Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 21:01:19 +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/Jun/02/t1275512719nv6bzfqlpcs1z30.htm/, Retrieved Fri, 26 Apr 2024 07:10:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77329, Retrieved Fri, 26 Apr 2024 07:10:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-06-02 21:01:19] [703cc945e3db15433e6894138e0ac090] [Current]
Feedback Forum

Post a new message
Dataseries X:
225
243
270
289
273
274
220
271
288
276
266
239
201
242
239
273
280
294
212
264
272
262
238
227
250
245
270
288
298
281
218
284
281
277
276
222
255
267
261
263
264
278
248
320
305
301
274
220
235
252
272
280
305
299
246
307
325
302
274
251
272
253
292
288
258
295
231
250
268




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77329&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77329&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77329&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.34126575693962
beta0
gamma0.660091540095026

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.34126575693962 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.660091540095026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77329&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]0.34126575693962[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.660091540095026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77329&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77329&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
alpha0.34126575693962
beta0
gamma0.660091540095026







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13201201.63706732081-0.637067320809876
14242242.488883213482-0.488883213482097
15239239.61359667665-0.613596676650189
16273274.115023149593-1.11502314959273
17280281.985390904853-1.98539090485286
18294296.581420610356-2.58142061035574
19212212.790148615504-0.790148615504137
20264262.1658222915841.83417770841567
21272280.002229273858-8.00222927385767
22262267.057972290363-5.05797229036318
23238255.423546961307-17.4235469613072
24227222.5722185024824.42778149751754
25250187.32721121270262.6727887872979
26245251.420246684895-6.4202466848952
27270246.40276364184223.5972363581584
28288291.201448650303-3.20144865030318
29298298.508750191992-0.508750191991851
30281314.351749950383-33.3517499503829
31218218.513780594727-0.513780594726995
32284270.61736009839113.3826399016089
33281288.682131665687-7.68213166568745
34277276.7429617462950.257038253705332
35276260.59365149915615.4063485008438
36222246.770044116115-24.7700441161146
37255223.35098868510931.6490113148906
38267246.68692559233920.3130744076611
39261263.826998694924-2.8269986949245
40263287.769491070318-24.7694910703182
41264288.552323159868-24.5523231598683
42278281.249581308694-3.24958130869396
43248211.97317424998936.0268257500108
44320284.1546730565535.8453269434504
45305300.9693370560634.03066294393693
46301296.1201349374814.8798650625194
47274287.31717017368-13.3171701736804
48220244.475945031834-24.475945031834
49235245.414214163067-10.4142141630666
50252249.0298595453492.97014045465119
51272250.14885813605721.8511418639427
52280272.4044068545537.59559314544714
53305284.24035776522220.7596422347779
54299302.553013704055-3.55301370405482
55246245.2252556490560.774744350943848
56307306.041151631790.958848368209772
57325297.2621720713527.7378279286503
58302300.8160470467771.18395295322267
59274282.668197088828-8.66819708882787
60251235.7616286325315.2383713674699
61272257.39458906686614.6054109331338
62253276.799370819002-23.7993708190017
63292277.3170862861114.6829137138899
64288291.422901204502-3.42290120450195
65258305.667026345426-47.6670263454264
66295290.0005045364844.9994954635165
67231238.92048890566-7.92048890565954
68250294.450211543451-44.4502115434515
69268281.186686679723-13.1866866797228

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 201 & 201.63706732081 & -0.637067320809876 \tabularnewline
14 & 242 & 242.488883213482 & -0.488883213482097 \tabularnewline
15 & 239 & 239.61359667665 & -0.613596676650189 \tabularnewline
16 & 273 & 274.115023149593 & -1.11502314959273 \tabularnewline
17 & 280 & 281.985390904853 & -1.98539090485286 \tabularnewline
18 & 294 & 296.581420610356 & -2.58142061035574 \tabularnewline
19 & 212 & 212.790148615504 & -0.790148615504137 \tabularnewline
20 & 264 & 262.165822291584 & 1.83417770841567 \tabularnewline
21 & 272 & 280.002229273858 & -8.00222927385767 \tabularnewline
22 & 262 & 267.057972290363 & -5.05797229036318 \tabularnewline
23 & 238 & 255.423546961307 & -17.4235469613072 \tabularnewline
24 & 227 & 222.572218502482 & 4.42778149751754 \tabularnewline
25 & 250 & 187.327211212702 & 62.6727887872979 \tabularnewline
26 & 245 & 251.420246684895 & -6.4202466848952 \tabularnewline
27 & 270 & 246.402763641842 & 23.5972363581584 \tabularnewline
28 & 288 & 291.201448650303 & -3.20144865030318 \tabularnewline
29 & 298 & 298.508750191992 & -0.508750191991851 \tabularnewline
30 & 281 & 314.351749950383 & -33.3517499503829 \tabularnewline
31 & 218 & 218.513780594727 & -0.513780594726995 \tabularnewline
32 & 284 & 270.617360098391 & 13.3826399016089 \tabularnewline
33 & 281 & 288.682131665687 & -7.68213166568745 \tabularnewline
34 & 277 & 276.742961746295 & 0.257038253705332 \tabularnewline
35 & 276 & 260.593651499156 & 15.4063485008438 \tabularnewline
36 & 222 & 246.770044116115 & -24.7700441161146 \tabularnewline
37 & 255 & 223.350988685109 & 31.6490113148906 \tabularnewline
38 & 267 & 246.686925592339 & 20.3130744076611 \tabularnewline
39 & 261 & 263.826998694924 & -2.8269986949245 \tabularnewline
40 & 263 & 287.769491070318 & -24.7694910703182 \tabularnewline
41 & 264 & 288.552323159868 & -24.5523231598683 \tabularnewline
42 & 278 & 281.249581308694 & -3.24958130869396 \tabularnewline
43 & 248 & 211.973174249989 & 36.0268257500108 \tabularnewline
44 & 320 & 284.15467305655 & 35.8453269434504 \tabularnewline
45 & 305 & 300.969337056063 & 4.03066294393693 \tabularnewline
46 & 301 & 296.120134937481 & 4.8798650625194 \tabularnewline
47 & 274 & 287.31717017368 & -13.3171701736804 \tabularnewline
48 & 220 & 244.475945031834 & -24.475945031834 \tabularnewline
49 & 235 & 245.414214163067 & -10.4142141630666 \tabularnewline
50 & 252 & 249.029859545349 & 2.97014045465119 \tabularnewline
51 & 272 & 250.148858136057 & 21.8511418639427 \tabularnewline
52 & 280 & 272.404406854553 & 7.59559314544714 \tabularnewline
53 & 305 & 284.240357765222 & 20.7596422347779 \tabularnewline
54 & 299 & 302.553013704055 & -3.55301370405482 \tabularnewline
55 & 246 & 245.225255649056 & 0.774744350943848 \tabularnewline
56 & 307 & 306.04115163179 & 0.958848368209772 \tabularnewline
57 & 325 & 297.26217207135 & 27.7378279286503 \tabularnewline
58 & 302 & 300.816047046777 & 1.18395295322267 \tabularnewline
59 & 274 & 282.668197088828 & -8.66819708882787 \tabularnewline
60 & 251 & 235.76162863253 & 15.2383713674699 \tabularnewline
61 & 272 & 257.394589066866 & 14.6054109331338 \tabularnewline
62 & 253 & 276.799370819002 & -23.7993708190017 \tabularnewline
63 & 292 & 277.31708628611 & 14.6829137138899 \tabularnewline
64 & 288 & 291.422901204502 & -3.42290120450195 \tabularnewline
65 & 258 & 305.667026345426 & -47.6670263454264 \tabularnewline
66 & 295 & 290.000504536484 & 4.9994954635165 \tabularnewline
67 & 231 & 238.92048890566 & -7.92048890565954 \tabularnewline
68 & 250 & 294.450211543451 & -44.4502115434515 \tabularnewline
69 & 268 & 281.186686679723 & -13.1866866797228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77329&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]201[/C][C]201.63706732081[/C][C]-0.637067320809876[/C][/ROW]
[ROW][C]14[/C][C]242[/C][C]242.488883213482[/C][C]-0.488883213482097[/C][/ROW]
[ROW][C]15[/C][C]239[/C][C]239.61359667665[/C][C]-0.613596676650189[/C][/ROW]
[ROW][C]16[/C][C]273[/C][C]274.115023149593[/C][C]-1.11502314959273[/C][/ROW]
[ROW][C]17[/C][C]280[/C][C]281.985390904853[/C][C]-1.98539090485286[/C][/ROW]
[ROW][C]18[/C][C]294[/C][C]296.581420610356[/C][C]-2.58142061035574[/C][/ROW]
[ROW][C]19[/C][C]212[/C][C]212.790148615504[/C][C]-0.790148615504137[/C][/ROW]
[ROW][C]20[/C][C]264[/C][C]262.165822291584[/C][C]1.83417770841567[/C][/ROW]
[ROW][C]21[/C][C]272[/C][C]280.002229273858[/C][C]-8.00222927385767[/C][/ROW]
[ROW][C]22[/C][C]262[/C][C]267.057972290363[/C][C]-5.05797229036318[/C][/ROW]
[ROW][C]23[/C][C]238[/C][C]255.423546961307[/C][C]-17.4235469613072[/C][/ROW]
[ROW][C]24[/C][C]227[/C][C]222.572218502482[/C][C]4.42778149751754[/C][/ROW]
[ROW][C]25[/C][C]250[/C][C]187.327211212702[/C][C]62.6727887872979[/C][/ROW]
[ROW][C]26[/C][C]245[/C][C]251.420246684895[/C][C]-6.4202466848952[/C][/ROW]
[ROW][C]27[/C][C]270[/C][C]246.402763641842[/C][C]23.5972363581584[/C][/ROW]
[ROW][C]28[/C][C]288[/C][C]291.201448650303[/C][C]-3.20144865030318[/C][/ROW]
[ROW][C]29[/C][C]298[/C][C]298.508750191992[/C][C]-0.508750191991851[/C][/ROW]
[ROW][C]30[/C][C]281[/C][C]314.351749950383[/C][C]-33.3517499503829[/C][/ROW]
[ROW][C]31[/C][C]218[/C][C]218.513780594727[/C][C]-0.513780594726995[/C][/ROW]
[ROW][C]32[/C][C]284[/C][C]270.617360098391[/C][C]13.3826399016089[/C][/ROW]
[ROW][C]33[/C][C]281[/C][C]288.682131665687[/C][C]-7.68213166568745[/C][/ROW]
[ROW][C]34[/C][C]277[/C][C]276.742961746295[/C][C]0.257038253705332[/C][/ROW]
[ROW][C]35[/C][C]276[/C][C]260.593651499156[/C][C]15.4063485008438[/C][/ROW]
[ROW][C]36[/C][C]222[/C][C]246.770044116115[/C][C]-24.7700441161146[/C][/ROW]
[ROW][C]37[/C][C]255[/C][C]223.350988685109[/C][C]31.6490113148906[/C][/ROW]
[ROW][C]38[/C][C]267[/C][C]246.686925592339[/C][C]20.3130744076611[/C][/ROW]
[ROW][C]39[/C][C]261[/C][C]263.826998694924[/C][C]-2.8269986949245[/C][/ROW]
[ROW][C]40[/C][C]263[/C][C]287.769491070318[/C][C]-24.7694910703182[/C][/ROW]
[ROW][C]41[/C][C]264[/C][C]288.552323159868[/C][C]-24.5523231598683[/C][/ROW]
[ROW][C]42[/C][C]278[/C][C]281.249581308694[/C][C]-3.24958130869396[/C][/ROW]
[ROW][C]43[/C][C]248[/C][C]211.973174249989[/C][C]36.0268257500108[/C][/ROW]
[ROW][C]44[/C][C]320[/C][C]284.15467305655[/C][C]35.8453269434504[/C][/ROW]
[ROW][C]45[/C][C]305[/C][C]300.969337056063[/C][C]4.03066294393693[/C][/ROW]
[ROW][C]46[/C][C]301[/C][C]296.120134937481[/C][C]4.8798650625194[/C][/ROW]
[ROW][C]47[/C][C]274[/C][C]287.31717017368[/C][C]-13.3171701736804[/C][/ROW]
[ROW][C]48[/C][C]220[/C][C]244.475945031834[/C][C]-24.475945031834[/C][/ROW]
[ROW][C]49[/C][C]235[/C][C]245.414214163067[/C][C]-10.4142141630666[/C][/ROW]
[ROW][C]50[/C][C]252[/C][C]249.029859545349[/C][C]2.97014045465119[/C][/ROW]
[ROW][C]51[/C][C]272[/C][C]250.148858136057[/C][C]21.8511418639427[/C][/ROW]
[ROW][C]52[/C][C]280[/C][C]272.404406854553[/C][C]7.59559314544714[/C][/ROW]
[ROW][C]53[/C][C]305[/C][C]284.240357765222[/C][C]20.7596422347779[/C][/ROW]
[ROW][C]54[/C][C]299[/C][C]302.553013704055[/C][C]-3.55301370405482[/C][/ROW]
[ROW][C]55[/C][C]246[/C][C]245.225255649056[/C][C]0.774744350943848[/C][/ROW]
[ROW][C]56[/C][C]307[/C][C]306.04115163179[/C][C]0.958848368209772[/C][/ROW]
[ROW][C]57[/C][C]325[/C][C]297.26217207135[/C][C]27.7378279286503[/C][/ROW]
[ROW][C]58[/C][C]302[/C][C]300.816047046777[/C][C]1.18395295322267[/C][/ROW]
[ROW][C]59[/C][C]274[/C][C]282.668197088828[/C][C]-8.66819708882787[/C][/ROW]
[ROW][C]60[/C][C]251[/C][C]235.76162863253[/C][C]15.2383713674699[/C][/ROW]
[ROW][C]61[/C][C]272[/C][C]257.394589066866[/C][C]14.6054109331338[/C][/ROW]
[ROW][C]62[/C][C]253[/C][C]276.799370819002[/C][C]-23.7993708190017[/C][/ROW]
[ROW][C]63[/C][C]292[/C][C]277.31708628611[/C][C]14.6829137138899[/C][/ROW]
[ROW][C]64[/C][C]288[/C][C]291.422901204502[/C][C]-3.42290120450195[/C][/ROW]
[ROW][C]65[/C][C]258[/C][C]305.667026345426[/C][C]-47.6670263454264[/C][/ROW]
[ROW][C]66[/C][C]295[/C][C]290.000504536484[/C][C]4.9994954635165[/C][/ROW]
[ROW][C]67[/C][C]231[/C][C]238.92048890566[/C][C]-7.92048890565954[/C][/ROW]
[ROW][C]68[/C][C]250[/C][C]294.450211543451[/C][C]-44.4502115434515[/C][/ROW]
[ROW][C]69[/C][C]268[/C][C]281.186686679723[/C][C]-13.1866866797228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77329&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77329&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
13201201.63706732081-0.637067320809876
14242242.488883213482-0.488883213482097
15239239.61359667665-0.613596676650189
16273274.115023149593-1.11502314959273
17280281.985390904853-1.98539090485286
18294296.581420610356-2.58142061035574
19212212.790148615504-0.790148615504137
20264262.1658222915841.83417770841567
21272280.002229273858-8.00222927385767
22262267.057972290363-5.05797229036318
23238255.423546961307-17.4235469613072
24227222.5722185024824.42778149751754
25250187.32721121270262.6727887872979
26245251.420246684895-6.4202466848952
27270246.40276364184223.5972363581584
28288291.201448650303-3.20144865030318
29298298.508750191992-0.508750191991851
30281314.351749950383-33.3517499503829
31218218.513780594727-0.513780594726995
32284270.61736009839113.3826399016089
33281288.682131665687-7.68213166568745
34277276.7429617462950.257038253705332
35276260.59365149915615.4063485008438
36222246.770044116115-24.7700441161146
37255223.35098868510931.6490113148906
38267246.68692559233920.3130744076611
39261263.826998694924-2.8269986949245
40263287.769491070318-24.7694910703182
41264288.552323159868-24.5523231598683
42278281.249581308694-3.24958130869396
43248211.97317424998936.0268257500108
44320284.1546730565535.8453269434504
45305300.9693370560634.03066294393693
46301296.1201349374814.8798650625194
47274287.31717017368-13.3171701736804
48220244.475945031834-24.475945031834
49235245.414214163067-10.4142141630666
50252249.0298595453492.97014045465119
51272250.14885813605721.8511418639427
52280272.4044068545537.59559314544714
53305284.24035776522220.7596422347779
54299302.553013704055-3.55301370405482
55246245.2252556490560.774744350943848
56307306.041151631790.958848368209772
57325297.2621720713527.7378279286503
58302300.8160470467771.18395295322267
59274282.668197088828-8.66819708882787
60251235.7616286325315.2383713674699
61272257.39458906686614.6054109331338
62253276.799370819002-23.7993708190017
63292277.3170862861114.6829137138899
64288291.422901204502-3.42290120450195
65258305.667026345426-47.6670263454264
66295290.0005045364844.9994954635165
67231238.92048890566-7.92048890565954
68250294.450211543451-44.4502115434515
69268281.186686679723-13.1866866797228







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
70261.441490444896232.052786489386290.830194400405
71241.534605288313209.801421745394273.267788831233
72211.969218632856178.743330365976245.195106899736
73225.611899135989189.176350181303262.047448090675
74223.339726755872184.800981073848261.878472437896
75245.088421844246202.445563513779287.731280174714
76246.020424798304201.298196593896290.742653002711
77241.671118341207195.538420324883287.80381635753
78262.727368689373212.084006447435313.370730931311
79210.418487076428164.937932987881255.899041164974
80247.6861486502195.009494059684300.362803240716
81262.331946860743192.501922094577332.161971626909

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
70 & 261.441490444896 & 232.052786489386 & 290.830194400405 \tabularnewline
71 & 241.534605288313 & 209.801421745394 & 273.267788831233 \tabularnewline
72 & 211.969218632856 & 178.743330365976 & 245.195106899736 \tabularnewline
73 & 225.611899135989 & 189.176350181303 & 262.047448090675 \tabularnewline
74 & 223.339726755872 & 184.800981073848 & 261.878472437896 \tabularnewline
75 & 245.088421844246 & 202.445563513779 & 287.731280174714 \tabularnewline
76 & 246.020424798304 & 201.298196593896 & 290.742653002711 \tabularnewline
77 & 241.671118341207 & 195.538420324883 & 287.80381635753 \tabularnewline
78 & 262.727368689373 & 212.084006447435 & 313.370730931311 \tabularnewline
79 & 210.418487076428 & 164.937932987881 & 255.899041164974 \tabularnewline
80 & 247.6861486502 & 195.009494059684 & 300.362803240716 \tabularnewline
81 & 262.331946860743 & 192.501922094577 & 332.161971626909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77329&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]70[/C][C]261.441490444896[/C][C]232.052786489386[/C][C]290.830194400405[/C][/ROW]
[ROW][C]71[/C][C]241.534605288313[/C][C]209.801421745394[/C][C]273.267788831233[/C][/ROW]
[ROW][C]72[/C][C]211.969218632856[/C][C]178.743330365976[/C][C]245.195106899736[/C][/ROW]
[ROW][C]73[/C][C]225.611899135989[/C][C]189.176350181303[/C][C]262.047448090675[/C][/ROW]
[ROW][C]74[/C][C]223.339726755872[/C][C]184.800981073848[/C][C]261.878472437896[/C][/ROW]
[ROW][C]75[/C][C]245.088421844246[/C][C]202.445563513779[/C][C]287.731280174714[/C][/ROW]
[ROW][C]76[/C][C]246.020424798304[/C][C]201.298196593896[/C][C]290.742653002711[/C][/ROW]
[ROW][C]77[/C][C]241.671118341207[/C][C]195.538420324883[/C][C]287.80381635753[/C][/ROW]
[ROW][C]78[/C][C]262.727368689373[/C][C]212.084006447435[/C][C]313.370730931311[/C][/ROW]
[ROW][C]79[/C][C]210.418487076428[/C][C]164.937932987881[/C][C]255.899041164974[/C][/ROW]
[ROW][C]80[/C][C]247.6861486502[/C][C]195.009494059684[/C][C]300.362803240716[/C][/ROW]
[ROW][C]81[/C][C]262.331946860743[/C][C]192.501922094577[/C][C]332.161971626909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77329&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77329&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
70261.441490444896232.052786489386290.830194400405
71241.534605288313209.801421745394273.267788831233
72211.969218632856178.743330365976245.195106899736
73225.611899135989189.176350181303262.047448090675
74223.339726755872184.800981073848261.878472437896
75245.088421844246202.445563513779287.731280174714
76246.020424798304201.298196593896290.742653002711
77241.671118341207195.538420324883287.80381635753
78262.727368689373212.084006447435313.370730931311
79210.418487076428164.937932987881255.899041164974
80247.6861486502195.009494059684300.362803240716
81262.331946860743192.501922094577332.161971626909



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')