Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Jan 2011 18:13:18 +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/2011/Jan/16/t12952020631tpd0qi7rqgq4rf.htm/, Retrieved Thu, 16 May 2024 23:29:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117452, Retrieved Thu, 16 May 2024 23:29:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [opgave 9 oefening 1] [2011-01-02 09:52:21] [29d16baa26cbc27967659afeae618f55]
-    D  [Classical Decomposition] [opgave 9 oefening 2] [2011-01-02 09:56:53] [29d16baa26cbc27967659afeae618f55]
- RMPD      [Exponential Smoothing] [opgave10; oefening 2] [2011-01-16 18:13:18] [e8fe41381a545d3d3a7b09800c89aa00] [Current]
Feedback Forum

Post a new message
Dataseries X:
17.88
18.11
18.16
18.27
18.29
18.35
18.35
18.38
18.41
18.41
18.42
18.43
18.48
18.54
18.65
18.66
18.69
18.72
18.72
18.73
18.84
18.83
18.91
18.91
18.94
18.97
19
19.08
19.18
19.24
19.23
19.25
19.3
19.33
19.35
19.35
19.31
19.47
19.7
19.76
19.9
19.97
20.1
20.26
20.44
20.43
20.57
20.6
20.69
20.93
20.98
21.11
21.14
21.16
21.32
21.32
21.48
21.58
21.74
21.75
21.81
21.89
22.21
22.37
22.47
22.51
22.55
22.61
22.58
22.85
22.93
22.98
23.01
23.11
23.18
23.18
23.21
23.22
23.12
23.15
23.16
23.21
23.21
23.22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117452&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117452&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.967403347699123
beta0.315348716873752
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.967403347699123 \tabularnewline
beta & 0.315348716873752 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117452&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]0.967403347699123[/C][/ROW]
[ROW][C]beta[/C][C]0.315348716873752[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117452&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
alpha0.967403347699123
beta0.315348716873752
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
318.1618.34-0.180000000000000
418.2718.3409549046228-0.0709549046228268
518.2918.4257542290714-0.13575422907142
618.3518.4064520083127-0.0564520083127036
718.3518.4466452408430-0.0966452408430172
818.3818.4184718996069-0.0384718996069395
918.4118.4348390439304-0.0248390439303989
1018.4118.4568170261364-0.0468170261364271
1118.4218.4432509925016-0.0232509925016231
1218.4318.4453896522630-0.0153896522630284
1318.4818.45043848683890.0295615131610951
1418.5418.50799154254220.0320084574578345
1518.6518.57767658140200.0723234185979713
1618.6618.7084261108668-0.0484261108668029
1718.6918.7075888164949-0.0175888164948965
1818.7218.7312178141602-0.0112178141602293
1918.7218.7575879289278-0.0375879289278238
2018.7318.7469805792995-0.0169805792995348
2118.8418.75112859347560.0888714065243548
2218.8318.8847901201546-0.0547901201546352
2318.9118.86275821566640.0472417843335755
2418.9118.9538443401615-0.0438443401614919
2518.9418.9434378761519-0.00343787615187807
2618.9718.9710719698638-0.00107196986380487
271919.0006678240313-0.000667824031275188
2819.0819.03045091755060.0495490824493672
2919.1819.12392992358170.0560700764183331
3019.2419.240822625826-0.000822625826000234
3119.2319.3024261794887-0.0724261794887333
3219.2519.2726652041917-0.0226652041916608
3319.319.28412870263850.0158712973615209
3419.3319.3377143889295-0.00771438892953569
3519.3519.3661297793088-0.0161297793088231
3619.3519.3814833906962-0.0314833906962093
3719.3119.3723792477801-0.0623792477801004
3819.4719.31435634932400.155643650675966
3919.719.51473164851920.185268351480786
4019.7619.8002856880873-0.0402856880872875
4119.919.85534806381970.0446519361803333
4219.9720.0062013211898-0.0362013211898251
4320.120.06779295121400.0322070487860273
4420.2620.20538845255390.0546115474460791
4520.4420.38131845315370.0586815468463442
4620.4320.5790877293438-0.149087729343808
4720.5720.53037820740490.0396217925951312
4820.620.6763143054005-0.0763143054004729
4920.6920.68681227438050.00318772561948322
5020.9320.77519325187430.154806748125740
5120.9821.0574777817627-0.0774777817626742
5221.1121.09141337908200.0185866209179686
5321.1421.2239522105225-0.0839522105225434
5421.1621.2316833822965-0.0716833822964844
5521.3221.22941505282640.0905849471736389
5621.3221.4117603443927-0.0917603443927106
5721.4821.38971091684950.0902890831504841
5821.5821.57132115177850.00867884822147147
5921.7421.67662902328850.0633709767115356
6021.7521.8541787891139-0.104178789113881
6121.8121.8378585894279-0.0278585894278898
6221.8921.88687200313110.00312799686889775
6322.2121.96681620029330.243183799706657
6422.3722.35317912169080.0168208783092325
6522.4722.5256893304606-0.055689330460595
6622.5122.6110638096493-0.101063809649279
6722.5522.621711389555-0.0717113895550021
6822.6122.6388776480230-0.0288776480230304
6922.5822.6886717245608-0.108671724560814
7022.8522.62812032604290.221879673957105
7122.9322.9550341570196-0.0250341570195793
7222.9823.0354455659447-0.0554455659446766
7323.0123.0695221302882-0.0595221302882294
7423.1123.08149663180330.0285033681967093
7523.1823.1873228007946-0.00732280079462555
7623.1823.2562566514916-0.0762566514915797
7723.2123.2352400930027-0.025240093002715
7823.2223.2558771438448-0.0358771438448215
7923.1223.2552788571885-0.135278857188450
8023.1523.11724957988650.0327504201134659
8123.1623.15176353911570.00823646088430507
8223.2123.16507530433750.044924695662484
8323.2123.2275845408534-0.0175845408533561
8423.2223.2242576272969-0.00425762729694057

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 18.16 & 18.34 & -0.180000000000000 \tabularnewline
4 & 18.27 & 18.3409549046228 & -0.0709549046228268 \tabularnewline
5 & 18.29 & 18.4257542290714 & -0.13575422907142 \tabularnewline
6 & 18.35 & 18.4064520083127 & -0.0564520083127036 \tabularnewline
7 & 18.35 & 18.4466452408430 & -0.0966452408430172 \tabularnewline
8 & 18.38 & 18.4184718996069 & -0.0384718996069395 \tabularnewline
9 & 18.41 & 18.4348390439304 & -0.0248390439303989 \tabularnewline
10 & 18.41 & 18.4568170261364 & -0.0468170261364271 \tabularnewline
11 & 18.42 & 18.4432509925016 & -0.0232509925016231 \tabularnewline
12 & 18.43 & 18.4453896522630 & -0.0153896522630284 \tabularnewline
13 & 18.48 & 18.4504384868389 & 0.0295615131610951 \tabularnewline
14 & 18.54 & 18.5079915425422 & 0.0320084574578345 \tabularnewline
15 & 18.65 & 18.5776765814020 & 0.0723234185979713 \tabularnewline
16 & 18.66 & 18.7084261108668 & -0.0484261108668029 \tabularnewline
17 & 18.69 & 18.7075888164949 & -0.0175888164948965 \tabularnewline
18 & 18.72 & 18.7312178141602 & -0.0112178141602293 \tabularnewline
19 & 18.72 & 18.7575879289278 & -0.0375879289278238 \tabularnewline
20 & 18.73 & 18.7469805792995 & -0.0169805792995348 \tabularnewline
21 & 18.84 & 18.7511285934756 & 0.0888714065243548 \tabularnewline
22 & 18.83 & 18.8847901201546 & -0.0547901201546352 \tabularnewline
23 & 18.91 & 18.8627582156664 & 0.0472417843335755 \tabularnewline
24 & 18.91 & 18.9538443401615 & -0.0438443401614919 \tabularnewline
25 & 18.94 & 18.9434378761519 & -0.00343787615187807 \tabularnewline
26 & 18.97 & 18.9710719698638 & -0.00107196986380487 \tabularnewline
27 & 19 & 19.0006678240313 & -0.000667824031275188 \tabularnewline
28 & 19.08 & 19.0304509175506 & 0.0495490824493672 \tabularnewline
29 & 19.18 & 19.1239299235817 & 0.0560700764183331 \tabularnewline
30 & 19.24 & 19.240822625826 & -0.000822625826000234 \tabularnewline
31 & 19.23 & 19.3024261794887 & -0.0724261794887333 \tabularnewline
32 & 19.25 & 19.2726652041917 & -0.0226652041916608 \tabularnewline
33 & 19.3 & 19.2841287026385 & 0.0158712973615209 \tabularnewline
34 & 19.33 & 19.3377143889295 & -0.00771438892953569 \tabularnewline
35 & 19.35 & 19.3661297793088 & -0.0161297793088231 \tabularnewline
36 & 19.35 & 19.3814833906962 & -0.0314833906962093 \tabularnewline
37 & 19.31 & 19.3723792477801 & -0.0623792477801004 \tabularnewline
38 & 19.47 & 19.3143563493240 & 0.155643650675966 \tabularnewline
39 & 19.7 & 19.5147316485192 & 0.185268351480786 \tabularnewline
40 & 19.76 & 19.8002856880873 & -0.0402856880872875 \tabularnewline
41 & 19.9 & 19.8553480638197 & 0.0446519361803333 \tabularnewline
42 & 19.97 & 20.0062013211898 & -0.0362013211898251 \tabularnewline
43 & 20.1 & 20.0677929512140 & 0.0322070487860273 \tabularnewline
44 & 20.26 & 20.2053884525539 & 0.0546115474460791 \tabularnewline
45 & 20.44 & 20.3813184531537 & 0.0586815468463442 \tabularnewline
46 & 20.43 & 20.5790877293438 & -0.149087729343808 \tabularnewline
47 & 20.57 & 20.5303782074049 & 0.0396217925951312 \tabularnewline
48 & 20.6 & 20.6763143054005 & -0.0763143054004729 \tabularnewline
49 & 20.69 & 20.6868122743805 & 0.00318772561948322 \tabularnewline
50 & 20.93 & 20.7751932518743 & 0.154806748125740 \tabularnewline
51 & 20.98 & 21.0574777817627 & -0.0774777817626742 \tabularnewline
52 & 21.11 & 21.0914133790820 & 0.0185866209179686 \tabularnewline
53 & 21.14 & 21.2239522105225 & -0.0839522105225434 \tabularnewline
54 & 21.16 & 21.2316833822965 & -0.0716833822964844 \tabularnewline
55 & 21.32 & 21.2294150528264 & 0.0905849471736389 \tabularnewline
56 & 21.32 & 21.4117603443927 & -0.0917603443927106 \tabularnewline
57 & 21.48 & 21.3897109168495 & 0.0902890831504841 \tabularnewline
58 & 21.58 & 21.5713211517785 & 0.00867884822147147 \tabularnewline
59 & 21.74 & 21.6766290232885 & 0.0633709767115356 \tabularnewline
60 & 21.75 & 21.8541787891139 & -0.104178789113881 \tabularnewline
61 & 21.81 & 21.8378585894279 & -0.0278585894278898 \tabularnewline
62 & 21.89 & 21.8868720031311 & 0.00312799686889775 \tabularnewline
63 & 22.21 & 21.9668162002933 & 0.243183799706657 \tabularnewline
64 & 22.37 & 22.3531791216908 & 0.0168208783092325 \tabularnewline
65 & 22.47 & 22.5256893304606 & -0.055689330460595 \tabularnewline
66 & 22.51 & 22.6110638096493 & -0.101063809649279 \tabularnewline
67 & 22.55 & 22.621711389555 & -0.0717113895550021 \tabularnewline
68 & 22.61 & 22.6388776480230 & -0.0288776480230304 \tabularnewline
69 & 22.58 & 22.6886717245608 & -0.108671724560814 \tabularnewline
70 & 22.85 & 22.6281203260429 & 0.221879673957105 \tabularnewline
71 & 22.93 & 22.9550341570196 & -0.0250341570195793 \tabularnewline
72 & 22.98 & 23.0354455659447 & -0.0554455659446766 \tabularnewline
73 & 23.01 & 23.0695221302882 & -0.0595221302882294 \tabularnewline
74 & 23.11 & 23.0814966318033 & 0.0285033681967093 \tabularnewline
75 & 23.18 & 23.1873228007946 & -0.00732280079462555 \tabularnewline
76 & 23.18 & 23.2562566514916 & -0.0762566514915797 \tabularnewline
77 & 23.21 & 23.2352400930027 & -0.025240093002715 \tabularnewline
78 & 23.22 & 23.2558771438448 & -0.0358771438448215 \tabularnewline
79 & 23.12 & 23.2552788571885 & -0.135278857188450 \tabularnewline
80 & 23.15 & 23.1172495798865 & 0.0327504201134659 \tabularnewline
81 & 23.16 & 23.1517635391157 & 0.00823646088430507 \tabularnewline
82 & 23.21 & 23.1650753043375 & 0.044924695662484 \tabularnewline
83 & 23.21 & 23.2275845408534 & -0.0175845408533561 \tabularnewline
84 & 23.22 & 23.2242576272969 & -0.00425762729694057 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117452&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]18.16[/C][C]18.34[/C][C]-0.180000000000000[/C][/ROW]
[ROW][C]4[/C][C]18.27[/C][C]18.3409549046228[/C][C]-0.0709549046228268[/C][/ROW]
[ROW][C]5[/C][C]18.29[/C][C]18.4257542290714[/C][C]-0.13575422907142[/C][/ROW]
[ROW][C]6[/C][C]18.35[/C][C]18.4064520083127[/C][C]-0.0564520083127036[/C][/ROW]
[ROW][C]7[/C][C]18.35[/C][C]18.4466452408430[/C][C]-0.0966452408430172[/C][/ROW]
[ROW][C]8[/C][C]18.38[/C][C]18.4184718996069[/C][C]-0.0384718996069395[/C][/ROW]
[ROW][C]9[/C][C]18.41[/C][C]18.4348390439304[/C][C]-0.0248390439303989[/C][/ROW]
[ROW][C]10[/C][C]18.41[/C][C]18.4568170261364[/C][C]-0.0468170261364271[/C][/ROW]
[ROW][C]11[/C][C]18.42[/C][C]18.4432509925016[/C][C]-0.0232509925016231[/C][/ROW]
[ROW][C]12[/C][C]18.43[/C][C]18.4453896522630[/C][C]-0.0153896522630284[/C][/ROW]
[ROW][C]13[/C][C]18.48[/C][C]18.4504384868389[/C][C]0.0295615131610951[/C][/ROW]
[ROW][C]14[/C][C]18.54[/C][C]18.5079915425422[/C][C]0.0320084574578345[/C][/ROW]
[ROW][C]15[/C][C]18.65[/C][C]18.5776765814020[/C][C]0.0723234185979713[/C][/ROW]
[ROW][C]16[/C][C]18.66[/C][C]18.7084261108668[/C][C]-0.0484261108668029[/C][/ROW]
[ROW][C]17[/C][C]18.69[/C][C]18.7075888164949[/C][C]-0.0175888164948965[/C][/ROW]
[ROW][C]18[/C][C]18.72[/C][C]18.7312178141602[/C][C]-0.0112178141602293[/C][/ROW]
[ROW][C]19[/C][C]18.72[/C][C]18.7575879289278[/C][C]-0.0375879289278238[/C][/ROW]
[ROW][C]20[/C][C]18.73[/C][C]18.7469805792995[/C][C]-0.0169805792995348[/C][/ROW]
[ROW][C]21[/C][C]18.84[/C][C]18.7511285934756[/C][C]0.0888714065243548[/C][/ROW]
[ROW][C]22[/C][C]18.83[/C][C]18.8847901201546[/C][C]-0.0547901201546352[/C][/ROW]
[ROW][C]23[/C][C]18.91[/C][C]18.8627582156664[/C][C]0.0472417843335755[/C][/ROW]
[ROW][C]24[/C][C]18.91[/C][C]18.9538443401615[/C][C]-0.0438443401614919[/C][/ROW]
[ROW][C]25[/C][C]18.94[/C][C]18.9434378761519[/C][C]-0.00343787615187807[/C][/ROW]
[ROW][C]26[/C][C]18.97[/C][C]18.9710719698638[/C][C]-0.00107196986380487[/C][/ROW]
[ROW][C]27[/C][C]19[/C][C]19.0006678240313[/C][C]-0.000667824031275188[/C][/ROW]
[ROW][C]28[/C][C]19.08[/C][C]19.0304509175506[/C][C]0.0495490824493672[/C][/ROW]
[ROW][C]29[/C][C]19.18[/C][C]19.1239299235817[/C][C]0.0560700764183331[/C][/ROW]
[ROW][C]30[/C][C]19.24[/C][C]19.240822625826[/C][C]-0.000822625826000234[/C][/ROW]
[ROW][C]31[/C][C]19.23[/C][C]19.3024261794887[/C][C]-0.0724261794887333[/C][/ROW]
[ROW][C]32[/C][C]19.25[/C][C]19.2726652041917[/C][C]-0.0226652041916608[/C][/ROW]
[ROW][C]33[/C][C]19.3[/C][C]19.2841287026385[/C][C]0.0158712973615209[/C][/ROW]
[ROW][C]34[/C][C]19.33[/C][C]19.3377143889295[/C][C]-0.00771438892953569[/C][/ROW]
[ROW][C]35[/C][C]19.35[/C][C]19.3661297793088[/C][C]-0.0161297793088231[/C][/ROW]
[ROW][C]36[/C][C]19.35[/C][C]19.3814833906962[/C][C]-0.0314833906962093[/C][/ROW]
[ROW][C]37[/C][C]19.31[/C][C]19.3723792477801[/C][C]-0.0623792477801004[/C][/ROW]
[ROW][C]38[/C][C]19.47[/C][C]19.3143563493240[/C][C]0.155643650675966[/C][/ROW]
[ROW][C]39[/C][C]19.7[/C][C]19.5147316485192[/C][C]0.185268351480786[/C][/ROW]
[ROW][C]40[/C][C]19.76[/C][C]19.8002856880873[/C][C]-0.0402856880872875[/C][/ROW]
[ROW][C]41[/C][C]19.9[/C][C]19.8553480638197[/C][C]0.0446519361803333[/C][/ROW]
[ROW][C]42[/C][C]19.97[/C][C]20.0062013211898[/C][C]-0.0362013211898251[/C][/ROW]
[ROW][C]43[/C][C]20.1[/C][C]20.0677929512140[/C][C]0.0322070487860273[/C][/ROW]
[ROW][C]44[/C][C]20.26[/C][C]20.2053884525539[/C][C]0.0546115474460791[/C][/ROW]
[ROW][C]45[/C][C]20.44[/C][C]20.3813184531537[/C][C]0.0586815468463442[/C][/ROW]
[ROW][C]46[/C][C]20.43[/C][C]20.5790877293438[/C][C]-0.149087729343808[/C][/ROW]
[ROW][C]47[/C][C]20.57[/C][C]20.5303782074049[/C][C]0.0396217925951312[/C][/ROW]
[ROW][C]48[/C][C]20.6[/C][C]20.6763143054005[/C][C]-0.0763143054004729[/C][/ROW]
[ROW][C]49[/C][C]20.69[/C][C]20.6868122743805[/C][C]0.00318772561948322[/C][/ROW]
[ROW][C]50[/C][C]20.93[/C][C]20.7751932518743[/C][C]0.154806748125740[/C][/ROW]
[ROW][C]51[/C][C]20.98[/C][C]21.0574777817627[/C][C]-0.0774777817626742[/C][/ROW]
[ROW][C]52[/C][C]21.11[/C][C]21.0914133790820[/C][C]0.0185866209179686[/C][/ROW]
[ROW][C]53[/C][C]21.14[/C][C]21.2239522105225[/C][C]-0.0839522105225434[/C][/ROW]
[ROW][C]54[/C][C]21.16[/C][C]21.2316833822965[/C][C]-0.0716833822964844[/C][/ROW]
[ROW][C]55[/C][C]21.32[/C][C]21.2294150528264[/C][C]0.0905849471736389[/C][/ROW]
[ROW][C]56[/C][C]21.32[/C][C]21.4117603443927[/C][C]-0.0917603443927106[/C][/ROW]
[ROW][C]57[/C][C]21.48[/C][C]21.3897109168495[/C][C]0.0902890831504841[/C][/ROW]
[ROW][C]58[/C][C]21.58[/C][C]21.5713211517785[/C][C]0.00867884822147147[/C][/ROW]
[ROW][C]59[/C][C]21.74[/C][C]21.6766290232885[/C][C]0.0633709767115356[/C][/ROW]
[ROW][C]60[/C][C]21.75[/C][C]21.8541787891139[/C][C]-0.104178789113881[/C][/ROW]
[ROW][C]61[/C][C]21.81[/C][C]21.8378585894279[/C][C]-0.0278585894278898[/C][/ROW]
[ROW][C]62[/C][C]21.89[/C][C]21.8868720031311[/C][C]0.00312799686889775[/C][/ROW]
[ROW][C]63[/C][C]22.21[/C][C]21.9668162002933[/C][C]0.243183799706657[/C][/ROW]
[ROW][C]64[/C][C]22.37[/C][C]22.3531791216908[/C][C]0.0168208783092325[/C][/ROW]
[ROW][C]65[/C][C]22.47[/C][C]22.5256893304606[/C][C]-0.055689330460595[/C][/ROW]
[ROW][C]66[/C][C]22.51[/C][C]22.6110638096493[/C][C]-0.101063809649279[/C][/ROW]
[ROW][C]67[/C][C]22.55[/C][C]22.621711389555[/C][C]-0.0717113895550021[/C][/ROW]
[ROW][C]68[/C][C]22.61[/C][C]22.6388776480230[/C][C]-0.0288776480230304[/C][/ROW]
[ROW][C]69[/C][C]22.58[/C][C]22.6886717245608[/C][C]-0.108671724560814[/C][/ROW]
[ROW][C]70[/C][C]22.85[/C][C]22.6281203260429[/C][C]0.221879673957105[/C][/ROW]
[ROW][C]71[/C][C]22.93[/C][C]22.9550341570196[/C][C]-0.0250341570195793[/C][/ROW]
[ROW][C]72[/C][C]22.98[/C][C]23.0354455659447[/C][C]-0.0554455659446766[/C][/ROW]
[ROW][C]73[/C][C]23.01[/C][C]23.0695221302882[/C][C]-0.0595221302882294[/C][/ROW]
[ROW][C]74[/C][C]23.11[/C][C]23.0814966318033[/C][C]0.0285033681967093[/C][/ROW]
[ROW][C]75[/C][C]23.18[/C][C]23.1873228007946[/C][C]-0.00732280079462555[/C][/ROW]
[ROW][C]76[/C][C]23.18[/C][C]23.2562566514916[/C][C]-0.0762566514915797[/C][/ROW]
[ROW][C]77[/C][C]23.21[/C][C]23.2352400930027[/C][C]-0.025240093002715[/C][/ROW]
[ROW][C]78[/C][C]23.22[/C][C]23.2558771438448[/C][C]-0.0358771438448215[/C][/ROW]
[ROW][C]79[/C][C]23.12[/C][C]23.2552788571885[/C][C]-0.135278857188450[/C][/ROW]
[ROW][C]80[/C][C]23.15[/C][C]23.1172495798865[/C][C]0.0327504201134659[/C][/ROW]
[ROW][C]81[/C][C]23.16[/C][C]23.1517635391157[/C][C]0.00823646088430507[/C][/ROW]
[ROW][C]82[/C][C]23.21[/C][C]23.1650753043375[/C][C]0.044924695662484[/C][/ROW]
[ROW][C]83[/C][C]23.21[/C][C]23.2275845408534[/C][C]-0.0175845408533561[/C][/ROW]
[ROW][C]84[/C][C]23.22[/C][C]23.2242576272969[/C][C]-0.00425762729694057[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117452&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117452&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
318.1618.34-0.180000000000000
418.2718.3409549046228-0.0709549046228268
518.2918.4257542290714-0.13575422907142
618.3518.4064520083127-0.0564520083127036
718.3518.4466452408430-0.0966452408430172
818.3818.4184718996069-0.0384718996069395
918.4118.4348390439304-0.0248390439303989
1018.4118.4568170261364-0.0468170261364271
1118.4218.4432509925016-0.0232509925016231
1218.4318.4453896522630-0.0153896522630284
1318.4818.45043848683890.0295615131610951
1418.5418.50799154254220.0320084574578345
1518.6518.57767658140200.0723234185979713
1618.6618.7084261108668-0.0484261108668029
1718.6918.7075888164949-0.0175888164948965
1818.7218.7312178141602-0.0112178141602293
1918.7218.7575879289278-0.0375879289278238
2018.7318.7469805792995-0.0169805792995348
2118.8418.75112859347560.0888714065243548
2218.8318.8847901201546-0.0547901201546352
2318.9118.86275821566640.0472417843335755
2418.9118.9538443401615-0.0438443401614919
2518.9418.9434378761519-0.00343787615187807
2618.9718.9710719698638-0.00107196986380487
271919.0006678240313-0.000667824031275188
2819.0819.03045091755060.0495490824493672
2919.1819.12392992358170.0560700764183331
3019.2419.240822625826-0.000822625826000234
3119.2319.3024261794887-0.0724261794887333
3219.2519.2726652041917-0.0226652041916608
3319.319.28412870263850.0158712973615209
3419.3319.3377143889295-0.00771438892953569
3519.3519.3661297793088-0.0161297793088231
3619.3519.3814833906962-0.0314833906962093
3719.3119.3723792477801-0.0623792477801004
3819.4719.31435634932400.155643650675966
3919.719.51473164851920.185268351480786
4019.7619.8002856880873-0.0402856880872875
4119.919.85534806381970.0446519361803333
4219.9720.0062013211898-0.0362013211898251
4320.120.06779295121400.0322070487860273
4420.2620.20538845255390.0546115474460791
4520.4420.38131845315370.0586815468463442
4620.4320.5790877293438-0.149087729343808
4720.5720.53037820740490.0396217925951312
4820.620.6763143054005-0.0763143054004729
4920.6920.68681227438050.00318772561948322
5020.9320.77519325187430.154806748125740
5120.9821.0574777817627-0.0774777817626742
5221.1121.09141337908200.0185866209179686
5321.1421.2239522105225-0.0839522105225434
5421.1621.2316833822965-0.0716833822964844
5521.3221.22941505282640.0905849471736389
5621.3221.4117603443927-0.0917603443927106
5721.4821.38971091684950.0902890831504841
5821.5821.57132115177850.00867884822147147
5921.7421.67662902328850.0633709767115356
6021.7521.8541787891139-0.104178789113881
6121.8121.8378585894279-0.0278585894278898
6221.8921.88687200313110.00312799686889775
6322.2121.96681620029330.243183799706657
6422.3722.35317912169080.0168208783092325
6522.4722.5256893304606-0.055689330460595
6622.5122.6110638096493-0.101063809649279
6722.5522.621711389555-0.0717113895550021
6822.6122.6388776480230-0.0288776480230304
6922.5822.6886717245608-0.108671724560814
7022.8522.62812032604290.221879673957105
7122.9322.9550341570196-0.0250341570195793
7222.9823.0354455659447-0.0554455659446766
7323.0123.0695221302882-0.0595221302882294
7423.1123.08149663180330.0285033681967093
7523.1823.1873228007946-0.00732280079462555
7623.1823.2562566514916-0.0762566514915797
7723.2123.2352400930027-0.025240093002715
7823.2223.2558771438448-0.0358771438448215
7923.1223.2552788571885-0.135278857188450
8023.1523.11724957988650.0327504201134659
8123.1623.15176353911570.00823646088430507
8223.2123.16507530433750.044924695662484
8323.2123.2275845408534-0.0175845408533561
8423.2223.2242576272969-0.00425762729694057







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8523.232524342705923.082954745854823.382093939557
8623.244909901015123.002847928232723.4869718737976
8723.257295459324422.919260686738323.5953302319104
8823.269681017633622.829731450416823.7096305848505
8923.282066575942922.733776167235523.8303569846503
9023.294452134252222.631404782852323.9574994856520
9123.306837692561422.522779080970624.0908963041522
9223.319223250870722.408105941257424.2303405604839
9323.331608809179922.287599059435124.3756185589247
9423.343994367489222.161464556267624.5265241787108
9523.356379925798422.029895861274524.6828639903223
9623.368765484107721.893072411159024.8444585570563

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 23.2325243427059 & 23.0829547458548 & 23.382093939557 \tabularnewline
86 & 23.2449099010151 & 23.0028479282327 & 23.4869718737976 \tabularnewline
87 & 23.2572954593244 & 22.9192606867383 & 23.5953302319104 \tabularnewline
88 & 23.2696810176336 & 22.8297314504168 & 23.7096305848505 \tabularnewline
89 & 23.2820665759429 & 22.7337761672355 & 23.8303569846503 \tabularnewline
90 & 23.2944521342522 & 22.6314047828523 & 23.9574994856520 \tabularnewline
91 & 23.3068376925614 & 22.5227790809706 & 24.0908963041522 \tabularnewline
92 & 23.3192232508707 & 22.4081059412574 & 24.2303405604839 \tabularnewline
93 & 23.3316088091799 & 22.2875990594351 & 24.3756185589247 \tabularnewline
94 & 23.3439943674892 & 22.1614645562676 & 24.5265241787108 \tabularnewline
95 & 23.3563799257984 & 22.0298958612745 & 24.6828639903223 \tabularnewline
96 & 23.3687654841077 & 21.8930724111590 & 24.8444585570563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117452&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]23.2325243427059[/C][C]23.0829547458548[/C][C]23.382093939557[/C][/ROW]
[ROW][C]86[/C][C]23.2449099010151[/C][C]23.0028479282327[/C][C]23.4869718737976[/C][/ROW]
[ROW][C]87[/C][C]23.2572954593244[/C][C]22.9192606867383[/C][C]23.5953302319104[/C][/ROW]
[ROW][C]88[/C][C]23.2696810176336[/C][C]22.8297314504168[/C][C]23.7096305848505[/C][/ROW]
[ROW][C]89[/C][C]23.2820665759429[/C][C]22.7337761672355[/C][C]23.8303569846503[/C][/ROW]
[ROW][C]90[/C][C]23.2944521342522[/C][C]22.6314047828523[/C][C]23.9574994856520[/C][/ROW]
[ROW][C]91[/C][C]23.3068376925614[/C][C]22.5227790809706[/C][C]24.0908963041522[/C][/ROW]
[ROW][C]92[/C][C]23.3192232508707[/C][C]22.4081059412574[/C][C]24.2303405604839[/C][/ROW]
[ROW][C]93[/C][C]23.3316088091799[/C][C]22.2875990594351[/C][C]24.3756185589247[/C][/ROW]
[ROW][C]94[/C][C]23.3439943674892[/C][C]22.1614645562676[/C][C]24.5265241787108[/C][/ROW]
[ROW][C]95[/C][C]23.3563799257984[/C][C]22.0298958612745[/C][C]24.6828639903223[/C][/ROW]
[ROW][C]96[/C][C]23.3687654841077[/C][C]21.8930724111590[/C][C]24.8444585570563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117452&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117452&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
8523.232524342705923.082954745854823.382093939557
8623.244909901015123.002847928232723.4869718737976
8723.257295459324422.919260686738323.5953302319104
8823.269681017633622.829731450416823.7096305848505
8923.282066575942922.733776167235523.8303569846503
9023.294452134252222.631404782852323.9574994856520
9123.306837692561422.522779080970624.0908963041522
9223.319223250870722.408105941257424.2303405604839
9323.331608809179922.287599059435124.3756185589247
9423.343994367489222.161464556267624.5265241787108
9523.356379925798422.029895861274524.6828639903223
9623.368765484107721.893072411159024.8444585570563



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')