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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 computationFri, 14 Dec 2012 10:11:56 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/14/t1355497929m0a8th4ad5u7tl0.htm/, Retrieved Thu, 25 Apr 2024 21:53:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=199624, Retrieved Thu, 25 Apr 2024 21:53:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-14 15:11:56] [195a7509fef65339447329cdcf8835cc] [Current]
- R PD    [Exponential Smoothing] [] [2012-12-19 15:07:49] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
59,8
60,7
59,7
60,2
61,3
59,8
61,2
59,3
59,4
63,1
68
69,4
70,2
72,6
72,1
69,7
71,5
75,7
76
76,4
83,8
86,2
88,5
95,9
103,1
113,5
115,7
113,1
112,7
121,9
120,3
108,7
102,8
83,4
79,4
77,8
85,7
83,2
82
86,9
95,7
97,9
89,3
91,5
86,8
91
93,8
96,8
95,7
91,4
88,7
88,2
87,7
89,5
95,6
100,5
106,3
112
117,7
125
132,4
138,1
134,7
136,7
134,3
131,6
129,8
131,9
129,8
119,4
116,7
112,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199624&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199624&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199624&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199624&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[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199624&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199624&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1370.264.03555021367526.16444978632481
1472.672.5947989510490.00520104895103657
1572.171.69479895104890.405201048951056
1669.769.04479895104890.655201048951056
1771.571.0072989510490.492701048951048
1875.775.06563228438230.634367715617728
197677.3781322843823-1.37813228438229
2076.474.49479895104891.90520104895107
2183.876.81146561771566.98853438228437
2286.287.9114656177156-1.7114656177156
2388.591.6031322843823-3.1031322843823
2495.990.13646561771565.76353438228438
25103.196.74479895104896.35520104895106
26113.5105.4947989510498.00520104895105
27115.7112.5947989510493.10520104895106
28113.1112.6447989510490.455201048951039
29112.7114.407298951049-1.70729895104894
30121.9116.2656322843825.63436771561773
31120.3123.578132284382-3.27813228438229
32108.7118.794798951049-10.0947989510489
33102.8109.111465617716-6.31146561771563
3483.4106.911465617716-23.5114656177156
3579.488.8031322843823-9.40313228438229
3677.881.0364656177156-3.23646561771564
3785.778.64479895104897.05520104895108
3883.288.094798951049-4.89479895104895
398282.2947989510489-0.294798951048946
4086.978.9447989510497.95520104895105
4195.788.2072989510497.49270104895105
4297.999.2656322843823-1.36563228438227
4389.399.5781322843823-10.2781322843823
4491.587.79479895104893.70520104895107
4586.891.9114656177156-5.11146561771562
469190.91146561771560.0885343822843936
4793.896.4031322843823-2.6031322843823
4896.895.43646561771561.36353438228437
4995.797.6447989510489-1.94479895104892
5091.498.094798951049-6.69479895104895
5188.790.4947989510489-1.79479895104895
5288.285.6447989510492.55520104895105
5387.789.507298951049-1.80729895104895
5489.591.2656322843823-1.76563228438228
5595.691.17813228438234.42186771561771
56100.594.09479895104896.40520104895107
57106.3100.9114656177165.38853438228438
58112110.4114656177161.58853438228439
59117.7117.4031322843820.296867715617708
60125119.3364656177165.66353438228437
61132.4125.8447989510496.55520104895108
62138.1134.7947989510493.30520104895103
63134.7137.194798951049-2.49479895104898
64136.7131.6447989510495.05520104895103
65134.3138.007298951049-3.70729895104893
66131.6137.865632284382-6.26563228438232
67129.8133.278132284382-3.47813228438227
68131.9128.2947989510493.60520104895105
69129.8132.311465617716-2.51146561771563
70119.4133.911465617716-14.5114656177156
71116.7124.803132284382-8.1031322843823
72112.8118.336465617716-5.53646561771563

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 70.2 & 64.0355502136752 & 6.16444978632481 \tabularnewline
14 & 72.6 & 72.594798951049 & 0.00520104895103657 \tabularnewline
15 & 72.1 & 71.6947989510489 & 0.405201048951056 \tabularnewline
16 & 69.7 & 69.0447989510489 & 0.655201048951056 \tabularnewline
17 & 71.5 & 71.007298951049 & 0.492701048951048 \tabularnewline
18 & 75.7 & 75.0656322843823 & 0.634367715617728 \tabularnewline
19 & 76 & 77.3781322843823 & -1.37813228438229 \tabularnewline
20 & 76.4 & 74.4947989510489 & 1.90520104895107 \tabularnewline
21 & 83.8 & 76.8114656177156 & 6.98853438228437 \tabularnewline
22 & 86.2 & 87.9114656177156 & -1.7114656177156 \tabularnewline
23 & 88.5 & 91.6031322843823 & -3.1031322843823 \tabularnewline
24 & 95.9 & 90.1364656177156 & 5.76353438228438 \tabularnewline
25 & 103.1 & 96.7447989510489 & 6.35520104895106 \tabularnewline
26 & 113.5 & 105.494798951049 & 8.00520104895105 \tabularnewline
27 & 115.7 & 112.594798951049 & 3.10520104895106 \tabularnewline
28 & 113.1 & 112.644798951049 & 0.455201048951039 \tabularnewline
29 & 112.7 & 114.407298951049 & -1.70729895104894 \tabularnewline
30 & 121.9 & 116.265632284382 & 5.63436771561773 \tabularnewline
31 & 120.3 & 123.578132284382 & -3.27813228438229 \tabularnewline
32 & 108.7 & 118.794798951049 & -10.0947989510489 \tabularnewline
33 & 102.8 & 109.111465617716 & -6.31146561771563 \tabularnewline
34 & 83.4 & 106.911465617716 & -23.5114656177156 \tabularnewline
35 & 79.4 & 88.8031322843823 & -9.40313228438229 \tabularnewline
36 & 77.8 & 81.0364656177156 & -3.23646561771564 \tabularnewline
37 & 85.7 & 78.6447989510489 & 7.05520104895108 \tabularnewline
38 & 83.2 & 88.094798951049 & -4.89479895104895 \tabularnewline
39 & 82 & 82.2947989510489 & -0.294798951048946 \tabularnewline
40 & 86.9 & 78.944798951049 & 7.95520104895105 \tabularnewline
41 & 95.7 & 88.207298951049 & 7.49270104895105 \tabularnewline
42 & 97.9 & 99.2656322843823 & -1.36563228438227 \tabularnewline
43 & 89.3 & 99.5781322843823 & -10.2781322843823 \tabularnewline
44 & 91.5 & 87.7947989510489 & 3.70520104895107 \tabularnewline
45 & 86.8 & 91.9114656177156 & -5.11146561771562 \tabularnewline
46 & 91 & 90.9114656177156 & 0.0885343822843936 \tabularnewline
47 & 93.8 & 96.4031322843823 & -2.6031322843823 \tabularnewline
48 & 96.8 & 95.4364656177156 & 1.36353438228437 \tabularnewline
49 & 95.7 & 97.6447989510489 & -1.94479895104892 \tabularnewline
50 & 91.4 & 98.094798951049 & -6.69479895104895 \tabularnewline
51 & 88.7 & 90.4947989510489 & -1.79479895104895 \tabularnewline
52 & 88.2 & 85.644798951049 & 2.55520104895105 \tabularnewline
53 & 87.7 & 89.507298951049 & -1.80729895104895 \tabularnewline
54 & 89.5 & 91.2656322843823 & -1.76563228438228 \tabularnewline
55 & 95.6 & 91.1781322843823 & 4.42186771561771 \tabularnewline
56 & 100.5 & 94.0947989510489 & 6.40520104895107 \tabularnewline
57 & 106.3 & 100.911465617716 & 5.38853438228438 \tabularnewline
58 & 112 & 110.411465617716 & 1.58853438228439 \tabularnewline
59 & 117.7 & 117.403132284382 & 0.296867715617708 \tabularnewline
60 & 125 & 119.336465617716 & 5.66353438228437 \tabularnewline
61 & 132.4 & 125.844798951049 & 6.55520104895108 \tabularnewline
62 & 138.1 & 134.794798951049 & 3.30520104895103 \tabularnewline
63 & 134.7 & 137.194798951049 & -2.49479895104898 \tabularnewline
64 & 136.7 & 131.644798951049 & 5.05520104895103 \tabularnewline
65 & 134.3 & 138.007298951049 & -3.70729895104893 \tabularnewline
66 & 131.6 & 137.865632284382 & -6.26563228438232 \tabularnewline
67 & 129.8 & 133.278132284382 & -3.47813228438227 \tabularnewline
68 & 131.9 & 128.294798951049 & 3.60520104895105 \tabularnewline
69 & 129.8 & 132.311465617716 & -2.51146561771563 \tabularnewline
70 & 119.4 & 133.911465617716 & -14.5114656177156 \tabularnewline
71 & 116.7 & 124.803132284382 & -8.1031322843823 \tabularnewline
72 & 112.8 & 118.336465617716 & -5.53646561771563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199624&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]70.2[/C][C]64.0355502136752[/C][C]6.16444978632481[/C][/ROW]
[ROW][C]14[/C][C]72.6[/C][C]72.594798951049[/C][C]0.00520104895103657[/C][/ROW]
[ROW][C]15[/C][C]72.1[/C][C]71.6947989510489[/C][C]0.405201048951056[/C][/ROW]
[ROW][C]16[/C][C]69.7[/C][C]69.0447989510489[/C][C]0.655201048951056[/C][/ROW]
[ROW][C]17[/C][C]71.5[/C][C]71.007298951049[/C][C]0.492701048951048[/C][/ROW]
[ROW][C]18[/C][C]75.7[/C][C]75.0656322843823[/C][C]0.634367715617728[/C][/ROW]
[ROW][C]19[/C][C]76[/C][C]77.3781322843823[/C][C]-1.37813228438229[/C][/ROW]
[ROW][C]20[/C][C]76.4[/C][C]74.4947989510489[/C][C]1.90520104895107[/C][/ROW]
[ROW][C]21[/C][C]83.8[/C][C]76.8114656177156[/C][C]6.98853438228437[/C][/ROW]
[ROW][C]22[/C][C]86.2[/C][C]87.9114656177156[/C][C]-1.7114656177156[/C][/ROW]
[ROW][C]23[/C][C]88.5[/C][C]91.6031322843823[/C][C]-3.1031322843823[/C][/ROW]
[ROW][C]24[/C][C]95.9[/C][C]90.1364656177156[/C][C]5.76353438228438[/C][/ROW]
[ROW][C]25[/C][C]103.1[/C][C]96.7447989510489[/C][C]6.35520104895106[/C][/ROW]
[ROW][C]26[/C][C]113.5[/C][C]105.494798951049[/C][C]8.00520104895105[/C][/ROW]
[ROW][C]27[/C][C]115.7[/C][C]112.594798951049[/C][C]3.10520104895106[/C][/ROW]
[ROW][C]28[/C][C]113.1[/C][C]112.644798951049[/C][C]0.455201048951039[/C][/ROW]
[ROW][C]29[/C][C]112.7[/C][C]114.407298951049[/C][C]-1.70729895104894[/C][/ROW]
[ROW][C]30[/C][C]121.9[/C][C]116.265632284382[/C][C]5.63436771561773[/C][/ROW]
[ROW][C]31[/C][C]120.3[/C][C]123.578132284382[/C][C]-3.27813228438229[/C][/ROW]
[ROW][C]32[/C][C]108.7[/C][C]118.794798951049[/C][C]-10.0947989510489[/C][/ROW]
[ROW][C]33[/C][C]102.8[/C][C]109.111465617716[/C][C]-6.31146561771563[/C][/ROW]
[ROW][C]34[/C][C]83.4[/C][C]106.911465617716[/C][C]-23.5114656177156[/C][/ROW]
[ROW][C]35[/C][C]79.4[/C][C]88.8031322843823[/C][C]-9.40313228438229[/C][/ROW]
[ROW][C]36[/C][C]77.8[/C][C]81.0364656177156[/C][C]-3.23646561771564[/C][/ROW]
[ROW][C]37[/C][C]85.7[/C][C]78.6447989510489[/C][C]7.05520104895108[/C][/ROW]
[ROW][C]38[/C][C]83.2[/C][C]88.094798951049[/C][C]-4.89479895104895[/C][/ROW]
[ROW][C]39[/C][C]82[/C][C]82.2947989510489[/C][C]-0.294798951048946[/C][/ROW]
[ROW][C]40[/C][C]86.9[/C][C]78.944798951049[/C][C]7.95520104895105[/C][/ROW]
[ROW][C]41[/C][C]95.7[/C][C]88.207298951049[/C][C]7.49270104895105[/C][/ROW]
[ROW][C]42[/C][C]97.9[/C][C]99.2656322843823[/C][C]-1.36563228438227[/C][/ROW]
[ROW][C]43[/C][C]89.3[/C][C]99.5781322843823[/C][C]-10.2781322843823[/C][/ROW]
[ROW][C]44[/C][C]91.5[/C][C]87.7947989510489[/C][C]3.70520104895107[/C][/ROW]
[ROW][C]45[/C][C]86.8[/C][C]91.9114656177156[/C][C]-5.11146561771562[/C][/ROW]
[ROW][C]46[/C][C]91[/C][C]90.9114656177156[/C][C]0.0885343822843936[/C][/ROW]
[ROW][C]47[/C][C]93.8[/C][C]96.4031322843823[/C][C]-2.6031322843823[/C][/ROW]
[ROW][C]48[/C][C]96.8[/C][C]95.4364656177156[/C][C]1.36353438228437[/C][/ROW]
[ROW][C]49[/C][C]95.7[/C][C]97.6447989510489[/C][C]-1.94479895104892[/C][/ROW]
[ROW][C]50[/C][C]91.4[/C][C]98.094798951049[/C][C]-6.69479895104895[/C][/ROW]
[ROW][C]51[/C][C]88.7[/C][C]90.4947989510489[/C][C]-1.79479895104895[/C][/ROW]
[ROW][C]52[/C][C]88.2[/C][C]85.644798951049[/C][C]2.55520104895105[/C][/ROW]
[ROW][C]53[/C][C]87.7[/C][C]89.507298951049[/C][C]-1.80729895104895[/C][/ROW]
[ROW][C]54[/C][C]89.5[/C][C]91.2656322843823[/C][C]-1.76563228438228[/C][/ROW]
[ROW][C]55[/C][C]95.6[/C][C]91.1781322843823[/C][C]4.42186771561771[/C][/ROW]
[ROW][C]56[/C][C]100.5[/C][C]94.0947989510489[/C][C]6.40520104895107[/C][/ROW]
[ROW][C]57[/C][C]106.3[/C][C]100.911465617716[/C][C]5.38853438228438[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]110.411465617716[/C][C]1.58853438228439[/C][/ROW]
[ROW][C]59[/C][C]117.7[/C][C]117.403132284382[/C][C]0.296867715617708[/C][/ROW]
[ROW][C]60[/C][C]125[/C][C]119.336465617716[/C][C]5.66353438228437[/C][/ROW]
[ROW][C]61[/C][C]132.4[/C][C]125.844798951049[/C][C]6.55520104895108[/C][/ROW]
[ROW][C]62[/C][C]138.1[/C][C]134.794798951049[/C][C]3.30520104895103[/C][/ROW]
[ROW][C]63[/C][C]134.7[/C][C]137.194798951049[/C][C]-2.49479895104898[/C][/ROW]
[ROW][C]64[/C][C]136.7[/C][C]131.644798951049[/C][C]5.05520104895103[/C][/ROW]
[ROW][C]65[/C][C]134.3[/C][C]138.007298951049[/C][C]-3.70729895104893[/C][/ROW]
[ROW][C]66[/C][C]131.6[/C][C]137.865632284382[/C][C]-6.26563228438232[/C][/ROW]
[ROW][C]67[/C][C]129.8[/C][C]133.278132284382[/C][C]-3.47813228438227[/C][/ROW]
[ROW][C]68[/C][C]131.9[/C][C]128.294798951049[/C][C]3.60520104895105[/C][/ROW]
[ROW][C]69[/C][C]129.8[/C][C]132.311465617716[/C][C]-2.51146561771563[/C][/ROW]
[ROW][C]70[/C][C]119.4[/C][C]133.911465617716[/C][C]-14.5114656177156[/C][/ROW]
[ROW][C]71[/C][C]116.7[/C][C]124.803132284382[/C][C]-8.1031322843823[/C][/ROW]
[ROW][C]72[/C][C]112.8[/C][C]118.336465617716[/C][C]-5.53646561771563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199624&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199624&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
1370.264.03555021367526.16444978632481
1472.672.5947989510490.00520104895103657
1572.171.69479895104890.405201048951056
1669.769.04479895104890.655201048951056
1771.571.0072989510490.492701048951048
1875.775.06563228438230.634367715617728
197677.3781322843823-1.37813228438229
2076.474.49479895104891.90520104895107
2183.876.81146561771566.98853438228437
2286.287.9114656177156-1.7114656177156
2388.591.6031322843823-3.1031322843823
2495.990.13646561771565.76353438228438
25103.196.74479895104896.35520104895106
26113.5105.4947989510498.00520104895105
27115.7112.5947989510493.10520104895106
28113.1112.6447989510490.455201048951039
29112.7114.407298951049-1.70729895104894
30121.9116.2656322843825.63436771561773
31120.3123.578132284382-3.27813228438229
32108.7118.794798951049-10.0947989510489
33102.8109.111465617716-6.31146561771563
3483.4106.911465617716-23.5114656177156
3579.488.8031322843823-9.40313228438229
3677.881.0364656177156-3.23646561771564
3785.778.64479895104897.05520104895108
3883.288.094798951049-4.89479895104895
398282.2947989510489-0.294798951048946
4086.978.9447989510497.95520104895105
4195.788.2072989510497.49270104895105
4297.999.2656322843823-1.36563228438227
4389.399.5781322843823-10.2781322843823
4491.587.79479895104893.70520104895107
4586.891.9114656177156-5.11146561771562
469190.91146561771560.0885343822843936
4793.896.4031322843823-2.6031322843823
4896.895.43646561771561.36353438228437
4995.797.6447989510489-1.94479895104892
5091.498.094798951049-6.69479895104895
5188.790.4947989510489-1.79479895104895
5288.285.6447989510492.55520104895105
5387.789.507298951049-1.80729895104895
5489.591.2656322843823-1.76563228438228
5595.691.17813228438234.42186771561771
56100.594.09479895104896.40520104895107
57106.3100.9114656177165.38853438228438
58112110.4114656177161.58853438228439
59117.7117.4031322843820.296867715617708
60125119.3364656177165.66353438228437
61132.4125.8447989510496.55520104895108
62138.1134.7947989510493.30520104895103
63134.7137.194798951049-2.49479895104898
64136.7131.6447989510495.05520104895103
65134.3138.007298951049-3.70729895104893
66131.6137.865632284382-6.26563228438232
67129.8133.278132284382-3.47813228438227
68131.9128.2947989510493.60520104895105
69129.8132.311465617716-2.51146561771563
70119.4133.911465617716-14.5114656177156
71116.7124.803132284382-8.1031322843823
72112.8118.336465617716-5.53646561771563







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73113.644798951049101.971226681291125.318371220807
74116.03959790209899.5306736768633132.548522127332
75115.13439685314794.9151765760985135.353617130195
76112.07919580419688.7320512646794135.426340343712
77113.38649475524587.2835936198089139.489395890681
78116.95212703962788.3578315032161145.546422576038
79118.63025932400987.7448901864893149.515628461529
80117.12505827505884.1072098245892150.142906725527
81117.53652389277482.5158070834992152.557240702048
82121.64798951048984.732912707472158.563066313507
83127.05112179487288.3342626129864165.767980976757
84128.68758741258788.2491468584907169.126027966684

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 113.644798951049 & 101.971226681291 & 125.318371220807 \tabularnewline
74 & 116.039597902098 & 99.5306736768633 & 132.548522127332 \tabularnewline
75 & 115.134396853147 & 94.9151765760985 & 135.353617130195 \tabularnewline
76 & 112.079195804196 & 88.7320512646794 & 135.426340343712 \tabularnewline
77 & 113.386494755245 & 87.2835936198089 & 139.489395890681 \tabularnewline
78 & 116.952127039627 & 88.3578315032161 & 145.546422576038 \tabularnewline
79 & 118.630259324009 & 87.7448901864893 & 149.515628461529 \tabularnewline
80 & 117.125058275058 & 84.1072098245892 & 150.142906725527 \tabularnewline
81 & 117.536523892774 & 82.5158070834992 & 152.557240702048 \tabularnewline
82 & 121.647989510489 & 84.732912707472 & 158.563066313507 \tabularnewline
83 & 127.051121794872 & 88.3342626129864 & 165.767980976757 \tabularnewline
84 & 128.687587412587 & 88.2491468584907 & 169.126027966684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199624&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]113.644798951049[/C][C]101.971226681291[/C][C]125.318371220807[/C][/ROW]
[ROW][C]74[/C][C]116.039597902098[/C][C]99.5306736768633[/C][C]132.548522127332[/C][/ROW]
[ROW][C]75[/C][C]115.134396853147[/C][C]94.9151765760985[/C][C]135.353617130195[/C][/ROW]
[ROW][C]76[/C][C]112.079195804196[/C][C]88.7320512646794[/C][C]135.426340343712[/C][/ROW]
[ROW][C]77[/C][C]113.386494755245[/C][C]87.2835936198089[/C][C]139.489395890681[/C][/ROW]
[ROW][C]78[/C][C]116.952127039627[/C][C]88.3578315032161[/C][C]145.546422576038[/C][/ROW]
[ROW][C]79[/C][C]118.630259324009[/C][C]87.7448901864893[/C][C]149.515628461529[/C][/ROW]
[ROW][C]80[/C][C]117.125058275058[/C][C]84.1072098245892[/C][C]150.142906725527[/C][/ROW]
[ROW][C]81[/C][C]117.536523892774[/C][C]82.5158070834992[/C][C]152.557240702048[/C][/ROW]
[ROW][C]82[/C][C]121.647989510489[/C][C]84.732912707472[/C][C]158.563066313507[/C][/ROW]
[ROW][C]83[/C][C]127.051121794872[/C][C]88.3342626129864[/C][C]165.767980976757[/C][/ROW]
[ROW][C]84[/C][C]128.687587412587[/C][C]88.2491468584907[/C][C]169.126027966684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199624&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199624&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
73113.644798951049101.971226681291125.318371220807
74116.03959790209899.5306736768633132.548522127332
75115.13439685314794.9151765760985135.353617130195
76112.07919580419688.7320512646794135.426340343712
77113.38649475524587.2835936198089139.489395890681
78116.95212703962788.3578315032161145.546422576038
79118.63025932400987.7448901864893149.515628461529
80117.12505827505884.1072098245892150.142906725527
81117.53652389277482.5158070834992152.557240702048
82121.64798951048984.732912707472158.563066313507
83127.05112179487288.3342626129864165.767980976757
84128.68758741258788.2491468584907169.126027966684



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')