Free Statistics

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 17:01:56 +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/2014/Nov/28/t1417194136szw7gq98y2ipe3m.htm/, Retrieved Sun, 19 May 2024 13:54:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260978, Retrieved Sun, 19 May 2024 13:54:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 11 (2)] [2014-11-28 17:01:56] [76c30f62b7052b57088120e90a652e05] [Current]
Feedback Forum

Post a new message
Dataseries X:
219
231
247
259
278
289
252
224
242
303
305
283
259
224
252
273
252
265
285
224
283
279
296
269
252
226
259
301
260
282
311
263
276
296
310
290
273
267
302
322
314
300
316
299
295
340
333
316
294
309
354
335
313
338
357
324
296
378
343
301
309
271
308
326
336
310
335
298
288
319
328
315




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260978&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260978&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260978&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.271708073363645
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.271708073363645 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260978&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]0.271708073363645[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260978&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260978&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
alpha0.271708073363645
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
223121912
3247222.26049688036424.7395031196363
4259228.98241960897430.017580391026
5278237.13843854405840.8615614559419
6289248.24085468188240.7591453181178
7252259.315443528217-7.31544352821686
8224257.327778461365-33.3277784613645
9242248.272351986137-6.27235198613678
10303246.56810331252556.4318966874751
11305261.90110523773543.0988947622649
12283273.6114228976939.38857710230741
13259276.162375093787-17.1623750937866
14224271.49921922271-47.4992192227096
15252258.59329788143-6.59329788142975
16273256.80184561695416.1981543830461
17252261.203014936418-9.20301493641824
18265258.7024814789076.2975185210928
19285260.41356810324524.5864318967548
20224267.093900144799-43.093900144799
21283255.3849395627327.6150604372697
22279262.88817442996216.1118255700385
23296267.26588751396828.7341124860322
24269275.073177857362-6.07317785736188
25252273.423046402543-21.4230464025433
26226267.602231738928-41.6022317389283
27259256.2985695055162.70143049448382
28301257.03256998049843.9674300195018
29260268.978875681848-8.97887568184797
30282266.53924266936115.4607573306386
31311270.74005525641240.2599447435879
32263281.679007276419-18.6790072764192
33276276.603770196998-0.603770196997857
34296276.43972096001719.5602790399828
35310281.75440669242628.2455933075738
36290289.428962431040.57103756895981
37273289.584117948721-16.5841179487205
38267285.078079212438-18.0780792124382
39302280.16611913951121.8338808604887
40322286.09856084216635.9014391578339
41314295.85327170672318.1467282932767
42300300.783884289143-0.783884289143089
43316300.570896599215.4291034008
44299304.76310855796-5.76310855795987
45295303.197225435091-8.19722543509107
46340300.96997310519539.030026894805
47333311.57474651611421.4252534838863
48316317.396160861548-1.39616086154825
49294317.016812683751-23.0168126837513
50309310.762958854477-1.76295885447735
51354310.28394870070843.7160512992921
52335322.16195277430512.8380472256951
53313325.65015385175-12.65015385175
54338322.21300492093715.7869950790626
55357326.50245893807130.4975410619292
56324334.788887062336-10.7888870623363
57296331.857459344891-35.857459344891
58378322.11469815057555.8853018494246
59343337.2991858454285.70081415457162
60301338.848143075971-37.8481430759713
61309328.564497040408-19.5644970404076
62271323.24866524323-52.2486652432297
63308309.05228107417-1.05228107416974
64326308.7663678108717.2336321891299
65336313.44888481003622.5511151899638
66310319.576204870503-9.57620487050292
67335316.97427269500318.025727304997
68298321.872008332022-23.8720083320222
69288315.385790940808-27.3857909408076
70319307.94485044674111.0551495532587
71328310.94862383260417.0513761673958
72315315.581620399246-0.581620399246106

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 231 & 219 & 12 \tabularnewline
3 & 247 & 222.260496880364 & 24.7395031196363 \tabularnewline
4 & 259 & 228.982419608974 & 30.017580391026 \tabularnewline
5 & 278 & 237.138438544058 & 40.8615614559419 \tabularnewline
6 & 289 & 248.240854681882 & 40.7591453181178 \tabularnewline
7 & 252 & 259.315443528217 & -7.31544352821686 \tabularnewline
8 & 224 & 257.327778461365 & -33.3277784613645 \tabularnewline
9 & 242 & 248.272351986137 & -6.27235198613678 \tabularnewline
10 & 303 & 246.568103312525 & 56.4318966874751 \tabularnewline
11 & 305 & 261.901105237735 & 43.0988947622649 \tabularnewline
12 & 283 & 273.611422897693 & 9.38857710230741 \tabularnewline
13 & 259 & 276.162375093787 & -17.1623750937866 \tabularnewline
14 & 224 & 271.49921922271 & -47.4992192227096 \tabularnewline
15 & 252 & 258.59329788143 & -6.59329788142975 \tabularnewline
16 & 273 & 256.801845616954 & 16.1981543830461 \tabularnewline
17 & 252 & 261.203014936418 & -9.20301493641824 \tabularnewline
18 & 265 & 258.702481478907 & 6.2975185210928 \tabularnewline
19 & 285 & 260.413568103245 & 24.5864318967548 \tabularnewline
20 & 224 & 267.093900144799 & -43.093900144799 \tabularnewline
21 & 283 & 255.38493956273 & 27.6150604372697 \tabularnewline
22 & 279 & 262.888174429962 & 16.1118255700385 \tabularnewline
23 & 296 & 267.265887513968 & 28.7341124860322 \tabularnewline
24 & 269 & 275.073177857362 & -6.07317785736188 \tabularnewline
25 & 252 & 273.423046402543 & -21.4230464025433 \tabularnewline
26 & 226 & 267.602231738928 & -41.6022317389283 \tabularnewline
27 & 259 & 256.298569505516 & 2.70143049448382 \tabularnewline
28 & 301 & 257.032569980498 & 43.9674300195018 \tabularnewline
29 & 260 & 268.978875681848 & -8.97887568184797 \tabularnewline
30 & 282 & 266.539242669361 & 15.4607573306386 \tabularnewline
31 & 311 & 270.740055256412 & 40.2599447435879 \tabularnewline
32 & 263 & 281.679007276419 & -18.6790072764192 \tabularnewline
33 & 276 & 276.603770196998 & -0.603770196997857 \tabularnewline
34 & 296 & 276.439720960017 & 19.5602790399828 \tabularnewline
35 & 310 & 281.754406692426 & 28.2455933075738 \tabularnewline
36 & 290 & 289.42896243104 & 0.57103756895981 \tabularnewline
37 & 273 & 289.584117948721 & -16.5841179487205 \tabularnewline
38 & 267 & 285.078079212438 & -18.0780792124382 \tabularnewline
39 & 302 & 280.166119139511 & 21.8338808604887 \tabularnewline
40 & 322 & 286.098560842166 & 35.9014391578339 \tabularnewline
41 & 314 & 295.853271706723 & 18.1467282932767 \tabularnewline
42 & 300 & 300.783884289143 & -0.783884289143089 \tabularnewline
43 & 316 & 300.5708965992 & 15.4291034008 \tabularnewline
44 & 299 & 304.76310855796 & -5.76310855795987 \tabularnewline
45 & 295 & 303.197225435091 & -8.19722543509107 \tabularnewline
46 & 340 & 300.969973105195 & 39.030026894805 \tabularnewline
47 & 333 & 311.574746516114 & 21.4252534838863 \tabularnewline
48 & 316 & 317.396160861548 & -1.39616086154825 \tabularnewline
49 & 294 & 317.016812683751 & -23.0168126837513 \tabularnewline
50 & 309 & 310.762958854477 & -1.76295885447735 \tabularnewline
51 & 354 & 310.283948700708 & 43.7160512992921 \tabularnewline
52 & 335 & 322.161952774305 & 12.8380472256951 \tabularnewline
53 & 313 & 325.65015385175 & -12.65015385175 \tabularnewline
54 & 338 & 322.213004920937 & 15.7869950790626 \tabularnewline
55 & 357 & 326.502458938071 & 30.4975410619292 \tabularnewline
56 & 324 & 334.788887062336 & -10.7888870623363 \tabularnewline
57 & 296 & 331.857459344891 & -35.857459344891 \tabularnewline
58 & 378 & 322.114698150575 & 55.8853018494246 \tabularnewline
59 & 343 & 337.299185845428 & 5.70081415457162 \tabularnewline
60 & 301 & 338.848143075971 & -37.8481430759713 \tabularnewline
61 & 309 & 328.564497040408 & -19.5644970404076 \tabularnewline
62 & 271 & 323.24866524323 & -52.2486652432297 \tabularnewline
63 & 308 & 309.05228107417 & -1.05228107416974 \tabularnewline
64 & 326 & 308.76636781087 & 17.2336321891299 \tabularnewline
65 & 336 & 313.448884810036 & 22.5511151899638 \tabularnewline
66 & 310 & 319.576204870503 & -9.57620487050292 \tabularnewline
67 & 335 & 316.974272695003 & 18.025727304997 \tabularnewline
68 & 298 & 321.872008332022 & -23.8720083320222 \tabularnewline
69 & 288 & 315.385790940808 & -27.3857909408076 \tabularnewline
70 & 319 & 307.944850446741 & 11.0551495532587 \tabularnewline
71 & 328 & 310.948623832604 & 17.0513761673958 \tabularnewline
72 & 315 & 315.581620399246 & -0.581620399246106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260978&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]2[/C][C]231[/C][C]219[/C][C]12[/C][/ROW]
[ROW][C]3[/C][C]247[/C][C]222.260496880364[/C][C]24.7395031196363[/C][/ROW]
[ROW][C]4[/C][C]259[/C][C]228.982419608974[/C][C]30.017580391026[/C][/ROW]
[ROW][C]5[/C][C]278[/C][C]237.138438544058[/C][C]40.8615614559419[/C][/ROW]
[ROW][C]6[/C][C]289[/C][C]248.240854681882[/C][C]40.7591453181178[/C][/ROW]
[ROW][C]7[/C][C]252[/C][C]259.315443528217[/C][C]-7.31544352821686[/C][/ROW]
[ROW][C]8[/C][C]224[/C][C]257.327778461365[/C][C]-33.3277784613645[/C][/ROW]
[ROW][C]9[/C][C]242[/C][C]248.272351986137[/C][C]-6.27235198613678[/C][/ROW]
[ROW][C]10[/C][C]303[/C][C]246.568103312525[/C][C]56.4318966874751[/C][/ROW]
[ROW][C]11[/C][C]305[/C][C]261.901105237735[/C][C]43.0988947622649[/C][/ROW]
[ROW][C]12[/C][C]283[/C][C]273.611422897693[/C][C]9.38857710230741[/C][/ROW]
[ROW][C]13[/C][C]259[/C][C]276.162375093787[/C][C]-17.1623750937866[/C][/ROW]
[ROW][C]14[/C][C]224[/C][C]271.49921922271[/C][C]-47.4992192227096[/C][/ROW]
[ROW][C]15[/C][C]252[/C][C]258.59329788143[/C][C]-6.59329788142975[/C][/ROW]
[ROW][C]16[/C][C]273[/C][C]256.801845616954[/C][C]16.1981543830461[/C][/ROW]
[ROW][C]17[/C][C]252[/C][C]261.203014936418[/C][C]-9.20301493641824[/C][/ROW]
[ROW][C]18[/C][C]265[/C][C]258.702481478907[/C][C]6.2975185210928[/C][/ROW]
[ROW][C]19[/C][C]285[/C][C]260.413568103245[/C][C]24.5864318967548[/C][/ROW]
[ROW][C]20[/C][C]224[/C][C]267.093900144799[/C][C]-43.093900144799[/C][/ROW]
[ROW][C]21[/C][C]283[/C][C]255.38493956273[/C][C]27.6150604372697[/C][/ROW]
[ROW][C]22[/C][C]279[/C][C]262.888174429962[/C][C]16.1118255700385[/C][/ROW]
[ROW][C]23[/C][C]296[/C][C]267.265887513968[/C][C]28.7341124860322[/C][/ROW]
[ROW][C]24[/C][C]269[/C][C]275.073177857362[/C][C]-6.07317785736188[/C][/ROW]
[ROW][C]25[/C][C]252[/C][C]273.423046402543[/C][C]-21.4230464025433[/C][/ROW]
[ROW][C]26[/C][C]226[/C][C]267.602231738928[/C][C]-41.6022317389283[/C][/ROW]
[ROW][C]27[/C][C]259[/C][C]256.298569505516[/C][C]2.70143049448382[/C][/ROW]
[ROW][C]28[/C][C]301[/C][C]257.032569980498[/C][C]43.9674300195018[/C][/ROW]
[ROW][C]29[/C][C]260[/C][C]268.978875681848[/C][C]-8.97887568184797[/C][/ROW]
[ROW][C]30[/C][C]282[/C][C]266.539242669361[/C][C]15.4607573306386[/C][/ROW]
[ROW][C]31[/C][C]311[/C][C]270.740055256412[/C][C]40.2599447435879[/C][/ROW]
[ROW][C]32[/C][C]263[/C][C]281.679007276419[/C][C]-18.6790072764192[/C][/ROW]
[ROW][C]33[/C][C]276[/C][C]276.603770196998[/C][C]-0.603770196997857[/C][/ROW]
[ROW][C]34[/C][C]296[/C][C]276.439720960017[/C][C]19.5602790399828[/C][/ROW]
[ROW][C]35[/C][C]310[/C][C]281.754406692426[/C][C]28.2455933075738[/C][/ROW]
[ROW][C]36[/C][C]290[/C][C]289.42896243104[/C][C]0.57103756895981[/C][/ROW]
[ROW][C]37[/C][C]273[/C][C]289.584117948721[/C][C]-16.5841179487205[/C][/ROW]
[ROW][C]38[/C][C]267[/C][C]285.078079212438[/C][C]-18.0780792124382[/C][/ROW]
[ROW][C]39[/C][C]302[/C][C]280.166119139511[/C][C]21.8338808604887[/C][/ROW]
[ROW][C]40[/C][C]322[/C][C]286.098560842166[/C][C]35.9014391578339[/C][/ROW]
[ROW][C]41[/C][C]314[/C][C]295.853271706723[/C][C]18.1467282932767[/C][/ROW]
[ROW][C]42[/C][C]300[/C][C]300.783884289143[/C][C]-0.783884289143089[/C][/ROW]
[ROW][C]43[/C][C]316[/C][C]300.5708965992[/C][C]15.4291034008[/C][/ROW]
[ROW][C]44[/C][C]299[/C][C]304.76310855796[/C][C]-5.76310855795987[/C][/ROW]
[ROW][C]45[/C][C]295[/C][C]303.197225435091[/C][C]-8.19722543509107[/C][/ROW]
[ROW][C]46[/C][C]340[/C][C]300.969973105195[/C][C]39.030026894805[/C][/ROW]
[ROW][C]47[/C][C]333[/C][C]311.574746516114[/C][C]21.4252534838863[/C][/ROW]
[ROW][C]48[/C][C]316[/C][C]317.396160861548[/C][C]-1.39616086154825[/C][/ROW]
[ROW][C]49[/C][C]294[/C][C]317.016812683751[/C][C]-23.0168126837513[/C][/ROW]
[ROW][C]50[/C][C]309[/C][C]310.762958854477[/C][C]-1.76295885447735[/C][/ROW]
[ROW][C]51[/C][C]354[/C][C]310.283948700708[/C][C]43.7160512992921[/C][/ROW]
[ROW][C]52[/C][C]335[/C][C]322.161952774305[/C][C]12.8380472256951[/C][/ROW]
[ROW][C]53[/C][C]313[/C][C]325.65015385175[/C][C]-12.65015385175[/C][/ROW]
[ROW][C]54[/C][C]338[/C][C]322.213004920937[/C][C]15.7869950790626[/C][/ROW]
[ROW][C]55[/C][C]357[/C][C]326.502458938071[/C][C]30.4975410619292[/C][/ROW]
[ROW][C]56[/C][C]324[/C][C]334.788887062336[/C][C]-10.7888870623363[/C][/ROW]
[ROW][C]57[/C][C]296[/C][C]331.857459344891[/C][C]-35.857459344891[/C][/ROW]
[ROW][C]58[/C][C]378[/C][C]322.114698150575[/C][C]55.8853018494246[/C][/ROW]
[ROW][C]59[/C][C]343[/C][C]337.299185845428[/C][C]5.70081415457162[/C][/ROW]
[ROW][C]60[/C][C]301[/C][C]338.848143075971[/C][C]-37.8481430759713[/C][/ROW]
[ROW][C]61[/C][C]309[/C][C]328.564497040408[/C][C]-19.5644970404076[/C][/ROW]
[ROW][C]62[/C][C]271[/C][C]323.24866524323[/C][C]-52.2486652432297[/C][/ROW]
[ROW][C]63[/C][C]308[/C][C]309.05228107417[/C][C]-1.05228107416974[/C][/ROW]
[ROW][C]64[/C][C]326[/C][C]308.76636781087[/C][C]17.2336321891299[/C][/ROW]
[ROW][C]65[/C][C]336[/C][C]313.448884810036[/C][C]22.5511151899638[/C][/ROW]
[ROW][C]66[/C][C]310[/C][C]319.576204870503[/C][C]-9.57620487050292[/C][/ROW]
[ROW][C]67[/C][C]335[/C][C]316.974272695003[/C][C]18.025727304997[/C][/ROW]
[ROW][C]68[/C][C]298[/C][C]321.872008332022[/C][C]-23.8720083320222[/C][/ROW]
[ROW][C]69[/C][C]288[/C][C]315.385790940808[/C][C]-27.3857909408076[/C][/ROW]
[ROW][C]70[/C][C]319[/C][C]307.944850446741[/C][C]11.0551495532587[/C][/ROW]
[ROW][C]71[/C][C]328[/C][C]310.948623832604[/C][C]17.0513761673958[/C][/ROW]
[ROW][C]72[/C][C]315[/C][C]315.581620399246[/C][C]-0.581620399246106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260978&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260978&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
223121912
3247222.26049688036424.7395031196363
4259228.98241960897430.017580391026
5278237.13843854405840.8615614559419
6289248.24085468188240.7591453181178
7252259.315443528217-7.31544352821686
8224257.327778461365-33.3277784613645
9242248.272351986137-6.27235198613678
10303246.56810331252556.4318966874751
11305261.90110523773543.0988947622649
12283273.6114228976939.38857710230741
13259276.162375093787-17.1623750937866
14224271.49921922271-47.4992192227096
15252258.59329788143-6.59329788142975
16273256.80184561695416.1981543830461
17252261.203014936418-9.20301493641824
18265258.7024814789076.2975185210928
19285260.41356810324524.5864318967548
20224267.093900144799-43.093900144799
21283255.3849395627327.6150604372697
22279262.88817442996216.1118255700385
23296267.26588751396828.7341124860322
24269275.073177857362-6.07317785736188
25252273.423046402543-21.4230464025433
26226267.602231738928-41.6022317389283
27259256.2985695055162.70143049448382
28301257.03256998049843.9674300195018
29260268.978875681848-8.97887568184797
30282266.53924266936115.4607573306386
31311270.74005525641240.2599447435879
32263281.679007276419-18.6790072764192
33276276.603770196998-0.603770196997857
34296276.43972096001719.5602790399828
35310281.75440669242628.2455933075738
36290289.428962431040.57103756895981
37273289.584117948721-16.5841179487205
38267285.078079212438-18.0780792124382
39302280.16611913951121.8338808604887
40322286.09856084216635.9014391578339
41314295.85327170672318.1467282932767
42300300.783884289143-0.783884289143089
43316300.570896599215.4291034008
44299304.76310855796-5.76310855795987
45295303.197225435091-8.19722543509107
46340300.96997310519539.030026894805
47333311.57474651611421.4252534838863
48316317.396160861548-1.39616086154825
49294317.016812683751-23.0168126837513
50309310.762958854477-1.76295885447735
51354310.28394870070843.7160512992921
52335322.16195277430512.8380472256951
53313325.65015385175-12.65015385175
54338322.21300492093715.7869950790626
55357326.50245893807130.4975410619292
56324334.788887062336-10.7888870623363
57296331.857459344891-35.857459344891
58378322.11469815057555.8853018494246
59343337.2991858454285.70081415457162
60301338.848143075971-37.8481430759713
61309328.564497040408-19.5644970404076
62271323.24866524323-52.2486652432297
63308309.05228107417-1.05228107416974
64326308.7663678108717.2336321891299
65336313.44888481003622.5511151899638
66310319.576204870503-9.57620487050292
67335316.97427269500318.025727304997
68298321.872008332022-23.8720083320222
69288315.385790940808-27.3857909408076
70319307.94485044674111.0551495532587
71328310.94862383260417.0513761673958
72315315.581620399246-0.581620399246106







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73315.423589441138265.452048529511365.395130352765
74315.423589441138263.640309768121367.206869114155
75315.423589441138261.889850487976368.9573283943
76315.423589441138260.194843674855370.65233520742
77315.423589441138258.550331124702372.296847757574
78315.423589441138256.952052227383373.895126654892
79315.423589441138255.396313834537375.450865047739
80315.423589441138253.879889768773376.967289113503
81315.423589441138252.399942117505378.447236764771
82315.423589441138250.953958803255379.893220079021
83315.423589441138249.539703496269381.307475386007
84315.423589441138248.155175012017382.692003870259

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 315.423589441138 & 265.452048529511 & 365.395130352765 \tabularnewline
74 & 315.423589441138 & 263.640309768121 & 367.206869114155 \tabularnewline
75 & 315.423589441138 & 261.889850487976 & 368.9573283943 \tabularnewline
76 & 315.423589441138 & 260.194843674855 & 370.65233520742 \tabularnewline
77 & 315.423589441138 & 258.550331124702 & 372.296847757574 \tabularnewline
78 & 315.423589441138 & 256.952052227383 & 373.895126654892 \tabularnewline
79 & 315.423589441138 & 255.396313834537 & 375.450865047739 \tabularnewline
80 & 315.423589441138 & 253.879889768773 & 376.967289113503 \tabularnewline
81 & 315.423589441138 & 252.399942117505 & 378.447236764771 \tabularnewline
82 & 315.423589441138 & 250.953958803255 & 379.893220079021 \tabularnewline
83 & 315.423589441138 & 249.539703496269 & 381.307475386007 \tabularnewline
84 & 315.423589441138 & 248.155175012017 & 382.692003870259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260978&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]315.423589441138[/C][C]265.452048529511[/C][C]365.395130352765[/C][/ROW]
[ROW][C]74[/C][C]315.423589441138[/C][C]263.640309768121[/C][C]367.206869114155[/C][/ROW]
[ROW][C]75[/C][C]315.423589441138[/C][C]261.889850487976[/C][C]368.9573283943[/C][/ROW]
[ROW][C]76[/C][C]315.423589441138[/C][C]260.194843674855[/C][C]370.65233520742[/C][/ROW]
[ROW][C]77[/C][C]315.423589441138[/C][C]258.550331124702[/C][C]372.296847757574[/C][/ROW]
[ROW][C]78[/C][C]315.423589441138[/C][C]256.952052227383[/C][C]373.895126654892[/C][/ROW]
[ROW][C]79[/C][C]315.423589441138[/C][C]255.396313834537[/C][C]375.450865047739[/C][/ROW]
[ROW][C]80[/C][C]315.423589441138[/C][C]253.879889768773[/C][C]376.967289113503[/C][/ROW]
[ROW][C]81[/C][C]315.423589441138[/C][C]252.399942117505[/C][C]378.447236764771[/C][/ROW]
[ROW][C]82[/C][C]315.423589441138[/C][C]250.953958803255[/C][C]379.893220079021[/C][/ROW]
[ROW][C]83[/C][C]315.423589441138[/C][C]249.539703496269[/C][C]381.307475386007[/C][/ROW]
[ROW][C]84[/C][C]315.423589441138[/C][C]248.155175012017[/C][C]382.692003870259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260978&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260978&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
73315.423589441138265.452048529511365.395130352765
74315.423589441138263.640309768121367.206869114155
75315.423589441138261.889850487976368.9573283943
76315.423589441138260.194843674855370.65233520742
77315.423589441138258.550331124702372.296847757574
78315.423589441138256.952052227383373.895126654892
79315.423589441138255.396313834537375.450865047739
80315.423589441138253.879889768773376.967289113503
81315.423589441138252.399942117505378.447236764771
82315.423589441138250.953958803255379.893220079021
83315.423589441138249.539703496269381.307475386007
84315.423589441138248.155175012017382.692003870259



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