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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 13:33:33 -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/t1233002242g13yne2ovlw7ddy.htm/, Retrieved Sun, 05 May 2024 18:15:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36974, Retrieved Sun, 05 May 2024 18:15:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact216
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Nieuwe personenwa...] [2009-01-16 12:08:15] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [opgave 10-oefenin...] [2009-01-26 20:33:33] [59eb7d50a05a673a4523845c066501a9] [Current]
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Dataseries X:
101.6
101.8
102.1
102.1
101.9
102.1
102
102.1
102.2
102.3
102.7
102.8
103.1
103.1
103.3
103.5
103.3
103.5
103.8
103.9
103.9
104.2
104.6
104.9
105.2
105.2
105.6
105.6
106.2
106.3
106.4
106.9
107.2
107.3
107.3
107.4
107.55
107.87
108.37
108.38
107.92
108.03
108.14
108.3
108.64
108.66
109.04
109.03
109.03
109.54
109.75
109.83
109.65
109.82
109.95
110.12
110.15
110.2
109.99
110.14
110.14
110.81
110.97
110.99
109.73
109.81
110.02
110.18
110.21
110.25
110.36
110.51
110.64
110.95
111.18
111.19
111.69
111.7
111.83
111.77
111.73
112.01
111.86
112.04




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36974&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36974&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 time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0314493769982561
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0314493769982561 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36974&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]0.0314493769982561[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36974&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
beta0.0314493769982561
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3102.11020.0999999999999943
4102.1102.303144937700-0.203144937699832
5101.9102.296756155969-0.396756155968802
6102.1102.0842784220430.0157215779566116
7102102.284772855876-0.284772855875531
8102.1102.175816926972-0.0758169269722515
9102.2102.273432531853-0.0734325318530296
10102.3102.371123124475-0.071123124474866
11102.7102.468886346520.231113653480051
12102.8102.876154726938-0.0761547269377019
13103.1102.973759708220.126240291779965
14103.1103.277729886749-0.177729886748594
15103.3103.2721403925360.0278596074636255
16103.5103.4730165598350.0269834401654805
17103.3103.673865172217-0.373865172216995
18103.5103.4621073454690.0378926545305802
19103.8103.6632990458470.136700954152772
20103.9103.967598205690-0.0675982056903877
21103.9104.065472284235-0.165472284235236
22104.2104.0602682839860.139731716014438
23104.6104.3646627594010.235337240598881
24104.9104.7720639690020.127936030997574
25105.2105.0760874774730.123912522527064
26105.2105.379984449109-0.179984449108687
27105.6105.3743240503150.22567594968514
28105.6105.781421418336-0.181421418335944
29106.2105.7757158277550.424284172244882
30106.3106.389059300642-0.089059300642461
31106.4106.486258441121-0.0862584411213447
32106.9106.5835456668870.316454333112759
33107.2107.0934979585120.106502041487957
34107.3107.396847381366-0.0968473813658761
35107.3107.493801591558-0.193801591558000
36107.4107.487706652242-0.0877066522422325
37107.55107.584948332671-0.0349483326706235
38107.87107.7338492293810.136150770619011
39108.37108.0581310862950.311868913705197
40108.38108.567939169336-0.187939169335962
41107.92108.572028599547-0.652028599546753
42108.03108.091522706306-0.0615227063059791
43108.14108.199587855521-0.0595878555214
44108.3108.307713854589-0.00771385458860152
45108.64108.4674712586680.172528741332471
46108.66108.812897180097-0.152897180096730
47109.04108.8280886590380.211911340962118
48109.03109.21475313869-0.184753138690027
49109.03109.198942767580-0.168942767579750
50109.54109.1936296227910.346370377209013
51109.75109.7145227553650.0354772446351177
52109.83109.925638492606-0.0956384926062697
53109.65110.002630721597-0.352630721596739
54109.82109.8115407050920.00845929490790809
55109.95109.981806744647-0.0318067446467722
56110.12110.1108064423430.00919355765670105
57110.15110.281095574004-0.131095574003993
58110.2110.306972699874-0.106972699874348
59109.99110.353608475107-0.363608475107483
60110.14110.1321732150940.00782678490594435
61110.14110.282419362603-0.142419362603249
62110.81110.2779403623770.532059637623121
63110.97110.9646733065060.00532669349394155
64110.99111.124840827698-0.1348408276979
65109.73111.140600167673-1.41060016767285
66109.81109.836237671206-0.0262376712059194
67110.02109.9154125127930.104587487207382
68110.18110.1287017241070.0512982758929184
69110.21110.290315022925-0.0803150229250207
70110.25110.317789165490-0.0677891654904101
71110.36110.3556572384690.00434276153148971
72110.51110.4657938156130.0442061843868800
73110.64110.6171840725720.0228159274284252
74110.95110.7479016192750.202098380725175
75111.18111.0642574874410.115742512559009
76111.19111.297897517353-0.107897517353194
77111.69111.3045042076530.385495792347228
78111.7111.816627810158-0.116627810157539
79111.83111.8229599381870.00704006181257455
80111.77111.953181343745-0.183181343745446
81111.73111.887420404607-0.157420404606938
82112.01111.8424696309550.167530369044755
83111.86112.12773835669-0.267738356690003
84112.04111.9693181521740.0706818478264495

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 102.1 & 102 & 0.0999999999999943 \tabularnewline
4 & 102.1 & 102.303144937700 & -0.203144937699832 \tabularnewline
5 & 101.9 & 102.296756155969 & -0.396756155968802 \tabularnewline
6 & 102.1 & 102.084278422043 & 0.0157215779566116 \tabularnewline
7 & 102 & 102.284772855876 & -0.284772855875531 \tabularnewline
8 & 102.1 & 102.175816926972 & -0.0758169269722515 \tabularnewline
9 & 102.2 & 102.273432531853 & -0.0734325318530296 \tabularnewline
10 & 102.3 & 102.371123124475 & -0.071123124474866 \tabularnewline
11 & 102.7 & 102.46888634652 & 0.231113653480051 \tabularnewline
12 & 102.8 & 102.876154726938 & -0.0761547269377019 \tabularnewline
13 & 103.1 & 102.97375970822 & 0.126240291779965 \tabularnewline
14 & 103.1 & 103.277729886749 & -0.177729886748594 \tabularnewline
15 & 103.3 & 103.272140392536 & 0.0278596074636255 \tabularnewline
16 & 103.5 & 103.473016559835 & 0.0269834401654805 \tabularnewline
17 & 103.3 & 103.673865172217 & -0.373865172216995 \tabularnewline
18 & 103.5 & 103.462107345469 & 0.0378926545305802 \tabularnewline
19 & 103.8 & 103.663299045847 & 0.136700954152772 \tabularnewline
20 & 103.9 & 103.967598205690 & -0.0675982056903877 \tabularnewline
21 & 103.9 & 104.065472284235 & -0.165472284235236 \tabularnewline
22 & 104.2 & 104.060268283986 & 0.139731716014438 \tabularnewline
23 & 104.6 & 104.364662759401 & 0.235337240598881 \tabularnewline
24 & 104.9 & 104.772063969002 & 0.127936030997574 \tabularnewline
25 & 105.2 & 105.076087477473 & 0.123912522527064 \tabularnewline
26 & 105.2 & 105.379984449109 & -0.179984449108687 \tabularnewline
27 & 105.6 & 105.374324050315 & 0.22567594968514 \tabularnewline
28 & 105.6 & 105.781421418336 & -0.181421418335944 \tabularnewline
29 & 106.2 & 105.775715827755 & 0.424284172244882 \tabularnewline
30 & 106.3 & 106.389059300642 & -0.089059300642461 \tabularnewline
31 & 106.4 & 106.486258441121 & -0.0862584411213447 \tabularnewline
32 & 106.9 & 106.583545666887 & 0.316454333112759 \tabularnewline
33 & 107.2 & 107.093497958512 & 0.106502041487957 \tabularnewline
34 & 107.3 & 107.396847381366 & -0.0968473813658761 \tabularnewline
35 & 107.3 & 107.493801591558 & -0.193801591558000 \tabularnewline
36 & 107.4 & 107.487706652242 & -0.0877066522422325 \tabularnewline
37 & 107.55 & 107.584948332671 & -0.0349483326706235 \tabularnewline
38 & 107.87 & 107.733849229381 & 0.136150770619011 \tabularnewline
39 & 108.37 & 108.058131086295 & 0.311868913705197 \tabularnewline
40 & 108.38 & 108.567939169336 & -0.187939169335962 \tabularnewline
41 & 107.92 & 108.572028599547 & -0.652028599546753 \tabularnewline
42 & 108.03 & 108.091522706306 & -0.0615227063059791 \tabularnewline
43 & 108.14 & 108.199587855521 & -0.0595878555214 \tabularnewline
44 & 108.3 & 108.307713854589 & -0.00771385458860152 \tabularnewline
45 & 108.64 & 108.467471258668 & 0.172528741332471 \tabularnewline
46 & 108.66 & 108.812897180097 & -0.152897180096730 \tabularnewline
47 & 109.04 & 108.828088659038 & 0.211911340962118 \tabularnewline
48 & 109.03 & 109.21475313869 & -0.184753138690027 \tabularnewline
49 & 109.03 & 109.198942767580 & -0.168942767579750 \tabularnewline
50 & 109.54 & 109.193629622791 & 0.346370377209013 \tabularnewline
51 & 109.75 & 109.714522755365 & 0.0354772446351177 \tabularnewline
52 & 109.83 & 109.925638492606 & -0.0956384926062697 \tabularnewline
53 & 109.65 & 110.002630721597 & -0.352630721596739 \tabularnewline
54 & 109.82 & 109.811540705092 & 0.00845929490790809 \tabularnewline
55 & 109.95 & 109.981806744647 & -0.0318067446467722 \tabularnewline
56 & 110.12 & 110.110806442343 & 0.00919355765670105 \tabularnewline
57 & 110.15 & 110.281095574004 & -0.131095574003993 \tabularnewline
58 & 110.2 & 110.306972699874 & -0.106972699874348 \tabularnewline
59 & 109.99 & 110.353608475107 & -0.363608475107483 \tabularnewline
60 & 110.14 & 110.132173215094 & 0.00782678490594435 \tabularnewline
61 & 110.14 & 110.282419362603 & -0.142419362603249 \tabularnewline
62 & 110.81 & 110.277940362377 & 0.532059637623121 \tabularnewline
63 & 110.97 & 110.964673306506 & 0.00532669349394155 \tabularnewline
64 & 110.99 & 111.124840827698 & -0.1348408276979 \tabularnewline
65 & 109.73 & 111.140600167673 & -1.41060016767285 \tabularnewline
66 & 109.81 & 109.836237671206 & -0.0262376712059194 \tabularnewline
67 & 110.02 & 109.915412512793 & 0.104587487207382 \tabularnewline
68 & 110.18 & 110.128701724107 & 0.0512982758929184 \tabularnewline
69 & 110.21 & 110.290315022925 & -0.0803150229250207 \tabularnewline
70 & 110.25 & 110.317789165490 & -0.0677891654904101 \tabularnewline
71 & 110.36 & 110.355657238469 & 0.00434276153148971 \tabularnewline
72 & 110.51 & 110.465793815613 & 0.0442061843868800 \tabularnewline
73 & 110.64 & 110.617184072572 & 0.0228159274284252 \tabularnewline
74 & 110.95 & 110.747901619275 & 0.202098380725175 \tabularnewline
75 & 111.18 & 111.064257487441 & 0.115742512559009 \tabularnewline
76 & 111.19 & 111.297897517353 & -0.107897517353194 \tabularnewline
77 & 111.69 & 111.304504207653 & 0.385495792347228 \tabularnewline
78 & 111.7 & 111.816627810158 & -0.116627810157539 \tabularnewline
79 & 111.83 & 111.822959938187 & 0.00704006181257455 \tabularnewline
80 & 111.77 & 111.953181343745 & -0.183181343745446 \tabularnewline
81 & 111.73 & 111.887420404607 & -0.157420404606938 \tabularnewline
82 & 112.01 & 111.842469630955 & 0.167530369044755 \tabularnewline
83 & 111.86 & 112.12773835669 & -0.267738356690003 \tabularnewline
84 & 112.04 & 111.969318152174 & 0.0706818478264495 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36974&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]102.1[/C][C]102[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]4[/C][C]102.1[/C][C]102.303144937700[/C][C]-0.203144937699832[/C][/ROW]
[ROW][C]5[/C][C]101.9[/C][C]102.296756155969[/C][C]-0.396756155968802[/C][/ROW]
[ROW][C]6[/C][C]102.1[/C][C]102.084278422043[/C][C]0.0157215779566116[/C][/ROW]
[ROW][C]7[/C][C]102[/C][C]102.284772855876[/C][C]-0.284772855875531[/C][/ROW]
[ROW][C]8[/C][C]102.1[/C][C]102.175816926972[/C][C]-0.0758169269722515[/C][/ROW]
[ROW][C]9[/C][C]102.2[/C][C]102.273432531853[/C][C]-0.0734325318530296[/C][/ROW]
[ROW][C]10[/C][C]102.3[/C][C]102.371123124475[/C][C]-0.071123124474866[/C][/ROW]
[ROW][C]11[/C][C]102.7[/C][C]102.46888634652[/C][C]0.231113653480051[/C][/ROW]
[ROW][C]12[/C][C]102.8[/C][C]102.876154726938[/C][C]-0.0761547269377019[/C][/ROW]
[ROW][C]13[/C][C]103.1[/C][C]102.97375970822[/C][C]0.126240291779965[/C][/ROW]
[ROW][C]14[/C][C]103.1[/C][C]103.277729886749[/C][C]-0.177729886748594[/C][/ROW]
[ROW][C]15[/C][C]103.3[/C][C]103.272140392536[/C][C]0.0278596074636255[/C][/ROW]
[ROW][C]16[/C][C]103.5[/C][C]103.473016559835[/C][C]0.0269834401654805[/C][/ROW]
[ROW][C]17[/C][C]103.3[/C][C]103.673865172217[/C][C]-0.373865172216995[/C][/ROW]
[ROW][C]18[/C][C]103.5[/C][C]103.462107345469[/C][C]0.0378926545305802[/C][/ROW]
[ROW][C]19[/C][C]103.8[/C][C]103.663299045847[/C][C]0.136700954152772[/C][/ROW]
[ROW][C]20[/C][C]103.9[/C][C]103.967598205690[/C][C]-0.0675982056903877[/C][/ROW]
[ROW][C]21[/C][C]103.9[/C][C]104.065472284235[/C][C]-0.165472284235236[/C][/ROW]
[ROW][C]22[/C][C]104.2[/C][C]104.060268283986[/C][C]0.139731716014438[/C][/ROW]
[ROW][C]23[/C][C]104.6[/C][C]104.364662759401[/C][C]0.235337240598881[/C][/ROW]
[ROW][C]24[/C][C]104.9[/C][C]104.772063969002[/C][C]0.127936030997574[/C][/ROW]
[ROW][C]25[/C][C]105.2[/C][C]105.076087477473[/C][C]0.123912522527064[/C][/ROW]
[ROW][C]26[/C][C]105.2[/C][C]105.379984449109[/C][C]-0.179984449108687[/C][/ROW]
[ROW][C]27[/C][C]105.6[/C][C]105.374324050315[/C][C]0.22567594968514[/C][/ROW]
[ROW][C]28[/C][C]105.6[/C][C]105.781421418336[/C][C]-0.181421418335944[/C][/ROW]
[ROW][C]29[/C][C]106.2[/C][C]105.775715827755[/C][C]0.424284172244882[/C][/ROW]
[ROW][C]30[/C][C]106.3[/C][C]106.389059300642[/C][C]-0.089059300642461[/C][/ROW]
[ROW][C]31[/C][C]106.4[/C][C]106.486258441121[/C][C]-0.0862584411213447[/C][/ROW]
[ROW][C]32[/C][C]106.9[/C][C]106.583545666887[/C][C]0.316454333112759[/C][/ROW]
[ROW][C]33[/C][C]107.2[/C][C]107.093497958512[/C][C]0.106502041487957[/C][/ROW]
[ROW][C]34[/C][C]107.3[/C][C]107.396847381366[/C][C]-0.0968473813658761[/C][/ROW]
[ROW][C]35[/C][C]107.3[/C][C]107.493801591558[/C][C]-0.193801591558000[/C][/ROW]
[ROW][C]36[/C][C]107.4[/C][C]107.487706652242[/C][C]-0.0877066522422325[/C][/ROW]
[ROW][C]37[/C][C]107.55[/C][C]107.584948332671[/C][C]-0.0349483326706235[/C][/ROW]
[ROW][C]38[/C][C]107.87[/C][C]107.733849229381[/C][C]0.136150770619011[/C][/ROW]
[ROW][C]39[/C][C]108.37[/C][C]108.058131086295[/C][C]0.311868913705197[/C][/ROW]
[ROW][C]40[/C][C]108.38[/C][C]108.567939169336[/C][C]-0.187939169335962[/C][/ROW]
[ROW][C]41[/C][C]107.92[/C][C]108.572028599547[/C][C]-0.652028599546753[/C][/ROW]
[ROW][C]42[/C][C]108.03[/C][C]108.091522706306[/C][C]-0.0615227063059791[/C][/ROW]
[ROW][C]43[/C][C]108.14[/C][C]108.199587855521[/C][C]-0.0595878555214[/C][/ROW]
[ROW][C]44[/C][C]108.3[/C][C]108.307713854589[/C][C]-0.00771385458860152[/C][/ROW]
[ROW][C]45[/C][C]108.64[/C][C]108.467471258668[/C][C]0.172528741332471[/C][/ROW]
[ROW][C]46[/C][C]108.66[/C][C]108.812897180097[/C][C]-0.152897180096730[/C][/ROW]
[ROW][C]47[/C][C]109.04[/C][C]108.828088659038[/C][C]0.211911340962118[/C][/ROW]
[ROW][C]48[/C][C]109.03[/C][C]109.21475313869[/C][C]-0.184753138690027[/C][/ROW]
[ROW][C]49[/C][C]109.03[/C][C]109.198942767580[/C][C]-0.168942767579750[/C][/ROW]
[ROW][C]50[/C][C]109.54[/C][C]109.193629622791[/C][C]0.346370377209013[/C][/ROW]
[ROW][C]51[/C][C]109.75[/C][C]109.714522755365[/C][C]0.0354772446351177[/C][/ROW]
[ROW][C]52[/C][C]109.83[/C][C]109.925638492606[/C][C]-0.0956384926062697[/C][/ROW]
[ROW][C]53[/C][C]109.65[/C][C]110.002630721597[/C][C]-0.352630721596739[/C][/ROW]
[ROW][C]54[/C][C]109.82[/C][C]109.811540705092[/C][C]0.00845929490790809[/C][/ROW]
[ROW][C]55[/C][C]109.95[/C][C]109.981806744647[/C][C]-0.0318067446467722[/C][/ROW]
[ROW][C]56[/C][C]110.12[/C][C]110.110806442343[/C][C]0.00919355765670105[/C][/ROW]
[ROW][C]57[/C][C]110.15[/C][C]110.281095574004[/C][C]-0.131095574003993[/C][/ROW]
[ROW][C]58[/C][C]110.2[/C][C]110.306972699874[/C][C]-0.106972699874348[/C][/ROW]
[ROW][C]59[/C][C]109.99[/C][C]110.353608475107[/C][C]-0.363608475107483[/C][/ROW]
[ROW][C]60[/C][C]110.14[/C][C]110.132173215094[/C][C]0.00782678490594435[/C][/ROW]
[ROW][C]61[/C][C]110.14[/C][C]110.282419362603[/C][C]-0.142419362603249[/C][/ROW]
[ROW][C]62[/C][C]110.81[/C][C]110.277940362377[/C][C]0.532059637623121[/C][/ROW]
[ROW][C]63[/C][C]110.97[/C][C]110.964673306506[/C][C]0.00532669349394155[/C][/ROW]
[ROW][C]64[/C][C]110.99[/C][C]111.124840827698[/C][C]-0.1348408276979[/C][/ROW]
[ROW][C]65[/C][C]109.73[/C][C]111.140600167673[/C][C]-1.41060016767285[/C][/ROW]
[ROW][C]66[/C][C]109.81[/C][C]109.836237671206[/C][C]-0.0262376712059194[/C][/ROW]
[ROW][C]67[/C][C]110.02[/C][C]109.915412512793[/C][C]0.104587487207382[/C][/ROW]
[ROW][C]68[/C][C]110.18[/C][C]110.128701724107[/C][C]0.0512982758929184[/C][/ROW]
[ROW][C]69[/C][C]110.21[/C][C]110.290315022925[/C][C]-0.0803150229250207[/C][/ROW]
[ROW][C]70[/C][C]110.25[/C][C]110.317789165490[/C][C]-0.0677891654904101[/C][/ROW]
[ROW][C]71[/C][C]110.36[/C][C]110.355657238469[/C][C]0.00434276153148971[/C][/ROW]
[ROW][C]72[/C][C]110.51[/C][C]110.465793815613[/C][C]0.0442061843868800[/C][/ROW]
[ROW][C]73[/C][C]110.64[/C][C]110.617184072572[/C][C]0.0228159274284252[/C][/ROW]
[ROW][C]74[/C][C]110.95[/C][C]110.747901619275[/C][C]0.202098380725175[/C][/ROW]
[ROW][C]75[/C][C]111.18[/C][C]111.064257487441[/C][C]0.115742512559009[/C][/ROW]
[ROW][C]76[/C][C]111.19[/C][C]111.297897517353[/C][C]-0.107897517353194[/C][/ROW]
[ROW][C]77[/C][C]111.69[/C][C]111.304504207653[/C][C]0.385495792347228[/C][/ROW]
[ROW][C]78[/C][C]111.7[/C][C]111.816627810158[/C][C]-0.116627810157539[/C][/ROW]
[ROW][C]79[/C][C]111.83[/C][C]111.822959938187[/C][C]0.00704006181257455[/C][/ROW]
[ROW][C]80[/C][C]111.77[/C][C]111.953181343745[/C][C]-0.183181343745446[/C][/ROW]
[ROW][C]81[/C][C]111.73[/C][C]111.887420404607[/C][C]-0.157420404606938[/C][/ROW]
[ROW][C]82[/C][C]112.01[/C][C]111.842469630955[/C][C]0.167530369044755[/C][/ROW]
[ROW][C]83[/C][C]111.86[/C][C]112.12773835669[/C][C]-0.267738356690003[/C][/ROW]
[ROW][C]84[/C][C]112.04[/C][C]111.969318152174[/C][C]0.0706818478264495[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36974&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36974&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
3102.11020.0999999999999943
4102.1102.303144937700-0.203144937699832
5101.9102.296756155969-0.396756155968802
6102.1102.0842784220430.0157215779566116
7102102.284772855876-0.284772855875531
8102.1102.175816926972-0.0758169269722515
9102.2102.273432531853-0.0734325318530296
10102.3102.371123124475-0.071123124474866
11102.7102.468886346520.231113653480051
12102.8102.876154726938-0.0761547269377019
13103.1102.973759708220.126240291779965
14103.1103.277729886749-0.177729886748594
15103.3103.2721403925360.0278596074636255
16103.5103.4730165598350.0269834401654805
17103.3103.673865172217-0.373865172216995
18103.5103.4621073454690.0378926545305802
19103.8103.6632990458470.136700954152772
20103.9103.967598205690-0.0675982056903877
21103.9104.065472284235-0.165472284235236
22104.2104.0602682839860.139731716014438
23104.6104.3646627594010.235337240598881
24104.9104.7720639690020.127936030997574
25105.2105.0760874774730.123912522527064
26105.2105.379984449109-0.179984449108687
27105.6105.3743240503150.22567594968514
28105.6105.781421418336-0.181421418335944
29106.2105.7757158277550.424284172244882
30106.3106.389059300642-0.089059300642461
31106.4106.486258441121-0.0862584411213447
32106.9106.5835456668870.316454333112759
33107.2107.0934979585120.106502041487957
34107.3107.396847381366-0.0968473813658761
35107.3107.493801591558-0.193801591558000
36107.4107.487706652242-0.0877066522422325
37107.55107.584948332671-0.0349483326706235
38107.87107.7338492293810.136150770619011
39108.37108.0581310862950.311868913705197
40108.38108.567939169336-0.187939169335962
41107.92108.572028599547-0.652028599546753
42108.03108.091522706306-0.0615227063059791
43108.14108.199587855521-0.0595878555214
44108.3108.307713854589-0.00771385458860152
45108.64108.4674712586680.172528741332471
46108.66108.812897180097-0.152897180096730
47109.04108.8280886590380.211911340962118
48109.03109.21475313869-0.184753138690027
49109.03109.198942767580-0.168942767579750
50109.54109.1936296227910.346370377209013
51109.75109.7145227553650.0354772446351177
52109.83109.925638492606-0.0956384926062697
53109.65110.002630721597-0.352630721596739
54109.82109.8115407050920.00845929490790809
55109.95109.981806744647-0.0318067446467722
56110.12110.1108064423430.00919355765670105
57110.15110.281095574004-0.131095574003993
58110.2110.306972699874-0.106972699874348
59109.99110.353608475107-0.363608475107483
60110.14110.1321732150940.00782678490594435
61110.14110.282419362603-0.142419362603249
62110.81110.2779403623770.532059637623121
63110.97110.9646733065060.00532669349394155
64110.99111.124840827698-0.1348408276979
65109.73111.140600167673-1.41060016767285
66109.81109.836237671206-0.0262376712059194
67110.02109.9154125127930.104587487207382
68110.18110.1287017241070.0512982758929184
69110.21110.290315022925-0.0803150229250207
70110.25110.317789165490-0.0677891654904101
71110.36110.3556572384690.00434276153148971
72110.51110.4657938156130.0442061843868800
73110.64110.6171840725720.0228159274284252
74110.95110.7479016192750.202098380725175
75111.18111.0642574874410.115742512559009
76111.19111.297897517353-0.107897517353194
77111.69111.3045042076530.385495792347228
78111.7111.816627810158-0.116627810157539
79111.83111.8229599381870.00704006181257455
80111.77111.953181343745-0.183181343745446
81111.73111.887420404607-0.157420404606938
82112.01111.8424696309550.167530369044755
83111.86112.12773835669-0.267738356690003
84112.04111.9693181521740.0706818478264495







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85112.151541052253111.665217398609112.637864705897
86112.263082104506111.564417990405112.961746218606
87112.374623156758111.505525698001113.243720615516
88112.486164209011111.467059165524113.505269252498
89112.597705261264111.440841620655113.754568901873
90112.709246313517111.422749744989113.995742882044
91112.820787365770111.410375102857114.231199628682
92112.932328418022111.402175052280114.462481783764
93113.043869470275111.397096570665114.690642369886
94113.155410522528111.394386507904114.916434537151
95113.266951574781111.393486613175115.140416536386
96113.378492627033111.393971279745115.363013974322

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 112.151541052253 & 111.665217398609 & 112.637864705897 \tabularnewline
86 & 112.263082104506 & 111.564417990405 & 112.961746218606 \tabularnewline
87 & 112.374623156758 & 111.505525698001 & 113.243720615516 \tabularnewline
88 & 112.486164209011 & 111.467059165524 & 113.505269252498 \tabularnewline
89 & 112.597705261264 & 111.440841620655 & 113.754568901873 \tabularnewline
90 & 112.709246313517 & 111.422749744989 & 113.995742882044 \tabularnewline
91 & 112.820787365770 & 111.410375102857 & 114.231199628682 \tabularnewline
92 & 112.932328418022 & 111.402175052280 & 114.462481783764 \tabularnewline
93 & 113.043869470275 & 111.397096570665 & 114.690642369886 \tabularnewline
94 & 113.155410522528 & 111.394386507904 & 114.916434537151 \tabularnewline
95 & 113.266951574781 & 111.393486613175 & 115.140416536386 \tabularnewline
96 & 113.378492627033 & 111.393971279745 & 115.363013974322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36974&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]112.151541052253[/C][C]111.665217398609[/C][C]112.637864705897[/C][/ROW]
[ROW][C]86[/C][C]112.263082104506[/C][C]111.564417990405[/C][C]112.961746218606[/C][/ROW]
[ROW][C]87[/C][C]112.374623156758[/C][C]111.505525698001[/C][C]113.243720615516[/C][/ROW]
[ROW][C]88[/C][C]112.486164209011[/C][C]111.467059165524[/C][C]113.505269252498[/C][/ROW]
[ROW][C]89[/C][C]112.597705261264[/C][C]111.440841620655[/C][C]113.754568901873[/C][/ROW]
[ROW][C]90[/C][C]112.709246313517[/C][C]111.422749744989[/C][C]113.995742882044[/C][/ROW]
[ROW][C]91[/C][C]112.820787365770[/C][C]111.410375102857[/C][C]114.231199628682[/C][/ROW]
[ROW][C]92[/C][C]112.932328418022[/C][C]111.402175052280[/C][C]114.462481783764[/C][/ROW]
[ROW][C]93[/C][C]113.043869470275[/C][C]111.397096570665[/C][C]114.690642369886[/C][/ROW]
[ROW][C]94[/C][C]113.155410522528[/C][C]111.394386507904[/C][C]114.916434537151[/C][/ROW]
[ROW][C]95[/C][C]113.266951574781[/C][C]111.393486613175[/C][C]115.140416536386[/C][/ROW]
[ROW][C]96[/C][C]113.378492627033[/C][C]111.393971279745[/C][C]115.363013974322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36974&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36974&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
85112.151541052253111.665217398609112.637864705897
86112.263082104506111.564417990405112.961746218606
87112.374623156758111.505525698001113.243720615516
88112.486164209011111.467059165524113.505269252498
89112.597705261264111.440841620655113.754568901873
90112.709246313517111.422749744989113.995742882044
91112.820787365770111.410375102857114.231199628682
92112.932328418022111.402175052280114.462481783764
93113.043869470275111.397096570665114.690642369886
94113.155410522528111.394386507904114.916434537151
95113.266951574781111.393486613175115.140416536386
96113.378492627033111.393971279745115.363013974322



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=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')