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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 computationTue, 27 Dec 2011 12:19:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/27/t1325006497agfvv7s9t9m9rzq.htm/, Retrieved Sat, 18 May 2024 04:24:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160865, Retrieved Sat, 18 May 2024 04:24:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-27 17:19:17] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
47460
50104
61465
53726
39477
43895
31481
29896
33842
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577
23872
57276
56389
57657
62300
48929
51168
39636
33213
38127
43291
30600
21956
48033
46148
50736
48114
38390
44112
36287
30333
35908
40005
35263
26591
49709
47840
64781
57802
48154
54353
39737
37732
37163
43782
40649
29412




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'AstonUniversity' @ aston.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 & 12 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160865&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]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160865&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160865&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 time12 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.243019798407211
beta0
gamma0.341904622231544

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.243019798407211 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.341904622231544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160865&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]0.243019798407211[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.341904622231544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160865&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160865&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
alpha0.243019798407211
beta0
gamma0.341904622231544







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135144251813.3655217552-371.365521755157
144559445632.5963151448-38.596315144845
155251852282.7595170525235.24048294752
164856448427.7848578868136.215142113186
174174541673.328542424471.6714575755686
184958549644.2760792111-59.2760792110566
193274731243.86639824981503.13360175017
203337930042.66952117833336.33047882167
213564535421.2409659106223.759034089439
223703441626.5023389194-4592.50233891937
233568135016.2749352751664.725064724946
242097225983.2044183067-5011.20441830674
255855250324.67015669978227.32984330033
265495546238.422149198716.57785080996
276554055490.94377324710049.056226753
285157053578.0083247755-2008.00832477546
295114545640.0295594795504.97044052099
304664155895.993652243-9254.99365224295
313570434198.17279639861505.8272036014
323325333359.2812024481-106.281202448095
333519337286.7845860057-2093.78458600573
344166841819.7751721882-151.77517218815
353486537389.1895224921-2524.18952249207
362121025615.3555813842-4405.3555813842
375612654773.9544312771352.04556872305
384923148972.2953529558258.704647044171
395972356175.4264201113547.57357988899
404810349990.0570673106-1887.05706731059
414747244306.70322102593165.29677897408
425049749731.0404150801765.959584919925
434005933683.6371230986375.362876902
443414933597.8541270509551.145872949084
453686037206.978597251-346.978597251007
464635642802.44006478373553.55993521628
473657738415.8218766784-1838.82187667839
482387225673.6683595933-1801.66835959332
495727659433.3995030754-2157.39950307542
505638952095.15301917794293.84698082209
515765761770.6828786755-4113.68287867548
526230051900.819485682110399.1805143179
534892950063.8418371644-1134.84183716443
545116854162.3536782749-2994.35367827488
553963637595.87014316482040.12985683522
563321334845.2821764542-1632.28217645424
573812737745.9297862732381.070213726816
584329144654.5307232199-1363.53072321994
593060037710.9620533543-7110.96205335426
602195624184.5499571474-2228.54995714736
614803356193.2787234067-8160.27872340668
624614849411.6899365021-3263.68993650205
635073654390.4186304456-3654.41863044563
644811448809.2579415269-695.257941526928
653839042382.4560732175-3992.45607321751
664411244662.9792513608-550.979251360768
673628732233.34302895834053.65697104171
683033329605.6375256366727.362474363355
693590833125.61424009682782.38575990323
704000539471.4105644895533.589435510548
713526332227.53947121393035.46052878609
722659122781.25109827433809.74890172572
734970955504.1263382184-5795.12633821839
744784050414.3728450426-2574.3728450426
756478155681.62351793079099.37648206932
765780253564.81590999314237.1840900069
774815446554.31394818191599.68605181809
785435351755.04211406272597.95788593731
793973739242.5042996718494.495700328225
803773234221.15515093793510.84484906206
813716339590.7356063763-2427.73560637631
824378244746.3764226137-964.3764226137
834064936957.31145134063691.68854865943
842941226613.01587214592798.98412785407

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 51442 & 51813.3655217552 & -371.365521755157 \tabularnewline
14 & 45594 & 45632.5963151448 & -38.596315144845 \tabularnewline
15 & 52518 & 52282.7595170525 & 235.24048294752 \tabularnewline
16 & 48564 & 48427.7848578868 & 136.215142113186 \tabularnewline
17 & 41745 & 41673.3285424244 & 71.6714575755686 \tabularnewline
18 & 49585 & 49644.2760792111 & -59.2760792110566 \tabularnewline
19 & 32747 & 31243.8663982498 & 1503.13360175017 \tabularnewline
20 & 33379 & 30042.6695211783 & 3336.33047882167 \tabularnewline
21 & 35645 & 35421.2409659106 & 223.759034089439 \tabularnewline
22 & 37034 & 41626.5023389194 & -4592.50233891937 \tabularnewline
23 & 35681 & 35016.2749352751 & 664.725064724946 \tabularnewline
24 & 20972 & 25983.2044183067 & -5011.20441830674 \tabularnewline
25 & 58552 & 50324.6701566997 & 8227.32984330033 \tabularnewline
26 & 54955 & 46238.42214919 & 8716.57785080996 \tabularnewline
27 & 65540 & 55490.943773247 & 10049.056226753 \tabularnewline
28 & 51570 & 53578.0083247755 & -2008.00832477546 \tabularnewline
29 & 51145 & 45640.029559479 & 5504.97044052099 \tabularnewline
30 & 46641 & 55895.993652243 & -9254.99365224295 \tabularnewline
31 & 35704 & 34198.1727963986 & 1505.8272036014 \tabularnewline
32 & 33253 & 33359.2812024481 & -106.281202448095 \tabularnewline
33 & 35193 & 37286.7845860057 & -2093.78458600573 \tabularnewline
34 & 41668 & 41819.7751721882 & -151.77517218815 \tabularnewline
35 & 34865 & 37389.1895224921 & -2524.18952249207 \tabularnewline
36 & 21210 & 25615.3555813842 & -4405.3555813842 \tabularnewline
37 & 56126 & 54773.954431277 & 1352.04556872305 \tabularnewline
38 & 49231 & 48972.2953529558 & 258.704647044171 \tabularnewline
39 & 59723 & 56175.426420111 & 3547.57357988899 \tabularnewline
40 & 48103 & 49990.0570673106 & -1887.05706731059 \tabularnewline
41 & 47472 & 44306.7032210259 & 3165.29677897408 \tabularnewline
42 & 50497 & 49731.0404150801 & 765.959584919925 \tabularnewline
43 & 40059 & 33683.637123098 & 6375.362876902 \tabularnewline
44 & 34149 & 33597.8541270509 & 551.145872949084 \tabularnewline
45 & 36860 & 37206.978597251 & -346.978597251007 \tabularnewline
46 & 46356 & 42802.4400647837 & 3553.55993521628 \tabularnewline
47 & 36577 & 38415.8218766784 & -1838.82187667839 \tabularnewline
48 & 23872 & 25673.6683595933 & -1801.66835959332 \tabularnewline
49 & 57276 & 59433.3995030754 & -2157.39950307542 \tabularnewline
50 & 56389 & 52095.1530191779 & 4293.84698082209 \tabularnewline
51 & 57657 & 61770.6828786755 & -4113.68287867548 \tabularnewline
52 & 62300 & 51900.8194856821 & 10399.1805143179 \tabularnewline
53 & 48929 & 50063.8418371644 & -1134.84183716443 \tabularnewline
54 & 51168 & 54162.3536782749 & -2994.35367827488 \tabularnewline
55 & 39636 & 37595.8701431648 & 2040.12985683522 \tabularnewline
56 & 33213 & 34845.2821764542 & -1632.28217645424 \tabularnewline
57 & 38127 & 37745.9297862732 & 381.070213726816 \tabularnewline
58 & 43291 & 44654.5307232199 & -1363.53072321994 \tabularnewline
59 & 30600 & 37710.9620533543 & -7110.96205335426 \tabularnewline
60 & 21956 & 24184.5499571474 & -2228.54995714736 \tabularnewline
61 & 48033 & 56193.2787234067 & -8160.27872340668 \tabularnewline
62 & 46148 & 49411.6899365021 & -3263.68993650205 \tabularnewline
63 & 50736 & 54390.4186304456 & -3654.41863044563 \tabularnewline
64 & 48114 & 48809.2579415269 & -695.257941526928 \tabularnewline
65 & 38390 & 42382.4560732175 & -3992.45607321751 \tabularnewline
66 & 44112 & 44662.9792513608 & -550.979251360768 \tabularnewline
67 & 36287 & 32233.3430289583 & 4053.65697104171 \tabularnewline
68 & 30333 & 29605.6375256366 & 727.362474363355 \tabularnewline
69 & 35908 & 33125.6142400968 & 2782.38575990323 \tabularnewline
70 & 40005 & 39471.4105644895 & 533.589435510548 \tabularnewline
71 & 35263 & 32227.5394712139 & 3035.46052878609 \tabularnewline
72 & 26591 & 22781.2510982743 & 3809.74890172572 \tabularnewline
73 & 49709 & 55504.1263382184 & -5795.12633821839 \tabularnewline
74 & 47840 & 50414.3728450426 & -2574.3728450426 \tabularnewline
75 & 64781 & 55681.6235179307 & 9099.37648206932 \tabularnewline
76 & 57802 & 53564.8159099931 & 4237.1840900069 \tabularnewline
77 & 48154 & 46554.3139481819 & 1599.68605181809 \tabularnewline
78 & 54353 & 51755.0421140627 & 2597.95788593731 \tabularnewline
79 & 39737 & 39242.5042996718 & 494.495700328225 \tabularnewline
80 & 37732 & 34221.1551509379 & 3510.84484906206 \tabularnewline
81 & 37163 & 39590.7356063763 & -2427.73560637631 \tabularnewline
82 & 43782 & 44746.3764226137 & -964.3764226137 \tabularnewline
83 & 40649 & 36957.3114513406 & 3691.68854865943 \tabularnewline
84 & 29412 & 26613.0158721459 & 2798.98412785407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160865&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]51442[/C][C]51813.3655217552[/C][C]-371.365521755157[/C][/ROW]
[ROW][C]14[/C][C]45594[/C][C]45632.5963151448[/C][C]-38.596315144845[/C][/ROW]
[ROW][C]15[/C][C]52518[/C][C]52282.7595170525[/C][C]235.24048294752[/C][/ROW]
[ROW][C]16[/C][C]48564[/C][C]48427.7848578868[/C][C]136.215142113186[/C][/ROW]
[ROW][C]17[/C][C]41745[/C][C]41673.3285424244[/C][C]71.6714575755686[/C][/ROW]
[ROW][C]18[/C][C]49585[/C][C]49644.2760792111[/C][C]-59.2760792110566[/C][/ROW]
[ROW][C]19[/C][C]32747[/C][C]31243.8663982498[/C][C]1503.13360175017[/C][/ROW]
[ROW][C]20[/C][C]33379[/C][C]30042.6695211783[/C][C]3336.33047882167[/C][/ROW]
[ROW][C]21[/C][C]35645[/C][C]35421.2409659106[/C][C]223.759034089439[/C][/ROW]
[ROW][C]22[/C][C]37034[/C][C]41626.5023389194[/C][C]-4592.50233891937[/C][/ROW]
[ROW][C]23[/C][C]35681[/C][C]35016.2749352751[/C][C]664.725064724946[/C][/ROW]
[ROW][C]24[/C][C]20972[/C][C]25983.2044183067[/C][C]-5011.20441830674[/C][/ROW]
[ROW][C]25[/C][C]58552[/C][C]50324.6701566997[/C][C]8227.32984330033[/C][/ROW]
[ROW][C]26[/C][C]54955[/C][C]46238.42214919[/C][C]8716.57785080996[/C][/ROW]
[ROW][C]27[/C][C]65540[/C][C]55490.943773247[/C][C]10049.056226753[/C][/ROW]
[ROW][C]28[/C][C]51570[/C][C]53578.0083247755[/C][C]-2008.00832477546[/C][/ROW]
[ROW][C]29[/C][C]51145[/C][C]45640.029559479[/C][C]5504.97044052099[/C][/ROW]
[ROW][C]30[/C][C]46641[/C][C]55895.993652243[/C][C]-9254.99365224295[/C][/ROW]
[ROW][C]31[/C][C]35704[/C][C]34198.1727963986[/C][C]1505.8272036014[/C][/ROW]
[ROW][C]32[/C][C]33253[/C][C]33359.2812024481[/C][C]-106.281202448095[/C][/ROW]
[ROW][C]33[/C][C]35193[/C][C]37286.7845860057[/C][C]-2093.78458600573[/C][/ROW]
[ROW][C]34[/C][C]41668[/C][C]41819.7751721882[/C][C]-151.77517218815[/C][/ROW]
[ROW][C]35[/C][C]34865[/C][C]37389.1895224921[/C][C]-2524.18952249207[/C][/ROW]
[ROW][C]36[/C][C]21210[/C][C]25615.3555813842[/C][C]-4405.3555813842[/C][/ROW]
[ROW][C]37[/C][C]56126[/C][C]54773.954431277[/C][C]1352.04556872305[/C][/ROW]
[ROW][C]38[/C][C]49231[/C][C]48972.2953529558[/C][C]258.704647044171[/C][/ROW]
[ROW][C]39[/C][C]59723[/C][C]56175.426420111[/C][C]3547.57357988899[/C][/ROW]
[ROW][C]40[/C][C]48103[/C][C]49990.0570673106[/C][C]-1887.05706731059[/C][/ROW]
[ROW][C]41[/C][C]47472[/C][C]44306.7032210259[/C][C]3165.29677897408[/C][/ROW]
[ROW][C]42[/C][C]50497[/C][C]49731.0404150801[/C][C]765.959584919925[/C][/ROW]
[ROW][C]43[/C][C]40059[/C][C]33683.637123098[/C][C]6375.362876902[/C][/ROW]
[ROW][C]44[/C][C]34149[/C][C]33597.8541270509[/C][C]551.145872949084[/C][/ROW]
[ROW][C]45[/C][C]36860[/C][C]37206.978597251[/C][C]-346.978597251007[/C][/ROW]
[ROW][C]46[/C][C]46356[/C][C]42802.4400647837[/C][C]3553.55993521628[/C][/ROW]
[ROW][C]47[/C][C]36577[/C][C]38415.8218766784[/C][C]-1838.82187667839[/C][/ROW]
[ROW][C]48[/C][C]23872[/C][C]25673.6683595933[/C][C]-1801.66835959332[/C][/ROW]
[ROW][C]49[/C][C]57276[/C][C]59433.3995030754[/C][C]-2157.39950307542[/C][/ROW]
[ROW][C]50[/C][C]56389[/C][C]52095.1530191779[/C][C]4293.84698082209[/C][/ROW]
[ROW][C]51[/C][C]57657[/C][C]61770.6828786755[/C][C]-4113.68287867548[/C][/ROW]
[ROW][C]52[/C][C]62300[/C][C]51900.8194856821[/C][C]10399.1805143179[/C][/ROW]
[ROW][C]53[/C][C]48929[/C][C]50063.8418371644[/C][C]-1134.84183716443[/C][/ROW]
[ROW][C]54[/C][C]51168[/C][C]54162.3536782749[/C][C]-2994.35367827488[/C][/ROW]
[ROW][C]55[/C][C]39636[/C][C]37595.8701431648[/C][C]2040.12985683522[/C][/ROW]
[ROW][C]56[/C][C]33213[/C][C]34845.2821764542[/C][C]-1632.28217645424[/C][/ROW]
[ROW][C]57[/C][C]38127[/C][C]37745.9297862732[/C][C]381.070213726816[/C][/ROW]
[ROW][C]58[/C][C]43291[/C][C]44654.5307232199[/C][C]-1363.53072321994[/C][/ROW]
[ROW][C]59[/C][C]30600[/C][C]37710.9620533543[/C][C]-7110.96205335426[/C][/ROW]
[ROW][C]60[/C][C]21956[/C][C]24184.5499571474[/C][C]-2228.54995714736[/C][/ROW]
[ROW][C]61[/C][C]48033[/C][C]56193.2787234067[/C][C]-8160.27872340668[/C][/ROW]
[ROW][C]62[/C][C]46148[/C][C]49411.6899365021[/C][C]-3263.68993650205[/C][/ROW]
[ROW][C]63[/C][C]50736[/C][C]54390.4186304456[/C][C]-3654.41863044563[/C][/ROW]
[ROW][C]64[/C][C]48114[/C][C]48809.2579415269[/C][C]-695.257941526928[/C][/ROW]
[ROW][C]65[/C][C]38390[/C][C]42382.4560732175[/C][C]-3992.45607321751[/C][/ROW]
[ROW][C]66[/C][C]44112[/C][C]44662.9792513608[/C][C]-550.979251360768[/C][/ROW]
[ROW][C]67[/C][C]36287[/C][C]32233.3430289583[/C][C]4053.65697104171[/C][/ROW]
[ROW][C]68[/C][C]30333[/C][C]29605.6375256366[/C][C]727.362474363355[/C][/ROW]
[ROW][C]69[/C][C]35908[/C][C]33125.6142400968[/C][C]2782.38575990323[/C][/ROW]
[ROW][C]70[/C][C]40005[/C][C]39471.4105644895[/C][C]533.589435510548[/C][/ROW]
[ROW][C]71[/C][C]35263[/C][C]32227.5394712139[/C][C]3035.46052878609[/C][/ROW]
[ROW][C]72[/C][C]26591[/C][C]22781.2510982743[/C][C]3809.74890172572[/C][/ROW]
[ROW][C]73[/C][C]49709[/C][C]55504.1263382184[/C][C]-5795.12633821839[/C][/ROW]
[ROW][C]74[/C][C]47840[/C][C]50414.3728450426[/C][C]-2574.3728450426[/C][/ROW]
[ROW][C]75[/C][C]64781[/C][C]55681.6235179307[/C][C]9099.37648206932[/C][/ROW]
[ROW][C]76[/C][C]57802[/C][C]53564.8159099931[/C][C]4237.1840900069[/C][/ROW]
[ROW][C]77[/C][C]48154[/C][C]46554.3139481819[/C][C]1599.68605181809[/C][/ROW]
[ROW][C]78[/C][C]54353[/C][C]51755.0421140627[/C][C]2597.95788593731[/C][/ROW]
[ROW][C]79[/C][C]39737[/C][C]39242.5042996718[/C][C]494.495700328225[/C][/ROW]
[ROW][C]80[/C][C]37732[/C][C]34221.1551509379[/C][C]3510.84484906206[/C][/ROW]
[ROW][C]81[/C][C]37163[/C][C]39590.7356063763[/C][C]-2427.73560637631[/C][/ROW]
[ROW][C]82[/C][C]43782[/C][C]44746.3764226137[/C][C]-964.3764226137[/C][/ROW]
[ROW][C]83[/C][C]40649[/C][C]36957.3114513406[/C][C]3691.68854865943[/C][/ROW]
[ROW][C]84[/C][C]29412[/C][C]26613.0158721459[/C][C]2798.98412785407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160865&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160865&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
135144251813.3655217552-371.365521755157
144559445632.5963151448-38.596315144845
155251852282.7595170525235.24048294752
164856448427.7848578868136.215142113186
174174541673.328542424471.6714575755686
184958549644.2760792111-59.2760792110566
193274731243.86639824981503.13360175017
203337930042.66952117833336.33047882167
213564535421.2409659106223.759034089439
223703441626.5023389194-4592.50233891937
233568135016.2749352751664.725064724946
242097225983.2044183067-5011.20441830674
255855250324.67015669978227.32984330033
265495546238.422149198716.57785080996
276554055490.94377324710049.056226753
285157053578.0083247755-2008.00832477546
295114545640.0295594795504.97044052099
304664155895.993652243-9254.99365224295
313570434198.17279639861505.8272036014
323325333359.2812024481-106.281202448095
333519337286.7845860057-2093.78458600573
344166841819.7751721882-151.77517218815
353486537389.1895224921-2524.18952249207
362121025615.3555813842-4405.3555813842
375612654773.9544312771352.04556872305
384923148972.2953529558258.704647044171
395972356175.4264201113547.57357988899
404810349990.0570673106-1887.05706731059
414747244306.70322102593165.29677897408
425049749731.0404150801765.959584919925
434005933683.6371230986375.362876902
443414933597.8541270509551.145872949084
453686037206.978597251-346.978597251007
464635642802.44006478373553.55993521628
473657738415.8218766784-1838.82187667839
482387225673.6683595933-1801.66835959332
495727659433.3995030754-2157.39950307542
505638952095.15301917794293.84698082209
515765761770.6828786755-4113.68287867548
526230051900.819485682110399.1805143179
534892950063.8418371644-1134.84183716443
545116854162.3536782749-2994.35367827488
553963637595.87014316482040.12985683522
563321334845.2821764542-1632.28217645424
573812737745.9297862732381.070213726816
584329144654.5307232199-1363.53072321994
593060037710.9620533543-7110.96205335426
602195624184.5499571474-2228.54995714736
614803356193.2787234067-8160.27872340668
624614849411.6899365021-3263.68993650205
635073654390.4186304456-3654.41863044563
644811448809.2579415269-695.257941526928
653839042382.4560732175-3992.45607321751
664411244662.9792513608-550.979251360768
673628732233.34302895834053.65697104171
683033329605.6375256366727.362474363355
693590833125.61424009682782.38575990323
704000539471.4105644895533.589435510548
713526332227.53947121393035.46052878609
722659122781.25109827433809.74890172572
734970955504.1263382184-5795.12633821839
744784050414.3728450426-2574.3728450426
756478155681.62351793079099.37648206932
765780253564.81590999314237.1840900069
774815446554.31394818191599.68605181809
785435351755.04211406272597.95788593731
793973739242.5042996718494.495700328225
803773234221.15515093793510.84484906206
813716339590.7356063763-2427.73560637631
824378244746.3764226137-964.3764226137
834064936957.31145134063691.68854865943
842941226613.01587214592798.98412785407







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8559646.011141906755765.702599461163526.3196843524
8656405.049765541452137.393582858860672.705948224
8766535.072012256261599.810177476571470.3338470359
8860341.137036024355281.022818113665401.251253935
8950885.19711875745878.811131011155891.5831065028
9056323.522117846150699.02536050161948.0188751911
9141791.916028983236680.892803155846902.9392548106
9237153.017089383731996.745149301442309.289029466
9340219.133399142834500.934705685545937.3320926
9446636.306380968140040.114669681653232.4980922546
9539921.725189265933718.331343985946125.1190345459
9628101.803761623924443.12750143731760.4800218108

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 59646.0111419067 & 55765.7025994611 & 63526.3196843524 \tabularnewline
86 & 56405.0497655414 & 52137.3935828588 & 60672.705948224 \tabularnewline
87 & 66535.0720122562 & 61599.8101774765 & 71470.3338470359 \tabularnewline
88 & 60341.1370360243 & 55281.0228181136 & 65401.251253935 \tabularnewline
89 & 50885.197118757 & 45878.8111310111 & 55891.5831065028 \tabularnewline
90 & 56323.5221178461 & 50699.025360501 & 61948.0188751911 \tabularnewline
91 & 41791.9160289832 & 36680.8928031558 & 46902.9392548106 \tabularnewline
92 & 37153.0170893837 & 31996.7451493014 & 42309.289029466 \tabularnewline
93 & 40219.1333991428 & 34500.9347056855 & 45937.3320926 \tabularnewline
94 & 46636.3063809681 & 40040.1146696816 & 53232.4980922546 \tabularnewline
95 & 39921.7251892659 & 33718.3313439859 & 46125.1190345459 \tabularnewline
96 & 28101.8037616239 & 24443.127501437 & 31760.4800218108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160865&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]59646.0111419067[/C][C]55765.7025994611[/C][C]63526.3196843524[/C][/ROW]
[ROW][C]86[/C][C]56405.0497655414[/C][C]52137.3935828588[/C][C]60672.705948224[/C][/ROW]
[ROW][C]87[/C][C]66535.0720122562[/C][C]61599.8101774765[/C][C]71470.3338470359[/C][/ROW]
[ROW][C]88[/C][C]60341.1370360243[/C][C]55281.0228181136[/C][C]65401.251253935[/C][/ROW]
[ROW][C]89[/C][C]50885.197118757[/C][C]45878.8111310111[/C][C]55891.5831065028[/C][/ROW]
[ROW][C]90[/C][C]56323.5221178461[/C][C]50699.025360501[/C][C]61948.0188751911[/C][/ROW]
[ROW][C]91[/C][C]41791.9160289832[/C][C]36680.8928031558[/C][C]46902.9392548106[/C][/ROW]
[ROW][C]92[/C][C]37153.0170893837[/C][C]31996.7451493014[/C][C]42309.289029466[/C][/ROW]
[ROW][C]93[/C][C]40219.1333991428[/C][C]34500.9347056855[/C][C]45937.3320926[/C][/ROW]
[ROW][C]94[/C][C]46636.3063809681[/C][C]40040.1146696816[/C][C]53232.4980922546[/C][/ROW]
[ROW][C]95[/C][C]39921.7251892659[/C][C]33718.3313439859[/C][C]46125.1190345459[/C][/ROW]
[ROW][C]96[/C][C]28101.8037616239[/C][C]24443.127501437[/C][C]31760.4800218108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160865&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160865&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
8559646.011141906755765.702599461163526.3196843524
8656405.049765541452137.393582858860672.705948224
8766535.072012256261599.810177476571470.3338470359
8860341.137036024355281.022818113665401.251253935
8950885.19711875745878.811131011155891.5831065028
9056323.522117846150699.02536050161948.0188751911
9141791.916028983236680.892803155846902.9392548106
9237153.017089383731996.745149301442309.289029466
9340219.133399142834500.934705685545937.3320926
9446636.306380968140040.114669681653232.4980922546
9539921.725189265933718.331343985946125.1190345459
9628101.803761623924443.12750143731760.4800218108



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')