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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Jan 2012 04:40:37 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/16/t1326706900l3cr0mddixxq8dp.htm/, Retrieved Sun, 28 Apr 2024 05:13:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161204, Retrieved Sun, 28 Apr 2024 05:13:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKEYWORD: KDGP2W102
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oef 2] [2012-01-16 09:40:37] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
11,8
11,87
11,86
12,11
11,92
12,61
13,34
13,31
13,47
13,24
13,18
13,3
13,15
13,47
13,65
13,52
14,13
14,84
15,29
15,51
15,43
15,42
15,56
15,43
15,36
15,18
15,41
15,15
15,21
15,09
15,09
15,5
15,41
15,42
15,47
15,23
15,59
15,22
15,45
15,02
15,5
15,59
15,98
15,76
15,43
15,45
15,32
15,4
15,42
15,54
15,6
15,67
15,61
16,01
16,06
16,15
15,87
15,89
15,73
15,78
16,07
16,2
16,42
16,61
16,89
17,62
17,83
17,94
18,07
17,85
17,86
17,85




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161204&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161204&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161204&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161204&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]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161204&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161204&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
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
311.8611.94-0.0799999999999983
412.1111.930.180000000000001
511.9212.18-0.259999999999998
612.6111.990.620000000000001
713.3412.680.660000000000002
813.3113.41-0.0999999999999979
913.4713.380.0900000000000016
1013.2413.54-0.299999999999999
1113.1813.31-0.129999999999999
1213.313.250.0500000000000025
1313.1513.37-0.219999999999999
1413.4713.220.250000000000002
1513.6513.540.110000000000001
1613.5213.72-0.199999999999999
1714.1313.590.540000000000003
1814.8414.20.640000000000001
1915.2914.910.380000000000001
2015.5115.360.150000000000002
2115.4315.58-0.149999999999999
2215.4215.5-0.0799999999999983
2315.5615.490.0700000000000021
2415.4315.63-0.199999999999999
2515.3615.5-0.139999999999999
2615.1815.43-0.249999999999998
2715.4115.250.160000000000002
2815.1515.48-0.329999999999998
2915.2115.22-0.00999999999999801
3015.0915.28-0.19
3115.0915.16-0.0699999999999985
3215.515.160.340000000000002
3315.4115.57-0.159999999999998
3415.4215.48-0.0599999999999987
3515.4715.49-0.0199999999999978
3615.2315.54-0.309999999999999
3715.5915.30.290000000000001
3815.2215.66-0.439999999999998
3915.4515.290.16
4015.0215.52-0.499999999999998
4115.515.090.410000000000002
4215.5915.570.0200000000000014
4315.9815.660.320000000000002
4415.7616.05-0.289999999999997
4515.4315.83-0.399999999999999
4615.4515.5-0.0499999999999989
4715.3215.52-0.199999999999998
4815.415.390.0100000000000016
4915.4215.47-0.0499999999999989
5015.5415.490.0500000000000007
5115.615.61-0.00999999999999801
5215.6715.671.77635683940025e-15
5315.6115.74-0.129999999999999
5416.0115.680.330000000000004
5516.0616.08-0.0199999999999996
5616.1516.130.0200000000000031
5715.8716.22-0.35
5815.8915.94-0.0499999999999972
5915.7315.96-0.229999999999999
6015.7815.8-0.0199999999999996
6116.0715.850.220000000000002
6216.216.140.0599999999999987
6316.4216.270.150000000000006
6416.6116.490.119999999999997
6516.8916.680.210000000000001
6617.6216.960.66
6717.8317.690.140000000000001
6817.9417.90.0400000000000027
6918.0718.010.0600000000000023
7017.8518.14-0.289999999999999
7117.8617.92-0.0600000000000023
7217.8517.93-0.0799999999999983

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 11.86 & 11.94 & -0.0799999999999983 \tabularnewline
4 & 12.11 & 11.93 & 0.180000000000001 \tabularnewline
5 & 11.92 & 12.18 & -0.259999999999998 \tabularnewline
6 & 12.61 & 11.99 & 0.620000000000001 \tabularnewline
7 & 13.34 & 12.68 & 0.660000000000002 \tabularnewline
8 & 13.31 & 13.41 & -0.0999999999999979 \tabularnewline
9 & 13.47 & 13.38 & 0.0900000000000016 \tabularnewline
10 & 13.24 & 13.54 & -0.299999999999999 \tabularnewline
11 & 13.18 & 13.31 & -0.129999999999999 \tabularnewline
12 & 13.3 & 13.25 & 0.0500000000000025 \tabularnewline
13 & 13.15 & 13.37 & -0.219999999999999 \tabularnewline
14 & 13.47 & 13.22 & 0.250000000000002 \tabularnewline
15 & 13.65 & 13.54 & 0.110000000000001 \tabularnewline
16 & 13.52 & 13.72 & -0.199999999999999 \tabularnewline
17 & 14.13 & 13.59 & 0.540000000000003 \tabularnewline
18 & 14.84 & 14.2 & 0.640000000000001 \tabularnewline
19 & 15.29 & 14.91 & 0.380000000000001 \tabularnewline
20 & 15.51 & 15.36 & 0.150000000000002 \tabularnewline
21 & 15.43 & 15.58 & -0.149999999999999 \tabularnewline
22 & 15.42 & 15.5 & -0.0799999999999983 \tabularnewline
23 & 15.56 & 15.49 & 0.0700000000000021 \tabularnewline
24 & 15.43 & 15.63 & -0.199999999999999 \tabularnewline
25 & 15.36 & 15.5 & -0.139999999999999 \tabularnewline
26 & 15.18 & 15.43 & -0.249999999999998 \tabularnewline
27 & 15.41 & 15.25 & 0.160000000000002 \tabularnewline
28 & 15.15 & 15.48 & -0.329999999999998 \tabularnewline
29 & 15.21 & 15.22 & -0.00999999999999801 \tabularnewline
30 & 15.09 & 15.28 & -0.19 \tabularnewline
31 & 15.09 & 15.16 & -0.0699999999999985 \tabularnewline
32 & 15.5 & 15.16 & 0.340000000000002 \tabularnewline
33 & 15.41 & 15.57 & -0.159999999999998 \tabularnewline
34 & 15.42 & 15.48 & -0.0599999999999987 \tabularnewline
35 & 15.47 & 15.49 & -0.0199999999999978 \tabularnewline
36 & 15.23 & 15.54 & -0.309999999999999 \tabularnewline
37 & 15.59 & 15.3 & 0.290000000000001 \tabularnewline
38 & 15.22 & 15.66 & -0.439999999999998 \tabularnewline
39 & 15.45 & 15.29 & 0.16 \tabularnewline
40 & 15.02 & 15.52 & -0.499999999999998 \tabularnewline
41 & 15.5 & 15.09 & 0.410000000000002 \tabularnewline
42 & 15.59 & 15.57 & 0.0200000000000014 \tabularnewline
43 & 15.98 & 15.66 & 0.320000000000002 \tabularnewline
44 & 15.76 & 16.05 & -0.289999999999997 \tabularnewline
45 & 15.43 & 15.83 & -0.399999999999999 \tabularnewline
46 & 15.45 & 15.5 & -0.0499999999999989 \tabularnewline
47 & 15.32 & 15.52 & -0.199999999999998 \tabularnewline
48 & 15.4 & 15.39 & 0.0100000000000016 \tabularnewline
49 & 15.42 & 15.47 & -0.0499999999999989 \tabularnewline
50 & 15.54 & 15.49 & 0.0500000000000007 \tabularnewline
51 & 15.6 & 15.61 & -0.00999999999999801 \tabularnewline
52 & 15.67 & 15.67 & 1.77635683940025e-15 \tabularnewline
53 & 15.61 & 15.74 & -0.129999999999999 \tabularnewline
54 & 16.01 & 15.68 & 0.330000000000004 \tabularnewline
55 & 16.06 & 16.08 & -0.0199999999999996 \tabularnewline
56 & 16.15 & 16.13 & 0.0200000000000031 \tabularnewline
57 & 15.87 & 16.22 & -0.35 \tabularnewline
58 & 15.89 & 15.94 & -0.0499999999999972 \tabularnewline
59 & 15.73 & 15.96 & -0.229999999999999 \tabularnewline
60 & 15.78 & 15.8 & -0.0199999999999996 \tabularnewline
61 & 16.07 & 15.85 & 0.220000000000002 \tabularnewline
62 & 16.2 & 16.14 & 0.0599999999999987 \tabularnewline
63 & 16.42 & 16.27 & 0.150000000000006 \tabularnewline
64 & 16.61 & 16.49 & 0.119999999999997 \tabularnewline
65 & 16.89 & 16.68 & 0.210000000000001 \tabularnewline
66 & 17.62 & 16.96 & 0.66 \tabularnewline
67 & 17.83 & 17.69 & 0.140000000000001 \tabularnewline
68 & 17.94 & 17.9 & 0.0400000000000027 \tabularnewline
69 & 18.07 & 18.01 & 0.0600000000000023 \tabularnewline
70 & 17.85 & 18.14 & -0.289999999999999 \tabularnewline
71 & 17.86 & 17.92 & -0.0600000000000023 \tabularnewline
72 & 17.85 & 17.93 & -0.0799999999999983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161204&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]11.86[/C][C]11.94[/C][C]-0.0799999999999983[/C][/ROW]
[ROW][C]4[/C][C]12.11[/C][C]11.93[/C][C]0.180000000000001[/C][/ROW]
[ROW][C]5[/C][C]11.92[/C][C]12.18[/C][C]-0.259999999999998[/C][/ROW]
[ROW][C]6[/C][C]12.61[/C][C]11.99[/C][C]0.620000000000001[/C][/ROW]
[ROW][C]7[/C][C]13.34[/C][C]12.68[/C][C]0.660000000000002[/C][/ROW]
[ROW][C]8[/C][C]13.31[/C][C]13.41[/C][C]-0.0999999999999979[/C][/ROW]
[ROW][C]9[/C][C]13.47[/C][C]13.38[/C][C]0.0900000000000016[/C][/ROW]
[ROW][C]10[/C][C]13.24[/C][C]13.54[/C][C]-0.299999999999999[/C][/ROW]
[ROW][C]11[/C][C]13.18[/C][C]13.31[/C][C]-0.129999999999999[/C][/ROW]
[ROW][C]12[/C][C]13.3[/C][C]13.25[/C][C]0.0500000000000025[/C][/ROW]
[ROW][C]13[/C][C]13.15[/C][C]13.37[/C][C]-0.219999999999999[/C][/ROW]
[ROW][C]14[/C][C]13.47[/C][C]13.22[/C][C]0.250000000000002[/C][/ROW]
[ROW][C]15[/C][C]13.65[/C][C]13.54[/C][C]0.110000000000001[/C][/ROW]
[ROW][C]16[/C][C]13.52[/C][C]13.72[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]17[/C][C]14.13[/C][C]13.59[/C][C]0.540000000000003[/C][/ROW]
[ROW][C]18[/C][C]14.84[/C][C]14.2[/C][C]0.640000000000001[/C][/ROW]
[ROW][C]19[/C][C]15.29[/C][C]14.91[/C][C]0.380000000000001[/C][/ROW]
[ROW][C]20[/C][C]15.51[/C][C]15.36[/C][C]0.150000000000002[/C][/ROW]
[ROW][C]21[/C][C]15.43[/C][C]15.58[/C][C]-0.149999999999999[/C][/ROW]
[ROW][C]22[/C][C]15.42[/C][C]15.5[/C][C]-0.0799999999999983[/C][/ROW]
[ROW][C]23[/C][C]15.56[/C][C]15.49[/C][C]0.0700000000000021[/C][/ROW]
[ROW][C]24[/C][C]15.43[/C][C]15.63[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]25[/C][C]15.36[/C][C]15.5[/C][C]-0.139999999999999[/C][/ROW]
[ROW][C]26[/C][C]15.18[/C][C]15.43[/C][C]-0.249999999999998[/C][/ROW]
[ROW][C]27[/C][C]15.41[/C][C]15.25[/C][C]0.160000000000002[/C][/ROW]
[ROW][C]28[/C][C]15.15[/C][C]15.48[/C][C]-0.329999999999998[/C][/ROW]
[ROW][C]29[/C][C]15.21[/C][C]15.22[/C][C]-0.00999999999999801[/C][/ROW]
[ROW][C]30[/C][C]15.09[/C][C]15.28[/C][C]-0.19[/C][/ROW]
[ROW][C]31[/C][C]15.09[/C][C]15.16[/C][C]-0.0699999999999985[/C][/ROW]
[ROW][C]32[/C][C]15.5[/C][C]15.16[/C][C]0.340000000000002[/C][/ROW]
[ROW][C]33[/C][C]15.41[/C][C]15.57[/C][C]-0.159999999999998[/C][/ROW]
[ROW][C]34[/C][C]15.42[/C][C]15.48[/C][C]-0.0599999999999987[/C][/ROW]
[ROW][C]35[/C][C]15.47[/C][C]15.49[/C][C]-0.0199999999999978[/C][/ROW]
[ROW][C]36[/C][C]15.23[/C][C]15.54[/C][C]-0.309999999999999[/C][/ROW]
[ROW][C]37[/C][C]15.59[/C][C]15.3[/C][C]0.290000000000001[/C][/ROW]
[ROW][C]38[/C][C]15.22[/C][C]15.66[/C][C]-0.439999999999998[/C][/ROW]
[ROW][C]39[/C][C]15.45[/C][C]15.29[/C][C]0.16[/C][/ROW]
[ROW][C]40[/C][C]15.02[/C][C]15.52[/C][C]-0.499999999999998[/C][/ROW]
[ROW][C]41[/C][C]15.5[/C][C]15.09[/C][C]0.410000000000002[/C][/ROW]
[ROW][C]42[/C][C]15.59[/C][C]15.57[/C][C]0.0200000000000014[/C][/ROW]
[ROW][C]43[/C][C]15.98[/C][C]15.66[/C][C]0.320000000000002[/C][/ROW]
[ROW][C]44[/C][C]15.76[/C][C]16.05[/C][C]-0.289999999999997[/C][/ROW]
[ROW][C]45[/C][C]15.43[/C][C]15.83[/C][C]-0.399999999999999[/C][/ROW]
[ROW][C]46[/C][C]15.45[/C][C]15.5[/C][C]-0.0499999999999989[/C][/ROW]
[ROW][C]47[/C][C]15.32[/C][C]15.52[/C][C]-0.199999999999998[/C][/ROW]
[ROW][C]48[/C][C]15.4[/C][C]15.39[/C][C]0.0100000000000016[/C][/ROW]
[ROW][C]49[/C][C]15.42[/C][C]15.47[/C][C]-0.0499999999999989[/C][/ROW]
[ROW][C]50[/C][C]15.54[/C][C]15.49[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]51[/C][C]15.6[/C][C]15.61[/C][C]-0.00999999999999801[/C][/ROW]
[ROW][C]52[/C][C]15.67[/C][C]15.67[/C][C]1.77635683940025e-15[/C][/ROW]
[ROW][C]53[/C][C]15.61[/C][C]15.74[/C][C]-0.129999999999999[/C][/ROW]
[ROW][C]54[/C][C]16.01[/C][C]15.68[/C][C]0.330000000000004[/C][/ROW]
[ROW][C]55[/C][C]16.06[/C][C]16.08[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]56[/C][C]16.15[/C][C]16.13[/C][C]0.0200000000000031[/C][/ROW]
[ROW][C]57[/C][C]15.87[/C][C]16.22[/C][C]-0.35[/C][/ROW]
[ROW][C]58[/C][C]15.89[/C][C]15.94[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]59[/C][C]15.73[/C][C]15.96[/C][C]-0.229999999999999[/C][/ROW]
[ROW][C]60[/C][C]15.78[/C][C]15.8[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]61[/C][C]16.07[/C][C]15.85[/C][C]0.220000000000002[/C][/ROW]
[ROW][C]62[/C][C]16.2[/C][C]16.14[/C][C]0.0599999999999987[/C][/ROW]
[ROW][C]63[/C][C]16.42[/C][C]16.27[/C][C]0.150000000000006[/C][/ROW]
[ROW][C]64[/C][C]16.61[/C][C]16.49[/C][C]0.119999999999997[/C][/ROW]
[ROW][C]65[/C][C]16.89[/C][C]16.68[/C][C]0.210000000000001[/C][/ROW]
[ROW][C]66[/C][C]17.62[/C][C]16.96[/C][C]0.66[/C][/ROW]
[ROW][C]67[/C][C]17.83[/C][C]17.69[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]68[/C][C]17.94[/C][C]17.9[/C][C]0.0400000000000027[/C][/ROW]
[ROW][C]69[/C][C]18.07[/C][C]18.01[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]70[/C][C]17.85[/C][C]18.14[/C][C]-0.289999999999999[/C][/ROW]
[ROW][C]71[/C][C]17.86[/C][C]17.92[/C][C]-0.0600000000000023[/C][/ROW]
[ROW][C]72[/C][C]17.85[/C][C]17.93[/C][C]-0.0799999999999983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161204&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161204&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
311.8611.94-0.0799999999999983
412.1111.930.180000000000001
511.9212.18-0.259999999999998
612.6111.990.620000000000001
713.3412.680.660000000000002
813.3113.41-0.0999999999999979
913.4713.380.0900000000000016
1013.2413.54-0.299999999999999
1113.1813.31-0.129999999999999
1213.313.250.0500000000000025
1313.1513.37-0.219999999999999
1413.4713.220.250000000000002
1513.6513.540.110000000000001
1613.5213.72-0.199999999999999
1714.1313.590.540000000000003
1814.8414.20.640000000000001
1915.2914.910.380000000000001
2015.5115.360.150000000000002
2115.4315.58-0.149999999999999
2215.4215.5-0.0799999999999983
2315.5615.490.0700000000000021
2415.4315.63-0.199999999999999
2515.3615.5-0.139999999999999
2615.1815.43-0.249999999999998
2715.4115.250.160000000000002
2815.1515.48-0.329999999999998
2915.2115.22-0.00999999999999801
3015.0915.28-0.19
3115.0915.16-0.0699999999999985
3215.515.160.340000000000002
3315.4115.57-0.159999999999998
3415.4215.48-0.0599999999999987
3515.4715.49-0.0199999999999978
3615.2315.54-0.309999999999999
3715.5915.30.290000000000001
3815.2215.66-0.439999999999998
3915.4515.290.16
4015.0215.52-0.499999999999998
4115.515.090.410000000000002
4215.5915.570.0200000000000014
4315.9815.660.320000000000002
4415.7616.05-0.289999999999997
4515.4315.83-0.399999999999999
4615.4515.5-0.0499999999999989
4715.3215.52-0.199999999999998
4815.415.390.0100000000000016
4915.4215.47-0.0499999999999989
5015.5415.490.0500000000000007
5115.615.61-0.00999999999999801
5215.6715.671.77635683940025e-15
5315.6115.74-0.129999999999999
5416.0115.680.330000000000004
5516.0616.08-0.0199999999999996
5616.1516.130.0200000000000031
5715.8716.22-0.35
5815.8915.94-0.0499999999999972
5915.7315.96-0.229999999999999
6015.7815.8-0.0199999999999996
6116.0715.850.220000000000002
6216.216.140.0599999999999987
6316.4216.270.150000000000006
6416.6116.490.119999999999997
6516.8916.680.210000000000001
6617.6216.960.66
6717.8317.690.140000000000001
6817.9417.90.0400000000000027
6918.0718.010.0600000000000023
7017.8518.14-0.289999999999999
7117.8617.92-0.0600000000000023
7217.8517.93-0.0799999999999983







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7317.9217.405779732646518.4342202673535
7417.9917.262782723861518.7172172761385
7518.0617.16934437066218.950655629338
7618.1317.101559465292919.1584405347071
7718.217.050168526789419.3498314732106
7818.2717.010422729586319.5295772704137
7918.3416.979501053473419.7004989465266
8018.4116.95556544772319.864434552277
8118.4816.937339197939420.0226608020606
8218.5516.923892736142120.1761072638579
8318.6216.914524313592120.3254756864079
8418.6916.90868874132420.4713112586759

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 17.92 & 17.4057797326465 & 18.4342202673535 \tabularnewline
74 & 17.99 & 17.2627827238615 & 18.7172172761385 \tabularnewline
75 & 18.06 & 17.169344370662 & 18.950655629338 \tabularnewline
76 & 18.13 & 17.1015594652929 & 19.1584405347071 \tabularnewline
77 & 18.2 & 17.0501685267894 & 19.3498314732106 \tabularnewline
78 & 18.27 & 17.0104227295863 & 19.5295772704137 \tabularnewline
79 & 18.34 & 16.9795010534734 & 19.7004989465266 \tabularnewline
80 & 18.41 & 16.955565447723 & 19.864434552277 \tabularnewline
81 & 18.48 & 16.9373391979394 & 20.0226608020606 \tabularnewline
82 & 18.55 & 16.9238927361421 & 20.1761072638579 \tabularnewline
83 & 18.62 & 16.9145243135921 & 20.3254756864079 \tabularnewline
84 & 18.69 & 16.908688741324 & 20.4713112586759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161204&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]73[/C][C]17.92[/C][C]17.4057797326465[/C][C]18.4342202673535[/C][/ROW]
[ROW][C]74[/C][C]17.99[/C][C]17.2627827238615[/C][C]18.7172172761385[/C][/ROW]
[ROW][C]75[/C][C]18.06[/C][C]17.169344370662[/C][C]18.950655629338[/C][/ROW]
[ROW][C]76[/C][C]18.13[/C][C]17.1015594652929[/C][C]19.1584405347071[/C][/ROW]
[ROW][C]77[/C][C]18.2[/C][C]17.0501685267894[/C][C]19.3498314732106[/C][/ROW]
[ROW][C]78[/C][C]18.27[/C][C]17.0104227295863[/C][C]19.5295772704137[/C][/ROW]
[ROW][C]79[/C][C]18.34[/C][C]16.9795010534734[/C][C]19.7004989465266[/C][/ROW]
[ROW][C]80[/C][C]18.41[/C][C]16.955565447723[/C][C]19.864434552277[/C][/ROW]
[ROW][C]81[/C][C]18.48[/C][C]16.9373391979394[/C][C]20.0226608020606[/C][/ROW]
[ROW][C]82[/C][C]18.55[/C][C]16.9238927361421[/C][C]20.1761072638579[/C][/ROW]
[ROW][C]83[/C][C]18.62[/C][C]16.9145243135921[/C][C]20.3254756864079[/C][/ROW]
[ROW][C]84[/C][C]18.69[/C][C]16.908688741324[/C][C]20.4713112586759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161204&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161204&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
7317.9217.405779732646518.4342202673535
7417.9917.262782723861518.7172172761385
7518.0617.16934437066218.950655629338
7618.1317.101559465292919.1584405347071
7718.217.050168526789419.3498314732106
7818.2717.010422729586319.5295772704137
7918.3416.979501053473419.7004989465266
8018.4116.95556544772319.864434552277
8118.4816.937339197939420.0226608020606
8218.5516.923892736142120.1761072638579
8318.6216.914524313592120.3254756864079
8418.6916.90868874132420.4713112586759



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