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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Dec 2013 13:02:18 -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/2013/Dec/16/t1387216987gw3v5x167uqweq5.htm/, Retrieved Fri, 29 Mar 2024 08:33:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232395, Retrieved Fri, 29 Mar 2024 08:33:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-16 18:02:18] [23be8e4142dc0b2e5f6a7ba847207dc8] [Current]
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Dataseries X:
1,65
1,66
1,66
1,67
1,68
1,68
1,68
1,68
1,69
1,7
1,7
1,71
1,72
1,73
1,74
1,74
1,75
1,75
1,75
1,76
1,79
1,83
1,84
1,85
1,87
1,87
1,87
1,88
1,88
1,88
1,88
1,89
1,89
1,89
1,9
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,9
1,9
1,92
1,93
1,92
1,95
1,96
1,96
1,96
1,96
1,96
1,97
1,97
1,97
1,97
1,97
1,97
1,98
1,98
1,98
1,98
1,98
1,98
1,97
1,98
1,98
1,99
2
2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232395&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232395&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232395&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.838349047626254
beta0.166586826882942
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.838349047626254 \tabularnewline
beta & 0.166586826882942 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232395&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]0.838349047626254[/C][/ROW]
[ROW][C]beta[/C][C]0.166586826882942[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232395&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232395&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
alpha0.838349047626254
beta0.166586826882942
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.721.683816773504270.0361832264957267
141.731.7300506659034-5.06659033958634e-05
151.741.74465083322386-0.00465083322386417
161.741.74266159568202-0.00266159568202218
171.751.75030165398822-0.000301653988219019
181.751.749461372134370.000538627865630747
191.751.77315076341316-0.0231507634131556
201.761.755830322228750.00416967777125499
211.791.771579608698520.0184203913014842
221.831.801848520591870.028151479408127
231.841.834623724310260.00537627568973575
241.851.8590561970957-0.00905619709570393
251.871.87597350355179-0.00597350355178494
261.871.88251797329288-0.012517973292884
271.871.88569128088713-0.0156912808871252
281.881.872994687862870.00700531213712563
291.881.88869736723302-0.00869736723301817
301.881.879358743070990.000641256929010181
311.881.89772345715901-0.017723457159011
321.891.888546031069440.00145396893056082
331.891.9031196395474-0.0131196395474034
341.891.90291261407479-0.0129126140747911
351.91.886237793180830.0137622068191743
361.891.90519639438884-0.0151963943888371
371.891.90643567955025-0.0164356795502503
381.891.89066143554196-0.000661435541962074
391.891.89242771262894-0.00242771262894137
401.891.885537928047070.00446207195293225
411.891.887233330500090.00276666949991355
421.891.881279410632410.00872058936759346
431.891.89684133704476-0.00684133704475776
441.891.89479933449808-0.00479933449807812
451.891.8958136903568-0.0058136903568029
461.891.89682443591707-0.00682443591707393
471.891.885475275430440.00452472456956232
481.891.886628001129390.00337199887061246
491.891.90044651682256-0.0104465168225609
501.891.89029240453859-0.000292404538592139
511.891.89018327742889-0.000183277428885686
521.891.884703045709040.00529695429096422
531.891.88535509798460.0046449020153998
541.891.880731349828450.00926865017154954
551.891.89310678374765-0.00310678374765039
561.91.8939169334360.00608306656399682
571.91.90480158301176-0.00480158301176359
581.921.907549803353930.0124501966460746
591.931.917938333711530.0120616662884661
601.921.93002012001641-0.0100201200164072
611.951.933304085970730.0166959140292704
621.961.954263378362530.00573662163746658
631.961.96678547298752-0.00678547298752052
641.961.96329328564855-0.00329328564854658
651.961.96207572270727-0.00207572270726875
661.961.95706399924810.00293600075190126
671.971.965744378050090.00425562194990725
681.971.97885497594516-0.0088549759451626
691.971.97801323642524-0.00801323642524299
701.971.98296562258832-0.0129656225883212
711.971.97054238444753-0.000542384447528077
721.971.96528614533520.0047138546648049
731.981.9840968236538-0.00409682365379616
741.981.98180492029495-0.00180492029495172
751.981.98087908207054-0.000879082070544879
761.981.978626621707380.00137337829262307
771.981.977893503134040.00210649686596187
781.981.974157500264480.00584249973551576
791.971.98285318423465-0.0128531842346542
801.981.974477236538480.00552276346151803
811.981.98280904057023-0.00280904057023235
821.991.989034519954440.000965480045563183
8321.989954943883680.0100450561163226
8421.995559278507440.00444072149256258

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.72 & 1.68381677350427 & 0.0361832264957267 \tabularnewline
14 & 1.73 & 1.7300506659034 & -5.06659033958634e-05 \tabularnewline
15 & 1.74 & 1.74465083322386 & -0.00465083322386417 \tabularnewline
16 & 1.74 & 1.74266159568202 & -0.00266159568202218 \tabularnewline
17 & 1.75 & 1.75030165398822 & -0.000301653988219019 \tabularnewline
18 & 1.75 & 1.74946137213437 & 0.000538627865630747 \tabularnewline
19 & 1.75 & 1.77315076341316 & -0.0231507634131556 \tabularnewline
20 & 1.76 & 1.75583032222875 & 0.00416967777125499 \tabularnewline
21 & 1.79 & 1.77157960869852 & 0.0184203913014842 \tabularnewline
22 & 1.83 & 1.80184852059187 & 0.028151479408127 \tabularnewline
23 & 1.84 & 1.83462372431026 & 0.00537627568973575 \tabularnewline
24 & 1.85 & 1.8590561970957 & -0.00905619709570393 \tabularnewline
25 & 1.87 & 1.87597350355179 & -0.00597350355178494 \tabularnewline
26 & 1.87 & 1.88251797329288 & -0.012517973292884 \tabularnewline
27 & 1.87 & 1.88569128088713 & -0.0156912808871252 \tabularnewline
28 & 1.88 & 1.87299468786287 & 0.00700531213712563 \tabularnewline
29 & 1.88 & 1.88869736723302 & -0.00869736723301817 \tabularnewline
30 & 1.88 & 1.87935874307099 & 0.000641256929010181 \tabularnewline
31 & 1.88 & 1.89772345715901 & -0.017723457159011 \tabularnewline
32 & 1.89 & 1.88854603106944 & 0.00145396893056082 \tabularnewline
33 & 1.89 & 1.9031196395474 & -0.0131196395474034 \tabularnewline
34 & 1.89 & 1.90291261407479 & -0.0129126140747911 \tabularnewline
35 & 1.9 & 1.88623779318083 & 0.0137622068191743 \tabularnewline
36 & 1.89 & 1.90519639438884 & -0.0151963943888371 \tabularnewline
37 & 1.89 & 1.90643567955025 & -0.0164356795502503 \tabularnewline
38 & 1.89 & 1.89066143554196 & -0.000661435541962074 \tabularnewline
39 & 1.89 & 1.89242771262894 & -0.00242771262894137 \tabularnewline
40 & 1.89 & 1.88553792804707 & 0.00446207195293225 \tabularnewline
41 & 1.89 & 1.88723333050009 & 0.00276666949991355 \tabularnewline
42 & 1.89 & 1.88127941063241 & 0.00872058936759346 \tabularnewline
43 & 1.89 & 1.89684133704476 & -0.00684133704475776 \tabularnewline
44 & 1.89 & 1.89479933449808 & -0.00479933449807812 \tabularnewline
45 & 1.89 & 1.8958136903568 & -0.0058136903568029 \tabularnewline
46 & 1.89 & 1.89682443591707 & -0.00682443591707393 \tabularnewline
47 & 1.89 & 1.88547527543044 & 0.00452472456956232 \tabularnewline
48 & 1.89 & 1.88662800112939 & 0.00337199887061246 \tabularnewline
49 & 1.89 & 1.90044651682256 & -0.0104465168225609 \tabularnewline
50 & 1.89 & 1.89029240453859 & -0.000292404538592139 \tabularnewline
51 & 1.89 & 1.89018327742889 & -0.000183277428885686 \tabularnewline
52 & 1.89 & 1.88470304570904 & 0.00529695429096422 \tabularnewline
53 & 1.89 & 1.8853550979846 & 0.0046449020153998 \tabularnewline
54 & 1.89 & 1.88073134982845 & 0.00926865017154954 \tabularnewline
55 & 1.89 & 1.89310678374765 & -0.00310678374765039 \tabularnewline
56 & 1.9 & 1.893916933436 & 0.00608306656399682 \tabularnewline
57 & 1.9 & 1.90480158301176 & -0.00480158301176359 \tabularnewline
58 & 1.92 & 1.90754980335393 & 0.0124501966460746 \tabularnewline
59 & 1.93 & 1.91793833371153 & 0.0120616662884661 \tabularnewline
60 & 1.92 & 1.93002012001641 & -0.0100201200164072 \tabularnewline
61 & 1.95 & 1.93330408597073 & 0.0166959140292704 \tabularnewline
62 & 1.96 & 1.95426337836253 & 0.00573662163746658 \tabularnewline
63 & 1.96 & 1.96678547298752 & -0.00678547298752052 \tabularnewline
64 & 1.96 & 1.96329328564855 & -0.00329328564854658 \tabularnewline
65 & 1.96 & 1.96207572270727 & -0.00207572270726875 \tabularnewline
66 & 1.96 & 1.9570639992481 & 0.00293600075190126 \tabularnewline
67 & 1.97 & 1.96574437805009 & 0.00425562194990725 \tabularnewline
68 & 1.97 & 1.97885497594516 & -0.0088549759451626 \tabularnewline
69 & 1.97 & 1.97801323642524 & -0.00801323642524299 \tabularnewline
70 & 1.97 & 1.98296562258832 & -0.0129656225883212 \tabularnewline
71 & 1.97 & 1.97054238444753 & -0.000542384447528077 \tabularnewline
72 & 1.97 & 1.9652861453352 & 0.0047138546648049 \tabularnewline
73 & 1.98 & 1.9840968236538 & -0.00409682365379616 \tabularnewline
74 & 1.98 & 1.98180492029495 & -0.00180492029495172 \tabularnewline
75 & 1.98 & 1.98087908207054 & -0.000879082070544879 \tabularnewline
76 & 1.98 & 1.97862662170738 & 0.00137337829262307 \tabularnewline
77 & 1.98 & 1.97789350313404 & 0.00210649686596187 \tabularnewline
78 & 1.98 & 1.97415750026448 & 0.00584249973551576 \tabularnewline
79 & 1.97 & 1.98285318423465 & -0.0128531842346542 \tabularnewline
80 & 1.98 & 1.97447723653848 & 0.00552276346151803 \tabularnewline
81 & 1.98 & 1.98280904057023 & -0.00280904057023235 \tabularnewline
82 & 1.99 & 1.98903451995444 & 0.000965480045563183 \tabularnewline
83 & 2 & 1.98995494388368 & 0.0100450561163226 \tabularnewline
84 & 2 & 1.99555927850744 & 0.00444072149256258 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232395&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]13[/C][C]1.72[/C][C]1.68381677350427[/C][C]0.0361832264957267[/C][/ROW]
[ROW][C]14[/C][C]1.73[/C][C]1.7300506659034[/C][C]-5.06659033958634e-05[/C][/ROW]
[ROW][C]15[/C][C]1.74[/C][C]1.74465083322386[/C][C]-0.00465083322386417[/C][/ROW]
[ROW][C]16[/C][C]1.74[/C][C]1.74266159568202[/C][C]-0.00266159568202218[/C][/ROW]
[ROW][C]17[/C][C]1.75[/C][C]1.75030165398822[/C][C]-0.000301653988219019[/C][/ROW]
[ROW][C]18[/C][C]1.75[/C][C]1.74946137213437[/C][C]0.000538627865630747[/C][/ROW]
[ROW][C]19[/C][C]1.75[/C][C]1.77315076341316[/C][C]-0.0231507634131556[/C][/ROW]
[ROW][C]20[/C][C]1.76[/C][C]1.75583032222875[/C][C]0.00416967777125499[/C][/ROW]
[ROW][C]21[/C][C]1.79[/C][C]1.77157960869852[/C][C]0.0184203913014842[/C][/ROW]
[ROW][C]22[/C][C]1.83[/C][C]1.80184852059187[/C][C]0.028151479408127[/C][/ROW]
[ROW][C]23[/C][C]1.84[/C][C]1.83462372431026[/C][C]0.00537627568973575[/C][/ROW]
[ROW][C]24[/C][C]1.85[/C][C]1.8590561970957[/C][C]-0.00905619709570393[/C][/ROW]
[ROW][C]25[/C][C]1.87[/C][C]1.87597350355179[/C][C]-0.00597350355178494[/C][/ROW]
[ROW][C]26[/C][C]1.87[/C][C]1.88251797329288[/C][C]-0.012517973292884[/C][/ROW]
[ROW][C]27[/C][C]1.87[/C][C]1.88569128088713[/C][C]-0.0156912808871252[/C][/ROW]
[ROW][C]28[/C][C]1.88[/C][C]1.87299468786287[/C][C]0.00700531213712563[/C][/ROW]
[ROW][C]29[/C][C]1.88[/C][C]1.88869736723302[/C][C]-0.00869736723301817[/C][/ROW]
[ROW][C]30[/C][C]1.88[/C][C]1.87935874307099[/C][C]0.000641256929010181[/C][/ROW]
[ROW][C]31[/C][C]1.88[/C][C]1.89772345715901[/C][C]-0.017723457159011[/C][/ROW]
[ROW][C]32[/C][C]1.89[/C][C]1.88854603106944[/C][C]0.00145396893056082[/C][/ROW]
[ROW][C]33[/C][C]1.89[/C][C]1.9031196395474[/C][C]-0.0131196395474034[/C][/ROW]
[ROW][C]34[/C][C]1.89[/C][C]1.90291261407479[/C][C]-0.0129126140747911[/C][/ROW]
[ROW][C]35[/C][C]1.9[/C][C]1.88623779318083[/C][C]0.0137622068191743[/C][/ROW]
[ROW][C]36[/C][C]1.89[/C][C]1.90519639438884[/C][C]-0.0151963943888371[/C][/ROW]
[ROW][C]37[/C][C]1.89[/C][C]1.90643567955025[/C][C]-0.0164356795502503[/C][/ROW]
[ROW][C]38[/C][C]1.89[/C][C]1.89066143554196[/C][C]-0.000661435541962074[/C][/ROW]
[ROW][C]39[/C][C]1.89[/C][C]1.89242771262894[/C][C]-0.00242771262894137[/C][/ROW]
[ROW][C]40[/C][C]1.89[/C][C]1.88553792804707[/C][C]0.00446207195293225[/C][/ROW]
[ROW][C]41[/C][C]1.89[/C][C]1.88723333050009[/C][C]0.00276666949991355[/C][/ROW]
[ROW][C]42[/C][C]1.89[/C][C]1.88127941063241[/C][C]0.00872058936759346[/C][/ROW]
[ROW][C]43[/C][C]1.89[/C][C]1.89684133704476[/C][C]-0.00684133704475776[/C][/ROW]
[ROW][C]44[/C][C]1.89[/C][C]1.89479933449808[/C][C]-0.00479933449807812[/C][/ROW]
[ROW][C]45[/C][C]1.89[/C][C]1.8958136903568[/C][C]-0.0058136903568029[/C][/ROW]
[ROW][C]46[/C][C]1.89[/C][C]1.89682443591707[/C][C]-0.00682443591707393[/C][/ROW]
[ROW][C]47[/C][C]1.89[/C][C]1.88547527543044[/C][C]0.00452472456956232[/C][/ROW]
[ROW][C]48[/C][C]1.89[/C][C]1.88662800112939[/C][C]0.00337199887061246[/C][/ROW]
[ROW][C]49[/C][C]1.89[/C][C]1.90044651682256[/C][C]-0.0104465168225609[/C][/ROW]
[ROW][C]50[/C][C]1.89[/C][C]1.89029240453859[/C][C]-0.000292404538592139[/C][/ROW]
[ROW][C]51[/C][C]1.89[/C][C]1.89018327742889[/C][C]-0.000183277428885686[/C][/ROW]
[ROW][C]52[/C][C]1.89[/C][C]1.88470304570904[/C][C]0.00529695429096422[/C][/ROW]
[ROW][C]53[/C][C]1.89[/C][C]1.8853550979846[/C][C]0.0046449020153998[/C][/ROW]
[ROW][C]54[/C][C]1.89[/C][C]1.88073134982845[/C][C]0.00926865017154954[/C][/ROW]
[ROW][C]55[/C][C]1.89[/C][C]1.89310678374765[/C][C]-0.00310678374765039[/C][/ROW]
[ROW][C]56[/C][C]1.9[/C][C]1.893916933436[/C][C]0.00608306656399682[/C][/ROW]
[ROW][C]57[/C][C]1.9[/C][C]1.90480158301176[/C][C]-0.00480158301176359[/C][/ROW]
[ROW][C]58[/C][C]1.92[/C][C]1.90754980335393[/C][C]0.0124501966460746[/C][/ROW]
[ROW][C]59[/C][C]1.93[/C][C]1.91793833371153[/C][C]0.0120616662884661[/C][/ROW]
[ROW][C]60[/C][C]1.92[/C][C]1.93002012001641[/C][C]-0.0100201200164072[/C][/ROW]
[ROW][C]61[/C][C]1.95[/C][C]1.93330408597073[/C][C]0.0166959140292704[/C][/ROW]
[ROW][C]62[/C][C]1.96[/C][C]1.95426337836253[/C][C]0.00573662163746658[/C][/ROW]
[ROW][C]63[/C][C]1.96[/C][C]1.96678547298752[/C][C]-0.00678547298752052[/C][/ROW]
[ROW][C]64[/C][C]1.96[/C][C]1.96329328564855[/C][C]-0.00329328564854658[/C][/ROW]
[ROW][C]65[/C][C]1.96[/C][C]1.96207572270727[/C][C]-0.00207572270726875[/C][/ROW]
[ROW][C]66[/C][C]1.96[/C][C]1.9570639992481[/C][C]0.00293600075190126[/C][/ROW]
[ROW][C]67[/C][C]1.97[/C][C]1.96574437805009[/C][C]0.00425562194990725[/C][/ROW]
[ROW][C]68[/C][C]1.97[/C][C]1.97885497594516[/C][C]-0.0088549759451626[/C][/ROW]
[ROW][C]69[/C][C]1.97[/C][C]1.97801323642524[/C][C]-0.00801323642524299[/C][/ROW]
[ROW][C]70[/C][C]1.97[/C][C]1.98296562258832[/C][C]-0.0129656225883212[/C][/ROW]
[ROW][C]71[/C][C]1.97[/C][C]1.97054238444753[/C][C]-0.000542384447528077[/C][/ROW]
[ROW][C]72[/C][C]1.97[/C][C]1.9652861453352[/C][C]0.0047138546648049[/C][/ROW]
[ROW][C]73[/C][C]1.98[/C][C]1.9840968236538[/C][C]-0.00409682365379616[/C][/ROW]
[ROW][C]74[/C][C]1.98[/C][C]1.98180492029495[/C][C]-0.00180492029495172[/C][/ROW]
[ROW][C]75[/C][C]1.98[/C][C]1.98087908207054[/C][C]-0.000879082070544879[/C][/ROW]
[ROW][C]76[/C][C]1.98[/C][C]1.97862662170738[/C][C]0.00137337829262307[/C][/ROW]
[ROW][C]77[/C][C]1.98[/C][C]1.97789350313404[/C][C]0.00210649686596187[/C][/ROW]
[ROW][C]78[/C][C]1.98[/C][C]1.97415750026448[/C][C]0.00584249973551576[/C][/ROW]
[ROW][C]79[/C][C]1.97[/C][C]1.98285318423465[/C][C]-0.0128531842346542[/C][/ROW]
[ROW][C]80[/C][C]1.98[/C][C]1.97447723653848[/C][C]0.00552276346151803[/C][/ROW]
[ROW][C]81[/C][C]1.98[/C][C]1.98280904057023[/C][C]-0.00280904057023235[/C][/ROW]
[ROW][C]82[/C][C]1.99[/C][C]1.98903451995444[/C][C]0.000965480045563183[/C][/ROW]
[ROW][C]83[/C][C]2[/C][C]1.98995494388368[/C][C]0.0100450561163226[/C][/ROW]
[ROW][C]84[/C][C]2[/C][C]1.99555927850744[/C][C]0.00444072149256258[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232395&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232395&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
131.721.683816773504270.0361832264957267
141.731.7300506659034-5.06659033958634e-05
151.741.74465083322386-0.00465083322386417
161.741.74266159568202-0.00266159568202218
171.751.75030165398822-0.000301653988219019
181.751.749461372134370.000538627865630747
191.751.77315076341316-0.0231507634131556
201.761.755830322228750.00416967777125499
211.791.771579608698520.0184203913014842
221.831.801848520591870.028151479408127
231.841.834623724310260.00537627568973575
241.851.8590561970957-0.00905619709570393
251.871.87597350355179-0.00597350355178494
261.871.88251797329288-0.012517973292884
271.871.88569128088713-0.0156912808871252
281.881.872994687862870.00700531213712563
291.881.88869736723302-0.00869736723301817
301.881.879358743070990.000641256929010181
311.881.89772345715901-0.017723457159011
321.891.888546031069440.00145396893056082
331.891.9031196395474-0.0131196395474034
341.891.90291261407479-0.0129126140747911
351.91.886237793180830.0137622068191743
361.891.90519639438884-0.0151963943888371
371.891.90643567955025-0.0164356795502503
381.891.89066143554196-0.000661435541962074
391.891.89242771262894-0.00242771262894137
401.891.885537928047070.00446207195293225
411.891.887233330500090.00276666949991355
421.891.881279410632410.00872058936759346
431.891.89684133704476-0.00684133704475776
441.891.89479933449808-0.00479933449807812
451.891.8958136903568-0.0058136903568029
461.891.89682443591707-0.00682443591707393
471.891.885475275430440.00452472456956232
481.891.886628001129390.00337199887061246
491.891.90044651682256-0.0104465168225609
501.891.89029240453859-0.000292404538592139
511.891.89018327742889-0.000183277428885686
521.891.884703045709040.00529695429096422
531.891.88535509798460.0046449020153998
541.891.880731349828450.00926865017154954
551.891.89310678374765-0.00310678374765039
561.91.8939169334360.00608306656399682
571.91.90480158301176-0.00480158301176359
581.921.907549803353930.0124501966460746
591.931.917938333711530.0120616662884661
601.921.93002012001641-0.0100201200164072
611.951.933304085970730.0166959140292704
621.961.954263378362530.00573662163746658
631.961.96678547298752-0.00678547298752052
641.961.96329328564855-0.00329328564854658
651.961.96207572270727-0.00207572270726875
661.961.95706399924810.00293600075190126
671.971.965744378050090.00425562194990725
681.971.97885497594516-0.0088549759451626
691.971.97801323642524-0.00801323642524299
701.971.98296562258832-0.0129656225883212
711.971.97054238444753-0.000542384447528077
721.971.96528614533520.0047138546648049
731.981.9840968236538-0.00409682365379616
741.981.98180492029495-0.00180492029495172
751.981.98087908207054-0.000879082070544879
761.981.978626621707380.00137337829262307
771.981.977893503134040.00210649686596187
781.981.974157500264480.00584249973551576
791.971.98285318423465-0.0128531842346542
801.981.974477236538480.00552276346151803
811.981.98280904057023-0.00280904057023235
821.991.989034519954440.000965480045563183
8321.989954943883680.0100450561163226
8421.995559278507440.00444072149256258







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
852.013813503106781.994129274021582.03349773219199
862.016995591893481.989462304309812.04452887947715
872.019653576478391.984410162083212.05489699087356
882.020545983825651.977480539251432.06361142839988
892.020631978776391.969535997113392.07172796043938
902.01729171033471.957913992477582.07666942819181
912.018808999455531.950878967317162.0867390315939
922.026715879143081.949954940835822.10347681745034
932.03083642121611.944963927535692.11670891489652
942.04218490225421.946921402045212.13744840246319
952.045786692417481.940855742760872.1507176420741
962.042683999655591.927813163562582.1575548357486

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2.01381350310678 & 1.99412927402158 & 2.03349773219199 \tabularnewline
86 & 2.01699559189348 & 1.98946230430981 & 2.04452887947715 \tabularnewline
87 & 2.01965357647839 & 1.98441016208321 & 2.05489699087356 \tabularnewline
88 & 2.02054598382565 & 1.97748053925143 & 2.06361142839988 \tabularnewline
89 & 2.02063197877639 & 1.96953599711339 & 2.07172796043938 \tabularnewline
90 & 2.0172917103347 & 1.95791399247758 & 2.07666942819181 \tabularnewline
91 & 2.01880899945553 & 1.95087896731716 & 2.0867390315939 \tabularnewline
92 & 2.02671587914308 & 1.94995494083582 & 2.10347681745034 \tabularnewline
93 & 2.0308364212161 & 1.94496392753569 & 2.11670891489652 \tabularnewline
94 & 2.0421849022542 & 1.94692140204521 & 2.13744840246319 \tabularnewline
95 & 2.04578669241748 & 1.94085574276087 & 2.1507176420741 \tabularnewline
96 & 2.04268399965559 & 1.92781316356258 & 2.1575548357486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232395&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]2.01381350310678[/C][C]1.99412927402158[/C][C]2.03349773219199[/C][/ROW]
[ROW][C]86[/C][C]2.01699559189348[/C][C]1.98946230430981[/C][C]2.04452887947715[/C][/ROW]
[ROW][C]87[/C][C]2.01965357647839[/C][C]1.98441016208321[/C][C]2.05489699087356[/C][/ROW]
[ROW][C]88[/C][C]2.02054598382565[/C][C]1.97748053925143[/C][C]2.06361142839988[/C][/ROW]
[ROW][C]89[/C][C]2.02063197877639[/C][C]1.96953599711339[/C][C]2.07172796043938[/C][/ROW]
[ROW][C]90[/C][C]2.0172917103347[/C][C]1.95791399247758[/C][C]2.07666942819181[/C][/ROW]
[ROW][C]91[/C][C]2.01880899945553[/C][C]1.95087896731716[/C][C]2.0867390315939[/C][/ROW]
[ROW][C]92[/C][C]2.02671587914308[/C][C]1.94995494083582[/C][C]2.10347681745034[/C][/ROW]
[ROW][C]93[/C][C]2.0308364212161[/C][C]1.94496392753569[/C][C]2.11670891489652[/C][/ROW]
[ROW][C]94[/C][C]2.0421849022542[/C][C]1.94692140204521[/C][C]2.13744840246319[/C][/ROW]
[ROW][C]95[/C][C]2.04578669241748[/C][C]1.94085574276087[/C][C]2.1507176420741[/C][/ROW]
[ROW][C]96[/C][C]2.04268399965559[/C][C]1.92781316356258[/C][C]2.1575548357486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232395&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232395&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
852.013813503106781.994129274021582.03349773219199
862.016995591893481.989462304309812.04452887947715
872.019653576478391.984410162083212.05489699087356
882.020545983825651.977480539251432.06361142839988
892.020631978776391.969535997113392.07172796043938
902.01729171033471.957913992477582.07666942819181
912.018808999455531.950878967317162.0867390315939
922.026715879143081.949954940835822.10347681745034
932.03083642121611.944963927535692.11670891489652
942.04218490225421.946921402045212.13744840246319
952.045786692417481.940855742760872.1507176420741
962.042683999655591.927813163562582.1575548357486



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