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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 computationWed, 28 Dec 2011 12:11:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/28/t1325092333w5f6lvduv95ya5v.htm/, Retrieved Fri, 03 May 2024 12:32:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160875, Retrieved Fri, 03 May 2024 12:32:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [KDGP2W102] [2011-12-28 17:11:20] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
2144
2207
1864
2061
2025
2068
2054
2095
2151
2065
2147
1994
2273
2119
1969
1821
1942
1802
1737
1650
1720
1491
1570
1649
1409
1480
1495
1490
1415
1448
1354
1330
1183
1264
1197
1037
1084
1103
1005
1013
973
1046
923
844
820
777
652
560
490
582
505
478
540
585
594
586
585
534
588
581
615
603
626
687
580
539
550
606
597
539
551
526




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160875&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160875&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160875&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.557172259021654
beta0.221851978873936
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.557172259021654 \tabularnewline
beta & 0.221851978873936 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160875&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]0.557172259021654[/C][/ROW]
[ROW][C]beta[/C][C]0.221851978873936[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160875&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160875&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
alpha0.557172259021654
beta0.221851978873936
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
318642270-406
420612056.602496932744.39750306726364
520252072.41067208128-47.4106720812752
620682053.4923470585614.5076529414432
720542070.86648268135-16.866482681347
820952068.6749582691126.3250417308896
921512093.8025853914357.1974146085699
1020652143.20160141492-78.2016014149212
1121472107.4935599845939.5064400154142
1219942142.2525557972-148.252555797204
1322732054.07198369854218.928016301458
1421192197.5358817807-78.5358817806987
1519692165.55334564578-196.553345645784
1618212043.51883906355-222.51883906355
1719421879.5115777319862.4884222680212
1818021882.02663542818-80.0266354281785
1917371795.24418262507-58.244182625072
2016501713.39875834183-63.3987583418302
2117201620.84464163799.1553583630023
2214911631.11774021663-140.117740216635
2315701490.7545845433979.2454154566119
2416491482.41000130121166.589998698792
2514091543.32354794724-134.323547947241
2614801419.9727114076760.0272885923268
2714951412.3287287364382.6712712635654
2814901427.5203217241862.4796782758244
2914151439.18481778493-24.1848177849265
3014481399.5727810772748.4272189227281
3113541406.40423420162-52.4042342016151
3213301350.5775235639-20.5775235639007
3311831309.94019027079-126.940190270792
3412641194.3494821936369.6505178063737
3511971196.903147402160.0968525978425987
3610371160.71541177039-123.715411770388
3710841040.2504837296343.749516270374
3811031018.5002355189284.4997644810769
3910051029.89989146311-24.8998914631097
401013977.26722415578535.7327758442148
41973962.83431720318110.1656827968187
421046935.412712955235110.587287044765
43923977.612909722325-54.6129097223252
44844921.017450552316-77.0174505523156
45820842.418693542694-22.4186935426936
46777791.469679802895-14.4696798028947
47652743.161042238585-91.1610422385853
48560640.853709715123-80.8537097151228
49490534.295028619208-44.2950286192075
50582442.630532234657139.369467765343
51505470.52622581263534.4737741873654
52478444.23824407570333.7617559242967
53540421.726828339771118.273171660229
54585460.922548360194124.077451639806
55594518.68943720954375.3105627904567
56586558.59388964561527.406110354385
57585575.1949730498859.80502695011455
58534583.201218161437-49.2012181614372
59588552.24906921385735.7509307861434
60581573.0490652728987.95093472710221
61615579.34248792581935.6575120741807
62603605.48086367239-2.48086367239023
63626610.06293546525415.9370645347457
64687626.87694277731560.1230572226852
65580675.741956621462-95.7419566214619
66539625.928667531029-86.9286675310293
67550570.280666185809-20.2806661858086
68606549.26019386245156.7398061375493
69597578.16698638092318.8330136190774
70539588.281110128282-49.2811101282823
71551554.352307074596-3.35230707459573
72526545.59938107194-19.5993810719403

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1864 & 2270 & -406 \tabularnewline
4 & 2061 & 2056.60249693274 & 4.39750306726364 \tabularnewline
5 & 2025 & 2072.41067208128 & -47.4106720812752 \tabularnewline
6 & 2068 & 2053.49234705856 & 14.5076529414432 \tabularnewline
7 & 2054 & 2070.86648268135 & -16.866482681347 \tabularnewline
8 & 2095 & 2068.67495826911 & 26.3250417308896 \tabularnewline
9 & 2151 & 2093.80258539143 & 57.1974146085699 \tabularnewline
10 & 2065 & 2143.20160141492 & -78.2016014149212 \tabularnewline
11 & 2147 & 2107.49355998459 & 39.5064400154142 \tabularnewline
12 & 1994 & 2142.2525557972 & -148.252555797204 \tabularnewline
13 & 2273 & 2054.07198369854 & 218.928016301458 \tabularnewline
14 & 2119 & 2197.5358817807 & -78.5358817806987 \tabularnewline
15 & 1969 & 2165.55334564578 & -196.553345645784 \tabularnewline
16 & 1821 & 2043.51883906355 & -222.51883906355 \tabularnewline
17 & 1942 & 1879.51157773198 & 62.4884222680212 \tabularnewline
18 & 1802 & 1882.02663542818 & -80.0266354281785 \tabularnewline
19 & 1737 & 1795.24418262507 & -58.244182625072 \tabularnewline
20 & 1650 & 1713.39875834183 & -63.3987583418302 \tabularnewline
21 & 1720 & 1620.844641637 & 99.1553583630023 \tabularnewline
22 & 1491 & 1631.11774021663 & -140.117740216635 \tabularnewline
23 & 1570 & 1490.75458454339 & 79.2454154566119 \tabularnewline
24 & 1649 & 1482.41000130121 & 166.589998698792 \tabularnewline
25 & 1409 & 1543.32354794724 & -134.323547947241 \tabularnewline
26 & 1480 & 1419.97271140767 & 60.0272885923268 \tabularnewline
27 & 1495 & 1412.32872873643 & 82.6712712635654 \tabularnewline
28 & 1490 & 1427.52032172418 & 62.4796782758244 \tabularnewline
29 & 1415 & 1439.18481778493 & -24.1848177849265 \tabularnewline
30 & 1448 & 1399.57278107727 & 48.4272189227281 \tabularnewline
31 & 1354 & 1406.40423420162 & -52.4042342016151 \tabularnewline
32 & 1330 & 1350.5775235639 & -20.5775235639007 \tabularnewline
33 & 1183 & 1309.94019027079 & -126.940190270792 \tabularnewline
34 & 1264 & 1194.34948219363 & 69.6505178063737 \tabularnewline
35 & 1197 & 1196.90314740216 & 0.0968525978425987 \tabularnewline
36 & 1037 & 1160.71541177039 & -123.715411770388 \tabularnewline
37 & 1084 & 1040.25048372963 & 43.749516270374 \tabularnewline
38 & 1103 & 1018.50023551892 & 84.4997644810769 \tabularnewline
39 & 1005 & 1029.89989146311 & -24.8998914631097 \tabularnewline
40 & 1013 & 977.267224155785 & 35.7327758442148 \tabularnewline
41 & 973 & 962.834317203181 & 10.1656827968187 \tabularnewline
42 & 1046 & 935.412712955235 & 110.587287044765 \tabularnewline
43 & 923 & 977.612909722325 & -54.6129097223252 \tabularnewline
44 & 844 & 921.017450552316 & -77.0174505523156 \tabularnewline
45 & 820 & 842.418693542694 & -22.4186935426936 \tabularnewline
46 & 777 & 791.469679802895 & -14.4696798028947 \tabularnewline
47 & 652 & 743.161042238585 & -91.1610422385853 \tabularnewline
48 & 560 & 640.853709715123 & -80.8537097151228 \tabularnewline
49 & 490 & 534.295028619208 & -44.2950286192075 \tabularnewline
50 & 582 & 442.630532234657 & 139.369467765343 \tabularnewline
51 & 505 & 470.526225812635 & 34.4737741873654 \tabularnewline
52 & 478 & 444.238244075703 & 33.7617559242967 \tabularnewline
53 & 540 & 421.726828339771 & 118.273171660229 \tabularnewline
54 & 585 & 460.922548360194 & 124.077451639806 \tabularnewline
55 & 594 & 518.689437209543 & 75.3105627904567 \tabularnewline
56 & 586 & 558.593889645615 & 27.406110354385 \tabularnewline
57 & 585 & 575.194973049885 & 9.80502695011455 \tabularnewline
58 & 534 & 583.201218161437 & -49.2012181614372 \tabularnewline
59 & 588 & 552.249069213857 & 35.7509307861434 \tabularnewline
60 & 581 & 573.049065272898 & 7.95093472710221 \tabularnewline
61 & 615 & 579.342487925819 & 35.6575120741807 \tabularnewline
62 & 603 & 605.48086367239 & -2.48086367239023 \tabularnewline
63 & 626 & 610.062935465254 & 15.9370645347457 \tabularnewline
64 & 687 & 626.876942777315 & 60.1230572226852 \tabularnewline
65 & 580 & 675.741956621462 & -95.7419566214619 \tabularnewline
66 & 539 & 625.928667531029 & -86.9286675310293 \tabularnewline
67 & 550 & 570.280666185809 & -20.2806661858086 \tabularnewline
68 & 606 & 549.260193862451 & 56.7398061375493 \tabularnewline
69 & 597 & 578.166986380923 & 18.8330136190774 \tabularnewline
70 & 539 & 588.281110128282 & -49.2811101282823 \tabularnewline
71 & 551 & 554.352307074596 & -3.35230707459573 \tabularnewline
72 & 526 & 545.59938107194 & -19.5993810719403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160875&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]3[/C][C]1864[/C][C]2270[/C][C]-406[/C][/ROW]
[ROW][C]4[/C][C]2061[/C][C]2056.60249693274[/C][C]4.39750306726364[/C][/ROW]
[ROW][C]5[/C][C]2025[/C][C]2072.41067208128[/C][C]-47.4106720812752[/C][/ROW]
[ROW][C]6[/C][C]2068[/C][C]2053.49234705856[/C][C]14.5076529414432[/C][/ROW]
[ROW][C]7[/C][C]2054[/C][C]2070.86648268135[/C][C]-16.866482681347[/C][/ROW]
[ROW][C]8[/C][C]2095[/C][C]2068.67495826911[/C][C]26.3250417308896[/C][/ROW]
[ROW][C]9[/C][C]2151[/C][C]2093.80258539143[/C][C]57.1974146085699[/C][/ROW]
[ROW][C]10[/C][C]2065[/C][C]2143.20160141492[/C][C]-78.2016014149212[/C][/ROW]
[ROW][C]11[/C][C]2147[/C][C]2107.49355998459[/C][C]39.5064400154142[/C][/ROW]
[ROW][C]12[/C][C]1994[/C][C]2142.2525557972[/C][C]-148.252555797204[/C][/ROW]
[ROW][C]13[/C][C]2273[/C][C]2054.07198369854[/C][C]218.928016301458[/C][/ROW]
[ROW][C]14[/C][C]2119[/C][C]2197.5358817807[/C][C]-78.5358817806987[/C][/ROW]
[ROW][C]15[/C][C]1969[/C][C]2165.55334564578[/C][C]-196.553345645784[/C][/ROW]
[ROW][C]16[/C][C]1821[/C][C]2043.51883906355[/C][C]-222.51883906355[/C][/ROW]
[ROW][C]17[/C][C]1942[/C][C]1879.51157773198[/C][C]62.4884222680212[/C][/ROW]
[ROW][C]18[/C][C]1802[/C][C]1882.02663542818[/C][C]-80.0266354281785[/C][/ROW]
[ROW][C]19[/C][C]1737[/C][C]1795.24418262507[/C][C]-58.244182625072[/C][/ROW]
[ROW][C]20[/C][C]1650[/C][C]1713.39875834183[/C][C]-63.3987583418302[/C][/ROW]
[ROW][C]21[/C][C]1720[/C][C]1620.844641637[/C][C]99.1553583630023[/C][/ROW]
[ROW][C]22[/C][C]1491[/C][C]1631.11774021663[/C][C]-140.117740216635[/C][/ROW]
[ROW][C]23[/C][C]1570[/C][C]1490.75458454339[/C][C]79.2454154566119[/C][/ROW]
[ROW][C]24[/C][C]1649[/C][C]1482.41000130121[/C][C]166.589998698792[/C][/ROW]
[ROW][C]25[/C][C]1409[/C][C]1543.32354794724[/C][C]-134.323547947241[/C][/ROW]
[ROW][C]26[/C][C]1480[/C][C]1419.97271140767[/C][C]60.0272885923268[/C][/ROW]
[ROW][C]27[/C][C]1495[/C][C]1412.32872873643[/C][C]82.6712712635654[/C][/ROW]
[ROW][C]28[/C][C]1490[/C][C]1427.52032172418[/C][C]62.4796782758244[/C][/ROW]
[ROW][C]29[/C][C]1415[/C][C]1439.18481778493[/C][C]-24.1848177849265[/C][/ROW]
[ROW][C]30[/C][C]1448[/C][C]1399.57278107727[/C][C]48.4272189227281[/C][/ROW]
[ROW][C]31[/C][C]1354[/C][C]1406.40423420162[/C][C]-52.4042342016151[/C][/ROW]
[ROW][C]32[/C][C]1330[/C][C]1350.5775235639[/C][C]-20.5775235639007[/C][/ROW]
[ROW][C]33[/C][C]1183[/C][C]1309.94019027079[/C][C]-126.940190270792[/C][/ROW]
[ROW][C]34[/C][C]1264[/C][C]1194.34948219363[/C][C]69.6505178063737[/C][/ROW]
[ROW][C]35[/C][C]1197[/C][C]1196.90314740216[/C][C]0.0968525978425987[/C][/ROW]
[ROW][C]36[/C][C]1037[/C][C]1160.71541177039[/C][C]-123.715411770388[/C][/ROW]
[ROW][C]37[/C][C]1084[/C][C]1040.25048372963[/C][C]43.749516270374[/C][/ROW]
[ROW][C]38[/C][C]1103[/C][C]1018.50023551892[/C][C]84.4997644810769[/C][/ROW]
[ROW][C]39[/C][C]1005[/C][C]1029.89989146311[/C][C]-24.8998914631097[/C][/ROW]
[ROW][C]40[/C][C]1013[/C][C]977.267224155785[/C][C]35.7327758442148[/C][/ROW]
[ROW][C]41[/C][C]973[/C][C]962.834317203181[/C][C]10.1656827968187[/C][/ROW]
[ROW][C]42[/C][C]1046[/C][C]935.412712955235[/C][C]110.587287044765[/C][/ROW]
[ROW][C]43[/C][C]923[/C][C]977.612909722325[/C][C]-54.6129097223252[/C][/ROW]
[ROW][C]44[/C][C]844[/C][C]921.017450552316[/C][C]-77.0174505523156[/C][/ROW]
[ROW][C]45[/C][C]820[/C][C]842.418693542694[/C][C]-22.4186935426936[/C][/ROW]
[ROW][C]46[/C][C]777[/C][C]791.469679802895[/C][C]-14.4696798028947[/C][/ROW]
[ROW][C]47[/C][C]652[/C][C]743.161042238585[/C][C]-91.1610422385853[/C][/ROW]
[ROW][C]48[/C][C]560[/C][C]640.853709715123[/C][C]-80.8537097151228[/C][/ROW]
[ROW][C]49[/C][C]490[/C][C]534.295028619208[/C][C]-44.2950286192075[/C][/ROW]
[ROW][C]50[/C][C]582[/C][C]442.630532234657[/C][C]139.369467765343[/C][/ROW]
[ROW][C]51[/C][C]505[/C][C]470.526225812635[/C][C]34.4737741873654[/C][/ROW]
[ROW][C]52[/C][C]478[/C][C]444.238244075703[/C][C]33.7617559242967[/C][/ROW]
[ROW][C]53[/C][C]540[/C][C]421.726828339771[/C][C]118.273171660229[/C][/ROW]
[ROW][C]54[/C][C]585[/C][C]460.922548360194[/C][C]124.077451639806[/C][/ROW]
[ROW][C]55[/C][C]594[/C][C]518.689437209543[/C][C]75.3105627904567[/C][/ROW]
[ROW][C]56[/C][C]586[/C][C]558.593889645615[/C][C]27.406110354385[/C][/ROW]
[ROW][C]57[/C][C]585[/C][C]575.194973049885[/C][C]9.80502695011455[/C][/ROW]
[ROW][C]58[/C][C]534[/C][C]583.201218161437[/C][C]-49.2012181614372[/C][/ROW]
[ROW][C]59[/C][C]588[/C][C]552.249069213857[/C][C]35.7509307861434[/C][/ROW]
[ROW][C]60[/C][C]581[/C][C]573.049065272898[/C][C]7.95093472710221[/C][/ROW]
[ROW][C]61[/C][C]615[/C][C]579.342487925819[/C][C]35.6575120741807[/C][/ROW]
[ROW][C]62[/C][C]603[/C][C]605.48086367239[/C][C]-2.48086367239023[/C][/ROW]
[ROW][C]63[/C][C]626[/C][C]610.062935465254[/C][C]15.9370645347457[/C][/ROW]
[ROW][C]64[/C][C]687[/C][C]626.876942777315[/C][C]60.1230572226852[/C][/ROW]
[ROW][C]65[/C][C]580[/C][C]675.741956621462[/C][C]-95.7419566214619[/C][/ROW]
[ROW][C]66[/C][C]539[/C][C]625.928667531029[/C][C]-86.9286675310293[/C][/ROW]
[ROW][C]67[/C][C]550[/C][C]570.280666185809[/C][C]-20.2806661858086[/C][/ROW]
[ROW][C]68[/C][C]606[/C][C]549.260193862451[/C][C]56.7398061375493[/C][/ROW]
[ROW][C]69[/C][C]597[/C][C]578.166986380923[/C][C]18.8330136190774[/C][/ROW]
[ROW][C]70[/C][C]539[/C][C]588.281110128282[/C][C]-49.2811101282823[/C][/ROW]
[ROW][C]71[/C][C]551[/C][C]554.352307074596[/C][C]-3.35230707459573[/C][/ROW]
[ROW][C]72[/C][C]526[/C][C]545.59938107194[/C][C]-19.5993810719403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160875&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160875&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
318642270-406
420612056.602496932744.39750306726364
520252072.41067208128-47.4106720812752
620682053.4923470585614.5076529414432
720542070.86648268135-16.866482681347
820952068.6749582691126.3250417308896
921512093.8025853914357.1974146085699
1020652143.20160141492-78.2016014149212
1121472107.4935599845939.5064400154142
1219942142.2525557972-148.252555797204
1322732054.07198369854218.928016301458
1421192197.5358817807-78.5358817806987
1519692165.55334564578-196.553345645784
1618212043.51883906355-222.51883906355
1719421879.5115777319862.4884222680212
1818021882.02663542818-80.0266354281785
1917371795.24418262507-58.244182625072
2016501713.39875834183-63.3987583418302
2117201620.84464163799.1553583630023
2214911631.11774021663-140.117740216635
2315701490.7545845433979.2454154566119
2416491482.41000130121166.589998698792
2514091543.32354794724-134.323547947241
2614801419.9727114076760.0272885923268
2714951412.3287287364382.6712712635654
2814901427.5203217241862.4796782758244
2914151439.18481778493-24.1848177849265
3014481399.5727810772748.4272189227281
3113541406.40423420162-52.4042342016151
3213301350.5775235639-20.5775235639007
3311831309.94019027079-126.940190270792
3412641194.3494821936369.6505178063737
3511971196.903147402160.0968525978425987
3610371160.71541177039-123.715411770388
3710841040.2504837296343.749516270374
3811031018.5002355189284.4997644810769
3910051029.89989146311-24.8998914631097
401013977.26722415578535.7327758442148
41973962.83431720318110.1656827968187
421046935.412712955235110.587287044765
43923977.612909722325-54.6129097223252
44844921.017450552316-77.0174505523156
45820842.418693542694-22.4186935426936
46777791.469679802895-14.4696798028947
47652743.161042238585-91.1610422385853
48560640.853709715123-80.8537097151228
49490534.295028619208-44.2950286192075
50582442.630532234657139.369467765343
51505470.52622581263534.4737741873654
52478444.23824407570333.7617559242967
53540421.726828339771118.273171660229
54585460.922548360194124.077451639806
55594518.68943720954375.3105627904567
56586558.59388964561527.406110354385
57585575.1949730498859.80502695011455
58534583.201218161437-49.2012181614372
59588552.24906921385735.7509307861434
60581573.0490652728987.95093472710221
61615579.34248792581935.6575120741807
62603605.48086367239-2.48086367239023
63626610.06293546525415.9370645347457
64687626.87694277731560.1230572226852
65580675.741956621462-95.7419566214619
66539625.928667531029-86.9286675310293
67550570.280666185809-20.2806661858086
68606549.26019386245156.7398061375493
69597578.16698638092318.8330136190774
70539588.281110128282-49.2811101282823
71551554.352307074596-3.35230707459573
72526545.59938107194-19.5993810719403







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73525.371361195789337.443014998449713.29970739313
74516.063572746917288.719655547332743.407489946502
75506.755784298045233.741083403223779.770485192867
76497.447995849173173.485622648252821.410369050095
77488.140207400301108.655979772989867.624435027614
78478.8324189514339.7581069006591917.9067310022
79469.524630502558-32.8345855960875971.883846601203
80460.216842053686-108.837738633841029.27142274121
81450.909053604814-188.0279528393921089.84606004902
82441.601265155942-270.2246788085361153.42720912042
83432.29347670707-355.2783549292341219.86530834337
84422.985688258198-443.0624570295811289.03383354598

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 525.371361195789 & 337.443014998449 & 713.29970739313 \tabularnewline
74 & 516.063572746917 & 288.719655547332 & 743.407489946502 \tabularnewline
75 & 506.755784298045 & 233.741083403223 & 779.770485192867 \tabularnewline
76 & 497.447995849173 & 173.485622648252 & 821.410369050095 \tabularnewline
77 & 488.140207400301 & 108.655979772989 & 867.624435027614 \tabularnewline
78 & 478.83241895143 & 39.7581069006591 & 917.9067310022 \tabularnewline
79 & 469.524630502558 & -32.8345855960875 & 971.883846601203 \tabularnewline
80 & 460.216842053686 & -108.83773863384 & 1029.27142274121 \tabularnewline
81 & 450.909053604814 & -188.027952839392 & 1089.84606004902 \tabularnewline
82 & 441.601265155942 & -270.224678808536 & 1153.42720912042 \tabularnewline
83 & 432.29347670707 & -355.278354929234 & 1219.86530834337 \tabularnewline
84 & 422.985688258198 & -443.062457029581 & 1289.03383354598 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160875&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]73[/C][C]525.371361195789[/C][C]337.443014998449[/C][C]713.29970739313[/C][/ROW]
[ROW][C]74[/C][C]516.063572746917[/C][C]288.719655547332[/C][C]743.407489946502[/C][/ROW]
[ROW][C]75[/C][C]506.755784298045[/C][C]233.741083403223[/C][C]779.770485192867[/C][/ROW]
[ROW][C]76[/C][C]497.447995849173[/C][C]173.485622648252[/C][C]821.410369050095[/C][/ROW]
[ROW][C]77[/C][C]488.140207400301[/C][C]108.655979772989[/C][C]867.624435027614[/C][/ROW]
[ROW][C]78[/C][C]478.83241895143[/C][C]39.7581069006591[/C][C]917.9067310022[/C][/ROW]
[ROW][C]79[/C][C]469.524630502558[/C][C]-32.8345855960875[/C][C]971.883846601203[/C][/ROW]
[ROW][C]80[/C][C]460.216842053686[/C][C]-108.83773863384[/C][C]1029.27142274121[/C][/ROW]
[ROW][C]81[/C][C]450.909053604814[/C][C]-188.027952839392[/C][C]1089.84606004902[/C][/ROW]
[ROW][C]82[/C][C]441.601265155942[/C][C]-270.224678808536[/C][C]1153.42720912042[/C][/ROW]
[ROW][C]83[/C][C]432.29347670707[/C][C]-355.278354929234[/C][C]1219.86530834337[/C][/ROW]
[ROW][C]84[/C][C]422.985688258198[/C][C]-443.062457029581[/C][C]1289.03383354598[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160875&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160875&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
73525.371361195789337.443014998449713.29970739313
74516.063572746917288.719655547332743.407489946502
75506.755784298045233.741083403223779.770485192867
76497.447995849173173.485622648252821.410369050095
77488.140207400301108.655979772989867.624435027614
78478.8324189514339.7581069006591917.9067310022
79469.524630502558-32.8345855960875971.883846601203
80460.216842053686-108.837738633841029.27142274121
81450.909053604814-188.0279528393921089.84606004902
82441.601265155942-270.2246788085361153.42720912042
83432.29347670707-355.2783549292341219.86530834337
84422.985688258198-443.0624570295811289.03383354598



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')