Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Dec 2015 13:26:58 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/12/t1449926874kdzpb83qtez0iiw.htm/, Retrieved Thu, 16 May 2024 06:52:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286079, Retrieved Thu, 16 May 2024 06:52:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2015-11-25 14:34:15] [fbceac9f0608ffc2a284e55c3c8d1045]
- R P     [Exponential Smoothing] [] [2015-12-12 13:26:58] [bd97b182bc123d4050d70da6fa7efb72] [Current]
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Dataseries X:
98.41
98.94
99.09
100.45
101.99
102.35
102.69
102.6
102.62
102.73
102.74
103.45
103.9
103.45
103.5
103.33
103.56
103.58
103.86
103.77
103.73
104.21
104.55
104.5
104.66
104.99
104.99
105.62
106.52
106.1
106.73
106.63
106.72
106.5
107.12
106.84
107.25
108.19
108.21
107.98
109.12
109.79
109.69
109.69
109.24
108.55
106.47
107.27
105.95
108.55
110.81
111.54
110.38
106.67
106.45
105.44
105.37
103.72
106.57
108.54
110.36
106.64
103.45
101.36
101.9
100.86
100.37
100.16
99.5
99.52
99.2
99.35
99.37
99.85
99.76
100.07
99.77
99.93
99.16
99.4
99.81
99.67
99.37
99.49
99.28
99.33
99.19
98.11
99.12
99.06
97.41
98.45
100.33
103.18
103.06
103.48
102.8
103.92
103.9
103.96
103.62
103.83
104.09
104.07
103.22
104.01
104.01
104.24




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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286079&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286079&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286079&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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.049663457334581
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.049663457334581 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286079&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.049663457334581[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286079&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286079&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
alpha1
beta0.049663457334581
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
399.0999.47-0.379999999999995
4100.4599.60112788621290.848872113787138
5101.99101.0032858102180.986714189781551
6102.35102.592289448284-0.242289448284083
7102.69102.940256516607-0.250256516606612
8102.6103.267827912771-0.667827912771415
9102.62103.144661269719-0.524661269718635
10102.73103.138604777135-0.408604777134869
11102.74103.228312051219-0.488312051218941
12103.45103.2140607864970.235939213502746
13103.9103.935778343561-0.0357783435605938
14103.45104.384001467322-0.934001467321679
15103.5103.887615725299-0.387615725298915
16103.33103.918365388263-0.588365388263313
17103.56103.719145128906-0.159145128906161
18103.58103.941241431587-0.36124143158672
19103.86103.943300933162-0.0833009331616239
20103.77104.219163920822-0.449163920821633
21103.73104.106856887604-0.376856887603665
22104.21104.0481408716450.161859128355061
23104.55104.536179355560.0138206444398037
24104.5104.876865736546-0.376865736545668
25104.66104.808149281118-0.148149281117867
26104.99104.9607916756160.0292083243840722
27104.99105.292242261988-0.302242261987786
28105.62105.2772318663050.342768133695159
29106.52105.9242549168880.595745083111723
30106.1106.853841677406-0.753841677405674
31106.73106.3964032934230.333596706577197
32106.63107.042970859227-0.412970859226874
33106.72106.922461298579-0.202461298579223
34106.5107.002406370515-0.502406370515331
35107.12106.7574551331690.362544866831385
36106.84107.395460364694-0.555460364694369
37107.25107.0878742825710.16212571742868
38108.19107.5059260062220.684073993778313
39108.21108.479899485825-0.269899485825391
40107.98108.486495344226-0.506495344226465
41109.12108.2313410343080.88865896569169
42109.79109.4154749109360.374525089064065
43109.69110.104075121717-0.414075121717417
44109.69109.983510719577-0.293510719576673
45109.24109.968933962478-0.72893396247774
46108.55109.482732581732-0.932732581732495
47106.47108.746409856955-2.27640985695506
48107.27106.5533554731480.716644526851852
49105.95107.388946518032-1.43894651803151
50108.55105.9974834590272.55251654097349
51110.81108.7242502553552.08574974464504
52111.54111.0878357988090.452164201191252
53110.38111.840291836323-1.46029183632285
54106.67110.607768695014-3.93776869501357
55106.45106.702205487435-0.252205487435333
56105.44106.469680090971-1.02968009097054
57105.37105.408542617704-0.0385426177043513
58103.72105.336628458054-1.61662845805444
59106.57103.6063410996022.96365890039802
60108.54106.6035266469561.93647335304387
61110.36108.6696986087051.69030139129541
62106.64110.573644819734-3.93364481973377
63103.45106.65828641806-3.20828641805953
64101.36103.308951822419-1.94895182241912
65101.9101.1221601367390.777839863260752
66100.86101.700790353601-0.840790353601435
67100.37100.619033797748-0.249033797748012
68100.16100.1166659183590.0433340816412908
6999.599.9088180386734-0.408818038673417
7099.5299.22851472145220.291485278547839
7199.299.262990888147-0.0629908881469703
7299.3598.9398625428610.410137457138973
7399.3799.1102313869650.25976861303505
7499.8599.14313239439530.7068676056047
7599.7699.65823788356740.101762116432582
76100.0799.57329174209520.496708257904828
7799.7799.9079599914693-0.137959991469344
7899.9399.60110842131910.328891578680881
7999.1699.7774423142047-0.617442314204666
8099.498.97677799417660.423222005823419
8199.8199.23779666220590.57220333779415
8299.6799.6762142582591-0.00621425825909228
8399.3799.5359056367092-0.165905636709184
8499.4999.22766618919890.262333810801081
8599.2899.360694593219-0.0806945932190359
8699.3399.14668702073160.183312979268422
8799.1999.2057909770564-0.0157909770563549
8898.1199.065006742541-0.955006742541045
8999.1297.93757780592861.18242219407139
9099.0699.00630098011530.053699019884661
9197.4198.9489678590983-1.53896785909831
9298.4597.22253739448871.22746260551133
93100.3398.32349743122732.00650256877272
94103.18100.3031472859432.87685271405675
95103.06103.296021737966-0.236021737965686
96103.48103.1643000824520.315699917547818
97102.8103.599978831838-0.799978831837862
98103.92102.8802491172541.03975088274569
99103.9104.051886740858-0.151886740858131
100103.96104.024343520184-0.0643435201838543
101103.62104.081147998514-0.46114799851442
102103.83103.7182457945650.111754205434707
103104.09103.9337958947790.15620410522115
104104.07104.201553530694-0.131553530694006
105103.22104.175020127535-0.95502012753515
106104.01103.2775905261780.732409473822358
107104.01104.103964512832-0.0939645128322724
108104.24104.0992979102580.140702089741737

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 99.09 & 99.47 & -0.379999999999995 \tabularnewline
4 & 100.45 & 99.6011278862129 & 0.848872113787138 \tabularnewline
5 & 101.99 & 101.003285810218 & 0.986714189781551 \tabularnewline
6 & 102.35 & 102.592289448284 & -0.242289448284083 \tabularnewline
7 & 102.69 & 102.940256516607 & -0.250256516606612 \tabularnewline
8 & 102.6 & 103.267827912771 & -0.667827912771415 \tabularnewline
9 & 102.62 & 103.144661269719 & -0.524661269718635 \tabularnewline
10 & 102.73 & 103.138604777135 & -0.408604777134869 \tabularnewline
11 & 102.74 & 103.228312051219 & -0.488312051218941 \tabularnewline
12 & 103.45 & 103.214060786497 & 0.235939213502746 \tabularnewline
13 & 103.9 & 103.935778343561 & -0.0357783435605938 \tabularnewline
14 & 103.45 & 104.384001467322 & -0.934001467321679 \tabularnewline
15 & 103.5 & 103.887615725299 & -0.387615725298915 \tabularnewline
16 & 103.33 & 103.918365388263 & -0.588365388263313 \tabularnewline
17 & 103.56 & 103.719145128906 & -0.159145128906161 \tabularnewline
18 & 103.58 & 103.941241431587 & -0.36124143158672 \tabularnewline
19 & 103.86 & 103.943300933162 & -0.0833009331616239 \tabularnewline
20 & 103.77 & 104.219163920822 & -0.449163920821633 \tabularnewline
21 & 103.73 & 104.106856887604 & -0.376856887603665 \tabularnewline
22 & 104.21 & 104.048140871645 & 0.161859128355061 \tabularnewline
23 & 104.55 & 104.53617935556 & 0.0138206444398037 \tabularnewline
24 & 104.5 & 104.876865736546 & -0.376865736545668 \tabularnewline
25 & 104.66 & 104.808149281118 & -0.148149281117867 \tabularnewline
26 & 104.99 & 104.960791675616 & 0.0292083243840722 \tabularnewline
27 & 104.99 & 105.292242261988 & -0.302242261987786 \tabularnewline
28 & 105.62 & 105.277231866305 & 0.342768133695159 \tabularnewline
29 & 106.52 & 105.924254916888 & 0.595745083111723 \tabularnewline
30 & 106.1 & 106.853841677406 & -0.753841677405674 \tabularnewline
31 & 106.73 & 106.396403293423 & 0.333596706577197 \tabularnewline
32 & 106.63 & 107.042970859227 & -0.412970859226874 \tabularnewline
33 & 106.72 & 106.922461298579 & -0.202461298579223 \tabularnewline
34 & 106.5 & 107.002406370515 & -0.502406370515331 \tabularnewline
35 & 107.12 & 106.757455133169 & 0.362544866831385 \tabularnewline
36 & 106.84 & 107.395460364694 & -0.555460364694369 \tabularnewline
37 & 107.25 & 107.087874282571 & 0.16212571742868 \tabularnewline
38 & 108.19 & 107.505926006222 & 0.684073993778313 \tabularnewline
39 & 108.21 & 108.479899485825 & -0.269899485825391 \tabularnewline
40 & 107.98 & 108.486495344226 & -0.506495344226465 \tabularnewline
41 & 109.12 & 108.231341034308 & 0.88865896569169 \tabularnewline
42 & 109.79 & 109.415474910936 & 0.374525089064065 \tabularnewline
43 & 109.69 & 110.104075121717 & -0.414075121717417 \tabularnewline
44 & 109.69 & 109.983510719577 & -0.293510719576673 \tabularnewline
45 & 109.24 & 109.968933962478 & -0.72893396247774 \tabularnewline
46 & 108.55 & 109.482732581732 & -0.932732581732495 \tabularnewline
47 & 106.47 & 108.746409856955 & -2.27640985695506 \tabularnewline
48 & 107.27 & 106.553355473148 & 0.716644526851852 \tabularnewline
49 & 105.95 & 107.388946518032 & -1.43894651803151 \tabularnewline
50 & 108.55 & 105.997483459027 & 2.55251654097349 \tabularnewline
51 & 110.81 & 108.724250255355 & 2.08574974464504 \tabularnewline
52 & 111.54 & 111.087835798809 & 0.452164201191252 \tabularnewline
53 & 110.38 & 111.840291836323 & -1.46029183632285 \tabularnewline
54 & 106.67 & 110.607768695014 & -3.93776869501357 \tabularnewline
55 & 106.45 & 106.702205487435 & -0.252205487435333 \tabularnewline
56 & 105.44 & 106.469680090971 & -1.02968009097054 \tabularnewline
57 & 105.37 & 105.408542617704 & -0.0385426177043513 \tabularnewline
58 & 103.72 & 105.336628458054 & -1.61662845805444 \tabularnewline
59 & 106.57 & 103.606341099602 & 2.96365890039802 \tabularnewline
60 & 108.54 & 106.603526646956 & 1.93647335304387 \tabularnewline
61 & 110.36 & 108.669698608705 & 1.69030139129541 \tabularnewline
62 & 106.64 & 110.573644819734 & -3.93364481973377 \tabularnewline
63 & 103.45 & 106.65828641806 & -3.20828641805953 \tabularnewline
64 & 101.36 & 103.308951822419 & -1.94895182241912 \tabularnewline
65 & 101.9 & 101.122160136739 & 0.777839863260752 \tabularnewline
66 & 100.86 & 101.700790353601 & -0.840790353601435 \tabularnewline
67 & 100.37 & 100.619033797748 & -0.249033797748012 \tabularnewline
68 & 100.16 & 100.116665918359 & 0.0433340816412908 \tabularnewline
69 & 99.5 & 99.9088180386734 & -0.408818038673417 \tabularnewline
70 & 99.52 & 99.2285147214522 & 0.291485278547839 \tabularnewline
71 & 99.2 & 99.262990888147 & -0.0629908881469703 \tabularnewline
72 & 99.35 & 98.939862542861 & 0.410137457138973 \tabularnewline
73 & 99.37 & 99.110231386965 & 0.25976861303505 \tabularnewline
74 & 99.85 & 99.1431323943953 & 0.7068676056047 \tabularnewline
75 & 99.76 & 99.6582378835674 & 0.101762116432582 \tabularnewline
76 & 100.07 & 99.5732917420952 & 0.496708257904828 \tabularnewline
77 & 99.77 & 99.9079599914693 & -0.137959991469344 \tabularnewline
78 & 99.93 & 99.6011084213191 & 0.328891578680881 \tabularnewline
79 & 99.16 & 99.7774423142047 & -0.617442314204666 \tabularnewline
80 & 99.4 & 98.9767779941766 & 0.423222005823419 \tabularnewline
81 & 99.81 & 99.2377966622059 & 0.57220333779415 \tabularnewline
82 & 99.67 & 99.6762142582591 & -0.00621425825909228 \tabularnewline
83 & 99.37 & 99.5359056367092 & -0.165905636709184 \tabularnewline
84 & 99.49 & 99.2276661891989 & 0.262333810801081 \tabularnewline
85 & 99.28 & 99.360694593219 & -0.0806945932190359 \tabularnewline
86 & 99.33 & 99.1466870207316 & 0.183312979268422 \tabularnewline
87 & 99.19 & 99.2057909770564 & -0.0157909770563549 \tabularnewline
88 & 98.11 & 99.065006742541 & -0.955006742541045 \tabularnewline
89 & 99.12 & 97.9375778059286 & 1.18242219407139 \tabularnewline
90 & 99.06 & 99.0063009801153 & 0.053699019884661 \tabularnewline
91 & 97.41 & 98.9489678590983 & -1.53896785909831 \tabularnewline
92 & 98.45 & 97.2225373944887 & 1.22746260551133 \tabularnewline
93 & 100.33 & 98.3234974312273 & 2.00650256877272 \tabularnewline
94 & 103.18 & 100.303147285943 & 2.87685271405675 \tabularnewline
95 & 103.06 & 103.296021737966 & -0.236021737965686 \tabularnewline
96 & 103.48 & 103.164300082452 & 0.315699917547818 \tabularnewline
97 & 102.8 & 103.599978831838 & -0.799978831837862 \tabularnewline
98 & 103.92 & 102.880249117254 & 1.03975088274569 \tabularnewline
99 & 103.9 & 104.051886740858 & -0.151886740858131 \tabularnewline
100 & 103.96 & 104.024343520184 & -0.0643435201838543 \tabularnewline
101 & 103.62 & 104.081147998514 & -0.46114799851442 \tabularnewline
102 & 103.83 & 103.718245794565 & 0.111754205434707 \tabularnewline
103 & 104.09 & 103.933795894779 & 0.15620410522115 \tabularnewline
104 & 104.07 & 104.201553530694 & -0.131553530694006 \tabularnewline
105 & 103.22 & 104.175020127535 & -0.95502012753515 \tabularnewline
106 & 104.01 & 103.277590526178 & 0.732409473822358 \tabularnewline
107 & 104.01 & 104.103964512832 & -0.0939645128322724 \tabularnewline
108 & 104.24 & 104.099297910258 & 0.140702089741737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286079&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]3[/C][C]99.09[/C][C]99.47[/C][C]-0.379999999999995[/C][/ROW]
[ROW][C]4[/C][C]100.45[/C][C]99.6011278862129[/C][C]0.848872113787138[/C][/ROW]
[ROW][C]5[/C][C]101.99[/C][C]101.003285810218[/C][C]0.986714189781551[/C][/ROW]
[ROW][C]6[/C][C]102.35[/C][C]102.592289448284[/C][C]-0.242289448284083[/C][/ROW]
[ROW][C]7[/C][C]102.69[/C][C]102.940256516607[/C][C]-0.250256516606612[/C][/ROW]
[ROW][C]8[/C][C]102.6[/C][C]103.267827912771[/C][C]-0.667827912771415[/C][/ROW]
[ROW][C]9[/C][C]102.62[/C][C]103.144661269719[/C][C]-0.524661269718635[/C][/ROW]
[ROW][C]10[/C][C]102.73[/C][C]103.138604777135[/C][C]-0.408604777134869[/C][/ROW]
[ROW][C]11[/C][C]102.74[/C][C]103.228312051219[/C][C]-0.488312051218941[/C][/ROW]
[ROW][C]12[/C][C]103.45[/C][C]103.214060786497[/C][C]0.235939213502746[/C][/ROW]
[ROW][C]13[/C][C]103.9[/C][C]103.935778343561[/C][C]-0.0357783435605938[/C][/ROW]
[ROW][C]14[/C][C]103.45[/C][C]104.384001467322[/C][C]-0.934001467321679[/C][/ROW]
[ROW][C]15[/C][C]103.5[/C][C]103.887615725299[/C][C]-0.387615725298915[/C][/ROW]
[ROW][C]16[/C][C]103.33[/C][C]103.918365388263[/C][C]-0.588365388263313[/C][/ROW]
[ROW][C]17[/C][C]103.56[/C][C]103.719145128906[/C][C]-0.159145128906161[/C][/ROW]
[ROW][C]18[/C][C]103.58[/C][C]103.941241431587[/C][C]-0.36124143158672[/C][/ROW]
[ROW][C]19[/C][C]103.86[/C][C]103.943300933162[/C][C]-0.0833009331616239[/C][/ROW]
[ROW][C]20[/C][C]103.77[/C][C]104.219163920822[/C][C]-0.449163920821633[/C][/ROW]
[ROW][C]21[/C][C]103.73[/C][C]104.106856887604[/C][C]-0.376856887603665[/C][/ROW]
[ROW][C]22[/C][C]104.21[/C][C]104.048140871645[/C][C]0.161859128355061[/C][/ROW]
[ROW][C]23[/C][C]104.55[/C][C]104.53617935556[/C][C]0.0138206444398037[/C][/ROW]
[ROW][C]24[/C][C]104.5[/C][C]104.876865736546[/C][C]-0.376865736545668[/C][/ROW]
[ROW][C]25[/C][C]104.66[/C][C]104.808149281118[/C][C]-0.148149281117867[/C][/ROW]
[ROW][C]26[/C][C]104.99[/C][C]104.960791675616[/C][C]0.0292083243840722[/C][/ROW]
[ROW][C]27[/C][C]104.99[/C][C]105.292242261988[/C][C]-0.302242261987786[/C][/ROW]
[ROW][C]28[/C][C]105.62[/C][C]105.277231866305[/C][C]0.342768133695159[/C][/ROW]
[ROW][C]29[/C][C]106.52[/C][C]105.924254916888[/C][C]0.595745083111723[/C][/ROW]
[ROW][C]30[/C][C]106.1[/C][C]106.853841677406[/C][C]-0.753841677405674[/C][/ROW]
[ROW][C]31[/C][C]106.73[/C][C]106.396403293423[/C][C]0.333596706577197[/C][/ROW]
[ROW][C]32[/C][C]106.63[/C][C]107.042970859227[/C][C]-0.412970859226874[/C][/ROW]
[ROW][C]33[/C][C]106.72[/C][C]106.922461298579[/C][C]-0.202461298579223[/C][/ROW]
[ROW][C]34[/C][C]106.5[/C][C]107.002406370515[/C][C]-0.502406370515331[/C][/ROW]
[ROW][C]35[/C][C]107.12[/C][C]106.757455133169[/C][C]0.362544866831385[/C][/ROW]
[ROW][C]36[/C][C]106.84[/C][C]107.395460364694[/C][C]-0.555460364694369[/C][/ROW]
[ROW][C]37[/C][C]107.25[/C][C]107.087874282571[/C][C]0.16212571742868[/C][/ROW]
[ROW][C]38[/C][C]108.19[/C][C]107.505926006222[/C][C]0.684073993778313[/C][/ROW]
[ROW][C]39[/C][C]108.21[/C][C]108.479899485825[/C][C]-0.269899485825391[/C][/ROW]
[ROW][C]40[/C][C]107.98[/C][C]108.486495344226[/C][C]-0.506495344226465[/C][/ROW]
[ROW][C]41[/C][C]109.12[/C][C]108.231341034308[/C][C]0.88865896569169[/C][/ROW]
[ROW][C]42[/C][C]109.79[/C][C]109.415474910936[/C][C]0.374525089064065[/C][/ROW]
[ROW][C]43[/C][C]109.69[/C][C]110.104075121717[/C][C]-0.414075121717417[/C][/ROW]
[ROW][C]44[/C][C]109.69[/C][C]109.983510719577[/C][C]-0.293510719576673[/C][/ROW]
[ROW][C]45[/C][C]109.24[/C][C]109.968933962478[/C][C]-0.72893396247774[/C][/ROW]
[ROW][C]46[/C][C]108.55[/C][C]109.482732581732[/C][C]-0.932732581732495[/C][/ROW]
[ROW][C]47[/C][C]106.47[/C][C]108.746409856955[/C][C]-2.27640985695506[/C][/ROW]
[ROW][C]48[/C][C]107.27[/C][C]106.553355473148[/C][C]0.716644526851852[/C][/ROW]
[ROW][C]49[/C][C]105.95[/C][C]107.388946518032[/C][C]-1.43894651803151[/C][/ROW]
[ROW][C]50[/C][C]108.55[/C][C]105.997483459027[/C][C]2.55251654097349[/C][/ROW]
[ROW][C]51[/C][C]110.81[/C][C]108.724250255355[/C][C]2.08574974464504[/C][/ROW]
[ROW][C]52[/C][C]111.54[/C][C]111.087835798809[/C][C]0.452164201191252[/C][/ROW]
[ROW][C]53[/C][C]110.38[/C][C]111.840291836323[/C][C]-1.46029183632285[/C][/ROW]
[ROW][C]54[/C][C]106.67[/C][C]110.607768695014[/C][C]-3.93776869501357[/C][/ROW]
[ROW][C]55[/C][C]106.45[/C][C]106.702205487435[/C][C]-0.252205487435333[/C][/ROW]
[ROW][C]56[/C][C]105.44[/C][C]106.469680090971[/C][C]-1.02968009097054[/C][/ROW]
[ROW][C]57[/C][C]105.37[/C][C]105.408542617704[/C][C]-0.0385426177043513[/C][/ROW]
[ROW][C]58[/C][C]103.72[/C][C]105.336628458054[/C][C]-1.61662845805444[/C][/ROW]
[ROW][C]59[/C][C]106.57[/C][C]103.606341099602[/C][C]2.96365890039802[/C][/ROW]
[ROW][C]60[/C][C]108.54[/C][C]106.603526646956[/C][C]1.93647335304387[/C][/ROW]
[ROW][C]61[/C][C]110.36[/C][C]108.669698608705[/C][C]1.69030139129541[/C][/ROW]
[ROW][C]62[/C][C]106.64[/C][C]110.573644819734[/C][C]-3.93364481973377[/C][/ROW]
[ROW][C]63[/C][C]103.45[/C][C]106.65828641806[/C][C]-3.20828641805953[/C][/ROW]
[ROW][C]64[/C][C]101.36[/C][C]103.308951822419[/C][C]-1.94895182241912[/C][/ROW]
[ROW][C]65[/C][C]101.9[/C][C]101.122160136739[/C][C]0.777839863260752[/C][/ROW]
[ROW][C]66[/C][C]100.86[/C][C]101.700790353601[/C][C]-0.840790353601435[/C][/ROW]
[ROW][C]67[/C][C]100.37[/C][C]100.619033797748[/C][C]-0.249033797748012[/C][/ROW]
[ROW][C]68[/C][C]100.16[/C][C]100.116665918359[/C][C]0.0433340816412908[/C][/ROW]
[ROW][C]69[/C][C]99.5[/C][C]99.9088180386734[/C][C]-0.408818038673417[/C][/ROW]
[ROW][C]70[/C][C]99.52[/C][C]99.2285147214522[/C][C]0.291485278547839[/C][/ROW]
[ROW][C]71[/C][C]99.2[/C][C]99.262990888147[/C][C]-0.0629908881469703[/C][/ROW]
[ROW][C]72[/C][C]99.35[/C][C]98.939862542861[/C][C]0.410137457138973[/C][/ROW]
[ROW][C]73[/C][C]99.37[/C][C]99.110231386965[/C][C]0.25976861303505[/C][/ROW]
[ROW][C]74[/C][C]99.85[/C][C]99.1431323943953[/C][C]0.7068676056047[/C][/ROW]
[ROW][C]75[/C][C]99.76[/C][C]99.6582378835674[/C][C]0.101762116432582[/C][/ROW]
[ROW][C]76[/C][C]100.07[/C][C]99.5732917420952[/C][C]0.496708257904828[/C][/ROW]
[ROW][C]77[/C][C]99.77[/C][C]99.9079599914693[/C][C]-0.137959991469344[/C][/ROW]
[ROW][C]78[/C][C]99.93[/C][C]99.6011084213191[/C][C]0.328891578680881[/C][/ROW]
[ROW][C]79[/C][C]99.16[/C][C]99.7774423142047[/C][C]-0.617442314204666[/C][/ROW]
[ROW][C]80[/C][C]99.4[/C][C]98.9767779941766[/C][C]0.423222005823419[/C][/ROW]
[ROW][C]81[/C][C]99.81[/C][C]99.2377966622059[/C][C]0.57220333779415[/C][/ROW]
[ROW][C]82[/C][C]99.67[/C][C]99.6762142582591[/C][C]-0.00621425825909228[/C][/ROW]
[ROW][C]83[/C][C]99.37[/C][C]99.5359056367092[/C][C]-0.165905636709184[/C][/ROW]
[ROW][C]84[/C][C]99.49[/C][C]99.2276661891989[/C][C]0.262333810801081[/C][/ROW]
[ROW][C]85[/C][C]99.28[/C][C]99.360694593219[/C][C]-0.0806945932190359[/C][/ROW]
[ROW][C]86[/C][C]99.33[/C][C]99.1466870207316[/C][C]0.183312979268422[/C][/ROW]
[ROW][C]87[/C][C]99.19[/C][C]99.2057909770564[/C][C]-0.0157909770563549[/C][/ROW]
[ROW][C]88[/C][C]98.11[/C][C]99.065006742541[/C][C]-0.955006742541045[/C][/ROW]
[ROW][C]89[/C][C]99.12[/C][C]97.9375778059286[/C][C]1.18242219407139[/C][/ROW]
[ROW][C]90[/C][C]99.06[/C][C]99.0063009801153[/C][C]0.053699019884661[/C][/ROW]
[ROW][C]91[/C][C]97.41[/C][C]98.9489678590983[/C][C]-1.53896785909831[/C][/ROW]
[ROW][C]92[/C][C]98.45[/C][C]97.2225373944887[/C][C]1.22746260551133[/C][/ROW]
[ROW][C]93[/C][C]100.33[/C][C]98.3234974312273[/C][C]2.00650256877272[/C][/ROW]
[ROW][C]94[/C][C]103.18[/C][C]100.303147285943[/C][C]2.87685271405675[/C][/ROW]
[ROW][C]95[/C][C]103.06[/C][C]103.296021737966[/C][C]-0.236021737965686[/C][/ROW]
[ROW][C]96[/C][C]103.48[/C][C]103.164300082452[/C][C]0.315699917547818[/C][/ROW]
[ROW][C]97[/C][C]102.8[/C][C]103.599978831838[/C][C]-0.799978831837862[/C][/ROW]
[ROW][C]98[/C][C]103.92[/C][C]102.880249117254[/C][C]1.03975088274569[/C][/ROW]
[ROW][C]99[/C][C]103.9[/C][C]104.051886740858[/C][C]-0.151886740858131[/C][/ROW]
[ROW][C]100[/C][C]103.96[/C][C]104.024343520184[/C][C]-0.0643435201838543[/C][/ROW]
[ROW][C]101[/C][C]103.62[/C][C]104.081147998514[/C][C]-0.46114799851442[/C][/ROW]
[ROW][C]102[/C][C]103.83[/C][C]103.718245794565[/C][C]0.111754205434707[/C][/ROW]
[ROW][C]103[/C][C]104.09[/C][C]103.933795894779[/C][C]0.15620410522115[/C][/ROW]
[ROW][C]104[/C][C]104.07[/C][C]104.201553530694[/C][C]-0.131553530694006[/C][/ROW]
[ROW][C]105[/C][C]103.22[/C][C]104.175020127535[/C][C]-0.95502012753515[/C][/ROW]
[ROW][C]106[/C][C]104.01[/C][C]103.277590526178[/C][C]0.732409473822358[/C][/ROW]
[ROW][C]107[/C][C]104.01[/C][C]104.103964512832[/C][C]-0.0939645128322724[/C][/ROW]
[ROW][C]108[/C][C]104.24[/C][C]104.099297910258[/C][C]0.140702089741737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286079&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286079&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
399.0999.47-0.379999999999995
4100.4599.60112788621290.848872113787138
5101.99101.0032858102180.986714189781551
6102.35102.592289448284-0.242289448284083
7102.69102.940256516607-0.250256516606612
8102.6103.267827912771-0.667827912771415
9102.62103.144661269719-0.524661269718635
10102.73103.138604777135-0.408604777134869
11102.74103.228312051219-0.488312051218941
12103.45103.2140607864970.235939213502746
13103.9103.935778343561-0.0357783435605938
14103.45104.384001467322-0.934001467321679
15103.5103.887615725299-0.387615725298915
16103.33103.918365388263-0.588365388263313
17103.56103.719145128906-0.159145128906161
18103.58103.941241431587-0.36124143158672
19103.86103.943300933162-0.0833009331616239
20103.77104.219163920822-0.449163920821633
21103.73104.106856887604-0.376856887603665
22104.21104.0481408716450.161859128355061
23104.55104.536179355560.0138206444398037
24104.5104.876865736546-0.376865736545668
25104.66104.808149281118-0.148149281117867
26104.99104.9607916756160.0292083243840722
27104.99105.292242261988-0.302242261987786
28105.62105.2772318663050.342768133695159
29106.52105.9242549168880.595745083111723
30106.1106.853841677406-0.753841677405674
31106.73106.3964032934230.333596706577197
32106.63107.042970859227-0.412970859226874
33106.72106.922461298579-0.202461298579223
34106.5107.002406370515-0.502406370515331
35107.12106.7574551331690.362544866831385
36106.84107.395460364694-0.555460364694369
37107.25107.0878742825710.16212571742868
38108.19107.5059260062220.684073993778313
39108.21108.479899485825-0.269899485825391
40107.98108.486495344226-0.506495344226465
41109.12108.2313410343080.88865896569169
42109.79109.4154749109360.374525089064065
43109.69110.104075121717-0.414075121717417
44109.69109.983510719577-0.293510719576673
45109.24109.968933962478-0.72893396247774
46108.55109.482732581732-0.932732581732495
47106.47108.746409856955-2.27640985695506
48107.27106.5533554731480.716644526851852
49105.95107.388946518032-1.43894651803151
50108.55105.9974834590272.55251654097349
51110.81108.7242502553552.08574974464504
52111.54111.0878357988090.452164201191252
53110.38111.840291836323-1.46029183632285
54106.67110.607768695014-3.93776869501357
55106.45106.702205487435-0.252205487435333
56105.44106.469680090971-1.02968009097054
57105.37105.408542617704-0.0385426177043513
58103.72105.336628458054-1.61662845805444
59106.57103.6063410996022.96365890039802
60108.54106.6035266469561.93647335304387
61110.36108.6696986087051.69030139129541
62106.64110.573644819734-3.93364481973377
63103.45106.65828641806-3.20828641805953
64101.36103.308951822419-1.94895182241912
65101.9101.1221601367390.777839863260752
66100.86101.700790353601-0.840790353601435
67100.37100.619033797748-0.249033797748012
68100.16100.1166659183590.0433340816412908
6999.599.9088180386734-0.408818038673417
7099.5299.22851472145220.291485278547839
7199.299.262990888147-0.0629908881469703
7299.3598.9398625428610.410137457138973
7399.3799.1102313869650.25976861303505
7499.8599.14313239439530.7068676056047
7599.7699.65823788356740.101762116432582
76100.0799.57329174209520.496708257904828
7799.7799.9079599914693-0.137959991469344
7899.9399.60110842131910.328891578680881
7999.1699.7774423142047-0.617442314204666
8099.498.97677799417660.423222005823419
8199.8199.23779666220590.57220333779415
8299.6799.6762142582591-0.00621425825909228
8399.3799.5359056367092-0.165905636709184
8499.4999.22766618919890.262333810801081
8599.2899.360694593219-0.0806945932190359
8699.3399.14668702073160.183312979268422
8799.1999.2057909770564-0.0157909770563549
8898.1199.065006742541-0.955006742541045
8999.1297.93757780592861.18242219407139
9099.0699.00630098011530.053699019884661
9197.4198.9489678590983-1.53896785909831
9298.4597.22253739448871.22746260551133
93100.3398.32349743122732.00650256877272
94103.18100.3031472859432.87685271405675
95103.06103.296021737966-0.236021737965686
96103.48103.1643000824520.315699917547818
97102.8103.599978831838-0.799978831837862
98103.92102.8802491172541.03975088274569
99103.9104.051886740858-0.151886740858131
100103.96104.024343520184-0.0643435201838543
101103.62104.081147998514-0.46114799851442
102103.83103.7182457945650.111754205434707
103104.09103.9337958947790.15620410522115
104104.07104.201553530694-0.131553530694006
105103.22104.175020127535-0.95502012753515
106104.01103.2775905261780.732409473822358
107104.01104.103964512832-0.0939645128322724
108104.24104.0992979102580.140702089741737







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109104.336285662489102.231123233153106.441448091825
110104.432571324978101.380598798381107.484543851575
111104.528856987467100.698668532054108.35904544288
112104.625142649956100.095132494025109.155152805888
113104.72142831244599.5360312412446109.906825383646
114104.81771397493499.0044311519652110.630996797903
115104.91399963742398.4905584685011111.337440806345
116105.01028529991297.9882327613255112.032337838499
117105.10657096240197.4932934389978112.719848485805
118105.2028566248997.0028093025883113.402903947192
119105.29914228737996.5146430170796114.083641557679
120105.39542794986896.0271938617171114.76366203802

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 104.336285662489 & 102.231123233153 & 106.441448091825 \tabularnewline
110 & 104.432571324978 & 101.380598798381 & 107.484543851575 \tabularnewline
111 & 104.528856987467 & 100.698668532054 & 108.35904544288 \tabularnewline
112 & 104.625142649956 & 100.095132494025 & 109.155152805888 \tabularnewline
113 & 104.721428312445 & 99.5360312412446 & 109.906825383646 \tabularnewline
114 & 104.817713974934 & 99.0044311519652 & 110.630996797903 \tabularnewline
115 & 104.913999637423 & 98.4905584685011 & 111.337440806345 \tabularnewline
116 & 105.010285299912 & 97.9882327613255 & 112.032337838499 \tabularnewline
117 & 105.106570962401 & 97.4932934389978 & 112.719848485805 \tabularnewline
118 & 105.20285662489 & 97.0028093025883 & 113.402903947192 \tabularnewline
119 & 105.299142287379 & 96.5146430170796 & 114.083641557679 \tabularnewline
120 & 105.395427949868 & 96.0271938617171 & 114.76366203802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286079&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]109[/C][C]104.336285662489[/C][C]102.231123233153[/C][C]106.441448091825[/C][/ROW]
[ROW][C]110[/C][C]104.432571324978[/C][C]101.380598798381[/C][C]107.484543851575[/C][/ROW]
[ROW][C]111[/C][C]104.528856987467[/C][C]100.698668532054[/C][C]108.35904544288[/C][/ROW]
[ROW][C]112[/C][C]104.625142649956[/C][C]100.095132494025[/C][C]109.155152805888[/C][/ROW]
[ROW][C]113[/C][C]104.721428312445[/C][C]99.5360312412446[/C][C]109.906825383646[/C][/ROW]
[ROW][C]114[/C][C]104.817713974934[/C][C]99.0044311519652[/C][C]110.630996797903[/C][/ROW]
[ROW][C]115[/C][C]104.913999637423[/C][C]98.4905584685011[/C][C]111.337440806345[/C][/ROW]
[ROW][C]116[/C][C]105.010285299912[/C][C]97.9882327613255[/C][C]112.032337838499[/C][/ROW]
[ROW][C]117[/C][C]105.106570962401[/C][C]97.4932934389978[/C][C]112.719848485805[/C][/ROW]
[ROW][C]118[/C][C]105.20285662489[/C][C]97.0028093025883[/C][C]113.402903947192[/C][/ROW]
[ROW][C]119[/C][C]105.299142287379[/C][C]96.5146430170796[/C][C]114.083641557679[/C][/ROW]
[ROW][C]120[/C][C]105.395427949868[/C][C]96.0271938617171[/C][C]114.76366203802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286079&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286079&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
109104.336285662489102.231123233153106.441448091825
110104.432571324978101.380598798381107.484543851575
111104.528856987467100.698668532054108.35904544288
112104.625142649956100.095132494025109.155152805888
113104.72142831244599.5360312412446109.906825383646
114104.81771397493499.0044311519652110.630996797903
115104.91399963742398.4905584685011111.337440806345
116105.01028529991297.9882327613255112.032337838499
117105.10657096240197.4932934389978112.719848485805
118105.2028566248997.0028093025883113.402903947192
119105.29914228737996.5146430170796114.083641557679
120105.39542794986896.0271938617171114.76366203802



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')