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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 03:23:27 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211793899wbidkn7k50y6jqc.htm/, Retrieved Tue, 14 May 2024 02:40:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13254, Retrieved Tue, 14 May 2024 02:40:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact209
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exp smoothing eig...] [2008-05-26 09:23:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3722.7
3707.1
3697.4
3691.4
3679.4
3660.6
3647.5
3639
3623.5
3612.2
3604.2
3596.9
3603.9
3606.9
3607.7
3611.4
3611.9
3618.4
3629.5
3640.6
3646.8
3647.3
3649.5
3649.7
3652.5
3665.8
3674.3
3705.8
3735.8
3735.4
3747.7
3765.5
3779.7
3795.5
3813.1
3826.9
3833.3
3844.8
3851.3
3851.8
3854.1
3858.4
3861.6
3856.3
3855.8
3860.4
3855.1
3839.5
3833
3833.6
3826.8
3818.2
3811.4
3806.8
3810.3
3818.2
3858.7
3868.7
3872.6
3872.4
3876.4
3883.2
3883.4
3881.8
3887.1
3893.3
3902.8
3914.7
3929.8
3947.3
3971.8
3991.3
3993
3997.2
4016.2
4041.7
4060.5
4076.7
4102.7
4125.8
4140.1
4146.7
4157.9
4154.7
4145.3
4149
4142.4
4141
4146.1
4147.6
4142.7
4148.1
4159
4167
4178.5
4192.5
4209.2
4223.7
4231.6
4236.9
4253
4270.5
4285.7
4302.8
4321.5
4340.3
4356.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 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 & 9 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13254&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]9 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=13254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13254&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 time9 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13254&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]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13254&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23707.13722.7-15.5999999999999
33697.43707.1-9.69999999999982
43691.43697.4-6
53679.43691.4-12
63660.63679.4-18.8000000000002
73647.53660.6-13.0999999999999
836393647.5-8.5
93623.53639-15.5
103612.23623.5-11.3000000000002
113604.23612.2-8
123596.93604.2-7.29999999999973
133603.93596.97
143606.93603.93
153607.73606.90.799999999999727
163611.43607.73.70000000000027
173611.93611.40.5
183618.43611.96.5
193629.53618.411.0999999999999
203640.63629.511.0999999999999
213646.83640.66.20000000000027
223647.33646.80.5
233649.53647.32.19999999999982
243649.73649.50.199999999999818
253652.53649.72.80000000000018
263665.83652.513.3000000000002
273674.33665.88.5
283705.83674.331.5
293735.83705.830
303735.43735.8-0.400000000000091
313747.73735.412.2999999999997
323765.53747.717.8000000000002
333779.73765.514.1999999999998
343795.53779.715.8000000000002
353813.13795.517.5999999999999
363826.93813.113.8000000000002
373833.33826.96.40000000000009
383844.83833.311.5
393851.33844.86.5
403851.83851.30.5
413854.13851.82.29999999999973
423858.43854.14.30000000000018
433861.63858.43.19999999999982
443856.33861.6-5.29999999999973
453855.83856.3-0.5
463860.43855.84.59999999999991
473855.13860.4-5.30000000000018
483839.53855.1-15.5999999999999
4938333839.5-6.5
503833.638330.599999999999909
513826.83833.6-6.79999999999973
523818.23826.8-8.60000000000036
533811.43818.2-6.79999999999973
543806.83811.4-4.59999999999991
553810.33806.83.5
563818.23810.37.89999999999964
573858.73818.240.5
583868.73858.710
593872.63868.73.90000000000009
603872.43872.6-0.199999999999818
613876.43872.44
623883.23876.46.79999999999973
633883.43883.20.200000000000273
643881.83883.4-1.59999999999991
653887.13881.85.29999999999973
663893.33887.16.20000000000027
673902.83893.39.5
683914.73902.811.8999999999996
693929.83914.715.1000000000004
703947.33929.817.5
713971.83947.324.5
723991.33971.819.5
7339933991.31.69999999999982
743997.239934.19999999999982
754016.23997.219
764041.74016.225.5
774060.54041.718.8000000000002
784076.74060.516.1999999999998
794102.74076.726
804125.84102.723.1000000000004
814140.14125.814.3000000000002
824146.74140.16.59999999999945
834157.94146.711.1999999999998
844154.74157.9-3.19999999999982
854145.34154.7-9.39999999999964
8641494145.33.69999999999982
874142.44149-6.60000000000036
8841414142.4-1.39999999999964
894146.141415.10000000000036
904147.64146.11.5
914142.74147.6-4.90000000000055
924148.14142.75.40000000000055
9341594148.110.8999999999996
94416741598
954178.5416711.5
964192.54178.514
974209.24192.516.6999999999998
984223.74209.214.5
994231.64223.77.90000000000055
1004236.94231.65.29999999999927
10142534236.916.1000000000004
1024270.5425317.5
1034285.74270.515.1999999999998
1044302.84285.717.1000000000004
1054321.54302.818.6999999999998
1064340.34321.518.8000000000002
1074356.54340.316.1999999999998

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3707.1 & 3722.7 & -15.5999999999999 \tabularnewline
3 & 3697.4 & 3707.1 & -9.69999999999982 \tabularnewline
4 & 3691.4 & 3697.4 & -6 \tabularnewline
5 & 3679.4 & 3691.4 & -12 \tabularnewline
6 & 3660.6 & 3679.4 & -18.8000000000002 \tabularnewline
7 & 3647.5 & 3660.6 & -13.0999999999999 \tabularnewline
8 & 3639 & 3647.5 & -8.5 \tabularnewline
9 & 3623.5 & 3639 & -15.5 \tabularnewline
10 & 3612.2 & 3623.5 & -11.3000000000002 \tabularnewline
11 & 3604.2 & 3612.2 & -8 \tabularnewline
12 & 3596.9 & 3604.2 & -7.29999999999973 \tabularnewline
13 & 3603.9 & 3596.9 & 7 \tabularnewline
14 & 3606.9 & 3603.9 & 3 \tabularnewline
15 & 3607.7 & 3606.9 & 0.799999999999727 \tabularnewline
16 & 3611.4 & 3607.7 & 3.70000000000027 \tabularnewline
17 & 3611.9 & 3611.4 & 0.5 \tabularnewline
18 & 3618.4 & 3611.9 & 6.5 \tabularnewline
19 & 3629.5 & 3618.4 & 11.0999999999999 \tabularnewline
20 & 3640.6 & 3629.5 & 11.0999999999999 \tabularnewline
21 & 3646.8 & 3640.6 & 6.20000000000027 \tabularnewline
22 & 3647.3 & 3646.8 & 0.5 \tabularnewline
23 & 3649.5 & 3647.3 & 2.19999999999982 \tabularnewline
24 & 3649.7 & 3649.5 & 0.199999999999818 \tabularnewline
25 & 3652.5 & 3649.7 & 2.80000000000018 \tabularnewline
26 & 3665.8 & 3652.5 & 13.3000000000002 \tabularnewline
27 & 3674.3 & 3665.8 & 8.5 \tabularnewline
28 & 3705.8 & 3674.3 & 31.5 \tabularnewline
29 & 3735.8 & 3705.8 & 30 \tabularnewline
30 & 3735.4 & 3735.8 & -0.400000000000091 \tabularnewline
31 & 3747.7 & 3735.4 & 12.2999999999997 \tabularnewline
32 & 3765.5 & 3747.7 & 17.8000000000002 \tabularnewline
33 & 3779.7 & 3765.5 & 14.1999999999998 \tabularnewline
34 & 3795.5 & 3779.7 & 15.8000000000002 \tabularnewline
35 & 3813.1 & 3795.5 & 17.5999999999999 \tabularnewline
36 & 3826.9 & 3813.1 & 13.8000000000002 \tabularnewline
37 & 3833.3 & 3826.9 & 6.40000000000009 \tabularnewline
38 & 3844.8 & 3833.3 & 11.5 \tabularnewline
39 & 3851.3 & 3844.8 & 6.5 \tabularnewline
40 & 3851.8 & 3851.3 & 0.5 \tabularnewline
41 & 3854.1 & 3851.8 & 2.29999999999973 \tabularnewline
42 & 3858.4 & 3854.1 & 4.30000000000018 \tabularnewline
43 & 3861.6 & 3858.4 & 3.19999999999982 \tabularnewline
44 & 3856.3 & 3861.6 & -5.29999999999973 \tabularnewline
45 & 3855.8 & 3856.3 & -0.5 \tabularnewline
46 & 3860.4 & 3855.8 & 4.59999999999991 \tabularnewline
47 & 3855.1 & 3860.4 & -5.30000000000018 \tabularnewline
48 & 3839.5 & 3855.1 & -15.5999999999999 \tabularnewline
49 & 3833 & 3839.5 & -6.5 \tabularnewline
50 & 3833.6 & 3833 & 0.599999999999909 \tabularnewline
51 & 3826.8 & 3833.6 & -6.79999999999973 \tabularnewline
52 & 3818.2 & 3826.8 & -8.60000000000036 \tabularnewline
53 & 3811.4 & 3818.2 & -6.79999999999973 \tabularnewline
54 & 3806.8 & 3811.4 & -4.59999999999991 \tabularnewline
55 & 3810.3 & 3806.8 & 3.5 \tabularnewline
56 & 3818.2 & 3810.3 & 7.89999999999964 \tabularnewline
57 & 3858.7 & 3818.2 & 40.5 \tabularnewline
58 & 3868.7 & 3858.7 & 10 \tabularnewline
59 & 3872.6 & 3868.7 & 3.90000000000009 \tabularnewline
60 & 3872.4 & 3872.6 & -0.199999999999818 \tabularnewline
61 & 3876.4 & 3872.4 & 4 \tabularnewline
62 & 3883.2 & 3876.4 & 6.79999999999973 \tabularnewline
63 & 3883.4 & 3883.2 & 0.200000000000273 \tabularnewline
64 & 3881.8 & 3883.4 & -1.59999999999991 \tabularnewline
65 & 3887.1 & 3881.8 & 5.29999999999973 \tabularnewline
66 & 3893.3 & 3887.1 & 6.20000000000027 \tabularnewline
67 & 3902.8 & 3893.3 & 9.5 \tabularnewline
68 & 3914.7 & 3902.8 & 11.8999999999996 \tabularnewline
69 & 3929.8 & 3914.7 & 15.1000000000004 \tabularnewline
70 & 3947.3 & 3929.8 & 17.5 \tabularnewline
71 & 3971.8 & 3947.3 & 24.5 \tabularnewline
72 & 3991.3 & 3971.8 & 19.5 \tabularnewline
73 & 3993 & 3991.3 & 1.69999999999982 \tabularnewline
74 & 3997.2 & 3993 & 4.19999999999982 \tabularnewline
75 & 4016.2 & 3997.2 & 19 \tabularnewline
76 & 4041.7 & 4016.2 & 25.5 \tabularnewline
77 & 4060.5 & 4041.7 & 18.8000000000002 \tabularnewline
78 & 4076.7 & 4060.5 & 16.1999999999998 \tabularnewline
79 & 4102.7 & 4076.7 & 26 \tabularnewline
80 & 4125.8 & 4102.7 & 23.1000000000004 \tabularnewline
81 & 4140.1 & 4125.8 & 14.3000000000002 \tabularnewline
82 & 4146.7 & 4140.1 & 6.59999999999945 \tabularnewline
83 & 4157.9 & 4146.7 & 11.1999999999998 \tabularnewline
84 & 4154.7 & 4157.9 & -3.19999999999982 \tabularnewline
85 & 4145.3 & 4154.7 & -9.39999999999964 \tabularnewline
86 & 4149 & 4145.3 & 3.69999999999982 \tabularnewline
87 & 4142.4 & 4149 & -6.60000000000036 \tabularnewline
88 & 4141 & 4142.4 & -1.39999999999964 \tabularnewline
89 & 4146.1 & 4141 & 5.10000000000036 \tabularnewline
90 & 4147.6 & 4146.1 & 1.5 \tabularnewline
91 & 4142.7 & 4147.6 & -4.90000000000055 \tabularnewline
92 & 4148.1 & 4142.7 & 5.40000000000055 \tabularnewline
93 & 4159 & 4148.1 & 10.8999999999996 \tabularnewline
94 & 4167 & 4159 & 8 \tabularnewline
95 & 4178.5 & 4167 & 11.5 \tabularnewline
96 & 4192.5 & 4178.5 & 14 \tabularnewline
97 & 4209.2 & 4192.5 & 16.6999999999998 \tabularnewline
98 & 4223.7 & 4209.2 & 14.5 \tabularnewline
99 & 4231.6 & 4223.7 & 7.90000000000055 \tabularnewline
100 & 4236.9 & 4231.6 & 5.29999999999927 \tabularnewline
101 & 4253 & 4236.9 & 16.1000000000004 \tabularnewline
102 & 4270.5 & 4253 & 17.5 \tabularnewline
103 & 4285.7 & 4270.5 & 15.1999999999998 \tabularnewline
104 & 4302.8 & 4285.7 & 17.1000000000004 \tabularnewline
105 & 4321.5 & 4302.8 & 18.6999999999998 \tabularnewline
106 & 4340.3 & 4321.5 & 18.8000000000002 \tabularnewline
107 & 4356.5 & 4340.3 & 16.1999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13254&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]2[/C][C]3707.1[/C][C]3722.7[/C][C]-15.5999999999999[/C][/ROW]
[ROW][C]3[/C][C]3697.4[/C][C]3707.1[/C][C]-9.69999999999982[/C][/ROW]
[ROW][C]4[/C][C]3691.4[/C][C]3697.4[/C][C]-6[/C][/ROW]
[ROW][C]5[/C][C]3679.4[/C][C]3691.4[/C][C]-12[/C][/ROW]
[ROW][C]6[/C][C]3660.6[/C][C]3679.4[/C][C]-18.8000000000002[/C][/ROW]
[ROW][C]7[/C][C]3647.5[/C][C]3660.6[/C][C]-13.0999999999999[/C][/ROW]
[ROW][C]8[/C][C]3639[/C][C]3647.5[/C][C]-8.5[/C][/ROW]
[ROW][C]9[/C][C]3623.5[/C][C]3639[/C][C]-15.5[/C][/ROW]
[ROW][C]10[/C][C]3612.2[/C][C]3623.5[/C][C]-11.3000000000002[/C][/ROW]
[ROW][C]11[/C][C]3604.2[/C][C]3612.2[/C][C]-8[/C][/ROW]
[ROW][C]12[/C][C]3596.9[/C][C]3604.2[/C][C]-7.29999999999973[/C][/ROW]
[ROW][C]13[/C][C]3603.9[/C][C]3596.9[/C][C]7[/C][/ROW]
[ROW][C]14[/C][C]3606.9[/C][C]3603.9[/C][C]3[/C][/ROW]
[ROW][C]15[/C][C]3607.7[/C][C]3606.9[/C][C]0.799999999999727[/C][/ROW]
[ROW][C]16[/C][C]3611.4[/C][C]3607.7[/C][C]3.70000000000027[/C][/ROW]
[ROW][C]17[/C][C]3611.9[/C][C]3611.4[/C][C]0.5[/C][/ROW]
[ROW][C]18[/C][C]3618.4[/C][C]3611.9[/C][C]6.5[/C][/ROW]
[ROW][C]19[/C][C]3629.5[/C][C]3618.4[/C][C]11.0999999999999[/C][/ROW]
[ROW][C]20[/C][C]3640.6[/C][C]3629.5[/C][C]11.0999999999999[/C][/ROW]
[ROW][C]21[/C][C]3646.8[/C][C]3640.6[/C][C]6.20000000000027[/C][/ROW]
[ROW][C]22[/C][C]3647.3[/C][C]3646.8[/C][C]0.5[/C][/ROW]
[ROW][C]23[/C][C]3649.5[/C][C]3647.3[/C][C]2.19999999999982[/C][/ROW]
[ROW][C]24[/C][C]3649.7[/C][C]3649.5[/C][C]0.199999999999818[/C][/ROW]
[ROW][C]25[/C][C]3652.5[/C][C]3649.7[/C][C]2.80000000000018[/C][/ROW]
[ROW][C]26[/C][C]3665.8[/C][C]3652.5[/C][C]13.3000000000002[/C][/ROW]
[ROW][C]27[/C][C]3674.3[/C][C]3665.8[/C][C]8.5[/C][/ROW]
[ROW][C]28[/C][C]3705.8[/C][C]3674.3[/C][C]31.5[/C][/ROW]
[ROW][C]29[/C][C]3735.8[/C][C]3705.8[/C][C]30[/C][/ROW]
[ROW][C]30[/C][C]3735.4[/C][C]3735.8[/C][C]-0.400000000000091[/C][/ROW]
[ROW][C]31[/C][C]3747.7[/C][C]3735.4[/C][C]12.2999999999997[/C][/ROW]
[ROW][C]32[/C][C]3765.5[/C][C]3747.7[/C][C]17.8000000000002[/C][/ROW]
[ROW][C]33[/C][C]3779.7[/C][C]3765.5[/C][C]14.1999999999998[/C][/ROW]
[ROW][C]34[/C][C]3795.5[/C][C]3779.7[/C][C]15.8000000000002[/C][/ROW]
[ROW][C]35[/C][C]3813.1[/C][C]3795.5[/C][C]17.5999999999999[/C][/ROW]
[ROW][C]36[/C][C]3826.9[/C][C]3813.1[/C][C]13.8000000000002[/C][/ROW]
[ROW][C]37[/C][C]3833.3[/C][C]3826.9[/C][C]6.40000000000009[/C][/ROW]
[ROW][C]38[/C][C]3844.8[/C][C]3833.3[/C][C]11.5[/C][/ROW]
[ROW][C]39[/C][C]3851.3[/C][C]3844.8[/C][C]6.5[/C][/ROW]
[ROW][C]40[/C][C]3851.8[/C][C]3851.3[/C][C]0.5[/C][/ROW]
[ROW][C]41[/C][C]3854.1[/C][C]3851.8[/C][C]2.29999999999973[/C][/ROW]
[ROW][C]42[/C][C]3858.4[/C][C]3854.1[/C][C]4.30000000000018[/C][/ROW]
[ROW][C]43[/C][C]3861.6[/C][C]3858.4[/C][C]3.19999999999982[/C][/ROW]
[ROW][C]44[/C][C]3856.3[/C][C]3861.6[/C][C]-5.29999999999973[/C][/ROW]
[ROW][C]45[/C][C]3855.8[/C][C]3856.3[/C][C]-0.5[/C][/ROW]
[ROW][C]46[/C][C]3860.4[/C][C]3855.8[/C][C]4.59999999999991[/C][/ROW]
[ROW][C]47[/C][C]3855.1[/C][C]3860.4[/C][C]-5.30000000000018[/C][/ROW]
[ROW][C]48[/C][C]3839.5[/C][C]3855.1[/C][C]-15.5999999999999[/C][/ROW]
[ROW][C]49[/C][C]3833[/C][C]3839.5[/C][C]-6.5[/C][/ROW]
[ROW][C]50[/C][C]3833.6[/C][C]3833[/C][C]0.599999999999909[/C][/ROW]
[ROW][C]51[/C][C]3826.8[/C][C]3833.6[/C][C]-6.79999999999973[/C][/ROW]
[ROW][C]52[/C][C]3818.2[/C][C]3826.8[/C][C]-8.60000000000036[/C][/ROW]
[ROW][C]53[/C][C]3811.4[/C][C]3818.2[/C][C]-6.79999999999973[/C][/ROW]
[ROW][C]54[/C][C]3806.8[/C][C]3811.4[/C][C]-4.59999999999991[/C][/ROW]
[ROW][C]55[/C][C]3810.3[/C][C]3806.8[/C][C]3.5[/C][/ROW]
[ROW][C]56[/C][C]3818.2[/C][C]3810.3[/C][C]7.89999999999964[/C][/ROW]
[ROW][C]57[/C][C]3858.7[/C][C]3818.2[/C][C]40.5[/C][/ROW]
[ROW][C]58[/C][C]3868.7[/C][C]3858.7[/C][C]10[/C][/ROW]
[ROW][C]59[/C][C]3872.6[/C][C]3868.7[/C][C]3.90000000000009[/C][/ROW]
[ROW][C]60[/C][C]3872.4[/C][C]3872.6[/C][C]-0.199999999999818[/C][/ROW]
[ROW][C]61[/C][C]3876.4[/C][C]3872.4[/C][C]4[/C][/ROW]
[ROW][C]62[/C][C]3883.2[/C][C]3876.4[/C][C]6.79999999999973[/C][/ROW]
[ROW][C]63[/C][C]3883.4[/C][C]3883.2[/C][C]0.200000000000273[/C][/ROW]
[ROW][C]64[/C][C]3881.8[/C][C]3883.4[/C][C]-1.59999999999991[/C][/ROW]
[ROW][C]65[/C][C]3887.1[/C][C]3881.8[/C][C]5.29999999999973[/C][/ROW]
[ROW][C]66[/C][C]3893.3[/C][C]3887.1[/C][C]6.20000000000027[/C][/ROW]
[ROW][C]67[/C][C]3902.8[/C][C]3893.3[/C][C]9.5[/C][/ROW]
[ROW][C]68[/C][C]3914.7[/C][C]3902.8[/C][C]11.8999999999996[/C][/ROW]
[ROW][C]69[/C][C]3929.8[/C][C]3914.7[/C][C]15.1000000000004[/C][/ROW]
[ROW][C]70[/C][C]3947.3[/C][C]3929.8[/C][C]17.5[/C][/ROW]
[ROW][C]71[/C][C]3971.8[/C][C]3947.3[/C][C]24.5[/C][/ROW]
[ROW][C]72[/C][C]3991.3[/C][C]3971.8[/C][C]19.5[/C][/ROW]
[ROW][C]73[/C][C]3993[/C][C]3991.3[/C][C]1.69999999999982[/C][/ROW]
[ROW][C]74[/C][C]3997.2[/C][C]3993[/C][C]4.19999999999982[/C][/ROW]
[ROW][C]75[/C][C]4016.2[/C][C]3997.2[/C][C]19[/C][/ROW]
[ROW][C]76[/C][C]4041.7[/C][C]4016.2[/C][C]25.5[/C][/ROW]
[ROW][C]77[/C][C]4060.5[/C][C]4041.7[/C][C]18.8000000000002[/C][/ROW]
[ROW][C]78[/C][C]4076.7[/C][C]4060.5[/C][C]16.1999999999998[/C][/ROW]
[ROW][C]79[/C][C]4102.7[/C][C]4076.7[/C][C]26[/C][/ROW]
[ROW][C]80[/C][C]4125.8[/C][C]4102.7[/C][C]23.1000000000004[/C][/ROW]
[ROW][C]81[/C][C]4140.1[/C][C]4125.8[/C][C]14.3000000000002[/C][/ROW]
[ROW][C]82[/C][C]4146.7[/C][C]4140.1[/C][C]6.59999999999945[/C][/ROW]
[ROW][C]83[/C][C]4157.9[/C][C]4146.7[/C][C]11.1999999999998[/C][/ROW]
[ROW][C]84[/C][C]4154.7[/C][C]4157.9[/C][C]-3.19999999999982[/C][/ROW]
[ROW][C]85[/C][C]4145.3[/C][C]4154.7[/C][C]-9.39999999999964[/C][/ROW]
[ROW][C]86[/C][C]4149[/C][C]4145.3[/C][C]3.69999999999982[/C][/ROW]
[ROW][C]87[/C][C]4142.4[/C][C]4149[/C][C]-6.60000000000036[/C][/ROW]
[ROW][C]88[/C][C]4141[/C][C]4142.4[/C][C]-1.39999999999964[/C][/ROW]
[ROW][C]89[/C][C]4146.1[/C][C]4141[/C][C]5.10000000000036[/C][/ROW]
[ROW][C]90[/C][C]4147.6[/C][C]4146.1[/C][C]1.5[/C][/ROW]
[ROW][C]91[/C][C]4142.7[/C][C]4147.6[/C][C]-4.90000000000055[/C][/ROW]
[ROW][C]92[/C][C]4148.1[/C][C]4142.7[/C][C]5.40000000000055[/C][/ROW]
[ROW][C]93[/C][C]4159[/C][C]4148.1[/C][C]10.8999999999996[/C][/ROW]
[ROW][C]94[/C][C]4167[/C][C]4159[/C][C]8[/C][/ROW]
[ROW][C]95[/C][C]4178.5[/C][C]4167[/C][C]11.5[/C][/ROW]
[ROW][C]96[/C][C]4192.5[/C][C]4178.5[/C][C]14[/C][/ROW]
[ROW][C]97[/C][C]4209.2[/C][C]4192.5[/C][C]16.6999999999998[/C][/ROW]
[ROW][C]98[/C][C]4223.7[/C][C]4209.2[/C][C]14.5[/C][/ROW]
[ROW][C]99[/C][C]4231.6[/C][C]4223.7[/C][C]7.90000000000055[/C][/ROW]
[ROW][C]100[/C][C]4236.9[/C][C]4231.6[/C][C]5.29999999999927[/C][/ROW]
[ROW][C]101[/C][C]4253[/C][C]4236.9[/C][C]16.1000000000004[/C][/ROW]
[ROW][C]102[/C][C]4270.5[/C][C]4253[/C][C]17.5[/C][/ROW]
[ROW][C]103[/C][C]4285.7[/C][C]4270.5[/C][C]15.1999999999998[/C][/ROW]
[ROW][C]104[/C][C]4302.8[/C][C]4285.7[/C][C]17.1000000000004[/C][/ROW]
[ROW][C]105[/C][C]4321.5[/C][C]4302.8[/C][C]18.6999999999998[/C][/ROW]
[ROW][C]106[/C][C]4340.3[/C][C]4321.5[/C][C]18.8000000000002[/C][/ROW]
[ROW][C]107[/C][C]4356.5[/C][C]4340.3[/C][C]16.1999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13254&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13254&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
23707.13722.7-15.5999999999999
33697.43707.1-9.69999999999982
43691.43697.4-6
53679.43691.4-12
63660.63679.4-18.8000000000002
73647.53660.6-13.0999999999999
836393647.5-8.5
93623.53639-15.5
103612.23623.5-11.3000000000002
113604.23612.2-8
123596.93604.2-7.29999999999973
133603.93596.97
143606.93603.93
153607.73606.90.799999999999727
163611.43607.73.70000000000027
173611.93611.40.5
183618.43611.96.5
193629.53618.411.0999999999999
203640.63629.511.0999999999999
213646.83640.66.20000000000027
223647.33646.80.5
233649.53647.32.19999999999982
243649.73649.50.199999999999818
253652.53649.72.80000000000018
263665.83652.513.3000000000002
273674.33665.88.5
283705.83674.331.5
293735.83705.830
303735.43735.8-0.400000000000091
313747.73735.412.2999999999997
323765.53747.717.8000000000002
333779.73765.514.1999999999998
343795.53779.715.8000000000002
353813.13795.517.5999999999999
363826.93813.113.8000000000002
373833.33826.96.40000000000009
383844.83833.311.5
393851.33844.86.5
403851.83851.30.5
413854.13851.82.29999999999973
423858.43854.14.30000000000018
433861.63858.43.19999999999982
443856.33861.6-5.29999999999973
453855.83856.3-0.5
463860.43855.84.59999999999991
473855.13860.4-5.30000000000018
483839.53855.1-15.5999999999999
4938333839.5-6.5
503833.638330.599999999999909
513826.83833.6-6.79999999999973
523818.23826.8-8.60000000000036
533811.43818.2-6.79999999999973
543806.83811.4-4.59999999999991
553810.33806.83.5
563818.23810.37.89999999999964
573858.73818.240.5
583868.73858.710
593872.63868.73.90000000000009
603872.43872.6-0.199999999999818
613876.43872.44
623883.23876.46.79999999999973
633883.43883.20.200000000000273
643881.83883.4-1.59999999999991
653887.13881.85.29999999999973
663893.33887.16.20000000000027
673902.83893.39.5
683914.73902.811.8999999999996
693929.83914.715.1000000000004
703947.33929.817.5
713971.83947.324.5
723991.33971.819.5
7339933991.31.69999999999982
743997.239934.19999999999982
754016.23997.219
764041.74016.225.5
774060.54041.718.8000000000002
784076.74060.516.1999999999998
794102.74076.726
804125.84102.723.1000000000004
814140.14125.814.3000000000002
824146.74140.16.59999999999945
834157.94146.711.1999999999998
844154.74157.9-3.19999999999982
854145.34154.7-9.39999999999964
8641494145.33.69999999999982
874142.44149-6.60000000000036
8841414142.4-1.39999999999964
894146.141415.10000000000036
904147.64146.11.5
914142.74147.6-4.90000000000055
924148.14142.75.40000000000055
9341594148.110.8999999999996
94416741598
954178.5416711.5
964192.54178.514
974209.24192.516.6999999999998
984223.74209.214.5
994231.64223.77.90000000000055
1004236.94231.65.29999999999927
10142534236.916.1000000000004
1024270.5425317.5
1034285.74270.515.1999999999998
1044302.84285.717.1000000000004
1054321.54302.818.6999999999998
1064340.34321.518.8000000000002
1074356.54340.316.1999999999998







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1084356.54334.768524370714378.23147562929
1094356.54325.767052434684387.23294756532
1104356.54318.859980086634394.14001991337
1114356.54313.037048741424399.96295125858
1124356.54307.906943241534405.09305675847
1134356.54303.268973350524409.73102664948
1144356.54299.003919862444413.99608013756
1154356.54295.034104869364417.96589513064
1164356.54291.305573112144421.69442688786
1174356.54287.779040095014425.22095990499
1184356.54284.42484919694428.5751508031
1194356.54281.219960173264431.78003982674

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
108 & 4356.5 & 4334.76852437071 & 4378.23147562929 \tabularnewline
109 & 4356.5 & 4325.76705243468 & 4387.23294756532 \tabularnewline
110 & 4356.5 & 4318.85998008663 & 4394.14001991337 \tabularnewline
111 & 4356.5 & 4313.03704874142 & 4399.96295125858 \tabularnewline
112 & 4356.5 & 4307.90694324153 & 4405.09305675847 \tabularnewline
113 & 4356.5 & 4303.26897335052 & 4409.73102664948 \tabularnewline
114 & 4356.5 & 4299.00391986244 & 4413.99608013756 \tabularnewline
115 & 4356.5 & 4295.03410486936 & 4417.96589513064 \tabularnewline
116 & 4356.5 & 4291.30557311214 & 4421.69442688786 \tabularnewline
117 & 4356.5 & 4287.77904009501 & 4425.22095990499 \tabularnewline
118 & 4356.5 & 4284.4248491969 & 4428.5751508031 \tabularnewline
119 & 4356.5 & 4281.21996017326 & 4431.78003982674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13254&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]108[/C][C]4356.5[/C][C]4334.76852437071[/C][C]4378.23147562929[/C][/ROW]
[ROW][C]109[/C][C]4356.5[/C][C]4325.76705243468[/C][C]4387.23294756532[/C][/ROW]
[ROW][C]110[/C][C]4356.5[/C][C]4318.85998008663[/C][C]4394.14001991337[/C][/ROW]
[ROW][C]111[/C][C]4356.5[/C][C]4313.03704874142[/C][C]4399.96295125858[/C][/ROW]
[ROW][C]112[/C][C]4356.5[/C][C]4307.90694324153[/C][C]4405.09305675847[/C][/ROW]
[ROW][C]113[/C][C]4356.5[/C][C]4303.26897335052[/C][C]4409.73102664948[/C][/ROW]
[ROW][C]114[/C][C]4356.5[/C][C]4299.00391986244[/C][C]4413.99608013756[/C][/ROW]
[ROW][C]115[/C][C]4356.5[/C][C]4295.03410486936[/C][C]4417.96589513064[/C][/ROW]
[ROW][C]116[/C][C]4356.5[/C][C]4291.30557311214[/C][C]4421.69442688786[/C][/ROW]
[ROW][C]117[/C][C]4356.5[/C][C]4287.77904009501[/C][C]4425.22095990499[/C][/ROW]
[ROW][C]118[/C][C]4356.5[/C][C]4284.4248491969[/C][C]4428.5751508031[/C][/ROW]
[ROW][C]119[/C][C]4356.5[/C][C]4281.21996017326[/C][C]4431.78003982674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13254&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13254&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
1084356.54334.768524370714378.23147562929
1094356.54325.767052434684387.23294756532
1104356.54318.859980086634394.14001991337
1114356.54313.037048741424399.96295125858
1124356.54307.906943241534405.09305675847
1134356.54303.268973350524409.73102664948
1144356.54299.003919862444413.99608013756
1154356.54295.034104869364417.96589513064
1164356.54291.305573112144421.69442688786
1174356.54287.779040095014425.22095990499
1184356.54284.42484919694428.5751508031
1194356.54281.219960173264431.78003982674



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')