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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Apr 2008 11:48:35 -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/Apr/15/t1208281771q0q3lnlfd7zcr2g.htm/, Retrieved Mon, 13 May 2024 14:48:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10127, Retrieved Mon, 13 May 2024 14:48:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact293
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
- R PD    [Exponential Smoothing] [steve] [2008-04-15 17:48:35] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
13328
12873
14000
13477
14237
13674
13529
14058
12975
14326
14008
16193
14483
14011
15057
14884
15414
14440
14900
15074
14442
15307
14938
17193
15528
14765
15838
15723
16150
15486
15986
15983
15692
16490
15686
18897
16316
15636
17163
16534
16518
16375
16290
16352
15943
16362
16393
19051
16747
16320
17910
16961
17480
17049
16879
17473
16998
17307
17418
20169
17871
17226
19062
17804
19100
18522
18060
18869
18127
18871
18890
21263
19547
18450
20254
19240
20216
19420
19415
20018
18652
19978
19509
21971




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10127&T=0

[TABLE]
[ROW][C]Summary of compuational 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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10127&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10127&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.440051506383271
beta0.000510357792765983
gamma0.96961246768094

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.440051506383271 \tabularnewline
beta & 0.000510357792765983 \tabularnewline
gamma & 0.96961246768094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10127&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]0.440051506383271[/C][/ROW]
[ROW][C]beta[/C][C]0.000510357792765983[/C][/ROW]
[ROW][C]gamma[/C][C]0.96961246768094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10127&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10127&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
alpha0.440051506383271
beta0.000510357792765983
gamma0.96961246768094







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131448313950.0064127244532.99358727564
141401113710.3180276631300.681972336923
151505714858.4539887854198.546011214616
161488414757.8307940623126.169205937656
171541415346.879194846867.1208051532321
181444014409.496592874930.5034071250557
191490014882.374378915417.6256210845550
201507415074.1789431871-0.178943187094774
211444214462.2002026381-20.2002026381178
221530715336.5931238976-29.5931238976209
231493814973.0809767451-35.0809767451483
241719317227.6015232390-34.6015232389509
251552815796.1793597407-268.179359740729
261476515019.3832309771-254.383230977075
271583815923.2660255571-85.2660255571136
281572315640.763094344282.2369056557509
291615016200.2974877907-50.2974877906727
301548615138.1294300757347.870569924342
311598615765.3156185356220.684381464374
321598316042.5739394614-59.5739394614156
331569215349.5587830128342.441216987201
341649016436.547282223753.4527177762684
351568616073.7925925926-387.792592592596
361889718313.7834502124583.216549787649
371631616895.9028379536-579.902837953625
381563615936.0503022295-300.050302229527
391716316983.0463333618179.953666638183
401653416889.6413325147-355.641332514726
411651817207.8578450826-689.857845082581
421637516035.9966343466339.0033656534
431629016603.8926137906-313.892613790649
441635216491.7088311064-139.708831106396
451594315964.7551711969-21.7551711968772
461636216746.0563229809-384.056322980894
471639315944.7054354089448.294564591091
481905119156.356226812-105.356226812008
491674716770.4584969015-23.4584969015123
501632016188.8764249218131.123575078169
511791017737.8757527058172.124247294203
521696117327.2676307849-366.267630784881
531748017460.009975119019.9900248809681
541704917134.9256386618-85.9256386617926
551687917158.8465352256-279.846535225559
561747317157.4450247848315.554975215218
571699816867.0219923134130.978007686579
581730717547.9730593578-240.973059357799
591741817241.1132802831176.886719716909
602016920181.7132615435-12.7132615435185
611787117740.7680291172130.231970882836
621722617274.8412128554-48.8412128553646
631906218848.1932548180213.806745181970
641780418111.7650355626-307.765035562628
651910018504.8029249480595.197075051976
661852218340.3783130128181.621686987244
671806018365.5852249802-305.585224980157
681886918703.5773108711165.422689128878
691812718200.9628220799-73.962822079895
701887118612.3533893378258.646610662221
711889018747.3054779326142.694522067351
722126321783.5634715529-520.563471552898
731954719028.8903805263518.1096194737
741845018582.0878468767-132.087846876704
752025420385.1178385464-131.117838546423
761924019132.7870737035107.212926296495
772021620265.7094088722-49.7094088721533
781942019548.1138197171-128.113819717128
791941519150.0971746055264.902825394514
802001820037.3628166547-19.3628166547314
811865219274.9496496977-622.949649697675
821997819650.4021559329327.597844067142
831950919746.2597465847-237.259746584718
842197122352.5260978328-381.526097832812

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14483 & 13950.0064127244 & 532.99358727564 \tabularnewline
14 & 14011 & 13710.3180276631 & 300.681972336923 \tabularnewline
15 & 15057 & 14858.4539887854 & 198.546011214616 \tabularnewline
16 & 14884 & 14757.8307940623 & 126.169205937656 \tabularnewline
17 & 15414 & 15346.8791948468 & 67.1208051532321 \tabularnewline
18 & 14440 & 14409.4965928749 & 30.5034071250557 \tabularnewline
19 & 14900 & 14882.3743789154 & 17.6256210845550 \tabularnewline
20 & 15074 & 15074.1789431871 & -0.178943187094774 \tabularnewline
21 & 14442 & 14462.2002026381 & -20.2002026381178 \tabularnewline
22 & 15307 & 15336.5931238976 & -29.5931238976209 \tabularnewline
23 & 14938 & 14973.0809767451 & -35.0809767451483 \tabularnewline
24 & 17193 & 17227.6015232390 & -34.6015232389509 \tabularnewline
25 & 15528 & 15796.1793597407 & -268.179359740729 \tabularnewline
26 & 14765 & 15019.3832309771 & -254.383230977075 \tabularnewline
27 & 15838 & 15923.2660255571 & -85.2660255571136 \tabularnewline
28 & 15723 & 15640.7630943442 & 82.2369056557509 \tabularnewline
29 & 16150 & 16200.2974877907 & -50.2974877906727 \tabularnewline
30 & 15486 & 15138.1294300757 & 347.870569924342 \tabularnewline
31 & 15986 & 15765.3156185356 & 220.684381464374 \tabularnewline
32 & 15983 & 16042.5739394614 & -59.5739394614156 \tabularnewline
33 & 15692 & 15349.5587830128 & 342.441216987201 \tabularnewline
34 & 16490 & 16436.5472822237 & 53.4527177762684 \tabularnewline
35 & 15686 & 16073.7925925926 & -387.792592592596 \tabularnewline
36 & 18897 & 18313.7834502124 & 583.216549787649 \tabularnewline
37 & 16316 & 16895.9028379536 & -579.902837953625 \tabularnewline
38 & 15636 & 15936.0503022295 & -300.050302229527 \tabularnewline
39 & 17163 & 16983.0463333618 & 179.953666638183 \tabularnewline
40 & 16534 & 16889.6413325147 & -355.641332514726 \tabularnewline
41 & 16518 & 17207.8578450826 & -689.857845082581 \tabularnewline
42 & 16375 & 16035.9966343466 & 339.0033656534 \tabularnewline
43 & 16290 & 16603.8926137906 & -313.892613790649 \tabularnewline
44 & 16352 & 16491.7088311064 & -139.708831106396 \tabularnewline
45 & 15943 & 15964.7551711969 & -21.7551711968772 \tabularnewline
46 & 16362 & 16746.0563229809 & -384.056322980894 \tabularnewline
47 & 16393 & 15944.7054354089 & 448.294564591091 \tabularnewline
48 & 19051 & 19156.356226812 & -105.356226812008 \tabularnewline
49 & 16747 & 16770.4584969015 & -23.4584969015123 \tabularnewline
50 & 16320 & 16188.8764249218 & 131.123575078169 \tabularnewline
51 & 17910 & 17737.8757527058 & 172.124247294203 \tabularnewline
52 & 16961 & 17327.2676307849 & -366.267630784881 \tabularnewline
53 & 17480 & 17460.0099751190 & 19.9900248809681 \tabularnewline
54 & 17049 & 17134.9256386618 & -85.9256386617926 \tabularnewline
55 & 16879 & 17158.8465352256 & -279.846535225559 \tabularnewline
56 & 17473 & 17157.4450247848 & 315.554975215218 \tabularnewline
57 & 16998 & 16867.0219923134 & 130.978007686579 \tabularnewline
58 & 17307 & 17547.9730593578 & -240.973059357799 \tabularnewline
59 & 17418 & 17241.1132802831 & 176.886719716909 \tabularnewline
60 & 20169 & 20181.7132615435 & -12.7132615435185 \tabularnewline
61 & 17871 & 17740.7680291172 & 130.231970882836 \tabularnewline
62 & 17226 & 17274.8412128554 & -48.8412128553646 \tabularnewline
63 & 19062 & 18848.1932548180 & 213.806745181970 \tabularnewline
64 & 17804 & 18111.7650355626 & -307.765035562628 \tabularnewline
65 & 19100 & 18504.8029249480 & 595.197075051976 \tabularnewline
66 & 18522 & 18340.3783130128 & 181.621686987244 \tabularnewline
67 & 18060 & 18365.5852249802 & -305.585224980157 \tabularnewline
68 & 18869 & 18703.5773108711 & 165.422689128878 \tabularnewline
69 & 18127 & 18200.9628220799 & -73.962822079895 \tabularnewline
70 & 18871 & 18612.3533893378 & 258.646610662221 \tabularnewline
71 & 18890 & 18747.3054779326 & 142.694522067351 \tabularnewline
72 & 21263 & 21783.5634715529 & -520.563471552898 \tabularnewline
73 & 19547 & 19028.8903805263 & 518.1096194737 \tabularnewline
74 & 18450 & 18582.0878468767 & -132.087846876704 \tabularnewline
75 & 20254 & 20385.1178385464 & -131.117838546423 \tabularnewline
76 & 19240 & 19132.7870737035 & 107.212926296495 \tabularnewline
77 & 20216 & 20265.7094088722 & -49.7094088721533 \tabularnewline
78 & 19420 & 19548.1138197171 & -128.113819717128 \tabularnewline
79 & 19415 & 19150.0971746055 & 264.902825394514 \tabularnewline
80 & 20018 & 20037.3628166547 & -19.3628166547314 \tabularnewline
81 & 18652 & 19274.9496496977 & -622.949649697675 \tabularnewline
82 & 19978 & 19650.4021559329 & 327.597844067142 \tabularnewline
83 & 19509 & 19746.2597465847 & -237.259746584718 \tabularnewline
84 & 21971 & 22352.5260978328 & -381.526097832812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10127&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]14483[/C][C]13950.0064127244[/C][C]532.99358727564[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]13710.3180276631[/C][C]300.681972336923[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14858.4539887854[/C][C]198.546011214616[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14757.8307940623[/C][C]126.169205937656[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]15346.8791948468[/C][C]67.1208051532321[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14409.4965928749[/C][C]30.5034071250557[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14882.3743789154[/C][C]17.6256210845550[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]15074.1789431871[/C][C]-0.178943187094774[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14462.2002026381[/C][C]-20.2002026381178[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]15336.5931238976[/C][C]-29.5931238976209[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14973.0809767451[/C][C]-35.0809767451483[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]17227.6015232390[/C][C]-34.6015232389509[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15796.1793597407[/C][C]-268.179359740729[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15019.3832309771[/C][C]-254.383230977075[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15923.2660255571[/C][C]-85.2660255571136[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15640.7630943442[/C][C]82.2369056557509[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]16200.2974877907[/C][C]-50.2974877906727[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15138.1294300757[/C][C]347.870569924342[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15765.3156185356[/C][C]220.684381464374[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]16042.5739394614[/C][C]-59.5739394614156[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15349.5587830128[/C][C]342.441216987201[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]16436.5472822237[/C][C]53.4527177762684[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]16073.7925925926[/C][C]-387.792592592596[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]18313.7834502124[/C][C]583.216549787649[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16895.9028379536[/C][C]-579.902837953625[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]15936.0503022295[/C][C]-300.050302229527[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16983.0463333618[/C][C]179.953666638183[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16889.6413325147[/C][C]-355.641332514726[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]17207.8578450826[/C][C]-689.857845082581[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16035.9966343466[/C][C]339.0033656534[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16603.8926137906[/C][C]-313.892613790649[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16491.7088311064[/C][C]-139.708831106396[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]15964.7551711969[/C][C]-21.7551711968772[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16746.0563229809[/C][C]-384.056322980894[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]15944.7054354089[/C][C]448.294564591091[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]19156.356226812[/C][C]-105.356226812008[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]16770.4584969015[/C][C]-23.4584969015123[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]16188.8764249218[/C][C]131.123575078169[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]17737.8757527058[/C][C]172.124247294203[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17327.2676307849[/C][C]-366.267630784881[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17460.0099751190[/C][C]19.9900248809681[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17134.9256386618[/C][C]-85.9256386617926[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17158.8465352256[/C][C]-279.846535225559[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17157.4450247848[/C][C]315.554975215218[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]16867.0219923134[/C][C]130.978007686579[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17547.9730593578[/C][C]-240.973059357799[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17241.1132802831[/C][C]176.886719716909[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]20181.7132615435[/C][C]-12.7132615435185[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]17740.7680291172[/C][C]130.231970882836[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]17274.8412128554[/C][C]-48.8412128553646[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]18848.1932548180[/C][C]213.806745181970[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18111.7650355626[/C][C]-307.765035562628[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18504.8029249480[/C][C]595.197075051976[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18340.3783130128[/C][C]181.621686987244[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18365.5852249802[/C][C]-305.585224980157[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18703.5773108711[/C][C]165.422689128878[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18200.9628220799[/C][C]-73.962822079895[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18612.3533893378[/C][C]258.646610662221[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18747.3054779326[/C][C]142.694522067351[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]21783.5634715529[/C][C]-520.563471552898[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19028.8903805263[/C][C]518.1096194737[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]18582.0878468767[/C][C]-132.087846876704[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]20385.1178385464[/C][C]-131.117838546423[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19132.7870737035[/C][C]107.212926296495[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]20265.7094088722[/C][C]-49.7094088721533[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19548.1138197171[/C][C]-128.113819717128[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19150.0971746055[/C][C]264.902825394514[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]20037.3628166547[/C][C]-19.3628166547314[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19274.9496496977[/C][C]-622.949649697675[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19650.4021559329[/C][C]327.597844067142[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19746.2597465847[/C][C]-237.259746584718[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]22352.5260978328[/C][C]-381.526097832812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10127&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10127&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
131448313950.0064127244532.99358727564
141401113710.3180276631300.681972336923
151505714858.4539887854198.546011214616
161488414757.8307940623126.169205937656
171541415346.879194846867.1208051532321
181444014409.496592874930.5034071250557
191490014882.374378915417.6256210845550
201507415074.1789431871-0.178943187094774
211444214462.2002026381-20.2002026381178
221530715336.5931238976-29.5931238976209
231493814973.0809767451-35.0809767451483
241719317227.6015232390-34.6015232389509
251552815796.1793597407-268.179359740729
261476515019.3832309771-254.383230977075
271583815923.2660255571-85.2660255571136
281572315640.763094344282.2369056557509
291615016200.2974877907-50.2974877906727
301548615138.1294300757347.870569924342
311598615765.3156185356220.684381464374
321598316042.5739394614-59.5739394614156
331569215349.5587830128342.441216987201
341649016436.547282223753.4527177762684
351568616073.7925925926-387.792592592596
361889718313.7834502124583.216549787649
371631616895.9028379536-579.902837953625
381563615936.0503022295-300.050302229527
391716316983.0463333618179.953666638183
401653416889.6413325147-355.641332514726
411651817207.8578450826-689.857845082581
421637516035.9966343466339.0033656534
431629016603.8926137906-313.892613790649
441635216491.7088311064-139.708831106396
451594315964.7551711969-21.7551711968772
461636216746.0563229809-384.056322980894
471639315944.7054354089448.294564591091
481905119156.356226812-105.356226812008
491674716770.4584969015-23.4584969015123
501632016188.8764249218131.123575078169
511791017737.8757527058172.124247294203
521696117327.2676307849-366.267630784881
531748017460.009975119019.9900248809681
541704917134.9256386618-85.9256386617926
551687917158.8465352256-279.846535225559
561747317157.4450247848315.554975215218
571699816867.0219923134130.978007686579
581730717547.9730593578-240.973059357799
591741817241.1132802831176.886719716909
602016920181.7132615435-12.7132615435185
611787117740.7680291172130.231970882836
621722617274.8412128554-48.8412128553646
631906218848.1932548180213.806745181970
641780418111.7650355626-307.765035562628
651910018504.8029249480595.197075051976
661852218340.3783130128181.621686987244
671806018365.5852249802-305.585224980157
681886918703.5773108711165.422689128878
691812718200.9628220799-73.962822079895
701887118612.3533893378258.646610662221
711889018747.3054779326142.694522067351
722126321783.5634715529-520.563471552898
731954719028.8903805263518.1096194737
741845018582.0878468767-132.087846876704
752025420385.1178385464-131.117838546423
761924019132.7870737035107.212926296495
772021620265.7094088722-49.7094088721533
781942019548.1138197171-128.113819717128
791941519150.0971746055264.902825394514
802001820037.3628166547-19.3628166547314
811865219274.9496496977-622.949649697675
821997819650.4021559329327.597844067142
831950919746.2597465847-237.259746584718
842197122352.5260978328-381.526097832812







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520131.543851707219588.764074227120674.3236291872
8619069.624411246818480.392591081919658.8562314118
8720990.227487978720335.357782441721645.0971935157
8819883.062559206019199.857931331020566.2671870810
8920913.994213540820173.362229942421654.6261971393
9020146.972887516419383.476170342620910.4696046901
9120009.788200345819213.063017879620806.5133828120
9220642.330661550519795.935049378421488.7262737226
9319519.289666735118669.910167723020368.6691657471
9420733.159856054819817.256158960921649.0635531486
9520360.655569500819426.686977071021294.6241619306
9623101.553534085222199.36634409224003.7407240785

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20131.5438517072 & 19588.7640742271 & 20674.3236291872 \tabularnewline
86 & 19069.6244112468 & 18480.3925910819 & 19658.8562314118 \tabularnewline
87 & 20990.2274879787 & 20335.3577824417 & 21645.0971935157 \tabularnewline
88 & 19883.0625592060 & 19199.8579313310 & 20566.2671870810 \tabularnewline
89 & 20913.9942135408 & 20173.3622299424 & 21654.6261971393 \tabularnewline
90 & 20146.9728875164 & 19383.4761703426 & 20910.4696046901 \tabularnewline
91 & 20009.7882003458 & 19213.0630178796 & 20806.5133828120 \tabularnewline
92 & 20642.3306615505 & 19795.9350493784 & 21488.7262737226 \tabularnewline
93 & 19519.2896667351 & 18669.9101677230 & 20368.6691657471 \tabularnewline
94 & 20733.1598560548 & 19817.2561589609 & 21649.0635531486 \tabularnewline
95 & 20360.6555695008 & 19426.6869770710 & 21294.6241619306 \tabularnewline
96 & 23101.5535340852 & 22199.366344092 & 24003.7407240785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10127&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]85[/C][C]20131.5438517072[/C][C]19588.7640742271[/C][C]20674.3236291872[/C][/ROW]
[ROW][C]86[/C][C]19069.6244112468[/C][C]18480.3925910819[/C][C]19658.8562314118[/C][/ROW]
[ROW][C]87[/C][C]20990.2274879787[/C][C]20335.3577824417[/C][C]21645.0971935157[/C][/ROW]
[ROW][C]88[/C][C]19883.0625592060[/C][C]19199.8579313310[/C][C]20566.2671870810[/C][/ROW]
[ROW][C]89[/C][C]20913.9942135408[/C][C]20173.3622299424[/C][C]21654.6261971393[/C][/ROW]
[ROW][C]90[/C][C]20146.9728875164[/C][C]19383.4761703426[/C][C]20910.4696046901[/C][/ROW]
[ROW][C]91[/C][C]20009.7882003458[/C][C]19213.0630178796[/C][C]20806.5133828120[/C][/ROW]
[ROW][C]92[/C][C]20642.3306615505[/C][C]19795.9350493784[/C][C]21488.7262737226[/C][/ROW]
[ROW][C]93[/C][C]19519.2896667351[/C][C]18669.9101677230[/C][C]20368.6691657471[/C][/ROW]
[ROW][C]94[/C][C]20733.1598560548[/C][C]19817.2561589609[/C][C]21649.0635531486[/C][/ROW]
[ROW][C]95[/C][C]20360.6555695008[/C][C]19426.6869770710[/C][C]21294.6241619306[/C][/ROW]
[ROW][C]96[/C][C]23101.5535340852[/C][C]22199.366344092[/C][C]24003.7407240785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10127&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10127&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
8520131.543851707219588.764074227120674.3236291872
8619069.624411246818480.392591081919658.8562314118
8720990.227487978720335.357782441721645.0971935157
8819883.062559206019199.857931331020566.2671870810
8920913.994213540820173.362229942421654.6261971393
9020146.972887516419383.476170342620910.4696046901
9120009.788200345819213.063017879620806.5133828120
9220642.330661550519795.935049378421488.7262737226
9319519.289666735118669.910167723020368.6691657471
9420733.159856054819817.256158960921649.0635531486
9520360.655569500819426.686977071021294.6241619306
9623101.553534085222199.36634409224003.7407240785



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=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()

bitmap(file="myhist.png")
hist(myresid)
grid()
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')