Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 17:54:06 -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/May/27/t1211846069h3hhulk8arkbbsl.htm/, Retrieved Mon, 20 May 2024 00:09:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13317, Retrieved Mon, 20 May 2024 00:09:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact236
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10: Goudkoers] [2008-05-26 23:54:06] [f38aed22bcf737d6f431a6f90e40d4b2] [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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13317&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13317&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13317&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.989310479959035
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.989310479959035 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13317&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]0.989310479959035[/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=13317&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13317&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
alpha0.989310479959035
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21089310236657
31075610885.9769853331-129.976985333085
41094010757.3893915896182.610608410418
51099710938.047980241758.9520197582951
61082710996.3698312033-169.369831203338
71016610828.8104822050-662.810482204983
81018610173.085125932912.9148740671080
91045710185.8619461948271.138053805165
101036810454.1016643400-86.1016643399817
111024410368.9203854665-124.920385466521
121051110245.3353389640265.664661036031
131081210508.1601722817303.839827718321
141073810808.7520980724-70.752098072362
151017110738.7563059703-567.756305970284
16972110177.0690424111-456.069042411053
1798979725.87515916892171.124840831084
1898289895.17075758443-67.1707575844284
1999249828.7180231593795.2819768406334
20103719922.98148139902448.01851860098
211084610366.2108970667479.789102933308
221041310840.8712847688-427.871284768757
231070910417.5737386735291.426261326511
241066210705.8847931391-43.8847931390883
251057010662.4691073758-92.4691073757549
261029710570.9884503765-273.988450376462
271063510299.9288050313335.071194968708
281087210631.4182497462240.581750253768
291029610869.4282965592-573.428296559172
301038310302.129673268180.8703267318742
311043110382.135535021748.8644649783182
321057410430.4776623223143.522337677678
331065310572.465815095180.534184904931
341080510652.1391282165152.860871783525
351087210803.365990647668.6340093524104
361062510871.2663353815-246.266335381535
371040710627.6324689275-220.632468927477
381046310409.358455198353.6415448017124
391055610462.426597631893.5734023681871
401064610554.999745240191.000254759916
411070210645.02725095356.9727490469886
421135310701.3909886573651.609011342727
431134611346.0346124144-0.0346124143779889
441145111346.0003699901104.999630009903
451196411449.8776043507514.122395649285
461257411958.5042783482615.495721651803
471303112567.4206461483463.579353851725
481381213026.0445592064785.955440793576
491454413803.5985135643740.401486435669
501493114536.0854634724394.914536527614
511488614926.7785531473-40.7785531473201
521600514886.43590316111118.56409683889
531706415993.04308666971070.95691333026
541516817052.5519846119-1884.55198461195
551605015188.1449562078861.85504379225
561583916040.7871832370-201.787183236975
571513715841.1570081392-704.157008139222
581495415144.5271004505-190.527100450490
591564814956.0366432586691.963356741388
601530515640.6032438305-335.603243830499
611557915308.5874376007270.412562399262
621634815576.1094194949771.890580505096
631592816339.7488601703-411.748860170259
641617115932.4013976926238.598602307366
651593716168.4494954589-231.449495458888
661571315939.4740840202-226.474084020179
671559415715.4208992599-121.420899259894
681568315595.297931136087.7020688639677
691643815682.0625069772755.937493022757
701703216429.9193910186602.080608981381
711769617025.564047264670.435952735985
721774517688.833361447056.1666385529534
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 & -129.976985333085 \tabularnewline
4 & 10940 & 10757.3893915896 & 182.610608410418 \tabularnewline
5 & 10997 & 10938.0479802417 & 58.9520197582951 \tabularnewline
6 & 10827 & 10996.3698312033 & -169.369831203338 \tabularnewline
7 & 10166 & 10828.8104822050 & -662.810482204983 \tabularnewline
8 & 10186 & 10173.0851259329 & 12.9148740671080 \tabularnewline
9 & 10457 & 10185.8619461948 & 271.138053805165 \tabularnewline
10 & 10368 & 10454.1016643400 & -86.1016643399817 \tabularnewline
11 & 10244 & 10368.9203854665 & -124.920385466521 \tabularnewline
12 & 10511 & 10245.3353389640 & 265.664661036031 \tabularnewline
13 & 10812 & 10508.1601722817 & 303.839827718321 \tabularnewline
14 & 10738 & 10808.7520980724 & -70.752098072362 \tabularnewline
15 & 10171 & 10738.7563059703 & -567.756305970284 \tabularnewline
16 & 9721 & 10177.0690424111 & -456.069042411053 \tabularnewline
17 & 9897 & 9725.87515916892 & 171.124840831084 \tabularnewline
18 & 9828 & 9895.17075758443 & -67.1707575844284 \tabularnewline
19 & 9924 & 9828.71802315937 & 95.2819768406334 \tabularnewline
20 & 10371 & 9922.98148139902 & 448.01851860098 \tabularnewline
21 & 10846 & 10366.2108970667 & 479.789102933308 \tabularnewline
22 & 10413 & 10840.8712847688 & -427.871284768757 \tabularnewline
23 & 10709 & 10417.5737386735 & 291.426261326511 \tabularnewline
24 & 10662 & 10705.8847931391 & -43.8847931390883 \tabularnewline
25 & 10570 & 10662.4691073758 & -92.4691073757549 \tabularnewline
26 & 10297 & 10570.9884503765 & -273.988450376462 \tabularnewline
27 & 10635 & 10299.9288050313 & 335.071194968708 \tabularnewline
28 & 10872 & 10631.4182497462 & 240.581750253768 \tabularnewline
29 & 10296 & 10869.4282965592 & -573.428296559172 \tabularnewline
30 & 10383 & 10302.1296732681 & 80.8703267318742 \tabularnewline
31 & 10431 & 10382.1355350217 & 48.8644649783182 \tabularnewline
32 & 10574 & 10430.4776623223 & 143.522337677678 \tabularnewline
33 & 10653 & 10572.4658150951 & 80.534184904931 \tabularnewline
34 & 10805 & 10652.1391282165 & 152.860871783525 \tabularnewline
35 & 10872 & 10803.3659906476 & 68.6340093524104 \tabularnewline
36 & 10625 & 10871.2663353815 & -246.266335381535 \tabularnewline
37 & 10407 & 10627.6324689275 & -220.632468927477 \tabularnewline
38 & 10463 & 10409.3584551983 & 53.6415448017124 \tabularnewline
39 & 10556 & 10462.4265976318 & 93.5734023681871 \tabularnewline
40 & 10646 & 10554.9997452401 & 91.000254759916 \tabularnewline
41 & 10702 & 10645.027250953 & 56.9727490469886 \tabularnewline
42 & 11353 & 10701.3909886573 & 651.609011342727 \tabularnewline
43 & 11346 & 11346.0346124144 & -0.0346124143779889 \tabularnewline
44 & 11451 & 11346.0003699901 & 104.999630009903 \tabularnewline
45 & 11964 & 11449.8776043507 & 514.122395649285 \tabularnewline
46 & 12574 & 11958.5042783482 & 615.495721651803 \tabularnewline
47 & 13031 & 12567.4206461483 & 463.579353851725 \tabularnewline
48 & 13812 & 13026.0445592064 & 785.955440793576 \tabularnewline
49 & 14544 & 13803.5985135643 & 740.401486435669 \tabularnewline
50 & 14931 & 14536.0854634724 & 394.914536527614 \tabularnewline
51 & 14886 & 14926.7785531473 & -40.7785531473201 \tabularnewline
52 & 16005 & 14886.4359031611 & 1118.56409683889 \tabularnewline
53 & 17064 & 15993.0430866697 & 1070.95691333026 \tabularnewline
54 & 15168 & 17052.5519846119 & -1884.55198461195 \tabularnewline
55 & 16050 & 15188.1449562078 & 861.85504379225 \tabularnewline
56 & 15839 & 16040.7871832370 & -201.787183236975 \tabularnewline
57 & 15137 & 15841.1570081392 & -704.157008139222 \tabularnewline
58 & 14954 & 15144.5271004505 & -190.527100450490 \tabularnewline
59 & 15648 & 14956.0366432586 & 691.963356741388 \tabularnewline
60 & 15305 & 15640.6032438305 & -335.603243830499 \tabularnewline
61 & 15579 & 15308.5874376007 & 270.412562399262 \tabularnewline
62 & 16348 & 15576.1094194949 & 771.890580505096 \tabularnewline
63 & 15928 & 16339.7488601703 & -411.748860170259 \tabularnewline
64 & 16171 & 15932.4013976926 & 238.598602307366 \tabularnewline
65 & 15937 & 16168.4494954589 & -231.449495458888 \tabularnewline
66 & 15713 & 15939.4740840202 & -226.474084020179 \tabularnewline
67 & 15594 & 15715.4208992599 & -121.420899259894 \tabularnewline
68 & 15683 & 15595.2979311360 & 87.7020688639677 \tabularnewline
69 & 16438 & 15682.0625069772 & 755.937493022757 \tabularnewline
70 & 17032 & 16429.9193910186 & 602.080608981381 \tabularnewline
71 & 17696 & 17025.564047264 & 670.435952735985 \tabularnewline
72 & 17745 & 17688.8333614470 & 56.1666385529534 \tabularnewline
73 & 19394 & 17744.3996055916 & 1649.60039440844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13317&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]-129.976985333085[/C][/ROW]
[ROW][C]4[/C][C]10940[/C][C]10757.3893915896[/C][C]182.610608410418[/C][/ROW]
[ROW][C]5[/C][C]10997[/C][C]10938.0479802417[/C][C]58.9520197582951[/C][/ROW]
[ROW][C]6[/C][C]10827[/C][C]10996.3698312033[/C][C]-169.369831203338[/C][/ROW]
[ROW][C]7[/C][C]10166[/C][C]10828.8104822050[/C][C]-662.810482204983[/C][/ROW]
[ROW][C]8[/C][C]10186[/C][C]10173.0851259329[/C][C]12.9148740671080[/C][/ROW]
[ROW][C]9[/C][C]10457[/C][C]10185.8619461948[/C][C]271.138053805165[/C][/ROW]
[ROW][C]10[/C][C]10368[/C][C]10454.1016643400[/C][C]-86.1016643399817[/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]265.664661036031[/C][/ROW]
[ROW][C]13[/C][C]10812[/C][C]10508.1601722817[/C][C]303.839827718321[/C][/ROW]
[ROW][C]14[/C][C]10738[/C][C]10808.7520980724[/C][C]-70.752098072362[/C][/ROW]
[ROW][C]15[/C][C]10171[/C][C]10738.7563059703[/C][C]-567.756305970284[/C][/ROW]
[ROW][C]16[/C][C]9721[/C][C]10177.0690424111[/C][C]-456.069042411053[/C][/ROW]
[ROW][C]17[/C][C]9897[/C][C]9725.87515916892[/C][C]171.124840831084[/C][/ROW]
[ROW][C]18[/C][C]9828[/C][C]9895.17075758443[/C][C]-67.1707575844284[/C][/ROW]
[ROW][C]19[/C][C]9924[/C][C]9828.71802315937[/C][C]95.2819768406334[/C][/ROW]
[ROW][C]20[/C][C]10371[/C][C]9922.98148139902[/C][C]448.01851860098[/C][/ROW]
[ROW][C]21[/C][C]10846[/C][C]10366.2108970667[/C][C]479.789102933308[/C][/ROW]
[ROW][C]22[/C][C]10413[/C][C]10840.8712847688[/C][C]-427.871284768757[/C][/ROW]
[ROW][C]23[/C][C]10709[/C][C]10417.5737386735[/C][C]291.426261326511[/C][/ROW]
[ROW][C]24[/C][C]10662[/C][C]10705.8847931391[/C][C]-43.8847931390883[/C][/ROW]
[ROW][C]25[/C][C]10570[/C][C]10662.4691073758[/C][C]-92.4691073757549[/C][/ROW]
[ROW][C]26[/C][C]10297[/C][C]10570.9884503765[/C][C]-273.988450376462[/C][/ROW]
[ROW][C]27[/C][C]10635[/C][C]10299.9288050313[/C][C]335.071194968708[/C][/ROW]
[ROW][C]28[/C][C]10872[/C][C]10631.4182497462[/C][C]240.581750253768[/C][/ROW]
[ROW][C]29[/C][C]10296[/C][C]10869.4282965592[/C][C]-573.428296559172[/C][/ROW]
[ROW][C]30[/C][C]10383[/C][C]10302.1296732681[/C][C]80.8703267318742[/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]143.522337677678[/C][/ROW]
[ROW][C]33[/C][C]10653[/C][C]10572.4658150951[/C][C]80.534184904931[/C][/ROW]
[ROW][C]34[/C][C]10805[/C][C]10652.1391282165[/C][C]152.860871783525[/C][/ROW]
[ROW][C]35[/C][C]10872[/C][C]10803.3659906476[/C][C]68.6340093524104[/C][/ROW]
[ROW][C]36[/C][C]10625[/C][C]10871.2663353815[/C][C]-246.266335381535[/C][/ROW]
[ROW][C]37[/C][C]10407[/C][C]10627.6324689275[/C][C]-220.632468927477[/C][/ROW]
[ROW][C]38[/C][C]10463[/C][C]10409.3584551983[/C][C]53.6415448017124[/C][/ROW]
[ROW][C]39[/C][C]10556[/C][C]10462.4265976318[/C][C]93.5734023681871[/C][/ROW]
[ROW][C]40[/C][C]10646[/C][C]10554.9997452401[/C][C]91.000254759916[/C][/ROW]
[ROW][C]41[/C][C]10702[/C][C]10645.027250953[/C][C]56.9727490469886[/C][/ROW]
[ROW][C]42[/C][C]11353[/C][C]10701.3909886573[/C][C]651.609011342727[/C][/ROW]
[ROW][C]43[/C][C]11346[/C][C]11346.0346124144[/C][C]-0.0346124143779889[/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]514.122395649285[/C][/ROW]
[ROW][C]46[/C][C]12574[/C][C]11958.5042783482[/C][C]615.495721651803[/C][/ROW]
[ROW][C]47[/C][C]13031[/C][C]12567.4206461483[/C][C]463.579353851725[/C][/ROW]
[ROW][C]48[/C][C]13812[/C][C]13026.0445592064[/C][C]785.955440793576[/C][/ROW]
[ROW][C]49[/C][C]14544[/C][C]13803.5985135643[/C][C]740.401486435669[/C][/ROW]
[ROW][C]50[/C][C]14931[/C][C]14536.0854634724[/C][C]394.914536527614[/C][/ROW]
[ROW][C]51[/C][C]14886[/C][C]14926.7785531473[/C][C]-40.7785531473201[/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]15993.0430866697[/C][C]1070.95691333026[/C][/ROW]
[ROW][C]54[/C][C]15168[/C][C]17052.5519846119[/C][C]-1884.55198461195[/C][/ROW]
[ROW][C]55[/C][C]16050[/C][C]15188.1449562078[/C][C]861.85504379225[/C][/ROW]
[ROW][C]56[/C][C]15839[/C][C]16040.7871832370[/C][C]-201.787183236975[/C][/ROW]
[ROW][C]57[/C][C]15137[/C][C]15841.1570081392[/C][C]-704.157008139222[/C][/ROW]
[ROW][C]58[/C][C]14954[/C][C]15144.5271004505[/C][C]-190.527100450490[/C][/ROW]
[ROW][C]59[/C][C]15648[/C][C]14956.0366432586[/C][C]691.963356741388[/C][/ROW]
[ROW][C]60[/C][C]15305[/C][C]15640.6032438305[/C][C]-335.603243830499[/C][/ROW]
[ROW][C]61[/C][C]15579[/C][C]15308.5874376007[/C][C]270.412562399262[/C][/ROW]
[ROW][C]62[/C][C]16348[/C][C]15576.1094194949[/C][C]771.890580505096[/C][/ROW]
[ROW][C]63[/C][C]15928[/C][C]16339.7488601703[/C][C]-411.748860170259[/C][/ROW]
[ROW][C]64[/C][C]16171[/C][C]15932.4013976926[/C][C]238.598602307366[/C][/ROW]
[ROW][C]65[/C][C]15937[/C][C]16168.4494954589[/C][C]-231.449495458888[/C][/ROW]
[ROW][C]66[/C][C]15713[/C][C]15939.4740840202[/C][C]-226.474084020179[/C][/ROW]
[ROW][C]67[/C][C]15594[/C][C]15715.4208992599[/C][C]-121.420899259894[/C][/ROW]
[ROW][C]68[/C][C]15683[/C][C]15595.2979311360[/C][C]87.7020688639677[/C][/ROW]
[ROW][C]69[/C][C]16438[/C][C]15682.0625069772[/C][C]755.937493022757[/C][/ROW]
[ROW][C]70[/C][C]17032[/C][C]16429.9193910186[/C][C]602.080608981381[/C][/ROW]
[ROW][C]71[/C][C]17696[/C][C]17025.564047264[/C][C]670.435952735985[/C][/ROW]
[ROW][C]72[/C][C]17745[/C][C]17688.8333614470[/C][C]56.1666385529534[/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=13317&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13317&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
31075610885.9769853331-129.976985333085
41094010757.3893915896182.610608410418
51099710938.047980241758.9520197582951
61082710996.3698312033-169.369831203338
71016610828.8104822050-662.810482204983
81018610173.085125932912.9148740671080
91045710185.8619461948271.138053805165
101036810454.1016643400-86.1016643399817
111024410368.9203854665-124.920385466521
121051110245.3353389640265.664661036031
131081210508.1601722817303.839827718321
141073810808.7520980724-70.752098072362
151017110738.7563059703-567.756305970284
16972110177.0690424111-456.069042411053
1798979725.87515916892171.124840831084
1898289895.17075758443-67.1707575844284
1999249828.7180231593795.2819768406334
20103719922.98148139902448.01851860098
211084610366.2108970667479.789102933308
221041310840.8712847688-427.871284768757
231070910417.5737386735291.426261326511
241066210705.8847931391-43.8847931390883
251057010662.4691073758-92.4691073757549
261029710570.9884503765-273.988450376462
271063510299.9288050313335.071194968708
281087210631.4182497462240.581750253768
291029610869.4282965592-573.428296559172
301038310302.129673268180.8703267318742
311043110382.135535021748.8644649783182
321057410430.4776623223143.522337677678
331065310572.465815095180.534184904931
341080510652.1391282165152.860871783525
351087210803.365990647668.6340093524104
361062510871.2663353815-246.266335381535
371040710627.6324689275-220.632468927477
381046310409.358455198353.6415448017124
391055610462.426597631893.5734023681871
401064610554.999745240191.000254759916
411070210645.02725095356.9727490469886
421135310701.3909886573651.609011342727
431134611346.0346124144-0.0346124143779889
441145111346.0003699901104.999630009903
451196411449.8776043507514.122395649285
461257411958.5042783482615.495721651803
471303112567.4206461483463.579353851725
481381213026.0445592064785.955440793576
491454413803.5985135643740.401486435669
501493114536.0854634724394.914536527614
511488614926.7785531473-40.7785531473201
521600514886.43590316111118.56409683889
531706415993.04308666971070.95691333026
541516817052.5519846119-1884.55198461195
551605015188.1449562078861.85504379225
561583916040.7871832370-201.787183236975
571513715841.1570081392-704.157008139222
581495415144.5271004505-190.527100450490
591564814956.0366432586691.963356741388
601530515640.6032438305-335.603243830499
611557915308.5874376007270.412562399262
621634815576.1094194949771.890580505096
631592816339.7488601703-411.748860170259
641617115932.4013976926238.598602307366
651593716168.4494954589-231.449495458888
661571315939.4740840202-226.474084020179
671559415715.4208992599-121.420899259894
681568315595.297931136087.7020688639677
691643815682.0625069772755.937493022757
701703216429.9193910186602.080608981381
711769617025.564047264670.435952735985
721774517688.833361447056.1666385529534
731939417744.39960559161649.60039440844







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7419376.366563524418398.040100349420354.6930266993
7519376.366563524418000.178952903320752.5541741455
7619376.366563524417693.909428645221058.8236984035
7719376.366563524417435.379267897621317.3538591511
7819376.366563524417207.449471318421545.2836557303
7919376.366563524417001.293717495921751.4394095528
8019376.366563524416811.655918047921941.0772090009
8119376.366563524416635.105837854722117.6272891941
8219376.366563524416469.258028024322283.4750990245
8319376.366563524416312.374117669422440.3590093794
8419376.366563524416163.140866606322589.5922604425
8519376.366563524416020.537448325922732.1956787228

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 19376.3665635244 & 18398.0401003494 & 20354.6930266993 \tabularnewline
75 & 19376.3665635244 & 18000.1789529033 & 20752.5541741455 \tabularnewline
76 & 19376.3665635244 & 17693.9094286452 & 21058.8236984035 \tabularnewline
77 & 19376.3665635244 & 17435.3792678976 & 21317.3538591511 \tabularnewline
78 & 19376.3665635244 & 17207.4494713184 & 21545.2836557303 \tabularnewline
79 & 19376.3665635244 & 17001.2937174959 & 21751.4394095528 \tabularnewline
80 & 19376.3665635244 & 16811.6559180479 & 21941.0772090009 \tabularnewline
81 & 19376.3665635244 & 16635.1058378547 & 22117.6272891941 \tabularnewline
82 & 19376.3665635244 & 16469.2580280243 & 22283.4750990245 \tabularnewline
83 & 19376.3665635244 & 16312.3741176694 & 22440.3590093794 \tabularnewline
84 & 19376.3665635244 & 16163.1408666063 & 22589.5922604425 \tabularnewline
85 & 19376.3665635244 & 16020.5374483259 & 22732.1956787228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13317&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]18398.0401003494[/C][C]20354.6930266993[/C][/ROW]
[ROW][C]75[/C][C]19376.3665635244[/C][C]18000.1789529033[/C][C]20752.5541741455[/C][/ROW]
[ROW][C]76[/C][C]19376.3665635244[/C][C]17693.9094286452[/C][C]21058.8236984035[/C][/ROW]
[ROW][C]77[/C][C]19376.3665635244[/C][C]17435.3792678976[/C][C]21317.3538591511[/C][/ROW]
[ROW][C]78[/C][C]19376.3665635244[/C][C]17207.4494713184[/C][C]21545.2836557303[/C][/ROW]
[ROW][C]79[/C][C]19376.3665635244[/C][C]17001.2937174959[/C][C]21751.4394095528[/C][/ROW]
[ROW][C]80[/C][C]19376.3665635244[/C][C]16811.6559180479[/C][C]21941.0772090009[/C][/ROW]
[ROW][C]81[/C][C]19376.3665635244[/C][C]16635.1058378547[/C][C]22117.6272891941[/C][/ROW]
[ROW][C]82[/C][C]19376.3665635244[/C][C]16469.2580280243[/C][C]22283.4750990245[/C][/ROW]
[ROW][C]83[/C][C]19376.3665635244[/C][C]16312.3741176694[/C][C]22440.3590093794[/C][/ROW]
[ROW][C]84[/C][C]19376.3665635244[/C][C]16163.1408666063[/C][C]22589.5922604425[/C][/ROW]
[ROW][C]85[/C][C]19376.3665635244[/C][C]16020.5374483259[/C][C]22732.1956787228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13317&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13317&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
7419376.366563524418398.040100349420354.6930266993
7519376.366563524418000.178952903320752.5541741455
7619376.366563524417693.909428645221058.8236984035
7719376.366563524417435.379267897621317.3538591511
7819376.366563524417207.449471318421545.2836557303
7919376.366563524417001.293717495921751.4394095528
8019376.366563524416811.655918047921941.0772090009
8119376.366563524416635.105837854722117.6272891941
8219376.366563524416469.258028024322283.4750990245
8319376.366563524416312.374117669422440.3590093794
8419376.366563524416163.140866606322589.5922604425
8519376.366563524416020.537448325922732.1956787228



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=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')