Free Statistics

of Irreproducible Research!

Author's title

werkloosheid voor jongeren -25jaar (additief, triple), Jonas Janssens, MAR ...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 02:16:39 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211789862bjia1an2o4u5sje.htm/, Retrieved Tue, 14 May 2024 11:34:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13249, Retrieved Tue, 14 May 2024 11:34:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact202
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [werkloosheid voor...] [2008-05-26 08:16:39] [2fa459907c4dcce485bca7190e4cae85] [Current]
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Dataseries X:
18.3
15.3
18.6
18.2
16.1
13.1
16.5
16.5
14.7
12.1
15.7
15.7
14
11.7
15.2
15.6
14.3
12.5
16.6
18.1
18.5
17.6
22.6
23.9
23.2
20.6
24.2
24.5
22.9
20.4
23.9
24.1
22.3
19.5
23.3
23.4
21.8
19.8
23.3
23.2
21.2
19
23.8
24.3
23.1
21.6
22.2
17.4
15.6
14.5
20.3
16.1
14.1
15.3
17.8
19.6
17.8
15.7
18.9
18.4
20.8
19
24.5
22.6
19.6
17.5
25
22.3
20.5
19.9
23.4
22.1
20
18.9
23
20
18.6
19.2
20.3
17.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13249&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13249&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13249&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.859340004640999
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.859340004640999 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13249&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]0.859340004640999[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13249&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13249&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
alpha0.859340004640999
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
516.117.4075892857143-1.30758928571429
613.113.7589255028600-0.658925502860049
716.516.9801844581742-0.480184458174222
816.516.8675427436583-0.367542743658252
914.714.8052730577572-0.105273057757156
1012.112.2810487525014-0.181048752501376
1115.715.9381080312026-0.238108031202568
1215.716.0493364576049-0.349336457604942
131414.0396030144470-0.0396030144470458
1411.711.56115299564310.138847004356897
1515.215.4850855376502-0.285085537650222
1615.615.54029892350230.0597010764977011
1714.313.92563490147560.374365098524372
1812.511.82802502161050.671974978389455
1916.616.15046540990580.449534590094203
2018.116.88546494328901.21453505671097
2118.516.30745659905632.19254340094367
2217.615.81414187435101.78585812564897
2322.621.06249814759651.53750185240346
2423.922.84003643530581.05996356469418
2523.222.26676527356690.93323472643312
2620.620.6340718777277-0.0340718777277047
2724.224.2835557011831-0.0835557011831192
2824.524.6008838499370-0.100883849937041
2922.923.0122243877198-0.112224387719767
3020.420.34506480942050.054935190579517
3123.924.0640755729905-0.164075572990519
3224.124.3097723974085-0.209772397408468
3322.322.6259454903099-0.325945490309859
3419.519.7986394842267-0.298639484226719
3523.323.18300333212050.116996667879508
3623.423.6638090622016-0.263809062201602
3721.821.9172053806205-0.117205380620526
3819.819.27311896405550.526881035944491
3923.323.4253489988107-0.125348998810740
4023.223.6443332703276-0.444333270327633
4121.221.7632191880685-0.56321918806853
421918.82645245650600.173547543493971
4323.822.58330621255731.21669378744266
4424.323.91069321209050.389306787909518
4523.122.72923688870810.370763111291872
4621.620.69871211565490.901287884345145
4722.225.2276712054232-3.02767120542324
4817.422.7913253207745-5.39132532077448
4915.616.6397322208207-1.03973222082073
5014.513.47173599463921.02826400536079
5120.317.55716337749802.74283662250205
5216.119.7471741395838-3.64717413958384
5314.115.7064949890128-1.60649498901282
5415.312.34234118255992.95765881744011
5517.818.3269464885550-0.526946488554952
5619.616.80828293267112.79171706732891
5717.818.5878425015799-0.787842501579892
5815.716.5691833807104-0.869183380710382
5918.918.77508552821720.124914471782787
6018.418.28339537338400.116604626616027
6120.817.26062297272543.53937702727461
621918.94907529418330.0509247058166657
6324.522.08549292835462.41450707164538
6422.623.5601724261307-0.960172426130704
6519.622.093529577959-2.49352957795898
6617.518.1069782219304-0.606978221930408
672521.01049503572633.98950496427371
6822.323.3639508273679-1.06395082736787
6920.521.5924450375355-1.09244503753551
7019.919.07526398196040.824736018039633
7123.423.8556514210159-0.455651421015883
7222.121.67838743569350.421612564306486
732021.1794777022872-1.17947770228715
7418.918.85717667456000.0428233254400254
752322.78553596549280.214464034507188
762021.3075249469337-1.30752494693371
7718.619.0974888271249-0.497488827124869
7819.217.53317697943221.66682302056783
7920.322.8812471572539-2.58124715725392
8017.818.786686707126-0.986686707126008

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 16.1 & 17.4075892857143 & -1.30758928571429 \tabularnewline
6 & 13.1 & 13.7589255028600 & -0.658925502860049 \tabularnewline
7 & 16.5 & 16.9801844581742 & -0.480184458174222 \tabularnewline
8 & 16.5 & 16.8675427436583 & -0.367542743658252 \tabularnewline
9 & 14.7 & 14.8052730577572 & -0.105273057757156 \tabularnewline
10 & 12.1 & 12.2810487525014 & -0.181048752501376 \tabularnewline
11 & 15.7 & 15.9381080312026 & -0.238108031202568 \tabularnewline
12 & 15.7 & 16.0493364576049 & -0.349336457604942 \tabularnewline
13 & 14 & 14.0396030144470 & -0.0396030144470458 \tabularnewline
14 & 11.7 & 11.5611529956431 & 0.138847004356897 \tabularnewline
15 & 15.2 & 15.4850855376502 & -0.285085537650222 \tabularnewline
16 & 15.6 & 15.5402989235023 & 0.0597010764977011 \tabularnewline
17 & 14.3 & 13.9256349014756 & 0.374365098524372 \tabularnewline
18 & 12.5 & 11.8280250216105 & 0.671974978389455 \tabularnewline
19 & 16.6 & 16.1504654099058 & 0.449534590094203 \tabularnewline
20 & 18.1 & 16.8854649432890 & 1.21453505671097 \tabularnewline
21 & 18.5 & 16.3074565990563 & 2.19254340094367 \tabularnewline
22 & 17.6 & 15.8141418743510 & 1.78585812564897 \tabularnewline
23 & 22.6 & 21.0624981475965 & 1.53750185240346 \tabularnewline
24 & 23.9 & 22.8400364353058 & 1.05996356469418 \tabularnewline
25 & 23.2 & 22.2667652735669 & 0.93323472643312 \tabularnewline
26 & 20.6 & 20.6340718777277 & -0.0340718777277047 \tabularnewline
27 & 24.2 & 24.2835557011831 & -0.0835557011831192 \tabularnewline
28 & 24.5 & 24.6008838499370 & -0.100883849937041 \tabularnewline
29 & 22.9 & 23.0122243877198 & -0.112224387719767 \tabularnewline
30 & 20.4 & 20.3450648094205 & 0.054935190579517 \tabularnewline
31 & 23.9 & 24.0640755729905 & -0.164075572990519 \tabularnewline
32 & 24.1 & 24.3097723974085 & -0.209772397408468 \tabularnewline
33 & 22.3 & 22.6259454903099 & -0.325945490309859 \tabularnewline
34 & 19.5 & 19.7986394842267 & -0.298639484226719 \tabularnewline
35 & 23.3 & 23.1830033321205 & 0.116996667879508 \tabularnewline
36 & 23.4 & 23.6638090622016 & -0.263809062201602 \tabularnewline
37 & 21.8 & 21.9172053806205 & -0.117205380620526 \tabularnewline
38 & 19.8 & 19.2731189640555 & 0.526881035944491 \tabularnewline
39 & 23.3 & 23.4253489988107 & -0.125348998810740 \tabularnewline
40 & 23.2 & 23.6443332703276 & -0.444333270327633 \tabularnewline
41 & 21.2 & 21.7632191880685 & -0.56321918806853 \tabularnewline
42 & 19 & 18.8264524565060 & 0.173547543493971 \tabularnewline
43 & 23.8 & 22.5833062125573 & 1.21669378744266 \tabularnewline
44 & 24.3 & 23.9106932120905 & 0.389306787909518 \tabularnewline
45 & 23.1 & 22.7292368887081 & 0.370763111291872 \tabularnewline
46 & 21.6 & 20.6987121156549 & 0.901287884345145 \tabularnewline
47 & 22.2 & 25.2276712054232 & -3.02767120542324 \tabularnewline
48 & 17.4 & 22.7913253207745 & -5.39132532077448 \tabularnewline
49 & 15.6 & 16.6397322208207 & -1.03973222082073 \tabularnewline
50 & 14.5 & 13.4717359946392 & 1.02826400536079 \tabularnewline
51 & 20.3 & 17.5571633774980 & 2.74283662250205 \tabularnewline
52 & 16.1 & 19.7471741395838 & -3.64717413958384 \tabularnewline
53 & 14.1 & 15.7064949890128 & -1.60649498901282 \tabularnewline
54 & 15.3 & 12.3423411825599 & 2.95765881744011 \tabularnewline
55 & 17.8 & 18.3269464885550 & -0.526946488554952 \tabularnewline
56 & 19.6 & 16.8082829326711 & 2.79171706732891 \tabularnewline
57 & 17.8 & 18.5878425015799 & -0.787842501579892 \tabularnewline
58 & 15.7 & 16.5691833807104 & -0.869183380710382 \tabularnewline
59 & 18.9 & 18.7750855282172 & 0.124914471782787 \tabularnewline
60 & 18.4 & 18.2833953733840 & 0.116604626616027 \tabularnewline
61 & 20.8 & 17.2606229727254 & 3.53937702727461 \tabularnewline
62 & 19 & 18.9490752941833 & 0.0509247058166657 \tabularnewline
63 & 24.5 & 22.0854929283546 & 2.41450707164538 \tabularnewline
64 & 22.6 & 23.5601724261307 & -0.960172426130704 \tabularnewline
65 & 19.6 & 22.093529577959 & -2.49352957795898 \tabularnewline
66 & 17.5 & 18.1069782219304 & -0.606978221930408 \tabularnewline
67 & 25 & 21.0104950357263 & 3.98950496427371 \tabularnewline
68 & 22.3 & 23.3639508273679 & -1.06395082736787 \tabularnewline
69 & 20.5 & 21.5924450375355 & -1.09244503753551 \tabularnewline
70 & 19.9 & 19.0752639819604 & 0.824736018039633 \tabularnewline
71 & 23.4 & 23.8556514210159 & -0.455651421015883 \tabularnewline
72 & 22.1 & 21.6783874356935 & 0.421612564306486 \tabularnewline
73 & 20 & 21.1794777022872 & -1.17947770228715 \tabularnewline
74 & 18.9 & 18.8571766745600 & 0.0428233254400254 \tabularnewline
75 & 23 & 22.7855359654928 & 0.214464034507188 \tabularnewline
76 & 20 & 21.3075249469337 & -1.30752494693371 \tabularnewline
77 & 18.6 & 19.0974888271249 & -0.497488827124869 \tabularnewline
78 & 19.2 & 17.5331769794322 & 1.66682302056783 \tabularnewline
79 & 20.3 & 22.8812471572539 & -2.58124715725392 \tabularnewline
80 & 17.8 & 18.786686707126 & -0.986686707126008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13249&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]5[/C][C]16.1[/C][C]17.4075892857143[/C][C]-1.30758928571429[/C][/ROW]
[ROW][C]6[/C][C]13.1[/C][C]13.7589255028600[/C][C]-0.658925502860049[/C][/ROW]
[ROW][C]7[/C][C]16.5[/C][C]16.9801844581742[/C][C]-0.480184458174222[/C][/ROW]
[ROW][C]8[/C][C]16.5[/C][C]16.8675427436583[/C][C]-0.367542743658252[/C][/ROW]
[ROW][C]9[/C][C]14.7[/C][C]14.8052730577572[/C][C]-0.105273057757156[/C][/ROW]
[ROW][C]10[/C][C]12.1[/C][C]12.2810487525014[/C][C]-0.181048752501376[/C][/ROW]
[ROW][C]11[/C][C]15.7[/C][C]15.9381080312026[/C][C]-0.238108031202568[/C][/ROW]
[ROW][C]12[/C][C]15.7[/C][C]16.0493364576049[/C][C]-0.349336457604942[/C][/ROW]
[ROW][C]13[/C][C]14[/C][C]14.0396030144470[/C][C]-0.0396030144470458[/C][/ROW]
[ROW][C]14[/C][C]11.7[/C][C]11.5611529956431[/C][C]0.138847004356897[/C][/ROW]
[ROW][C]15[/C][C]15.2[/C][C]15.4850855376502[/C][C]-0.285085537650222[/C][/ROW]
[ROW][C]16[/C][C]15.6[/C][C]15.5402989235023[/C][C]0.0597010764977011[/C][/ROW]
[ROW][C]17[/C][C]14.3[/C][C]13.9256349014756[/C][C]0.374365098524372[/C][/ROW]
[ROW][C]18[/C][C]12.5[/C][C]11.8280250216105[/C][C]0.671974978389455[/C][/ROW]
[ROW][C]19[/C][C]16.6[/C][C]16.1504654099058[/C][C]0.449534590094203[/C][/ROW]
[ROW][C]20[/C][C]18.1[/C][C]16.8854649432890[/C][C]1.21453505671097[/C][/ROW]
[ROW][C]21[/C][C]18.5[/C][C]16.3074565990563[/C][C]2.19254340094367[/C][/ROW]
[ROW][C]22[/C][C]17.6[/C][C]15.8141418743510[/C][C]1.78585812564897[/C][/ROW]
[ROW][C]23[/C][C]22.6[/C][C]21.0624981475965[/C][C]1.53750185240346[/C][/ROW]
[ROW][C]24[/C][C]23.9[/C][C]22.8400364353058[/C][C]1.05996356469418[/C][/ROW]
[ROW][C]25[/C][C]23.2[/C][C]22.2667652735669[/C][C]0.93323472643312[/C][/ROW]
[ROW][C]26[/C][C]20.6[/C][C]20.6340718777277[/C][C]-0.0340718777277047[/C][/ROW]
[ROW][C]27[/C][C]24.2[/C][C]24.2835557011831[/C][C]-0.0835557011831192[/C][/ROW]
[ROW][C]28[/C][C]24.5[/C][C]24.6008838499370[/C][C]-0.100883849937041[/C][/ROW]
[ROW][C]29[/C][C]22.9[/C][C]23.0122243877198[/C][C]-0.112224387719767[/C][/ROW]
[ROW][C]30[/C][C]20.4[/C][C]20.3450648094205[/C][C]0.054935190579517[/C][/ROW]
[ROW][C]31[/C][C]23.9[/C][C]24.0640755729905[/C][C]-0.164075572990519[/C][/ROW]
[ROW][C]32[/C][C]24.1[/C][C]24.3097723974085[/C][C]-0.209772397408468[/C][/ROW]
[ROW][C]33[/C][C]22.3[/C][C]22.6259454903099[/C][C]-0.325945490309859[/C][/ROW]
[ROW][C]34[/C][C]19.5[/C][C]19.7986394842267[/C][C]-0.298639484226719[/C][/ROW]
[ROW][C]35[/C][C]23.3[/C][C]23.1830033321205[/C][C]0.116996667879508[/C][/ROW]
[ROW][C]36[/C][C]23.4[/C][C]23.6638090622016[/C][C]-0.263809062201602[/C][/ROW]
[ROW][C]37[/C][C]21.8[/C][C]21.9172053806205[/C][C]-0.117205380620526[/C][/ROW]
[ROW][C]38[/C][C]19.8[/C][C]19.2731189640555[/C][C]0.526881035944491[/C][/ROW]
[ROW][C]39[/C][C]23.3[/C][C]23.4253489988107[/C][C]-0.125348998810740[/C][/ROW]
[ROW][C]40[/C][C]23.2[/C][C]23.6443332703276[/C][C]-0.444333270327633[/C][/ROW]
[ROW][C]41[/C][C]21.2[/C][C]21.7632191880685[/C][C]-0.56321918806853[/C][/ROW]
[ROW][C]42[/C][C]19[/C][C]18.8264524565060[/C][C]0.173547543493971[/C][/ROW]
[ROW][C]43[/C][C]23.8[/C][C]22.5833062125573[/C][C]1.21669378744266[/C][/ROW]
[ROW][C]44[/C][C]24.3[/C][C]23.9106932120905[/C][C]0.389306787909518[/C][/ROW]
[ROW][C]45[/C][C]23.1[/C][C]22.7292368887081[/C][C]0.370763111291872[/C][/ROW]
[ROW][C]46[/C][C]21.6[/C][C]20.6987121156549[/C][C]0.901287884345145[/C][/ROW]
[ROW][C]47[/C][C]22.2[/C][C]25.2276712054232[/C][C]-3.02767120542324[/C][/ROW]
[ROW][C]48[/C][C]17.4[/C][C]22.7913253207745[/C][C]-5.39132532077448[/C][/ROW]
[ROW][C]49[/C][C]15.6[/C][C]16.6397322208207[/C][C]-1.03973222082073[/C][/ROW]
[ROW][C]50[/C][C]14.5[/C][C]13.4717359946392[/C][C]1.02826400536079[/C][/ROW]
[ROW][C]51[/C][C]20.3[/C][C]17.5571633774980[/C][C]2.74283662250205[/C][/ROW]
[ROW][C]52[/C][C]16.1[/C][C]19.7471741395838[/C][C]-3.64717413958384[/C][/ROW]
[ROW][C]53[/C][C]14.1[/C][C]15.7064949890128[/C][C]-1.60649498901282[/C][/ROW]
[ROW][C]54[/C][C]15.3[/C][C]12.3423411825599[/C][C]2.95765881744011[/C][/ROW]
[ROW][C]55[/C][C]17.8[/C][C]18.3269464885550[/C][C]-0.526946488554952[/C][/ROW]
[ROW][C]56[/C][C]19.6[/C][C]16.8082829326711[/C][C]2.79171706732891[/C][/ROW]
[ROW][C]57[/C][C]17.8[/C][C]18.5878425015799[/C][C]-0.787842501579892[/C][/ROW]
[ROW][C]58[/C][C]15.7[/C][C]16.5691833807104[/C][C]-0.869183380710382[/C][/ROW]
[ROW][C]59[/C][C]18.9[/C][C]18.7750855282172[/C][C]0.124914471782787[/C][/ROW]
[ROW][C]60[/C][C]18.4[/C][C]18.2833953733840[/C][C]0.116604626616027[/C][/ROW]
[ROW][C]61[/C][C]20.8[/C][C]17.2606229727254[/C][C]3.53937702727461[/C][/ROW]
[ROW][C]62[/C][C]19[/C][C]18.9490752941833[/C][C]0.0509247058166657[/C][/ROW]
[ROW][C]63[/C][C]24.5[/C][C]22.0854929283546[/C][C]2.41450707164538[/C][/ROW]
[ROW][C]64[/C][C]22.6[/C][C]23.5601724261307[/C][C]-0.960172426130704[/C][/ROW]
[ROW][C]65[/C][C]19.6[/C][C]22.093529577959[/C][C]-2.49352957795898[/C][/ROW]
[ROW][C]66[/C][C]17.5[/C][C]18.1069782219304[/C][C]-0.606978221930408[/C][/ROW]
[ROW][C]67[/C][C]25[/C][C]21.0104950357263[/C][C]3.98950496427371[/C][/ROW]
[ROW][C]68[/C][C]22.3[/C][C]23.3639508273679[/C][C]-1.06395082736787[/C][/ROW]
[ROW][C]69[/C][C]20.5[/C][C]21.5924450375355[/C][C]-1.09244503753551[/C][/ROW]
[ROW][C]70[/C][C]19.9[/C][C]19.0752639819604[/C][C]0.824736018039633[/C][/ROW]
[ROW][C]71[/C][C]23.4[/C][C]23.8556514210159[/C][C]-0.455651421015883[/C][/ROW]
[ROW][C]72[/C][C]22.1[/C][C]21.6783874356935[/C][C]0.421612564306486[/C][/ROW]
[ROW][C]73[/C][C]20[/C][C]21.1794777022872[/C][C]-1.17947770228715[/C][/ROW]
[ROW][C]74[/C][C]18.9[/C][C]18.8571766745600[/C][C]0.0428233254400254[/C][/ROW]
[ROW][C]75[/C][C]23[/C][C]22.7855359654928[/C][C]0.214464034507188[/C][/ROW]
[ROW][C]76[/C][C]20[/C][C]21.3075249469337[/C][C]-1.30752494693371[/C][/ROW]
[ROW][C]77[/C][C]18.6[/C][C]19.0974888271249[/C][C]-0.497488827124869[/C][/ROW]
[ROW][C]78[/C][C]19.2[/C][C]17.5331769794322[/C][C]1.66682302056783[/C][/ROW]
[ROW][C]79[/C][C]20.3[/C][C]22.8812471572539[/C][C]-2.58124715725392[/C][/ROW]
[ROW][C]80[/C][C]17.8[/C][C]18.786686707126[/C][C]-0.986686707126008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13249&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13249&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
516.117.4075892857143-1.30758928571429
613.113.7589255028600-0.658925502860049
716.516.9801844581742-0.480184458174222
816.516.8675427436583-0.367542743658252
914.714.8052730577572-0.105273057757156
1012.112.2810487525014-0.181048752501376
1115.715.9381080312026-0.238108031202568
1215.716.0493364576049-0.349336457604942
131414.0396030144470-0.0396030144470458
1411.711.56115299564310.138847004356897
1515.215.4850855376502-0.285085537650222
1615.615.54029892350230.0597010764977011
1714.313.92563490147560.374365098524372
1812.511.82802502161050.671974978389455
1916.616.15046540990580.449534590094203
2018.116.88546494328901.21453505671097
2118.516.30745659905632.19254340094367
2217.615.81414187435101.78585812564897
2322.621.06249814759651.53750185240346
2423.922.84003643530581.05996356469418
2523.222.26676527356690.93323472643312
2620.620.6340718777277-0.0340718777277047
2724.224.2835557011831-0.0835557011831192
2824.524.6008838499370-0.100883849937041
2922.923.0122243877198-0.112224387719767
3020.420.34506480942050.054935190579517
3123.924.0640755729905-0.164075572990519
3224.124.3097723974085-0.209772397408468
3322.322.6259454903099-0.325945490309859
3419.519.7986394842267-0.298639484226719
3523.323.18300333212050.116996667879508
3623.423.6638090622016-0.263809062201602
3721.821.9172053806205-0.117205380620526
3819.819.27311896405550.526881035944491
3923.323.4253489988107-0.125348998810740
4023.223.6443332703276-0.444333270327633
4121.221.7632191880685-0.56321918806853
421918.82645245650600.173547543493971
4323.822.58330621255731.21669378744266
4424.323.91069321209050.389306787909518
4523.122.72923688870810.370763111291872
4621.620.69871211565490.901287884345145
4722.225.2276712054232-3.02767120542324
4817.422.7913253207745-5.39132532077448
4915.616.6397322208207-1.03973222082073
5014.513.47173599463921.02826400536079
5120.317.55716337749802.74283662250205
5216.119.7471741395838-3.64717413958384
5314.115.7064949890128-1.60649498901282
5415.312.34234118255992.95765881744011
5517.818.3269464885550-0.526946488554952
5619.616.80828293267112.79171706732891
5717.818.5878425015799-0.787842501579892
5815.716.5691833807104-0.869183380710382
5918.918.77508552821720.124914471782787
6018.418.28339537338400.116604626616027
6120.817.26062297272543.53937702727461
621918.94907529418330.0509247058166657
6324.522.08549292835462.41450707164538
6422.623.5601724261307-0.960172426130704
6519.622.093529577959-2.49352957795898
6617.518.1069782219304-0.606978221930408
672521.01049503572633.98950496427371
6822.323.3639508273679-1.06395082736787
6920.521.5924450375355-1.09244503753551
7019.919.07526398196040.824736018039633
7123.423.8556514210159-0.455651421015883
7222.121.67838743569350.421612564306486
732021.1794777022872-1.17947770228715
7418.918.85717667456000.0428233254400254
752322.78553596549280.214464034507188
762021.3075249469337-1.30752494693371
7718.619.0974888271249-0.497488827124869
7819.217.53317697943221.66682302056783
7920.322.8812471572539-2.58124715725392
8017.818.786686707126-0.986686707126008







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8116.966299398655514.083387745563619.8492110517473
8216.133931696425012.332787544079719.9350758487702
8319.452100640519114.914897302086523.9893039789518
8417.812.630499888610122.9695001113899

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 16.9662993986555 & 14.0833877455636 & 19.8492110517473 \tabularnewline
82 & 16.1339316964250 & 12.3327875440797 & 19.9350758487702 \tabularnewline
83 & 19.4521006405191 & 14.9148973020865 & 23.9893039789518 \tabularnewline
84 & 17.8 & 12.6304998886101 & 22.9695001113899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13249&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]81[/C][C]16.9662993986555[/C][C]14.0833877455636[/C][C]19.8492110517473[/C][/ROW]
[ROW][C]82[/C][C]16.1339316964250[/C][C]12.3327875440797[/C][C]19.9350758487702[/C][/ROW]
[ROW][C]83[/C][C]19.4521006405191[/C][C]14.9148973020865[/C][C]23.9893039789518[/C][/ROW]
[ROW][C]84[/C][C]17.8[/C][C]12.6304998886101[/C][C]22.9695001113899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13249&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13249&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
8116.966299398655514.083387745563619.8492110517473
8216.133931696425012.332787544079719.9350758487702
8319.452100640519114.914897302086523.9893039789518
8417.812.630499888610122.9695001113899



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; 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')