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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Jan 2013 10:06:26 -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/12/t1358003229jrgdnaajvdtnlpf.htm/, Retrieved Sun, 28 Apr 2024 08:57:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205229, Retrieved Sun, 28 Apr 2024 08:57:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exp smoothing eig...] [2013-01-12 15:06:26] [21b9ad762194a0cf58934491430d34cc] [Current]
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Dataseries X:
46,56
46,72
47,01
47,26
47,49
47,51
47,52
47,66
47,71
47,87
48
48
48,05
48,25
48,72
48,94
49,16
49,18
49,25
49,34
49,49
49,57
49,63
49,67
49,7
49,8
50,09
50,49
50,73
51,12
51,15
51,41
51,61
52,06
52,17
52,18
52,19
52,74
53,05
53,38
53,78
53,82
53,88
53,96
54,14
54,2
54,35
54,36
54,39
54,77
54,91
55,06
55,38
55,41
55,47
55,58
55,67
55,97
56,03
56,06
56,08
56,43
56,65
56,96
57,37
57,51
57,61
57,7
57,91
58,12
58,18
58,16




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=205229&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=205229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205229&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=205229&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=205229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205229&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
347.0146.880.130000000000003
447.2647.170.0900000000000034
547.4947.420.0700000000000074
647.5147.65-0.140000000000001
747.5247.67-0.149999999999991
847.6647.68-0.0200000000000031
947.7147.82-0.109999999999992
1047.8747.870
114848.03-0.029999999999994
124848.16-0.159999999999997
1348.0548.16-0.109999999999999
1448.2548.210.0400000000000063
1548.7248.410.310000000000002
1648.9448.880.0600000000000023
1749.1649.10.0600000000000023
1849.1849.32-0.139999999999993
1949.2549.34-0.0899999999999963
2049.3449.41-0.0699999999999932
2149.4949.5-0.00999999999999801
2249.5749.65-0.0799999999999983
2349.6349.73-0.0999999999999943
2449.6749.79-0.119999999999997
2549.749.83-0.129999999999995
2649.849.86-0.0600000000000023
2750.0949.960.13000000000001
2850.4950.250.240000000000002
2950.7350.650.0799999999999983
3051.1250.890.230000000000004
3151.1551.28-0.129999999999995
3251.4151.310.100000000000001
3351.6151.570.0400000000000063
3452.0651.770.290000000000006
3552.1752.22-0.0499999999999972
3652.1852.33-0.149999999999999
3752.1952.34-0.149999999999999
3852.7452.350.390000000000008
3953.0552.90.149999999999999
4053.3853.210.170000000000009
4153.7853.540.240000000000002
4253.8253.94-0.119999999999997
4353.8853.98-0.0999999999999943
4453.9654.04-0.0799999999999983
4554.1454.120.0200000000000031
4654.254.3-0.0999999999999943
4754.3554.36-0.00999999999999801
4854.3654.51-0.149999999999999
4954.3954.52-0.129999999999995
5054.7754.550.220000000000006
5154.9154.93-0.0200000000000031
5255.0655.07-0.00999999999999091
5355.3855.220.160000000000004
5455.4155.54-0.130000000000003
5555.4755.57-0.0999999999999943
5655.5855.63-0.0499999999999972
5755.6755.74-0.0699999999999932
5855.9755.830.140000000000001
5956.0356.13-0.0999999999999943
6056.0656.19-0.129999999999995
6156.0856.22-0.140000000000001
6256.4356.240.190000000000005
6356.6556.590.0600000000000023
6456.9656.810.150000000000006
6557.3757.120.25
6657.5157.53-0.019999999999996
6757.6157.67-0.0599999999999952
6857.757.77-0.0699999999999932
6957.9157.860.0499999999999972
7058.1258.070.0500000000000043
7158.1858.28-0.0999999999999943
7258.1658.34-0.18

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 47.01 & 46.88 & 0.130000000000003 \tabularnewline
4 & 47.26 & 47.17 & 0.0900000000000034 \tabularnewline
5 & 47.49 & 47.42 & 0.0700000000000074 \tabularnewline
6 & 47.51 & 47.65 & -0.140000000000001 \tabularnewline
7 & 47.52 & 47.67 & -0.149999999999991 \tabularnewline
8 & 47.66 & 47.68 & -0.0200000000000031 \tabularnewline
9 & 47.71 & 47.82 & -0.109999999999992 \tabularnewline
10 & 47.87 & 47.87 & 0 \tabularnewline
11 & 48 & 48.03 & -0.029999999999994 \tabularnewline
12 & 48 & 48.16 & -0.159999999999997 \tabularnewline
13 & 48.05 & 48.16 & -0.109999999999999 \tabularnewline
14 & 48.25 & 48.21 & 0.0400000000000063 \tabularnewline
15 & 48.72 & 48.41 & 0.310000000000002 \tabularnewline
16 & 48.94 & 48.88 & 0.0600000000000023 \tabularnewline
17 & 49.16 & 49.1 & 0.0600000000000023 \tabularnewline
18 & 49.18 & 49.32 & -0.139999999999993 \tabularnewline
19 & 49.25 & 49.34 & -0.0899999999999963 \tabularnewline
20 & 49.34 & 49.41 & -0.0699999999999932 \tabularnewline
21 & 49.49 & 49.5 & -0.00999999999999801 \tabularnewline
22 & 49.57 & 49.65 & -0.0799999999999983 \tabularnewline
23 & 49.63 & 49.73 & -0.0999999999999943 \tabularnewline
24 & 49.67 & 49.79 & -0.119999999999997 \tabularnewline
25 & 49.7 & 49.83 & -0.129999999999995 \tabularnewline
26 & 49.8 & 49.86 & -0.0600000000000023 \tabularnewline
27 & 50.09 & 49.96 & 0.13000000000001 \tabularnewline
28 & 50.49 & 50.25 & 0.240000000000002 \tabularnewline
29 & 50.73 & 50.65 & 0.0799999999999983 \tabularnewline
30 & 51.12 & 50.89 & 0.230000000000004 \tabularnewline
31 & 51.15 & 51.28 & -0.129999999999995 \tabularnewline
32 & 51.41 & 51.31 & 0.100000000000001 \tabularnewline
33 & 51.61 & 51.57 & 0.0400000000000063 \tabularnewline
34 & 52.06 & 51.77 & 0.290000000000006 \tabularnewline
35 & 52.17 & 52.22 & -0.0499999999999972 \tabularnewline
36 & 52.18 & 52.33 & -0.149999999999999 \tabularnewline
37 & 52.19 & 52.34 & -0.149999999999999 \tabularnewline
38 & 52.74 & 52.35 & 0.390000000000008 \tabularnewline
39 & 53.05 & 52.9 & 0.149999999999999 \tabularnewline
40 & 53.38 & 53.21 & 0.170000000000009 \tabularnewline
41 & 53.78 & 53.54 & 0.240000000000002 \tabularnewline
42 & 53.82 & 53.94 & -0.119999999999997 \tabularnewline
43 & 53.88 & 53.98 & -0.0999999999999943 \tabularnewline
44 & 53.96 & 54.04 & -0.0799999999999983 \tabularnewline
45 & 54.14 & 54.12 & 0.0200000000000031 \tabularnewline
46 & 54.2 & 54.3 & -0.0999999999999943 \tabularnewline
47 & 54.35 & 54.36 & -0.00999999999999801 \tabularnewline
48 & 54.36 & 54.51 & -0.149999999999999 \tabularnewline
49 & 54.39 & 54.52 & -0.129999999999995 \tabularnewline
50 & 54.77 & 54.55 & 0.220000000000006 \tabularnewline
51 & 54.91 & 54.93 & -0.0200000000000031 \tabularnewline
52 & 55.06 & 55.07 & -0.00999999999999091 \tabularnewline
53 & 55.38 & 55.22 & 0.160000000000004 \tabularnewline
54 & 55.41 & 55.54 & -0.130000000000003 \tabularnewline
55 & 55.47 & 55.57 & -0.0999999999999943 \tabularnewline
56 & 55.58 & 55.63 & -0.0499999999999972 \tabularnewline
57 & 55.67 & 55.74 & -0.0699999999999932 \tabularnewline
58 & 55.97 & 55.83 & 0.140000000000001 \tabularnewline
59 & 56.03 & 56.13 & -0.0999999999999943 \tabularnewline
60 & 56.06 & 56.19 & -0.129999999999995 \tabularnewline
61 & 56.08 & 56.22 & -0.140000000000001 \tabularnewline
62 & 56.43 & 56.24 & 0.190000000000005 \tabularnewline
63 & 56.65 & 56.59 & 0.0600000000000023 \tabularnewline
64 & 56.96 & 56.81 & 0.150000000000006 \tabularnewline
65 & 57.37 & 57.12 & 0.25 \tabularnewline
66 & 57.51 & 57.53 & -0.019999999999996 \tabularnewline
67 & 57.61 & 57.67 & -0.0599999999999952 \tabularnewline
68 & 57.7 & 57.77 & -0.0699999999999932 \tabularnewline
69 & 57.91 & 57.86 & 0.0499999999999972 \tabularnewline
70 & 58.12 & 58.07 & 0.0500000000000043 \tabularnewline
71 & 58.18 & 58.28 & -0.0999999999999943 \tabularnewline
72 & 58.16 & 58.34 & -0.18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205229&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]47.01[/C][C]46.88[/C][C]0.130000000000003[/C][/ROW]
[ROW][C]4[/C][C]47.26[/C][C]47.17[/C][C]0.0900000000000034[/C][/ROW]
[ROW][C]5[/C][C]47.49[/C][C]47.42[/C][C]0.0700000000000074[/C][/ROW]
[ROW][C]6[/C][C]47.51[/C][C]47.65[/C][C]-0.140000000000001[/C][/ROW]
[ROW][C]7[/C][C]47.52[/C][C]47.67[/C][C]-0.149999999999991[/C][/ROW]
[ROW][C]8[/C][C]47.66[/C][C]47.68[/C][C]-0.0200000000000031[/C][/ROW]
[ROW][C]9[/C][C]47.71[/C][C]47.82[/C][C]-0.109999999999992[/C][/ROW]
[ROW][C]10[/C][C]47.87[/C][C]47.87[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]48[/C][C]48.03[/C][C]-0.029999999999994[/C][/ROW]
[ROW][C]12[/C][C]48[/C][C]48.16[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]13[/C][C]48.05[/C][C]48.16[/C][C]-0.109999999999999[/C][/ROW]
[ROW][C]14[/C][C]48.25[/C][C]48.21[/C][C]0.0400000000000063[/C][/ROW]
[ROW][C]15[/C][C]48.72[/C][C]48.41[/C][C]0.310000000000002[/C][/ROW]
[ROW][C]16[/C][C]48.94[/C][C]48.88[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]17[/C][C]49.16[/C][C]49.1[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]18[/C][C]49.18[/C][C]49.32[/C][C]-0.139999999999993[/C][/ROW]
[ROW][C]19[/C][C]49.25[/C][C]49.34[/C][C]-0.0899999999999963[/C][/ROW]
[ROW][C]20[/C][C]49.34[/C][C]49.41[/C][C]-0.0699999999999932[/C][/ROW]
[ROW][C]21[/C][C]49.49[/C][C]49.5[/C][C]-0.00999999999999801[/C][/ROW]
[ROW][C]22[/C][C]49.57[/C][C]49.65[/C][C]-0.0799999999999983[/C][/ROW]
[ROW][C]23[/C][C]49.63[/C][C]49.73[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]24[/C][C]49.67[/C][C]49.79[/C][C]-0.119999999999997[/C][/ROW]
[ROW][C]25[/C][C]49.7[/C][C]49.83[/C][C]-0.129999999999995[/C][/ROW]
[ROW][C]26[/C][C]49.8[/C][C]49.86[/C][C]-0.0600000000000023[/C][/ROW]
[ROW][C]27[/C][C]50.09[/C][C]49.96[/C][C]0.13000000000001[/C][/ROW]
[ROW][C]28[/C][C]50.49[/C][C]50.25[/C][C]0.240000000000002[/C][/ROW]
[ROW][C]29[/C][C]50.73[/C][C]50.65[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]30[/C][C]51.12[/C][C]50.89[/C][C]0.230000000000004[/C][/ROW]
[ROW][C]31[/C][C]51.15[/C][C]51.28[/C][C]-0.129999999999995[/C][/ROW]
[ROW][C]32[/C][C]51.41[/C][C]51.31[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]33[/C][C]51.61[/C][C]51.57[/C][C]0.0400000000000063[/C][/ROW]
[ROW][C]34[/C][C]52.06[/C][C]51.77[/C][C]0.290000000000006[/C][/ROW]
[ROW][C]35[/C][C]52.17[/C][C]52.22[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]36[/C][C]52.18[/C][C]52.33[/C][C]-0.149999999999999[/C][/ROW]
[ROW][C]37[/C][C]52.19[/C][C]52.34[/C][C]-0.149999999999999[/C][/ROW]
[ROW][C]38[/C][C]52.74[/C][C]52.35[/C][C]0.390000000000008[/C][/ROW]
[ROW][C]39[/C][C]53.05[/C][C]52.9[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]40[/C][C]53.38[/C][C]53.21[/C][C]0.170000000000009[/C][/ROW]
[ROW][C]41[/C][C]53.78[/C][C]53.54[/C][C]0.240000000000002[/C][/ROW]
[ROW][C]42[/C][C]53.82[/C][C]53.94[/C][C]-0.119999999999997[/C][/ROW]
[ROW][C]43[/C][C]53.88[/C][C]53.98[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]44[/C][C]53.96[/C][C]54.04[/C][C]-0.0799999999999983[/C][/ROW]
[ROW][C]45[/C][C]54.14[/C][C]54.12[/C][C]0.0200000000000031[/C][/ROW]
[ROW][C]46[/C][C]54.2[/C][C]54.3[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]47[/C][C]54.35[/C][C]54.36[/C][C]-0.00999999999999801[/C][/ROW]
[ROW][C]48[/C][C]54.36[/C][C]54.51[/C][C]-0.149999999999999[/C][/ROW]
[ROW][C]49[/C][C]54.39[/C][C]54.52[/C][C]-0.129999999999995[/C][/ROW]
[ROW][C]50[/C][C]54.77[/C][C]54.55[/C][C]0.220000000000006[/C][/ROW]
[ROW][C]51[/C][C]54.91[/C][C]54.93[/C][C]-0.0200000000000031[/C][/ROW]
[ROW][C]52[/C][C]55.06[/C][C]55.07[/C][C]-0.00999999999999091[/C][/ROW]
[ROW][C]53[/C][C]55.38[/C][C]55.22[/C][C]0.160000000000004[/C][/ROW]
[ROW][C]54[/C][C]55.41[/C][C]55.54[/C][C]-0.130000000000003[/C][/ROW]
[ROW][C]55[/C][C]55.47[/C][C]55.57[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]56[/C][C]55.58[/C][C]55.63[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]57[/C][C]55.67[/C][C]55.74[/C][C]-0.0699999999999932[/C][/ROW]
[ROW][C]58[/C][C]55.97[/C][C]55.83[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]59[/C][C]56.03[/C][C]56.13[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]60[/C][C]56.06[/C][C]56.19[/C][C]-0.129999999999995[/C][/ROW]
[ROW][C]61[/C][C]56.08[/C][C]56.22[/C][C]-0.140000000000001[/C][/ROW]
[ROW][C]62[/C][C]56.43[/C][C]56.24[/C][C]0.190000000000005[/C][/ROW]
[ROW][C]63[/C][C]56.65[/C][C]56.59[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]64[/C][C]56.96[/C][C]56.81[/C][C]0.150000000000006[/C][/ROW]
[ROW][C]65[/C][C]57.37[/C][C]57.12[/C][C]0.25[/C][/ROW]
[ROW][C]66[/C][C]57.51[/C][C]57.53[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]67[/C][C]57.61[/C][C]57.67[/C][C]-0.0599999999999952[/C][/ROW]
[ROW][C]68[/C][C]57.7[/C][C]57.77[/C][C]-0.0699999999999932[/C][/ROW]
[ROW][C]69[/C][C]57.91[/C][C]57.86[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]70[/C][C]58.12[/C][C]58.07[/C][C]0.0500000000000043[/C][/ROW]
[ROW][C]71[/C][C]58.18[/C][C]58.28[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]72[/C][C]58.16[/C][C]58.34[/C][C]-0.18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205229&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205229&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
347.0146.880.130000000000003
447.2647.170.0900000000000034
547.4947.420.0700000000000074
647.5147.65-0.140000000000001
747.5247.67-0.149999999999991
847.6647.68-0.0200000000000031
947.7147.82-0.109999999999992
1047.8747.870
114848.03-0.029999999999994
124848.16-0.159999999999997
1348.0548.16-0.109999999999999
1448.2548.210.0400000000000063
1548.7248.410.310000000000002
1648.9448.880.0600000000000023
1749.1649.10.0600000000000023
1849.1849.32-0.139999999999993
1949.2549.34-0.0899999999999963
2049.3449.41-0.0699999999999932
2149.4949.5-0.00999999999999801
2249.5749.65-0.0799999999999983
2349.6349.73-0.0999999999999943
2449.6749.79-0.119999999999997
2549.749.83-0.129999999999995
2649.849.86-0.0600000000000023
2750.0949.960.13000000000001
2850.4950.250.240000000000002
2950.7350.650.0799999999999983
3051.1250.890.230000000000004
3151.1551.28-0.129999999999995
3251.4151.310.100000000000001
3351.6151.570.0400000000000063
3452.0651.770.290000000000006
3552.1752.22-0.0499999999999972
3652.1852.33-0.149999999999999
3752.1952.34-0.149999999999999
3852.7452.350.390000000000008
3953.0552.90.149999999999999
4053.3853.210.170000000000009
4153.7853.540.240000000000002
4253.8253.94-0.119999999999997
4353.8853.98-0.0999999999999943
4453.9654.04-0.0799999999999983
4554.1454.120.0200000000000031
4654.254.3-0.0999999999999943
4754.3554.36-0.00999999999999801
4854.3654.51-0.149999999999999
4954.3954.52-0.129999999999995
5054.7754.550.220000000000006
5154.9154.93-0.0200000000000031
5255.0655.07-0.00999999999999091
5355.3855.220.160000000000004
5455.4155.54-0.130000000000003
5555.4755.57-0.0999999999999943
5655.5855.63-0.0499999999999972
5755.6755.74-0.0699999999999932
5855.9755.830.140000000000001
5956.0356.13-0.0999999999999943
6056.0656.19-0.129999999999995
6156.0856.22-0.140000000000001
6256.4356.240.190000000000005
6356.6556.590.0600000000000023
6456.9656.810.150000000000006
6557.3757.120.25
6657.5157.53-0.019999999999996
6757.6157.67-0.0599999999999952
6857.757.77-0.0699999999999932
6957.9157.860.0499999999999972
7058.1258.070.0500000000000043
7158.1858.28-0.0999999999999943
7258.1658.34-0.18







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7358.3258.050686198149758.5893138018503
7458.4858.09913276888958.8608672311109
7558.6458.173534812015759.1064651879842
7658.858.261372396299459.3386276037006
7758.9658.357796031783859.5622039682162
7859.1258.460318604777759.7796813952222
7959.2858.567462655666859.9925373443332
8059.4458.678265537778160.2017344622219
8159.658.792058594449160.4079414055509
8259.7658.908354980833760.6116450191662
8359.9259.026787168398460.8132128316015
8460.0859.147069624031461.0129303759685

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 58.32 & 58.0506861981497 & 58.5893138018503 \tabularnewline
74 & 58.48 & 58.099132768889 & 58.8608672311109 \tabularnewline
75 & 58.64 & 58.1735348120157 & 59.1064651879842 \tabularnewline
76 & 58.8 & 58.2613723962994 & 59.3386276037006 \tabularnewline
77 & 58.96 & 58.3577960317838 & 59.5622039682162 \tabularnewline
78 & 59.12 & 58.4603186047777 & 59.7796813952222 \tabularnewline
79 & 59.28 & 58.5674626556668 & 59.9925373443332 \tabularnewline
80 & 59.44 & 58.6782655377781 & 60.2017344622219 \tabularnewline
81 & 59.6 & 58.7920585944491 & 60.4079414055509 \tabularnewline
82 & 59.76 & 58.9083549808337 & 60.6116450191662 \tabularnewline
83 & 59.92 & 59.0267871683984 & 60.8132128316015 \tabularnewline
84 & 60.08 & 59.1470696240314 & 61.0129303759685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205229&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]58.32[/C][C]58.0506861981497[/C][C]58.5893138018503[/C][/ROW]
[ROW][C]74[/C][C]58.48[/C][C]58.099132768889[/C][C]58.8608672311109[/C][/ROW]
[ROW][C]75[/C][C]58.64[/C][C]58.1735348120157[/C][C]59.1064651879842[/C][/ROW]
[ROW][C]76[/C][C]58.8[/C][C]58.2613723962994[/C][C]59.3386276037006[/C][/ROW]
[ROW][C]77[/C][C]58.96[/C][C]58.3577960317838[/C][C]59.5622039682162[/C][/ROW]
[ROW][C]78[/C][C]59.12[/C][C]58.4603186047777[/C][C]59.7796813952222[/C][/ROW]
[ROW][C]79[/C][C]59.28[/C][C]58.5674626556668[/C][C]59.9925373443332[/C][/ROW]
[ROW][C]80[/C][C]59.44[/C][C]58.6782655377781[/C][C]60.2017344622219[/C][/ROW]
[ROW][C]81[/C][C]59.6[/C][C]58.7920585944491[/C][C]60.4079414055509[/C][/ROW]
[ROW][C]82[/C][C]59.76[/C][C]58.9083549808337[/C][C]60.6116450191662[/C][/ROW]
[ROW][C]83[/C][C]59.92[/C][C]59.0267871683984[/C][C]60.8132128316015[/C][/ROW]
[ROW][C]84[/C][C]60.08[/C][C]59.1470696240314[/C][C]61.0129303759685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205229&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205229&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
7358.3258.050686198149758.5893138018503
7458.4858.09913276888958.8608672311109
7558.6458.173534812015759.1064651879842
7658.858.261372396299459.3386276037006
7758.9658.357796031783859.5622039682162
7859.1258.460318604777759.7796813952222
7959.2858.567462655666859.9925373443332
8059.4458.678265537778160.2017344622219
8159.658.792058594449160.4079414055509
8259.7658.908354980833760.6116450191662
8359.9259.026787168398460.8132128316015
8460.0859.147069624031461.0129303759685



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')