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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Dec 2009 10:51:35 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/03/t1259862719c9l0dhvblrdtm1n.htm/, Retrieved Sat, 20 Apr 2024 11:59:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62988, Retrieved Sat, 20 Apr 2024 11:59:23 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
- R PD      [Exponential Smoothing] [] [2009-12-03 17:51:35] [0f1f1142419956a95ff6f880845f2408] [Current]
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Dataseries X:
115.47
103.34
102.60
100.69
105.67
123.61
113.08
106.46
123.38
109.87
95.74
123.06
123.39
120.28
115.33
110.4
114.49
132.03
123.16
118.82
128.32
112.24
104.53
132.57
122.52
131.8
124.55
120.96
122.6
145.52
118.57
134.25
136.7
121.37
111.63
134.42
137.65
137.86
119.77
130.69
128.28
147.45
128.42
136.9
143.95
135.64
122.48
136.83
153.04
142.71
123.46
144.37
146.15
147.61
158.51
147.4
165.05
154.64
126.2
157.36
154.15
123.21
113.07
110.45
113.57
122.44
114.93
111.85
126.04
121.34




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62988&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62988&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.558149525043339
beta0
gamma0.210439498485435

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.558149525043339 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.210439498485435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62988&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]0.558149525043339[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.210439498485435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62988&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
alpha0.558149525043339
beta0
gamma0.210439498485435







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13123.39118.3241426282055.06585737179483
14120.28117.8782059151422.40179408485788
15115.33114.3194902104571.01050978954348
16110.4110.420479837141-0.0204798371409112
17114.49114.805606426700-0.315606426700157
18132.03132.178508250469-0.148508250469234
19123.16122.5734258419370.586574158062803
20118.82116.0165459972622.80345400273828
21128.32134.036599918303-5.71659991830336
22112.24117.172439789972-4.93243978997194
23104.53100.2888749314934.24112506850672
24132.57130.0292809417292.54071905827124
25122.52132.249143709074-9.72914370907434
26131.8123.2976721262778.50232787372252
27124.55123.0146009596191.53539904038105
28120.96119.312692977981.64730702201990
29122.6124.601252316458-2.00125231645791
30145.52141.0488489424914.47115105750910
31118.57134.090577197526-15.5205771975257
32134.25118.74963015220215.5003698477983
33136.7143.064243217082-6.36424321708157
34121.37125.911514687526-4.54151468752563
35111.63110.09912816571.53087183430006
36134.42138.168699121546-3.74869912154617
37137.65135.7372400171021.91275998289802
38137.86134.9789045870972.88109541290305
39119.77130.910540695208-11.1405406952082
40130.69120.14396848729210.5460315127081
41128.28130.060093438373-1.78009343837269
42147.45147.2329519261300.217048073869762
43128.42136.041367904197-7.62136790419717
44136.9127.9937750519478.9062249480534
45143.95146.594836496423-2.64483649642332
46135.64131.6875754498303.95242455017018
47122.48121.1807045343321.29929546566818
48136.83148.630112000102-11.8001120001017
49153.04142.23117889790110.8088211020988
50142.71146.528214288553-3.81821428855315
51123.46137.416862989954-13.9568629899545
52144.37127.09483987136617.2751601286337
53146.15139.6207072465086.52929275349192
54147.61161.617145485194-14.0071454851938
55158.51141.75749677886116.7525032211392
56147.4148.850950253000-1.45095025300023
57165.05160.5971093304424.4528906695584
58154.64150.2648730844384.37512691556196
59126.2139.747237942662-13.5472379426617
60157.36157.692040353663-0.332040353663331
61154.15159.796247726105-5.64624772610517
62123.21153.548831671235-30.3388316712351
63113.07128.692290509669-15.6222905096693
64110.45120.344750532434-9.89475053243387
65113.57116.706564421809-3.13656442180904
66122.44131.398473696496-8.9584736964959
67114.93117.216856779711-2.28685677971127
68111.85111.990892577709-0.140892577709209
69126.04125.0172153389951.02278466100462
70121.34112.7632363624798.57676363752145

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 123.39 & 118.324142628205 & 5.06585737179483 \tabularnewline
14 & 120.28 & 117.878205915142 & 2.40179408485788 \tabularnewline
15 & 115.33 & 114.319490210457 & 1.01050978954348 \tabularnewline
16 & 110.4 & 110.420479837141 & -0.0204798371409112 \tabularnewline
17 & 114.49 & 114.805606426700 & -0.315606426700157 \tabularnewline
18 & 132.03 & 132.178508250469 & -0.148508250469234 \tabularnewline
19 & 123.16 & 122.573425841937 & 0.586574158062803 \tabularnewline
20 & 118.82 & 116.016545997262 & 2.80345400273828 \tabularnewline
21 & 128.32 & 134.036599918303 & -5.71659991830336 \tabularnewline
22 & 112.24 & 117.172439789972 & -4.93243978997194 \tabularnewline
23 & 104.53 & 100.288874931493 & 4.24112506850672 \tabularnewline
24 & 132.57 & 130.029280941729 & 2.54071905827124 \tabularnewline
25 & 122.52 & 132.249143709074 & -9.72914370907434 \tabularnewline
26 & 131.8 & 123.297672126277 & 8.50232787372252 \tabularnewline
27 & 124.55 & 123.014600959619 & 1.53539904038105 \tabularnewline
28 & 120.96 & 119.31269297798 & 1.64730702201990 \tabularnewline
29 & 122.6 & 124.601252316458 & -2.00125231645791 \tabularnewline
30 & 145.52 & 141.048848942491 & 4.47115105750910 \tabularnewline
31 & 118.57 & 134.090577197526 & -15.5205771975257 \tabularnewline
32 & 134.25 & 118.749630152202 & 15.5003698477983 \tabularnewline
33 & 136.7 & 143.064243217082 & -6.36424321708157 \tabularnewline
34 & 121.37 & 125.911514687526 & -4.54151468752563 \tabularnewline
35 & 111.63 & 110.0991281657 & 1.53087183430006 \tabularnewline
36 & 134.42 & 138.168699121546 & -3.74869912154617 \tabularnewline
37 & 137.65 & 135.737240017102 & 1.91275998289802 \tabularnewline
38 & 137.86 & 134.978904587097 & 2.88109541290305 \tabularnewline
39 & 119.77 & 130.910540695208 & -11.1405406952082 \tabularnewline
40 & 130.69 & 120.143968487292 & 10.5460315127081 \tabularnewline
41 & 128.28 & 130.060093438373 & -1.78009343837269 \tabularnewline
42 & 147.45 & 147.232951926130 & 0.217048073869762 \tabularnewline
43 & 128.42 & 136.041367904197 & -7.62136790419717 \tabularnewline
44 & 136.9 & 127.993775051947 & 8.9062249480534 \tabularnewline
45 & 143.95 & 146.594836496423 & -2.64483649642332 \tabularnewline
46 & 135.64 & 131.687575449830 & 3.95242455017018 \tabularnewline
47 & 122.48 & 121.180704534332 & 1.29929546566818 \tabularnewline
48 & 136.83 & 148.630112000102 & -11.8001120001017 \tabularnewline
49 & 153.04 & 142.231178897901 & 10.8088211020988 \tabularnewline
50 & 142.71 & 146.528214288553 & -3.81821428855315 \tabularnewline
51 & 123.46 & 137.416862989954 & -13.9568629899545 \tabularnewline
52 & 144.37 & 127.094839871366 & 17.2751601286337 \tabularnewline
53 & 146.15 & 139.620707246508 & 6.52929275349192 \tabularnewline
54 & 147.61 & 161.617145485194 & -14.0071454851938 \tabularnewline
55 & 158.51 & 141.757496778861 & 16.7525032211392 \tabularnewline
56 & 147.4 & 148.850950253000 & -1.45095025300023 \tabularnewline
57 & 165.05 & 160.597109330442 & 4.4528906695584 \tabularnewline
58 & 154.64 & 150.264873084438 & 4.37512691556196 \tabularnewline
59 & 126.2 & 139.747237942662 & -13.5472379426617 \tabularnewline
60 & 157.36 & 157.692040353663 & -0.332040353663331 \tabularnewline
61 & 154.15 & 159.796247726105 & -5.64624772610517 \tabularnewline
62 & 123.21 & 153.548831671235 & -30.3388316712351 \tabularnewline
63 & 113.07 & 128.692290509669 & -15.6222905096693 \tabularnewline
64 & 110.45 & 120.344750532434 & -9.89475053243387 \tabularnewline
65 & 113.57 & 116.706564421809 & -3.13656442180904 \tabularnewline
66 & 122.44 & 131.398473696496 & -8.9584736964959 \tabularnewline
67 & 114.93 & 117.216856779711 & -2.28685677971127 \tabularnewline
68 & 111.85 & 111.990892577709 & -0.140892577709209 \tabularnewline
69 & 126.04 & 125.017215338995 & 1.02278466100462 \tabularnewline
70 & 121.34 & 112.763236362479 & 8.57676363752145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62988&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]123.39[/C][C]118.324142628205[/C][C]5.06585737179483[/C][/ROW]
[ROW][C]14[/C][C]120.28[/C][C]117.878205915142[/C][C]2.40179408485788[/C][/ROW]
[ROW][C]15[/C][C]115.33[/C][C]114.319490210457[/C][C]1.01050978954348[/C][/ROW]
[ROW][C]16[/C][C]110.4[/C][C]110.420479837141[/C][C]-0.0204798371409112[/C][/ROW]
[ROW][C]17[/C][C]114.49[/C][C]114.805606426700[/C][C]-0.315606426700157[/C][/ROW]
[ROW][C]18[/C][C]132.03[/C][C]132.178508250469[/C][C]-0.148508250469234[/C][/ROW]
[ROW][C]19[/C][C]123.16[/C][C]122.573425841937[/C][C]0.586574158062803[/C][/ROW]
[ROW][C]20[/C][C]118.82[/C][C]116.016545997262[/C][C]2.80345400273828[/C][/ROW]
[ROW][C]21[/C][C]128.32[/C][C]134.036599918303[/C][C]-5.71659991830336[/C][/ROW]
[ROW][C]22[/C][C]112.24[/C][C]117.172439789972[/C][C]-4.93243978997194[/C][/ROW]
[ROW][C]23[/C][C]104.53[/C][C]100.288874931493[/C][C]4.24112506850672[/C][/ROW]
[ROW][C]24[/C][C]132.57[/C][C]130.029280941729[/C][C]2.54071905827124[/C][/ROW]
[ROW][C]25[/C][C]122.52[/C][C]132.249143709074[/C][C]-9.72914370907434[/C][/ROW]
[ROW][C]26[/C][C]131.8[/C][C]123.297672126277[/C][C]8.50232787372252[/C][/ROW]
[ROW][C]27[/C][C]124.55[/C][C]123.014600959619[/C][C]1.53539904038105[/C][/ROW]
[ROW][C]28[/C][C]120.96[/C][C]119.31269297798[/C][C]1.64730702201990[/C][/ROW]
[ROW][C]29[/C][C]122.6[/C][C]124.601252316458[/C][C]-2.00125231645791[/C][/ROW]
[ROW][C]30[/C][C]145.52[/C][C]141.048848942491[/C][C]4.47115105750910[/C][/ROW]
[ROW][C]31[/C][C]118.57[/C][C]134.090577197526[/C][C]-15.5205771975257[/C][/ROW]
[ROW][C]32[/C][C]134.25[/C][C]118.749630152202[/C][C]15.5003698477983[/C][/ROW]
[ROW][C]33[/C][C]136.7[/C][C]143.064243217082[/C][C]-6.36424321708157[/C][/ROW]
[ROW][C]34[/C][C]121.37[/C][C]125.911514687526[/C][C]-4.54151468752563[/C][/ROW]
[ROW][C]35[/C][C]111.63[/C][C]110.0991281657[/C][C]1.53087183430006[/C][/ROW]
[ROW][C]36[/C][C]134.42[/C][C]138.168699121546[/C][C]-3.74869912154617[/C][/ROW]
[ROW][C]37[/C][C]137.65[/C][C]135.737240017102[/C][C]1.91275998289802[/C][/ROW]
[ROW][C]38[/C][C]137.86[/C][C]134.978904587097[/C][C]2.88109541290305[/C][/ROW]
[ROW][C]39[/C][C]119.77[/C][C]130.910540695208[/C][C]-11.1405406952082[/C][/ROW]
[ROW][C]40[/C][C]130.69[/C][C]120.143968487292[/C][C]10.5460315127081[/C][/ROW]
[ROW][C]41[/C][C]128.28[/C][C]130.060093438373[/C][C]-1.78009343837269[/C][/ROW]
[ROW][C]42[/C][C]147.45[/C][C]147.232951926130[/C][C]0.217048073869762[/C][/ROW]
[ROW][C]43[/C][C]128.42[/C][C]136.041367904197[/C][C]-7.62136790419717[/C][/ROW]
[ROW][C]44[/C][C]136.9[/C][C]127.993775051947[/C][C]8.9062249480534[/C][/ROW]
[ROW][C]45[/C][C]143.95[/C][C]146.594836496423[/C][C]-2.64483649642332[/C][/ROW]
[ROW][C]46[/C][C]135.64[/C][C]131.687575449830[/C][C]3.95242455017018[/C][/ROW]
[ROW][C]47[/C][C]122.48[/C][C]121.180704534332[/C][C]1.29929546566818[/C][/ROW]
[ROW][C]48[/C][C]136.83[/C][C]148.630112000102[/C][C]-11.8001120001017[/C][/ROW]
[ROW][C]49[/C][C]153.04[/C][C]142.231178897901[/C][C]10.8088211020988[/C][/ROW]
[ROW][C]50[/C][C]142.71[/C][C]146.528214288553[/C][C]-3.81821428855315[/C][/ROW]
[ROW][C]51[/C][C]123.46[/C][C]137.416862989954[/C][C]-13.9568629899545[/C][/ROW]
[ROW][C]52[/C][C]144.37[/C][C]127.094839871366[/C][C]17.2751601286337[/C][/ROW]
[ROW][C]53[/C][C]146.15[/C][C]139.620707246508[/C][C]6.52929275349192[/C][/ROW]
[ROW][C]54[/C][C]147.61[/C][C]161.617145485194[/C][C]-14.0071454851938[/C][/ROW]
[ROW][C]55[/C][C]158.51[/C][C]141.757496778861[/C][C]16.7525032211392[/C][/ROW]
[ROW][C]56[/C][C]147.4[/C][C]148.850950253000[/C][C]-1.45095025300023[/C][/ROW]
[ROW][C]57[/C][C]165.05[/C][C]160.597109330442[/C][C]4.4528906695584[/C][/ROW]
[ROW][C]58[/C][C]154.64[/C][C]150.264873084438[/C][C]4.37512691556196[/C][/ROW]
[ROW][C]59[/C][C]126.2[/C][C]139.747237942662[/C][C]-13.5472379426617[/C][/ROW]
[ROW][C]60[/C][C]157.36[/C][C]157.692040353663[/C][C]-0.332040353663331[/C][/ROW]
[ROW][C]61[/C][C]154.15[/C][C]159.796247726105[/C][C]-5.64624772610517[/C][/ROW]
[ROW][C]62[/C][C]123.21[/C][C]153.548831671235[/C][C]-30.3388316712351[/C][/ROW]
[ROW][C]63[/C][C]113.07[/C][C]128.692290509669[/C][C]-15.6222905096693[/C][/ROW]
[ROW][C]64[/C][C]110.45[/C][C]120.344750532434[/C][C]-9.89475053243387[/C][/ROW]
[ROW][C]65[/C][C]113.57[/C][C]116.706564421809[/C][C]-3.13656442180904[/C][/ROW]
[ROW][C]66[/C][C]122.44[/C][C]131.398473696496[/C][C]-8.9584736964959[/C][/ROW]
[ROW][C]67[/C][C]114.93[/C][C]117.216856779711[/C][C]-2.28685677971127[/C][/ROW]
[ROW][C]68[/C][C]111.85[/C][C]111.990892577709[/C][C]-0.140892577709209[/C][/ROW]
[ROW][C]69[/C][C]126.04[/C][C]125.017215338995[/C][C]1.02278466100462[/C][/ROW]
[ROW][C]70[/C][C]121.34[/C][C]112.763236362479[/C][C]8.57676363752145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62988&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62988&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
13123.39118.3241426282055.06585737179483
14120.28117.8782059151422.40179408485788
15115.33114.3194902104571.01050978954348
16110.4110.420479837141-0.0204798371409112
17114.49114.805606426700-0.315606426700157
18132.03132.178508250469-0.148508250469234
19123.16122.5734258419370.586574158062803
20118.82116.0165459972622.80345400273828
21128.32134.036599918303-5.71659991830336
22112.24117.172439789972-4.93243978997194
23104.53100.2888749314934.24112506850672
24132.57130.0292809417292.54071905827124
25122.52132.249143709074-9.72914370907434
26131.8123.2976721262778.50232787372252
27124.55123.0146009596191.53539904038105
28120.96119.312692977981.64730702201990
29122.6124.601252316458-2.00125231645791
30145.52141.0488489424914.47115105750910
31118.57134.090577197526-15.5205771975257
32134.25118.74963015220215.5003698477983
33136.7143.064243217082-6.36424321708157
34121.37125.911514687526-4.54151468752563
35111.63110.09912816571.53087183430006
36134.42138.168699121546-3.74869912154617
37137.65135.7372400171021.91275998289802
38137.86134.9789045870972.88109541290305
39119.77130.910540695208-11.1405406952082
40130.69120.14396848729210.5460315127081
41128.28130.060093438373-1.78009343837269
42147.45147.2329519261300.217048073869762
43128.42136.041367904197-7.62136790419717
44136.9127.9937750519478.9062249480534
45143.95146.594836496423-2.64483649642332
46135.64131.6875754498303.95242455017018
47122.48121.1807045343321.29929546566818
48136.83148.630112000102-11.8001120001017
49153.04142.23117889790110.8088211020988
50142.71146.528214288553-3.81821428855315
51123.46137.416862989954-13.9568629899545
52144.37127.09483987136617.2751601286337
53146.15139.6207072465086.52929275349192
54147.61161.617145485194-14.0071454851938
55158.51141.75749677886116.7525032211392
56147.4148.850950253000-1.45095025300023
57165.05160.5971093304424.4528906695584
58154.64150.2648730844384.37512691556196
59126.2139.747237942662-13.5472379426617
60157.36157.692040353663-0.332040353663331
61154.15159.796247726105-5.64624772610517
62123.21153.548831671235-30.3388316712351
63113.07128.692290509669-15.6222905096693
64110.45120.344750532434-9.89475053243387
65113.57116.706564421809-3.13656442180904
66122.44131.398473696496-8.9584736964959
67114.93117.216856779711-2.28685677971127
68111.85111.990892577709-0.140892577709209
69126.04125.0172153389951.02278466100462
70121.34112.7632363624798.57676363752145







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
71102.92427123133886.1005462509806119.747996211696
72129.659244039039110.392362704154148.926125373924
73131.454649736528110.021317971952152.887981501104
74126.062698762572102.662640970160149.462756554983
75119.50814717969194.2943077488146144.721986610568
76120.41274389092893.5071182151721147.318369566683
77122.92570310622794.4285508421546151.422855370299
78138.826946942014108.822569239426168.831324644602
79130.2658434344998.826414758425161.705272110555
80126.51582500172393.7040486152604159.327601388185
81139.728988847396105.600003163771173.85797453102
82127.60653315674892.2093205835683163.003745729928

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
71 & 102.924271231338 & 86.1005462509806 & 119.747996211696 \tabularnewline
72 & 129.659244039039 & 110.392362704154 & 148.926125373924 \tabularnewline
73 & 131.454649736528 & 110.021317971952 & 152.887981501104 \tabularnewline
74 & 126.062698762572 & 102.662640970160 & 149.462756554983 \tabularnewline
75 & 119.508147179691 & 94.2943077488146 & 144.721986610568 \tabularnewline
76 & 120.412743890928 & 93.5071182151721 & 147.318369566683 \tabularnewline
77 & 122.925703106227 & 94.4285508421546 & 151.422855370299 \tabularnewline
78 & 138.826946942014 & 108.822569239426 & 168.831324644602 \tabularnewline
79 & 130.26584343449 & 98.826414758425 & 161.705272110555 \tabularnewline
80 & 126.515825001723 & 93.7040486152604 & 159.327601388185 \tabularnewline
81 & 139.728988847396 & 105.600003163771 & 173.85797453102 \tabularnewline
82 & 127.606533156748 & 92.2093205835683 & 163.003745729928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62988&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]71[/C][C]102.924271231338[/C][C]86.1005462509806[/C][C]119.747996211696[/C][/ROW]
[ROW][C]72[/C][C]129.659244039039[/C][C]110.392362704154[/C][C]148.926125373924[/C][/ROW]
[ROW][C]73[/C][C]131.454649736528[/C][C]110.021317971952[/C][C]152.887981501104[/C][/ROW]
[ROW][C]74[/C][C]126.062698762572[/C][C]102.662640970160[/C][C]149.462756554983[/C][/ROW]
[ROW][C]75[/C][C]119.508147179691[/C][C]94.2943077488146[/C][C]144.721986610568[/C][/ROW]
[ROW][C]76[/C][C]120.412743890928[/C][C]93.5071182151721[/C][C]147.318369566683[/C][/ROW]
[ROW][C]77[/C][C]122.925703106227[/C][C]94.4285508421546[/C][C]151.422855370299[/C][/ROW]
[ROW][C]78[/C][C]138.826946942014[/C][C]108.822569239426[/C][C]168.831324644602[/C][/ROW]
[ROW][C]79[/C][C]130.26584343449[/C][C]98.826414758425[/C][C]161.705272110555[/C][/ROW]
[ROW][C]80[/C][C]126.515825001723[/C][C]93.7040486152604[/C][C]159.327601388185[/C][/ROW]
[ROW][C]81[/C][C]139.728988847396[/C][C]105.600003163771[/C][C]173.85797453102[/C][/ROW]
[ROW][C]82[/C][C]127.606533156748[/C][C]92.2093205835683[/C][C]163.003745729928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62988&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62988&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
71102.92427123133886.1005462509806119.747996211696
72129.659244039039110.392362704154148.926125373924
73131.454649736528110.021317971952152.887981501104
74126.062698762572102.662640970160149.462756554983
75119.50814717969194.2943077488146144.721986610568
76120.41274389092893.5071182151721147.318369566683
77122.92570310622794.4285508421546151.422855370299
78138.826946942014108.822569239426168.831324644602
79130.2658434344998.826414758425161.705272110555
80126.51582500172393.7040486152604159.327601388185
81139.728988847396105.600003163771173.85797453102
82127.60653315674892.2093205835683163.003745729928



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')