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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 02:50:05 -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/04/t12599203801qhvw1b2uve15w6.htm/, Retrieved Sun, 28 Apr 2024 05:37:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63218, Retrieved Sun, 28 Apr 2024 05:37:43 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws9p2.2es
Estimated Impact101
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]
- R  D      [Exponential Smoothing] [] [2009-12-04 09:50:05] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
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Dataseries X:
2756.76
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45
1862.83
1905.41
1810.99
1670.07
1864.44
2052.02
2029.6
2070.83
2293.41
2443.27




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=63218&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=63218&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63218&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
alpha0.960596258085363
beta0.155180585289121
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.960596258085363 \tabularnewline
beta & 0.155180585289121 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63218&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]0.960596258085363[/C][/ROW]
[ROW][C]beta[/C][C]0.155180585289121[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63218&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63218&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
alpha0.960596258085363
beta0.155180585289121
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133295.322962.76559155129332.554408448710
143363.993392.98879678833-28.9987967883330
153494.173546.58680895763-52.4168089576297
163667.033722.78042621769-55.7504262176926
173813.063855.97632952237-42.9163295223652
183917.963947.54155853685-29.5815585368532
193895.513794.2083205011101.301679498902
203801.063854.59220615474-53.5322061547413
213570.123873.8904436771-303.770443677099
223701.613632.8712788352268.7387211647838
233862.273788.5754174266773.6945825733328
243970.13865.00887974193105.091120258073
254138.523998.12875106984140.391248930162
264199.754217.02339826659-17.2733982665886
274290.894391.40027088035-100.510270880351
284443.914533.88370146698-89.9737014669781
294502.644632.48542203175-129.845422031752
304356.984613.6483417335-256.668341733503
314591.274158.21487503664433.055124963359
324696.964491.69926816083205.260731839172
334621.44765.9242492627-144.524249262704
344562.844747.24615518697-184.406155186975
354202.524678.39475203288-475.874752032879
364296.494150.75837033177145.731629668234
374435.234255.07810908536180.151890914637
384105.184445.09564869543-339.91564869543
394116.684193.94661730321-77.2666173032057
403844.494241.83793067068-397.347930670677
413720.983867.54902688718-146.569026887182
423674.43653.1528287467221.2471712532843
433857.623402.43741968196455.182580318040
443801.063663.70342094598137.356579054023
453504.373746.06217649642-241.69217649642
463032.63487.58628066273-454.986280662727
473047.032954.2750807090492.7549192909573
482962.342912.9302198235149.4097801764929
492197.822832.39247361421-634.572473614209
502014.452011.172170360973.27782963902678
511862.831867.95929153018-5.12929153018263
521905.411721.00559015236184.404409847640
531810.991769.7858781369841.2041218630247
541670.071654.4828060271715.5871939728315
551864.441433.03442239943431.40557760057
562052.021674.65573155100377.364268448996
572029.61967.7010036355761.8989963644285
582070.832001.8054930077869.0245069922157
592293.412076.08781223182217.322187768176
602443.272274.38036988952168.889630110483

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3295.32 & 2962.76559155129 & 332.554408448710 \tabularnewline
14 & 3363.99 & 3392.98879678833 & -28.9987967883330 \tabularnewline
15 & 3494.17 & 3546.58680895763 & -52.4168089576297 \tabularnewline
16 & 3667.03 & 3722.78042621769 & -55.7504262176926 \tabularnewline
17 & 3813.06 & 3855.97632952237 & -42.9163295223652 \tabularnewline
18 & 3917.96 & 3947.54155853685 & -29.5815585368532 \tabularnewline
19 & 3895.51 & 3794.2083205011 & 101.301679498902 \tabularnewline
20 & 3801.06 & 3854.59220615474 & -53.5322061547413 \tabularnewline
21 & 3570.12 & 3873.8904436771 & -303.770443677099 \tabularnewline
22 & 3701.61 & 3632.87127883522 & 68.7387211647838 \tabularnewline
23 & 3862.27 & 3788.57541742667 & 73.6945825733328 \tabularnewline
24 & 3970.1 & 3865.00887974193 & 105.091120258073 \tabularnewline
25 & 4138.52 & 3998.12875106984 & 140.391248930162 \tabularnewline
26 & 4199.75 & 4217.02339826659 & -17.2733982665886 \tabularnewline
27 & 4290.89 & 4391.40027088035 & -100.510270880351 \tabularnewline
28 & 4443.91 & 4533.88370146698 & -89.9737014669781 \tabularnewline
29 & 4502.64 & 4632.48542203175 & -129.845422031752 \tabularnewline
30 & 4356.98 & 4613.6483417335 & -256.668341733503 \tabularnewline
31 & 4591.27 & 4158.21487503664 & 433.055124963359 \tabularnewline
32 & 4696.96 & 4491.69926816083 & 205.260731839172 \tabularnewline
33 & 4621.4 & 4765.9242492627 & -144.524249262704 \tabularnewline
34 & 4562.84 & 4747.24615518697 & -184.406155186975 \tabularnewline
35 & 4202.52 & 4678.39475203288 & -475.874752032879 \tabularnewline
36 & 4296.49 & 4150.75837033177 & 145.731629668234 \tabularnewline
37 & 4435.23 & 4255.07810908536 & 180.151890914637 \tabularnewline
38 & 4105.18 & 4445.09564869543 & -339.91564869543 \tabularnewline
39 & 4116.68 & 4193.94661730321 & -77.2666173032057 \tabularnewline
40 & 3844.49 & 4241.83793067068 & -397.347930670677 \tabularnewline
41 & 3720.98 & 3867.54902688718 & -146.569026887182 \tabularnewline
42 & 3674.4 & 3653.15282874672 & 21.2471712532843 \tabularnewline
43 & 3857.62 & 3402.43741968196 & 455.182580318040 \tabularnewline
44 & 3801.06 & 3663.70342094598 & 137.356579054023 \tabularnewline
45 & 3504.37 & 3746.06217649642 & -241.69217649642 \tabularnewline
46 & 3032.6 & 3487.58628066273 & -454.986280662727 \tabularnewline
47 & 3047.03 & 2954.27508070904 & 92.7549192909573 \tabularnewline
48 & 2962.34 & 2912.93021982351 & 49.4097801764929 \tabularnewline
49 & 2197.82 & 2832.39247361421 & -634.572473614209 \tabularnewline
50 & 2014.45 & 2011.17217036097 & 3.27782963902678 \tabularnewline
51 & 1862.83 & 1867.95929153018 & -5.12929153018263 \tabularnewline
52 & 1905.41 & 1721.00559015236 & 184.404409847640 \tabularnewline
53 & 1810.99 & 1769.78587813698 & 41.2041218630247 \tabularnewline
54 & 1670.07 & 1654.48280602717 & 15.5871939728315 \tabularnewline
55 & 1864.44 & 1433.03442239943 & 431.40557760057 \tabularnewline
56 & 2052.02 & 1674.65573155100 & 377.364268448996 \tabularnewline
57 & 2029.6 & 1967.70100363557 & 61.8989963644285 \tabularnewline
58 & 2070.83 & 2001.80549300778 & 69.0245069922157 \tabularnewline
59 & 2293.41 & 2076.08781223182 & 217.322187768176 \tabularnewline
60 & 2443.27 & 2274.38036988952 & 168.889630110483 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63218&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]3295.32[/C][C]2962.76559155129[/C][C]332.554408448710[/C][/ROW]
[ROW][C]14[/C][C]3363.99[/C][C]3392.98879678833[/C][C]-28.9987967883330[/C][/ROW]
[ROW][C]15[/C][C]3494.17[/C][C]3546.58680895763[/C][C]-52.4168089576297[/C][/ROW]
[ROW][C]16[/C][C]3667.03[/C][C]3722.78042621769[/C][C]-55.7504262176926[/C][/ROW]
[ROW][C]17[/C][C]3813.06[/C][C]3855.97632952237[/C][C]-42.9163295223652[/C][/ROW]
[ROW][C]18[/C][C]3917.96[/C][C]3947.54155853685[/C][C]-29.5815585368532[/C][/ROW]
[ROW][C]19[/C][C]3895.51[/C][C]3794.2083205011[/C][C]101.301679498902[/C][/ROW]
[ROW][C]20[/C][C]3801.06[/C][C]3854.59220615474[/C][C]-53.5322061547413[/C][/ROW]
[ROW][C]21[/C][C]3570.12[/C][C]3873.8904436771[/C][C]-303.770443677099[/C][/ROW]
[ROW][C]22[/C][C]3701.61[/C][C]3632.87127883522[/C][C]68.7387211647838[/C][/ROW]
[ROW][C]23[/C][C]3862.27[/C][C]3788.57541742667[/C][C]73.6945825733328[/C][/ROW]
[ROW][C]24[/C][C]3970.1[/C][C]3865.00887974193[/C][C]105.091120258073[/C][/ROW]
[ROW][C]25[/C][C]4138.52[/C][C]3998.12875106984[/C][C]140.391248930162[/C][/ROW]
[ROW][C]26[/C][C]4199.75[/C][C]4217.02339826659[/C][C]-17.2733982665886[/C][/ROW]
[ROW][C]27[/C][C]4290.89[/C][C]4391.40027088035[/C][C]-100.510270880351[/C][/ROW]
[ROW][C]28[/C][C]4443.91[/C][C]4533.88370146698[/C][C]-89.9737014669781[/C][/ROW]
[ROW][C]29[/C][C]4502.64[/C][C]4632.48542203175[/C][C]-129.845422031752[/C][/ROW]
[ROW][C]30[/C][C]4356.98[/C][C]4613.6483417335[/C][C]-256.668341733503[/C][/ROW]
[ROW][C]31[/C][C]4591.27[/C][C]4158.21487503664[/C][C]433.055124963359[/C][/ROW]
[ROW][C]32[/C][C]4696.96[/C][C]4491.69926816083[/C][C]205.260731839172[/C][/ROW]
[ROW][C]33[/C][C]4621.4[/C][C]4765.9242492627[/C][C]-144.524249262704[/C][/ROW]
[ROW][C]34[/C][C]4562.84[/C][C]4747.24615518697[/C][C]-184.406155186975[/C][/ROW]
[ROW][C]35[/C][C]4202.52[/C][C]4678.39475203288[/C][C]-475.874752032879[/C][/ROW]
[ROW][C]36[/C][C]4296.49[/C][C]4150.75837033177[/C][C]145.731629668234[/C][/ROW]
[ROW][C]37[/C][C]4435.23[/C][C]4255.07810908536[/C][C]180.151890914637[/C][/ROW]
[ROW][C]38[/C][C]4105.18[/C][C]4445.09564869543[/C][C]-339.91564869543[/C][/ROW]
[ROW][C]39[/C][C]4116.68[/C][C]4193.94661730321[/C][C]-77.2666173032057[/C][/ROW]
[ROW][C]40[/C][C]3844.49[/C][C]4241.83793067068[/C][C]-397.347930670677[/C][/ROW]
[ROW][C]41[/C][C]3720.98[/C][C]3867.54902688718[/C][C]-146.569026887182[/C][/ROW]
[ROW][C]42[/C][C]3674.4[/C][C]3653.15282874672[/C][C]21.2471712532843[/C][/ROW]
[ROW][C]43[/C][C]3857.62[/C][C]3402.43741968196[/C][C]455.182580318040[/C][/ROW]
[ROW][C]44[/C][C]3801.06[/C][C]3663.70342094598[/C][C]137.356579054023[/C][/ROW]
[ROW][C]45[/C][C]3504.37[/C][C]3746.06217649642[/C][C]-241.69217649642[/C][/ROW]
[ROW][C]46[/C][C]3032.6[/C][C]3487.58628066273[/C][C]-454.986280662727[/C][/ROW]
[ROW][C]47[/C][C]3047.03[/C][C]2954.27508070904[/C][C]92.7549192909573[/C][/ROW]
[ROW][C]48[/C][C]2962.34[/C][C]2912.93021982351[/C][C]49.4097801764929[/C][/ROW]
[ROW][C]49[/C][C]2197.82[/C][C]2832.39247361421[/C][C]-634.572473614209[/C][/ROW]
[ROW][C]50[/C][C]2014.45[/C][C]2011.17217036097[/C][C]3.27782963902678[/C][/ROW]
[ROW][C]51[/C][C]1862.83[/C][C]1867.95929153018[/C][C]-5.12929153018263[/C][/ROW]
[ROW][C]52[/C][C]1905.41[/C][C]1721.00559015236[/C][C]184.404409847640[/C][/ROW]
[ROW][C]53[/C][C]1810.99[/C][C]1769.78587813698[/C][C]41.2041218630247[/C][/ROW]
[ROW][C]54[/C][C]1670.07[/C][C]1654.48280602717[/C][C]15.5871939728315[/C][/ROW]
[ROW][C]55[/C][C]1864.44[/C][C]1433.03442239943[/C][C]431.40557760057[/C][/ROW]
[ROW][C]56[/C][C]2052.02[/C][C]1674.65573155100[/C][C]377.364268448996[/C][/ROW]
[ROW][C]57[/C][C]2029.6[/C][C]1967.70100363557[/C][C]61.8989963644285[/C][/ROW]
[ROW][C]58[/C][C]2070.83[/C][C]2001.80549300778[/C][C]69.0245069922157[/C][/ROW]
[ROW][C]59[/C][C]2293.41[/C][C]2076.08781223182[/C][C]217.322187768176[/C][/ROW]
[ROW][C]60[/C][C]2443.27[/C][C]2274.38036988952[/C][C]168.889630110483[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63218&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63218&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
133295.322962.76559155129332.554408448710
143363.993392.98879678833-28.9987967883330
153494.173546.58680895763-52.4168089576297
163667.033722.78042621769-55.7504262176926
173813.063855.97632952237-42.9163295223652
183917.963947.54155853685-29.5815585368532
193895.513794.2083205011101.301679498902
203801.063854.59220615474-53.5322061547413
213570.123873.8904436771-303.770443677099
223701.613632.8712788352268.7387211647838
233862.273788.5754174266773.6945825733328
243970.13865.00887974193105.091120258073
254138.523998.12875106984140.391248930162
264199.754217.02339826659-17.2733982665886
274290.894391.40027088035-100.510270880351
284443.914533.88370146698-89.9737014669781
294502.644632.48542203175-129.845422031752
304356.984613.6483417335-256.668341733503
314591.274158.21487503664433.055124963359
324696.964491.69926816083205.260731839172
334621.44765.9242492627-144.524249262704
344562.844747.24615518697-184.406155186975
354202.524678.39475203288-475.874752032879
364296.494150.75837033177145.731629668234
374435.234255.07810908536180.151890914637
384105.184445.09564869543-339.91564869543
394116.684193.94661730321-77.2666173032057
403844.494241.83793067068-397.347930670677
413720.983867.54902688718-146.569026887182
423674.43653.1528287467221.2471712532843
433857.623402.43741968196455.182580318040
443801.063663.70342094598137.356579054023
453504.373746.06217649642-241.69217649642
463032.63487.58628066273-454.986280662727
473047.032954.2750807090492.7549192909573
482962.342912.9302198235149.4097801764929
492197.822832.39247361421-634.572473614209
502014.452011.172170360973.27782963902678
511862.831867.95929153018-5.12929153018263
521905.411721.00559015236184.404409847640
531810.991769.7858781369841.2041218630247
541670.071654.4828060271715.5871939728315
551864.441433.03442239943431.40557760057
562052.021674.65573155100377.364268448996
572029.61967.7010036355761.8989963644285
582070.832001.8054930077869.0245069922157
592293.412076.08781223182217.322187768176
602443.272274.38036988952168.889630110483







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
612416.715703949951956.869696991562876.56171090834
622455.791793582731767.762600193103143.82098697235
632550.312728690581634.173441135233466.45201624593
642680.659770594811519.489779576183841.82976161344
652783.786122077901377.614315063054189.95792909274
662854.029881297761208.619073671764499.44068892377
672797.38145038882980.6607444459784614.10215633167
682716.01911918143749.0980261067814682.94021225608
692697.94865330974539.532987186934856.36431943255
702743.24951877555339.4586142706985147.0404232804
712826.65811423442134.0224409952865519.29378747356
722834.39557499779-47.75510127534025716.54625127091

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 2416.71570394995 & 1956.86969699156 & 2876.56171090834 \tabularnewline
62 & 2455.79179358273 & 1767.76260019310 & 3143.82098697235 \tabularnewline
63 & 2550.31272869058 & 1634.17344113523 & 3466.45201624593 \tabularnewline
64 & 2680.65977059481 & 1519.48977957618 & 3841.82976161344 \tabularnewline
65 & 2783.78612207790 & 1377.61431506305 & 4189.95792909274 \tabularnewline
66 & 2854.02988129776 & 1208.61907367176 & 4499.44068892377 \tabularnewline
67 & 2797.38145038882 & 980.660744445978 & 4614.10215633167 \tabularnewline
68 & 2716.01911918143 & 749.098026106781 & 4682.94021225608 \tabularnewline
69 & 2697.94865330974 & 539.53298718693 & 4856.36431943255 \tabularnewline
70 & 2743.24951877555 & 339.458614270698 & 5147.0404232804 \tabularnewline
71 & 2826.65811423442 & 134.022440995286 & 5519.29378747356 \tabularnewline
72 & 2834.39557499779 & -47.7551012753402 & 5716.54625127091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63218&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]2416.71570394995[/C][C]1956.86969699156[/C][C]2876.56171090834[/C][/ROW]
[ROW][C]62[/C][C]2455.79179358273[/C][C]1767.76260019310[/C][C]3143.82098697235[/C][/ROW]
[ROW][C]63[/C][C]2550.31272869058[/C][C]1634.17344113523[/C][C]3466.45201624593[/C][/ROW]
[ROW][C]64[/C][C]2680.65977059481[/C][C]1519.48977957618[/C][C]3841.82976161344[/C][/ROW]
[ROW][C]65[/C][C]2783.78612207790[/C][C]1377.61431506305[/C][C]4189.95792909274[/C][/ROW]
[ROW][C]66[/C][C]2854.02988129776[/C][C]1208.61907367176[/C][C]4499.44068892377[/C][/ROW]
[ROW][C]67[/C][C]2797.38145038882[/C][C]980.660744445978[/C][C]4614.10215633167[/C][/ROW]
[ROW][C]68[/C][C]2716.01911918143[/C][C]749.098026106781[/C][C]4682.94021225608[/C][/ROW]
[ROW][C]69[/C][C]2697.94865330974[/C][C]539.53298718693[/C][C]4856.36431943255[/C][/ROW]
[ROW][C]70[/C][C]2743.24951877555[/C][C]339.458614270698[/C][C]5147.0404232804[/C][/ROW]
[ROW][C]71[/C][C]2826.65811423442[/C][C]134.022440995286[/C][C]5519.29378747356[/C][/ROW]
[ROW][C]72[/C][C]2834.39557499779[/C][C]-47.7551012753402[/C][C]5716.54625127091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63218&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63218&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
612416.715703949951956.869696991562876.56171090834
622455.791793582731767.762600193103143.82098697235
632550.312728690581634.173441135233466.45201624593
642680.659770594811519.489779576183841.82976161344
652783.786122077901377.614315063054189.95792909274
662854.029881297761208.619073671764499.44068892377
672797.38145038882980.6607444459784614.10215633167
682716.01911918143749.0980261067814682.94021225608
692697.94865330974539.532987186934856.36431943255
702743.24951877555339.4586142706985147.0404232804
712826.65811423442134.0224409952865519.29378747356
722834.39557499779-47.75510127534025716.54625127091



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')