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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 22:20:07 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t14488356499e57nhk64zkz0sc.htm/, Retrieved Wed, 15 May 2024 01:59:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284546, Retrieved Wed, 15 May 2024 01:59:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-29 22:20:07] [06d8efd1cada8e807c830d2ff46bf732] [Current]
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Dataseries X:
28100
27900
28078
28479
28156
29219
28782
27078
30031
29579
26532
23995
22067
21818
23787
21551
21309
22395
22906
21430
23492
24144
24438
24689
24569
23754
28473
27051
27081
29635
27715
26373
28009
29472
30005
29777
28886
28549
33348
29017
30924
30435
29431
30290
31286
30622
31742
30391
30740
32086
33947
31312
33239
32362
32170
32665
31412
34891
33919
30706
32846
31368
33130
31665
33139
32201
32230
30287
31918
33853
32232
31484
31902
30260
32823
32018
32100
31952
33274
29491
32751
33643
31226
30976




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284546&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284546&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284546&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.756870207622303
beta0.021687702481385
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.756870207622303 \tabularnewline
beta & 0.021687702481385 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284546&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]0.756870207622303[/C][/ROW]
[ROW][C]beta[/C][C]0.021687702481385[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284546&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284546&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
alpha0.756870207622303
beta0.021687702481385
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132206724971.8204541955-2904.82045419548
142181822477.5946359339-659.594635933914
152378723922.7657862992-135.765786299198
162155121531.60204013219.397959867998
172130921081.9224199767227.077580023342
182239521855.70966167539.290338329985
192290622962.9476920096-56.9476920095767
202143021425.51627495134.48372504872532
212349223543.9483569644-51.9483569643999
222414422954.32925415981189.67074584016
232443821335.02220466083102.97779533916
242468921451.75385512383237.24614487621
252456921394.11428578523174.88571421483
262375424262.2849451563-508.284945156254
272847326380.46313730572092.53686269429
282705125612.65299646871438.34700353129
292708126539.7436868049541.256313195143
302963528193.90064881121441.09935118881
312771530455.8727821526-2740.8727821526
322637326897.8889129812-524.888912981183
332800929481.4958123088-1472.49581230879
342947228400.66518859561071.33481140443
353000526954.90617879353050.09382120653
362977726811.03402451142965.96597548861
372888626224.30886065652661.69113934351
382854927942.0199739243606.980026075697
393334832384.6548297973963.345170202709
402901730391.2825834689-1374.2825834689
413092429077.4792218211846.52077817899
423043532290.5396939982-1855.53969399815
432943131101.0315562843-1670.03155628432
443029028948.93275896011341.06724103994
453128633275.7858075011-1989.78580750111
463062232705.1541186193-2083.15411861928
473174229305.17749239042436.82250760965
483039128611.47323838611779.52676161389
493074027040.17654743743699.82345256258
503208629085.61888309223000.38111690776
513394735958.2685886485-2011.26858864848
523131231094.3363218276217.663678172394
533323931891.09070593741347.90929406257
543236233959.3194893223-1597.31948932228
553217033116.5532267763-946.553226776268
563266532340.0862301772324.913769822771
573141235361.8519218134-3949.85192181338
583489133361.56372928911529.43627071087
593391933817.6549147668101.345085233181
603070631081.6237257793-375.623725779282
613284628265.48988103634580.51011896367
623136830773.186779563594.813220436965
633313034499.7941195009-1369.79411950094
643166530717.1913107097947.808689290316
653313932363.3677826603775.632217339684
663220133283.6618343515-1082.66183435154
673223033013.0488246165-783.048824616526
683028732702.1094842767-2415.10948427675
693191832410.5025607513-492.502560751287
703385334439.0110369367-586.011036936732
713223232977.1484550203-745.148455020273
723148429601.56750590351882.43249409648
733190229593.97948921572308.02051078428
743026029486.7984011392773.201598860778
753282332735.785276797387.2147232026946
763201830650.52489310121367.47510689884
773210032592.5405752188-492.540575218838
783195232098.7243968633-146.724396863294
793327432618.8533332962655.146666703808
802949133003.7697214214-3512.76972142135
813275132375.2244947981375.775505201938
823364335135.7424312599-1492.74243125986
833122632966.9429578603-1740.94295786029
843097629500.81906114021475.18093885983

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 22067 & 24971.8204541955 & -2904.82045419548 \tabularnewline
14 & 21818 & 22477.5946359339 & -659.594635933914 \tabularnewline
15 & 23787 & 23922.7657862992 & -135.765786299198 \tabularnewline
16 & 21551 & 21531.602040132 & 19.397959867998 \tabularnewline
17 & 21309 & 21081.9224199767 & 227.077580023342 \tabularnewline
18 & 22395 & 21855.70966167 & 539.290338329985 \tabularnewline
19 & 22906 & 22962.9476920096 & -56.9476920095767 \tabularnewline
20 & 21430 & 21425.5162749513 & 4.48372504872532 \tabularnewline
21 & 23492 & 23543.9483569644 & -51.9483569643999 \tabularnewline
22 & 24144 & 22954.3292541598 & 1189.67074584016 \tabularnewline
23 & 24438 & 21335.0222046608 & 3102.97779533916 \tabularnewline
24 & 24689 & 21451.7538551238 & 3237.24614487621 \tabularnewline
25 & 24569 & 21394.1142857852 & 3174.88571421483 \tabularnewline
26 & 23754 & 24262.2849451563 & -508.284945156254 \tabularnewline
27 & 28473 & 26380.4631373057 & 2092.53686269429 \tabularnewline
28 & 27051 & 25612.6529964687 & 1438.34700353129 \tabularnewline
29 & 27081 & 26539.7436868049 & 541.256313195143 \tabularnewline
30 & 29635 & 28193.9006488112 & 1441.09935118881 \tabularnewline
31 & 27715 & 30455.8727821526 & -2740.8727821526 \tabularnewline
32 & 26373 & 26897.8889129812 & -524.888912981183 \tabularnewline
33 & 28009 & 29481.4958123088 & -1472.49581230879 \tabularnewline
34 & 29472 & 28400.6651885956 & 1071.33481140443 \tabularnewline
35 & 30005 & 26954.9061787935 & 3050.09382120653 \tabularnewline
36 & 29777 & 26811.0340245114 & 2965.96597548861 \tabularnewline
37 & 28886 & 26224.3088606565 & 2661.69113934351 \tabularnewline
38 & 28549 & 27942.0199739243 & 606.980026075697 \tabularnewline
39 & 33348 & 32384.6548297973 & 963.345170202709 \tabularnewline
40 & 29017 & 30391.2825834689 & -1374.2825834689 \tabularnewline
41 & 30924 & 29077.479221821 & 1846.52077817899 \tabularnewline
42 & 30435 & 32290.5396939982 & -1855.53969399815 \tabularnewline
43 & 29431 & 31101.0315562843 & -1670.03155628432 \tabularnewline
44 & 30290 & 28948.9327589601 & 1341.06724103994 \tabularnewline
45 & 31286 & 33275.7858075011 & -1989.78580750111 \tabularnewline
46 & 30622 & 32705.1541186193 & -2083.15411861928 \tabularnewline
47 & 31742 & 29305.1774923904 & 2436.82250760965 \tabularnewline
48 & 30391 & 28611.4732383861 & 1779.52676161389 \tabularnewline
49 & 30740 & 27040.1765474374 & 3699.82345256258 \tabularnewline
50 & 32086 & 29085.6188830922 & 3000.38111690776 \tabularnewline
51 & 33947 & 35958.2685886485 & -2011.26858864848 \tabularnewline
52 & 31312 & 31094.3363218276 & 217.663678172394 \tabularnewline
53 & 33239 & 31891.0907059374 & 1347.90929406257 \tabularnewline
54 & 32362 & 33959.3194893223 & -1597.31948932228 \tabularnewline
55 & 32170 & 33116.5532267763 & -946.553226776268 \tabularnewline
56 & 32665 & 32340.0862301772 & 324.913769822771 \tabularnewline
57 & 31412 & 35361.8519218134 & -3949.85192181338 \tabularnewline
58 & 34891 & 33361.5637292891 & 1529.43627071087 \tabularnewline
59 & 33919 & 33817.6549147668 & 101.345085233181 \tabularnewline
60 & 30706 & 31081.6237257793 & -375.623725779282 \tabularnewline
61 & 32846 & 28265.4898810363 & 4580.51011896367 \tabularnewline
62 & 31368 & 30773.186779563 & 594.813220436965 \tabularnewline
63 & 33130 & 34499.7941195009 & -1369.79411950094 \tabularnewline
64 & 31665 & 30717.1913107097 & 947.808689290316 \tabularnewline
65 & 33139 & 32363.3677826603 & 775.632217339684 \tabularnewline
66 & 32201 & 33283.6618343515 & -1082.66183435154 \tabularnewline
67 & 32230 & 33013.0488246165 & -783.048824616526 \tabularnewline
68 & 30287 & 32702.1094842767 & -2415.10948427675 \tabularnewline
69 & 31918 & 32410.5025607513 & -492.502560751287 \tabularnewline
70 & 33853 & 34439.0110369367 & -586.011036936732 \tabularnewline
71 & 32232 & 32977.1484550203 & -745.148455020273 \tabularnewline
72 & 31484 & 29601.5675059035 & 1882.43249409648 \tabularnewline
73 & 31902 & 29593.9794892157 & 2308.02051078428 \tabularnewline
74 & 30260 & 29486.7984011392 & 773.201598860778 \tabularnewline
75 & 32823 & 32735.7852767973 & 87.2147232026946 \tabularnewline
76 & 32018 & 30650.5248931012 & 1367.47510689884 \tabularnewline
77 & 32100 & 32592.5405752188 & -492.540575218838 \tabularnewline
78 & 31952 & 32098.7243968633 & -146.724396863294 \tabularnewline
79 & 33274 & 32618.8533332962 & 655.146666703808 \tabularnewline
80 & 29491 & 33003.7697214214 & -3512.76972142135 \tabularnewline
81 & 32751 & 32375.2244947981 & 375.775505201938 \tabularnewline
82 & 33643 & 35135.7424312599 & -1492.74243125986 \tabularnewline
83 & 31226 & 32966.9429578603 & -1740.94295786029 \tabularnewline
84 & 30976 & 29500.8190611402 & 1475.18093885983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284546&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]13[/C][C]22067[/C][C]24971.8204541955[/C][C]-2904.82045419548[/C][/ROW]
[ROW][C]14[/C][C]21818[/C][C]22477.5946359339[/C][C]-659.594635933914[/C][/ROW]
[ROW][C]15[/C][C]23787[/C][C]23922.7657862992[/C][C]-135.765786299198[/C][/ROW]
[ROW][C]16[/C][C]21551[/C][C]21531.602040132[/C][C]19.397959867998[/C][/ROW]
[ROW][C]17[/C][C]21309[/C][C]21081.9224199767[/C][C]227.077580023342[/C][/ROW]
[ROW][C]18[/C][C]22395[/C][C]21855.70966167[/C][C]539.290338329985[/C][/ROW]
[ROW][C]19[/C][C]22906[/C][C]22962.9476920096[/C][C]-56.9476920095767[/C][/ROW]
[ROW][C]20[/C][C]21430[/C][C]21425.5162749513[/C][C]4.48372504872532[/C][/ROW]
[ROW][C]21[/C][C]23492[/C][C]23543.9483569644[/C][C]-51.9483569643999[/C][/ROW]
[ROW][C]22[/C][C]24144[/C][C]22954.3292541598[/C][C]1189.67074584016[/C][/ROW]
[ROW][C]23[/C][C]24438[/C][C]21335.0222046608[/C][C]3102.97779533916[/C][/ROW]
[ROW][C]24[/C][C]24689[/C][C]21451.7538551238[/C][C]3237.24614487621[/C][/ROW]
[ROW][C]25[/C][C]24569[/C][C]21394.1142857852[/C][C]3174.88571421483[/C][/ROW]
[ROW][C]26[/C][C]23754[/C][C]24262.2849451563[/C][C]-508.284945156254[/C][/ROW]
[ROW][C]27[/C][C]28473[/C][C]26380.4631373057[/C][C]2092.53686269429[/C][/ROW]
[ROW][C]28[/C][C]27051[/C][C]25612.6529964687[/C][C]1438.34700353129[/C][/ROW]
[ROW][C]29[/C][C]27081[/C][C]26539.7436868049[/C][C]541.256313195143[/C][/ROW]
[ROW][C]30[/C][C]29635[/C][C]28193.9006488112[/C][C]1441.09935118881[/C][/ROW]
[ROW][C]31[/C][C]27715[/C][C]30455.8727821526[/C][C]-2740.8727821526[/C][/ROW]
[ROW][C]32[/C][C]26373[/C][C]26897.8889129812[/C][C]-524.888912981183[/C][/ROW]
[ROW][C]33[/C][C]28009[/C][C]29481.4958123088[/C][C]-1472.49581230879[/C][/ROW]
[ROW][C]34[/C][C]29472[/C][C]28400.6651885956[/C][C]1071.33481140443[/C][/ROW]
[ROW][C]35[/C][C]30005[/C][C]26954.9061787935[/C][C]3050.09382120653[/C][/ROW]
[ROW][C]36[/C][C]29777[/C][C]26811.0340245114[/C][C]2965.96597548861[/C][/ROW]
[ROW][C]37[/C][C]28886[/C][C]26224.3088606565[/C][C]2661.69113934351[/C][/ROW]
[ROW][C]38[/C][C]28549[/C][C]27942.0199739243[/C][C]606.980026075697[/C][/ROW]
[ROW][C]39[/C][C]33348[/C][C]32384.6548297973[/C][C]963.345170202709[/C][/ROW]
[ROW][C]40[/C][C]29017[/C][C]30391.2825834689[/C][C]-1374.2825834689[/C][/ROW]
[ROW][C]41[/C][C]30924[/C][C]29077.479221821[/C][C]1846.52077817899[/C][/ROW]
[ROW][C]42[/C][C]30435[/C][C]32290.5396939982[/C][C]-1855.53969399815[/C][/ROW]
[ROW][C]43[/C][C]29431[/C][C]31101.0315562843[/C][C]-1670.03155628432[/C][/ROW]
[ROW][C]44[/C][C]30290[/C][C]28948.9327589601[/C][C]1341.06724103994[/C][/ROW]
[ROW][C]45[/C][C]31286[/C][C]33275.7858075011[/C][C]-1989.78580750111[/C][/ROW]
[ROW][C]46[/C][C]30622[/C][C]32705.1541186193[/C][C]-2083.15411861928[/C][/ROW]
[ROW][C]47[/C][C]31742[/C][C]29305.1774923904[/C][C]2436.82250760965[/C][/ROW]
[ROW][C]48[/C][C]30391[/C][C]28611.4732383861[/C][C]1779.52676161389[/C][/ROW]
[ROW][C]49[/C][C]30740[/C][C]27040.1765474374[/C][C]3699.82345256258[/C][/ROW]
[ROW][C]50[/C][C]32086[/C][C]29085.6188830922[/C][C]3000.38111690776[/C][/ROW]
[ROW][C]51[/C][C]33947[/C][C]35958.2685886485[/C][C]-2011.26858864848[/C][/ROW]
[ROW][C]52[/C][C]31312[/C][C]31094.3363218276[/C][C]217.663678172394[/C][/ROW]
[ROW][C]53[/C][C]33239[/C][C]31891.0907059374[/C][C]1347.90929406257[/C][/ROW]
[ROW][C]54[/C][C]32362[/C][C]33959.3194893223[/C][C]-1597.31948932228[/C][/ROW]
[ROW][C]55[/C][C]32170[/C][C]33116.5532267763[/C][C]-946.553226776268[/C][/ROW]
[ROW][C]56[/C][C]32665[/C][C]32340.0862301772[/C][C]324.913769822771[/C][/ROW]
[ROW][C]57[/C][C]31412[/C][C]35361.8519218134[/C][C]-3949.85192181338[/C][/ROW]
[ROW][C]58[/C][C]34891[/C][C]33361.5637292891[/C][C]1529.43627071087[/C][/ROW]
[ROW][C]59[/C][C]33919[/C][C]33817.6549147668[/C][C]101.345085233181[/C][/ROW]
[ROW][C]60[/C][C]30706[/C][C]31081.6237257793[/C][C]-375.623725779282[/C][/ROW]
[ROW][C]61[/C][C]32846[/C][C]28265.4898810363[/C][C]4580.51011896367[/C][/ROW]
[ROW][C]62[/C][C]31368[/C][C]30773.186779563[/C][C]594.813220436965[/C][/ROW]
[ROW][C]63[/C][C]33130[/C][C]34499.7941195009[/C][C]-1369.79411950094[/C][/ROW]
[ROW][C]64[/C][C]31665[/C][C]30717.1913107097[/C][C]947.808689290316[/C][/ROW]
[ROW][C]65[/C][C]33139[/C][C]32363.3677826603[/C][C]775.632217339684[/C][/ROW]
[ROW][C]66[/C][C]32201[/C][C]33283.6618343515[/C][C]-1082.66183435154[/C][/ROW]
[ROW][C]67[/C][C]32230[/C][C]33013.0488246165[/C][C]-783.048824616526[/C][/ROW]
[ROW][C]68[/C][C]30287[/C][C]32702.1094842767[/C][C]-2415.10948427675[/C][/ROW]
[ROW][C]69[/C][C]31918[/C][C]32410.5025607513[/C][C]-492.502560751287[/C][/ROW]
[ROW][C]70[/C][C]33853[/C][C]34439.0110369367[/C][C]-586.011036936732[/C][/ROW]
[ROW][C]71[/C][C]32232[/C][C]32977.1484550203[/C][C]-745.148455020273[/C][/ROW]
[ROW][C]72[/C][C]31484[/C][C]29601.5675059035[/C][C]1882.43249409648[/C][/ROW]
[ROW][C]73[/C][C]31902[/C][C]29593.9794892157[/C][C]2308.02051078428[/C][/ROW]
[ROW][C]74[/C][C]30260[/C][C]29486.7984011392[/C][C]773.201598860778[/C][/ROW]
[ROW][C]75[/C][C]32823[/C][C]32735.7852767973[/C][C]87.2147232026946[/C][/ROW]
[ROW][C]76[/C][C]32018[/C][C]30650.5248931012[/C][C]1367.47510689884[/C][/ROW]
[ROW][C]77[/C][C]32100[/C][C]32592.5405752188[/C][C]-492.540575218838[/C][/ROW]
[ROW][C]78[/C][C]31952[/C][C]32098.7243968633[/C][C]-146.724396863294[/C][/ROW]
[ROW][C]79[/C][C]33274[/C][C]32618.8533332962[/C][C]655.146666703808[/C][/ROW]
[ROW][C]80[/C][C]29491[/C][C]33003.7697214214[/C][C]-3512.76972142135[/C][/ROW]
[ROW][C]81[/C][C]32751[/C][C]32375.2244947981[/C][C]375.775505201938[/C][/ROW]
[ROW][C]82[/C][C]33643[/C][C]35135.7424312599[/C][C]-1492.74243125986[/C][/ROW]
[ROW][C]83[/C][C]31226[/C][C]32966.9429578603[/C][C]-1740.94295786029[/C][/ROW]
[ROW][C]84[/C][C]30976[/C][C]29500.8190611402[/C][C]1475.18093885983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284546&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284546&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
132206724971.8204541955-2904.82045419548
142181822477.5946359339-659.594635933914
152378723922.7657862992-135.765786299198
162155121531.60204013219.397959867998
172130921081.9224199767227.077580023342
182239521855.70966167539.290338329985
192290622962.9476920096-56.9476920095767
202143021425.51627495134.48372504872532
212349223543.9483569644-51.9483569643999
222414422954.32925415981189.67074584016
232443821335.02220466083102.97779533916
242468921451.75385512383237.24614487621
252456921394.11428578523174.88571421483
262375424262.2849451563-508.284945156254
272847326380.46313730572092.53686269429
282705125612.65299646871438.34700353129
292708126539.7436868049541.256313195143
302963528193.90064881121441.09935118881
312771530455.8727821526-2740.8727821526
322637326897.8889129812-524.888912981183
332800929481.4958123088-1472.49581230879
342947228400.66518859561071.33481140443
353000526954.90617879353050.09382120653
362977726811.03402451142965.96597548861
372888626224.30886065652661.69113934351
382854927942.0199739243606.980026075697
393334832384.6548297973963.345170202709
402901730391.2825834689-1374.2825834689
413092429077.4792218211846.52077817899
423043532290.5396939982-1855.53969399815
432943131101.0315562843-1670.03155628432
443029028948.93275896011341.06724103994
453128633275.7858075011-1989.78580750111
463062232705.1541186193-2083.15411861928
473174229305.17749239042436.82250760965
483039128611.47323838611779.52676161389
493074027040.17654743743699.82345256258
503208629085.61888309223000.38111690776
513394735958.2685886485-2011.26858864848
523131231094.3363218276217.663678172394
533323931891.09070593741347.90929406257
543236233959.3194893223-1597.31948932228
553217033116.5532267763-946.553226776268
563266532340.0862301772324.913769822771
573141235361.8519218134-3949.85192181338
583489133361.56372928911529.43627071087
593391933817.6549147668101.345085233181
603070631081.6237257793-375.623725779282
613284628265.48988103634580.51011896367
623136830773.186779563594.813220436965
633313034499.7941195009-1369.79411950094
643166530717.1913107097947.808689290316
653313932363.3677826603775.632217339684
663220133283.6618343515-1082.66183435154
673223033013.0488246165-783.048824616526
683028732702.1094842767-2415.10948427675
693191832410.5025607513-492.502560751287
703385334439.0110369367-586.011036936732
713223232977.1484550203-745.148455020273
723148429601.56750590351882.43249409648
733190229593.97948921572308.02051078428
743026029486.7984011392773.201598860778
753282332735.785276797387.2147232026946
763201830650.52489310121367.47510689884
773210032592.5405752188-492.540575218838
783195232098.7243968633-146.724396863294
793327432618.8533332962655.146666703808
802949133003.7697214214-3512.76972142135
813275132375.2244947981375.775505201938
823364335135.7424312599-1492.74243125986
833122632966.9429578603-1740.94295786029
843097629500.81906114021475.18093885983







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8529292.690408430725777.752616059932807.6282008016
8627203.791499260222870.77220894731536.8107895733
8729390.754162100924013.065683977434768.4426402243
8827677.380918752421813.254160211333541.5076772935
8927990.746473370921385.348668599634596.1442781421
9027887.11669586520653.129118135235121.1042735948
9128535.022227704320530.992708826236539.0517465824
9227428.515103925719101.280528749935755.7496791015
9330169.166233626820492.16662243839846.1658448157
9431985.713039946821192.919220002642778.506859891
9530915.228379872819905.482029500741924.9747302449
9629572.44942544119031.276943462440113.6219074196

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 29292.6904084307 & 25777.7526160599 & 32807.6282008016 \tabularnewline
86 & 27203.7914992602 & 22870.772208947 & 31536.8107895733 \tabularnewline
87 & 29390.7541621009 & 24013.0656839774 & 34768.4426402243 \tabularnewline
88 & 27677.3809187524 & 21813.2541602113 & 33541.5076772935 \tabularnewline
89 & 27990.7464733709 & 21385.3486685996 & 34596.1442781421 \tabularnewline
90 & 27887.116695865 & 20653.1291181352 & 35121.1042735948 \tabularnewline
91 & 28535.0222277043 & 20530.9927088262 & 36539.0517465824 \tabularnewline
92 & 27428.5151039257 & 19101.2805287499 & 35755.7496791015 \tabularnewline
93 & 30169.1662336268 & 20492.166622438 & 39846.1658448157 \tabularnewline
94 & 31985.7130399468 & 21192.9192200026 & 42778.506859891 \tabularnewline
95 & 30915.2283798728 & 19905.4820295007 & 41924.9747302449 \tabularnewline
96 & 29572.449425441 & 19031.2769434624 & 40113.6219074196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284546&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]29292.6904084307[/C][C]25777.7526160599[/C][C]32807.6282008016[/C][/ROW]
[ROW][C]86[/C][C]27203.7914992602[/C][C]22870.772208947[/C][C]31536.8107895733[/C][/ROW]
[ROW][C]87[/C][C]29390.7541621009[/C][C]24013.0656839774[/C][C]34768.4426402243[/C][/ROW]
[ROW][C]88[/C][C]27677.3809187524[/C][C]21813.2541602113[/C][C]33541.5076772935[/C][/ROW]
[ROW][C]89[/C][C]27990.7464733709[/C][C]21385.3486685996[/C][C]34596.1442781421[/C][/ROW]
[ROW][C]90[/C][C]27887.116695865[/C][C]20653.1291181352[/C][C]35121.1042735948[/C][/ROW]
[ROW][C]91[/C][C]28535.0222277043[/C][C]20530.9927088262[/C][C]36539.0517465824[/C][/ROW]
[ROW][C]92[/C][C]27428.5151039257[/C][C]19101.2805287499[/C][C]35755.7496791015[/C][/ROW]
[ROW][C]93[/C][C]30169.1662336268[/C][C]20492.166622438[/C][C]39846.1658448157[/C][/ROW]
[ROW][C]94[/C][C]31985.7130399468[/C][C]21192.9192200026[/C][C]42778.506859891[/C][/ROW]
[ROW][C]95[/C][C]30915.2283798728[/C][C]19905.4820295007[/C][C]41924.9747302449[/C][/ROW]
[ROW][C]96[/C][C]29572.449425441[/C][C]19031.2769434624[/C][C]40113.6219074196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284546&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284546&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
8529292.690408430725777.752616059932807.6282008016
8627203.791499260222870.77220894731536.8107895733
8729390.754162100924013.065683977434768.4426402243
8827677.380918752421813.254160211333541.5076772935
8927990.746473370921385.348668599634596.1442781421
9027887.11669586520653.129118135235121.1042735948
9128535.022227704320530.992708826236539.0517465824
9227428.515103925719101.280528749935755.7496791015
9330169.166233626820492.16662243839846.1658448157
9431985.713039946821192.919220002642778.506859891
9530915.228379872819905.482029500741924.9747302449
9629572.44942544119031.276943462440113.6219074196



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')