Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 11:18:12 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/02/t1493720310wh2qe8jvowjh952.htm/, Retrieved Fri, 17 May 2024 08:59:55 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 08:59:55 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
78,46
78,59
81,37
83,61
83,85
84,08
84,56
84,65
85,41
85,75
86,21
86,38
86,65
87,30
87,87
88,23
88,33
88,62
88,67
88,85
88,87
89,20
89,38
89,65
90,37
90,38
91,43
92,09
92,21
92,31
92,62
93,13
93,17
93,42
93,50
95,75
97,29
98,01
98,02
98,20
98,29
98,39
98,42
98,70
98,90
99,04
99,31
99,34
99,35
99,51
99,88
99,91
100,30
100,74
101,16
101,30
101,37
101,68
101,68
101,89
101,93
102,66
102,68
103,13
103,14
104,01
104,17
104,41
104,71
105,51
105,98
106,25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.876399052238814
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.876399052238814 \tabularnewline
beta & 0 \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]0.876399052238814[/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=&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
alpha0.876399052238814
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1386.6584.00561431623932.64438568376067
1487.387.01070387079350.289296129206463
1587.8787.8988785051322-0.0288785051322122
1688.2388.32945519149-0.0994551914900228
1788.3388.4502618701471-0.120261870147061
1888.6288.7503335953488-0.130333595348816
1988.6789.3740784701294-0.70407847012936
2088.8588.5266605470920.323339452907987
2188.8789.3200873847244-0.450087384724412
2289.289.18610034154640.013899658453596
2389.3889.6629177699273-0.282917769927337
2489.6589.59293801872060.0570619812793609
2590.3790.26318144267740.106818557322569
2690.3890.7532582716235-0.373258271623527
2791.4391.02144417066030.40855582933969
2892.0991.82666454784230.263335452157662
2992.2192.2628488775515-0.0528488775515541
3092.3192.6207564107921-0.310756410792052
3192.6293.0154634908199-0.395463490819878
3293.1392.56550527219030.564494727809688
3393.1793.4746840740337-0.304684074033659
3493.4293.5254775928231-0.105477592823121
3593.593.8609859958663-0.360985995866329
3695.7593.76460914490551.98539085509449
3797.2996.13098812623491.15901187376508
3898.0197.48386822942730.526131770572675
3998.0298.63691167289-0.616911672890012
4098.298.5254639267623-0.325463926762282
4198.2998.406544356008-0.11654435600795
4298.3998.6767516167541-0.286751616754103
4398.4299.0820266001525-0.662026600152458
4498.798.51710447077570.182895529224282
4598.998.984418772962-0.0844187729619676
4699.0499.2528747027295-0.212874702729536
4799.3199.4626792996605-0.152679299660477
4899.3499.8388766424131-0.498876642413123
4999.3599.9259047181169-0.575904718116945
5099.5199.6800809838968-0.170080983896767
5199.88100.081682976242-0.201682976241656
5299.91100.370164483963-0.460164483963155
53100.3100.1590161294930.140983870506957
54100.74100.6338831051380.106116894862467
55101.16101.337083336152-0.177083336152037
56101.3101.30159819971-0.00159819971023012
57101.37101.574182071614-0.204182071613928
58101.68101.721800285285-0.041800285285106
59101.68102.088974548397-0.408974548396856
60101.89102.197764658387-0.307764658386986
61101.93102.442762352602-0.512762352601555
62102.66102.3024367258490.357563274151204
63102.68103.162559609661-0.482559609661195
64103.13103.172932542725-0.042932542724671
65103.14103.401748372477-0.261748372477314
66104.01103.5193516008290.490648399170865
67104.17104.524551060816-0.354551060815908
68104.41104.3552235078580.0547764921420679
69104.71104.6521745477030.0578254522971662
70105.51105.0494864496990.460513550301485
71105.98105.8115049953310.168495004669325
72106.25106.438898512653-0.188898512652813

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 86.65 & 84.0056143162393 & 2.64438568376067 \tabularnewline
14 & 87.3 & 87.0107038707935 & 0.289296129206463 \tabularnewline
15 & 87.87 & 87.8988785051322 & -0.0288785051322122 \tabularnewline
16 & 88.23 & 88.32945519149 & -0.0994551914900228 \tabularnewline
17 & 88.33 & 88.4502618701471 & -0.120261870147061 \tabularnewline
18 & 88.62 & 88.7503335953488 & -0.130333595348816 \tabularnewline
19 & 88.67 & 89.3740784701294 & -0.70407847012936 \tabularnewline
20 & 88.85 & 88.526660547092 & 0.323339452907987 \tabularnewline
21 & 88.87 & 89.3200873847244 & -0.450087384724412 \tabularnewline
22 & 89.2 & 89.1861003415464 & 0.013899658453596 \tabularnewline
23 & 89.38 & 89.6629177699273 & -0.282917769927337 \tabularnewline
24 & 89.65 & 89.5929380187206 & 0.0570619812793609 \tabularnewline
25 & 90.37 & 90.2631814426774 & 0.106818557322569 \tabularnewline
26 & 90.38 & 90.7532582716235 & -0.373258271623527 \tabularnewline
27 & 91.43 & 91.0214441706603 & 0.40855582933969 \tabularnewline
28 & 92.09 & 91.8266645478423 & 0.263335452157662 \tabularnewline
29 & 92.21 & 92.2628488775515 & -0.0528488775515541 \tabularnewline
30 & 92.31 & 92.6207564107921 & -0.310756410792052 \tabularnewline
31 & 92.62 & 93.0154634908199 & -0.395463490819878 \tabularnewline
32 & 93.13 & 92.5655052721903 & 0.564494727809688 \tabularnewline
33 & 93.17 & 93.4746840740337 & -0.304684074033659 \tabularnewline
34 & 93.42 & 93.5254775928231 & -0.105477592823121 \tabularnewline
35 & 93.5 & 93.8609859958663 & -0.360985995866329 \tabularnewline
36 & 95.75 & 93.7646091449055 & 1.98539085509449 \tabularnewline
37 & 97.29 & 96.1309881262349 & 1.15901187376508 \tabularnewline
38 & 98.01 & 97.4838682294273 & 0.526131770572675 \tabularnewline
39 & 98.02 & 98.63691167289 & -0.616911672890012 \tabularnewline
40 & 98.2 & 98.5254639267623 & -0.325463926762282 \tabularnewline
41 & 98.29 & 98.406544356008 & -0.11654435600795 \tabularnewline
42 & 98.39 & 98.6767516167541 & -0.286751616754103 \tabularnewline
43 & 98.42 & 99.0820266001525 & -0.662026600152458 \tabularnewline
44 & 98.7 & 98.5171044707757 & 0.182895529224282 \tabularnewline
45 & 98.9 & 98.984418772962 & -0.0844187729619676 \tabularnewline
46 & 99.04 & 99.2528747027295 & -0.212874702729536 \tabularnewline
47 & 99.31 & 99.4626792996605 & -0.152679299660477 \tabularnewline
48 & 99.34 & 99.8388766424131 & -0.498876642413123 \tabularnewline
49 & 99.35 & 99.9259047181169 & -0.575904718116945 \tabularnewline
50 & 99.51 & 99.6800809838968 & -0.170080983896767 \tabularnewline
51 & 99.88 & 100.081682976242 & -0.201682976241656 \tabularnewline
52 & 99.91 & 100.370164483963 & -0.460164483963155 \tabularnewline
53 & 100.3 & 100.159016129493 & 0.140983870506957 \tabularnewline
54 & 100.74 & 100.633883105138 & 0.106116894862467 \tabularnewline
55 & 101.16 & 101.337083336152 & -0.177083336152037 \tabularnewline
56 & 101.3 & 101.30159819971 & -0.00159819971023012 \tabularnewline
57 & 101.37 & 101.574182071614 & -0.204182071613928 \tabularnewline
58 & 101.68 & 101.721800285285 & -0.041800285285106 \tabularnewline
59 & 101.68 & 102.088974548397 & -0.408974548396856 \tabularnewline
60 & 101.89 & 102.197764658387 & -0.307764658386986 \tabularnewline
61 & 101.93 & 102.442762352602 & -0.512762352601555 \tabularnewline
62 & 102.66 & 102.302436725849 & 0.357563274151204 \tabularnewline
63 & 102.68 & 103.162559609661 & -0.482559609661195 \tabularnewline
64 & 103.13 & 103.172932542725 & -0.042932542724671 \tabularnewline
65 & 103.14 & 103.401748372477 & -0.261748372477314 \tabularnewline
66 & 104.01 & 103.519351600829 & 0.490648399170865 \tabularnewline
67 & 104.17 & 104.524551060816 & -0.354551060815908 \tabularnewline
68 & 104.41 & 104.355223507858 & 0.0547764921420679 \tabularnewline
69 & 104.71 & 104.652174547703 & 0.0578254522971662 \tabularnewline
70 & 105.51 & 105.049486449699 & 0.460513550301485 \tabularnewline
71 & 105.98 & 105.811504995331 & 0.168495004669325 \tabularnewline
72 & 106.25 & 106.438898512653 & -0.188898512652813 \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]86.65[/C][C]84.0056143162393[/C][C]2.64438568376067[/C][/ROW]
[ROW][C]14[/C][C]87.3[/C][C]87.0107038707935[/C][C]0.289296129206463[/C][/ROW]
[ROW][C]15[/C][C]87.87[/C][C]87.8988785051322[/C][C]-0.0288785051322122[/C][/ROW]
[ROW][C]16[/C][C]88.23[/C][C]88.32945519149[/C][C]-0.0994551914900228[/C][/ROW]
[ROW][C]17[/C][C]88.33[/C][C]88.4502618701471[/C][C]-0.120261870147061[/C][/ROW]
[ROW][C]18[/C][C]88.62[/C][C]88.7503335953488[/C][C]-0.130333595348816[/C][/ROW]
[ROW][C]19[/C][C]88.67[/C][C]89.3740784701294[/C][C]-0.70407847012936[/C][/ROW]
[ROW][C]20[/C][C]88.85[/C][C]88.526660547092[/C][C]0.323339452907987[/C][/ROW]
[ROW][C]21[/C][C]88.87[/C][C]89.3200873847244[/C][C]-0.450087384724412[/C][/ROW]
[ROW][C]22[/C][C]89.2[/C][C]89.1861003415464[/C][C]0.013899658453596[/C][/ROW]
[ROW][C]23[/C][C]89.38[/C][C]89.6629177699273[/C][C]-0.282917769927337[/C][/ROW]
[ROW][C]24[/C][C]89.65[/C][C]89.5929380187206[/C][C]0.0570619812793609[/C][/ROW]
[ROW][C]25[/C][C]90.37[/C][C]90.2631814426774[/C][C]0.106818557322569[/C][/ROW]
[ROW][C]26[/C][C]90.38[/C][C]90.7532582716235[/C][C]-0.373258271623527[/C][/ROW]
[ROW][C]27[/C][C]91.43[/C][C]91.0214441706603[/C][C]0.40855582933969[/C][/ROW]
[ROW][C]28[/C][C]92.09[/C][C]91.8266645478423[/C][C]0.263335452157662[/C][/ROW]
[ROW][C]29[/C][C]92.21[/C][C]92.2628488775515[/C][C]-0.0528488775515541[/C][/ROW]
[ROW][C]30[/C][C]92.31[/C][C]92.6207564107921[/C][C]-0.310756410792052[/C][/ROW]
[ROW][C]31[/C][C]92.62[/C][C]93.0154634908199[/C][C]-0.395463490819878[/C][/ROW]
[ROW][C]32[/C][C]93.13[/C][C]92.5655052721903[/C][C]0.564494727809688[/C][/ROW]
[ROW][C]33[/C][C]93.17[/C][C]93.4746840740337[/C][C]-0.304684074033659[/C][/ROW]
[ROW][C]34[/C][C]93.42[/C][C]93.5254775928231[/C][C]-0.105477592823121[/C][/ROW]
[ROW][C]35[/C][C]93.5[/C][C]93.8609859958663[/C][C]-0.360985995866329[/C][/ROW]
[ROW][C]36[/C][C]95.75[/C][C]93.7646091449055[/C][C]1.98539085509449[/C][/ROW]
[ROW][C]37[/C][C]97.29[/C][C]96.1309881262349[/C][C]1.15901187376508[/C][/ROW]
[ROW][C]38[/C][C]98.01[/C][C]97.4838682294273[/C][C]0.526131770572675[/C][/ROW]
[ROW][C]39[/C][C]98.02[/C][C]98.63691167289[/C][C]-0.616911672890012[/C][/ROW]
[ROW][C]40[/C][C]98.2[/C][C]98.5254639267623[/C][C]-0.325463926762282[/C][/ROW]
[ROW][C]41[/C][C]98.29[/C][C]98.406544356008[/C][C]-0.11654435600795[/C][/ROW]
[ROW][C]42[/C][C]98.39[/C][C]98.6767516167541[/C][C]-0.286751616754103[/C][/ROW]
[ROW][C]43[/C][C]98.42[/C][C]99.0820266001525[/C][C]-0.662026600152458[/C][/ROW]
[ROW][C]44[/C][C]98.7[/C][C]98.5171044707757[/C][C]0.182895529224282[/C][/ROW]
[ROW][C]45[/C][C]98.9[/C][C]98.984418772962[/C][C]-0.0844187729619676[/C][/ROW]
[ROW][C]46[/C][C]99.04[/C][C]99.2528747027295[/C][C]-0.212874702729536[/C][/ROW]
[ROW][C]47[/C][C]99.31[/C][C]99.4626792996605[/C][C]-0.152679299660477[/C][/ROW]
[ROW][C]48[/C][C]99.34[/C][C]99.8388766424131[/C][C]-0.498876642413123[/C][/ROW]
[ROW][C]49[/C][C]99.35[/C][C]99.9259047181169[/C][C]-0.575904718116945[/C][/ROW]
[ROW][C]50[/C][C]99.51[/C][C]99.6800809838968[/C][C]-0.170080983896767[/C][/ROW]
[ROW][C]51[/C][C]99.88[/C][C]100.081682976242[/C][C]-0.201682976241656[/C][/ROW]
[ROW][C]52[/C][C]99.91[/C][C]100.370164483963[/C][C]-0.460164483963155[/C][/ROW]
[ROW][C]53[/C][C]100.3[/C][C]100.159016129493[/C][C]0.140983870506957[/C][/ROW]
[ROW][C]54[/C][C]100.74[/C][C]100.633883105138[/C][C]0.106116894862467[/C][/ROW]
[ROW][C]55[/C][C]101.16[/C][C]101.337083336152[/C][C]-0.177083336152037[/C][/ROW]
[ROW][C]56[/C][C]101.3[/C][C]101.30159819971[/C][C]-0.00159819971023012[/C][/ROW]
[ROW][C]57[/C][C]101.37[/C][C]101.574182071614[/C][C]-0.204182071613928[/C][/ROW]
[ROW][C]58[/C][C]101.68[/C][C]101.721800285285[/C][C]-0.041800285285106[/C][/ROW]
[ROW][C]59[/C][C]101.68[/C][C]102.088974548397[/C][C]-0.408974548396856[/C][/ROW]
[ROW][C]60[/C][C]101.89[/C][C]102.197764658387[/C][C]-0.307764658386986[/C][/ROW]
[ROW][C]61[/C][C]101.93[/C][C]102.442762352602[/C][C]-0.512762352601555[/C][/ROW]
[ROW][C]62[/C][C]102.66[/C][C]102.302436725849[/C][C]0.357563274151204[/C][/ROW]
[ROW][C]63[/C][C]102.68[/C][C]103.162559609661[/C][C]-0.482559609661195[/C][/ROW]
[ROW][C]64[/C][C]103.13[/C][C]103.172932542725[/C][C]-0.042932542724671[/C][/ROW]
[ROW][C]65[/C][C]103.14[/C][C]103.401748372477[/C][C]-0.261748372477314[/C][/ROW]
[ROW][C]66[/C][C]104.01[/C][C]103.519351600829[/C][C]0.490648399170865[/C][/ROW]
[ROW][C]67[/C][C]104.17[/C][C]104.524551060816[/C][C]-0.354551060815908[/C][/ROW]
[ROW][C]68[/C][C]104.41[/C][C]104.355223507858[/C][C]0.0547764921420679[/C][/ROW]
[ROW][C]69[/C][C]104.71[/C][C]104.652174547703[/C][C]0.0578254522971662[/C][/ROW]
[ROW][C]70[/C][C]105.51[/C][C]105.049486449699[/C][C]0.460513550301485[/C][/ROW]
[ROW][C]71[/C][C]105.98[/C][C]105.811504995331[/C][C]0.168495004669325[/C][/ROW]
[ROW][C]72[/C][C]106.25[/C][C]106.438898512653[/C][C]-0.188898512652813[/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
1386.6584.00561431623932.64438568376067
1487.387.01070387079350.289296129206463
1587.8787.8988785051322-0.0288785051322122
1688.2388.32945519149-0.0994551914900228
1788.3388.4502618701471-0.120261870147061
1888.6288.7503335953488-0.130333595348816
1988.6789.3740784701294-0.70407847012936
2088.8588.5266605470920.323339452907987
2188.8789.3200873847244-0.450087384724412
2289.289.18610034154640.013899658453596
2389.3889.6629177699273-0.282917769927337
2489.6589.59293801872060.0570619812793609
2590.3790.26318144267740.106818557322569
2690.3890.7532582716235-0.373258271623527
2791.4391.02144417066030.40855582933969
2892.0991.82666454784230.263335452157662
2992.2192.2628488775515-0.0528488775515541
3092.3192.6207564107921-0.310756410792052
3192.6293.0154634908199-0.395463490819878
3293.1392.56550527219030.564494727809688
3393.1793.4746840740337-0.304684074033659
3493.4293.5254775928231-0.105477592823121
3593.593.8609859958663-0.360985995866329
3695.7593.76460914490551.98539085509449
3797.2996.13098812623491.15901187376508
3898.0197.48386822942730.526131770572675
3998.0298.63691167289-0.616911672890012
4098.298.5254639267623-0.325463926762282
4198.2998.406544356008-0.11654435600795
4298.3998.6767516167541-0.286751616754103
4398.4299.0820266001525-0.662026600152458
4498.798.51710447077570.182895529224282
4598.998.984418772962-0.0844187729619676
4699.0499.2528747027295-0.212874702729536
4799.3199.4626792996605-0.152679299660477
4899.3499.8388766424131-0.498876642413123
4999.3599.9259047181169-0.575904718116945
5099.5199.6800809838968-0.170080983896767
5199.88100.081682976242-0.201682976241656
5299.91100.370164483963-0.460164483963155
53100.3100.1590161294930.140983870506957
54100.74100.6338831051380.106116894862467
55101.16101.337083336152-0.177083336152037
56101.3101.30159819971-0.00159819971023012
57101.37101.574182071614-0.204182071613928
58101.68101.721800285285-0.041800285285106
59101.68102.088974548397-0.408974548396856
60101.89102.197764658387-0.307764658386986
61101.93102.442762352602-0.512762352601555
62102.66102.3024367258490.357563274151204
63102.68103.162559609661-0.482559609661195
64103.13103.172932542725-0.042932542724671
65103.14103.401748372477-0.261748372477314
66104.01103.5193516008290.490648399170865
67104.17104.524551060816-0.354551060815908
68104.41104.3552235078580.0547764921420679
69104.71104.6521745477030.0578254522971662
70105.51105.0494864496990.460513550301485
71105.98105.8115049953310.168495004669325
72106.25106.438898512653-0.188898512652813







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73106.762732475038105.666506971851107.858957978226
74107.179364360457105.721724352467108.637004368446
75107.622279145013105.876507558594109.368050731431
76108.109905184767106.117238009597110.102572359936
77108.349301210331106.137124339110.561478081662
78108.789297418315106.377507512642111.201087323988
79109.260025631984106.663925751749111.85612551222
80109.452019566186106.683854356663112.220184775709
81109.701341394598106.771197598422112.631485190773
82110.09774775557107.014122177567113.181373333574
83110.420078893171107.190256801419113.649900984924
84110.855629370629107.485947667052114.225311074207

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 106.762732475038 & 105.666506971851 & 107.858957978226 \tabularnewline
74 & 107.179364360457 & 105.721724352467 & 108.637004368446 \tabularnewline
75 & 107.622279145013 & 105.876507558594 & 109.368050731431 \tabularnewline
76 & 108.109905184767 & 106.117238009597 & 110.102572359936 \tabularnewline
77 & 108.349301210331 & 106.137124339 & 110.561478081662 \tabularnewline
78 & 108.789297418315 & 106.377507512642 & 111.201087323988 \tabularnewline
79 & 109.260025631984 & 106.663925751749 & 111.85612551222 \tabularnewline
80 & 109.452019566186 & 106.683854356663 & 112.220184775709 \tabularnewline
81 & 109.701341394598 & 106.771197598422 & 112.631485190773 \tabularnewline
82 & 110.09774775557 & 107.014122177567 & 113.181373333574 \tabularnewline
83 & 110.420078893171 & 107.190256801419 & 113.649900984924 \tabularnewline
84 & 110.855629370629 & 107.485947667052 & 114.225311074207 \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]106.762732475038[/C][C]105.666506971851[/C][C]107.858957978226[/C][/ROW]
[ROW][C]74[/C][C]107.179364360457[/C][C]105.721724352467[/C][C]108.637004368446[/C][/ROW]
[ROW][C]75[/C][C]107.622279145013[/C][C]105.876507558594[/C][C]109.368050731431[/C][/ROW]
[ROW][C]76[/C][C]108.109905184767[/C][C]106.117238009597[/C][C]110.102572359936[/C][/ROW]
[ROW][C]77[/C][C]108.349301210331[/C][C]106.137124339[/C][C]110.561478081662[/C][/ROW]
[ROW][C]78[/C][C]108.789297418315[/C][C]106.377507512642[/C][C]111.201087323988[/C][/ROW]
[ROW][C]79[/C][C]109.260025631984[/C][C]106.663925751749[/C][C]111.85612551222[/C][/ROW]
[ROW][C]80[/C][C]109.452019566186[/C][C]106.683854356663[/C][C]112.220184775709[/C][/ROW]
[ROW][C]81[/C][C]109.701341394598[/C][C]106.771197598422[/C][C]112.631485190773[/C][/ROW]
[ROW][C]82[/C][C]110.09774775557[/C][C]107.014122177567[/C][C]113.181373333574[/C][/ROW]
[ROW][C]83[/C][C]110.420078893171[/C][C]107.190256801419[/C][C]113.649900984924[/C][/ROW]
[ROW][C]84[/C][C]110.855629370629[/C][C]107.485947667052[/C][C]114.225311074207[/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
73106.762732475038105.666506971851107.858957978226
74107.179364360457105.721724352467108.637004368446
75107.622279145013105.876507558594109.368050731431
76108.109905184767106.117238009597110.102572359936
77108.349301210331106.137124339110.561478081662
78108.789297418315106.377507512642111.201087323988
79109.260025631984106.663925751749111.85612551222
80109.452019566186106.683854356663112.220184775709
81109.701341394598106.771197598422112.631485190773
82110.09774775557107.014122177567113.181373333574
83110.420078893171107.190256801419113.649900984924
84110.855629370629107.485947667052114.225311074207



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')