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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 17:49:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/28/t1417197024pql0xfmvhjmbeg5.htm/, Retrieved Sun, 19 May 2024 13:08:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260999, Retrieved Sun, 19 May 2024 13:08:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gemiddelde consum...] [2014-11-28 17:49:51] [1ab96e54865215824aa8065210e49a0c] [Current]
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Dataseries X:
48,74
48,79
48,82
48,82
49,20
49,30
49,30
49,34
49,47
49,65
49,70
49,75
49,75
49,70
50,09
50,19
50,53
50,55
50,55
50,55
50,58
50,61
50,94
51,01
51,01
51,04
51,15
51,31
51,31
51,34
51,34
51,34
51,47
51,95
51,97
51,92
51,92
51,91
51,97
52,14
52,33
52,40
52,40
52,41
52,71
53,17
53,33
53,32
53,32
53,30
53,31
53,72
53,87
53,91
53,91
53,96
54,02
54,33
54,48
54,54
52,40
52,45
52,38
52,45
52,83
52,76
52,86
52,88
53,32
53,20
53,22
53,22




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=260999&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=260999&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260999&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=260999&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=260999&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260999&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
348.8248.84-0.019999999999996
448.8248.87-0.0499999999999972
549.248.870.330000000000005
649.349.250.0499999999999972
749.349.35-0.0499999999999972
849.3449.35-0.00999999999999091
949.4749.390.0799999999999983
1049.6549.520.130000000000003
1149.749.77.105427357601e-15
1249.7549.750
1349.7549.8-0.0499999999999972
1449.749.8-0.0999999999999943
1550.0949.750.340000000000003
1650.1950.140.0499999999999972
1750.5350.240.290000000000006
1850.5550.58-0.0300000000000011
1950.5550.6-0.0499999999999972
2050.5550.6-0.0499999999999972
2150.5850.6-0.019999999999996
2250.6150.63-0.019999999999996
2350.9450.660.280000000000001
2451.0150.990.0200000000000031
2551.0151.06-0.0499999999999972
2651.0451.06-0.019999999999996
2751.1551.090.0600000000000023
2851.3151.20.110000000000007
2951.3151.36-0.0499999999999972
3051.3451.36-0.019999999999996
3151.3451.39-0.0499999999999972
3251.3451.39-0.0499999999999972
3351.4751.390.0799999999999983
3451.9551.520.430000000000007
3551.9752-0.0300000000000011
3651.9252.02-0.0999999999999943
3751.9251.97-0.0499999999999972
3851.9151.97-0.0600000000000023
3951.9751.960.0100000000000051
4052.1452.020.120000000000005
4152.3352.190.140000000000001
4252.452.380.0200000000000031
4352.452.45-0.0499999999999972
4452.4152.45-0.0399999999999991
4552.7152.460.250000000000007
4653.1752.760.410000000000004
4753.3353.220.109999999999999
4853.3253.38-0.0599999999999952
4953.3253.37-0.0499999999999972
5053.353.37-0.0700000000000003
5153.3153.35-0.039999999999992
5253.7253.360.359999999999999
5353.8753.770.100000000000001
5453.9153.92-0.00999999999999801
5553.9153.96-0.0499999999999972
5653.9653.967.105427357601e-15
5754.0254.010.0100000000000051
5854.3354.070.259999999999998
5954.4854.380.100000000000001
6054.5454.530.0100000000000051
6152.454.59-2.19
6252.4552.457.105427357601e-15
6352.3852.5-0.119999999999997
6452.4552.430.0200000000000031
6552.8352.50.329999999999998
6652.7652.88-0.119999999999997
6752.8652.810.0500000000000043
6852.8852.91-0.029999999999994
6953.3252.930.390000000000001
7053.253.37-0.169999999999995
7153.2253.25-0.0300000000000011
7253.2253.27-0.0499999999999972

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 48.82 & 48.84 & -0.019999999999996 \tabularnewline
4 & 48.82 & 48.87 & -0.0499999999999972 \tabularnewline
5 & 49.2 & 48.87 & 0.330000000000005 \tabularnewline
6 & 49.3 & 49.25 & 0.0499999999999972 \tabularnewline
7 & 49.3 & 49.35 & -0.0499999999999972 \tabularnewline
8 & 49.34 & 49.35 & -0.00999999999999091 \tabularnewline
9 & 49.47 & 49.39 & 0.0799999999999983 \tabularnewline
10 & 49.65 & 49.52 & 0.130000000000003 \tabularnewline
11 & 49.7 & 49.7 & 7.105427357601e-15 \tabularnewline
12 & 49.75 & 49.75 & 0 \tabularnewline
13 & 49.75 & 49.8 & -0.0499999999999972 \tabularnewline
14 & 49.7 & 49.8 & -0.0999999999999943 \tabularnewline
15 & 50.09 & 49.75 & 0.340000000000003 \tabularnewline
16 & 50.19 & 50.14 & 0.0499999999999972 \tabularnewline
17 & 50.53 & 50.24 & 0.290000000000006 \tabularnewline
18 & 50.55 & 50.58 & -0.0300000000000011 \tabularnewline
19 & 50.55 & 50.6 & -0.0499999999999972 \tabularnewline
20 & 50.55 & 50.6 & -0.0499999999999972 \tabularnewline
21 & 50.58 & 50.6 & -0.019999999999996 \tabularnewline
22 & 50.61 & 50.63 & -0.019999999999996 \tabularnewline
23 & 50.94 & 50.66 & 0.280000000000001 \tabularnewline
24 & 51.01 & 50.99 & 0.0200000000000031 \tabularnewline
25 & 51.01 & 51.06 & -0.0499999999999972 \tabularnewline
26 & 51.04 & 51.06 & -0.019999999999996 \tabularnewline
27 & 51.15 & 51.09 & 0.0600000000000023 \tabularnewline
28 & 51.31 & 51.2 & 0.110000000000007 \tabularnewline
29 & 51.31 & 51.36 & -0.0499999999999972 \tabularnewline
30 & 51.34 & 51.36 & -0.019999999999996 \tabularnewline
31 & 51.34 & 51.39 & -0.0499999999999972 \tabularnewline
32 & 51.34 & 51.39 & -0.0499999999999972 \tabularnewline
33 & 51.47 & 51.39 & 0.0799999999999983 \tabularnewline
34 & 51.95 & 51.52 & 0.430000000000007 \tabularnewline
35 & 51.97 & 52 & -0.0300000000000011 \tabularnewline
36 & 51.92 & 52.02 & -0.0999999999999943 \tabularnewline
37 & 51.92 & 51.97 & -0.0499999999999972 \tabularnewline
38 & 51.91 & 51.97 & -0.0600000000000023 \tabularnewline
39 & 51.97 & 51.96 & 0.0100000000000051 \tabularnewline
40 & 52.14 & 52.02 & 0.120000000000005 \tabularnewline
41 & 52.33 & 52.19 & 0.140000000000001 \tabularnewline
42 & 52.4 & 52.38 & 0.0200000000000031 \tabularnewline
43 & 52.4 & 52.45 & -0.0499999999999972 \tabularnewline
44 & 52.41 & 52.45 & -0.0399999999999991 \tabularnewline
45 & 52.71 & 52.46 & 0.250000000000007 \tabularnewline
46 & 53.17 & 52.76 & 0.410000000000004 \tabularnewline
47 & 53.33 & 53.22 & 0.109999999999999 \tabularnewline
48 & 53.32 & 53.38 & -0.0599999999999952 \tabularnewline
49 & 53.32 & 53.37 & -0.0499999999999972 \tabularnewline
50 & 53.3 & 53.37 & -0.0700000000000003 \tabularnewline
51 & 53.31 & 53.35 & -0.039999999999992 \tabularnewline
52 & 53.72 & 53.36 & 0.359999999999999 \tabularnewline
53 & 53.87 & 53.77 & 0.100000000000001 \tabularnewline
54 & 53.91 & 53.92 & -0.00999999999999801 \tabularnewline
55 & 53.91 & 53.96 & -0.0499999999999972 \tabularnewline
56 & 53.96 & 53.96 & 7.105427357601e-15 \tabularnewline
57 & 54.02 & 54.01 & 0.0100000000000051 \tabularnewline
58 & 54.33 & 54.07 & 0.259999999999998 \tabularnewline
59 & 54.48 & 54.38 & 0.100000000000001 \tabularnewline
60 & 54.54 & 54.53 & 0.0100000000000051 \tabularnewline
61 & 52.4 & 54.59 & -2.19 \tabularnewline
62 & 52.45 & 52.45 & 7.105427357601e-15 \tabularnewline
63 & 52.38 & 52.5 & -0.119999999999997 \tabularnewline
64 & 52.45 & 52.43 & 0.0200000000000031 \tabularnewline
65 & 52.83 & 52.5 & 0.329999999999998 \tabularnewline
66 & 52.76 & 52.88 & -0.119999999999997 \tabularnewline
67 & 52.86 & 52.81 & 0.0500000000000043 \tabularnewline
68 & 52.88 & 52.91 & -0.029999999999994 \tabularnewline
69 & 53.32 & 52.93 & 0.390000000000001 \tabularnewline
70 & 53.2 & 53.37 & -0.169999999999995 \tabularnewline
71 & 53.22 & 53.25 & -0.0300000000000011 \tabularnewline
72 & 53.22 & 53.27 & -0.0499999999999972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260999&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]48.82[/C][C]48.84[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]4[/C][C]48.82[/C][C]48.87[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]5[/C][C]49.2[/C][C]48.87[/C][C]0.330000000000005[/C][/ROW]
[ROW][C]6[/C][C]49.3[/C][C]49.25[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]7[/C][C]49.3[/C][C]49.35[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]8[/C][C]49.34[/C][C]49.35[/C][C]-0.00999999999999091[/C][/ROW]
[ROW][C]9[/C][C]49.47[/C][C]49.39[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]10[/C][C]49.65[/C][C]49.52[/C][C]0.130000000000003[/C][/ROW]
[ROW][C]11[/C][C]49.7[/C][C]49.7[/C][C]7.105427357601e-15[/C][/ROW]
[ROW][C]12[/C][C]49.75[/C][C]49.75[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]49.75[/C][C]49.8[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]14[/C][C]49.7[/C][C]49.8[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]15[/C][C]50.09[/C][C]49.75[/C][C]0.340000000000003[/C][/ROW]
[ROW][C]16[/C][C]50.19[/C][C]50.14[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]17[/C][C]50.53[/C][C]50.24[/C][C]0.290000000000006[/C][/ROW]
[ROW][C]18[/C][C]50.55[/C][C]50.58[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]19[/C][C]50.55[/C][C]50.6[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]20[/C][C]50.55[/C][C]50.6[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]21[/C][C]50.58[/C][C]50.6[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]22[/C][C]50.61[/C][C]50.63[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]23[/C][C]50.94[/C][C]50.66[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]24[/C][C]51.01[/C][C]50.99[/C][C]0.0200000000000031[/C][/ROW]
[ROW][C]25[/C][C]51.01[/C][C]51.06[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]26[/C][C]51.04[/C][C]51.06[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]27[/C][C]51.15[/C][C]51.09[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]28[/C][C]51.31[/C][C]51.2[/C][C]0.110000000000007[/C][/ROW]
[ROW][C]29[/C][C]51.31[/C][C]51.36[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]30[/C][C]51.34[/C][C]51.36[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]31[/C][C]51.34[/C][C]51.39[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]32[/C][C]51.34[/C][C]51.39[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]33[/C][C]51.47[/C][C]51.39[/C][C]0.0799999999999983[/C][/ROW]
[ROW][C]34[/C][C]51.95[/C][C]51.52[/C][C]0.430000000000007[/C][/ROW]
[ROW][C]35[/C][C]51.97[/C][C]52[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]36[/C][C]51.92[/C][C]52.02[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]37[/C][C]51.92[/C][C]51.97[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]38[/C][C]51.91[/C][C]51.97[/C][C]-0.0600000000000023[/C][/ROW]
[ROW][C]39[/C][C]51.97[/C][C]51.96[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]40[/C][C]52.14[/C][C]52.02[/C][C]0.120000000000005[/C][/ROW]
[ROW][C]41[/C][C]52.33[/C][C]52.19[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]42[/C][C]52.4[/C][C]52.38[/C][C]0.0200000000000031[/C][/ROW]
[ROW][C]43[/C][C]52.4[/C][C]52.45[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]44[/C][C]52.41[/C][C]52.45[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]45[/C][C]52.71[/C][C]52.46[/C][C]0.250000000000007[/C][/ROW]
[ROW][C]46[/C][C]53.17[/C][C]52.76[/C][C]0.410000000000004[/C][/ROW]
[ROW][C]47[/C][C]53.33[/C][C]53.22[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]48[/C][C]53.32[/C][C]53.38[/C][C]-0.0599999999999952[/C][/ROW]
[ROW][C]49[/C][C]53.32[/C][C]53.37[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]50[/C][C]53.3[/C][C]53.37[/C][C]-0.0700000000000003[/C][/ROW]
[ROW][C]51[/C][C]53.31[/C][C]53.35[/C][C]-0.039999999999992[/C][/ROW]
[ROW][C]52[/C][C]53.72[/C][C]53.36[/C][C]0.359999999999999[/C][/ROW]
[ROW][C]53[/C][C]53.87[/C][C]53.77[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]54[/C][C]53.91[/C][C]53.92[/C][C]-0.00999999999999801[/C][/ROW]
[ROW][C]55[/C][C]53.91[/C][C]53.96[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]56[/C][C]53.96[/C][C]53.96[/C][C]7.105427357601e-15[/C][/ROW]
[ROW][C]57[/C][C]54.02[/C][C]54.01[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]58[/C][C]54.33[/C][C]54.07[/C][C]0.259999999999998[/C][/ROW]
[ROW][C]59[/C][C]54.48[/C][C]54.38[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]60[/C][C]54.54[/C][C]54.53[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]61[/C][C]52.4[/C][C]54.59[/C][C]-2.19[/C][/ROW]
[ROW][C]62[/C][C]52.45[/C][C]52.45[/C][C]7.105427357601e-15[/C][/ROW]
[ROW][C]63[/C][C]52.38[/C][C]52.5[/C][C]-0.119999999999997[/C][/ROW]
[ROW][C]64[/C][C]52.45[/C][C]52.43[/C][C]0.0200000000000031[/C][/ROW]
[ROW][C]65[/C][C]52.83[/C][C]52.5[/C][C]0.329999999999998[/C][/ROW]
[ROW][C]66[/C][C]52.76[/C][C]52.88[/C][C]-0.119999999999997[/C][/ROW]
[ROW][C]67[/C][C]52.86[/C][C]52.81[/C][C]0.0500000000000043[/C][/ROW]
[ROW][C]68[/C][C]52.88[/C][C]52.91[/C][C]-0.029999999999994[/C][/ROW]
[ROW][C]69[/C][C]53.32[/C][C]52.93[/C][C]0.390000000000001[/C][/ROW]
[ROW][C]70[/C][C]53.2[/C][C]53.37[/C][C]-0.169999999999995[/C][/ROW]
[ROW][C]71[/C][C]53.22[/C][C]53.25[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]72[/C][C]53.22[/C][C]53.27[/C][C]-0.0499999999999972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260999&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260999&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
348.8248.84-0.019999999999996
448.8248.87-0.0499999999999972
549.248.870.330000000000005
649.349.250.0499999999999972
749.349.35-0.0499999999999972
849.3449.35-0.00999999999999091
949.4749.390.0799999999999983
1049.6549.520.130000000000003
1149.749.77.105427357601e-15
1249.7549.750
1349.7549.8-0.0499999999999972
1449.749.8-0.0999999999999943
1550.0949.750.340000000000003
1650.1950.140.0499999999999972
1750.5350.240.290000000000006
1850.5550.58-0.0300000000000011
1950.5550.6-0.0499999999999972
2050.5550.6-0.0499999999999972
2150.5850.6-0.019999999999996
2250.6150.63-0.019999999999996
2350.9450.660.280000000000001
2451.0150.990.0200000000000031
2551.0151.06-0.0499999999999972
2651.0451.06-0.019999999999996
2751.1551.090.0600000000000023
2851.3151.20.110000000000007
2951.3151.36-0.0499999999999972
3051.3451.36-0.019999999999996
3151.3451.39-0.0499999999999972
3251.3451.39-0.0499999999999972
3351.4751.390.0799999999999983
3451.9551.520.430000000000007
3551.9752-0.0300000000000011
3651.9252.02-0.0999999999999943
3751.9251.97-0.0499999999999972
3851.9151.97-0.0600000000000023
3951.9751.960.0100000000000051
4052.1452.020.120000000000005
4152.3352.190.140000000000001
4252.452.380.0200000000000031
4352.452.45-0.0499999999999972
4452.4152.45-0.0399999999999991
4552.7152.460.250000000000007
4653.1752.760.410000000000004
4753.3353.220.109999999999999
4853.3253.38-0.0599999999999952
4953.3253.37-0.0499999999999972
5053.353.37-0.0700000000000003
5153.3153.35-0.039999999999992
5253.7253.360.359999999999999
5353.8753.770.100000000000001
5453.9153.92-0.00999999999999801
5553.9153.96-0.0499999999999972
5653.9653.967.105427357601e-15
5754.0254.010.0100000000000051
5854.3354.070.259999999999998
5954.4854.380.100000000000001
6054.5454.530.0100000000000051
6152.454.59-2.19
6252.4552.457.105427357601e-15
6352.3852.5-0.119999999999997
6452.4552.430.0200000000000031
6552.8352.50.329999999999998
6652.7652.88-0.119999999999997
6752.8652.810.0500000000000043
6852.8852.91-0.029999999999994
6953.3252.930.390000000000001
7053.253.37-0.169999999999995
7153.2253.25-0.0300000000000011
7253.2253.27-0.0499999999999972







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7353.2752.677824365119853.8621756348801
7453.3252.482537185845654.1574628141544
7553.3752.344321713383254.3956782866168
7653.4252.235648730239754.6043512697603
7753.4752.145855025788954.7941449742111
7853.5252.069471856434954.970528143565
7953.5752.003250537635355.1367494623646
8053.6251.945074371691255.2949256283088
8153.6751.893473095359555.4465269046404
8253.7251.847376218922455.5926237810775
8353.7751.80597560911255.7340243908879
8453.8251.768643426766455.8713565732335

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 53.27 & 52.6778243651198 & 53.8621756348801 \tabularnewline
74 & 53.32 & 52.4825371858456 & 54.1574628141544 \tabularnewline
75 & 53.37 & 52.3443217133832 & 54.3956782866168 \tabularnewline
76 & 53.42 & 52.2356487302397 & 54.6043512697603 \tabularnewline
77 & 53.47 & 52.1458550257889 & 54.7941449742111 \tabularnewline
78 & 53.52 & 52.0694718564349 & 54.970528143565 \tabularnewline
79 & 53.57 & 52.0032505376353 & 55.1367494623646 \tabularnewline
80 & 53.62 & 51.9450743716912 & 55.2949256283088 \tabularnewline
81 & 53.67 & 51.8934730953595 & 55.4465269046404 \tabularnewline
82 & 53.72 & 51.8473762189224 & 55.5926237810775 \tabularnewline
83 & 53.77 & 51.805975609112 & 55.7340243908879 \tabularnewline
84 & 53.82 & 51.7686434267664 & 55.8713565732335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260999&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]53.27[/C][C]52.6778243651198[/C][C]53.8621756348801[/C][/ROW]
[ROW][C]74[/C][C]53.32[/C][C]52.4825371858456[/C][C]54.1574628141544[/C][/ROW]
[ROW][C]75[/C][C]53.37[/C][C]52.3443217133832[/C][C]54.3956782866168[/C][/ROW]
[ROW][C]76[/C][C]53.42[/C][C]52.2356487302397[/C][C]54.6043512697603[/C][/ROW]
[ROW][C]77[/C][C]53.47[/C][C]52.1458550257889[/C][C]54.7941449742111[/C][/ROW]
[ROW][C]78[/C][C]53.52[/C][C]52.0694718564349[/C][C]54.970528143565[/C][/ROW]
[ROW][C]79[/C][C]53.57[/C][C]52.0032505376353[/C][C]55.1367494623646[/C][/ROW]
[ROW][C]80[/C][C]53.62[/C][C]51.9450743716912[/C][C]55.2949256283088[/C][/ROW]
[ROW][C]81[/C][C]53.67[/C][C]51.8934730953595[/C][C]55.4465269046404[/C][/ROW]
[ROW][C]82[/C][C]53.72[/C][C]51.8473762189224[/C][C]55.5926237810775[/C][/ROW]
[ROW][C]83[/C][C]53.77[/C][C]51.805975609112[/C][C]55.7340243908879[/C][/ROW]
[ROW][C]84[/C][C]53.82[/C][C]51.7686434267664[/C][C]55.8713565732335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260999&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260999&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
7353.2752.677824365119853.8621756348801
7453.3252.482537185845654.1574628141544
7553.3752.344321713383254.3956782866168
7653.4252.235648730239754.6043512697603
7753.4752.145855025788954.7941449742111
7853.5252.069471856434954.970528143565
7953.5752.003250537635355.1367494623646
8053.6251.945074371691255.2949256283088
8153.6751.893473095359555.4465269046404
8253.7251.847376218922455.5926237810775
8353.7751.80597560911255.7340243908879
8453.8251.768643426766455.8713565732335



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')