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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Nov 2013 15:12:12 -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/2013/Nov/25/t1385410384uq6du7hlhcb91ah.htm/, Retrieved Mon, 29 Apr 2024 22:17:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=228434, Retrieved Mon, 29 Apr 2024 22:17:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD    [Exponential Smoothing] [WS8: Smoothing Mu...] [2013-11-25 20:12:12] [0d4b5c001fcd12491258e86d922016e4] [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





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=228434&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=228434&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228434&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.290822481652029
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.290822481652029 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228434&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]0.290822481652029[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228434&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228434&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
alpha0.290822481652029
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21287313328-455
31400013195.6757708483804.324229151673
41347713429.591339223147.4086607769277
51423713443.378843602793.621156397983
61367413674.1817177972-0.181717797231613
71352913674.1288701765-145.128870176481
81405813631.9221319924426.077868007598
91297513755.8351549434-780.835154943377
101432613528.7507374216797.249262578402
111400813760.6087464599247.391253540101
121619313832.55568475342360.44431524656
131448314519.0259583149-36.0259583148654
141401114508.5487997138-497.548799713844
151505714363.8504230381693.149576961923
161488414565.4339031662318.566096833803
171541414658.0800860176755.919913982396
181444014877.9185913322-437.918591332153
191490014750.5620198394149.437980160625
201507414794.0219440828279.978055917245
211444214875.4458571127-433.445857112718
221530714749.3900572854557.609942714593
231493814911.555564619526.4444353804902
241719314919.24620094282273.75379905725
251552815580.5049234503-52.5049234503076
261476515565.2353113135-800.23531131354
271583815332.5088921718505.491107828248
281572315479.5170706034243.482929396603
291615015550.3273803704599.672619629577
301548615724.7256597899-238.72565978987
311598615655.2988709758330.701129024237
321598315751.4741940037231.525805996282
331569215818.80710347-126.807103470042
341649015781.9287469478708.071253052221
351568615987.8517859469-301.851785946887
361889715900.06650046672996.93349953328
371631616771.6421381471-455.642138147083
381563616639.1311607859-1003.13116078591
391716316347.3980671837815.601932816326
401653416584.5934453255-50.5934453255104
411651816569.8797340006-51.8797340006204
421637516554.7919410111-179.791941011114
431629016502.5044025452-212.504402545226
441635216440.703344835-88.7033448350412
451594316414.9064179593-471.906417959279
461636216277.665422380884.3345776191582
471639316302.191813533190.8081864668784
481905116328.60087567572722.39912432426
491674717120.335745059-373.33574505903
501632017011.7613171916-691.761317191555
511791016810.5815742151099.41842578497
521696117130.3171691758-169.317169175782
531748017081.0759298498398.924070150217
541704917197.0920179216-148.092017921597
551687917154.0235297568-275.023529756781
561747317074.0405043202398.959495679785
571699817190.0668949325-192.066894932454
581730717134.209523905172.790476095
591741817184.4608789688233.539121031215
602016917252.37930570992916.62069429008
611787118100.598174061-229.598174061022
621722618033.8258632978-807.825863297821
631906217798.89194099091263.10805900914
641780418166.2321613066-362.232161306572
651910018060.88690522121039.11309477878
661852218363.0843541619158.915645838097
671806018409.3005966579-349.300596657875
681886918307.7161302953561.283869704701
691812718470.9500981941-343.950098194073
701887118370.9216770728500.078322927187
711889018516.3556959669373.644304033118
722126318625.01985972092637.98014027906

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 12873 & 13328 & -455 \tabularnewline
3 & 14000 & 13195.6757708483 & 804.324229151673 \tabularnewline
4 & 13477 & 13429.5913392231 & 47.4086607769277 \tabularnewline
5 & 14237 & 13443.378843602 & 793.621156397983 \tabularnewline
6 & 13674 & 13674.1817177972 & -0.181717797231613 \tabularnewline
7 & 13529 & 13674.1288701765 & -145.128870176481 \tabularnewline
8 & 14058 & 13631.9221319924 & 426.077868007598 \tabularnewline
9 & 12975 & 13755.8351549434 & -780.835154943377 \tabularnewline
10 & 14326 & 13528.7507374216 & 797.249262578402 \tabularnewline
11 & 14008 & 13760.6087464599 & 247.391253540101 \tabularnewline
12 & 16193 & 13832.5556847534 & 2360.44431524656 \tabularnewline
13 & 14483 & 14519.0259583149 & -36.0259583148654 \tabularnewline
14 & 14011 & 14508.5487997138 & -497.548799713844 \tabularnewline
15 & 15057 & 14363.8504230381 & 693.149576961923 \tabularnewline
16 & 14884 & 14565.4339031662 & 318.566096833803 \tabularnewline
17 & 15414 & 14658.0800860176 & 755.919913982396 \tabularnewline
18 & 14440 & 14877.9185913322 & -437.918591332153 \tabularnewline
19 & 14900 & 14750.5620198394 & 149.437980160625 \tabularnewline
20 & 15074 & 14794.0219440828 & 279.978055917245 \tabularnewline
21 & 14442 & 14875.4458571127 & -433.445857112718 \tabularnewline
22 & 15307 & 14749.3900572854 & 557.609942714593 \tabularnewline
23 & 14938 & 14911.5555646195 & 26.4444353804902 \tabularnewline
24 & 17193 & 14919.2462009428 & 2273.75379905725 \tabularnewline
25 & 15528 & 15580.5049234503 & -52.5049234503076 \tabularnewline
26 & 14765 & 15565.2353113135 & -800.23531131354 \tabularnewline
27 & 15838 & 15332.5088921718 & 505.491107828248 \tabularnewline
28 & 15723 & 15479.5170706034 & 243.482929396603 \tabularnewline
29 & 16150 & 15550.3273803704 & 599.672619629577 \tabularnewline
30 & 15486 & 15724.7256597899 & -238.72565978987 \tabularnewline
31 & 15986 & 15655.2988709758 & 330.701129024237 \tabularnewline
32 & 15983 & 15751.4741940037 & 231.525805996282 \tabularnewline
33 & 15692 & 15818.80710347 & -126.807103470042 \tabularnewline
34 & 16490 & 15781.9287469478 & 708.071253052221 \tabularnewline
35 & 15686 & 15987.8517859469 & -301.851785946887 \tabularnewline
36 & 18897 & 15900.0665004667 & 2996.93349953328 \tabularnewline
37 & 16316 & 16771.6421381471 & -455.642138147083 \tabularnewline
38 & 15636 & 16639.1311607859 & -1003.13116078591 \tabularnewline
39 & 17163 & 16347.3980671837 & 815.601932816326 \tabularnewline
40 & 16534 & 16584.5934453255 & -50.5934453255104 \tabularnewline
41 & 16518 & 16569.8797340006 & -51.8797340006204 \tabularnewline
42 & 16375 & 16554.7919410111 & -179.791941011114 \tabularnewline
43 & 16290 & 16502.5044025452 & -212.504402545226 \tabularnewline
44 & 16352 & 16440.703344835 & -88.7033448350412 \tabularnewline
45 & 15943 & 16414.9064179593 & -471.906417959279 \tabularnewline
46 & 16362 & 16277.6654223808 & 84.3345776191582 \tabularnewline
47 & 16393 & 16302.1918135331 & 90.8081864668784 \tabularnewline
48 & 19051 & 16328.6008756757 & 2722.39912432426 \tabularnewline
49 & 16747 & 17120.335745059 & -373.33574505903 \tabularnewline
50 & 16320 & 17011.7613171916 & -691.761317191555 \tabularnewline
51 & 17910 & 16810.581574215 & 1099.41842578497 \tabularnewline
52 & 16961 & 17130.3171691758 & -169.317169175782 \tabularnewline
53 & 17480 & 17081.0759298498 & 398.924070150217 \tabularnewline
54 & 17049 & 17197.0920179216 & -148.092017921597 \tabularnewline
55 & 16879 & 17154.0235297568 & -275.023529756781 \tabularnewline
56 & 17473 & 17074.0405043202 & 398.959495679785 \tabularnewline
57 & 16998 & 17190.0668949325 & -192.066894932454 \tabularnewline
58 & 17307 & 17134.209523905 & 172.790476095 \tabularnewline
59 & 17418 & 17184.4608789688 & 233.539121031215 \tabularnewline
60 & 20169 & 17252.3793057099 & 2916.62069429008 \tabularnewline
61 & 17871 & 18100.598174061 & -229.598174061022 \tabularnewline
62 & 17226 & 18033.8258632978 & -807.825863297821 \tabularnewline
63 & 19062 & 17798.8919409909 & 1263.10805900914 \tabularnewline
64 & 17804 & 18166.2321613066 & -362.232161306572 \tabularnewline
65 & 19100 & 18060.8869052212 & 1039.11309477878 \tabularnewline
66 & 18522 & 18363.0843541619 & 158.915645838097 \tabularnewline
67 & 18060 & 18409.3005966579 & -349.300596657875 \tabularnewline
68 & 18869 & 18307.7161302953 & 561.283869704701 \tabularnewline
69 & 18127 & 18470.9500981941 & -343.950098194073 \tabularnewline
70 & 18871 & 18370.9216770728 & 500.078322927187 \tabularnewline
71 & 18890 & 18516.3556959669 & 373.644304033118 \tabularnewline
72 & 21263 & 18625.0198597209 & 2637.98014027906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228434&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]12873[/C][C]13328[/C][C]-455[/C][/ROW]
[ROW][C]3[/C][C]14000[/C][C]13195.6757708483[/C][C]804.324229151673[/C][/ROW]
[ROW][C]4[/C][C]13477[/C][C]13429.5913392231[/C][C]47.4086607769277[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]13443.378843602[/C][C]793.621156397983[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]13674.1817177972[/C][C]-0.181717797231613[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]13674.1288701765[/C][C]-145.128870176481[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]13631.9221319924[/C][C]426.077868007598[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13755.8351549434[/C][C]-780.835154943377[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]13528.7507374216[/C][C]797.249262578402[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]13760.6087464599[/C][C]247.391253540101[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]13832.5556847534[/C][C]2360.44431524656[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14519.0259583149[/C][C]-36.0259583148654[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14508.5487997138[/C][C]-497.548799713844[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14363.8504230381[/C][C]693.149576961923[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14565.4339031662[/C][C]318.566096833803[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]14658.0800860176[/C][C]755.919913982396[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14877.9185913322[/C][C]-437.918591332153[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14750.5620198394[/C][C]149.437980160625[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]14794.0219440828[/C][C]279.978055917245[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14875.4458571127[/C][C]-433.445857112718[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]14749.3900572854[/C][C]557.609942714593[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14911.5555646195[/C][C]26.4444353804902[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]14919.2462009428[/C][C]2273.75379905725[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15580.5049234503[/C][C]-52.5049234503076[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15565.2353113135[/C][C]-800.23531131354[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15332.5088921718[/C][C]505.491107828248[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15479.5170706034[/C][C]243.482929396603[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]15550.3273803704[/C][C]599.672619629577[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15724.7256597899[/C][C]-238.72565978987[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15655.2988709758[/C][C]330.701129024237[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]15751.4741940037[/C][C]231.525805996282[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15818.80710347[/C][C]-126.807103470042[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]15781.9287469478[/C][C]708.071253052221[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]15987.8517859469[/C][C]-301.851785946887[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]15900.0665004667[/C][C]2996.93349953328[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16771.6421381471[/C][C]-455.642138147083[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]16639.1311607859[/C][C]-1003.13116078591[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16347.3980671837[/C][C]815.601932816326[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16584.5934453255[/C][C]-50.5934453255104[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16569.8797340006[/C][C]-51.8797340006204[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16554.7919410111[/C][C]-179.791941011114[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16502.5044025452[/C][C]-212.504402545226[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16440.703344835[/C][C]-88.7033448350412[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16414.9064179593[/C][C]-471.906417959279[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16277.6654223808[/C][C]84.3345776191582[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16302.1918135331[/C][C]90.8081864668784[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]16328.6008756757[/C][C]2722.39912432426[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]17120.335745059[/C][C]-373.33574505903[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]17011.7613171916[/C][C]-691.761317191555[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]16810.581574215[/C][C]1099.41842578497[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17130.3171691758[/C][C]-169.317169175782[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17081.0759298498[/C][C]398.924070150217[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17197.0920179216[/C][C]-148.092017921597[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17154.0235297568[/C][C]-275.023529756781[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17074.0405043202[/C][C]398.959495679785[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17190.0668949325[/C][C]-192.066894932454[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17134.209523905[/C][C]172.790476095[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17184.4608789688[/C][C]233.539121031215[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]17252.3793057099[/C][C]2916.62069429008[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]18100.598174061[/C][C]-229.598174061022[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]18033.8258632978[/C][C]-807.825863297821[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]17798.8919409909[/C][C]1263.10805900914[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18166.2321613066[/C][C]-362.232161306572[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18060.8869052212[/C][C]1039.11309477878[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18363.0843541619[/C][C]158.915645838097[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18409.3005966579[/C][C]-349.300596657875[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18307.7161302953[/C][C]561.283869704701[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18470.9500981941[/C][C]-343.950098194073[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18370.9216770728[/C][C]500.078322927187[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18516.3556959669[/C][C]373.644304033118[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]18625.0198597209[/C][C]2637.98014027906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228434&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228434&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
21287313328-455
31400013195.6757708483804.324229151673
41347713429.591339223147.4086607769277
51423713443.378843602793.621156397983
61367413674.1817177972-0.181717797231613
71352913674.1288701765-145.128870176481
81405813631.9221319924426.077868007598
91297513755.8351549434-780.835154943377
101432613528.7507374216797.249262578402
111400813760.6087464599247.391253540101
121619313832.55568475342360.44431524656
131448314519.0259583149-36.0259583148654
141401114508.5487997138-497.548799713844
151505714363.8504230381693.149576961923
161488414565.4339031662318.566096833803
171541414658.0800860176755.919913982396
181444014877.9185913322-437.918591332153
191490014750.5620198394149.437980160625
201507414794.0219440828279.978055917245
211444214875.4458571127-433.445857112718
221530714749.3900572854557.609942714593
231493814911.555564619526.4444353804902
241719314919.24620094282273.75379905725
251552815580.5049234503-52.5049234503076
261476515565.2353113135-800.23531131354
271583815332.5088921718505.491107828248
281572315479.5170706034243.482929396603
291615015550.3273803704599.672619629577
301548615724.7256597899-238.72565978987
311598615655.2988709758330.701129024237
321598315751.4741940037231.525805996282
331569215818.80710347-126.807103470042
341649015781.9287469478708.071253052221
351568615987.8517859469-301.851785946887
361889715900.06650046672996.93349953328
371631616771.6421381471-455.642138147083
381563616639.1311607859-1003.13116078591
391716316347.3980671837815.601932816326
401653416584.5934453255-50.5934453255104
411651816569.8797340006-51.8797340006204
421637516554.7919410111-179.791941011114
431629016502.5044025452-212.504402545226
441635216440.703344835-88.7033448350412
451594316414.9064179593-471.906417959279
461636216277.665422380884.3345776191582
471639316302.191813533190.8081864668784
481905116328.60087567572722.39912432426
491674717120.335745059-373.33574505903
501632017011.7613171916-691.761317191555
511791016810.5815742151099.41842578497
521696117130.3171691758-169.317169175782
531748017081.0759298498398.924070150217
541704917197.0920179216-148.092017921597
551687917154.0235297568-275.023529756781
561747317074.0405043202398.959495679785
571699817190.0668949325-192.066894932454
581730717134.209523905172.790476095
591741817184.4608789688233.539121031215
602016917252.37930570992916.62069429008
611787118100.598174061-229.598174061022
621722618033.8258632978-807.825863297821
631906217798.89194099091263.10805900914
641780418166.2321613066-362.232161306572
651910018060.88690522121039.11309477878
661852218363.0843541619158.915645838097
671806018409.3005966579-349.300596657875
681886918307.7161302953561.283869704701
691812718470.9500981941-343.950098194073
701887118370.9216770728500.078322927187
711889018516.3556959669373.644304033118
722126318625.01985972092637.98014027906







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7319392.203790665717688.467766697421095.9398146339
7419392.203790665717617.88094362721166.5266377043
7519392.203790665717549.996774155421234.4108071759
7619392.203790665717484.526716883121299.8808644482
7719392.203790665717421.230187597421363.1773937339
7819392.203790665717359.904090781821424.5034905495
7919392.203790665717300.375117876221484.0324634552
8019392.203790665717242.49396781521541.9136135163
8119392.203790665717186.130934068121598.2766472632
8219392.203790665717131.172482883121653.2350984482
8319392.203790665717077.518563484921706.8890178465
8419392.203790665717025.080467497821759.3271138335

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 19392.2037906657 & 17688.4677666974 & 21095.9398146339 \tabularnewline
74 & 19392.2037906657 & 17617.880943627 & 21166.5266377043 \tabularnewline
75 & 19392.2037906657 & 17549.9967741554 & 21234.4108071759 \tabularnewline
76 & 19392.2037906657 & 17484.5267168831 & 21299.8808644482 \tabularnewline
77 & 19392.2037906657 & 17421.2301875974 & 21363.1773937339 \tabularnewline
78 & 19392.2037906657 & 17359.9040907818 & 21424.5034905495 \tabularnewline
79 & 19392.2037906657 & 17300.3751178762 & 21484.0324634552 \tabularnewline
80 & 19392.2037906657 & 17242.493967815 & 21541.9136135163 \tabularnewline
81 & 19392.2037906657 & 17186.1309340681 & 21598.2766472632 \tabularnewline
82 & 19392.2037906657 & 17131.1724828831 & 21653.2350984482 \tabularnewline
83 & 19392.2037906657 & 17077.5185634849 & 21706.8890178465 \tabularnewline
84 & 19392.2037906657 & 17025.0804674978 & 21759.3271138335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228434&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]19392.2037906657[/C][C]17688.4677666974[/C][C]21095.9398146339[/C][/ROW]
[ROW][C]74[/C][C]19392.2037906657[/C][C]17617.880943627[/C][C]21166.5266377043[/C][/ROW]
[ROW][C]75[/C][C]19392.2037906657[/C][C]17549.9967741554[/C][C]21234.4108071759[/C][/ROW]
[ROW][C]76[/C][C]19392.2037906657[/C][C]17484.5267168831[/C][C]21299.8808644482[/C][/ROW]
[ROW][C]77[/C][C]19392.2037906657[/C][C]17421.2301875974[/C][C]21363.1773937339[/C][/ROW]
[ROW][C]78[/C][C]19392.2037906657[/C][C]17359.9040907818[/C][C]21424.5034905495[/C][/ROW]
[ROW][C]79[/C][C]19392.2037906657[/C][C]17300.3751178762[/C][C]21484.0324634552[/C][/ROW]
[ROW][C]80[/C][C]19392.2037906657[/C][C]17242.493967815[/C][C]21541.9136135163[/C][/ROW]
[ROW][C]81[/C][C]19392.2037906657[/C][C]17186.1309340681[/C][C]21598.2766472632[/C][/ROW]
[ROW][C]82[/C][C]19392.2037906657[/C][C]17131.1724828831[/C][C]21653.2350984482[/C][/ROW]
[ROW][C]83[/C][C]19392.2037906657[/C][C]17077.5185634849[/C][C]21706.8890178465[/C][/ROW]
[ROW][C]84[/C][C]19392.2037906657[/C][C]17025.0804674978[/C][C]21759.3271138335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228434&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228434&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
7319392.203790665717688.467766697421095.9398146339
7419392.203790665717617.88094362721166.5266377043
7519392.203790665717549.996774155421234.4108071759
7619392.203790665717484.526716883121299.8808644482
7719392.203790665717421.230187597421363.1773937339
7819392.203790665717359.904090781821424.5034905495
7919392.203790665717300.375117876221484.0324634552
8019392.203790665717242.49396781521541.9136135163
8119392.203790665717186.130934068121598.2766472632
8219392.203790665717131.172482883121653.2350984482
8319392.203790665717077.518563484921706.8890178465
8419392.203790665717025.080467497821759.3271138335



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