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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 25 May 2008 10:43:42 -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/2008/May/25/t1211733872inrq0sz5siz4r4v.htm/, Retrieved Wed, 15 May 2024 03:18:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13181, Retrieved Wed, 15 May 2024 03:18:07 +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] [Exponential Smoot...] [2008-05-25 16:43:42] [f1ad3272590ff3a9e1233970549442f0] [Current]
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Dataseries X:
23.11
18.64
14.94
16.90
15.46
11.15
13.13
12.48
12.95
12.59
10.58
10.58
12.39
15.53
13.06
10.22
16.33
19.72
21.31
18.84
24.84
15.67
15.57
12.73
13.56
15.54
17.22
12.14
11.07
12.02
11.55
6.92
10.33
8.38
12.11
11.46
12.75
13.32
13.00
11.90
11.79
12.55
11.84
11.25
11.15
10.99
11.70
14.01
17.51
17.27
16.90
15.79
15.45
16.24
16.71
16.77
16.64
17.80
16.87
16.13
15.76
15.66
15.54
15.30
15.05
14.69
14.39
14.18
13.70
13.66
13.27
13.56
13.14
14.19
22.57
23.09
23.31
22.91
22.36
43.06
64.67
64.68
56.90
48.79
45.21
41.40
22.17
25.52
20.28
22.87
27.63
22.95
21.35
18.38
17.15
18.27
19.40
20.52




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13181&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13181&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 time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.874143869308098
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.874143869308098 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13181&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]0.874143869308098[/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=13181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13181&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
alpha0.874143869308098
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1312.3912.4368674516908-0.0468674516908294
1415.5314.93006522279190.599934777208135
1513.0612.22407786360640.835922136393592
1610.229.49104407435380.728955925646206
1716.3315.90200642775320.427993572246763
1819.7219.3686343850360.351365614963981
1921.3121.12744514990910.182554850090881
2018.8418.76785768626190.0721423137381407
2124.8424.65717044753380.182829552466245
2215.6715.39365644661710.276343553382862
2315.5715.6743871362962-0.104387136296246
2412.7313.2831377610683-0.553137761068253
2513.5615.0128838888891-1.45288388888910
2615.5416.3584250371190-0.818425037118974
2717.2212.44228759768584.77771240231422
2812.1413.1414832500866-1.00148325008658
2911.0718.0019148495259-6.93191484952586
3012.0215.0252798830406-3.00527988304063
3111.5513.8286536947063-2.2786536947063
326.929.30371977593065-2.38371977593065
3310.3313.0601864152357-2.73018641523568
348.381.262046675276717.11795332472329
3512.117.475411311332764.63458868866724
3611.469.17023058301652.28976941698349
3712.7513.2718480252907-0.521848025290724
3813.3215.5110990019581-2.19109900195810
391311.09935523654911.90064476345090
4011.98.556232647530183.34376735246982
4111.7916.4686572473630-4.67865724736305
4212.5515.9558846833017-3.40588468330166
4311.8414.5005226253269-2.66052262532692
4411.259.628557111520151.62144288847985
4511.1516.8425071888646-5.69250718886455
4610.993.694321667898277.29567833210173
4711.79.75049686538581.94950313461420
4814.018.803055180720435.20694481927957
4917.5115.10084432433772.40915567566235
5017.2719.6921287480355-2.42212874803547
5116.915.59340278456221.30659721543778
5215.7912.71262299853813.07737700146188
5315.4519.3825127872921-3.93251278729207
5416.2419.6821640587835-3.44216405878350
5516.7118.2888969917302-1.57889699173023
5616.7714.90133950574241.86866049425762
5716.6421.4108878807541-4.77088788075414
5817.810.70297300218597.09702699781405
5916.8715.91264942931920.957350570680763
6016.1314.50789266985961.62210733014036
6115.7617.3198991837725-1.55989918377251
6215.6617.8336118713092-2.17361187130917
6315.5414.4214084342191.11859156578101
6415.311.59914815432863.70085184567144
6515.0517.9318070504269-2.88180705042688
6614.6919.2116396939056-4.52163969390565
6714.3917.1092592018479-2.71925920184786
6814.1813.15875732661941.02124267338062
6913.718.0919127407484-4.3919127407484
7013.669.208926503433854.45107349656615
7113.2711.33294298015771.93705701984229
7213.5610.86825432055112.69174567944886
7313.1414.2148036122114-1.07480361221137
7414.1915.0753201154468-0.885320115446817
7522.5713.20361300466669.36638699533338
7623.0917.91610582209315.17389417790685
7723.3124.7079476638188-1.39794766381879
7822.9127.0785039015258-4.16850390152578
7922.3625.5116555321751-3.15165553217508
8043.0621.653942148541821.4060578514582
8164.6743.725079982309820.9449200176902
8264.6858.10307480005916.57692519994091
8356.961.76898712409-4.86898712409003
8448.7955.4498188963999-6.65981889639988
8545.2150.1477120257345-4.93771202573446
8641.447.6553384813228-6.25533848132279
8722.1742.3797029278897-20.2097029278897
8825.5220.71078713687094.80921286312914
8920.2826.3567384573136-6.07673845731362
9022.8724.2886669191698-1.41866691916982
9127.6325.25354829080912.37645170919089
9222.9529.3189347461984-6.36893474619842
9321.3527.0526960571734-5.70269605717339
9418.3816.32854041784152.05145958215847
9517.1514.59800647898212.55199352101793
9618.2714.54045582888413.72954417111595
9719.418.53688469708350.863115302916533
9820.5220.9494374315293-0.429437431529294

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 12.39 & 12.4368674516908 & -0.0468674516908294 \tabularnewline
14 & 15.53 & 14.9300652227919 & 0.599934777208135 \tabularnewline
15 & 13.06 & 12.2240778636064 & 0.835922136393592 \tabularnewline
16 & 10.22 & 9.4910440743538 & 0.728955925646206 \tabularnewline
17 & 16.33 & 15.9020064277532 & 0.427993572246763 \tabularnewline
18 & 19.72 & 19.368634385036 & 0.351365614963981 \tabularnewline
19 & 21.31 & 21.1274451499091 & 0.182554850090881 \tabularnewline
20 & 18.84 & 18.7678576862619 & 0.0721423137381407 \tabularnewline
21 & 24.84 & 24.6571704475338 & 0.182829552466245 \tabularnewline
22 & 15.67 & 15.3936564466171 & 0.276343553382862 \tabularnewline
23 & 15.57 & 15.6743871362962 & -0.104387136296246 \tabularnewline
24 & 12.73 & 13.2831377610683 & -0.553137761068253 \tabularnewline
25 & 13.56 & 15.0128838888891 & -1.45288388888910 \tabularnewline
26 & 15.54 & 16.3584250371190 & -0.818425037118974 \tabularnewline
27 & 17.22 & 12.4422875976858 & 4.77771240231422 \tabularnewline
28 & 12.14 & 13.1414832500866 & -1.00148325008658 \tabularnewline
29 & 11.07 & 18.0019148495259 & -6.93191484952586 \tabularnewline
30 & 12.02 & 15.0252798830406 & -3.00527988304063 \tabularnewline
31 & 11.55 & 13.8286536947063 & -2.2786536947063 \tabularnewline
32 & 6.92 & 9.30371977593065 & -2.38371977593065 \tabularnewline
33 & 10.33 & 13.0601864152357 & -2.73018641523568 \tabularnewline
34 & 8.38 & 1.26204667527671 & 7.11795332472329 \tabularnewline
35 & 12.11 & 7.47541131133276 & 4.63458868866724 \tabularnewline
36 & 11.46 & 9.1702305830165 & 2.28976941698349 \tabularnewline
37 & 12.75 & 13.2718480252907 & -0.521848025290724 \tabularnewline
38 & 13.32 & 15.5110990019581 & -2.19109900195810 \tabularnewline
39 & 13 & 11.0993552365491 & 1.90064476345090 \tabularnewline
40 & 11.9 & 8.55623264753018 & 3.34376735246982 \tabularnewline
41 & 11.79 & 16.4686572473630 & -4.67865724736305 \tabularnewline
42 & 12.55 & 15.9558846833017 & -3.40588468330166 \tabularnewline
43 & 11.84 & 14.5005226253269 & -2.66052262532692 \tabularnewline
44 & 11.25 & 9.62855711152015 & 1.62144288847985 \tabularnewline
45 & 11.15 & 16.8425071888646 & -5.69250718886455 \tabularnewline
46 & 10.99 & 3.69432166789827 & 7.29567833210173 \tabularnewline
47 & 11.7 & 9.7504968653858 & 1.94950313461420 \tabularnewline
48 & 14.01 & 8.80305518072043 & 5.20694481927957 \tabularnewline
49 & 17.51 & 15.1008443243377 & 2.40915567566235 \tabularnewline
50 & 17.27 & 19.6921287480355 & -2.42212874803547 \tabularnewline
51 & 16.9 & 15.5934027845622 & 1.30659721543778 \tabularnewline
52 & 15.79 & 12.7126229985381 & 3.07737700146188 \tabularnewline
53 & 15.45 & 19.3825127872921 & -3.93251278729207 \tabularnewline
54 & 16.24 & 19.6821640587835 & -3.44216405878350 \tabularnewline
55 & 16.71 & 18.2888969917302 & -1.57889699173023 \tabularnewline
56 & 16.77 & 14.9013395057424 & 1.86866049425762 \tabularnewline
57 & 16.64 & 21.4108878807541 & -4.77088788075414 \tabularnewline
58 & 17.8 & 10.7029730021859 & 7.09702699781405 \tabularnewline
59 & 16.87 & 15.9126494293192 & 0.957350570680763 \tabularnewline
60 & 16.13 & 14.5078926698596 & 1.62210733014036 \tabularnewline
61 & 15.76 & 17.3198991837725 & -1.55989918377251 \tabularnewline
62 & 15.66 & 17.8336118713092 & -2.17361187130917 \tabularnewline
63 & 15.54 & 14.421408434219 & 1.11859156578101 \tabularnewline
64 & 15.3 & 11.5991481543286 & 3.70085184567144 \tabularnewline
65 & 15.05 & 17.9318070504269 & -2.88180705042688 \tabularnewline
66 & 14.69 & 19.2116396939056 & -4.52163969390565 \tabularnewline
67 & 14.39 & 17.1092592018479 & -2.71925920184786 \tabularnewline
68 & 14.18 & 13.1587573266194 & 1.02124267338062 \tabularnewline
69 & 13.7 & 18.0919127407484 & -4.3919127407484 \tabularnewline
70 & 13.66 & 9.20892650343385 & 4.45107349656615 \tabularnewline
71 & 13.27 & 11.3329429801577 & 1.93705701984229 \tabularnewline
72 & 13.56 & 10.8682543205511 & 2.69174567944886 \tabularnewline
73 & 13.14 & 14.2148036122114 & -1.07480361221137 \tabularnewline
74 & 14.19 & 15.0753201154468 & -0.885320115446817 \tabularnewline
75 & 22.57 & 13.2036130046666 & 9.36638699533338 \tabularnewline
76 & 23.09 & 17.9161058220931 & 5.17389417790685 \tabularnewline
77 & 23.31 & 24.7079476638188 & -1.39794766381879 \tabularnewline
78 & 22.91 & 27.0785039015258 & -4.16850390152578 \tabularnewline
79 & 22.36 & 25.5116555321751 & -3.15165553217508 \tabularnewline
80 & 43.06 & 21.6539421485418 & 21.4060578514582 \tabularnewline
81 & 64.67 & 43.7250799823098 & 20.9449200176902 \tabularnewline
82 & 64.68 & 58.1030748000591 & 6.57692519994091 \tabularnewline
83 & 56.9 & 61.76898712409 & -4.86898712409003 \tabularnewline
84 & 48.79 & 55.4498188963999 & -6.65981889639988 \tabularnewline
85 & 45.21 & 50.1477120257345 & -4.93771202573446 \tabularnewline
86 & 41.4 & 47.6553384813228 & -6.25533848132279 \tabularnewline
87 & 22.17 & 42.3797029278897 & -20.2097029278897 \tabularnewline
88 & 25.52 & 20.7107871368709 & 4.80921286312914 \tabularnewline
89 & 20.28 & 26.3567384573136 & -6.07673845731362 \tabularnewline
90 & 22.87 & 24.2886669191698 & -1.41866691916982 \tabularnewline
91 & 27.63 & 25.2535482908091 & 2.37645170919089 \tabularnewline
92 & 22.95 & 29.3189347461984 & -6.36893474619842 \tabularnewline
93 & 21.35 & 27.0526960571734 & -5.70269605717339 \tabularnewline
94 & 18.38 & 16.3285404178415 & 2.05145958215847 \tabularnewline
95 & 17.15 & 14.5980064789821 & 2.55199352101793 \tabularnewline
96 & 18.27 & 14.5404558288841 & 3.72954417111595 \tabularnewline
97 & 19.4 & 18.5368846970835 & 0.863115302916533 \tabularnewline
98 & 20.52 & 20.9494374315293 & -0.429437431529294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13181&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]12.39[/C][C]12.4368674516908[/C][C]-0.0468674516908294[/C][/ROW]
[ROW][C]14[/C][C]15.53[/C][C]14.9300652227919[/C][C]0.599934777208135[/C][/ROW]
[ROW][C]15[/C][C]13.06[/C][C]12.2240778636064[/C][C]0.835922136393592[/C][/ROW]
[ROW][C]16[/C][C]10.22[/C][C]9.4910440743538[/C][C]0.728955925646206[/C][/ROW]
[ROW][C]17[/C][C]16.33[/C][C]15.9020064277532[/C][C]0.427993572246763[/C][/ROW]
[ROW][C]18[/C][C]19.72[/C][C]19.368634385036[/C][C]0.351365614963981[/C][/ROW]
[ROW][C]19[/C][C]21.31[/C][C]21.1274451499091[/C][C]0.182554850090881[/C][/ROW]
[ROW][C]20[/C][C]18.84[/C][C]18.7678576862619[/C][C]0.0721423137381407[/C][/ROW]
[ROW][C]21[/C][C]24.84[/C][C]24.6571704475338[/C][C]0.182829552466245[/C][/ROW]
[ROW][C]22[/C][C]15.67[/C][C]15.3936564466171[/C][C]0.276343553382862[/C][/ROW]
[ROW][C]23[/C][C]15.57[/C][C]15.6743871362962[/C][C]-0.104387136296246[/C][/ROW]
[ROW][C]24[/C][C]12.73[/C][C]13.2831377610683[/C][C]-0.553137761068253[/C][/ROW]
[ROW][C]25[/C][C]13.56[/C][C]15.0128838888891[/C][C]-1.45288388888910[/C][/ROW]
[ROW][C]26[/C][C]15.54[/C][C]16.3584250371190[/C][C]-0.818425037118974[/C][/ROW]
[ROW][C]27[/C][C]17.22[/C][C]12.4422875976858[/C][C]4.77771240231422[/C][/ROW]
[ROW][C]28[/C][C]12.14[/C][C]13.1414832500866[/C][C]-1.00148325008658[/C][/ROW]
[ROW][C]29[/C][C]11.07[/C][C]18.0019148495259[/C][C]-6.93191484952586[/C][/ROW]
[ROW][C]30[/C][C]12.02[/C][C]15.0252798830406[/C][C]-3.00527988304063[/C][/ROW]
[ROW][C]31[/C][C]11.55[/C][C]13.8286536947063[/C][C]-2.2786536947063[/C][/ROW]
[ROW][C]32[/C][C]6.92[/C][C]9.30371977593065[/C][C]-2.38371977593065[/C][/ROW]
[ROW][C]33[/C][C]10.33[/C][C]13.0601864152357[/C][C]-2.73018641523568[/C][/ROW]
[ROW][C]34[/C][C]8.38[/C][C]1.26204667527671[/C][C]7.11795332472329[/C][/ROW]
[ROW][C]35[/C][C]12.11[/C][C]7.47541131133276[/C][C]4.63458868866724[/C][/ROW]
[ROW][C]36[/C][C]11.46[/C][C]9.1702305830165[/C][C]2.28976941698349[/C][/ROW]
[ROW][C]37[/C][C]12.75[/C][C]13.2718480252907[/C][C]-0.521848025290724[/C][/ROW]
[ROW][C]38[/C][C]13.32[/C][C]15.5110990019581[/C][C]-2.19109900195810[/C][/ROW]
[ROW][C]39[/C][C]13[/C][C]11.0993552365491[/C][C]1.90064476345090[/C][/ROW]
[ROW][C]40[/C][C]11.9[/C][C]8.55623264753018[/C][C]3.34376735246982[/C][/ROW]
[ROW][C]41[/C][C]11.79[/C][C]16.4686572473630[/C][C]-4.67865724736305[/C][/ROW]
[ROW][C]42[/C][C]12.55[/C][C]15.9558846833017[/C][C]-3.40588468330166[/C][/ROW]
[ROW][C]43[/C][C]11.84[/C][C]14.5005226253269[/C][C]-2.66052262532692[/C][/ROW]
[ROW][C]44[/C][C]11.25[/C][C]9.62855711152015[/C][C]1.62144288847985[/C][/ROW]
[ROW][C]45[/C][C]11.15[/C][C]16.8425071888646[/C][C]-5.69250718886455[/C][/ROW]
[ROW][C]46[/C][C]10.99[/C][C]3.69432166789827[/C][C]7.29567833210173[/C][/ROW]
[ROW][C]47[/C][C]11.7[/C][C]9.7504968653858[/C][C]1.94950313461420[/C][/ROW]
[ROW][C]48[/C][C]14.01[/C][C]8.80305518072043[/C][C]5.20694481927957[/C][/ROW]
[ROW][C]49[/C][C]17.51[/C][C]15.1008443243377[/C][C]2.40915567566235[/C][/ROW]
[ROW][C]50[/C][C]17.27[/C][C]19.6921287480355[/C][C]-2.42212874803547[/C][/ROW]
[ROW][C]51[/C][C]16.9[/C][C]15.5934027845622[/C][C]1.30659721543778[/C][/ROW]
[ROW][C]52[/C][C]15.79[/C][C]12.7126229985381[/C][C]3.07737700146188[/C][/ROW]
[ROW][C]53[/C][C]15.45[/C][C]19.3825127872921[/C][C]-3.93251278729207[/C][/ROW]
[ROW][C]54[/C][C]16.24[/C][C]19.6821640587835[/C][C]-3.44216405878350[/C][/ROW]
[ROW][C]55[/C][C]16.71[/C][C]18.2888969917302[/C][C]-1.57889699173023[/C][/ROW]
[ROW][C]56[/C][C]16.77[/C][C]14.9013395057424[/C][C]1.86866049425762[/C][/ROW]
[ROW][C]57[/C][C]16.64[/C][C]21.4108878807541[/C][C]-4.77088788075414[/C][/ROW]
[ROW][C]58[/C][C]17.8[/C][C]10.7029730021859[/C][C]7.09702699781405[/C][/ROW]
[ROW][C]59[/C][C]16.87[/C][C]15.9126494293192[/C][C]0.957350570680763[/C][/ROW]
[ROW][C]60[/C][C]16.13[/C][C]14.5078926698596[/C][C]1.62210733014036[/C][/ROW]
[ROW][C]61[/C][C]15.76[/C][C]17.3198991837725[/C][C]-1.55989918377251[/C][/ROW]
[ROW][C]62[/C][C]15.66[/C][C]17.8336118713092[/C][C]-2.17361187130917[/C][/ROW]
[ROW][C]63[/C][C]15.54[/C][C]14.421408434219[/C][C]1.11859156578101[/C][/ROW]
[ROW][C]64[/C][C]15.3[/C][C]11.5991481543286[/C][C]3.70085184567144[/C][/ROW]
[ROW][C]65[/C][C]15.05[/C][C]17.9318070504269[/C][C]-2.88180705042688[/C][/ROW]
[ROW][C]66[/C][C]14.69[/C][C]19.2116396939056[/C][C]-4.52163969390565[/C][/ROW]
[ROW][C]67[/C][C]14.39[/C][C]17.1092592018479[/C][C]-2.71925920184786[/C][/ROW]
[ROW][C]68[/C][C]14.18[/C][C]13.1587573266194[/C][C]1.02124267338062[/C][/ROW]
[ROW][C]69[/C][C]13.7[/C][C]18.0919127407484[/C][C]-4.3919127407484[/C][/ROW]
[ROW][C]70[/C][C]13.66[/C][C]9.20892650343385[/C][C]4.45107349656615[/C][/ROW]
[ROW][C]71[/C][C]13.27[/C][C]11.3329429801577[/C][C]1.93705701984229[/C][/ROW]
[ROW][C]72[/C][C]13.56[/C][C]10.8682543205511[/C][C]2.69174567944886[/C][/ROW]
[ROW][C]73[/C][C]13.14[/C][C]14.2148036122114[/C][C]-1.07480361221137[/C][/ROW]
[ROW][C]74[/C][C]14.19[/C][C]15.0753201154468[/C][C]-0.885320115446817[/C][/ROW]
[ROW][C]75[/C][C]22.57[/C][C]13.2036130046666[/C][C]9.36638699533338[/C][/ROW]
[ROW][C]76[/C][C]23.09[/C][C]17.9161058220931[/C][C]5.17389417790685[/C][/ROW]
[ROW][C]77[/C][C]23.31[/C][C]24.7079476638188[/C][C]-1.39794766381879[/C][/ROW]
[ROW][C]78[/C][C]22.91[/C][C]27.0785039015258[/C][C]-4.16850390152578[/C][/ROW]
[ROW][C]79[/C][C]22.36[/C][C]25.5116555321751[/C][C]-3.15165553217508[/C][/ROW]
[ROW][C]80[/C][C]43.06[/C][C]21.6539421485418[/C][C]21.4060578514582[/C][/ROW]
[ROW][C]81[/C][C]64.67[/C][C]43.7250799823098[/C][C]20.9449200176902[/C][/ROW]
[ROW][C]82[/C][C]64.68[/C][C]58.1030748000591[/C][C]6.57692519994091[/C][/ROW]
[ROW][C]83[/C][C]56.9[/C][C]61.76898712409[/C][C]-4.86898712409003[/C][/ROW]
[ROW][C]84[/C][C]48.79[/C][C]55.4498188963999[/C][C]-6.65981889639988[/C][/ROW]
[ROW][C]85[/C][C]45.21[/C][C]50.1477120257345[/C][C]-4.93771202573446[/C][/ROW]
[ROW][C]86[/C][C]41.4[/C][C]47.6553384813228[/C][C]-6.25533848132279[/C][/ROW]
[ROW][C]87[/C][C]22.17[/C][C]42.3797029278897[/C][C]-20.2097029278897[/C][/ROW]
[ROW][C]88[/C][C]25.52[/C][C]20.7107871368709[/C][C]4.80921286312914[/C][/ROW]
[ROW][C]89[/C][C]20.28[/C][C]26.3567384573136[/C][C]-6.07673845731362[/C][/ROW]
[ROW][C]90[/C][C]22.87[/C][C]24.2886669191698[/C][C]-1.41866691916982[/C][/ROW]
[ROW][C]91[/C][C]27.63[/C][C]25.2535482908091[/C][C]2.37645170919089[/C][/ROW]
[ROW][C]92[/C][C]22.95[/C][C]29.3189347461984[/C][C]-6.36893474619842[/C][/ROW]
[ROW][C]93[/C][C]21.35[/C][C]27.0526960571734[/C][C]-5.70269605717339[/C][/ROW]
[ROW][C]94[/C][C]18.38[/C][C]16.3285404178415[/C][C]2.05145958215847[/C][/ROW]
[ROW][C]95[/C][C]17.15[/C][C]14.5980064789821[/C][C]2.55199352101793[/C][/ROW]
[ROW][C]96[/C][C]18.27[/C][C]14.5404558288841[/C][C]3.72954417111595[/C][/ROW]
[ROW][C]97[/C][C]19.4[/C][C]18.5368846970835[/C][C]0.863115302916533[/C][/ROW]
[ROW][C]98[/C][C]20.52[/C][C]20.9494374315293[/C][C]-0.429437431529294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13181&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13181&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
1312.3912.4368674516908-0.0468674516908294
1415.5314.93006522279190.599934777208135
1513.0612.22407786360640.835922136393592
1610.229.49104407435380.728955925646206
1716.3315.90200642775320.427993572246763
1819.7219.3686343850360.351365614963981
1921.3121.12744514990910.182554850090881
2018.8418.76785768626190.0721423137381407
2124.8424.65717044753380.182829552466245
2215.6715.39365644661710.276343553382862
2315.5715.6743871362962-0.104387136296246
2412.7313.2831377610683-0.553137761068253
2513.5615.0128838888891-1.45288388888910
2615.5416.3584250371190-0.818425037118974
2717.2212.44228759768584.77771240231422
2812.1413.1414832500866-1.00148325008658
2911.0718.0019148495259-6.93191484952586
3012.0215.0252798830406-3.00527988304063
3111.5513.8286536947063-2.2786536947063
326.929.30371977593065-2.38371977593065
3310.3313.0601864152357-2.73018641523568
348.381.262046675276717.11795332472329
3512.117.475411311332764.63458868866724
3611.469.17023058301652.28976941698349
3712.7513.2718480252907-0.521848025290724
3813.3215.5110990019581-2.19109900195810
391311.09935523654911.90064476345090
4011.98.556232647530183.34376735246982
4111.7916.4686572473630-4.67865724736305
4212.5515.9558846833017-3.40588468330166
4311.8414.5005226253269-2.66052262532692
4411.259.628557111520151.62144288847985
4511.1516.8425071888646-5.69250718886455
4610.993.694321667898277.29567833210173
4711.79.75049686538581.94950313461420
4814.018.803055180720435.20694481927957
4917.5115.10084432433772.40915567566235
5017.2719.6921287480355-2.42212874803547
5116.915.59340278456221.30659721543778
5215.7912.71262299853813.07737700146188
5315.4519.3825127872921-3.93251278729207
5416.2419.6821640587835-3.44216405878350
5516.7118.2888969917302-1.57889699173023
5616.7714.90133950574241.86866049425762
5716.6421.4108878807541-4.77088788075414
5817.810.70297300218597.09702699781405
5916.8715.91264942931920.957350570680763
6016.1314.50789266985961.62210733014036
6115.7617.3198991837725-1.55989918377251
6215.6617.8336118713092-2.17361187130917
6315.5414.4214084342191.11859156578101
6415.311.59914815432863.70085184567144
6515.0517.9318070504269-2.88180705042688
6614.6919.2116396939056-4.52163969390565
6714.3917.1092592018479-2.71925920184786
6814.1813.15875732661941.02124267338062
6913.718.0919127407484-4.3919127407484
7013.669.208926503433854.45107349656615
7113.2711.33294298015771.93705701984229
7213.5610.86825432055112.69174567944886
7313.1414.2148036122114-1.07480361221137
7414.1915.0753201154468-0.885320115446817
7522.5713.20361300466669.36638699533338
7623.0917.91610582209315.17389417790685
7723.3124.7079476638188-1.39794766381879
7822.9127.0785039015258-4.16850390152578
7922.3625.5116555321751-3.15165553217508
8043.0621.653942148541821.4060578514582
8164.6743.725079982309820.9449200176902
8264.6858.10307480005916.57692519994091
8356.961.76898712409-4.86898712409003
8448.7955.4498188963999-6.65981889639988
8545.2150.1477120257345-4.93771202573446
8641.447.6553384813228-6.25533848132279
8722.1742.3797029278897-20.2097029278897
8825.5220.71078713687094.80921286312914
8920.2826.3567384573136-6.07673845731362
9022.8724.2886669191698-1.41866691916982
9127.6325.25354829080912.37645170919089
9222.9529.3189347461984-6.36893474619842
9321.3527.0526960571734-5.70269605717339
9418.3816.32854041784152.05145958215847
9517.1514.59800647898212.55199352101793
9618.2714.54045582888413.72954417111595
9719.418.53688469708350.863115302916533
9820.5220.9494374315293-0.429437431529294







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9919.01023524845928.6064615467365429.4140089501819
10018.15629130795724.3379510445597131.9746315713548
10118.22823497580671.6857276678618134.7707422837516
10222.05835396578923.1807861025345140.9359218290439
10324.74099327349323.7869819909210345.6950045560654
10425.62835853590592.785884737550848.470832334261
10529.01333533281154.4270255318894353.5996451337336
10624.2500645159343-1.9643332460836650.4644622779523
10720.7892550250225-6.957865013346748.5363750633917
10818.6490968525277-10.550401273673847.8485949787293
10919.0246099019773-11.558370842554949.6075906465094
11020.52-11.386531174961652.4265311749616

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
99 & 19.0102352484592 & 8.60646154673654 & 29.4140089501819 \tabularnewline
100 & 18.1562913079572 & 4.33795104455971 & 31.9746315713548 \tabularnewline
101 & 18.2282349758067 & 1.68572766786181 & 34.7707422837516 \tabularnewline
102 & 22.0583539657892 & 3.18078610253451 & 40.9359218290439 \tabularnewline
103 & 24.7409932734932 & 3.78698199092103 & 45.6950045560654 \tabularnewline
104 & 25.6283585359059 & 2.7858847375508 & 48.470832334261 \tabularnewline
105 & 29.0133353328115 & 4.42702553188943 & 53.5996451337336 \tabularnewline
106 & 24.2500645159343 & -1.96433324608366 & 50.4644622779523 \tabularnewline
107 & 20.7892550250225 & -6.9578650133467 & 48.5363750633917 \tabularnewline
108 & 18.6490968525277 & -10.5504012736738 & 47.8485949787293 \tabularnewline
109 & 19.0246099019773 & -11.5583708425549 & 49.6075906465094 \tabularnewline
110 & 20.52 & -11.3865311749616 & 52.4265311749616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13181&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]99[/C][C]19.0102352484592[/C][C]8.60646154673654[/C][C]29.4140089501819[/C][/ROW]
[ROW][C]100[/C][C]18.1562913079572[/C][C]4.33795104455971[/C][C]31.9746315713548[/C][/ROW]
[ROW][C]101[/C][C]18.2282349758067[/C][C]1.68572766786181[/C][C]34.7707422837516[/C][/ROW]
[ROW][C]102[/C][C]22.0583539657892[/C][C]3.18078610253451[/C][C]40.9359218290439[/C][/ROW]
[ROW][C]103[/C][C]24.7409932734932[/C][C]3.78698199092103[/C][C]45.6950045560654[/C][/ROW]
[ROW][C]104[/C][C]25.6283585359059[/C][C]2.7858847375508[/C][C]48.470832334261[/C][/ROW]
[ROW][C]105[/C][C]29.0133353328115[/C][C]4.42702553188943[/C][C]53.5996451337336[/C][/ROW]
[ROW][C]106[/C][C]24.2500645159343[/C][C]-1.96433324608366[/C][C]50.4644622779523[/C][/ROW]
[ROW][C]107[/C][C]20.7892550250225[/C][C]-6.9578650133467[/C][C]48.5363750633917[/C][/ROW]
[ROW][C]108[/C][C]18.6490968525277[/C][C]-10.5504012736738[/C][C]47.8485949787293[/C][/ROW]
[ROW][C]109[/C][C]19.0246099019773[/C][C]-11.5583708425549[/C][C]49.6075906465094[/C][/ROW]
[ROW][C]110[/C][C]20.52[/C][C]-11.3865311749616[/C][C]52.4265311749616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13181&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13181&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
9919.01023524845928.6064615467365429.4140089501819
10018.15629130795724.3379510445597131.9746315713548
10118.22823497580671.6857276678618134.7707422837516
10222.05835396578923.1807861025345140.9359218290439
10324.74099327349323.7869819909210345.6950045560654
10425.62835853590592.785884737550848.470832334261
10529.01333533281154.4270255318894353.5996451337336
10624.2500645159343-1.9643332460836650.4644622779523
10720.7892550250225-6.957865013346748.5363750633917
10818.6490968525277-10.550401273673847.8485949787293
10919.0246099019773-11.558370842554949.6075906465094
11020.52-11.386531174961652.4265311749616



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')