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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 13 Jan 2014 06:09:55 -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/2014/Jan/13/t138961147436or1ec6qy4uh6e.htm/, Retrieved Tue, 28 May 2024 05:21:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233135, Retrieved Tue, 28 May 2024 05:21:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-13 11:09:55] [ef6034d7f955a1620c5a7f0f2c706f38] [Current]
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Dataseries X:
101,16
101,16
101,16
101,16
101,16
101,16
101,16
101,16
101,16
101,21
101,21
101,21
103,16
103,16
103,16
103,16
101,13
101,13
100,53
100,53
100,53
100,53
100,53
100,53
100,53
100,53
100,53
99,42
99,42
99,42
99,42
100,31
100,31
102,25
102,25
102,25
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,94
101,94
101,94
101,94
101,94
102
102
102
102
102
102
102
102
102
102
102
102
109,67
109,67
109,67
109,67
109,67
109,67
109,67
109,67
109,67
109,67
109,67
109,67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233135&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]5 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=233135&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233135&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 time5 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=233135&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=233135&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233135&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
3101.16101.160
4101.16101.160
5101.16101.160
6101.16101.160
7101.16101.160
8101.16101.160
9101.16101.160
10101.21101.160.0499999999999972
11101.21101.210
12101.21101.210
13103.16101.211.95
14103.16103.160
15103.16103.160
16103.16103.160
17101.13103.16-2.03
18101.13101.130
19100.53101.13-0.599999999999994
20100.53100.530
21100.53100.530
22100.53100.530
23100.53100.530
24100.53100.530
25100.53100.530
26100.53100.530
27100.53100.530
2899.42100.53-1.11
2999.4299.420
3099.4299.420
3199.4299.420
32100.3199.420.890000000000001
33100.31100.310
34102.25100.311.94
35102.25102.250
36102.25102.250
37101.81102.25-0.439999999999998
38101.81101.810
39101.81101.810
40101.81101.810
41101.81101.810
42101.81101.810
43101.81101.810
44101.81101.810
45101.81101.810
46101.81101.810
47101.81101.810
48101.81101.810
49101.81101.810
50101.81101.810
51101.81101.810
52101.81101.810
53101.81101.810
54101.81101.810
55101.81101.810
56101.94101.810.129999999999995
57101.94101.940
58101.94101.940
59101.94101.940
60101.94101.940
61102101.940.0600000000000023
621021020
631021020
641021020
651021020
661021020
671021020
681021020
691021020
701021020
711021020
721021020
73109.671027.67
74109.67109.670
75109.67109.670
76109.67109.670
77109.67109.670
78109.67109.670
79109.67109.670
80109.67109.670
81109.67109.670
82109.67109.670
83109.67109.670
84109.67109.670

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 101.16 & 101.16 & 0 \tabularnewline
4 & 101.16 & 101.16 & 0 \tabularnewline
5 & 101.16 & 101.16 & 0 \tabularnewline
6 & 101.16 & 101.16 & 0 \tabularnewline
7 & 101.16 & 101.16 & 0 \tabularnewline
8 & 101.16 & 101.16 & 0 \tabularnewline
9 & 101.16 & 101.16 & 0 \tabularnewline
10 & 101.21 & 101.16 & 0.0499999999999972 \tabularnewline
11 & 101.21 & 101.21 & 0 \tabularnewline
12 & 101.21 & 101.21 & 0 \tabularnewline
13 & 103.16 & 101.21 & 1.95 \tabularnewline
14 & 103.16 & 103.16 & 0 \tabularnewline
15 & 103.16 & 103.16 & 0 \tabularnewline
16 & 103.16 & 103.16 & 0 \tabularnewline
17 & 101.13 & 103.16 & -2.03 \tabularnewline
18 & 101.13 & 101.13 & 0 \tabularnewline
19 & 100.53 & 101.13 & -0.599999999999994 \tabularnewline
20 & 100.53 & 100.53 & 0 \tabularnewline
21 & 100.53 & 100.53 & 0 \tabularnewline
22 & 100.53 & 100.53 & 0 \tabularnewline
23 & 100.53 & 100.53 & 0 \tabularnewline
24 & 100.53 & 100.53 & 0 \tabularnewline
25 & 100.53 & 100.53 & 0 \tabularnewline
26 & 100.53 & 100.53 & 0 \tabularnewline
27 & 100.53 & 100.53 & 0 \tabularnewline
28 & 99.42 & 100.53 & -1.11 \tabularnewline
29 & 99.42 & 99.42 & 0 \tabularnewline
30 & 99.42 & 99.42 & 0 \tabularnewline
31 & 99.42 & 99.42 & 0 \tabularnewline
32 & 100.31 & 99.42 & 0.890000000000001 \tabularnewline
33 & 100.31 & 100.31 & 0 \tabularnewline
34 & 102.25 & 100.31 & 1.94 \tabularnewline
35 & 102.25 & 102.25 & 0 \tabularnewline
36 & 102.25 & 102.25 & 0 \tabularnewline
37 & 101.81 & 102.25 & -0.439999999999998 \tabularnewline
38 & 101.81 & 101.81 & 0 \tabularnewline
39 & 101.81 & 101.81 & 0 \tabularnewline
40 & 101.81 & 101.81 & 0 \tabularnewline
41 & 101.81 & 101.81 & 0 \tabularnewline
42 & 101.81 & 101.81 & 0 \tabularnewline
43 & 101.81 & 101.81 & 0 \tabularnewline
44 & 101.81 & 101.81 & 0 \tabularnewline
45 & 101.81 & 101.81 & 0 \tabularnewline
46 & 101.81 & 101.81 & 0 \tabularnewline
47 & 101.81 & 101.81 & 0 \tabularnewline
48 & 101.81 & 101.81 & 0 \tabularnewline
49 & 101.81 & 101.81 & 0 \tabularnewline
50 & 101.81 & 101.81 & 0 \tabularnewline
51 & 101.81 & 101.81 & 0 \tabularnewline
52 & 101.81 & 101.81 & 0 \tabularnewline
53 & 101.81 & 101.81 & 0 \tabularnewline
54 & 101.81 & 101.81 & 0 \tabularnewline
55 & 101.81 & 101.81 & 0 \tabularnewline
56 & 101.94 & 101.81 & 0.129999999999995 \tabularnewline
57 & 101.94 & 101.94 & 0 \tabularnewline
58 & 101.94 & 101.94 & 0 \tabularnewline
59 & 101.94 & 101.94 & 0 \tabularnewline
60 & 101.94 & 101.94 & 0 \tabularnewline
61 & 102 & 101.94 & 0.0600000000000023 \tabularnewline
62 & 102 & 102 & 0 \tabularnewline
63 & 102 & 102 & 0 \tabularnewline
64 & 102 & 102 & 0 \tabularnewline
65 & 102 & 102 & 0 \tabularnewline
66 & 102 & 102 & 0 \tabularnewline
67 & 102 & 102 & 0 \tabularnewline
68 & 102 & 102 & 0 \tabularnewline
69 & 102 & 102 & 0 \tabularnewline
70 & 102 & 102 & 0 \tabularnewline
71 & 102 & 102 & 0 \tabularnewline
72 & 102 & 102 & 0 \tabularnewline
73 & 109.67 & 102 & 7.67 \tabularnewline
74 & 109.67 & 109.67 & 0 \tabularnewline
75 & 109.67 & 109.67 & 0 \tabularnewline
76 & 109.67 & 109.67 & 0 \tabularnewline
77 & 109.67 & 109.67 & 0 \tabularnewline
78 & 109.67 & 109.67 & 0 \tabularnewline
79 & 109.67 & 109.67 & 0 \tabularnewline
80 & 109.67 & 109.67 & 0 \tabularnewline
81 & 109.67 & 109.67 & 0 \tabularnewline
82 & 109.67 & 109.67 & 0 \tabularnewline
83 & 109.67 & 109.67 & 0 \tabularnewline
84 & 109.67 & 109.67 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233135&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]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]101.21[/C][C]101.16[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]11[/C][C]101.21[/C][C]101.21[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]101.21[/C][C]101.21[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]103.16[/C][C]101.21[/C][C]1.95[/C][/ROW]
[ROW][C]14[/C][C]103.16[/C][C]103.16[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]103.16[/C][C]103.16[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]103.16[/C][C]103.16[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]101.13[/C][C]103.16[/C][C]-2.03[/C][/ROW]
[ROW][C]18[/C][C]101.13[/C][C]101.13[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]100.53[/C][C]101.13[/C][C]-0.599999999999994[/C][/ROW]
[ROW][C]20[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]99.42[/C][C]100.53[/C][C]-1.11[/C][/ROW]
[ROW][C]29[/C][C]99.42[/C][C]99.42[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]99.42[/C][C]99.42[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]99.42[/C][C]99.42[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]100.31[/C][C]99.42[/C][C]0.890000000000001[/C][/ROW]
[ROW][C]33[/C][C]100.31[/C][C]100.31[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]102.25[/C][C]100.31[/C][C]1.94[/C][/ROW]
[ROW][C]35[/C][C]102.25[/C][C]102.25[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]102.25[/C][C]102.25[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]101.81[/C][C]102.25[/C][C]-0.439999999999998[/C][/ROW]
[ROW][C]38[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]101.94[/C][C]101.81[/C][C]0.129999999999995[/C][/ROW]
[ROW][C]57[/C][C]101.94[/C][C]101.94[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]101.94[/C][C]101.94[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]101.94[/C][C]101.94[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]101.94[/C][C]101.94[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]102[/C][C]101.94[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]62[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]64[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]102[/C][C]102[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]109.67[/C][C]102[/C][C]7.67[/C][/ROW]
[ROW][C]74[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]75[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]76[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]77[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]78[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]80[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]82[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]83[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[ROW][C]84[/C][C]109.67[/C][C]109.67[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233135&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233135&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
3101.16101.160
4101.16101.160
5101.16101.160
6101.16101.160
7101.16101.160
8101.16101.160
9101.16101.160
10101.21101.160.0499999999999972
11101.21101.210
12101.21101.210
13103.16101.211.95
14103.16103.160
15103.16103.160
16103.16103.160
17101.13103.16-2.03
18101.13101.130
19100.53101.13-0.599999999999994
20100.53100.530
21100.53100.530
22100.53100.530
23100.53100.530
24100.53100.530
25100.53100.530
26100.53100.530
27100.53100.530
2899.42100.53-1.11
2999.4299.420
3099.4299.420
3199.4299.420
32100.3199.420.890000000000001
33100.31100.310
34102.25100.311.94
35102.25102.250
36102.25102.250
37101.81102.25-0.439999999999998
38101.81101.810
39101.81101.810
40101.81101.810
41101.81101.810
42101.81101.810
43101.81101.810
44101.81101.810
45101.81101.810
46101.81101.810
47101.81101.810
48101.81101.810
49101.81101.810
50101.81101.810
51101.81101.810
52101.81101.810
53101.81101.810
54101.81101.810
55101.81101.810
56101.94101.810.129999999999995
57101.94101.940
58101.94101.940
59101.94101.940
60101.94101.940
61102101.940.0600000000000023
621021020
631021020
641021020
651021020
661021020
671021020
681021020
691021020
701021020
711021020
721021020
73109.671027.67
74109.67109.670
75109.67109.670
76109.67109.670
77109.67109.670
78109.67109.670
79109.67109.670
80109.67109.670
81109.67109.670
82109.67109.670
83109.67109.670
84109.67109.670







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85109.67107.819133924872111.520866075128
86109.67107.052480094418112.287519905582
87109.67106.464205919873112.875794080127
88109.67105.968267849744113.371732150256
89109.67105.531337638766113.808662361234
90109.67105.136322533709114.203677466291
91109.67104.773068655125114.566931344875
92109.67104.434960188835114.905039811165
93109.67104.117401774616115.222598225384
94109.67103.817047558659115.522952441341
95109.67103.531371691603115.808628308397
96109.67103.258411839745116.081588160255

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 109.67 & 107.819133924872 & 111.520866075128 \tabularnewline
86 & 109.67 & 107.052480094418 & 112.287519905582 \tabularnewline
87 & 109.67 & 106.464205919873 & 112.875794080127 \tabularnewline
88 & 109.67 & 105.968267849744 & 113.371732150256 \tabularnewline
89 & 109.67 & 105.531337638766 & 113.808662361234 \tabularnewline
90 & 109.67 & 105.136322533709 & 114.203677466291 \tabularnewline
91 & 109.67 & 104.773068655125 & 114.566931344875 \tabularnewline
92 & 109.67 & 104.434960188835 & 114.905039811165 \tabularnewline
93 & 109.67 & 104.117401774616 & 115.222598225384 \tabularnewline
94 & 109.67 & 103.817047558659 & 115.522952441341 \tabularnewline
95 & 109.67 & 103.531371691603 & 115.808628308397 \tabularnewline
96 & 109.67 & 103.258411839745 & 116.081588160255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233135&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]85[/C][C]109.67[/C][C]107.819133924872[/C][C]111.520866075128[/C][/ROW]
[ROW][C]86[/C][C]109.67[/C][C]107.052480094418[/C][C]112.287519905582[/C][/ROW]
[ROW][C]87[/C][C]109.67[/C][C]106.464205919873[/C][C]112.875794080127[/C][/ROW]
[ROW][C]88[/C][C]109.67[/C][C]105.968267849744[/C][C]113.371732150256[/C][/ROW]
[ROW][C]89[/C][C]109.67[/C][C]105.531337638766[/C][C]113.808662361234[/C][/ROW]
[ROW][C]90[/C][C]109.67[/C][C]105.136322533709[/C][C]114.203677466291[/C][/ROW]
[ROW][C]91[/C][C]109.67[/C][C]104.773068655125[/C][C]114.566931344875[/C][/ROW]
[ROW][C]92[/C][C]109.67[/C][C]104.434960188835[/C][C]114.905039811165[/C][/ROW]
[ROW][C]93[/C][C]109.67[/C][C]104.117401774616[/C][C]115.222598225384[/C][/ROW]
[ROW][C]94[/C][C]109.67[/C][C]103.817047558659[/C][C]115.522952441341[/C][/ROW]
[ROW][C]95[/C][C]109.67[/C][C]103.531371691603[/C][C]115.808628308397[/C][/ROW]
[ROW][C]96[/C][C]109.67[/C][C]103.258411839745[/C][C]116.081588160255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233135&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233135&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
85109.67107.819133924872111.520866075128
86109.67107.052480094418112.287519905582
87109.67106.464205919873112.875794080127
88109.67105.968267849744113.371732150256
89109.67105.531337638766113.808662361234
90109.67105.136322533709114.203677466291
91109.67104.773068655125114.566931344875
92109.67104.434960188835114.905039811165
93109.67104.117401774616115.222598225384
94109.67103.817047558659115.522952441341
95109.67103.531371691603115.808628308397
96109.67103.258411839745116.081588160255



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')