Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 02 Jul 2010 13:20:58 +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/02/t1278076870qnz6ummbakhvre9.htm/, Retrieved Fri, 03 May 2024 18:20:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77920, Retrieved Fri, 03 May 2024 18:20:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSteffi Poppe
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks2-Stap27] [2010-07-02 13:20:58] [b37bab310ab56201887748d7a7c0dc58] [Current]
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Dataseries X:
59
58
57
55
53
52
53
55
56
56
57
59
68
68
68
70
66
64
72
80
84
82
83
86
99
100
95
98
103
107
114
123
132
137
141
146
156
156
143
143
151
149
156
166
177
180
189
195
205
209
199
191
198
200
208
224
234
243
249
258
274
270
261
258
261
258
264
270
267
287
297
306
322
323
309
303
306
301
316
327
330
342
359
379




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=77920&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=77920&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77920&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
alpha0.594886274163376
beta0.0322225119939658
gamma0.93989494567203

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.594886274163376 \tabularnewline
beta & 0.0322225119939658 \tabularnewline
gamma & 0.93989494567203 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77920&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]0.594886274163376[/C][/ROW]
[ROW][C]beta[/C][C]0.0322225119939658[/C][/ROW]
[ROW][C]gamma[/C][C]0.93989494567203[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77920&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77920&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
alpha0.594886274163376
beta0.0322225119939658
gamma0.93989494567203







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136860.88949394743177.11050605256828
146865.05549887559082.94450112440924
156866.37663566699761.62336433300239
167068.86561900231981.13438099768018
176665.23904596464970.760954035350323
186463.36676059966040.633239400339569
197270.40015962326811.59984037673190
208074.8131012737165.18689872628394
218480.01771194668453.98228805331553
228282.8146920752238-0.814692075223775
238384.0966887782759-1.09668877827586
248686.8359440422374-0.835944042237401
2599103.758392118631-4.75839211863149
2610097.76829963304892.23170036695112
279597.0994417215807-2.09944172158070
289897.11609257320980.883907426790188
2910390.890354515793812.1096454842062
3010794.10157766126312.8984223387371
31114112.5027899000961.49721009990445
32123120.4324281515752.56757184842461
33132123.9698178312358.03018216876497
34137126.17684162869710.8231583713033
35141134.9460645139516.05393548604906
36146144.0691412793861.93085872061408
37156171.700550261588-15.7005502615883
38156161.174781575277-5.17478157527711
39143151.933368234723-8.93336823472342
40143149.907629134552-6.90762913455166
41151141.1666705749679.83332942503304
42149140.7359860798948.26401392010578
43156153.8178446242332.18215537576663
44166164.6758903766721.32410962332764
45177170.2464781292476.75352187075276
46180171.4397395408618.56026045913947
47189176.53121745562412.4687825443758
48195188.5532489091406.4467510908604
49205217.427781000438-12.4277810004377
50209213.276833343379-4.27683334337857
51199199.880640003582-0.880640003581846
52191204.567872881927-13.5678728819266
53198198.317350814738-0.317350814737949
54200188.49512040367211.5048795963284
55208202.5569457880865.44305421191393
56224217.5366683444496.46333165555052
57234230.0408786800193.95912131998134
58243229.03941151044513.9605884895547
59249238.66300937057210.3369906294276
60258247.30859898310710.6914010168932
61274276.252714267061-2.25271426706104
62270283.068945235288-13.0689452352884
63261262.352714727390-1.35271472738958
64258261.422039730643-3.42203973064284
65261268.490490350596-7.49049035059602
66258256.7240475432221.27595245677782
67264263.3634422988440.636557701156278
68270278.593349651185-8.5933496511854
69267282.218345610810-15.2183456108104
70287272.63677644389214.3632235561081
71297280.16164350682716.8383564931733
72306292.35764402730813.6423559726915
73322320.2627417984151.73725820158489
74323325.1333943394-2.13339433939996
75309313.14001495548-4.14001495548018
76303309.007880394555-6.00788039455495
77306313.727655202529-7.72765520252904
78301303.872604393695-2.87260439369464
79316308.1660433893547.83395661064583
80327325.660335022471.33966497752999
81330333.338934680628-3.3389346806278
82342344.229696292912-2.22969629291248
83359342.09736201100616.9026379889937
84379352.64876999809826.3512300019017

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 68 & 60.8894939474317 & 7.11050605256828 \tabularnewline
14 & 68 & 65.0554988755908 & 2.94450112440924 \tabularnewline
15 & 68 & 66.3766356669976 & 1.62336433300239 \tabularnewline
16 & 70 & 68.8656190023198 & 1.13438099768018 \tabularnewline
17 & 66 & 65.2390459646497 & 0.760954035350323 \tabularnewline
18 & 64 & 63.3667605996604 & 0.633239400339569 \tabularnewline
19 & 72 & 70.4001596232681 & 1.59984037673190 \tabularnewline
20 & 80 & 74.813101273716 & 5.18689872628394 \tabularnewline
21 & 84 & 80.0177119466845 & 3.98228805331553 \tabularnewline
22 & 82 & 82.8146920752238 & -0.814692075223775 \tabularnewline
23 & 83 & 84.0966887782759 & -1.09668877827586 \tabularnewline
24 & 86 & 86.8359440422374 & -0.835944042237401 \tabularnewline
25 & 99 & 103.758392118631 & -4.75839211863149 \tabularnewline
26 & 100 & 97.7682996330489 & 2.23170036695112 \tabularnewline
27 & 95 & 97.0994417215807 & -2.09944172158070 \tabularnewline
28 & 98 & 97.1160925732098 & 0.883907426790188 \tabularnewline
29 & 103 & 90.8903545157938 & 12.1096454842062 \tabularnewline
30 & 107 & 94.101577661263 & 12.8984223387371 \tabularnewline
31 & 114 & 112.502789900096 & 1.49721009990445 \tabularnewline
32 & 123 & 120.432428151575 & 2.56757184842461 \tabularnewline
33 & 132 & 123.969817831235 & 8.03018216876497 \tabularnewline
34 & 137 & 126.176841628697 & 10.8231583713033 \tabularnewline
35 & 141 & 134.946064513951 & 6.05393548604906 \tabularnewline
36 & 146 & 144.069141279386 & 1.93085872061408 \tabularnewline
37 & 156 & 171.700550261588 & -15.7005502615883 \tabularnewline
38 & 156 & 161.174781575277 & -5.17478157527711 \tabularnewline
39 & 143 & 151.933368234723 & -8.93336823472342 \tabularnewline
40 & 143 & 149.907629134552 & -6.90762913455166 \tabularnewline
41 & 151 & 141.166670574967 & 9.83332942503304 \tabularnewline
42 & 149 & 140.735986079894 & 8.26401392010578 \tabularnewline
43 & 156 & 153.817844624233 & 2.18215537576663 \tabularnewline
44 & 166 & 164.675890376672 & 1.32410962332764 \tabularnewline
45 & 177 & 170.246478129247 & 6.75352187075276 \tabularnewline
46 & 180 & 171.439739540861 & 8.56026045913947 \tabularnewline
47 & 189 & 176.531217455624 & 12.4687825443758 \tabularnewline
48 & 195 & 188.553248909140 & 6.4467510908604 \tabularnewline
49 & 205 & 217.427781000438 & -12.4277810004377 \tabularnewline
50 & 209 & 213.276833343379 & -4.27683334337857 \tabularnewline
51 & 199 & 199.880640003582 & -0.880640003581846 \tabularnewline
52 & 191 & 204.567872881927 & -13.5678728819266 \tabularnewline
53 & 198 & 198.317350814738 & -0.317350814737949 \tabularnewline
54 & 200 & 188.495120403672 & 11.5048795963284 \tabularnewline
55 & 208 & 202.556945788086 & 5.44305421191393 \tabularnewline
56 & 224 & 217.536668344449 & 6.46333165555052 \tabularnewline
57 & 234 & 230.040878680019 & 3.95912131998134 \tabularnewline
58 & 243 & 229.039411510445 & 13.9605884895547 \tabularnewline
59 & 249 & 238.663009370572 & 10.3369906294276 \tabularnewline
60 & 258 & 247.308598983107 & 10.6914010168932 \tabularnewline
61 & 274 & 276.252714267061 & -2.25271426706104 \tabularnewline
62 & 270 & 283.068945235288 & -13.0689452352884 \tabularnewline
63 & 261 & 262.352714727390 & -1.35271472738958 \tabularnewline
64 & 258 & 261.422039730643 & -3.42203973064284 \tabularnewline
65 & 261 & 268.490490350596 & -7.49049035059602 \tabularnewline
66 & 258 & 256.724047543222 & 1.27595245677782 \tabularnewline
67 & 264 & 263.363442298844 & 0.636557701156278 \tabularnewline
68 & 270 & 278.593349651185 & -8.5933496511854 \tabularnewline
69 & 267 & 282.218345610810 & -15.2183456108104 \tabularnewline
70 & 287 & 272.636776443892 & 14.3632235561081 \tabularnewline
71 & 297 & 280.161643506827 & 16.8383564931733 \tabularnewline
72 & 306 & 292.357644027308 & 13.6423559726915 \tabularnewline
73 & 322 & 320.262741798415 & 1.73725820158489 \tabularnewline
74 & 323 & 325.1333943394 & -2.13339433939996 \tabularnewline
75 & 309 & 313.14001495548 & -4.14001495548018 \tabularnewline
76 & 303 & 309.007880394555 & -6.00788039455495 \tabularnewline
77 & 306 & 313.727655202529 & -7.72765520252904 \tabularnewline
78 & 301 & 303.872604393695 & -2.87260439369464 \tabularnewline
79 & 316 & 308.166043389354 & 7.83395661064583 \tabularnewline
80 & 327 & 325.66033502247 & 1.33966497752999 \tabularnewline
81 & 330 & 333.338934680628 & -3.3389346806278 \tabularnewline
82 & 342 & 344.229696292912 & -2.22969629291248 \tabularnewline
83 & 359 & 342.097362011006 & 16.9026379889937 \tabularnewline
84 & 379 & 352.648769998098 & 26.3512300019017 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77920&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]68[/C][C]60.8894939474317[/C][C]7.11050605256828[/C][/ROW]
[ROW][C]14[/C][C]68[/C][C]65.0554988755908[/C][C]2.94450112440924[/C][/ROW]
[ROW][C]15[/C][C]68[/C][C]66.3766356669976[/C][C]1.62336433300239[/C][/ROW]
[ROW][C]16[/C][C]70[/C][C]68.8656190023198[/C][C]1.13438099768018[/C][/ROW]
[ROW][C]17[/C][C]66[/C][C]65.2390459646497[/C][C]0.760954035350323[/C][/ROW]
[ROW][C]18[/C][C]64[/C][C]63.3667605996604[/C][C]0.633239400339569[/C][/ROW]
[ROW][C]19[/C][C]72[/C][C]70.4001596232681[/C][C]1.59984037673190[/C][/ROW]
[ROW][C]20[/C][C]80[/C][C]74.813101273716[/C][C]5.18689872628394[/C][/ROW]
[ROW][C]21[/C][C]84[/C][C]80.0177119466845[/C][C]3.98228805331553[/C][/ROW]
[ROW][C]22[/C][C]82[/C][C]82.8146920752238[/C][C]-0.814692075223775[/C][/ROW]
[ROW][C]23[/C][C]83[/C][C]84.0966887782759[/C][C]-1.09668877827586[/C][/ROW]
[ROW][C]24[/C][C]86[/C][C]86.8359440422374[/C][C]-0.835944042237401[/C][/ROW]
[ROW][C]25[/C][C]99[/C][C]103.758392118631[/C][C]-4.75839211863149[/C][/ROW]
[ROW][C]26[/C][C]100[/C][C]97.7682996330489[/C][C]2.23170036695112[/C][/ROW]
[ROW][C]27[/C][C]95[/C][C]97.0994417215807[/C][C]-2.09944172158070[/C][/ROW]
[ROW][C]28[/C][C]98[/C][C]97.1160925732098[/C][C]0.883907426790188[/C][/ROW]
[ROW][C]29[/C][C]103[/C][C]90.8903545157938[/C][C]12.1096454842062[/C][/ROW]
[ROW][C]30[/C][C]107[/C][C]94.101577661263[/C][C]12.8984223387371[/C][/ROW]
[ROW][C]31[/C][C]114[/C][C]112.502789900096[/C][C]1.49721009990445[/C][/ROW]
[ROW][C]32[/C][C]123[/C][C]120.432428151575[/C][C]2.56757184842461[/C][/ROW]
[ROW][C]33[/C][C]132[/C][C]123.969817831235[/C][C]8.03018216876497[/C][/ROW]
[ROW][C]34[/C][C]137[/C][C]126.176841628697[/C][C]10.8231583713033[/C][/ROW]
[ROW][C]35[/C][C]141[/C][C]134.946064513951[/C][C]6.05393548604906[/C][/ROW]
[ROW][C]36[/C][C]146[/C][C]144.069141279386[/C][C]1.93085872061408[/C][/ROW]
[ROW][C]37[/C][C]156[/C][C]171.700550261588[/C][C]-15.7005502615883[/C][/ROW]
[ROW][C]38[/C][C]156[/C][C]161.174781575277[/C][C]-5.17478157527711[/C][/ROW]
[ROW][C]39[/C][C]143[/C][C]151.933368234723[/C][C]-8.93336823472342[/C][/ROW]
[ROW][C]40[/C][C]143[/C][C]149.907629134552[/C][C]-6.90762913455166[/C][/ROW]
[ROW][C]41[/C][C]151[/C][C]141.166670574967[/C][C]9.83332942503304[/C][/ROW]
[ROW][C]42[/C][C]149[/C][C]140.735986079894[/C][C]8.26401392010578[/C][/ROW]
[ROW][C]43[/C][C]156[/C][C]153.817844624233[/C][C]2.18215537576663[/C][/ROW]
[ROW][C]44[/C][C]166[/C][C]164.675890376672[/C][C]1.32410962332764[/C][/ROW]
[ROW][C]45[/C][C]177[/C][C]170.246478129247[/C][C]6.75352187075276[/C][/ROW]
[ROW][C]46[/C][C]180[/C][C]171.439739540861[/C][C]8.56026045913947[/C][/ROW]
[ROW][C]47[/C][C]189[/C][C]176.531217455624[/C][C]12.4687825443758[/C][/ROW]
[ROW][C]48[/C][C]195[/C][C]188.553248909140[/C][C]6.4467510908604[/C][/ROW]
[ROW][C]49[/C][C]205[/C][C]217.427781000438[/C][C]-12.4277810004377[/C][/ROW]
[ROW][C]50[/C][C]209[/C][C]213.276833343379[/C][C]-4.27683334337857[/C][/ROW]
[ROW][C]51[/C][C]199[/C][C]199.880640003582[/C][C]-0.880640003581846[/C][/ROW]
[ROW][C]52[/C][C]191[/C][C]204.567872881927[/C][C]-13.5678728819266[/C][/ROW]
[ROW][C]53[/C][C]198[/C][C]198.317350814738[/C][C]-0.317350814737949[/C][/ROW]
[ROW][C]54[/C][C]200[/C][C]188.495120403672[/C][C]11.5048795963284[/C][/ROW]
[ROW][C]55[/C][C]208[/C][C]202.556945788086[/C][C]5.44305421191393[/C][/ROW]
[ROW][C]56[/C][C]224[/C][C]217.536668344449[/C][C]6.46333165555052[/C][/ROW]
[ROW][C]57[/C][C]234[/C][C]230.040878680019[/C][C]3.95912131998134[/C][/ROW]
[ROW][C]58[/C][C]243[/C][C]229.039411510445[/C][C]13.9605884895547[/C][/ROW]
[ROW][C]59[/C][C]249[/C][C]238.663009370572[/C][C]10.3369906294276[/C][/ROW]
[ROW][C]60[/C][C]258[/C][C]247.308598983107[/C][C]10.6914010168932[/C][/ROW]
[ROW][C]61[/C][C]274[/C][C]276.252714267061[/C][C]-2.25271426706104[/C][/ROW]
[ROW][C]62[/C][C]270[/C][C]283.068945235288[/C][C]-13.0689452352884[/C][/ROW]
[ROW][C]63[/C][C]261[/C][C]262.352714727390[/C][C]-1.35271472738958[/C][/ROW]
[ROW][C]64[/C][C]258[/C][C]261.422039730643[/C][C]-3.42203973064284[/C][/ROW]
[ROW][C]65[/C][C]261[/C][C]268.490490350596[/C][C]-7.49049035059602[/C][/ROW]
[ROW][C]66[/C][C]258[/C][C]256.724047543222[/C][C]1.27595245677782[/C][/ROW]
[ROW][C]67[/C][C]264[/C][C]263.363442298844[/C][C]0.636557701156278[/C][/ROW]
[ROW][C]68[/C][C]270[/C][C]278.593349651185[/C][C]-8.5933496511854[/C][/ROW]
[ROW][C]69[/C][C]267[/C][C]282.218345610810[/C][C]-15.2183456108104[/C][/ROW]
[ROW][C]70[/C][C]287[/C][C]272.636776443892[/C][C]14.3632235561081[/C][/ROW]
[ROW][C]71[/C][C]297[/C][C]280.161643506827[/C][C]16.8383564931733[/C][/ROW]
[ROW][C]72[/C][C]306[/C][C]292.357644027308[/C][C]13.6423559726915[/C][/ROW]
[ROW][C]73[/C][C]322[/C][C]320.262741798415[/C][C]1.73725820158489[/C][/ROW]
[ROW][C]74[/C][C]323[/C][C]325.1333943394[/C][C]-2.13339433939996[/C][/ROW]
[ROW][C]75[/C][C]309[/C][C]313.14001495548[/C][C]-4.14001495548018[/C][/ROW]
[ROW][C]76[/C][C]303[/C][C]309.007880394555[/C][C]-6.00788039455495[/C][/ROW]
[ROW][C]77[/C][C]306[/C][C]313.727655202529[/C][C]-7.72765520252904[/C][/ROW]
[ROW][C]78[/C][C]301[/C][C]303.872604393695[/C][C]-2.87260439369464[/C][/ROW]
[ROW][C]79[/C][C]316[/C][C]308.166043389354[/C][C]7.83395661064583[/C][/ROW]
[ROW][C]80[/C][C]327[/C][C]325.66033502247[/C][C]1.33966497752999[/C][/ROW]
[ROW][C]81[/C][C]330[/C][C]333.338934680628[/C][C]-3.3389346806278[/C][/ROW]
[ROW][C]82[/C][C]342[/C][C]344.229696292912[/C][C]-2.22969629291248[/C][/ROW]
[ROW][C]83[/C][C]359[/C][C]342.097362011006[/C][C]16.9026379889937[/C][/ROW]
[ROW][C]84[/C][C]379[/C][C]352.648769998098[/C][C]26.3512300019017[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77920&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77920&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
136860.88949394743177.11050605256828
146865.05549887559082.94450112440924
156866.37663566699761.62336433300239
167068.86561900231981.13438099768018
176665.23904596464970.760954035350323
186463.36676059966040.633239400339569
197270.40015962326811.59984037673190
208074.8131012737165.18689872628394
218480.01771194668453.98228805331553
228282.8146920752238-0.814692075223775
238384.0966887782759-1.09668877827586
248686.8359440422374-0.835944042237401
2599103.758392118631-4.75839211863149
2610097.76829963304892.23170036695112
279597.0994417215807-2.09944172158070
289897.11609257320980.883907426790188
2910390.890354515793812.1096454842062
3010794.10157766126312.8984223387371
31114112.5027899000961.49721009990445
32123120.4324281515752.56757184842461
33132123.9698178312358.03018216876497
34137126.17684162869710.8231583713033
35141134.9460645139516.05393548604906
36146144.0691412793861.93085872061408
37156171.700550261588-15.7005502615883
38156161.174781575277-5.17478157527711
39143151.933368234723-8.93336823472342
40143149.907629134552-6.90762913455166
41151141.1666705749679.83332942503304
42149140.7359860798948.26401392010578
43156153.8178446242332.18215537576663
44166164.6758903766721.32410962332764
45177170.2464781292476.75352187075276
46180171.4397395408618.56026045913947
47189176.53121745562412.4687825443758
48195188.5532489091406.4467510908604
49205217.427781000438-12.4277810004377
50209213.276833343379-4.27683334337857
51199199.880640003582-0.880640003581846
52191204.567872881927-13.5678728819266
53198198.317350814738-0.317350814737949
54200188.49512040367211.5048795963284
55208202.5569457880865.44305421191393
56224217.5366683444496.46333165555052
57234230.0408786800193.95912131998134
58243229.03941151044513.9605884895547
59249238.66300937057210.3369906294276
60258247.30859898310710.6914010168932
61274276.252714267061-2.25271426706104
62270283.068945235288-13.0689452352884
63261262.352714727390-1.35271472738958
64258261.422039730643-3.42203973064284
65261268.490490350596-7.49049035059602
66258256.7240475432221.27595245677782
67264263.3634422988440.636557701156278
68270278.593349651185-8.5933496511854
69267282.218345610810-15.2183456108104
70287272.63677644389214.3632235561081
71297280.16164350682716.8383564931733
72306292.35764402730813.6423559726915
73322320.2627417984151.73725820158489
74323325.1333943394-2.13339433939996
75309313.14001495548-4.14001495548018
76303309.007880394555-6.00788039455495
77306313.727655202529-7.72765520252904
78301303.872604393695-2.87260439369464
79316308.1660433893547.83395661064583
80327325.660335022471.33966497752999
81330333.338934680628-3.3389346806278
82342344.229696292912-2.22969629291248
83359342.09736201100616.9026379889937
84379352.64876999809826.3512300019017







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85386.329402892636370.782252790757401.876552994515
86388.768981491809370.430228513682407.107734469936
87374.587468006574354.1033094465395.071626566647
88371.396187099717348.703553699606394.088820499829
89380.513364866514355.271503287684405.755226445344
90376.197351854313349.113589100998403.281114607627
91388.708029511585358.955777148597418.460281874572
92401.309581687412368.888120753673433.731042621151
93407.391412059784372.739049688733442.043774430835
94423.681805832528386.064980205328461.298631459728
95431.394258390896391.453971874856471.334544906935
96435.463717291297396.313699677362474.613734905232

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 386.329402892636 & 370.782252790757 & 401.876552994515 \tabularnewline
86 & 388.768981491809 & 370.430228513682 & 407.107734469936 \tabularnewline
87 & 374.587468006574 & 354.1033094465 & 395.071626566647 \tabularnewline
88 & 371.396187099717 & 348.703553699606 & 394.088820499829 \tabularnewline
89 & 380.513364866514 & 355.271503287684 & 405.755226445344 \tabularnewline
90 & 376.197351854313 & 349.113589100998 & 403.281114607627 \tabularnewline
91 & 388.708029511585 & 358.955777148597 & 418.460281874572 \tabularnewline
92 & 401.309581687412 & 368.888120753673 & 433.731042621151 \tabularnewline
93 & 407.391412059784 & 372.739049688733 & 442.043774430835 \tabularnewline
94 & 423.681805832528 & 386.064980205328 & 461.298631459728 \tabularnewline
95 & 431.394258390896 & 391.453971874856 & 471.334544906935 \tabularnewline
96 & 435.463717291297 & 396.313699677362 & 474.613734905232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77920&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]386.329402892636[/C][C]370.782252790757[/C][C]401.876552994515[/C][/ROW]
[ROW][C]86[/C][C]388.768981491809[/C][C]370.430228513682[/C][C]407.107734469936[/C][/ROW]
[ROW][C]87[/C][C]374.587468006574[/C][C]354.1033094465[/C][C]395.071626566647[/C][/ROW]
[ROW][C]88[/C][C]371.396187099717[/C][C]348.703553699606[/C][C]394.088820499829[/C][/ROW]
[ROW][C]89[/C][C]380.513364866514[/C][C]355.271503287684[/C][C]405.755226445344[/C][/ROW]
[ROW][C]90[/C][C]376.197351854313[/C][C]349.113589100998[/C][C]403.281114607627[/C][/ROW]
[ROW][C]91[/C][C]388.708029511585[/C][C]358.955777148597[/C][C]418.460281874572[/C][/ROW]
[ROW][C]92[/C][C]401.309581687412[/C][C]368.888120753673[/C][C]433.731042621151[/C][/ROW]
[ROW][C]93[/C][C]407.391412059784[/C][C]372.739049688733[/C][C]442.043774430835[/C][/ROW]
[ROW][C]94[/C][C]423.681805832528[/C][C]386.064980205328[/C][C]461.298631459728[/C][/ROW]
[ROW][C]95[/C][C]431.394258390896[/C][C]391.453971874856[/C][C]471.334544906935[/C][/ROW]
[ROW][C]96[/C][C]435.463717291297[/C][C]396.313699677362[/C][C]474.613734905232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77920&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77920&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
85386.329402892636370.782252790757401.876552994515
86388.768981491809370.430228513682407.107734469936
87374.587468006574354.1033094465395.071626566647
88371.396187099717348.703553699606394.088820499829
89380.513364866514355.271503287684405.755226445344
90376.197351854313349.113589100998403.281114607627
91388.708029511585358.955777148597418.460281874572
92401.309581687412368.888120753673433.731042621151
93407.391412059784372.739049688733442.043774430835
94423.681805832528386.064980205328461.298631459728
95431.394258390896391.453971874856471.334544906935
96435.463717291297396.313699677362474.613734905232



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