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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 13:05:26 -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/2009/Jun/02/t1243969573b314re07dxo1nu2.htm/, Retrieved Thu, 09 May 2024 21:54:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41379, Retrieved Thu, 09 May 2024 21:54:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave10oef2-Mere...] [2009-06-02 19:05:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
672.1
674.4
676.6
678.7
680.8
682.9
684
684.1
684.1
684.2
685.9
689.2
692.4
695.7
697.2
696.8
696.4
695.9
696.2
697.2
705.2
706.2
707.4
708.7
710
711.3
711.5
710.7
710
709.2
707.9
706.1
704.4
702.7
701.5
700.8
700
699.3
698.8
698.4
696.8
695.1
694.3
693.4
692.4
691
689.7
688.3
686
683.6
682.6
681.9
681
679.9
678.5
677.5
678
679
679.8
681.3
684.2
687
688.4
689.5
691.1
693.3
695.9
698
699.6
701.6
703.5
705.5
708.1
709.6
710.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41379&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41379&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.90268835297018
beta0.176277296760850
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.90268835297018 \tabularnewline
beta & 0.176277296760850 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41379&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]0.90268835297018[/C][/ROW]
[ROW][C]beta[/C][C]0.176277296760850[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41379&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
alpha0.90268835297018
beta0.176277296760850
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13692.4684.0051451236528.39485487634829
14695.7696.594880733925-0.894880733925334
15697.2698.486464448622-1.28646444862147
16696.8697.544674972548-0.744674972548069
17696.4696.955381403424-0.555381403424462
18695.9696.451132961243-0.551132961242729
19696.2702.754426404273-6.55442640427282
20697.2696.2530129881380.946987011861552
21705.2696.5600814596238.63991854037715
22706.2705.4056564459390.794343554061243
23707.4709.157720691802-1.75772069180198
24708.7712.198845026445-3.49884502644522
25710713.99324936466-3.99324936466064
26711.3713.02706703545-1.72706703544986
27711.5712.493418892771-0.993418892770933
28710.7710.2395793643260.460420635674041
29710709.3241377416630.67586225833702
30709.2708.6998413141630.500158685837505
31707.9714.412560412607-6.51256041260751
32706.1707.641520449921-1.54152044992099
33704.4705.013467569147-0.613467569147474
34702.7701.8657908119070.834209188093041
35701.5702.531651568538-1.03165156853834
36700.8703.275296545231-2.47529654523146
37700703.297219569422-3.29721956942183
38699.3700.648722065727-1.34872206572754
39698.8698.0768571280410.723142871959453
40698.4695.3808600797033.01913992029665
41696.8695.0780227810151.72197721898533
42695.1693.8377133105251.26228668947465
43694.3698.009258771678-3.70925877167838
44693.4693.2350551356970.164944864302583
45692.4691.5016138783110.898386121688645
46691689.3854936474551.61450635254516
47689.7690.189028164016-0.489028164015735
48688.3690.948805642573-2.64880564257339
49686690.351764831617-4.35176483161717
50683.6686.406798071727-2.80679807172692
51682.6681.9814128099020.618587190098424
52681.9678.7080195382643.19198046173631
53681677.772730799733.2272692002698
54679.9677.4223595591032.47764044089661
55678.5681.856404706074-3.35640470607404
56677.5677.551304835978-0.0513048359782715
57678675.4515836915932.54841630840667
58679674.9381546780454.06184532195516
59679.8678.1413212729751.65867872702495
60681.3681.338164067972-0.0381640679718203
61684.2684.0550264798380.144973520162011
62687686.1863625892320.813637410768251
63688.4687.8163706829440.583629317056079
64689.5687.187912744862.31208725513989
65691.1687.7283570040583.37164299594247
66693.3689.7089479504413.59105204955858
67695.9697.115371278848-1.21537127884847
68698697.9048086265930.0951913734072605
69699.6699.0261304018350.573869598164947
70701.6699.3492915243352.25070847566496
71703.5702.9082447566690.591755243331249
72705.5707.103683877399-1.60368387739868
73708.1710.35574720215-2.25574720215036
74709.6711.910659925909-2.31065992590914
75710.3711.67951757201-1.37951757200995

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 692.4 & 684.005145123652 & 8.39485487634829 \tabularnewline
14 & 695.7 & 696.594880733925 & -0.894880733925334 \tabularnewline
15 & 697.2 & 698.486464448622 & -1.28646444862147 \tabularnewline
16 & 696.8 & 697.544674972548 & -0.744674972548069 \tabularnewline
17 & 696.4 & 696.955381403424 & -0.555381403424462 \tabularnewline
18 & 695.9 & 696.451132961243 & -0.551132961242729 \tabularnewline
19 & 696.2 & 702.754426404273 & -6.55442640427282 \tabularnewline
20 & 697.2 & 696.253012988138 & 0.946987011861552 \tabularnewline
21 & 705.2 & 696.560081459623 & 8.63991854037715 \tabularnewline
22 & 706.2 & 705.405656445939 & 0.794343554061243 \tabularnewline
23 & 707.4 & 709.157720691802 & -1.75772069180198 \tabularnewline
24 & 708.7 & 712.198845026445 & -3.49884502644522 \tabularnewline
25 & 710 & 713.99324936466 & -3.99324936466064 \tabularnewline
26 & 711.3 & 713.02706703545 & -1.72706703544986 \tabularnewline
27 & 711.5 & 712.493418892771 & -0.993418892770933 \tabularnewline
28 & 710.7 & 710.239579364326 & 0.460420635674041 \tabularnewline
29 & 710 & 709.324137741663 & 0.67586225833702 \tabularnewline
30 & 709.2 & 708.699841314163 & 0.500158685837505 \tabularnewline
31 & 707.9 & 714.412560412607 & -6.51256041260751 \tabularnewline
32 & 706.1 & 707.641520449921 & -1.54152044992099 \tabularnewline
33 & 704.4 & 705.013467569147 & -0.613467569147474 \tabularnewline
34 & 702.7 & 701.865790811907 & 0.834209188093041 \tabularnewline
35 & 701.5 & 702.531651568538 & -1.03165156853834 \tabularnewline
36 & 700.8 & 703.275296545231 & -2.47529654523146 \tabularnewline
37 & 700 & 703.297219569422 & -3.29721956942183 \tabularnewline
38 & 699.3 & 700.648722065727 & -1.34872206572754 \tabularnewline
39 & 698.8 & 698.076857128041 & 0.723142871959453 \tabularnewline
40 & 698.4 & 695.380860079703 & 3.01913992029665 \tabularnewline
41 & 696.8 & 695.078022781015 & 1.72197721898533 \tabularnewline
42 & 695.1 & 693.837713310525 & 1.26228668947465 \tabularnewline
43 & 694.3 & 698.009258771678 & -3.70925877167838 \tabularnewline
44 & 693.4 & 693.235055135697 & 0.164944864302583 \tabularnewline
45 & 692.4 & 691.501613878311 & 0.898386121688645 \tabularnewline
46 & 691 & 689.385493647455 & 1.61450635254516 \tabularnewline
47 & 689.7 & 690.189028164016 & -0.489028164015735 \tabularnewline
48 & 688.3 & 690.948805642573 & -2.64880564257339 \tabularnewline
49 & 686 & 690.351764831617 & -4.35176483161717 \tabularnewline
50 & 683.6 & 686.406798071727 & -2.80679807172692 \tabularnewline
51 & 682.6 & 681.981412809902 & 0.618587190098424 \tabularnewline
52 & 681.9 & 678.708019538264 & 3.19198046173631 \tabularnewline
53 & 681 & 677.77273079973 & 3.2272692002698 \tabularnewline
54 & 679.9 & 677.422359559103 & 2.47764044089661 \tabularnewline
55 & 678.5 & 681.856404706074 & -3.35640470607404 \tabularnewline
56 & 677.5 & 677.551304835978 & -0.0513048359782715 \tabularnewline
57 & 678 & 675.451583691593 & 2.54841630840667 \tabularnewline
58 & 679 & 674.938154678045 & 4.06184532195516 \tabularnewline
59 & 679.8 & 678.141321272975 & 1.65867872702495 \tabularnewline
60 & 681.3 & 681.338164067972 & -0.0381640679718203 \tabularnewline
61 & 684.2 & 684.055026479838 & 0.144973520162011 \tabularnewline
62 & 687 & 686.186362589232 & 0.813637410768251 \tabularnewline
63 & 688.4 & 687.816370682944 & 0.583629317056079 \tabularnewline
64 & 689.5 & 687.18791274486 & 2.31208725513989 \tabularnewline
65 & 691.1 & 687.728357004058 & 3.37164299594247 \tabularnewline
66 & 693.3 & 689.708947950441 & 3.59105204955858 \tabularnewline
67 & 695.9 & 697.115371278848 & -1.21537127884847 \tabularnewline
68 & 698 & 697.904808626593 & 0.0951913734072605 \tabularnewline
69 & 699.6 & 699.026130401835 & 0.573869598164947 \tabularnewline
70 & 701.6 & 699.349291524335 & 2.25070847566496 \tabularnewline
71 & 703.5 & 702.908244756669 & 0.591755243331249 \tabularnewline
72 & 705.5 & 707.103683877399 & -1.60368387739868 \tabularnewline
73 & 708.1 & 710.35574720215 & -2.25574720215036 \tabularnewline
74 & 709.6 & 711.910659925909 & -2.31065992590914 \tabularnewline
75 & 710.3 & 711.67951757201 & -1.37951757200995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41379&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]692.4[/C][C]684.005145123652[/C][C]8.39485487634829[/C][/ROW]
[ROW][C]14[/C][C]695.7[/C][C]696.594880733925[/C][C]-0.894880733925334[/C][/ROW]
[ROW][C]15[/C][C]697.2[/C][C]698.486464448622[/C][C]-1.28646444862147[/C][/ROW]
[ROW][C]16[/C][C]696.8[/C][C]697.544674972548[/C][C]-0.744674972548069[/C][/ROW]
[ROW][C]17[/C][C]696.4[/C][C]696.955381403424[/C][C]-0.555381403424462[/C][/ROW]
[ROW][C]18[/C][C]695.9[/C][C]696.451132961243[/C][C]-0.551132961242729[/C][/ROW]
[ROW][C]19[/C][C]696.2[/C][C]702.754426404273[/C][C]-6.55442640427282[/C][/ROW]
[ROW][C]20[/C][C]697.2[/C][C]696.253012988138[/C][C]0.946987011861552[/C][/ROW]
[ROW][C]21[/C][C]705.2[/C][C]696.560081459623[/C][C]8.63991854037715[/C][/ROW]
[ROW][C]22[/C][C]706.2[/C][C]705.405656445939[/C][C]0.794343554061243[/C][/ROW]
[ROW][C]23[/C][C]707.4[/C][C]709.157720691802[/C][C]-1.75772069180198[/C][/ROW]
[ROW][C]24[/C][C]708.7[/C][C]712.198845026445[/C][C]-3.49884502644522[/C][/ROW]
[ROW][C]25[/C][C]710[/C][C]713.99324936466[/C][C]-3.99324936466064[/C][/ROW]
[ROW][C]26[/C][C]711.3[/C][C]713.02706703545[/C][C]-1.72706703544986[/C][/ROW]
[ROW][C]27[/C][C]711.5[/C][C]712.493418892771[/C][C]-0.993418892770933[/C][/ROW]
[ROW][C]28[/C][C]710.7[/C][C]710.239579364326[/C][C]0.460420635674041[/C][/ROW]
[ROW][C]29[/C][C]710[/C][C]709.324137741663[/C][C]0.67586225833702[/C][/ROW]
[ROW][C]30[/C][C]709.2[/C][C]708.699841314163[/C][C]0.500158685837505[/C][/ROW]
[ROW][C]31[/C][C]707.9[/C][C]714.412560412607[/C][C]-6.51256041260751[/C][/ROW]
[ROW][C]32[/C][C]706.1[/C][C]707.641520449921[/C][C]-1.54152044992099[/C][/ROW]
[ROW][C]33[/C][C]704.4[/C][C]705.013467569147[/C][C]-0.613467569147474[/C][/ROW]
[ROW][C]34[/C][C]702.7[/C][C]701.865790811907[/C][C]0.834209188093041[/C][/ROW]
[ROW][C]35[/C][C]701.5[/C][C]702.531651568538[/C][C]-1.03165156853834[/C][/ROW]
[ROW][C]36[/C][C]700.8[/C][C]703.275296545231[/C][C]-2.47529654523146[/C][/ROW]
[ROW][C]37[/C][C]700[/C][C]703.297219569422[/C][C]-3.29721956942183[/C][/ROW]
[ROW][C]38[/C][C]699.3[/C][C]700.648722065727[/C][C]-1.34872206572754[/C][/ROW]
[ROW][C]39[/C][C]698.8[/C][C]698.076857128041[/C][C]0.723142871959453[/C][/ROW]
[ROW][C]40[/C][C]698.4[/C][C]695.380860079703[/C][C]3.01913992029665[/C][/ROW]
[ROW][C]41[/C][C]696.8[/C][C]695.078022781015[/C][C]1.72197721898533[/C][/ROW]
[ROW][C]42[/C][C]695.1[/C][C]693.837713310525[/C][C]1.26228668947465[/C][/ROW]
[ROW][C]43[/C][C]694.3[/C][C]698.009258771678[/C][C]-3.70925877167838[/C][/ROW]
[ROW][C]44[/C][C]693.4[/C][C]693.235055135697[/C][C]0.164944864302583[/C][/ROW]
[ROW][C]45[/C][C]692.4[/C][C]691.501613878311[/C][C]0.898386121688645[/C][/ROW]
[ROW][C]46[/C][C]691[/C][C]689.385493647455[/C][C]1.61450635254516[/C][/ROW]
[ROW][C]47[/C][C]689.7[/C][C]690.189028164016[/C][C]-0.489028164015735[/C][/ROW]
[ROW][C]48[/C][C]688.3[/C][C]690.948805642573[/C][C]-2.64880564257339[/C][/ROW]
[ROW][C]49[/C][C]686[/C][C]690.351764831617[/C][C]-4.35176483161717[/C][/ROW]
[ROW][C]50[/C][C]683.6[/C][C]686.406798071727[/C][C]-2.80679807172692[/C][/ROW]
[ROW][C]51[/C][C]682.6[/C][C]681.981412809902[/C][C]0.618587190098424[/C][/ROW]
[ROW][C]52[/C][C]681.9[/C][C]678.708019538264[/C][C]3.19198046173631[/C][/ROW]
[ROW][C]53[/C][C]681[/C][C]677.77273079973[/C][C]3.2272692002698[/C][/ROW]
[ROW][C]54[/C][C]679.9[/C][C]677.422359559103[/C][C]2.47764044089661[/C][/ROW]
[ROW][C]55[/C][C]678.5[/C][C]681.856404706074[/C][C]-3.35640470607404[/C][/ROW]
[ROW][C]56[/C][C]677.5[/C][C]677.551304835978[/C][C]-0.0513048359782715[/C][/ROW]
[ROW][C]57[/C][C]678[/C][C]675.451583691593[/C][C]2.54841630840667[/C][/ROW]
[ROW][C]58[/C][C]679[/C][C]674.938154678045[/C][C]4.06184532195516[/C][/ROW]
[ROW][C]59[/C][C]679.8[/C][C]678.141321272975[/C][C]1.65867872702495[/C][/ROW]
[ROW][C]60[/C][C]681.3[/C][C]681.338164067972[/C][C]-0.0381640679718203[/C][/ROW]
[ROW][C]61[/C][C]684.2[/C][C]684.055026479838[/C][C]0.144973520162011[/C][/ROW]
[ROW][C]62[/C][C]687[/C][C]686.186362589232[/C][C]0.813637410768251[/C][/ROW]
[ROW][C]63[/C][C]688.4[/C][C]687.816370682944[/C][C]0.583629317056079[/C][/ROW]
[ROW][C]64[/C][C]689.5[/C][C]687.18791274486[/C][C]2.31208725513989[/C][/ROW]
[ROW][C]65[/C][C]691.1[/C][C]687.728357004058[/C][C]3.37164299594247[/C][/ROW]
[ROW][C]66[/C][C]693.3[/C][C]689.708947950441[/C][C]3.59105204955858[/C][/ROW]
[ROW][C]67[/C][C]695.9[/C][C]697.115371278848[/C][C]-1.21537127884847[/C][/ROW]
[ROW][C]68[/C][C]698[/C][C]697.904808626593[/C][C]0.0951913734072605[/C][/ROW]
[ROW][C]69[/C][C]699.6[/C][C]699.026130401835[/C][C]0.573869598164947[/C][/ROW]
[ROW][C]70[/C][C]701.6[/C][C]699.349291524335[/C][C]2.25070847566496[/C][/ROW]
[ROW][C]71[/C][C]703.5[/C][C]702.908244756669[/C][C]0.591755243331249[/C][/ROW]
[ROW][C]72[/C][C]705.5[/C][C]707.103683877399[/C][C]-1.60368387739868[/C][/ROW]
[ROW][C]73[/C][C]708.1[/C][C]710.35574720215[/C][C]-2.25574720215036[/C][/ROW]
[ROW][C]74[/C][C]709.6[/C][C]711.910659925909[/C][C]-2.31065992590914[/C][/ROW]
[ROW][C]75[/C][C]710.3[/C][C]711.67951757201[/C][C]-1.37951757200995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41379&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41379&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
13692.4684.0051451236528.39485487634829
14695.7696.594880733925-0.894880733925334
15697.2698.486464448622-1.28646444862147
16696.8697.544674972548-0.744674972548069
17696.4696.955381403424-0.555381403424462
18695.9696.451132961243-0.551132961242729
19696.2702.754426404273-6.55442640427282
20697.2696.2530129881380.946987011861552
21705.2696.5600814596238.63991854037715
22706.2705.4056564459390.794343554061243
23707.4709.157720691802-1.75772069180198
24708.7712.198845026445-3.49884502644522
25710713.99324936466-3.99324936466064
26711.3713.02706703545-1.72706703544986
27711.5712.493418892771-0.993418892770933
28710.7710.2395793643260.460420635674041
29710709.3241377416630.67586225833702
30709.2708.6998413141630.500158685837505
31707.9714.412560412607-6.51256041260751
32706.1707.641520449921-1.54152044992099
33704.4705.013467569147-0.613467569147474
34702.7701.8657908119070.834209188093041
35701.5702.531651568538-1.03165156853834
36700.8703.275296545231-2.47529654523146
37700703.297219569422-3.29721956942183
38699.3700.648722065727-1.34872206572754
39698.8698.0768571280410.723142871959453
40698.4695.3808600797033.01913992029665
41696.8695.0780227810151.72197721898533
42695.1693.8377133105251.26228668947465
43694.3698.009258771678-3.70925877167838
44693.4693.2350551356970.164944864302583
45692.4691.5016138783110.898386121688645
46691689.3854936474551.61450635254516
47689.7690.189028164016-0.489028164015735
48688.3690.948805642573-2.64880564257339
49686690.351764831617-4.35176483161717
50683.6686.406798071727-2.80679807172692
51682.6681.9814128099020.618587190098424
52681.9678.7080195382643.19198046173631
53681677.772730799733.2272692002698
54679.9677.4223595591032.47764044089661
55678.5681.856404706074-3.35640470607404
56677.5677.551304835978-0.0513048359782715
57678675.4515836915932.54841630840667
58679674.9381546780454.06184532195516
59679.8678.1413212729751.65867872702495
60681.3681.338164067972-0.0381640679718203
61684.2684.0550264798380.144973520162011
62687686.1863625892320.813637410768251
63688.4687.8163706829440.583629317056079
64689.5687.187912744862.31208725513989
65691.1687.7283570040583.37164299594247
66693.3689.7089479504413.59105204955858
67695.9697.115371278848-1.21537127884847
68698697.9048086265930.0951913734072605
69699.6699.0261304018350.573869598164947
70701.6699.3492915243352.25070847566496
71703.5702.9082447566690.591755243331249
72705.5707.103683877399-1.60368387739868
73708.1710.35574720215-2.25574720215036
74709.6711.910659925909-2.31065992590914
75710.3711.67951757201-1.37951757200995







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
76710.051098077342704.612480579747715.489715574936
77708.820264466602700.900829447093716.739699486111
78707.460950791398697.154156568736717.767745014059
79710.364874086449697.59574101564723.134007157258
80711.748664191939696.475068322154727.022260061723
81712.16666262262694.330986273687730.002338971553
82711.360379630604690.913822607338731.806936653871
83711.616771213069688.44968128461734.783861141527
84713.883003828457687.841054684109739.924952972805
85717.606573058886688.535385202097746.677760915676
86720.63167034423688.454354912587752.808985775873
87722.368428596778687.041333199465757.695523994091

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 710.051098077342 & 704.612480579747 & 715.489715574936 \tabularnewline
77 & 708.820264466602 & 700.900829447093 & 716.739699486111 \tabularnewline
78 & 707.460950791398 & 697.154156568736 & 717.767745014059 \tabularnewline
79 & 710.364874086449 & 697.59574101564 & 723.134007157258 \tabularnewline
80 & 711.748664191939 & 696.475068322154 & 727.022260061723 \tabularnewline
81 & 712.16666262262 & 694.330986273687 & 730.002338971553 \tabularnewline
82 & 711.360379630604 & 690.913822607338 & 731.806936653871 \tabularnewline
83 & 711.616771213069 & 688.44968128461 & 734.783861141527 \tabularnewline
84 & 713.883003828457 & 687.841054684109 & 739.924952972805 \tabularnewline
85 & 717.606573058886 & 688.535385202097 & 746.677760915676 \tabularnewline
86 & 720.63167034423 & 688.454354912587 & 752.808985775873 \tabularnewline
87 & 722.368428596778 & 687.041333199465 & 757.695523994091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41379&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]76[/C][C]710.051098077342[/C][C]704.612480579747[/C][C]715.489715574936[/C][/ROW]
[ROW][C]77[/C][C]708.820264466602[/C][C]700.900829447093[/C][C]716.739699486111[/C][/ROW]
[ROW][C]78[/C][C]707.460950791398[/C][C]697.154156568736[/C][C]717.767745014059[/C][/ROW]
[ROW][C]79[/C][C]710.364874086449[/C][C]697.59574101564[/C][C]723.134007157258[/C][/ROW]
[ROW][C]80[/C][C]711.748664191939[/C][C]696.475068322154[/C][C]727.022260061723[/C][/ROW]
[ROW][C]81[/C][C]712.16666262262[/C][C]694.330986273687[/C][C]730.002338971553[/C][/ROW]
[ROW][C]82[/C][C]711.360379630604[/C][C]690.913822607338[/C][C]731.806936653871[/C][/ROW]
[ROW][C]83[/C][C]711.616771213069[/C][C]688.44968128461[/C][C]734.783861141527[/C][/ROW]
[ROW][C]84[/C][C]713.883003828457[/C][C]687.841054684109[/C][C]739.924952972805[/C][/ROW]
[ROW][C]85[/C][C]717.606573058886[/C][C]688.535385202097[/C][C]746.677760915676[/C][/ROW]
[ROW][C]86[/C][C]720.63167034423[/C][C]688.454354912587[/C][C]752.808985775873[/C][/ROW]
[ROW][C]87[/C][C]722.368428596778[/C][C]687.041333199465[/C][C]757.695523994091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41379&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41379&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
76710.051098077342704.612480579747715.489715574936
77708.820264466602700.900829447093716.739699486111
78707.460950791398697.154156568736717.767745014059
79710.364874086449697.59574101564723.134007157258
80711.748664191939696.475068322154727.022260061723
81712.16666262262694.330986273687730.002338971553
82711.360379630604690.913822607338731.806936653871
83711.616771213069688.44968128461734.783861141527
84713.883003828457687.841054684109739.924952972805
85717.606573058886688.535385202097746.677760915676
86720.63167034423688.454354912587752.808985775873
87722.368428596778687.041333199465757.695523994091



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