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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 21:20:14 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t14616158124ibqqwsl008jykb.htm/, Retrieved Mon, 06 May 2024 05:40:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294786, Retrieved Mon, 06 May 2024 05:40:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 20:20:14] [409a9d71664281dd1fd3bb0995266dd0] [Current]
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Dataseries X:
100.57
100.27
100.27
100.18
100.16
100.18
100.18
100.59
100.69
101.06
101.15
101.16
101.16
100.81
100.94
101.13
101.29
101.34
101.35
101.7
102.05
102.48
102.66
102.72
102.73
102.18
102.22
102.37
102.53
102.61
102.62
103
103.17
103.52
103.69
103.73
99.57
99.09
99.14
99.36
99.6
99.65
99.8
100.15
100.45
100.89
101.13
101.17
101.21
101.1
101.17
101.11
101.2
101.15
100.92
101.1
101.22
101.25
101.39
101.43
101.95
101.92
102.05
102.07
102.1
102.16
101.63
101.43
101.4
101.6
101.72
101.73





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=294786&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=294786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294786&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999945481003755
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999945481003755 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294786&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]0.999945481003755[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294786&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
alpha0.999945481003755
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2100.27100.57-0.299999999999997
3100.27100.270016355699-1.63556988752589e-05
4100.18100.270000000892-0.0900000008916919
5100.16100.18000490671-0.0200049067097297
6100.18100.1600010906470.0199989093525801
7100.18100.179998909681.09032046680113e-06
8100.59100.1799999999410.410000000059441
9100.69100.5899776472120.100022352788457
10101.06100.6899945468820.370005453118281
11101.15101.0599798276740.0900201723259215
12101.16101.1499950921910.0100049078094315
13101.16101.1599994545425.45457538692062e-07
14100.81101.15999999997-0.349999999970251
15100.94100.8100190816490.129980918351308
16101.13100.9399929135710.190007086429205
17101.29101.1299896410040.160010358995649
18101.34101.2899912763960.0500087236041651
19101.35101.3399972735750.0100027264254123
20101.7101.3499994546610.350000545338617
21102.05101.6999809183220.350019081678411
22102.48102.0499809173110.430019082689
23102.66102.4799765557910.180023444208743
24102.72102.6599901853030.0600098146974801
25102.73102.7199967283250.0100032716748615
26102.18102.729999454632-0.54999945463166
27102.22102.1800299854180.0399700145817832
28102.37102.2199978208750.150002179125082
29102.53102.3699918220320.160008177968237
30102.61102.5299912765150.0800087234852498
31102.62102.6099956380050.0100043619952999
32103102.6199994545720.380000545427762
33103.17102.9999792827520.170020717248306
34103.52103.1699907306410.350009269358836
35103.69103.5199809178460.170019082154042
36103.73103.689990730730.0400092692697172
3799.57103.729997818735-4.15999781873481
3899.0999.5702267989055-0.480226798905449
3999.1499.0900261814830.0499738185169605
4099.3699.13999727547760.220002724522431
4199.699.35998800567230.240011994327716
4299.6599.5999869147870.0500130852130241
4399.899.64999727333680.150002726663189
44100.1599.79999182200190.350008177998092
45100.45100.1499809179050.300019082094536
46100.89100.4499836432610.440016356739207
47101.13100.889976010750.240023989250091
48101.17101.1299869141330.0400130858669741
49101.21101.1699978185270.0400021814732696
50101.1101.209997819121-0.109997819121219
51101.17101.1000059969710.069994003029322
52101.11101.169996183997-0.0599961839972138
53101.2101.1100032709320.0899967290682753
54101.15101.199995093469-0.0499950934686524
55100.92101.150002725682-0.230002725682311
56101.1100.9200125395180.179987460482252
57101.22101.0999901872640.120009812735688
58101.25101.2199934571850.0300065428145331
59101.39101.2499983640730.140001635926595
60101.43101.3899923672510.0400076327486687
61101.95101.4299978188240.520002181175983
62101.92101.949971650003-0.0299716500030485
63102.05101.9200016340240.129998365975709
64102.07102.049992912620.0200070873804208
65102.1102.0699989092340.0300010907663193
66102.16102.0999983643710.060001635629348
67101.63102.159996728771-0.529996728771053
68101.43101.63002889489-0.200028894889641
69101.4101.430010905375-0.0300109053745672
70101.6101.4000016361640.199998363835562
71101.72101.599989096290.120010903710053
72101.73101.7199934571260.0100065428740095

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 100.27 & 100.57 & -0.299999999999997 \tabularnewline
3 & 100.27 & 100.270016355699 & -1.63556988752589e-05 \tabularnewline
4 & 100.18 & 100.270000000892 & -0.0900000008916919 \tabularnewline
5 & 100.16 & 100.18000490671 & -0.0200049067097297 \tabularnewline
6 & 100.18 & 100.160001090647 & 0.0199989093525801 \tabularnewline
7 & 100.18 & 100.17999890968 & 1.09032046680113e-06 \tabularnewline
8 & 100.59 & 100.179999999941 & 0.410000000059441 \tabularnewline
9 & 100.69 & 100.589977647212 & 0.100022352788457 \tabularnewline
10 & 101.06 & 100.689994546882 & 0.370005453118281 \tabularnewline
11 & 101.15 & 101.059979827674 & 0.0900201723259215 \tabularnewline
12 & 101.16 & 101.149995092191 & 0.0100049078094315 \tabularnewline
13 & 101.16 & 101.159999454542 & 5.45457538692062e-07 \tabularnewline
14 & 100.81 & 101.15999999997 & -0.349999999970251 \tabularnewline
15 & 100.94 & 100.810019081649 & 0.129980918351308 \tabularnewline
16 & 101.13 & 100.939992913571 & 0.190007086429205 \tabularnewline
17 & 101.29 & 101.129989641004 & 0.160010358995649 \tabularnewline
18 & 101.34 & 101.289991276396 & 0.0500087236041651 \tabularnewline
19 & 101.35 & 101.339997273575 & 0.0100027264254123 \tabularnewline
20 & 101.7 & 101.349999454661 & 0.350000545338617 \tabularnewline
21 & 102.05 & 101.699980918322 & 0.350019081678411 \tabularnewline
22 & 102.48 & 102.049980917311 & 0.430019082689 \tabularnewline
23 & 102.66 & 102.479976555791 & 0.180023444208743 \tabularnewline
24 & 102.72 & 102.659990185303 & 0.0600098146974801 \tabularnewline
25 & 102.73 & 102.719996728325 & 0.0100032716748615 \tabularnewline
26 & 102.18 & 102.729999454632 & -0.54999945463166 \tabularnewline
27 & 102.22 & 102.180029985418 & 0.0399700145817832 \tabularnewline
28 & 102.37 & 102.219997820875 & 0.150002179125082 \tabularnewline
29 & 102.53 & 102.369991822032 & 0.160008177968237 \tabularnewline
30 & 102.61 & 102.529991276515 & 0.0800087234852498 \tabularnewline
31 & 102.62 & 102.609995638005 & 0.0100043619952999 \tabularnewline
32 & 103 & 102.619999454572 & 0.380000545427762 \tabularnewline
33 & 103.17 & 102.999979282752 & 0.170020717248306 \tabularnewline
34 & 103.52 & 103.169990730641 & 0.350009269358836 \tabularnewline
35 & 103.69 & 103.519980917846 & 0.170019082154042 \tabularnewline
36 & 103.73 & 103.68999073073 & 0.0400092692697172 \tabularnewline
37 & 99.57 & 103.729997818735 & -4.15999781873481 \tabularnewline
38 & 99.09 & 99.5702267989055 & -0.480226798905449 \tabularnewline
39 & 99.14 & 99.090026181483 & 0.0499738185169605 \tabularnewline
40 & 99.36 & 99.1399972754776 & 0.220002724522431 \tabularnewline
41 & 99.6 & 99.3599880056723 & 0.240011994327716 \tabularnewline
42 & 99.65 & 99.599986914787 & 0.0500130852130241 \tabularnewline
43 & 99.8 & 99.6499972733368 & 0.150002726663189 \tabularnewline
44 & 100.15 & 99.7999918220019 & 0.350008177998092 \tabularnewline
45 & 100.45 & 100.149980917905 & 0.300019082094536 \tabularnewline
46 & 100.89 & 100.449983643261 & 0.440016356739207 \tabularnewline
47 & 101.13 & 100.88997601075 & 0.240023989250091 \tabularnewline
48 & 101.17 & 101.129986914133 & 0.0400130858669741 \tabularnewline
49 & 101.21 & 101.169997818527 & 0.0400021814732696 \tabularnewline
50 & 101.1 & 101.209997819121 & -0.109997819121219 \tabularnewline
51 & 101.17 & 101.100005996971 & 0.069994003029322 \tabularnewline
52 & 101.11 & 101.169996183997 & -0.0599961839972138 \tabularnewline
53 & 101.2 & 101.110003270932 & 0.0899967290682753 \tabularnewline
54 & 101.15 & 101.199995093469 & -0.0499950934686524 \tabularnewline
55 & 100.92 & 101.150002725682 & -0.230002725682311 \tabularnewline
56 & 101.1 & 100.920012539518 & 0.179987460482252 \tabularnewline
57 & 101.22 & 101.099990187264 & 0.120009812735688 \tabularnewline
58 & 101.25 & 101.219993457185 & 0.0300065428145331 \tabularnewline
59 & 101.39 & 101.249998364073 & 0.140001635926595 \tabularnewline
60 & 101.43 & 101.389992367251 & 0.0400076327486687 \tabularnewline
61 & 101.95 & 101.429997818824 & 0.520002181175983 \tabularnewline
62 & 101.92 & 101.949971650003 & -0.0299716500030485 \tabularnewline
63 & 102.05 & 101.920001634024 & 0.129998365975709 \tabularnewline
64 & 102.07 & 102.04999291262 & 0.0200070873804208 \tabularnewline
65 & 102.1 & 102.069998909234 & 0.0300010907663193 \tabularnewline
66 & 102.16 & 102.099998364371 & 0.060001635629348 \tabularnewline
67 & 101.63 & 102.159996728771 & -0.529996728771053 \tabularnewline
68 & 101.43 & 101.63002889489 & -0.200028894889641 \tabularnewline
69 & 101.4 & 101.430010905375 & -0.0300109053745672 \tabularnewline
70 & 101.6 & 101.400001636164 & 0.199998363835562 \tabularnewline
71 & 101.72 & 101.59998909629 & 0.120010903710053 \tabularnewline
72 & 101.73 & 101.719993457126 & 0.0100065428740095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294786&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]2[/C][C]100.27[/C][C]100.57[/C][C]-0.299999999999997[/C][/ROW]
[ROW][C]3[/C][C]100.27[/C][C]100.270016355699[/C][C]-1.63556988752589e-05[/C][/ROW]
[ROW][C]4[/C][C]100.18[/C][C]100.270000000892[/C][C]-0.0900000008916919[/C][/ROW]
[ROW][C]5[/C][C]100.16[/C][C]100.18000490671[/C][C]-0.0200049067097297[/C][/ROW]
[ROW][C]6[/C][C]100.18[/C][C]100.160001090647[/C][C]0.0199989093525801[/C][/ROW]
[ROW][C]7[/C][C]100.18[/C][C]100.17999890968[/C][C]1.09032046680113e-06[/C][/ROW]
[ROW][C]8[/C][C]100.59[/C][C]100.179999999941[/C][C]0.410000000059441[/C][/ROW]
[ROW][C]9[/C][C]100.69[/C][C]100.589977647212[/C][C]0.100022352788457[/C][/ROW]
[ROW][C]10[/C][C]101.06[/C][C]100.689994546882[/C][C]0.370005453118281[/C][/ROW]
[ROW][C]11[/C][C]101.15[/C][C]101.059979827674[/C][C]0.0900201723259215[/C][/ROW]
[ROW][C]12[/C][C]101.16[/C][C]101.149995092191[/C][C]0.0100049078094315[/C][/ROW]
[ROW][C]13[/C][C]101.16[/C][C]101.159999454542[/C][C]5.45457538692062e-07[/C][/ROW]
[ROW][C]14[/C][C]100.81[/C][C]101.15999999997[/C][C]-0.349999999970251[/C][/ROW]
[ROW][C]15[/C][C]100.94[/C][C]100.810019081649[/C][C]0.129980918351308[/C][/ROW]
[ROW][C]16[/C][C]101.13[/C][C]100.939992913571[/C][C]0.190007086429205[/C][/ROW]
[ROW][C]17[/C][C]101.29[/C][C]101.129989641004[/C][C]0.160010358995649[/C][/ROW]
[ROW][C]18[/C][C]101.34[/C][C]101.289991276396[/C][C]0.0500087236041651[/C][/ROW]
[ROW][C]19[/C][C]101.35[/C][C]101.339997273575[/C][C]0.0100027264254123[/C][/ROW]
[ROW][C]20[/C][C]101.7[/C][C]101.349999454661[/C][C]0.350000545338617[/C][/ROW]
[ROW][C]21[/C][C]102.05[/C][C]101.699980918322[/C][C]0.350019081678411[/C][/ROW]
[ROW][C]22[/C][C]102.48[/C][C]102.049980917311[/C][C]0.430019082689[/C][/ROW]
[ROW][C]23[/C][C]102.66[/C][C]102.479976555791[/C][C]0.180023444208743[/C][/ROW]
[ROW][C]24[/C][C]102.72[/C][C]102.659990185303[/C][C]0.0600098146974801[/C][/ROW]
[ROW][C]25[/C][C]102.73[/C][C]102.719996728325[/C][C]0.0100032716748615[/C][/ROW]
[ROW][C]26[/C][C]102.18[/C][C]102.729999454632[/C][C]-0.54999945463166[/C][/ROW]
[ROW][C]27[/C][C]102.22[/C][C]102.180029985418[/C][C]0.0399700145817832[/C][/ROW]
[ROW][C]28[/C][C]102.37[/C][C]102.219997820875[/C][C]0.150002179125082[/C][/ROW]
[ROW][C]29[/C][C]102.53[/C][C]102.369991822032[/C][C]0.160008177968237[/C][/ROW]
[ROW][C]30[/C][C]102.61[/C][C]102.529991276515[/C][C]0.0800087234852498[/C][/ROW]
[ROW][C]31[/C][C]102.62[/C][C]102.609995638005[/C][C]0.0100043619952999[/C][/ROW]
[ROW][C]32[/C][C]103[/C][C]102.619999454572[/C][C]0.380000545427762[/C][/ROW]
[ROW][C]33[/C][C]103.17[/C][C]102.999979282752[/C][C]0.170020717248306[/C][/ROW]
[ROW][C]34[/C][C]103.52[/C][C]103.169990730641[/C][C]0.350009269358836[/C][/ROW]
[ROW][C]35[/C][C]103.69[/C][C]103.519980917846[/C][C]0.170019082154042[/C][/ROW]
[ROW][C]36[/C][C]103.73[/C][C]103.68999073073[/C][C]0.0400092692697172[/C][/ROW]
[ROW][C]37[/C][C]99.57[/C][C]103.729997818735[/C][C]-4.15999781873481[/C][/ROW]
[ROW][C]38[/C][C]99.09[/C][C]99.5702267989055[/C][C]-0.480226798905449[/C][/ROW]
[ROW][C]39[/C][C]99.14[/C][C]99.090026181483[/C][C]0.0499738185169605[/C][/ROW]
[ROW][C]40[/C][C]99.36[/C][C]99.1399972754776[/C][C]0.220002724522431[/C][/ROW]
[ROW][C]41[/C][C]99.6[/C][C]99.3599880056723[/C][C]0.240011994327716[/C][/ROW]
[ROW][C]42[/C][C]99.65[/C][C]99.599986914787[/C][C]0.0500130852130241[/C][/ROW]
[ROW][C]43[/C][C]99.8[/C][C]99.6499972733368[/C][C]0.150002726663189[/C][/ROW]
[ROW][C]44[/C][C]100.15[/C][C]99.7999918220019[/C][C]0.350008177998092[/C][/ROW]
[ROW][C]45[/C][C]100.45[/C][C]100.149980917905[/C][C]0.300019082094536[/C][/ROW]
[ROW][C]46[/C][C]100.89[/C][C]100.449983643261[/C][C]0.440016356739207[/C][/ROW]
[ROW][C]47[/C][C]101.13[/C][C]100.88997601075[/C][C]0.240023989250091[/C][/ROW]
[ROW][C]48[/C][C]101.17[/C][C]101.129986914133[/C][C]0.0400130858669741[/C][/ROW]
[ROW][C]49[/C][C]101.21[/C][C]101.169997818527[/C][C]0.0400021814732696[/C][/ROW]
[ROW][C]50[/C][C]101.1[/C][C]101.209997819121[/C][C]-0.109997819121219[/C][/ROW]
[ROW][C]51[/C][C]101.17[/C][C]101.100005996971[/C][C]0.069994003029322[/C][/ROW]
[ROW][C]52[/C][C]101.11[/C][C]101.169996183997[/C][C]-0.0599961839972138[/C][/ROW]
[ROW][C]53[/C][C]101.2[/C][C]101.110003270932[/C][C]0.0899967290682753[/C][/ROW]
[ROW][C]54[/C][C]101.15[/C][C]101.199995093469[/C][C]-0.0499950934686524[/C][/ROW]
[ROW][C]55[/C][C]100.92[/C][C]101.150002725682[/C][C]-0.230002725682311[/C][/ROW]
[ROW][C]56[/C][C]101.1[/C][C]100.920012539518[/C][C]0.179987460482252[/C][/ROW]
[ROW][C]57[/C][C]101.22[/C][C]101.099990187264[/C][C]0.120009812735688[/C][/ROW]
[ROW][C]58[/C][C]101.25[/C][C]101.219993457185[/C][C]0.0300065428145331[/C][/ROW]
[ROW][C]59[/C][C]101.39[/C][C]101.249998364073[/C][C]0.140001635926595[/C][/ROW]
[ROW][C]60[/C][C]101.43[/C][C]101.389992367251[/C][C]0.0400076327486687[/C][/ROW]
[ROW][C]61[/C][C]101.95[/C][C]101.429997818824[/C][C]0.520002181175983[/C][/ROW]
[ROW][C]62[/C][C]101.92[/C][C]101.949971650003[/C][C]-0.0299716500030485[/C][/ROW]
[ROW][C]63[/C][C]102.05[/C][C]101.920001634024[/C][C]0.129998365975709[/C][/ROW]
[ROW][C]64[/C][C]102.07[/C][C]102.04999291262[/C][C]0.0200070873804208[/C][/ROW]
[ROW][C]65[/C][C]102.1[/C][C]102.069998909234[/C][C]0.0300010907663193[/C][/ROW]
[ROW][C]66[/C][C]102.16[/C][C]102.099998364371[/C][C]0.060001635629348[/C][/ROW]
[ROW][C]67[/C][C]101.63[/C][C]102.159996728771[/C][C]-0.529996728771053[/C][/ROW]
[ROW][C]68[/C][C]101.43[/C][C]101.63002889489[/C][C]-0.200028894889641[/C][/ROW]
[ROW][C]69[/C][C]101.4[/C][C]101.430010905375[/C][C]-0.0300109053745672[/C][/ROW]
[ROW][C]70[/C][C]101.6[/C][C]101.400001636164[/C][C]0.199998363835562[/C][/ROW]
[ROW][C]71[/C][C]101.72[/C][C]101.59998909629[/C][C]0.120010903710053[/C][/ROW]
[ROW][C]72[/C][C]101.73[/C][C]101.719993457126[/C][C]0.0100065428740095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294786&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294786&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
2100.27100.57-0.299999999999997
3100.27100.270016355699-1.63556988752589e-05
4100.18100.270000000892-0.0900000008916919
5100.16100.18000490671-0.0200049067097297
6100.18100.1600010906470.0199989093525801
7100.18100.179998909681.09032046680113e-06
8100.59100.1799999999410.410000000059441
9100.69100.5899776472120.100022352788457
10101.06100.6899945468820.370005453118281
11101.15101.0599798276740.0900201723259215
12101.16101.1499950921910.0100049078094315
13101.16101.1599994545425.45457538692062e-07
14100.81101.15999999997-0.349999999970251
15100.94100.8100190816490.129980918351308
16101.13100.9399929135710.190007086429205
17101.29101.1299896410040.160010358995649
18101.34101.2899912763960.0500087236041651
19101.35101.3399972735750.0100027264254123
20101.7101.3499994546610.350000545338617
21102.05101.6999809183220.350019081678411
22102.48102.0499809173110.430019082689
23102.66102.4799765557910.180023444208743
24102.72102.6599901853030.0600098146974801
25102.73102.7199967283250.0100032716748615
26102.18102.729999454632-0.54999945463166
27102.22102.1800299854180.0399700145817832
28102.37102.2199978208750.150002179125082
29102.53102.3699918220320.160008177968237
30102.61102.5299912765150.0800087234852498
31102.62102.6099956380050.0100043619952999
32103102.6199994545720.380000545427762
33103.17102.9999792827520.170020717248306
34103.52103.1699907306410.350009269358836
35103.69103.5199809178460.170019082154042
36103.73103.689990730730.0400092692697172
3799.57103.729997818735-4.15999781873481
3899.0999.5702267989055-0.480226798905449
3999.1499.0900261814830.0499738185169605
4099.3699.13999727547760.220002724522431
4199.699.35998800567230.240011994327716
4299.6599.5999869147870.0500130852130241
4399.899.64999727333680.150002726663189
44100.1599.79999182200190.350008177998092
45100.45100.1499809179050.300019082094536
46100.89100.4499836432610.440016356739207
47101.13100.889976010750.240023989250091
48101.17101.1299869141330.0400130858669741
49101.21101.1699978185270.0400021814732696
50101.1101.209997819121-0.109997819121219
51101.17101.1000059969710.069994003029322
52101.11101.169996183997-0.0599961839972138
53101.2101.1100032709320.0899967290682753
54101.15101.199995093469-0.0499950934686524
55100.92101.150002725682-0.230002725682311
56101.1100.9200125395180.179987460482252
57101.22101.0999901872640.120009812735688
58101.25101.2199934571850.0300065428145331
59101.39101.2499983640730.140001635926595
60101.43101.3899923672510.0400076327486687
61101.95101.4299978188240.520002181175983
62101.92101.949971650003-0.0299716500030485
63102.05101.9200016340240.129998365975709
64102.07102.049992912620.0200070873804208
65102.1102.0699989092340.0300010907663193
66102.16102.0999983643710.060001635629348
67101.63102.159996728771-0.529996728771053
68101.43101.63002889489-0.200028894889641
69101.4101.430010905375-0.0300109053745672
70101.6101.4000016361640.199998363835562
71101.72101.599989096290.120010903710053
72101.73101.7199934571260.0100065428740095







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.729999454453100.663741407825102.796257501081
74101.729999454453100.222123968412103.237874940495
75101.72999945445399.8832534673692103.576745441537
76101.72999945445399.5975705575807103.862428351326
77101.72999945445399.3458779685337104.114120940373
78101.72999945445399.1183299655958104.341668943311
79101.72999945445398.9090776585796104.550921250327
80101.72999945445398.7143101405747104.745688768332
81101.72999945445398.5313803309489104.928618577958
82101.72999945445398.3583608978085105.101638011098
83101.72999945445398.1937968561764105.26620205273
84101.72999945445398.0365578242842105.423441084622

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.729999454453 & 100.663741407825 & 102.796257501081 \tabularnewline
74 & 101.729999454453 & 100.222123968412 & 103.237874940495 \tabularnewline
75 & 101.729999454453 & 99.8832534673692 & 103.576745441537 \tabularnewline
76 & 101.729999454453 & 99.5975705575807 & 103.862428351326 \tabularnewline
77 & 101.729999454453 & 99.3458779685337 & 104.114120940373 \tabularnewline
78 & 101.729999454453 & 99.1183299655958 & 104.341668943311 \tabularnewline
79 & 101.729999454453 & 98.9090776585796 & 104.550921250327 \tabularnewline
80 & 101.729999454453 & 98.7143101405747 & 104.745688768332 \tabularnewline
81 & 101.729999454453 & 98.5313803309489 & 104.928618577958 \tabularnewline
82 & 101.729999454453 & 98.3583608978085 & 105.101638011098 \tabularnewline
83 & 101.729999454453 & 98.1937968561764 & 105.26620205273 \tabularnewline
84 & 101.729999454453 & 98.0365578242842 & 105.423441084622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294786&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]73[/C][C]101.729999454453[/C][C]100.663741407825[/C][C]102.796257501081[/C][/ROW]
[ROW][C]74[/C][C]101.729999454453[/C][C]100.222123968412[/C][C]103.237874940495[/C][/ROW]
[ROW][C]75[/C][C]101.729999454453[/C][C]99.8832534673692[/C][C]103.576745441537[/C][/ROW]
[ROW][C]76[/C][C]101.729999454453[/C][C]99.5975705575807[/C][C]103.862428351326[/C][/ROW]
[ROW][C]77[/C][C]101.729999454453[/C][C]99.3458779685337[/C][C]104.114120940373[/C][/ROW]
[ROW][C]78[/C][C]101.729999454453[/C][C]99.1183299655958[/C][C]104.341668943311[/C][/ROW]
[ROW][C]79[/C][C]101.729999454453[/C][C]98.9090776585796[/C][C]104.550921250327[/C][/ROW]
[ROW][C]80[/C][C]101.729999454453[/C][C]98.7143101405747[/C][C]104.745688768332[/C][/ROW]
[ROW][C]81[/C][C]101.729999454453[/C][C]98.5313803309489[/C][C]104.928618577958[/C][/ROW]
[ROW][C]82[/C][C]101.729999454453[/C][C]98.3583608978085[/C][C]105.101638011098[/C][/ROW]
[ROW][C]83[/C][C]101.729999454453[/C][C]98.1937968561764[/C][C]105.26620205273[/C][/ROW]
[ROW][C]84[/C][C]101.729999454453[/C][C]98.0365578242842[/C][C]105.423441084622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294786&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294786&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
73101.729999454453100.663741407825102.796257501081
74101.729999454453100.222123968412103.237874940495
75101.72999945445399.8832534673692103.576745441537
76101.72999945445399.5975705575807103.862428351326
77101.72999945445399.3458779685337104.114120940373
78101.72999945445399.1183299655958104.341668943311
79101.72999945445398.9090776585796104.550921250327
80101.72999945445398.7143101405747104.745688768332
81101.72999945445398.5313803309489104.928618577958
82101.72999945445398.3583608978085105.101638011098
83101.72999945445398.1937968561764105.26620205273
84101.72999945445398.0365578242842105.423441084622



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')