Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 Aug 2010 07:49:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/20/t1282290529aviw0rmst0356i8.htm/, Retrieved Wed, 08 May 2024 06:07:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79444, Retrieved Wed, 08 May 2024 06:07:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B Stap 2] [2010-08-20 07:49:05] [6b796205aa6c71fffca3ea7e892beea1] [Current]
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Dataseries X:
76
75
74
72
70
69
70
72
73
73
74
76
74
67
66
58
55
58
64
68
66
76
75
88
85
83
77
66
65
65
63
62
57
68
69
79
74
76
82
75
75
76
78
77
67
74
68
87
76
88
95
96
96
105
108
113
101
107
102
116
105
121
134
140
131
141
131
128
123
129
125
144
135
141
156
159
146
154
145
133
126
127
122
148




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79444&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79444&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79444&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.853661782423506
beta0.00329071622036451
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.853661782423506 \tabularnewline
beta & 0.00329071622036451 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79444&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]0.853661782423506[/C][/ROW]
[ROW][C]beta[/C][C]0.00329071622036451[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79444&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79444&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
alpha0.853661782423506
beta0.00329071622036451
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137480.240411948487-6.24041194848706
146767.632330326825-0.632330326824984
156665.9331569263830.0668430736170222
165857.59821411589110.401785884108882
175554.29940496014020.700595039859763
185856.89749646635671.10250353364327
196464.0993687803489-0.0993687803488683
206865.6137652082172.38623479178297
216668.6120576315391-2.6120576315391
227666.61051137709219.38948862290788
237576.3382818181108-1.33828181811079
248877.794940185377310.2050598146227
258583.46419376386821.53580623613183
268377.51925956600545.48074043399458
277781.1128249630908-4.11282496309083
286667.940679940157-1.94067994015697
296562.28842064933152.71157935066854
306567.1641148449105-2.16411484491054
316372.2921996125122-9.29219961251218
326266.3506539610196-4.35065396101965
335762.7932770504556-5.79327705045564
346859.37433072847428.62566927152582
356966.77756770067012.22243229932992
367972.41097377234756.58902622765245
377474.133741985889-0.133741985889046
387668.0804862848777.91951371512306
398272.51573371330699.4842662866931
407570.87589887085824.12410112914178
417570.74854614940824.25145385059177
427676.6013714626525-0.601371462652509
437882.9872341082717-4.98723410827175
447782.2958932680294-5.29589326802939
456777.8421144404391-10.8421144404391
467472.99293008076381.00706991923616
476872.96481777294-4.96481777294001
488773.035801813325813.9641981866742
497679.7902153235534-3.79021532355343
508871.570844757725116.4291552422749
519583.198529559337211.8014704406628
529681.386930013322914.6130699866771
539689.46500223782986.53499776217018
5410597.1590008033157.840999196685
55108112.637161530114-4.63716153011377
56113113.843811412907-0.843811412907115
57101112.092463834908-11.0924638349082
58107112.4920597365-5.4920597365
59102105.567425895142-3.56742589514207
60116113.2468519250262.75314807497436
61105105.542226559521-0.542226559521424
62121102.06357085947118.9364291405286
63134114.13426313550519.8657368644951
64140115.14321737964224.8567826203578
65131128.6454881031002.35451189690014
66141133.9478404055147.05215959448597
67131149.461821142014-18.4618211420136
68128140.975067209160-12.9750672091596
69123126.940551140281-3.94055114028126
70129136.807948893198-7.80794889319833
71125127.933651460175-2.93365146017474
72144139.9658384766584.03416152334179
73135130.5887325657774.41126743422339
74141133.8989330406527.10106695934772
75156135.08265372769120.9173462723091
76159135.03167594217623.968324057824
77146143.3389928276622.66100717233786
78154150.0685167657053.93148323429509
79145159.416466608536-14.4164666085359
80133156.097421860839-23.0974218608394
81126134.677514939105-8.67751493910461
82127140.353222925781-13.3532229257807
83122127.461348104025-5.46134810402451
84148138.0646668679369.93533313206424

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 74 & 80.240411948487 & -6.24041194848706 \tabularnewline
14 & 67 & 67.632330326825 & -0.632330326824984 \tabularnewline
15 & 66 & 65.933156926383 & 0.0668430736170222 \tabularnewline
16 & 58 & 57.5982141158911 & 0.401785884108882 \tabularnewline
17 & 55 & 54.2994049601402 & 0.700595039859763 \tabularnewline
18 & 58 & 56.8974964663567 & 1.10250353364327 \tabularnewline
19 & 64 & 64.0993687803489 & -0.0993687803488683 \tabularnewline
20 & 68 & 65.613765208217 & 2.38623479178297 \tabularnewline
21 & 66 & 68.6120576315391 & -2.6120576315391 \tabularnewline
22 & 76 & 66.6105113770921 & 9.38948862290788 \tabularnewline
23 & 75 & 76.3382818181108 & -1.33828181811079 \tabularnewline
24 & 88 & 77.7949401853773 & 10.2050598146227 \tabularnewline
25 & 85 & 83.4641937638682 & 1.53580623613183 \tabularnewline
26 & 83 & 77.5192595660054 & 5.48074043399458 \tabularnewline
27 & 77 & 81.1128249630908 & -4.11282496309083 \tabularnewline
28 & 66 & 67.940679940157 & -1.94067994015697 \tabularnewline
29 & 65 & 62.2884206493315 & 2.71157935066854 \tabularnewline
30 & 65 & 67.1641148449105 & -2.16411484491054 \tabularnewline
31 & 63 & 72.2921996125122 & -9.29219961251218 \tabularnewline
32 & 62 & 66.3506539610196 & -4.35065396101965 \tabularnewline
33 & 57 & 62.7932770504556 & -5.79327705045564 \tabularnewline
34 & 68 & 59.3743307284742 & 8.62566927152582 \tabularnewline
35 & 69 & 66.7775677006701 & 2.22243229932992 \tabularnewline
36 & 79 & 72.4109737723475 & 6.58902622765245 \tabularnewline
37 & 74 & 74.133741985889 & -0.133741985889046 \tabularnewline
38 & 76 & 68.080486284877 & 7.91951371512306 \tabularnewline
39 & 82 & 72.5157337133069 & 9.4842662866931 \tabularnewline
40 & 75 & 70.8758988708582 & 4.12410112914178 \tabularnewline
41 & 75 & 70.7485461494082 & 4.25145385059177 \tabularnewline
42 & 76 & 76.6013714626525 & -0.601371462652509 \tabularnewline
43 & 78 & 82.9872341082717 & -4.98723410827175 \tabularnewline
44 & 77 & 82.2958932680294 & -5.29589326802939 \tabularnewline
45 & 67 & 77.8421144404391 & -10.8421144404391 \tabularnewline
46 & 74 & 72.9929300807638 & 1.00706991923616 \tabularnewline
47 & 68 & 72.96481777294 & -4.96481777294001 \tabularnewline
48 & 87 & 73.0358018133258 & 13.9641981866742 \tabularnewline
49 & 76 & 79.7902153235534 & -3.79021532355343 \tabularnewline
50 & 88 & 71.5708447577251 & 16.4291552422749 \tabularnewline
51 & 95 & 83.1985295593372 & 11.8014704406628 \tabularnewline
52 & 96 & 81.3869300133229 & 14.6130699866771 \tabularnewline
53 & 96 & 89.4650022378298 & 6.53499776217018 \tabularnewline
54 & 105 & 97.159000803315 & 7.840999196685 \tabularnewline
55 & 108 & 112.637161530114 & -4.63716153011377 \tabularnewline
56 & 113 & 113.843811412907 & -0.843811412907115 \tabularnewline
57 & 101 & 112.092463834908 & -11.0924638349082 \tabularnewline
58 & 107 & 112.4920597365 & -5.4920597365 \tabularnewline
59 & 102 & 105.567425895142 & -3.56742589514207 \tabularnewline
60 & 116 & 113.246851925026 & 2.75314807497436 \tabularnewline
61 & 105 & 105.542226559521 & -0.542226559521424 \tabularnewline
62 & 121 & 102.063570859471 & 18.9364291405286 \tabularnewline
63 & 134 & 114.134263135505 & 19.8657368644951 \tabularnewline
64 & 140 & 115.143217379642 & 24.8567826203578 \tabularnewline
65 & 131 & 128.645488103100 & 2.35451189690014 \tabularnewline
66 & 141 & 133.947840405514 & 7.05215959448597 \tabularnewline
67 & 131 & 149.461821142014 & -18.4618211420136 \tabularnewline
68 & 128 & 140.975067209160 & -12.9750672091596 \tabularnewline
69 & 123 & 126.940551140281 & -3.94055114028126 \tabularnewline
70 & 129 & 136.807948893198 & -7.80794889319833 \tabularnewline
71 & 125 & 127.933651460175 & -2.93365146017474 \tabularnewline
72 & 144 & 139.965838476658 & 4.03416152334179 \tabularnewline
73 & 135 & 130.588732565777 & 4.41126743422339 \tabularnewline
74 & 141 & 133.898933040652 & 7.10106695934772 \tabularnewline
75 & 156 & 135.082653727691 & 20.9173462723091 \tabularnewline
76 & 159 & 135.031675942176 & 23.968324057824 \tabularnewline
77 & 146 & 143.338992827662 & 2.66100717233786 \tabularnewline
78 & 154 & 150.068516765705 & 3.93148323429509 \tabularnewline
79 & 145 & 159.416466608536 & -14.4164666085359 \tabularnewline
80 & 133 & 156.097421860839 & -23.0974218608394 \tabularnewline
81 & 126 & 134.677514939105 & -8.67751493910461 \tabularnewline
82 & 127 & 140.353222925781 & -13.3532229257807 \tabularnewline
83 & 122 & 127.461348104025 & -5.46134810402451 \tabularnewline
84 & 148 & 138.064666867936 & 9.93533313206424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79444&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]74[/C][C]80.240411948487[/C][C]-6.24041194848706[/C][/ROW]
[ROW][C]14[/C][C]67[/C][C]67.632330326825[/C][C]-0.632330326824984[/C][/ROW]
[ROW][C]15[/C][C]66[/C][C]65.933156926383[/C][C]0.0668430736170222[/C][/ROW]
[ROW][C]16[/C][C]58[/C][C]57.5982141158911[/C][C]0.401785884108882[/C][/ROW]
[ROW][C]17[/C][C]55[/C][C]54.2994049601402[/C][C]0.700595039859763[/C][/ROW]
[ROW][C]18[/C][C]58[/C][C]56.8974964663567[/C][C]1.10250353364327[/C][/ROW]
[ROW][C]19[/C][C]64[/C][C]64.0993687803489[/C][C]-0.0993687803488683[/C][/ROW]
[ROW][C]20[/C][C]68[/C][C]65.613765208217[/C][C]2.38623479178297[/C][/ROW]
[ROW][C]21[/C][C]66[/C][C]68.6120576315391[/C][C]-2.6120576315391[/C][/ROW]
[ROW][C]22[/C][C]76[/C][C]66.6105113770921[/C][C]9.38948862290788[/C][/ROW]
[ROW][C]23[/C][C]75[/C][C]76.3382818181108[/C][C]-1.33828181811079[/C][/ROW]
[ROW][C]24[/C][C]88[/C][C]77.7949401853773[/C][C]10.2050598146227[/C][/ROW]
[ROW][C]25[/C][C]85[/C][C]83.4641937638682[/C][C]1.53580623613183[/C][/ROW]
[ROW][C]26[/C][C]83[/C][C]77.5192595660054[/C][C]5.48074043399458[/C][/ROW]
[ROW][C]27[/C][C]77[/C][C]81.1128249630908[/C][C]-4.11282496309083[/C][/ROW]
[ROW][C]28[/C][C]66[/C][C]67.940679940157[/C][C]-1.94067994015697[/C][/ROW]
[ROW][C]29[/C][C]65[/C][C]62.2884206493315[/C][C]2.71157935066854[/C][/ROW]
[ROW][C]30[/C][C]65[/C][C]67.1641148449105[/C][C]-2.16411484491054[/C][/ROW]
[ROW][C]31[/C][C]63[/C][C]72.2921996125122[/C][C]-9.29219961251218[/C][/ROW]
[ROW][C]32[/C][C]62[/C][C]66.3506539610196[/C][C]-4.35065396101965[/C][/ROW]
[ROW][C]33[/C][C]57[/C][C]62.7932770504556[/C][C]-5.79327705045564[/C][/ROW]
[ROW][C]34[/C][C]68[/C][C]59.3743307284742[/C][C]8.62566927152582[/C][/ROW]
[ROW][C]35[/C][C]69[/C][C]66.7775677006701[/C][C]2.22243229932992[/C][/ROW]
[ROW][C]36[/C][C]79[/C][C]72.4109737723475[/C][C]6.58902622765245[/C][/ROW]
[ROW][C]37[/C][C]74[/C][C]74.133741985889[/C][C]-0.133741985889046[/C][/ROW]
[ROW][C]38[/C][C]76[/C][C]68.080486284877[/C][C]7.91951371512306[/C][/ROW]
[ROW][C]39[/C][C]82[/C][C]72.5157337133069[/C][C]9.4842662866931[/C][/ROW]
[ROW][C]40[/C][C]75[/C][C]70.8758988708582[/C][C]4.12410112914178[/C][/ROW]
[ROW][C]41[/C][C]75[/C][C]70.7485461494082[/C][C]4.25145385059177[/C][/ROW]
[ROW][C]42[/C][C]76[/C][C]76.6013714626525[/C][C]-0.601371462652509[/C][/ROW]
[ROW][C]43[/C][C]78[/C][C]82.9872341082717[/C][C]-4.98723410827175[/C][/ROW]
[ROW][C]44[/C][C]77[/C][C]82.2958932680294[/C][C]-5.29589326802939[/C][/ROW]
[ROW][C]45[/C][C]67[/C][C]77.8421144404391[/C][C]-10.8421144404391[/C][/ROW]
[ROW][C]46[/C][C]74[/C][C]72.9929300807638[/C][C]1.00706991923616[/C][/ROW]
[ROW][C]47[/C][C]68[/C][C]72.96481777294[/C][C]-4.96481777294001[/C][/ROW]
[ROW][C]48[/C][C]87[/C][C]73.0358018133258[/C][C]13.9641981866742[/C][/ROW]
[ROW][C]49[/C][C]76[/C][C]79.7902153235534[/C][C]-3.79021532355343[/C][/ROW]
[ROW][C]50[/C][C]88[/C][C]71.5708447577251[/C][C]16.4291552422749[/C][/ROW]
[ROW][C]51[/C][C]95[/C][C]83.1985295593372[/C][C]11.8014704406628[/C][/ROW]
[ROW][C]52[/C][C]96[/C][C]81.3869300133229[/C][C]14.6130699866771[/C][/ROW]
[ROW][C]53[/C][C]96[/C][C]89.4650022378298[/C][C]6.53499776217018[/C][/ROW]
[ROW][C]54[/C][C]105[/C][C]97.159000803315[/C][C]7.840999196685[/C][/ROW]
[ROW][C]55[/C][C]108[/C][C]112.637161530114[/C][C]-4.63716153011377[/C][/ROW]
[ROW][C]56[/C][C]113[/C][C]113.843811412907[/C][C]-0.843811412907115[/C][/ROW]
[ROW][C]57[/C][C]101[/C][C]112.092463834908[/C][C]-11.0924638349082[/C][/ROW]
[ROW][C]58[/C][C]107[/C][C]112.4920597365[/C][C]-5.4920597365[/C][/ROW]
[ROW][C]59[/C][C]102[/C][C]105.567425895142[/C][C]-3.56742589514207[/C][/ROW]
[ROW][C]60[/C][C]116[/C][C]113.246851925026[/C][C]2.75314807497436[/C][/ROW]
[ROW][C]61[/C][C]105[/C][C]105.542226559521[/C][C]-0.542226559521424[/C][/ROW]
[ROW][C]62[/C][C]121[/C][C]102.063570859471[/C][C]18.9364291405286[/C][/ROW]
[ROW][C]63[/C][C]134[/C][C]114.134263135505[/C][C]19.8657368644951[/C][/ROW]
[ROW][C]64[/C][C]140[/C][C]115.143217379642[/C][C]24.8567826203578[/C][/ROW]
[ROW][C]65[/C][C]131[/C][C]128.645488103100[/C][C]2.35451189690014[/C][/ROW]
[ROW][C]66[/C][C]141[/C][C]133.947840405514[/C][C]7.05215959448597[/C][/ROW]
[ROW][C]67[/C][C]131[/C][C]149.461821142014[/C][C]-18.4618211420136[/C][/ROW]
[ROW][C]68[/C][C]128[/C][C]140.975067209160[/C][C]-12.9750672091596[/C][/ROW]
[ROW][C]69[/C][C]123[/C][C]126.940551140281[/C][C]-3.94055114028126[/C][/ROW]
[ROW][C]70[/C][C]129[/C][C]136.807948893198[/C][C]-7.80794889319833[/C][/ROW]
[ROW][C]71[/C][C]125[/C][C]127.933651460175[/C][C]-2.93365146017474[/C][/ROW]
[ROW][C]72[/C][C]144[/C][C]139.965838476658[/C][C]4.03416152334179[/C][/ROW]
[ROW][C]73[/C][C]135[/C][C]130.588732565777[/C][C]4.41126743422339[/C][/ROW]
[ROW][C]74[/C][C]141[/C][C]133.898933040652[/C][C]7.10106695934772[/C][/ROW]
[ROW][C]75[/C][C]156[/C][C]135.082653727691[/C][C]20.9173462723091[/C][/ROW]
[ROW][C]76[/C][C]159[/C][C]135.031675942176[/C][C]23.968324057824[/C][/ROW]
[ROW][C]77[/C][C]146[/C][C]143.338992827662[/C][C]2.66100717233786[/C][/ROW]
[ROW][C]78[/C][C]154[/C][C]150.068516765705[/C][C]3.93148323429509[/C][/ROW]
[ROW][C]79[/C][C]145[/C][C]159.416466608536[/C][C]-14.4164666085359[/C][/ROW]
[ROW][C]80[/C][C]133[/C][C]156.097421860839[/C][C]-23.0974218608394[/C][/ROW]
[ROW][C]81[/C][C]126[/C][C]134.677514939105[/C][C]-8.67751493910461[/C][/ROW]
[ROW][C]82[/C][C]127[/C][C]140.353222925781[/C][C]-13.3532229257807[/C][/ROW]
[ROW][C]83[/C][C]122[/C][C]127.461348104025[/C][C]-5.46134810402451[/C][/ROW]
[ROW][C]84[/C][C]148[/C][C]138.064666867936[/C][C]9.93533313206424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79444&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79444&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
137480.240411948487-6.24041194848706
146767.632330326825-0.632330326824984
156665.9331569263830.0668430736170222
165857.59821411589110.401785884108882
175554.29940496014020.700595039859763
185856.89749646635671.10250353364327
196464.0993687803489-0.0993687803488683
206865.6137652082172.38623479178297
216668.6120576315391-2.6120576315391
227666.61051137709219.38948862290788
237576.3382818181108-1.33828181811079
248877.794940185377310.2050598146227
258583.46419376386821.53580623613183
268377.51925956600545.48074043399458
277781.1128249630908-4.11282496309083
286667.940679940157-1.94067994015697
296562.28842064933152.71157935066854
306567.1641148449105-2.16411484491054
316372.2921996125122-9.29219961251218
326266.3506539610196-4.35065396101965
335762.7932770504556-5.79327705045564
346859.37433072847428.62566927152582
356966.77756770067012.22243229932992
367972.41097377234756.58902622765245
377474.133741985889-0.133741985889046
387668.0804862848777.91951371512306
398272.51573371330699.4842662866931
407570.87589887085824.12410112914178
417570.74854614940824.25145385059177
427676.6013714626525-0.601371462652509
437882.9872341082717-4.98723410827175
447782.2958932680294-5.29589326802939
456777.8421144404391-10.8421144404391
467472.99293008076381.00706991923616
476872.96481777294-4.96481777294001
488773.035801813325813.9641981866742
497679.7902153235534-3.79021532355343
508871.570844757725116.4291552422749
519583.198529559337211.8014704406628
529681.386930013322914.6130699866771
539689.46500223782986.53499776217018
5410597.1590008033157.840999196685
55108112.637161530114-4.63716153011377
56113113.843811412907-0.843811412907115
57101112.092463834908-11.0924638349082
58107112.4920597365-5.4920597365
59102105.567425895142-3.56742589514207
60116113.2468519250262.75314807497436
61105105.542226559521-0.542226559521424
62121102.06357085947118.9364291405286
63134114.13426313550519.8657368644951
64140115.14321737964224.8567826203578
65131128.6454881031002.35451189690014
66141133.9478404055147.05215959448597
67131149.461821142014-18.4618211420136
68128140.975067209160-12.9750672091596
69123126.940551140281-3.94055114028126
70129136.807948893198-7.80794889319833
71125127.933651460175-2.93365146017474
72144139.9658384766584.03416152334179
73135130.5887325657774.41126743422339
74141133.8989330406527.10106695934772
75156135.08265372769120.9173462723091
76159135.03167594217623.968324057824
77146143.3389928276622.66100717233786
78154150.0685167657053.93148323429509
79145159.416466608536-14.4164666085359
80133156.097421860839-23.0974218608394
81126134.677514939105-8.67751493910461
82127140.353222925781-13.3532229257807
83122127.461348104025-5.46134810402451
84148138.0646668679369.93533313206424







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85133.561981257641115.204119823497151.919842691785
86133.459104619344109.269193710852157.649015527836
87130.386347762239101.857488712259158.915206812219
88115.30211132755885.1568190588556145.447403596261
89104.05916092653572.2682384314985135.850083421571
90107.18307471393370.797189837427143.568959590438
91109.17051765646968.7855548293011149.555480483636
92114.45234631339169.1826047770838159.722087849698
93114.65403334440866.4320877355408162.875978953275
94125.72373004003970.4490874561326180.998372623946
95125.36506605802367.7519959965753182.978136119471
96143.32011251063048.2934173403048238.346807680956

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 133.561981257641 & 115.204119823497 & 151.919842691785 \tabularnewline
86 & 133.459104619344 & 109.269193710852 & 157.649015527836 \tabularnewline
87 & 130.386347762239 & 101.857488712259 & 158.915206812219 \tabularnewline
88 & 115.302111327558 & 85.1568190588556 & 145.447403596261 \tabularnewline
89 & 104.059160926535 & 72.2682384314985 & 135.850083421571 \tabularnewline
90 & 107.183074713933 & 70.797189837427 & 143.568959590438 \tabularnewline
91 & 109.170517656469 & 68.7855548293011 & 149.555480483636 \tabularnewline
92 & 114.452346313391 & 69.1826047770838 & 159.722087849698 \tabularnewline
93 & 114.654033344408 & 66.4320877355408 & 162.875978953275 \tabularnewline
94 & 125.723730040039 & 70.4490874561326 & 180.998372623946 \tabularnewline
95 & 125.365066058023 & 67.7519959965753 & 182.978136119471 \tabularnewline
96 & 143.320112510630 & 48.2934173403048 & 238.346807680956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79444&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]133.561981257641[/C][C]115.204119823497[/C][C]151.919842691785[/C][/ROW]
[ROW][C]86[/C][C]133.459104619344[/C][C]109.269193710852[/C][C]157.649015527836[/C][/ROW]
[ROW][C]87[/C][C]130.386347762239[/C][C]101.857488712259[/C][C]158.915206812219[/C][/ROW]
[ROW][C]88[/C][C]115.302111327558[/C][C]85.1568190588556[/C][C]145.447403596261[/C][/ROW]
[ROW][C]89[/C][C]104.059160926535[/C][C]72.2682384314985[/C][C]135.850083421571[/C][/ROW]
[ROW][C]90[/C][C]107.183074713933[/C][C]70.797189837427[/C][C]143.568959590438[/C][/ROW]
[ROW][C]91[/C][C]109.170517656469[/C][C]68.7855548293011[/C][C]149.555480483636[/C][/ROW]
[ROW][C]92[/C][C]114.452346313391[/C][C]69.1826047770838[/C][C]159.722087849698[/C][/ROW]
[ROW][C]93[/C][C]114.654033344408[/C][C]66.4320877355408[/C][C]162.875978953275[/C][/ROW]
[ROW][C]94[/C][C]125.723730040039[/C][C]70.4490874561326[/C][C]180.998372623946[/C][/ROW]
[ROW][C]95[/C][C]125.365066058023[/C][C]67.7519959965753[/C][C]182.978136119471[/C][/ROW]
[ROW][C]96[/C][C]143.320112510630[/C][C]48.2934173403048[/C][C]238.346807680956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79444&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79444&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
85133.561981257641115.204119823497151.919842691785
86133.459104619344109.269193710852157.649015527836
87130.386347762239101.857488712259158.915206812219
88115.30211132755885.1568190588556145.447403596261
89104.05916092653572.2682384314985135.850083421571
90107.18307471393370.797189837427143.568959590438
91109.17051765646968.7855548293011149.555480483636
92114.45234631339169.1826047770838159.722087849698
93114.65403334440866.4320877355408162.875978953275
94125.72373004003970.4490874561326180.998372623946
95125.36506605802367.7519959965753182.978136119471
96143.32011251063048.2934173403048238.346807680956



Parameters (Session):
par1 = 12 ;
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=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')