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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 18 Aug 2008 05:00:08 -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/Aug/18/t1219057293rgd83u2b6esmq6o.htm/, Retrieved Tue, 14 May 2024 01:12:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14219, Retrieved Tue, 14 May 2024 01:12:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact284
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Toon Raeman - Opg...] [2008-08-18 11:00:08] [b46ff5180a79ecd706507099e9497e04] [Current]
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Dataseries X:
12.11
11.42
11.71
12.04
12.21
12
12.36
12.32
12.96
12.79
13.19
12.34
13.25
12.54
12.77
12.96
13
13.61
13.8
14.16
14.27
14.69
15.01
15.09
15.14
14.2
13.83
14.31
14.04
14.9
14.92
15.36
15.5
15.65
16.18
15.44
15.58
15.24
15.33
16.07
15.82
15.87
15.72
17.07
16.83
17.52
17.76
17.36
17.95
16.71
17.14
16.72
17.26
17.24
17.69
18.13
18.08
18.18
18.18
17.64
17.89
16.82
16.61
16.66
17.02
16.91
17.18
18.06
17.58
17.48
17.54
17.44
17.79
16.79
16.19
16.62
16.39
16.54
17.26
18
17.29
18.16
17.82
17.48
18.31
17.04
17.03
16.97
17.11
17.12
17.69
18.5
18.27
18.45
18.35
18.03




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14219&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14219&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.553590492930469
beta0.0620502955838186
gamma0.64547702995407

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.553590492930469 \tabularnewline
beta & 0.0620502955838186 \tabularnewline
gamma & 0.64547702995407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14219&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]0.553590492930469[/C][/ROW]
[ROW][C]beta[/C][C]0.0620502955838186[/C][/ROW]
[ROW][C]gamma[/C][C]0.64547702995407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14219&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
alpha0.553590492930469
beta0.0620502955838186
gamma0.64547702995407







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1313.2512.54172222222220.708277777777772
1412.5412.2342147583650.305785241635011
1512.7712.65981178148100.110188218519037
1612.9612.93841316745500.0215868325449780
171312.99745718598560.00254281401435286
1813.6113.58062929705900.0293707029410264
1913.813.75674530269290.0432546973071055
2014.1614.15744984075640.00255015924358837
2114.2714.3202916659892-0.0502916659892492
2214.6914.7750698842658-0.0850698842657582
2315.0115.1085063557543-0.0985063557543349
2415.0915.1936207863540-0.103620786353964
2515.1415.1522660045593-0.0122660045592724
2614.214.3355811263814-0.135581126381437
2713.8314.4510059011042-0.621005901104201
2814.3114.26470278175380.0452972182462172
2914.0414.2976074671984-0.257607467198365
3014.914.70177925478520.198220745214778
3114.9214.9384557675841-0.0184557675841415
3215.3615.25423539916060.105764600839418
3315.515.42350131719360.0764986828063652
3415.6515.9073153080154-0.257315308015365
3516.1816.10447704494330.0755229550566767
3615.4416.2533870995686-0.813387099568642
3715.5815.7899836138805-0.20998361388048
3815.2414.76606713012860.47393286987136
3915.3315.03773228391050.292267716089532
4016.0715.53906637784610.530933622153883
4115.8215.76027981014870.0597201898513191
4215.8716.4891132425697-0.619113242569734
4315.7216.2004574328931-0.480457432893106
4417.0716.26997181257370.800028187426346
4516.8316.81269157297870.0173084270212485
4617.5217.16306667129530.356933328704734
4717.7617.8127925057252-0.0527925057251615
4817.3617.6467393251675-0.286739325167499
4917.9517.67905040772760.270949592272448
5016.7117.1652612012099-0.455261201209886
5117.1416.88508751604110.254912483958851
5216.7217.4481302730138-0.728130273013786
5317.2616.80692699083870.453073009161255
5417.2417.5417926427331-0.301792642733119
5517.6917.46353558555510.226464414444894
5618.1318.3124262795372-0.182426279537186
5718.0818.07104531936240.0089546806375509
5818.1818.4996859804297-0.319685980429693
5918.1818.6185665064751-0.438566506475077
6017.6418.1200759135896-0.480075913589573
6117.8918.1479474344342-0.257947434434232
6216.8217.0558357886584-0.235835788658363
6316.6117.0330312119843-0.423031211984252
6416.6616.8454850184927-0.185485018492692
6517.0216.77166051787690.248339482123114
6616.9117.0952578583092-0.185257858309193
6717.1817.15731466074400.0226853392560216
6818.0617.69216021259430.367839787405742
6917.5817.7460347472905-0.16603474729051
7017.4817.9125826769409-0.432582676940886
7117.5417.8603081356006-0.320308135600616
7217.4417.34498421393280.0950157860672505
7317.7917.70464214231120.0853578576887912
7416.7916.77016057797390.0198394220261022
7516.1916.8049462408868-0.614946240886802
7616.6216.54300427511560.0769957248843589
7716.3916.7119065360177-0.32190653601765
7816.5416.5477077371023-0.00770773710234351
7917.2616.72689819530420.533101804695839
801817.62021910525740.379780894742595
8117.2917.5037383242314-0.213738324231358
8218.1617.54230294986740.617697050132616
8317.8218.1151123980704-0.295112398070394
8417.4817.7455839947709-0.265583994770950
8518.3117.90262066393170.407379336068335
8617.0417.1383760214255-0.0983760214254765
8717.0316.93159418664100.0984058133590189
8816.9717.2952292466832-0.325229246683243
8917.1117.1439955058378-0.0339955058378081
9017.1217.2570812991928-0.137081299192847
9117.6917.54340475046600.146595249533977
9218.518.18822393284090.311776067159077
9318.2717.87038309734020.399616902659787
9418.4518.5164476564008-0.0664476564008467
9518.3518.4523736719747-0.102373671974746
9618.0318.2095487333393-0.179548733339342

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13.25 & 12.5417222222222 & 0.708277777777772 \tabularnewline
14 & 12.54 & 12.234214758365 & 0.305785241635011 \tabularnewline
15 & 12.77 & 12.6598117814810 & 0.110188218519037 \tabularnewline
16 & 12.96 & 12.9384131674550 & 0.0215868325449780 \tabularnewline
17 & 13 & 12.9974571859856 & 0.00254281401435286 \tabularnewline
18 & 13.61 & 13.5806292970590 & 0.0293707029410264 \tabularnewline
19 & 13.8 & 13.7567453026929 & 0.0432546973071055 \tabularnewline
20 & 14.16 & 14.1574498407564 & 0.00255015924358837 \tabularnewline
21 & 14.27 & 14.3202916659892 & -0.0502916659892492 \tabularnewline
22 & 14.69 & 14.7750698842658 & -0.0850698842657582 \tabularnewline
23 & 15.01 & 15.1085063557543 & -0.0985063557543349 \tabularnewline
24 & 15.09 & 15.1936207863540 & -0.103620786353964 \tabularnewline
25 & 15.14 & 15.1522660045593 & -0.0122660045592724 \tabularnewline
26 & 14.2 & 14.3355811263814 & -0.135581126381437 \tabularnewline
27 & 13.83 & 14.4510059011042 & -0.621005901104201 \tabularnewline
28 & 14.31 & 14.2647027817538 & 0.0452972182462172 \tabularnewline
29 & 14.04 & 14.2976074671984 & -0.257607467198365 \tabularnewline
30 & 14.9 & 14.7017792547852 & 0.198220745214778 \tabularnewline
31 & 14.92 & 14.9384557675841 & -0.0184557675841415 \tabularnewline
32 & 15.36 & 15.2542353991606 & 0.105764600839418 \tabularnewline
33 & 15.5 & 15.4235013171936 & 0.0764986828063652 \tabularnewline
34 & 15.65 & 15.9073153080154 & -0.257315308015365 \tabularnewline
35 & 16.18 & 16.1044770449433 & 0.0755229550566767 \tabularnewline
36 & 15.44 & 16.2533870995686 & -0.813387099568642 \tabularnewline
37 & 15.58 & 15.7899836138805 & -0.20998361388048 \tabularnewline
38 & 15.24 & 14.7660671301286 & 0.47393286987136 \tabularnewline
39 & 15.33 & 15.0377322839105 & 0.292267716089532 \tabularnewline
40 & 16.07 & 15.5390663778461 & 0.530933622153883 \tabularnewline
41 & 15.82 & 15.7602798101487 & 0.0597201898513191 \tabularnewline
42 & 15.87 & 16.4891132425697 & -0.619113242569734 \tabularnewline
43 & 15.72 & 16.2004574328931 & -0.480457432893106 \tabularnewline
44 & 17.07 & 16.2699718125737 & 0.800028187426346 \tabularnewline
45 & 16.83 & 16.8126915729787 & 0.0173084270212485 \tabularnewline
46 & 17.52 & 17.1630666712953 & 0.356933328704734 \tabularnewline
47 & 17.76 & 17.8127925057252 & -0.0527925057251615 \tabularnewline
48 & 17.36 & 17.6467393251675 & -0.286739325167499 \tabularnewline
49 & 17.95 & 17.6790504077276 & 0.270949592272448 \tabularnewline
50 & 16.71 & 17.1652612012099 & -0.455261201209886 \tabularnewline
51 & 17.14 & 16.8850875160411 & 0.254912483958851 \tabularnewline
52 & 16.72 & 17.4481302730138 & -0.728130273013786 \tabularnewline
53 & 17.26 & 16.8069269908387 & 0.453073009161255 \tabularnewline
54 & 17.24 & 17.5417926427331 & -0.301792642733119 \tabularnewline
55 & 17.69 & 17.4635355855551 & 0.226464414444894 \tabularnewline
56 & 18.13 & 18.3124262795372 & -0.182426279537186 \tabularnewline
57 & 18.08 & 18.0710453193624 & 0.0089546806375509 \tabularnewline
58 & 18.18 & 18.4996859804297 & -0.319685980429693 \tabularnewline
59 & 18.18 & 18.6185665064751 & -0.438566506475077 \tabularnewline
60 & 17.64 & 18.1200759135896 & -0.480075913589573 \tabularnewline
61 & 17.89 & 18.1479474344342 & -0.257947434434232 \tabularnewline
62 & 16.82 & 17.0558357886584 & -0.235835788658363 \tabularnewline
63 & 16.61 & 17.0330312119843 & -0.423031211984252 \tabularnewline
64 & 16.66 & 16.8454850184927 & -0.185485018492692 \tabularnewline
65 & 17.02 & 16.7716605178769 & 0.248339482123114 \tabularnewline
66 & 16.91 & 17.0952578583092 & -0.185257858309193 \tabularnewline
67 & 17.18 & 17.1573146607440 & 0.0226853392560216 \tabularnewline
68 & 18.06 & 17.6921602125943 & 0.367839787405742 \tabularnewline
69 & 17.58 & 17.7460347472905 & -0.16603474729051 \tabularnewline
70 & 17.48 & 17.9125826769409 & -0.432582676940886 \tabularnewline
71 & 17.54 & 17.8603081356006 & -0.320308135600616 \tabularnewline
72 & 17.44 & 17.3449842139328 & 0.0950157860672505 \tabularnewline
73 & 17.79 & 17.7046421423112 & 0.0853578576887912 \tabularnewline
74 & 16.79 & 16.7701605779739 & 0.0198394220261022 \tabularnewline
75 & 16.19 & 16.8049462408868 & -0.614946240886802 \tabularnewline
76 & 16.62 & 16.5430042751156 & 0.0769957248843589 \tabularnewline
77 & 16.39 & 16.7119065360177 & -0.32190653601765 \tabularnewline
78 & 16.54 & 16.5477077371023 & -0.00770773710234351 \tabularnewline
79 & 17.26 & 16.7268981953042 & 0.533101804695839 \tabularnewline
80 & 18 & 17.6202191052574 & 0.379780894742595 \tabularnewline
81 & 17.29 & 17.5037383242314 & -0.213738324231358 \tabularnewline
82 & 18.16 & 17.5423029498674 & 0.617697050132616 \tabularnewline
83 & 17.82 & 18.1151123980704 & -0.295112398070394 \tabularnewline
84 & 17.48 & 17.7455839947709 & -0.265583994770950 \tabularnewline
85 & 18.31 & 17.9026206639317 & 0.407379336068335 \tabularnewline
86 & 17.04 & 17.1383760214255 & -0.0983760214254765 \tabularnewline
87 & 17.03 & 16.9315941866410 & 0.0984058133590189 \tabularnewline
88 & 16.97 & 17.2952292466832 & -0.325229246683243 \tabularnewline
89 & 17.11 & 17.1439955058378 & -0.0339955058378081 \tabularnewline
90 & 17.12 & 17.2570812991928 & -0.137081299192847 \tabularnewline
91 & 17.69 & 17.5434047504660 & 0.146595249533977 \tabularnewline
92 & 18.5 & 18.1882239328409 & 0.311776067159077 \tabularnewline
93 & 18.27 & 17.8703830973402 & 0.399616902659787 \tabularnewline
94 & 18.45 & 18.5164476564008 & -0.0664476564008467 \tabularnewline
95 & 18.35 & 18.4523736719747 & -0.102373671974746 \tabularnewline
96 & 18.03 & 18.2095487333393 & -0.179548733339342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14219&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]13.25[/C][C]12.5417222222222[/C][C]0.708277777777772[/C][/ROW]
[ROW][C]14[/C][C]12.54[/C][C]12.234214758365[/C][C]0.305785241635011[/C][/ROW]
[ROW][C]15[/C][C]12.77[/C][C]12.6598117814810[/C][C]0.110188218519037[/C][/ROW]
[ROW][C]16[/C][C]12.96[/C][C]12.9384131674550[/C][C]0.0215868325449780[/C][/ROW]
[ROW][C]17[/C][C]13[/C][C]12.9974571859856[/C][C]0.00254281401435286[/C][/ROW]
[ROW][C]18[/C][C]13.61[/C][C]13.5806292970590[/C][C]0.0293707029410264[/C][/ROW]
[ROW][C]19[/C][C]13.8[/C][C]13.7567453026929[/C][C]0.0432546973071055[/C][/ROW]
[ROW][C]20[/C][C]14.16[/C][C]14.1574498407564[/C][C]0.00255015924358837[/C][/ROW]
[ROW][C]21[/C][C]14.27[/C][C]14.3202916659892[/C][C]-0.0502916659892492[/C][/ROW]
[ROW][C]22[/C][C]14.69[/C][C]14.7750698842658[/C][C]-0.0850698842657582[/C][/ROW]
[ROW][C]23[/C][C]15.01[/C][C]15.1085063557543[/C][C]-0.0985063557543349[/C][/ROW]
[ROW][C]24[/C][C]15.09[/C][C]15.1936207863540[/C][C]-0.103620786353964[/C][/ROW]
[ROW][C]25[/C][C]15.14[/C][C]15.1522660045593[/C][C]-0.0122660045592724[/C][/ROW]
[ROW][C]26[/C][C]14.2[/C][C]14.3355811263814[/C][C]-0.135581126381437[/C][/ROW]
[ROW][C]27[/C][C]13.83[/C][C]14.4510059011042[/C][C]-0.621005901104201[/C][/ROW]
[ROW][C]28[/C][C]14.31[/C][C]14.2647027817538[/C][C]0.0452972182462172[/C][/ROW]
[ROW][C]29[/C][C]14.04[/C][C]14.2976074671984[/C][C]-0.257607467198365[/C][/ROW]
[ROW][C]30[/C][C]14.9[/C][C]14.7017792547852[/C][C]0.198220745214778[/C][/ROW]
[ROW][C]31[/C][C]14.92[/C][C]14.9384557675841[/C][C]-0.0184557675841415[/C][/ROW]
[ROW][C]32[/C][C]15.36[/C][C]15.2542353991606[/C][C]0.105764600839418[/C][/ROW]
[ROW][C]33[/C][C]15.5[/C][C]15.4235013171936[/C][C]0.0764986828063652[/C][/ROW]
[ROW][C]34[/C][C]15.65[/C][C]15.9073153080154[/C][C]-0.257315308015365[/C][/ROW]
[ROW][C]35[/C][C]16.18[/C][C]16.1044770449433[/C][C]0.0755229550566767[/C][/ROW]
[ROW][C]36[/C][C]15.44[/C][C]16.2533870995686[/C][C]-0.813387099568642[/C][/ROW]
[ROW][C]37[/C][C]15.58[/C][C]15.7899836138805[/C][C]-0.20998361388048[/C][/ROW]
[ROW][C]38[/C][C]15.24[/C][C]14.7660671301286[/C][C]0.47393286987136[/C][/ROW]
[ROW][C]39[/C][C]15.33[/C][C]15.0377322839105[/C][C]0.292267716089532[/C][/ROW]
[ROW][C]40[/C][C]16.07[/C][C]15.5390663778461[/C][C]0.530933622153883[/C][/ROW]
[ROW][C]41[/C][C]15.82[/C][C]15.7602798101487[/C][C]0.0597201898513191[/C][/ROW]
[ROW][C]42[/C][C]15.87[/C][C]16.4891132425697[/C][C]-0.619113242569734[/C][/ROW]
[ROW][C]43[/C][C]15.72[/C][C]16.2004574328931[/C][C]-0.480457432893106[/C][/ROW]
[ROW][C]44[/C][C]17.07[/C][C]16.2699718125737[/C][C]0.800028187426346[/C][/ROW]
[ROW][C]45[/C][C]16.83[/C][C]16.8126915729787[/C][C]0.0173084270212485[/C][/ROW]
[ROW][C]46[/C][C]17.52[/C][C]17.1630666712953[/C][C]0.356933328704734[/C][/ROW]
[ROW][C]47[/C][C]17.76[/C][C]17.8127925057252[/C][C]-0.0527925057251615[/C][/ROW]
[ROW][C]48[/C][C]17.36[/C][C]17.6467393251675[/C][C]-0.286739325167499[/C][/ROW]
[ROW][C]49[/C][C]17.95[/C][C]17.6790504077276[/C][C]0.270949592272448[/C][/ROW]
[ROW][C]50[/C][C]16.71[/C][C]17.1652612012099[/C][C]-0.455261201209886[/C][/ROW]
[ROW][C]51[/C][C]17.14[/C][C]16.8850875160411[/C][C]0.254912483958851[/C][/ROW]
[ROW][C]52[/C][C]16.72[/C][C]17.4481302730138[/C][C]-0.728130273013786[/C][/ROW]
[ROW][C]53[/C][C]17.26[/C][C]16.8069269908387[/C][C]0.453073009161255[/C][/ROW]
[ROW][C]54[/C][C]17.24[/C][C]17.5417926427331[/C][C]-0.301792642733119[/C][/ROW]
[ROW][C]55[/C][C]17.69[/C][C]17.4635355855551[/C][C]0.226464414444894[/C][/ROW]
[ROW][C]56[/C][C]18.13[/C][C]18.3124262795372[/C][C]-0.182426279537186[/C][/ROW]
[ROW][C]57[/C][C]18.08[/C][C]18.0710453193624[/C][C]0.0089546806375509[/C][/ROW]
[ROW][C]58[/C][C]18.18[/C][C]18.4996859804297[/C][C]-0.319685980429693[/C][/ROW]
[ROW][C]59[/C][C]18.18[/C][C]18.6185665064751[/C][C]-0.438566506475077[/C][/ROW]
[ROW][C]60[/C][C]17.64[/C][C]18.1200759135896[/C][C]-0.480075913589573[/C][/ROW]
[ROW][C]61[/C][C]17.89[/C][C]18.1479474344342[/C][C]-0.257947434434232[/C][/ROW]
[ROW][C]62[/C][C]16.82[/C][C]17.0558357886584[/C][C]-0.235835788658363[/C][/ROW]
[ROW][C]63[/C][C]16.61[/C][C]17.0330312119843[/C][C]-0.423031211984252[/C][/ROW]
[ROW][C]64[/C][C]16.66[/C][C]16.8454850184927[/C][C]-0.185485018492692[/C][/ROW]
[ROW][C]65[/C][C]17.02[/C][C]16.7716605178769[/C][C]0.248339482123114[/C][/ROW]
[ROW][C]66[/C][C]16.91[/C][C]17.0952578583092[/C][C]-0.185257858309193[/C][/ROW]
[ROW][C]67[/C][C]17.18[/C][C]17.1573146607440[/C][C]0.0226853392560216[/C][/ROW]
[ROW][C]68[/C][C]18.06[/C][C]17.6921602125943[/C][C]0.367839787405742[/C][/ROW]
[ROW][C]69[/C][C]17.58[/C][C]17.7460347472905[/C][C]-0.16603474729051[/C][/ROW]
[ROW][C]70[/C][C]17.48[/C][C]17.9125826769409[/C][C]-0.432582676940886[/C][/ROW]
[ROW][C]71[/C][C]17.54[/C][C]17.8603081356006[/C][C]-0.320308135600616[/C][/ROW]
[ROW][C]72[/C][C]17.44[/C][C]17.3449842139328[/C][C]0.0950157860672505[/C][/ROW]
[ROW][C]73[/C][C]17.79[/C][C]17.7046421423112[/C][C]0.0853578576887912[/C][/ROW]
[ROW][C]74[/C][C]16.79[/C][C]16.7701605779739[/C][C]0.0198394220261022[/C][/ROW]
[ROW][C]75[/C][C]16.19[/C][C]16.8049462408868[/C][C]-0.614946240886802[/C][/ROW]
[ROW][C]76[/C][C]16.62[/C][C]16.5430042751156[/C][C]0.0769957248843589[/C][/ROW]
[ROW][C]77[/C][C]16.39[/C][C]16.7119065360177[/C][C]-0.32190653601765[/C][/ROW]
[ROW][C]78[/C][C]16.54[/C][C]16.5477077371023[/C][C]-0.00770773710234351[/C][/ROW]
[ROW][C]79[/C][C]17.26[/C][C]16.7268981953042[/C][C]0.533101804695839[/C][/ROW]
[ROW][C]80[/C][C]18[/C][C]17.6202191052574[/C][C]0.379780894742595[/C][/ROW]
[ROW][C]81[/C][C]17.29[/C][C]17.5037383242314[/C][C]-0.213738324231358[/C][/ROW]
[ROW][C]82[/C][C]18.16[/C][C]17.5423029498674[/C][C]0.617697050132616[/C][/ROW]
[ROW][C]83[/C][C]17.82[/C][C]18.1151123980704[/C][C]-0.295112398070394[/C][/ROW]
[ROW][C]84[/C][C]17.48[/C][C]17.7455839947709[/C][C]-0.265583994770950[/C][/ROW]
[ROW][C]85[/C][C]18.31[/C][C]17.9026206639317[/C][C]0.407379336068335[/C][/ROW]
[ROW][C]86[/C][C]17.04[/C][C]17.1383760214255[/C][C]-0.0983760214254765[/C][/ROW]
[ROW][C]87[/C][C]17.03[/C][C]16.9315941866410[/C][C]0.0984058133590189[/C][/ROW]
[ROW][C]88[/C][C]16.97[/C][C]17.2952292466832[/C][C]-0.325229246683243[/C][/ROW]
[ROW][C]89[/C][C]17.11[/C][C]17.1439955058378[/C][C]-0.0339955058378081[/C][/ROW]
[ROW][C]90[/C][C]17.12[/C][C]17.2570812991928[/C][C]-0.137081299192847[/C][/ROW]
[ROW][C]91[/C][C]17.69[/C][C]17.5434047504660[/C][C]0.146595249533977[/C][/ROW]
[ROW][C]92[/C][C]18.5[/C][C]18.1882239328409[/C][C]0.311776067159077[/C][/ROW]
[ROW][C]93[/C][C]18.27[/C][C]17.8703830973402[/C][C]0.399616902659787[/C][/ROW]
[ROW][C]94[/C][C]18.45[/C][C]18.5164476564008[/C][C]-0.0664476564008467[/C][/ROW]
[ROW][C]95[/C][C]18.35[/C][C]18.4523736719747[/C][C]-0.102373671974746[/C][/ROW]
[ROW][C]96[/C][C]18.03[/C][C]18.2095487333393[/C][C]-0.179548733339342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14219&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14219&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
1313.2512.54172222222220.708277777777772
1412.5412.2342147583650.305785241635011
1512.7712.65981178148100.110188218519037
1612.9612.93841316745500.0215868325449780
171312.99745718598560.00254281401435286
1813.6113.58062929705900.0293707029410264
1913.813.75674530269290.0432546973071055
2014.1614.15744984075640.00255015924358837
2114.2714.3202916659892-0.0502916659892492
2214.6914.7750698842658-0.0850698842657582
2315.0115.1085063557543-0.0985063557543349
2415.0915.1936207863540-0.103620786353964
2515.1415.1522660045593-0.0122660045592724
2614.214.3355811263814-0.135581126381437
2713.8314.4510059011042-0.621005901104201
2814.3114.26470278175380.0452972182462172
2914.0414.2976074671984-0.257607467198365
3014.914.70177925478520.198220745214778
3114.9214.9384557675841-0.0184557675841415
3215.3615.25423539916060.105764600839418
3315.515.42350131719360.0764986828063652
3415.6515.9073153080154-0.257315308015365
3516.1816.10447704494330.0755229550566767
3615.4416.2533870995686-0.813387099568642
3715.5815.7899836138805-0.20998361388048
3815.2414.76606713012860.47393286987136
3915.3315.03773228391050.292267716089532
4016.0715.53906637784610.530933622153883
4115.8215.76027981014870.0597201898513191
4215.8716.4891132425697-0.619113242569734
4315.7216.2004574328931-0.480457432893106
4417.0716.26997181257370.800028187426346
4516.8316.81269157297870.0173084270212485
4617.5217.16306667129530.356933328704734
4717.7617.8127925057252-0.0527925057251615
4817.3617.6467393251675-0.286739325167499
4917.9517.67905040772760.270949592272448
5016.7117.1652612012099-0.455261201209886
5117.1416.88508751604110.254912483958851
5216.7217.4481302730138-0.728130273013786
5317.2616.80692699083870.453073009161255
5417.2417.5417926427331-0.301792642733119
5517.6917.46353558555510.226464414444894
5618.1318.3124262795372-0.182426279537186
5718.0818.07104531936240.0089546806375509
5818.1818.4996859804297-0.319685980429693
5918.1818.6185665064751-0.438566506475077
6017.6418.1200759135896-0.480075913589573
6117.8918.1479474344342-0.257947434434232
6216.8217.0558357886584-0.235835788658363
6316.6117.0330312119843-0.423031211984252
6416.6616.8454850184927-0.185485018492692
6517.0216.77166051787690.248339482123114
6616.9117.0952578583092-0.185257858309193
6717.1817.15731466074400.0226853392560216
6818.0617.69216021259430.367839787405742
6917.5817.7460347472905-0.16603474729051
7017.4817.9125826769409-0.432582676940886
7117.5417.8603081356006-0.320308135600616
7217.4417.34498421393280.0950157860672505
7317.7917.70464214231120.0853578576887912
7416.7916.77016057797390.0198394220261022
7516.1916.8049462408868-0.614946240886802
7616.6216.54300427511560.0769957248843589
7716.3916.7119065360177-0.32190653601765
7816.5416.5477077371023-0.00770773710234351
7917.2616.72689819530420.533101804695839
801817.62021910525740.379780894742595
8117.2917.5037383242314-0.213738324231358
8218.1617.54230294986740.617697050132616
8317.8218.1151123980704-0.295112398070394
8417.4817.7455839947709-0.265583994770950
8518.3117.90262066393170.407379336068335
8617.0417.1383760214255-0.0983760214254765
8717.0316.93159418664100.0984058133590189
8816.9717.2952292466832-0.325229246683243
8917.1117.1439955058378-0.0339955058378081
9017.1217.2570812991928-0.137081299192847
9117.6917.54340475046600.146595249533977
9218.518.18822393284090.311776067159077
9318.2717.87038309734020.399616902659787
9418.4518.5164476564008-0.0664476564008467
9518.3518.4523736719747-0.102373671974746
9618.0318.2095487333393-0.179548733339342







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9718.6225780911517.986183133966819.2589730483332
9817.487538490569616.749299888995518.2257770921436
9917.395756358829016.558003092175018.233509625483
10017.583302966316316.647110032479618.5194959001530
10117.707660246350016.673333406026118.7419870866739
10217.822658568023916.690002086752218.9553150492955
10318.284115108191817.052592049433219.5156381669505
10418.907846926447317.576680974843820.2390128780507
10518.444481256979417.012724398095919.876238115863
10618.723059885157217.189639023149220.2564807471652
10718.675734552473017.039484552936520.3119845520096
10818.461177356119916.720865020699220.2014896915405

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 18.62257809115 & 17.9861831339668 & 19.2589730483332 \tabularnewline
98 & 17.4875384905696 & 16.7492998889955 & 18.2257770921436 \tabularnewline
99 & 17.3957563588290 & 16.5580030921750 & 18.233509625483 \tabularnewline
100 & 17.5833029663163 & 16.6471100324796 & 18.5194959001530 \tabularnewline
101 & 17.7076602463500 & 16.6733334060261 & 18.7419870866739 \tabularnewline
102 & 17.8226585680239 & 16.6900020867522 & 18.9553150492955 \tabularnewline
103 & 18.2841151081918 & 17.0525920494332 & 19.5156381669505 \tabularnewline
104 & 18.9078469264473 & 17.5766809748438 & 20.2390128780507 \tabularnewline
105 & 18.4444812569794 & 17.0127243980959 & 19.876238115863 \tabularnewline
106 & 18.7230598851572 & 17.1896390231492 & 20.2564807471652 \tabularnewline
107 & 18.6757345524730 & 17.0394845529365 & 20.3119845520096 \tabularnewline
108 & 18.4611773561199 & 16.7208650206992 & 20.2014896915405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14219&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]97[/C][C]18.62257809115[/C][C]17.9861831339668[/C][C]19.2589730483332[/C][/ROW]
[ROW][C]98[/C][C]17.4875384905696[/C][C]16.7492998889955[/C][C]18.2257770921436[/C][/ROW]
[ROW][C]99[/C][C]17.3957563588290[/C][C]16.5580030921750[/C][C]18.233509625483[/C][/ROW]
[ROW][C]100[/C][C]17.5833029663163[/C][C]16.6471100324796[/C][C]18.5194959001530[/C][/ROW]
[ROW][C]101[/C][C]17.7076602463500[/C][C]16.6733334060261[/C][C]18.7419870866739[/C][/ROW]
[ROW][C]102[/C][C]17.8226585680239[/C][C]16.6900020867522[/C][C]18.9553150492955[/C][/ROW]
[ROW][C]103[/C][C]18.2841151081918[/C][C]17.0525920494332[/C][C]19.5156381669505[/C][/ROW]
[ROW][C]104[/C][C]18.9078469264473[/C][C]17.5766809748438[/C][C]20.2390128780507[/C][/ROW]
[ROW][C]105[/C][C]18.4444812569794[/C][C]17.0127243980959[/C][C]19.876238115863[/C][/ROW]
[ROW][C]106[/C][C]18.7230598851572[/C][C]17.1896390231492[/C][C]20.2564807471652[/C][/ROW]
[ROW][C]107[/C][C]18.6757345524730[/C][C]17.0394845529365[/C][C]20.3119845520096[/C][/ROW]
[ROW][C]108[/C][C]18.4611773561199[/C][C]16.7208650206992[/C][C]20.2014896915405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14219&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14219&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
9718.6225780911517.986183133966819.2589730483332
9817.487538490569616.749299888995518.2257770921436
9917.395756358829016.558003092175018.233509625483
10017.583302966316316.647110032479618.5194959001530
10117.707660246350016.673333406026118.7419870866739
10217.822658568023916.690002086752218.9553150492955
10318.284115108191817.052592049433219.5156381669505
10418.907846926447317.576680974843820.2390128780507
10518.444481256979417.012724398095919.876238115863
10618.723059885157217.189639023149220.2564807471652
10718.675734552473017.039484552936520.3119845520096
10818.461177356119916.720865020699220.2014896915405



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')