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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 computationMon, 17 Dec 2012 03:17:38 -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/2012/Dec/17/t1355732611qtgaexkx6vm4vpa.htm/, Retrieved Tue, 23 Apr 2024 06:58:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200702, Retrieved Tue, 23 Apr 2024 06:58:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [single additief m...] [2012-12-17 08:17:38] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
124275
58605
21828
42811
65963
128457
26867
143540
107458
258558
22475
294584
159848
289458
117950
78351
84589
44324
52285
185486
23846
13257
166999
148488
74747
55700
218584
187888
44788
18840
48787
69100
41892
90588
148574
50201
86828
102785
118844
145288
56790
287525
187880
87740
55258
58769
43366
77051
91574
15533
18425
65192
81059
73322
91261
86166
61842
25192
21059
15855
12618
101667
224275
55700
60748
41848
61781
120077
42032
46485
36861
55027
48999
68352
126987
86526
125340
69029
153287
135724
92108
119906
79798
97206




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200702&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200702&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200702&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0632137222254264
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0632137222254264 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200702&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]0.0632137222254264[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200702&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200702&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
alpha0.0632137222254264
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
258605124275-65670
321828120123.754861456-98295.7548614562
442811113910.114317706-71099.1143177055
565963109415.674654752-43452.6746547523
6128457106668.86934917521788.1306508251
726867108046.178187947-81179.1781879475
8143540102914.54016748640625.4598325138
9107458105482.6267006191975.37329938107
10258558105607.497399658152950.502600342
1122475115276.067985275-92801.0679852749
12294584109409.767051431185174.232948569
13159848121115.31957634838732.6804236519
14289458123563.756477695165894.243522305
15117950134050.549106511-16100.5491065113
1678351133032.773467615-54681.7734676155
1784589129576.13502884-44987.1350288399
1844324126732.330771409-82408.3307714091
1952285121522.993440964-69237.9934409642
20185486117146.20215614168339.7978438588
2123846121466.215153985-97620.2151539846
2213257115295.277989654-102038.277989654
23166999108845.05862845558153.9413715446
24148488112521.1857246335966.81427537
2574747114794.781931567-40047.7819315667
2655700112263.2125688-56563.2125688002
27218584108687.641361298109896.358638702
28187888115634.59924987172253.4007501289
2944788120202.005654732-75414.0056547321
3018840115434.805649367-96594.8056493672
3148787109328.688436629-60541.688436629
3269100105501.622960738-36401.6229607376
3341892103200.540878343-61308.5408783429
349058899324.9998052131-8736.99980521311
3514857498772.701526442849801.2984735572
3650201101920.826974616-51719.8269746158
378682898651.4241986953-11823.4241986953
3810278597904.02154564564880.97845435442
3911884498212.566361847420631.4336381526
4014528899516.756076961945771.2439230381
4156790102410.126776225-45620.1267762251
4228752599526.3087543041187998.691245696
43187880111410.40580145376469.5941985468
4487740116244.333487811-28504.3334878112
4555258114442.468468492-59184.4684684918
4658769110701.197918665-51932.197918665
4743366107418.370384879-64052.3703848787
4877051103369.381635489-26318.3816354888
4991574101705.69876936-10131.6987693603
5015533101065.236377682-85532.2363776822
511842595658.4253459839-77233.4253459839
526519290776.2130496447-25584.2130496447
538105989158.9397125683-8099.9397125683
547332288646.9123735353-15324.9123735353
559126187678.16761962563582.83238037436
568616687904.6517904989-1738.65179049889
576184287794.7451391676-25952.7451391676
582519286154.1755169529-60962.1755169529
592105982300.5294875666-61241.5294875666
601585578429.2244538793-62574.2244538793
611261874473.6748107803-61855.6748107803
6210166770563.547365225331103.4526347747
6322427572529.7123803316151745.287619668
645570082122.0968409388-26422.0968409388
656074880451.8577506224-19703.8577506224
664184879206.3035600052-37358.3035600052
676178176844.7461359499-15063.7461359499
6812007775892.510672037644184.4893279624
694203278685.5767070877-36653.5767070877
704648576368.5676905575-29883.5676905575
713686174479.5161434619-37618.5161434619
725502772101.5097134364-17074.5097134364
734899971022.1663992759-22023.1663992759
746835269630.0000759877-1278.0000759877
7512698769549.212934180157437.7870658199
768652673180.069251002113345.9307489979
7712534074023.71521020951316.284789791
786902977267.6085825517-8238.60858255171
7915328776746.815468090376540.1845319097
8013572481585.205432173354138.7945678267
819210885007.52015360337100.47984639669
8211990685456.367914280734449.6320857193
837979887634.0573877155-7836.05738771547
849720687138.711032665910067.2889673341

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 58605 & 124275 & -65670 \tabularnewline
3 & 21828 & 120123.754861456 & -98295.7548614562 \tabularnewline
4 & 42811 & 113910.114317706 & -71099.1143177055 \tabularnewline
5 & 65963 & 109415.674654752 & -43452.6746547523 \tabularnewline
6 & 128457 & 106668.869349175 & 21788.1306508251 \tabularnewline
7 & 26867 & 108046.178187947 & -81179.1781879475 \tabularnewline
8 & 143540 & 102914.540167486 & 40625.4598325138 \tabularnewline
9 & 107458 & 105482.626700619 & 1975.37329938107 \tabularnewline
10 & 258558 & 105607.497399658 & 152950.502600342 \tabularnewline
11 & 22475 & 115276.067985275 & -92801.0679852749 \tabularnewline
12 & 294584 & 109409.767051431 & 185174.232948569 \tabularnewline
13 & 159848 & 121115.319576348 & 38732.6804236519 \tabularnewline
14 & 289458 & 123563.756477695 & 165894.243522305 \tabularnewline
15 & 117950 & 134050.549106511 & -16100.5491065113 \tabularnewline
16 & 78351 & 133032.773467615 & -54681.7734676155 \tabularnewline
17 & 84589 & 129576.13502884 & -44987.1350288399 \tabularnewline
18 & 44324 & 126732.330771409 & -82408.3307714091 \tabularnewline
19 & 52285 & 121522.993440964 & -69237.9934409642 \tabularnewline
20 & 185486 & 117146.202156141 & 68339.7978438588 \tabularnewline
21 & 23846 & 121466.215153985 & -97620.2151539846 \tabularnewline
22 & 13257 & 115295.277989654 & -102038.277989654 \tabularnewline
23 & 166999 & 108845.058628455 & 58153.9413715446 \tabularnewline
24 & 148488 & 112521.18572463 & 35966.81427537 \tabularnewline
25 & 74747 & 114794.781931567 & -40047.7819315667 \tabularnewline
26 & 55700 & 112263.2125688 & -56563.2125688002 \tabularnewline
27 & 218584 & 108687.641361298 & 109896.358638702 \tabularnewline
28 & 187888 & 115634.599249871 & 72253.4007501289 \tabularnewline
29 & 44788 & 120202.005654732 & -75414.0056547321 \tabularnewline
30 & 18840 & 115434.805649367 & -96594.8056493672 \tabularnewline
31 & 48787 & 109328.688436629 & -60541.688436629 \tabularnewline
32 & 69100 & 105501.622960738 & -36401.6229607376 \tabularnewline
33 & 41892 & 103200.540878343 & -61308.5408783429 \tabularnewline
34 & 90588 & 99324.9998052131 & -8736.99980521311 \tabularnewline
35 & 148574 & 98772.7015264428 & 49801.2984735572 \tabularnewline
36 & 50201 & 101920.826974616 & -51719.8269746158 \tabularnewline
37 & 86828 & 98651.4241986953 & -11823.4241986953 \tabularnewline
38 & 102785 & 97904.0215456456 & 4880.97845435442 \tabularnewline
39 & 118844 & 98212.5663618474 & 20631.4336381526 \tabularnewline
40 & 145288 & 99516.7560769619 & 45771.2439230381 \tabularnewline
41 & 56790 & 102410.126776225 & -45620.1267762251 \tabularnewline
42 & 287525 & 99526.3087543041 & 187998.691245696 \tabularnewline
43 & 187880 & 111410.405801453 & 76469.5941985468 \tabularnewline
44 & 87740 & 116244.333487811 & -28504.3334878112 \tabularnewline
45 & 55258 & 114442.468468492 & -59184.4684684918 \tabularnewline
46 & 58769 & 110701.197918665 & -51932.197918665 \tabularnewline
47 & 43366 & 107418.370384879 & -64052.3703848787 \tabularnewline
48 & 77051 & 103369.381635489 & -26318.3816354888 \tabularnewline
49 & 91574 & 101705.69876936 & -10131.6987693603 \tabularnewline
50 & 15533 & 101065.236377682 & -85532.2363776822 \tabularnewline
51 & 18425 & 95658.4253459839 & -77233.4253459839 \tabularnewline
52 & 65192 & 90776.2130496447 & -25584.2130496447 \tabularnewline
53 & 81059 & 89158.9397125683 & -8099.9397125683 \tabularnewline
54 & 73322 & 88646.9123735353 & -15324.9123735353 \tabularnewline
55 & 91261 & 87678.1676196256 & 3582.83238037436 \tabularnewline
56 & 86166 & 87904.6517904989 & -1738.65179049889 \tabularnewline
57 & 61842 & 87794.7451391676 & -25952.7451391676 \tabularnewline
58 & 25192 & 86154.1755169529 & -60962.1755169529 \tabularnewline
59 & 21059 & 82300.5294875666 & -61241.5294875666 \tabularnewline
60 & 15855 & 78429.2244538793 & -62574.2244538793 \tabularnewline
61 & 12618 & 74473.6748107803 & -61855.6748107803 \tabularnewline
62 & 101667 & 70563.5473652253 & 31103.4526347747 \tabularnewline
63 & 224275 & 72529.7123803316 & 151745.287619668 \tabularnewline
64 & 55700 & 82122.0968409388 & -26422.0968409388 \tabularnewline
65 & 60748 & 80451.8577506224 & -19703.8577506224 \tabularnewline
66 & 41848 & 79206.3035600052 & -37358.3035600052 \tabularnewline
67 & 61781 & 76844.7461359499 & -15063.7461359499 \tabularnewline
68 & 120077 & 75892.5106720376 & 44184.4893279624 \tabularnewline
69 & 42032 & 78685.5767070877 & -36653.5767070877 \tabularnewline
70 & 46485 & 76368.5676905575 & -29883.5676905575 \tabularnewline
71 & 36861 & 74479.5161434619 & -37618.5161434619 \tabularnewline
72 & 55027 & 72101.5097134364 & -17074.5097134364 \tabularnewline
73 & 48999 & 71022.1663992759 & -22023.1663992759 \tabularnewline
74 & 68352 & 69630.0000759877 & -1278.0000759877 \tabularnewline
75 & 126987 & 69549.2129341801 & 57437.7870658199 \tabularnewline
76 & 86526 & 73180.0692510021 & 13345.9307489979 \tabularnewline
77 & 125340 & 74023.715210209 & 51316.284789791 \tabularnewline
78 & 69029 & 77267.6085825517 & -8238.60858255171 \tabularnewline
79 & 153287 & 76746.8154680903 & 76540.1845319097 \tabularnewline
80 & 135724 & 81585.2054321733 & 54138.7945678267 \tabularnewline
81 & 92108 & 85007.5201536033 & 7100.47984639669 \tabularnewline
82 & 119906 & 85456.3679142807 & 34449.6320857193 \tabularnewline
83 & 79798 & 87634.0573877155 & -7836.05738771547 \tabularnewline
84 & 97206 & 87138.7110326659 & 10067.2889673341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200702&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]58605[/C][C]124275[/C][C]-65670[/C][/ROW]
[ROW][C]3[/C][C]21828[/C][C]120123.754861456[/C][C]-98295.7548614562[/C][/ROW]
[ROW][C]4[/C][C]42811[/C][C]113910.114317706[/C][C]-71099.1143177055[/C][/ROW]
[ROW][C]5[/C][C]65963[/C][C]109415.674654752[/C][C]-43452.6746547523[/C][/ROW]
[ROW][C]6[/C][C]128457[/C][C]106668.869349175[/C][C]21788.1306508251[/C][/ROW]
[ROW][C]7[/C][C]26867[/C][C]108046.178187947[/C][C]-81179.1781879475[/C][/ROW]
[ROW][C]8[/C][C]143540[/C][C]102914.540167486[/C][C]40625.4598325138[/C][/ROW]
[ROW][C]9[/C][C]107458[/C][C]105482.626700619[/C][C]1975.37329938107[/C][/ROW]
[ROW][C]10[/C][C]258558[/C][C]105607.497399658[/C][C]152950.502600342[/C][/ROW]
[ROW][C]11[/C][C]22475[/C][C]115276.067985275[/C][C]-92801.0679852749[/C][/ROW]
[ROW][C]12[/C][C]294584[/C][C]109409.767051431[/C][C]185174.232948569[/C][/ROW]
[ROW][C]13[/C][C]159848[/C][C]121115.319576348[/C][C]38732.6804236519[/C][/ROW]
[ROW][C]14[/C][C]289458[/C][C]123563.756477695[/C][C]165894.243522305[/C][/ROW]
[ROW][C]15[/C][C]117950[/C][C]134050.549106511[/C][C]-16100.5491065113[/C][/ROW]
[ROW][C]16[/C][C]78351[/C][C]133032.773467615[/C][C]-54681.7734676155[/C][/ROW]
[ROW][C]17[/C][C]84589[/C][C]129576.13502884[/C][C]-44987.1350288399[/C][/ROW]
[ROW][C]18[/C][C]44324[/C][C]126732.330771409[/C][C]-82408.3307714091[/C][/ROW]
[ROW][C]19[/C][C]52285[/C][C]121522.993440964[/C][C]-69237.9934409642[/C][/ROW]
[ROW][C]20[/C][C]185486[/C][C]117146.202156141[/C][C]68339.7978438588[/C][/ROW]
[ROW][C]21[/C][C]23846[/C][C]121466.215153985[/C][C]-97620.2151539846[/C][/ROW]
[ROW][C]22[/C][C]13257[/C][C]115295.277989654[/C][C]-102038.277989654[/C][/ROW]
[ROW][C]23[/C][C]166999[/C][C]108845.058628455[/C][C]58153.9413715446[/C][/ROW]
[ROW][C]24[/C][C]148488[/C][C]112521.18572463[/C][C]35966.81427537[/C][/ROW]
[ROW][C]25[/C][C]74747[/C][C]114794.781931567[/C][C]-40047.7819315667[/C][/ROW]
[ROW][C]26[/C][C]55700[/C][C]112263.2125688[/C][C]-56563.2125688002[/C][/ROW]
[ROW][C]27[/C][C]218584[/C][C]108687.641361298[/C][C]109896.358638702[/C][/ROW]
[ROW][C]28[/C][C]187888[/C][C]115634.599249871[/C][C]72253.4007501289[/C][/ROW]
[ROW][C]29[/C][C]44788[/C][C]120202.005654732[/C][C]-75414.0056547321[/C][/ROW]
[ROW][C]30[/C][C]18840[/C][C]115434.805649367[/C][C]-96594.8056493672[/C][/ROW]
[ROW][C]31[/C][C]48787[/C][C]109328.688436629[/C][C]-60541.688436629[/C][/ROW]
[ROW][C]32[/C][C]69100[/C][C]105501.622960738[/C][C]-36401.6229607376[/C][/ROW]
[ROW][C]33[/C][C]41892[/C][C]103200.540878343[/C][C]-61308.5408783429[/C][/ROW]
[ROW][C]34[/C][C]90588[/C][C]99324.9998052131[/C][C]-8736.99980521311[/C][/ROW]
[ROW][C]35[/C][C]148574[/C][C]98772.7015264428[/C][C]49801.2984735572[/C][/ROW]
[ROW][C]36[/C][C]50201[/C][C]101920.826974616[/C][C]-51719.8269746158[/C][/ROW]
[ROW][C]37[/C][C]86828[/C][C]98651.4241986953[/C][C]-11823.4241986953[/C][/ROW]
[ROW][C]38[/C][C]102785[/C][C]97904.0215456456[/C][C]4880.97845435442[/C][/ROW]
[ROW][C]39[/C][C]118844[/C][C]98212.5663618474[/C][C]20631.4336381526[/C][/ROW]
[ROW][C]40[/C][C]145288[/C][C]99516.7560769619[/C][C]45771.2439230381[/C][/ROW]
[ROW][C]41[/C][C]56790[/C][C]102410.126776225[/C][C]-45620.1267762251[/C][/ROW]
[ROW][C]42[/C][C]287525[/C][C]99526.3087543041[/C][C]187998.691245696[/C][/ROW]
[ROW][C]43[/C][C]187880[/C][C]111410.405801453[/C][C]76469.5941985468[/C][/ROW]
[ROW][C]44[/C][C]87740[/C][C]116244.333487811[/C][C]-28504.3334878112[/C][/ROW]
[ROW][C]45[/C][C]55258[/C][C]114442.468468492[/C][C]-59184.4684684918[/C][/ROW]
[ROW][C]46[/C][C]58769[/C][C]110701.197918665[/C][C]-51932.197918665[/C][/ROW]
[ROW][C]47[/C][C]43366[/C][C]107418.370384879[/C][C]-64052.3703848787[/C][/ROW]
[ROW][C]48[/C][C]77051[/C][C]103369.381635489[/C][C]-26318.3816354888[/C][/ROW]
[ROW][C]49[/C][C]91574[/C][C]101705.69876936[/C][C]-10131.6987693603[/C][/ROW]
[ROW][C]50[/C][C]15533[/C][C]101065.236377682[/C][C]-85532.2363776822[/C][/ROW]
[ROW][C]51[/C][C]18425[/C][C]95658.4253459839[/C][C]-77233.4253459839[/C][/ROW]
[ROW][C]52[/C][C]65192[/C][C]90776.2130496447[/C][C]-25584.2130496447[/C][/ROW]
[ROW][C]53[/C][C]81059[/C][C]89158.9397125683[/C][C]-8099.9397125683[/C][/ROW]
[ROW][C]54[/C][C]73322[/C][C]88646.9123735353[/C][C]-15324.9123735353[/C][/ROW]
[ROW][C]55[/C][C]91261[/C][C]87678.1676196256[/C][C]3582.83238037436[/C][/ROW]
[ROW][C]56[/C][C]86166[/C][C]87904.6517904989[/C][C]-1738.65179049889[/C][/ROW]
[ROW][C]57[/C][C]61842[/C][C]87794.7451391676[/C][C]-25952.7451391676[/C][/ROW]
[ROW][C]58[/C][C]25192[/C][C]86154.1755169529[/C][C]-60962.1755169529[/C][/ROW]
[ROW][C]59[/C][C]21059[/C][C]82300.5294875666[/C][C]-61241.5294875666[/C][/ROW]
[ROW][C]60[/C][C]15855[/C][C]78429.2244538793[/C][C]-62574.2244538793[/C][/ROW]
[ROW][C]61[/C][C]12618[/C][C]74473.6748107803[/C][C]-61855.6748107803[/C][/ROW]
[ROW][C]62[/C][C]101667[/C][C]70563.5473652253[/C][C]31103.4526347747[/C][/ROW]
[ROW][C]63[/C][C]224275[/C][C]72529.7123803316[/C][C]151745.287619668[/C][/ROW]
[ROW][C]64[/C][C]55700[/C][C]82122.0968409388[/C][C]-26422.0968409388[/C][/ROW]
[ROW][C]65[/C][C]60748[/C][C]80451.8577506224[/C][C]-19703.8577506224[/C][/ROW]
[ROW][C]66[/C][C]41848[/C][C]79206.3035600052[/C][C]-37358.3035600052[/C][/ROW]
[ROW][C]67[/C][C]61781[/C][C]76844.7461359499[/C][C]-15063.7461359499[/C][/ROW]
[ROW][C]68[/C][C]120077[/C][C]75892.5106720376[/C][C]44184.4893279624[/C][/ROW]
[ROW][C]69[/C][C]42032[/C][C]78685.5767070877[/C][C]-36653.5767070877[/C][/ROW]
[ROW][C]70[/C][C]46485[/C][C]76368.5676905575[/C][C]-29883.5676905575[/C][/ROW]
[ROW][C]71[/C][C]36861[/C][C]74479.5161434619[/C][C]-37618.5161434619[/C][/ROW]
[ROW][C]72[/C][C]55027[/C][C]72101.5097134364[/C][C]-17074.5097134364[/C][/ROW]
[ROW][C]73[/C][C]48999[/C][C]71022.1663992759[/C][C]-22023.1663992759[/C][/ROW]
[ROW][C]74[/C][C]68352[/C][C]69630.0000759877[/C][C]-1278.0000759877[/C][/ROW]
[ROW][C]75[/C][C]126987[/C][C]69549.2129341801[/C][C]57437.7870658199[/C][/ROW]
[ROW][C]76[/C][C]86526[/C][C]73180.0692510021[/C][C]13345.9307489979[/C][/ROW]
[ROW][C]77[/C][C]125340[/C][C]74023.715210209[/C][C]51316.284789791[/C][/ROW]
[ROW][C]78[/C][C]69029[/C][C]77267.6085825517[/C][C]-8238.60858255171[/C][/ROW]
[ROW][C]79[/C][C]153287[/C][C]76746.8154680903[/C][C]76540.1845319097[/C][/ROW]
[ROW][C]80[/C][C]135724[/C][C]81585.2054321733[/C][C]54138.7945678267[/C][/ROW]
[ROW][C]81[/C][C]92108[/C][C]85007.5201536033[/C][C]7100.47984639669[/C][/ROW]
[ROW][C]82[/C][C]119906[/C][C]85456.3679142807[/C][C]34449.6320857193[/C][/ROW]
[ROW][C]83[/C][C]79798[/C][C]87634.0573877155[/C][C]-7836.05738771547[/C][/ROW]
[ROW][C]84[/C][C]97206[/C][C]87138.7110326659[/C][C]10067.2889673341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200702&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200702&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
258605124275-65670
321828120123.754861456-98295.7548614562
442811113910.114317706-71099.1143177055
565963109415.674654752-43452.6746547523
6128457106668.86934917521788.1306508251
726867108046.178187947-81179.1781879475
8143540102914.54016748640625.4598325138
9107458105482.6267006191975.37329938107
10258558105607.497399658152950.502600342
1122475115276.067985275-92801.0679852749
12294584109409.767051431185174.232948569
13159848121115.31957634838732.6804236519
14289458123563.756477695165894.243522305
15117950134050.549106511-16100.5491065113
1678351133032.773467615-54681.7734676155
1784589129576.13502884-44987.1350288399
1844324126732.330771409-82408.3307714091
1952285121522.993440964-69237.9934409642
20185486117146.20215614168339.7978438588
2123846121466.215153985-97620.2151539846
2213257115295.277989654-102038.277989654
23166999108845.05862845558153.9413715446
24148488112521.1857246335966.81427537
2574747114794.781931567-40047.7819315667
2655700112263.2125688-56563.2125688002
27218584108687.641361298109896.358638702
28187888115634.59924987172253.4007501289
2944788120202.005654732-75414.0056547321
3018840115434.805649367-96594.8056493672
3148787109328.688436629-60541.688436629
3269100105501.622960738-36401.6229607376
3341892103200.540878343-61308.5408783429
349058899324.9998052131-8736.99980521311
3514857498772.701526442849801.2984735572
3650201101920.826974616-51719.8269746158
378682898651.4241986953-11823.4241986953
3810278597904.02154564564880.97845435442
3911884498212.566361847420631.4336381526
4014528899516.756076961945771.2439230381
4156790102410.126776225-45620.1267762251
4228752599526.3087543041187998.691245696
43187880111410.40580145376469.5941985468
4487740116244.333487811-28504.3334878112
4555258114442.468468492-59184.4684684918
4658769110701.197918665-51932.197918665
4743366107418.370384879-64052.3703848787
4877051103369.381635489-26318.3816354888
4991574101705.69876936-10131.6987693603
5015533101065.236377682-85532.2363776822
511842595658.4253459839-77233.4253459839
526519290776.2130496447-25584.2130496447
538105989158.9397125683-8099.9397125683
547332288646.9123735353-15324.9123735353
559126187678.16761962563582.83238037436
568616687904.6517904989-1738.65179049889
576184287794.7451391676-25952.7451391676
582519286154.1755169529-60962.1755169529
592105982300.5294875666-61241.5294875666
601585578429.2244538793-62574.2244538793
611261874473.6748107803-61855.6748107803
6210166770563.547365225331103.4526347747
6322427572529.7123803316151745.287619668
645570082122.0968409388-26422.0968409388
656074880451.8577506224-19703.8577506224
664184879206.3035600052-37358.3035600052
676178176844.7461359499-15063.7461359499
6812007775892.510672037644184.4893279624
694203278685.5767070877-36653.5767070877
704648576368.5676905575-29883.5676905575
713686174479.5161434619-37618.5161434619
725502772101.5097134364-17074.5097134364
734899971022.1663992759-22023.1663992759
746835269630.0000759877-1278.0000759877
7512698769549.212934180157437.7870658199
768652673180.069251002113345.9307489979
7712534074023.71521020951316.284789791
786902977267.6085825517-8238.60858255171
7915328776746.815468090376540.1845319097
8013572481585.205432173354138.7945678267
819210885007.52015360337100.47984639669
8211990685456.367914280734449.6320857193
837979887634.0573877155-7836.05738771547
849720687138.711032665910067.2889673341







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8587775.1018410101-41300.2878764155216850.491558436
8687775.1018410101-41557.9217528128217108.125434833
8787775.1018410101-41815.0434368442217365.247118864
8887775.1018410101-42071.6559712296217621.85965325
8987775.1018410101-42327.7623686817217877.966050702
9087775.1018410101-42583.3656123186218133.569294339
9187775.1018410101-42838.4686560696218388.67233809
9287775.1018410101-43093.0744250732218643.278107093
9387775.1018410101-43347.1858160686218897.389498089
9487775.1018410101-43600.8056977801219151.0093798
9587775.1018410101-43853.9369112949219404.140593315
9687775.1018410101-44106.5822704345219656.785952455

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 87775.1018410101 & -41300.2878764155 & 216850.491558436 \tabularnewline
86 & 87775.1018410101 & -41557.9217528128 & 217108.125434833 \tabularnewline
87 & 87775.1018410101 & -41815.0434368442 & 217365.247118864 \tabularnewline
88 & 87775.1018410101 & -42071.6559712296 & 217621.85965325 \tabularnewline
89 & 87775.1018410101 & -42327.7623686817 & 217877.966050702 \tabularnewline
90 & 87775.1018410101 & -42583.3656123186 & 218133.569294339 \tabularnewline
91 & 87775.1018410101 & -42838.4686560696 & 218388.67233809 \tabularnewline
92 & 87775.1018410101 & -43093.0744250732 & 218643.278107093 \tabularnewline
93 & 87775.1018410101 & -43347.1858160686 & 218897.389498089 \tabularnewline
94 & 87775.1018410101 & -43600.8056977801 & 219151.0093798 \tabularnewline
95 & 87775.1018410101 & -43853.9369112949 & 219404.140593315 \tabularnewline
96 & 87775.1018410101 & -44106.5822704345 & 219656.785952455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200702&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]87775.1018410101[/C][C]-41300.2878764155[/C][C]216850.491558436[/C][/ROW]
[ROW][C]86[/C][C]87775.1018410101[/C][C]-41557.9217528128[/C][C]217108.125434833[/C][/ROW]
[ROW][C]87[/C][C]87775.1018410101[/C][C]-41815.0434368442[/C][C]217365.247118864[/C][/ROW]
[ROW][C]88[/C][C]87775.1018410101[/C][C]-42071.6559712296[/C][C]217621.85965325[/C][/ROW]
[ROW][C]89[/C][C]87775.1018410101[/C][C]-42327.7623686817[/C][C]217877.966050702[/C][/ROW]
[ROW][C]90[/C][C]87775.1018410101[/C][C]-42583.3656123186[/C][C]218133.569294339[/C][/ROW]
[ROW][C]91[/C][C]87775.1018410101[/C][C]-42838.4686560696[/C][C]218388.67233809[/C][/ROW]
[ROW][C]92[/C][C]87775.1018410101[/C][C]-43093.0744250732[/C][C]218643.278107093[/C][/ROW]
[ROW][C]93[/C][C]87775.1018410101[/C][C]-43347.1858160686[/C][C]218897.389498089[/C][/ROW]
[ROW][C]94[/C][C]87775.1018410101[/C][C]-43600.8056977801[/C][C]219151.0093798[/C][/ROW]
[ROW][C]95[/C][C]87775.1018410101[/C][C]-43853.9369112949[/C][C]219404.140593315[/C][/ROW]
[ROW][C]96[/C][C]87775.1018410101[/C][C]-44106.5822704345[/C][C]219656.785952455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200702&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200702&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
8587775.1018410101-41300.2878764155216850.491558436
8687775.1018410101-41557.9217528128217108.125434833
8787775.1018410101-41815.0434368442217365.247118864
8887775.1018410101-42071.6559712296217621.85965325
8987775.1018410101-42327.7623686817217877.966050702
9087775.1018410101-42583.3656123186218133.569294339
9187775.1018410101-42838.4686560696218388.67233809
9287775.1018410101-43093.0744250732218643.278107093
9387775.1018410101-43347.1858160686218897.389498089
9487775.1018410101-43600.8056977801219151.0093798
9587775.1018410101-43853.9369112949219404.140593315
9687775.1018410101-44106.5822704345219656.785952455



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')