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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 17 Apr 2008 07:27:08 -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/17/t1208438934da4lvnmdyh0073a.htm/, Retrieved Fri, 03 May 2024 07:37:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10164, Retrieved Fri, 03 May 2024 07:37:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsEXPONENTIAL SMOOTHING
Estimated Impact363
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] [test kuleuven] [2008-04-17 13:27:08] [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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10164&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10164&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10164&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.257593917038981
beta0.275620602016356
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.257593917038981 \tabularnewline
beta & 0.275620602016356 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10164&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]0.257593917038981[/C][/ROW]
[ROW][C]beta[/C][C]0.275620602016356[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10164&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10164&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
alpha0.257593917038981
beta0.275620602016356
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
314000124181582
41347712482.8327141109994.167285889096
51423712466.82737517281770.17262482716
61367412776.3953443527897.604655647281
71352912924.9234187952604.076581204808
81405813040.72879096411017.27120903593
91297513335.1950008946-360.195000894586
101432613249.26110093321076.73889906681
111400813609.9191462529398.080853747075
121619313824.02202763352368.97797236650
131448314714.0091672289-231.009167228871
141401114917.8542024250-906.854202425036
151505714883.2206602832173.779339716792
161488415139.2897638098-255.289763809847
171541415266.7081649975147.291835002472
181444015508.2865909102-1068.28659091022
191490015360.8929937446-460.892993744594
201507415337.2377238919-263.237723891854
211444215345.8078471588-903.807847158841
221530715125.2022815364181.797718463629
231493815197.1494149680-259.149414968046
241719315137.11210956272055.88789043734
251552815819.3786518194-291.378651819447
261476515876.3162540952-1111.31625409515
271583815643.1414745702194.858525429809
281572315760.2639755477-37.2639755476648
291615015814.9474574311335.052542568883
301548615989.325533836-503.325533836001
311598615912.007315450473.992684549643
321598315988.6561050292-5.65610502916206
331569216044.3862776907-352.386277690657
341649015985.7820789511504.21792104888
351568616183.6324711241-497.632471124056
361889716088.08129151122808.91870848877
371631617043.7057276810-727.705727681048
381563617036.6514323675-1400.65143236751
391716316756.8066998239406.193300176132
401653416971.2331687191-437.233168719074
411651816937.3553459559-419.35534595593
421637516878.3092708513-503.309270851274
431629016761.9031278947-471.903127894733
441635216620.0827481543-268.082748154338
451594316511.7318683831-568.731868383089
461636216285.556670548676.443329451422
471639316231.0020171667161.997982833258
481905116209.98728571462841.01271428535
491674717080.7772146159-333.777214615868
501632017110.062991691-790.062991690986
511791016965.7192853769944.280714623052
521696117335.1741899171-374.174189917117
531748017338.4374407453141.562559254660
541704917484.6020265019-435.602026501892
551687917451.1655701818-572.165570181805
561747317341.9284555769131.071544423117
571699817423.146786409-425.146786409005
581730717330.9020061455-23.9020061455049
591741817340.318441336177.6815586638913
602016917381.41743499232787.58256500767
611787118318.4837616176-447.483761617645
621722618390.4461439381-1164.44614393811
631906218195.0498086843866.950191315664
641780418584.4807073156-780.480707315615
651910018494.1307097856605.869290214378
661852218803.9116617851-281.911661785070
671806018864.9904230216-804.990423021602
681886918734.1744138350134.825586165025
691812718855.0216644002-728.021664400152
701887118701.9164910760169.083508924028
711889018791.904776519698.0952234803808
722126318870.57149481482392.42850518523
731954719710.1026048821-163.102604882108
741845019879.7644563814-1429.76445638138
752025419621.6312307591632.368769240937
761924019939.5880185195-699.588018519546
772021619864.7713565907351.228643409253
781942020085.5752728283-665.575272828344
791941519997.202045416-582.202045415997
802001819888.9699625048129.030037495155
811865219973.1078369356-1321.10783693559
821997819589.9027501805388.097249819497
831950919674.5326992170-165.532699216954
842197119604.79841897972366.20158102032

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14000 & 12418 & 1582 \tabularnewline
4 & 13477 & 12482.8327141109 & 994.167285889096 \tabularnewline
5 & 14237 & 12466.8273751728 & 1770.17262482716 \tabularnewline
6 & 13674 & 12776.3953443527 & 897.604655647281 \tabularnewline
7 & 13529 & 12924.9234187952 & 604.076581204808 \tabularnewline
8 & 14058 & 13040.7287909641 & 1017.27120903593 \tabularnewline
9 & 12975 & 13335.1950008946 & -360.195000894586 \tabularnewline
10 & 14326 & 13249.2611009332 & 1076.73889906681 \tabularnewline
11 & 14008 & 13609.9191462529 & 398.080853747075 \tabularnewline
12 & 16193 & 13824.0220276335 & 2368.97797236650 \tabularnewline
13 & 14483 & 14714.0091672289 & -231.009167228871 \tabularnewline
14 & 14011 & 14917.8542024250 & -906.854202425036 \tabularnewline
15 & 15057 & 14883.2206602832 & 173.779339716792 \tabularnewline
16 & 14884 & 15139.2897638098 & -255.289763809847 \tabularnewline
17 & 15414 & 15266.7081649975 & 147.291835002472 \tabularnewline
18 & 14440 & 15508.2865909102 & -1068.28659091022 \tabularnewline
19 & 14900 & 15360.8929937446 & -460.892993744594 \tabularnewline
20 & 15074 & 15337.2377238919 & -263.237723891854 \tabularnewline
21 & 14442 & 15345.8078471588 & -903.807847158841 \tabularnewline
22 & 15307 & 15125.2022815364 & 181.797718463629 \tabularnewline
23 & 14938 & 15197.1494149680 & -259.149414968046 \tabularnewline
24 & 17193 & 15137.1121095627 & 2055.88789043734 \tabularnewline
25 & 15528 & 15819.3786518194 & -291.378651819447 \tabularnewline
26 & 14765 & 15876.3162540952 & -1111.31625409515 \tabularnewline
27 & 15838 & 15643.1414745702 & 194.858525429809 \tabularnewline
28 & 15723 & 15760.2639755477 & -37.2639755476648 \tabularnewline
29 & 16150 & 15814.9474574311 & 335.052542568883 \tabularnewline
30 & 15486 & 15989.325533836 & -503.325533836001 \tabularnewline
31 & 15986 & 15912.0073154504 & 73.992684549643 \tabularnewline
32 & 15983 & 15988.6561050292 & -5.65610502916206 \tabularnewline
33 & 15692 & 16044.3862776907 & -352.386277690657 \tabularnewline
34 & 16490 & 15985.7820789511 & 504.21792104888 \tabularnewline
35 & 15686 & 16183.6324711241 & -497.632471124056 \tabularnewline
36 & 18897 & 16088.0812915112 & 2808.91870848877 \tabularnewline
37 & 16316 & 17043.7057276810 & -727.705727681048 \tabularnewline
38 & 15636 & 17036.6514323675 & -1400.65143236751 \tabularnewline
39 & 17163 & 16756.8066998239 & 406.193300176132 \tabularnewline
40 & 16534 & 16971.2331687191 & -437.233168719074 \tabularnewline
41 & 16518 & 16937.3553459559 & -419.35534595593 \tabularnewline
42 & 16375 & 16878.3092708513 & -503.309270851274 \tabularnewline
43 & 16290 & 16761.9031278947 & -471.903127894733 \tabularnewline
44 & 16352 & 16620.0827481543 & -268.082748154338 \tabularnewline
45 & 15943 & 16511.7318683831 & -568.731868383089 \tabularnewline
46 & 16362 & 16285.5566705486 & 76.443329451422 \tabularnewline
47 & 16393 & 16231.0020171667 & 161.997982833258 \tabularnewline
48 & 19051 & 16209.9872857146 & 2841.01271428535 \tabularnewline
49 & 16747 & 17080.7772146159 & -333.777214615868 \tabularnewline
50 & 16320 & 17110.062991691 & -790.062991690986 \tabularnewline
51 & 17910 & 16965.7192853769 & 944.280714623052 \tabularnewline
52 & 16961 & 17335.1741899171 & -374.174189917117 \tabularnewline
53 & 17480 & 17338.4374407453 & 141.562559254660 \tabularnewline
54 & 17049 & 17484.6020265019 & -435.602026501892 \tabularnewline
55 & 16879 & 17451.1655701818 & -572.165570181805 \tabularnewline
56 & 17473 & 17341.9284555769 & 131.071544423117 \tabularnewline
57 & 16998 & 17423.146786409 & -425.146786409005 \tabularnewline
58 & 17307 & 17330.9020061455 & -23.9020061455049 \tabularnewline
59 & 17418 & 17340.3184413361 & 77.6815586638913 \tabularnewline
60 & 20169 & 17381.4174349923 & 2787.58256500767 \tabularnewline
61 & 17871 & 18318.4837616176 & -447.483761617645 \tabularnewline
62 & 17226 & 18390.4461439381 & -1164.44614393811 \tabularnewline
63 & 19062 & 18195.0498086843 & 866.950191315664 \tabularnewline
64 & 17804 & 18584.4807073156 & -780.480707315615 \tabularnewline
65 & 19100 & 18494.1307097856 & 605.869290214378 \tabularnewline
66 & 18522 & 18803.9116617851 & -281.911661785070 \tabularnewline
67 & 18060 & 18864.9904230216 & -804.990423021602 \tabularnewline
68 & 18869 & 18734.1744138350 & 134.825586165025 \tabularnewline
69 & 18127 & 18855.0216644002 & -728.021664400152 \tabularnewline
70 & 18871 & 18701.9164910760 & 169.083508924028 \tabularnewline
71 & 18890 & 18791.9047765196 & 98.0952234803808 \tabularnewline
72 & 21263 & 18870.5714948148 & 2392.42850518523 \tabularnewline
73 & 19547 & 19710.1026048821 & -163.102604882108 \tabularnewline
74 & 18450 & 19879.7644563814 & -1429.76445638138 \tabularnewline
75 & 20254 & 19621.6312307591 & 632.368769240937 \tabularnewline
76 & 19240 & 19939.5880185195 & -699.588018519546 \tabularnewline
77 & 20216 & 19864.7713565907 & 351.228643409253 \tabularnewline
78 & 19420 & 20085.5752728283 & -665.575272828344 \tabularnewline
79 & 19415 & 19997.202045416 & -582.202045415997 \tabularnewline
80 & 20018 & 19888.9699625048 & 129.030037495155 \tabularnewline
81 & 18652 & 19973.1078369356 & -1321.10783693559 \tabularnewline
82 & 19978 & 19589.9027501805 & 388.097249819497 \tabularnewline
83 & 19509 & 19674.5326992170 & -165.532699216954 \tabularnewline
84 & 21971 & 19604.7984189797 & 2366.20158102032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10164&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]12482.8327141109[/C][C]994.167285889096[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]12466.8273751728[/C][C]1770.17262482716[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]12776.3953443527[/C][C]897.604655647281[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]12924.9234187952[/C][C]604.076581204808[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]13040.7287909641[/C][C]1017.27120903593[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13335.1950008946[/C][C]-360.195000894586[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]13249.2611009332[/C][C]1076.73889906681[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]13609.9191462529[/C][C]398.080853747075[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]13824.0220276335[/C][C]2368.97797236650[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14714.0091672289[/C][C]-231.009167228871[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14917.8542024250[/C][C]-906.854202425036[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14883.2206602832[/C][C]173.779339716792[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]15139.2897638098[/C][C]-255.289763809847[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]15266.7081649975[/C][C]147.291835002472[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]15508.2865909102[/C][C]-1068.28659091022[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]15360.8929937446[/C][C]-460.892993744594[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]15337.2377238919[/C][C]-263.237723891854[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]15345.8078471588[/C][C]-903.807847158841[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]15125.2022815364[/C][C]181.797718463629[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]15197.1494149680[/C][C]-259.149414968046[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]15137.1121095627[/C][C]2055.88789043734[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15819.3786518194[/C][C]-291.378651819447[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15876.3162540952[/C][C]-1111.31625409515[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15643.1414745702[/C][C]194.858525429809[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15760.2639755477[/C][C]-37.2639755476648[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]15814.9474574311[/C][C]335.052542568883[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15989.325533836[/C][C]-503.325533836001[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15912.0073154504[/C][C]73.992684549643[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]15988.6561050292[/C][C]-5.65610502916206[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]16044.3862776907[/C][C]-352.386277690657[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]15985.7820789511[/C][C]504.21792104888[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]16183.6324711241[/C][C]-497.632471124056[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]16088.0812915112[/C][C]2808.91870848877[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]17043.7057276810[/C][C]-727.705727681048[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]17036.6514323675[/C][C]-1400.65143236751[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16756.8066998239[/C][C]406.193300176132[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16971.2331687191[/C][C]-437.233168719074[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16937.3553459559[/C][C]-419.35534595593[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16878.3092708513[/C][C]-503.309270851274[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16761.9031278947[/C][C]-471.903127894733[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16620.0827481543[/C][C]-268.082748154338[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16511.7318683831[/C][C]-568.731868383089[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16285.5566705486[/C][C]76.443329451422[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16231.0020171667[/C][C]161.997982833258[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]16209.9872857146[/C][C]2841.01271428535[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]17080.7772146159[/C][C]-333.777214615868[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]17110.062991691[/C][C]-790.062991690986[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]16965.7192853769[/C][C]944.280714623052[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17335.1741899171[/C][C]-374.174189917117[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17338.4374407453[/C][C]141.562559254660[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17484.6020265019[/C][C]-435.602026501892[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17451.1655701818[/C][C]-572.165570181805[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17341.9284555769[/C][C]131.071544423117[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17423.146786409[/C][C]-425.146786409005[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17330.9020061455[/C][C]-23.9020061455049[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17340.3184413361[/C][C]77.6815586638913[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]17381.4174349923[/C][C]2787.58256500767[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]18318.4837616176[/C][C]-447.483761617645[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]18390.4461439381[/C][C]-1164.44614393811[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]18195.0498086843[/C][C]866.950191315664[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18584.4807073156[/C][C]-780.480707315615[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18494.1307097856[/C][C]605.869290214378[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18803.9116617851[/C][C]-281.911661785070[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18864.9904230216[/C][C]-804.990423021602[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18734.1744138350[/C][C]134.825586165025[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18855.0216644002[/C][C]-728.021664400152[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18701.9164910760[/C][C]169.083508924028[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18791.9047765196[/C][C]98.0952234803808[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]18870.5714948148[/C][C]2392.42850518523[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19710.1026048821[/C][C]-163.102604882108[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]19879.7644563814[/C][C]-1429.76445638138[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]19621.6312307591[/C][C]632.368769240937[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19939.5880185195[/C][C]-699.588018519546[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]19864.7713565907[/C][C]351.228643409253[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]20085.5752728283[/C][C]-665.575272828344[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19997.202045416[/C][C]-582.202045415997[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]19888.9699625048[/C][C]129.030037495155[/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]19589.9027501805[/C][C]388.097249819497[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19674.5326992170[/C][C]-165.532699216954[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]19604.7984189797[/C][C]2366.20158102032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10164&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10164&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
41347712482.8327141109994.167285889096
51423712466.82737517281770.17262482716
61367412776.3953443527897.604655647281
71352912924.9234187952604.076581204808
81405813040.72879096411017.27120903593
91297513335.1950008946-360.195000894586
101432613249.26110093321076.73889906681
111400813609.9191462529398.080853747075
121619313824.02202763352368.97797236650
131448314714.0091672289-231.009167228871
141401114917.8542024250-906.854202425036
151505714883.2206602832173.779339716792
161488415139.2897638098-255.289763809847
171541415266.7081649975147.291835002472
181444015508.2865909102-1068.28659091022
191490015360.8929937446-460.892993744594
201507415337.2377238919-263.237723891854
211444215345.8078471588-903.807847158841
221530715125.2022815364181.797718463629
231493815197.1494149680-259.149414968046
241719315137.11210956272055.88789043734
251552815819.3786518194-291.378651819447
261476515876.3162540952-1111.31625409515
271583815643.1414745702194.858525429809
281572315760.2639755477-37.2639755476648
291615015814.9474574311335.052542568883
301548615989.325533836-503.325533836001
311598615912.007315450473.992684549643
321598315988.6561050292-5.65610502916206
331569216044.3862776907-352.386277690657
341649015985.7820789511504.21792104888
351568616183.6324711241-497.632471124056
361889716088.08129151122808.91870848877
371631617043.7057276810-727.705727681048
381563617036.6514323675-1400.65143236751
391716316756.8066998239406.193300176132
401653416971.2331687191-437.233168719074
411651816937.3553459559-419.35534595593
421637516878.3092708513-503.309270851274
431629016761.9031278947-471.903127894733
441635216620.0827481543-268.082748154338
451594316511.7318683831-568.731868383089
461636216285.556670548676.443329451422
471639316231.0020171667161.997982833258
481905116209.98728571462841.01271428535
491674717080.7772146159-333.777214615868
501632017110.062991691-790.062991690986
511791016965.7192853769944.280714623052
521696117335.1741899171-374.174189917117
531748017338.4374407453141.562559254660
541704917484.6020265019-435.602026501892
551687917451.1655701818-572.165570181805
561747317341.9284555769131.071544423117
571699817423.146786409-425.146786409005
581730717330.9020061455-23.9020061455049
591741817340.318441336177.6815586638913
602016917381.41743499232787.58256500767
611787118318.4837616176-447.483761617645
621722618390.4461439381-1164.44614393811
631906218195.0498086843866.950191315664
641780418584.4807073156-780.480707315615
651910018494.1307097856605.869290214378
661852218803.9116617851-281.911661785070
671806018864.9904230216-804.990423021602
681886918734.1744138350134.825586165025
691812718855.0216644002-728.021664400152
701887118701.9164910760169.083508924028
711889018791.904776519698.0952234803808
722126318870.57149481482392.42850518523
731954719710.1026048821-163.102604882108
741845019879.7644563814-1429.76445638138
752025419621.6312307591632.368769240937
761924019939.5880185195-699.588018519546
772021619864.7713565907351.228643409253
781942020085.5752728283-665.575272828344
791941519997.202045416-582.202045415997
802001819888.9699625048129.030037495155
811865219973.1078369356-1321.10783693559
821997819589.9027501805388.097249819497
831950919674.5326992170-165.532699216954
842197119604.79841897972366.20158102032







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520355.219519477718446.244952239522264.1940867159
8620496.121486216818486.729404102122505.5135683316
8720637.02345295618487.713761075722786.3331448364
8820777.925419695218448.429868393023107.4209709973
8920918.827386434318370.210615560323467.4441573083
9021059.729353173518255.631511677923863.8271946691
9121200.631319912618107.762086890624293.5005529347
9221341.533286651817929.669807876424753.3967654272
9321482.435253391017724.161659079625240.7088477024
9421623.337220130117493.687971392025752.9864688683
9521764.239186869317240.336147362926288.1422263757
9621905.141153608416965.865237161626844.4170700553

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20355.2195194777 & 18446.2449522395 & 22264.1940867159 \tabularnewline
86 & 20496.1214862168 & 18486.7294041021 & 22505.5135683316 \tabularnewline
87 & 20637.023452956 & 18487.7137610757 & 22786.3331448364 \tabularnewline
88 & 20777.9254196952 & 18448.4298683930 & 23107.4209709973 \tabularnewline
89 & 20918.8273864343 & 18370.2106155603 & 23467.4441573083 \tabularnewline
90 & 21059.7293531735 & 18255.6315116779 & 23863.8271946691 \tabularnewline
91 & 21200.6313199126 & 18107.7620868906 & 24293.5005529347 \tabularnewline
92 & 21341.5332866518 & 17929.6698078764 & 24753.3967654272 \tabularnewline
93 & 21482.4352533910 & 17724.1616590796 & 25240.7088477024 \tabularnewline
94 & 21623.3372201301 & 17493.6879713920 & 25752.9864688683 \tabularnewline
95 & 21764.2391868693 & 17240.3361473629 & 26288.1422263757 \tabularnewline
96 & 21905.1411536084 & 16965.8652371616 & 26844.4170700553 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10164&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]20355.2195194777[/C][C]18446.2449522395[/C][C]22264.1940867159[/C][/ROW]
[ROW][C]86[/C][C]20496.1214862168[/C][C]18486.7294041021[/C][C]22505.5135683316[/C][/ROW]
[ROW][C]87[/C][C]20637.023452956[/C][C]18487.7137610757[/C][C]22786.3331448364[/C][/ROW]
[ROW][C]88[/C][C]20777.9254196952[/C][C]18448.4298683930[/C][C]23107.4209709973[/C][/ROW]
[ROW][C]89[/C][C]20918.8273864343[/C][C]18370.2106155603[/C][C]23467.4441573083[/C][/ROW]
[ROW][C]90[/C][C]21059.7293531735[/C][C]18255.6315116779[/C][C]23863.8271946691[/C][/ROW]
[ROW][C]91[/C][C]21200.6313199126[/C][C]18107.7620868906[/C][C]24293.5005529347[/C][/ROW]
[ROW][C]92[/C][C]21341.5332866518[/C][C]17929.6698078764[/C][C]24753.3967654272[/C][/ROW]
[ROW][C]93[/C][C]21482.4352533910[/C][C]17724.1616590796[/C][C]25240.7088477024[/C][/ROW]
[ROW][C]94[/C][C]21623.3372201301[/C][C]17493.6879713920[/C][C]25752.9864688683[/C][/ROW]
[ROW][C]95[/C][C]21764.2391868693[/C][C]17240.3361473629[/C][C]26288.1422263757[/C][/ROW]
[ROW][C]96[/C][C]21905.1411536084[/C][C]16965.8652371616[/C][C]26844.4170700553[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10164&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10164&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
8520355.219519477718446.244952239522264.1940867159
8620496.121486216818486.729404102122505.5135683316
8720637.02345295618487.713761075722786.3331448364
8820777.925419695218448.429868393023107.4209709973
8920918.827386434318370.210615560323467.4441573083
9021059.729353173518255.631511677923863.8271946691
9121200.631319912618107.762086890624293.5005529347
9221341.533286651817929.669807876424753.3967654272
9321482.435253391017724.161659079625240.7088477024
9421623.337220130117493.687971392025752.9864688683
9521764.239186869317240.336147362926288.1422263757
9621905.141153608416965.865237161626844.4170700553



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')