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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 computationTue, 01 Dec 2009 14:25:38 -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/01/t1259702811s5eiuo3u5752m6p.htm/, Retrieved Thu, 28 Mar 2024 20:01:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62267, Retrieved Thu, 28 Mar 2024 20:01:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
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]
-   PD      [Exponential Smoothing] [] [2009-12-01 21:25:38] [fc845972e0ebdb725d2fb9537c0c51aa] [Current]
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Dataseries X:
111.4
87.4
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1
115.9
96
99.8
116.8
115.7
99.4
94.3
91
93.2
103.1
94.1
91.8
102.7




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=62267&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=62267&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62267&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
alpha0.0788162596370837
beta1
gamma0.94734822479976

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0788162596370837 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.94734822479976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62267&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]0.0788162596370837[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.94734822479976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62267&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62267&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
alpha0.0788162596370837
beta1
gamma0.94734822479976







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13113.9114.216458260221-0.31645826022131
1480.981.0333726382371-0.133372638237091
1595.795.58574335436530.114256645634683
16113.2112.4882293296210.711770670379039
17105.9105.0885193957470.811480604253163
18108.8107.8516815332320.948318466767887
19102.3102.547234564864-0.247234564863732
209995.88191633054673.11808366945326
21100.798.2689635412342.43103645876596
22115.5108.3571384443777.14286155562264
23100.7108.491888077685-7.79188807768526
24109.9103.5929004116406.30709958835989
25114.6121.631916200956-7.03191620095613
2685.486.4651102279986-1.06511022799863
27100.5102.617812933350-2.11781293335015
28114.8121.426526702188-6.62652670218807
29116.5112.7970173681053.70298263189542
30112.9116.088093552074-3.18809355207401
31102108.675136681084-6.67513668108393
32106103.4292155302422.57078446975783
33105.3104.3832519707880.916748029212187
34118.8117.8545800333000.945419966700314
35106.1102.6744506679053.42554933209513
36109.3110.477944750928-1.17794475092815
37117.2115.0305356986582.16946430134215
3892.585.3105092380287.189490761972
39104.2101.5387846484882.66121535151179
40112.5117.670919879155-5.17091987915531
41122.4119.0168942507143.38310574928613
42113.3116.960839569567-3.66083956956676
43100106.782729872856-6.78272987285611
44110.7110.3988844126790.301115587321064
45112.8110.1866664032712.61333359672884
46109.8125.169538689621-15.3695386896213
47117.3109.7577382182037.54226178179738
48109.1113.783215130895-4.68321513089481
49115.9120.719702352607-4.81970235260694
509693.22384380705732.77615619294272
5199.8103.912189953244-4.11218995324450
52116.8110.5499140940396.25008590596083
53115.7118.849790024212-3.14979002421187
5499.4108.746156607763-9.34615660776292
5594.394.13758735326080.162412646739227
5691102.367887695294-11.3678876952937
5793.2100.673154186207-7.47315418620667
58103.195.99455770589637.10544229410374
5994.199.8373772191616-5.73737721916159
6091.890.63780450787871.16219549212130
61102.794.32818404045218.37181595954787

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 113.9 & 114.216458260221 & -0.31645826022131 \tabularnewline
14 & 80.9 & 81.0333726382371 & -0.133372638237091 \tabularnewline
15 & 95.7 & 95.5857433543653 & 0.114256645634683 \tabularnewline
16 & 113.2 & 112.488229329621 & 0.711770670379039 \tabularnewline
17 & 105.9 & 105.088519395747 & 0.811480604253163 \tabularnewline
18 & 108.8 & 107.851681533232 & 0.948318466767887 \tabularnewline
19 & 102.3 & 102.547234564864 & -0.247234564863732 \tabularnewline
20 & 99 & 95.8819163305467 & 3.11808366945326 \tabularnewline
21 & 100.7 & 98.268963541234 & 2.43103645876596 \tabularnewline
22 & 115.5 & 108.357138444377 & 7.14286155562264 \tabularnewline
23 & 100.7 & 108.491888077685 & -7.79188807768526 \tabularnewline
24 & 109.9 & 103.592900411640 & 6.30709958835989 \tabularnewline
25 & 114.6 & 121.631916200956 & -7.03191620095613 \tabularnewline
26 & 85.4 & 86.4651102279986 & -1.06511022799863 \tabularnewline
27 & 100.5 & 102.617812933350 & -2.11781293335015 \tabularnewline
28 & 114.8 & 121.426526702188 & -6.62652670218807 \tabularnewline
29 & 116.5 & 112.797017368105 & 3.70298263189542 \tabularnewline
30 & 112.9 & 116.088093552074 & -3.18809355207401 \tabularnewline
31 & 102 & 108.675136681084 & -6.67513668108393 \tabularnewline
32 & 106 & 103.429215530242 & 2.57078446975783 \tabularnewline
33 & 105.3 & 104.383251970788 & 0.916748029212187 \tabularnewline
34 & 118.8 & 117.854580033300 & 0.945419966700314 \tabularnewline
35 & 106.1 & 102.674450667905 & 3.42554933209513 \tabularnewline
36 & 109.3 & 110.477944750928 & -1.17794475092815 \tabularnewline
37 & 117.2 & 115.030535698658 & 2.16946430134215 \tabularnewline
38 & 92.5 & 85.310509238028 & 7.189490761972 \tabularnewline
39 & 104.2 & 101.538784648488 & 2.66121535151179 \tabularnewline
40 & 112.5 & 117.670919879155 & -5.17091987915531 \tabularnewline
41 & 122.4 & 119.016894250714 & 3.38310574928613 \tabularnewline
42 & 113.3 & 116.960839569567 & -3.66083956956676 \tabularnewline
43 & 100 & 106.782729872856 & -6.78272987285611 \tabularnewline
44 & 110.7 & 110.398884412679 & 0.301115587321064 \tabularnewline
45 & 112.8 & 110.186666403271 & 2.61333359672884 \tabularnewline
46 & 109.8 & 125.169538689621 & -15.3695386896213 \tabularnewline
47 & 117.3 & 109.757738218203 & 7.54226178179738 \tabularnewline
48 & 109.1 & 113.783215130895 & -4.68321513089481 \tabularnewline
49 & 115.9 & 120.719702352607 & -4.81970235260694 \tabularnewline
50 & 96 & 93.2238438070573 & 2.77615619294272 \tabularnewline
51 & 99.8 & 103.912189953244 & -4.11218995324450 \tabularnewline
52 & 116.8 & 110.549914094039 & 6.25008590596083 \tabularnewline
53 & 115.7 & 118.849790024212 & -3.14979002421187 \tabularnewline
54 & 99.4 & 108.746156607763 & -9.34615660776292 \tabularnewline
55 & 94.3 & 94.1375873532608 & 0.162412646739227 \tabularnewline
56 & 91 & 102.367887695294 & -11.3678876952937 \tabularnewline
57 & 93.2 & 100.673154186207 & -7.47315418620667 \tabularnewline
58 & 103.1 & 95.9945577058963 & 7.10544229410374 \tabularnewline
59 & 94.1 & 99.8373772191616 & -5.73737721916159 \tabularnewline
60 & 91.8 & 90.6378045078787 & 1.16219549212130 \tabularnewline
61 & 102.7 & 94.3281840404521 & 8.37181595954787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62267&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]113.9[/C][C]114.216458260221[/C][C]-0.31645826022131[/C][/ROW]
[ROW][C]14[/C][C]80.9[/C][C]81.0333726382371[/C][C]-0.133372638237091[/C][/ROW]
[ROW][C]15[/C][C]95.7[/C][C]95.5857433543653[/C][C]0.114256645634683[/C][/ROW]
[ROW][C]16[/C][C]113.2[/C][C]112.488229329621[/C][C]0.711770670379039[/C][/ROW]
[ROW][C]17[/C][C]105.9[/C][C]105.088519395747[/C][C]0.811480604253163[/C][/ROW]
[ROW][C]18[/C][C]108.8[/C][C]107.851681533232[/C][C]0.948318466767887[/C][/ROW]
[ROW][C]19[/C][C]102.3[/C][C]102.547234564864[/C][C]-0.247234564863732[/C][/ROW]
[ROW][C]20[/C][C]99[/C][C]95.8819163305467[/C][C]3.11808366945326[/C][/ROW]
[ROW][C]21[/C][C]100.7[/C][C]98.268963541234[/C][C]2.43103645876596[/C][/ROW]
[ROW][C]22[/C][C]115.5[/C][C]108.357138444377[/C][C]7.14286155562264[/C][/ROW]
[ROW][C]23[/C][C]100.7[/C][C]108.491888077685[/C][C]-7.79188807768526[/C][/ROW]
[ROW][C]24[/C][C]109.9[/C][C]103.592900411640[/C][C]6.30709958835989[/C][/ROW]
[ROW][C]25[/C][C]114.6[/C][C]121.631916200956[/C][C]-7.03191620095613[/C][/ROW]
[ROW][C]26[/C][C]85.4[/C][C]86.4651102279986[/C][C]-1.06511022799863[/C][/ROW]
[ROW][C]27[/C][C]100.5[/C][C]102.617812933350[/C][C]-2.11781293335015[/C][/ROW]
[ROW][C]28[/C][C]114.8[/C][C]121.426526702188[/C][C]-6.62652670218807[/C][/ROW]
[ROW][C]29[/C][C]116.5[/C][C]112.797017368105[/C][C]3.70298263189542[/C][/ROW]
[ROW][C]30[/C][C]112.9[/C][C]116.088093552074[/C][C]-3.18809355207401[/C][/ROW]
[ROW][C]31[/C][C]102[/C][C]108.675136681084[/C][C]-6.67513668108393[/C][/ROW]
[ROW][C]32[/C][C]106[/C][C]103.429215530242[/C][C]2.57078446975783[/C][/ROW]
[ROW][C]33[/C][C]105.3[/C][C]104.383251970788[/C][C]0.916748029212187[/C][/ROW]
[ROW][C]34[/C][C]118.8[/C][C]117.854580033300[/C][C]0.945419966700314[/C][/ROW]
[ROW][C]35[/C][C]106.1[/C][C]102.674450667905[/C][C]3.42554933209513[/C][/ROW]
[ROW][C]36[/C][C]109.3[/C][C]110.477944750928[/C][C]-1.17794475092815[/C][/ROW]
[ROW][C]37[/C][C]117.2[/C][C]115.030535698658[/C][C]2.16946430134215[/C][/ROW]
[ROW][C]38[/C][C]92.5[/C][C]85.310509238028[/C][C]7.189490761972[/C][/ROW]
[ROW][C]39[/C][C]104.2[/C][C]101.538784648488[/C][C]2.66121535151179[/C][/ROW]
[ROW][C]40[/C][C]112.5[/C][C]117.670919879155[/C][C]-5.17091987915531[/C][/ROW]
[ROW][C]41[/C][C]122.4[/C][C]119.016894250714[/C][C]3.38310574928613[/C][/ROW]
[ROW][C]42[/C][C]113.3[/C][C]116.960839569567[/C][C]-3.66083956956676[/C][/ROW]
[ROW][C]43[/C][C]100[/C][C]106.782729872856[/C][C]-6.78272987285611[/C][/ROW]
[ROW][C]44[/C][C]110.7[/C][C]110.398884412679[/C][C]0.301115587321064[/C][/ROW]
[ROW][C]45[/C][C]112.8[/C][C]110.186666403271[/C][C]2.61333359672884[/C][/ROW]
[ROW][C]46[/C][C]109.8[/C][C]125.169538689621[/C][C]-15.3695386896213[/C][/ROW]
[ROW][C]47[/C][C]117.3[/C][C]109.757738218203[/C][C]7.54226178179738[/C][/ROW]
[ROW][C]48[/C][C]109.1[/C][C]113.783215130895[/C][C]-4.68321513089481[/C][/ROW]
[ROW][C]49[/C][C]115.9[/C][C]120.719702352607[/C][C]-4.81970235260694[/C][/ROW]
[ROW][C]50[/C][C]96[/C][C]93.2238438070573[/C][C]2.77615619294272[/C][/ROW]
[ROW][C]51[/C][C]99.8[/C][C]103.912189953244[/C][C]-4.11218995324450[/C][/ROW]
[ROW][C]52[/C][C]116.8[/C][C]110.549914094039[/C][C]6.25008590596083[/C][/ROW]
[ROW][C]53[/C][C]115.7[/C][C]118.849790024212[/C][C]-3.14979002421187[/C][/ROW]
[ROW][C]54[/C][C]99.4[/C][C]108.746156607763[/C][C]-9.34615660776292[/C][/ROW]
[ROW][C]55[/C][C]94.3[/C][C]94.1375873532608[/C][C]0.162412646739227[/C][/ROW]
[ROW][C]56[/C][C]91[/C][C]102.367887695294[/C][C]-11.3678876952937[/C][/ROW]
[ROW][C]57[/C][C]93.2[/C][C]100.673154186207[/C][C]-7.47315418620667[/C][/ROW]
[ROW][C]58[/C][C]103.1[/C][C]95.9945577058963[/C][C]7.10544229410374[/C][/ROW]
[ROW][C]59[/C][C]94.1[/C][C]99.8373772191616[/C][C]-5.73737721916159[/C][/ROW]
[ROW][C]60[/C][C]91.8[/C][C]90.6378045078787[/C][C]1.16219549212130[/C][/ROW]
[ROW][C]61[/C][C]102.7[/C][C]94.3281840404521[/C][C]8.37181595954787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62267&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62267&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
13113.9114.216458260221-0.31645826022131
1480.981.0333726382371-0.133372638237091
1595.795.58574335436530.114256645634683
16113.2112.4882293296210.711770670379039
17105.9105.0885193957470.811480604253163
18108.8107.8516815332320.948318466767887
19102.3102.547234564864-0.247234564863732
209995.88191633054673.11808366945326
21100.798.2689635412342.43103645876596
22115.5108.3571384443777.14286155562264
23100.7108.491888077685-7.79188807768526
24109.9103.5929004116406.30709958835989
25114.6121.631916200956-7.03191620095613
2685.486.4651102279986-1.06511022799863
27100.5102.617812933350-2.11781293335015
28114.8121.426526702188-6.62652670218807
29116.5112.7970173681053.70298263189542
30112.9116.088093552074-3.18809355207401
31102108.675136681084-6.67513668108393
32106103.4292155302422.57078446975783
33105.3104.3832519707880.916748029212187
34118.8117.8545800333000.945419966700314
35106.1102.6744506679053.42554933209513
36109.3110.477944750928-1.17794475092815
37117.2115.0305356986582.16946430134215
3892.585.3105092380287.189490761972
39104.2101.5387846484882.66121535151179
40112.5117.670919879155-5.17091987915531
41122.4119.0168942507143.38310574928613
42113.3116.960839569567-3.66083956956676
43100106.782729872856-6.78272987285611
44110.7110.3988844126790.301115587321064
45112.8110.1866664032712.61333359672884
46109.8125.169538689621-15.3695386896213
47117.3109.7577382182037.54226178179738
48109.1113.783215130895-4.68321513089481
49115.9120.719702352607-4.81970235260694
509693.22384380705732.77615619294272
5199.8103.912189953244-4.11218995324450
52116.8110.5499140940396.25008590596083
53115.7118.849790024212-3.14979002421187
5499.4108.746156607763-9.34615660776292
5594.394.13758735326080.162412646739227
5691102.367887695294-11.3678876952937
5793.2100.673154186207-7.47315418620667
58103.195.99455770589637.10544229410374
5994.199.8373772191616-5.73737721916159
6091.890.63780450787871.16219549212130
61102.794.32818404045218.37181595954787







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6277.064416129242267.20021894896886.9286133095164
6379.216506432641869.203667872642689.229344992641
6490.494576127984380.0041618165221100.984990439446
6588.383992182689777.23117962493199.5368047404484
6675.283164523619763.69243682439286.8738922228474
6770.213630273528957.855202702193382.5720578448646
6867.89331550506954.44672067427481.3399103358642
6969.492809772387254.277612912770684.7080066320037
7076.003085063000757.729924930635694.2762451953657
7169.817352806979750.274763867303989.3599417466554
7267.81051875208346.123637408305689.4974000958605
7375.015573858394549.4887353110272100.542412405762

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 77.0644161292422 & 67.200218948968 & 86.9286133095164 \tabularnewline
63 & 79.2165064326418 & 69.2036678726426 & 89.229344992641 \tabularnewline
64 & 90.4945761279843 & 80.0041618165221 & 100.984990439446 \tabularnewline
65 & 88.3839921826897 & 77.231179624931 & 99.5368047404484 \tabularnewline
66 & 75.2831645236197 & 63.692436824392 & 86.8738922228474 \tabularnewline
67 & 70.2136302735289 & 57.8552027021933 & 82.5720578448646 \tabularnewline
68 & 67.893315505069 & 54.446720674274 & 81.3399103358642 \tabularnewline
69 & 69.4928097723872 & 54.2776129127706 & 84.7080066320037 \tabularnewline
70 & 76.0030850630007 & 57.7299249306356 & 94.2762451953657 \tabularnewline
71 & 69.8173528069797 & 50.2747638673039 & 89.3599417466554 \tabularnewline
72 & 67.810518752083 & 46.1236374083056 & 89.4974000958605 \tabularnewline
73 & 75.0155738583945 & 49.4887353110272 & 100.542412405762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62267&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]62[/C][C]77.0644161292422[/C][C]67.200218948968[/C][C]86.9286133095164[/C][/ROW]
[ROW][C]63[/C][C]79.2165064326418[/C][C]69.2036678726426[/C][C]89.229344992641[/C][/ROW]
[ROW][C]64[/C][C]90.4945761279843[/C][C]80.0041618165221[/C][C]100.984990439446[/C][/ROW]
[ROW][C]65[/C][C]88.3839921826897[/C][C]77.231179624931[/C][C]99.5368047404484[/C][/ROW]
[ROW][C]66[/C][C]75.2831645236197[/C][C]63.692436824392[/C][C]86.8738922228474[/C][/ROW]
[ROW][C]67[/C][C]70.2136302735289[/C][C]57.8552027021933[/C][C]82.5720578448646[/C][/ROW]
[ROW][C]68[/C][C]67.893315505069[/C][C]54.446720674274[/C][C]81.3399103358642[/C][/ROW]
[ROW][C]69[/C][C]69.4928097723872[/C][C]54.2776129127706[/C][C]84.7080066320037[/C][/ROW]
[ROW][C]70[/C][C]76.0030850630007[/C][C]57.7299249306356[/C][C]94.2762451953657[/C][/ROW]
[ROW][C]71[/C][C]69.8173528069797[/C][C]50.2747638673039[/C][C]89.3599417466554[/C][/ROW]
[ROW][C]72[/C][C]67.810518752083[/C][C]46.1236374083056[/C][C]89.4974000958605[/C][/ROW]
[ROW][C]73[/C][C]75.0155738583945[/C][C]49.4887353110272[/C][C]100.542412405762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62267&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62267&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
6277.064416129242267.20021894896886.9286133095164
6379.216506432641869.203667872642689.229344992641
6490.494576127984380.0041618165221100.984990439446
6588.383992182689777.23117962493199.5368047404484
6675.283164523619763.69243682439286.8738922228474
6770.213630273528957.855202702193382.5720578448646
6867.89331550506954.44672067427481.3399103358642
6969.492809772387254.277612912770684.7080066320037
7076.003085063000757.729924930635694.2762451953657
7169.817352806979750.274763867303989.3599417466554
7267.81051875208346.123637408305689.4974000958605
7375.015573858394549.4887353110272100.542412405762



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
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')