Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 16:41:50 +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/28/t14803513485os9zottly3ogtt.htm/, Retrieved Sat, 04 May 2024 19:52:04 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 19:52:04 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
831,5
831
830
828,4
828,1
827,6
828,2
828,2
828,7
830,5
831
831,9
832,2
831,9
830,6
829,7
828,8
826,7
825,8
825,4
825
825,6
824,6
824,5
822,6
822
821,2
820,4
819,4
819,7
818,2
817,7
817,5
817,7
817,5
816,9
820,3
819,7
819,4
818,6
818,2
817,6
817,3
816,7
817
817,6
817,8
817,8
820,9
820,7
820,6
820,8
820,4
820,2
819,8
819,6
819,6
819,8
819,9
820,3
822,9
821,9
820,6
818,9
817,3
815,6
813,8
812,1
810,8
809,6
808,7
807,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.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]'Herman Ole Andreas Wold' @ wold.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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.777073915251965
beta0.376349008968854
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.777073915251965 \tabularnewline
beta & 0.376349008968854 \tabularnewline
gamma & 1 \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]0.777073915251965[/C][/ROW]
[ROW][C]beta[/C][C]0.376349008968854[/C][/ROW]
[ROW][C]gamma[/C][C]1[/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
alpha0.777073915251965
beta0.376349008968854
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13832.2832.0958600427350.104139957264579
14831.9831.983624354119-0.0836243541185695
15830.6830.755192557766-0.155192557766441
16829.7829.913260758813-0.21326075881268
17828.8829.076337353792-0.276337353792201
18826.7827.013750303944-0.313750303943493
19825.8826.109500703626-0.309500703626327
20825.4825.2972062339060.10279376609401
21825825.339523848147-0.339523848146655
22825.6826.222167227236-0.622167227236446
23824.6825.399055715984-0.799055715983854
24824.5824.696470799366-0.196470799366125
25822.6823.957063001449-1.35706300144921
26822821.3330084389960.66699156100367
27821.2819.5569260377061.64307396229378
28820.4819.5103599322170.889640067783262
29819.4819.2498796243810.150120375618826
30819.7817.3685284701342.33147152986646
31818.2819.152543909266-0.952543909265955
32817.7818.376194708359-0.676194708359162
33817.5817.930486786554-0.430486786553615
34817.7818.868744676654-1.16874467665411
35817.5817.61092992763-0.110929927630309
36816.9817.808105480299-0.9081054802989
37820.3816.2795643590164.02043564098358
38819.7819.880678823989-0.180678823988956
39819.4819.0108266000830.389173399917127
40818.6818.802561030478-0.202561030477909
41818.2818.1897202317580.0102797682418441
42817.6817.306304858680.293695141320086
43817.3816.7990971759080.500902824092123
44816.7817.663223370498-0.963223370498213
45817817.414740255161-0.41474025516095
46817.6818.570755099654-0.970755099653729
47817.8818.130607312731-0.330607312730649
48817.8818.343121130298-0.543121130298459
49820.9818.6673952953842.23260470461605
50820.7819.8903371269720.809662873027719
51820.6820.1543570971220.445642902878262
52820.8820.1118425969460.688157403054333
53820.4820.752878250875-0.352878250875165
54820.2820.0585116346020.141488365398118
55819.8819.842775711578-0.0427757115785425
56819.6820.162587924978-0.562587924977834
57819.6820.669421940467-1.06942194046712
58819.8821.323010783131-1.52301078313076
59819.9820.565177695058-0.66517769505765
60820.3820.341237825449-0.0412378254492296
61822.9821.6919774843291.20802251567102
62821.9821.5195756643120.380424335687962
63820.6820.961408071172-0.361408071171809
64818.9819.702307310298-0.802307310297579
65817.3817.873669010205-0.573669010204753
66815.6815.973969689171-0.373969689170849
67813.8814.021892086708-0.221892086707953
68812.1812.739539771428-0.639539771427962
69810.8811.703987183101-0.903987183101322
70809.6811.06379302697-1.4637930269696
71808.7809.239306927463-0.539306927463372
72807.3807.985178495127-0.685178495127502

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 832.2 & 832.095860042735 & 0.104139957264579 \tabularnewline
14 & 831.9 & 831.983624354119 & -0.0836243541185695 \tabularnewline
15 & 830.6 & 830.755192557766 & -0.155192557766441 \tabularnewline
16 & 829.7 & 829.913260758813 & -0.21326075881268 \tabularnewline
17 & 828.8 & 829.076337353792 & -0.276337353792201 \tabularnewline
18 & 826.7 & 827.013750303944 & -0.313750303943493 \tabularnewline
19 & 825.8 & 826.109500703626 & -0.309500703626327 \tabularnewline
20 & 825.4 & 825.297206233906 & 0.10279376609401 \tabularnewline
21 & 825 & 825.339523848147 & -0.339523848146655 \tabularnewline
22 & 825.6 & 826.222167227236 & -0.622167227236446 \tabularnewline
23 & 824.6 & 825.399055715984 & -0.799055715983854 \tabularnewline
24 & 824.5 & 824.696470799366 & -0.196470799366125 \tabularnewline
25 & 822.6 & 823.957063001449 & -1.35706300144921 \tabularnewline
26 & 822 & 821.333008438996 & 0.66699156100367 \tabularnewline
27 & 821.2 & 819.556926037706 & 1.64307396229378 \tabularnewline
28 & 820.4 & 819.510359932217 & 0.889640067783262 \tabularnewline
29 & 819.4 & 819.249879624381 & 0.150120375618826 \tabularnewline
30 & 819.7 & 817.368528470134 & 2.33147152986646 \tabularnewline
31 & 818.2 & 819.152543909266 & -0.952543909265955 \tabularnewline
32 & 817.7 & 818.376194708359 & -0.676194708359162 \tabularnewline
33 & 817.5 & 817.930486786554 & -0.430486786553615 \tabularnewline
34 & 817.7 & 818.868744676654 & -1.16874467665411 \tabularnewline
35 & 817.5 & 817.61092992763 & -0.110929927630309 \tabularnewline
36 & 816.9 & 817.808105480299 & -0.9081054802989 \tabularnewline
37 & 820.3 & 816.279564359016 & 4.02043564098358 \tabularnewline
38 & 819.7 & 819.880678823989 & -0.180678823988956 \tabularnewline
39 & 819.4 & 819.010826600083 & 0.389173399917127 \tabularnewline
40 & 818.6 & 818.802561030478 & -0.202561030477909 \tabularnewline
41 & 818.2 & 818.189720231758 & 0.0102797682418441 \tabularnewline
42 & 817.6 & 817.30630485868 & 0.293695141320086 \tabularnewline
43 & 817.3 & 816.799097175908 & 0.500902824092123 \tabularnewline
44 & 816.7 & 817.663223370498 & -0.963223370498213 \tabularnewline
45 & 817 & 817.414740255161 & -0.41474025516095 \tabularnewline
46 & 817.6 & 818.570755099654 & -0.970755099653729 \tabularnewline
47 & 817.8 & 818.130607312731 & -0.330607312730649 \tabularnewline
48 & 817.8 & 818.343121130298 & -0.543121130298459 \tabularnewline
49 & 820.9 & 818.667395295384 & 2.23260470461605 \tabularnewline
50 & 820.7 & 819.890337126972 & 0.809662873027719 \tabularnewline
51 & 820.6 & 820.154357097122 & 0.445642902878262 \tabularnewline
52 & 820.8 & 820.111842596946 & 0.688157403054333 \tabularnewline
53 & 820.4 & 820.752878250875 & -0.352878250875165 \tabularnewline
54 & 820.2 & 820.058511634602 & 0.141488365398118 \tabularnewline
55 & 819.8 & 819.842775711578 & -0.0427757115785425 \tabularnewline
56 & 819.6 & 820.162587924978 & -0.562587924977834 \tabularnewline
57 & 819.6 & 820.669421940467 & -1.06942194046712 \tabularnewline
58 & 819.8 & 821.323010783131 & -1.52301078313076 \tabularnewline
59 & 819.9 & 820.565177695058 & -0.66517769505765 \tabularnewline
60 & 820.3 & 820.341237825449 & -0.0412378254492296 \tabularnewline
61 & 822.9 & 821.691977484329 & 1.20802251567102 \tabularnewline
62 & 821.9 & 821.519575664312 & 0.380424335687962 \tabularnewline
63 & 820.6 & 820.961408071172 & -0.361408071171809 \tabularnewline
64 & 818.9 & 819.702307310298 & -0.802307310297579 \tabularnewline
65 & 817.3 & 817.873669010205 & -0.573669010204753 \tabularnewline
66 & 815.6 & 815.973969689171 & -0.373969689170849 \tabularnewline
67 & 813.8 & 814.021892086708 & -0.221892086707953 \tabularnewline
68 & 812.1 & 812.739539771428 & -0.639539771427962 \tabularnewline
69 & 810.8 & 811.703987183101 & -0.903987183101322 \tabularnewline
70 & 809.6 & 811.06379302697 & -1.4637930269696 \tabularnewline
71 & 808.7 & 809.239306927463 & -0.539306927463372 \tabularnewline
72 & 807.3 & 807.985178495127 & -0.685178495127502 \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]13[/C][C]832.2[/C][C]832.095860042735[/C][C]0.104139957264579[/C][/ROW]
[ROW][C]14[/C][C]831.9[/C][C]831.983624354119[/C][C]-0.0836243541185695[/C][/ROW]
[ROW][C]15[/C][C]830.6[/C][C]830.755192557766[/C][C]-0.155192557766441[/C][/ROW]
[ROW][C]16[/C][C]829.7[/C][C]829.913260758813[/C][C]-0.21326075881268[/C][/ROW]
[ROW][C]17[/C][C]828.8[/C][C]829.076337353792[/C][C]-0.276337353792201[/C][/ROW]
[ROW][C]18[/C][C]826.7[/C][C]827.013750303944[/C][C]-0.313750303943493[/C][/ROW]
[ROW][C]19[/C][C]825.8[/C][C]826.109500703626[/C][C]-0.309500703626327[/C][/ROW]
[ROW][C]20[/C][C]825.4[/C][C]825.297206233906[/C][C]0.10279376609401[/C][/ROW]
[ROW][C]21[/C][C]825[/C][C]825.339523848147[/C][C]-0.339523848146655[/C][/ROW]
[ROW][C]22[/C][C]825.6[/C][C]826.222167227236[/C][C]-0.622167227236446[/C][/ROW]
[ROW][C]23[/C][C]824.6[/C][C]825.399055715984[/C][C]-0.799055715983854[/C][/ROW]
[ROW][C]24[/C][C]824.5[/C][C]824.696470799366[/C][C]-0.196470799366125[/C][/ROW]
[ROW][C]25[/C][C]822.6[/C][C]823.957063001449[/C][C]-1.35706300144921[/C][/ROW]
[ROW][C]26[/C][C]822[/C][C]821.333008438996[/C][C]0.66699156100367[/C][/ROW]
[ROW][C]27[/C][C]821.2[/C][C]819.556926037706[/C][C]1.64307396229378[/C][/ROW]
[ROW][C]28[/C][C]820.4[/C][C]819.510359932217[/C][C]0.889640067783262[/C][/ROW]
[ROW][C]29[/C][C]819.4[/C][C]819.249879624381[/C][C]0.150120375618826[/C][/ROW]
[ROW][C]30[/C][C]819.7[/C][C]817.368528470134[/C][C]2.33147152986646[/C][/ROW]
[ROW][C]31[/C][C]818.2[/C][C]819.152543909266[/C][C]-0.952543909265955[/C][/ROW]
[ROW][C]32[/C][C]817.7[/C][C]818.376194708359[/C][C]-0.676194708359162[/C][/ROW]
[ROW][C]33[/C][C]817.5[/C][C]817.930486786554[/C][C]-0.430486786553615[/C][/ROW]
[ROW][C]34[/C][C]817.7[/C][C]818.868744676654[/C][C]-1.16874467665411[/C][/ROW]
[ROW][C]35[/C][C]817.5[/C][C]817.61092992763[/C][C]-0.110929927630309[/C][/ROW]
[ROW][C]36[/C][C]816.9[/C][C]817.808105480299[/C][C]-0.9081054802989[/C][/ROW]
[ROW][C]37[/C][C]820.3[/C][C]816.279564359016[/C][C]4.02043564098358[/C][/ROW]
[ROW][C]38[/C][C]819.7[/C][C]819.880678823989[/C][C]-0.180678823988956[/C][/ROW]
[ROW][C]39[/C][C]819.4[/C][C]819.010826600083[/C][C]0.389173399917127[/C][/ROW]
[ROW][C]40[/C][C]818.6[/C][C]818.802561030478[/C][C]-0.202561030477909[/C][/ROW]
[ROW][C]41[/C][C]818.2[/C][C]818.189720231758[/C][C]0.0102797682418441[/C][/ROW]
[ROW][C]42[/C][C]817.6[/C][C]817.30630485868[/C][C]0.293695141320086[/C][/ROW]
[ROW][C]43[/C][C]817.3[/C][C]816.799097175908[/C][C]0.500902824092123[/C][/ROW]
[ROW][C]44[/C][C]816.7[/C][C]817.663223370498[/C][C]-0.963223370498213[/C][/ROW]
[ROW][C]45[/C][C]817[/C][C]817.414740255161[/C][C]-0.41474025516095[/C][/ROW]
[ROW][C]46[/C][C]817.6[/C][C]818.570755099654[/C][C]-0.970755099653729[/C][/ROW]
[ROW][C]47[/C][C]817.8[/C][C]818.130607312731[/C][C]-0.330607312730649[/C][/ROW]
[ROW][C]48[/C][C]817.8[/C][C]818.343121130298[/C][C]-0.543121130298459[/C][/ROW]
[ROW][C]49[/C][C]820.9[/C][C]818.667395295384[/C][C]2.23260470461605[/C][/ROW]
[ROW][C]50[/C][C]820.7[/C][C]819.890337126972[/C][C]0.809662873027719[/C][/ROW]
[ROW][C]51[/C][C]820.6[/C][C]820.154357097122[/C][C]0.445642902878262[/C][/ROW]
[ROW][C]52[/C][C]820.8[/C][C]820.111842596946[/C][C]0.688157403054333[/C][/ROW]
[ROW][C]53[/C][C]820.4[/C][C]820.752878250875[/C][C]-0.352878250875165[/C][/ROW]
[ROW][C]54[/C][C]820.2[/C][C]820.058511634602[/C][C]0.141488365398118[/C][/ROW]
[ROW][C]55[/C][C]819.8[/C][C]819.842775711578[/C][C]-0.0427757115785425[/C][/ROW]
[ROW][C]56[/C][C]819.6[/C][C]820.162587924978[/C][C]-0.562587924977834[/C][/ROW]
[ROW][C]57[/C][C]819.6[/C][C]820.669421940467[/C][C]-1.06942194046712[/C][/ROW]
[ROW][C]58[/C][C]819.8[/C][C]821.323010783131[/C][C]-1.52301078313076[/C][/ROW]
[ROW][C]59[/C][C]819.9[/C][C]820.565177695058[/C][C]-0.66517769505765[/C][/ROW]
[ROW][C]60[/C][C]820.3[/C][C]820.341237825449[/C][C]-0.0412378254492296[/C][/ROW]
[ROW][C]61[/C][C]822.9[/C][C]821.691977484329[/C][C]1.20802251567102[/C][/ROW]
[ROW][C]62[/C][C]821.9[/C][C]821.519575664312[/C][C]0.380424335687962[/C][/ROW]
[ROW][C]63[/C][C]820.6[/C][C]820.961408071172[/C][C]-0.361408071171809[/C][/ROW]
[ROW][C]64[/C][C]818.9[/C][C]819.702307310298[/C][C]-0.802307310297579[/C][/ROW]
[ROW][C]65[/C][C]817.3[/C][C]817.873669010205[/C][C]-0.573669010204753[/C][/ROW]
[ROW][C]66[/C][C]815.6[/C][C]815.973969689171[/C][C]-0.373969689170849[/C][/ROW]
[ROW][C]67[/C][C]813.8[/C][C]814.021892086708[/C][C]-0.221892086707953[/C][/ROW]
[ROW][C]68[/C][C]812.1[/C][C]812.739539771428[/C][C]-0.639539771427962[/C][/ROW]
[ROW][C]69[/C][C]810.8[/C][C]811.703987183101[/C][C]-0.903987183101322[/C][/ROW]
[ROW][C]70[/C][C]809.6[/C][C]811.06379302697[/C][C]-1.4637930269696[/C][/ROW]
[ROW][C]71[/C][C]808.7[/C][C]809.239306927463[/C][C]-0.539306927463372[/C][/ROW]
[ROW][C]72[/C][C]807.3[/C][C]807.985178495127[/C][C]-0.685178495127502[/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
13832.2832.0958600427350.104139957264579
14831.9831.983624354119-0.0836243541185695
15830.6830.755192557766-0.155192557766441
16829.7829.913260758813-0.21326075881268
17828.8829.076337353792-0.276337353792201
18826.7827.013750303944-0.313750303943493
19825.8826.109500703626-0.309500703626327
20825.4825.2972062339060.10279376609401
21825825.339523848147-0.339523848146655
22825.6826.222167227236-0.622167227236446
23824.6825.399055715984-0.799055715983854
24824.5824.696470799366-0.196470799366125
25822.6823.957063001449-1.35706300144921
26822821.3330084389960.66699156100367
27821.2819.5569260377061.64307396229378
28820.4819.5103599322170.889640067783262
29819.4819.2498796243810.150120375618826
30819.7817.3685284701342.33147152986646
31818.2819.152543909266-0.952543909265955
32817.7818.376194708359-0.676194708359162
33817.5817.930486786554-0.430486786553615
34817.7818.868744676654-1.16874467665411
35817.5817.61092992763-0.110929927630309
36816.9817.808105480299-0.9081054802989
37820.3816.2795643590164.02043564098358
38819.7819.880678823989-0.180678823988956
39819.4819.0108266000830.389173399917127
40818.6818.802561030478-0.202561030477909
41818.2818.1897202317580.0102797682418441
42817.6817.306304858680.293695141320086
43817.3816.7990971759080.500902824092123
44816.7817.663223370498-0.963223370498213
45817817.414740255161-0.41474025516095
46817.6818.570755099654-0.970755099653729
47817.8818.130607312731-0.330607312730649
48817.8818.343121130298-0.543121130298459
49820.9818.6673952953842.23260470461605
50820.7819.8903371269720.809662873027719
51820.6820.1543570971220.445642902878262
52820.8820.1118425969460.688157403054333
53820.4820.752878250875-0.352878250875165
54820.2820.0585116346020.141488365398118
55819.8819.842775711578-0.0427757115785425
56819.6820.162587924978-0.562587924977834
57819.6820.669421940467-1.06942194046712
58819.8821.323010783131-1.52301078313076
59819.9820.565177695058-0.66517769505765
60820.3820.341237825449-0.0412378254492296
61822.9821.6919774843291.20802251567102
62821.9821.5195756643120.380424335687962
63820.6820.961408071172-0.361408071171809
64818.9819.702307310298-0.802307310297579
65817.3817.873669010205-0.573669010204753
66815.6815.973969689171-0.373969689170849
67813.8814.021892086708-0.221892086707953
68812.1812.739539771428-0.639539771427962
69810.8811.703987183101-0.903987183101322
70809.6811.06379302697-1.4637930269696
71808.7809.239306927463-0.539306927463372
72807.3807.985178495127-0.685178495127502







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73807.658608356704805.805369194379809.511847519028
74804.554290121915801.840776138116807.267804105714
75801.615175023388797.909224018863805.321126027913
76798.724365373904793.914508024969803.534222722839
77795.990522438909789.977818309393802.003226568426
78793.169268445145785.863434423948800.475102466342
79790.239206722195781.556464338193798.921949106198
80787.798580682991777.660310966938797.936850399045
81786.150483873705774.482313857284797.818653890126
82785.301769537082772.032913535215798.570625538949
83784.462748898977769.525512031495799.39998576646
84783.394802100192766.72419333373800.065410866654

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 807.658608356704 & 805.805369194379 & 809.511847519028 \tabularnewline
74 & 804.554290121915 & 801.840776138116 & 807.267804105714 \tabularnewline
75 & 801.615175023388 & 797.909224018863 & 805.321126027913 \tabularnewline
76 & 798.724365373904 & 793.914508024969 & 803.534222722839 \tabularnewline
77 & 795.990522438909 & 789.977818309393 & 802.003226568426 \tabularnewline
78 & 793.169268445145 & 785.863434423948 & 800.475102466342 \tabularnewline
79 & 790.239206722195 & 781.556464338193 & 798.921949106198 \tabularnewline
80 & 787.798580682991 & 777.660310966938 & 797.936850399045 \tabularnewline
81 & 786.150483873705 & 774.482313857284 & 797.818653890126 \tabularnewline
82 & 785.301769537082 & 772.032913535215 & 798.570625538949 \tabularnewline
83 & 784.462748898977 & 769.525512031495 & 799.39998576646 \tabularnewline
84 & 783.394802100192 & 766.72419333373 & 800.065410866654 \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]73[/C][C]807.658608356704[/C][C]805.805369194379[/C][C]809.511847519028[/C][/ROW]
[ROW][C]74[/C][C]804.554290121915[/C][C]801.840776138116[/C][C]807.267804105714[/C][/ROW]
[ROW][C]75[/C][C]801.615175023388[/C][C]797.909224018863[/C][C]805.321126027913[/C][/ROW]
[ROW][C]76[/C][C]798.724365373904[/C][C]793.914508024969[/C][C]803.534222722839[/C][/ROW]
[ROW][C]77[/C][C]795.990522438909[/C][C]789.977818309393[/C][C]802.003226568426[/C][/ROW]
[ROW][C]78[/C][C]793.169268445145[/C][C]785.863434423948[/C][C]800.475102466342[/C][/ROW]
[ROW][C]79[/C][C]790.239206722195[/C][C]781.556464338193[/C][C]798.921949106198[/C][/ROW]
[ROW][C]80[/C][C]787.798580682991[/C][C]777.660310966938[/C][C]797.936850399045[/C][/ROW]
[ROW][C]81[/C][C]786.150483873705[/C][C]774.482313857284[/C][C]797.818653890126[/C][/ROW]
[ROW][C]82[/C][C]785.301769537082[/C][C]772.032913535215[/C][C]798.570625538949[/C][/ROW]
[ROW][C]83[/C][C]784.462748898977[/C][C]769.525512031495[/C][C]799.39998576646[/C][/ROW]
[ROW][C]84[/C][C]783.394802100192[/C][C]766.72419333373[/C][C]800.065410866654[/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
73807.658608356704805.805369194379809.511847519028
74804.554290121915801.840776138116807.267804105714
75801.615175023388797.909224018863805.321126027913
76798.724365373904793.914508024969803.534222722839
77795.990522438909789.977818309393802.003226568426
78793.169268445145785.863434423948800.475102466342
79790.239206722195781.556464338193798.921949106198
80787.798580682991777.660310966938797.936850399045
81786.150483873705774.482313857284797.818653890126
82785.301769537082772.032913535215798.570625538949
83784.462748898977769.525512031495799.39998576646
84783.394802100192766.72419333373800.065410866654



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; 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=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')