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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, 20 Aug 2013 03:36:49 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/20/t1376984227jb9jmqul17fy383.htm/, Retrieved Sat, 27 Apr 2024 06:47:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211236, Retrieved Sat, 27 Apr 2024 06:47:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJespers Eva
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2013-08-20 07:36:49] [987ccabfb1247e6edeac48c68eb55107] [Current]
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Dataseries X:
19570
18845
19932
15946
20657
20294
21744
22469
25006
21744
20657
25730
21744
16308
19207
14496
20294
16670
22106
19932
21019
23556
23194
27542
19932
16670
18482
13409
19207
14858
21019
19932
17758
25368
22831
26093
19570
18120
16308
13409
17758
15946
21744
21019
18120
24281
22469
28992
23194
14134
14134
14134
16670
16670
22469
20657
18482
23194
21382
30804
24281
14134
14858
12322
17033
19570
24643
24281
19570
22831
20294
28992
22106
17758
15946
11959
17758
21382
25006
23556
17395
25006
19570
30079
25006
18120
16670
11234
17758
17033
25730
25730
19570
25368
18845
29354
25006
18482
14134
9785
19207
18482
24281
27905
20657
23194
17395
30079




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211236&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211236&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211236&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00923748353743334
beta1
gamma0.929544161839171

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00923748353743334 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929544161839171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211236&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]0.00923748353743334[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929544161839171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211236&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211236&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
alpha0.00923748353743334
beta1
gamma0.929544161839171







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132174422487.7216880342-743.721688034188
141630817033.654531258-725.654531257973
151920720089.259381092-882.259381092012
161449615344.0594063619-848.059406361912
172029420828.508085197-534.508085197001
181667016888.9156795619-218.915679561862
192210621119.5079902589986.492009741069
201993221746.3896050083-1814.3896050083
212101924263.429394511-3244.42939451103
222355620892.99718521352663.00281478647
232319419761.65089502633432.34910497369
242754224919.70103021452622.29896978546
251993220320.3473747081-388.347374708148
261667014895.87906391741774.12093608263
271848217863.1177680323618.882231967658
281340913209.9166914212199.08330857882
291920719049.1141458694157.885854130618
301485815469.2692595661-611.269259566085
312101920865.4464631356153.553536864449
321993218956.526586026975.473413973959
331775820259.4888445426-2501.48884454255
342536822420.43355608092947.56644391913
352283122086.8997599377744.100240062344
362609326535.9114241912-442.911424191203
371957019169.0666793558400.933320644166
381812015784.22285176842335.77714823165
391630817738.7044505498-1430.70445054977
401340912707.0007234948701.999276505234
411775818544.5957739199-786.595773919889
421594614270.63546324591675.36453675409
432174420436.39584106071307.60415893928
442101919349.84142881111669.1585711889
451812017518.2366389267601.763361073252
462428124816.0217997531-535.021799753133
472246922478.6743472609-9.67434726090141
482899225878.22819086793113.7718091321
492319419404.93067902543789.06932097459
501413417948.1387845451-3814.1387845451
511413416435.0764863674-2301.07648636738
521413413409.4575609292724.542439070807
531667017926.531628764-1256.53162876398
541667015961.4536840778708.546315922225
552246921816.522990201652.47700979904
562065721087.7729563612-430.772956361223
571848218265.226214971216.773785028978
582319424520.4496410354-1326.44964103539
592138222660.2287030919-1278.22870309189
603080428913.52188368081890.47811631919
612428123028.44076109151252.55923890853
621413414500.1515266794-366.15152667937
631485814398.4220280994459.577971900622
641232214196.2885665818-1874.28856658178
651703316852.3817537906180.618246209364
661957016711.11922689312858.88077310685
672464322555.06491538582087.9350846142
682428120875.8578794223405.142120578
691957018754.4527515237815.547248476316
702283123668.8396638711-837.839663871076
712029421936.9307489099-1642.9307489099
722899231181.1194841544-2189.11948415443
732210624709.191879553-2603.19187955298
741775814657.23884578593100.76115421413
751594615382.7397091983563.260290801722
761195913067.8728800758-1108.8728800758
771775817666.289756048991.7102439510527
782138220032.72195884251349.27804115746
792500625180.719582783-174.719582782996
802355624700.8068819381-1144.80688193812
811739520117.5385975578-2722.53859755784
822500623408.9341671331597.06583286698
831957020912.9461334003-1342.94613340034
843007929614.5436204892464.45637951079
852500622767.95192726092238.04807273909
861812018040.705673621279.294326378782
871667016400.3420584262269.657941573769
881123412539.0640849438-1305.0640849438
891775818235.8069917313-477.806991731279
901703321744.3361890741-4711.33618907409
912573025366.0184929373363.981507062734
922573023935.85565620161794.14434379841
931957017892.04333006831677.9566699317
942536825208.2413795782159.758620421791
951884519984.053858118-1139.05385811801
962935430346.6628939373-992.662893937333
972500625101.1407388962-95.1407388962471
981848218323.7954761785158.204523821543
991413416819.7807913605-2685.78079136046
100978511413.9523005926-1628.95230059265
1011920717799.5823988731407.41760112701
1021848217374.0510063451107.94899365495
1032428125724.8215747689-1443.82157476891
1042790525579.55959548392325.44040451611
1052065719423.04023484891233.95976515114
1062319425322.2285943674-2128.22859436744
1071739518844.9070983706-1449.9070983706
1083007929300.7453688151778.254631184926

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 21744 & 22487.7216880342 & -743.721688034188 \tabularnewline
14 & 16308 & 17033.654531258 & -725.654531257973 \tabularnewline
15 & 19207 & 20089.259381092 & -882.259381092012 \tabularnewline
16 & 14496 & 15344.0594063619 & -848.059406361912 \tabularnewline
17 & 20294 & 20828.508085197 & -534.508085197001 \tabularnewline
18 & 16670 & 16888.9156795619 & -218.915679561862 \tabularnewline
19 & 22106 & 21119.5079902589 & 986.492009741069 \tabularnewline
20 & 19932 & 21746.3896050083 & -1814.3896050083 \tabularnewline
21 & 21019 & 24263.429394511 & -3244.42939451103 \tabularnewline
22 & 23556 & 20892.9971852135 & 2663.00281478647 \tabularnewline
23 & 23194 & 19761.6508950263 & 3432.34910497369 \tabularnewline
24 & 27542 & 24919.7010302145 & 2622.29896978546 \tabularnewline
25 & 19932 & 20320.3473747081 & -388.347374708148 \tabularnewline
26 & 16670 & 14895.8790639174 & 1774.12093608263 \tabularnewline
27 & 18482 & 17863.1177680323 & 618.882231967658 \tabularnewline
28 & 13409 & 13209.9166914212 & 199.08330857882 \tabularnewline
29 & 19207 & 19049.1141458694 & 157.885854130618 \tabularnewline
30 & 14858 & 15469.2692595661 & -611.269259566085 \tabularnewline
31 & 21019 & 20865.4464631356 & 153.553536864449 \tabularnewline
32 & 19932 & 18956.526586026 & 975.473413973959 \tabularnewline
33 & 17758 & 20259.4888445426 & -2501.48884454255 \tabularnewline
34 & 25368 & 22420.4335560809 & 2947.56644391913 \tabularnewline
35 & 22831 & 22086.8997599377 & 744.100240062344 \tabularnewline
36 & 26093 & 26535.9114241912 & -442.911424191203 \tabularnewline
37 & 19570 & 19169.0666793558 & 400.933320644166 \tabularnewline
38 & 18120 & 15784.2228517684 & 2335.77714823165 \tabularnewline
39 & 16308 & 17738.7044505498 & -1430.70445054977 \tabularnewline
40 & 13409 & 12707.0007234948 & 701.999276505234 \tabularnewline
41 & 17758 & 18544.5957739199 & -786.595773919889 \tabularnewline
42 & 15946 & 14270.6354632459 & 1675.36453675409 \tabularnewline
43 & 21744 & 20436.3958410607 & 1307.60415893928 \tabularnewline
44 & 21019 & 19349.8414288111 & 1669.1585711889 \tabularnewline
45 & 18120 & 17518.2366389267 & 601.763361073252 \tabularnewline
46 & 24281 & 24816.0217997531 & -535.021799753133 \tabularnewline
47 & 22469 & 22478.6743472609 & -9.67434726090141 \tabularnewline
48 & 28992 & 25878.2281908679 & 3113.7718091321 \tabularnewline
49 & 23194 & 19404.9306790254 & 3789.06932097459 \tabularnewline
50 & 14134 & 17948.1387845451 & -3814.1387845451 \tabularnewline
51 & 14134 & 16435.0764863674 & -2301.07648636738 \tabularnewline
52 & 14134 & 13409.4575609292 & 724.542439070807 \tabularnewline
53 & 16670 & 17926.531628764 & -1256.53162876398 \tabularnewline
54 & 16670 & 15961.4536840778 & 708.546315922225 \tabularnewline
55 & 22469 & 21816.522990201 & 652.47700979904 \tabularnewline
56 & 20657 & 21087.7729563612 & -430.772956361223 \tabularnewline
57 & 18482 & 18265.226214971 & 216.773785028978 \tabularnewline
58 & 23194 & 24520.4496410354 & -1326.44964103539 \tabularnewline
59 & 21382 & 22660.2287030919 & -1278.22870309189 \tabularnewline
60 & 30804 & 28913.5218836808 & 1890.47811631919 \tabularnewline
61 & 24281 & 23028.4407610915 & 1252.55923890853 \tabularnewline
62 & 14134 & 14500.1515266794 & -366.15152667937 \tabularnewline
63 & 14858 & 14398.4220280994 & 459.577971900622 \tabularnewline
64 & 12322 & 14196.2885665818 & -1874.28856658178 \tabularnewline
65 & 17033 & 16852.3817537906 & 180.618246209364 \tabularnewline
66 & 19570 & 16711.1192268931 & 2858.88077310685 \tabularnewline
67 & 24643 & 22555.0649153858 & 2087.9350846142 \tabularnewline
68 & 24281 & 20875.857879422 & 3405.142120578 \tabularnewline
69 & 19570 & 18754.4527515237 & 815.547248476316 \tabularnewline
70 & 22831 & 23668.8396638711 & -837.839663871076 \tabularnewline
71 & 20294 & 21936.9307489099 & -1642.9307489099 \tabularnewline
72 & 28992 & 31181.1194841544 & -2189.11948415443 \tabularnewline
73 & 22106 & 24709.191879553 & -2603.19187955298 \tabularnewline
74 & 17758 & 14657.2388457859 & 3100.76115421413 \tabularnewline
75 & 15946 & 15382.7397091983 & 563.260290801722 \tabularnewline
76 & 11959 & 13067.8728800758 & -1108.8728800758 \tabularnewline
77 & 17758 & 17666.2897560489 & 91.7102439510527 \tabularnewline
78 & 21382 & 20032.7219588425 & 1349.27804115746 \tabularnewline
79 & 25006 & 25180.719582783 & -174.719582782996 \tabularnewline
80 & 23556 & 24700.8068819381 & -1144.80688193812 \tabularnewline
81 & 17395 & 20117.5385975578 & -2722.53859755784 \tabularnewline
82 & 25006 & 23408.934167133 & 1597.06583286698 \tabularnewline
83 & 19570 & 20912.9461334003 & -1342.94613340034 \tabularnewline
84 & 30079 & 29614.5436204892 & 464.45637951079 \tabularnewline
85 & 25006 & 22767.9519272609 & 2238.04807273909 \tabularnewline
86 & 18120 & 18040.7056736212 & 79.294326378782 \tabularnewline
87 & 16670 & 16400.3420584262 & 269.657941573769 \tabularnewline
88 & 11234 & 12539.0640849438 & -1305.0640849438 \tabularnewline
89 & 17758 & 18235.8069917313 & -477.806991731279 \tabularnewline
90 & 17033 & 21744.3361890741 & -4711.33618907409 \tabularnewline
91 & 25730 & 25366.0184929373 & 363.981507062734 \tabularnewline
92 & 25730 & 23935.8556562016 & 1794.14434379841 \tabularnewline
93 & 19570 & 17892.0433300683 & 1677.9566699317 \tabularnewline
94 & 25368 & 25208.2413795782 & 159.758620421791 \tabularnewline
95 & 18845 & 19984.053858118 & -1139.05385811801 \tabularnewline
96 & 29354 & 30346.6628939373 & -992.662893937333 \tabularnewline
97 & 25006 & 25101.1407388962 & -95.1407388962471 \tabularnewline
98 & 18482 & 18323.7954761785 & 158.204523821543 \tabularnewline
99 & 14134 & 16819.7807913605 & -2685.78079136046 \tabularnewline
100 & 9785 & 11413.9523005926 & -1628.95230059265 \tabularnewline
101 & 19207 & 17799.582398873 & 1407.41760112701 \tabularnewline
102 & 18482 & 17374.051006345 & 1107.94899365495 \tabularnewline
103 & 24281 & 25724.8215747689 & -1443.82157476891 \tabularnewline
104 & 27905 & 25579.5595954839 & 2325.44040451611 \tabularnewline
105 & 20657 & 19423.0402348489 & 1233.95976515114 \tabularnewline
106 & 23194 & 25322.2285943674 & -2128.22859436744 \tabularnewline
107 & 17395 & 18844.9070983706 & -1449.9070983706 \tabularnewline
108 & 30079 & 29300.7453688151 & 778.254631184926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211236&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]21744[/C][C]22487.7216880342[/C][C]-743.721688034188[/C][/ROW]
[ROW][C]14[/C][C]16308[/C][C]17033.654531258[/C][C]-725.654531257973[/C][/ROW]
[ROW][C]15[/C][C]19207[/C][C]20089.259381092[/C][C]-882.259381092012[/C][/ROW]
[ROW][C]16[/C][C]14496[/C][C]15344.0594063619[/C][C]-848.059406361912[/C][/ROW]
[ROW][C]17[/C][C]20294[/C][C]20828.508085197[/C][C]-534.508085197001[/C][/ROW]
[ROW][C]18[/C][C]16670[/C][C]16888.9156795619[/C][C]-218.915679561862[/C][/ROW]
[ROW][C]19[/C][C]22106[/C][C]21119.5079902589[/C][C]986.492009741069[/C][/ROW]
[ROW][C]20[/C][C]19932[/C][C]21746.3896050083[/C][C]-1814.3896050083[/C][/ROW]
[ROW][C]21[/C][C]21019[/C][C]24263.429394511[/C][C]-3244.42939451103[/C][/ROW]
[ROW][C]22[/C][C]23556[/C][C]20892.9971852135[/C][C]2663.00281478647[/C][/ROW]
[ROW][C]23[/C][C]23194[/C][C]19761.6508950263[/C][C]3432.34910497369[/C][/ROW]
[ROW][C]24[/C][C]27542[/C][C]24919.7010302145[/C][C]2622.29896978546[/C][/ROW]
[ROW][C]25[/C][C]19932[/C][C]20320.3473747081[/C][C]-388.347374708148[/C][/ROW]
[ROW][C]26[/C][C]16670[/C][C]14895.8790639174[/C][C]1774.12093608263[/C][/ROW]
[ROW][C]27[/C][C]18482[/C][C]17863.1177680323[/C][C]618.882231967658[/C][/ROW]
[ROW][C]28[/C][C]13409[/C][C]13209.9166914212[/C][C]199.08330857882[/C][/ROW]
[ROW][C]29[/C][C]19207[/C][C]19049.1141458694[/C][C]157.885854130618[/C][/ROW]
[ROW][C]30[/C][C]14858[/C][C]15469.2692595661[/C][C]-611.269259566085[/C][/ROW]
[ROW][C]31[/C][C]21019[/C][C]20865.4464631356[/C][C]153.553536864449[/C][/ROW]
[ROW][C]32[/C][C]19932[/C][C]18956.526586026[/C][C]975.473413973959[/C][/ROW]
[ROW][C]33[/C][C]17758[/C][C]20259.4888445426[/C][C]-2501.48884454255[/C][/ROW]
[ROW][C]34[/C][C]25368[/C][C]22420.4335560809[/C][C]2947.56644391913[/C][/ROW]
[ROW][C]35[/C][C]22831[/C][C]22086.8997599377[/C][C]744.100240062344[/C][/ROW]
[ROW][C]36[/C][C]26093[/C][C]26535.9114241912[/C][C]-442.911424191203[/C][/ROW]
[ROW][C]37[/C][C]19570[/C][C]19169.0666793558[/C][C]400.933320644166[/C][/ROW]
[ROW][C]38[/C][C]18120[/C][C]15784.2228517684[/C][C]2335.77714823165[/C][/ROW]
[ROW][C]39[/C][C]16308[/C][C]17738.7044505498[/C][C]-1430.70445054977[/C][/ROW]
[ROW][C]40[/C][C]13409[/C][C]12707.0007234948[/C][C]701.999276505234[/C][/ROW]
[ROW][C]41[/C][C]17758[/C][C]18544.5957739199[/C][C]-786.595773919889[/C][/ROW]
[ROW][C]42[/C][C]15946[/C][C]14270.6354632459[/C][C]1675.36453675409[/C][/ROW]
[ROW][C]43[/C][C]21744[/C][C]20436.3958410607[/C][C]1307.60415893928[/C][/ROW]
[ROW][C]44[/C][C]21019[/C][C]19349.8414288111[/C][C]1669.1585711889[/C][/ROW]
[ROW][C]45[/C][C]18120[/C][C]17518.2366389267[/C][C]601.763361073252[/C][/ROW]
[ROW][C]46[/C][C]24281[/C][C]24816.0217997531[/C][C]-535.021799753133[/C][/ROW]
[ROW][C]47[/C][C]22469[/C][C]22478.6743472609[/C][C]-9.67434726090141[/C][/ROW]
[ROW][C]48[/C][C]28992[/C][C]25878.2281908679[/C][C]3113.7718091321[/C][/ROW]
[ROW][C]49[/C][C]23194[/C][C]19404.9306790254[/C][C]3789.06932097459[/C][/ROW]
[ROW][C]50[/C][C]14134[/C][C]17948.1387845451[/C][C]-3814.1387845451[/C][/ROW]
[ROW][C]51[/C][C]14134[/C][C]16435.0764863674[/C][C]-2301.07648636738[/C][/ROW]
[ROW][C]52[/C][C]14134[/C][C]13409.4575609292[/C][C]724.542439070807[/C][/ROW]
[ROW][C]53[/C][C]16670[/C][C]17926.531628764[/C][C]-1256.53162876398[/C][/ROW]
[ROW][C]54[/C][C]16670[/C][C]15961.4536840778[/C][C]708.546315922225[/C][/ROW]
[ROW][C]55[/C][C]22469[/C][C]21816.522990201[/C][C]652.47700979904[/C][/ROW]
[ROW][C]56[/C][C]20657[/C][C]21087.7729563612[/C][C]-430.772956361223[/C][/ROW]
[ROW][C]57[/C][C]18482[/C][C]18265.226214971[/C][C]216.773785028978[/C][/ROW]
[ROW][C]58[/C][C]23194[/C][C]24520.4496410354[/C][C]-1326.44964103539[/C][/ROW]
[ROW][C]59[/C][C]21382[/C][C]22660.2287030919[/C][C]-1278.22870309189[/C][/ROW]
[ROW][C]60[/C][C]30804[/C][C]28913.5218836808[/C][C]1890.47811631919[/C][/ROW]
[ROW][C]61[/C][C]24281[/C][C]23028.4407610915[/C][C]1252.55923890853[/C][/ROW]
[ROW][C]62[/C][C]14134[/C][C]14500.1515266794[/C][C]-366.15152667937[/C][/ROW]
[ROW][C]63[/C][C]14858[/C][C]14398.4220280994[/C][C]459.577971900622[/C][/ROW]
[ROW][C]64[/C][C]12322[/C][C]14196.2885665818[/C][C]-1874.28856658178[/C][/ROW]
[ROW][C]65[/C][C]17033[/C][C]16852.3817537906[/C][C]180.618246209364[/C][/ROW]
[ROW][C]66[/C][C]19570[/C][C]16711.1192268931[/C][C]2858.88077310685[/C][/ROW]
[ROW][C]67[/C][C]24643[/C][C]22555.0649153858[/C][C]2087.9350846142[/C][/ROW]
[ROW][C]68[/C][C]24281[/C][C]20875.857879422[/C][C]3405.142120578[/C][/ROW]
[ROW][C]69[/C][C]19570[/C][C]18754.4527515237[/C][C]815.547248476316[/C][/ROW]
[ROW][C]70[/C][C]22831[/C][C]23668.8396638711[/C][C]-837.839663871076[/C][/ROW]
[ROW][C]71[/C][C]20294[/C][C]21936.9307489099[/C][C]-1642.9307489099[/C][/ROW]
[ROW][C]72[/C][C]28992[/C][C]31181.1194841544[/C][C]-2189.11948415443[/C][/ROW]
[ROW][C]73[/C][C]22106[/C][C]24709.191879553[/C][C]-2603.19187955298[/C][/ROW]
[ROW][C]74[/C][C]17758[/C][C]14657.2388457859[/C][C]3100.76115421413[/C][/ROW]
[ROW][C]75[/C][C]15946[/C][C]15382.7397091983[/C][C]563.260290801722[/C][/ROW]
[ROW][C]76[/C][C]11959[/C][C]13067.8728800758[/C][C]-1108.8728800758[/C][/ROW]
[ROW][C]77[/C][C]17758[/C][C]17666.2897560489[/C][C]91.7102439510527[/C][/ROW]
[ROW][C]78[/C][C]21382[/C][C]20032.7219588425[/C][C]1349.27804115746[/C][/ROW]
[ROW][C]79[/C][C]25006[/C][C]25180.719582783[/C][C]-174.719582782996[/C][/ROW]
[ROW][C]80[/C][C]23556[/C][C]24700.8068819381[/C][C]-1144.80688193812[/C][/ROW]
[ROW][C]81[/C][C]17395[/C][C]20117.5385975578[/C][C]-2722.53859755784[/C][/ROW]
[ROW][C]82[/C][C]25006[/C][C]23408.934167133[/C][C]1597.06583286698[/C][/ROW]
[ROW][C]83[/C][C]19570[/C][C]20912.9461334003[/C][C]-1342.94613340034[/C][/ROW]
[ROW][C]84[/C][C]30079[/C][C]29614.5436204892[/C][C]464.45637951079[/C][/ROW]
[ROW][C]85[/C][C]25006[/C][C]22767.9519272609[/C][C]2238.04807273909[/C][/ROW]
[ROW][C]86[/C][C]18120[/C][C]18040.7056736212[/C][C]79.294326378782[/C][/ROW]
[ROW][C]87[/C][C]16670[/C][C]16400.3420584262[/C][C]269.657941573769[/C][/ROW]
[ROW][C]88[/C][C]11234[/C][C]12539.0640849438[/C][C]-1305.0640849438[/C][/ROW]
[ROW][C]89[/C][C]17758[/C][C]18235.8069917313[/C][C]-477.806991731279[/C][/ROW]
[ROW][C]90[/C][C]17033[/C][C]21744.3361890741[/C][C]-4711.33618907409[/C][/ROW]
[ROW][C]91[/C][C]25730[/C][C]25366.0184929373[/C][C]363.981507062734[/C][/ROW]
[ROW][C]92[/C][C]25730[/C][C]23935.8556562016[/C][C]1794.14434379841[/C][/ROW]
[ROW][C]93[/C][C]19570[/C][C]17892.0433300683[/C][C]1677.9566699317[/C][/ROW]
[ROW][C]94[/C][C]25368[/C][C]25208.2413795782[/C][C]159.758620421791[/C][/ROW]
[ROW][C]95[/C][C]18845[/C][C]19984.053858118[/C][C]-1139.05385811801[/C][/ROW]
[ROW][C]96[/C][C]29354[/C][C]30346.6628939373[/C][C]-992.662893937333[/C][/ROW]
[ROW][C]97[/C][C]25006[/C][C]25101.1407388962[/C][C]-95.1407388962471[/C][/ROW]
[ROW][C]98[/C][C]18482[/C][C]18323.7954761785[/C][C]158.204523821543[/C][/ROW]
[ROW][C]99[/C][C]14134[/C][C]16819.7807913605[/C][C]-2685.78079136046[/C][/ROW]
[ROW][C]100[/C][C]9785[/C][C]11413.9523005926[/C][C]-1628.95230059265[/C][/ROW]
[ROW][C]101[/C][C]19207[/C][C]17799.582398873[/C][C]1407.41760112701[/C][/ROW]
[ROW][C]102[/C][C]18482[/C][C]17374.051006345[/C][C]1107.94899365495[/C][/ROW]
[ROW][C]103[/C][C]24281[/C][C]25724.8215747689[/C][C]-1443.82157476891[/C][/ROW]
[ROW][C]104[/C][C]27905[/C][C]25579.5595954839[/C][C]2325.44040451611[/C][/ROW]
[ROW][C]105[/C][C]20657[/C][C]19423.0402348489[/C][C]1233.95976515114[/C][/ROW]
[ROW][C]106[/C][C]23194[/C][C]25322.2285943674[/C][C]-2128.22859436744[/C][/ROW]
[ROW][C]107[/C][C]17395[/C][C]18844.9070983706[/C][C]-1449.9070983706[/C][/ROW]
[ROW][C]108[/C][C]30079[/C][C]29300.7453688151[/C][C]778.254631184926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211236&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211236&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
132174422487.7216880342-743.721688034188
141630817033.654531258-725.654531257973
151920720089.259381092-882.259381092012
161449615344.0594063619-848.059406361912
172029420828.508085197-534.508085197001
181667016888.9156795619-218.915679561862
192210621119.5079902589986.492009741069
201993221746.3896050083-1814.3896050083
212101924263.429394511-3244.42939451103
222355620892.99718521352663.00281478647
232319419761.65089502633432.34910497369
242754224919.70103021452622.29896978546
251993220320.3473747081-388.347374708148
261667014895.87906391741774.12093608263
271848217863.1177680323618.882231967658
281340913209.9166914212199.08330857882
291920719049.1141458694157.885854130618
301485815469.2692595661-611.269259566085
312101920865.4464631356153.553536864449
321993218956.526586026975.473413973959
331775820259.4888445426-2501.48884454255
342536822420.43355608092947.56644391913
352283122086.8997599377744.100240062344
362609326535.9114241912-442.911424191203
371957019169.0666793558400.933320644166
381812015784.22285176842335.77714823165
391630817738.7044505498-1430.70445054977
401340912707.0007234948701.999276505234
411775818544.5957739199-786.595773919889
421594614270.63546324591675.36453675409
432174420436.39584106071307.60415893928
442101919349.84142881111669.1585711889
451812017518.2366389267601.763361073252
462428124816.0217997531-535.021799753133
472246922478.6743472609-9.67434726090141
482899225878.22819086793113.7718091321
492319419404.93067902543789.06932097459
501413417948.1387845451-3814.1387845451
511413416435.0764863674-2301.07648636738
521413413409.4575609292724.542439070807
531667017926.531628764-1256.53162876398
541667015961.4536840778708.546315922225
552246921816.522990201652.47700979904
562065721087.7729563612-430.772956361223
571848218265.226214971216.773785028978
582319424520.4496410354-1326.44964103539
592138222660.2287030919-1278.22870309189
603080428913.52188368081890.47811631919
612428123028.44076109151252.55923890853
621413414500.1515266794-366.15152667937
631485814398.4220280994459.577971900622
641232214196.2885665818-1874.28856658178
651703316852.3817537906180.618246209364
661957016711.11922689312858.88077310685
672464322555.06491538582087.9350846142
682428120875.8578794223405.142120578
691957018754.4527515237815.547248476316
702283123668.8396638711-837.839663871076
712029421936.9307489099-1642.9307489099
722899231181.1194841544-2189.11948415443
732210624709.191879553-2603.19187955298
741775814657.23884578593100.76115421413
751594615382.7397091983563.260290801722
761195913067.8728800758-1108.8728800758
771775817666.289756048991.7102439510527
782138220032.72195884251349.27804115746
792500625180.719582783-174.719582782996
802355624700.8068819381-1144.80688193812
811739520117.5385975578-2722.53859755784
822500623408.9341671331597.06583286698
831957020912.9461334003-1342.94613340034
843007929614.5436204892464.45637951079
852500622767.95192726092238.04807273909
861812018040.705673621279.294326378782
871667016400.3420584262269.657941573769
881123412539.0640849438-1305.0640849438
891775818235.8069917313-477.806991731279
901703321744.3361890741-4711.33618907409
912573025366.0184929373363.981507062734
922573023935.85565620161794.14434379841
931957017892.04333006831677.9566699317
942536825208.2413795782159.758620421791
951884519984.053858118-1139.05385811801
962935430346.6628939373-992.662893937333
972500625101.1407388962-95.1407388962471
981848218323.7954761785158.204523821543
991413416819.7807913605-2685.78079136046
100978511413.9523005926-1628.95230059265
1011920717799.5823988731407.41760112701
1021848217374.0510063451107.94899365495
1032428125724.8215747689-1443.82157476891
1042790525579.55959548392325.44040451611
1052065719423.04023484891233.95976515114
1062319425322.2285943674-2128.22859436744
1071739518844.9070983706-1449.9070983706
1083007929300.7453688151778.254631184926







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10924875.801506489121553.911569894728197.6914430835
11018311.173888368614988.717079083221633.630697654
11114163.565297973110839.833378626117487.2972173201
1129757.707806199096431.7102315510913083.7053808471
11318971.667422353415642.132847737722301.2019969692
11418261.250596780514926.629333122821595.8718604382
11524245.392995538220903.860625299427586.9253657769
11627591.814477626224241.276825119230942.3521301331
11720394.141432281517032.241053040823756.0418115222
11823159.634623929619783.758940802626535.5103070567
11917320.473503860313927.764672528520713.182335192
12029848.936666495126436.303201251333261.5701317389

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 24875.8015064891 & 21553.9115698947 & 28197.6914430835 \tabularnewline
110 & 18311.1738883686 & 14988.7170790832 & 21633.630697654 \tabularnewline
111 & 14163.5652979731 & 10839.8333786261 & 17487.2972173201 \tabularnewline
112 & 9757.70780619909 & 6431.71023155109 & 13083.7053808471 \tabularnewline
113 & 18971.6674223534 & 15642.1328477377 & 22301.2019969692 \tabularnewline
114 & 18261.2505967805 & 14926.6293331228 & 21595.8718604382 \tabularnewline
115 & 24245.3929955382 & 20903.8606252994 & 27586.9253657769 \tabularnewline
116 & 27591.8144776262 & 24241.2768251192 & 30942.3521301331 \tabularnewline
117 & 20394.1414322815 & 17032.2410530408 & 23756.0418115222 \tabularnewline
118 & 23159.6346239296 & 19783.7589408026 & 26535.5103070567 \tabularnewline
119 & 17320.4735038603 & 13927.7646725285 & 20713.182335192 \tabularnewline
120 & 29848.9366664951 & 26436.3032012513 & 33261.5701317389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211236&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]109[/C][C]24875.8015064891[/C][C]21553.9115698947[/C][C]28197.6914430835[/C][/ROW]
[ROW][C]110[/C][C]18311.1738883686[/C][C]14988.7170790832[/C][C]21633.630697654[/C][/ROW]
[ROW][C]111[/C][C]14163.5652979731[/C][C]10839.8333786261[/C][C]17487.2972173201[/C][/ROW]
[ROW][C]112[/C][C]9757.70780619909[/C][C]6431.71023155109[/C][C]13083.7053808471[/C][/ROW]
[ROW][C]113[/C][C]18971.6674223534[/C][C]15642.1328477377[/C][C]22301.2019969692[/C][/ROW]
[ROW][C]114[/C][C]18261.2505967805[/C][C]14926.6293331228[/C][C]21595.8718604382[/C][/ROW]
[ROW][C]115[/C][C]24245.3929955382[/C][C]20903.8606252994[/C][C]27586.9253657769[/C][/ROW]
[ROW][C]116[/C][C]27591.8144776262[/C][C]24241.2768251192[/C][C]30942.3521301331[/C][/ROW]
[ROW][C]117[/C][C]20394.1414322815[/C][C]17032.2410530408[/C][C]23756.0418115222[/C][/ROW]
[ROW][C]118[/C][C]23159.6346239296[/C][C]19783.7589408026[/C][C]26535.5103070567[/C][/ROW]
[ROW][C]119[/C][C]17320.4735038603[/C][C]13927.7646725285[/C][C]20713.182335192[/C][/ROW]
[ROW][C]120[/C][C]29848.9366664951[/C][C]26436.3032012513[/C][C]33261.5701317389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211236&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211236&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
10924875.801506489121553.911569894728197.6914430835
11018311.173888368614988.717079083221633.630697654
11114163.565297973110839.833378626117487.2972173201
1129757.707806199096431.7102315510913083.7053808471
11318971.667422353415642.132847737722301.2019969692
11418261.250596780514926.629333122821595.8718604382
11524245.392995538220903.860625299427586.9253657769
11627591.814477626224241.276825119230942.3521301331
11720394.141432281517032.241053040823756.0418115222
11823159.634623929619783.758940802626535.5103070567
11917320.473503860313927.764672528520713.182335192
12029848.936666495126436.303201251333261.5701317389



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