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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 24 Apr 2016 20:10:30 +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/2016/Apr/24/t1461525076ca5qkuz7n1brnq6.htm/, Retrieved Tue, 30 Apr 2024 16:05:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294657, Retrieved Tue, 30 Apr 2024 16:05:05 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-04-24 19:10:30] [214f5f03d61b6cc2dcf3be3cf135b694] [Current]
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Dataseries X:
78,21
75,50
79,87
85,76
77,02
75,47
75,29
77,52
78,44
83,50
86,29
92,14
96,91
104,23
114,60
122,09
114,52
113,77
117,03
109,84
109,90
108,74
110,49
107,82
111,26
119,06
124,54
120,60
110,28
95,93
102,72
112,68
113,03
111,48
109,56
109,16
112,32
116,08
109,63
109,63
103,27
103,32
107,38
110,45
111,24
109,44
107,94
110,58
107,31
108,70
107,70
108,08
109,32
111,95
108,07
103,38
98,54
88,16
79,70
63,30




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294657&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294657&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294657&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999935045734029
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999935045734029 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294657&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]0.999935045734029[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294657&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294657&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
alpha0.999935045734029
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
275.578.21-2.70999999999999
379.8775.50017602606084.36982397393922
485.7679.86971616129145.89028383870864
577.0285.7596174009369-8.73961740093691
675.4777.0205676754331-1.55056767543314
775.2975.4701007159852-0.180100715985191
877.5275.29001169830982.22998830169018
978.4477.51985515274670.920144847253269
1083.578.43994023266695.06005976733314
1186.2983.4996713275322.79032867246796
1292.1486.28981875624935.85018124375074
1396.9192.13962000577154.77037999422848
14104.2396.90969014346917.32030985653093
15114.6104.22952451464710.3704754853534
16122.09114.5993263933777.49067360662292
17114.52122.089513448794-7.56951344879427
18113.77114.52049167219-0.750491672189824
19117.03113.7700487476363.25995125236432
20109.84117.029788252259-7.18978825225931
21109.9109.8404670074180.0595329925815946
22108.74109.899996133078-1.15999613307818
23110.49108.7400753466971.74992465330264
24107.82110.489886334929-2.66988633492865
25111.26107.8201734205073.4398265794929
26119.06111.2597765685897.80022343141054
27124.54119.0594933422135.48050665778739
28120.6124.539644017713-3.93964401771291
29110.28120.600255896685-10.3202558966854
3095.93110.280670344646-14.3506703446464
31102.7295.93093213725846.78906786274156
32112.68102.719559021089.96044097891965
33113.03112.6793530268670.350646973132527
34111.48113.029977223983-1.54997722398323
35109.56111.480100677633-1.92010067763286
36109.16109.56012471873-0.400124718730112
37112.32109.1600259898073.1599740101926
38116.08112.3197947462083.76020525379234
39109.63116.079755758628-6.44975575862784
40109.63109.630418939151-0.000418939151003883
41103.27109.630000027212-6.3600000272119
42103.32103.2704131091330.0495868908666495
43107.38103.319996779124.06000322088011
44110.45107.3797362854713.07026371452905
45111.24110.4498005732740.790199426725906
46109.44111.239948673176-1.79994867317626
47107.94109.440116914345-1.50011691434484
48110.58107.9400974389932.63990256100696
49107.31110.579828527067-3.26982852706691
50108.7107.3102123893121.38978761068817
51107.7108.699909727366-0.999909727365889
52108.08107.7000649484020.379935051597627
53109.32108.0799753215981.24002467840239
54111.95109.3199194551072.63008054489279
55108.07111.949829165049-3.87982916504878
56103.38108.070252011455-4.6902520114555
5798.54103.380304651877-4.84030465187661
5888.1698.5403143984358-10.3803143984358
5979.788.1606742457023-8.46067424570229
6063.379.7005495568852-16.4005495568853

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 75.5 & 78.21 & -2.70999999999999 \tabularnewline
3 & 79.87 & 75.5001760260608 & 4.36982397393922 \tabularnewline
4 & 85.76 & 79.8697161612914 & 5.89028383870864 \tabularnewline
5 & 77.02 & 85.7596174009369 & -8.73961740093691 \tabularnewline
6 & 75.47 & 77.0205676754331 & -1.55056767543314 \tabularnewline
7 & 75.29 & 75.4701007159852 & -0.180100715985191 \tabularnewline
8 & 77.52 & 75.2900116983098 & 2.22998830169018 \tabularnewline
9 & 78.44 & 77.5198551527467 & 0.920144847253269 \tabularnewline
10 & 83.5 & 78.4399402326669 & 5.06005976733314 \tabularnewline
11 & 86.29 & 83.499671327532 & 2.79032867246796 \tabularnewline
12 & 92.14 & 86.2898187562493 & 5.85018124375074 \tabularnewline
13 & 96.91 & 92.1396200057715 & 4.77037999422848 \tabularnewline
14 & 104.23 & 96.9096901434691 & 7.32030985653093 \tabularnewline
15 & 114.6 & 104.229524514647 & 10.3704754853534 \tabularnewline
16 & 122.09 & 114.599326393377 & 7.49067360662292 \tabularnewline
17 & 114.52 & 122.089513448794 & -7.56951344879427 \tabularnewline
18 & 113.77 & 114.52049167219 & -0.750491672189824 \tabularnewline
19 & 117.03 & 113.770048747636 & 3.25995125236432 \tabularnewline
20 & 109.84 & 117.029788252259 & -7.18978825225931 \tabularnewline
21 & 109.9 & 109.840467007418 & 0.0595329925815946 \tabularnewline
22 & 108.74 & 109.899996133078 & -1.15999613307818 \tabularnewline
23 & 110.49 & 108.740075346697 & 1.74992465330264 \tabularnewline
24 & 107.82 & 110.489886334929 & -2.66988633492865 \tabularnewline
25 & 111.26 & 107.820173420507 & 3.4398265794929 \tabularnewline
26 & 119.06 & 111.259776568589 & 7.80022343141054 \tabularnewline
27 & 124.54 & 119.059493342213 & 5.48050665778739 \tabularnewline
28 & 120.6 & 124.539644017713 & -3.93964401771291 \tabularnewline
29 & 110.28 & 120.600255896685 & -10.3202558966854 \tabularnewline
30 & 95.93 & 110.280670344646 & -14.3506703446464 \tabularnewline
31 & 102.72 & 95.9309321372584 & 6.78906786274156 \tabularnewline
32 & 112.68 & 102.71955902108 & 9.96044097891965 \tabularnewline
33 & 113.03 & 112.679353026867 & 0.350646973132527 \tabularnewline
34 & 111.48 & 113.029977223983 & -1.54997722398323 \tabularnewline
35 & 109.56 & 111.480100677633 & -1.92010067763286 \tabularnewline
36 & 109.16 & 109.56012471873 & -0.400124718730112 \tabularnewline
37 & 112.32 & 109.160025989807 & 3.1599740101926 \tabularnewline
38 & 116.08 & 112.319794746208 & 3.76020525379234 \tabularnewline
39 & 109.63 & 116.079755758628 & -6.44975575862784 \tabularnewline
40 & 109.63 & 109.630418939151 & -0.000418939151003883 \tabularnewline
41 & 103.27 & 109.630000027212 & -6.3600000272119 \tabularnewline
42 & 103.32 & 103.270413109133 & 0.0495868908666495 \tabularnewline
43 & 107.38 & 103.31999677912 & 4.06000322088011 \tabularnewline
44 & 110.45 & 107.379736285471 & 3.07026371452905 \tabularnewline
45 & 111.24 & 110.449800573274 & 0.790199426725906 \tabularnewline
46 & 109.44 & 111.239948673176 & -1.79994867317626 \tabularnewline
47 & 107.94 & 109.440116914345 & -1.50011691434484 \tabularnewline
48 & 110.58 & 107.940097438993 & 2.63990256100696 \tabularnewline
49 & 107.31 & 110.579828527067 & -3.26982852706691 \tabularnewline
50 & 108.7 & 107.310212389312 & 1.38978761068817 \tabularnewline
51 & 107.7 & 108.699909727366 & -0.999909727365889 \tabularnewline
52 & 108.08 & 107.700064948402 & 0.379935051597627 \tabularnewline
53 & 109.32 & 108.079975321598 & 1.24002467840239 \tabularnewline
54 & 111.95 & 109.319919455107 & 2.63008054489279 \tabularnewline
55 & 108.07 & 111.949829165049 & -3.87982916504878 \tabularnewline
56 & 103.38 & 108.070252011455 & -4.6902520114555 \tabularnewline
57 & 98.54 & 103.380304651877 & -4.84030465187661 \tabularnewline
58 & 88.16 & 98.5403143984358 & -10.3803143984358 \tabularnewline
59 & 79.7 & 88.1606742457023 & -8.46067424570229 \tabularnewline
60 & 63.3 & 79.7005495568852 & -16.4005495568853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294657&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]75.5[/C][C]78.21[/C][C]-2.70999999999999[/C][/ROW]
[ROW][C]3[/C][C]79.87[/C][C]75.5001760260608[/C][C]4.36982397393922[/C][/ROW]
[ROW][C]4[/C][C]85.76[/C][C]79.8697161612914[/C][C]5.89028383870864[/C][/ROW]
[ROW][C]5[/C][C]77.02[/C][C]85.7596174009369[/C][C]-8.73961740093691[/C][/ROW]
[ROW][C]6[/C][C]75.47[/C][C]77.0205676754331[/C][C]-1.55056767543314[/C][/ROW]
[ROW][C]7[/C][C]75.29[/C][C]75.4701007159852[/C][C]-0.180100715985191[/C][/ROW]
[ROW][C]8[/C][C]77.52[/C][C]75.2900116983098[/C][C]2.22998830169018[/C][/ROW]
[ROW][C]9[/C][C]78.44[/C][C]77.5198551527467[/C][C]0.920144847253269[/C][/ROW]
[ROW][C]10[/C][C]83.5[/C][C]78.4399402326669[/C][C]5.06005976733314[/C][/ROW]
[ROW][C]11[/C][C]86.29[/C][C]83.499671327532[/C][C]2.79032867246796[/C][/ROW]
[ROW][C]12[/C][C]92.14[/C][C]86.2898187562493[/C][C]5.85018124375074[/C][/ROW]
[ROW][C]13[/C][C]96.91[/C][C]92.1396200057715[/C][C]4.77037999422848[/C][/ROW]
[ROW][C]14[/C][C]104.23[/C][C]96.9096901434691[/C][C]7.32030985653093[/C][/ROW]
[ROW][C]15[/C][C]114.6[/C][C]104.229524514647[/C][C]10.3704754853534[/C][/ROW]
[ROW][C]16[/C][C]122.09[/C][C]114.599326393377[/C][C]7.49067360662292[/C][/ROW]
[ROW][C]17[/C][C]114.52[/C][C]122.089513448794[/C][C]-7.56951344879427[/C][/ROW]
[ROW][C]18[/C][C]113.77[/C][C]114.52049167219[/C][C]-0.750491672189824[/C][/ROW]
[ROW][C]19[/C][C]117.03[/C][C]113.770048747636[/C][C]3.25995125236432[/C][/ROW]
[ROW][C]20[/C][C]109.84[/C][C]117.029788252259[/C][C]-7.18978825225931[/C][/ROW]
[ROW][C]21[/C][C]109.9[/C][C]109.840467007418[/C][C]0.0595329925815946[/C][/ROW]
[ROW][C]22[/C][C]108.74[/C][C]109.899996133078[/C][C]-1.15999613307818[/C][/ROW]
[ROW][C]23[/C][C]110.49[/C][C]108.740075346697[/C][C]1.74992465330264[/C][/ROW]
[ROW][C]24[/C][C]107.82[/C][C]110.489886334929[/C][C]-2.66988633492865[/C][/ROW]
[ROW][C]25[/C][C]111.26[/C][C]107.820173420507[/C][C]3.4398265794929[/C][/ROW]
[ROW][C]26[/C][C]119.06[/C][C]111.259776568589[/C][C]7.80022343141054[/C][/ROW]
[ROW][C]27[/C][C]124.54[/C][C]119.059493342213[/C][C]5.48050665778739[/C][/ROW]
[ROW][C]28[/C][C]120.6[/C][C]124.539644017713[/C][C]-3.93964401771291[/C][/ROW]
[ROW][C]29[/C][C]110.28[/C][C]120.600255896685[/C][C]-10.3202558966854[/C][/ROW]
[ROW][C]30[/C][C]95.93[/C][C]110.280670344646[/C][C]-14.3506703446464[/C][/ROW]
[ROW][C]31[/C][C]102.72[/C][C]95.9309321372584[/C][C]6.78906786274156[/C][/ROW]
[ROW][C]32[/C][C]112.68[/C][C]102.71955902108[/C][C]9.96044097891965[/C][/ROW]
[ROW][C]33[/C][C]113.03[/C][C]112.679353026867[/C][C]0.350646973132527[/C][/ROW]
[ROW][C]34[/C][C]111.48[/C][C]113.029977223983[/C][C]-1.54997722398323[/C][/ROW]
[ROW][C]35[/C][C]109.56[/C][C]111.480100677633[/C][C]-1.92010067763286[/C][/ROW]
[ROW][C]36[/C][C]109.16[/C][C]109.56012471873[/C][C]-0.400124718730112[/C][/ROW]
[ROW][C]37[/C][C]112.32[/C][C]109.160025989807[/C][C]3.1599740101926[/C][/ROW]
[ROW][C]38[/C][C]116.08[/C][C]112.319794746208[/C][C]3.76020525379234[/C][/ROW]
[ROW][C]39[/C][C]109.63[/C][C]116.079755758628[/C][C]-6.44975575862784[/C][/ROW]
[ROW][C]40[/C][C]109.63[/C][C]109.630418939151[/C][C]-0.000418939151003883[/C][/ROW]
[ROW][C]41[/C][C]103.27[/C][C]109.630000027212[/C][C]-6.3600000272119[/C][/ROW]
[ROW][C]42[/C][C]103.32[/C][C]103.270413109133[/C][C]0.0495868908666495[/C][/ROW]
[ROW][C]43[/C][C]107.38[/C][C]103.31999677912[/C][C]4.06000322088011[/C][/ROW]
[ROW][C]44[/C][C]110.45[/C][C]107.379736285471[/C][C]3.07026371452905[/C][/ROW]
[ROW][C]45[/C][C]111.24[/C][C]110.449800573274[/C][C]0.790199426725906[/C][/ROW]
[ROW][C]46[/C][C]109.44[/C][C]111.239948673176[/C][C]-1.79994867317626[/C][/ROW]
[ROW][C]47[/C][C]107.94[/C][C]109.440116914345[/C][C]-1.50011691434484[/C][/ROW]
[ROW][C]48[/C][C]110.58[/C][C]107.940097438993[/C][C]2.63990256100696[/C][/ROW]
[ROW][C]49[/C][C]107.31[/C][C]110.579828527067[/C][C]-3.26982852706691[/C][/ROW]
[ROW][C]50[/C][C]108.7[/C][C]107.310212389312[/C][C]1.38978761068817[/C][/ROW]
[ROW][C]51[/C][C]107.7[/C][C]108.699909727366[/C][C]-0.999909727365889[/C][/ROW]
[ROW][C]52[/C][C]108.08[/C][C]107.700064948402[/C][C]0.379935051597627[/C][/ROW]
[ROW][C]53[/C][C]109.32[/C][C]108.079975321598[/C][C]1.24002467840239[/C][/ROW]
[ROW][C]54[/C][C]111.95[/C][C]109.319919455107[/C][C]2.63008054489279[/C][/ROW]
[ROW][C]55[/C][C]108.07[/C][C]111.949829165049[/C][C]-3.87982916504878[/C][/ROW]
[ROW][C]56[/C][C]103.38[/C][C]108.070252011455[/C][C]-4.6902520114555[/C][/ROW]
[ROW][C]57[/C][C]98.54[/C][C]103.380304651877[/C][C]-4.84030465187661[/C][/ROW]
[ROW][C]58[/C][C]88.16[/C][C]98.5403143984358[/C][C]-10.3803143984358[/C][/ROW]
[ROW][C]59[/C][C]79.7[/C][C]88.1606742457023[/C][C]-8.46067424570229[/C][/ROW]
[ROW][C]60[/C][C]63.3[/C][C]79.7005495568852[/C][C]-16.4005495568853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294657&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294657&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
275.578.21-2.70999999999999
379.8775.50017602606084.36982397393922
485.7679.86971616129145.89028383870864
577.0285.7596174009369-8.73961740093691
675.4777.0205676754331-1.55056767543314
775.2975.4701007159852-0.180100715985191
877.5275.29001169830982.22998830169018
978.4477.51985515274670.920144847253269
1083.578.43994023266695.06005976733314
1186.2983.4996713275322.79032867246796
1292.1486.28981875624935.85018124375074
1396.9192.13962000577154.77037999422848
14104.2396.90969014346917.32030985653093
15114.6104.22952451464710.3704754853534
16122.09114.5993263933777.49067360662292
17114.52122.089513448794-7.56951344879427
18113.77114.52049167219-0.750491672189824
19117.03113.7700487476363.25995125236432
20109.84117.029788252259-7.18978825225931
21109.9109.8404670074180.0595329925815946
22108.74109.899996133078-1.15999613307818
23110.49108.7400753466971.74992465330264
24107.82110.489886334929-2.66988633492865
25111.26107.8201734205073.4398265794929
26119.06111.2597765685897.80022343141054
27124.54119.0594933422135.48050665778739
28120.6124.539644017713-3.93964401771291
29110.28120.600255896685-10.3202558966854
3095.93110.280670344646-14.3506703446464
31102.7295.93093213725846.78906786274156
32112.68102.719559021089.96044097891965
33113.03112.6793530268670.350646973132527
34111.48113.029977223983-1.54997722398323
35109.56111.480100677633-1.92010067763286
36109.16109.56012471873-0.400124718730112
37112.32109.1600259898073.1599740101926
38116.08112.3197947462083.76020525379234
39109.63116.079755758628-6.44975575862784
40109.63109.630418939151-0.000418939151003883
41103.27109.630000027212-6.3600000272119
42103.32103.2704131091330.0495868908666495
43107.38103.319996779124.06000322088011
44110.45107.3797362854713.07026371452905
45111.24110.4498005732740.790199426725906
46109.44111.239948673176-1.79994867317626
47107.94109.440116914345-1.50011691434484
48110.58107.9400974389932.63990256100696
49107.31110.579828527067-3.26982852706691
50108.7107.3102123893121.38978761068817
51107.7108.699909727366-0.999909727365889
52108.08107.7000649484020.379935051597627
53109.32108.0799753215981.24002467840239
54111.95109.3199194551072.63008054489279
55108.07111.949829165049-3.87982916504878
56103.38108.070252011455-4.6902520114555
5798.54103.380304651877-4.84030465187661
5888.1698.5403143984358-10.3803143984358
5979.788.1606742457023-8.46067424570229
6063.379.7005495568852-16.4005495568853







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6163.30106528565852.262086281163874.3400442901521
6263.30106528565847.690098470428478.9120321008875
6363.30106528565844.181820730740782.4203098405752
6463.30106528565841.22418281110485.3779477602119
6563.30106528565838.618440481156387.9836900901597
6663.30106528565836.262663064292690.3394675070234
6763.30106528565834.096298172584392.5058323987317
6863.30106528565832.079892188328694.5222383829874
6963.30106528565830.186040342017496.4160902292986
7063.30106528565828.394789281728998.207341289587
7163.30106528565826.691075775866999.911054795449
7263.30106528565825.0631971527254101.538933418591

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 63.301065285658 & 52.2620862811638 & 74.3400442901521 \tabularnewline
62 & 63.301065285658 & 47.6900984704284 & 78.9120321008875 \tabularnewline
63 & 63.301065285658 & 44.1818207307407 & 82.4203098405752 \tabularnewline
64 & 63.301065285658 & 41.224182811104 & 85.3779477602119 \tabularnewline
65 & 63.301065285658 & 38.6184404811563 & 87.9836900901597 \tabularnewline
66 & 63.301065285658 & 36.2626630642926 & 90.3394675070234 \tabularnewline
67 & 63.301065285658 & 34.0962981725843 & 92.5058323987317 \tabularnewline
68 & 63.301065285658 & 32.0798921883286 & 94.5222383829874 \tabularnewline
69 & 63.301065285658 & 30.1860403420174 & 96.4160902292986 \tabularnewline
70 & 63.301065285658 & 28.3947892817289 & 98.207341289587 \tabularnewline
71 & 63.301065285658 & 26.6910757758669 & 99.911054795449 \tabularnewline
72 & 63.301065285658 & 25.0631971527254 & 101.538933418591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294657&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]63.301065285658[/C][C]52.2620862811638[/C][C]74.3400442901521[/C][/ROW]
[ROW][C]62[/C][C]63.301065285658[/C][C]47.6900984704284[/C][C]78.9120321008875[/C][/ROW]
[ROW][C]63[/C][C]63.301065285658[/C][C]44.1818207307407[/C][C]82.4203098405752[/C][/ROW]
[ROW][C]64[/C][C]63.301065285658[/C][C]41.224182811104[/C][C]85.3779477602119[/C][/ROW]
[ROW][C]65[/C][C]63.301065285658[/C][C]38.6184404811563[/C][C]87.9836900901597[/C][/ROW]
[ROW][C]66[/C][C]63.301065285658[/C][C]36.2626630642926[/C][C]90.3394675070234[/C][/ROW]
[ROW][C]67[/C][C]63.301065285658[/C][C]34.0962981725843[/C][C]92.5058323987317[/C][/ROW]
[ROW][C]68[/C][C]63.301065285658[/C][C]32.0798921883286[/C][C]94.5222383829874[/C][/ROW]
[ROW][C]69[/C][C]63.301065285658[/C][C]30.1860403420174[/C][C]96.4160902292986[/C][/ROW]
[ROW][C]70[/C][C]63.301065285658[/C][C]28.3947892817289[/C][C]98.207341289587[/C][/ROW]
[ROW][C]71[/C][C]63.301065285658[/C][C]26.6910757758669[/C][C]99.911054795449[/C][/ROW]
[ROW][C]72[/C][C]63.301065285658[/C][C]25.0631971527254[/C][C]101.538933418591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294657&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294657&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
6163.30106528565852.262086281163874.3400442901521
6263.30106528565847.690098470428478.9120321008875
6363.30106528565844.181820730740782.4203098405752
6463.30106528565841.22418281110485.3779477602119
6563.30106528565838.618440481156387.9836900901597
6663.30106528565836.262663064292690.3394675070234
6763.30106528565834.096298172584392.5058323987317
6863.30106528565832.079892188328694.5222383829874
6963.30106528565830.186040342017496.4160902292986
7063.30106528565828.394789281728998.207341289587
7163.30106528565826.691075775866999.911054795449
7263.30106528565825.0631971527254101.538933418591



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