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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 21:00:03 -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/2013/Jan/15/t1358301757qxwgq5ye5ueqimx.htm/, Retrieved Sun, 28 Apr 2024 13:11:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205603, Retrieved Sun, 28 Apr 2024 13:11:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [double exponentia...] [2013-01-16 02:00:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
73.97
73.97
73.97
73.97
73.97
73.97
73.96
74.44
75.43
75.77
75.82
75.85
75.85
75.85
77.95
82.07
84.82
85.08
85.34
85.65
85.65
85.72
85.73
85.73
85.73
85.73
85.74
86.32
87.59
87.81
87.87
87.94
87.96
88.01
88.01
88.01
88.01
88.01
88.59
89.43
89.63
89.73
89.88
89.89
89.9
89.91
89.86
90.07
90.17
90.17
90.28
90.87
92.05
92.1
92.16
92.22
92.25
92.29
92.29
92.29
92.29
92.29
91.95
91.82
92.16
92.31
92.33
92.4
92.54
92.49
92.54
92.58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205603&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]3 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=205603&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205603&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205603&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]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205603&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205603&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
beta1
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
373.9773.970
473.9773.970
573.9773.970
673.9773.970
773.9673.97-0.0100000000000051
874.4473.950.490000000000009
975.4374.920.510000000000005
1075.7776.42-0.65000000000002
1175.8276.11-0.289999999999992
1275.8575.87-0.019999999999996
1375.8575.88-0.0300000000000011
1475.8575.850
1577.9575.852.10000000000001
1682.0780.052.01999999999998
1784.8286.19-1.36999999999999
1885.0887.57-2.48999999999999
1985.3485.340
2085.6585.60.0499999999999972
2185.6585.96-0.310000000000002
2285.7285.650.0699999999999932
2385.7385.79-0.0599999999999881
2485.7385.74-0.0100000000000051
2585.7385.730
2685.7385.730
2785.7485.730.00999999999999091
2886.3285.750.570000000000007
2987.5986.90.690000000000012
3087.8188.86-1.05000000000001
3187.8788.03-0.159999999999997
3287.9487.930.00999999999999091
3387.9688.01-0.0499999999999972
3488.0187.980.0300000000000153
3588.0188.06-0.0500000000000114
3688.0188.010
3788.0188.010
3888.0188.010
3988.5988.010.579999999999998
4089.4389.170.260000000000005
4189.6390.27-0.640000000000015
4289.7389.83-0.0999999999999801
4389.8889.830.0499999999999829
4489.8990.03-0.139999999999986
4589.989.90
4689.9189.91-1.4210854715202e-14
4789.8689.92-0.0599999999999881
4890.0789.810.259999999999991
4990.1790.28-0.109999999999985
5090.1790.27-0.100000000000009
5190.2890.170.109999999999999
5290.8790.390.480000000000004
5392.0591.460.589999999999989
5492.193.23-1.13
5592.1692.150.0100000000000051
5692.2292.220
5792.2592.28-0.0300000000000011
5892.2992.280.0100000000000051
5992.2992.33-0.0400000000000063
6092.2992.290
6192.2992.290
6292.2992.290
6391.9592.29-0.340000000000003
6491.8291.610.209999999999994
6592.1691.690.470000000000013
6692.3192.5-0.189999999999998
6792.3392.46-0.13000000000001
6892.492.350.0500000000000114
6992.5492.470.0699999999999932
7092.4992.68-0.190000000000012
7192.5492.440.100000000000023
7292.5892.59-0.0100000000000193

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 73.97 & 73.97 & 0 \tabularnewline
4 & 73.97 & 73.97 & 0 \tabularnewline
5 & 73.97 & 73.97 & 0 \tabularnewline
6 & 73.97 & 73.97 & 0 \tabularnewline
7 & 73.96 & 73.97 & -0.0100000000000051 \tabularnewline
8 & 74.44 & 73.95 & 0.490000000000009 \tabularnewline
9 & 75.43 & 74.92 & 0.510000000000005 \tabularnewline
10 & 75.77 & 76.42 & -0.65000000000002 \tabularnewline
11 & 75.82 & 76.11 & -0.289999999999992 \tabularnewline
12 & 75.85 & 75.87 & -0.019999999999996 \tabularnewline
13 & 75.85 & 75.88 & -0.0300000000000011 \tabularnewline
14 & 75.85 & 75.85 & 0 \tabularnewline
15 & 77.95 & 75.85 & 2.10000000000001 \tabularnewline
16 & 82.07 & 80.05 & 2.01999999999998 \tabularnewline
17 & 84.82 & 86.19 & -1.36999999999999 \tabularnewline
18 & 85.08 & 87.57 & -2.48999999999999 \tabularnewline
19 & 85.34 & 85.34 & 0 \tabularnewline
20 & 85.65 & 85.6 & 0.0499999999999972 \tabularnewline
21 & 85.65 & 85.96 & -0.310000000000002 \tabularnewline
22 & 85.72 & 85.65 & 0.0699999999999932 \tabularnewline
23 & 85.73 & 85.79 & -0.0599999999999881 \tabularnewline
24 & 85.73 & 85.74 & -0.0100000000000051 \tabularnewline
25 & 85.73 & 85.73 & 0 \tabularnewline
26 & 85.73 & 85.73 & 0 \tabularnewline
27 & 85.74 & 85.73 & 0.00999999999999091 \tabularnewline
28 & 86.32 & 85.75 & 0.570000000000007 \tabularnewline
29 & 87.59 & 86.9 & 0.690000000000012 \tabularnewline
30 & 87.81 & 88.86 & -1.05000000000001 \tabularnewline
31 & 87.87 & 88.03 & -0.159999999999997 \tabularnewline
32 & 87.94 & 87.93 & 0.00999999999999091 \tabularnewline
33 & 87.96 & 88.01 & -0.0499999999999972 \tabularnewline
34 & 88.01 & 87.98 & 0.0300000000000153 \tabularnewline
35 & 88.01 & 88.06 & -0.0500000000000114 \tabularnewline
36 & 88.01 & 88.01 & 0 \tabularnewline
37 & 88.01 & 88.01 & 0 \tabularnewline
38 & 88.01 & 88.01 & 0 \tabularnewline
39 & 88.59 & 88.01 & 0.579999999999998 \tabularnewline
40 & 89.43 & 89.17 & 0.260000000000005 \tabularnewline
41 & 89.63 & 90.27 & -0.640000000000015 \tabularnewline
42 & 89.73 & 89.83 & -0.0999999999999801 \tabularnewline
43 & 89.88 & 89.83 & 0.0499999999999829 \tabularnewline
44 & 89.89 & 90.03 & -0.139999999999986 \tabularnewline
45 & 89.9 & 89.9 & 0 \tabularnewline
46 & 89.91 & 89.91 & -1.4210854715202e-14 \tabularnewline
47 & 89.86 & 89.92 & -0.0599999999999881 \tabularnewline
48 & 90.07 & 89.81 & 0.259999999999991 \tabularnewline
49 & 90.17 & 90.28 & -0.109999999999985 \tabularnewline
50 & 90.17 & 90.27 & -0.100000000000009 \tabularnewline
51 & 90.28 & 90.17 & 0.109999999999999 \tabularnewline
52 & 90.87 & 90.39 & 0.480000000000004 \tabularnewline
53 & 92.05 & 91.46 & 0.589999999999989 \tabularnewline
54 & 92.1 & 93.23 & -1.13 \tabularnewline
55 & 92.16 & 92.15 & 0.0100000000000051 \tabularnewline
56 & 92.22 & 92.22 & 0 \tabularnewline
57 & 92.25 & 92.28 & -0.0300000000000011 \tabularnewline
58 & 92.29 & 92.28 & 0.0100000000000051 \tabularnewline
59 & 92.29 & 92.33 & -0.0400000000000063 \tabularnewline
60 & 92.29 & 92.29 & 0 \tabularnewline
61 & 92.29 & 92.29 & 0 \tabularnewline
62 & 92.29 & 92.29 & 0 \tabularnewline
63 & 91.95 & 92.29 & -0.340000000000003 \tabularnewline
64 & 91.82 & 91.61 & 0.209999999999994 \tabularnewline
65 & 92.16 & 91.69 & 0.470000000000013 \tabularnewline
66 & 92.31 & 92.5 & -0.189999999999998 \tabularnewline
67 & 92.33 & 92.46 & -0.13000000000001 \tabularnewline
68 & 92.4 & 92.35 & 0.0500000000000114 \tabularnewline
69 & 92.54 & 92.47 & 0.0699999999999932 \tabularnewline
70 & 92.49 & 92.68 & -0.190000000000012 \tabularnewline
71 & 92.54 & 92.44 & 0.100000000000023 \tabularnewline
72 & 92.58 & 92.59 & -0.0100000000000193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205603&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]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]73.97[/C][C]73.97[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]73.96[/C][C]73.97[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]8[/C][C]74.44[/C][C]73.95[/C][C]0.490000000000009[/C][/ROW]
[ROW][C]9[/C][C]75.43[/C][C]74.92[/C][C]0.510000000000005[/C][/ROW]
[ROW][C]10[/C][C]75.77[/C][C]76.42[/C][C]-0.65000000000002[/C][/ROW]
[ROW][C]11[/C][C]75.82[/C][C]76.11[/C][C]-0.289999999999992[/C][/ROW]
[ROW][C]12[/C][C]75.85[/C][C]75.87[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]13[/C][C]75.85[/C][C]75.88[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]14[/C][C]75.85[/C][C]75.85[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]77.95[/C][C]75.85[/C][C]2.10000000000001[/C][/ROW]
[ROW][C]16[/C][C]82.07[/C][C]80.05[/C][C]2.01999999999998[/C][/ROW]
[ROW][C]17[/C][C]84.82[/C][C]86.19[/C][C]-1.36999999999999[/C][/ROW]
[ROW][C]18[/C][C]85.08[/C][C]87.57[/C][C]-2.48999999999999[/C][/ROW]
[ROW][C]19[/C][C]85.34[/C][C]85.34[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]85.65[/C][C]85.6[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]21[/C][C]85.65[/C][C]85.96[/C][C]-0.310000000000002[/C][/ROW]
[ROW][C]22[/C][C]85.72[/C][C]85.65[/C][C]0.0699999999999932[/C][/ROW]
[ROW][C]23[/C][C]85.73[/C][C]85.79[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]24[/C][C]85.73[/C][C]85.74[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]25[/C][C]85.73[/C][C]85.73[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]85.73[/C][C]85.73[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]85.74[/C][C]85.73[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]28[/C][C]86.32[/C][C]85.75[/C][C]0.570000000000007[/C][/ROW]
[ROW][C]29[/C][C]87.59[/C][C]86.9[/C][C]0.690000000000012[/C][/ROW]
[ROW][C]30[/C][C]87.81[/C][C]88.86[/C][C]-1.05000000000001[/C][/ROW]
[ROW][C]31[/C][C]87.87[/C][C]88.03[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]32[/C][C]87.94[/C][C]87.93[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]33[/C][C]87.96[/C][C]88.01[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]34[/C][C]88.01[/C][C]87.98[/C][C]0.0300000000000153[/C][/ROW]
[ROW][C]35[/C][C]88.01[/C][C]88.06[/C][C]-0.0500000000000114[/C][/ROW]
[ROW][C]36[/C][C]88.01[/C][C]88.01[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]88.01[/C][C]88.01[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]88.01[/C][C]88.01[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]88.59[/C][C]88.01[/C][C]0.579999999999998[/C][/ROW]
[ROW][C]40[/C][C]89.43[/C][C]89.17[/C][C]0.260000000000005[/C][/ROW]
[ROW][C]41[/C][C]89.63[/C][C]90.27[/C][C]-0.640000000000015[/C][/ROW]
[ROW][C]42[/C][C]89.73[/C][C]89.83[/C][C]-0.0999999999999801[/C][/ROW]
[ROW][C]43[/C][C]89.88[/C][C]89.83[/C][C]0.0499999999999829[/C][/ROW]
[ROW][C]44[/C][C]89.89[/C][C]90.03[/C][C]-0.139999999999986[/C][/ROW]
[ROW][C]45[/C][C]89.9[/C][C]89.9[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]89.91[/C][C]89.91[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]47[/C][C]89.86[/C][C]89.92[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]48[/C][C]90.07[/C][C]89.81[/C][C]0.259999999999991[/C][/ROW]
[ROW][C]49[/C][C]90.17[/C][C]90.28[/C][C]-0.109999999999985[/C][/ROW]
[ROW][C]50[/C][C]90.17[/C][C]90.27[/C][C]-0.100000000000009[/C][/ROW]
[ROW][C]51[/C][C]90.28[/C][C]90.17[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]52[/C][C]90.87[/C][C]90.39[/C][C]0.480000000000004[/C][/ROW]
[ROW][C]53[/C][C]92.05[/C][C]91.46[/C][C]0.589999999999989[/C][/ROW]
[ROW][C]54[/C][C]92.1[/C][C]93.23[/C][C]-1.13[/C][/ROW]
[ROW][C]55[/C][C]92.16[/C][C]92.15[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]56[/C][C]92.22[/C][C]92.22[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]92.25[/C][C]92.28[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]58[/C][C]92.29[/C][C]92.28[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]59[/C][C]92.29[/C][C]92.33[/C][C]-0.0400000000000063[/C][/ROW]
[ROW][C]60[/C][C]92.29[/C][C]92.29[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]92.29[/C][C]92.29[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]92.29[/C][C]92.29[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]91.95[/C][C]92.29[/C][C]-0.340000000000003[/C][/ROW]
[ROW][C]64[/C][C]91.82[/C][C]91.61[/C][C]0.209999999999994[/C][/ROW]
[ROW][C]65[/C][C]92.16[/C][C]91.69[/C][C]0.470000000000013[/C][/ROW]
[ROW][C]66[/C][C]92.31[/C][C]92.5[/C][C]-0.189999999999998[/C][/ROW]
[ROW][C]67[/C][C]92.33[/C][C]92.46[/C][C]-0.13000000000001[/C][/ROW]
[ROW][C]68[/C][C]92.4[/C][C]92.35[/C][C]0.0500000000000114[/C][/ROW]
[ROW][C]69[/C][C]92.54[/C][C]92.47[/C][C]0.0699999999999932[/C][/ROW]
[ROW][C]70[/C][C]92.49[/C][C]92.68[/C][C]-0.190000000000012[/C][/ROW]
[ROW][C]71[/C][C]92.54[/C][C]92.44[/C][C]0.100000000000023[/C][/ROW]
[ROW][C]72[/C][C]92.58[/C][C]92.59[/C][C]-0.0100000000000193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205603&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205603&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
373.9773.970
473.9773.970
573.9773.970
673.9773.970
773.9673.97-0.0100000000000051
874.4473.950.490000000000009
975.4374.920.510000000000005
1075.7776.42-0.65000000000002
1175.8276.11-0.289999999999992
1275.8575.87-0.019999999999996
1375.8575.88-0.0300000000000011
1475.8575.850
1577.9575.852.10000000000001
1682.0780.052.01999999999998
1784.8286.19-1.36999999999999
1885.0887.57-2.48999999999999
1985.3485.340
2085.6585.60.0499999999999972
2185.6585.96-0.310000000000002
2285.7285.650.0699999999999932
2385.7385.79-0.0599999999999881
2485.7385.74-0.0100000000000051
2585.7385.730
2685.7385.730
2785.7485.730.00999999999999091
2886.3285.750.570000000000007
2987.5986.90.690000000000012
3087.8188.86-1.05000000000001
3187.8788.03-0.159999999999997
3287.9487.930.00999999999999091
3387.9688.01-0.0499999999999972
3488.0187.980.0300000000000153
3588.0188.06-0.0500000000000114
3688.0188.010
3788.0188.010
3888.0188.010
3988.5988.010.579999999999998
4089.4389.170.260000000000005
4189.6390.27-0.640000000000015
4289.7389.83-0.0999999999999801
4389.8889.830.0499999999999829
4489.8990.03-0.139999999999986
4589.989.90
4689.9189.91-1.4210854715202e-14
4789.8689.92-0.0599999999999881
4890.0789.810.259999999999991
4990.1790.28-0.109999999999985
5090.1790.27-0.100000000000009
5190.2890.170.109999999999999
5290.8790.390.480000000000004
5392.0591.460.589999999999989
5492.193.23-1.13
5592.1692.150.0100000000000051
5692.2292.220
5792.2592.28-0.0300000000000011
5892.2992.280.0100000000000051
5992.2992.33-0.0400000000000063
6092.2992.290
6192.2992.290
6292.2992.290
6391.9592.29-0.340000000000003
6491.8291.610.209999999999994
6592.1691.690.470000000000013
6692.3192.5-0.189999999999998
6792.3392.46-0.13000000000001
6892.492.350.0500000000000114
6992.5492.470.0699999999999932
7092.4992.68-0.190000000000012
7192.5492.440.100000000000023
7292.5892.59-0.0100000000000193







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7392.6291.490522525606993.7494774743931
7492.6690.134411588202295.1855884117978
7592.788.473882264742296.9261177352578
7692.7486.553597090809298.9264029091907
7792.7884.4035708631971101.156429136803
7892.8282.04547160059103.59452839941
7992.859999999999979.4958422965529106.224157703447
8092.899999999999976.7678349099404109.03216509006
8192.939999999999973.8722256392882112.007774360712
8292.979999999999970.8180516292641115.141948370736
8393.019999999999967.6130324758798118.42696752412
8493.059999999999964.2638615895299121.85613841047

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 92.62 & 91.4905225256069 & 93.7494774743931 \tabularnewline
74 & 92.66 & 90.1344115882022 & 95.1855884117978 \tabularnewline
75 & 92.7 & 88.4738822647422 & 96.9261177352578 \tabularnewline
76 & 92.74 & 86.5535970908092 & 98.9264029091907 \tabularnewline
77 & 92.78 & 84.4035708631971 & 101.156429136803 \tabularnewline
78 & 92.82 & 82.04547160059 & 103.59452839941 \tabularnewline
79 & 92.8599999999999 & 79.4958422965529 & 106.224157703447 \tabularnewline
80 & 92.8999999999999 & 76.7678349099404 & 109.03216509006 \tabularnewline
81 & 92.9399999999999 & 73.8722256392882 & 112.007774360712 \tabularnewline
82 & 92.9799999999999 & 70.8180516292641 & 115.141948370736 \tabularnewline
83 & 93.0199999999999 & 67.6130324758798 & 118.42696752412 \tabularnewline
84 & 93.0599999999999 & 64.2638615895299 & 121.85613841047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205603&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]92.62[/C][C]91.4905225256069[/C][C]93.7494774743931[/C][/ROW]
[ROW][C]74[/C][C]92.66[/C][C]90.1344115882022[/C][C]95.1855884117978[/C][/ROW]
[ROW][C]75[/C][C]92.7[/C][C]88.4738822647422[/C][C]96.9261177352578[/C][/ROW]
[ROW][C]76[/C][C]92.74[/C][C]86.5535970908092[/C][C]98.9264029091907[/C][/ROW]
[ROW][C]77[/C][C]92.78[/C][C]84.4035708631971[/C][C]101.156429136803[/C][/ROW]
[ROW][C]78[/C][C]92.82[/C][C]82.04547160059[/C][C]103.59452839941[/C][/ROW]
[ROW][C]79[/C][C]92.8599999999999[/C][C]79.4958422965529[/C][C]106.224157703447[/C][/ROW]
[ROW][C]80[/C][C]92.8999999999999[/C][C]76.7678349099404[/C][C]109.03216509006[/C][/ROW]
[ROW][C]81[/C][C]92.9399999999999[/C][C]73.8722256392882[/C][C]112.007774360712[/C][/ROW]
[ROW][C]82[/C][C]92.9799999999999[/C][C]70.8180516292641[/C][C]115.141948370736[/C][/ROW]
[ROW][C]83[/C][C]93.0199999999999[/C][C]67.6130324758798[/C][C]118.42696752412[/C][/ROW]
[ROW][C]84[/C][C]93.0599999999999[/C][C]64.2638615895299[/C][C]121.85613841047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205603&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205603&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
7392.6291.490522525606993.7494774743931
7492.6690.134411588202295.1855884117978
7592.788.473882264742296.9261177352578
7692.7486.553597090809298.9264029091907
7792.7884.4035708631971101.156429136803
7892.8282.04547160059103.59452839941
7992.859999999999979.4958422965529106.224157703447
8092.899999999999976.7678349099404109.03216509006
8192.939999999999973.8722256392882112.007774360712
8292.979999999999970.8180516292641115.141948370736
8393.019999999999967.6130324758798118.42696752412
8493.059999999999964.2638615895299121.85613841047



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')