35146146.946123303462-0.946123303461746
36159151.3977478057687.60225219423216
37146151.253594164881-5.2535941648807
38151151.760008587292-0.760008587291765
39156153.0216567557242.97834324427649
40152156.274237268001-4.27423726800109
41152154.903684124029-2.9036841240287
42143150.093746917097-7.09374691709718
43127139.268797712543-12.2687977125427
44126135.445913664715-9.4459136647145
45122122.780358420159-0.780358420159331
46122124.851842927184-2.85184292718409
47114118.719417983047-4.71941798304671
48127122.9356313322524.06436866774831
49125114.67536989148710.3246301085129
50123125.930594672566-2.93059467256623
51124126.437493018267-2.43749301826719
52123122.6774052639530.32259473604698
53127123.9107779223443.08922207765633
54117120.676561420825-3.67656142082477
55104109.530089069581-5.53008906958102
56110110.616031918222-0.616031918221893
57106106.570550405005-0.570550405004965
58107107.862465025745-0.862465025745081
59100102.197338571444-2.19733857144375
60115111.231132186093.76886781390998
61117105.07224976051711.9277502394833
62123112.42829645741410.5717035425861
63130121.9709928663288.02900713367222
64129126.4486600039082.55133999609151
65125130.796957775159-5.7969577751586
66112119.919157790429-7.91915779042853
6790105.762308221345-15.7623082213452
6896102.313548291892-6.31354829189227
699994.63342764582144.3665723541786
7010898.98472375693359.0152762430665
7110199.35689563379431.6431043662057
72113113.436383977466-0.436383977465894
73113107.9650403702155.03495962978531
74120110.6106425219629.38935747803775
75131118.56511245063412.4348875493656
76135123.9964607867811.0035392132201
77137130.9989826215136.00101737848746
78120127.495167577491-7.49516757749142
79102111.445560897239-9.44556089723908
80114116.3876032177-2.38760321769955
81121116.1524427485724.84755725142803
82134123.55710454899510.4428954510045
83122123.157701531511-1.15770153151095
84131135.695170433302-4.69517043330245







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85130.454034707349118.314640487486142.593428927211
86132.296755827628117.784366395379146.809145259877
87135.979829744022119.277750696334152.681908791709
88133.241058661304114.463065326114152.019051996494
89131.364472486531110.585435843744152.143509129317
90118.82383758167896.0944824641646141.553192699191
91106.70469573055682.0596791209231131.349712340188
92120.38972991135993.8524675823117146.926992240407
93124.58444227744596.170183920447152.998700634443
94131.132979019595100.850866294637161.415091744552
95119.70962494622687.5641235428816151.85512634957
96131.54199910618797.5339271914234165.55007102095

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 130.454034707349 & 118.314640487486 & 142.593428927211 \tabularnewline
86 & 132.296755827628 & 117.784366395379 & 146.809145259877 \tabularnewline
87 & 135.979829744022 & 119.277750696334 & 152.681908791709 \tabularnewline
88 & 133.241058661304 & 114.463065326114 & 152.019051996494 \tabularnewline
89 & 131.364472486531 & 110.585435843744 & 152.143509129317 \tabularnewline
90 & 118.823837581678 & 96.0944824641646 & 141.553192699191 \tabularnewline
91 & 106.704695730556 & 82.0596791209231 & 131.349712340188 \tabularnewline
92 & 120.389729911359 & 93.8524675823117 & 146.926992240407 \tabularnewline
93 & 124.584442277445 & 96.170183920447 & 152.998700634443 \tabularnewline
94 & 131.132979019595 & 100.850866294637 & 161.415091744552 \tabularnewline
95 & 119.709624946226 & 87.5641235428816 & 151.85512634957 \tabularnewline
96 & 131.541999106187 & 97.5339271914234 & 165.55007102095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78503&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]85[/C][C]130.454034707349[/C][C]118.314640487486[/C][C]142.593428927211[/C][/ROW]
[ROW][C]86[/C][C]132.296755827628[/C][C]117.784366395379[/C][C]146.809145259877[/C][/ROW]
[ROW][C]87[/C][C]135.979829744022[/C][C]119.277750696334[/C][C]152.681908791709[/C][/ROW]
[ROW][C]88[/C][C]133.241058661304[/C][C]114.463065326114[/C][C]152.019051996494[/C][/ROW]
[ROW][C]89[/C][C]131.364472486531[/C][C]110.585435843744[/C][C]152.143509129317[/C][/ROW]
[ROW][C]90[/C][C]118.823837581678[/C][C]96.0944824641646[/C][C]141.553192699191[/C][/ROW]
[ROW][C]91[/C][C]106.704695730556[/C][C]82.0596791209231[/C][C]131.349712340188[/C][/ROW]
[ROW][C]92[/C][C]120.389729911359[/C][C]93.8524675823117[/C][C]146.926992240407[/C][/ROW]
[ROW][C]93[/C][C]124.584442277445[/C][C]96.170183920447[/C][C]152.998700634443[/C][/ROW]
[ROW][C]94[/C][C]131.132979019595[/C][C]100.850866294637[/C][C]161.415091744552[/C][/ROW]
[ROW][C]95[/C][C]119.709624946226[/C][C]87.5641235428816[/C][C]151.85512634957[/C][/ROW]
[ROW][C]96[/C][C]131.541999106187[/C][C]97.5339271914234[/C][C]165.55007102095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78503&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78503&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
85130.454034707349118.314640487486142.593428927211
86132.296755827628117.784366395379146.809145259877
87135.979829744022119.277750696334152.681908791709
88133.241058661304114.463065326114152.019051996494
89131.364472486531110.585435843744152.143509129317
90118.82383758167896.0944824641646141.553192699191
91106.70469573055682.0596791209231131.349712340188
92120.38972991135993.8524675823117146.926992240407
93124.58444227744596.170183920447152.998700634443
94131.132979019595100.850866294637161.415091744552
95119.70962494622687.5641235428816151.85512634957
96131.54199910618797.5339271914234165.55007102095



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')