Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 Nov 2016 13:02:22 +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/2016/Nov/27/t1480251775lvdm52epkh4mlaz.htm/, Retrieved Mon, 29 Apr 2024 22:41:08 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 22:41:08 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
88
90
82
75
79
70
71
75
89
92
94
90
102
98
100
98
100
91
93
92
106
109
108
108
118
119
124
118
119
113
114
115
125
125
118
122
132
133
136
128
126
114
108
107
117
119
113
114
124
125
124
118
111
99
94
93
107
107
103
97




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999924222782354
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999924222782354 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.999924222782354[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.999924222782354
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
290882
38289.9998484455647-7.99984844556471
47582.0006062062568-7.00060620625679
57975.00053048646013.99946951353985
67078.9996969313282-8.99969693132822
77170.00068197199310.999318028006883
87570.99992427446034.0000757255397
98974.999696885391114.0003031146089
109288.99893909598383.00106090401623
119491.99977258795472.00022741204529
129093.9998484283321-3.99984842833206
1310290.000303097384911.9996969026151
1498101.999090696356-3.99909069635612
1510098.00030303996611.99969696003392
169899.9998484685282-1.99984846852824
1710098.00015154295271.99984845704734
189199.9998484570482-8.99984845704822
199391.00068198347531.9993180165247
209292.9998484972435-0.999848497243519
2110692.000075765737213.9999242342628
22109105.9989391246943.00106087530573
23108108.999772587957-0.999772587956883
24108108.000075759985-7.5759984994761e-05
25118108.0000000057419.99999999425911
26119117.9992422278241.00075777217603
27124118.999924165365.00007583463952
28118123.999621108165-5.99962110816523
29119118.0004546345950.999545365405496
30113118.999924257233-5.99992425723329
31114113.0004546575660.999545342433706
32115113.9999242572351.00007574276496
33125114.99992421704310.0000757829572
34125124.9992422220810.00075777791907683
35118124.999999942578-6.9999999425777
36122118.0005304405193.99946955948083
37132121.99969693132510.0003030686753
38133131.9992422048581.00075779514216
39136132.9999241653593.00007583464128
40128135.999772662601-7.99977266260052
41126128.000606200514-2.00060620051417
42114126.000151600371-12.0001516003715
43108114.0009093381-6.0009093380996
44107108.000454732213-1.00045473221299
45117107.0000758116769.999924188324
46119116.9992422335682.00075776643166
47113118.999848388143-5.99984838814328
48114113.0004546518170.999545348182849
49124113.99992425723510.0000757427654
50125123.9992422220841.00075777791604
51124124.99992416536-0.999924165360056
52118124.000075771471-6.0000757714711
53111118.000454669048-7.00045466904763
5499111.000530474977-12.0005304749771
559499.0009093668097-5.00090936680967
569394.0003789549975-1.00037895499752
5710793.000075805933813.9999241940662
58107106.9989391246970.00106087530268439
59103106.99999991961-3.99999991960982
6097103.000303108865-6.0003031088645

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 90 & 88 & 2 \tabularnewline
3 & 82 & 89.9998484455647 & -7.99984844556471 \tabularnewline
4 & 75 & 82.0006062062568 & -7.00060620625679 \tabularnewline
5 & 79 & 75.0005304864601 & 3.99946951353985 \tabularnewline
6 & 70 & 78.9996969313282 & -8.99969693132822 \tabularnewline
7 & 71 & 70.0006819719931 & 0.999318028006883 \tabularnewline
8 & 75 & 70.9999242744603 & 4.0000757255397 \tabularnewline
9 & 89 & 74.9996968853911 & 14.0003031146089 \tabularnewline
10 & 92 & 88.9989390959838 & 3.00106090401623 \tabularnewline
11 & 94 & 91.9997725879547 & 2.00022741204529 \tabularnewline
12 & 90 & 93.9998484283321 & -3.99984842833206 \tabularnewline
13 & 102 & 90.0003030973849 & 11.9996969026151 \tabularnewline
14 & 98 & 101.999090696356 & -3.99909069635612 \tabularnewline
15 & 100 & 98.0003030399661 & 1.99969696003392 \tabularnewline
16 & 98 & 99.9998484685282 & -1.99984846852824 \tabularnewline
17 & 100 & 98.0001515429527 & 1.99984845704734 \tabularnewline
18 & 91 & 99.9998484570482 & -8.99984845704822 \tabularnewline
19 & 93 & 91.0006819834753 & 1.9993180165247 \tabularnewline
20 & 92 & 92.9998484972435 & -0.999848497243519 \tabularnewline
21 & 106 & 92.0000757657372 & 13.9999242342628 \tabularnewline
22 & 109 & 105.998939124694 & 3.00106087530573 \tabularnewline
23 & 108 & 108.999772587957 & -0.999772587956883 \tabularnewline
24 & 108 & 108.000075759985 & -7.5759984994761e-05 \tabularnewline
25 & 118 & 108.000000005741 & 9.99999999425911 \tabularnewline
26 & 119 & 117.999242227824 & 1.00075777217603 \tabularnewline
27 & 124 & 118.99992416536 & 5.00007583463952 \tabularnewline
28 & 118 & 123.999621108165 & -5.99962110816523 \tabularnewline
29 & 119 & 118.000454634595 & 0.999545365405496 \tabularnewline
30 & 113 & 118.999924257233 & -5.99992425723329 \tabularnewline
31 & 114 & 113.000454657566 & 0.999545342433706 \tabularnewline
32 & 115 & 113.999924257235 & 1.00007574276496 \tabularnewline
33 & 125 & 114.999924217043 & 10.0000757829572 \tabularnewline
34 & 125 & 124.999242222081 & 0.00075777791907683 \tabularnewline
35 & 118 & 124.999999942578 & -6.9999999425777 \tabularnewline
36 & 122 & 118.000530440519 & 3.99946955948083 \tabularnewline
37 & 132 & 121.999696931325 & 10.0003030686753 \tabularnewline
38 & 133 & 131.999242204858 & 1.00075779514216 \tabularnewline
39 & 136 & 132.999924165359 & 3.00007583464128 \tabularnewline
40 & 128 & 135.999772662601 & -7.99977266260052 \tabularnewline
41 & 126 & 128.000606200514 & -2.00060620051417 \tabularnewline
42 & 114 & 126.000151600371 & -12.0001516003715 \tabularnewline
43 & 108 & 114.0009093381 & -6.0009093380996 \tabularnewline
44 & 107 & 108.000454732213 & -1.00045473221299 \tabularnewline
45 & 117 & 107.000075811676 & 9.999924188324 \tabularnewline
46 & 119 & 116.999242233568 & 2.00075776643166 \tabularnewline
47 & 113 & 118.999848388143 & -5.99984838814328 \tabularnewline
48 & 114 & 113.000454651817 & 0.999545348182849 \tabularnewline
49 & 124 & 113.999924257235 & 10.0000757427654 \tabularnewline
50 & 125 & 123.999242222084 & 1.00075777791604 \tabularnewline
51 & 124 & 124.99992416536 & -0.999924165360056 \tabularnewline
52 & 118 & 124.000075771471 & -6.0000757714711 \tabularnewline
53 & 111 & 118.000454669048 & -7.00045466904763 \tabularnewline
54 & 99 & 111.000530474977 & -12.0005304749771 \tabularnewline
55 & 94 & 99.0009093668097 & -5.00090936680967 \tabularnewline
56 & 93 & 94.0003789549975 & -1.00037895499752 \tabularnewline
57 & 107 & 93.0000758059338 & 13.9999241940662 \tabularnewline
58 & 107 & 106.998939124697 & 0.00106087530268439 \tabularnewline
59 & 103 & 106.99999991961 & -3.99999991960982 \tabularnewline
60 & 97 & 103.000303108865 & -6.0003031088645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]90[/C][C]88[/C][C]2[/C][/ROW]
[ROW][C]3[/C][C]82[/C][C]89.9998484455647[/C][C]-7.99984844556471[/C][/ROW]
[ROW][C]4[/C][C]75[/C][C]82.0006062062568[/C][C]-7.00060620625679[/C][/ROW]
[ROW][C]5[/C][C]79[/C][C]75.0005304864601[/C][C]3.99946951353985[/C][/ROW]
[ROW][C]6[/C][C]70[/C][C]78.9996969313282[/C][C]-8.99969693132822[/C][/ROW]
[ROW][C]7[/C][C]71[/C][C]70.0006819719931[/C][C]0.999318028006883[/C][/ROW]
[ROW][C]8[/C][C]75[/C][C]70.9999242744603[/C][C]4.0000757255397[/C][/ROW]
[ROW][C]9[/C][C]89[/C][C]74.9996968853911[/C][C]14.0003031146089[/C][/ROW]
[ROW][C]10[/C][C]92[/C][C]88.9989390959838[/C][C]3.00106090401623[/C][/ROW]
[ROW][C]11[/C][C]94[/C][C]91.9997725879547[/C][C]2.00022741204529[/C][/ROW]
[ROW][C]12[/C][C]90[/C][C]93.9998484283321[/C][C]-3.99984842833206[/C][/ROW]
[ROW][C]13[/C][C]102[/C][C]90.0003030973849[/C][C]11.9996969026151[/C][/ROW]
[ROW][C]14[/C][C]98[/C][C]101.999090696356[/C][C]-3.99909069635612[/C][/ROW]
[ROW][C]15[/C][C]100[/C][C]98.0003030399661[/C][C]1.99969696003392[/C][/ROW]
[ROW][C]16[/C][C]98[/C][C]99.9998484685282[/C][C]-1.99984846852824[/C][/ROW]
[ROW][C]17[/C][C]100[/C][C]98.0001515429527[/C][C]1.99984845704734[/C][/ROW]
[ROW][C]18[/C][C]91[/C][C]99.9998484570482[/C][C]-8.99984845704822[/C][/ROW]
[ROW][C]19[/C][C]93[/C][C]91.0006819834753[/C][C]1.9993180165247[/C][/ROW]
[ROW][C]20[/C][C]92[/C][C]92.9998484972435[/C][C]-0.999848497243519[/C][/ROW]
[ROW][C]21[/C][C]106[/C][C]92.0000757657372[/C][C]13.9999242342628[/C][/ROW]
[ROW][C]22[/C][C]109[/C][C]105.998939124694[/C][C]3.00106087530573[/C][/ROW]
[ROW][C]23[/C][C]108[/C][C]108.999772587957[/C][C]-0.999772587956883[/C][/ROW]
[ROW][C]24[/C][C]108[/C][C]108.000075759985[/C][C]-7.5759984994761e-05[/C][/ROW]
[ROW][C]25[/C][C]118[/C][C]108.000000005741[/C][C]9.99999999425911[/C][/ROW]
[ROW][C]26[/C][C]119[/C][C]117.999242227824[/C][C]1.00075777217603[/C][/ROW]
[ROW][C]27[/C][C]124[/C][C]118.99992416536[/C][C]5.00007583463952[/C][/ROW]
[ROW][C]28[/C][C]118[/C][C]123.999621108165[/C][C]-5.99962110816523[/C][/ROW]
[ROW][C]29[/C][C]119[/C][C]118.000454634595[/C][C]0.999545365405496[/C][/ROW]
[ROW][C]30[/C][C]113[/C][C]118.999924257233[/C][C]-5.99992425723329[/C][/ROW]
[ROW][C]31[/C][C]114[/C][C]113.000454657566[/C][C]0.999545342433706[/C][/ROW]
[ROW][C]32[/C][C]115[/C][C]113.999924257235[/C][C]1.00007574276496[/C][/ROW]
[ROW][C]33[/C][C]125[/C][C]114.999924217043[/C][C]10.0000757829572[/C][/ROW]
[ROW][C]34[/C][C]125[/C][C]124.999242222081[/C][C]0.00075777791907683[/C][/ROW]
[ROW][C]35[/C][C]118[/C][C]124.999999942578[/C][C]-6.9999999425777[/C][/ROW]
[ROW][C]36[/C][C]122[/C][C]118.000530440519[/C][C]3.99946955948083[/C][/ROW]
[ROW][C]37[/C][C]132[/C][C]121.999696931325[/C][C]10.0003030686753[/C][/ROW]
[ROW][C]38[/C][C]133[/C][C]131.999242204858[/C][C]1.00075779514216[/C][/ROW]
[ROW][C]39[/C][C]136[/C][C]132.999924165359[/C][C]3.00007583464128[/C][/ROW]
[ROW][C]40[/C][C]128[/C][C]135.999772662601[/C][C]-7.99977266260052[/C][/ROW]
[ROW][C]41[/C][C]126[/C][C]128.000606200514[/C][C]-2.00060620051417[/C][/ROW]
[ROW][C]42[/C][C]114[/C][C]126.000151600371[/C][C]-12.0001516003715[/C][/ROW]
[ROW][C]43[/C][C]108[/C][C]114.0009093381[/C][C]-6.0009093380996[/C][/ROW]
[ROW][C]44[/C][C]107[/C][C]108.000454732213[/C][C]-1.00045473221299[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]107.000075811676[/C][C]9.999924188324[/C][/ROW]
[ROW][C]46[/C][C]119[/C][C]116.999242233568[/C][C]2.00075776643166[/C][/ROW]
[ROW][C]47[/C][C]113[/C][C]118.999848388143[/C][C]-5.99984838814328[/C][/ROW]
[ROW][C]48[/C][C]114[/C][C]113.000454651817[/C][C]0.999545348182849[/C][/ROW]
[ROW][C]49[/C][C]124[/C][C]113.999924257235[/C][C]10.0000757427654[/C][/ROW]
[ROW][C]50[/C][C]125[/C][C]123.999242222084[/C][C]1.00075777791604[/C][/ROW]
[ROW][C]51[/C][C]124[/C][C]124.99992416536[/C][C]-0.999924165360056[/C][/ROW]
[ROW][C]52[/C][C]118[/C][C]124.000075771471[/C][C]-6.0000757714711[/C][/ROW]
[ROW][C]53[/C][C]111[/C][C]118.000454669048[/C][C]-7.00045466904763[/C][/ROW]
[ROW][C]54[/C][C]99[/C][C]111.000530474977[/C][C]-12.0005304749771[/C][/ROW]
[ROW][C]55[/C][C]94[/C][C]99.0009093668097[/C][C]-5.00090936680967[/C][/ROW]
[ROW][C]56[/C][C]93[/C][C]94.0003789549975[/C][C]-1.00037895499752[/C][/ROW]
[ROW][C]57[/C][C]107[/C][C]93.0000758059338[/C][C]13.9999241940662[/C][/ROW]
[ROW][C]58[/C][C]107[/C][C]106.998939124697[/C][C]0.00106087530268439[/C][/ROW]
[ROW][C]59[/C][C]103[/C][C]106.99999991961[/C][C]-3.99999991960982[/C][/ROW]
[ROW][C]60[/C][C]97[/C][C]103.000303108865[/C][C]-6.0003031088645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
290882
38289.9998484455647-7.99984844556471
47582.0006062062568-7.00060620625679
57975.00053048646013.99946951353985
67078.9996969313282-8.99969693132822
77170.00068197199310.999318028006883
87570.99992427446034.0000757255397
98974.999696885391114.0003031146089
109288.99893909598383.00106090401623
119491.99977258795472.00022741204529
129093.9998484283321-3.99984842833206
1310290.000303097384911.9996969026151
1498101.999090696356-3.99909069635612
1510098.00030303996611.99969696003392
169899.9998484685282-1.99984846852824
1710098.00015154295271.99984845704734
189199.9998484570482-8.99984845704822
199391.00068198347531.9993180165247
209292.9998484972435-0.999848497243519
2110692.000075765737213.9999242342628
22109105.9989391246943.00106087530573
23108108.999772587957-0.999772587956883
24108108.000075759985-7.5759984994761e-05
25118108.0000000057419.99999999425911
26119117.9992422278241.00075777217603
27124118.999924165365.00007583463952
28118123.999621108165-5.99962110816523
29119118.0004546345950.999545365405496
30113118.999924257233-5.99992425723329
31114113.0004546575660.999545342433706
32115113.9999242572351.00007574276496
33125114.99992421704310.0000757829572
34125124.9992422220810.00075777791907683
35118124.999999942578-6.9999999425777
36122118.0005304405193.99946955948083
37132121.99969693132510.0003030686753
38133131.9992422048581.00075779514216
39136132.9999241653593.00007583464128
40128135.999772662601-7.99977266260052
41126128.000606200514-2.00060620051417
42114126.000151600371-12.0001516003715
43108114.0009093381-6.0009093380996
44107108.000454732213-1.00045473221299
45117107.0000758116769.999924188324
46119116.9992422335682.00075776643166
47113118.999848388143-5.99984838814328
48114113.0004546518170.999545348182849
49124113.99992425723510.0000757427654
50125123.9992422220841.00075777791604
51124124.99992416536-0.999924165360056
52118124.000075771471-6.0000757714711
53111118.000454669048-7.00045466904763
5499111.000530474977-12.0005304749771
559499.0009093668097-5.00090936680967
569394.0003789549975-1.00037895499752
5710793.000075805933813.9999241940662
58107106.9989391246970.00106087530268439
59103106.99999991961-3.99999991960982
6097103.000303108865-6.0003031088645







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6197.000454686274684.4198164994623109.581092873087
6297.000454686274679.2094196295131114.791489743036
6397.000454686274675.2112509469372118.789658425612
6497.000454686274671.8406082877412122.160301084808
6597.000454686274668.8709978482688125.12991152428
6697.000454686274666.1862564457773127.814652926772
6797.000454686274663.7173766373905130.283532735159
6897.000454686274661.4193957417807132.581513630768
6997.000454686274659.2610823171561134.739827055393
7097.000454686274657.2196967998489136.7812125727
7197.000454686274655.2780725728111138.722836799738
7297.000454686274653.4228728301723140.578036542377

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 97.0004546862746 & 84.4198164994623 & 109.581092873087 \tabularnewline
62 & 97.0004546862746 & 79.2094196295131 & 114.791489743036 \tabularnewline
63 & 97.0004546862746 & 75.2112509469372 & 118.789658425612 \tabularnewline
64 & 97.0004546862746 & 71.8406082877412 & 122.160301084808 \tabularnewline
65 & 97.0004546862746 & 68.8709978482688 & 125.12991152428 \tabularnewline
66 & 97.0004546862746 & 66.1862564457773 & 127.814652926772 \tabularnewline
67 & 97.0004546862746 & 63.7173766373905 & 130.283532735159 \tabularnewline
68 & 97.0004546862746 & 61.4193957417807 & 132.581513630768 \tabularnewline
69 & 97.0004546862746 & 59.2610823171561 & 134.739827055393 \tabularnewline
70 & 97.0004546862746 & 57.2196967998489 & 136.7812125727 \tabularnewline
71 & 97.0004546862746 & 55.2780725728111 & 138.722836799738 \tabularnewline
72 & 97.0004546862746 & 53.4228728301723 & 140.578036542377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]97.0004546862746[/C][C]84.4198164994623[/C][C]109.581092873087[/C][/ROW]
[ROW][C]62[/C][C]97.0004546862746[/C][C]79.2094196295131[/C][C]114.791489743036[/C][/ROW]
[ROW][C]63[/C][C]97.0004546862746[/C][C]75.2112509469372[/C][C]118.789658425612[/C][/ROW]
[ROW][C]64[/C][C]97.0004546862746[/C][C]71.8406082877412[/C][C]122.160301084808[/C][/ROW]
[ROW][C]65[/C][C]97.0004546862746[/C][C]68.8709978482688[/C][C]125.12991152428[/C][/ROW]
[ROW][C]66[/C][C]97.0004546862746[/C][C]66.1862564457773[/C][C]127.814652926772[/C][/ROW]
[ROW][C]67[/C][C]97.0004546862746[/C][C]63.7173766373905[/C][C]130.283532735159[/C][/ROW]
[ROW][C]68[/C][C]97.0004546862746[/C][C]61.4193957417807[/C][C]132.581513630768[/C][/ROW]
[ROW][C]69[/C][C]97.0004546862746[/C][C]59.2610823171561[/C][C]134.739827055393[/C][/ROW]
[ROW][C]70[/C][C]97.0004546862746[/C][C]57.2196967998489[/C][C]136.7812125727[/C][/ROW]
[ROW][C]71[/C][C]97.0004546862746[/C][C]55.2780725728111[/C][C]138.722836799738[/C][/ROW]
[ROW][C]72[/C][C]97.0004546862746[/C][C]53.4228728301723[/C][C]140.578036542377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
6197.000454686274684.4198164994623109.581092873087
6297.000454686274679.2094196295131114.791489743036
6397.000454686274675.2112509469372118.789658425612
6497.000454686274671.8406082877412122.160301084808
6597.000454686274668.8709978482688125.12991152428
6697.000454686274666.1862564457773127.814652926772
6797.000454686274663.7173766373905130.283532735159
6897.000454686274661.4193957417807132.581513630768
6997.000454686274659.2610823171561134.739827055393
7097.000454686274657.2196967998489136.7812125727
7197.000454686274655.2780725728111138.722836799738
7297.000454686274653.4228728301723140.578036542377



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')