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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Jan 2010 12:22:55 -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/2010/Jan/26/t1264533846xtugkgavdu4vxb8.htm/, Retrieved Fri, 03 May 2024 00:15:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72651, Retrieved Fri, 03 May 2024 00:15:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKEYWORD: KDGP2W62
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [eigen reeks opgave 8] [2010-01-26 19:22:55] [4c49eeca41cf2bf23e101541a1a2b4ce] [Current]
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Dataseries X:
124.9
122.7
148.1
176.9
234.6
254.6
279.7
275.8
283
295.4
297.6
276.8
250.1
239.1
258.9
276.1
264.1
265.5
287.7
285.1
304.5
301.5
274.2
258.6
253.9
269.6
266.9
269.6
257.9
258.2
254.7
237.2
267.2
228.8
196.3
194.8
186.6
176.7
162.1
154.9
150.1
150.5
143.6
143.8
141.5
147.9
151.4
144.6
140.4
139.5
138.1
136.7
130
128.5
130.4
125.7
121.7
129.9
129.6
128.2
119.7
112.2
105.6
101.2
94.9
95.1
93.1
91.4
89.8
85.9
89.7
91.6
88.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72651&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72651&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72651&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.357504192131878
beta0.200940707428541
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.357504192131878 \tabularnewline
beta & 0.200940707428541 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72651&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]0.357504192131878[/C][/ROW]
[ROW][C]beta[/C][C]0.200940707428541[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72651&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72651&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
alpha0.357504192131878
beta0.200940707428541
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13250.1220.44169337606929.6583066239315
14239.1224.45805383380314.6419461661969
15258.9254.3953380911944.50466190880641
16276.1278.565436115028-2.46543611502847
17264.1272.737418316742-8.63741831674241
18265.5278.494903533154-12.9949035331539
19287.7329.644386077925-41.9443860779247
20285.1302.44780896338-17.3478089633801
21304.5294.49839420666410.0016057933361
22301.5302.961663352859-1.46166335285932
23274.2300.409264001131-26.2092640011305
24258.6267.805861633489-9.20586163348867
25253.9254.671095080908-0.771095080908253
26269.6231.55978000997338.0402199900274
27266.9258.4286595937798.4713404062208
28269.6274.903334892304-5.30333489230384
29257.9259.256148990486-1.35614899048585
30258.2260.500983430093-2.3009834300928
31254.7293.325817658484-38.6258176584837
32237.2279.809388422839-42.6093884228392
33267.2275.276565757883-8.07656575788258
34228.8263.488854501053-34.6888545010526
35196.3224.347562875663-28.0475628756633
36194.8193.0697150772741.73028492272587
37186.6181.1077298461875.49227015381257
38176.7177.465404544223-0.765404544222918
39162.1160.9692474253871.13075257461261
40154.9154.948151715486-0.0481517154864548
41150.1133.07197463005217.0280253699478
42150.5130.95905131558019.5409486844196
43143.6140.4998511860953.10014881390546
44143.8134.5846137440549.21538625594638
45141.5169.732914322033-28.2329143220331
46147.9131.15932070304816.7406792969519
47151.4115.88423663174535.5157633682552
48144.6132.24182630456012.3581736954404
49140.4133.0390322885607.3609677114396
50139.5132.7211030198036.7788969801968
51138.1127.35915799019810.7408420098019
52136.7131.9254495343734.77455046562679
53130131.000411103601-1.00041110360144
54128.5131.017307672957-2.5173076729574
55130.4127.4849600689762.91503993102424
56125.7130.795178791412-5.09517879141232
57121.7141.101605045243-19.4016050452431
58129.9139.549591732372-9.64959173237216
59129.6129.975991063662-0.375991063661814
60128.2119.118315720559.08168427944997
61119.7115.7929474024793.90705259752085
62112.2113.877599890108-1.67759989010841
63105.6107.441813150535-1.84181315053543
64101.2102.176391693773-0.976391693773166
6594.993.57180373878721.32819626121280
6695.191.70069302697673.3993069730233
6793.192.452958741330.647041258669972
6891.488.32203814799463.07796185200536
6989.891.461924309446-1.66192430944595
7085.9102.895263679034-16.9952636790344
7189.796.5038267266136-6.8038267266136
7291.688.81295526121872.78704473878125
7388.678.84862413478789.75137586521217

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 250.1 & 220.441693376069 & 29.6583066239315 \tabularnewline
14 & 239.1 & 224.458053833803 & 14.6419461661969 \tabularnewline
15 & 258.9 & 254.395338091194 & 4.50466190880641 \tabularnewline
16 & 276.1 & 278.565436115028 & -2.46543611502847 \tabularnewline
17 & 264.1 & 272.737418316742 & -8.63741831674241 \tabularnewline
18 & 265.5 & 278.494903533154 & -12.9949035331539 \tabularnewline
19 & 287.7 & 329.644386077925 & -41.9443860779247 \tabularnewline
20 & 285.1 & 302.44780896338 & -17.3478089633801 \tabularnewline
21 & 304.5 & 294.498394206664 & 10.0016057933361 \tabularnewline
22 & 301.5 & 302.961663352859 & -1.46166335285932 \tabularnewline
23 & 274.2 & 300.409264001131 & -26.2092640011305 \tabularnewline
24 & 258.6 & 267.805861633489 & -9.20586163348867 \tabularnewline
25 & 253.9 & 254.671095080908 & -0.771095080908253 \tabularnewline
26 & 269.6 & 231.559780009973 & 38.0402199900274 \tabularnewline
27 & 266.9 & 258.428659593779 & 8.4713404062208 \tabularnewline
28 & 269.6 & 274.903334892304 & -5.30333489230384 \tabularnewline
29 & 257.9 & 259.256148990486 & -1.35614899048585 \tabularnewline
30 & 258.2 & 260.500983430093 & -2.3009834300928 \tabularnewline
31 & 254.7 & 293.325817658484 & -38.6258176584837 \tabularnewline
32 & 237.2 & 279.809388422839 & -42.6093884228392 \tabularnewline
33 & 267.2 & 275.276565757883 & -8.07656575788258 \tabularnewline
34 & 228.8 & 263.488854501053 & -34.6888545010526 \tabularnewline
35 & 196.3 & 224.347562875663 & -28.0475628756633 \tabularnewline
36 & 194.8 & 193.069715077274 & 1.73028492272587 \tabularnewline
37 & 186.6 & 181.107729846187 & 5.49227015381257 \tabularnewline
38 & 176.7 & 177.465404544223 & -0.765404544222918 \tabularnewline
39 & 162.1 & 160.969247425387 & 1.13075257461261 \tabularnewline
40 & 154.9 & 154.948151715486 & -0.0481517154864548 \tabularnewline
41 & 150.1 & 133.071974630052 & 17.0280253699478 \tabularnewline
42 & 150.5 & 130.959051315580 & 19.5409486844196 \tabularnewline
43 & 143.6 & 140.499851186095 & 3.10014881390546 \tabularnewline
44 & 143.8 & 134.584613744054 & 9.21538625594638 \tabularnewline
45 & 141.5 & 169.732914322033 & -28.2329143220331 \tabularnewline
46 & 147.9 & 131.159320703048 & 16.7406792969519 \tabularnewline
47 & 151.4 & 115.884236631745 & 35.5157633682552 \tabularnewline
48 & 144.6 & 132.241826304560 & 12.3581736954404 \tabularnewline
49 & 140.4 & 133.039032288560 & 7.3609677114396 \tabularnewline
50 & 139.5 & 132.721103019803 & 6.7788969801968 \tabularnewline
51 & 138.1 & 127.359157990198 & 10.7408420098019 \tabularnewline
52 & 136.7 & 131.925449534373 & 4.77455046562679 \tabularnewline
53 & 130 & 131.000411103601 & -1.00041110360144 \tabularnewline
54 & 128.5 & 131.017307672957 & -2.5173076729574 \tabularnewline
55 & 130.4 & 127.484960068976 & 2.91503993102424 \tabularnewline
56 & 125.7 & 130.795178791412 & -5.09517879141232 \tabularnewline
57 & 121.7 & 141.101605045243 & -19.4016050452431 \tabularnewline
58 & 129.9 & 139.549591732372 & -9.64959173237216 \tabularnewline
59 & 129.6 & 129.975991063662 & -0.375991063661814 \tabularnewline
60 & 128.2 & 119.11831572055 & 9.08168427944997 \tabularnewline
61 & 119.7 & 115.792947402479 & 3.90705259752085 \tabularnewline
62 & 112.2 & 113.877599890108 & -1.67759989010841 \tabularnewline
63 & 105.6 & 107.441813150535 & -1.84181315053543 \tabularnewline
64 & 101.2 & 102.176391693773 & -0.976391693773166 \tabularnewline
65 & 94.9 & 93.5718037387872 & 1.32819626121280 \tabularnewline
66 & 95.1 & 91.7006930269767 & 3.3993069730233 \tabularnewline
67 & 93.1 & 92.45295874133 & 0.647041258669972 \tabularnewline
68 & 91.4 & 88.3220381479946 & 3.07796185200536 \tabularnewline
69 & 89.8 & 91.461924309446 & -1.66192430944595 \tabularnewline
70 & 85.9 & 102.895263679034 & -16.9952636790344 \tabularnewline
71 & 89.7 & 96.5038267266136 & -6.8038267266136 \tabularnewline
72 & 91.6 & 88.8129552612187 & 2.78704473878125 \tabularnewline
73 & 88.6 & 78.8486241347878 & 9.75137586521217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72651&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]250.1[/C][C]220.441693376069[/C][C]29.6583066239315[/C][/ROW]
[ROW][C]14[/C][C]239.1[/C][C]224.458053833803[/C][C]14.6419461661969[/C][/ROW]
[ROW][C]15[/C][C]258.9[/C][C]254.395338091194[/C][C]4.50466190880641[/C][/ROW]
[ROW][C]16[/C][C]276.1[/C][C]278.565436115028[/C][C]-2.46543611502847[/C][/ROW]
[ROW][C]17[/C][C]264.1[/C][C]272.737418316742[/C][C]-8.63741831674241[/C][/ROW]
[ROW][C]18[/C][C]265.5[/C][C]278.494903533154[/C][C]-12.9949035331539[/C][/ROW]
[ROW][C]19[/C][C]287.7[/C][C]329.644386077925[/C][C]-41.9443860779247[/C][/ROW]
[ROW][C]20[/C][C]285.1[/C][C]302.44780896338[/C][C]-17.3478089633801[/C][/ROW]
[ROW][C]21[/C][C]304.5[/C][C]294.498394206664[/C][C]10.0016057933361[/C][/ROW]
[ROW][C]22[/C][C]301.5[/C][C]302.961663352859[/C][C]-1.46166335285932[/C][/ROW]
[ROW][C]23[/C][C]274.2[/C][C]300.409264001131[/C][C]-26.2092640011305[/C][/ROW]
[ROW][C]24[/C][C]258.6[/C][C]267.805861633489[/C][C]-9.20586163348867[/C][/ROW]
[ROW][C]25[/C][C]253.9[/C][C]254.671095080908[/C][C]-0.771095080908253[/C][/ROW]
[ROW][C]26[/C][C]269.6[/C][C]231.559780009973[/C][C]38.0402199900274[/C][/ROW]
[ROW][C]27[/C][C]266.9[/C][C]258.428659593779[/C][C]8.4713404062208[/C][/ROW]
[ROW][C]28[/C][C]269.6[/C][C]274.903334892304[/C][C]-5.30333489230384[/C][/ROW]
[ROW][C]29[/C][C]257.9[/C][C]259.256148990486[/C][C]-1.35614899048585[/C][/ROW]
[ROW][C]30[/C][C]258.2[/C][C]260.500983430093[/C][C]-2.3009834300928[/C][/ROW]
[ROW][C]31[/C][C]254.7[/C][C]293.325817658484[/C][C]-38.6258176584837[/C][/ROW]
[ROW][C]32[/C][C]237.2[/C][C]279.809388422839[/C][C]-42.6093884228392[/C][/ROW]
[ROW][C]33[/C][C]267.2[/C][C]275.276565757883[/C][C]-8.07656575788258[/C][/ROW]
[ROW][C]34[/C][C]228.8[/C][C]263.488854501053[/C][C]-34.6888545010526[/C][/ROW]
[ROW][C]35[/C][C]196.3[/C][C]224.347562875663[/C][C]-28.0475628756633[/C][/ROW]
[ROW][C]36[/C][C]194.8[/C][C]193.069715077274[/C][C]1.73028492272587[/C][/ROW]
[ROW][C]37[/C][C]186.6[/C][C]181.107729846187[/C][C]5.49227015381257[/C][/ROW]
[ROW][C]38[/C][C]176.7[/C][C]177.465404544223[/C][C]-0.765404544222918[/C][/ROW]
[ROW][C]39[/C][C]162.1[/C][C]160.969247425387[/C][C]1.13075257461261[/C][/ROW]
[ROW][C]40[/C][C]154.9[/C][C]154.948151715486[/C][C]-0.0481517154864548[/C][/ROW]
[ROW][C]41[/C][C]150.1[/C][C]133.071974630052[/C][C]17.0280253699478[/C][/ROW]
[ROW][C]42[/C][C]150.5[/C][C]130.959051315580[/C][C]19.5409486844196[/C][/ROW]
[ROW][C]43[/C][C]143.6[/C][C]140.499851186095[/C][C]3.10014881390546[/C][/ROW]
[ROW][C]44[/C][C]143.8[/C][C]134.584613744054[/C][C]9.21538625594638[/C][/ROW]
[ROW][C]45[/C][C]141.5[/C][C]169.732914322033[/C][C]-28.2329143220331[/C][/ROW]
[ROW][C]46[/C][C]147.9[/C][C]131.159320703048[/C][C]16.7406792969519[/C][/ROW]
[ROW][C]47[/C][C]151.4[/C][C]115.884236631745[/C][C]35.5157633682552[/C][/ROW]
[ROW][C]48[/C][C]144.6[/C][C]132.241826304560[/C][C]12.3581736954404[/C][/ROW]
[ROW][C]49[/C][C]140.4[/C][C]133.039032288560[/C][C]7.3609677114396[/C][/ROW]
[ROW][C]50[/C][C]139.5[/C][C]132.721103019803[/C][C]6.7788969801968[/C][/ROW]
[ROW][C]51[/C][C]138.1[/C][C]127.359157990198[/C][C]10.7408420098019[/C][/ROW]
[ROW][C]52[/C][C]136.7[/C][C]131.925449534373[/C][C]4.77455046562679[/C][/ROW]
[ROW][C]53[/C][C]130[/C][C]131.000411103601[/C][C]-1.00041110360144[/C][/ROW]
[ROW][C]54[/C][C]128.5[/C][C]131.017307672957[/C][C]-2.5173076729574[/C][/ROW]
[ROW][C]55[/C][C]130.4[/C][C]127.484960068976[/C][C]2.91503993102424[/C][/ROW]
[ROW][C]56[/C][C]125.7[/C][C]130.795178791412[/C][C]-5.09517879141232[/C][/ROW]
[ROW][C]57[/C][C]121.7[/C][C]141.101605045243[/C][C]-19.4016050452431[/C][/ROW]
[ROW][C]58[/C][C]129.9[/C][C]139.549591732372[/C][C]-9.64959173237216[/C][/ROW]
[ROW][C]59[/C][C]129.6[/C][C]129.975991063662[/C][C]-0.375991063661814[/C][/ROW]
[ROW][C]60[/C][C]128.2[/C][C]119.11831572055[/C][C]9.08168427944997[/C][/ROW]
[ROW][C]61[/C][C]119.7[/C][C]115.792947402479[/C][C]3.90705259752085[/C][/ROW]
[ROW][C]62[/C][C]112.2[/C][C]113.877599890108[/C][C]-1.67759989010841[/C][/ROW]
[ROW][C]63[/C][C]105.6[/C][C]107.441813150535[/C][C]-1.84181315053543[/C][/ROW]
[ROW][C]64[/C][C]101.2[/C][C]102.176391693773[/C][C]-0.976391693773166[/C][/ROW]
[ROW][C]65[/C][C]94.9[/C][C]93.5718037387872[/C][C]1.32819626121280[/C][/ROW]
[ROW][C]66[/C][C]95.1[/C][C]91.7006930269767[/C][C]3.3993069730233[/C][/ROW]
[ROW][C]67[/C][C]93.1[/C][C]92.45295874133[/C][C]0.647041258669972[/C][/ROW]
[ROW][C]68[/C][C]91.4[/C][C]88.3220381479946[/C][C]3.07796185200536[/C][/ROW]
[ROW][C]69[/C][C]89.8[/C][C]91.461924309446[/C][C]-1.66192430944595[/C][/ROW]
[ROW][C]70[/C][C]85.9[/C][C]102.895263679034[/C][C]-16.9952636790344[/C][/ROW]
[ROW][C]71[/C][C]89.7[/C][C]96.5038267266136[/C][C]-6.8038267266136[/C][/ROW]
[ROW][C]72[/C][C]91.6[/C][C]88.8129552612187[/C][C]2.78704473878125[/C][/ROW]
[ROW][C]73[/C][C]88.6[/C][C]78.8486241347878[/C][C]9.75137586521217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72651&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72651&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
13250.1220.44169337606929.6583066239315
14239.1224.45805383380314.6419461661969
15258.9254.3953380911944.50466190880641
16276.1278.565436115028-2.46543611502847
17264.1272.737418316742-8.63741831674241
18265.5278.494903533154-12.9949035331539
19287.7329.644386077925-41.9443860779247
20285.1302.44780896338-17.3478089633801
21304.5294.49839420666410.0016057933361
22301.5302.961663352859-1.46166335285932
23274.2300.409264001131-26.2092640011305
24258.6267.805861633489-9.20586163348867
25253.9254.671095080908-0.771095080908253
26269.6231.55978000997338.0402199900274
27266.9258.4286595937798.4713404062208
28269.6274.903334892304-5.30333489230384
29257.9259.256148990486-1.35614899048585
30258.2260.500983430093-2.3009834300928
31254.7293.325817658484-38.6258176584837
32237.2279.809388422839-42.6093884228392
33267.2275.276565757883-8.07656575788258
34228.8263.488854501053-34.6888545010526
35196.3224.347562875663-28.0475628756633
36194.8193.0697150772741.73028492272587
37186.6181.1077298461875.49227015381257
38176.7177.465404544223-0.765404544222918
39162.1160.9692474253871.13075257461261
40154.9154.948151715486-0.0481517154864548
41150.1133.07197463005217.0280253699478
42150.5130.95905131558019.5409486844196
43143.6140.4998511860953.10014881390546
44143.8134.5846137440549.21538625594638
45141.5169.732914322033-28.2329143220331
46147.9131.15932070304816.7406792969519
47151.4115.88423663174535.5157633682552
48144.6132.24182630456012.3581736954404
49140.4133.0390322885607.3609677114396
50139.5132.7211030198036.7788969801968
51138.1127.35915799019810.7408420098019
52136.7131.9254495343734.77455046562679
53130131.000411103601-1.00041110360144
54128.5131.017307672957-2.5173076729574
55130.4127.4849600689762.91503993102424
56125.7130.795178791412-5.09517879141232
57121.7141.101605045243-19.4016050452431
58129.9139.549591732372-9.64959173237216
59129.6129.975991063662-0.375991063661814
60128.2119.118315720559.08168427944997
61119.7115.7929474024793.90705259752085
62112.2113.877599890108-1.67759989010841
63105.6107.441813150535-1.84181315053543
64101.2102.176391693773-0.976391693773166
6594.993.57180373878721.32819626121280
6695.191.70069302697673.3993069730233
6793.192.452958741330.647041258669972
6891.488.32203814799463.07796185200536
6989.891.461924309446-1.66192430944595
7085.9102.895263679034-16.9952636790344
7189.796.5038267266136-6.8038267266136
7291.688.81295526121872.78704473878125
7388.678.84862413478789.75137586521217







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7474.790446756996643.0784411307395106.502452383254
7568.325332544364933.8140733432684102.836591745461
7663.883137131845425.8880535529317101.878220710759
7756.787183056233314.670335201470398.9040309109964
7855.35538439100848.53643543212566102.174333349891
7952.46333574766810.419496725554822104.507174769781
8048.9557412045722-8.7837595524323106.695241961577
8147.0215638417077-16.8396901621975110.882817845613
8248.3885074809065-21.9831494899258118.760164451739
8355.032860911676-22.2067691501459132.272490973498
8456.8372050763588-27.6021831471619141.276593299880
8551.0515583301586-40.8978792867074143.000995947025

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 74.7904467569966 & 43.0784411307395 & 106.502452383254 \tabularnewline
75 & 68.3253325443649 & 33.8140733432684 & 102.836591745461 \tabularnewline
76 & 63.8831371318454 & 25.8880535529317 & 101.878220710759 \tabularnewline
77 & 56.7871830562333 & 14.6703352014703 & 98.9040309109964 \tabularnewline
78 & 55.3553843910084 & 8.53643543212566 & 102.174333349891 \tabularnewline
79 & 52.4633357476681 & 0.419496725554822 & 104.507174769781 \tabularnewline
80 & 48.9557412045722 & -8.7837595524323 & 106.695241961577 \tabularnewline
81 & 47.0215638417077 & -16.8396901621975 & 110.882817845613 \tabularnewline
82 & 48.3885074809065 & -21.9831494899258 & 118.760164451739 \tabularnewline
83 & 55.032860911676 & -22.2067691501459 & 132.272490973498 \tabularnewline
84 & 56.8372050763588 & -27.6021831471619 & 141.276593299880 \tabularnewline
85 & 51.0515583301586 & -40.8978792867074 & 143.000995947025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72651&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]74[/C][C]74.7904467569966[/C][C]43.0784411307395[/C][C]106.502452383254[/C][/ROW]
[ROW][C]75[/C][C]68.3253325443649[/C][C]33.8140733432684[/C][C]102.836591745461[/C][/ROW]
[ROW][C]76[/C][C]63.8831371318454[/C][C]25.8880535529317[/C][C]101.878220710759[/C][/ROW]
[ROW][C]77[/C][C]56.7871830562333[/C][C]14.6703352014703[/C][C]98.9040309109964[/C][/ROW]
[ROW][C]78[/C][C]55.3553843910084[/C][C]8.53643543212566[/C][C]102.174333349891[/C][/ROW]
[ROW][C]79[/C][C]52.4633357476681[/C][C]0.419496725554822[/C][C]104.507174769781[/C][/ROW]
[ROW][C]80[/C][C]48.9557412045722[/C][C]-8.7837595524323[/C][C]106.695241961577[/C][/ROW]
[ROW][C]81[/C][C]47.0215638417077[/C][C]-16.8396901621975[/C][C]110.882817845613[/C][/ROW]
[ROW][C]82[/C][C]48.3885074809065[/C][C]-21.9831494899258[/C][C]118.760164451739[/C][/ROW]
[ROW][C]83[/C][C]55.032860911676[/C][C]-22.2067691501459[/C][C]132.272490973498[/C][/ROW]
[ROW][C]84[/C][C]56.8372050763588[/C][C]-27.6021831471619[/C][C]141.276593299880[/C][/ROW]
[ROW][C]85[/C][C]51.0515583301586[/C][C]-40.8978792867074[/C][C]143.000995947025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72651&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72651&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
7474.790446756996643.0784411307395106.502452383254
7568.325332544364933.8140733432684102.836591745461
7663.883137131845425.8880535529317101.878220710759
7756.787183056233314.670335201470398.9040309109964
7855.35538439100848.53643543212566102.174333349891
7952.46333574766810.419496725554822104.507174769781
8048.9557412045722-8.7837595524323106.695241961577
8147.0215638417077-16.8396901621975110.882817845613
8248.3885074809065-21.9831494899258118.760164451739
8355.032860911676-22.2067691501459132.272490973498
8456.8372050763588-27.6021831471619141.276593299880
8551.0515583301586-40.8978792867074143.000995947025



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')