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Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwareExponential Smoothing
Date of computationSun, 09 Dec 2012 06:48:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/09/t1355053746b63lhirxj950vw9.htm/, Retrieved Tue, 30 Apr 2024 09:43:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=197815, Retrieved Tue, 30 Apr 2024 09:43:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Workshop 8] [2012-11-23 16:59:10] [498ff5d3288f0a3191251bab12f09e42]
- R P   [Exponential Smoothing] [Workshop 8] [2012-11-23 17:11:28] [498ff5d3288f0a3191251bab12f09e42]
-  M        [Exponential Smoothing] [Paper - triple ex...] [2012-12-09 11:48:06] [88970af05b38e2e8b1d3faaed6004b57] [Current]
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Dataseries X:
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810
32242
32700
32819
33947
34148
35261
39506
41591
39148
41216
40225
41126
42362
40740
40256
39804
41002
41702
42254
43605
43271




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=197815&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=197815&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=197815&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0116432278326306
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0116432278326306 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=197815&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0116432278326306[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=197815&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=197815&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0116432278326306
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131939417905.69204059831488.30795940171
142014820146.68899420421.31100579578197
152010820170.8292585434-62.8292585433846
161858418637.0977231716-53.0977231716133
171844118516.2294942833-75.2294942833287
181839118494.811913475-103.81191347499
191917818386.0198743813791.980125618677
201807919203.3660794228-1124.36607942282
211848318742.0664956595-259.066495659485
221964419039.8417920934604.158207906617
231919520347.7094770883-1152.70947708833
241965019259.2465513551390.753448644904
252083021273.796182784-443.796182784045
262359521565.37896271662029.62103728335
272293723624.1353028676-687.135302867631
282181421465.1348299845348.865170015495
292192821749.9467466419178.053253358139
302177721988.4781945704-211.478194570387
312138321777.432572436-394.432572436035
322146721399.965104130667.0348958694485
332205222135.5372733626-83.5372733625627
342268022616.35629652363.6437034770497
352432023384.930647996935.069352004019
362497724409.776206834567.223793165984
372520426628.3805226899-1424.38052268992
382573925955.5461357439-216.546135743891
392643425758.1498397491675.850160250855
402752524968.01891714572556.98108285433
413069527492.54043045713202.45956954293
423243630822.28573018341613.71426981662
433016032524.4912397503-2364.49123975028
443023630242.0859295376-6.08592953761399
453129330968.8067363401324.193263659898
463107731926.3730590374-849.37305903736
473222631840.3169483294385.683051670574
483386532367.76587730461497.23412269545
493281035579.1985153139-2769.19851531387
503224233608.7061060863-1366.7061060863
513270032294.9182355129405.081764487117
523281931264.63469478771554.36530521234
533394732805.48252417141141.51747582862
543414834069.231805550778.7681944492942
553526134213.56558825131047.43441174868
563950635359.8861057474146.11389425296
574159140303.95192110451287.04807889547
583914842300.7289817853-3152.72898178532
594121639960.85437328921255.1456267108
604022541417.4266531175-1192.42665311747
614112641967.5429579215-841.542957921505
624236241975.4946815315386.505318468517
634074042486.1198510129-1746.11985101293
644025639350.7893797645905.210620235484
653980440281.0789532524-477.078953252436
664100239945.98254763891056.01745236111
674170241098.6946660986603.305333901364
684225441826.8440875539427.155912446113
694360543034.6092278292570.39077217078
704327144289.0420842099-1018.0420842099

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 19394 & 17905.6920405983 & 1488.30795940171 \tabularnewline
14 & 20148 & 20146.6889942042 & 1.31100579578197 \tabularnewline
15 & 20108 & 20170.8292585434 & -62.8292585433846 \tabularnewline
16 & 18584 & 18637.0977231716 & -53.0977231716133 \tabularnewline
17 & 18441 & 18516.2294942833 & -75.2294942833287 \tabularnewline
18 & 18391 & 18494.811913475 & -103.81191347499 \tabularnewline
19 & 19178 & 18386.0198743813 & 791.980125618677 \tabularnewline
20 & 18079 & 19203.3660794228 & -1124.36607942282 \tabularnewline
21 & 18483 & 18742.0664956595 & -259.066495659485 \tabularnewline
22 & 19644 & 19039.8417920934 & 604.158207906617 \tabularnewline
23 & 19195 & 20347.7094770883 & -1152.70947708833 \tabularnewline
24 & 19650 & 19259.2465513551 & 390.753448644904 \tabularnewline
25 & 20830 & 21273.796182784 & -443.796182784045 \tabularnewline
26 & 23595 & 21565.3789627166 & 2029.62103728335 \tabularnewline
27 & 22937 & 23624.1353028676 & -687.135302867631 \tabularnewline
28 & 21814 & 21465.1348299845 & 348.865170015495 \tabularnewline
29 & 21928 & 21749.9467466419 & 178.053253358139 \tabularnewline
30 & 21777 & 21988.4781945704 & -211.478194570387 \tabularnewline
31 & 21383 & 21777.432572436 & -394.432572436035 \tabularnewline
32 & 21467 & 21399.9651041306 & 67.0348958694485 \tabularnewline
33 & 22052 & 22135.5372733626 & -83.5372733625627 \tabularnewline
34 & 22680 & 22616.356296523 & 63.6437034770497 \tabularnewline
35 & 24320 & 23384.930647996 & 935.069352004019 \tabularnewline
36 & 24977 & 24409.776206834 & 567.223793165984 \tabularnewline
37 & 25204 & 26628.3805226899 & -1424.38052268992 \tabularnewline
38 & 25739 & 25955.5461357439 & -216.546135743891 \tabularnewline
39 & 26434 & 25758.1498397491 & 675.850160250855 \tabularnewline
40 & 27525 & 24968.0189171457 & 2556.98108285433 \tabularnewline
41 & 30695 & 27492.5404304571 & 3202.45956954293 \tabularnewline
42 & 32436 & 30822.2857301834 & 1613.71426981662 \tabularnewline
43 & 30160 & 32524.4912397503 & -2364.49123975028 \tabularnewline
44 & 30236 & 30242.0859295376 & -6.08592953761399 \tabularnewline
45 & 31293 & 30968.8067363401 & 324.193263659898 \tabularnewline
46 & 31077 & 31926.3730590374 & -849.37305903736 \tabularnewline
47 & 32226 & 31840.3169483294 & 385.683051670574 \tabularnewline
48 & 33865 & 32367.7658773046 & 1497.23412269545 \tabularnewline
49 & 32810 & 35579.1985153139 & -2769.19851531387 \tabularnewline
50 & 32242 & 33608.7061060863 & -1366.7061060863 \tabularnewline
51 & 32700 & 32294.9182355129 & 405.081764487117 \tabularnewline
52 & 32819 & 31264.6346947877 & 1554.36530521234 \tabularnewline
53 & 33947 & 32805.4825241714 & 1141.51747582862 \tabularnewline
54 & 34148 & 34069.2318055507 & 78.7681944492942 \tabularnewline
55 & 35261 & 34213.5655882513 & 1047.43441174868 \tabularnewline
56 & 39506 & 35359.886105747 & 4146.11389425296 \tabularnewline
57 & 41591 & 40303.9519211045 & 1287.04807889547 \tabularnewline
58 & 39148 & 42300.7289817853 & -3152.72898178532 \tabularnewline
59 & 41216 & 39960.8543732892 & 1255.1456267108 \tabularnewline
60 & 40225 & 41417.4266531175 & -1192.42665311747 \tabularnewline
61 & 41126 & 41967.5429579215 & -841.542957921505 \tabularnewline
62 & 42362 & 41975.4946815315 & 386.505318468517 \tabularnewline
63 & 40740 & 42486.1198510129 & -1746.11985101293 \tabularnewline
64 & 40256 & 39350.7893797645 & 905.210620235484 \tabularnewline
65 & 39804 & 40281.0789532524 & -477.078953252436 \tabularnewline
66 & 41002 & 39945.9825476389 & 1056.01745236111 \tabularnewline
67 & 41702 & 41098.6946660986 & 603.305333901364 \tabularnewline
68 & 42254 & 41826.8440875539 & 427.155912446113 \tabularnewline
69 & 43605 & 43034.6092278292 & 570.39077217078 \tabularnewline
70 & 43271 & 44289.0420842099 & -1018.0420842099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=197815&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]19394[/C][C]17905.6920405983[/C][C]1488.30795940171[/C][/ROW]
[ROW][C]14[/C][C]20148[/C][C]20146.6889942042[/C][C]1.31100579578197[/C][/ROW]
[ROW][C]15[/C][C]20108[/C][C]20170.8292585434[/C][C]-62.8292585433846[/C][/ROW]
[ROW][C]16[/C][C]18584[/C][C]18637.0977231716[/C][C]-53.0977231716133[/C][/ROW]
[ROW][C]17[/C][C]18441[/C][C]18516.2294942833[/C][C]-75.2294942833287[/C][/ROW]
[ROW][C]18[/C][C]18391[/C][C]18494.811913475[/C][C]-103.81191347499[/C][/ROW]
[ROW][C]19[/C][C]19178[/C][C]18386.0198743813[/C][C]791.980125618677[/C][/ROW]
[ROW][C]20[/C][C]18079[/C][C]19203.3660794228[/C][C]-1124.36607942282[/C][/ROW]
[ROW][C]21[/C][C]18483[/C][C]18742.0664956595[/C][C]-259.066495659485[/C][/ROW]
[ROW][C]22[/C][C]19644[/C][C]19039.8417920934[/C][C]604.158207906617[/C][/ROW]
[ROW][C]23[/C][C]19195[/C][C]20347.7094770883[/C][C]-1152.70947708833[/C][/ROW]
[ROW][C]24[/C][C]19650[/C][C]19259.2465513551[/C][C]390.753448644904[/C][/ROW]
[ROW][C]25[/C][C]20830[/C][C]21273.796182784[/C][C]-443.796182784045[/C][/ROW]
[ROW][C]26[/C][C]23595[/C][C]21565.3789627166[/C][C]2029.62103728335[/C][/ROW]
[ROW][C]27[/C][C]22937[/C][C]23624.1353028676[/C][C]-687.135302867631[/C][/ROW]
[ROW][C]28[/C][C]21814[/C][C]21465.1348299845[/C][C]348.865170015495[/C][/ROW]
[ROW][C]29[/C][C]21928[/C][C]21749.9467466419[/C][C]178.053253358139[/C][/ROW]
[ROW][C]30[/C][C]21777[/C][C]21988.4781945704[/C][C]-211.478194570387[/C][/ROW]
[ROW][C]31[/C][C]21383[/C][C]21777.432572436[/C][C]-394.432572436035[/C][/ROW]
[ROW][C]32[/C][C]21467[/C][C]21399.9651041306[/C][C]67.0348958694485[/C][/ROW]
[ROW][C]33[/C][C]22052[/C][C]22135.5372733626[/C][C]-83.5372733625627[/C][/ROW]
[ROW][C]34[/C][C]22680[/C][C]22616.356296523[/C][C]63.6437034770497[/C][/ROW]
[ROW][C]35[/C][C]24320[/C][C]23384.930647996[/C][C]935.069352004019[/C][/ROW]
[ROW][C]36[/C][C]24977[/C][C]24409.776206834[/C][C]567.223793165984[/C][/ROW]
[ROW][C]37[/C][C]25204[/C][C]26628.3805226899[/C][C]-1424.38052268992[/C][/ROW]
[ROW][C]38[/C][C]25739[/C][C]25955.5461357439[/C][C]-216.546135743891[/C][/ROW]
[ROW][C]39[/C][C]26434[/C][C]25758.1498397491[/C][C]675.850160250855[/C][/ROW]
[ROW][C]40[/C][C]27525[/C][C]24968.0189171457[/C][C]2556.98108285433[/C][/ROW]
[ROW][C]41[/C][C]30695[/C][C]27492.5404304571[/C][C]3202.45956954293[/C][/ROW]
[ROW][C]42[/C][C]32436[/C][C]30822.2857301834[/C][C]1613.71426981662[/C][/ROW]
[ROW][C]43[/C][C]30160[/C][C]32524.4912397503[/C][C]-2364.49123975028[/C][/ROW]
[ROW][C]44[/C][C]30236[/C][C]30242.0859295376[/C][C]-6.08592953761399[/C][/ROW]
[ROW][C]45[/C][C]31293[/C][C]30968.8067363401[/C][C]324.193263659898[/C][/ROW]
[ROW][C]46[/C][C]31077[/C][C]31926.3730590374[/C][C]-849.37305903736[/C][/ROW]
[ROW][C]47[/C][C]32226[/C][C]31840.3169483294[/C][C]385.683051670574[/C][/ROW]
[ROW][C]48[/C][C]33865[/C][C]32367.7658773046[/C][C]1497.23412269545[/C][/ROW]
[ROW][C]49[/C][C]32810[/C][C]35579.1985153139[/C][C]-2769.19851531387[/C][/ROW]
[ROW][C]50[/C][C]32242[/C][C]33608.7061060863[/C][C]-1366.7061060863[/C][/ROW]
[ROW][C]51[/C][C]32700[/C][C]32294.9182355129[/C][C]405.081764487117[/C][/ROW]
[ROW][C]52[/C][C]32819[/C][C]31264.6346947877[/C][C]1554.36530521234[/C][/ROW]
[ROW][C]53[/C][C]33947[/C][C]32805.4825241714[/C][C]1141.51747582862[/C][/ROW]
[ROW][C]54[/C][C]34148[/C][C]34069.2318055507[/C][C]78.7681944492942[/C][/ROW]
[ROW][C]55[/C][C]35261[/C][C]34213.5655882513[/C][C]1047.43441174868[/C][/ROW]
[ROW][C]56[/C][C]39506[/C][C]35359.886105747[/C][C]4146.11389425296[/C][/ROW]
[ROW][C]57[/C][C]41591[/C][C]40303.9519211045[/C][C]1287.04807889547[/C][/ROW]
[ROW][C]58[/C][C]39148[/C][C]42300.7289817853[/C][C]-3152.72898178532[/C][/ROW]
[ROW][C]59[/C][C]41216[/C][C]39960.8543732892[/C][C]1255.1456267108[/C][/ROW]
[ROW][C]60[/C][C]40225[/C][C]41417.4266531175[/C][C]-1192.42665311747[/C][/ROW]
[ROW][C]61[/C][C]41126[/C][C]41967.5429579215[/C][C]-841.542957921505[/C][/ROW]
[ROW][C]62[/C][C]42362[/C][C]41975.4946815315[/C][C]386.505318468517[/C][/ROW]
[ROW][C]63[/C][C]40740[/C][C]42486.1198510129[/C][C]-1746.11985101293[/C][/ROW]
[ROW][C]64[/C][C]40256[/C][C]39350.7893797645[/C][C]905.210620235484[/C][/ROW]
[ROW][C]65[/C][C]39804[/C][C]40281.0789532524[/C][C]-477.078953252436[/C][/ROW]
[ROW][C]66[/C][C]41002[/C][C]39945.9825476389[/C][C]1056.01745236111[/C][/ROW]
[ROW][C]67[/C][C]41702[/C][C]41098.6946660986[/C][C]603.305333901364[/C][/ROW]
[ROW][C]68[/C][C]42254[/C][C]41826.8440875539[/C][C]427.155912446113[/C][/ROW]
[ROW][C]69[/C][C]43605[/C][C]43034.6092278292[/C][C]570.39077217078[/C][/ROW]
[ROW][C]70[/C][C]43271[/C][C]44289.0420842099[/C][C]-1018.0420842099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=197815&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=197815&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
131939417905.69204059831488.30795940171
142014820146.68899420421.31100579578197
152010820170.8292585434-62.8292585433846
161858418637.0977231716-53.0977231716133
171844118516.2294942833-75.2294942833287
181839118494.811913475-103.81191347499
191917818386.0198743813791.980125618677
201807919203.3660794228-1124.36607942282
211848318742.0664956595-259.066495659485
221964419039.8417920934604.158207906617
231919520347.7094770883-1152.70947708833
241965019259.2465513551390.753448644904
252083021273.796182784-443.796182784045
262359521565.37896271662029.62103728335
272293723624.1353028676-687.135302867631
282181421465.1348299845348.865170015495
292192821749.9467466419178.053253358139
302177721988.4781945704-211.478194570387
312138321777.432572436-394.432572436035
322146721399.965104130667.0348958694485
332205222135.5372733626-83.5372733625627
342268022616.35629652363.6437034770497
352432023384.930647996935.069352004019
362497724409.776206834567.223793165984
372520426628.3805226899-1424.38052268992
382573925955.5461357439-216.546135743891
392643425758.1498397491675.850160250855
402752524968.01891714572556.98108285433
413069527492.54043045713202.45956954293
423243630822.28573018341613.71426981662
433016032524.4912397503-2364.49123975028
443023630242.0859295376-6.08592953761399
453129330968.8067363401324.193263659898
463107731926.3730590374-849.37305903736
473222631840.3169483294385.683051670574
483386532367.76587730461497.23412269545
493281035579.1985153139-2769.19851531387
503224233608.7061060863-1366.7061060863
513270032294.9182355129405.081764487117
523281931264.63469478771554.36530521234
533394732805.48252417141141.51747582862
543414834069.231805550778.7681944492942
553526134213.56558825131047.43441174868
563950635359.8861057474146.11389425296
574159140303.95192110451287.04807889547
583914842300.7289817853-3152.72898178532
594121639960.85437328921255.1456267108
604022541417.4266531175-1192.42665311747
614112641967.5429579215-841.542957921505
624236241975.4946815315386.505318468517
634074042486.1198510129-1746.11985101293
644025639350.7893797645905.210620235484
653980440281.0789532524-477.078953252436
664100239945.98254763891056.01745236111
674170241098.6946660986603.305333901364
684225441826.8440875539427.155912446113
694360543034.6092278292570.39077217078
704327144289.0420842099-1018.0420842099







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7144083.022121613641545.878096936846620.1661462903
7244269.002576560540659.990317380647878.0148357403
7346009.983031507441564.158659967450455.8074030474
7446867.713486454341704.381262331352031.0457105772
7546995.568941401241189.481556864352801.6563259381
7645630.424396348139233.624195394252027.224597302
7745669.02985129538720.148558129452617.9111444606
7845830.093639575338359.076891411953301.1103877386
7945933.574094522237964.369731907353902.778457137
8046058.179549469137610.394201843254505.9648970949
8146833.576671082637923.559058396855743.5942837684
8247505.765459362938147.348221536156864.1826971897

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
71 & 44083.0221216136 & 41545.8780969368 & 46620.1661462903 \tabularnewline
72 & 44269.0025765605 & 40659.9903173806 & 47878.0148357403 \tabularnewline
73 & 46009.9830315074 & 41564.1586599674 & 50455.8074030474 \tabularnewline
74 & 46867.7134864543 & 41704.3812623313 & 52031.0457105772 \tabularnewline
75 & 46995.5689414012 & 41189.4815568643 & 52801.6563259381 \tabularnewline
76 & 45630.4243963481 & 39233.6241953942 & 52027.224597302 \tabularnewline
77 & 45669.029851295 & 38720.1485581294 & 52617.9111444606 \tabularnewline
78 & 45830.0936395753 & 38359.0768914119 & 53301.1103877386 \tabularnewline
79 & 45933.5740945222 & 37964.3697319073 & 53902.778457137 \tabularnewline
80 & 46058.1795494691 & 37610.3942018432 & 54505.9648970949 \tabularnewline
81 & 46833.5766710826 & 37923.5590583968 & 55743.5942837684 \tabularnewline
82 & 47505.7654593629 & 38147.3482215361 & 56864.1826971897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=197815&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]71[/C][C]44083.0221216136[/C][C]41545.8780969368[/C][C]46620.1661462903[/C][/ROW]
[ROW][C]72[/C][C]44269.0025765605[/C][C]40659.9903173806[/C][C]47878.0148357403[/C][/ROW]
[ROW][C]73[/C][C]46009.9830315074[/C][C]41564.1586599674[/C][C]50455.8074030474[/C][/ROW]
[ROW][C]74[/C][C]46867.7134864543[/C][C]41704.3812623313[/C][C]52031.0457105772[/C][/ROW]
[ROW][C]75[/C][C]46995.5689414012[/C][C]41189.4815568643[/C][C]52801.6563259381[/C][/ROW]
[ROW][C]76[/C][C]45630.4243963481[/C][C]39233.6241953942[/C][C]52027.224597302[/C][/ROW]
[ROW][C]77[/C][C]45669.029851295[/C][C]38720.1485581294[/C][C]52617.9111444606[/C][/ROW]
[ROW][C]78[/C][C]45830.0936395753[/C][C]38359.0768914119[/C][C]53301.1103877386[/C][/ROW]
[ROW][C]79[/C][C]45933.5740945222[/C][C]37964.3697319073[/C][C]53902.778457137[/C][/ROW]
[ROW][C]80[/C][C]46058.1795494691[/C][C]37610.3942018432[/C][C]54505.9648970949[/C][/ROW]
[ROW][C]81[/C][C]46833.5766710826[/C][C]37923.5590583968[/C][C]55743.5942837684[/C][/ROW]
[ROW][C]82[/C][C]47505.7654593629[/C][C]38147.3482215361[/C][C]56864.1826971897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=197815&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=197815&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
7144083.022121613641545.878096936846620.1661462903
7244269.002576560540659.990317380647878.0148357403
7346009.983031507441564.158659967450455.8074030474
7446867.713486454341704.381262331352031.0457105772
7546995.568941401241189.481556864352801.6563259381
7645630.424396348139233.624195394252027.224597302
7745669.02985129538720.148558129452617.9111444606
7845830.093639575338359.076891411953301.1103877386
7945933.574094522237964.369731907353902.778457137
8046058.179549469137610.394201843254505.9648970949
8146833.576671082637923.559058396855743.5942837684
8247505.765459362938147.348221536156864.1826971897



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')