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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, 16 Aug 2015 15:25:44 +0100
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/Aug/16/t1439735166sa1u6bny0fy4d3c.htm/, Retrieved Sun, 19 May 2024 14:33:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280155, Retrieved Sun, 19 May 2024 14:33:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2015-08-16 14:25:44] [0d8529ada52922935dd1fcf0fb375c74] [Current]
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Dataseries X:
133448.00
132951.00
132447.00
131404.00
141722.00
141176.00
133448.00
128310.00
128807.00
128807.00
129360.00
130354.00
131901.00
131901.00
130907.00
128310.00
141722.00
143766.00
140679.00
133448.00
136542.00
131901.00
133994.00
134995.00
136038.00
133448.00
133994.00
130354.00
141722.00
145313.00
142226.00
136542.00
142723.00
136038.00
142226.00
141722.00
143269.00
137585.00
143766.00
143269.00
152544.00
150451.00
142226.00
138082.00
143766.00
136038.00
141722.00
142723.00
144816.00
140182.00
142723.00
144270.00
149954.00
145313.00
139132.00
132447.00
138635.00
121625.00
129857.00
134491.00
139132.00
132447.00
132447.00
132447.00
136038.00
130907.00
124173.00
118538.00
122626.00
106666.00
116445.00
122129.00
123172.00
117488.00
117985.00
116445.00
121625.00
117985.00
110810.00
105623.00
114394.00
95347.00
107716.00
113351.00
113351.00
106666.00
100485.00
99988.00
105623.00
100485.00
90713.00
83979.00
91210.00
74207.00
89663.00
97888.00
100485.00
94801.00
87619.00
92757.00
94801.00
93254.00
77791.00
70616.00
75747.00
60291.00
76251.00
81935.00
86569.00
78841.00
71610.00
75747.00
77791.00
73703.00
58247.00
51513.00
57694.00
40691.00
59241.00
70616.00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280155&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]1 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=280155&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280155&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.379244790290872
beta0.0506954647933669
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.379244790290872 \tabularnewline
beta & 0.0506954647933669 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280155&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]0.379244790290872[/C][/ROW]
[ROW][C]beta[/C][C]0.0506954647933669[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280155&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280155&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
alpha0.379244790290872
beta0.0506954647933669
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13131901131911.039942534-10.0399425340293
14131901131619.02904282281.970957179554
15130907130433.911712833473.088287166785
16128310127820.367827504489.632172496102
17141722141310.274434993411.725565007073
18143766143369.041711089396.958288910741
19140679135685.0030069664993.99699303432
20133448132737.747383033710.252616967278
21136542133994.3062170982547.69378290157
22131901135570.364657747-3669.3646577473
23133994135230.383265171-1236.38326517076
24134995136008.582699965-1013.58269996496
25136038137109.355986803-1071.35598680258
26133448136645.459002346-3197.45900234563
27133994134216.194199657-222.194199656806
28130354131256.274249541-902.274249541311
29141722144383.695886947-2661.69588694657
30145313145176.333629742136.666370257648
31142226140039.9053733492186.09462665126
32136542133199.5021543113342.49784568939
33142723136488.506823566234.49317643984
34136038135480.488853316557.511146683944
35142226138358.5368569863867.46314301417
36141722141397.895754419324.104245581228
37143269143193.24419354975.7558064506156
38137585141927.785378739-4342.78537873927
39143766141098.9990714982667.00092850157
40143269138815.3139419444453.68605805596
41152544154166.055822731-1622.05582273088
42150451157749.347052454-7298.34705245381
43142226151013.629873568-8787.62987356764
44138082140450.803766888-2368.80376688816
45143766143282.602187232483.397812768206
46136038136330.605164581-292.605164581415
47141722140697.7252934881024.27470651228
48142723140190.2816287312532.71837126918
49144816142428.023602292387.97639771001
50140182139076.6411898271105.35881017262
51142723144633.772459773-1910.77245977335
52144270141515.789078982754.21092101964
53149954152181.106361855-2227.10636185462
54145313151698.78208626-6385.78208626018
55139132144093.765441182-4961.76544118195
56132447138818.185079912-6371.18507991187
57138635141612.496641716-2977.49664171616
58121625132768.249195753-11143.249195753
59129857133051.153432608-3194.15343260812
60134491131297.6132724383193.38672756249
61139132133044.8990843136087.10091568722
62132447130161.0177612752285.98223872458
63132447133621.965297378-1174.96529737808
64132447133191.929856733-744.929856732604
65136038138393.160971463-2355.16097146345
66130907134886.551485379-3979.55148537891
67124173128922.23222872-4749.23222871992
68118538122695.050224849-4157.05022484885
69122626127339.206533114-4713.20653311428
70106666113317.543189966-6651.54318996619
71116445118955.92132869-2510.92132869003
72122129120666.4146996921462.58530030806
73123172122794.112099581377.887900419388
74117488115710.2680506191777.73194938064
75117985116219.496942861765.50305713979
76116445116635.757771759-190.757771758988
77121625119990.6825887031634.31741129687
78117985116947.3437607841037.65623921571
79110810112556.172327911-1746.17232791097
80105623107937.52123637-2314.5212363703
81114394112073.662837282320.33716272016
8295347100382.274518873-5035.27451887298
83107716108269.134587186-553.134587185501
84113351112750.416384899600.583615100812
85113351113727.054340776-376.054340775649
86106666107620.422987033-954.422987032929
87100485106942.994510317-6457.99451031692
8899988102870.087881005-2882.0878810047
89105623105357.108365324265.891634676227
90100485101542.176693241-1057.17669324094
919071395115.3623997588-4402.3623997588
928397989316.3149803951-5337.31498039508
939121093196.443022733-1986.44302273302
947420777950.5811540883-3743.58115408834
958966385949.16171785233713.83828214766
969788891116.86720349666771.13279650344
9710048593306.07185993047178.92814006956
989480190351.08911586094449.91088413911
998761988537.7497337323-918.749733732257
1009275788592.74656230274164.25343769735
1019480195214.058677824-413.058677823952
1029325490827.41262268572426.58737731431
1037779184410.4704613824-6619.47046138236
1047061677619.3781983073-7003.3781983073
1057574782064.4917144144-6317.49171441441
1066029165911.7989780586-5620.79897805862
1077625175616.6508561256634.349143874366
1088193580252.03536567981682.96463432019
1098656980278.00497653856290.99502346152
1107884176177.40637706942663.59362293055
1117161071238.0874577971371.912542202859
1127574773861.20096300751885.79903699248
1137779175911.54440566191879.45559433814
1147370374236.9531397412-533.953139741221
1155824763268.7500393247-5021.75003932466
1165151357310.016233421-5797.01623342096
1175769460460.5345476127-2766.53454761267
1184069148541.843395267-7850.84339526699
1195924156894.17251111692346.82748888308
1207061661047.72793587049568.27206412957

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 131901 & 131911.039942534 & -10.0399425340293 \tabularnewline
14 & 131901 & 131619.02904282 & 281.970957179554 \tabularnewline
15 & 130907 & 130433.911712833 & 473.088287166785 \tabularnewline
16 & 128310 & 127820.367827504 & 489.632172496102 \tabularnewline
17 & 141722 & 141310.274434993 & 411.725565007073 \tabularnewline
18 & 143766 & 143369.041711089 & 396.958288910741 \tabularnewline
19 & 140679 & 135685.003006966 & 4993.99699303432 \tabularnewline
20 & 133448 & 132737.747383033 & 710.252616967278 \tabularnewline
21 & 136542 & 133994.306217098 & 2547.69378290157 \tabularnewline
22 & 131901 & 135570.364657747 & -3669.3646577473 \tabularnewline
23 & 133994 & 135230.383265171 & -1236.38326517076 \tabularnewline
24 & 134995 & 136008.582699965 & -1013.58269996496 \tabularnewline
25 & 136038 & 137109.355986803 & -1071.35598680258 \tabularnewline
26 & 133448 & 136645.459002346 & -3197.45900234563 \tabularnewline
27 & 133994 & 134216.194199657 & -222.194199656806 \tabularnewline
28 & 130354 & 131256.274249541 & -902.274249541311 \tabularnewline
29 & 141722 & 144383.695886947 & -2661.69588694657 \tabularnewline
30 & 145313 & 145176.333629742 & 136.666370257648 \tabularnewline
31 & 142226 & 140039.905373349 & 2186.09462665126 \tabularnewline
32 & 136542 & 133199.502154311 & 3342.49784568939 \tabularnewline
33 & 142723 & 136488.50682356 & 6234.49317643984 \tabularnewline
34 & 136038 & 135480.488853316 & 557.511146683944 \tabularnewline
35 & 142226 & 138358.536856986 & 3867.46314301417 \tabularnewline
36 & 141722 & 141397.895754419 & 324.104245581228 \tabularnewline
37 & 143269 & 143193.244193549 & 75.7558064506156 \tabularnewline
38 & 137585 & 141927.785378739 & -4342.78537873927 \tabularnewline
39 & 143766 & 141098.999071498 & 2667.00092850157 \tabularnewline
40 & 143269 & 138815.313941944 & 4453.68605805596 \tabularnewline
41 & 152544 & 154166.055822731 & -1622.05582273088 \tabularnewline
42 & 150451 & 157749.347052454 & -7298.34705245381 \tabularnewline
43 & 142226 & 151013.629873568 & -8787.62987356764 \tabularnewline
44 & 138082 & 140450.803766888 & -2368.80376688816 \tabularnewline
45 & 143766 & 143282.602187232 & 483.397812768206 \tabularnewline
46 & 136038 & 136330.605164581 & -292.605164581415 \tabularnewline
47 & 141722 & 140697.725293488 & 1024.27470651228 \tabularnewline
48 & 142723 & 140190.281628731 & 2532.71837126918 \tabularnewline
49 & 144816 & 142428.02360229 & 2387.97639771001 \tabularnewline
50 & 140182 & 139076.641189827 & 1105.35881017262 \tabularnewline
51 & 142723 & 144633.772459773 & -1910.77245977335 \tabularnewline
52 & 144270 & 141515.78907898 & 2754.21092101964 \tabularnewline
53 & 149954 & 152181.106361855 & -2227.10636185462 \tabularnewline
54 & 145313 & 151698.78208626 & -6385.78208626018 \tabularnewline
55 & 139132 & 144093.765441182 & -4961.76544118195 \tabularnewline
56 & 132447 & 138818.185079912 & -6371.18507991187 \tabularnewline
57 & 138635 & 141612.496641716 & -2977.49664171616 \tabularnewline
58 & 121625 & 132768.249195753 & -11143.249195753 \tabularnewline
59 & 129857 & 133051.153432608 & -3194.15343260812 \tabularnewline
60 & 134491 & 131297.613272438 & 3193.38672756249 \tabularnewline
61 & 139132 & 133044.899084313 & 6087.10091568722 \tabularnewline
62 & 132447 & 130161.017761275 & 2285.98223872458 \tabularnewline
63 & 132447 & 133621.965297378 & -1174.96529737808 \tabularnewline
64 & 132447 & 133191.929856733 & -744.929856732604 \tabularnewline
65 & 136038 & 138393.160971463 & -2355.16097146345 \tabularnewline
66 & 130907 & 134886.551485379 & -3979.55148537891 \tabularnewline
67 & 124173 & 128922.23222872 & -4749.23222871992 \tabularnewline
68 & 118538 & 122695.050224849 & -4157.05022484885 \tabularnewline
69 & 122626 & 127339.206533114 & -4713.20653311428 \tabularnewline
70 & 106666 & 113317.543189966 & -6651.54318996619 \tabularnewline
71 & 116445 & 118955.92132869 & -2510.92132869003 \tabularnewline
72 & 122129 & 120666.414699692 & 1462.58530030806 \tabularnewline
73 & 123172 & 122794.112099581 & 377.887900419388 \tabularnewline
74 & 117488 & 115710.268050619 & 1777.73194938064 \tabularnewline
75 & 117985 & 116219.49694286 & 1765.50305713979 \tabularnewline
76 & 116445 & 116635.757771759 & -190.757771758988 \tabularnewline
77 & 121625 & 119990.682588703 & 1634.31741129687 \tabularnewline
78 & 117985 & 116947.343760784 & 1037.65623921571 \tabularnewline
79 & 110810 & 112556.172327911 & -1746.17232791097 \tabularnewline
80 & 105623 & 107937.52123637 & -2314.5212363703 \tabularnewline
81 & 114394 & 112073.66283728 & 2320.33716272016 \tabularnewline
82 & 95347 & 100382.274518873 & -5035.27451887298 \tabularnewline
83 & 107716 & 108269.134587186 & -553.134587185501 \tabularnewline
84 & 113351 & 112750.416384899 & 600.583615100812 \tabularnewline
85 & 113351 & 113727.054340776 & -376.054340775649 \tabularnewline
86 & 106666 & 107620.422987033 & -954.422987032929 \tabularnewline
87 & 100485 & 106942.994510317 & -6457.99451031692 \tabularnewline
88 & 99988 & 102870.087881005 & -2882.0878810047 \tabularnewline
89 & 105623 & 105357.108365324 & 265.891634676227 \tabularnewline
90 & 100485 & 101542.176693241 & -1057.17669324094 \tabularnewline
91 & 90713 & 95115.3623997588 & -4402.3623997588 \tabularnewline
92 & 83979 & 89316.3149803951 & -5337.31498039508 \tabularnewline
93 & 91210 & 93196.443022733 & -1986.44302273302 \tabularnewline
94 & 74207 & 77950.5811540883 & -3743.58115408834 \tabularnewline
95 & 89663 & 85949.1617178523 & 3713.83828214766 \tabularnewline
96 & 97888 & 91116.8672034966 & 6771.13279650344 \tabularnewline
97 & 100485 & 93306.0718599304 & 7178.92814006956 \tabularnewline
98 & 94801 & 90351.0891158609 & 4449.91088413911 \tabularnewline
99 & 87619 & 88537.7497337323 & -918.749733732257 \tabularnewline
100 & 92757 & 88592.7465623027 & 4164.25343769735 \tabularnewline
101 & 94801 & 95214.058677824 & -413.058677823952 \tabularnewline
102 & 93254 & 90827.4126226857 & 2426.58737731431 \tabularnewline
103 & 77791 & 84410.4704613824 & -6619.47046138236 \tabularnewline
104 & 70616 & 77619.3781983073 & -7003.3781983073 \tabularnewline
105 & 75747 & 82064.4917144144 & -6317.49171441441 \tabularnewline
106 & 60291 & 65911.7989780586 & -5620.79897805862 \tabularnewline
107 & 76251 & 75616.6508561256 & 634.349143874366 \tabularnewline
108 & 81935 & 80252.0353656798 & 1682.96463432019 \tabularnewline
109 & 86569 & 80278.0049765385 & 6290.99502346152 \tabularnewline
110 & 78841 & 76177.4063770694 & 2663.59362293055 \tabularnewline
111 & 71610 & 71238.0874577971 & 371.912542202859 \tabularnewline
112 & 75747 & 73861.2009630075 & 1885.79903699248 \tabularnewline
113 & 77791 & 75911.5444056619 & 1879.45559433814 \tabularnewline
114 & 73703 & 74236.9531397412 & -533.953139741221 \tabularnewline
115 & 58247 & 63268.7500393247 & -5021.75003932466 \tabularnewline
116 & 51513 & 57310.016233421 & -5797.01623342096 \tabularnewline
117 & 57694 & 60460.5345476127 & -2766.53454761267 \tabularnewline
118 & 40691 & 48541.843395267 & -7850.84339526699 \tabularnewline
119 & 59241 & 56894.1725111169 & 2346.82748888308 \tabularnewline
120 & 70616 & 61047.7279358704 & 9568.27206412957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280155&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]131901[/C][C]131911.039942534[/C][C]-10.0399425340293[/C][/ROW]
[ROW][C]14[/C][C]131901[/C][C]131619.02904282[/C][C]281.970957179554[/C][/ROW]
[ROW][C]15[/C][C]130907[/C][C]130433.911712833[/C][C]473.088287166785[/C][/ROW]
[ROW][C]16[/C][C]128310[/C][C]127820.367827504[/C][C]489.632172496102[/C][/ROW]
[ROW][C]17[/C][C]141722[/C][C]141310.274434993[/C][C]411.725565007073[/C][/ROW]
[ROW][C]18[/C][C]143766[/C][C]143369.041711089[/C][C]396.958288910741[/C][/ROW]
[ROW][C]19[/C][C]140679[/C][C]135685.003006966[/C][C]4993.99699303432[/C][/ROW]
[ROW][C]20[/C][C]133448[/C][C]132737.747383033[/C][C]710.252616967278[/C][/ROW]
[ROW][C]21[/C][C]136542[/C][C]133994.306217098[/C][C]2547.69378290157[/C][/ROW]
[ROW][C]22[/C][C]131901[/C][C]135570.364657747[/C][C]-3669.3646577473[/C][/ROW]
[ROW][C]23[/C][C]133994[/C][C]135230.383265171[/C][C]-1236.38326517076[/C][/ROW]
[ROW][C]24[/C][C]134995[/C][C]136008.582699965[/C][C]-1013.58269996496[/C][/ROW]
[ROW][C]25[/C][C]136038[/C][C]137109.355986803[/C][C]-1071.35598680258[/C][/ROW]
[ROW][C]26[/C][C]133448[/C][C]136645.459002346[/C][C]-3197.45900234563[/C][/ROW]
[ROW][C]27[/C][C]133994[/C][C]134216.194199657[/C][C]-222.194199656806[/C][/ROW]
[ROW][C]28[/C][C]130354[/C][C]131256.274249541[/C][C]-902.274249541311[/C][/ROW]
[ROW][C]29[/C][C]141722[/C][C]144383.695886947[/C][C]-2661.69588694657[/C][/ROW]
[ROW][C]30[/C][C]145313[/C][C]145176.333629742[/C][C]136.666370257648[/C][/ROW]
[ROW][C]31[/C][C]142226[/C][C]140039.905373349[/C][C]2186.09462665126[/C][/ROW]
[ROW][C]32[/C][C]136542[/C][C]133199.502154311[/C][C]3342.49784568939[/C][/ROW]
[ROW][C]33[/C][C]142723[/C][C]136488.50682356[/C][C]6234.49317643984[/C][/ROW]
[ROW][C]34[/C][C]136038[/C][C]135480.488853316[/C][C]557.511146683944[/C][/ROW]
[ROW][C]35[/C][C]142226[/C][C]138358.536856986[/C][C]3867.46314301417[/C][/ROW]
[ROW][C]36[/C][C]141722[/C][C]141397.895754419[/C][C]324.104245581228[/C][/ROW]
[ROW][C]37[/C][C]143269[/C][C]143193.244193549[/C][C]75.7558064506156[/C][/ROW]
[ROW][C]38[/C][C]137585[/C][C]141927.785378739[/C][C]-4342.78537873927[/C][/ROW]
[ROW][C]39[/C][C]143766[/C][C]141098.999071498[/C][C]2667.00092850157[/C][/ROW]
[ROW][C]40[/C][C]143269[/C][C]138815.313941944[/C][C]4453.68605805596[/C][/ROW]
[ROW][C]41[/C][C]152544[/C][C]154166.055822731[/C][C]-1622.05582273088[/C][/ROW]
[ROW][C]42[/C][C]150451[/C][C]157749.347052454[/C][C]-7298.34705245381[/C][/ROW]
[ROW][C]43[/C][C]142226[/C][C]151013.629873568[/C][C]-8787.62987356764[/C][/ROW]
[ROW][C]44[/C][C]138082[/C][C]140450.803766888[/C][C]-2368.80376688816[/C][/ROW]
[ROW][C]45[/C][C]143766[/C][C]143282.602187232[/C][C]483.397812768206[/C][/ROW]
[ROW][C]46[/C][C]136038[/C][C]136330.605164581[/C][C]-292.605164581415[/C][/ROW]
[ROW][C]47[/C][C]141722[/C][C]140697.725293488[/C][C]1024.27470651228[/C][/ROW]
[ROW][C]48[/C][C]142723[/C][C]140190.281628731[/C][C]2532.71837126918[/C][/ROW]
[ROW][C]49[/C][C]144816[/C][C]142428.02360229[/C][C]2387.97639771001[/C][/ROW]
[ROW][C]50[/C][C]140182[/C][C]139076.641189827[/C][C]1105.35881017262[/C][/ROW]
[ROW][C]51[/C][C]142723[/C][C]144633.772459773[/C][C]-1910.77245977335[/C][/ROW]
[ROW][C]52[/C][C]144270[/C][C]141515.78907898[/C][C]2754.21092101964[/C][/ROW]
[ROW][C]53[/C][C]149954[/C][C]152181.106361855[/C][C]-2227.10636185462[/C][/ROW]
[ROW][C]54[/C][C]145313[/C][C]151698.78208626[/C][C]-6385.78208626018[/C][/ROW]
[ROW][C]55[/C][C]139132[/C][C]144093.765441182[/C][C]-4961.76544118195[/C][/ROW]
[ROW][C]56[/C][C]132447[/C][C]138818.185079912[/C][C]-6371.18507991187[/C][/ROW]
[ROW][C]57[/C][C]138635[/C][C]141612.496641716[/C][C]-2977.49664171616[/C][/ROW]
[ROW][C]58[/C][C]121625[/C][C]132768.249195753[/C][C]-11143.249195753[/C][/ROW]
[ROW][C]59[/C][C]129857[/C][C]133051.153432608[/C][C]-3194.15343260812[/C][/ROW]
[ROW][C]60[/C][C]134491[/C][C]131297.613272438[/C][C]3193.38672756249[/C][/ROW]
[ROW][C]61[/C][C]139132[/C][C]133044.899084313[/C][C]6087.10091568722[/C][/ROW]
[ROW][C]62[/C][C]132447[/C][C]130161.017761275[/C][C]2285.98223872458[/C][/ROW]
[ROW][C]63[/C][C]132447[/C][C]133621.965297378[/C][C]-1174.96529737808[/C][/ROW]
[ROW][C]64[/C][C]132447[/C][C]133191.929856733[/C][C]-744.929856732604[/C][/ROW]
[ROW][C]65[/C][C]136038[/C][C]138393.160971463[/C][C]-2355.16097146345[/C][/ROW]
[ROW][C]66[/C][C]130907[/C][C]134886.551485379[/C][C]-3979.55148537891[/C][/ROW]
[ROW][C]67[/C][C]124173[/C][C]128922.23222872[/C][C]-4749.23222871992[/C][/ROW]
[ROW][C]68[/C][C]118538[/C][C]122695.050224849[/C][C]-4157.05022484885[/C][/ROW]
[ROW][C]69[/C][C]122626[/C][C]127339.206533114[/C][C]-4713.20653311428[/C][/ROW]
[ROW][C]70[/C][C]106666[/C][C]113317.543189966[/C][C]-6651.54318996619[/C][/ROW]
[ROW][C]71[/C][C]116445[/C][C]118955.92132869[/C][C]-2510.92132869003[/C][/ROW]
[ROW][C]72[/C][C]122129[/C][C]120666.414699692[/C][C]1462.58530030806[/C][/ROW]
[ROW][C]73[/C][C]123172[/C][C]122794.112099581[/C][C]377.887900419388[/C][/ROW]
[ROW][C]74[/C][C]117488[/C][C]115710.268050619[/C][C]1777.73194938064[/C][/ROW]
[ROW][C]75[/C][C]117985[/C][C]116219.49694286[/C][C]1765.50305713979[/C][/ROW]
[ROW][C]76[/C][C]116445[/C][C]116635.757771759[/C][C]-190.757771758988[/C][/ROW]
[ROW][C]77[/C][C]121625[/C][C]119990.682588703[/C][C]1634.31741129687[/C][/ROW]
[ROW][C]78[/C][C]117985[/C][C]116947.343760784[/C][C]1037.65623921571[/C][/ROW]
[ROW][C]79[/C][C]110810[/C][C]112556.172327911[/C][C]-1746.17232791097[/C][/ROW]
[ROW][C]80[/C][C]105623[/C][C]107937.52123637[/C][C]-2314.5212363703[/C][/ROW]
[ROW][C]81[/C][C]114394[/C][C]112073.66283728[/C][C]2320.33716272016[/C][/ROW]
[ROW][C]82[/C][C]95347[/C][C]100382.274518873[/C][C]-5035.27451887298[/C][/ROW]
[ROW][C]83[/C][C]107716[/C][C]108269.134587186[/C][C]-553.134587185501[/C][/ROW]
[ROW][C]84[/C][C]113351[/C][C]112750.416384899[/C][C]600.583615100812[/C][/ROW]
[ROW][C]85[/C][C]113351[/C][C]113727.054340776[/C][C]-376.054340775649[/C][/ROW]
[ROW][C]86[/C][C]106666[/C][C]107620.422987033[/C][C]-954.422987032929[/C][/ROW]
[ROW][C]87[/C][C]100485[/C][C]106942.994510317[/C][C]-6457.99451031692[/C][/ROW]
[ROW][C]88[/C][C]99988[/C][C]102870.087881005[/C][C]-2882.0878810047[/C][/ROW]
[ROW][C]89[/C][C]105623[/C][C]105357.108365324[/C][C]265.891634676227[/C][/ROW]
[ROW][C]90[/C][C]100485[/C][C]101542.176693241[/C][C]-1057.17669324094[/C][/ROW]
[ROW][C]91[/C][C]90713[/C][C]95115.3623997588[/C][C]-4402.3623997588[/C][/ROW]
[ROW][C]92[/C][C]83979[/C][C]89316.3149803951[/C][C]-5337.31498039508[/C][/ROW]
[ROW][C]93[/C][C]91210[/C][C]93196.443022733[/C][C]-1986.44302273302[/C][/ROW]
[ROW][C]94[/C][C]74207[/C][C]77950.5811540883[/C][C]-3743.58115408834[/C][/ROW]
[ROW][C]95[/C][C]89663[/C][C]85949.1617178523[/C][C]3713.83828214766[/C][/ROW]
[ROW][C]96[/C][C]97888[/C][C]91116.8672034966[/C][C]6771.13279650344[/C][/ROW]
[ROW][C]97[/C][C]100485[/C][C]93306.0718599304[/C][C]7178.92814006956[/C][/ROW]
[ROW][C]98[/C][C]94801[/C][C]90351.0891158609[/C][C]4449.91088413911[/C][/ROW]
[ROW][C]99[/C][C]87619[/C][C]88537.7497337323[/C][C]-918.749733732257[/C][/ROW]
[ROW][C]100[/C][C]92757[/C][C]88592.7465623027[/C][C]4164.25343769735[/C][/ROW]
[ROW][C]101[/C][C]94801[/C][C]95214.058677824[/C][C]-413.058677823952[/C][/ROW]
[ROW][C]102[/C][C]93254[/C][C]90827.4126226857[/C][C]2426.58737731431[/C][/ROW]
[ROW][C]103[/C][C]77791[/C][C]84410.4704613824[/C][C]-6619.47046138236[/C][/ROW]
[ROW][C]104[/C][C]70616[/C][C]77619.3781983073[/C][C]-7003.3781983073[/C][/ROW]
[ROW][C]105[/C][C]75747[/C][C]82064.4917144144[/C][C]-6317.49171441441[/C][/ROW]
[ROW][C]106[/C][C]60291[/C][C]65911.7989780586[/C][C]-5620.79897805862[/C][/ROW]
[ROW][C]107[/C][C]76251[/C][C]75616.6508561256[/C][C]634.349143874366[/C][/ROW]
[ROW][C]108[/C][C]81935[/C][C]80252.0353656798[/C][C]1682.96463432019[/C][/ROW]
[ROW][C]109[/C][C]86569[/C][C]80278.0049765385[/C][C]6290.99502346152[/C][/ROW]
[ROW][C]110[/C][C]78841[/C][C]76177.4063770694[/C][C]2663.59362293055[/C][/ROW]
[ROW][C]111[/C][C]71610[/C][C]71238.0874577971[/C][C]371.912542202859[/C][/ROW]
[ROW][C]112[/C][C]75747[/C][C]73861.2009630075[/C][C]1885.79903699248[/C][/ROW]
[ROW][C]113[/C][C]77791[/C][C]75911.5444056619[/C][C]1879.45559433814[/C][/ROW]
[ROW][C]114[/C][C]73703[/C][C]74236.9531397412[/C][C]-533.953139741221[/C][/ROW]
[ROW][C]115[/C][C]58247[/C][C]63268.7500393247[/C][C]-5021.75003932466[/C][/ROW]
[ROW][C]116[/C][C]51513[/C][C]57310.016233421[/C][C]-5797.01623342096[/C][/ROW]
[ROW][C]117[/C][C]57694[/C][C]60460.5345476127[/C][C]-2766.53454761267[/C][/ROW]
[ROW][C]118[/C][C]40691[/C][C]48541.843395267[/C][C]-7850.84339526699[/C][/ROW]
[ROW][C]119[/C][C]59241[/C][C]56894.1725111169[/C][C]2346.82748888308[/C][/ROW]
[ROW][C]120[/C][C]70616[/C][C]61047.7279358704[/C][C]9568.27206412957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280155&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280155&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
13131901131911.039942534-10.0399425340293
14131901131619.02904282281.970957179554
15130907130433.911712833473.088287166785
16128310127820.367827504489.632172496102
17141722141310.274434993411.725565007073
18143766143369.041711089396.958288910741
19140679135685.0030069664993.99699303432
20133448132737.747383033710.252616967278
21136542133994.3062170982547.69378290157
22131901135570.364657747-3669.3646577473
23133994135230.383265171-1236.38326517076
24134995136008.582699965-1013.58269996496
25136038137109.355986803-1071.35598680258
26133448136645.459002346-3197.45900234563
27133994134216.194199657-222.194199656806
28130354131256.274249541-902.274249541311
29141722144383.695886947-2661.69588694657
30145313145176.333629742136.666370257648
31142226140039.9053733492186.09462665126
32136542133199.5021543113342.49784568939
33142723136488.506823566234.49317643984
34136038135480.488853316557.511146683944
35142226138358.5368569863867.46314301417
36141722141397.895754419324.104245581228
37143269143193.24419354975.7558064506156
38137585141927.785378739-4342.78537873927
39143766141098.9990714982667.00092850157
40143269138815.3139419444453.68605805596
41152544154166.055822731-1622.05582273088
42150451157749.347052454-7298.34705245381
43142226151013.629873568-8787.62987356764
44138082140450.803766888-2368.80376688816
45143766143282.602187232483.397812768206
46136038136330.605164581-292.605164581415
47141722140697.7252934881024.27470651228
48142723140190.2816287312532.71837126918
49144816142428.023602292387.97639771001
50140182139076.6411898271105.35881017262
51142723144633.772459773-1910.77245977335
52144270141515.789078982754.21092101964
53149954152181.106361855-2227.10636185462
54145313151698.78208626-6385.78208626018
55139132144093.765441182-4961.76544118195
56132447138818.185079912-6371.18507991187
57138635141612.496641716-2977.49664171616
58121625132768.249195753-11143.249195753
59129857133051.153432608-3194.15343260812
60134491131297.6132724383193.38672756249
61139132133044.8990843136087.10091568722
62132447130161.0177612752285.98223872458
63132447133621.965297378-1174.96529737808
64132447133191.929856733-744.929856732604
65136038138393.160971463-2355.16097146345
66130907134886.551485379-3979.55148537891
67124173128922.23222872-4749.23222871992
68118538122695.050224849-4157.05022484885
69122626127339.206533114-4713.20653311428
70106666113317.543189966-6651.54318996619
71116445118955.92132869-2510.92132869003
72122129120666.4146996921462.58530030806
73123172122794.112099581377.887900419388
74117488115710.2680506191777.73194938064
75117985116219.496942861765.50305713979
76116445116635.757771759-190.757771758988
77121625119990.6825887031634.31741129687
78117985116947.3437607841037.65623921571
79110810112556.172327911-1746.17232791097
80105623107937.52123637-2314.5212363703
81114394112073.662837282320.33716272016
8295347100382.274518873-5035.27451887298
83107716108269.134587186-553.134587185501
84113351112750.416384899600.583615100812
85113351113727.054340776-376.054340775649
86106666107620.422987033-954.422987032929
87100485106942.994510317-6457.99451031692
8899988102870.087881005-2882.0878810047
89105623105357.108365324265.891634676227
90100485101542.176693241-1057.17669324094
919071395115.3623997588-4402.3623997588
928397989316.3149803951-5337.31498039508
939121093196.443022733-1986.44302273302
947420777950.5811540883-3743.58115408834
958966385949.16171785233713.83828214766
969788891116.86720349666771.13279650344
9710048593306.07185993047178.92814006956
989480190351.08911586094449.91088413911
998761988537.7497337323-918.749733732257
1009275788592.74656230274164.25343769735
1019480195214.058677824-413.058677823952
1029325490827.41262268572426.58737731431
1037779184410.4704613824-6619.47046138236
1047061677619.3781983073-7003.3781983073
1057574782064.4917144144-6317.49171441441
1066029165911.7989780586-5620.79897805862
1077625175616.6508561256634.349143874366
1088193580252.03536567981682.96463432019
1098656980278.00497653856290.99502346152
1107884176177.40637706942663.59362293055
1117161071238.0874577971371.912542202859
1127574773861.20096300751885.79903699248
1137779175911.54440566191879.45559433814
1147370374236.9531397412-533.953139741221
1155824763268.7500393247-5021.75003932466
1165151357310.016233421-5797.01623342096
1175769460460.5345476127-2766.53454761267
1184069148541.843395267-7850.84339526699
1195924156894.17251111692346.82748888308
1207061661047.72793587049568.27206412957







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12165996.414444133458617.821656045173375.0072322216
12258859.888893458251008.133245810766711.6445411058
12352880.117134260544605.427534506261154.8067340148
12454877.648975145845842.960442154663912.3375081371
12555252.18685775545485.829739537165018.543975973
12651890.009651696341691.63358418162088.3857192115
12741783.850296808731920.09068148751647.6099121305
12838034.793096542527895.755765901548173.8304271834
12943006.328781702531293.893723919554718.7638394854
13032085.439131592121479.464133172442691.4141300118
13145873.475834594731396.14229803160350.8093711585
13251408.138475502936054.386938784366761.8900122216

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 65996.4144441334 & 58617.8216560451 & 73375.0072322216 \tabularnewline
122 & 58859.8888934582 & 51008.1332458107 & 66711.6445411058 \tabularnewline
123 & 52880.1171342605 & 44605.4275345062 & 61154.8067340148 \tabularnewline
124 & 54877.6489751458 & 45842.9604421546 & 63912.3375081371 \tabularnewline
125 & 55252.186857755 & 45485.8297395371 & 65018.543975973 \tabularnewline
126 & 51890.0096516963 & 41691.633584181 & 62088.3857192115 \tabularnewline
127 & 41783.8502968087 & 31920.090681487 & 51647.6099121305 \tabularnewline
128 & 38034.7930965425 & 27895.7557659015 & 48173.8304271834 \tabularnewline
129 & 43006.3287817025 & 31293.8937239195 & 54718.7638394854 \tabularnewline
130 & 32085.4391315921 & 21479.4641331724 & 42691.4141300118 \tabularnewline
131 & 45873.4758345947 & 31396.142298031 & 60350.8093711585 \tabularnewline
132 & 51408.1384755029 & 36054.3869387843 & 66761.8900122216 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280155&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]121[/C][C]65996.4144441334[/C][C]58617.8216560451[/C][C]73375.0072322216[/C][/ROW]
[ROW][C]122[/C][C]58859.8888934582[/C][C]51008.1332458107[/C][C]66711.6445411058[/C][/ROW]
[ROW][C]123[/C][C]52880.1171342605[/C][C]44605.4275345062[/C][C]61154.8067340148[/C][/ROW]
[ROW][C]124[/C][C]54877.6489751458[/C][C]45842.9604421546[/C][C]63912.3375081371[/C][/ROW]
[ROW][C]125[/C][C]55252.186857755[/C][C]45485.8297395371[/C][C]65018.543975973[/C][/ROW]
[ROW][C]126[/C][C]51890.0096516963[/C][C]41691.633584181[/C][C]62088.3857192115[/C][/ROW]
[ROW][C]127[/C][C]41783.8502968087[/C][C]31920.090681487[/C][C]51647.6099121305[/C][/ROW]
[ROW][C]128[/C][C]38034.7930965425[/C][C]27895.7557659015[/C][C]48173.8304271834[/C][/ROW]
[ROW][C]129[/C][C]43006.3287817025[/C][C]31293.8937239195[/C][C]54718.7638394854[/C][/ROW]
[ROW][C]130[/C][C]32085.4391315921[/C][C]21479.4641331724[/C][C]42691.4141300118[/C][/ROW]
[ROW][C]131[/C][C]45873.4758345947[/C][C]31396.142298031[/C][C]60350.8093711585[/C][/ROW]
[ROW][C]132[/C][C]51408.1384755029[/C][C]36054.3869387843[/C][C]66761.8900122216[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280155&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280155&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
12165996.414444133458617.821656045173375.0072322216
12258859.888893458251008.133245810766711.6445411058
12352880.117134260544605.427534506261154.8067340148
12454877.648975145845842.960442154663912.3375081371
12555252.18685775545485.829739537165018.543975973
12651890.009651696341691.63358418162088.3857192115
12741783.850296808731920.09068148751647.6099121305
12838034.793096542527895.755765901548173.8304271834
12943006.328781702531293.893723919554718.7638394854
13032085.439131592121479.464133172442691.4141300118
13145873.475834594731396.14229803160350.8093711585
13251408.138475502936054.386938784366761.8900122216



Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
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')