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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Dec 2009 12:32:46 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t12599552236zjkziyrfx0pvtn.htm/, Retrieved Sun, 28 Apr 2024 02:25:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64078, Retrieved Sun, 28 Apr 2024 02:25:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D    [Exponential Smoothing] [Exponential smoot...] [2009-12-03 16:44:51] [d46757a0a8c9b00540ab7e7e0c34bfc4]
-    D        [Exponential Smoothing] [Exponential Smoot...] [2009-12-04 19:32:46] [d1818fb1d9a1b0f34f8553ada228d3d5] [Current]
-    D          [Exponential Smoothing] [Experimental smoo...] [2009-12-11 16:09:28] [4f1a20f787b3465111b61213cdeef1a9]
-   PD          [Exponential Smoothing] [Exponential Smoot...] [2009-12-11 16:49:18] [4f1a20f787b3465111b61213cdeef1a9]
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Dataseries X:
107.11
107.57
107.81
108.75
109.43
109.62
109.54
109.53
109.84
109.67
109.79
109.56
110.22
110.40
110.69
110.72
110.89
110.58
110.94
110.91
111.22
111.09
111.00
111.06
111.55
112.32
112.64
112.36
112.04
112.37
112.59
112.89
113.22
112.85
113.06
112.99
113.32
113.74
113.91
114.52
114.96
114.91
115.30
115.44
115.52
116.08
115.94
115.56
115.88
116.66
117.41
117.68
117.85
118.21
118.92
119.03
119.17
118.95
118.92
118.90




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64078&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64078&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.693734207502508
beta0.0445082090570031
gamma0.0518931374312389

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.693734207502508 \tabularnewline
beta & 0.0445082090570031 \tabularnewline
gamma & 0.0518931374312389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64078&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]0.693734207502508[/C][/ROW]
[ROW][C]beta[/C][C]0.0445082090570031[/C][/ROW]
[ROW][C]gamma[/C][C]0.0518931374312389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64078&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
alpha0.693734207502508
beta0.0445082090570031
gamma0.0518931374312389







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13110.22109.3177508271440.902249172856173
14110.4110.1715182021070.228481797893451
15110.69110.6758973493090.0141026506911146
16110.72110.770390033708-0.0503900337077852
17110.89110.965719613761-0.0757196137607536
18110.58110.657493240438-0.0774932404384288
19110.94111.334770951348-0.394770951347823
20110.91110.952557258342-0.0425572583422138
21111.22111.1474013276910.072598672308743
22111.09110.9749325862180.115067413782285
23111111.188862771837-0.188862771836739
24111.06110.8744451385590.185554861441247
25111.55111.744077360525-0.194077360524957
26112.32111.8148215437510.505178456248714
27112.64112.5065772698090.133422730191214
28112.36112.680974317223-0.320974317222678
29112.04112.680430511491-0.64043051149099
30112.37111.9493436458020.420656354198258
31112.59112.964752946192-0.374752946192004
32112.89112.5881673180210.301832681979249
33113.22113.0255915055630.194408494436843
34112.85112.935997133788-0.085997133787842
35113.06113.0032693404690.056730659530956
36112.99112.8649832712740.125016728726294
37113.32113.700536695131-0.380536695130701
38113.74113.6521573414870.0878426585131962
39113.91114.035955916242-0.125955916241807
40114.52113.9992010238990.52079897610065
41114.96114.5816182070390.378381792961264
42114.91114.5990704752220.310929524778132
43115.3115.569682311137-0.269682311136762
44115.44115.3052362964440.134763703556359
45115.52115.656039960459-0.136039960458888
46116.08115.3435703247950.73642967520479
47115.94116.027376225578-0.0873762255783106
48115.56115.821428656575-0.261428656574793
49115.88116.422677370127-0.542677370126768
50116.66116.2940122419950.365987758004977
51117.41116.9032238856350.506776114365152
52117.68117.3643170496790.315682950320891
53117.85117.8485620416420.00143795835791138
54118.21117.6255342650500.584465734949717
55118.92118.8340848856120.0859151143882713
56119.03118.8678168064240.162183193576496
57119.17119.289056769990-0.119056769989569
58118.95119.044007853194-0.0940078531937871
59118.92119.165750250126-0.245750250125667
60118.9118.8614036366200.0385963633795683

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 110.22 & 109.317750827144 & 0.902249172856173 \tabularnewline
14 & 110.4 & 110.171518202107 & 0.228481797893451 \tabularnewline
15 & 110.69 & 110.675897349309 & 0.0141026506911146 \tabularnewline
16 & 110.72 & 110.770390033708 & -0.0503900337077852 \tabularnewline
17 & 110.89 & 110.965719613761 & -0.0757196137607536 \tabularnewline
18 & 110.58 & 110.657493240438 & -0.0774932404384288 \tabularnewline
19 & 110.94 & 111.334770951348 & -0.394770951347823 \tabularnewline
20 & 110.91 & 110.952557258342 & -0.0425572583422138 \tabularnewline
21 & 111.22 & 111.147401327691 & 0.072598672308743 \tabularnewline
22 & 111.09 & 110.974932586218 & 0.115067413782285 \tabularnewline
23 & 111 & 111.188862771837 & -0.188862771836739 \tabularnewline
24 & 111.06 & 110.874445138559 & 0.185554861441247 \tabularnewline
25 & 111.55 & 111.744077360525 & -0.194077360524957 \tabularnewline
26 & 112.32 & 111.814821543751 & 0.505178456248714 \tabularnewline
27 & 112.64 & 112.506577269809 & 0.133422730191214 \tabularnewline
28 & 112.36 & 112.680974317223 & -0.320974317222678 \tabularnewline
29 & 112.04 & 112.680430511491 & -0.64043051149099 \tabularnewline
30 & 112.37 & 111.949343645802 & 0.420656354198258 \tabularnewline
31 & 112.59 & 112.964752946192 & -0.374752946192004 \tabularnewline
32 & 112.89 & 112.588167318021 & 0.301832681979249 \tabularnewline
33 & 113.22 & 113.025591505563 & 0.194408494436843 \tabularnewline
34 & 112.85 & 112.935997133788 & -0.085997133787842 \tabularnewline
35 & 113.06 & 113.003269340469 & 0.056730659530956 \tabularnewline
36 & 112.99 & 112.864983271274 & 0.125016728726294 \tabularnewline
37 & 113.32 & 113.700536695131 & -0.380536695130701 \tabularnewline
38 & 113.74 & 113.652157341487 & 0.0878426585131962 \tabularnewline
39 & 113.91 & 114.035955916242 & -0.125955916241807 \tabularnewline
40 & 114.52 & 113.999201023899 & 0.52079897610065 \tabularnewline
41 & 114.96 & 114.581618207039 & 0.378381792961264 \tabularnewline
42 & 114.91 & 114.599070475222 & 0.310929524778132 \tabularnewline
43 & 115.3 & 115.569682311137 & -0.269682311136762 \tabularnewline
44 & 115.44 & 115.305236296444 & 0.134763703556359 \tabularnewline
45 & 115.52 & 115.656039960459 & -0.136039960458888 \tabularnewline
46 & 116.08 & 115.343570324795 & 0.73642967520479 \tabularnewline
47 & 115.94 & 116.027376225578 & -0.0873762255783106 \tabularnewline
48 & 115.56 & 115.821428656575 & -0.261428656574793 \tabularnewline
49 & 115.88 & 116.422677370127 & -0.542677370126768 \tabularnewline
50 & 116.66 & 116.294012241995 & 0.365987758004977 \tabularnewline
51 & 117.41 & 116.903223885635 & 0.506776114365152 \tabularnewline
52 & 117.68 & 117.364317049679 & 0.315682950320891 \tabularnewline
53 & 117.85 & 117.848562041642 & 0.00143795835791138 \tabularnewline
54 & 118.21 & 117.625534265050 & 0.584465734949717 \tabularnewline
55 & 118.92 & 118.834084885612 & 0.0859151143882713 \tabularnewline
56 & 119.03 & 118.867816806424 & 0.162183193576496 \tabularnewline
57 & 119.17 & 119.289056769990 & -0.119056769989569 \tabularnewline
58 & 118.95 & 119.044007853194 & -0.0940078531937871 \tabularnewline
59 & 118.92 & 119.165750250126 & -0.245750250125667 \tabularnewline
60 & 118.9 & 118.861403636620 & 0.0385963633795683 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64078&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]110.22[/C][C]109.317750827144[/C][C]0.902249172856173[/C][/ROW]
[ROW][C]14[/C][C]110.4[/C][C]110.171518202107[/C][C]0.228481797893451[/C][/ROW]
[ROW][C]15[/C][C]110.69[/C][C]110.675897349309[/C][C]0.0141026506911146[/C][/ROW]
[ROW][C]16[/C][C]110.72[/C][C]110.770390033708[/C][C]-0.0503900337077852[/C][/ROW]
[ROW][C]17[/C][C]110.89[/C][C]110.965719613761[/C][C]-0.0757196137607536[/C][/ROW]
[ROW][C]18[/C][C]110.58[/C][C]110.657493240438[/C][C]-0.0774932404384288[/C][/ROW]
[ROW][C]19[/C][C]110.94[/C][C]111.334770951348[/C][C]-0.394770951347823[/C][/ROW]
[ROW][C]20[/C][C]110.91[/C][C]110.952557258342[/C][C]-0.0425572583422138[/C][/ROW]
[ROW][C]21[/C][C]111.22[/C][C]111.147401327691[/C][C]0.072598672308743[/C][/ROW]
[ROW][C]22[/C][C]111.09[/C][C]110.974932586218[/C][C]0.115067413782285[/C][/ROW]
[ROW][C]23[/C][C]111[/C][C]111.188862771837[/C][C]-0.188862771836739[/C][/ROW]
[ROW][C]24[/C][C]111.06[/C][C]110.874445138559[/C][C]0.185554861441247[/C][/ROW]
[ROW][C]25[/C][C]111.55[/C][C]111.744077360525[/C][C]-0.194077360524957[/C][/ROW]
[ROW][C]26[/C][C]112.32[/C][C]111.814821543751[/C][C]0.505178456248714[/C][/ROW]
[ROW][C]27[/C][C]112.64[/C][C]112.506577269809[/C][C]0.133422730191214[/C][/ROW]
[ROW][C]28[/C][C]112.36[/C][C]112.680974317223[/C][C]-0.320974317222678[/C][/ROW]
[ROW][C]29[/C][C]112.04[/C][C]112.680430511491[/C][C]-0.64043051149099[/C][/ROW]
[ROW][C]30[/C][C]112.37[/C][C]111.949343645802[/C][C]0.420656354198258[/C][/ROW]
[ROW][C]31[/C][C]112.59[/C][C]112.964752946192[/C][C]-0.374752946192004[/C][/ROW]
[ROW][C]32[/C][C]112.89[/C][C]112.588167318021[/C][C]0.301832681979249[/C][/ROW]
[ROW][C]33[/C][C]113.22[/C][C]113.025591505563[/C][C]0.194408494436843[/C][/ROW]
[ROW][C]34[/C][C]112.85[/C][C]112.935997133788[/C][C]-0.085997133787842[/C][/ROW]
[ROW][C]35[/C][C]113.06[/C][C]113.003269340469[/C][C]0.056730659530956[/C][/ROW]
[ROW][C]36[/C][C]112.99[/C][C]112.864983271274[/C][C]0.125016728726294[/C][/ROW]
[ROW][C]37[/C][C]113.32[/C][C]113.700536695131[/C][C]-0.380536695130701[/C][/ROW]
[ROW][C]38[/C][C]113.74[/C][C]113.652157341487[/C][C]0.0878426585131962[/C][/ROW]
[ROW][C]39[/C][C]113.91[/C][C]114.035955916242[/C][C]-0.125955916241807[/C][/ROW]
[ROW][C]40[/C][C]114.52[/C][C]113.999201023899[/C][C]0.52079897610065[/C][/ROW]
[ROW][C]41[/C][C]114.96[/C][C]114.581618207039[/C][C]0.378381792961264[/C][/ROW]
[ROW][C]42[/C][C]114.91[/C][C]114.599070475222[/C][C]0.310929524778132[/C][/ROW]
[ROW][C]43[/C][C]115.3[/C][C]115.569682311137[/C][C]-0.269682311136762[/C][/ROW]
[ROW][C]44[/C][C]115.44[/C][C]115.305236296444[/C][C]0.134763703556359[/C][/ROW]
[ROW][C]45[/C][C]115.52[/C][C]115.656039960459[/C][C]-0.136039960458888[/C][/ROW]
[ROW][C]46[/C][C]116.08[/C][C]115.343570324795[/C][C]0.73642967520479[/C][/ROW]
[ROW][C]47[/C][C]115.94[/C][C]116.027376225578[/C][C]-0.0873762255783106[/C][/ROW]
[ROW][C]48[/C][C]115.56[/C][C]115.821428656575[/C][C]-0.261428656574793[/C][/ROW]
[ROW][C]49[/C][C]115.88[/C][C]116.422677370127[/C][C]-0.542677370126768[/C][/ROW]
[ROW][C]50[/C][C]116.66[/C][C]116.294012241995[/C][C]0.365987758004977[/C][/ROW]
[ROW][C]51[/C][C]117.41[/C][C]116.903223885635[/C][C]0.506776114365152[/C][/ROW]
[ROW][C]52[/C][C]117.68[/C][C]117.364317049679[/C][C]0.315682950320891[/C][/ROW]
[ROW][C]53[/C][C]117.85[/C][C]117.848562041642[/C][C]0.00143795835791138[/C][/ROW]
[ROW][C]54[/C][C]118.21[/C][C]117.625534265050[/C][C]0.584465734949717[/C][/ROW]
[ROW][C]55[/C][C]118.92[/C][C]118.834084885612[/C][C]0.0859151143882713[/C][/ROW]
[ROW][C]56[/C][C]119.03[/C][C]118.867816806424[/C][C]0.162183193576496[/C][/ROW]
[ROW][C]57[/C][C]119.17[/C][C]119.289056769990[/C][C]-0.119056769989569[/C][/ROW]
[ROW][C]58[/C][C]118.95[/C][C]119.044007853194[/C][C]-0.0940078531937871[/C][/ROW]
[ROW][C]59[/C][C]118.92[/C][C]119.165750250126[/C][C]-0.245750250125667[/C][/ROW]
[ROW][C]60[/C][C]118.9[/C][C]118.861403636620[/C][C]0.0385963633795683[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64078&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64078&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
13110.22109.3177508271440.902249172856173
14110.4110.1715182021070.228481797893451
15110.69110.6758973493090.0141026506911146
16110.72110.770390033708-0.0503900337077852
17110.89110.965719613761-0.0757196137607536
18110.58110.657493240438-0.0774932404384288
19110.94111.334770951348-0.394770951347823
20110.91110.952557258342-0.0425572583422138
21111.22111.1474013276910.072598672308743
22111.09110.9749325862180.115067413782285
23111111.188862771837-0.188862771836739
24111.06110.8744451385590.185554861441247
25111.55111.744077360525-0.194077360524957
26112.32111.8148215437510.505178456248714
27112.64112.5065772698090.133422730191214
28112.36112.680974317223-0.320974317222678
29112.04112.680430511491-0.64043051149099
30112.37111.9493436458020.420656354198258
31112.59112.964752946192-0.374752946192004
32112.89112.5881673180210.301832681979249
33113.22113.0255915055630.194408494436843
34112.85112.935997133788-0.085997133787842
35113.06113.0032693404690.056730659530956
36112.99112.8649832712740.125016728726294
37113.32113.700536695131-0.380536695130701
38113.74113.6521573414870.0878426585131962
39113.91114.035955916242-0.125955916241807
40114.52113.9992010238990.52079897610065
41114.96114.5816182070390.378381792961264
42114.91114.5990704752220.310929524778132
43115.3115.569682311137-0.269682311136762
44115.44115.3052362964440.134763703556359
45115.52115.656039960459-0.136039960458888
46116.08115.3435703247950.73642967520479
47115.94116.027376225578-0.0873762255783106
48115.56115.821428656575-0.261428656574793
49115.88116.422677370127-0.542677370126768
50116.66116.2940122419950.365987758004977
51117.41116.9032238856350.506776114365152
52117.68117.3643170496790.315682950320891
53117.85117.8485620416420.00143795835791138
54118.21117.6255342650500.584465734949717
55118.92118.8340848856120.0859151143882713
56119.03118.8678168064240.162183193576496
57119.17119.289056769990-0.119056769989569
58118.95119.044007853194-0.0940078531937871
59118.92119.165750250126-0.245750250125667
60118.9118.8614036366200.0385963633795683







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61119.715526388584119.265755301009120.165297476159
62120.030070086460119.386993676115120.673146496806
63120.430987892013119.628383733995121.233592050031
64120.557502867448119.613241721418121.501764013477
65120.831846414456119.754435663872121.909257165039
66120.619057419030119.418663259217121.819451578844
67121.421259612919120.092477631224122.750041594614
68121.383198111863119.937282012311122.829114211414
69121.675843897272120.110991648490123.240696146053
70121.496344954675119.819776112444123.172913796907
71121.673578752966119.881564311948123.465593193985
72121.537564003874118.801891422596124.273236585151

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 119.715526388584 & 119.265755301009 & 120.165297476159 \tabularnewline
62 & 120.030070086460 & 119.386993676115 & 120.673146496806 \tabularnewline
63 & 120.430987892013 & 119.628383733995 & 121.233592050031 \tabularnewline
64 & 120.557502867448 & 119.613241721418 & 121.501764013477 \tabularnewline
65 & 120.831846414456 & 119.754435663872 & 121.909257165039 \tabularnewline
66 & 120.619057419030 & 119.418663259217 & 121.819451578844 \tabularnewline
67 & 121.421259612919 & 120.092477631224 & 122.750041594614 \tabularnewline
68 & 121.383198111863 & 119.937282012311 & 122.829114211414 \tabularnewline
69 & 121.675843897272 & 120.110991648490 & 123.240696146053 \tabularnewline
70 & 121.496344954675 & 119.819776112444 & 123.172913796907 \tabularnewline
71 & 121.673578752966 & 119.881564311948 & 123.465593193985 \tabularnewline
72 & 121.537564003874 & 118.801891422596 & 124.273236585151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64078&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]61[/C][C]119.715526388584[/C][C]119.265755301009[/C][C]120.165297476159[/C][/ROW]
[ROW][C]62[/C][C]120.030070086460[/C][C]119.386993676115[/C][C]120.673146496806[/C][/ROW]
[ROW][C]63[/C][C]120.430987892013[/C][C]119.628383733995[/C][C]121.233592050031[/C][/ROW]
[ROW][C]64[/C][C]120.557502867448[/C][C]119.613241721418[/C][C]121.501764013477[/C][/ROW]
[ROW][C]65[/C][C]120.831846414456[/C][C]119.754435663872[/C][C]121.909257165039[/C][/ROW]
[ROW][C]66[/C][C]120.619057419030[/C][C]119.418663259217[/C][C]121.819451578844[/C][/ROW]
[ROW][C]67[/C][C]121.421259612919[/C][C]120.092477631224[/C][C]122.750041594614[/C][/ROW]
[ROW][C]68[/C][C]121.383198111863[/C][C]119.937282012311[/C][C]122.829114211414[/C][/ROW]
[ROW][C]69[/C][C]121.675843897272[/C][C]120.110991648490[/C][C]123.240696146053[/C][/ROW]
[ROW][C]70[/C][C]121.496344954675[/C][C]119.819776112444[/C][C]123.172913796907[/C][/ROW]
[ROW][C]71[/C][C]121.673578752966[/C][C]119.881564311948[/C][C]123.465593193985[/C][/ROW]
[ROW][C]72[/C][C]121.537564003874[/C][C]118.801891422596[/C][C]124.273236585151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64078&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64078&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
61119.715526388584119.265755301009120.165297476159
62120.030070086460119.386993676115120.673146496806
63120.430987892013119.628383733995121.233592050031
64120.557502867448119.613241721418121.501764013477
65120.831846414456119.754435663872121.909257165039
66120.619057419030119.418663259217121.819451578844
67121.421259612919120.092477631224122.750041594614
68121.383198111863119.937282012311122.829114211414
69121.675843897272120.110991648490123.240696146053
70121.496344954675119.819776112444123.172913796907
71121.673578752966119.881564311948123.465593193985
72121.537564003874118.801891422596124.273236585151



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')