Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 11:53:19 +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/26/t1461668028vepja8e2t778jo8.htm/, Retrieved Sat, 04 May 2024 03:50:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294849, Retrieved Sat, 04 May 2024 03:50:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 10:53:19] [a8cf284534efea996701e15b66911faf] [Current]
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Dataseries X:
92.09
93.77
94.44
94.91
94.78
94.51
94.36
96.6
96.72
96.71
97.44
97.83
98.92
97.98
98.76
99.76
99.87
100.09
100.07
99.46
100.4
101.25
102.29
102.1
105.91
108.95
110.07
109.92
109.87
110.54
110.79
110.32
110.76
110.24
110.27
110.11
110.39
111.05
110.85
110.24
108.7
109.93
109.53
109.83
107.86
104.61
103.61
103.11
102.59
102.91
101.94
101.8
102.25
102.6
102.49
102.13
100.76
100.86
101.12
100.74
99.99
99.39
99.52
99.21
99.38
99.37
99.38
99.26
99.36
99.2
98.53
98.65
99.15
100.17
99.98
100.07
99.94
100.05
99.13
98.74
98.64
98.44
98.81
98.88
99.63
100.08
100.07
100.55
99.98
99.89
99.86
99.61
100.12
100.24
100.1
99.86
97.99
97.57
98.28
97.97
97.99
97.84
97.33
96.7
96.79
96.76
96.23
96.29
96.46
97.23
97.59
97.13
97.37
96.12
96.96
96.7
97
97.15
96.51
96.68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294849&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294849&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294849&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.850141679872731
beta0.0816759489554359
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.850141679872731 \tabularnewline
beta & 0.0816759489554359 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294849&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]0.850141679872731[/C][/ROW]
[ROW][C]beta[/C][C]0.0816759489554359[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294849&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294849&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
alpha0.850141679872731
beta0.0816759489554359
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1398.9296.37004006410262.54995993589739
1497.9897.80491934888410.175080651115948
1598.7699.0375550249198-0.277555024919835
1699.76100.016113900598-0.25611390059791
1799.87100.056367212026-0.186367212025573
18100.09100.264224472769-0.174224472768572
19100.0799.17030730939150.899692690608518
2099.46102.291843064563-2.83184306456269
21100.4100.0289958588790.371004141120878
22101.25100.3581169815430.891883018457193
23102.29101.8999045184940.390095481505782
24102.1102.671771609138-0.571771609137556
25105.91103.6425131676832.26748683231712
26108.95104.5297773750134.4202226249873
27110.07109.6467426828280.423257317172357
28109.92111.616154891819-1.69615489181932
29109.87110.734481006888-0.86448100688763
30110.54110.612439110284-0.0724391102839803
31110.79110.0178308823750.772169117625197
32110.32112.714738644387-2.39473864438699
33110.76111.57680305645-0.816803056450084
34110.24111.165038703039-0.925038703039348
35110.27111.15168920478-0.881689204780415
36110.11110.674608421209-0.564608421208874
37110.39112.053816670664-1.6638166706642
38111.05109.6254372542851.42456274571479
39110.85111.09259768004-0.242597680039651
40110.24111.628001803405-1.38800180340526
41108.7110.604006464987-1.90400646498698
42109.93109.1158056050050.814194394994558
43109.53108.8619883306120.668011669388193
44109.83110.448983023147-0.61898302314701
45107.86110.633682669736-2.77368266973593
46104.61107.982719829376-3.37271982937644
47103.61105.165679815449-1.55567981544907
48103.11103.38701836274-0.277018362740435
49102.59104.089852193389-1.49985219338873
50102.91101.5189290104251.39107098957494
51101.94101.960697145696-0.0206971456959906
52101.8101.7814260464340.0185739535660474
53102.25101.2418851902241.0081148097758
54102.6102.2049448413760.395055158623975
55102.49101.1119895528961.37801044710433
56102.13102.698112920832-0.568112920831922
57100.76102.195087899642-1.43508789964218
58100.86100.2772246091610.582775390839004
59101.12101.0547438305620.065256169438257
60100.74100.917806515576-0.177806515576364
6199.99101.600702374794-1.61070237479427
6299.3999.4400424425914-0.050042442591419
6399.5298.41630216358441.10369783641558
6499.2199.2480922196188-0.038092219618818
6599.3898.85401435387320.525985646126756
6699.3799.32719297164730.0428070283526694
6799.3898.06949130102011.31050869897993
6899.2699.2893091874408-0.0293091874408162
6999.3699.13455605531090.225443944689104
7099.299.06621039379810.133789606201873
7198.5399.4887343846299-0.958734384629906
7298.6598.47799397430340.172006025696646
7399.1599.3009972372993-0.150997237299308
74100.1798.7739761806411.39602381935902
7599.9899.41170874766910.568291252330951
76100.0799.8392581156320.230741884367973
7799.9499.9989633918872-0.0589633918872039
78100.05100.102531823172-0.0525318231715346
7999.1399.1472220105027-0.0172220105027492
8098.7499.1387730898866-0.398773089886603
8198.6498.7837212949961-0.143721294996098
8298.4498.43778542975540.00221457024458971
8398.8198.62557984591350.184420154086482
8498.8898.87636149665490.00363850334510119
8599.6399.61636087884380.0136391211562454
86100.0899.58110683448560.498893165514374
87100.0799.38978415426480.680215845735162
88100.5599.92734783917030.622652160829674
8999.98100.469477498812-0.489477498811496
9099.89100.270778403909-0.380778403908877
9199.8699.08167842494580.778321575054193
9299.6199.7875895914179-0.177589591417899
93100.1299.76936879746430.350631202535723
94100.24100.0104702785150.229529721485022
95100.1100.579501665941-0.479501665940845
9699.86100.353345774053-0.493345774053111
9797.99100.75240982269-2.76240982268962
9897.5798.317155169795-0.747155169794979
9998.2896.89448175265591.38551824734409
10097.9797.87279365292290.0972063470770621
10197.9997.61484076416320.375159235836776
10297.8498.0408146074078-0.200814607407779
10397.3397.06422586602780.265774133972215
10496.797.0413742759722-0.341374275972186
10596.7996.8019254292441-0.0119254292440871
10696.7696.53033366618630.229666333813682
10796.2396.8069157510378-0.576915751037831
10896.2996.3027941837197-0.0127941837196914
10996.4696.6106494372938-0.150649437293808
11097.2396.71940674763340.510593252366647
11197.5996.79457264849710.795427351502894
11297.1397.1461619047377-0.0161619047377286
11397.3796.89361411904040.476385880959583
11496.1297.3864898922854-1.26648989228543
11596.9695.5670114254811.39298857451898
11696.796.48289802587790.217101974122073
1179796.8778146491220.122185350878041
11897.1596.87596360089920.274036399100794
11996.5197.1919973920265-0.681997392026531
12096.6896.798387290736-0.118387290736038

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 98.92 & 96.3700400641026 & 2.54995993589739 \tabularnewline
14 & 97.98 & 97.8049193488841 & 0.175080651115948 \tabularnewline
15 & 98.76 & 99.0375550249198 & -0.277555024919835 \tabularnewline
16 & 99.76 & 100.016113900598 & -0.25611390059791 \tabularnewline
17 & 99.87 & 100.056367212026 & -0.186367212025573 \tabularnewline
18 & 100.09 & 100.264224472769 & -0.174224472768572 \tabularnewline
19 & 100.07 & 99.1703073093915 & 0.899692690608518 \tabularnewline
20 & 99.46 & 102.291843064563 & -2.83184306456269 \tabularnewline
21 & 100.4 & 100.028995858879 & 0.371004141120878 \tabularnewline
22 & 101.25 & 100.358116981543 & 0.891883018457193 \tabularnewline
23 & 102.29 & 101.899904518494 & 0.390095481505782 \tabularnewline
24 & 102.1 & 102.671771609138 & -0.571771609137556 \tabularnewline
25 & 105.91 & 103.642513167683 & 2.26748683231712 \tabularnewline
26 & 108.95 & 104.529777375013 & 4.4202226249873 \tabularnewline
27 & 110.07 & 109.646742682828 & 0.423257317172357 \tabularnewline
28 & 109.92 & 111.616154891819 & -1.69615489181932 \tabularnewline
29 & 109.87 & 110.734481006888 & -0.86448100688763 \tabularnewline
30 & 110.54 & 110.612439110284 & -0.0724391102839803 \tabularnewline
31 & 110.79 & 110.017830882375 & 0.772169117625197 \tabularnewline
32 & 110.32 & 112.714738644387 & -2.39473864438699 \tabularnewline
33 & 110.76 & 111.57680305645 & -0.816803056450084 \tabularnewline
34 & 110.24 & 111.165038703039 & -0.925038703039348 \tabularnewline
35 & 110.27 & 111.15168920478 & -0.881689204780415 \tabularnewline
36 & 110.11 & 110.674608421209 & -0.564608421208874 \tabularnewline
37 & 110.39 & 112.053816670664 & -1.6638166706642 \tabularnewline
38 & 111.05 & 109.625437254285 & 1.42456274571479 \tabularnewline
39 & 110.85 & 111.09259768004 & -0.242597680039651 \tabularnewline
40 & 110.24 & 111.628001803405 & -1.38800180340526 \tabularnewline
41 & 108.7 & 110.604006464987 & -1.90400646498698 \tabularnewline
42 & 109.93 & 109.115805605005 & 0.814194394994558 \tabularnewline
43 & 109.53 & 108.861988330612 & 0.668011669388193 \tabularnewline
44 & 109.83 & 110.448983023147 & -0.61898302314701 \tabularnewline
45 & 107.86 & 110.633682669736 & -2.77368266973593 \tabularnewline
46 & 104.61 & 107.982719829376 & -3.37271982937644 \tabularnewline
47 & 103.61 & 105.165679815449 & -1.55567981544907 \tabularnewline
48 & 103.11 & 103.38701836274 & -0.277018362740435 \tabularnewline
49 & 102.59 & 104.089852193389 & -1.49985219338873 \tabularnewline
50 & 102.91 & 101.518929010425 & 1.39107098957494 \tabularnewline
51 & 101.94 & 101.960697145696 & -0.0206971456959906 \tabularnewline
52 & 101.8 & 101.781426046434 & 0.0185739535660474 \tabularnewline
53 & 102.25 & 101.241885190224 & 1.0081148097758 \tabularnewline
54 & 102.6 & 102.204944841376 & 0.395055158623975 \tabularnewline
55 & 102.49 & 101.111989552896 & 1.37801044710433 \tabularnewline
56 & 102.13 & 102.698112920832 & -0.568112920831922 \tabularnewline
57 & 100.76 & 102.195087899642 & -1.43508789964218 \tabularnewline
58 & 100.86 & 100.277224609161 & 0.582775390839004 \tabularnewline
59 & 101.12 & 101.054743830562 & 0.065256169438257 \tabularnewline
60 & 100.74 & 100.917806515576 & -0.177806515576364 \tabularnewline
61 & 99.99 & 101.600702374794 & -1.61070237479427 \tabularnewline
62 & 99.39 & 99.4400424425914 & -0.050042442591419 \tabularnewline
63 & 99.52 & 98.4163021635844 & 1.10369783641558 \tabularnewline
64 & 99.21 & 99.2480922196188 & -0.038092219618818 \tabularnewline
65 & 99.38 & 98.8540143538732 & 0.525985646126756 \tabularnewline
66 & 99.37 & 99.3271929716473 & 0.0428070283526694 \tabularnewline
67 & 99.38 & 98.0694913010201 & 1.31050869897993 \tabularnewline
68 & 99.26 & 99.2893091874408 & -0.0293091874408162 \tabularnewline
69 & 99.36 & 99.1345560553109 & 0.225443944689104 \tabularnewline
70 & 99.2 & 99.0662103937981 & 0.133789606201873 \tabularnewline
71 & 98.53 & 99.4887343846299 & -0.958734384629906 \tabularnewline
72 & 98.65 & 98.4779939743034 & 0.172006025696646 \tabularnewline
73 & 99.15 & 99.3009972372993 & -0.150997237299308 \tabularnewline
74 & 100.17 & 98.773976180641 & 1.39602381935902 \tabularnewline
75 & 99.98 & 99.4117087476691 & 0.568291252330951 \tabularnewline
76 & 100.07 & 99.839258115632 & 0.230741884367973 \tabularnewline
77 & 99.94 & 99.9989633918872 & -0.0589633918872039 \tabularnewline
78 & 100.05 & 100.102531823172 & -0.0525318231715346 \tabularnewline
79 & 99.13 & 99.1472220105027 & -0.0172220105027492 \tabularnewline
80 & 98.74 & 99.1387730898866 & -0.398773089886603 \tabularnewline
81 & 98.64 & 98.7837212949961 & -0.143721294996098 \tabularnewline
82 & 98.44 & 98.4377854297554 & 0.00221457024458971 \tabularnewline
83 & 98.81 & 98.6255798459135 & 0.184420154086482 \tabularnewline
84 & 98.88 & 98.8763614966549 & 0.00363850334510119 \tabularnewline
85 & 99.63 & 99.6163608788438 & 0.0136391211562454 \tabularnewline
86 & 100.08 & 99.5811068344856 & 0.498893165514374 \tabularnewline
87 & 100.07 & 99.3897841542648 & 0.680215845735162 \tabularnewline
88 & 100.55 & 99.9273478391703 & 0.622652160829674 \tabularnewline
89 & 99.98 & 100.469477498812 & -0.489477498811496 \tabularnewline
90 & 99.89 & 100.270778403909 & -0.380778403908877 \tabularnewline
91 & 99.86 & 99.0816784249458 & 0.778321575054193 \tabularnewline
92 & 99.61 & 99.7875895914179 & -0.177589591417899 \tabularnewline
93 & 100.12 & 99.7693687974643 & 0.350631202535723 \tabularnewline
94 & 100.24 & 100.010470278515 & 0.229529721485022 \tabularnewline
95 & 100.1 & 100.579501665941 & -0.479501665940845 \tabularnewline
96 & 99.86 & 100.353345774053 & -0.493345774053111 \tabularnewline
97 & 97.99 & 100.75240982269 & -2.76240982268962 \tabularnewline
98 & 97.57 & 98.317155169795 & -0.747155169794979 \tabularnewline
99 & 98.28 & 96.8944817526559 & 1.38551824734409 \tabularnewline
100 & 97.97 & 97.8727936529229 & 0.0972063470770621 \tabularnewline
101 & 97.99 & 97.6148407641632 & 0.375159235836776 \tabularnewline
102 & 97.84 & 98.0408146074078 & -0.200814607407779 \tabularnewline
103 & 97.33 & 97.0642258660278 & 0.265774133972215 \tabularnewline
104 & 96.7 & 97.0413742759722 & -0.341374275972186 \tabularnewline
105 & 96.79 & 96.8019254292441 & -0.0119254292440871 \tabularnewline
106 & 96.76 & 96.5303336661863 & 0.229666333813682 \tabularnewline
107 & 96.23 & 96.8069157510378 & -0.576915751037831 \tabularnewline
108 & 96.29 & 96.3027941837197 & -0.0127941837196914 \tabularnewline
109 & 96.46 & 96.6106494372938 & -0.150649437293808 \tabularnewline
110 & 97.23 & 96.7194067476334 & 0.510593252366647 \tabularnewline
111 & 97.59 & 96.7945726484971 & 0.795427351502894 \tabularnewline
112 & 97.13 & 97.1461619047377 & -0.0161619047377286 \tabularnewline
113 & 97.37 & 96.8936141190404 & 0.476385880959583 \tabularnewline
114 & 96.12 & 97.3864898922854 & -1.26648989228543 \tabularnewline
115 & 96.96 & 95.567011425481 & 1.39298857451898 \tabularnewline
116 & 96.7 & 96.4828980258779 & 0.217101974122073 \tabularnewline
117 & 97 & 96.877814649122 & 0.122185350878041 \tabularnewline
118 & 97.15 & 96.8759636008992 & 0.274036399100794 \tabularnewline
119 & 96.51 & 97.1919973920265 & -0.681997392026531 \tabularnewline
120 & 96.68 & 96.798387290736 & -0.118387290736038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294849&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]98.92[/C][C]96.3700400641026[/C][C]2.54995993589739[/C][/ROW]
[ROW][C]14[/C][C]97.98[/C][C]97.8049193488841[/C][C]0.175080651115948[/C][/ROW]
[ROW][C]15[/C][C]98.76[/C][C]99.0375550249198[/C][C]-0.277555024919835[/C][/ROW]
[ROW][C]16[/C][C]99.76[/C][C]100.016113900598[/C][C]-0.25611390059791[/C][/ROW]
[ROW][C]17[/C][C]99.87[/C][C]100.056367212026[/C][C]-0.186367212025573[/C][/ROW]
[ROW][C]18[/C][C]100.09[/C][C]100.264224472769[/C][C]-0.174224472768572[/C][/ROW]
[ROW][C]19[/C][C]100.07[/C][C]99.1703073093915[/C][C]0.899692690608518[/C][/ROW]
[ROW][C]20[/C][C]99.46[/C][C]102.291843064563[/C][C]-2.83184306456269[/C][/ROW]
[ROW][C]21[/C][C]100.4[/C][C]100.028995858879[/C][C]0.371004141120878[/C][/ROW]
[ROW][C]22[/C][C]101.25[/C][C]100.358116981543[/C][C]0.891883018457193[/C][/ROW]
[ROW][C]23[/C][C]102.29[/C][C]101.899904518494[/C][C]0.390095481505782[/C][/ROW]
[ROW][C]24[/C][C]102.1[/C][C]102.671771609138[/C][C]-0.571771609137556[/C][/ROW]
[ROW][C]25[/C][C]105.91[/C][C]103.642513167683[/C][C]2.26748683231712[/C][/ROW]
[ROW][C]26[/C][C]108.95[/C][C]104.529777375013[/C][C]4.4202226249873[/C][/ROW]
[ROW][C]27[/C][C]110.07[/C][C]109.646742682828[/C][C]0.423257317172357[/C][/ROW]
[ROW][C]28[/C][C]109.92[/C][C]111.616154891819[/C][C]-1.69615489181932[/C][/ROW]
[ROW][C]29[/C][C]109.87[/C][C]110.734481006888[/C][C]-0.86448100688763[/C][/ROW]
[ROW][C]30[/C][C]110.54[/C][C]110.612439110284[/C][C]-0.0724391102839803[/C][/ROW]
[ROW][C]31[/C][C]110.79[/C][C]110.017830882375[/C][C]0.772169117625197[/C][/ROW]
[ROW][C]32[/C][C]110.32[/C][C]112.714738644387[/C][C]-2.39473864438699[/C][/ROW]
[ROW][C]33[/C][C]110.76[/C][C]111.57680305645[/C][C]-0.816803056450084[/C][/ROW]
[ROW][C]34[/C][C]110.24[/C][C]111.165038703039[/C][C]-0.925038703039348[/C][/ROW]
[ROW][C]35[/C][C]110.27[/C][C]111.15168920478[/C][C]-0.881689204780415[/C][/ROW]
[ROW][C]36[/C][C]110.11[/C][C]110.674608421209[/C][C]-0.564608421208874[/C][/ROW]
[ROW][C]37[/C][C]110.39[/C][C]112.053816670664[/C][C]-1.6638166706642[/C][/ROW]
[ROW][C]38[/C][C]111.05[/C][C]109.625437254285[/C][C]1.42456274571479[/C][/ROW]
[ROW][C]39[/C][C]110.85[/C][C]111.09259768004[/C][C]-0.242597680039651[/C][/ROW]
[ROW][C]40[/C][C]110.24[/C][C]111.628001803405[/C][C]-1.38800180340526[/C][/ROW]
[ROW][C]41[/C][C]108.7[/C][C]110.604006464987[/C][C]-1.90400646498698[/C][/ROW]
[ROW][C]42[/C][C]109.93[/C][C]109.115805605005[/C][C]0.814194394994558[/C][/ROW]
[ROW][C]43[/C][C]109.53[/C][C]108.861988330612[/C][C]0.668011669388193[/C][/ROW]
[ROW][C]44[/C][C]109.83[/C][C]110.448983023147[/C][C]-0.61898302314701[/C][/ROW]
[ROW][C]45[/C][C]107.86[/C][C]110.633682669736[/C][C]-2.77368266973593[/C][/ROW]
[ROW][C]46[/C][C]104.61[/C][C]107.982719829376[/C][C]-3.37271982937644[/C][/ROW]
[ROW][C]47[/C][C]103.61[/C][C]105.165679815449[/C][C]-1.55567981544907[/C][/ROW]
[ROW][C]48[/C][C]103.11[/C][C]103.38701836274[/C][C]-0.277018362740435[/C][/ROW]
[ROW][C]49[/C][C]102.59[/C][C]104.089852193389[/C][C]-1.49985219338873[/C][/ROW]
[ROW][C]50[/C][C]102.91[/C][C]101.518929010425[/C][C]1.39107098957494[/C][/ROW]
[ROW][C]51[/C][C]101.94[/C][C]101.960697145696[/C][C]-0.0206971456959906[/C][/ROW]
[ROW][C]52[/C][C]101.8[/C][C]101.781426046434[/C][C]0.0185739535660474[/C][/ROW]
[ROW][C]53[/C][C]102.25[/C][C]101.241885190224[/C][C]1.0081148097758[/C][/ROW]
[ROW][C]54[/C][C]102.6[/C][C]102.204944841376[/C][C]0.395055158623975[/C][/ROW]
[ROW][C]55[/C][C]102.49[/C][C]101.111989552896[/C][C]1.37801044710433[/C][/ROW]
[ROW][C]56[/C][C]102.13[/C][C]102.698112920832[/C][C]-0.568112920831922[/C][/ROW]
[ROW][C]57[/C][C]100.76[/C][C]102.195087899642[/C][C]-1.43508789964218[/C][/ROW]
[ROW][C]58[/C][C]100.86[/C][C]100.277224609161[/C][C]0.582775390839004[/C][/ROW]
[ROW][C]59[/C][C]101.12[/C][C]101.054743830562[/C][C]0.065256169438257[/C][/ROW]
[ROW][C]60[/C][C]100.74[/C][C]100.917806515576[/C][C]-0.177806515576364[/C][/ROW]
[ROW][C]61[/C][C]99.99[/C][C]101.600702374794[/C][C]-1.61070237479427[/C][/ROW]
[ROW][C]62[/C][C]99.39[/C][C]99.4400424425914[/C][C]-0.050042442591419[/C][/ROW]
[ROW][C]63[/C][C]99.52[/C][C]98.4163021635844[/C][C]1.10369783641558[/C][/ROW]
[ROW][C]64[/C][C]99.21[/C][C]99.2480922196188[/C][C]-0.038092219618818[/C][/ROW]
[ROW][C]65[/C][C]99.38[/C][C]98.8540143538732[/C][C]0.525985646126756[/C][/ROW]
[ROW][C]66[/C][C]99.37[/C][C]99.3271929716473[/C][C]0.0428070283526694[/C][/ROW]
[ROW][C]67[/C][C]99.38[/C][C]98.0694913010201[/C][C]1.31050869897993[/C][/ROW]
[ROW][C]68[/C][C]99.26[/C][C]99.2893091874408[/C][C]-0.0293091874408162[/C][/ROW]
[ROW][C]69[/C][C]99.36[/C][C]99.1345560553109[/C][C]0.225443944689104[/C][/ROW]
[ROW][C]70[/C][C]99.2[/C][C]99.0662103937981[/C][C]0.133789606201873[/C][/ROW]
[ROW][C]71[/C][C]98.53[/C][C]99.4887343846299[/C][C]-0.958734384629906[/C][/ROW]
[ROW][C]72[/C][C]98.65[/C][C]98.4779939743034[/C][C]0.172006025696646[/C][/ROW]
[ROW][C]73[/C][C]99.15[/C][C]99.3009972372993[/C][C]-0.150997237299308[/C][/ROW]
[ROW][C]74[/C][C]100.17[/C][C]98.773976180641[/C][C]1.39602381935902[/C][/ROW]
[ROW][C]75[/C][C]99.98[/C][C]99.4117087476691[/C][C]0.568291252330951[/C][/ROW]
[ROW][C]76[/C][C]100.07[/C][C]99.839258115632[/C][C]0.230741884367973[/C][/ROW]
[ROW][C]77[/C][C]99.94[/C][C]99.9989633918872[/C][C]-0.0589633918872039[/C][/ROW]
[ROW][C]78[/C][C]100.05[/C][C]100.102531823172[/C][C]-0.0525318231715346[/C][/ROW]
[ROW][C]79[/C][C]99.13[/C][C]99.1472220105027[/C][C]-0.0172220105027492[/C][/ROW]
[ROW][C]80[/C][C]98.74[/C][C]99.1387730898866[/C][C]-0.398773089886603[/C][/ROW]
[ROW][C]81[/C][C]98.64[/C][C]98.7837212949961[/C][C]-0.143721294996098[/C][/ROW]
[ROW][C]82[/C][C]98.44[/C][C]98.4377854297554[/C][C]0.00221457024458971[/C][/ROW]
[ROW][C]83[/C][C]98.81[/C][C]98.6255798459135[/C][C]0.184420154086482[/C][/ROW]
[ROW][C]84[/C][C]98.88[/C][C]98.8763614966549[/C][C]0.00363850334510119[/C][/ROW]
[ROW][C]85[/C][C]99.63[/C][C]99.6163608788438[/C][C]0.0136391211562454[/C][/ROW]
[ROW][C]86[/C][C]100.08[/C][C]99.5811068344856[/C][C]0.498893165514374[/C][/ROW]
[ROW][C]87[/C][C]100.07[/C][C]99.3897841542648[/C][C]0.680215845735162[/C][/ROW]
[ROW][C]88[/C][C]100.55[/C][C]99.9273478391703[/C][C]0.622652160829674[/C][/ROW]
[ROW][C]89[/C][C]99.98[/C][C]100.469477498812[/C][C]-0.489477498811496[/C][/ROW]
[ROW][C]90[/C][C]99.89[/C][C]100.270778403909[/C][C]-0.380778403908877[/C][/ROW]
[ROW][C]91[/C][C]99.86[/C][C]99.0816784249458[/C][C]0.778321575054193[/C][/ROW]
[ROW][C]92[/C][C]99.61[/C][C]99.7875895914179[/C][C]-0.177589591417899[/C][/ROW]
[ROW][C]93[/C][C]100.12[/C][C]99.7693687974643[/C][C]0.350631202535723[/C][/ROW]
[ROW][C]94[/C][C]100.24[/C][C]100.010470278515[/C][C]0.229529721485022[/C][/ROW]
[ROW][C]95[/C][C]100.1[/C][C]100.579501665941[/C][C]-0.479501665940845[/C][/ROW]
[ROW][C]96[/C][C]99.86[/C][C]100.353345774053[/C][C]-0.493345774053111[/C][/ROW]
[ROW][C]97[/C][C]97.99[/C][C]100.75240982269[/C][C]-2.76240982268962[/C][/ROW]
[ROW][C]98[/C][C]97.57[/C][C]98.317155169795[/C][C]-0.747155169794979[/C][/ROW]
[ROW][C]99[/C][C]98.28[/C][C]96.8944817526559[/C][C]1.38551824734409[/C][/ROW]
[ROW][C]100[/C][C]97.97[/C][C]97.8727936529229[/C][C]0.0972063470770621[/C][/ROW]
[ROW][C]101[/C][C]97.99[/C][C]97.6148407641632[/C][C]0.375159235836776[/C][/ROW]
[ROW][C]102[/C][C]97.84[/C][C]98.0408146074078[/C][C]-0.200814607407779[/C][/ROW]
[ROW][C]103[/C][C]97.33[/C][C]97.0642258660278[/C][C]0.265774133972215[/C][/ROW]
[ROW][C]104[/C][C]96.7[/C][C]97.0413742759722[/C][C]-0.341374275972186[/C][/ROW]
[ROW][C]105[/C][C]96.79[/C][C]96.8019254292441[/C][C]-0.0119254292440871[/C][/ROW]
[ROW][C]106[/C][C]96.76[/C][C]96.5303336661863[/C][C]0.229666333813682[/C][/ROW]
[ROW][C]107[/C][C]96.23[/C][C]96.8069157510378[/C][C]-0.576915751037831[/C][/ROW]
[ROW][C]108[/C][C]96.29[/C][C]96.3027941837197[/C][C]-0.0127941837196914[/C][/ROW]
[ROW][C]109[/C][C]96.46[/C][C]96.6106494372938[/C][C]-0.150649437293808[/C][/ROW]
[ROW][C]110[/C][C]97.23[/C][C]96.7194067476334[/C][C]0.510593252366647[/C][/ROW]
[ROW][C]111[/C][C]97.59[/C][C]96.7945726484971[/C][C]0.795427351502894[/C][/ROW]
[ROW][C]112[/C][C]97.13[/C][C]97.1461619047377[/C][C]-0.0161619047377286[/C][/ROW]
[ROW][C]113[/C][C]97.37[/C][C]96.8936141190404[/C][C]0.476385880959583[/C][/ROW]
[ROW][C]114[/C][C]96.12[/C][C]97.3864898922854[/C][C]-1.26648989228543[/C][/ROW]
[ROW][C]115[/C][C]96.96[/C][C]95.567011425481[/C][C]1.39298857451898[/C][/ROW]
[ROW][C]116[/C][C]96.7[/C][C]96.4828980258779[/C][C]0.217101974122073[/C][/ROW]
[ROW][C]117[/C][C]97[/C][C]96.877814649122[/C][C]0.122185350878041[/C][/ROW]
[ROW][C]118[/C][C]97.15[/C][C]96.8759636008992[/C][C]0.274036399100794[/C][/ROW]
[ROW][C]119[/C][C]96.51[/C][C]97.1919973920265[/C][C]-0.681997392026531[/C][/ROW]
[ROW][C]120[/C][C]96.68[/C][C]96.798387290736[/C][C]-0.118387290736038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294849&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294849&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
1398.9296.37004006410262.54995993589739
1497.9897.80491934888410.175080651115948
1598.7699.0375550249198-0.277555024919835
1699.76100.016113900598-0.25611390059791
1799.87100.056367212026-0.186367212025573
18100.09100.264224472769-0.174224472768572
19100.0799.17030730939150.899692690608518
2099.46102.291843064563-2.83184306456269
21100.4100.0289958588790.371004141120878
22101.25100.3581169815430.891883018457193
23102.29101.8999045184940.390095481505782
24102.1102.671771609138-0.571771609137556
25105.91103.6425131676832.26748683231712
26108.95104.5297773750134.4202226249873
27110.07109.6467426828280.423257317172357
28109.92111.616154891819-1.69615489181932
29109.87110.734481006888-0.86448100688763
30110.54110.612439110284-0.0724391102839803
31110.79110.0178308823750.772169117625197
32110.32112.714738644387-2.39473864438699
33110.76111.57680305645-0.816803056450084
34110.24111.165038703039-0.925038703039348
35110.27111.15168920478-0.881689204780415
36110.11110.674608421209-0.564608421208874
37110.39112.053816670664-1.6638166706642
38111.05109.6254372542851.42456274571479
39110.85111.09259768004-0.242597680039651
40110.24111.628001803405-1.38800180340526
41108.7110.604006464987-1.90400646498698
42109.93109.1158056050050.814194394994558
43109.53108.8619883306120.668011669388193
44109.83110.448983023147-0.61898302314701
45107.86110.633682669736-2.77368266973593
46104.61107.982719829376-3.37271982937644
47103.61105.165679815449-1.55567981544907
48103.11103.38701836274-0.277018362740435
49102.59104.089852193389-1.49985219338873
50102.91101.5189290104251.39107098957494
51101.94101.960697145696-0.0206971456959906
52101.8101.7814260464340.0185739535660474
53102.25101.2418851902241.0081148097758
54102.6102.2049448413760.395055158623975
55102.49101.1119895528961.37801044710433
56102.13102.698112920832-0.568112920831922
57100.76102.195087899642-1.43508789964218
58100.86100.2772246091610.582775390839004
59101.12101.0547438305620.065256169438257
60100.74100.917806515576-0.177806515576364
6199.99101.600702374794-1.61070237479427
6299.3999.4400424425914-0.050042442591419
6399.5298.41630216358441.10369783641558
6499.2199.2480922196188-0.038092219618818
6599.3898.85401435387320.525985646126756
6699.3799.32719297164730.0428070283526694
6799.3898.06949130102011.31050869897993
6899.2699.2893091874408-0.0293091874408162
6999.3699.13455605531090.225443944689104
7099.299.06621039379810.133789606201873
7198.5399.4887343846299-0.958734384629906
7298.6598.47799397430340.172006025696646
7399.1599.3009972372993-0.150997237299308
74100.1798.7739761806411.39602381935902
7599.9899.41170874766910.568291252330951
76100.0799.8392581156320.230741884367973
7799.9499.9989633918872-0.0589633918872039
78100.05100.102531823172-0.0525318231715346
7999.1399.1472220105027-0.0172220105027492
8098.7499.1387730898866-0.398773089886603
8198.6498.7837212949961-0.143721294996098
8298.4498.43778542975540.00221457024458971
8398.8198.62557984591350.184420154086482
8498.8898.87636149665490.00363850334510119
8599.6399.61636087884380.0136391211562454
86100.0899.58110683448560.498893165514374
87100.0799.38978415426480.680215845735162
88100.5599.92734783917030.622652160829674
8999.98100.469477498812-0.489477498811496
9099.89100.270778403909-0.380778403908877
9199.8699.08167842494580.778321575054193
9299.6199.7875895914179-0.177589591417899
93100.1299.76936879746430.350631202535723
94100.24100.0104702785150.229529721485022
95100.1100.579501665941-0.479501665940845
9699.86100.353345774053-0.493345774053111
9797.99100.75240982269-2.76240982268962
9897.5798.317155169795-0.747155169794979
9998.2896.89448175265591.38551824734409
10097.9797.87279365292290.0972063470770621
10197.9997.61484076416320.375159235836776
10297.8498.0408146074078-0.200814607407779
10397.3397.06422586602780.265774133972215
10496.797.0413742759722-0.341374275972186
10596.7996.8019254292441-0.0119254292440871
10696.7696.53033366618630.229666333813682
10796.2396.8069157510378-0.576915751037831
10896.2996.3027941837197-0.0127941837196914
10996.4696.6106494372938-0.150649437293808
11097.2396.71940674763340.510593252366647
11197.5996.79457264849710.795427351502894
11297.1397.1461619047377-0.0161619047377286
11397.3796.89361411904040.476385880959583
11496.1297.3864898922854-1.26648989228543
11596.9695.5670114254811.39298857451898
11696.796.48289802587790.217101974122073
1179796.8778146491220.122185350878041
11897.1596.87596360089920.274036399100794
11996.5197.1919973920265-0.681997392026531
12096.6896.798387290736-0.118387290736038







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12197.103790148060494.977947999128899.2296322969921
12297.558149518294194.6701138606049100.446185175983
12397.32490593034693.7526232286228100.897188632069
12496.906396800313192.6845318526925101.128261747934
12596.770274488423491.9150559211732101.625493055674
12696.592765122987491.1108136117613102.074716634214
12796.332262421038690.2245904984584102.439934343619
12895.874706195301289.1388085762732102.610603814329
12996.042767826534388.6738227729446103.411712880124
13095.923250474822687.9148587953901103.931642154255
13195.80746926970787.152132617092104.462805922322
13296.069894884802586.7593377258325105.380452043773

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 97.1037901480604 & 94.9779479991288 & 99.2296322969921 \tabularnewline
122 & 97.5581495182941 & 94.6701138606049 & 100.446185175983 \tabularnewline
123 & 97.324905930346 & 93.7526232286228 & 100.897188632069 \tabularnewline
124 & 96.9063968003131 & 92.6845318526925 & 101.128261747934 \tabularnewline
125 & 96.7702744884234 & 91.9150559211732 & 101.625493055674 \tabularnewline
126 & 96.5927651229874 & 91.1108136117613 & 102.074716634214 \tabularnewline
127 & 96.3322624210386 & 90.2245904984584 & 102.439934343619 \tabularnewline
128 & 95.8747061953012 & 89.1388085762732 & 102.610603814329 \tabularnewline
129 & 96.0427678265343 & 88.6738227729446 & 103.411712880124 \tabularnewline
130 & 95.9232504748226 & 87.9148587953901 & 103.931642154255 \tabularnewline
131 & 95.807469269707 & 87.152132617092 & 104.462805922322 \tabularnewline
132 & 96.0698948848025 & 86.7593377258325 & 105.380452043773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294849&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]121[/C][C]97.1037901480604[/C][C]94.9779479991288[/C][C]99.2296322969921[/C][/ROW]
[ROW][C]122[/C][C]97.5581495182941[/C][C]94.6701138606049[/C][C]100.446185175983[/C][/ROW]
[ROW][C]123[/C][C]97.324905930346[/C][C]93.7526232286228[/C][C]100.897188632069[/C][/ROW]
[ROW][C]124[/C][C]96.9063968003131[/C][C]92.6845318526925[/C][C]101.128261747934[/C][/ROW]
[ROW][C]125[/C][C]96.7702744884234[/C][C]91.9150559211732[/C][C]101.625493055674[/C][/ROW]
[ROW][C]126[/C][C]96.5927651229874[/C][C]91.1108136117613[/C][C]102.074716634214[/C][/ROW]
[ROW][C]127[/C][C]96.3322624210386[/C][C]90.2245904984584[/C][C]102.439934343619[/C][/ROW]
[ROW][C]128[/C][C]95.8747061953012[/C][C]89.1388085762732[/C][C]102.610603814329[/C][/ROW]
[ROW][C]129[/C][C]96.0427678265343[/C][C]88.6738227729446[/C][C]103.411712880124[/C][/ROW]
[ROW][C]130[/C][C]95.9232504748226[/C][C]87.9148587953901[/C][C]103.931642154255[/C][/ROW]
[ROW][C]131[/C][C]95.807469269707[/C][C]87.152132617092[/C][C]104.462805922322[/C][/ROW]
[ROW][C]132[/C][C]96.0698948848025[/C][C]86.7593377258325[/C][C]105.380452043773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294849&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294849&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
12197.103790148060494.977947999128899.2296322969921
12297.558149518294194.6701138606049100.446185175983
12397.32490593034693.7526232286228100.897188632069
12496.906396800313192.6845318526925101.128261747934
12596.770274488423491.9150559211732101.625493055674
12696.592765122987491.1108136117613102.074716634214
12796.332262421038690.2245904984584102.439934343619
12895.874706195301289.1388085762732102.610603814329
12996.042767826534388.6738227729446103.411712880124
13095.923250474822687.9148587953901103.931642154255
13195.80746926970787.152132617092104.462805922322
13296.069894884802586.7593377258325105.380452043773



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')