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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 computationTue, 29 Nov 2011 05:57:03 -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/Nov/29/t1322564244x2314wkaourssqf.htm/, Retrieved Thu, 28 Mar 2024 14:54:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148187, Retrieved Thu, 28 Mar 2024 14:54:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Single] [2011-11-29 10:45:34] [f2faabc3a2466a29562900bc59f67898]
- R P     [Exponential Smoothing] [Double] [2011-11-29 10:57:03] [5988e21ec0676b551e455a86717edc1d] [Current]
-   P       [Exponential Smoothing] [Triple] [2011-11-29 11:02:24] [f2faabc3a2466a29562900bc59f67898]
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Dataseries X:
16111
15554
15220
14807
14291
14653
17006
18032
16558
16102
15055
15484
14596
14609
13923
14226
14056
14278
16142
16509
15680
14086
13129
13086
13096
12280
11534
11135
10903
10926
13220
13581
11788
11088
10434
11061
10828
10270
10360
9899
9395
9944
12117
12474
11106
10643
10227
11273
11516
11583
11605
11414
11181
12000
14007
14582
13251
12806
12645
13869
13342
13079
12513
12331
11882
12388
14394
14635
13218
12554
12031
12429




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=148187&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=148187&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148187&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
beta0.0502034740466688
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0502034740466688 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148187&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]0.0502034740466688[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148187&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148187&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
beta0.0502034740466688
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31522014997223
41480714674.1953747124132.804625287594
51429114267.862628271323.1373717286897
61465313753.0242047124899.975795287601
71700614160.20611619382845.79388380625
81803216656.07485558161375.92514441841
91655817751.1510778596-1193.15107785955
101610216217.2507486885-115.250748688479
111505515755.4647607178-700.464760717838
121548414673.2989962825810.701003717466
131459615142.9990030823-546.999003082272
141460914227.5377528275381.462247172523
151392314259.6884828532-336.688482853187
161422613556.7855513425669.214448657545
171405613893.3824415473162.61755845271
181427813731.5464079226546.453592077398
191614213980.98027665022161.01972334983
201650915953.4709742457555.529025754298
211568016348.3604612723-668.360461272328
221408615485.806444201-1399.80644420102
231312913821.5312977092-692.531297709218
241308612829.7638206782256.236179321833
251309612799.6277670566296.372232943431
261228012824.5066827613-544.506682761297
271153411981.1705556451-447.170555645052
281113511212.7210402603-77.7210402602923
291090310809.819174032793.1808259672962
301092610582.4971752108343.502824789199
311322010622.74221036012597.25778963994
321358113047.1335743948533.86642560524
331178813434.935523637-1646.93552363702
341108811559.2536388196-471.253638819573
351043410835.5950689937-401.595068993696
361106110161.4336013702899.5663986298
371082810833.5949597171-5.59495971706747
381027010600.3140733021-330.314073302119
391036010025.7311592958334.268840704153
40989910132.5126163647-233.512616364747
4193959659.78947178951-264.789471789511
4299449142.49612041469801.503879585305
43121179731.734399631762385.26560036824
441247412024.4830192943449.516980705741
451110612404.0503333687-1298.05033336866
461064310970.8836971461-327.883697146113
471022710491.4227964661-264.422796466113
481127310062.14785346641210.85214653362
491151611168.9368377792347.063162220767
501158311429.3606142363153.639385763663
511160511504.0738451521100.92615484793
521141411531.1406887476-117.140688747608
531118111334.2598192203-153.259819220259
541200011093.5656438636906.434356136364
551400711958.07179753692048.92820246306
561458214067.9351113728514.064888627219
571325114668.7429546673-1417.74295466728
581280613266.5673330378-460.567333037794
591264512798.4452528869-153.445252886888
601386912629.7417681161239.258231884
611334213915.9568365975-573.956836597505
621307913360.1422094475-281.142209447475
631251313083.0278938321-570.027893832055
641233112488.4105132582-157.410513258181
651188212298.5079586412-416.50795864115
661238811828.5978121493559.402187850721
671439412362.68174536872031.31825463131
681463514470.6609786456164.339021354401
691321814719.911368439-1501.91136843902
701255413227.5102000332-673.510200033195
711203112529.6976481857-498.697648185662
721242911981.6612937478447.338706252162

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15220 & 14997 & 223 \tabularnewline
4 & 14807 & 14674.1953747124 & 132.804625287594 \tabularnewline
5 & 14291 & 14267.8626282713 & 23.1373717286897 \tabularnewline
6 & 14653 & 13753.0242047124 & 899.975795287601 \tabularnewline
7 & 17006 & 14160.2061161938 & 2845.79388380625 \tabularnewline
8 & 18032 & 16656.0748555816 & 1375.92514441841 \tabularnewline
9 & 16558 & 17751.1510778596 & -1193.15107785955 \tabularnewline
10 & 16102 & 16217.2507486885 & -115.250748688479 \tabularnewline
11 & 15055 & 15755.4647607178 & -700.464760717838 \tabularnewline
12 & 15484 & 14673.2989962825 & 810.701003717466 \tabularnewline
13 & 14596 & 15142.9990030823 & -546.999003082272 \tabularnewline
14 & 14609 & 14227.5377528275 & 381.462247172523 \tabularnewline
15 & 13923 & 14259.6884828532 & -336.688482853187 \tabularnewline
16 & 14226 & 13556.7855513425 & 669.214448657545 \tabularnewline
17 & 14056 & 13893.3824415473 & 162.61755845271 \tabularnewline
18 & 14278 & 13731.5464079226 & 546.453592077398 \tabularnewline
19 & 16142 & 13980.9802766502 & 2161.01972334983 \tabularnewline
20 & 16509 & 15953.4709742457 & 555.529025754298 \tabularnewline
21 & 15680 & 16348.3604612723 & -668.360461272328 \tabularnewline
22 & 14086 & 15485.806444201 & -1399.80644420102 \tabularnewline
23 & 13129 & 13821.5312977092 & -692.531297709218 \tabularnewline
24 & 13086 & 12829.7638206782 & 256.236179321833 \tabularnewline
25 & 13096 & 12799.6277670566 & 296.372232943431 \tabularnewline
26 & 12280 & 12824.5066827613 & -544.506682761297 \tabularnewline
27 & 11534 & 11981.1705556451 & -447.170555645052 \tabularnewline
28 & 11135 & 11212.7210402603 & -77.7210402602923 \tabularnewline
29 & 10903 & 10809.8191740327 & 93.1808259672962 \tabularnewline
30 & 10926 & 10582.4971752108 & 343.502824789199 \tabularnewline
31 & 13220 & 10622.7422103601 & 2597.25778963994 \tabularnewline
32 & 13581 & 13047.1335743948 & 533.86642560524 \tabularnewline
33 & 11788 & 13434.935523637 & -1646.93552363702 \tabularnewline
34 & 11088 & 11559.2536388196 & -471.253638819573 \tabularnewline
35 & 10434 & 10835.5950689937 & -401.595068993696 \tabularnewline
36 & 11061 & 10161.4336013702 & 899.5663986298 \tabularnewline
37 & 10828 & 10833.5949597171 & -5.59495971706747 \tabularnewline
38 & 10270 & 10600.3140733021 & -330.314073302119 \tabularnewline
39 & 10360 & 10025.7311592958 & 334.268840704153 \tabularnewline
40 & 9899 & 10132.5126163647 & -233.512616364747 \tabularnewline
41 & 9395 & 9659.78947178951 & -264.789471789511 \tabularnewline
42 & 9944 & 9142.49612041469 & 801.503879585305 \tabularnewline
43 & 12117 & 9731.73439963176 & 2385.26560036824 \tabularnewline
44 & 12474 & 12024.4830192943 & 449.516980705741 \tabularnewline
45 & 11106 & 12404.0503333687 & -1298.05033336866 \tabularnewline
46 & 10643 & 10970.8836971461 & -327.883697146113 \tabularnewline
47 & 10227 & 10491.4227964661 & -264.422796466113 \tabularnewline
48 & 11273 & 10062.1478534664 & 1210.85214653362 \tabularnewline
49 & 11516 & 11168.9368377792 & 347.063162220767 \tabularnewline
50 & 11583 & 11429.3606142363 & 153.639385763663 \tabularnewline
51 & 11605 & 11504.0738451521 & 100.92615484793 \tabularnewline
52 & 11414 & 11531.1406887476 & -117.140688747608 \tabularnewline
53 & 11181 & 11334.2598192203 & -153.259819220259 \tabularnewline
54 & 12000 & 11093.5656438636 & 906.434356136364 \tabularnewline
55 & 14007 & 11958.0717975369 & 2048.92820246306 \tabularnewline
56 & 14582 & 14067.9351113728 & 514.064888627219 \tabularnewline
57 & 13251 & 14668.7429546673 & -1417.74295466728 \tabularnewline
58 & 12806 & 13266.5673330378 & -460.567333037794 \tabularnewline
59 & 12645 & 12798.4452528869 & -153.445252886888 \tabularnewline
60 & 13869 & 12629.741768116 & 1239.258231884 \tabularnewline
61 & 13342 & 13915.9568365975 & -573.956836597505 \tabularnewline
62 & 13079 & 13360.1422094475 & -281.142209447475 \tabularnewline
63 & 12513 & 13083.0278938321 & -570.027893832055 \tabularnewline
64 & 12331 & 12488.4105132582 & -157.410513258181 \tabularnewline
65 & 11882 & 12298.5079586412 & -416.50795864115 \tabularnewline
66 & 12388 & 11828.5978121493 & 559.402187850721 \tabularnewline
67 & 14394 & 12362.6817453687 & 2031.31825463131 \tabularnewline
68 & 14635 & 14470.6609786456 & 164.339021354401 \tabularnewline
69 & 13218 & 14719.911368439 & -1501.91136843902 \tabularnewline
70 & 12554 & 13227.5102000332 & -673.510200033195 \tabularnewline
71 & 12031 & 12529.6976481857 & -498.697648185662 \tabularnewline
72 & 12429 & 11981.6612937478 & 447.338706252162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148187&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]15220[/C][C]14997[/C][C]223[/C][/ROW]
[ROW][C]4[/C][C]14807[/C][C]14674.1953747124[/C][C]132.804625287594[/C][/ROW]
[ROW][C]5[/C][C]14291[/C][C]14267.8626282713[/C][C]23.1373717286897[/C][/ROW]
[ROW][C]6[/C][C]14653[/C][C]13753.0242047124[/C][C]899.975795287601[/C][/ROW]
[ROW][C]7[/C][C]17006[/C][C]14160.2061161938[/C][C]2845.79388380625[/C][/ROW]
[ROW][C]8[/C][C]18032[/C][C]16656.0748555816[/C][C]1375.92514441841[/C][/ROW]
[ROW][C]9[/C][C]16558[/C][C]17751.1510778596[/C][C]-1193.15107785955[/C][/ROW]
[ROW][C]10[/C][C]16102[/C][C]16217.2507486885[/C][C]-115.250748688479[/C][/ROW]
[ROW][C]11[/C][C]15055[/C][C]15755.4647607178[/C][C]-700.464760717838[/C][/ROW]
[ROW][C]12[/C][C]15484[/C][C]14673.2989962825[/C][C]810.701003717466[/C][/ROW]
[ROW][C]13[/C][C]14596[/C][C]15142.9990030823[/C][C]-546.999003082272[/C][/ROW]
[ROW][C]14[/C][C]14609[/C][C]14227.5377528275[/C][C]381.462247172523[/C][/ROW]
[ROW][C]15[/C][C]13923[/C][C]14259.6884828532[/C][C]-336.688482853187[/C][/ROW]
[ROW][C]16[/C][C]14226[/C][C]13556.7855513425[/C][C]669.214448657545[/C][/ROW]
[ROW][C]17[/C][C]14056[/C][C]13893.3824415473[/C][C]162.61755845271[/C][/ROW]
[ROW][C]18[/C][C]14278[/C][C]13731.5464079226[/C][C]546.453592077398[/C][/ROW]
[ROW][C]19[/C][C]16142[/C][C]13980.9802766502[/C][C]2161.01972334983[/C][/ROW]
[ROW][C]20[/C][C]16509[/C][C]15953.4709742457[/C][C]555.529025754298[/C][/ROW]
[ROW][C]21[/C][C]15680[/C][C]16348.3604612723[/C][C]-668.360461272328[/C][/ROW]
[ROW][C]22[/C][C]14086[/C][C]15485.806444201[/C][C]-1399.80644420102[/C][/ROW]
[ROW][C]23[/C][C]13129[/C][C]13821.5312977092[/C][C]-692.531297709218[/C][/ROW]
[ROW][C]24[/C][C]13086[/C][C]12829.7638206782[/C][C]256.236179321833[/C][/ROW]
[ROW][C]25[/C][C]13096[/C][C]12799.6277670566[/C][C]296.372232943431[/C][/ROW]
[ROW][C]26[/C][C]12280[/C][C]12824.5066827613[/C][C]-544.506682761297[/C][/ROW]
[ROW][C]27[/C][C]11534[/C][C]11981.1705556451[/C][C]-447.170555645052[/C][/ROW]
[ROW][C]28[/C][C]11135[/C][C]11212.7210402603[/C][C]-77.7210402602923[/C][/ROW]
[ROW][C]29[/C][C]10903[/C][C]10809.8191740327[/C][C]93.1808259672962[/C][/ROW]
[ROW][C]30[/C][C]10926[/C][C]10582.4971752108[/C][C]343.502824789199[/C][/ROW]
[ROW][C]31[/C][C]13220[/C][C]10622.7422103601[/C][C]2597.25778963994[/C][/ROW]
[ROW][C]32[/C][C]13581[/C][C]13047.1335743948[/C][C]533.86642560524[/C][/ROW]
[ROW][C]33[/C][C]11788[/C][C]13434.935523637[/C][C]-1646.93552363702[/C][/ROW]
[ROW][C]34[/C][C]11088[/C][C]11559.2536388196[/C][C]-471.253638819573[/C][/ROW]
[ROW][C]35[/C][C]10434[/C][C]10835.5950689937[/C][C]-401.595068993696[/C][/ROW]
[ROW][C]36[/C][C]11061[/C][C]10161.4336013702[/C][C]899.5663986298[/C][/ROW]
[ROW][C]37[/C][C]10828[/C][C]10833.5949597171[/C][C]-5.59495971706747[/C][/ROW]
[ROW][C]38[/C][C]10270[/C][C]10600.3140733021[/C][C]-330.314073302119[/C][/ROW]
[ROW][C]39[/C][C]10360[/C][C]10025.7311592958[/C][C]334.268840704153[/C][/ROW]
[ROW][C]40[/C][C]9899[/C][C]10132.5126163647[/C][C]-233.512616364747[/C][/ROW]
[ROW][C]41[/C][C]9395[/C][C]9659.78947178951[/C][C]-264.789471789511[/C][/ROW]
[ROW][C]42[/C][C]9944[/C][C]9142.49612041469[/C][C]801.503879585305[/C][/ROW]
[ROW][C]43[/C][C]12117[/C][C]9731.73439963176[/C][C]2385.26560036824[/C][/ROW]
[ROW][C]44[/C][C]12474[/C][C]12024.4830192943[/C][C]449.516980705741[/C][/ROW]
[ROW][C]45[/C][C]11106[/C][C]12404.0503333687[/C][C]-1298.05033336866[/C][/ROW]
[ROW][C]46[/C][C]10643[/C][C]10970.8836971461[/C][C]-327.883697146113[/C][/ROW]
[ROW][C]47[/C][C]10227[/C][C]10491.4227964661[/C][C]-264.422796466113[/C][/ROW]
[ROW][C]48[/C][C]11273[/C][C]10062.1478534664[/C][C]1210.85214653362[/C][/ROW]
[ROW][C]49[/C][C]11516[/C][C]11168.9368377792[/C][C]347.063162220767[/C][/ROW]
[ROW][C]50[/C][C]11583[/C][C]11429.3606142363[/C][C]153.639385763663[/C][/ROW]
[ROW][C]51[/C][C]11605[/C][C]11504.0738451521[/C][C]100.92615484793[/C][/ROW]
[ROW][C]52[/C][C]11414[/C][C]11531.1406887476[/C][C]-117.140688747608[/C][/ROW]
[ROW][C]53[/C][C]11181[/C][C]11334.2598192203[/C][C]-153.259819220259[/C][/ROW]
[ROW][C]54[/C][C]12000[/C][C]11093.5656438636[/C][C]906.434356136364[/C][/ROW]
[ROW][C]55[/C][C]14007[/C][C]11958.0717975369[/C][C]2048.92820246306[/C][/ROW]
[ROW][C]56[/C][C]14582[/C][C]14067.9351113728[/C][C]514.064888627219[/C][/ROW]
[ROW][C]57[/C][C]13251[/C][C]14668.7429546673[/C][C]-1417.74295466728[/C][/ROW]
[ROW][C]58[/C][C]12806[/C][C]13266.5673330378[/C][C]-460.567333037794[/C][/ROW]
[ROW][C]59[/C][C]12645[/C][C]12798.4452528869[/C][C]-153.445252886888[/C][/ROW]
[ROW][C]60[/C][C]13869[/C][C]12629.741768116[/C][C]1239.258231884[/C][/ROW]
[ROW][C]61[/C][C]13342[/C][C]13915.9568365975[/C][C]-573.956836597505[/C][/ROW]
[ROW][C]62[/C][C]13079[/C][C]13360.1422094475[/C][C]-281.142209447475[/C][/ROW]
[ROW][C]63[/C][C]12513[/C][C]13083.0278938321[/C][C]-570.027893832055[/C][/ROW]
[ROW][C]64[/C][C]12331[/C][C]12488.4105132582[/C][C]-157.410513258181[/C][/ROW]
[ROW][C]65[/C][C]11882[/C][C]12298.5079586412[/C][C]-416.50795864115[/C][/ROW]
[ROW][C]66[/C][C]12388[/C][C]11828.5978121493[/C][C]559.402187850721[/C][/ROW]
[ROW][C]67[/C][C]14394[/C][C]12362.6817453687[/C][C]2031.31825463131[/C][/ROW]
[ROW][C]68[/C][C]14635[/C][C]14470.6609786456[/C][C]164.339021354401[/C][/ROW]
[ROW][C]69[/C][C]13218[/C][C]14719.911368439[/C][C]-1501.91136843902[/C][/ROW]
[ROW][C]70[/C][C]12554[/C][C]13227.5102000332[/C][C]-673.510200033195[/C][/ROW]
[ROW][C]71[/C][C]12031[/C][C]12529.6976481857[/C][C]-498.697648185662[/C][/ROW]
[ROW][C]72[/C][C]12429[/C][C]11981.6612937478[/C][C]447.338706252162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148187&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148187&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
31522014997223
41480714674.1953747124132.804625287594
51429114267.862628271323.1373717286897
61465313753.0242047124899.975795287601
71700614160.20611619382845.79388380625
81803216656.07485558161375.92514441841
91655817751.1510778596-1193.15107785955
101610216217.2507486885-115.250748688479
111505515755.4647607178-700.464760717838
121548414673.2989962825810.701003717466
131459615142.9990030823-546.999003082272
141460914227.5377528275381.462247172523
151392314259.6884828532-336.688482853187
161422613556.7855513425669.214448657545
171405613893.3824415473162.61755845271
181427813731.5464079226546.453592077398
191614213980.98027665022161.01972334983
201650915953.4709742457555.529025754298
211568016348.3604612723-668.360461272328
221408615485.806444201-1399.80644420102
231312913821.5312977092-692.531297709218
241308612829.7638206782256.236179321833
251309612799.6277670566296.372232943431
261228012824.5066827613-544.506682761297
271153411981.1705556451-447.170555645052
281113511212.7210402603-77.7210402602923
291090310809.819174032793.1808259672962
301092610582.4971752108343.502824789199
311322010622.74221036012597.25778963994
321358113047.1335743948533.86642560524
331178813434.935523637-1646.93552363702
341108811559.2536388196-471.253638819573
351043410835.5950689937-401.595068993696
361106110161.4336013702899.5663986298
371082810833.5949597171-5.59495971706747
381027010600.3140733021-330.314073302119
391036010025.7311592958334.268840704153
40989910132.5126163647-233.512616364747
4193959659.78947178951-264.789471789511
4299449142.49612041469801.503879585305
43121179731.734399631762385.26560036824
441247412024.4830192943449.516980705741
451110612404.0503333687-1298.05033336866
461064310970.8836971461-327.883697146113
471022710491.4227964661-264.422796466113
481127310062.14785346641210.85214653362
491151611168.9368377792347.063162220767
501158311429.3606142363153.639385763663
511160511504.0738451521100.92615484793
521141411531.1406887476-117.140688747608
531118111334.2598192203-153.259819220259
541200011093.5656438636906.434356136364
551400711958.07179753692048.92820246306
561458214067.9351113728514.064888627219
571325114668.7429546673-1417.74295466728
581280613266.5673330378-460.567333037794
591264512798.4452528869-153.445252886888
601386912629.7417681161239.258231884
611334213915.9568365975-573.956836597505
621307913360.1422094475-281.142209447475
631251313083.0278938321-570.027893832055
641233112488.4105132582-157.410513258181
651188212298.5079586412-416.50795864115
661238811828.5978121493559.402187850721
671439412362.68174536872031.31825463131
681463514470.6609786456164.339021354401
691321814719.911368439-1501.91136843902
701255413227.5102000332-673.510200033195
711203112529.6976481857-498.697648185662
721242911981.6612937478447.338706252162







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7312402.119250877210562.357822322414241.8806794321
7412375.23850175459707.3133413844415043.1636621245
7512348.35775263178999.2729114445515697.4425938189
7612321.4770035098359.4803374505216283.4736695674
7712294.59625438627758.2947633079816830.8977454644
7812267.71550526347180.9413002069617354.4897103199
7912240.83475614076618.8955000543717862.774012227
8012213.95400701796066.7692524245818361.1387616112
8112187.07325789515520.9370705204318853.2094452699
8212160.19250877244978.8460879994619341.5389295453
8312133.31175964964438.6359199455219827.9875993537
8412106.43101052693898.914157725520313.9478633282

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 12402.1192508772 & 10562.3578223224 & 14241.8806794321 \tabularnewline
74 & 12375.2385017545 & 9707.31334138444 & 15043.1636621245 \tabularnewline
75 & 12348.3577526317 & 8999.27291144455 & 15697.4425938189 \tabularnewline
76 & 12321.477003509 & 8359.48033745052 & 16283.4736695674 \tabularnewline
77 & 12294.5962543862 & 7758.29476330798 & 16830.8977454644 \tabularnewline
78 & 12267.7155052634 & 7180.94130020696 & 17354.4897103199 \tabularnewline
79 & 12240.8347561407 & 6618.89550005437 & 17862.774012227 \tabularnewline
80 & 12213.9540070179 & 6066.76925242458 & 18361.1387616112 \tabularnewline
81 & 12187.0732578951 & 5520.93707052043 & 18853.2094452699 \tabularnewline
82 & 12160.1925087724 & 4978.84608799946 & 19341.5389295453 \tabularnewline
83 & 12133.3117596496 & 4438.63591994552 & 19827.9875993537 \tabularnewline
84 & 12106.4310105269 & 3898.9141577255 & 20313.9478633282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148187&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]12402.1192508772[/C][C]10562.3578223224[/C][C]14241.8806794321[/C][/ROW]
[ROW][C]74[/C][C]12375.2385017545[/C][C]9707.31334138444[/C][C]15043.1636621245[/C][/ROW]
[ROW][C]75[/C][C]12348.3577526317[/C][C]8999.27291144455[/C][C]15697.4425938189[/C][/ROW]
[ROW][C]76[/C][C]12321.477003509[/C][C]8359.48033745052[/C][C]16283.4736695674[/C][/ROW]
[ROW][C]77[/C][C]12294.5962543862[/C][C]7758.29476330798[/C][C]16830.8977454644[/C][/ROW]
[ROW][C]78[/C][C]12267.7155052634[/C][C]7180.94130020696[/C][C]17354.4897103199[/C][/ROW]
[ROW][C]79[/C][C]12240.8347561407[/C][C]6618.89550005437[/C][C]17862.774012227[/C][/ROW]
[ROW][C]80[/C][C]12213.9540070179[/C][C]6066.76925242458[/C][C]18361.1387616112[/C][/ROW]
[ROW][C]81[/C][C]12187.0732578951[/C][C]5520.93707052043[/C][C]18853.2094452699[/C][/ROW]
[ROW][C]82[/C][C]12160.1925087724[/C][C]4978.84608799946[/C][C]19341.5389295453[/C][/ROW]
[ROW][C]83[/C][C]12133.3117596496[/C][C]4438.63591994552[/C][C]19827.9875993537[/C][/ROW]
[ROW][C]84[/C][C]12106.4310105269[/C][C]3898.9141577255[/C][C]20313.9478633282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148187&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148187&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
7312402.119250877210562.357822322414241.8806794321
7412375.23850175459707.3133413844415043.1636621245
7512348.35775263178999.2729114445515697.4425938189
7612321.4770035098359.4803374505216283.4736695674
7712294.59625438627758.2947633079816830.8977454644
7812267.71550526347180.9413002069617354.4897103199
7912240.83475614076618.8955000543717862.774012227
8012213.95400701796066.7692524245818361.1387616112
8112187.07325789515520.9370705204318853.2094452699
8212160.19250877244978.8460879994619341.5389295453
8312133.31175964964438.6359199455219827.9875993537
8412106.43101052693898.914157725520313.9478633282



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