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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 28 Nov 2015 11:17:46 +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/2015/Nov/28/t1448709601cef9r1uw8po7al3.htm/, Retrieved Tue, 14 May 2024 18:50:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284371, Retrieved Tue, 14 May 2024 18:50:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-28 11:17:46] [5a70237751c59f15349851dd3eb2a645] [Current]
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Dataseries X:
92.51
92.51
92.51
92.51
92.51
92.51
92.51
92.51
92.51
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.67
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
96.19
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.13
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
99.58
101.27
101.27
101.27
101.25
101.25
101.25
101.25
101.25
101.25
101.25
101.25
101.25
102.55
102.55
102.55




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284371&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284371&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284371&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919662212077
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999919662212077 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284371&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]0.999919662212077[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284371&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284371&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
alpha0.999919662212077
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
292.5192.510
392.5192.510
492.5192.510
592.5192.510
692.5192.510
792.5192.510
892.5192.510
992.5192.510
1096.6792.514.16
1196.6796.66966579480220.000334205197759729
1296.6796.66999997315072.68493067778763e-08
1396.6796.66999999999792.1458390619955e-12
1496.6796.670
1596.6796.670
1696.6796.670
1796.6796.670
1896.6796.670
1996.6796.670
2096.6796.670
2196.6796.670
2296.1996.67-0.480000000000004
2396.1996.1900385621382-3.85621382008594e-05
2496.1996.190000003098-3.09799474962347e-09
2596.1996.1900000000003-2.55795384873636e-13
2696.1996.190
2796.1996.190
2896.1996.190
2996.1996.190
3096.1996.190
3196.1996.190
3296.1996.190
3396.1996.190
3499.1396.192.94
3599.1399.12976380690350.000236193096498027
3699.1399.12999998102481.89752284995848e-08
3799.1399.12999999999851.52056145452661e-12
3899.1399.130
3999.1399.130
4099.1399.130
4199.1399.130
4299.1399.130
4399.1399.130
4499.1399.130
4599.1399.130
4699.5899.130.450000000000003
4799.5899.57996384799543.61520045686348e-05
4899.5899.57999999709562.90437185412884e-09
4999.5899.57999999999982.41584530158434e-13
5099.5899.580
5199.5899.580
5299.5899.580
5399.5899.580
5499.5899.580
5599.5899.580
5699.5899.580
5799.5899.580
58101.2799.581.69
59101.27101.2698642291380.00013577086158989
60101.27101.2699999890921.09075415366533e-08
61101.25101.269999999999-0.0199999999991149
62101.25101.250001606756-1.60675575955338e-06
63101.25101.250000000129-1.2907719337818e-10
64101.25101.250
65101.25101.250
66101.25101.250
67101.25101.250
68101.25101.250
69101.25101.250
70102.55101.251.3
71102.55102.5498955608760.000104439124299915
72102.55102.549999991618.39041547351371e-09

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 92.51 & 92.51 & 0 \tabularnewline
3 & 92.51 & 92.51 & 0 \tabularnewline
4 & 92.51 & 92.51 & 0 \tabularnewline
5 & 92.51 & 92.51 & 0 \tabularnewline
6 & 92.51 & 92.51 & 0 \tabularnewline
7 & 92.51 & 92.51 & 0 \tabularnewline
8 & 92.51 & 92.51 & 0 \tabularnewline
9 & 92.51 & 92.51 & 0 \tabularnewline
10 & 96.67 & 92.51 & 4.16 \tabularnewline
11 & 96.67 & 96.6696657948022 & 0.000334205197759729 \tabularnewline
12 & 96.67 & 96.6699999731507 & 2.68493067778763e-08 \tabularnewline
13 & 96.67 & 96.6699999999979 & 2.1458390619955e-12 \tabularnewline
14 & 96.67 & 96.67 & 0 \tabularnewline
15 & 96.67 & 96.67 & 0 \tabularnewline
16 & 96.67 & 96.67 & 0 \tabularnewline
17 & 96.67 & 96.67 & 0 \tabularnewline
18 & 96.67 & 96.67 & 0 \tabularnewline
19 & 96.67 & 96.67 & 0 \tabularnewline
20 & 96.67 & 96.67 & 0 \tabularnewline
21 & 96.67 & 96.67 & 0 \tabularnewline
22 & 96.19 & 96.67 & -0.480000000000004 \tabularnewline
23 & 96.19 & 96.1900385621382 & -3.85621382008594e-05 \tabularnewline
24 & 96.19 & 96.190000003098 & -3.09799474962347e-09 \tabularnewline
25 & 96.19 & 96.1900000000003 & -2.55795384873636e-13 \tabularnewline
26 & 96.19 & 96.19 & 0 \tabularnewline
27 & 96.19 & 96.19 & 0 \tabularnewline
28 & 96.19 & 96.19 & 0 \tabularnewline
29 & 96.19 & 96.19 & 0 \tabularnewline
30 & 96.19 & 96.19 & 0 \tabularnewline
31 & 96.19 & 96.19 & 0 \tabularnewline
32 & 96.19 & 96.19 & 0 \tabularnewline
33 & 96.19 & 96.19 & 0 \tabularnewline
34 & 99.13 & 96.19 & 2.94 \tabularnewline
35 & 99.13 & 99.1297638069035 & 0.000236193096498027 \tabularnewline
36 & 99.13 & 99.1299999810248 & 1.89752284995848e-08 \tabularnewline
37 & 99.13 & 99.1299999999985 & 1.52056145452661e-12 \tabularnewline
38 & 99.13 & 99.13 & 0 \tabularnewline
39 & 99.13 & 99.13 & 0 \tabularnewline
40 & 99.13 & 99.13 & 0 \tabularnewline
41 & 99.13 & 99.13 & 0 \tabularnewline
42 & 99.13 & 99.13 & 0 \tabularnewline
43 & 99.13 & 99.13 & 0 \tabularnewline
44 & 99.13 & 99.13 & 0 \tabularnewline
45 & 99.13 & 99.13 & 0 \tabularnewline
46 & 99.58 & 99.13 & 0.450000000000003 \tabularnewline
47 & 99.58 & 99.5799638479954 & 3.61520045686348e-05 \tabularnewline
48 & 99.58 & 99.5799999970956 & 2.90437185412884e-09 \tabularnewline
49 & 99.58 & 99.5799999999998 & 2.41584530158434e-13 \tabularnewline
50 & 99.58 & 99.58 & 0 \tabularnewline
51 & 99.58 & 99.58 & 0 \tabularnewline
52 & 99.58 & 99.58 & 0 \tabularnewline
53 & 99.58 & 99.58 & 0 \tabularnewline
54 & 99.58 & 99.58 & 0 \tabularnewline
55 & 99.58 & 99.58 & 0 \tabularnewline
56 & 99.58 & 99.58 & 0 \tabularnewline
57 & 99.58 & 99.58 & 0 \tabularnewline
58 & 101.27 & 99.58 & 1.69 \tabularnewline
59 & 101.27 & 101.269864229138 & 0.00013577086158989 \tabularnewline
60 & 101.27 & 101.269999989092 & 1.09075415366533e-08 \tabularnewline
61 & 101.25 & 101.269999999999 & -0.0199999999991149 \tabularnewline
62 & 101.25 & 101.250001606756 & -1.60675575955338e-06 \tabularnewline
63 & 101.25 & 101.250000000129 & -1.2907719337818e-10 \tabularnewline
64 & 101.25 & 101.25 & 0 \tabularnewline
65 & 101.25 & 101.25 & 0 \tabularnewline
66 & 101.25 & 101.25 & 0 \tabularnewline
67 & 101.25 & 101.25 & 0 \tabularnewline
68 & 101.25 & 101.25 & 0 \tabularnewline
69 & 101.25 & 101.25 & 0 \tabularnewline
70 & 102.55 & 101.25 & 1.3 \tabularnewline
71 & 102.55 & 102.549895560876 & 0.000104439124299915 \tabularnewline
72 & 102.55 & 102.54999999161 & 8.39041547351371e-09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284371&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]2[/C][C]92.51[/C][C]92.51[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]92.51[/C][C]92.51[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]92.51[/C][C]92.51[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]92.51[/C][C]92.51[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]92.51[/C][C]92.51[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]92.51[/C][C]92.51[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]92.51[/C][C]92.51[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]92.51[/C][C]92.51[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]96.67[/C][C]92.51[/C][C]4.16[/C][/ROW]
[ROW][C]11[/C][C]96.67[/C][C]96.6696657948022[/C][C]0.000334205197759729[/C][/ROW]
[ROW][C]12[/C][C]96.67[/C][C]96.6699999731507[/C][C]2.68493067778763e-08[/C][/ROW]
[ROW][C]13[/C][C]96.67[/C][C]96.6699999999979[/C][C]2.1458390619955e-12[/C][/ROW]
[ROW][C]14[/C][C]96.67[/C][C]96.67[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]96.67[/C][C]96.67[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]96.67[/C][C]96.67[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]96.67[/C][C]96.67[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]96.67[/C][C]96.67[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]96.67[/C][C]96.67[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]96.67[/C][C]96.67[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]96.67[/C][C]96.67[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]96.19[/C][C]96.67[/C][C]-0.480000000000004[/C][/ROW]
[ROW][C]23[/C][C]96.19[/C][C]96.1900385621382[/C][C]-3.85621382008594e-05[/C][/ROW]
[ROW][C]24[/C][C]96.19[/C][C]96.190000003098[/C][C]-3.09799474962347e-09[/C][/ROW]
[ROW][C]25[/C][C]96.19[/C][C]96.1900000000003[/C][C]-2.55795384873636e-13[/C][/ROW]
[ROW][C]26[/C][C]96.19[/C][C]96.19[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]96.19[/C][C]96.19[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]96.19[/C][C]96.19[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]96.19[/C][C]96.19[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]96.19[/C][C]96.19[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]96.19[/C][C]96.19[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]96.19[/C][C]96.19[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]96.19[/C][C]96.19[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]99.13[/C][C]96.19[/C][C]2.94[/C][/ROW]
[ROW][C]35[/C][C]99.13[/C][C]99.1297638069035[/C][C]0.000236193096498027[/C][/ROW]
[ROW][C]36[/C][C]99.13[/C][C]99.1299999810248[/C][C]1.89752284995848e-08[/C][/ROW]
[ROW][C]37[/C][C]99.13[/C][C]99.1299999999985[/C][C]1.52056145452661e-12[/C][/ROW]
[ROW][C]38[/C][C]99.13[/C][C]99.13[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]99.13[/C][C]99.13[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]99.13[/C][C]99.13[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]99.13[/C][C]99.13[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]99.13[/C][C]99.13[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]99.13[/C][C]99.13[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]99.13[/C][C]99.13[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]99.13[/C][C]99.13[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]99.58[/C][C]99.13[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]47[/C][C]99.58[/C][C]99.5799638479954[/C][C]3.61520045686348e-05[/C][/ROW]
[ROW][C]48[/C][C]99.58[/C][C]99.5799999970956[/C][C]2.90437185412884e-09[/C][/ROW]
[ROW][C]49[/C][C]99.58[/C][C]99.5799999999998[/C][C]2.41584530158434e-13[/C][/ROW]
[ROW][C]50[/C][C]99.58[/C][C]99.58[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]99.58[/C][C]99.58[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]99.58[/C][C]99.58[/C][C]0[/C][/ROW]
[ROW][C]53[/C][C]99.58[/C][C]99.58[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]99.58[/C][C]99.58[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]99.58[/C][C]99.58[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]99.58[/C][C]99.58[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]99.58[/C][C]99.58[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]101.27[/C][C]99.58[/C][C]1.69[/C][/ROW]
[ROW][C]59[/C][C]101.27[/C][C]101.269864229138[/C][C]0.00013577086158989[/C][/ROW]
[ROW][C]60[/C][C]101.27[/C][C]101.269999989092[/C][C]1.09075415366533e-08[/C][/ROW]
[ROW][C]61[/C][C]101.25[/C][C]101.269999999999[/C][C]-0.0199999999991149[/C][/ROW]
[ROW][C]62[/C][C]101.25[/C][C]101.250001606756[/C][C]-1.60675575955338e-06[/C][/ROW]
[ROW][C]63[/C][C]101.25[/C][C]101.250000000129[/C][C]-1.2907719337818e-10[/C][/ROW]
[ROW][C]64[/C][C]101.25[/C][C]101.25[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]101.25[/C][C]101.25[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]101.25[/C][C]101.25[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]101.25[/C][C]101.25[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]101.25[/C][C]101.25[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]101.25[/C][C]101.25[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]102.55[/C][C]101.25[/C][C]1.3[/C][/ROW]
[ROW][C]71[/C][C]102.55[/C][C]102.549895560876[/C][C]0.000104439124299915[/C][/ROW]
[ROW][C]72[/C][C]102.55[/C][C]102.54999999161[/C][C]8.39041547351371e-09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284371&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284371&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
292.5192.510
392.5192.510
492.5192.510
592.5192.510
692.5192.510
792.5192.510
892.5192.510
992.5192.510
1096.6792.514.16
1196.6796.66966579480220.000334205197759729
1296.6796.66999997315072.68493067778763e-08
1396.6796.66999999999792.1458390619955e-12
1496.6796.670
1596.6796.670
1696.6796.670
1796.6796.670
1896.6796.670
1996.6796.670
2096.6796.670
2196.6796.670
2296.1996.67-0.480000000000004
2396.1996.1900385621382-3.85621382008594e-05
2496.1996.190000003098-3.09799474962347e-09
2596.1996.1900000000003-2.55795384873636e-13
2696.1996.190
2796.1996.190
2896.1996.190
2996.1996.190
3096.1996.190
3196.1996.190
3296.1996.190
3396.1996.190
3499.1396.192.94
3599.1399.12976380690350.000236193096498027
3699.1399.12999998102481.89752284995848e-08
3799.1399.12999999999851.52056145452661e-12
3899.1399.130
3999.1399.130
4099.1399.130
4199.1399.130
4299.1399.130
4399.1399.130
4499.1399.130
4599.1399.130
4699.5899.130.450000000000003
4799.5899.57996384799543.61520045686348e-05
4899.5899.57999999709562.90437185412884e-09
4999.5899.57999999999982.41584530158434e-13
5099.5899.580
5199.5899.580
5299.5899.580
5399.5899.580
5499.5899.580
5599.5899.580
5699.5899.580
5799.5899.580
58101.2799.581.69
59101.27101.2698642291380.00013577086158989
60101.27101.2699999890921.09075415366533e-08
61101.25101.269999999999-0.0199999999991149
62101.25101.250001606756-1.60675575955338e-06
63101.25101.250000000129-1.2907719337818e-10
64101.25101.250
65101.25101.250
66101.25101.250
67101.25101.250
68101.25101.250
69101.25101.250
70102.55101.251.3
71102.55102.5498955608760.000104439124299915
72102.55102.549999991618.39041547351371e-09







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.549999999999101.277453668281103.822546331718
74102.549999999999100.750420007525104.349579992474
75102.549999999999100.346003146041104.753996853958
76102.549999999999100.005060685359105.09493931464
77102.54999999999999.704682777237105.395317222762
78102.54999999999999.4331194952169105.666880504782
79102.54999999999999.1833907170505105.916609282948
80102.54999999999998.9509484517464106.149051548252
81102.54999999999998.7326336264472106.367366373551
82102.54999999999998.5261461243136106.573853875685
83102.54999999999998.3297495339943106.770250466004
84102.54999999999998.1420948310148106.957905168984

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.549999999999 & 101.277453668281 & 103.822546331718 \tabularnewline
74 & 102.549999999999 & 100.750420007525 & 104.349579992474 \tabularnewline
75 & 102.549999999999 & 100.346003146041 & 104.753996853958 \tabularnewline
76 & 102.549999999999 & 100.005060685359 & 105.09493931464 \tabularnewline
77 & 102.549999999999 & 99.704682777237 & 105.395317222762 \tabularnewline
78 & 102.549999999999 & 99.4331194952169 & 105.666880504782 \tabularnewline
79 & 102.549999999999 & 99.1833907170505 & 105.916609282948 \tabularnewline
80 & 102.549999999999 & 98.9509484517464 & 106.149051548252 \tabularnewline
81 & 102.549999999999 & 98.7326336264472 & 106.367366373551 \tabularnewline
82 & 102.549999999999 & 98.5261461243136 & 106.573853875685 \tabularnewline
83 & 102.549999999999 & 98.3297495339943 & 106.770250466004 \tabularnewline
84 & 102.549999999999 & 98.1420948310148 & 106.957905168984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284371&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]102.549999999999[/C][C]101.277453668281[/C][C]103.822546331718[/C][/ROW]
[ROW][C]74[/C][C]102.549999999999[/C][C]100.750420007525[/C][C]104.349579992474[/C][/ROW]
[ROW][C]75[/C][C]102.549999999999[/C][C]100.346003146041[/C][C]104.753996853958[/C][/ROW]
[ROW][C]76[/C][C]102.549999999999[/C][C]100.005060685359[/C][C]105.09493931464[/C][/ROW]
[ROW][C]77[/C][C]102.549999999999[/C][C]99.704682777237[/C][C]105.395317222762[/C][/ROW]
[ROW][C]78[/C][C]102.549999999999[/C][C]99.4331194952169[/C][C]105.666880504782[/C][/ROW]
[ROW][C]79[/C][C]102.549999999999[/C][C]99.1833907170505[/C][C]105.916609282948[/C][/ROW]
[ROW][C]80[/C][C]102.549999999999[/C][C]98.9509484517464[/C][C]106.149051548252[/C][/ROW]
[ROW][C]81[/C][C]102.549999999999[/C][C]98.7326336264472[/C][C]106.367366373551[/C][/ROW]
[ROW][C]82[/C][C]102.549999999999[/C][C]98.5261461243136[/C][C]106.573853875685[/C][/ROW]
[ROW][C]83[/C][C]102.549999999999[/C][C]98.3297495339943[/C][C]106.770250466004[/C][/ROW]
[ROW][C]84[/C][C]102.549999999999[/C][C]98.1420948310148[/C][C]106.957905168984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284371&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284371&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
73102.549999999999101.277453668281103.822546331718
74102.549999999999100.750420007525104.349579992474
75102.549999999999100.346003146041104.753996853958
76102.549999999999100.005060685359105.09493931464
77102.54999999999999.704682777237105.395317222762
78102.54999999999999.4331194952169105.666880504782
79102.54999999999999.1833907170505105.916609282948
80102.54999999999998.9509484517464106.149051548252
81102.54999999999998.7326336264472106.367366373551
82102.54999999999998.5261461243136106.573853875685
83102.54999999999998.3297495339943106.770250466004
84102.54999999999998.1420948310148106.957905168984



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')