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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 Dec 2011 09:04:00 -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/2011/Dec/27/t13249947062tjzbp39p92bwb6.htm/, Retrieved Fri, 31 May 2024 16:16:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160853, Retrieved Fri, 31 May 2024 16:16:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [Standard deviatio...] [2011-12-07 16:21:53] [102faec22d2a25d9aaa52ca244269a51]
- RMPD    [Exponential Smoothing] [Goudkoers te Brus...] [2011-12-27 14:04:00] [b7d89a59d057204a66389ee14552eeec] [Current]
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Dataseries X:
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160853&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160853&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0405366126959024
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0405366126959024 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160853&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]0.0405366126959024[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160853&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
beta0.0405366126959024
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3105561051937
41064610613.499854669732.5001453302521
51070210704.8173004736-2.81730047356177
61135310760.7030966554592.296903344584
71134611435.7128068273-89.7128068272777
81145111425.076153523125.9238464769405
91196411531.1270184473432.872981552717
101257412061.674222847512.325777152995
111303112692.4421744496338.557825550417
121381213163.1661618991648.833838100913
131454413970.4676878982573.532312101819
141493114725.7167451024205.283254897562
151488615121.0382328992-235.038232899175
161600515066.5105790834938.489420916589
171706416223.5537612583840.446238741692
181516817316.6226049299-2148.62260492991
191605015333.5247225642716.475277435797
201583916244.5682033918-405.568203391807
211513716017.1278422091-880.12784220914
221495415279.4504407466-325.450440746628
231564815083.2577822784564.742217721629
241530515800.1505188312-495.150518831178
251557915437.0787940231141.921205976856
261634815716.8317989832631.168201016837
271592816511.4172198938-583.417219893752
281617116067.7674620108103.232537989201
291593716314.9521594209-377.952159420882
301571316065.6312591169-352.631259116857
311559415827.3367823416-233.33678234157
321568315698.8780995681-15.8780995680809
331643815787.2344551955650.765544804457
341703216568.6142860411463.38571395888
351769617181.3983732567514.601626743315
361774517866.2585800927-121.258580092661
371939417910.34316799541483.65683200461
382014819619.485590368528.514409632011
392010820394.9097742954-286.909774295444
401858420343.2794238962-1759.27942389616
411844118747.9641952658-306.964195265813
421839118592.5209065708-201.520906570815
431917818534.351931631643.648068368973
441807919347.443244091-1268.44324409096
451848318197.0248515785285.975148421487
461964418612.61731541071031.38268458927
471919519815.4260758372-620.426075837186
481965019341.2761042945308.723895705465
492083019808.79072528471021.20927471528
502359521030.18709013532564.81290986469
512293723899.1559176999-962.155917699947
522181423202.1533759111-1388.15337591108
532192822022.8823401493-94.8823401492591
542177722133.0361314749-356.036131474946
552138321967.6036327076-584.6036327076
562146721549.9057816679-82.905781667916
572205221630.5450621062421.45493789381
582268022232.6294176924447.370582307631
592432022878.76430571891441.23569428109
602497724577.1871188615399.812881138503
612520425250.394178775-46.3941787750409
622573925475.5135159187263.48648408131
632643426021.1943654745412.805634525499
642752526732.9281075999792.071892400054
653069527856.03601912952838.96398087052
663243631141.11800247961294.88199752036
673016032934.6081325-2774.60813250002
683023630546.13491725-310.134917249969
693129330609.5630982259683.436901774068
703107731694.2673152152-617.267315215235
713222631453.2453891285772.754610871485
723386532633.57024349841231.42975650162

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 10556 & 10519 & 37 \tabularnewline
4 & 10646 & 10613.4998546697 & 32.5001453302521 \tabularnewline
5 & 10702 & 10704.8173004736 & -2.81730047356177 \tabularnewline
6 & 11353 & 10760.7030966554 & 592.296903344584 \tabularnewline
7 & 11346 & 11435.7128068273 & -89.7128068272777 \tabularnewline
8 & 11451 & 11425.0761535231 & 25.9238464769405 \tabularnewline
9 & 11964 & 11531.1270184473 & 432.872981552717 \tabularnewline
10 & 12574 & 12061.674222847 & 512.325777152995 \tabularnewline
11 & 13031 & 12692.4421744496 & 338.557825550417 \tabularnewline
12 & 13812 & 13163.1661618991 & 648.833838100913 \tabularnewline
13 & 14544 & 13970.4676878982 & 573.532312101819 \tabularnewline
14 & 14931 & 14725.7167451024 & 205.283254897562 \tabularnewline
15 & 14886 & 15121.0382328992 & -235.038232899175 \tabularnewline
16 & 16005 & 15066.5105790834 & 938.489420916589 \tabularnewline
17 & 17064 & 16223.5537612583 & 840.446238741692 \tabularnewline
18 & 15168 & 17316.6226049299 & -2148.62260492991 \tabularnewline
19 & 16050 & 15333.5247225642 & 716.475277435797 \tabularnewline
20 & 15839 & 16244.5682033918 & -405.568203391807 \tabularnewline
21 & 15137 & 16017.1278422091 & -880.12784220914 \tabularnewline
22 & 14954 & 15279.4504407466 & -325.450440746628 \tabularnewline
23 & 15648 & 15083.2577822784 & 564.742217721629 \tabularnewline
24 & 15305 & 15800.1505188312 & -495.150518831178 \tabularnewline
25 & 15579 & 15437.0787940231 & 141.921205976856 \tabularnewline
26 & 16348 & 15716.8317989832 & 631.168201016837 \tabularnewline
27 & 15928 & 16511.4172198938 & -583.417219893752 \tabularnewline
28 & 16171 & 16067.7674620108 & 103.232537989201 \tabularnewline
29 & 15937 & 16314.9521594209 & -377.952159420882 \tabularnewline
30 & 15713 & 16065.6312591169 & -352.631259116857 \tabularnewline
31 & 15594 & 15827.3367823416 & -233.33678234157 \tabularnewline
32 & 15683 & 15698.8780995681 & -15.8780995680809 \tabularnewline
33 & 16438 & 15787.2344551955 & 650.765544804457 \tabularnewline
34 & 17032 & 16568.6142860411 & 463.38571395888 \tabularnewline
35 & 17696 & 17181.3983732567 & 514.601626743315 \tabularnewline
36 & 17745 & 17866.2585800927 & -121.258580092661 \tabularnewline
37 & 19394 & 17910.3431679954 & 1483.65683200461 \tabularnewline
38 & 20148 & 19619.485590368 & 528.514409632011 \tabularnewline
39 & 20108 & 20394.9097742954 & -286.909774295444 \tabularnewline
40 & 18584 & 20343.2794238962 & -1759.27942389616 \tabularnewline
41 & 18441 & 18747.9641952658 & -306.964195265813 \tabularnewline
42 & 18391 & 18592.5209065708 & -201.520906570815 \tabularnewline
43 & 19178 & 18534.351931631 & 643.648068368973 \tabularnewline
44 & 18079 & 19347.443244091 & -1268.44324409096 \tabularnewline
45 & 18483 & 18197.0248515785 & 285.975148421487 \tabularnewline
46 & 19644 & 18612.6173154107 & 1031.38268458927 \tabularnewline
47 & 19195 & 19815.4260758372 & -620.426075837186 \tabularnewline
48 & 19650 & 19341.2761042945 & 308.723895705465 \tabularnewline
49 & 20830 & 19808.7907252847 & 1021.20927471528 \tabularnewline
50 & 23595 & 21030.1870901353 & 2564.81290986469 \tabularnewline
51 & 22937 & 23899.1559176999 & -962.155917699947 \tabularnewline
52 & 21814 & 23202.1533759111 & -1388.15337591108 \tabularnewline
53 & 21928 & 22022.8823401493 & -94.8823401492591 \tabularnewline
54 & 21777 & 22133.0361314749 & -356.036131474946 \tabularnewline
55 & 21383 & 21967.6036327076 & -584.6036327076 \tabularnewline
56 & 21467 & 21549.9057816679 & -82.905781667916 \tabularnewline
57 & 22052 & 21630.5450621062 & 421.45493789381 \tabularnewline
58 & 22680 & 22232.6294176924 & 447.370582307631 \tabularnewline
59 & 24320 & 22878.7643057189 & 1441.23569428109 \tabularnewline
60 & 24977 & 24577.1871188615 & 399.812881138503 \tabularnewline
61 & 25204 & 25250.394178775 & -46.3941787750409 \tabularnewline
62 & 25739 & 25475.5135159187 & 263.48648408131 \tabularnewline
63 & 26434 & 26021.1943654745 & 412.805634525499 \tabularnewline
64 & 27525 & 26732.9281075999 & 792.071892400054 \tabularnewline
65 & 30695 & 27856.0360191295 & 2838.96398087052 \tabularnewline
66 & 32436 & 31141.1180024796 & 1294.88199752036 \tabularnewline
67 & 30160 & 32934.6081325 & -2774.60813250002 \tabularnewline
68 & 30236 & 30546.13491725 & -310.134917249969 \tabularnewline
69 & 31293 & 30609.5630982259 & 683.436901774068 \tabularnewline
70 & 31077 & 31694.2673152152 & -617.267315215235 \tabularnewline
71 & 32226 & 31453.2453891285 & 772.754610871485 \tabularnewline
72 & 33865 & 32633.5702434984 & 1231.42975650162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160853&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]3[/C][C]10556[/C][C]10519[/C][C]37[/C][/ROW]
[ROW][C]4[/C][C]10646[/C][C]10613.4998546697[/C][C]32.5001453302521[/C][/ROW]
[ROW][C]5[/C][C]10702[/C][C]10704.8173004736[/C][C]-2.81730047356177[/C][/ROW]
[ROW][C]6[/C][C]11353[/C][C]10760.7030966554[/C][C]592.296903344584[/C][/ROW]
[ROW][C]7[/C][C]11346[/C][C]11435.7128068273[/C][C]-89.7128068272777[/C][/ROW]
[ROW][C]8[/C][C]11451[/C][C]11425.0761535231[/C][C]25.9238464769405[/C][/ROW]
[ROW][C]9[/C][C]11964[/C][C]11531.1270184473[/C][C]432.872981552717[/C][/ROW]
[ROW][C]10[/C][C]12574[/C][C]12061.674222847[/C][C]512.325777152995[/C][/ROW]
[ROW][C]11[/C][C]13031[/C][C]12692.4421744496[/C][C]338.557825550417[/C][/ROW]
[ROW][C]12[/C][C]13812[/C][C]13163.1661618991[/C][C]648.833838100913[/C][/ROW]
[ROW][C]13[/C][C]14544[/C][C]13970.4676878982[/C][C]573.532312101819[/C][/ROW]
[ROW][C]14[/C][C]14931[/C][C]14725.7167451024[/C][C]205.283254897562[/C][/ROW]
[ROW][C]15[/C][C]14886[/C][C]15121.0382328992[/C][C]-235.038232899175[/C][/ROW]
[ROW][C]16[/C][C]16005[/C][C]15066.5105790834[/C][C]938.489420916589[/C][/ROW]
[ROW][C]17[/C][C]17064[/C][C]16223.5537612583[/C][C]840.446238741692[/C][/ROW]
[ROW][C]18[/C][C]15168[/C][C]17316.6226049299[/C][C]-2148.62260492991[/C][/ROW]
[ROW][C]19[/C][C]16050[/C][C]15333.5247225642[/C][C]716.475277435797[/C][/ROW]
[ROW][C]20[/C][C]15839[/C][C]16244.5682033918[/C][C]-405.568203391807[/C][/ROW]
[ROW][C]21[/C][C]15137[/C][C]16017.1278422091[/C][C]-880.12784220914[/C][/ROW]
[ROW][C]22[/C][C]14954[/C][C]15279.4504407466[/C][C]-325.450440746628[/C][/ROW]
[ROW][C]23[/C][C]15648[/C][C]15083.2577822784[/C][C]564.742217721629[/C][/ROW]
[ROW][C]24[/C][C]15305[/C][C]15800.1505188312[/C][C]-495.150518831178[/C][/ROW]
[ROW][C]25[/C][C]15579[/C][C]15437.0787940231[/C][C]141.921205976856[/C][/ROW]
[ROW][C]26[/C][C]16348[/C][C]15716.8317989832[/C][C]631.168201016837[/C][/ROW]
[ROW][C]27[/C][C]15928[/C][C]16511.4172198938[/C][C]-583.417219893752[/C][/ROW]
[ROW][C]28[/C][C]16171[/C][C]16067.7674620108[/C][C]103.232537989201[/C][/ROW]
[ROW][C]29[/C][C]15937[/C][C]16314.9521594209[/C][C]-377.952159420882[/C][/ROW]
[ROW][C]30[/C][C]15713[/C][C]16065.6312591169[/C][C]-352.631259116857[/C][/ROW]
[ROW][C]31[/C][C]15594[/C][C]15827.3367823416[/C][C]-233.33678234157[/C][/ROW]
[ROW][C]32[/C][C]15683[/C][C]15698.8780995681[/C][C]-15.8780995680809[/C][/ROW]
[ROW][C]33[/C][C]16438[/C][C]15787.2344551955[/C][C]650.765544804457[/C][/ROW]
[ROW][C]34[/C][C]17032[/C][C]16568.6142860411[/C][C]463.38571395888[/C][/ROW]
[ROW][C]35[/C][C]17696[/C][C]17181.3983732567[/C][C]514.601626743315[/C][/ROW]
[ROW][C]36[/C][C]17745[/C][C]17866.2585800927[/C][C]-121.258580092661[/C][/ROW]
[ROW][C]37[/C][C]19394[/C][C]17910.3431679954[/C][C]1483.65683200461[/C][/ROW]
[ROW][C]38[/C][C]20148[/C][C]19619.485590368[/C][C]528.514409632011[/C][/ROW]
[ROW][C]39[/C][C]20108[/C][C]20394.9097742954[/C][C]-286.909774295444[/C][/ROW]
[ROW][C]40[/C][C]18584[/C][C]20343.2794238962[/C][C]-1759.27942389616[/C][/ROW]
[ROW][C]41[/C][C]18441[/C][C]18747.9641952658[/C][C]-306.964195265813[/C][/ROW]
[ROW][C]42[/C][C]18391[/C][C]18592.5209065708[/C][C]-201.520906570815[/C][/ROW]
[ROW][C]43[/C][C]19178[/C][C]18534.351931631[/C][C]643.648068368973[/C][/ROW]
[ROW][C]44[/C][C]18079[/C][C]19347.443244091[/C][C]-1268.44324409096[/C][/ROW]
[ROW][C]45[/C][C]18483[/C][C]18197.0248515785[/C][C]285.975148421487[/C][/ROW]
[ROW][C]46[/C][C]19644[/C][C]18612.6173154107[/C][C]1031.38268458927[/C][/ROW]
[ROW][C]47[/C][C]19195[/C][C]19815.4260758372[/C][C]-620.426075837186[/C][/ROW]
[ROW][C]48[/C][C]19650[/C][C]19341.2761042945[/C][C]308.723895705465[/C][/ROW]
[ROW][C]49[/C][C]20830[/C][C]19808.7907252847[/C][C]1021.20927471528[/C][/ROW]
[ROW][C]50[/C][C]23595[/C][C]21030.1870901353[/C][C]2564.81290986469[/C][/ROW]
[ROW][C]51[/C][C]22937[/C][C]23899.1559176999[/C][C]-962.155917699947[/C][/ROW]
[ROW][C]52[/C][C]21814[/C][C]23202.1533759111[/C][C]-1388.15337591108[/C][/ROW]
[ROW][C]53[/C][C]21928[/C][C]22022.8823401493[/C][C]-94.8823401492591[/C][/ROW]
[ROW][C]54[/C][C]21777[/C][C]22133.0361314749[/C][C]-356.036131474946[/C][/ROW]
[ROW][C]55[/C][C]21383[/C][C]21967.6036327076[/C][C]-584.6036327076[/C][/ROW]
[ROW][C]56[/C][C]21467[/C][C]21549.9057816679[/C][C]-82.905781667916[/C][/ROW]
[ROW][C]57[/C][C]22052[/C][C]21630.5450621062[/C][C]421.45493789381[/C][/ROW]
[ROW][C]58[/C][C]22680[/C][C]22232.6294176924[/C][C]447.370582307631[/C][/ROW]
[ROW][C]59[/C][C]24320[/C][C]22878.7643057189[/C][C]1441.23569428109[/C][/ROW]
[ROW][C]60[/C][C]24977[/C][C]24577.1871188615[/C][C]399.812881138503[/C][/ROW]
[ROW][C]61[/C][C]25204[/C][C]25250.394178775[/C][C]-46.3941787750409[/C][/ROW]
[ROW][C]62[/C][C]25739[/C][C]25475.5135159187[/C][C]263.48648408131[/C][/ROW]
[ROW][C]63[/C][C]26434[/C][C]26021.1943654745[/C][C]412.805634525499[/C][/ROW]
[ROW][C]64[/C][C]27525[/C][C]26732.9281075999[/C][C]792.071892400054[/C][/ROW]
[ROW][C]65[/C][C]30695[/C][C]27856.0360191295[/C][C]2838.96398087052[/C][/ROW]
[ROW][C]66[/C][C]32436[/C][C]31141.1180024796[/C][C]1294.88199752036[/C][/ROW]
[ROW][C]67[/C][C]30160[/C][C]32934.6081325[/C][C]-2774.60813250002[/C][/ROW]
[ROW][C]68[/C][C]30236[/C][C]30546.13491725[/C][C]-310.134917249969[/C][/ROW]
[ROW][C]69[/C][C]31293[/C][C]30609.5630982259[/C][C]683.436901774068[/C][/ROW]
[ROW][C]70[/C][C]31077[/C][C]31694.2673152152[/C][C]-617.267315215235[/C][/ROW]
[ROW][C]71[/C][C]32226[/C][C]31453.2453891285[/C][C]772.754610871485[/C][/ROW]
[ROW][C]72[/C][C]33865[/C][C]32633.5702434984[/C][C]1231.42975650162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160853&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
3105561051937
41064610613.499854669732.5001453302521
51070210704.8173004736-2.81730047356177
61135310760.7030966554592.296903344584
71134611435.7128068273-89.7128068272777
81145111425.076153523125.9238464769405
91196411531.1270184473432.872981552717
101257412061.674222847512.325777152995
111303112692.4421744496338.557825550417
121381213163.1661618991648.833838100913
131454413970.4676878982573.532312101819
141493114725.7167451024205.283254897562
151488615121.0382328992-235.038232899175
161600515066.5105790834938.489420916589
171706416223.5537612583840.446238741692
181516817316.6226049299-2148.62260492991
191605015333.5247225642716.475277435797
201583916244.5682033918-405.568203391807
211513716017.1278422091-880.12784220914
221495415279.4504407466-325.450440746628
231564815083.2577822784564.742217721629
241530515800.1505188312-495.150518831178
251557915437.0787940231141.921205976856
261634815716.8317989832631.168201016837
271592816511.4172198938-583.417219893752
281617116067.7674620108103.232537989201
291593716314.9521594209-377.952159420882
301571316065.6312591169-352.631259116857
311559415827.3367823416-233.33678234157
321568315698.8780995681-15.8780995680809
331643815787.2344551955650.765544804457
341703216568.6142860411463.38571395888
351769617181.3983732567514.601626743315
361774517866.2585800927-121.258580092661
371939417910.34316799541483.65683200461
382014819619.485590368528.514409632011
392010820394.9097742954-286.909774295444
401858420343.2794238962-1759.27942389616
411844118747.9641952658-306.964195265813
421839118592.5209065708-201.520906570815
431917818534.351931631643.648068368973
441807919347.443244091-1268.44324409096
451848318197.0248515785285.975148421487
461964418612.61731541071031.38268458927
471919519815.4260758372-620.426075837186
481965019341.2761042945308.723895705465
492083019808.79072528471021.20927471528
502359521030.18709013532564.81290986469
512293723899.1559176999-962.155917699947
522181423202.1533759111-1388.15337591108
532192822022.8823401493-94.8823401492591
542177722133.0361314749-356.036131474946
552138321967.6036327076-584.6036327076
562146721549.9057816679-82.905781667916
572205221630.5450621062421.45493789381
582268022232.6294176924447.370582307631
592432022878.76430571891441.23569428109
602497724577.1871188615399.812881138503
612520425250.394178775-46.3941787750409
622573925475.5135159187263.48648408131
632643426021.1943654745412.805634525499
642752526732.9281075999792.071892400054
653069527856.03601912952838.96398087052
663243631141.11800247961294.88199752036
673016032934.6081325-2774.60813250002
683023630546.13491725-310.134917249969
693129330609.5630982259683.436901774068
703107731694.2673152152-617.267315215235
713222631453.2453891285772.754610871485
723386532633.57024349841231.42975650162







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7334322.488234599932571.275759306936073.7007098929
7434779.976469199832252.693241240737307.2596971589
7535237.464703799732079.724246227138395.2051613723
7635694.952938399631976.174020783139413.7318560161
7736152.441172999531913.194224334740391.6881216643
7836609.929407599431876.315818211241343.5429969876
7937067.417642199331857.135110606242277.7001737924
8037524.905876799231850.301689439443199.510064159
8137982.394111399131852.186762421744112.6014603765
8238439.88234599931860.212818653845019.5518733442
8338897.370580598931872.483522336545922.2576388613
8439354.858815198831887.564655093346822.1529753043

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 34322.4882345999 & 32571.2757593069 & 36073.7007098929 \tabularnewline
74 & 34779.9764691998 & 32252.6932412407 & 37307.2596971589 \tabularnewline
75 & 35237.4647037997 & 32079.7242462271 & 38395.2051613723 \tabularnewline
76 & 35694.9529383996 & 31976.1740207831 & 39413.7318560161 \tabularnewline
77 & 36152.4411729995 & 31913.1942243347 & 40391.6881216643 \tabularnewline
78 & 36609.9294075994 & 31876.3158182112 & 41343.5429969876 \tabularnewline
79 & 37067.4176421993 & 31857.1351106062 & 42277.7001737924 \tabularnewline
80 & 37524.9058767992 & 31850.3016894394 & 43199.510064159 \tabularnewline
81 & 37982.3941113991 & 31852.1867624217 & 44112.6014603765 \tabularnewline
82 & 38439.882345999 & 31860.2128186538 & 45019.5518733442 \tabularnewline
83 & 38897.3705805989 & 31872.4835223365 & 45922.2576388613 \tabularnewline
84 & 39354.8588151988 & 31887.5646550933 & 46822.1529753043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160853&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]34322.4882345999[/C][C]32571.2757593069[/C][C]36073.7007098929[/C][/ROW]
[ROW][C]74[/C][C]34779.9764691998[/C][C]32252.6932412407[/C][C]37307.2596971589[/C][/ROW]
[ROW][C]75[/C][C]35237.4647037997[/C][C]32079.7242462271[/C][C]38395.2051613723[/C][/ROW]
[ROW][C]76[/C][C]35694.9529383996[/C][C]31976.1740207831[/C][C]39413.7318560161[/C][/ROW]
[ROW][C]77[/C][C]36152.4411729995[/C][C]31913.1942243347[/C][C]40391.6881216643[/C][/ROW]
[ROW][C]78[/C][C]36609.9294075994[/C][C]31876.3158182112[/C][C]41343.5429969876[/C][/ROW]
[ROW][C]79[/C][C]37067.4176421993[/C][C]31857.1351106062[/C][C]42277.7001737924[/C][/ROW]
[ROW][C]80[/C][C]37524.9058767992[/C][C]31850.3016894394[/C][C]43199.510064159[/C][/ROW]
[ROW][C]81[/C][C]37982.3941113991[/C][C]31852.1867624217[/C][C]44112.6014603765[/C][/ROW]
[ROW][C]82[/C][C]38439.882345999[/C][C]31860.2128186538[/C][C]45019.5518733442[/C][/ROW]
[ROW][C]83[/C][C]38897.3705805989[/C][C]31872.4835223365[/C][C]45922.2576388613[/C][/ROW]
[ROW][C]84[/C][C]39354.8588151988[/C][C]31887.5646550933[/C][C]46822.1529753043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160853&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160853&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
7334322.488234599932571.275759306936073.7007098929
7434779.976469199832252.693241240737307.2596971589
7535237.464703799732079.724246227138395.2051613723
7635694.952938399631976.174020783139413.7318560161
7736152.441172999531913.194224334740391.6881216643
7836609.929407599431876.315818211241343.5429969876
7937067.417642199331857.135110606242277.7001737924
8037524.905876799231850.301689439443199.510064159
8137982.394111399131852.186762421744112.6014603765
8238439.88234599931860.212818653845019.5518733442
8338897.370580598931872.483522336545922.2576388613
8439354.858815198831887.564655093346822.1529753043



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')