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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Jun 2009 13:33:43 -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/07/t1244403265xhk1l9ag8xtuxuu.htm/, Retrieved Sun, 12 May 2024 17:39:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42242, Retrieved Sun, 12 May 2024 17:39:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Thomas Van den Bo...] [2009-06-07 19:33:43] [50e97696ebad247f45d73cd9926afb25] [Current]
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Dataseries X:
36.80
35.40
33.00
28.73
26.70
26.46
24.60
28.00
31.60
33.50
34.50
35.00
34.76
33.50
32.74
34.40
31.93
29.24
25.75
26.03
26.08
23.80
20.61
19.70
18.18
19.60
20.60
20.03
23.00
23.60
22.56
22.55
23.75
24.92
24.50
30.58
28.07
27.70
27.00
25.23
26.86
25.60
24.55
23.96
23.50
23.64
21.55
21.05
21.89
21.98
21.45
22.15
22.58
23.80
23.30
22.38
23.00
21.96
22.40
20.80
20.40
16.00
12.78
9.75
7.50
11.24
12.24
12.75
12.52
14.49
14.21
14.32
22.15
22.58
23.80
23.30
22.38
23.00
21.96
22.40
20.80
20.40
16.00
12.78
9.75
7.50
11.24
12.24
12.75
12.52
14.49
14.21
14.32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42242&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42242&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.777924358723283
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.777924358723283 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42242&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]0.777924358723283[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42242&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
alpha0.777924358723283
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1334.7633.4384214743591.32157852564102
1433.533.14713751517360.352862484826353
1532.7432.8801824178193-0.140182417819275
1634.434.9717590140859-0.571759014085856
1731.9332.9463516634618-1.01635166346177
1829.2430.5884181945122-1.34841819451218
1925.7522.54924541567513.20075458432493
2026.0328.5098182868696-2.47981828686955
2126.0830.1771684833925-4.09716848339253
2223.828.5709258987877-4.77092589878773
2320.6125.3118010088766-4.70180100887656
2419.721.7268667212880-2.02686672128803
2518.1819.946319372578-1.76631937257799
2619.617.03775618513872.56224381486130
2720.618.38003937919372.21996062080629
2820.0322.2117860859024-2.18178608590237
292318.83516626019124.16483373980877
3023.620.43405923567783.16594076432225
3122.5616.91697671707755.64302328292253
3222.5523.5159330362688-0.96593303626879
3323.7526.0017973634841-2.25179736348414
3424.9225.6814888138517-0.761488813851706
3524.525.5567536513359-1.05675365133595
3630.5825.40142823916755.1785717608325
3728.0729.2840282205289-1.21402822052886
3827.727.7663742190333-0.0663742190332997
392726.98777865492440.0122213450756092
4025.2328.1245504787021-2.89455047870205
4126.8625.60288353753581.25711646246424
4225.624.71796261659740.882037383402555
4324.5519.97427571382284.57572428617723
4423.9624.2752659326508-0.315265932650782
4523.526.9817409041293-3.4817409041293
4623.6426.0355905412344-2.39559054123443
4721.5524.5740767122251-3.02407671222508
4821.0524.2730366589892-3.22303665898924
4921.8920.20018005783031.68981994216971
5021.9821.19636627447770.78363372552229
5121.4521.09646675584790.353533244152104
5222.1521.85323020302870.296769796971251
5322.5822.7361531391231-0.15615313912307
5423.820.66851944265473.13148055734527
5523.318.4950070660634.80499293393699
5622.3821.88818116135050.491818838649493
572324.5193100761003-1.51931007610035
5821.9625.3409899950015-3.38098999500152
5922.422.9733384583778-0.57333845837784
6020.824.5346032318987-3.7346032318987
6120.421.1548123127678-0.754812312767822
621620.0480176650006-4.04801766500061
6312.7816.0939439966101-3.3139439966101
649.7513.9850817842050-4.23508178420502
657.511.2419838337016-3.74198383370162
6611.247.114948455089154.12505154491085
6712.246.086005486061576.15399451393843
6812.759.570749867239293.17925013276071
6912.5213.8458743046403-1.32587430464027
7014.4914.40459886016670.0854011398333014
7114.2115.3570484396707-1.14704843967073
7214.3215.7699703420760-1.44997034207604
7322.1514.82918997791517.3208100220849
7422.5819.27327796582663.3067220341734
7523.821.20365534214492.59634465785512
7623.323.4879883762498-0.187988376249788
7722.3824.0027280133935-1.62272801339346
782323.2713902864168-0.271390286416789
7921.9619.27292693605012.68707306394987
8022.419.40005040541712.99994959458285
8120.822.5352141881701-1.73521418817014
8220.423.0889131766513-2.68891317665128
831621.6094590398976-5.60945903989764
8412.7818.4836914620280-5.70369146202803
859.7516.1816144973090-6.43161449730903
867.59.03592529602405-1.53592529602405
8711.247.04133184208114.1986681579189
8812.249.953818813363582.28618118663642
8912.7512.07465449610440.675345503895638
9012.5213.4311433286635-0.911143328663542
9114.499.592003148892154.89799685110785
9214.2111.50854034375082.70145965624916
9314.3213.35993699903510.960063000964904

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 34.76 & 33.438421474359 & 1.32157852564102 \tabularnewline
14 & 33.5 & 33.1471375151736 & 0.352862484826353 \tabularnewline
15 & 32.74 & 32.8801824178193 & -0.140182417819275 \tabularnewline
16 & 34.4 & 34.9717590140859 & -0.571759014085856 \tabularnewline
17 & 31.93 & 32.9463516634618 & -1.01635166346177 \tabularnewline
18 & 29.24 & 30.5884181945122 & -1.34841819451218 \tabularnewline
19 & 25.75 & 22.5492454156751 & 3.20075458432493 \tabularnewline
20 & 26.03 & 28.5098182868696 & -2.47981828686955 \tabularnewline
21 & 26.08 & 30.1771684833925 & -4.09716848339253 \tabularnewline
22 & 23.8 & 28.5709258987877 & -4.77092589878773 \tabularnewline
23 & 20.61 & 25.3118010088766 & -4.70180100887656 \tabularnewline
24 & 19.7 & 21.7268667212880 & -2.02686672128803 \tabularnewline
25 & 18.18 & 19.946319372578 & -1.76631937257799 \tabularnewline
26 & 19.6 & 17.0377561851387 & 2.56224381486130 \tabularnewline
27 & 20.6 & 18.3800393791937 & 2.21996062080629 \tabularnewline
28 & 20.03 & 22.2117860859024 & -2.18178608590237 \tabularnewline
29 & 23 & 18.8351662601912 & 4.16483373980877 \tabularnewline
30 & 23.6 & 20.4340592356778 & 3.16594076432225 \tabularnewline
31 & 22.56 & 16.9169767170775 & 5.64302328292253 \tabularnewline
32 & 22.55 & 23.5159330362688 & -0.96593303626879 \tabularnewline
33 & 23.75 & 26.0017973634841 & -2.25179736348414 \tabularnewline
34 & 24.92 & 25.6814888138517 & -0.761488813851706 \tabularnewline
35 & 24.5 & 25.5567536513359 & -1.05675365133595 \tabularnewline
36 & 30.58 & 25.4014282391675 & 5.1785717608325 \tabularnewline
37 & 28.07 & 29.2840282205289 & -1.21402822052886 \tabularnewline
38 & 27.7 & 27.7663742190333 & -0.0663742190332997 \tabularnewline
39 & 27 & 26.9877786549244 & 0.0122213450756092 \tabularnewline
40 & 25.23 & 28.1245504787021 & -2.89455047870205 \tabularnewline
41 & 26.86 & 25.6028835375358 & 1.25711646246424 \tabularnewline
42 & 25.6 & 24.7179626165974 & 0.882037383402555 \tabularnewline
43 & 24.55 & 19.9742757138228 & 4.57572428617723 \tabularnewline
44 & 23.96 & 24.2752659326508 & -0.315265932650782 \tabularnewline
45 & 23.5 & 26.9817409041293 & -3.4817409041293 \tabularnewline
46 & 23.64 & 26.0355905412344 & -2.39559054123443 \tabularnewline
47 & 21.55 & 24.5740767122251 & -3.02407671222508 \tabularnewline
48 & 21.05 & 24.2730366589892 & -3.22303665898924 \tabularnewline
49 & 21.89 & 20.2001800578303 & 1.68981994216971 \tabularnewline
50 & 21.98 & 21.1963662744777 & 0.78363372552229 \tabularnewline
51 & 21.45 & 21.0964667558479 & 0.353533244152104 \tabularnewline
52 & 22.15 & 21.8532302030287 & 0.296769796971251 \tabularnewline
53 & 22.58 & 22.7361531391231 & -0.15615313912307 \tabularnewline
54 & 23.8 & 20.6685194426547 & 3.13148055734527 \tabularnewline
55 & 23.3 & 18.495007066063 & 4.80499293393699 \tabularnewline
56 & 22.38 & 21.8881811613505 & 0.491818838649493 \tabularnewline
57 & 23 & 24.5193100761003 & -1.51931007610035 \tabularnewline
58 & 21.96 & 25.3409899950015 & -3.38098999500152 \tabularnewline
59 & 22.4 & 22.9733384583778 & -0.57333845837784 \tabularnewline
60 & 20.8 & 24.5346032318987 & -3.7346032318987 \tabularnewline
61 & 20.4 & 21.1548123127678 & -0.754812312767822 \tabularnewline
62 & 16 & 20.0480176650006 & -4.04801766500061 \tabularnewline
63 & 12.78 & 16.0939439966101 & -3.3139439966101 \tabularnewline
64 & 9.75 & 13.9850817842050 & -4.23508178420502 \tabularnewline
65 & 7.5 & 11.2419838337016 & -3.74198383370162 \tabularnewline
66 & 11.24 & 7.11494845508915 & 4.12505154491085 \tabularnewline
67 & 12.24 & 6.08600548606157 & 6.15399451393843 \tabularnewline
68 & 12.75 & 9.57074986723929 & 3.17925013276071 \tabularnewline
69 & 12.52 & 13.8458743046403 & -1.32587430464027 \tabularnewline
70 & 14.49 & 14.4045988601667 & 0.0854011398333014 \tabularnewline
71 & 14.21 & 15.3570484396707 & -1.14704843967073 \tabularnewline
72 & 14.32 & 15.7699703420760 & -1.44997034207604 \tabularnewline
73 & 22.15 & 14.8291899779151 & 7.3208100220849 \tabularnewline
74 & 22.58 & 19.2732779658266 & 3.3067220341734 \tabularnewline
75 & 23.8 & 21.2036553421449 & 2.59634465785512 \tabularnewline
76 & 23.3 & 23.4879883762498 & -0.187988376249788 \tabularnewline
77 & 22.38 & 24.0027280133935 & -1.62272801339346 \tabularnewline
78 & 23 & 23.2713902864168 & -0.271390286416789 \tabularnewline
79 & 21.96 & 19.2729269360501 & 2.68707306394987 \tabularnewline
80 & 22.4 & 19.4000504054171 & 2.99994959458285 \tabularnewline
81 & 20.8 & 22.5352141881701 & -1.73521418817014 \tabularnewline
82 & 20.4 & 23.0889131766513 & -2.68891317665128 \tabularnewline
83 & 16 & 21.6094590398976 & -5.60945903989764 \tabularnewline
84 & 12.78 & 18.4836914620280 & -5.70369146202803 \tabularnewline
85 & 9.75 & 16.1816144973090 & -6.43161449730903 \tabularnewline
86 & 7.5 & 9.03592529602405 & -1.53592529602405 \tabularnewline
87 & 11.24 & 7.0413318420811 & 4.1986681579189 \tabularnewline
88 & 12.24 & 9.95381881336358 & 2.28618118663642 \tabularnewline
89 & 12.75 & 12.0746544961044 & 0.675345503895638 \tabularnewline
90 & 12.52 & 13.4311433286635 & -0.911143328663542 \tabularnewline
91 & 14.49 & 9.59200314889215 & 4.89799685110785 \tabularnewline
92 & 14.21 & 11.5085403437508 & 2.70145965624916 \tabularnewline
93 & 14.32 & 13.3599369990351 & 0.960063000964904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42242&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]34.76[/C][C]33.438421474359[/C][C]1.32157852564102[/C][/ROW]
[ROW][C]14[/C][C]33.5[/C][C]33.1471375151736[/C][C]0.352862484826353[/C][/ROW]
[ROW][C]15[/C][C]32.74[/C][C]32.8801824178193[/C][C]-0.140182417819275[/C][/ROW]
[ROW][C]16[/C][C]34.4[/C][C]34.9717590140859[/C][C]-0.571759014085856[/C][/ROW]
[ROW][C]17[/C][C]31.93[/C][C]32.9463516634618[/C][C]-1.01635166346177[/C][/ROW]
[ROW][C]18[/C][C]29.24[/C][C]30.5884181945122[/C][C]-1.34841819451218[/C][/ROW]
[ROW][C]19[/C][C]25.75[/C][C]22.5492454156751[/C][C]3.20075458432493[/C][/ROW]
[ROW][C]20[/C][C]26.03[/C][C]28.5098182868696[/C][C]-2.47981828686955[/C][/ROW]
[ROW][C]21[/C][C]26.08[/C][C]30.1771684833925[/C][C]-4.09716848339253[/C][/ROW]
[ROW][C]22[/C][C]23.8[/C][C]28.5709258987877[/C][C]-4.77092589878773[/C][/ROW]
[ROW][C]23[/C][C]20.61[/C][C]25.3118010088766[/C][C]-4.70180100887656[/C][/ROW]
[ROW][C]24[/C][C]19.7[/C][C]21.7268667212880[/C][C]-2.02686672128803[/C][/ROW]
[ROW][C]25[/C][C]18.18[/C][C]19.946319372578[/C][C]-1.76631937257799[/C][/ROW]
[ROW][C]26[/C][C]19.6[/C][C]17.0377561851387[/C][C]2.56224381486130[/C][/ROW]
[ROW][C]27[/C][C]20.6[/C][C]18.3800393791937[/C][C]2.21996062080629[/C][/ROW]
[ROW][C]28[/C][C]20.03[/C][C]22.2117860859024[/C][C]-2.18178608590237[/C][/ROW]
[ROW][C]29[/C][C]23[/C][C]18.8351662601912[/C][C]4.16483373980877[/C][/ROW]
[ROW][C]30[/C][C]23.6[/C][C]20.4340592356778[/C][C]3.16594076432225[/C][/ROW]
[ROW][C]31[/C][C]22.56[/C][C]16.9169767170775[/C][C]5.64302328292253[/C][/ROW]
[ROW][C]32[/C][C]22.55[/C][C]23.5159330362688[/C][C]-0.96593303626879[/C][/ROW]
[ROW][C]33[/C][C]23.75[/C][C]26.0017973634841[/C][C]-2.25179736348414[/C][/ROW]
[ROW][C]34[/C][C]24.92[/C][C]25.6814888138517[/C][C]-0.761488813851706[/C][/ROW]
[ROW][C]35[/C][C]24.5[/C][C]25.5567536513359[/C][C]-1.05675365133595[/C][/ROW]
[ROW][C]36[/C][C]30.58[/C][C]25.4014282391675[/C][C]5.1785717608325[/C][/ROW]
[ROW][C]37[/C][C]28.07[/C][C]29.2840282205289[/C][C]-1.21402822052886[/C][/ROW]
[ROW][C]38[/C][C]27.7[/C][C]27.7663742190333[/C][C]-0.0663742190332997[/C][/ROW]
[ROW][C]39[/C][C]27[/C][C]26.9877786549244[/C][C]0.0122213450756092[/C][/ROW]
[ROW][C]40[/C][C]25.23[/C][C]28.1245504787021[/C][C]-2.89455047870205[/C][/ROW]
[ROW][C]41[/C][C]26.86[/C][C]25.6028835375358[/C][C]1.25711646246424[/C][/ROW]
[ROW][C]42[/C][C]25.6[/C][C]24.7179626165974[/C][C]0.882037383402555[/C][/ROW]
[ROW][C]43[/C][C]24.55[/C][C]19.9742757138228[/C][C]4.57572428617723[/C][/ROW]
[ROW][C]44[/C][C]23.96[/C][C]24.2752659326508[/C][C]-0.315265932650782[/C][/ROW]
[ROW][C]45[/C][C]23.5[/C][C]26.9817409041293[/C][C]-3.4817409041293[/C][/ROW]
[ROW][C]46[/C][C]23.64[/C][C]26.0355905412344[/C][C]-2.39559054123443[/C][/ROW]
[ROW][C]47[/C][C]21.55[/C][C]24.5740767122251[/C][C]-3.02407671222508[/C][/ROW]
[ROW][C]48[/C][C]21.05[/C][C]24.2730366589892[/C][C]-3.22303665898924[/C][/ROW]
[ROW][C]49[/C][C]21.89[/C][C]20.2001800578303[/C][C]1.68981994216971[/C][/ROW]
[ROW][C]50[/C][C]21.98[/C][C]21.1963662744777[/C][C]0.78363372552229[/C][/ROW]
[ROW][C]51[/C][C]21.45[/C][C]21.0964667558479[/C][C]0.353533244152104[/C][/ROW]
[ROW][C]52[/C][C]22.15[/C][C]21.8532302030287[/C][C]0.296769796971251[/C][/ROW]
[ROW][C]53[/C][C]22.58[/C][C]22.7361531391231[/C][C]-0.15615313912307[/C][/ROW]
[ROW][C]54[/C][C]23.8[/C][C]20.6685194426547[/C][C]3.13148055734527[/C][/ROW]
[ROW][C]55[/C][C]23.3[/C][C]18.495007066063[/C][C]4.80499293393699[/C][/ROW]
[ROW][C]56[/C][C]22.38[/C][C]21.8881811613505[/C][C]0.491818838649493[/C][/ROW]
[ROW][C]57[/C][C]23[/C][C]24.5193100761003[/C][C]-1.51931007610035[/C][/ROW]
[ROW][C]58[/C][C]21.96[/C][C]25.3409899950015[/C][C]-3.38098999500152[/C][/ROW]
[ROW][C]59[/C][C]22.4[/C][C]22.9733384583778[/C][C]-0.57333845837784[/C][/ROW]
[ROW][C]60[/C][C]20.8[/C][C]24.5346032318987[/C][C]-3.7346032318987[/C][/ROW]
[ROW][C]61[/C][C]20.4[/C][C]21.1548123127678[/C][C]-0.754812312767822[/C][/ROW]
[ROW][C]62[/C][C]16[/C][C]20.0480176650006[/C][C]-4.04801766500061[/C][/ROW]
[ROW][C]63[/C][C]12.78[/C][C]16.0939439966101[/C][C]-3.3139439966101[/C][/ROW]
[ROW][C]64[/C][C]9.75[/C][C]13.9850817842050[/C][C]-4.23508178420502[/C][/ROW]
[ROW][C]65[/C][C]7.5[/C][C]11.2419838337016[/C][C]-3.74198383370162[/C][/ROW]
[ROW][C]66[/C][C]11.24[/C][C]7.11494845508915[/C][C]4.12505154491085[/C][/ROW]
[ROW][C]67[/C][C]12.24[/C][C]6.08600548606157[/C][C]6.15399451393843[/C][/ROW]
[ROW][C]68[/C][C]12.75[/C][C]9.57074986723929[/C][C]3.17925013276071[/C][/ROW]
[ROW][C]69[/C][C]12.52[/C][C]13.8458743046403[/C][C]-1.32587430464027[/C][/ROW]
[ROW][C]70[/C][C]14.49[/C][C]14.4045988601667[/C][C]0.0854011398333014[/C][/ROW]
[ROW][C]71[/C][C]14.21[/C][C]15.3570484396707[/C][C]-1.14704843967073[/C][/ROW]
[ROW][C]72[/C][C]14.32[/C][C]15.7699703420760[/C][C]-1.44997034207604[/C][/ROW]
[ROW][C]73[/C][C]22.15[/C][C]14.8291899779151[/C][C]7.3208100220849[/C][/ROW]
[ROW][C]74[/C][C]22.58[/C][C]19.2732779658266[/C][C]3.3067220341734[/C][/ROW]
[ROW][C]75[/C][C]23.8[/C][C]21.2036553421449[/C][C]2.59634465785512[/C][/ROW]
[ROW][C]76[/C][C]23.3[/C][C]23.4879883762498[/C][C]-0.187988376249788[/C][/ROW]
[ROW][C]77[/C][C]22.38[/C][C]24.0027280133935[/C][C]-1.62272801339346[/C][/ROW]
[ROW][C]78[/C][C]23[/C][C]23.2713902864168[/C][C]-0.271390286416789[/C][/ROW]
[ROW][C]79[/C][C]21.96[/C][C]19.2729269360501[/C][C]2.68707306394987[/C][/ROW]
[ROW][C]80[/C][C]22.4[/C][C]19.4000504054171[/C][C]2.99994959458285[/C][/ROW]
[ROW][C]81[/C][C]20.8[/C][C]22.5352141881701[/C][C]-1.73521418817014[/C][/ROW]
[ROW][C]82[/C][C]20.4[/C][C]23.0889131766513[/C][C]-2.68891317665128[/C][/ROW]
[ROW][C]83[/C][C]16[/C][C]21.6094590398976[/C][C]-5.60945903989764[/C][/ROW]
[ROW][C]84[/C][C]12.78[/C][C]18.4836914620280[/C][C]-5.70369146202803[/C][/ROW]
[ROW][C]85[/C][C]9.75[/C][C]16.1816144973090[/C][C]-6.43161449730903[/C][/ROW]
[ROW][C]86[/C][C]7.5[/C][C]9.03592529602405[/C][C]-1.53592529602405[/C][/ROW]
[ROW][C]87[/C][C]11.24[/C][C]7.0413318420811[/C][C]4.1986681579189[/C][/ROW]
[ROW][C]88[/C][C]12.24[/C][C]9.95381881336358[/C][C]2.28618118663642[/C][/ROW]
[ROW][C]89[/C][C]12.75[/C][C]12.0746544961044[/C][C]0.675345503895638[/C][/ROW]
[ROW][C]90[/C][C]12.52[/C][C]13.4311433286635[/C][C]-0.911143328663542[/C][/ROW]
[ROW][C]91[/C][C]14.49[/C][C]9.59200314889215[/C][C]4.89799685110785[/C][/ROW]
[ROW][C]92[/C][C]14.21[/C][C]11.5085403437508[/C][C]2.70145965624916[/C][/ROW]
[ROW][C]93[/C][C]14.32[/C][C]13.3599369990351[/C][C]0.960063000964904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42242&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42242&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
1334.7633.4384214743591.32157852564102
1433.533.14713751517360.352862484826353
1532.7432.8801824178193-0.140182417819275
1634.434.9717590140859-0.571759014085856
1731.9332.9463516634618-1.01635166346177
1829.2430.5884181945122-1.34841819451218
1925.7522.54924541567513.20075458432493
2026.0328.5098182868696-2.47981828686955
2126.0830.1771684833925-4.09716848339253
2223.828.5709258987877-4.77092589878773
2320.6125.3118010088766-4.70180100887656
2419.721.7268667212880-2.02686672128803
2518.1819.946319372578-1.76631937257799
2619.617.03775618513872.56224381486130
2720.618.38003937919372.21996062080629
2820.0322.2117860859024-2.18178608590237
292318.83516626019124.16483373980877
3023.620.43405923567783.16594076432225
3122.5616.91697671707755.64302328292253
3222.5523.5159330362688-0.96593303626879
3323.7526.0017973634841-2.25179736348414
3424.9225.6814888138517-0.761488813851706
3524.525.5567536513359-1.05675365133595
3630.5825.40142823916755.1785717608325
3728.0729.2840282205289-1.21402822052886
3827.727.7663742190333-0.0663742190332997
392726.98777865492440.0122213450756092
4025.2328.1245504787021-2.89455047870205
4126.8625.60288353753581.25711646246424
4225.624.71796261659740.882037383402555
4324.5519.97427571382284.57572428617723
4423.9624.2752659326508-0.315265932650782
4523.526.9817409041293-3.4817409041293
4623.6426.0355905412344-2.39559054123443
4721.5524.5740767122251-3.02407671222508
4821.0524.2730366589892-3.22303665898924
4921.8920.20018005783031.68981994216971
5021.9821.19636627447770.78363372552229
5121.4521.09646675584790.353533244152104
5222.1521.85323020302870.296769796971251
5322.5822.7361531391231-0.15615313912307
5423.820.66851944265473.13148055734527
5523.318.4950070660634.80499293393699
5622.3821.88818116135050.491818838649493
572324.5193100761003-1.51931007610035
5821.9625.3409899950015-3.38098999500152
5922.422.9733384583778-0.57333845837784
6020.824.5346032318987-3.7346032318987
6120.421.1548123127678-0.754812312767822
621620.0480176650006-4.04801766500061
6312.7816.0939439966101-3.3139439966101
649.7513.9850817842050-4.23508178420502
657.511.2419838337016-3.74198383370162
6611.247.114948455089154.12505154491085
6712.246.086005486061576.15399451393843
6812.759.570749867239293.17925013276071
6912.5213.8458743046403-1.32587430464027
7014.4914.40459886016670.0854011398333014
7114.2115.3570484396707-1.14704843967073
7214.3215.7699703420760-1.44997034207604
7322.1514.82918997791517.3208100220849
7422.5819.27327796582663.3067220341734
7523.821.20365534214492.59634465785512
7623.323.4879883762498-0.187988376249788
7722.3824.0027280133935-1.62272801339346
782323.2713902864168-0.271390286416789
7921.9619.27292693605012.68707306394987
8022.419.40005040541712.99994959458285
8120.822.5352141881701-1.73521418817014
8220.423.0889131766513-2.68891317665128
831621.6094590398976-5.60945903989764
8412.7818.4836914620280-5.70369146202803
859.7516.1816144973090-6.43161449730903
867.59.03592529602405-1.53592529602405
8711.247.04133184208114.1986681579189
8812.249.953818813363582.28618118663642
8912.7512.07465449610440.675345503895638
9012.5213.4311433286635-0.911143328663542
9114.499.592003148892154.89799685110785
9214.2111.50854034375082.70145965624916
9314.3213.35993699903510.960063000964904







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9415.79856445200379.879877731177621.7172511728298
9515.76229927840068.263609781649223.260988775152
9616.97933980135428.1799173295043525.7787622732041
9718.95264938472879.0214194756236428.8838792938338
9817.89748308568516.95084802385428.8441181475162
9918.37123685144426.49570272255930.2467709803293
10017.59276081790484.8558929723266330.3296286634830
10117.57739309987014.0338598021988831.1209263975414
10218.05619368952573.7514117668770332.3609756121744
10316.21592263009901.1884052861082131.2434399740897
10413.8343913593945-1.8826620919795529.5514448107686
10513.1975349650350-3.1800491322229929.5751190622929

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
94 & 15.7985644520037 & 9.8798777311776 & 21.7172511728298 \tabularnewline
95 & 15.7622992784006 & 8.2636097816492 & 23.260988775152 \tabularnewline
96 & 16.9793398013542 & 8.17991732950435 & 25.7787622732041 \tabularnewline
97 & 18.9526493847287 & 9.02141947562364 & 28.8838792938338 \tabularnewline
98 & 17.8974830856851 & 6.950848023854 & 28.8441181475162 \tabularnewline
99 & 18.3712368514442 & 6.495702722559 & 30.2467709803293 \tabularnewline
100 & 17.5927608179048 & 4.85589297232663 & 30.3296286634830 \tabularnewline
101 & 17.5773930998701 & 4.03385980219888 & 31.1209263975414 \tabularnewline
102 & 18.0561936895257 & 3.75141176687703 & 32.3609756121744 \tabularnewline
103 & 16.2159226300990 & 1.18840528610821 & 31.2434399740897 \tabularnewline
104 & 13.8343913593945 & -1.88266209197955 & 29.5514448107686 \tabularnewline
105 & 13.1975349650350 & -3.18004913222299 & 29.5751190622929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42242&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]94[/C][C]15.7985644520037[/C][C]9.8798777311776[/C][C]21.7172511728298[/C][/ROW]
[ROW][C]95[/C][C]15.7622992784006[/C][C]8.2636097816492[/C][C]23.260988775152[/C][/ROW]
[ROW][C]96[/C][C]16.9793398013542[/C][C]8.17991732950435[/C][C]25.7787622732041[/C][/ROW]
[ROW][C]97[/C][C]18.9526493847287[/C][C]9.02141947562364[/C][C]28.8838792938338[/C][/ROW]
[ROW][C]98[/C][C]17.8974830856851[/C][C]6.950848023854[/C][C]28.8441181475162[/C][/ROW]
[ROW][C]99[/C][C]18.3712368514442[/C][C]6.495702722559[/C][C]30.2467709803293[/C][/ROW]
[ROW][C]100[/C][C]17.5927608179048[/C][C]4.85589297232663[/C][C]30.3296286634830[/C][/ROW]
[ROW][C]101[/C][C]17.5773930998701[/C][C]4.03385980219888[/C][C]31.1209263975414[/C][/ROW]
[ROW][C]102[/C][C]18.0561936895257[/C][C]3.75141176687703[/C][C]32.3609756121744[/C][/ROW]
[ROW][C]103[/C][C]16.2159226300990[/C][C]1.18840528610821[/C][C]31.2434399740897[/C][/ROW]
[ROW][C]104[/C][C]13.8343913593945[/C][C]-1.88266209197955[/C][C]29.5514448107686[/C][/ROW]
[ROW][C]105[/C][C]13.1975349650350[/C][C]-3.18004913222299[/C][C]29.5751190622929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42242&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42242&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
9415.79856445200379.879877731177621.7172511728298
9515.76229927840068.263609781649223.260988775152
9616.97933980135428.1799173295043525.7787622732041
9718.95264938472879.0214194756236428.8838792938338
9817.89748308568516.95084802385428.8441181475162
9918.37123685144426.49570272255930.2467709803293
10017.59276081790484.8558929723266330.3296286634830
10117.57739309987014.0338598021988831.1209263975414
10218.05619368952573.7514117668770332.3609756121744
10316.21592263009901.1884052861082131.2434399740897
10413.8343913593945-1.8826620919795529.5514448107686
10513.1975349650350-3.1800491322229929.5751190622929



Parameters (Session):
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=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')