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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 02 Jun 2008 02:06:45 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jun/02/t1212394033fxya8smp2flydoe.htm/, Retrieved Sat, 18 May 2024 13:57:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13763, Retrieved Sat, 18 May 2024 13:57:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact318
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Opgave 10: Inschr...] [2008-05-26 23:51:15] [5a9957222b47d6f610c4aa164db8acb4]
-    D    [Exponential Smoothing] [Verbetering opgav...] [2008-06-02 08:06:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
10236
10893
10756
10940
10997
10827
10166
10186
10457
10368
10244
10511
10812
10738
10171
9721
9897
9828
9924
10371
10846
10413
10709
10662
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13763&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13763&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.989310479959063
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.989310479959063 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13763&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]0.989310479959063[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13763&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
alpha0.989310479959063
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21089310236657
31075610885.9769853331-129.976985333104
41094010757.3893915896182.610608410421
51099710938.047980241758.9520197582915
61082710996.3698312033-169.369831203339
71016610828.8104822050-662.810482204979
81018610173.085125932912.9148740671262
91045710185.8619461948271.138053805167
101036810454.1016643400-86.101664339989
111024410368.9203854665-124.920385466521
121051110245.3353389640265.664661036035
131081210508.1601722817303.839827718313
141073810808.7520980724-70.7520980723712
151017110738.7563059703-567.756305970282
16972110177.0690424110-456.069042411038
1798979725.8751591689171.124840831097
1898289895.17075758443-67.1707575844339
1999249828.7180231593695.281976840637
20103719922.98148139902448.018518600978
211084610366.2108970667479.789102933297
221041310840.8712847688-427.871284768771
231070910417.5737386735291.426261326524
241066210705.8847931391-43.8847931390956
251057010662.4691073758-92.469107375753
261029710570.9884503765-273.988450376461
271063510299.9288050313335.071194968716
281087210631.4182497462240.581750253759
291029610869.4282965592-573.428296559179
301038310302.129673268180.8703267318906
311043110382.135535021748.8644649783182
321057410430.4776623223143.522337677676
331065310572.465815095180.5341849049273
341080510652.1391282165152.860871783521
351087210803.365990647668.634009352405
361062510871.2663353815-246.266335381537
371040710627.6324689275-220.632468927470
381046310409.358455198353.6415448017178
391055610462.426597631893.5734023681853
401064610554.999745240191.0002547599142
411070210645.027250953056.9727490469868
421135310701.3909886573651.609011342725
431134611346.0346124144-0.0346124143961788
441145111346.0003699901104.999630009903
451196411449.8776043507514.122395649281
461257411958.5042783482615.495721651787
471303112567.4206461483463.579353851708
481381213026.0445592064785.955440793563
491454413803.5985135644740.401486435647
501493114536.0854634724394.914536527593
511488614926.7785531473-40.778553147331
521600514886.43590316111118.56409683889
531706415993.04308666981070.95691333023
541516817052.5519846120-1884.55198461198
551605015188.1449562077861.855043792302
561583916040.787183237-201.787183237
571513715841.1570081392-704.157008139216
581495415144.5271004505-190.527100450470
591564814956.0366432586691.963356741393
601530515640.6032438305-335.603243830519
611557915308.5874376007270.412562399270
621634815576.1094194949771.890580505087
631592816339.7488601703-411.748860170281
641617115932.4013976926238.598602307376
651593716168.4494954589-231.449495458895
661571315939.4740840202-226.474084020172
671559415715.4208992599-121.420899259887
681568315595.297931136087.7020688639732
691643815682.0625069772755.937493022753
701703216429.9193910186602.080608981363
711769617025.5640472640670.435952735967
721774517688.833361447156.1666385529352
731939417744.39960559161649.60039440844

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 10893 & 10236 & 657 \tabularnewline
3 & 10756 & 10885.9769853331 & -129.976985333104 \tabularnewline
4 & 10940 & 10757.3893915896 & 182.610608410421 \tabularnewline
5 & 10997 & 10938.0479802417 & 58.9520197582915 \tabularnewline
6 & 10827 & 10996.3698312033 & -169.369831203339 \tabularnewline
7 & 10166 & 10828.8104822050 & -662.810482204979 \tabularnewline
8 & 10186 & 10173.0851259329 & 12.9148740671262 \tabularnewline
9 & 10457 & 10185.8619461948 & 271.138053805167 \tabularnewline
10 & 10368 & 10454.1016643400 & -86.101664339989 \tabularnewline
11 & 10244 & 10368.9203854665 & -124.920385466521 \tabularnewline
12 & 10511 & 10245.3353389640 & 265.664661036035 \tabularnewline
13 & 10812 & 10508.1601722817 & 303.839827718313 \tabularnewline
14 & 10738 & 10808.7520980724 & -70.7520980723712 \tabularnewline
15 & 10171 & 10738.7563059703 & -567.756305970282 \tabularnewline
16 & 9721 & 10177.0690424110 & -456.069042411038 \tabularnewline
17 & 9897 & 9725.8751591689 & 171.124840831097 \tabularnewline
18 & 9828 & 9895.17075758443 & -67.1707575844339 \tabularnewline
19 & 9924 & 9828.71802315936 & 95.281976840637 \tabularnewline
20 & 10371 & 9922.98148139902 & 448.018518600978 \tabularnewline
21 & 10846 & 10366.2108970667 & 479.789102933297 \tabularnewline
22 & 10413 & 10840.8712847688 & -427.871284768771 \tabularnewline
23 & 10709 & 10417.5737386735 & 291.426261326524 \tabularnewline
24 & 10662 & 10705.8847931391 & -43.8847931390956 \tabularnewline
25 & 10570 & 10662.4691073758 & -92.469107375753 \tabularnewline
26 & 10297 & 10570.9884503765 & -273.988450376461 \tabularnewline
27 & 10635 & 10299.9288050313 & 335.071194968716 \tabularnewline
28 & 10872 & 10631.4182497462 & 240.581750253759 \tabularnewline
29 & 10296 & 10869.4282965592 & -573.428296559179 \tabularnewline
30 & 10383 & 10302.1296732681 & 80.8703267318906 \tabularnewline
31 & 10431 & 10382.1355350217 & 48.8644649783182 \tabularnewline
32 & 10574 & 10430.4776623223 & 143.522337677676 \tabularnewline
33 & 10653 & 10572.4658150951 & 80.5341849049273 \tabularnewline
34 & 10805 & 10652.1391282165 & 152.860871783521 \tabularnewline
35 & 10872 & 10803.3659906476 & 68.634009352405 \tabularnewline
36 & 10625 & 10871.2663353815 & -246.266335381537 \tabularnewline
37 & 10407 & 10627.6324689275 & -220.632468927470 \tabularnewline
38 & 10463 & 10409.3584551983 & 53.6415448017178 \tabularnewline
39 & 10556 & 10462.4265976318 & 93.5734023681853 \tabularnewline
40 & 10646 & 10554.9997452401 & 91.0002547599142 \tabularnewline
41 & 10702 & 10645.0272509530 & 56.9727490469868 \tabularnewline
42 & 11353 & 10701.3909886573 & 651.609011342725 \tabularnewline
43 & 11346 & 11346.0346124144 & -0.0346124143961788 \tabularnewline
44 & 11451 & 11346.0003699901 & 104.999630009903 \tabularnewline
45 & 11964 & 11449.8776043507 & 514.122395649281 \tabularnewline
46 & 12574 & 11958.5042783482 & 615.495721651787 \tabularnewline
47 & 13031 & 12567.4206461483 & 463.579353851708 \tabularnewline
48 & 13812 & 13026.0445592064 & 785.955440793563 \tabularnewline
49 & 14544 & 13803.5985135644 & 740.401486435647 \tabularnewline
50 & 14931 & 14536.0854634724 & 394.914536527593 \tabularnewline
51 & 14886 & 14926.7785531473 & -40.778553147331 \tabularnewline
52 & 16005 & 14886.4359031611 & 1118.56409683889 \tabularnewline
53 & 17064 & 15993.0430866698 & 1070.95691333023 \tabularnewline
54 & 15168 & 17052.5519846120 & -1884.55198461198 \tabularnewline
55 & 16050 & 15188.1449562077 & 861.855043792302 \tabularnewline
56 & 15839 & 16040.787183237 & -201.787183237 \tabularnewline
57 & 15137 & 15841.1570081392 & -704.157008139216 \tabularnewline
58 & 14954 & 15144.5271004505 & -190.527100450470 \tabularnewline
59 & 15648 & 14956.0366432586 & 691.963356741393 \tabularnewline
60 & 15305 & 15640.6032438305 & -335.603243830519 \tabularnewline
61 & 15579 & 15308.5874376007 & 270.412562399270 \tabularnewline
62 & 16348 & 15576.1094194949 & 771.890580505087 \tabularnewline
63 & 15928 & 16339.7488601703 & -411.748860170281 \tabularnewline
64 & 16171 & 15932.4013976926 & 238.598602307376 \tabularnewline
65 & 15937 & 16168.4494954589 & -231.449495458895 \tabularnewline
66 & 15713 & 15939.4740840202 & -226.474084020172 \tabularnewline
67 & 15594 & 15715.4208992599 & -121.420899259887 \tabularnewline
68 & 15683 & 15595.2979311360 & 87.7020688639732 \tabularnewline
69 & 16438 & 15682.0625069772 & 755.937493022753 \tabularnewline
70 & 17032 & 16429.9193910186 & 602.080608981363 \tabularnewline
71 & 17696 & 17025.5640472640 & 670.435952735967 \tabularnewline
72 & 17745 & 17688.8333614471 & 56.1666385529352 \tabularnewline
73 & 19394 & 17744.3996055916 & 1649.60039440844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13763&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]10893[/C][C]10236[/C][C]657[/C][/ROW]
[ROW][C]3[/C][C]10756[/C][C]10885.9769853331[/C][C]-129.976985333104[/C][/ROW]
[ROW][C]4[/C][C]10940[/C][C]10757.3893915896[/C][C]182.610608410421[/C][/ROW]
[ROW][C]5[/C][C]10997[/C][C]10938.0479802417[/C][C]58.9520197582915[/C][/ROW]
[ROW][C]6[/C][C]10827[/C][C]10996.3698312033[/C][C]-169.369831203339[/C][/ROW]
[ROW][C]7[/C][C]10166[/C][C]10828.8104822050[/C][C]-662.810482204979[/C][/ROW]
[ROW][C]8[/C][C]10186[/C][C]10173.0851259329[/C][C]12.9148740671262[/C][/ROW]
[ROW][C]9[/C][C]10457[/C][C]10185.8619461948[/C][C]271.138053805167[/C][/ROW]
[ROW][C]10[/C][C]10368[/C][C]10454.1016643400[/C][C]-86.101664339989[/C][/ROW]
[ROW][C]11[/C][C]10244[/C][C]10368.9203854665[/C][C]-124.920385466521[/C][/ROW]
[ROW][C]12[/C][C]10511[/C][C]10245.3353389640[/C][C]265.664661036035[/C][/ROW]
[ROW][C]13[/C][C]10812[/C][C]10508.1601722817[/C][C]303.839827718313[/C][/ROW]
[ROW][C]14[/C][C]10738[/C][C]10808.7520980724[/C][C]-70.7520980723712[/C][/ROW]
[ROW][C]15[/C][C]10171[/C][C]10738.7563059703[/C][C]-567.756305970282[/C][/ROW]
[ROW][C]16[/C][C]9721[/C][C]10177.0690424110[/C][C]-456.069042411038[/C][/ROW]
[ROW][C]17[/C][C]9897[/C][C]9725.8751591689[/C][C]171.124840831097[/C][/ROW]
[ROW][C]18[/C][C]9828[/C][C]9895.17075758443[/C][C]-67.1707575844339[/C][/ROW]
[ROW][C]19[/C][C]9924[/C][C]9828.71802315936[/C][C]95.281976840637[/C][/ROW]
[ROW][C]20[/C][C]10371[/C][C]9922.98148139902[/C][C]448.018518600978[/C][/ROW]
[ROW][C]21[/C][C]10846[/C][C]10366.2108970667[/C][C]479.789102933297[/C][/ROW]
[ROW][C]22[/C][C]10413[/C][C]10840.8712847688[/C][C]-427.871284768771[/C][/ROW]
[ROW][C]23[/C][C]10709[/C][C]10417.5737386735[/C][C]291.426261326524[/C][/ROW]
[ROW][C]24[/C][C]10662[/C][C]10705.8847931391[/C][C]-43.8847931390956[/C][/ROW]
[ROW][C]25[/C][C]10570[/C][C]10662.4691073758[/C][C]-92.469107375753[/C][/ROW]
[ROW][C]26[/C][C]10297[/C][C]10570.9884503765[/C][C]-273.988450376461[/C][/ROW]
[ROW][C]27[/C][C]10635[/C][C]10299.9288050313[/C][C]335.071194968716[/C][/ROW]
[ROW][C]28[/C][C]10872[/C][C]10631.4182497462[/C][C]240.581750253759[/C][/ROW]
[ROW][C]29[/C][C]10296[/C][C]10869.4282965592[/C][C]-573.428296559179[/C][/ROW]
[ROW][C]30[/C][C]10383[/C][C]10302.1296732681[/C][C]80.8703267318906[/C][/ROW]
[ROW][C]31[/C][C]10431[/C][C]10382.1355350217[/C][C]48.8644649783182[/C][/ROW]
[ROW][C]32[/C][C]10574[/C][C]10430.4776623223[/C][C]143.522337677676[/C][/ROW]
[ROW][C]33[/C][C]10653[/C][C]10572.4658150951[/C][C]80.5341849049273[/C][/ROW]
[ROW][C]34[/C][C]10805[/C][C]10652.1391282165[/C][C]152.860871783521[/C][/ROW]
[ROW][C]35[/C][C]10872[/C][C]10803.3659906476[/C][C]68.634009352405[/C][/ROW]
[ROW][C]36[/C][C]10625[/C][C]10871.2663353815[/C][C]-246.266335381537[/C][/ROW]
[ROW][C]37[/C][C]10407[/C][C]10627.6324689275[/C][C]-220.632468927470[/C][/ROW]
[ROW][C]38[/C][C]10463[/C][C]10409.3584551983[/C][C]53.6415448017178[/C][/ROW]
[ROW][C]39[/C][C]10556[/C][C]10462.4265976318[/C][C]93.5734023681853[/C][/ROW]
[ROW][C]40[/C][C]10646[/C][C]10554.9997452401[/C][C]91.0002547599142[/C][/ROW]
[ROW][C]41[/C][C]10702[/C][C]10645.0272509530[/C][C]56.9727490469868[/C][/ROW]
[ROW][C]42[/C][C]11353[/C][C]10701.3909886573[/C][C]651.609011342725[/C][/ROW]
[ROW][C]43[/C][C]11346[/C][C]11346.0346124144[/C][C]-0.0346124143961788[/C][/ROW]
[ROW][C]44[/C][C]11451[/C][C]11346.0003699901[/C][C]104.999630009903[/C][/ROW]
[ROW][C]45[/C][C]11964[/C][C]11449.8776043507[/C][C]514.122395649281[/C][/ROW]
[ROW][C]46[/C][C]12574[/C][C]11958.5042783482[/C][C]615.495721651787[/C][/ROW]
[ROW][C]47[/C][C]13031[/C][C]12567.4206461483[/C][C]463.579353851708[/C][/ROW]
[ROW][C]48[/C][C]13812[/C][C]13026.0445592064[/C][C]785.955440793563[/C][/ROW]
[ROW][C]49[/C][C]14544[/C][C]13803.5985135644[/C][C]740.401486435647[/C][/ROW]
[ROW][C]50[/C][C]14931[/C][C]14536.0854634724[/C][C]394.914536527593[/C][/ROW]
[ROW][C]51[/C][C]14886[/C][C]14926.7785531473[/C][C]-40.778553147331[/C][/ROW]
[ROW][C]52[/C][C]16005[/C][C]14886.4359031611[/C][C]1118.56409683889[/C][/ROW]
[ROW][C]53[/C][C]17064[/C][C]15993.0430866698[/C][C]1070.95691333023[/C][/ROW]
[ROW][C]54[/C][C]15168[/C][C]17052.5519846120[/C][C]-1884.55198461198[/C][/ROW]
[ROW][C]55[/C][C]16050[/C][C]15188.1449562077[/C][C]861.855043792302[/C][/ROW]
[ROW][C]56[/C][C]15839[/C][C]16040.787183237[/C][C]-201.787183237[/C][/ROW]
[ROW][C]57[/C][C]15137[/C][C]15841.1570081392[/C][C]-704.157008139216[/C][/ROW]
[ROW][C]58[/C][C]14954[/C][C]15144.5271004505[/C][C]-190.527100450470[/C][/ROW]
[ROW][C]59[/C][C]15648[/C][C]14956.0366432586[/C][C]691.963356741393[/C][/ROW]
[ROW][C]60[/C][C]15305[/C][C]15640.6032438305[/C][C]-335.603243830519[/C][/ROW]
[ROW][C]61[/C][C]15579[/C][C]15308.5874376007[/C][C]270.412562399270[/C][/ROW]
[ROW][C]62[/C][C]16348[/C][C]15576.1094194949[/C][C]771.890580505087[/C][/ROW]
[ROW][C]63[/C][C]15928[/C][C]16339.7488601703[/C][C]-411.748860170281[/C][/ROW]
[ROW][C]64[/C][C]16171[/C][C]15932.4013976926[/C][C]238.598602307376[/C][/ROW]
[ROW][C]65[/C][C]15937[/C][C]16168.4494954589[/C][C]-231.449495458895[/C][/ROW]
[ROW][C]66[/C][C]15713[/C][C]15939.4740840202[/C][C]-226.474084020172[/C][/ROW]
[ROW][C]67[/C][C]15594[/C][C]15715.4208992599[/C][C]-121.420899259887[/C][/ROW]
[ROW][C]68[/C][C]15683[/C][C]15595.2979311360[/C][C]87.7020688639732[/C][/ROW]
[ROW][C]69[/C][C]16438[/C][C]15682.0625069772[/C][C]755.937493022753[/C][/ROW]
[ROW][C]70[/C][C]17032[/C][C]16429.9193910186[/C][C]602.080608981363[/C][/ROW]
[ROW][C]71[/C][C]17696[/C][C]17025.5640472640[/C][C]670.435952735967[/C][/ROW]
[ROW][C]72[/C][C]17745[/C][C]17688.8333614471[/C][C]56.1666385529352[/C][/ROW]
[ROW][C]73[/C][C]19394[/C][C]17744.3996055916[/C][C]1649.60039440844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13763&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13763&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
21089310236657
31075610885.9769853331-129.976985333104
41094010757.3893915896182.610608410421
51099710938.047980241758.9520197582915
61082710996.3698312033-169.369831203339
71016610828.8104822050-662.810482204979
81018610173.085125932912.9148740671262
91045710185.8619461948271.138053805167
101036810454.1016643400-86.101664339989
111024410368.9203854665-124.920385466521
121051110245.3353389640265.664661036035
131081210508.1601722817303.839827718313
141073810808.7520980724-70.7520980723712
151017110738.7563059703-567.756305970282
16972110177.0690424110-456.069042411038
1798979725.8751591689171.124840831097
1898289895.17075758443-67.1707575844339
1999249828.7180231593695.281976840637
20103719922.98148139902448.018518600978
211084610366.2108970667479.789102933297
221041310840.8712847688-427.871284768771
231070910417.5737386735291.426261326524
241066210705.8847931391-43.8847931390956
251057010662.4691073758-92.469107375753
261029710570.9884503765-273.988450376461
271063510299.9288050313335.071194968716
281087210631.4182497462240.581750253759
291029610869.4282965592-573.428296559179
301038310302.129673268180.8703267318906
311043110382.135535021748.8644649783182
321057410430.4776623223143.522337677676
331065310572.465815095180.5341849049273
341080510652.1391282165152.860871783521
351087210803.365990647668.634009352405
361062510871.2663353815-246.266335381537
371040710627.6324689275-220.632468927470
381046310409.358455198353.6415448017178
391055610462.426597631893.5734023681853
401064610554.999745240191.0002547599142
411070210645.027250953056.9727490469868
421135310701.3909886573651.609011342725
431134611346.0346124144-0.0346124143961788
441145111346.0003699901104.999630009903
451196411449.8776043507514.122395649281
461257411958.5042783482615.495721651787
471303112567.4206461483463.579353851708
481381213026.0445592064785.955440793563
491454413803.5985135644740.401486435647
501493114536.0854634724394.914536527593
511488614926.7785531473-40.778553147331
521600514886.43590316111118.56409683889
531706415993.04308666981070.95691333023
541516817052.5519846120-1884.55198461198
551605015188.1449562077861.855043792302
561583916040.787183237-201.787183237
571513715841.1570081392-704.157008139216
581495415144.5271004505-190.527100450470
591564814956.0366432586691.963356741393
601530515640.6032438305-335.603243830519
611557915308.5874376007270.412562399270
621634815576.1094194949771.890580505087
631592816339.7488601703-411.748860170281
641617115932.4013976926238.598602307376
651593716168.4494954589-231.449495458895
661571315939.4740840202-226.474084020172
671559415715.4208992599-121.420899259887
681568315595.297931136087.7020688639732
691643815682.0625069772755.937493022753
701703216429.9193910186602.080608981363
711769617025.5640472640670.435952735967
721774517688.833361447156.1666385529352
731939417744.39960559161649.60039440844







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7419376.366563524418398.040100349520354.6930266994
7519376.366563524418000.178952903320752.5541741456
7619376.366563524417693.909428645321058.8236984036
7719376.366563524417435.379267897621317.3538591512
7819376.366563524417207.449471318421545.2836557304
7919376.366563524417001.293717495921751.4394095530
8019376.366563524416811.655918047921941.077209001
8119376.366563524416635.105837854722117.6272891942
8219376.366563524416469.258028024222283.4750990246
8319376.366563524416312.374117669422440.3590093795
8419376.366563524416163.140866606222589.5922604427
8519376.366563524416020.537448325922732.195678723

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 19376.3665635244 & 18398.0401003495 & 20354.6930266994 \tabularnewline
75 & 19376.3665635244 & 18000.1789529033 & 20752.5541741456 \tabularnewline
76 & 19376.3665635244 & 17693.9094286453 & 21058.8236984036 \tabularnewline
77 & 19376.3665635244 & 17435.3792678976 & 21317.3538591512 \tabularnewline
78 & 19376.3665635244 & 17207.4494713184 & 21545.2836557304 \tabularnewline
79 & 19376.3665635244 & 17001.2937174959 & 21751.4394095530 \tabularnewline
80 & 19376.3665635244 & 16811.6559180479 & 21941.077209001 \tabularnewline
81 & 19376.3665635244 & 16635.1058378547 & 22117.6272891942 \tabularnewline
82 & 19376.3665635244 & 16469.2580280242 & 22283.4750990246 \tabularnewline
83 & 19376.3665635244 & 16312.3741176694 & 22440.3590093795 \tabularnewline
84 & 19376.3665635244 & 16163.1408666062 & 22589.5922604427 \tabularnewline
85 & 19376.3665635244 & 16020.5374483259 & 22732.195678723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13763&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]74[/C][C]19376.3665635244[/C][C]18398.0401003495[/C][C]20354.6930266994[/C][/ROW]
[ROW][C]75[/C][C]19376.3665635244[/C][C]18000.1789529033[/C][C]20752.5541741456[/C][/ROW]
[ROW][C]76[/C][C]19376.3665635244[/C][C]17693.9094286453[/C][C]21058.8236984036[/C][/ROW]
[ROW][C]77[/C][C]19376.3665635244[/C][C]17435.3792678976[/C][C]21317.3538591512[/C][/ROW]
[ROW][C]78[/C][C]19376.3665635244[/C][C]17207.4494713184[/C][C]21545.2836557304[/C][/ROW]
[ROW][C]79[/C][C]19376.3665635244[/C][C]17001.2937174959[/C][C]21751.4394095530[/C][/ROW]
[ROW][C]80[/C][C]19376.3665635244[/C][C]16811.6559180479[/C][C]21941.077209001[/C][/ROW]
[ROW][C]81[/C][C]19376.3665635244[/C][C]16635.1058378547[/C][C]22117.6272891942[/C][/ROW]
[ROW][C]82[/C][C]19376.3665635244[/C][C]16469.2580280242[/C][C]22283.4750990246[/C][/ROW]
[ROW][C]83[/C][C]19376.3665635244[/C][C]16312.3741176694[/C][C]22440.3590093795[/C][/ROW]
[ROW][C]84[/C][C]19376.3665635244[/C][C]16163.1408666062[/C][C]22589.5922604427[/C][/ROW]
[ROW][C]85[/C][C]19376.3665635244[/C][C]16020.5374483259[/C][C]22732.195678723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13763&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13763&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
7419376.366563524418398.040100349520354.6930266994
7519376.366563524418000.178952903320752.5541741456
7619376.366563524417693.909428645321058.8236984036
7719376.366563524417435.379267897621317.3538591512
7819376.366563524417207.449471318421545.2836557304
7919376.366563524417001.293717495921751.4394095530
8019376.366563524416811.655918047921941.077209001
8119376.366563524416635.105837854722117.6272891942
8219376.366563524416469.258028024222283.4750990246
8319376.366563524416312.374117669422440.3590093795
8419376.366563524416163.140866606222589.5922604427
8519376.366563524416020.537448325922732.195678723



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')