Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 03:17:49 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211793590i2cpxxayjxrcqpo.htm/, Retrieved Tue, 14 May 2024 20:59:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13251, Retrieved Tue, 14 May 2024 20:59:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-05-26 09:17:49] [1e17f2ab0c3b2b3de21c4ac88dec2f8d] [Current]
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Dataseries X:
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13251&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13251&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.567279660412336
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.567279660412336 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13251&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]0.567279660412336[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13251&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
alpha0.567279660412336
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23969041086-1396
34312940294.07759406442834.92240593562
43786341902.2714137989-4039.27141379887
53595339610.8748978658-3657.87489786579
62913337535.8368679737-8402.83686797367
72469332769.0784230093-8076.07842300931
82220528187.6833977412-5982.6833977412
92172524793.8287915160-3068.82879151605
102719223052.94463680124139.05536319878
112179025400.9465576645-3610.94655766448
121325323352.5300206655-10099.5300206655
133770217623.272060218220078.7279397818
143036429013.52602740931350.47397259071
153260929779.62244397622829.37755602376
163021231384.6707831357-1172.67078313569
172996530719.438499503-754.438499503005
182835230291.4608837029-1939.46088370295
192581429191.2441722129-3377.24417221293
202241427275.4022450704-4861.40224507044
212050624517.6276303591-4011.62763035911
222880622241.91287050836564.08712949175
232222825965.5859882433-3737.58598824331
241397123845.3294780707-9874.32947807074
253684518243.823204951318601.1767950487
263533828795.89246051636542.10753948367
273502232507.09700389562514.90299610439
283477733933.7503214957843.249678504326
292688734412.1087127604-7525.10871276042
302397030143.2675976198-6173.26759761978
312278026641.2984512076-3861.29845120756
321735124450.8623770559-7099.86237705586
332138220423.2548588253958.74514117471
342456120967.13147693293593.86852306714
351740923005.8599922650-5596.85999226497
361151419830.8751564775-8316.87515647751
373151415112.881042019216401.1189579808
382707124416.90223488492654.09776511515
392946225922.51791378053539.48208621949
402610527930.3941096867-1825.39410968665
412239726894.8851590249-4497.88515902493
422384324343.3263934396-500.32639343958
432170524059.5014068738-2354.50140687385
441808922723.8406483421-4634.84064834208
452076420094.5898192853669.410180714702
462531620474.33259927774841.6674007223
471770423220.9120381889-5516.91203818892
481554820091.2800506404-4543.28005064038
492802917513.969686355010515.0303136450
502938323478.93251190495904.06748809506
513643826828.1899116039609.81008839698
523203432279.6397151759-245.639715175901
532267932140.2933009671-9461.29330096713
542431926773.094050133-2454.09405013299
551800425380.9364107536-7376.93641075361
561753721196.1504287779-3659.15042877791
572036619120.38881614311245.61118385688
582278219826.99870552732955.00129447274
591916921503.3108363738-2334.31083637377
601380720179.1037778188-6372.10377781882
612974316564.338910625613178.6610893744
622559124040.32529809521550.67470190483
632909624919.99151640174176.00848359826
642648227288.9561908564-806.956190856396
652240526831.1863569397-4426.18635693975
662704424320.30086345332723.69913654675
671797025865.3999846989-7895.39998469887
681873021386.5001625593-2656.50016255933
691968419879.5216524574-195.521652457359
701978519768.606195848116.3938041519104
711847919777.9060675003-1298.90606750025
721069819041.0630746212-8343.06307462119

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 39690 & 41086 & -1396 \tabularnewline
3 & 43129 & 40294.0775940644 & 2834.92240593562 \tabularnewline
4 & 37863 & 41902.2714137989 & -4039.27141379887 \tabularnewline
5 & 35953 & 39610.8748978658 & -3657.87489786579 \tabularnewline
6 & 29133 & 37535.8368679737 & -8402.83686797367 \tabularnewline
7 & 24693 & 32769.0784230093 & -8076.07842300931 \tabularnewline
8 & 22205 & 28187.6833977412 & -5982.6833977412 \tabularnewline
9 & 21725 & 24793.8287915160 & -3068.82879151605 \tabularnewline
10 & 27192 & 23052.9446368012 & 4139.05536319878 \tabularnewline
11 & 21790 & 25400.9465576645 & -3610.94655766448 \tabularnewline
12 & 13253 & 23352.5300206655 & -10099.5300206655 \tabularnewline
13 & 37702 & 17623.2720602182 & 20078.7279397818 \tabularnewline
14 & 30364 & 29013.5260274093 & 1350.47397259071 \tabularnewline
15 & 32609 & 29779.6224439762 & 2829.37755602376 \tabularnewline
16 & 30212 & 31384.6707831357 & -1172.67078313569 \tabularnewline
17 & 29965 & 30719.438499503 & -754.438499503005 \tabularnewline
18 & 28352 & 30291.4608837029 & -1939.46088370295 \tabularnewline
19 & 25814 & 29191.2441722129 & -3377.24417221293 \tabularnewline
20 & 22414 & 27275.4022450704 & -4861.40224507044 \tabularnewline
21 & 20506 & 24517.6276303591 & -4011.62763035911 \tabularnewline
22 & 28806 & 22241.9128705083 & 6564.08712949175 \tabularnewline
23 & 22228 & 25965.5859882433 & -3737.58598824331 \tabularnewline
24 & 13971 & 23845.3294780707 & -9874.32947807074 \tabularnewline
25 & 36845 & 18243.8232049513 & 18601.1767950487 \tabularnewline
26 & 35338 & 28795.8924605163 & 6542.10753948367 \tabularnewline
27 & 35022 & 32507.0970038956 & 2514.90299610439 \tabularnewline
28 & 34777 & 33933.7503214957 & 843.249678504326 \tabularnewline
29 & 26887 & 34412.1087127604 & -7525.10871276042 \tabularnewline
30 & 23970 & 30143.2675976198 & -6173.26759761978 \tabularnewline
31 & 22780 & 26641.2984512076 & -3861.29845120756 \tabularnewline
32 & 17351 & 24450.8623770559 & -7099.86237705586 \tabularnewline
33 & 21382 & 20423.2548588253 & 958.74514117471 \tabularnewline
34 & 24561 & 20967.1314769329 & 3593.86852306714 \tabularnewline
35 & 17409 & 23005.8599922650 & -5596.85999226497 \tabularnewline
36 & 11514 & 19830.8751564775 & -8316.87515647751 \tabularnewline
37 & 31514 & 15112.8810420192 & 16401.1189579808 \tabularnewline
38 & 27071 & 24416.9022348849 & 2654.09776511515 \tabularnewline
39 & 29462 & 25922.5179137805 & 3539.48208621949 \tabularnewline
40 & 26105 & 27930.3941096867 & -1825.39410968665 \tabularnewline
41 & 22397 & 26894.8851590249 & -4497.88515902493 \tabularnewline
42 & 23843 & 24343.3263934396 & -500.32639343958 \tabularnewline
43 & 21705 & 24059.5014068738 & -2354.50140687385 \tabularnewline
44 & 18089 & 22723.8406483421 & -4634.84064834208 \tabularnewline
45 & 20764 & 20094.5898192853 & 669.410180714702 \tabularnewline
46 & 25316 & 20474.3325992777 & 4841.6674007223 \tabularnewline
47 & 17704 & 23220.9120381889 & -5516.91203818892 \tabularnewline
48 & 15548 & 20091.2800506404 & -4543.28005064038 \tabularnewline
49 & 28029 & 17513.9696863550 & 10515.0303136450 \tabularnewline
50 & 29383 & 23478.9325119049 & 5904.06748809506 \tabularnewline
51 & 36438 & 26828.189911603 & 9609.81008839698 \tabularnewline
52 & 32034 & 32279.6397151759 & -245.639715175901 \tabularnewline
53 & 22679 & 32140.2933009671 & -9461.29330096713 \tabularnewline
54 & 24319 & 26773.094050133 & -2454.09405013299 \tabularnewline
55 & 18004 & 25380.9364107536 & -7376.93641075361 \tabularnewline
56 & 17537 & 21196.1504287779 & -3659.15042877791 \tabularnewline
57 & 20366 & 19120.3888161431 & 1245.61118385688 \tabularnewline
58 & 22782 & 19826.9987055273 & 2955.00129447274 \tabularnewline
59 & 19169 & 21503.3108363738 & -2334.31083637377 \tabularnewline
60 & 13807 & 20179.1037778188 & -6372.10377781882 \tabularnewline
61 & 29743 & 16564.3389106256 & 13178.6610893744 \tabularnewline
62 & 25591 & 24040.3252980952 & 1550.67470190483 \tabularnewline
63 & 29096 & 24919.9915164017 & 4176.00848359826 \tabularnewline
64 & 26482 & 27288.9561908564 & -806.956190856396 \tabularnewline
65 & 22405 & 26831.1863569397 & -4426.18635693975 \tabularnewline
66 & 27044 & 24320.3008634533 & 2723.69913654675 \tabularnewline
67 & 17970 & 25865.3999846989 & -7895.39998469887 \tabularnewline
68 & 18730 & 21386.5001625593 & -2656.50016255933 \tabularnewline
69 & 19684 & 19879.5216524574 & -195.521652457359 \tabularnewline
70 & 19785 & 19768.6061958481 & 16.3938041519104 \tabularnewline
71 & 18479 & 19777.9060675003 & -1298.90606750025 \tabularnewline
72 & 10698 & 19041.0630746212 & -8343.06307462119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13251&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]39690[/C][C]41086[/C][C]-1396[/C][/ROW]
[ROW][C]3[/C][C]43129[/C][C]40294.0775940644[/C][C]2834.92240593562[/C][/ROW]
[ROW][C]4[/C][C]37863[/C][C]41902.2714137989[/C][C]-4039.27141379887[/C][/ROW]
[ROW][C]5[/C][C]35953[/C][C]39610.8748978658[/C][C]-3657.87489786579[/C][/ROW]
[ROW][C]6[/C][C]29133[/C][C]37535.8368679737[/C][C]-8402.83686797367[/C][/ROW]
[ROW][C]7[/C][C]24693[/C][C]32769.0784230093[/C][C]-8076.07842300931[/C][/ROW]
[ROW][C]8[/C][C]22205[/C][C]28187.6833977412[/C][C]-5982.6833977412[/C][/ROW]
[ROW][C]9[/C][C]21725[/C][C]24793.8287915160[/C][C]-3068.82879151605[/C][/ROW]
[ROW][C]10[/C][C]27192[/C][C]23052.9446368012[/C][C]4139.05536319878[/C][/ROW]
[ROW][C]11[/C][C]21790[/C][C]25400.9465576645[/C][C]-3610.94655766448[/C][/ROW]
[ROW][C]12[/C][C]13253[/C][C]23352.5300206655[/C][C]-10099.5300206655[/C][/ROW]
[ROW][C]13[/C][C]37702[/C][C]17623.2720602182[/C][C]20078.7279397818[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]29013.5260274093[/C][C]1350.47397259071[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]29779.6224439762[/C][C]2829.37755602376[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]31384.6707831357[/C][C]-1172.67078313569[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30719.438499503[/C][C]-754.438499503005[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]30291.4608837029[/C][C]-1939.46088370295[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]29191.2441722129[/C][C]-3377.24417221293[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]27275.4022450704[/C][C]-4861.40224507044[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]24517.6276303591[/C][C]-4011.62763035911[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]22241.9128705083[/C][C]6564.08712949175[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]25965.5859882433[/C][C]-3737.58598824331[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]23845.3294780707[/C][C]-9874.32947807074[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]18243.8232049513[/C][C]18601.1767950487[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]28795.8924605163[/C][C]6542.10753948367[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]32507.0970038956[/C][C]2514.90299610439[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]33933.7503214957[/C][C]843.249678504326[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]34412.1087127604[/C][C]-7525.10871276042[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]30143.2675976198[/C][C]-6173.26759761978[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]26641.2984512076[/C][C]-3861.29845120756[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]24450.8623770559[/C][C]-7099.86237705586[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]20423.2548588253[/C][C]958.74514117471[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]20967.1314769329[/C][C]3593.86852306714[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]23005.8599922650[/C][C]-5596.85999226497[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]19830.8751564775[/C][C]-8316.87515647751[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]15112.8810420192[/C][C]16401.1189579808[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]24416.9022348849[/C][C]2654.09776511515[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]25922.5179137805[/C][C]3539.48208621949[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27930.3941096867[/C][C]-1825.39410968665[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]26894.8851590249[/C][C]-4497.88515902493[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]24343.3263934396[/C][C]-500.32639343958[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]24059.5014068738[/C][C]-2354.50140687385[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]22723.8406483421[/C][C]-4634.84064834208[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]20094.5898192853[/C][C]669.410180714702[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]20474.3325992777[/C][C]4841.6674007223[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]23220.9120381889[/C][C]-5516.91203818892[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]20091.2800506404[/C][C]-4543.28005064038[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]17513.9696863550[/C][C]10515.0303136450[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]23478.9325119049[/C][C]5904.06748809506[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]26828.189911603[/C][C]9609.81008839698[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]32279.6397151759[/C][C]-245.639715175901[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]32140.2933009671[/C][C]-9461.29330096713[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]26773.094050133[/C][C]-2454.09405013299[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]25380.9364107536[/C][C]-7376.93641075361[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]21196.1504287779[/C][C]-3659.15042877791[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]19120.3888161431[/C][C]1245.61118385688[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]19826.9987055273[/C][C]2955.00129447274[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]21503.3108363738[/C][C]-2334.31083637377[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]20179.1037778188[/C][C]-6372.10377781882[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]16564.3389106256[/C][C]13178.6610893744[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]24040.3252980952[/C][C]1550.67470190483[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]24919.9915164017[/C][C]4176.00848359826[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]27288.9561908564[/C][C]-806.956190856396[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]26831.1863569397[/C][C]-4426.18635693975[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]24320.3008634533[/C][C]2723.69913654675[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]25865.3999846989[/C][C]-7895.39998469887[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]21386.5001625593[/C][C]-2656.50016255933[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19879.5216524574[/C][C]-195.521652457359[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]19768.6061958481[/C][C]16.3938041519104[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]19777.9060675003[/C][C]-1298.90606750025[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]19041.0630746212[/C][C]-8343.06307462119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13251&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13251&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
23969041086-1396
34312940294.07759406442834.92240593562
43786341902.2714137989-4039.27141379887
53595339610.8748978658-3657.87489786579
62913337535.8368679737-8402.83686797367
72469332769.0784230093-8076.07842300931
82220528187.6833977412-5982.6833977412
92172524793.8287915160-3068.82879151605
102719223052.94463680124139.05536319878
112179025400.9465576645-3610.94655766448
121325323352.5300206655-10099.5300206655
133770217623.272060218220078.7279397818
143036429013.52602740931350.47397259071
153260929779.62244397622829.37755602376
163021231384.6707831357-1172.67078313569
172996530719.438499503-754.438499503005
182835230291.4608837029-1939.46088370295
192581429191.2441722129-3377.24417221293
202241427275.4022450704-4861.40224507044
212050624517.6276303591-4011.62763035911
222880622241.91287050836564.08712949175
232222825965.5859882433-3737.58598824331
241397123845.3294780707-9874.32947807074
253684518243.823204951318601.1767950487
263533828795.89246051636542.10753948367
273502232507.09700389562514.90299610439
283477733933.7503214957843.249678504326
292688734412.1087127604-7525.10871276042
302397030143.2675976198-6173.26759761978
312278026641.2984512076-3861.29845120756
321735124450.8623770559-7099.86237705586
332138220423.2548588253958.74514117471
342456120967.13147693293593.86852306714
351740923005.8599922650-5596.85999226497
361151419830.8751564775-8316.87515647751
373151415112.881042019216401.1189579808
382707124416.90223488492654.09776511515
392946225922.51791378053539.48208621949
402610527930.3941096867-1825.39410968665
412239726894.8851590249-4497.88515902493
422384324343.3263934396-500.32639343958
432170524059.5014068738-2354.50140687385
441808922723.8406483421-4634.84064834208
452076420094.5898192853669.410180714702
462531620474.33259927774841.6674007223
471770423220.9120381889-5516.91203818892
481554820091.2800506404-4543.28005064038
492802917513.969686355010515.0303136450
502938323478.93251190495904.06748809506
513643826828.1899116039609.81008839698
523203432279.6397151759-245.639715175901
532267932140.2933009671-9461.29330096713
542431926773.094050133-2454.09405013299
551800425380.9364107536-7376.93641075361
561753721196.1504287779-3659.15042877791
572036619120.38881614311245.61118385688
582278219826.99870552732955.00129447274
591916921503.3108363738-2334.31083637377
601380720179.1037778188-6372.10377781882
612974316564.338910625613178.6610893744
622559124040.32529809521550.67470190483
632909624919.99151640174176.00848359826
642648227288.9561908564-806.956190856396
652240526831.1863569397-4426.18635693975
662704424320.30086345332723.69913654675
671797025865.3999846989-7895.39998469887
681873021386.5001625593-2656.50016255933
691968419879.5216524574-195.521652457359
701978519768.606195848116.3938041519104
711847919777.9060675003-1298.90606750025
721069819041.0630746212-8343.06307462119







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7314308.21308685141802.3111108718826814.1150628309
7414308.2130868514-69.801329454465328686.2275031572
7514308.2130868514-1724.7845392380530341.2107129408
7614308.2130868514-3224.2347513964231840.6609250992
7714308.2130868514-4605.1800916232533221.606265326
7814308.2130868514-5891.9392850061534508.3654587089
7914308.2130868514-7101.5013009902335717.927474693
8014308.2130868514-8246.289445717236862.7156194200
8114308.2130868514-9335.7142268233437952.1404005261
8214308.2130868514-10377.106703198438993.5328769012
8314308.2130868514-11376.310024542339992.7361982450
8414308.2130868514-12338.070740024140954.4969137269

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 14308.2130868514 & 1802.31111087188 & 26814.1150628309 \tabularnewline
74 & 14308.2130868514 & -69.8013294544653 & 28686.2275031572 \tabularnewline
75 & 14308.2130868514 & -1724.78453923805 & 30341.2107129408 \tabularnewline
76 & 14308.2130868514 & -3224.23475139642 & 31840.6609250992 \tabularnewline
77 & 14308.2130868514 & -4605.18009162325 & 33221.606265326 \tabularnewline
78 & 14308.2130868514 & -5891.93928500615 & 34508.3654587089 \tabularnewline
79 & 14308.2130868514 & -7101.50130099023 & 35717.927474693 \tabularnewline
80 & 14308.2130868514 & -8246.2894457172 & 36862.7156194200 \tabularnewline
81 & 14308.2130868514 & -9335.71422682334 & 37952.1404005261 \tabularnewline
82 & 14308.2130868514 & -10377.1067031984 & 38993.5328769012 \tabularnewline
83 & 14308.2130868514 & -11376.3100245423 & 39992.7361982450 \tabularnewline
84 & 14308.2130868514 & -12338.0707400241 & 40954.4969137269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13251&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]14308.2130868514[/C][C]1802.31111087188[/C][C]26814.1150628309[/C][/ROW]
[ROW][C]74[/C][C]14308.2130868514[/C][C]-69.8013294544653[/C][C]28686.2275031572[/C][/ROW]
[ROW][C]75[/C][C]14308.2130868514[/C][C]-1724.78453923805[/C][C]30341.2107129408[/C][/ROW]
[ROW][C]76[/C][C]14308.2130868514[/C][C]-3224.23475139642[/C][C]31840.6609250992[/C][/ROW]
[ROW][C]77[/C][C]14308.2130868514[/C][C]-4605.18009162325[/C][C]33221.606265326[/C][/ROW]
[ROW][C]78[/C][C]14308.2130868514[/C][C]-5891.93928500615[/C][C]34508.3654587089[/C][/ROW]
[ROW][C]79[/C][C]14308.2130868514[/C][C]-7101.50130099023[/C][C]35717.927474693[/C][/ROW]
[ROW][C]80[/C][C]14308.2130868514[/C][C]-8246.2894457172[/C][C]36862.7156194200[/C][/ROW]
[ROW][C]81[/C][C]14308.2130868514[/C][C]-9335.71422682334[/C][C]37952.1404005261[/C][/ROW]
[ROW][C]82[/C][C]14308.2130868514[/C][C]-10377.1067031984[/C][C]38993.5328769012[/C][/ROW]
[ROW][C]83[/C][C]14308.2130868514[/C][C]-11376.3100245423[/C][C]39992.7361982450[/C][/ROW]
[ROW][C]84[/C][C]14308.2130868514[/C][C]-12338.0707400241[/C][C]40954.4969137269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13251&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13251&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
7314308.21308685141802.3111108718826814.1150628309
7414308.2130868514-69.801329454465328686.2275031572
7514308.2130868514-1724.7845392380530341.2107129408
7614308.2130868514-3224.2347513964231840.6609250992
7714308.2130868514-4605.1800916232533221.606265326
7814308.2130868514-5891.9392850061534508.3654587089
7914308.2130868514-7101.5013009902335717.927474693
8014308.2130868514-8246.289445717236862.7156194200
8114308.2130868514-9335.7142268233437952.1404005261
8214308.2130868514-10377.106703198438993.5328769012
8314308.2130868514-11376.310024542339992.7361982450
8414308.2130868514-12338.070740024140954.4969137269



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')