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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 03 Jun 2009 02:19:01 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/03/t1244017172r1wocut1zhjyxwq.htm/, Retrieved Sat, 11 May 2024 09:28:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41415, Retrieved Sat, 11 May 2024 09:28:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2009-06-03 08:19:01] [8c726525c89fb87c09aaacaddee1db18] [Current]
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Dataseries X:
104.9
110.9
104.8
94.1
95.8
99.3
101.1
104.0
99.0
105.4
107.1
110.7
117.1
118.7
126.5
127.5
134.6
131.8
135.9
142.7
141.7
153.4
145.0
137.7
148.3
152.2
169.4
168.6
161.1
174.1
179.0
190.6
190.0
181.6
174.8
180.5
196.8
193.8
197.0
216.3
221.4
217.9
229.7
227.4
204.2
196.6
198.8
207.5
190.7
201.6
210.5
223.5
223.8
231.2
244.0
234.7
250.2
265.7
287.6
283.3
295.4
312.3
333.8
347.7
383.2
407.1
413.6
362.7
321.9
239.4
191.0
159.7
166.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41415&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41415&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.957353257069885
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.957353257069885 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41415&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]0.957353257069885[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41415&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
alpha0.957353257069885
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13117.1102.17663081878414.9233691812163
14118.7117.895799141110.804200858889956
15126.5125.9445123739480.555487626051615
16127.5126.5792750466080.920724953391655
17134.6133.8443185730420.755681426957523
18131.8131.948238356519-0.148238356518533
19135.9132.8645553902993.03544460970102
20142.7141.4239187848841.27608121511639
21141.7136.9113804550694.78861954493138
22153.4150.2563509334963.14364906650397
23145154.300635295941-9.3006352959407
24137.7149.168704141094-11.4687041410942
25148.3146.3567136653651.94328633463502
26152.2148.5076530622943.69234693770568
27169.4160.5198599438988.8801400561016
28168.6168.2051485187050.394851481295092
29161.1176.055387922463-14.9553879224631
30174.1157.96845338679816.1315466132021
31179174.0895605192954.91043948070464
32190.6185.2216774321765.37832256782394
33190182.0074720519377.99252794806296
34181.6200.333118707867-18.7331187078675
35174.8182.444294692526-7.64429469252596
36180.5178.9427934068001.55720659320033
37196.8190.9804630555515.81953694444854
38193.8196.099520064709-2.29952006470918
39197204.141850797993-7.14185079799313
40216.3195.45502684454520.8449731554553
41221.4223.226498741323-1.82649874132269
42217.9216.9605283085130.93947169148717
43229.7217.39280782850212.3071921714979
44227.4236.619824888423-9.21982488842281
45204.2217.385637574193-13.1856375741935
46196.6214.734558725146-18.1345587251464
47198.8197.6811115749021.11888842509794
48207.5203.1547248830234.34527511697695
49190.7219.195992521388-28.4959925213879
50201.6191.20646277283010.3935372271696
51210.5211.451524222904-0.951524222904283
52223.5209.55142907948413.948570920516
53223.8229.871774609051-6.07177460905118
54231.2219.57211932768111.6278806723193
55244230.52806214368713.4719378563130
56234.7250.154272103299-15.4542721032990
57250.2224.28165499541325.9183450045866
58265.7260.3041910315355.39580896846536
59287.6266.02252462144521.5774753785553
60283.3291.985011157394-8.68501115739411
61295.4296.698905157106-1.29890515710639
62312.3295.31773744016216.9822625598378
63333.8325.1211475139178.67885248608269
64347.7331.10898771121316.5910122887865
65383.2354.83733862684628.3626613731541
66407.1373.54992552086633.5500744791339
67413.6403.3056698866410.2943301133598
68362.7420.409578669385-57.7095786693847
69321.9348.989932621302-27.0899326213023
70239.4335.578167141133-96.1781671411326
71191244.812215446257-53.812215446257
72159.7196.901756882860-37.2017568828596
73166.7170.130429651811-3.43042965181058

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 117.1 & 102.176630818784 & 14.9233691812163 \tabularnewline
14 & 118.7 & 117.89579914111 & 0.804200858889956 \tabularnewline
15 & 126.5 & 125.944512373948 & 0.555487626051615 \tabularnewline
16 & 127.5 & 126.579275046608 & 0.920724953391655 \tabularnewline
17 & 134.6 & 133.844318573042 & 0.755681426957523 \tabularnewline
18 & 131.8 & 131.948238356519 & -0.148238356518533 \tabularnewline
19 & 135.9 & 132.864555390299 & 3.03544460970102 \tabularnewline
20 & 142.7 & 141.423918784884 & 1.27608121511639 \tabularnewline
21 & 141.7 & 136.911380455069 & 4.78861954493138 \tabularnewline
22 & 153.4 & 150.256350933496 & 3.14364906650397 \tabularnewline
23 & 145 & 154.300635295941 & -9.3006352959407 \tabularnewline
24 & 137.7 & 149.168704141094 & -11.4687041410942 \tabularnewline
25 & 148.3 & 146.356713665365 & 1.94328633463502 \tabularnewline
26 & 152.2 & 148.507653062294 & 3.69234693770568 \tabularnewline
27 & 169.4 & 160.519859943898 & 8.8801400561016 \tabularnewline
28 & 168.6 & 168.205148518705 & 0.394851481295092 \tabularnewline
29 & 161.1 & 176.055387922463 & -14.9553879224631 \tabularnewline
30 & 174.1 & 157.968453386798 & 16.1315466132021 \tabularnewline
31 & 179 & 174.089560519295 & 4.91043948070464 \tabularnewline
32 & 190.6 & 185.221677432176 & 5.37832256782394 \tabularnewline
33 & 190 & 182.007472051937 & 7.99252794806296 \tabularnewline
34 & 181.6 & 200.333118707867 & -18.7331187078675 \tabularnewline
35 & 174.8 & 182.444294692526 & -7.64429469252596 \tabularnewline
36 & 180.5 & 178.942793406800 & 1.55720659320033 \tabularnewline
37 & 196.8 & 190.980463055551 & 5.81953694444854 \tabularnewline
38 & 193.8 & 196.099520064709 & -2.29952006470918 \tabularnewline
39 & 197 & 204.141850797993 & -7.14185079799313 \tabularnewline
40 & 216.3 & 195.455026844545 & 20.8449731554553 \tabularnewline
41 & 221.4 & 223.226498741323 & -1.82649874132269 \tabularnewline
42 & 217.9 & 216.960528308513 & 0.93947169148717 \tabularnewline
43 & 229.7 & 217.392807828502 & 12.3071921714979 \tabularnewline
44 & 227.4 & 236.619824888423 & -9.21982488842281 \tabularnewline
45 & 204.2 & 217.385637574193 & -13.1856375741935 \tabularnewline
46 & 196.6 & 214.734558725146 & -18.1345587251464 \tabularnewline
47 & 198.8 & 197.681111574902 & 1.11888842509794 \tabularnewline
48 & 207.5 & 203.154724883023 & 4.34527511697695 \tabularnewline
49 & 190.7 & 219.195992521388 & -28.4959925213879 \tabularnewline
50 & 201.6 & 191.206462772830 & 10.3935372271696 \tabularnewline
51 & 210.5 & 211.451524222904 & -0.951524222904283 \tabularnewline
52 & 223.5 & 209.551429079484 & 13.948570920516 \tabularnewline
53 & 223.8 & 229.871774609051 & -6.07177460905118 \tabularnewline
54 & 231.2 & 219.572119327681 & 11.6278806723193 \tabularnewline
55 & 244 & 230.528062143687 & 13.4719378563130 \tabularnewline
56 & 234.7 & 250.154272103299 & -15.4542721032990 \tabularnewline
57 & 250.2 & 224.281654995413 & 25.9183450045866 \tabularnewline
58 & 265.7 & 260.304191031535 & 5.39580896846536 \tabularnewline
59 & 287.6 & 266.022524621445 & 21.5774753785553 \tabularnewline
60 & 283.3 & 291.985011157394 & -8.68501115739411 \tabularnewline
61 & 295.4 & 296.698905157106 & -1.29890515710639 \tabularnewline
62 & 312.3 & 295.317737440162 & 16.9822625598378 \tabularnewline
63 & 333.8 & 325.121147513917 & 8.67885248608269 \tabularnewline
64 & 347.7 & 331.108987711213 & 16.5910122887865 \tabularnewline
65 & 383.2 & 354.837338626846 & 28.3626613731541 \tabularnewline
66 & 407.1 & 373.549925520866 & 33.5500744791339 \tabularnewline
67 & 413.6 & 403.30566988664 & 10.2943301133598 \tabularnewline
68 & 362.7 & 420.409578669385 & -57.7095786693847 \tabularnewline
69 & 321.9 & 348.989932621302 & -27.0899326213023 \tabularnewline
70 & 239.4 & 335.578167141133 & -96.1781671411326 \tabularnewline
71 & 191 & 244.812215446257 & -53.812215446257 \tabularnewline
72 & 159.7 & 196.901756882860 & -37.2017568828596 \tabularnewline
73 & 166.7 & 170.130429651811 & -3.43042965181058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41415&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]117.1[/C][C]102.176630818784[/C][C]14.9233691812163[/C][/ROW]
[ROW][C]14[/C][C]118.7[/C][C]117.89579914111[/C][C]0.804200858889956[/C][/ROW]
[ROW][C]15[/C][C]126.5[/C][C]125.944512373948[/C][C]0.555487626051615[/C][/ROW]
[ROW][C]16[/C][C]127.5[/C][C]126.579275046608[/C][C]0.920724953391655[/C][/ROW]
[ROW][C]17[/C][C]134.6[/C][C]133.844318573042[/C][C]0.755681426957523[/C][/ROW]
[ROW][C]18[/C][C]131.8[/C][C]131.948238356519[/C][C]-0.148238356518533[/C][/ROW]
[ROW][C]19[/C][C]135.9[/C][C]132.864555390299[/C][C]3.03544460970102[/C][/ROW]
[ROW][C]20[/C][C]142.7[/C][C]141.423918784884[/C][C]1.27608121511639[/C][/ROW]
[ROW][C]21[/C][C]141.7[/C][C]136.911380455069[/C][C]4.78861954493138[/C][/ROW]
[ROW][C]22[/C][C]153.4[/C][C]150.256350933496[/C][C]3.14364906650397[/C][/ROW]
[ROW][C]23[/C][C]145[/C][C]154.300635295941[/C][C]-9.3006352959407[/C][/ROW]
[ROW][C]24[/C][C]137.7[/C][C]149.168704141094[/C][C]-11.4687041410942[/C][/ROW]
[ROW][C]25[/C][C]148.3[/C][C]146.356713665365[/C][C]1.94328633463502[/C][/ROW]
[ROW][C]26[/C][C]152.2[/C][C]148.507653062294[/C][C]3.69234693770568[/C][/ROW]
[ROW][C]27[/C][C]169.4[/C][C]160.519859943898[/C][C]8.8801400561016[/C][/ROW]
[ROW][C]28[/C][C]168.6[/C][C]168.205148518705[/C][C]0.394851481295092[/C][/ROW]
[ROW][C]29[/C][C]161.1[/C][C]176.055387922463[/C][C]-14.9553879224631[/C][/ROW]
[ROW][C]30[/C][C]174.1[/C][C]157.968453386798[/C][C]16.1315466132021[/C][/ROW]
[ROW][C]31[/C][C]179[/C][C]174.089560519295[/C][C]4.91043948070464[/C][/ROW]
[ROW][C]32[/C][C]190.6[/C][C]185.221677432176[/C][C]5.37832256782394[/C][/ROW]
[ROW][C]33[/C][C]190[/C][C]182.007472051937[/C][C]7.99252794806296[/C][/ROW]
[ROW][C]34[/C][C]181.6[/C][C]200.333118707867[/C][C]-18.7331187078675[/C][/ROW]
[ROW][C]35[/C][C]174.8[/C][C]182.444294692526[/C][C]-7.64429469252596[/C][/ROW]
[ROW][C]36[/C][C]180.5[/C][C]178.942793406800[/C][C]1.55720659320033[/C][/ROW]
[ROW][C]37[/C][C]196.8[/C][C]190.980463055551[/C][C]5.81953694444854[/C][/ROW]
[ROW][C]38[/C][C]193.8[/C][C]196.099520064709[/C][C]-2.29952006470918[/C][/ROW]
[ROW][C]39[/C][C]197[/C][C]204.141850797993[/C][C]-7.14185079799313[/C][/ROW]
[ROW][C]40[/C][C]216.3[/C][C]195.455026844545[/C][C]20.8449731554553[/C][/ROW]
[ROW][C]41[/C][C]221.4[/C][C]223.226498741323[/C][C]-1.82649874132269[/C][/ROW]
[ROW][C]42[/C][C]217.9[/C][C]216.960528308513[/C][C]0.93947169148717[/C][/ROW]
[ROW][C]43[/C][C]229.7[/C][C]217.392807828502[/C][C]12.3071921714979[/C][/ROW]
[ROW][C]44[/C][C]227.4[/C][C]236.619824888423[/C][C]-9.21982488842281[/C][/ROW]
[ROW][C]45[/C][C]204.2[/C][C]217.385637574193[/C][C]-13.1856375741935[/C][/ROW]
[ROW][C]46[/C][C]196.6[/C][C]214.734558725146[/C][C]-18.1345587251464[/C][/ROW]
[ROW][C]47[/C][C]198.8[/C][C]197.681111574902[/C][C]1.11888842509794[/C][/ROW]
[ROW][C]48[/C][C]207.5[/C][C]203.154724883023[/C][C]4.34527511697695[/C][/ROW]
[ROW][C]49[/C][C]190.7[/C][C]219.195992521388[/C][C]-28.4959925213879[/C][/ROW]
[ROW][C]50[/C][C]201.6[/C][C]191.206462772830[/C][C]10.3935372271696[/C][/ROW]
[ROW][C]51[/C][C]210.5[/C][C]211.451524222904[/C][C]-0.951524222904283[/C][/ROW]
[ROW][C]52[/C][C]223.5[/C][C]209.551429079484[/C][C]13.948570920516[/C][/ROW]
[ROW][C]53[/C][C]223.8[/C][C]229.871774609051[/C][C]-6.07177460905118[/C][/ROW]
[ROW][C]54[/C][C]231.2[/C][C]219.572119327681[/C][C]11.6278806723193[/C][/ROW]
[ROW][C]55[/C][C]244[/C][C]230.528062143687[/C][C]13.4719378563130[/C][/ROW]
[ROW][C]56[/C][C]234.7[/C][C]250.154272103299[/C][C]-15.4542721032990[/C][/ROW]
[ROW][C]57[/C][C]250.2[/C][C]224.281654995413[/C][C]25.9183450045866[/C][/ROW]
[ROW][C]58[/C][C]265.7[/C][C]260.304191031535[/C][C]5.39580896846536[/C][/ROW]
[ROW][C]59[/C][C]287.6[/C][C]266.022524621445[/C][C]21.5774753785553[/C][/ROW]
[ROW][C]60[/C][C]283.3[/C][C]291.985011157394[/C][C]-8.68501115739411[/C][/ROW]
[ROW][C]61[/C][C]295.4[/C][C]296.698905157106[/C][C]-1.29890515710639[/C][/ROW]
[ROW][C]62[/C][C]312.3[/C][C]295.317737440162[/C][C]16.9822625598378[/C][/ROW]
[ROW][C]63[/C][C]333.8[/C][C]325.121147513917[/C][C]8.67885248608269[/C][/ROW]
[ROW][C]64[/C][C]347.7[/C][C]331.108987711213[/C][C]16.5910122887865[/C][/ROW]
[ROW][C]65[/C][C]383.2[/C][C]354.837338626846[/C][C]28.3626613731541[/C][/ROW]
[ROW][C]66[/C][C]407.1[/C][C]373.549925520866[/C][C]33.5500744791339[/C][/ROW]
[ROW][C]67[/C][C]413.6[/C][C]403.30566988664[/C][C]10.2943301133598[/C][/ROW]
[ROW][C]68[/C][C]362.7[/C][C]420.409578669385[/C][C]-57.7095786693847[/C][/ROW]
[ROW][C]69[/C][C]321.9[/C][C]348.989932621302[/C][C]-27.0899326213023[/C][/ROW]
[ROW][C]70[/C][C]239.4[/C][C]335.578167141133[/C][C]-96.1781671411326[/C][/ROW]
[ROW][C]71[/C][C]191[/C][C]244.812215446257[/C][C]-53.812215446257[/C][/ROW]
[ROW][C]72[/C][C]159.7[/C][C]196.901756882860[/C][C]-37.2017568828596[/C][/ROW]
[ROW][C]73[/C][C]166.7[/C][C]170.130429651811[/C][C]-3.43042965181058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41415&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41415&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
13117.1102.17663081878414.9233691812163
14118.7117.895799141110.804200858889956
15126.5125.9445123739480.555487626051615
16127.5126.5792750466080.920724953391655
17134.6133.8443185730420.755681426957523
18131.8131.948238356519-0.148238356518533
19135.9132.8645553902993.03544460970102
20142.7141.4239187848841.27608121511639
21141.7136.9113804550694.78861954493138
22153.4150.2563509334963.14364906650397
23145154.300635295941-9.3006352959407
24137.7149.168704141094-11.4687041410942
25148.3146.3567136653651.94328633463502
26152.2148.5076530622943.69234693770568
27169.4160.5198599438988.8801400561016
28168.6168.2051485187050.394851481295092
29161.1176.055387922463-14.9553879224631
30174.1157.96845338679816.1315466132021
31179174.0895605192954.91043948070464
32190.6185.2216774321765.37832256782394
33190182.0074720519377.99252794806296
34181.6200.333118707867-18.7331187078675
35174.8182.444294692526-7.64429469252596
36180.5178.9427934068001.55720659320033
37196.8190.9804630555515.81953694444854
38193.8196.099520064709-2.29952006470918
39197204.141850797993-7.14185079799313
40216.3195.45502684454520.8449731554553
41221.4223.226498741323-1.82649874132269
42217.9216.9605283085130.93947169148717
43229.7217.39280782850212.3071921714979
44227.4236.619824888423-9.21982488842281
45204.2217.385637574193-13.1856375741935
46196.6214.734558725146-18.1345587251464
47198.8197.6811115749021.11888842509794
48207.5203.1547248830234.34527511697695
49190.7219.195992521388-28.4959925213879
50201.6191.20646277283010.3935372271696
51210.5211.451524222904-0.951524222904283
52223.5209.55142907948413.948570920516
53223.8229.871774609051-6.07177460905118
54231.2219.57211932768111.6278806723193
55244230.52806214368713.4719378563130
56234.7250.154272103299-15.4542721032990
57250.2224.28165499541325.9183450045866
58265.7260.3041910315355.39580896846536
59287.6266.02252462144521.5774753785553
60283.3291.985011157394-8.68501115739411
61295.4296.698905157106-1.29890515710639
62312.3295.31773744016216.9822625598378
63333.8325.1211475139178.67885248608269
64347.7331.10898771121316.5910122887865
65383.2354.83733862684628.3626613731541
66407.1373.54992552086633.5500744791339
67413.6403.3056698866410.2943301133598
68362.7420.409578669385-57.7095786693847
69321.9348.989932621302-27.0899326213023
70239.4335.578167141133-96.1781671411326
71191244.812215446257-53.812215446257
72159.7196.901756882860-37.2017568828596
73166.7170.130429651811-3.43042965181058







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74168.438280600603127.694761980994209.181799220213
75176.915212761224119.620827371940234.209598150508
76177.221119879369108.579007853279245.86323190546
77182.887199178161103.05313031362262.721268042702
78180.41676182409093.6103414532014267.223182194979
79180.50529299976786.5206998067393274.489886192794
80183.84424879888781.853255678764285.83524191901
81177.59720128009872.9635156010914282.230886959105
82183.25836761434470.0029317216867296.513803507002
83185.8209810982766.1442313889135305.497730807626
84189.75335281850163.1727874231555316.333918213847
85201.42483570885868.7698022934731334.079869124243

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 168.438280600603 & 127.694761980994 & 209.181799220213 \tabularnewline
75 & 176.915212761224 & 119.620827371940 & 234.209598150508 \tabularnewline
76 & 177.221119879369 & 108.579007853279 & 245.86323190546 \tabularnewline
77 & 182.887199178161 & 103.05313031362 & 262.721268042702 \tabularnewline
78 & 180.416761824090 & 93.6103414532014 & 267.223182194979 \tabularnewline
79 & 180.505292999767 & 86.5206998067393 & 274.489886192794 \tabularnewline
80 & 183.844248798887 & 81.853255678764 & 285.83524191901 \tabularnewline
81 & 177.597201280098 & 72.9635156010914 & 282.230886959105 \tabularnewline
82 & 183.258367614344 & 70.0029317216867 & 296.513803507002 \tabularnewline
83 & 185.82098109827 & 66.1442313889135 & 305.497730807626 \tabularnewline
84 & 189.753352818501 & 63.1727874231555 & 316.333918213847 \tabularnewline
85 & 201.424835708858 & 68.7698022934731 & 334.079869124243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41415&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]168.438280600603[/C][C]127.694761980994[/C][C]209.181799220213[/C][/ROW]
[ROW][C]75[/C][C]176.915212761224[/C][C]119.620827371940[/C][C]234.209598150508[/C][/ROW]
[ROW][C]76[/C][C]177.221119879369[/C][C]108.579007853279[/C][C]245.86323190546[/C][/ROW]
[ROW][C]77[/C][C]182.887199178161[/C][C]103.05313031362[/C][C]262.721268042702[/C][/ROW]
[ROW][C]78[/C][C]180.416761824090[/C][C]93.6103414532014[/C][C]267.223182194979[/C][/ROW]
[ROW][C]79[/C][C]180.505292999767[/C][C]86.5206998067393[/C][C]274.489886192794[/C][/ROW]
[ROW][C]80[/C][C]183.844248798887[/C][C]81.853255678764[/C][C]285.83524191901[/C][/ROW]
[ROW][C]81[/C][C]177.597201280098[/C][C]72.9635156010914[/C][C]282.230886959105[/C][/ROW]
[ROW][C]82[/C][C]183.258367614344[/C][C]70.0029317216867[/C][C]296.513803507002[/C][/ROW]
[ROW][C]83[/C][C]185.82098109827[/C][C]66.1442313889135[/C][C]305.497730807626[/C][/ROW]
[ROW][C]84[/C][C]189.753352818501[/C][C]63.1727874231555[/C][C]316.333918213847[/C][/ROW]
[ROW][C]85[/C][C]201.424835708858[/C][C]68.7698022934731[/C][C]334.079869124243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41415&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41415&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
74168.438280600603127.694761980994209.181799220213
75176.915212761224119.620827371940234.209598150508
76177.221119879369108.579007853279245.86323190546
77182.887199178161103.05313031362262.721268042702
78180.41676182409093.6103414532014267.223182194979
79180.50529299976786.5206998067393274.489886192794
80183.84424879888781.853255678764285.83524191901
81177.59720128009872.9635156010914282.230886959105
82183.25836761434470.0029317216867296.513803507002
83185.8209810982766.1442313889135305.497730807626
84189.75335281850163.1727874231555316.333918213847
85201.42483570885868.7698022934731334.079869124243



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')