Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 13 Jan 2014 05:26:06 -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/2014/Jan/13/t13896087783t3icontu0llx9q.htm/, Retrieved Sun, 19 May 2024 12:18:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233133, Retrieved Sun, 19 May 2024 12:18:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-13 10:26:06] [76c30f62b7052b57088120e90a652e05] [Current]
Feedback Forum

Post a new message
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
116
117,5
118,8
118,7
116,3
115,2
131,7
133,7
132,5
126,9
122,2
120,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233133&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233133&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.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=233133&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=233133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233133&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
73116113.6447989510492.35520104895107
74117.5118.394798951049-0.894798951048955
75118.8116.5947989510492.20520104895105
76118.7115.7447989510492.95520104895105
77116.3120.007298951049-3.70729895104895
78115.2119.865632284382-4.66563228438227
79131.7116.87813228438214.8218677156177
80133.7130.1947989510493.50520104895105
81132.5134.111465617716-1.61146561771562
82126.9136.611465617716-9.71146561771562
83122.2132.303132284382-10.1031322843823
84120.2123.836465617716-3.63646561771563

\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
73 & 116 & 113.644798951049 & 2.35520104895107 \tabularnewline
74 & 117.5 & 118.394798951049 & -0.894798951048955 \tabularnewline
75 & 118.8 & 116.594798951049 & 2.20520104895105 \tabularnewline
76 & 118.7 & 115.744798951049 & 2.95520104895105 \tabularnewline
77 & 116.3 & 120.007298951049 & -3.70729895104895 \tabularnewline
78 & 115.2 & 119.865632284382 & -4.66563228438227 \tabularnewline
79 & 131.7 & 116.878132284382 & 14.8218677156177 \tabularnewline
80 & 133.7 & 130.194798951049 & 3.50520104895105 \tabularnewline
81 & 132.5 & 134.111465617716 & -1.61146561771562 \tabularnewline
82 & 126.9 & 136.611465617716 & -9.71146561771562 \tabularnewline
83 & 122.2 & 132.303132284382 & -10.1031322843823 \tabularnewline
84 & 120.2 & 123.836465617716 & -3.63646561771563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233133&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]
[ROW][C]73[/C][C]116[/C][C]113.644798951049[/C][C]2.35520104895107[/C][/ROW]
[ROW][C]74[/C][C]117.5[/C][C]118.394798951049[/C][C]-0.894798951048955[/C][/ROW]
[ROW][C]75[/C][C]118.8[/C][C]116.594798951049[/C][C]2.20520104895105[/C][/ROW]
[ROW][C]76[/C][C]118.7[/C][C]115.744798951049[/C][C]2.95520104895105[/C][/ROW]
[ROW][C]77[/C][C]116.3[/C][C]120.007298951049[/C][C]-3.70729895104895[/C][/ROW]
[ROW][C]78[/C][C]115.2[/C][C]119.865632284382[/C][C]-4.66563228438227[/C][/ROW]
[ROW][C]79[/C][C]131.7[/C][C]116.878132284382[/C][C]14.8218677156177[/C][/ROW]
[ROW][C]80[/C][C]133.7[/C][C]130.194798951049[/C][C]3.50520104895105[/C][/ROW]
[ROW][C]81[/C][C]132.5[/C][C]134.111465617716[/C][C]-1.61146561771562[/C][/ROW]
[ROW][C]82[/C][C]126.9[/C][C]136.611465617716[/C][C]-9.71146561771562[/C][/ROW]
[ROW][C]83[/C][C]122.2[/C][C]132.303132284382[/C][C]-10.1031322843823[/C][/ROW]
[ROW][C]84[/C][C]120.2[/C][C]123.836465617716[/C][C]-3.63646561771563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233133&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233133&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
73116113.6447989510492.35520104895107
74117.5118.394798951049-0.894798951048955
75118.8116.5947989510492.20520104895105
76118.7115.7447989510492.95520104895105
77116.3120.007298951049-3.70729895104895
78115.2119.865632284382-4.66563228438227
79131.7116.87813228438214.8218677156177
80133.7130.1947989510493.50520104895105
81132.5134.111465617716-1.61146561771562
82126.9136.611465617716-9.71146561771562
83122.2132.303132284382-10.1031322843823
84120.2123.836465617716-3.63646561771563







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85121.044798951049109.213809459594132.875788442504
86123.439597902098106.708052106989140.171143697207
87122.534396853147102.042521950134143.02627175616
88119.47919580419695.8172168212867143.141174787105
89120.78649475524594.3315980112667147.241391499223
90124.35212703962795.3722396333335153.332014445921
91126.03025932400994.728403365802157.332115282217
92124.52505827505891.061966684841157.988149865275
93124.93652389277489.4435554184102160.429492367138
94129.04798951048991.6351157439759166.460863277003
95134.45112179487295.2121687530793173.690074836664
96136.08758741258795.1038376065619177.071337218613

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 121.044798951049 & 109.213809459594 & 132.875788442504 \tabularnewline
86 & 123.439597902098 & 106.708052106989 & 140.171143697207 \tabularnewline
87 & 122.534396853147 & 102.042521950134 & 143.02627175616 \tabularnewline
88 & 119.479195804196 & 95.8172168212867 & 143.141174787105 \tabularnewline
89 & 120.786494755245 & 94.3315980112667 & 147.241391499223 \tabularnewline
90 & 124.352127039627 & 95.3722396333335 & 153.332014445921 \tabularnewline
91 & 126.030259324009 & 94.728403365802 & 157.332115282217 \tabularnewline
92 & 124.525058275058 & 91.061966684841 & 157.988149865275 \tabularnewline
93 & 124.936523892774 & 89.4435554184102 & 160.429492367138 \tabularnewline
94 & 129.047989510489 & 91.6351157439759 & 166.460863277003 \tabularnewline
95 & 134.451121794872 & 95.2121687530793 & 173.690074836664 \tabularnewline
96 & 136.087587412587 & 95.1038376065619 & 177.071337218613 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233133&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]85[/C][C]121.044798951049[/C][C]109.213809459594[/C][C]132.875788442504[/C][/ROW]
[ROW][C]86[/C][C]123.439597902098[/C][C]106.708052106989[/C][C]140.171143697207[/C][/ROW]
[ROW][C]87[/C][C]122.534396853147[/C][C]102.042521950134[/C][C]143.02627175616[/C][/ROW]
[ROW][C]88[/C][C]119.479195804196[/C][C]95.8172168212867[/C][C]143.141174787105[/C][/ROW]
[ROW][C]89[/C][C]120.786494755245[/C][C]94.3315980112667[/C][C]147.241391499223[/C][/ROW]
[ROW][C]90[/C][C]124.352127039627[/C][C]95.3722396333335[/C][C]153.332014445921[/C][/ROW]
[ROW][C]91[/C][C]126.030259324009[/C][C]94.728403365802[/C][C]157.332115282217[/C][/ROW]
[ROW][C]92[/C][C]124.525058275058[/C][C]91.061966684841[/C][C]157.988149865275[/C][/ROW]
[ROW][C]93[/C][C]124.936523892774[/C][C]89.4435554184102[/C][C]160.429492367138[/C][/ROW]
[ROW][C]94[/C][C]129.047989510489[/C][C]91.6351157439759[/C][C]166.460863277003[/C][/ROW]
[ROW][C]95[/C][C]134.451121794872[/C][C]95.2121687530793[/C][C]173.690074836664[/C][/ROW]
[ROW][C]96[/C][C]136.087587412587[/C][C]95.1038376065619[/C][C]177.071337218613[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233133&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233133&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
85121.044798951049109.213809459594132.875788442504
86123.439597902098106.708052106989140.171143697207
87122.534396853147102.042521950134143.02627175616
88119.47919580419695.8172168212867143.141174787105
89120.78649475524594.3315980112667147.241391499223
90124.35212703962795.3722396333335153.332014445921
91126.03025932400994.728403365802157.332115282217
92124.52505827505891.061966684841157.988149865275
93124.93652389277489.4435554184102160.429492367138
94129.04798951048991.6351157439759166.460863277003
95134.45112179487295.2121687530793173.690074836664
96136.08758741258795.1038376065619177.071337218613



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')