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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 16:02:13 -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/t1385413434uhovw71kf88c0ee.htm/, Retrieved Mon, 29 Apr 2024 20:15:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=228452, Retrieved Mon, 29 Apr 2024 20:15:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
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 17:50:48] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [WS8: Double Smoot...] [2013-11-25 21:02:13] [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
19547
18450
20254
19240
20216
19420
19415
20018
18652
19978
19509
21971




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228452&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228452&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.257593917038808
beta0.275620602016761
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.257593917038808 \tabularnewline
beta & 0.275620602016761 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228452&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]0.257593917038808[/C][/ROW]
[ROW][C]beta[/C][C]0.275620602016761[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228452&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
alpha0.257593917038808
beta0.275620602016761
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
314000124181582
41347712482.8327141107994.16728588928
51423712466.82737517271770.17262482731
61367412776.3953443526897.604655647427
71352912924.9234187953604.076581204739
81405813040.72879096441017.27120903563
91297513335.195000895-360.195000895035
101432613249.26110093391076.73889906607
111400813609.9191462536398.080853746354
121619313824.02202763432368.97797236571
131448314714.0091672295-231.009167229457
141401114917.8542024259-906.854202425859
151505714883.2206602842173.779339715784
161488415139.2897638107-255.289763810746
171541415266.7081649983147.291835001659
181444015508.2865909109-1068.28659091085
191490015360.8929937452-460.89299374519
201507415337.2377238923-263.237723892255
211444215345.807847159-903.80784715902
221530715125.2022815364181.797718463571
231493815197.1494149678-259.149414967833
241719315137.11210956232055.88789043767
251552815819.3786518188-291.378651818759
261476515876.3162540946-1111.31625409464
271583815643.1414745699194.858525430074
281572315760.2639755474-37.2639755473865
291615015814.9474574309335.052542569112
301548615989.3255338358-503.325533835779
311598615912.007315450373.9926845497248
321598315988.6561050291-5.65610502909112
331569216044.3862776906-352.386277690613
341649015985.7820789511504.217921048861
351568616183.632471124-497.632471124001
361889716088.08129151132808.91870848873
371631617043.7057276807-727.705727680743
381563617036.6514323675-1400.65143236754
391716316756.8066998242406.193300175819
401653416971.2331687193-437.233168719285
411651816937.3553459562-419.355345956166
421637516878.3092708515-503.309270851496
431629016761.9031278949-471.903127894908
441635216620.0827481544-268.082748154437
451594316511.7318683831-568.731868383074
461636216285.556670548576.443329451502
471639316231.0020171665161.997982833487
481905116209.98728571432841.01271428569
491674717080.7772146152-333.777214615184
501632017110.0629916906-790.062991690618
511791016965.7192853769944.280714623124
521696117335.174189917-374.174189917027
531748017338.4374407454141.562559254551
541704917484.6020265021-435.602026502056
551687917451.1655701821-572.165570182075
561747317341.9284555772131.071544422801
571699817423.1467864092-425.146786409223
581730717330.9020061457-23.9020061457049
591741817340.318441336277.6815586637858
602016917381.41743499232787.58256500765
611787118318.4837616173-447.483761617277
621722618390.446143938-1164.44614393801
631906218195.0498086845866.950191315489
641780418584.4807073157-780.480707315681
651910018494.1307097858605.869290214159
661852218803.9116617852-281.911661785176
671806018864.9904230218-804.990423021758
681886918734.1744138352134.825586164796
691812718855.0216644003-728.021664400261
701887118701.9164910761169.083508923904
711889018791.904776519698.0952234804063
722126318870.57149481472392.42850518534
731954719710.1026048817-163.102604881682
741845019879.7644563812-1429.76445638118
752025419621.6312307592632.368769240813
761924019939.5880185196-699.588018519578
772021619864.7713565909351.2286434091
781942020085.5752728284-665.57527282841
791941519997.2020454161-582.202045416136
802001819888.969962505129.03003749502
811865219973.1078369356-1321.10783693559
821997819589.9027501806388.09724981941
831950919674.5326992168-165.532699216819
842197119604.79841897952366.20158102052

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14000 & 12418 & 1582 \tabularnewline
4 & 13477 & 12482.8327141107 & 994.16728588928 \tabularnewline
5 & 14237 & 12466.8273751727 & 1770.17262482731 \tabularnewline
6 & 13674 & 12776.3953443526 & 897.604655647427 \tabularnewline
7 & 13529 & 12924.9234187953 & 604.076581204739 \tabularnewline
8 & 14058 & 13040.7287909644 & 1017.27120903563 \tabularnewline
9 & 12975 & 13335.195000895 & -360.195000895035 \tabularnewline
10 & 14326 & 13249.2611009339 & 1076.73889906607 \tabularnewline
11 & 14008 & 13609.9191462536 & 398.080853746354 \tabularnewline
12 & 16193 & 13824.0220276343 & 2368.97797236571 \tabularnewline
13 & 14483 & 14714.0091672295 & -231.009167229457 \tabularnewline
14 & 14011 & 14917.8542024259 & -906.854202425859 \tabularnewline
15 & 15057 & 14883.2206602842 & 173.779339715784 \tabularnewline
16 & 14884 & 15139.2897638107 & -255.289763810746 \tabularnewline
17 & 15414 & 15266.7081649983 & 147.291835001659 \tabularnewline
18 & 14440 & 15508.2865909109 & -1068.28659091085 \tabularnewline
19 & 14900 & 15360.8929937452 & -460.89299374519 \tabularnewline
20 & 15074 & 15337.2377238923 & -263.237723892255 \tabularnewline
21 & 14442 & 15345.807847159 & -903.80784715902 \tabularnewline
22 & 15307 & 15125.2022815364 & 181.797718463571 \tabularnewline
23 & 14938 & 15197.1494149678 & -259.149414967833 \tabularnewline
24 & 17193 & 15137.1121095623 & 2055.88789043767 \tabularnewline
25 & 15528 & 15819.3786518188 & -291.378651818759 \tabularnewline
26 & 14765 & 15876.3162540946 & -1111.31625409464 \tabularnewline
27 & 15838 & 15643.1414745699 & 194.858525430074 \tabularnewline
28 & 15723 & 15760.2639755474 & -37.2639755473865 \tabularnewline
29 & 16150 & 15814.9474574309 & 335.052542569112 \tabularnewline
30 & 15486 & 15989.3255338358 & -503.325533835779 \tabularnewline
31 & 15986 & 15912.0073154503 & 73.9926845497248 \tabularnewline
32 & 15983 & 15988.6561050291 & -5.65610502909112 \tabularnewline
33 & 15692 & 16044.3862776906 & -352.386277690613 \tabularnewline
34 & 16490 & 15985.7820789511 & 504.217921048861 \tabularnewline
35 & 15686 & 16183.632471124 & -497.632471124001 \tabularnewline
36 & 18897 & 16088.0812915113 & 2808.91870848873 \tabularnewline
37 & 16316 & 17043.7057276807 & -727.705727680743 \tabularnewline
38 & 15636 & 17036.6514323675 & -1400.65143236754 \tabularnewline
39 & 17163 & 16756.8066998242 & 406.193300175819 \tabularnewline
40 & 16534 & 16971.2331687193 & -437.233168719285 \tabularnewline
41 & 16518 & 16937.3553459562 & -419.355345956166 \tabularnewline
42 & 16375 & 16878.3092708515 & -503.309270851496 \tabularnewline
43 & 16290 & 16761.9031278949 & -471.903127894908 \tabularnewline
44 & 16352 & 16620.0827481544 & -268.082748154437 \tabularnewline
45 & 15943 & 16511.7318683831 & -568.731868383074 \tabularnewline
46 & 16362 & 16285.5566705485 & 76.443329451502 \tabularnewline
47 & 16393 & 16231.0020171665 & 161.997982833487 \tabularnewline
48 & 19051 & 16209.9872857143 & 2841.01271428569 \tabularnewline
49 & 16747 & 17080.7772146152 & -333.777214615184 \tabularnewline
50 & 16320 & 17110.0629916906 & -790.062991690618 \tabularnewline
51 & 17910 & 16965.7192853769 & 944.280714623124 \tabularnewline
52 & 16961 & 17335.174189917 & -374.174189917027 \tabularnewline
53 & 17480 & 17338.4374407454 & 141.562559254551 \tabularnewline
54 & 17049 & 17484.6020265021 & -435.602026502056 \tabularnewline
55 & 16879 & 17451.1655701821 & -572.165570182075 \tabularnewline
56 & 17473 & 17341.9284555772 & 131.071544422801 \tabularnewline
57 & 16998 & 17423.1467864092 & -425.146786409223 \tabularnewline
58 & 17307 & 17330.9020061457 & -23.9020061457049 \tabularnewline
59 & 17418 & 17340.3184413362 & 77.6815586637858 \tabularnewline
60 & 20169 & 17381.4174349923 & 2787.58256500765 \tabularnewline
61 & 17871 & 18318.4837616173 & -447.483761617277 \tabularnewline
62 & 17226 & 18390.446143938 & -1164.44614393801 \tabularnewline
63 & 19062 & 18195.0498086845 & 866.950191315489 \tabularnewline
64 & 17804 & 18584.4807073157 & -780.480707315681 \tabularnewline
65 & 19100 & 18494.1307097858 & 605.869290214159 \tabularnewline
66 & 18522 & 18803.9116617852 & -281.911661785176 \tabularnewline
67 & 18060 & 18864.9904230218 & -804.990423021758 \tabularnewline
68 & 18869 & 18734.1744138352 & 134.825586164796 \tabularnewline
69 & 18127 & 18855.0216644003 & -728.021664400261 \tabularnewline
70 & 18871 & 18701.9164910761 & 169.083508923904 \tabularnewline
71 & 18890 & 18791.9047765196 & 98.0952234804063 \tabularnewline
72 & 21263 & 18870.5714948147 & 2392.42850518534 \tabularnewline
73 & 19547 & 19710.1026048817 & -163.102604881682 \tabularnewline
74 & 18450 & 19879.7644563812 & -1429.76445638118 \tabularnewline
75 & 20254 & 19621.6312307592 & 632.368769240813 \tabularnewline
76 & 19240 & 19939.5880185196 & -699.588018519578 \tabularnewline
77 & 20216 & 19864.7713565909 & 351.2286434091 \tabularnewline
78 & 19420 & 20085.5752728284 & -665.57527282841 \tabularnewline
79 & 19415 & 19997.2020454161 & -582.202045416136 \tabularnewline
80 & 20018 & 19888.969962505 & 129.03003749502 \tabularnewline
81 & 18652 & 19973.1078369356 & -1321.10783693559 \tabularnewline
82 & 19978 & 19589.9027501806 & 388.09724981941 \tabularnewline
83 & 19509 & 19674.5326992168 & -165.532699216819 \tabularnewline
84 & 21971 & 19604.7984189795 & 2366.20158102052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228452&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]14000[/C][C]12418[/C][C]1582[/C][/ROW]
[ROW][C]4[/C][C]13477[/C][C]12482.8327141107[/C][C]994.16728588928[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]12466.8273751727[/C][C]1770.17262482731[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]12776.3953443526[/C][C]897.604655647427[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]12924.9234187953[/C][C]604.076581204739[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]13040.7287909644[/C][C]1017.27120903563[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13335.195000895[/C][C]-360.195000895035[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]13249.2611009339[/C][C]1076.73889906607[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]13609.9191462536[/C][C]398.080853746354[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]13824.0220276343[/C][C]2368.97797236571[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14714.0091672295[/C][C]-231.009167229457[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14917.8542024259[/C][C]-906.854202425859[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14883.2206602842[/C][C]173.779339715784[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]15139.2897638107[/C][C]-255.289763810746[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]15266.7081649983[/C][C]147.291835001659[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]15508.2865909109[/C][C]-1068.28659091085[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]15360.8929937452[/C][C]-460.89299374519[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]15337.2377238923[/C][C]-263.237723892255[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]15345.807847159[/C][C]-903.80784715902[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]15125.2022815364[/C][C]181.797718463571[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]15197.1494149678[/C][C]-259.149414967833[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]15137.1121095623[/C][C]2055.88789043767[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15819.3786518188[/C][C]-291.378651818759[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15876.3162540946[/C][C]-1111.31625409464[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15643.1414745699[/C][C]194.858525430074[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15760.2639755474[/C][C]-37.2639755473865[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]15814.9474574309[/C][C]335.052542569112[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15989.3255338358[/C][C]-503.325533835779[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15912.0073154503[/C][C]73.9926845497248[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]15988.6561050291[/C][C]-5.65610502909112[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]16044.3862776906[/C][C]-352.386277690613[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]15985.7820789511[/C][C]504.217921048861[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]16183.632471124[/C][C]-497.632471124001[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]16088.0812915113[/C][C]2808.91870848873[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]17043.7057276807[/C][C]-727.705727680743[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]17036.6514323675[/C][C]-1400.65143236754[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16756.8066998242[/C][C]406.193300175819[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16971.2331687193[/C][C]-437.233168719285[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16937.3553459562[/C][C]-419.355345956166[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16878.3092708515[/C][C]-503.309270851496[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16761.9031278949[/C][C]-471.903127894908[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16620.0827481544[/C][C]-268.082748154437[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16511.7318683831[/C][C]-568.731868383074[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16285.5566705485[/C][C]76.443329451502[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16231.0020171665[/C][C]161.997982833487[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]16209.9872857143[/C][C]2841.01271428569[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]17080.7772146152[/C][C]-333.777214615184[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]17110.0629916906[/C][C]-790.062991690618[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]16965.7192853769[/C][C]944.280714623124[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17335.174189917[/C][C]-374.174189917027[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17338.4374407454[/C][C]141.562559254551[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17484.6020265021[/C][C]-435.602026502056[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17451.1655701821[/C][C]-572.165570182075[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17341.9284555772[/C][C]131.071544422801[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17423.1467864092[/C][C]-425.146786409223[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17330.9020061457[/C][C]-23.9020061457049[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17340.3184413362[/C][C]77.6815586637858[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]17381.4174349923[/C][C]2787.58256500765[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]18318.4837616173[/C][C]-447.483761617277[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]18390.446143938[/C][C]-1164.44614393801[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]18195.0498086845[/C][C]866.950191315489[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18584.4807073157[/C][C]-780.480707315681[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18494.1307097858[/C][C]605.869290214159[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18803.9116617852[/C][C]-281.911661785176[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18864.9904230218[/C][C]-804.990423021758[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18734.1744138352[/C][C]134.825586164796[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18855.0216644003[/C][C]-728.021664400261[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18701.9164910761[/C][C]169.083508923904[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18791.9047765196[/C][C]98.0952234804063[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]18870.5714948147[/C][C]2392.42850518534[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19710.1026048817[/C][C]-163.102604881682[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]19879.7644563812[/C][C]-1429.76445638118[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]19621.6312307592[/C][C]632.368769240813[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19939.5880185196[/C][C]-699.588018519578[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]19864.7713565909[/C][C]351.2286434091[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]20085.5752728284[/C][C]-665.57527282841[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19997.2020454161[/C][C]-582.202045416136[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]19888.969962505[/C][C]129.03003749502[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19973.1078369356[/C][C]-1321.10783693559[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19589.9027501806[/C][C]388.09724981941[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19674.5326992168[/C][C]-165.532699216819[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]19604.7984189795[/C][C]2366.20158102052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228452&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228452&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
314000124181582
41347712482.8327141107994.16728588928
51423712466.82737517271770.17262482731
61367412776.3953443526897.604655647427
71352912924.9234187953604.076581204739
81405813040.72879096441017.27120903563
91297513335.195000895-360.195000895035
101432613249.26110093391076.73889906607
111400813609.9191462536398.080853746354
121619313824.02202763432368.97797236571
131448314714.0091672295-231.009167229457
141401114917.8542024259-906.854202425859
151505714883.2206602842173.779339715784
161488415139.2897638107-255.289763810746
171541415266.7081649983147.291835001659
181444015508.2865909109-1068.28659091085
191490015360.8929937452-460.89299374519
201507415337.2377238923-263.237723892255
211444215345.807847159-903.80784715902
221530715125.2022815364181.797718463571
231493815197.1494149678-259.149414967833
241719315137.11210956232055.88789043767
251552815819.3786518188-291.378651818759
261476515876.3162540946-1111.31625409464
271583815643.1414745699194.858525430074
281572315760.2639755474-37.2639755473865
291615015814.9474574309335.052542569112
301548615989.3255338358-503.325533835779
311598615912.007315450373.9926845497248
321598315988.6561050291-5.65610502909112
331569216044.3862776906-352.386277690613
341649015985.7820789511504.217921048861
351568616183.632471124-497.632471124001
361889716088.08129151132808.91870848873
371631617043.7057276807-727.705727680743
381563617036.6514323675-1400.65143236754
391716316756.8066998242406.193300175819
401653416971.2331687193-437.233168719285
411651816937.3553459562-419.355345956166
421637516878.3092708515-503.309270851496
431629016761.9031278949-471.903127894908
441635216620.0827481544-268.082748154437
451594316511.7318683831-568.731868383074
461636216285.556670548576.443329451502
471639316231.0020171665161.997982833487
481905116209.98728571432841.01271428569
491674717080.7772146152-333.777214615184
501632017110.0629916906-790.062991690618
511791016965.7192853769944.280714623124
521696117335.174189917-374.174189917027
531748017338.4374407454141.562559254551
541704917484.6020265021-435.602026502056
551687917451.1655701821-572.165570182075
561747317341.9284555772131.071544422801
571699817423.1467864092-425.146786409223
581730717330.9020061457-23.9020061457049
591741817340.318441336277.6815586637858
602016917381.41743499232787.58256500765
611787118318.4837616173-447.483761617277
621722618390.446143938-1164.44614393801
631906218195.0498086845866.950191315489
641780418584.4807073157-780.480707315681
651910018494.1307097858605.869290214159
661852218803.9116617852-281.911661785176
671806018864.9904230218-804.990423021758
681886918734.1744138352134.825586164796
691812718855.0216644003-728.021664400261
701887118701.9164910761169.083508923904
711889018791.904776519698.0952234804063
722126318870.57149481472392.42850518534
731954719710.1026048817-163.102604881682
741845019879.7644563812-1429.76445638118
752025419621.6312307592632.368769240813
761924019939.5880185196-699.588018519578
772021619864.7713565909351.2286434091
781942020085.5752728284-665.57527282841
791941519997.2020454161-582.202045416136
802001819888.969962505129.03003749502
811865219973.1078369356-1321.10783693559
821997819589.9027501806388.09724981941
831950919674.5326992168-165.532699216819
842197119604.79841897952366.20158102052







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520355.219519477218446.244952238922264.1940867154
8620496.121486216318486.729404101622505.513568331
8720637.023452955518487.713761075222786.3331448358
8820777.925419694718448.429868392623107.4209709967
8920918.827386433918370.210615559923467.4441573078
9021059.72935317318255.631511677423863.8271946687
9121200.631319912218107.762086889924293.5005529345
9221341.533286651417929.669807875624753.3967654272
9321482.435253390617724.161659078625240.7088477025
9421623.337220129817493.687971390825752.9864688687
9521764.239186868917240.336147361526288.1422263764
9621905.141153608116965.8652371626844.4170700562

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20355.2195194772 & 18446.2449522389 & 22264.1940867154 \tabularnewline
86 & 20496.1214862163 & 18486.7294041016 & 22505.513568331 \tabularnewline
87 & 20637.0234529555 & 18487.7137610752 & 22786.3331448358 \tabularnewline
88 & 20777.9254196947 & 18448.4298683926 & 23107.4209709967 \tabularnewline
89 & 20918.8273864339 & 18370.2106155599 & 23467.4441573078 \tabularnewline
90 & 21059.729353173 & 18255.6315116774 & 23863.8271946687 \tabularnewline
91 & 21200.6313199122 & 18107.7620868899 & 24293.5005529345 \tabularnewline
92 & 21341.5332866514 & 17929.6698078756 & 24753.3967654272 \tabularnewline
93 & 21482.4352533906 & 17724.1616590786 & 25240.7088477025 \tabularnewline
94 & 21623.3372201298 & 17493.6879713908 & 25752.9864688687 \tabularnewline
95 & 21764.2391868689 & 17240.3361473615 & 26288.1422263764 \tabularnewline
96 & 21905.1411536081 & 16965.86523716 & 26844.4170700562 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228452&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]20355.2195194772[/C][C]18446.2449522389[/C][C]22264.1940867154[/C][/ROW]
[ROW][C]86[/C][C]20496.1214862163[/C][C]18486.7294041016[/C][C]22505.513568331[/C][/ROW]
[ROW][C]87[/C][C]20637.0234529555[/C][C]18487.7137610752[/C][C]22786.3331448358[/C][/ROW]
[ROW][C]88[/C][C]20777.9254196947[/C][C]18448.4298683926[/C][C]23107.4209709967[/C][/ROW]
[ROW][C]89[/C][C]20918.8273864339[/C][C]18370.2106155599[/C][C]23467.4441573078[/C][/ROW]
[ROW][C]90[/C][C]21059.729353173[/C][C]18255.6315116774[/C][C]23863.8271946687[/C][/ROW]
[ROW][C]91[/C][C]21200.6313199122[/C][C]18107.7620868899[/C][C]24293.5005529345[/C][/ROW]
[ROW][C]92[/C][C]21341.5332866514[/C][C]17929.6698078756[/C][C]24753.3967654272[/C][/ROW]
[ROW][C]93[/C][C]21482.4352533906[/C][C]17724.1616590786[/C][C]25240.7088477025[/C][/ROW]
[ROW][C]94[/C][C]21623.3372201298[/C][C]17493.6879713908[/C][C]25752.9864688687[/C][/ROW]
[ROW][C]95[/C][C]21764.2391868689[/C][C]17240.3361473615[/C][C]26288.1422263764[/C][/ROW]
[ROW][C]96[/C][C]21905.1411536081[/C][C]16965.86523716[/C][C]26844.4170700562[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228452&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228452&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
8520355.219519477218446.244952238922264.1940867154
8620496.121486216318486.729404101622505.513568331
8720637.023452955518487.713761075222786.3331448358
8820777.925419694718448.429868392623107.4209709967
8920918.827386433918370.210615559923467.4441573078
9021059.72935317318255.631511677423863.8271946687
9121200.631319912218107.762086889924293.5005529345
9221341.533286651417929.669807875624753.3967654272
9321482.435253390617724.161659078625240.7088477025
9421623.337220129817493.687971390825752.9864688687
9521764.239186868917240.336147361526288.1422263764
9621905.141153608116965.8652371626844.4170700562



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')