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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 Jan 2009 13:14:17 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jan/26/t12330008984isqzv4iijxn8do.htm/, Retrieved Sun, 05 May 2024 10:35:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36971, Retrieved Sun, 05 May 2024 10:35:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact227
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [nick Follens MAR 203] [2009-01-26 20:11:26] [7b3d5b215418629d194620f174e04f44]
-    D    [Exponential Smoothing] [nick Follens MAR 203] [2009-01-26 20:14:17] [b3b27f5ee34edf98a28c70ba0002bc05] [Current]
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Dataseries X:
1,4369
1,4975
1,577
1,5553
1,5557
1,575
1,5527
1,4748
1,4718
1,457
1,4684
1,4227
1,3896
1,3622
1,3716
1,3419
1,3511
1,3516
1,3242
1,3074
1,2999
1,3213
1,2881
1,2611
1,2727
1,2811
1,2684
1,265
1,277
1,2271
1,202
1,1938
1,2103
1,1856
1,1786
1,2015
1,2256
1,2292
1,2037
1,2165
1,2694
1,2938
1,3201
1,3014
1,3119
1,3408
1,2991
1,249
1,2218
1,2176
1,2266
1,2138
1,2007
1,1985
1,2262
1,2646
1,2613
1,2286
1,1702
1,1692
1,1222
1,1139
1,1372
1,1663
1,1582
1,0848
1,0807
1,0773
1,0622
1,0183
1,0014
0,9811





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=36971&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=36971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36971&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36971&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]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36971&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21.49751.43690.0606
31.5771.49750.0794999999999999
41.55531.577-0.0217000000000001
51.55571.55530.000400000000000178
61.5751.55570.0192999999999999
71.55271.575-0.0223
81.47481.5527-0.0778999999999999
91.47181.4748-0.00300000000000011
101.4571.4718-0.0147999999999999
111.46841.4570.0113999999999999
121.42271.4684-0.0456999999999999
131.38961.4227-0.0331000000000001
141.36221.3896-0.0273999999999999
151.37161.36220.00939999999999985
161.34191.3716-0.0296999999999998
171.35111.34190.00919999999999987
181.35161.35110.000499999999999945
191.32421.3516-0.0273999999999999
201.30741.3242-0.0168000000000001
211.29991.3074-0.00749999999999984
221.32131.29990.0213999999999999
231.28811.3213-0.0331999999999999
241.26111.2881-0.0269999999999999
251.27271.26110.0115999999999998
261.28111.27270.00839999999999996
271.26841.2811-0.0126999999999999
281.2651.2684-0.00340000000000007
291.2771.2650.012
301.22711.277-0.0498999999999998
311.2021.2271-0.0251000000000001
321.19381.202-0.00819999999999999
331.21031.19380.0165000000000000
341.18561.2103-0.0246999999999999
351.17861.1856-0.0069999999999999
361.20151.17860.0228999999999999
371.22561.20150.0241
381.22921.22560.00360000000000005
391.20371.2292-0.0255000000000001
401.21651.20370.0127999999999999
411.26941.21650.0529000000000002
421.29381.26940.0244
431.32011.29380.0263
441.30141.3201-0.0187000000000002
451.31191.30140.0105000000000002
461.34081.31190.0288999999999999
471.29911.3408-0.0417000000000001
481.2491.2991-0.0500999999999998
491.22181.249-0.0272000000000001
501.21761.2218-0.00419999999999998
511.22661.21760.0089999999999999
521.21381.2266-0.0127999999999999
531.20071.2138-0.0130999999999999
541.19851.2007-0.0022000000000002
551.22621.19850.0277000000000001
561.26461.22620.0384
571.26131.2646-0.00329999999999986
581.22861.2613-0.0327000000000002
591.17021.2286-0.0584
601.16921.1702-0.00099999999999989
611.12221.1692-0.0469999999999999
621.11391.1222-0.0083000000000002
631.13721.11390.0233000000000001
641.16631.13720.0290999999999999
651.15821.1663-0.0081
661.08481.1582-0.0733999999999999
671.08071.0848-0.00409999999999999
681.07731.0807-0.00340000000000007
691.06221.0773-0.0150999999999999
701.01831.0622-0.0439000000000001
711.00141.0183-0.0168999999999999
720.98111.0014-0.0203000000000001

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.4975 & 1.4369 & 0.0606 \tabularnewline
3 & 1.577 & 1.4975 & 0.0794999999999999 \tabularnewline
4 & 1.5553 & 1.577 & -0.0217000000000001 \tabularnewline
5 & 1.5557 & 1.5553 & 0.000400000000000178 \tabularnewline
6 & 1.575 & 1.5557 & 0.0192999999999999 \tabularnewline
7 & 1.5527 & 1.575 & -0.0223 \tabularnewline
8 & 1.4748 & 1.5527 & -0.0778999999999999 \tabularnewline
9 & 1.4718 & 1.4748 & -0.00300000000000011 \tabularnewline
10 & 1.457 & 1.4718 & -0.0147999999999999 \tabularnewline
11 & 1.4684 & 1.457 & 0.0113999999999999 \tabularnewline
12 & 1.4227 & 1.4684 & -0.0456999999999999 \tabularnewline
13 & 1.3896 & 1.4227 & -0.0331000000000001 \tabularnewline
14 & 1.3622 & 1.3896 & -0.0273999999999999 \tabularnewline
15 & 1.3716 & 1.3622 & 0.00939999999999985 \tabularnewline
16 & 1.3419 & 1.3716 & -0.0296999999999998 \tabularnewline
17 & 1.3511 & 1.3419 & 0.00919999999999987 \tabularnewline
18 & 1.3516 & 1.3511 & 0.000499999999999945 \tabularnewline
19 & 1.3242 & 1.3516 & -0.0273999999999999 \tabularnewline
20 & 1.3074 & 1.3242 & -0.0168000000000001 \tabularnewline
21 & 1.2999 & 1.3074 & -0.00749999999999984 \tabularnewline
22 & 1.3213 & 1.2999 & 0.0213999999999999 \tabularnewline
23 & 1.2881 & 1.3213 & -0.0331999999999999 \tabularnewline
24 & 1.2611 & 1.2881 & -0.0269999999999999 \tabularnewline
25 & 1.2727 & 1.2611 & 0.0115999999999998 \tabularnewline
26 & 1.2811 & 1.2727 & 0.00839999999999996 \tabularnewline
27 & 1.2684 & 1.2811 & -0.0126999999999999 \tabularnewline
28 & 1.265 & 1.2684 & -0.00340000000000007 \tabularnewline
29 & 1.277 & 1.265 & 0.012 \tabularnewline
30 & 1.2271 & 1.277 & -0.0498999999999998 \tabularnewline
31 & 1.202 & 1.2271 & -0.0251000000000001 \tabularnewline
32 & 1.1938 & 1.202 & -0.00819999999999999 \tabularnewline
33 & 1.2103 & 1.1938 & 0.0165000000000000 \tabularnewline
34 & 1.1856 & 1.2103 & -0.0246999999999999 \tabularnewline
35 & 1.1786 & 1.1856 & -0.0069999999999999 \tabularnewline
36 & 1.2015 & 1.1786 & 0.0228999999999999 \tabularnewline
37 & 1.2256 & 1.2015 & 0.0241 \tabularnewline
38 & 1.2292 & 1.2256 & 0.00360000000000005 \tabularnewline
39 & 1.2037 & 1.2292 & -0.0255000000000001 \tabularnewline
40 & 1.2165 & 1.2037 & 0.0127999999999999 \tabularnewline
41 & 1.2694 & 1.2165 & 0.0529000000000002 \tabularnewline
42 & 1.2938 & 1.2694 & 0.0244 \tabularnewline
43 & 1.3201 & 1.2938 & 0.0263 \tabularnewline
44 & 1.3014 & 1.3201 & -0.0187000000000002 \tabularnewline
45 & 1.3119 & 1.3014 & 0.0105000000000002 \tabularnewline
46 & 1.3408 & 1.3119 & 0.0288999999999999 \tabularnewline
47 & 1.2991 & 1.3408 & -0.0417000000000001 \tabularnewline
48 & 1.249 & 1.2991 & -0.0500999999999998 \tabularnewline
49 & 1.2218 & 1.249 & -0.0272000000000001 \tabularnewline
50 & 1.2176 & 1.2218 & -0.00419999999999998 \tabularnewline
51 & 1.2266 & 1.2176 & 0.0089999999999999 \tabularnewline
52 & 1.2138 & 1.2266 & -0.0127999999999999 \tabularnewline
53 & 1.2007 & 1.2138 & -0.0130999999999999 \tabularnewline
54 & 1.1985 & 1.2007 & -0.0022000000000002 \tabularnewline
55 & 1.2262 & 1.1985 & 0.0277000000000001 \tabularnewline
56 & 1.2646 & 1.2262 & 0.0384 \tabularnewline
57 & 1.2613 & 1.2646 & -0.00329999999999986 \tabularnewline
58 & 1.2286 & 1.2613 & -0.0327000000000002 \tabularnewline
59 & 1.1702 & 1.2286 & -0.0584 \tabularnewline
60 & 1.1692 & 1.1702 & -0.00099999999999989 \tabularnewline
61 & 1.1222 & 1.1692 & -0.0469999999999999 \tabularnewline
62 & 1.1139 & 1.1222 & -0.0083000000000002 \tabularnewline
63 & 1.1372 & 1.1139 & 0.0233000000000001 \tabularnewline
64 & 1.1663 & 1.1372 & 0.0290999999999999 \tabularnewline
65 & 1.1582 & 1.1663 & -0.0081 \tabularnewline
66 & 1.0848 & 1.1582 & -0.0733999999999999 \tabularnewline
67 & 1.0807 & 1.0848 & -0.00409999999999999 \tabularnewline
68 & 1.0773 & 1.0807 & -0.00340000000000007 \tabularnewline
69 & 1.0622 & 1.0773 & -0.0150999999999999 \tabularnewline
70 & 1.0183 & 1.0622 & -0.0439000000000001 \tabularnewline
71 & 1.0014 & 1.0183 & -0.0168999999999999 \tabularnewline
72 & 0.9811 & 1.0014 & -0.0203000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36971&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]1.4975[/C][C]1.4369[/C][C]0.0606[/C][/ROW]
[ROW][C]3[/C][C]1.577[/C][C]1.4975[/C][C]0.0794999999999999[/C][/ROW]
[ROW][C]4[/C][C]1.5553[/C][C]1.577[/C][C]-0.0217000000000001[/C][/ROW]
[ROW][C]5[/C][C]1.5557[/C][C]1.5553[/C][C]0.000400000000000178[/C][/ROW]
[ROW][C]6[/C][C]1.575[/C][C]1.5557[/C][C]0.0192999999999999[/C][/ROW]
[ROW][C]7[/C][C]1.5527[/C][C]1.575[/C][C]-0.0223[/C][/ROW]
[ROW][C]8[/C][C]1.4748[/C][C]1.5527[/C][C]-0.0778999999999999[/C][/ROW]
[ROW][C]9[/C][C]1.4718[/C][C]1.4748[/C][C]-0.00300000000000011[/C][/ROW]
[ROW][C]10[/C][C]1.457[/C][C]1.4718[/C][C]-0.0147999999999999[/C][/ROW]
[ROW][C]11[/C][C]1.4684[/C][C]1.457[/C][C]0.0113999999999999[/C][/ROW]
[ROW][C]12[/C][C]1.4227[/C][C]1.4684[/C][C]-0.0456999999999999[/C][/ROW]
[ROW][C]13[/C][C]1.3896[/C][C]1.4227[/C][C]-0.0331000000000001[/C][/ROW]
[ROW][C]14[/C][C]1.3622[/C][C]1.3896[/C][C]-0.0273999999999999[/C][/ROW]
[ROW][C]15[/C][C]1.3716[/C][C]1.3622[/C][C]0.00939999999999985[/C][/ROW]
[ROW][C]16[/C][C]1.3419[/C][C]1.3716[/C][C]-0.0296999999999998[/C][/ROW]
[ROW][C]17[/C][C]1.3511[/C][C]1.3419[/C][C]0.00919999999999987[/C][/ROW]
[ROW][C]18[/C][C]1.3516[/C][C]1.3511[/C][C]0.000499999999999945[/C][/ROW]
[ROW][C]19[/C][C]1.3242[/C][C]1.3516[/C][C]-0.0273999999999999[/C][/ROW]
[ROW][C]20[/C][C]1.3074[/C][C]1.3242[/C][C]-0.0168000000000001[/C][/ROW]
[ROW][C]21[/C][C]1.2999[/C][C]1.3074[/C][C]-0.00749999999999984[/C][/ROW]
[ROW][C]22[/C][C]1.3213[/C][C]1.2999[/C][C]0.0213999999999999[/C][/ROW]
[ROW][C]23[/C][C]1.2881[/C][C]1.3213[/C][C]-0.0331999999999999[/C][/ROW]
[ROW][C]24[/C][C]1.2611[/C][C]1.2881[/C][C]-0.0269999999999999[/C][/ROW]
[ROW][C]25[/C][C]1.2727[/C][C]1.2611[/C][C]0.0115999999999998[/C][/ROW]
[ROW][C]26[/C][C]1.2811[/C][C]1.2727[/C][C]0.00839999999999996[/C][/ROW]
[ROW][C]27[/C][C]1.2684[/C][C]1.2811[/C][C]-0.0126999999999999[/C][/ROW]
[ROW][C]28[/C][C]1.265[/C][C]1.2684[/C][C]-0.00340000000000007[/C][/ROW]
[ROW][C]29[/C][C]1.277[/C][C]1.265[/C][C]0.012[/C][/ROW]
[ROW][C]30[/C][C]1.2271[/C][C]1.277[/C][C]-0.0498999999999998[/C][/ROW]
[ROW][C]31[/C][C]1.202[/C][C]1.2271[/C][C]-0.0251000000000001[/C][/ROW]
[ROW][C]32[/C][C]1.1938[/C][C]1.202[/C][C]-0.00819999999999999[/C][/ROW]
[ROW][C]33[/C][C]1.2103[/C][C]1.1938[/C][C]0.0165000000000000[/C][/ROW]
[ROW][C]34[/C][C]1.1856[/C][C]1.2103[/C][C]-0.0246999999999999[/C][/ROW]
[ROW][C]35[/C][C]1.1786[/C][C]1.1856[/C][C]-0.0069999999999999[/C][/ROW]
[ROW][C]36[/C][C]1.2015[/C][C]1.1786[/C][C]0.0228999999999999[/C][/ROW]
[ROW][C]37[/C][C]1.2256[/C][C]1.2015[/C][C]0.0241[/C][/ROW]
[ROW][C]38[/C][C]1.2292[/C][C]1.2256[/C][C]0.00360000000000005[/C][/ROW]
[ROW][C]39[/C][C]1.2037[/C][C]1.2292[/C][C]-0.0255000000000001[/C][/ROW]
[ROW][C]40[/C][C]1.2165[/C][C]1.2037[/C][C]0.0127999999999999[/C][/ROW]
[ROW][C]41[/C][C]1.2694[/C][C]1.2165[/C][C]0.0529000000000002[/C][/ROW]
[ROW][C]42[/C][C]1.2938[/C][C]1.2694[/C][C]0.0244[/C][/ROW]
[ROW][C]43[/C][C]1.3201[/C][C]1.2938[/C][C]0.0263[/C][/ROW]
[ROW][C]44[/C][C]1.3014[/C][C]1.3201[/C][C]-0.0187000000000002[/C][/ROW]
[ROW][C]45[/C][C]1.3119[/C][C]1.3014[/C][C]0.0105000000000002[/C][/ROW]
[ROW][C]46[/C][C]1.3408[/C][C]1.3119[/C][C]0.0288999999999999[/C][/ROW]
[ROW][C]47[/C][C]1.2991[/C][C]1.3408[/C][C]-0.0417000000000001[/C][/ROW]
[ROW][C]48[/C][C]1.249[/C][C]1.2991[/C][C]-0.0500999999999998[/C][/ROW]
[ROW][C]49[/C][C]1.2218[/C][C]1.249[/C][C]-0.0272000000000001[/C][/ROW]
[ROW][C]50[/C][C]1.2176[/C][C]1.2218[/C][C]-0.00419999999999998[/C][/ROW]
[ROW][C]51[/C][C]1.2266[/C][C]1.2176[/C][C]0.0089999999999999[/C][/ROW]
[ROW][C]52[/C][C]1.2138[/C][C]1.2266[/C][C]-0.0127999999999999[/C][/ROW]
[ROW][C]53[/C][C]1.2007[/C][C]1.2138[/C][C]-0.0130999999999999[/C][/ROW]
[ROW][C]54[/C][C]1.1985[/C][C]1.2007[/C][C]-0.0022000000000002[/C][/ROW]
[ROW][C]55[/C][C]1.2262[/C][C]1.1985[/C][C]0.0277000000000001[/C][/ROW]
[ROW][C]56[/C][C]1.2646[/C][C]1.2262[/C][C]0.0384[/C][/ROW]
[ROW][C]57[/C][C]1.2613[/C][C]1.2646[/C][C]-0.00329999999999986[/C][/ROW]
[ROW][C]58[/C][C]1.2286[/C][C]1.2613[/C][C]-0.0327000000000002[/C][/ROW]
[ROW][C]59[/C][C]1.1702[/C][C]1.2286[/C][C]-0.0584[/C][/ROW]
[ROW][C]60[/C][C]1.1692[/C][C]1.1702[/C][C]-0.00099999999999989[/C][/ROW]
[ROW][C]61[/C][C]1.1222[/C][C]1.1692[/C][C]-0.0469999999999999[/C][/ROW]
[ROW][C]62[/C][C]1.1139[/C][C]1.1222[/C][C]-0.0083000000000002[/C][/ROW]
[ROW][C]63[/C][C]1.1372[/C][C]1.1139[/C][C]0.0233000000000001[/C][/ROW]
[ROW][C]64[/C][C]1.1663[/C][C]1.1372[/C][C]0.0290999999999999[/C][/ROW]
[ROW][C]65[/C][C]1.1582[/C][C]1.1663[/C][C]-0.0081[/C][/ROW]
[ROW][C]66[/C][C]1.0848[/C][C]1.1582[/C][C]-0.0733999999999999[/C][/ROW]
[ROW][C]67[/C][C]1.0807[/C][C]1.0848[/C][C]-0.00409999999999999[/C][/ROW]
[ROW][C]68[/C][C]1.0773[/C][C]1.0807[/C][C]-0.00340000000000007[/C][/ROW]
[ROW][C]69[/C][C]1.0622[/C][C]1.0773[/C][C]-0.0150999999999999[/C][/ROW]
[ROW][C]70[/C][C]1.0183[/C][C]1.0622[/C][C]-0.0439000000000001[/C][/ROW]
[ROW][C]71[/C][C]1.0014[/C][C]1.0183[/C][C]-0.0168999999999999[/C][/ROW]
[ROW][C]72[/C][C]0.9811[/C][C]1.0014[/C][C]-0.0203000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36971&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36971&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
21.49751.43690.0606
31.5771.49750.0794999999999999
41.55531.577-0.0217000000000001
51.55571.55530.000400000000000178
61.5751.55570.0192999999999999
71.55271.575-0.0223
81.47481.5527-0.0778999999999999
91.47181.4748-0.00300000000000011
101.4571.4718-0.0147999999999999
111.46841.4570.0113999999999999
121.42271.4684-0.0456999999999999
131.38961.4227-0.0331000000000001
141.36221.3896-0.0273999999999999
151.37161.36220.00939999999999985
161.34191.3716-0.0296999999999998
171.35111.34190.00919999999999987
181.35161.35110.000499999999999945
191.32421.3516-0.0273999999999999
201.30741.3242-0.0168000000000001
211.29991.3074-0.00749999999999984
221.32131.29990.0213999999999999
231.28811.3213-0.0331999999999999
241.26111.2881-0.0269999999999999
251.27271.26110.0115999999999998
261.28111.27270.00839999999999996
271.26841.2811-0.0126999999999999
281.2651.2684-0.00340000000000007
291.2771.2650.012
301.22711.277-0.0498999999999998
311.2021.2271-0.0251000000000001
321.19381.202-0.00819999999999999
331.21031.19380.0165000000000000
341.18561.2103-0.0246999999999999
351.17861.1856-0.0069999999999999
361.20151.17860.0228999999999999
371.22561.20150.0241
381.22921.22560.00360000000000005
391.20371.2292-0.0255000000000001
401.21651.20370.0127999999999999
411.26941.21650.0529000000000002
421.29381.26940.0244
431.32011.29380.0263
441.30141.3201-0.0187000000000002
451.31191.30140.0105000000000002
461.34081.31190.0288999999999999
471.29911.3408-0.0417000000000001
481.2491.2991-0.0500999999999998
491.22181.249-0.0272000000000001
501.21761.2218-0.00419999999999998
511.22661.21760.0089999999999999
521.21381.2266-0.0127999999999999
531.20071.2138-0.0130999999999999
541.19851.2007-0.0022000000000002
551.22621.19850.0277000000000001
561.26461.22620.0384
571.26131.2646-0.00329999999999986
581.22861.2613-0.0327000000000002
591.17021.2286-0.0584
601.16921.1702-0.00099999999999989
611.12221.1692-0.0469999999999999
621.11391.1222-0.0083000000000002
631.13721.11390.0233000000000001
641.16631.13720.0290999999999999
651.15821.1663-0.0081
661.08481.1582-0.0733999999999999
671.08071.0848-0.00409999999999999
681.07731.0807-0.00340000000000007
691.06221.0773-0.0150999999999999
701.01831.0622-0.0439000000000001
711.00141.0183-0.0168999999999999
720.98111.0014-0.0203000000000001







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.98110.9240446282482111.03815537175179
740.98110.9004115194623821.06178848053762
750.98110.8822771972811721.07992280271883
760.98110.8669892564964231.09521074350358
770.98110.853520310281481.10867968971852
780.98110.8413434521233131.12085654787669
790.98110.8301456753844271.13205432461557
800.98110.8197230389247631.14247696107524
810.98110.8099338847446341.15226611525537
820.98110.8006750725167171.16152492748328
830.98110.7918687396250741.17033126037493
840.98110.7834543945623441.17874560543766

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.9811 & 0.924044628248211 & 1.03815537175179 \tabularnewline
74 & 0.9811 & 0.900411519462382 & 1.06178848053762 \tabularnewline
75 & 0.9811 & 0.882277197281172 & 1.07992280271883 \tabularnewline
76 & 0.9811 & 0.866989256496423 & 1.09521074350358 \tabularnewline
77 & 0.9811 & 0.85352031028148 & 1.10867968971852 \tabularnewline
78 & 0.9811 & 0.841343452123313 & 1.12085654787669 \tabularnewline
79 & 0.9811 & 0.830145675384427 & 1.13205432461557 \tabularnewline
80 & 0.9811 & 0.819723038924763 & 1.14247696107524 \tabularnewline
81 & 0.9811 & 0.809933884744634 & 1.15226611525537 \tabularnewline
82 & 0.9811 & 0.800675072516717 & 1.16152492748328 \tabularnewline
83 & 0.9811 & 0.791868739625074 & 1.17033126037493 \tabularnewline
84 & 0.9811 & 0.783454394562344 & 1.17874560543766 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36971&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]0.9811[/C][C]0.924044628248211[/C][C]1.03815537175179[/C][/ROW]
[ROW][C]74[/C][C]0.9811[/C][C]0.900411519462382[/C][C]1.06178848053762[/C][/ROW]
[ROW][C]75[/C][C]0.9811[/C][C]0.882277197281172[/C][C]1.07992280271883[/C][/ROW]
[ROW][C]76[/C][C]0.9811[/C][C]0.866989256496423[/C][C]1.09521074350358[/C][/ROW]
[ROW][C]77[/C][C]0.9811[/C][C]0.85352031028148[/C][C]1.10867968971852[/C][/ROW]
[ROW][C]78[/C][C]0.9811[/C][C]0.841343452123313[/C][C]1.12085654787669[/C][/ROW]
[ROW][C]79[/C][C]0.9811[/C][C]0.830145675384427[/C][C]1.13205432461557[/C][/ROW]
[ROW][C]80[/C][C]0.9811[/C][C]0.819723038924763[/C][C]1.14247696107524[/C][/ROW]
[ROW][C]81[/C][C]0.9811[/C][C]0.809933884744634[/C][C]1.15226611525537[/C][/ROW]
[ROW][C]82[/C][C]0.9811[/C][C]0.800675072516717[/C][C]1.16152492748328[/C][/ROW]
[ROW][C]83[/C][C]0.9811[/C][C]0.791868739625074[/C][C]1.17033126037493[/C][/ROW]
[ROW][C]84[/C][C]0.9811[/C][C]0.783454394562344[/C][C]1.17874560543766[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36971&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36971&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
730.98110.9240446282482111.03815537175179
740.98110.9004115194623821.06178848053762
750.98110.8822771972811721.07992280271883
760.98110.8669892564964231.09521074350358
770.98110.853520310281481.10867968971852
780.98110.8413434521233131.12085654787669
790.98110.8301456753844271.13205432461557
800.98110.8197230389247631.14247696107524
810.98110.8099338847446341.15226611525537
820.98110.8006750725167171.16152492748328
830.98110.7918687396250741.17033126037493
840.98110.7834543945623441.17874560543766



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')