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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 13:30:07 -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/28/t1212003091a1lhslv8h8vn2a9.htm/, Retrieved Mon, 13 May 2024 20:56:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13473, Retrieved Mon, 13 May 2024 20:56:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-05-28 19:30:07] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
430,00
433,87
434,55
434,55
434,55
434,55
434,71
434,71
434,71
434,71
434,73
436,34
437,55
439,58
439,65
439,76
439,76
439,76
440,06
440,13
441,18
441,14
441,14
441,19
449,06
456,46
456,79
456,87
457,25
455,93
456,00
456,22
456,22
456,58
457,61
457,61
460,43
460,43
462,18
462,37
462,59
463,19
463,48
464,30
461,41
463,35
463,35
463,35
464,27
472,28
472,36
472,56
472,56
472,56
474,15
474,59
474,97
474,99
474,99
474,99
478,34
485,70
485,75
485,85
485,84
485,85
485,84
486,00
488,79
489,71
489,71
489,71




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=13473&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=13473&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13473&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
alpha1
beta0.211289943060778
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.211289943060778 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13473&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.211289943060778[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13473&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13473&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
alpha1
beta0.211289943060778
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3434.55437.74-3.19
4434.55437.745985081636-3.19598508163614
5434.55437.070705575714-2.52070557571415
6434.55436.538105838149-1.9881058381485
7434.71436.118039068807-1.40803906880734
8434.71435.980534574132-1.27053457413166
9434.71435.712083396307-1.00208339630660
10434.71435.500353252559-0.790353252558873
11434.73435.333359558828-0.603359558827776
12436.34435.2258757519981.11412424800204
13437.55437.0712790009210.478720999079144
14439.58438.3824279335581.19757206644164
15439.65440.665462867288-1.01546286728797
16439.76440.520905775878-0.760905775878314
17439.76440.470134037818-0.71013403781842
18439.76440.320089857402-0.560089857402204
19440.06440.201748503323-0.141748503322788
20440.13440.471798470127-0.341798470126776
21441.18440.4695798908350.710420109164602
22441.14441.66968451525-0.52968451525004
23441.14441.517767504183-0.377767504182657
24441.19441.437949029734-0.247949029733718
25449.06441.4355598933597.62444010664069
26456.46450.9165274093625.54347259063826
27456.79459.487807417397-2.69780741739663
28456.87459.247787841786-2.37778784178602
29457.25458.825385184084-1.57538518408444
30455.93458.87252213824-2.94252213824041
31456456.930796803197-0.930796803196529
32456.22456.804128799648-0.584128799647942
33456.22456.90070825883-0.68070825883018
34456.58456.756881449581-0.176881449581003
35457.61457.079508178170.530491821829571
36457.61458.221595764999-0.611595764999038
37460.43458.0923717306362.33762826936379
38460.43461.406289074567-0.976289074567319
39462.18461.2000090115910.979990988408872
40462.37463.157071251732-0.78707125173213
41462.59463.180771011769-0.590771011768879
42463.19463.27594703833-0.0859470383302323
43463.48463.857787293495-0.377787293495203
44464.3464.0679646377640.232035362236445
45461.41464.936991376239-3.52699137623853
46463.35461.3017735691772.04822643082275
47463.35463.674543215121-0.324543215121366
48463.35463.605970497678-0.255970497677595
49464.27463.5518865057980.718113494201873
50472.28464.6236166650997.6563833349008
51472.36474.251333463982-1.89133346398182
52472.56473.931713724068-1.37171372406823
53472.56473.841884409414-1.28188440941415
54472.56473.571035125539-1.01103512553851
55474.15473.3574135714310.792586428568939
56474.59475.114879112794-0.52487911279411
57474.97475.443977434938-0.473977434937979
58474.99475.723830769698-0.733830769697931
59474.99475.588779708152-0.598779708152165
60474.99475.462263577711-0.472263577710748
61478.34475.3624790332672.97752096673338
62485.7479.341599268796.35840073121005
63485.75488.045065397245-2.29506539724491
64485.85487.61014116014-1.76014116014028
65485.84487.338241034635-1.49824103463538
66485.85487.011677771736-1.16167777173587
67485.84486.776226941491-0.93622694149093
68486486.568411604331-0.568411604331232
69488.79486.6083119488172.18168805118296
70489.71489.859280692928-0.149280692927903
71489.71490.747739183819-1.03773918381904
72489.71490.528475330758-0.81847533075802

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 434.55 & 437.74 & -3.19 \tabularnewline
4 & 434.55 & 437.745985081636 & -3.19598508163614 \tabularnewline
5 & 434.55 & 437.070705575714 & -2.52070557571415 \tabularnewline
6 & 434.55 & 436.538105838149 & -1.9881058381485 \tabularnewline
7 & 434.71 & 436.118039068807 & -1.40803906880734 \tabularnewline
8 & 434.71 & 435.980534574132 & -1.27053457413166 \tabularnewline
9 & 434.71 & 435.712083396307 & -1.00208339630660 \tabularnewline
10 & 434.71 & 435.500353252559 & -0.790353252558873 \tabularnewline
11 & 434.73 & 435.333359558828 & -0.603359558827776 \tabularnewline
12 & 436.34 & 435.225875751998 & 1.11412424800204 \tabularnewline
13 & 437.55 & 437.071279000921 & 0.478720999079144 \tabularnewline
14 & 439.58 & 438.382427933558 & 1.19757206644164 \tabularnewline
15 & 439.65 & 440.665462867288 & -1.01546286728797 \tabularnewline
16 & 439.76 & 440.520905775878 & -0.760905775878314 \tabularnewline
17 & 439.76 & 440.470134037818 & -0.71013403781842 \tabularnewline
18 & 439.76 & 440.320089857402 & -0.560089857402204 \tabularnewline
19 & 440.06 & 440.201748503323 & -0.141748503322788 \tabularnewline
20 & 440.13 & 440.471798470127 & -0.341798470126776 \tabularnewline
21 & 441.18 & 440.469579890835 & 0.710420109164602 \tabularnewline
22 & 441.14 & 441.66968451525 & -0.52968451525004 \tabularnewline
23 & 441.14 & 441.517767504183 & -0.377767504182657 \tabularnewline
24 & 441.19 & 441.437949029734 & -0.247949029733718 \tabularnewline
25 & 449.06 & 441.435559893359 & 7.62444010664069 \tabularnewline
26 & 456.46 & 450.916527409362 & 5.54347259063826 \tabularnewline
27 & 456.79 & 459.487807417397 & -2.69780741739663 \tabularnewline
28 & 456.87 & 459.247787841786 & -2.37778784178602 \tabularnewline
29 & 457.25 & 458.825385184084 & -1.57538518408444 \tabularnewline
30 & 455.93 & 458.87252213824 & -2.94252213824041 \tabularnewline
31 & 456 & 456.930796803197 & -0.930796803196529 \tabularnewline
32 & 456.22 & 456.804128799648 & -0.584128799647942 \tabularnewline
33 & 456.22 & 456.90070825883 & -0.68070825883018 \tabularnewline
34 & 456.58 & 456.756881449581 & -0.176881449581003 \tabularnewline
35 & 457.61 & 457.07950817817 & 0.530491821829571 \tabularnewline
36 & 457.61 & 458.221595764999 & -0.611595764999038 \tabularnewline
37 & 460.43 & 458.092371730636 & 2.33762826936379 \tabularnewline
38 & 460.43 & 461.406289074567 & -0.976289074567319 \tabularnewline
39 & 462.18 & 461.200009011591 & 0.979990988408872 \tabularnewline
40 & 462.37 & 463.157071251732 & -0.78707125173213 \tabularnewline
41 & 462.59 & 463.180771011769 & -0.590771011768879 \tabularnewline
42 & 463.19 & 463.27594703833 & -0.0859470383302323 \tabularnewline
43 & 463.48 & 463.857787293495 & -0.377787293495203 \tabularnewline
44 & 464.3 & 464.067964637764 & 0.232035362236445 \tabularnewline
45 & 461.41 & 464.936991376239 & -3.52699137623853 \tabularnewline
46 & 463.35 & 461.301773569177 & 2.04822643082275 \tabularnewline
47 & 463.35 & 463.674543215121 & -0.324543215121366 \tabularnewline
48 & 463.35 & 463.605970497678 & -0.255970497677595 \tabularnewline
49 & 464.27 & 463.551886505798 & 0.718113494201873 \tabularnewline
50 & 472.28 & 464.623616665099 & 7.6563833349008 \tabularnewline
51 & 472.36 & 474.251333463982 & -1.89133346398182 \tabularnewline
52 & 472.56 & 473.931713724068 & -1.37171372406823 \tabularnewline
53 & 472.56 & 473.841884409414 & -1.28188440941415 \tabularnewline
54 & 472.56 & 473.571035125539 & -1.01103512553851 \tabularnewline
55 & 474.15 & 473.357413571431 & 0.792586428568939 \tabularnewline
56 & 474.59 & 475.114879112794 & -0.52487911279411 \tabularnewline
57 & 474.97 & 475.443977434938 & -0.473977434937979 \tabularnewline
58 & 474.99 & 475.723830769698 & -0.733830769697931 \tabularnewline
59 & 474.99 & 475.588779708152 & -0.598779708152165 \tabularnewline
60 & 474.99 & 475.462263577711 & -0.472263577710748 \tabularnewline
61 & 478.34 & 475.362479033267 & 2.97752096673338 \tabularnewline
62 & 485.7 & 479.34159926879 & 6.35840073121005 \tabularnewline
63 & 485.75 & 488.045065397245 & -2.29506539724491 \tabularnewline
64 & 485.85 & 487.61014116014 & -1.76014116014028 \tabularnewline
65 & 485.84 & 487.338241034635 & -1.49824103463538 \tabularnewline
66 & 485.85 & 487.011677771736 & -1.16167777173587 \tabularnewline
67 & 485.84 & 486.776226941491 & -0.93622694149093 \tabularnewline
68 & 486 & 486.568411604331 & -0.568411604331232 \tabularnewline
69 & 488.79 & 486.608311948817 & 2.18168805118296 \tabularnewline
70 & 489.71 & 489.859280692928 & -0.149280692927903 \tabularnewline
71 & 489.71 & 490.747739183819 & -1.03773918381904 \tabularnewline
72 & 489.71 & 490.528475330758 & -0.81847533075802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13473&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]434.55[/C][C]437.74[/C][C]-3.19[/C][/ROW]
[ROW][C]4[/C][C]434.55[/C][C]437.745985081636[/C][C]-3.19598508163614[/C][/ROW]
[ROW][C]5[/C][C]434.55[/C][C]437.070705575714[/C][C]-2.52070557571415[/C][/ROW]
[ROW][C]6[/C][C]434.55[/C][C]436.538105838149[/C][C]-1.9881058381485[/C][/ROW]
[ROW][C]7[/C][C]434.71[/C][C]436.118039068807[/C][C]-1.40803906880734[/C][/ROW]
[ROW][C]8[/C][C]434.71[/C][C]435.980534574132[/C][C]-1.27053457413166[/C][/ROW]
[ROW][C]9[/C][C]434.71[/C][C]435.712083396307[/C][C]-1.00208339630660[/C][/ROW]
[ROW][C]10[/C][C]434.71[/C][C]435.500353252559[/C][C]-0.790353252558873[/C][/ROW]
[ROW][C]11[/C][C]434.73[/C][C]435.333359558828[/C][C]-0.603359558827776[/C][/ROW]
[ROW][C]12[/C][C]436.34[/C][C]435.225875751998[/C][C]1.11412424800204[/C][/ROW]
[ROW][C]13[/C][C]437.55[/C][C]437.071279000921[/C][C]0.478720999079144[/C][/ROW]
[ROW][C]14[/C][C]439.58[/C][C]438.382427933558[/C][C]1.19757206644164[/C][/ROW]
[ROW][C]15[/C][C]439.65[/C][C]440.665462867288[/C][C]-1.01546286728797[/C][/ROW]
[ROW][C]16[/C][C]439.76[/C][C]440.520905775878[/C][C]-0.760905775878314[/C][/ROW]
[ROW][C]17[/C][C]439.76[/C][C]440.470134037818[/C][C]-0.71013403781842[/C][/ROW]
[ROW][C]18[/C][C]439.76[/C][C]440.320089857402[/C][C]-0.560089857402204[/C][/ROW]
[ROW][C]19[/C][C]440.06[/C][C]440.201748503323[/C][C]-0.141748503322788[/C][/ROW]
[ROW][C]20[/C][C]440.13[/C][C]440.471798470127[/C][C]-0.341798470126776[/C][/ROW]
[ROW][C]21[/C][C]441.18[/C][C]440.469579890835[/C][C]0.710420109164602[/C][/ROW]
[ROW][C]22[/C][C]441.14[/C][C]441.66968451525[/C][C]-0.52968451525004[/C][/ROW]
[ROW][C]23[/C][C]441.14[/C][C]441.517767504183[/C][C]-0.377767504182657[/C][/ROW]
[ROW][C]24[/C][C]441.19[/C][C]441.437949029734[/C][C]-0.247949029733718[/C][/ROW]
[ROW][C]25[/C][C]449.06[/C][C]441.435559893359[/C][C]7.62444010664069[/C][/ROW]
[ROW][C]26[/C][C]456.46[/C][C]450.916527409362[/C][C]5.54347259063826[/C][/ROW]
[ROW][C]27[/C][C]456.79[/C][C]459.487807417397[/C][C]-2.69780741739663[/C][/ROW]
[ROW][C]28[/C][C]456.87[/C][C]459.247787841786[/C][C]-2.37778784178602[/C][/ROW]
[ROW][C]29[/C][C]457.25[/C][C]458.825385184084[/C][C]-1.57538518408444[/C][/ROW]
[ROW][C]30[/C][C]455.93[/C][C]458.87252213824[/C][C]-2.94252213824041[/C][/ROW]
[ROW][C]31[/C][C]456[/C][C]456.930796803197[/C][C]-0.930796803196529[/C][/ROW]
[ROW][C]32[/C][C]456.22[/C][C]456.804128799648[/C][C]-0.584128799647942[/C][/ROW]
[ROW][C]33[/C][C]456.22[/C][C]456.90070825883[/C][C]-0.68070825883018[/C][/ROW]
[ROW][C]34[/C][C]456.58[/C][C]456.756881449581[/C][C]-0.176881449581003[/C][/ROW]
[ROW][C]35[/C][C]457.61[/C][C]457.07950817817[/C][C]0.530491821829571[/C][/ROW]
[ROW][C]36[/C][C]457.61[/C][C]458.221595764999[/C][C]-0.611595764999038[/C][/ROW]
[ROW][C]37[/C][C]460.43[/C][C]458.092371730636[/C][C]2.33762826936379[/C][/ROW]
[ROW][C]38[/C][C]460.43[/C][C]461.406289074567[/C][C]-0.976289074567319[/C][/ROW]
[ROW][C]39[/C][C]462.18[/C][C]461.200009011591[/C][C]0.979990988408872[/C][/ROW]
[ROW][C]40[/C][C]462.37[/C][C]463.157071251732[/C][C]-0.78707125173213[/C][/ROW]
[ROW][C]41[/C][C]462.59[/C][C]463.180771011769[/C][C]-0.590771011768879[/C][/ROW]
[ROW][C]42[/C][C]463.19[/C][C]463.27594703833[/C][C]-0.0859470383302323[/C][/ROW]
[ROW][C]43[/C][C]463.48[/C][C]463.857787293495[/C][C]-0.377787293495203[/C][/ROW]
[ROW][C]44[/C][C]464.3[/C][C]464.067964637764[/C][C]0.232035362236445[/C][/ROW]
[ROW][C]45[/C][C]461.41[/C][C]464.936991376239[/C][C]-3.52699137623853[/C][/ROW]
[ROW][C]46[/C][C]463.35[/C][C]461.301773569177[/C][C]2.04822643082275[/C][/ROW]
[ROW][C]47[/C][C]463.35[/C][C]463.674543215121[/C][C]-0.324543215121366[/C][/ROW]
[ROW][C]48[/C][C]463.35[/C][C]463.605970497678[/C][C]-0.255970497677595[/C][/ROW]
[ROW][C]49[/C][C]464.27[/C][C]463.551886505798[/C][C]0.718113494201873[/C][/ROW]
[ROW][C]50[/C][C]472.28[/C][C]464.623616665099[/C][C]7.6563833349008[/C][/ROW]
[ROW][C]51[/C][C]472.36[/C][C]474.251333463982[/C][C]-1.89133346398182[/C][/ROW]
[ROW][C]52[/C][C]472.56[/C][C]473.931713724068[/C][C]-1.37171372406823[/C][/ROW]
[ROW][C]53[/C][C]472.56[/C][C]473.841884409414[/C][C]-1.28188440941415[/C][/ROW]
[ROW][C]54[/C][C]472.56[/C][C]473.571035125539[/C][C]-1.01103512553851[/C][/ROW]
[ROW][C]55[/C][C]474.15[/C][C]473.357413571431[/C][C]0.792586428568939[/C][/ROW]
[ROW][C]56[/C][C]474.59[/C][C]475.114879112794[/C][C]-0.52487911279411[/C][/ROW]
[ROW][C]57[/C][C]474.97[/C][C]475.443977434938[/C][C]-0.473977434937979[/C][/ROW]
[ROW][C]58[/C][C]474.99[/C][C]475.723830769698[/C][C]-0.733830769697931[/C][/ROW]
[ROW][C]59[/C][C]474.99[/C][C]475.588779708152[/C][C]-0.598779708152165[/C][/ROW]
[ROW][C]60[/C][C]474.99[/C][C]475.462263577711[/C][C]-0.472263577710748[/C][/ROW]
[ROW][C]61[/C][C]478.34[/C][C]475.362479033267[/C][C]2.97752096673338[/C][/ROW]
[ROW][C]62[/C][C]485.7[/C][C]479.34159926879[/C][C]6.35840073121005[/C][/ROW]
[ROW][C]63[/C][C]485.75[/C][C]488.045065397245[/C][C]-2.29506539724491[/C][/ROW]
[ROW][C]64[/C][C]485.85[/C][C]487.61014116014[/C][C]-1.76014116014028[/C][/ROW]
[ROW][C]65[/C][C]485.84[/C][C]487.338241034635[/C][C]-1.49824103463538[/C][/ROW]
[ROW][C]66[/C][C]485.85[/C][C]487.011677771736[/C][C]-1.16167777173587[/C][/ROW]
[ROW][C]67[/C][C]485.84[/C][C]486.776226941491[/C][C]-0.93622694149093[/C][/ROW]
[ROW][C]68[/C][C]486[/C][C]486.568411604331[/C][C]-0.568411604331232[/C][/ROW]
[ROW][C]69[/C][C]488.79[/C][C]486.608311948817[/C][C]2.18168805118296[/C][/ROW]
[ROW][C]70[/C][C]489.71[/C][C]489.859280692928[/C][C]-0.149280692927903[/C][/ROW]
[ROW][C]71[/C][C]489.71[/C][C]490.747739183819[/C][C]-1.03773918381904[/C][/ROW]
[ROW][C]72[/C][C]489.71[/C][C]490.528475330758[/C][C]-0.81847533075802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13473&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13473&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
3434.55437.74-3.19
4434.55437.745985081636-3.19598508163614
5434.55437.070705575714-2.52070557571415
6434.55436.538105838149-1.9881058381485
7434.71436.118039068807-1.40803906880734
8434.71435.980534574132-1.27053457413166
9434.71435.712083396307-1.00208339630660
10434.71435.500353252559-0.790353252558873
11434.73435.333359558828-0.603359558827776
12436.34435.2258757519981.11412424800204
13437.55437.0712790009210.478720999079144
14439.58438.3824279335581.19757206644164
15439.65440.665462867288-1.01546286728797
16439.76440.520905775878-0.760905775878314
17439.76440.470134037818-0.71013403781842
18439.76440.320089857402-0.560089857402204
19440.06440.201748503323-0.141748503322788
20440.13440.471798470127-0.341798470126776
21441.18440.4695798908350.710420109164602
22441.14441.66968451525-0.52968451525004
23441.14441.517767504183-0.377767504182657
24441.19441.437949029734-0.247949029733718
25449.06441.4355598933597.62444010664069
26456.46450.9165274093625.54347259063826
27456.79459.487807417397-2.69780741739663
28456.87459.247787841786-2.37778784178602
29457.25458.825385184084-1.57538518408444
30455.93458.87252213824-2.94252213824041
31456456.930796803197-0.930796803196529
32456.22456.804128799648-0.584128799647942
33456.22456.90070825883-0.68070825883018
34456.58456.756881449581-0.176881449581003
35457.61457.079508178170.530491821829571
36457.61458.221595764999-0.611595764999038
37460.43458.0923717306362.33762826936379
38460.43461.406289074567-0.976289074567319
39462.18461.2000090115910.979990988408872
40462.37463.157071251732-0.78707125173213
41462.59463.180771011769-0.590771011768879
42463.19463.27594703833-0.0859470383302323
43463.48463.857787293495-0.377787293495203
44464.3464.0679646377640.232035362236445
45461.41464.936991376239-3.52699137623853
46463.35461.3017735691772.04822643082275
47463.35463.674543215121-0.324543215121366
48463.35463.605970497678-0.255970497677595
49464.27463.5518865057980.718113494201873
50472.28464.6236166650997.6563833349008
51472.36474.251333463982-1.89133346398182
52472.56473.931713724068-1.37171372406823
53472.56473.841884409414-1.28188440941415
54472.56473.571035125539-1.01103512553851
55474.15473.3574135714310.792586428568939
56474.59475.114879112794-0.52487911279411
57474.97475.443977434938-0.473977434937979
58474.99475.723830769698-0.733830769697931
59474.99475.588779708152-0.598779708152165
60474.99475.462263577711-0.472263577710748
61478.34475.3624790332672.97752096673338
62485.7479.341599268796.35840073121005
63485.75488.045065397245-2.29506539724491
64485.85487.61014116014-1.76014116014028
65485.84487.338241034635-1.49824103463538
66485.85487.011677771736-1.16167777173587
67485.84486.776226941491-0.93622694149093
68486486.568411604331-0.568411604331232
69488.79486.6083119488172.18168805118296
70489.71489.859280692928-0.149280692927903
71489.71490.747739183819-1.03773918381904
72489.71490.528475330758-0.81847533075802







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73490.355539724725486.144219835997494.566859613454
74491.001079449451484.386191948613497.615966950289
75491.646619174176482.72204151673500.571196831623
76492.292158898902481.023051286338503.561266511465
77492.937698623627479.249223224916506.626174022339
78493.583238348353477.385203730852509.781272965853
79494.228778073078475.424996309759513.032559836398
80494.874317797804473.366748661039516.381886934569
81495.519857522529471.210603889119519.829111155939
82496.165397247255468.957703909563523.373090584947
83496.81093697198466.609689550074527.012184393887
84497.456476696706464.168436179268530.744517214143

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 490.355539724725 & 486.144219835997 & 494.566859613454 \tabularnewline
74 & 491.001079449451 & 484.386191948613 & 497.615966950289 \tabularnewline
75 & 491.646619174176 & 482.72204151673 & 500.571196831623 \tabularnewline
76 & 492.292158898902 & 481.023051286338 & 503.561266511465 \tabularnewline
77 & 492.937698623627 & 479.249223224916 & 506.626174022339 \tabularnewline
78 & 493.583238348353 & 477.385203730852 & 509.781272965853 \tabularnewline
79 & 494.228778073078 & 475.424996309759 & 513.032559836398 \tabularnewline
80 & 494.874317797804 & 473.366748661039 & 516.381886934569 \tabularnewline
81 & 495.519857522529 & 471.210603889119 & 519.829111155939 \tabularnewline
82 & 496.165397247255 & 468.957703909563 & 523.373090584947 \tabularnewline
83 & 496.81093697198 & 466.609689550074 & 527.012184393887 \tabularnewline
84 & 497.456476696706 & 464.168436179268 & 530.744517214143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13473&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]490.355539724725[/C][C]486.144219835997[/C][C]494.566859613454[/C][/ROW]
[ROW][C]74[/C][C]491.001079449451[/C][C]484.386191948613[/C][C]497.615966950289[/C][/ROW]
[ROW][C]75[/C][C]491.646619174176[/C][C]482.72204151673[/C][C]500.571196831623[/C][/ROW]
[ROW][C]76[/C][C]492.292158898902[/C][C]481.023051286338[/C][C]503.561266511465[/C][/ROW]
[ROW][C]77[/C][C]492.937698623627[/C][C]479.249223224916[/C][C]506.626174022339[/C][/ROW]
[ROW][C]78[/C][C]493.583238348353[/C][C]477.385203730852[/C][C]509.781272965853[/C][/ROW]
[ROW][C]79[/C][C]494.228778073078[/C][C]475.424996309759[/C][C]513.032559836398[/C][/ROW]
[ROW][C]80[/C][C]494.874317797804[/C][C]473.366748661039[/C][C]516.381886934569[/C][/ROW]
[ROW][C]81[/C][C]495.519857522529[/C][C]471.210603889119[/C][C]519.829111155939[/C][/ROW]
[ROW][C]82[/C][C]496.165397247255[/C][C]468.957703909563[/C][C]523.373090584947[/C][/ROW]
[ROW][C]83[/C][C]496.81093697198[/C][C]466.609689550074[/C][C]527.012184393887[/C][/ROW]
[ROW][C]84[/C][C]497.456476696706[/C][C]464.168436179268[/C][C]530.744517214143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13473&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13473&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
73490.355539724725486.144219835997494.566859613454
74491.001079449451484.386191948613497.615966950289
75491.646619174176482.72204151673500.571196831623
76492.292158898902481.023051286338503.561266511465
77492.937698623627479.249223224916506.626174022339
78493.583238348353477.385203730852509.781272965853
79494.228778073078475.424996309759513.032559836398
80494.874317797804473.366748661039516.381886934569
81495.519857522529471.210603889119519.829111155939
82496.165397247255468.957703909563523.373090584947
83496.81093697198466.609689550074527.012184393887
84497.456476696706464.168436179268530.744517214143



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