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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 computationMon, 21 Dec 2009 15:02:05 -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/21/t126143298259mzyyp9z5zyu76.htm/, Retrieved Sun, 05 May 2024 12:57:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70407, Retrieved Sun, 05 May 2024 12:57:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Exponential Smoothing] [Paper] [2009-12-21 22:02:05] [e339dd08bcbfc073ac7494f09a949034] [Current]
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Post a new message
Dataseries X:
25.6
23.7
22
21.3
20.7
20.4
20.3
20.4
19.8
19.5
23.1
23.5
23.5
22.9
21.9
21.5
20.5
20.2
19.4
19.2
18.8
18.8
22.6
23.3
23
21.4
19.9
18.8
18.6
18.4
18.6
19.9
19.2
18.4
21.1
20.5
19.1
18.1
17
17.1
17.4
16.8
15.3
14.3
13.4
15.3
22.1
23.7
22.2
19.5
16.6
17.3
19.8
21.2
21.5
20.6
19.1
19.6
23.5
24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70407&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70407&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70407&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[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70407&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
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1323.523.6301148459851-0.130114845985076
1422.922.9437996857881-0.0437996857881267
1521.921.9463706339436-0.0463706339436101
1621.521.5244856179741-0.0244856179740971
1720.520.5031491944293-0.00314919442930162
1820.220.18312323563790.0168767643621131
1919.419.7431788967428-0.343178896742813
2019.219.5608170367688-0.360817036768811
2118.818.62470765819150.175292341808486
2218.818.4690453485850.330954651414999
2322.622.22041171078940.379588289210556
2423.322.95795082530390.342049174696136
252323.2985525957402-0.298552595740205
2621.422.4545640949381-1.05456409493806
2719.920.5056726303232-0.605672630323188
2818.819.554435563383-0.754435563382998
2918.617.92262645556440.677373544435621
3018.418.30833504565070.0916649543492731
3118.617.97997047946910.620029520530938
3219.918.75235437239001.14764562760995
3319.219.3053074364747-0.105307436474696
3418.418.8629082197206-0.4629082197206
3521.121.7465655569433-0.646565556943287
3620.521.4307901943330-0.930790194332968
3719.120.4925522061045-1.39255220610451
3818.118.6385264863076-0.538526486307553
391717.3361370223583-0.336137022358262
4017.116.69786298422590.402137015774091
4117.416.29785287924201.10214712075797
4216.817.1242582940799-0.324258294079879
4315.316.4126741085591-1.11267410855907
4414.315.4174458818276-1.11744588182761
4513.413.8605092102093-0.460509210209255
4615.313.15189658825442.14810341174558
4722.118.07425786463564.0257421353644
4823.722.44889728164691.25110271835310
4922.223.6994097942596-1.49940979425959
5019.521.6717871495780-2.17178714957796
5116.618.680788492404-2.08078849240398
5217.316.30385297330770.996147026692313
5319.816.48900271175053.31099728824946
5421.219.49241179722161.70758820277844
5521.520.72273912856160.777260871438443
5620.621.6830315307631-1.08303153076309
5719.119.9859072147579-0.885907214757875
5819.618.76444250193670.835557498063299
5923.523.16810401848180.331895981518244
602423.87424720388640.125752796113602

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 23.5 & 23.6301148459851 & -0.130114845985076 \tabularnewline
14 & 22.9 & 22.9437996857881 & -0.0437996857881267 \tabularnewline
15 & 21.9 & 21.9463706339436 & -0.0463706339436101 \tabularnewline
16 & 21.5 & 21.5244856179741 & -0.0244856179740971 \tabularnewline
17 & 20.5 & 20.5031491944293 & -0.00314919442930162 \tabularnewline
18 & 20.2 & 20.1831232356379 & 0.0168767643621131 \tabularnewline
19 & 19.4 & 19.7431788967428 & -0.343178896742813 \tabularnewline
20 & 19.2 & 19.5608170367688 & -0.360817036768811 \tabularnewline
21 & 18.8 & 18.6247076581915 & 0.175292341808486 \tabularnewline
22 & 18.8 & 18.469045348585 & 0.330954651414999 \tabularnewline
23 & 22.6 & 22.2204117107894 & 0.379588289210556 \tabularnewline
24 & 23.3 & 22.9579508253039 & 0.342049174696136 \tabularnewline
25 & 23 & 23.2985525957402 & -0.298552595740205 \tabularnewline
26 & 21.4 & 22.4545640949381 & -1.05456409493806 \tabularnewline
27 & 19.9 & 20.5056726303232 & -0.605672630323188 \tabularnewline
28 & 18.8 & 19.554435563383 & -0.754435563382998 \tabularnewline
29 & 18.6 & 17.9226264555644 & 0.677373544435621 \tabularnewline
30 & 18.4 & 18.3083350456507 & 0.0916649543492731 \tabularnewline
31 & 18.6 & 17.9799704794691 & 0.620029520530938 \tabularnewline
32 & 19.9 & 18.7523543723900 & 1.14764562760995 \tabularnewline
33 & 19.2 & 19.3053074364747 & -0.105307436474696 \tabularnewline
34 & 18.4 & 18.8629082197206 & -0.4629082197206 \tabularnewline
35 & 21.1 & 21.7465655569433 & -0.646565556943287 \tabularnewline
36 & 20.5 & 21.4307901943330 & -0.930790194332968 \tabularnewline
37 & 19.1 & 20.4925522061045 & -1.39255220610451 \tabularnewline
38 & 18.1 & 18.6385264863076 & -0.538526486307553 \tabularnewline
39 & 17 & 17.3361370223583 & -0.336137022358262 \tabularnewline
40 & 17.1 & 16.6978629842259 & 0.402137015774091 \tabularnewline
41 & 17.4 & 16.2978528792420 & 1.10214712075797 \tabularnewline
42 & 16.8 & 17.1242582940799 & -0.324258294079879 \tabularnewline
43 & 15.3 & 16.4126741085591 & -1.11267410855907 \tabularnewline
44 & 14.3 & 15.4174458818276 & -1.11744588182761 \tabularnewline
45 & 13.4 & 13.8605092102093 & -0.460509210209255 \tabularnewline
46 & 15.3 & 13.1518965882544 & 2.14810341174558 \tabularnewline
47 & 22.1 & 18.0742578646356 & 4.0257421353644 \tabularnewline
48 & 23.7 & 22.4488972816469 & 1.25110271835310 \tabularnewline
49 & 22.2 & 23.6994097942596 & -1.49940979425959 \tabularnewline
50 & 19.5 & 21.6717871495780 & -2.17178714957796 \tabularnewline
51 & 16.6 & 18.680788492404 & -2.08078849240398 \tabularnewline
52 & 17.3 & 16.3038529733077 & 0.996147026692313 \tabularnewline
53 & 19.8 & 16.4890027117505 & 3.31099728824946 \tabularnewline
54 & 21.2 & 19.4924117972216 & 1.70758820277844 \tabularnewline
55 & 21.5 & 20.7227391285616 & 0.777260871438443 \tabularnewline
56 & 20.6 & 21.6830315307631 & -1.08303153076309 \tabularnewline
57 & 19.1 & 19.9859072147579 & -0.885907214757875 \tabularnewline
58 & 19.6 & 18.7644425019367 & 0.835557498063299 \tabularnewline
59 & 23.5 & 23.1681040184818 & 0.331895981518244 \tabularnewline
60 & 24 & 23.8742472038864 & 0.125752796113602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70407&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]23.5[/C][C]23.6301148459851[/C][C]-0.130114845985076[/C][/ROW]
[ROW][C]14[/C][C]22.9[/C][C]22.9437996857881[/C][C]-0.0437996857881267[/C][/ROW]
[ROW][C]15[/C][C]21.9[/C][C]21.9463706339436[/C][C]-0.0463706339436101[/C][/ROW]
[ROW][C]16[/C][C]21.5[/C][C]21.5244856179741[/C][C]-0.0244856179740971[/C][/ROW]
[ROW][C]17[/C][C]20.5[/C][C]20.5031491944293[/C][C]-0.00314919442930162[/C][/ROW]
[ROW][C]18[/C][C]20.2[/C][C]20.1831232356379[/C][C]0.0168767643621131[/C][/ROW]
[ROW][C]19[/C][C]19.4[/C][C]19.7431788967428[/C][C]-0.343178896742813[/C][/ROW]
[ROW][C]20[/C][C]19.2[/C][C]19.5608170367688[/C][C]-0.360817036768811[/C][/ROW]
[ROW][C]21[/C][C]18.8[/C][C]18.6247076581915[/C][C]0.175292341808486[/C][/ROW]
[ROW][C]22[/C][C]18.8[/C][C]18.469045348585[/C][C]0.330954651414999[/C][/ROW]
[ROW][C]23[/C][C]22.6[/C][C]22.2204117107894[/C][C]0.379588289210556[/C][/ROW]
[ROW][C]24[/C][C]23.3[/C][C]22.9579508253039[/C][C]0.342049174696136[/C][/ROW]
[ROW][C]25[/C][C]23[/C][C]23.2985525957402[/C][C]-0.298552595740205[/C][/ROW]
[ROW][C]26[/C][C]21.4[/C][C]22.4545640949381[/C][C]-1.05456409493806[/C][/ROW]
[ROW][C]27[/C][C]19.9[/C][C]20.5056726303232[/C][C]-0.605672630323188[/C][/ROW]
[ROW][C]28[/C][C]18.8[/C][C]19.554435563383[/C][C]-0.754435563382998[/C][/ROW]
[ROW][C]29[/C][C]18.6[/C][C]17.9226264555644[/C][C]0.677373544435621[/C][/ROW]
[ROW][C]30[/C][C]18.4[/C][C]18.3083350456507[/C][C]0.0916649543492731[/C][/ROW]
[ROW][C]31[/C][C]18.6[/C][C]17.9799704794691[/C][C]0.620029520530938[/C][/ROW]
[ROW][C]32[/C][C]19.9[/C][C]18.7523543723900[/C][C]1.14764562760995[/C][/ROW]
[ROW][C]33[/C][C]19.2[/C][C]19.3053074364747[/C][C]-0.105307436474696[/C][/ROW]
[ROW][C]34[/C][C]18.4[/C][C]18.8629082197206[/C][C]-0.4629082197206[/C][/ROW]
[ROW][C]35[/C][C]21.1[/C][C]21.7465655569433[/C][C]-0.646565556943287[/C][/ROW]
[ROW][C]36[/C][C]20.5[/C][C]21.4307901943330[/C][C]-0.930790194332968[/C][/ROW]
[ROW][C]37[/C][C]19.1[/C][C]20.4925522061045[/C][C]-1.39255220610451[/C][/ROW]
[ROW][C]38[/C][C]18.1[/C][C]18.6385264863076[/C][C]-0.538526486307553[/C][/ROW]
[ROW][C]39[/C][C]17[/C][C]17.3361370223583[/C][C]-0.336137022358262[/C][/ROW]
[ROW][C]40[/C][C]17.1[/C][C]16.6978629842259[/C][C]0.402137015774091[/C][/ROW]
[ROW][C]41[/C][C]17.4[/C][C]16.2978528792420[/C][C]1.10214712075797[/C][/ROW]
[ROW][C]42[/C][C]16.8[/C][C]17.1242582940799[/C][C]-0.324258294079879[/C][/ROW]
[ROW][C]43[/C][C]15.3[/C][C]16.4126741085591[/C][C]-1.11267410855907[/C][/ROW]
[ROW][C]44[/C][C]14.3[/C][C]15.4174458818276[/C][C]-1.11744588182761[/C][/ROW]
[ROW][C]45[/C][C]13.4[/C][C]13.8605092102093[/C][C]-0.460509210209255[/C][/ROW]
[ROW][C]46[/C][C]15.3[/C][C]13.1518965882544[/C][C]2.14810341174558[/C][/ROW]
[ROW][C]47[/C][C]22.1[/C][C]18.0742578646356[/C][C]4.0257421353644[/C][/ROW]
[ROW][C]48[/C][C]23.7[/C][C]22.4488972816469[/C][C]1.25110271835310[/C][/ROW]
[ROW][C]49[/C][C]22.2[/C][C]23.6994097942596[/C][C]-1.49940979425959[/C][/ROW]
[ROW][C]50[/C][C]19.5[/C][C]21.6717871495780[/C][C]-2.17178714957796[/C][/ROW]
[ROW][C]51[/C][C]16.6[/C][C]18.680788492404[/C][C]-2.08078849240398[/C][/ROW]
[ROW][C]52[/C][C]17.3[/C][C]16.3038529733077[/C][C]0.996147026692313[/C][/ROW]
[ROW][C]53[/C][C]19.8[/C][C]16.4890027117505[/C][C]3.31099728824946[/C][/ROW]
[ROW][C]54[/C][C]21.2[/C][C]19.4924117972216[/C][C]1.70758820277844[/C][/ROW]
[ROW][C]55[/C][C]21.5[/C][C]20.7227391285616[/C][C]0.777260871438443[/C][/ROW]
[ROW][C]56[/C][C]20.6[/C][C]21.6830315307631[/C][C]-1.08303153076309[/C][/ROW]
[ROW][C]57[/C][C]19.1[/C][C]19.9859072147579[/C][C]-0.885907214757875[/C][/ROW]
[ROW][C]58[/C][C]19.6[/C][C]18.7644425019367[/C][C]0.835557498063299[/C][/ROW]
[ROW][C]59[/C][C]23.5[/C][C]23.1681040184818[/C][C]0.331895981518244[/C][/ROW]
[ROW][C]60[/C][C]24[/C][C]23.8742472038864[/C][C]0.125752796113602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70407&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70407&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
1323.523.6301148459851-0.130114845985076
1422.922.9437996857881-0.0437996857881267
1521.921.9463706339436-0.0463706339436101
1621.521.5244856179741-0.0244856179740971
1720.520.5031491944293-0.00314919442930162
1820.220.18312323563790.0168767643621131
1919.419.7431788967428-0.343178896742813
2019.219.5608170367688-0.360817036768811
2118.818.62470765819150.175292341808486
2218.818.4690453485850.330954651414999
2322.622.22041171078940.379588289210556
2423.322.95795082530390.342049174696136
252323.2985525957402-0.298552595740205
2621.422.4545640949381-1.05456409493806
2719.920.5056726303232-0.605672630323188
2818.819.554435563383-0.754435563382998
2918.617.92262645556440.677373544435621
3018.418.30833504565070.0916649543492731
3118.617.97997047946910.620029520530938
3219.918.75235437239001.14764562760995
3319.219.3053074364747-0.105307436474696
3418.418.8629082197206-0.4629082197206
3521.121.7465655569433-0.646565556943287
3620.521.4307901943330-0.930790194332968
3719.120.4925522061045-1.39255220610451
3818.118.6385264863076-0.538526486307553
391717.3361370223583-0.336137022358262
4017.116.69786298422590.402137015774091
4117.416.29785287924201.10214712075797
4216.817.1242582940799-0.324258294079879
4315.316.4126741085591-1.11267410855907
4414.315.4174458818276-1.11744588182761
4513.413.8605092102093-0.460509210209255
4615.313.15189658825442.14810341174558
4722.118.07425786463564.0257421353644
4823.722.44889728164691.25110271835310
4922.223.6994097942596-1.49940979425959
5019.521.6717871495780-2.17178714957796
5116.618.680788492404-2.08078849240398
5217.316.30385297330770.996147026692313
5319.816.48900271175053.31099728824946
5421.219.49241179722161.70758820277844
5521.520.72273912856160.777260871438443
5620.621.6830315307631-1.08303153076309
5719.119.9859072147579-0.885907214757875
5819.618.76444250193670.835557498063299
5923.523.16810401848180.331895981518244
602423.87424720388640.125752796113602







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6124.000052693149121.697520001019726.3025853852786
6223.433086835366120.211675025328026.6544986454041
6322.458382060255818.601592037690526.315172082821
6422.074505922118917.632173040710926.5168388035268
6521.052232748370216.22231554150825.8821499552324
6620.728028201305515.435130508192926.0209258944181
6720.260414324020514.587417208953025.9334114390881
6820.430333107852914.252223608077026.6084426076288
6919.82094257307613.387877050054626.2540080960975
7019.474323781325712.734455393048226.2141921696032
7123.019226036359914.709693167847431.3287589048724
7223.3847678241084-30.821838726567377.5913743747842

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 24.0000526931491 & 21.6975200010197 & 26.3025853852786 \tabularnewline
62 & 23.4330868353661 & 20.2116750253280 & 26.6544986454041 \tabularnewline
63 & 22.4583820602558 & 18.6015920376905 & 26.315172082821 \tabularnewline
64 & 22.0745059221189 & 17.6321730407109 & 26.5168388035268 \tabularnewline
65 & 21.0522327483702 & 16.222315541508 & 25.8821499552324 \tabularnewline
66 & 20.7280282013055 & 15.4351305081929 & 26.0209258944181 \tabularnewline
67 & 20.2604143240205 & 14.5874172089530 & 25.9334114390881 \tabularnewline
68 & 20.4303331078529 & 14.2522236080770 & 26.6084426076288 \tabularnewline
69 & 19.820942573076 & 13.3878770500546 & 26.2540080960975 \tabularnewline
70 & 19.4743237813257 & 12.7344553930482 & 26.2141921696032 \tabularnewline
71 & 23.0192260363599 & 14.7096931678474 & 31.3287589048724 \tabularnewline
72 & 23.3847678241084 & -30.8218387265673 & 77.5913743747842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70407&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]24.0000526931491[/C][C]21.6975200010197[/C][C]26.3025853852786[/C][/ROW]
[ROW][C]62[/C][C]23.4330868353661[/C][C]20.2116750253280[/C][C]26.6544986454041[/C][/ROW]
[ROW][C]63[/C][C]22.4583820602558[/C][C]18.6015920376905[/C][C]26.315172082821[/C][/ROW]
[ROW][C]64[/C][C]22.0745059221189[/C][C]17.6321730407109[/C][C]26.5168388035268[/C][/ROW]
[ROW][C]65[/C][C]21.0522327483702[/C][C]16.222315541508[/C][C]25.8821499552324[/C][/ROW]
[ROW][C]66[/C][C]20.7280282013055[/C][C]15.4351305081929[/C][C]26.0209258944181[/C][/ROW]
[ROW][C]67[/C][C]20.2604143240205[/C][C]14.5874172089530[/C][C]25.9334114390881[/C][/ROW]
[ROW][C]68[/C][C]20.4303331078529[/C][C]14.2522236080770[/C][C]26.6084426076288[/C][/ROW]
[ROW][C]69[/C][C]19.820942573076[/C][C]13.3878770500546[/C][C]26.2540080960975[/C][/ROW]
[ROW][C]70[/C][C]19.4743237813257[/C][C]12.7344553930482[/C][C]26.2141921696032[/C][/ROW]
[ROW][C]71[/C][C]23.0192260363599[/C][C]14.7096931678474[/C][C]31.3287589048724[/C][/ROW]
[ROW][C]72[/C][C]23.3847678241084[/C][C]-30.8218387265673[/C][C]77.5913743747842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70407&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70407&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
6124.000052693149121.697520001019726.3025853852786
6223.433086835366120.211675025328026.6544986454041
6322.458382060255818.601592037690526.315172082821
6422.074505922118917.632173040710926.5168388035268
6521.052232748370216.22231554150825.8821499552324
6620.728028201305515.435130508192926.0209258944181
6720.260414324020514.587417208953025.9334114390881
6820.430333107852914.252223608077026.6084426076288
6919.82094257307613.387877050054626.2540080960975
7019.474323781325712.734455393048226.2141921696032
7123.019226036359914.709693167847431.3287589048724
7223.3847678241084-30.821838726567377.5913743747842



Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 1 ; par4 = 1 ;
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')