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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 Apr 2008 15:45:34 -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/27/t1209332797uek53m1r4zj46e7.htm/, Retrieved Sun, 05 May 2024 08:50:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10881, Retrieved Sun, 05 May 2024 08:50:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact234
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 17:43:04] [74be16979710d4c4e7c6647856088456]
-    D    [Exponential Smoothing] [test] [2008-04-27 21:45:34] [a5eabed6afc578bb0dc5ff43fff035a6] [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 time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10881&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10881&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.283890683571533
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.283890683571533 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10881&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]0.283890683571533[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10881&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
alpha0.283890683571533
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21287313328-455
31400013198.8297389750801.170261025047
41347713426.274512034550.7254879654629
51423713440.6750054876796.324994512448
61367413666.74425252487.25574747521205
71352913668.8040916353-139.804091635348
81405813629.1150124949428.884987505109
91297513750.8714647713-775.871464771284
101432613530.6087842737795.391215726282
111400813756.4129402130251.587059786954
121619313827.83616259372365.16383740628
131448314499.2841411537-16.2841411536556
141401114494.6612251902-483.66122519017
151505714357.3543093539699.645690646114
161488414555.9772027293328.022797270711
171541414649.0998188735764.900181126482
181444014866.2478541575-426.247854157504
191490014745.2400594698154.759940530170
201507414789.1749647764284.82503522357
211444214870.0341387243-428.034138724335
221530714748.5192344899558.480765510069
231493814907.066720772130.9332792278619
241719314915.84839055722277.15160944276
251552815562.3105175580-34.3105175579658
261476515552.5700812747-787.570081274742
271583815328.9862725412509.013727458832
281572315473.4905275767249.509472423251
291615015544.3239422606605.676057739442
301548615716.2697323151-230.269732315121
311598615650.8983006023335.101699397654
321598315746.0305511103236.969448889671
331569215813.3039699412-121.303969941187
341649015778.8669029946711.133097005357
351568615980.7509640138-294.750964013836
361889715897.07391135662999.92608864342
371631616748.7249793256-432.724979325634
381563616625.8783891464-989.8783891464
391716316344.8611365989818.138863401058
401653416577.1231377863-43.1231377863041
411651816564.8808807224-46.8808807224013
421637516551.5718354477-176.571835447685
431629016501.4447363830-211.444736382960
441635216441.4175456336-89.417545633598
451594316416.0327374804-473.032737480386
461636216281.743150285480.2568497146349
471639316304.527322212288.4726777878495
481905116329.64389118672721.35610881325
491674717102.2115371593-355.211537159306
501632017001.3702910627-681.370291062656
511791016807.93561336751102.06438663246
521696117120.8014254285-159.801425428472
531748017075.4352895279404.564710472121
541704917190.2874417327-141.287441732729
551687917150.1772533192-271.177253319151
561747317073.1925575053399.807442494675
571699817186.6941656521-188.694165652123
581730717133.1256499792173.874350020818
591741817182.4869580621235.513041937851
602016917249.34691652792919.65308347211
611787118078.2092261865-207.209226186525
621722618019.3844573221-793.384457322103
631906217794.15000139791267.84999860210
641780418154.0808041672-350.080804167217
651910018054.69612536691045.30387463309
661852218351.4481568765170.551843123529
671806018399.8662362052-339.866236205195
681886918303.381378086565.618621913982
691812718463.9552353020-336.955235301968
701887118368.2967832191502.703216780916
711889018511.0095430646378.990456935375
722126318618.60140295112644.39859704890
731954719369.3215283029177.678471697087
741845019419.7627910889-969.762791088946
752025419144.45616942451109.54383057553
761924019459.4453259391-219.445325939130
772021619397.1468423517818.853157648307
781942019629.6116250212-209.611625021178
791941519570.1048375094-155.104837509374
802001819526.0720191636491.927980836415
811865219665.7257899112-1013.72578991120
821997819377.9384824592600.061517540784
831950919548.2903568588-39.2903568588408
842197119537.13619059242433.86380940758

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 12873 & 13328 & -455 \tabularnewline
3 & 14000 & 13198.8297389750 & 801.170261025047 \tabularnewline
4 & 13477 & 13426.2745120345 & 50.7254879654629 \tabularnewline
5 & 14237 & 13440.6750054876 & 796.324994512448 \tabularnewline
6 & 13674 & 13666.7442525248 & 7.25574747521205 \tabularnewline
7 & 13529 & 13668.8040916353 & -139.804091635348 \tabularnewline
8 & 14058 & 13629.1150124949 & 428.884987505109 \tabularnewline
9 & 12975 & 13750.8714647713 & -775.871464771284 \tabularnewline
10 & 14326 & 13530.6087842737 & 795.391215726282 \tabularnewline
11 & 14008 & 13756.4129402130 & 251.587059786954 \tabularnewline
12 & 16193 & 13827.8361625937 & 2365.16383740628 \tabularnewline
13 & 14483 & 14499.2841411537 & -16.2841411536556 \tabularnewline
14 & 14011 & 14494.6612251902 & -483.66122519017 \tabularnewline
15 & 15057 & 14357.3543093539 & 699.645690646114 \tabularnewline
16 & 14884 & 14555.9772027293 & 328.022797270711 \tabularnewline
17 & 15414 & 14649.0998188735 & 764.900181126482 \tabularnewline
18 & 14440 & 14866.2478541575 & -426.247854157504 \tabularnewline
19 & 14900 & 14745.2400594698 & 154.759940530170 \tabularnewline
20 & 15074 & 14789.1749647764 & 284.82503522357 \tabularnewline
21 & 14442 & 14870.0341387243 & -428.034138724335 \tabularnewline
22 & 15307 & 14748.5192344899 & 558.480765510069 \tabularnewline
23 & 14938 & 14907.0667207721 & 30.9332792278619 \tabularnewline
24 & 17193 & 14915.8483905572 & 2277.15160944276 \tabularnewline
25 & 15528 & 15562.3105175580 & -34.3105175579658 \tabularnewline
26 & 14765 & 15552.5700812747 & -787.570081274742 \tabularnewline
27 & 15838 & 15328.9862725412 & 509.013727458832 \tabularnewline
28 & 15723 & 15473.4905275767 & 249.509472423251 \tabularnewline
29 & 16150 & 15544.3239422606 & 605.676057739442 \tabularnewline
30 & 15486 & 15716.2697323151 & -230.269732315121 \tabularnewline
31 & 15986 & 15650.8983006023 & 335.101699397654 \tabularnewline
32 & 15983 & 15746.0305511103 & 236.969448889671 \tabularnewline
33 & 15692 & 15813.3039699412 & -121.303969941187 \tabularnewline
34 & 16490 & 15778.8669029946 & 711.133097005357 \tabularnewline
35 & 15686 & 15980.7509640138 & -294.750964013836 \tabularnewline
36 & 18897 & 15897.0739113566 & 2999.92608864342 \tabularnewline
37 & 16316 & 16748.7249793256 & -432.724979325634 \tabularnewline
38 & 15636 & 16625.8783891464 & -989.8783891464 \tabularnewline
39 & 17163 & 16344.8611365989 & 818.138863401058 \tabularnewline
40 & 16534 & 16577.1231377863 & -43.1231377863041 \tabularnewline
41 & 16518 & 16564.8808807224 & -46.8808807224013 \tabularnewline
42 & 16375 & 16551.5718354477 & -176.571835447685 \tabularnewline
43 & 16290 & 16501.4447363830 & -211.444736382960 \tabularnewline
44 & 16352 & 16441.4175456336 & -89.417545633598 \tabularnewline
45 & 15943 & 16416.0327374804 & -473.032737480386 \tabularnewline
46 & 16362 & 16281.7431502854 & 80.2568497146349 \tabularnewline
47 & 16393 & 16304.5273222122 & 88.4726777878495 \tabularnewline
48 & 19051 & 16329.6438911867 & 2721.35610881325 \tabularnewline
49 & 16747 & 17102.2115371593 & -355.211537159306 \tabularnewline
50 & 16320 & 17001.3702910627 & -681.370291062656 \tabularnewline
51 & 17910 & 16807.9356133675 & 1102.06438663246 \tabularnewline
52 & 16961 & 17120.8014254285 & -159.801425428472 \tabularnewline
53 & 17480 & 17075.4352895279 & 404.564710472121 \tabularnewline
54 & 17049 & 17190.2874417327 & -141.287441732729 \tabularnewline
55 & 16879 & 17150.1772533192 & -271.177253319151 \tabularnewline
56 & 17473 & 17073.1925575053 & 399.807442494675 \tabularnewline
57 & 16998 & 17186.6941656521 & -188.694165652123 \tabularnewline
58 & 17307 & 17133.1256499792 & 173.874350020818 \tabularnewline
59 & 17418 & 17182.4869580621 & 235.513041937851 \tabularnewline
60 & 20169 & 17249.3469165279 & 2919.65308347211 \tabularnewline
61 & 17871 & 18078.2092261865 & -207.209226186525 \tabularnewline
62 & 17226 & 18019.3844573221 & -793.384457322103 \tabularnewline
63 & 19062 & 17794.1500013979 & 1267.84999860210 \tabularnewline
64 & 17804 & 18154.0808041672 & -350.080804167217 \tabularnewline
65 & 19100 & 18054.6961253669 & 1045.30387463309 \tabularnewline
66 & 18522 & 18351.4481568765 & 170.551843123529 \tabularnewline
67 & 18060 & 18399.8662362052 & -339.866236205195 \tabularnewline
68 & 18869 & 18303.381378086 & 565.618621913982 \tabularnewline
69 & 18127 & 18463.9552353020 & -336.955235301968 \tabularnewline
70 & 18871 & 18368.2967832191 & 502.703216780916 \tabularnewline
71 & 18890 & 18511.0095430646 & 378.990456935375 \tabularnewline
72 & 21263 & 18618.6014029511 & 2644.39859704890 \tabularnewline
73 & 19547 & 19369.3215283029 & 177.678471697087 \tabularnewline
74 & 18450 & 19419.7627910889 & -969.762791088946 \tabularnewline
75 & 20254 & 19144.4561694245 & 1109.54383057553 \tabularnewline
76 & 19240 & 19459.4453259391 & -219.445325939130 \tabularnewline
77 & 20216 & 19397.1468423517 & 818.853157648307 \tabularnewline
78 & 19420 & 19629.6116250212 & -209.611625021178 \tabularnewline
79 & 19415 & 19570.1048375094 & -155.104837509374 \tabularnewline
80 & 20018 & 19526.0720191636 & 491.927980836415 \tabularnewline
81 & 18652 & 19665.7257899112 & -1013.72578991120 \tabularnewline
82 & 19978 & 19377.9384824592 & 600.061517540784 \tabularnewline
83 & 19509 & 19548.2903568588 & -39.2903568588408 \tabularnewline
84 & 21971 & 19537.1361905924 & 2433.86380940758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10881&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]13198.8297389750[/C][C]801.170261025047[/C][/ROW]
[ROW][C]4[/C][C]13477[/C][C]13426.2745120345[/C][C]50.7254879654629[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]13440.6750054876[/C][C]796.324994512448[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]13666.7442525248[/C][C]7.25574747521205[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]13668.8040916353[/C][C]-139.804091635348[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]13629.1150124949[/C][C]428.884987505109[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13750.8714647713[/C][C]-775.871464771284[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]13530.6087842737[/C][C]795.391215726282[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]13756.4129402130[/C][C]251.587059786954[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]13827.8361625937[/C][C]2365.16383740628[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14499.2841411537[/C][C]-16.2841411536556[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14494.6612251902[/C][C]-483.66122519017[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14357.3543093539[/C][C]699.645690646114[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14555.9772027293[/C][C]328.022797270711[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]14649.0998188735[/C][C]764.900181126482[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14866.2478541575[/C][C]-426.247854157504[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14745.2400594698[/C][C]154.759940530170[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]14789.1749647764[/C][C]284.82503522357[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14870.0341387243[/C][C]-428.034138724335[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]14748.5192344899[/C][C]558.480765510069[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14907.0667207721[/C][C]30.9332792278619[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]14915.8483905572[/C][C]2277.15160944276[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15562.3105175580[/C][C]-34.3105175579658[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15552.5700812747[/C][C]-787.570081274742[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15328.9862725412[/C][C]509.013727458832[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15473.4905275767[/C][C]249.509472423251[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]15544.3239422606[/C][C]605.676057739442[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15716.2697323151[/C][C]-230.269732315121[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15650.8983006023[/C][C]335.101699397654[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]15746.0305511103[/C][C]236.969448889671[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15813.3039699412[/C][C]-121.303969941187[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]15778.8669029946[/C][C]711.133097005357[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]15980.7509640138[/C][C]-294.750964013836[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]15897.0739113566[/C][C]2999.92608864342[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16748.7249793256[/C][C]-432.724979325634[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]16625.8783891464[/C][C]-989.8783891464[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16344.8611365989[/C][C]818.138863401058[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16577.1231377863[/C][C]-43.1231377863041[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16564.8808807224[/C][C]-46.8808807224013[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16551.5718354477[/C][C]-176.571835447685[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16501.4447363830[/C][C]-211.444736382960[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16441.4175456336[/C][C]-89.417545633598[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16416.0327374804[/C][C]-473.032737480386[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16281.7431502854[/C][C]80.2568497146349[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16304.5273222122[/C][C]88.4726777878495[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]16329.6438911867[/C][C]2721.35610881325[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]17102.2115371593[/C][C]-355.211537159306[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]17001.3702910627[/C][C]-681.370291062656[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]16807.9356133675[/C][C]1102.06438663246[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17120.8014254285[/C][C]-159.801425428472[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17075.4352895279[/C][C]404.564710472121[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17190.2874417327[/C][C]-141.287441732729[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17150.1772533192[/C][C]-271.177253319151[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17073.1925575053[/C][C]399.807442494675[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17186.6941656521[/C][C]-188.694165652123[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17133.1256499792[/C][C]173.874350020818[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17182.4869580621[/C][C]235.513041937851[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]17249.3469165279[/C][C]2919.65308347211[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]18078.2092261865[/C][C]-207.209226186525[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]18019.3844573221[/C][C]-793.384457322103[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]17794.1500013979[/C][C]1267.84999860210[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18154.0808041672[/C][C]-350.080804167217[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18054.6961253669[/C][C]1045.30387463309[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18351.4481568765[/C][C]170.551843123529[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18399.8662362052[/C][C]-339.866236205195[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18303.381378086[/C][C]565.618621913982[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18463.9552353020[/C][C]-336.955235301968[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18368.2967832191[/C][C]502.703216780916[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18511.0095430646[/C][C]378.990456935375[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]18618.6014029511[/C][C]2644.39859704890[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19369.3215283029[/C][C]177.678471697087[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]19419.7627910889[/C][C]-969.762791088946[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]19144.4561694245[/C][C]1109.54383057553[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19459.4453259391[/C][C]-219.445325939130[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]19397.1468423517[/C][C]818.853157648307[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19629.6116250212[/C][C]-209.611625021178[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19570.1048375094[/C][C]-155.104837509374[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]19526.0720191636[/C][C]491.927980836415[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19665.7257899112[/C][C]-1013.72578991120[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19377.9384824592[/C][C]600.061517540784[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19548.2903568588[/C][C]-39.2903568588408[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]19537.1361905924[/C][C]2433.86380940758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10881&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
31400013198.8297389750801.170261025047
41347713426.274512034550.7254879654629
51423713440.6750054876796.324994512448
61367413666.74425252487.25574747521205
71352913668.8040916353-139.804091635348
81405813629.1150124949428.884987505109
91297513750.8714647713-775.871464771284
101432613530.6087842737795.391215726282
111400813756.4129402130251.587059786954
121619313827.83616259372365.16383740628
131448314499.2841411537-16.2841411536556
141401114494.6612251902-483.66122519017
151505714357.3543093539699.645690646114
161488414555.9772027293328.022797270711
171541414649.0998188735764.900181126482
181444014866.2478541575-426.247854157504
191490014745.2400594698154.759940530170
201507414789.1749647764284.82503522357
211444214870.0341387243-428.034138724335
221530714748.5192344899558.480765510069
231493814907.066720772130.9332792278619
241719314915.84839055722277.15160944276
251552815562.3105175580-34.3105175579658
261476515552.5700812747-787.570081274742
271583815328.9862725412509.013727458832
281572315473.4905275767249.509472423251
291615015544.3239422606605.676057739442
301548615716.2697323151-230.269732315121
311598615650.8983006023335.101699397654
321598315746.0305511103236.969448889671
331569215813.3039699412-121.303969941187
341649015778.8669029946711.133097005357
351568615980.7509640138-294.750964013836
361889715897.07391135662999.92608864342
371631616748.7249793256-432.724979325634
381563616625.8783891464-989.8783891464
391716316344.8611365989818.138863401058
401653416577.1231377863-43.1231377863041
411651816564.8808807224-46.8808807224013
421637516551.5718354477-176.571835447685
431629016501.4447363830-211.444736382960
441635216441.4175456336-89.417545633598
451594316416.0327374804-473.032737480386
461636216281.743150285480.2568497146349
471639316304.527322212288.4726777878495
481905116329.64389118672721.35610881325
491674717102.2115371593-355.211537159306
501632017001.3702910627-681.370291062656
511791016807.93561336751102.06438663246
521696117120.8014254285-159.801425428472
531748017075.4352895279404.564710472121
541704917190.2874417327-141.287441732729
551687917150.1772533192-271.177253319151
561747317073.1925575053399.807442494675
571699817186.6941656521-188.694165652123
581730717133.1256499792173.874350020818
591741817182.4869580621235.513041937851
602016917249.34691652792919.65308347211
611787118078.2092261865-207.209226186525
621722618019.3844573221-793.384457322103
631906217794.15000139791267.84999860210
641780418154.0808041672-350.080804167217
651910018054.69612536691045.30387463309
661852218351.4481568765170.551843123529
671806018399.8662362052-339.866236205195
681886918303.381378086565.618621913982
691812718463.9552353020-336.955235301968
701887118368.2967832191502.703216780916
711889018511.0095430646378.990456935375
722126318618.60140295112644.39859704890
731954719369.3215283029177.678471697087
741845019419.7627910889-969.762791088946
752025419144.45616942451109.54383057553
761924019459.4453259391-219.445325939130
772021619397.1468423517818.853157648307
781942019629.6116250212-209.611625021178
791941519570.1048375094-155.104837509374
802001819526.0720191636491.927980836415
811865219665.7257899112-1013.72578991120
821997819377.9384824592600.061517540784
831950919548.2903568588-39.2903568588408
842197119537.13619059242433.86380940758







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520228.087451165118517.586573958821938.5883283715
8620228.087451165118449.994087293722006.1808150366
8720228.087451165118384.878626760522071.2962755698
8820228.087451165118321.986317939822134.1885843905
8920228.087451165118261.103900191022195.0710021393
9020228.087451165118202.050173738422254.1247285919
9120228.087451165118144.669631993422311.5052703369
9220228.087451165118088.827633152822367.3472691775
9320228.087451165118034.406679338522421.7682229918
9420228.087451165117981.303507746922474.8713945834
9520228.087451165117929.426787186722526.7481151436
9620228.087451165117878.695272783422577.4796295469

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20228.0874511651 & 18517.5865739588 & 21938.5883283715 \tabularnewline
86 & 20228.0874511651 & 18449.9940872937 & 22006.1808150366 \tabularnewline
87 & 20228.0874511651 & 18384.8786267605 & 22071.2962755698 \tabularnewline
88 & 20228.0874511651 & 18321.9863179398 & 22134.1885843905 \tabularnewline
89 & 20228.0874511651 & 18261.1039001910 & 22195.0710021393 \tabularnewline
90 & 20228.0874511651 & 18202.0501737384 & 22254.1247285919 \tabularnewline
91 & 20228.0874511651 & 18144.6696319934 & 22311.5052703369 \tabularnewline
92 & 20228.0874511651 & 18088.8276331528 & 22367.3472691775 \tabularnewline
93 & 20228.0874511651 & 18034.4066793385 & 22421.7682229918 \tabularnewline
94 & 20228.0874511651 & 17981.3035077469 & 22474.8713945834 \tabularnewline
95 & 20228.0874511651 & 17929.4267871867 & 22526.7481151436 \tabularnewline
96 & 20228.0874511651 & 17878.6952727834 & 22577.4796295469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10881&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]20228.0874511651[/C][C]18517.5865739588[/C][C]21938.5883283715[/C][/ROW]
[ROW][C]86[/C][C]20228.0874511651[/C][C]18449.9940872937[/C][C]22006.1808150366[/C][/ROW]
[ROW][C]87[/C][C]20228.0874511651[/C][C]18384.8786267605[/C][C]22071.2962755698[/C][/ROW]
[ROW][C]88[/C][C]20228.0874511651[/C][C]18321.9863179398[/C][C]22134.1885843905[/C][/ROW]
[ROW][C]89[/C][C]20228.0874511651[/C][C]18261.1039001910[/C][C]22195.0710021393[/C][/ROW]
[ROW][C]90[/C][C]20228.0874511651[/C][C]18202.0501737384[/C][C]22254.1247285919[/C][/ROW]
[ROW][C]91[/C][C]20228.0874511651[/C][C]18144.6696319934[/C][C]22311.5052703369[/C][/ROW]
[ROW][C]92[/C][C]20228.0874511651[/C][C]18088.8276331528[/C][C]22367.3472691775[/C][/ROW]
[ROW][C]93[/C][C]20228.0874511651[/C][C]18034.4066793385[/C][C]22421.7682229918[/C][/ROW]
[ROW][C]94[/C][C]20228.0874511651[/C][C]17981.3035077469[/C][C]22474.8713945834[/C][/ROW]
[ROW][C]95[/C][C]20228.0874511651[/C][C]17929.4267871867[/C][C]22526.7481151436[/C][/ROW]
[ROW][C]96[/C][C]20228.0874511651[/C][C]17878.6952727834[/C][C]22577.4796295469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10881&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10881&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
8520228.087451165118517.586573958821938.5883283715
8620228.087451165118449.994087293722006.1808150366
8720228.087451165118384.878626760522071.2962755698
8820228.087451165118321.986317939822134.1885843905
8920228.087451165118261.103900191022195.0710021393
9020228.087451165118202.050173738422254.1247285919
9120228.087451165118144.669631993422311.5052703369
9220228.087451165118088.827633152822367.3472691775
9320228.087451165118034.406679338522421.7682229918
9420228.087451165117981.303507746922474.8713945834
9520228.087451165117929.426787186722526.7481151436
9620228.087451165117878.695272783422577.4796295469



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