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 09:13:48 +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/t1493712954glj7irimrmnf92s.htm/, Retrieved Fri, 17 May 2024 05:45:00 +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 05:45:00 +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
84.65
84.56
83.85
84.08
85.41
85.75
86.38
88.87
90.37
92.21
95.75
97.29
98.29
99.51
99.04
98.9
100.74
100.3
101.68
101.3
103.13
104.17
105.98
106.25
104.01
101.68
101.93
104.41
105.51
104.71
103.14
102.66
102.68
101.89
101.37
101.16
99.34
99.35
99.88
99.31
99.91
98.39
98.02
98.7
98.01
98.42
98.2
93.5
93.17
93.42
93.13
92.31
92.09
92.62
91.43
89.38
86.21
86.65
88.62
87.3
88.33
88.67
88.23
88.85
90.38
89.65
89.2
87.87




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 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]2 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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.120378446026332
gamma0.798277792400615

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.120378446026332 \tabularnewline
gamma & 0.798277792400615 \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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.120378446026332[/C][/ROW]
[ROW][C]gamma[/C][C]0.798277792400615[/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
alpha1
beta0.120378446026332
gamma0.798277792400615







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1390.3783.31741452991457.05258547008549
1492.2193.0151943143218-0.80519431432181
1595.7596.4524329406812-0.702432940681177
1697.2997.9191251548443-0.629125154844289
1798.2998.844642046348-0.554642046348036
1899.51100.086208432041-0.576208432041156
1999.0498.64809535640480.391904643595225
2098.999.9156888950579-1.01568889505788
21100.74100.6505051775580.0894948224420062
22100.3101.508778425211-1.20877842521095
23101.68101.2441008901270.435899109872736
24101.3104.483657080931-3.18365708093135
25103.13102.6658300555150.464169944485306
26104.17104.897122778791-0.727122778790658
27105.98107.543759535276-1.56375953527618
28106.25107.176766592461-0.926766592460766
29104.01106.796453870231-2.78645387023121
30101.68104.529358216742-2.84935821674206
31101.9399.26760690243832.66239309756169
32104.41101.5285183129012.88148168709935
33105.51105.352469933980.157530066019646
34104.71105.47893315853-0.768933158530217
35103.14104.907203513142-1.76720351314158
36102.66104.931553633751-2.27155363375067
37102.68103.123524203921-0.443524203920887
38101.89103.435550116145-1.54555011614454
39101.37104.153665861574-2.78366586157392
40101.16101.309822490901-0.149822490901101
4199.34100.543037092267-1.20303709226661
4299.3598.88655068992090.463449310079127
4399.8896.36358999768023.51641000231982
4499.3199.00730663601750.302693363982485
4599.9199.47082772612960.439172273870412
4698.3999.1311946019959-0.741194601995929
4798.0297.84280408093790.177195919062072
4898.799.3012179836502-0.601217983650159
4998.0198.8542609637219-0.844260963721865
5098.4298.4080468075350.0119531924649579
5198.2100.513652380936-2.31365238093571
5293.598.0263885026735-4.52638850267354
5393.1792.24275888861020.927241111389776
5493.4292.33271206602441.0872879339756
5593.1390.12484809789963.00515190210041
5692.3191.88702028061410.422979719385879
5792.0992.1150212552678-0.0250212552678164
5892.6290.8995092354411.72049076455897
5991.4391.9574525734147-0.527452573414664
6089.3892.5110419856078-3.13104198560777
6186.2189.0295486836037-2.8195486836037
6286.6585.86555246124260.784447538757433
6388.6288.09414970361410.525850296385926
6487.388.1387007451355-0.838700745135498
6588.3386.17898925275492.15101074724505
6688.6787.77625791722760.89374208277242
6788.2385.63509520030012.59490479969992
6888.8587.19788247434091.65211752565914
6990.3889.01384514806591.36615485193407
7089.6589.7158007461731-0.0658007461730534
7189.289.2987130879348-0.0987130879347546
7287.8790.64391349314-2.77391349314004

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 90.37 & 83.3174145299145 & 7.05258547008549 \tabularnewline
14 & 92.21 & 93.0151943143218 & -0.80519431432181 \tabularnewline
15 & 95.75 & 96.4524329406812 & -0.702432940681177 \tabularnewline
16 & 97.29 & 97.9191251548443 & -0.629125154844289 \tabularnewline
17 & 98.29 & 98.844642046348 & -0.554642046348036 \tabularnewline
18 & 99.51 & 100.086208432041 & -0.576208432041156 \tabularnewline
19 & 99.04 & 98.6480953564048 & 0.391904643595225 \tabularnewline
20 & 98.9 & 99.9156888950579 & -1.01568889505788 \tabularnewline
21 & 100.74 & 100.650505177558 & 0.0894948224420062 \tabularnewline
22 & 100.3 & 101.508778425211 & -1.20877842521095 \tabularnewline
23 & 101.68 & 101.244100890127 & 0.435899109872736 \tabularnewline
24 & 101.3 & 104.483657080931 & -3.18365708093135 \tabularnewline
25 & 103.13 & 102.665830055515 & 0.464169944485306 \tabularnewline
26 & 104.17 & 104.897122778791 & -0.727122778790658 \tabularnewline
27 & 105.98 & 107.543759535276 & -1.56375953527618 \tabularnewline
28 & 106.25 & 107.176766592461 & -0.926766592460766 \tabularnewline
29 & 104.01 & 106.796453870231 & -2.78645387023121 \tabularnewline
30 & 101.68 & 104.529358216742 & -2.84935821674206 \tabularnewline
31 & 101.93 & 99.2676069024383 & 2.66239309756169 \tabularnewline
32 & 104.41 & 101.528518312901 & 2.88148168709935 \tabularnewline
33 & 105.51 & 105.35246993398 & 0.157530066019646 \tabularnewline
34 & 104.71 & 105.47893315853 & -0.768933158530217 \tabularnewline
35 & 103.14 & 104.907203513142 & -1.76720351314158 \tabularnewline
36 & 102.66 & 104.931553633751 & -2.27155363375067 \tabularnewline
37 & 102.68 & 103.123524203921 & -0.443524203920887 \tabularnewline
38 & 101.89 & 103.435550116145 & -1.54555011614454 \tabularnewline
39 & 101.37 & 104.153665861574 & -2.78366586157392 \tabularnewline
40 & 101.16 & 101.309822490901 & -0.149822490901101 \tabularnewline
41 & 99.34 & 100.543037092267 & -1.20303709226661 \tabularnewline
42 & 99.35 & 98.8865506899209 & 0.463449310079127 \tabularnewline
43 & 99.88 & 96.3635899976802 & 3.51641000231982 \tabularnewline
44 & 99.31 & 99.0073066360175 & 0.302693363982485 \tabularnewline
45 & 99.91 & 99.4708277261296 & 0.439172273870412 \tabularnewline
46 & 98.39 & 99.1311946019959 & -0.741194601995929 \tabularnewline
47 & 98.02 & 97.8428040809379 & 0.177195919062072 \tabularnewline
48 & 98.7 & 99.3012179836502 & -0.601217983650159 \tabularnewline
49 & 98.01 & 98.8542609637219 & -0.844260963721865 \tabularnewline
50 & 98.42 & 98.408046807535 & 0.0119531924649579 \tabularnewline
51 & 98.2 & 100.513652380936 & -2.31365238093571 \tabularnewline
52 & 93.5 & 98.0263885026735 & -4.52638850267354 \tabularnewline
53 & 93.17 & 92.2427588886102 & 0.927241111389776 \tabularnewline
54 & 93.42 & 92.3327120660244 & 1.0872879339756 \tabularnewline
55 & 93.13 & 90.1248480978996 & 3.00515190210041 \tabularnewline
56 & 92.31 & 91.8870202806141 & 0.422979719385879 \tabularnewline
57 & 92.09 & 92.1150212552678 & -0.0250212552678164 \tabularnewline
58 & 92.62 & 90.899509235441 & 1.72049076455897 \tabularnewline
59 & 91.43 & 91.9574525734147 & -0.527452573414664 \tabularnewline
60 & 89.38 & 92.5110419856078 & -3.13104198560777 \tabularnewline
61 & 86.21 & 89.0295486836037 & -2.8195486836037 \tabularnewline
62 & 86.65 & 85.8655524612426 & 0.784447538757433 \tabularnewline
63 & 88.62 & 88.0941497036141 & 0.525850296385926 \tabularnewline
64 & 87.3 & 88.1387007451355 & -0.838700745135498 \tabularnewline
65 & 88.33 & 86.1789892527549 & 2.15101074724505 \tabularnewline
66 & 88.67 & 87.7762579172276 & 0.89374208277242 \tabularnewline
67 & 88.23 & 85.6350952003001 & 2.59490479969992 \tabularnewline
68 & 88.85 & 87.1978824743409 & 1.65211752565914 \tabularnewline
69 & 90.38 & 89.0138451480659 & 1.36615485193407 \tabularnewline
70 & 89.65 & 89.7158007461731 & -0.0658007461730534 \tabularnewline
71 & 89.2 & 89.2987130879348 & -0.0987130879347546 \tabularnewline
72 & 87.87 & 90.64391349314 & -2.77391349314004 \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]90.37[/C][C]83.3174145299145[/C][C]7.05258547008549[/C][/ROW]
[ROW][C]14[/C][C]92.21[/C][C]93.0151943143218[/C][C]-0.80519431432181[/C][/ROW]
[ROW][C]15[/C][C]95.75[/C][C]96.4524329406812[/C][C]-0.702432940681177[/C][/ROW]
[ROW][C]16[/C][C]97.29[/C][C]97.9191251548443[/C][C]-0.629125154844289[/C][/ROW]
[ROW][C]17[/C][C]98.29[/C][C]98.844642046348[/C][C]-0.554642046348036[/C][/ROW]
[ROW][C]18[/C][C]99.51[/C][C]100.086208432041[/C][C]-0.576208432041156[/C][/ROW]
[ROW][C]19[/C][C]99.04[/C][C]98.6480953564048[/C][C]0.391904643595225[/C][/ROW]
[ROW][C]20[/C][C]98.9[/C][C]99.9156888950579[/C][C]-1.01568889505788[/C][/ROW]
[ROW][C]21[/C][C]100.74[/C][C]100.650505177558[/C][C]0.0894948224420062[/C][/ROW]
[ROW][C]22[/C][C]100.3[/C][C]101.508778425211[/C][C]-1.20877842521095[/C][/ROW]
[ROW][C]23[/C][C]101.68[/C][C]101.244100890127[/C][C]0.435899109872736[/C][/ROW]
[ROW][C]24[/C][C]101.3[/C][C]104.483657080931[/C][C]-3.18365708093135[/C][/ROW]
[ROW][C]25[/C][C]103.13[/C][C]102.665830055515[/C][C]0.464169944485306[/C][/ROW]
[ROW][C]26[/C][C]104.17[/C][C]104.897122778791[/C][C]-0.727122778790658[/C][/ROW]
[ROW][C]27[/C][C]105.98[/C][C]107.543759535276[/C][C]-1.56375953527618[/C][/ROW]
[ROW][C]28[/C][C]106.25[/C][C]107.176766592461[/C][C]-0.926766592460766[/C][/ROW]
[ROW][C]29[/C][C]104.01[/C][C]106.796453870231[/C][C]-2.78645387023121[/C][/ROW]
[ROW][C]30[/C][C]101.68[/C][C]104.529358216742[/C][C]-2.84935821674206[/C][/ROW]
[ROW][C]31[/C][C]101.93[/C][C]99.2676069024383[/C][C]2.66239309756169[/C][/ROW]
[ROW][C]32[/C][C]104.41[/C][C]101.528518312901[/C][C]2.88148168709935[/C][/ROW]
[ROW][C]33[/C][C]105.51[/C][C]105.35246993398[/C][C]0.157530066019646[/C][/ROW]
[ROW][C]34[/C][C]104.71[/C][C]105.47893315853[/C][C]-0.768933158530217[/C][/ROW]
[ROW][C]35[/C][C]103.14[/C][C]104.907203513142[/C][C]-1.76720351314158[/C][/ROW]
[ROW][C]36[/C][C]102.66[/C][C]104.931553633751[/C][C]-2.27155363375067[/C][/ROW]
[ROW][C]37[/C][C]102.68[/C][C]103.123524203921[/C][C]-0.443524203920887[/C][/ROW]
[ROW][C]38[/C][C]101.89[/C][C]103.435550116145[/C][C]-1.54555011614454[/C][/ROW]
[ROW][C]39[/C][C]101.37[/C][C]104.153665861574[/C][C]-2.78366586157392[/C][/ROW]
[ROW][C]40[/C][C]101.16[/C][C]101.309822490901[/C][C]-0.149822490901101[/C][/ROW]
[ROW][C]41[/C][C]99.34[/C][C]100.543037092267[/C][C]-1.20303709226661[/C][/ROW]
[ROW][C]42[/C][C]99.35[/C][C]98.8865506899209[/C][C]0.463449310079127[/C][/ROW]
[ROW][C]43[/C][C]99.88[/C][C]96.3635899976802[/C][C]3.51641000231982[/C][/ROW]
[ROW][C]44[/C][C]99.31[/C][C]99.0073066360175[/C][C]0.302693363982485[/C][/ROW]
[ROW][C]45[/C][C]99.91[/C][C]99.4708277261296[/C][C]0.439172273870412[/C][/ROW]
[ROW][C]46[/C][C]98.39[/C][C]99.1311946019959[/C][C]-0.741194601995929[/C][/ROW]
[ROW][C]47[/C][C]98.02[/C][C]97.8428040809379[/C][C]0.177195919062072[/C][/ROW]
[ROW][C]48[/C][C]98.7[/C][C]99.3012179836502[/C][C]-0.601217983650159[/C][/ROW]
[ROW][C]49[/C][C]98.01[/C][C]98.8542609637219[/C][C]-0.844260963721865[/C][/ROW]
[ROW][C]50[/C][C]98.42[/C][C]98.408046807535[/C][C]0.0119531924649579[/C][/ROW]
[ROW][C]51[/C][C]98.2[/C][C]100.513652380936[/C][C]-2.31365238093571[/C][/ROW]
[ROW][C]52[/C][C]93.5[/C][C]98.0263885026735[/C][C]-4.52638850267354[/C][/ROW]
[ROW][C]53[/C][C]93.17[/C][C]92.2427588886102[/C][C]0.927241111389776[/C][/ROW]
[ROW][C]54[/C][C]93.42[/C][C]92.3327120660244[/C][C]1.0872879339756[/C][/ROW]
[ROW][C]55[/C][C]93.13[/C][C]90.1248480978996[/C][C]3.00515190210041[/C][/ROW]
[ROW][C]56[/C][C]92.31[/C][C]91.8870202806141[/C][C]0.422979719385879[/C][/ROW]
[ROW][C]57[/C][C]92.09[/C][C]92.1150212552678[/C][C]-0.0250212552678164[/C][/ROW]
[ROW][C]58[/C][C]92.62[/C][C]90.899509235441[/C][C]1.72049076455897[/C][/ROW]
[ROW][C]59[/C][C]91.43[/C][C]91.9574525734147[/C][C]-0.527452573414664[/C][/ROW]
[ROW][C]60[/C][C]89.38[/C][C]92.5110419856078[/C][C]-3.13104198560777[/C][/ROW]
[ROW][C]61[/C][C]86.21[/C][C]89.0295486836037[/C][C]-2.8195486836037[/C][/ROW]
[ROW][C]62[/C][C]86.65[/C][C]85.8655524612426[/C][C]0.784447538757433[/C][/ROW]
[ROW][C]63[/C][C]88.62[/C][C]88.0941497036141[/C][C]0.525850296385926[/C][/ROW]
[ROW][C]64[/C][C]87.3[/C][C]88.1387007451355[/C][C]-0.838700745135498[/C][/ROW]
[ROW][C]65[/C][C]88.33[/C][C]86.1789892527549[/C][C]2.15101074724505[/C][/ROW]
[ROW][C]66[/C][C]88.67[/C][C]87.7762579172276[/C][C]0.89374208277242[/C][/ROW]
[ROW][C]67[/C][C]88.23[/C][C]85.6350952003001[/C][C]2.59490479969992[/C][/ROW]
[ROW][C]68[/C][C]88.85[/C][C]87.1978824743409[/C][C]1.65211752565914[/C][/ROW]
[ROW][C]69[/C][C]90.38[/C][C]89.0138451480659[/C][C]1.36615485193407[/C][/ROW]
[ROW][C]70[/C][C]89.65[/C][C]89.7158007461731[/C][C]-0.0658007461730534[/C][/ROW]
[ROW][C]71[/C][C]89.2[/C][C]89.2987130879348[/C][C]-0.0987130879347546[/C][/ROW]
[ROW][C]72[/C][C]87.87[/C][C]90.64391349314[/C][C]-2.77391349314004[/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
1390.3783.31741452991457.05258547008549
1492.2193.0151943143218-0.80519431432181
1595.7596.4524329406812-0.702432940681177
1697.2997.9191251548443-0.629125154844289
1798.2998.844642046348-0.554642046348036
1899.51100.086208432041-0.576208432041156
1999.0498.64809535640480.391904643595225
2098.999.9156888950579-1.01568889505788
21100.74100.6505051775580.0894948224420062
22100.3101.508778425211-1.20877842521095
23101.68101.2441008901270.435899109872736
24101.3104.483657080931-3.18365708093135
25103.13102.6658300555150.464169944485306
26104.17104.897122778791-0.727122778790658
27105.98107.543759535276-1.56375953527618
28106.25107.176766592461-0.926766592460766
29104.01106.796453870231-2.78645387023121
30101.68104.529358216742-2.84935821674206
31101.9399.26760690243832.66239309756169
32104.41101.5285183129012.88148168709935
33105.51105.352469933980.157530066019646
34104.71105.47893315853-0.768933158530217
35103.14104.907203513142-1.76720351314158
36102.66104.931553633751-2.27155363375067
37102.68103.123524203921-0.443524203920887
38101.89103.435550116145-1.54555011614454
39101.37104.153665861574-2.78366586157392
40101.16101.309822490901-0.149822490901101
4199.34100.543037092267-1.20303709226661
4299.3598.88655068992090.463449310079127
4399.8896.36358999768023.51641000231982
4499.3199.00730663601750.302693363982485
4599.9199.47082772612960.439172273870412
4698.3999.1311946019959-0.741194601995929
4798.0297.84280408093790.177195919062072
4898.799.3012179836502-0.601217983650159
4998.0198.8542609637219-0.844260963721865
5098.4298.4080468075350.0119531924649579
5198.2100.513652380936-2.31365238093571
5293.598.0263885026735-4.52638850267354
5393.1792.24275888861020.927241111389776
5493.4292.33271206602441.0872879339756
5593.1390.12484809789963.00515190210041
5692.3191.88702028061410.422979719385879
5792.0992.1150212552678-0.0250212552678164
5892.6290.8995092354411.72049076455897
5991.4391.9574525734147-0.527452573414664
6089.3892.5110419856078-3.13104198560777
6186.2189.0295486836037-2.8195486836037
6286.6585.86555246124260.784447538757433
6388.6288.09414970361410.525850296385926
6487.388.1387007451355-0.838700745135498
6588.3386.17898925275492.15101074724505
6688.6787.77625791722760.89374208277242
6788.2385.63509520030012.59490479969992
6888.8587.19788247434091.65211752565914
6990.3889.01384514806591.36615485193407
7089.6589.7158007461731-0.0658007461730534
7189.289.2987130879348-0.0987130879347546
7287.8790.64391349314-2.77391349314004







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7387.92541076409184.163588379834191.6872331483479
7488.326238194848682.676927942413393.975548447284
7590.42123229227383.09318150167797.749283082869
7690.527476389697381.587772468907899.4671803104868
7790.094970487121779.5603242144377100.629616759806
7889.970797917879477.8344121937862102.107183641973
7987.257875348637173.5004156409583101.015335056316
8086.235369446061470.8302916487667101.640447243356
8186.209946876819169.126382734706103.293511018932
8285.192024307576766.3964648443362103.987583770817
8384.494935071667863.9522665616351105.0376035817
8485.604929169092163.2790961928032107.930762145381

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 87.925410764091 & 84.1635883798341 & 91.6872331483479 \tabularnewline
74 & 88.3262381948486 & 82.6769279424133 & 93.975548447284 \tabularnewline
75 & 90.421232292273 & 83.093181501677 & 97.749283082869 \tabularnewline
76 & 90.5274763896973 & 81.5877724689078 & 99.4671803104868 \tabularnewline
77 & 90.0949704871217 & 79.5603242144377 & 100.629616759806 \tabularnewline
78 & 89.9707979178794 & 77.8344121937862 & 102.107183641973 \tabularnewline
79 & 87.2578753486371 & 73.5004156409583 & 101.015335056316 \tabularnewline
80 & 86.2353694460614 & 70.8302916487667 & 101.640447243356 \tabularnewline
81 & 86.2099468768191 & 69.126382734706 & 103.293511018932 \tabularnewline
82 & 85.1920243075767 & 66.3964648443362 & 103.987583770817 \tabularnewline
83 & 84.4949350716678 & 63.9522665616351 & 105.0376035817 \tabularnewline
84 & 85.6049291690921 & 63.2790961928032 & 107.930762145381 \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]87.925410764091[/C][C]84.1635883798341[/C][C]91.6872331483479[/C][/ROW]
[ROW][C]74[/C][C]88.3262381948486[/C][C]82.6769279424133[/C][C]93.975548447284[/C][/ROW]
[ROW][C]75[/C][C]90.421232292273[/C][C]83.093181501677[/C][C]97.749283082869[/C][/ROW]
[ROW][C]76[/C][C]90.5274763896973[/C][C]81.5877724689078[/C][C]99.4671803104868[/C][/ROW]
[ROW][C]77[/C][C]90.0949704871217[/C][C]79.5603242144377[/C][C]100.629616759806[/C][/ROW]
[ROW][C]78[/C][C]89.9707979178794[/C][C]77.8344121937862[/C][C]102.107183641973[/C][/ROW]
[ROW][C]79[/C][C]87.2578753486371[/C][C]73.5004156409583[/C][C]101.015335056316[/C][/ROW]
[ROW][C]80[/C][C]86.2353694460614[/C][C]70.8302916487667[/C][C]101.640447243356[/C][/ROW]
[ROW][C]81[/C][C]86.2099468768191[/C][C]69.126382734706[/C][C]103.293511018932[/C][/ROW]
[ROW][C]82[/C][C]85.1920243075767[/C][C]66.3964648443362[/C][C]103.987583770817[/C][/ROW]
[ROW][C]83[/C][C]84.4949350716678[/C][C]63.9522665616351[/C][C]105.0376035817[/C][/ROW]
[ROW][C]84[/C][C]85.6049291690921[/C][C]63.2790961928032[/C][C]107.930762145381[/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
7387.92541076409184.163588379834191.6872331483479
7488.326238194848682.676927942413393.975548447284
7590.42123229227383.09318150167797.749283082869
7690.527476389697381.587772468907899.4671803104868
7790.094970487121779.5603242144377100.629616759806
7889.970797917879477.8344121937862102.107183641973
7987.257875348637173.5004156409583101.015335056316
8086.235369446061470.8302916487667101.640447243356
8186.209946876819169.126382734706103.293511018932
8285.192024307576766.3964648443362103.987583770817
8384.494935071667863.9522665616351105.0376035817
8485.604929169092163.2790961928032107.930762145381



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')