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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 Dec 2013 03:43:39 -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/18/t13873562543akbu4xcajwtw2x.htm/, Retrieved Fri, 19 Apr 2024 19:53:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232426, Retrieved Fri, 19 Apr 2024 19:53:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2013-12-13 13:40:20] [118d51f3b8c7238175a748a4b2235cf1]
- R PD    [Exponential Smoothing] [] [2013-12-18 08:43:39] [6e7c8e41ae9c2cf944b21192a5249437] [Current]
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Dataseries X:
26.73
26.85
27.01
27.09
27.11
27.16
27.13
27.19
27.49
27.63
27.72
27.77
27.81
27.92
28.07
28.14
28.17
28.20
28.21
28.20
28.19
28.24
28.25
28.26
28.33
28.67
28.81
28.99
29.16
29.25
29.25
29.38
29.48
29.65
29.69
29.73
29.81
30.05
30.29
30.37
30.50
30.67
30.76
30.84
30.86
31.09
31.20
31.19
31.18
31.31
31.39
31.39
31.37
31.36
31.37
31.35
31.34
31.47
31.48
31.54
31.55
31.55
31.57
31.66
31.74
31.78
31.80
31.68
31.70
31.70
31.75
31.73
31.82
31.90
31.82
31.51
31.42
30.97
30.99
30.92
30.95
30.82
30.72
30.73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232426&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232426&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232426&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.188533630779783
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.188533630779783 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232426&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]0.188533630779783[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232426&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232426&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
beta0.188533630779783
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
327.0126.970.0399999999999991
427.0927.1375413452312-0.0475413452311955
527.1127.2085782028026-0.0985782028025994
627.1627.2099928963125-0.0499928963124781
727.1327.2505675540575-0.120567554057491
827.1927.1978365153368-0.00783651533679119
927.4927.25635906864770.233640931352308
1027.6327.60040824173430.0295917582656919
1127.7227.7459872833613-0.025987283361296
1227.7727.8310878064751-0.0610878064750864
1327.8127.869570700524-0.0595707005239667
1427.9227.89833962006610.0216603799339126
1528.0728.01242333013910.0575766698609002
1628.1428.1732784687562-0.0332784687561833
1728.1728.2370043582148-0.0670043582147883
1828.228.2543717832825-0.0543717832824875
1928.2128.2741208735683-0.0641208735682639
2028.228.2720319324657-0.0720319324656735
2128.1928.2484514907058-0.0584514907058313
2228.2428.22743141893860.0125685810614264
2328.2528.2798010191598-0.0298010191598301
2428.2628.2841825248167-0.0241825248166911
2528.3328.28962330561160.0403766943884172
2628.6728.36723567040350.302764329596492
2728.8128.76431692873290.0456830712670495
2828.9928.91292972402410.0770702759759061
2929.1629.1074600629790.0525399370209705
3029.2529.2873656080665-0.037365608066537
3129.2529.3703209343115-0.120320934311458
3229.3829.34763639170690.032363608293096
3329.4829.4837380202835-0.00373802028353509
3429.6529.58303327774760.0669667222524453
3529.6929.7656587570352-0.0756587570352245
3629.7329.7913945368711-0.0613945368710915
3729.8129.8198196019247-0.00981960192474318
3830.0529.89796827672110.152031723278945
3930.2930.16663136950450.123368630495456
4030.3730.4298905053362-0.0598905053361776
4130.530.49859913091590.00140086908408321
4230.6730.62886324185060.0411367581494169
4330.7630.806618904223-0.0466189042230027
4430.8430.8878296729469-0.0478296729468681
4530.8630.9588121710472-0.0988121710471823
4631.0930.96018275367440.129817246325576
4731.231.214657670462-0.014657670462018
4831.1931.321894206631-0.131894206631038
4931.1831.2870277129761-0.107027712976073
5031.3131.25684938965460.0531506103453623
5131.3931.3968700672012-0.0068700672012092
5231.3931.4755748284881-0.0855748284880633
5331.3731.4594410953699-0.0894410953698532
5431.3631.4225784409189-0.0625784409188554
5531.3731.4007803002439-0.0307803002438831
5631.3531.4049771784824-0.0549771784824138
5731.3431.3746121314131-0.0346121314130983
5831.4731.35808658060880.111913419391243
5931.4831.5091860238996-0.029186023899566
6031.5431.51368347684580.0263165231542395
6131.5531.5786450265055-0.0286450265055258
6231.5531.5832444756547-0.0332444756546586
6331.5731.5769767739561-0.00697677395611507
6431.6631.5956614174310.0643385825689613
6531.7431.6977914040020.0422085959980087
6631.7831.7857491438556-0.00574914385560987
6731.831.8246652368906-0.0246652368906375
6831.6831.8400150102256-0.160015010225603
6931.731.68984679936850.0101532006314926
7031.731.7117610191476-0.0117610191475954
7131.7531.7095436715060.0404563284939705
7231.7331.767171050005-0.0371710500050177
7331.8231.74016305698770.0798369430123245
7431.931.84521500572410.0547849942758525
7531.8231.9355438196072-0.115543819607222
7631.5131.8337599237825-0.323759923782507
7731.4231.4627202898508-0.0427202898508057
7830.9731.3646660784973-0.394666078497274
7930.9930.84025824977260.149741750227438
8030.9230.88848960562230.0315103943777437
8130.9530.82443037468160.125569625318398
8230.8230.8781044720585-0.0581044720585311
8330.7230.7371498249768-0.0171498249767978
8430.7330.63391650620670.0960834937933193

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 27.01 & 26.97 & 0.0399999999999991 \tabularnewline
4 & 27.09 & 27.1375413452312 & -0.0475413452311955 \tabularnewline
5 & 27.11 & 27.2085782028026 & -0.0985782028025994 \tabularnewline
6 & 27.16 & 27.2099928963125 & -0.0499928963124781 \tabularnewline
7 & 27.13 & 27.2505675540575 & -0.120567554057491 \tabularnewline
8 & 27.19 & 27.1978365153368 & -0.00783651533679119 \tabularnewline
9 & 27.49 & 27.2563590686477 & 0.233640931352308 \tabularnewline
10 & 27.63 & 27.6004082417343 & 0.0295917582656919 \tabularnewline
11 & 27.72 & 27.7459872833613 & -0.025987283361296 \tabularnewline
12 & 27.77 & 27.8310878064751 & -0.0610878064750864 \tabularnewline
13 & 27.81 & 27.869570700524 & -0.0595707005239667 \tabularnewline
14 & 27.92 & 27.8983396200661 & 0.0216603799339126 \tabularnewline
15 & 28.07 & 28.0124233301391 & 0.0575766698609002 \tabularnewline
16 & 28.14 & 28.1732784687562 & -0.0332784687561833 \tabularnewline
17 & 28.17 & 28.2370043582148 & -0.0670043582147883 \tabularnewline
18 & 28.2 & 28.2543717832825 & -0.0543717832824875 \tabularnewline
19 & 28.21 & 28.2741208735683 & -0.0641208735682639 \tabularnewline
20 & 28.2 & 28.2720319324657 & -0.0720319324656735 \tabularnewline
21 & 28.19 & 28.2484514907058 & -0.0584514907058313 \tabularnewline
22 & 28.24 & 28.2274314189386 & 0.0125685810614264 \tabularnewline
23 & 28.25 & 28.2798010191598 & -0.0298010191598301 \tabularnewline
24 & 28.26 & 28.2841825248167 & -0.0241825248166911 \tabularnewline
25 & 28.33 & 28.2896233056116 & 0.0403766943884172 \tabularnewline
26 & 28.67 & 28.3672356704035 & 0.302764329596492 \tabularnewline
27 & 28.81 & 28.7643169287329 & 0.0456830712670495 \tabularnewline
28 & 28.99 & 28.9129297240241 & 0.0770702759759061 \tabularnewline
29 & 29.16 & 29.107460062979 & 0.0525399370209705 \tabularnewline
30 & 29.25 & 29.2873656080665 & -0.037365608066537 \tabularnewline
31 & 29.25 & 29.3703209343115 & -0.120320934311458 \tabularnewline
32 & 29.38 & 29.3476363917069 & 0.032363608293096 \tabularnewline
33 & 29.48 & 29.4837380202835 & -0.00373802028353509 \tabularnewline
34 & 29.65 & 29.5830332777476 & 0.0669667222524453 \tabularnewline
35 & 29.69 & 29.7656587570352 & -0.0756587570352245 \tabularnewline
36 & 29.73 & 29.7913945368711 & -0.0613945368710915 \tabularnewline
37 & 29.81 & 29.8198196019247 & -0.00981960192474318 \tabularnewline
38 & 30.05 & 29.8979682767211 & 0.152031723278945 \tabularnewline
39 & 30.29 & 30.1666313695045 & 0.123368630495456 \tabularnewline
40 & 30.37 & 30.4298905053362 & -0.0598905053361776 \tabularnewline
41 & 30.5 & 30.4985991309159 & 0.00140086908408321 \tabularnewline
42 & 30.67 & 30.6288632418506 & 0.0411367581494169 \tabularnewline
43 & 30.76 & 30.806618904223 & -0.0466189042230027 \tabularnewline
44 & 30.84 & 30.8878296729469 & -0.0478296729468681 \tabularnewline
45 & 30.86 & 30.9588121710472 & -0.0988121710471823 \tabularnewline
46 & 31.09 & 30.9601827536744 & 0.129817246325576 \tabularnewline
47 & 31.2 & 31.214657670462 & -0.014657670462018 \tabularnewline
48 & 31.19 & 31.321894206631 & -0.131894206631038 \tabularnewline
49 & 31.18 & 31.2870277129761 & -0.107027712976073 \tabularnewline
50 & 31.31 & 31.2568493896546 & 0.0531506103453623 \tabularnewline
51 & 31.39 & 31.3968700672012 & -0.0068700672012092 \tabularnewline
52 & 31.39 & 31.4755748284881 & -0.0855748284880633 \tabularnewline
53 & 31.37 & 31.4594410953699 & -0.0894410953698532 \tabularnewline
54 & 31.36 & 31.4225784409189 & -0.0625784409188554 \tabularnewline
55 & 31.37 & 31.4007803002439 & -0.0307803002438831 \tabularnewline
56 & 31.35 & 31.4049771784824 & -0.0549771784824138 \tabularnewline
57 & 31.34 & 31.3746121314131 & -0.0346121314130983 \tabularnewline
58 & 31.47 & 31.3580865806088 & 0.111913419391243 \tabularnewline
59 & 31.48 & 31.5091860238996 & -0.029186023899566 \tabularnewline
60 & 31.54 & 31.5136834768458 & 0.0263165231542395 \tabularnewline
61 & 31.55 & 31.5786450265055 & -0.0286450265055258 \tabularnewline
62 & 31.55 & 31.5832444756547 & -0.0332444756546586 \tabularnewline
63 & 31.57 & 31.5769767739561 & -0.00697677395611507 \tabularnewline
64 & 31.66 & 31.595661417431 & 0.0643385825689613 \tabularnewline
65 & 31.74 & 31.697791404002 & 0.0422085959980087 \tabularnewline
66 & 31.78 & 31.7857491438556 & -0.00574914385560987 \tabularnewline
67 & 31.8 & 31.8246652368906 & -0.0246652368906375 \tabularnewline
68 & 31.68 & 31.8400150102256 & -0.160015010225603 \tabularnewline
69 & 31.7 & 31.6898467993685 & 0.0101532006314926 \tabularnewline
70 & 31.7 & 31.7117610191476 & -0.0117610191475954 \tabularnewline
71 & 31.75 & 31.709543671506 & 0.0404563284939705 \tabularnewline
72 & 31.73 & 31.767171050005 & -0.0371710500050177 \tabularnewline
73 & 31.82 & 31.7401630569877 & 0.0798369430123245 \tabularnewline
74 & 31.9 & 31.8452150057241 & 0.0547849942758525 \tabularnewline
75 & 31.82 & 31.9355438196072 & -0.115543819607222 \tabularnewline
76 & 31.51 & 31.8337599237825 & -0.323759923782507 \tabularnewline
77 & 31.42 & 31.4627202898508 & -0.0427202898508057 \tabularnewline
78 & 30.97 & 31.3646660784973 & -0.394666078497274 \tabularnewline
79 & 30.99 & 30.8402582497726 & 0.149741750227438 \tabularnewline
80 & 30.92 & 30.8884896056223 & 0.0315103943777437 \tabularnewline
81 & 30.95 & 30.8244303746816 & 0.125569625318398 \tabularnewline
82 & 30.82 & 30.8781044720585 & -0.0581044720585311 \tabularnewline
83 & 30.72 & 30.7371498249768 & -0.0171498249767978 \tabularnewline
84 & 30.73 & 30.6339165062067 & 0.0960834937933193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232426&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]27.01[/C][C]26.97[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]4[/C][C]27.09[/C][C]27.1375413452312[/C][C]-0.0475413452311955[/C][/ROW]
[ROW][C]5[/C][C]27.11[/C][C]27.2085782028026[/C][C]-0.0985782028025994[/C][/ROW]
[ROW][C]6[/C][C]27.16[/C][C]27.2099928963125[/C][C]-0.0499928963124781[/C][/ROW]
[ROW][C]7[/C][C]27.13[/C][C]27.2505675540575[/C][C]-0.120567554057491[/C][/ROW]
[ROW][C]8[/C][C]27.19[/C][C]27.1978365153368[/C][C]-0.00783651533679119[/C][/ROW]
[ROW][C]9[/C][C]27.49[/C][C]27.2563590686477[/C][C]0.233640931352308[/C][/ROW]
[ROW][C]10[/C][C]27.63[/C][C]27.6004082417343[/C][C]0.0295917582656919[/C][/ROW]
[ROW][C]11[/C][C]27.72[/C][C]27.7459872833613[/C][C]-0.025987283361296[/C][/ROW]
[ROW][C]12[/C][C]27.77[/C][C]27.8310878064751[/C][C]-0.0610878064750864[/C][/ROW]
[ROW][C]13[/C][C]27.81[/C][C]27.869570700524[/C][C]-0.0595707005239667[/C][/ROW]
[ROW][C]14[/C][C]27.92[/C][C]27.8983396200661[/C][C]0.0216603799339126[/C][/ROW]
[ROW][C]15[/C][C]28.07[/C][C]28.0124233301391[/C][C]0.0575766698609002[/C][/ROW]
[ROW][C]16[/C][C]28.14[/C][C]28.1732784687562[/C][C]-0.0332784687561833[/C][/ROW]
[ROW][C]17[/C][C]28.17[/C][C]28.2370043582148[/C][C]-0.0670043582147883[/C][/ROW]
[ROW][C]18[/C][C]28.2[/C][C]28.2543717832825[/C][C]-0.0543717832824875[/C][/ROW]
[ROW][C]19[/C][C]28.21[/C][C]28.2741208735683[/C][C]-0.0641208735682639[/C][/ROW]
[ROW][C]20[/C][C]28.2[/C][C]28.2720319324657[/C][C]-0.0720319324656735[/C][/ROW]
[ROW][C]21[/C][C]28.19[/C][C]28.2484514907058[/C][C]-0.0584514907058313[/C][/ROW]
[ROW][C]22[/C][C]28.24[/C][C]28.2274314189386[/C][C]0.0125685810614264[/C][/ROW]
[ROW][C]23[/C][C]28.25[/C][C]28.2798010191598[/C][C]-0.0298010191598301[/C][/ROW]
[ROW][C]24[/C][C]28.26[/C][C]28.2841825248167[/C][C]-0.0241825248166911[/C][/ROW]
[ROW][C]25[/C][C]28.33[/C][C]28.2896233056116[/C][C]0.0403766943884172[/C][/ROW]
[ROW][C]26[/C][C]28.67[/C][C]28.3672356704035[/C][C]0.302764329596492[/C][/ROW]
[ROW][C]27[/C][C]28.81[/C][C]28.7643169287329[/C][C]0.0456830712670495[/C][/ROW]
[ROW][C]28[/C][C]28.99[/C][C]28.9129297240241[/C][C]0.0770702759759061[/C][/ROW]
[ROW][C]29[/C][C]29.16[/C][C]29.107460062979[/C][C]0.0525399370209705[/C][/ROW]
[ROW][C]30[/C][C]29.25[/C][C]29.2873656080665[/C][C]-0.037365608066537[/C][/ROW]
[ROW][C]31[/C][C]29.25[/C][C]29.3703209343115[/C][C]-0.120320934311458[/C][/ROW]
[ROW][C]32[/C][C]29.38[/C][C]29.3476363917069[/C][C]0.032363608293096[/C][/ROW]
[ROW][C]33[/C][C]29.48[/C][C]29.4837380202835[/C][C]-0.00373802028353509[/C][/ROW]
[ROW][C]34[/C][C]29.65[/C][C]29.5830332777476[/C][C]0.0669667222524453[/C][/ROW]
[ROW][C]35[/C][C]29.69[/C][C]29.7656587570352[/C][C]-0.0756587570352245[/C][/ROW]
[ROW][C]36[/C][C]29.73[/C][C]29.7913945368711[/C][C]-0.0613945368710915[/C][/ROW]
[ROW][C]37[/C][C]29.81[/C][C]29.8198196019247[/C][C]-0.00981960192474318[/C][/ROW]
[ROW][C]38[/C][C]30.05[/C][C]29.8979682767211[/C][C]0.152031723278945[/C][/ROW]
[ROW][C]39[/C][C]30.29[/C][C]30.1666313695045[/C][C]0.123368630495456[/C][/ROW]
[ROW][C]40[/C][C]30.37[/C][C]30.4298905053362[/C][C]-0.0598905053361776[/C][/ROW]
[ROW][C]41[/C][C]30.5[/C][C]30.4985991309159[/C][C]0.00140086908408321[/C][/ROW]
[ROW][C]42[/C][C]30.67[/C][C]30.6288632418506[/C][C]0.0411367581494169[/C][/ROW]
[ROW][C]43[/C][C]30.76[/C][C]30.806618904223[/C][C]-0.0466189042230027[/C][/ROW]
[ROW][C]44[/C][C]30.84[/C][C]30.8878296729469[/C][C]-0.0478296729468681[/C][/ROW]
[ROW][C]45[/C][C]30.86[/C][C]30.9588121710472[/C][C]-0.0988121710471823[/C][/ROW]
[ROW][C]46[/C][C]31.09[/C][C]30.9601827536744[/C][C]0.129817246325576[/C][/ROW]
[ROW][C]47[/C][C]31.2[/C][C]31.214657670462[/C][C]-0.014657670462018[/C][/ROW]
[ROW][C]48[/C][C]31.19[/C][C]31.321894206631[/C][C]-0.131894206631038[/C][/ROW]
[ROW][C]49[/C][C]31.18[/C][C]31.2870277129761[/C][C]-0.107027712976073[/C][/ROW]
[ROW][C]50[/C][C]31.31[/C][C]31.2568493896546[/C][C]0.0531506103453623[/C][/ROW]
[ROW][C]51[/C][C]31.39[/C][C]31.3968700672012[/C][C]-0.0068700672012092[/C][/ROW]
[ROW][C]52[/C][C]31.39[/C][C]31.4755748284881[/C][C]-0.0855748284880633[/C][/ROW]
[ROW][C]53[/C][C]31.37[/C][C]31.4594410953699[/C][C]-0.0894410953698532[/C][/ROW]
[ROW][C]54[/C][C]31.36[/C][C]31.4225784409189[/C][C]-0.0625784409188554[/C][/ROW]
[ROW][C]55[/C][C]31.37[/C][C]31.4007803002439[/C][C]-0.0307803002438831[/C][/ROW]
[ROW][C]56[/C][C]31.35[/C][C]31.4049771784824[/C][C]-0.0549771784824138[/C][/ROW]
[ROW][C]57[/C][C]31.34[/C][C]31.3746121314131[/C][C]-0.0346121314130983[/C][/ROW]
[ROW][C]58[/C][C]31.47[/C][C]31.3580865806088[/C][C]0.111913419391243[/C][/ROW]
[ROW][C]59[/C][C]31.48[/C][C]31.5091860238996[/C][C]-0.029186023899566[/C][/ROW]
[ROW][C]60[/C][C]31.54[/C][C]31.5136834768458[/C][C]0.0263165231542395[/C][/ROW]
[ROW][C]61[/C][C]31.55[/C][C]31.5786450265055[/C][C]-0.0286450265055258[/C][/ROW]
[ROW][C]62[/C][C]31.55[/C][C]31.5832444756547[/C][C]-0.0332444756546586[/C][/ROW]
[ROW][C]63[/C][C]31.57[/C][C]31.5769767739561[/C][C]-0.00697677395611507[/C][/ROW]
[ROW][C]64[/C][C]31.66[/C][C]31.595661417431[/C][C]0.0643385825689613[/C][/ROW]
[ROW][C]65[/C][C]31.74[/C][C]31.697791404002[/C][C]0.0422085959980087[/C][/ROW]
[ROW][C]66[/C][C]31.78[/C][C]31.7857491438556[/C][C]-0.00574914385560987[/C][/ROW]
[ROW][C]67[/C][C]31.8[/C][C]31.8246652368906[/C][C]-0.0246652368906375[/C][/ROW]
[ROW][C]68[/C][C]31.68[/C][C]31.8400150102256[/C][C]-0.160015010225603[/C][/ROW]
[ROW][C]69[/C][C]31.7[/C][C]31.6898467993685[/C][C]0.0101532006314926[/C][/ROW]
[ROW][C]70[/C][C]31.7[/C][C]31.7117610191476[/C][C]-0.0117610191475954[/C][/ROW]
[ROW][C]71[/C][C]31.75[/C][C]31.709543671506[/C][C]0.0404563284939705[/C][/ROW]
[ROW][C]72[/C][C]31.73[/C][C]31.767171050005[/C][C]-0.0371710500050177[/C][/ROW]
[ROW][C]73[/C][C]31.82[/C][C]31.7401630569877[/C][C]0.0798369430123245[/C][/ROW]
[ROW][C]74[/C][C]31.9[/C][C]31.8452150057241[/C][C]0.0547849942758525[/C][/ROW]
[ROW][C]75[/C][C]31.82[/C][C]31.9355438196072[/C][C]-0.115543819607222[/C][/ROW]
[ROW][C]76[/C][C]31.51[/C][C]31.8337599237825[/C][C]-0.323759923782507[/C][/ROW]
[ROW][C]77[/C][C]31.42[/C][C]31.4627202898508[/C][C]-0.0427202898508057[/C][/ROW]
[ROW][C]78[/C][C]30.97[/C][C]31.3646660784973[/C][C]-0.394666078497274[/C][/ROW]
[ROW][C]79[/C][C]30.99[/C][C]30.8402582497726[/C][C]0.149741750227438[/C][/ROW]
[ROW][C]80[/C][C]30.92[/C][C]30.8884896056223[/C][C]0.0315103943777437[/C][/ROW]
[ROW][C]81[/C][C]30.95[/C][C]30.8244303746816[/C][C]0.125569625318398[/C][/ROW]
[ROW][C]82[/C][C]30.82[/C][C]30.8781044720585[/C][C]-0.0581044720585311[/C][/ROW]
[ROW][C]83[/C][C]30.72[/C][C]30.7371498249768[/C][C]-0.0171498249767978[/C][/ROW]
[ROW][C]84[/C][C]30.73[/C][C]30.6339165062067[/C][C]0.0960834937933193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232426&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232426&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
327.0126.970.0399999999999991
427.0927.1375413452312-0.0475413452311955
527.1127.2085782028026-0.0985782028025994
627.1627.2099928963125-0.0499928963124781
727.1327.2505675540575-0.120567554057491
827.1927.1978365153368-0.00783651533679119
927.4927.25635906864770.233640931352308
1027.6327.60040824173430.0295917582656919
1127.7227.7459872833613-0.025987283361296
1227.7727.8310878064751-0.0610878064750864
1327.8127.869570700524-0.0595707005239667
1427.9227.89833962006610.0216603799339126
1528.0728.01242333013910.0575766698609002
1628.1428.1732784687562-0.0332784687561833
1728.1728.2370043582148-0.0670043582147883
1828.228.2543717832825-0.0543717832824875
1928.2128.2741208735683-0.0641208735682639
2028.228.2720319324657-0.0720319324656735
2128.1928.2484514907058-0.0584514907058313
2228.2428.22743141893860.0125685810614264
2328.2528.2798010191598-0.0298010191598301
2428.2628.2841825248167-0.0241825248166911
2528.3328.28962330561160.0403766943884172
2628.6728.36723567040350.302764329596492
2728.8128.76431692873290.0456830712670495
2828.9928.91292972402410.0770702759759061
2929.1629.1074600629790.0525399370209705
3029.2529.2873656080665-0.037365608066537
3129.2529.3703209343115-0.120320934311458
3229.3829.34763639170690.032363608293096
3329.4829.4837380202835-0.00373802028353509
3429.6529.58303327774760.0669667222524453
3529.6929.7656587570352-0.0756587570352245
3629.7329.7913945368711-0.0613945368710915
3729.8129.8198196019247-0.00981960192474318
3830.0529.89796827672110.152031723278945
3930.2930.16663136950450.123368630495456
4030.3730.4298905053362-0.0598905053361776
4130.530.49859913091590.00140086908408321
4230.6730.62886324185060.0411367581494169
4330.7630.806618904223-0.0466189042230027
4430.8430.8878296729469-0.0478296729468681
4530.8630.9588121710472-0.0988121710471823
4631.0930.96018275367440.129817246325576
4731.231.214657670462-0.014657670462018
4831.1931.321894206631-0.131894206631038
4931.1831.2870277129761-0.107027712976073
5031.3131.25684938965460.0531506103453623
5131.3931.3968700672012-0.0068700672012092
5231.3931.4755748284881-0.0855748284880633
5331.3731.4594410953699-0.0894410953698532
5431.3631.4225784409189-0.0625784409188554
5531.3731.4007803002439-0.0307803002438831
5631.3531.4049771784824-0.0549771784824138
5731.3431.3746121314131-0.0346121314130983
5831.4731.35808658060880.111913419391243
5931.4831.5091860238996-0.029186023899566
6031.5431.51368347684580.0263165231542395
6131.5531.5786450265055-0.0286450265055258
6231.5531.5832444756547-0.0332444756546586
6331.5731.5769767739561-0.00697677395611507
6431.6631.5956614174310.0643385825689613
6531.7431.6977914040020.0422085959980087
6631.7831.7857491438556-0.00574914385560987
6731.831.8246652368906-0.0246652368906375
6831.6831.8400150102256-0.160015010225603
6931.731.68984679936850.0101532006314926
7031.731.7117610191476-0.0117610191475954
7131.7531.7095436715060.0404563284939705
7231.7331.767171050005-0.0371710500050177
7331.8231.74016305698770.0798369430123245
7431.931.84521500572410.0547849942758525
7531.8231.9355438196072-0.115543819607222
7631.5131.8337599237825-0.323759923782507
7731.4231.4627202898508-0.0427202898508057
7830.9731.3646660784973-0.394666078497274
7930.9930.84025824977260.149741750227438
8030.9230.88848960562230.0315103943777437
8130.9530.82443037468160.125569625318398
8230.8230.8781044720585-0.0581044720585311
8330.7230.7371498249768-0.0171498249767978
8430.7330.63391650620670.0960834937933193







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8530.662031476149530.471747079341830.8523158729573
8630.594062952299130.298502081839330.8896238227588
8730.526094428448630.131102957827430.9210858990698
8830.458125904598229.963385280385330.952866528811
8930.390157380747729.793348926782630.9869658347129
9030.322188856897329.620171456311631.0242062574829
9130.254220333046829.443488183889731.0649524822039
9230.186251809196329.263143514353131.1093601040396
9330.118283285345929.0790867773931.1574797933017
9430.050314761495428.891322947666331.2093065753245
9529.98234623764528.69988731683631.2648051584539
9629.914377713794528.504831690532231.3239237370568

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 30.6620314761495 & 30.4717470793418 & 30.8523158729573 \tabularnewline
86 & 30.5940629522991 & 30.2985020818393 & 30.8896238227588 \tabularnewline
87 & 30.5260944284486 & 30.1311029578274 & 30.9210858990698 \tabularnewline
88 & 30.4581259045982 & 29.9633852803853 & 30.952866528811 \tabularnewline
89 & 30.3901573807477 & 29.7933489267826 & 30.9869658347129 \tabularnewline
90 & 30.3221888568973 & 29.6201714563116 & 31.0242062574829 \tabularnewline
91 & 30.2542203330468 & 29.4434881838897 & 31.0649524822039 \tabularnewline
92 & 30.1862518091963 & 29.2631435143531 & 31.1093601040396 \tabularnewline
93 & 30.1182832853459 & 29.07908677739 & 31.1574797933017 \tabularnewline
94 & 30.0503147614954 & 28.8913229476663 & 31.2093065753245 \tabularnewline
95 & 29.982346237645 & 28.699887316836 & 31.2648051584539 \tabularnewline
96 & 29.9143777137945 & 28.5048316905322 & 31.3239237370568 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232426&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]30.6620314761495[/C][C]30.4717470793418[/C][C]30.8523158729573[/C][/ROW]
[ROW][C]86[/C][C]30.5940629522991[/C][C]30.2985020818393[/C][C]30.8896238227588[/C][/ROW]
[ROW][C]87[/C][C]30.5260944284486[/C][C]30.1311029578274[/C][C]30.9210858990698[/C][/ROW]
[ROW][C]88[/C][C]30.4581259045982[/C][C]29.9633852803853[/C][C]30.952866528811[/C][/ROW]
[ROW][C]89[/C][C]30.3901573807477[/C][C]29.7933489267826[/C][C]30.9869658347129[/C][/ROW]
[ROW][C]90[/C][C]30.3221888568973[/C][C]29.6201714563116[/C][C]31.0242062574829[/C][/ROW]
[ROW][C]91[/C][C]30.2542203330468[/C][C]29.4434881838897[/C][C]31.0649524822039[/C][/ROW]
[ROW][C]92[/C][C]30.1862518091963[/C][C]29.2631435143531[/C][C]31.1093601040396[/C][/ROW]
[ROW][C]93[/C][C]30.1182832853459[/C][C]29.07908677739[/C][C]31.1574797933017[/C][/ROW]
[ROW][C]94[/C][C]30.0503147614954[/C][C]28.8913229476663[/C][C]31.2093065753245[/C][/ROW]
[ROW][C]95[/C][C]29.982346237645[/C][C]28.699887316836[/C][C]31.2648051584539[/C][/ROW]
[ROW][C]96[/C][C]29.9143777137945[/C][C]28.5048316905322[/C][C]31.3239237370568[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232426&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232426&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
8530.662031476149530.471747079341830.8523158729573
8630.594062952299130.298502081839330.8896238227588
8730.526094428448630.131102957827430.9210858990698
8830.458125904598229.963385280385330.952866528811
8930.390157380747729.793348926782630.9869658347129
9030.322188856897329.620171456311631.0242062574829
9130.254220333046829.443488183889731.0649524822039
9230.186251809196329.263143514353131.1093601040396
9330.118283285345929.0790867773931.1574797933017
9430.050314761495428.891322947666331.2093065753245
9529.98234623764528.69988731683631.2648051584539
9629.914377713794528.504831690532231.3239237370568



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