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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 computationWed, 08 Dec 2010 17:06:08 +0000
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/Dec/08/t1291829014j5sgph55xmzbiup.htm/, Retrieved Fri, 03 May 2024 15:01:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107023, Retrieved Fri, 03 May 2024 15:01:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-08 17:06:08] [b7dd4adfab743bef2d672ff51f950617] [Current]
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Dataseries X:
186448
190530
194207
190855
200779
204428
207617
212071
214239
215883
223484
221529
225247
226699
231406
232324
237192
236727
240698
240688
245283
243556
247826
245798
250479
249216
251896
247616
249994
246552
248771
247551
249745
245742
249019
245841
248771
244723
246878
246014
248496
244351
248016
246509
249426
247840
251035
250161
254278
250801
253985
249174
251287
247947
249992
243805
255812
250417
253033
248705
253950
251484
251093
245996
252721
248019
250464
245571
252690
250183
253639
254436
265280
268705
270643
271480




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107023&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107023&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107023&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.415713187131023
beta0.533706293812228
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.415713187131023 \tabularnewline
beta & 0.533706293812228 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107023&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]0.415713187131023[/C][/ROW]
[ROW][C]beta[/C][C]0.533706293812228[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107023&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107023&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
alpha0.415713187131023
beta0.533706293812228
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3194207194612-405
4190855198435.779317733-7580.77931773296
5200779197594.5545564003184.44544360027
6204428201935.1046029402492.89539705965
7207617206541.2637472211075.73625277937
8212071210796.9633986621274.03660133804
9214239215417.768021061-1178.76802106085
10215883218757.377635710-2874.37763570971
11223484220754.3654163782729.6345836221
12221529225686.635575184-4157.63557518445
13225247226833.327320933-1586.32732093311
14226699228696.989365262-1997.98936526186
15231406229946.2266773411459.77332265853
16232324232956.779610955-632.779610955215
17237192234957.0366775362234.96332246382
18236727238645.320804960-1918.32080495975
19240698240181.414522373516.585477627203
20240688242844.345062178-2156.34506217801
21245283243917.6775568781365.32244312158
22243556246757.936050369-3201.93605036903
23247826246989.115427959836.88457204125
24245798249084.964327941-3286.96432794144
25250479248737.2002101621741.79978983794
26249216250866.410583469-1650.41058346943
27251896251219.259847184676.740152816288
28247616252689.683848399-5073.68384839906
29249994250643.888895825-649.888895825279
30246552250292.933808889-3740.93380888866
31248771247826.994302543944.005697456509
32247551247518.09128869132.9087113087589
33249745246837.7346574002907.26534260032
34245742247997.317293432-2255.31729343228
35249019246510.3618319122508.63816808816
36245841247560.433879139-1719.43387913931
37248771246471.3519843642299.64801563646
38244723247563.275451180-2840.27545117974
39246878245888.296603914989.703396086057
40246014246025.0747197-11.0747197000892
41248496245743.3590412072752.64095879253
42244351247221.281409036-2870.28140903582
43248016245724.8550660682291.14493393217
44246509246882.43516799-373.435167990014
45249426246849.4605915422576.53940845776
46247840248614.482911658-774.482911657542
47251035248814.6075117682220.39248823244
48250161250752.377002849-591.377002848982
49254278251390.0487642302887.95123576961
50250801254114.86927131-3313.86927131008
51253985253526.267195070458.732804929517
52249174254607.764023163-5433.76402316292
53251287252034.089813545-747.089813544939
54247947251242.971997772-3295.97199777234
55249992248660.9770768741331.02292312571
56243805248297.797346093-4492.79734609343
57255812244516.76742392911295.2325760708
58250417249805.088808503611.911191497289
59253033250787.9765788872245.02342111259
60248705252947.871166762-4242.87116676228
61253950251469.3019193532480.69808064739
62251484253336.19844105-1852.19844105004
63251093252990.907797722-1897.90779772206
64245996252205.528751997-6209.52875199678
65252721248250.0516701944470.94832980601
66248019249726.553448325-1707.5534483254
67250464248255.7178210122208.28217898804
68245571248902.695496927-3331.69549692675
69252690246507.4322999516182.5677000492
70250183249439.092312525743.907687474944
71253639250274.8795021143364.12049788595
72254436252946.3169009321489.68309906818
73265280255169.04007334310110.9599266574
74268705263219.0476964205485.95230357972
75270643270563.54000939679.4599906041985
76271480275678.11186009-4198.11186008976

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 194207 & 194612 & -405 \tabularnewline
4 & 190855 & 198435.779317733 & -7580.77931773296 \tabularnewline
5 & 200779 & 197594.554556400 & 3184.44544360027 \tabularnewline
6 & 204428 & 201935.104602940 & 2492.89539705965 \tabularnewline
7 & 207617 & 206541.263747221 & 1075.73625277937 \tabularnewline
8 & 212071 & 210796.963398662 & 1274.03660133804 \tabularnewline
9 & 214239 & 215417.768021061 & -1178.76802106085 \tabularnewline
10 & 215883 & 218757.377635710 & -2874.37763570971 \tabularnewline
11 & 223484 & 220754.365416378 & 2729.6345836221 \tabularnewline
12 & 221529 & 225686.635575184 & -4157.63557518445 \tabularnewline
13 & 225247 & 226833.327320933 & -1586.32732093311 \tabularnewline
14 & 226699 & 228696.989365262 & -1997.98936526186 \tabularnewline
15 & 231406 & 229946.226677341 & 1459.77332265853 \tabularnewline
16 & 232324 & 232956.779610955 & -632.779610955215 \tabularnewline
17 & 237192 & 234957.036677536 & 2234.96332246382 \tabularnewline
18 & 236727 & 238645.320804960 & -1918.32080495975 \tabularnewline
19 & 240698 & 240181.414522373 & 516.585477627203 \tabularnewline
20 & 240688 & 242844.345062178 & -2156.34506217801 \tabularnewline
21 & 245283 & 243917.677556878 & 1365.32244312158 \tabularnewline
22 & 243556 & 246757.936050369 & -3201.93605036903 \tabularnewline
23 & 247826 & 246989.115427959 & 836.88457204125 \tabularnewline
24 & 245798 & 249084.964327941 & -3286.96432794144 \tabularnewline
25 & 250479 & 248737.200210162 & 1741.79978983794 \tabularnewline
26 & 249216 & 250866.410583469 & -1650.41058346943 \tabularnewline
27 & 251896 & 251219.259847184 & 676.740152816288 \tabularnewline
28 & 247616 & 252689.683848399 & -5073.68384839906 \tabularnewline
29 & 249994 & 250643.888895825 & -649.888895825279 \tabularnewline
30 & 246552 & 250292.933808889 & -3740.93380888866 \tabularnewline
31 & 248771 & 247826.994302543 & 944.005697456509 \tabularnewline
32 & 247551 & 247518.091288691 & 32.9087113087589 \tabularnewline
33 & 249745 & 246837.734657400 & 2907.26534260032 \tabularnewline
34 & 245742 & 247997.317293432 & -2255.31729343228 \tabularnewline
35 & 249019 & 246510.361831912 & 2508.63816808816 \tabularnewline
36 & 245841 & 247560.433879139 & -1719.43387913931 \tabularnewline
37 & 248771 & 246471.351984364 & 2299.64801563646 \tabularnewline
38 & 244723 & 247563.275451180 & -2840.27545117974 \tabularnewline
39 & 246878 & 245888.296603914 & 989.703396086057 \tabularnewline
40 & 246014 & 246025.0747197 & -11.0747197000892 \tabularnewline
41 & 248496 & 245743.359041207 & 2752.64095879253 \tabularnewline
42 & 244351 & 247221.281409036 & -2870.28140903582 \tabularnewline
43 & 248016 & 245724.855066068 & 2291.14493393217 \tabularnewline
44 & 246509 & 246882.43516799 & -373.435167990014 \tabularnewline
45 & 249426 & 246849.460591542 & 2576.53940845776 \tabularnewline
46 & 247840 & 248614.482911658 & -774.482911657542 \tabularnewline
47 & 251035 & 248814.607511768 & 2220.39248823244 \tabularnewline
48 & 250161 & 250752.377002849 & -591.377002848982 \tabularnewline
49 & 254278 & 251390.048764230 & 2887.95123576961 \tabularnewline
50 & 250801 & 254114.86927131 & -3313.86927131008 \tabularnewline
51 & 253985 & 253526.267195070 & 458.732804929517 \tabularnewline
52 & 249174 & 254607.764023163 & -5433.76402316292 \tabularnewline
53 & 251287 & 252034.089813545 & -747.089813544939 \tabularnewline
54 & 247947 & 251242.971997772 & -3295.97199777234 \tabularnewline
55 & 249992 & 248660.977076874 & 1331.02292312571 \tabularnewline
56 & 243805 & 248297.797346093 & -4492.79734609343 \tabularnewline
57 & 255812 & 244516.767423929 & 11295.2325760708 \tabularnewline
58 & 250417 & 249805.088808503 & 611.911191497289 \tabularnewline
59 & 253033 & 250787.976578887 & 2245.02342111259 \tabularnewline
60 & 248705 & 252947.871166762 & -4242.87116676228 \tabularnewline
61 & 253950 & 251469.301919353 & 2480.69808064739 \tabularnewline
62 & 251484 & 253336.19844105 & -1852.19844105004 \tabularnewline
63 & 251093 & 252990.907797722 & -1897.90779772206 \tabularnewline
64 & 245996 & 252205.528751997 & -6209.52875199678 \tabularnewline
65 & 252721 & 248250.051670194 & 4470.94832980601 \tabularnewline
66 & 248019 & 249726.553448325 & -1707.5534483254 \tabularnewline
67 & 250464 & 248255.717821012 & 2208.28217898804 \tabularnewline
68 & 245571 & 248902.695496927 & -3331.69549692675 \tabularnewline
69 & 252690 & 246507.432299951 & 6182.5677000492 \tabularnewline
70 & 250183 & 249439.092312525 & 743.907687474944 \tabularnewline
71 & 253639 & 250274.879502114 & 3364.12049788595 \tabularnewline
72 & 254436 & 252946.316900932 & 1489.68309906818 \tabularnewline
73 & 265280 & 255169.040073343 & 10110.9599266574 \tabularnewline
74 & 268705 & 263219.047696420 & 5485.95230357972 \tabularnewline
75 & 270643 & 270563.540009396 & 79.4599906041985 \tabularnewline
76 & 271480 & 275678.11186009 & -4198.11186008976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107023&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]3[/C][C]194207[/C][C]194612[/C][C]-405[/C][/ROW]
[ROW][C]4[/C][C]190855[/C][C]198435.779317733[/C][C]-7580.77931773296[/C][/ROW]
[ROW][C]5[/C][C]200779[/C][C]197594.554556400[/C][C]3184.44544360027[/C][/ROW]
[ROW][C]6[/C][C]204428[/C][C]201935.104602940[/C][C]2492.89539705965[/C][/ROW]
[ROW][C]7[/C][C]207617[/C][C]206541.263747221[/C][C]1075.73625277937[/C][/ROW]
[ROW][C]8[/C][C]212071[/C][C]210796.963398662[/C][C]1274.03660133804[/C][/ROW]
[ROW][C]9[/C][C]214239[/C][C]215417.768021061[/C][C]-1178.76802106085[/C][/ROW]
[ROW][C]10[/C][C]215883[/C][C]218757.377635710[/C][C]-2874.37763570971[/C][/ROW]
[ROW][C]11[/C][C]223484[/C][C]220754.365416378[/C][C]2729.6345836221[/C][/ROW]
[ROW][C]12[/C][C]221529[/C][C]225686.635575184[/C][C]-4157.63557518445[/C][/ROW]
[ROW][C]13[/C][C]225247[/C][C]226833.327320933[/C][C]-1586.32732093311[/C][/ROW]
[ROW][C]14[/C][C]226699[/C][C]228696.989365262[/C][C]-1997.98936526186[/C][/ROW]
[ROW][C]15[/C][C]231406[/C][C]229946.226677341[/C][C]1459.77332265853[/C][/ROW]
[ROW][C]16[/C][C]232324[/C][C]232956.779610955[/C][C]-632.779610955215[/C][/ROW]
[ROW][C]17[/C][C]237192[/C][C]234957.036677536[/C][C]2234.96332246382[/C][/ROW]
[ROW][C]18[/C][C]236727[/C][C]238645.320804960[/C][C]-1918.32080495975[/C][/ROW]
[ROW][C]19[/C][C]240698[/C][C]240181.414522373[/C][C]516.585477627203[/C][/ROW]
[ROW][C]20[/C][C]240688[/C][C]242844.345062178[/C][C]-2156.34506217801[/C][/ROW]
[ROW][C]21[/C][C]245283[/C][C]243917.677556878[/C][C]1365.32244312158[/C][/ROW]
[ROW][C]22[/C][C]243556[/C][C]246757.936050369[/C][C]-3201.93605036903[/C][/ROW]
[ROW][C]23[/C][C]247826[/C][C]246989.115427959[/C][C]836.88457204125[/C][/ROW]
[ROW][C]24[/C][C]245798[/C][C]249084.964327941[/C][C]-3286.96432794144[/C][/ROW]
[ROW][C]25[/C][C]250479[/C][C]248737.200210162[/C][C]1741.79978983794[/C][/ROW]
[ROW][C]26[/C][C]249216[/C][C]250866.410583469[/C][C]-1650.41058346943[/C][/ROW]
[ROW][C]27[/C][C]251896[/C][C]251219.259847184[/C][C]676.740152816288[/C][/ROW]
[ROW][C]28[/C][C]247616[/C][C]252689.683848399[/C][C]-5073.68384839906[/C][/ROW]
[ROW][C]29[/C][C]249994[/C][C]250643.888895825[/C][C]-649.888895825279[/C][/ROW]
[ROW][C]30[/C][C]246552[/C][C]250292.933808889[/C][C]-3740.93380888866[/C][/ROW]
[ROW][C]31[/C][C]248771[/C][C]247826.994302543[/C][C]944.005697456509[/C][/ROW]
[ROW][C]32[/C][C]247551[/C][C]247518.091288691[/C][C]32.9087113087589[/C][/ROW]
[ROW][C]33[/C][C]249745[/C][C]246837.734657400[/C][C]2907.26534260032[/C][/ROW]
[ROW][C]34[/C][C]245742[/C][C]247997.317293432[/C][C]-2255.31729343228[/C][/ROW]
[ROW][C]35[/C][C]249019[/C][C]246510.361831912[/C][C]2508.63816808816[/C][/ROW]
[ROW][C]36[/C][C]245841[/C][C]247560.433879139[/C][C]-1719.43387913931[/C][/ROW]
[ROW][C]37[/C][C]248771[/C][C]246471.351984364[/C][C]2299.64801563646[/C][/ROW]
[ROW][C]38[/C][C]244723[/C][C]247563.275451180[/C][C]-2840.27545117974[/C][/ROW]
[ROW][C]39[/C][C]246878[/C][C]245888.296603914[/C][C]989.703396086057[/C][/ROW]
[ROW][C]40[/C][C]246014[/C][C]246025.0747197[/C][C]-11.0747197000892[/C][/ROW]
[ROW][C]41[/C][C]248496[/C][C]245743.359041207[/C][C]2752.64095879253[/C][/ROW]
[ROW][C]42[/C][C]244351[/C][C]247221.281409036[/C][C]-2870.28140903582[/C][/ROW]
[ROW][C]43[/C][C]248016[/C][C]245724.855066068[/C][C]2291.14493393217[/C][/ROW]
[ROW][C]44[/C][C]246509[/C][C]246882.43516799[/C][C]-373.435167990014[/C][/ROW]
[ROW][C]45[/C][C]249426[/C][C]246849.460591542[/C][C]2576.53940845776[/C][/ROW]
[ROW][C]46[/C][C]247840[/C][C]248614.482911658[/C][C]-774.482911657542[/C][/ROW]
[ROW][C]47[/C][C]251035[/C][C]248814.607511768[/C][C]2220.39248823244[/C][/ROW]
[ROW][C]48[/C][C]250161[/C][C]250752.377002849[/C][C]-591.377002848982[/C][/ROW]
[ROW][C]49[/C][C]254278[/C][C]251390.048764230[/C][C]2887.95123576961[/C][/ROW]
[ROW][C]50[/C][C]250801[/C][C]254114.86927131[/C][C]-3313.86927131008[/C][/ROW]
[ROW][C]51[/C][C]253985[/C][C]253526.267195070[/C][C]458.732804929517[/C][/ROW]
[ROW][C]52[/C][C]249174[/C][C]254607.764023163[/C][C]-5433.76402316292[/C][/ROW]
[ROW][C]53[/C][C]251287[/C][C]252034.089813545[/C][C]-747.089813544939[/C][/ROW]
[ROW][C]54[/C][C]247947[/C][C]251242.971997772[/C][C]-3295.97199777234[/C][/ROW]
[ROW][C]55[/C][C]249992[/C][C]248660.977076874[/C][C]1331.02292312571[/C][/ROW]
[ROW][C]56[/C][C]243805[/C][C]248297.797346093[/C][C]-4492.79734609343[/C][/ROW]
[ROW][C]57[/C][C]255812[/C][C]244516.767423929[/C][C]11295.2325760708[/C][/ROW]
[ROW][C]58[/C][C]250417[/C][C]249805.088808503[/C][C]611.911191497289[/C][/ROW]
[ROW][C]59[/C][C]253033[/C][C]250787.976578887[/C][C]2245.02342111259[/C][/ROW]
[ROW][C]60[/C][C]248705[/C][C]252947.871166762[/C][C]-4242.87116676228[/C][/ROW]
[ROW][C]61[/C][C]253950[/C][C]251469.301919353[/C][C]2480.69808064739[/C][/ROW]
[ROW][C]62[/C][C]251484[/C][C]253336.19844105[/C][C]-1852.19844105004[/C][/ROW]
[ROW][C]63[/C][C]251093[/C][C]252990.907797722[/C][C]-1897.90779772206[/C][/ROW]
[ROW][C]64[/C][C]245996[/C][C]252205.528751997[/C][C]-6209.52875199678[/C][/ROW]
[ROW][C]65[/C][C]252721[/C][C]248250.051670194[/C][C]4470.94832980601[/C][/ROW]
[ROW][C]66[/C][C]248019[/C][C]249726.553448325[/C][C]-1707.5534483254[/C][/ROW]
[ROW][C]67[/C][C]250464[/C][C]248255.717821012[/C][C]2208.28217898804[/C][/ROW]
[ROW][C]68[/C][C]245571[/C][C]248902.695496927[/C][C]-3331.69549692675[/C][/ROW]
[ROW][C]69[/C][C]252690[/C][C]246507.432299951[/C][C]6182.5677000492[/C][/ROW]
[ROW][C]70[/C][C]250183[/C][C]249439.092312525[/C][C]743.907687474944[/C][/ROW]
[ROW][C]71[/C][C]253639[/C][C]250274.879502114[/C][C]3364.12049788595[/C][/ROW]
[ROW][C]72[/C][C]254436[/C][C]252946.316900932[/C][C]1489.68309906818[/C][/ROW]
[ROW][C]73[/C][C]265280[/C][C]255169.040073343[/C][C]10110.9599266574[/C][/ROW]
[ROW][C]74[/C][C]268705[/C][C]263219.047696420[/C][C]5485.95230357972[/C][/ROW]
[ROW][C]75[/C][C]270643[/C][C]270563.540009396[/C][C]79.4599906041985[/C][/ROW]
[ROW][C]76[/C][C]271480[/C][C]275678.11186009[/C][C]-4198.11186008976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107023&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107023&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
3194207194612-405
4190855198435.779317733-7580.77931773296
5200779197594.5545564003184.44544360027
6204428201935.1046029402492.89539705965
7207617206541.2637472211075.73625277937
8212071210796.9633986621274.03660133804
9214239215417.768021061-1178.76802106085
10215883218757.377635710-2874.37763570971
11223484220754.3654163782729.6345836221
12221529225686.635575184-4157.63557518445
13225247226833.327320933-1586.32732093311
14226699228696.989365262-1997.98936526186
15231406229946.2266773411459.77332265853
16232324232956.779610955-632.779610955215
17237192234957.0366775362234.96332246382
18236727238645.320804960-1918.32080495975
19240698240181.414522373516.585477627203
20240688242844.345062178-2156.34506217801
21245283243917.6775568781365.32244312158
22243556246757.936050369-3201.93605036903
23247826246989.115427959836.88457204125
24245798249084.964327941-3286.96432794144
25250479248737.2002101621741.79978983794
26249216250866.410583469-1650.41058346943
27251896251219.259847184676.740152816288
28247616252689.683848399-5073.68384839906
29249994250643.888895825-649.888895825279
30246552250292.933808889-3740.93380888866
31248771247826.994302543944.005697456509
32247551247518.09128869132.9087113087589
33249745246837.7346574002907.26534260032
34245742247997.317293432-2255.31729343228
35249019246510.3618319122508.63816808816
36245841247560.433879139-1719.43387913931
37248771246471.3519843642299.64801563646
38244723247563.275451180-2840.27545117974
39246878245888.296603914989.703396086057
40246014246025.0747197-11.0747197000892
41248496245743.3590412072752.64095879253
42244351247221.281409036-2870.28140903582
43248016245724.8550660682291.14493393217
44246509246882.43516799-373.435167990014
45249426246849.4605915422576.53940845776
46247840248614.482911658-774.482911657542
47251035248814.6075117682220.39248823244
48250161250752.377002849-591.377002848982
49254278251390.0487642302887.95123576961
50250801254114.86927131-3313.86927131008
51253985253526.267195070458.732804929517
52249174254607.764023163-5433.76402316292
53251287252034.089813545-747.089813544939
54247947251242.971997772-3295.97199777234
55249992248660.9770768741331.02292312571
56243805248297.797346093-4492.79734609343
57255812244516.76742392911295.2325760708
58250417249805.088808503611.911191497289
59253033250787.9765788872245.02342111259
60248705252947.871166762-4242.87116676228
61253950251469.3019193532480.69808064739
62251484253336.19844105-1852.19844105004
63251093252990.907797722-1897.90779772206
64245996252205.528751997-6209.52875199678
65252721248250.0516701944470.94832980601
66248019249726.553448325-1707.5534483254
67250464248255.7178210122208.28217898804
68245571248902.695496927-3331.69549692675
69252690246507.4322999516182.5677000492
70250183249439.092312525743.907687474944
71253639250274.8795021143364.12049788595
72254436252946.3169009321489.68309906818
73265280255169.04007334310110.9599266574
74268705263219.0476964205485.95230357972
75270643270563.54000939679.4599906041985
76271480275678.11186009-4198.11186008976







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
77278083.010876332271587.184362263284578.837390401
78282233.120353865274529.303656385289936.937051344
79286383.229831398276869.191679495295897.267983300
80290533.339308930278707.334571495302359.344046366

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 278083.010876332 & 271587.184362263 & 284578.837390401 \tabularnewline
78 & 282233.120353865 & 274529.303656385 & 289936.937051344 \tabularnewline
79 & 286383.229831398 & 276869.191679495 & 295897.267983300 \tabularnewline
80 & 290533.339308930 & 278707.334571495 & 302359.344046366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107023&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]77[/C][C]278083.010876332[/C][C]271587.184362263[/C][C]284578.837390401[/C][/ROW]
[ROW][C]78[/C][C]282233.120353865[/C][C]274529.303656385[/C][C]289936.937051344[/C][/ROW]
[ROW][C]79[/C][C]286383.229831398[/C][C]276869.191679495[/C][C]295897.267983300[/C][/ROW]
[ROW][C]80[/C][C]290533.339308930[/C][C]278707.334571495[/C][C]302359.344046366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107023&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107023&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
77278083.010876332271587.184362263284578.837390401
78282233.120353865274529.303656385289936.937051344
79286383.229831398276869.191679495295897.267983300
80290533.339308930278707.334571495302359.344046366



Parameters (Session):
par1 = 4 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Double ; 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')