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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 computationWed, 21 Dec 2016 16:56:25 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482335859z37cq3dlq53kywa.htm/, Retrieved Tue, 07 May 2024 03:40:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302402, Retrieved Tue, 07 May 2024 03:40:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-21 15:56:25] [361c8dad91b3f1ef2e651cd04783c23b] [Current]
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Dataseries X:
5300
3800
3900
5400
6100
4200
4000
4600
7300
4400
4000
5300
9300
4300
3400
6000
6500
3400
2900
5000
5800
3000
2300
4000
5800
2900
2200
3900
5300
3000
2000
3700
6000
2800
1800
3900
5400
2400
1700
3500
5400
3900
2900
4600
5400
2900
2700
4500
6300
2800
1900
5100
6200
3500
3500
6000
6000
3400
2800
4900




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302402&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302402&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302402&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.199833300600293
beta0.980755202967504
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.199833300600293 \tabularnewline
beta & 0.980755202967504 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302402&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]0.199833300600293[/C][/ROW]
[ROW][C]beta[/C][C]0.980755202967504[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302402&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302402&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
alpha0.199833300600293
beta0.980755202967504
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3390023001600
454001433.313359824323966.68664017568
561001816.99071585064283.0092841494
642003103.296363063131096.70363693687
740003967.812294172432.1877058275982
846004625.91088280893-25.9108828089338
973005267.321228296352032.67877170365
1044006718.48606998644-2318.48606998644
1140006845.74887698623-2845.74887698623
1253006309.91566868444-1009.91566868444
1393005943.012172854283356.98782714572
1443007106.68923323716-2806.68923323716
1534006488.5822183689-3088.5822183689
1660005208.81993810719791.180061892809
1765004859.424801232111640.57519876789
1834005001.29941070493-1601.29941070493
1929004181.50476965108-1281.50476965108
2050003174.456768026071825.54323197393
2158003146.084167846672653.91583215333
2230003803.38245845338-803.382458453385
2323003612.34446131363-1312.34446131363
2440003062.39573246513937.604267534865
2558003145.820446881782654.17955311822
2629004092.46021233646-1192.46021233646
2722004036.70590259845-1836.70590259845
2839003492.2383615613407.761638438702
2953003476.206381551861823.79361844814
3030004100.5855875535-1100.5855875535
3120003924.87537252457-1924.87537252457
3237003207.19300216417492.806997835828
3360003069.22811545482930.7718845452
3428003992.84459798395-1192.84459798395
3518003858.64249895695-2058.64249895695
3639003147.9568494911752.043150508904
3754003146.330884336382253.66911566362
3824003886.47087895489-1486.47087895489
3917003587.87656908445-1887.87656908445
4035002839.06773313897660.932266861025
4154002729.130274708392670.86972529161
4239003544.30246452866355.697535471337
4329003966.53844246463-1066.53844246463
4446003895.53605513505704.463944864949
4554004316.505082353721083.49491764628
4629005025.56863347059-2125.56863347059
4727004676.76943601028-1976.76943601028
4845003970.28307603029529.716923969705
4963003868.494080020932431.50591997907
5028004623.29074247004-1823.29074247004
5119004170.49506021915-2270.49506021915
5251003183.344300582571916.65569941743
5362003408.566350716542791.43364928346
5435004355.68440579304-855.684405793043
5535004406.28333258772-906.283332587723
5660004269.150659518031730.84934048197
5760004998.229833059841001.77016694016
5834005777.9491889242-2377.9491889242
5928005416.23963693031-2616.23963693031
6049004494.16132341276405.838676587243

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3900 & 2300 & 1600 \tabularnewline
4 & 5400 & 1433.31335982432 & 3966.68664017568 \tabularnewline
5 & 6100 & 1816.9907158506 & 4283.0092841494 \tabularnewline
6 & 4200 & 3103.29636306313 & 1096.70363693687 \tabularnewline
7 & 4000 & 3967.8122941724 & 32.1877058275982 \tabularnewline
8 & 4600 & 4625.91088280893 & -25.9108828089338 \tabularnewline
9 & 7300 & 5267.32122829635 & 2032.67877170365 \tabularnewline
10 & 4400 & 6718.48606998644 & -2318.48606998644 \tabularnewline
11 & 4000 & 6845.74887698623 & -2845.74887698623 \tabularnewline
12 & 5300 & 6309.91566868444 & -1009.91566868444 \tabularnewline
13 & 9300 & 5943.01217285428 & 3356.98782714572 \tabularnewline
14 & 4300 & 7106.68923323716 & -2806.68923323716 \tabularnewline
15 & 3400 & 6488.5822183689 & -3088.5822183689 \tabularnewline
16 & 6000 & 5208.81993810719 & 791.180061892809 \tabularnewline
17 & 6500 & 4859.42480123211 & 1640.57519876789 \tabularnewline
18 & 3400 & 5001.29941070493 & -1601.29941070493 \tabularnewline
19 & 2900 & 4181.50476965108 & -1281.50476965108 \tabularnewline
20 & 5000 & 3174.45676802607 & 1825.54323197393 \tabularnewline
21 & 5800 & 3146.08416784667 & 2653.91583215333 \tabularnewline
22 & 3000 & 3803.38245845338 & -803.382458453385 \tabularnewline
23 & 2300 & 3612.34446131363 & -1312.34446131363 \tabularnewline
24 & 4000 & 3062.39573246513 & 937.604267534865 \tabularnewline
25 & 5800 & 3145.82044688178 & 2654.17955311822 \tabularnewline
26 & 2900 & 4092.46021233646 & -1192.46021233646 \tabularnewline
27 & 2200 & 4036.70590259845 & -1836.70590259845 \tabularnewline
28 & 3900 & 3492.2383615613 & 407.761638438702 \tabularnewline
29 & 5300 & 3476.20638155186 & 1823.79361844814 \tabularnewline
30 & 3000 & 4100.5855875535 & -1100.5855875535 \tabularnewline
31 & 2000 & 3924.87537252457 & -1924.87537252457 \tabularnewline
32 & 3700 & 3207.19300216417 & 492.806997835828 \tabularnewline
33 & 6000 & 3069.2281154548 & 2930.7718845452 \tabularnewline
34 & 2800 & 3992.84459798395 & -1192.84459798395 \tabularnewline
35 & 1800 & 3858.64249895695 & -2058.64249895695 \tabularnewline
36 & 3900 & 3147.9568494911 & 752.043150508904 \tabularnewline
37 & 5400 & 3146.33088433638 & 2253.66911566362 \tabularnewline
38 & 2400 & 3886.47087895489 & -1486.47087895489 \tabularnewline
39 & 1700 & 3587.87656908445 & -1887.87656908445 \tabularnewline
40 & 3500 & 2839.06773313897 & 660.932266861025 \tabularnewline
41 & 5400 & 2729.13027470839 & 2670.86972529161 \tabularnewline
42 & 3900 & 3544.30246452866 & 355.697535471337 \tabularnewline
43 & 2900 & 3966.53844246463 & -1066.53844246463 \tabularnewline
44 & 4600 & 3895.53605513505 & 704.463944864949 \tabularnewline
45 & 5400 & 4316.50508235372 & 1083.49491764628 \tabularnewline
46 & 2900 & 5025.56863347059 & -2125.56863347059 \tabularnewline
47 & 2700 & 4676.76943601028 & -1976.76943601028 \tabularnewline
48 & 4500 & 3970.28307603029 & 529.716923969705 \tabularnewline
49 & 6300 & 3868.49408002093 & 2431.50591997907 \tabularnewline
50 & 2800 & 4623.29074247004 & -1823.29074247004 \tabularnewline
51 & 1900 & 4170.49506021915 & -2270.49506021915 \tabularnewline
52 & 5100 & 3183.34430058257 & 1916.65569941743 \tabularnewline
53 & 6200 & 3408.56635071654 & 2791.43364928346 \tabularnewline
54 & 3500 & 4355.68440579304 & -855.684405793043 \tabularnewline
55 & 3500 & 4406.28333258772 & -906.283332587723 \tabularnewline
56 & 6000 & 4269.15065951803 & 1730.84934048197 \tabularnewline
57 & 6000 & 4998.22983305984 & 1001.77016694016 \tabularnewline
58 & 3400 & 5777.9491889242 & -2377.9491889242 \tabularnewline
59 & 2800 & 5416.23963693031 & -2616.23963693031 \tabularnewline
60 & 4900 & 4494.16132341276 & 405.838676587243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302402&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]3900[/C][C]2300[/C][C]1600[/C][/ROW]
[ROW][C]4[/C][C]5400[/C][C]1433.31335982432[/C][C]3966.68664017568[/C][/ROW]
[ROW][C]5[/C][C]6100[/C][C]1816.9907158506[/C][C]4283.0092841494[/C][/ROW]
[ROW][C]6[/C][C]4200[/C][C]3103.29636306313[/C][C]1096.70363693687[/C][/ROW]
[ROW][C]7[/C][C]4000[/C][C]3967.8122941724[/C][C]32.1877058275982[/C][/ROW]
[ROW][C]8[/C][C]4600[/C][C]4625.91088280893[/C][C]-25.9108828089338[/C][/ROW]
[ROW][C]9[/C][C]7300[/C][C]5267.32122829635[/C][C]2032.67877170365[/C][/ROW]
[ROW][C]10[/C][C]4400[/C][C]6718.48606998644[/C][C]-2318.48606998644[/C][/ROW]
[ROW][C]11[/C][C]4000[/C][C]6845.74887698623[/C][C]-2845.74887698623[/C][/ROW]
[ROW][C]12[/C][C]5300[/C][C]6309.91566868444[/C][C]-1009.91566868444[/C][/ROW]
[ROW][C]13[/C][C]9300[/C][C]5943.01217285428[/C][C]3356.98782714572[/C][/ROW]
[ROW][C]14[/C][C]4300[/C][C]7106.68923323716[/C][C]-2806.68923323716[/C][/ROW]
[ROW][C]15[/C][C]3400[/C][C]6488.5822183689[/C][C]-3088.5822183689[/C][/ROW]
[ROW][C]16[/C][C]6000[/C][C]5208.81993810719[/C][C]791.180061892809[/C][/ROW]
[ROW][C]17[/C][C]6500[/C][C]4859.42480123211[/C][C]1640.57519876789[/C][/ROW]
[ROW][C]18[/C][C]3400[/C][C]5001.29941070493[/C][C]-1601.29941070493[/C][/ROW]
[ROW][C]19[/C][C]2900[/C][C]4181.50476965108[/C][C]-1281.50476965108[/C][/ROW]
[ROW][C]20[/C][C]5000[/C][C]3174.45676802607[/C][C]1825.54323197393[/C][/ROW]
[ROW][C]21[/C][C]5800[/C][C]3146.08416784667[/C][C]2653.91583215333[/C][/ROW]
[ROW][C]22[/C][C]3000[/C][C]3803.38245845338[/C][C]-803.382458453385[/C][/ROW]
[ROW][C]23[/C][C]2300[/C][C]3612.34446131363[/C][C]-1312.34446131363[/C][/ROW]
[ROW][C]24[/C][C]4000[/C][C]3062.39573246513[/C][C]937.604267534865[/C][/ROW]
[ROW][C]25[/C][C]5800[/C][C]3145.82044688178[/C][C]2654.17955311822[/C][/ROW]
[ROW][C]26[/C][C]2900[/C][C]4092.46021233646[/C][C]-1192.46021233646[/C][/ROW]
[ROW][C]27[/C][C]2200[/C][C]4036.70590259845[/C][C]-1836.70590259845[/C][/ROW]
[ROW][C]28[/C][C]3900[/C][C]3492.2383615613[/C][C]407.761638438702[/C][/ROW]
[ROW][C]29[/C][C]5300[/C][C]3476.20638155186[/C][C]1823.79361844814[/C][/ROW]
[ROW][C]30[/C][C]3000[/C][C]4100.5855875535[/C][C]-1100.5855875535[/C][/ROW]
[ROW][C]31[/C][C]2000[/C][C]3924.87537252457[/C][C]-1924.87537252457[/C][/ROW]
[ROW][C]32[/C][C]3700[/C][C]3207.19300216417[/C][C]492.806997835828[/C][/ROW]
[ROW][C]33[/C][C]6000[/C][C]3069.2281154548[/C][C]2930.7718845452[/C][/ROW]
[ROW][C]34[/C][C]2800[/C][C]3992.84459798395[/C][C]-1192.84459798395[/C][/ROW]
[ROW][C]35[/C][C]1800[/C][C]3858.64249895695[/C][C]-2058.64249895695[/C][/ROW]
[ROW][C]36[/C][C]3900[/C][C]3147.9568494911[/C][C]752.043150508904[/C][/ROW]
[ROW][C]37[/C][C]5400[/C][C]3146.33088433638[/C][C]2253.66911566362[/C][/ROW]
[ROW][C]38[/C][C]2400[/C][C]3886.47087895489[/C][C]-1486.47087895489[/C][/ROW]
[ROW][C]39[/C][C]1700[/C][C]3587.87656908445[/C][C]-1887.87656908445[/C][/ROW]
[ROW][C]40[/C][C]3500[/C][C]2839.06773313897[/C][C]660.932266861025[/C][/ROW]
[ROW][C]41[/C][C]5400[/C][C]2729.13027470839[/C][C]2670.86972529161[/C][/ROW]
[ROW][C]42[/C][C]3900[/C][C]3544.30246452866[/C][C]355.697535471337[/C][/ROW]
[ROW][C]43[/C][C]2900[/C][C]3966.53844246463[/C][C]-1066.53844246463[/C][/ROW]
[ROW][C]44[/C][C]4600[/C][C]3895.53605513505[/C][C]704.463944864949[/C][/ROW]
[ROW][C]45[/C][C]5400[/C][C]4316.50508235372[/C][C]1083.49491764628[/C][/ROW]
[ROW][C]46[/C][C]2900[/C][C]5025.56863347059[/C][C]-2125.56863347059[/C][/ROW]
[ROW][C]47[/C][C]2700[/C][C]4676.76943601028[/C][C]-1976.76943601028[/C][/ROW]
[ROW][C]48[/C][C]4500[/C][C]3970.28307603029[/C][C]529.716923969705[/C][/ROW]
[ROW][C]49[/C][C]6300[/C][C]3868.49408002093[/C][C]2431.50591997907[/C][/ROW]
[ROW][C]50[/C][C]2800[/C][C]4623.29074247004[/C][C]-1823.29074247004[/C][/ROW]
[ROW][C]51[/C][C]1900[/C][C]4170.49506021915[/C][C]-2270.49506021915[/C][/ROW]
[ROW][C]52[/C][C]5100[/C][C]3183.34430058257[/C][C]1916.65569941743[/C][/ROW]
[ROW][C]53[/C][C]6200[/C][C]3408.56635071654[/C][C]2791.43364928346[/C][/ROW]
[ROW][C]54[/C][C]3500[/C][C]4355.68440579304[/C][C]-855.684405793043[/C][/ROW]
[ROW][C]55[/C][C]3500[/C][C]4406.28333258772[/C][C]-906.283332587723[/C][/ROW]
[ROW][C]56[/C][C]6000[/C][C]4269.15065951803[/C][C]1730.84934048197[/C][/ROW]
[ROW][C]57[/C][C]6000[/C][C]4998.22983305984[/C][C]1001.77016694016[/C][/ROW]
[ROW][C]58[/C][C]3400[/C][C]5777.9491889242[/C][C]-2377.9491889242[/C][/ROW]
[ROW][C]59[/C][C]2800[/C][C]5416.23963693031[/C][C]-2616.23963693031[/C][/ROW]
[ROW][C]60[/C][C]4900[/C][C]4494.16132341276[/C][C]405.838676587243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302402&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302402&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
3390023001600
454001433.313359824323966.68664017568
561001816.99071585064283.0092841494
642003103.296363063131096.70363693687
740003967.812294172432.1877058275982
846004625.91088280893-25.9108828089338
973005267.321228296352032.67877170365
1044006718.48606998644-2318.48606998644
1140006845.74887698623-2845.74887698623
1253006309.91566868444-1009.91566868444
1393005943.012172854283356.98782714572
1443007106.68923323716-2806.68923323716
1534006488.5822183689-3088.5822183689
1660005208.81993810719791.180061892809
1765004859.424801232111640.57519876789
1834005001.29941070493-1601.29941070493
1929004181.50476965108-1281.50476965108
2050003174.456768026071825.54323197393
2158003146.084167846672653.91583215333
2230003803.38245845338-803.382458453385
2323003612.34446131363-1312.34446131363
2440003062.39573246513937.604267534865
2558003145.820446881782654.17955311822
2629004092.46021233646-1192.46021233646
2722004036.70590259845-1836.70590259845
2839003492.2383615613407.761638438702
2953003476.206381551861823.79361844814
3030004100.5855875535-1100.5855875535
3120003924.87537252457-1924.87537252457
3237003207.19300216417492.806997835828
3360003069.22811545482930.7718845452
3428003992.84459798395-1192.84459798395
3518003858.64249895695-2058.64249895695
3639003147.9568494911752.043150508904
3754003146.330884336382253.66911566362
3824003886.47087895489-1486.47087895489
3917003587.87656908445-1887.87656908445
4035002839.06773313897660.932266861025
4154002729.130274708392670.86972529161
4239003544.30246452866355.697535471337
4329003966.53844246463-1066.53844246463
4446003895.53605513505704.463944864949
4554004316.505082353721083.49491764628
4629005025.56863347059-2125.56863347059
4727004676.76943601028-1976.76943601028
4845003970.28307603029529.716923969705
4963003868.494080020932431.50591997907
5028004623.29074247004-1823.29074247004
5119004170.49506021915-2270.49506021915
5251003183.344300582571916.65569941743
5362003408.566350716542791.43364928346
5435004355.68440579304-855.684405793043
5535004406.28333258772-906.283332587723
5660004269.150659518031730.84934048197
5760004998.229833059841001.77016694016
5834005777.9491889242-2377.9491889242
5928005416.23963693031-2616.23963693031
6049004494.16132341276405.838676587243







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
614255.53422158937447.9201781848088063.14826499394
623935.8070375123-159.2356562510368030.84973127564
633616.07985343524-1058.006896635928290.16660350639
643296.35266935817-2257.459047811618850.16438652795
652976.6254852811-3722.355827380659675.60679794285
662656.89830120403-5408.7962191674110722.5928215755
672337.17111712696-7280.3036050311311954.6458392851
682017.4439330499-9310.0133928239813344.9012589238
691697.71674897283-11478.610487639214874.0439855848
701377.98956489576-13772.010864068616527.9899938601
711058.26238081869-16179.654928398418296.1796900358
72738.535196741624-18693.376777316520170.4471707998

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 4255.53422158937 & 447.920178184808 & 8063.14826499394 \tabularnewline
62 & 3935.8070375123 & -159.235656251036 & 8030.84973127564 \tabularnewline
63 & 3616.07985343524 & -1058.00689663592 & 8290.16660350639 \tabularnewline
64 & 3296.35266935817 & -2257.45904781161 & 8850.16438652795 \tabularnewline
65 & 2976.6254852811 & -3722.35582738065 & 9675.60679794285 \tabularnewline
66 & 2656.89830120403 & -5408.79621916741 & 10722.5928215755 \tabularnewline
67 & 2337.17111712696 & -7280.30360503113 & 11954.6458392851 \tabularnewline
68 & 2017.4439330499 & -9310.01339282398 & 13344.9012589238 \tabularnewline
69 & 1697.71674897283 & -11478.6104876392 & 14874.0439855848 \tabularnewline
70 & 1377.98956489576 & -13772.0108640686 & 16527.9899938601 \tabularnewline
71 & 1058.26238081869 & -16179.6549283984 & 18296.1796900358 \tabularnewline
72 & 738.535196741624 & -18693.3767773165 & 20170.4471707998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302402&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]4255.53422158937[/C][C]447.920178184808[/C][C]8063.14826499394[/C][/ROW]
[ROW][C]62[/C][C]3935.8070375123[/C][C]-159.235656251036[/C][C]8030.84973127564[/C][/ROW]
[ROW][C]63[/C][C]3616.07985343524[/C][C]-1058.00689663592[/C][C]8290.16660350639[/C][/ROW]
[ROW][C]64[/C][C]3296.35266935817[/C][C]-2257.45904781161[/C][C]8850.16438652795[/C][/ROW]
[ROW][C]65[/C][C]2976.6254852811[/C][C]-3722.35582738065[/C][C]9675.60679794285[/C][/ROW]
[ROW][C]66[/C][C]2656.89830120403[/C][C]-5408.79621916741[/C][C]10722.5928215755[/C][/ROW]
[ROW][C]67[/C][C]2337.17111712696[/C][C]-7280.30360503113[/C][C]11954.6458392851[/C][/ROW]
[ROW][C]68[/C][C]2017.4439330499[/C][C]-9310.01339282398[/C][C]13344.9012589238[/C][/ROW]
[ROW][C]69[/C][C]1697.71674897283[/C][C]-11478.6104876392[/C][C]14874.0439855848[/C][/ROW]
[ROW][C]70[/C][C]1377.98956489576[/C][C]-13772.0108640686[/C][C]16527.9899938601[/C][/ROW]
[ROW][C]71[/C][C]1058.26238081869[/C][C]-16179.6549283984[/C][C]18296.1796900358[/C][/ROW]
[ROW][C]72[/C][C]738.535196741624[/C][C]-18693.3767773165[/C][C]20170.4471707998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302402&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302402&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
614255.53422158937447.9201781848088063.14826499394
623935.8070375123-159.2356562510368030.84973127564
633616.07985343524-1058.006896635928290.16660350639
643296.35266935817-2257.459047811618850.16438652795
652976.6254852811-3722.355827380659675.60679794285
662656.89830120403-5408.7962191674110722.5928215755
672337.17111712696-7280.3036050311311954.6458392851
682017.4439330499-9310.0133928239813344.9012589238
691697.71674897283-11478.610487639214874.0439855848
701377.98956489576-13772.010864068616527.9899938601
711058.26238081869-16179.654928398418296.1796900358
72738.535196741624-18693.376777316520170.4471707998



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 4 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Double'
par1 <- '4'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')