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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 17:04:23 +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/t1291828475qvj7gtp2go1zq2a.htm/, Retrieved Mon, 07 Sep 2026 20:16:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107019, Retrieved Mon, 07 Sep 2026 20:16:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact514
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-08 17:04:23] [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=107019&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=107019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107019&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
alpha0.804058919867005
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.804058919867005 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107019&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]0.804058919867005[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107019&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
alpha0.804058919867005
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21905301864484082
3194207189730.1685108974476.83148910289
4190855193329.804802452-2474.80480245178
5200779191339.9159261119439.08407388927
6204428198929.4956710965498.504328904
7207617203350.6171226794266.38287732139
8212071206781.0403307575289.95966924325
9214239211034.4795885493204.52041145149
10215883213611.1028092722271.89719072802
11223484215437.8420104988046.15798950236
12221529221907.427112616-378.427112616191
13225247221603.1494171983643.85058280238
14226699224533.0199809622165.98001903755
15231406226274.5955355235131.40446447671
16232324230400.5470666311923.45293336883
17237192231947.1165546515244.88344534926
18236727236164.311872547562.68812745341
19240698236616.7462805294081.25371947122
20240688239898.31473791789.685262090003
21245283240533.2682167814749.73178321903
22243556244352.332424054-796.332424054039
23247826243712.0342353144113.96576468591
24245798247019.905104437-1221.90510443729
25250479246037.4214059834441.57859401655
26249216249608.712292793-392.712292792799
27251896249292.9484708312603.05152916868
28247616251385.955271733-3769.95527173285
29249994248354.6891079961639.31089200359
30246552249672.791653147-3120.79165314703
31248771247163.4912873881607.50871261233
32247551248456.023006528-905.02300652754
33249745247728.3311854442016.66881455577
34245742249349.851734205-3607.85173420541
35249019246448.926365762570.07363424011
36245841248515.416996086-2674.41699608567
37248771246365.0281549392405.97184506094
38244723248299.571277909-3576.57127790918
39246878245423.7972393661454.20276063384
40246014246593.061940349-579.061940349027
41248496246127.4620220562368.5379779441
42244351248031.906110266-3680.90611026561
43248016245072.2407191142943.75928088641
44246509247439.196626852-930.196626851597
45249426246691.2637318012734.73626819864
46247840248890.152821730-1050.15282173027
47251035248045.7680781952989.23192180545
48250161250449.286668473-288.286668473418
49254278250217.4872012094060.51279879137
50250801253482.378736311-2681.37873631096
51253985251326.3922458382658.60775416158
52249174253464.069525000-4290.06952499962
53251287250014.6008565741272.39914342592
54247947251037.684737477-3090.68473747684
55249992248552.5921058121439.40789418822
56243805249709.960862461-5904.96086246081
57255812244962.02440953410849.9755904664
58250417253686.044063387-3269.04406338738
59253033251057.5400247821975.45997521753
60248705252645.926238696-3940.92623869638
61253950249477.1893439354472.81065606538
62251484253073.59264882-1589.59264882017
63251093251795.466500581-702.4665005813
64245996251230.642044881-5234.64204488116
65252721247021.6814163845699.3185836164
66248019251604.269360704-3585.26936070414
67250464248721.5015511041742.4984488959
68245571250122.572971793-4551.57297179327
69252690246462.8401243976227.1598756027
70250183251469.843567814-1286.84356781357
71253639250435.1455186403203.85448136041
72254436253011.2332923331424.76670766668
73265280254156.82967236211123.1703276378
74268705263100.5139914995604.48600850062
75270643267606.8509579043036.14904209587
76271480270048.0936772471431.906322753

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 190530 & 186448 & 4082 \tabularnewline
3 & 194207 & 189730.168510897 & 4476.83148910289 \tabularnewline
4 & 190855 & 193329.804802452 & -2474.80480245178 \tabularnewline
5 & 200779 & 191339.915926111 & 9439.08407388927 \tabularnewline
6 & 204428 & 198929.495671096 & 5498.504328904 \tabularnewline
7 & 207617 & 203350.617122679 & 4266.38287732139 \tabularnewline
8 & 212071 & 206781.040330757 & 5289.95966924325 \tabularnewline
9 & 214239 & 211034.479588549 & 3204.52041145149 \tabularnewline
10 & 215883 & 213611.102809272 & 2271.89719072802 \tabularnewline
11 & 223484 & 215437.842010498 & 8046.15798950236 \tabularnewline
12 & 221529 & 221907.427112616 & -378.427112616191 \tabularnewline
13 & 225247 & 221603.149417198 & 3643.85058280238 \tabularnewline
14 & 226699 & 224533.019980962 & 2165.98001903755 \tabularnewline
15 & 231406 & 226274.595535523 & 5131.40446447671 \tabularnewline
16 & 232324 & 230400.547066631 & 1923.45293336883 \tabularnewline
17 & 237192 & 231947.116554651 & 5244.88344534926 \tabularnewline
18 & 236727 & 236164.311872547 & 562.68812745341 \tabularnewline
19 & 240698 & 236616.746280529 & 4081.25371947122 \tabularnewline
20 & 240688 & 239898.31473791 & 789.685262090003 \tabularnewline
21 & 245283 & 240533.268216781 & 4749.73178321903 \tabularnewline
22 & 243556 & 244352.332424054 & -796.332424054039 \tabularnewline
23 & 247826 & 243712.034235314 & 4113.96576468591 \tabularnewline
24 & 245798 & 247019.905104437 & -1221.90510443729 \tabularnewline
25 & 250479 & 246037.421405983 & 4441.57859401655 \tabularnewline
26 & 249216 & 249608.712292793 & -392.712292792799 \tabularnewline
27 & 251896 & 249292.948470831 & 2603.05152916868 \tabularnewline
28 & 247616 & 251385.955271733 & -3769.95527173285 \tabularnewline
29 & 249994 & 248354.689107996 & 1639.31089200359 \tabularnewline
30 & 246552 & 249672.791653147 & -3120.79165314703 \tabularnewline
31 & 248771 & 247163.491287388 & 1607.50871261233 \tabularnewline
32 & 247551 & 248456.023006528 & -905.02300652754 \tabularnewline
33 & 249745 & 247728.331185444 & 2016.66881455577 \tabularnewline
34 & 245742 & 249349.851734205 & -3607.85173420541 \tabularnewline
35 & 249019 & 246448.92636576 & 2570.07363424011 \tabularnewline
36 & 245841 & 248515.416996086 & -2674.41699608567 \tabularnewline
37 & 248771 & 246365.028154939 & 2405.97184506094 \tabularnewline
38 & 244723 & 248299.571277909 & -3576.57127790918 \tabularnewline
39 & 246878 & 245423.797239366 & 1454.20276063384 \tabularnewline
40 & 246014 & 246593.061940349 & -579.061940349027 \tabularnewline
41 & 248496 & 246127.462022056 & 2368.5379779441 \tabularnewline
42 & 244351 & 248031.906110266 & -3680.90611026561 \tabularnewline
43 & 248016 & 245072.240719114 & 2943.75928088641 \tabularnewline
44 & 246509 & 247439.196626852 & -930.196626851597 \tabularnewline
45 & 249426 & 246691.263731801 & 2734.73626819864 \tabularnewline
46 & 247840 & 248890.152821730 & -1050.15282173027 \tabularnewline
47 & 251035 & 248045.768078195 & 2989.23192180545 \tabularnewline
48 & 250161 & 250449.286668473 & -288.286668473418 \tabularnewline
49 & 254278 & 250217.487201209 & 4060.51279879137 \tabularnewline
50 & 250801 & 253482.378736311 & -2681.37873631096 \tabularnewline
51 & 253985 & 251326.392245838 & 2658.60775416158 \tabularnewline
52 & 249174 & 253464.069525000 & -4290.06952499962 \tabularnewline
53 & 251287 & 250014.600856574 & 1272.39914342592 \tabularnewline
54 & 247947 & 251037.684737477 & -3090.68473747684 \tabularnewline
55 & 249992 & 248552.592105812 & 1439.40789418822 \tabularnewline
56 & 243805 & 249709.960862461 & -5904.96086246081 \tabularnewline
57 & 255812 & 244962.024409534 & 10849.9755904664 \tabularnewline
58 & 250417 & 253686.044063387 & -3269.04406338738 \tabularnewline
59 & 253033 & 251057.540024782 & 1975.45997521753 \tabularnewline
60 & 248705 & 252645.926238696 & -3940.92623869638 \tabularnewline
61 & 253950 & 249477.189343935 & 4472.81065606538 \tabularnewline
62 & 251484 & 253073.59264882 & -1589.59264882017 \tabularnewline
63 & 251093 & 251795.466500581 & -702.4665005813 \tabularnewline
64 & 245996 & 251230.642044881 & -5234.64204488116 \tabularnewline
65 & 252721 & 247021.681416384 & 5699.3185836164 \tabularnewline
66 & 248019 & 251604.269360704 & -3585.26936070414 \tabularnewline
67 & 250464 & 248721.501551104 & 1742.4984488959 \tabularnewline
68 & 245571 & 250122.572971793 & -4551.57297179327 \tabularnewline
69 & 252690 & 246462.840124397 & 6227.1598756027 \tabularnewline
70 & 250183 & 251469.843567814 & -1286.84356781357 \tabularnewline
71 & 253639 & 250435.145518640 & 3203.85448136041 \tabularnewline
72 & 254436 & 253011.233292333 & 1424.76670766668 \tabularnewline
73 & 265280 & 254156.829672362 & 11123.1703276378 \tabularnewline
74 & 268705 & 263100.513991499 & 5604.48600850062 \tabularnewline
75 & 270643 & 267606.850957904 & 3036.14904209587 \tabularnewline
76 & 271480 & 270048.093677247 & 1431.906322753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107019&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]2[/C][C]190530[/C][C]186448[/C][C]4082[/C][/ROW]
[ROW][C]3[/C][C]194207[/C][C]189730.168510897[/C][C]4476.83148910289[/C][/ROW]
[ROW][C]4[/C][C]190855[/C][C]193329.804802452[/C][C]-2474.80480245178[/C][/ROW]
[ROW][C]5[/C][C]200779[/C][C]191339.915926111[/C][C]9439.08407388927[/C][/ROW]
[ROW][C]6[/C][C]204428[/C][C]198929.495671096[/C][C]5498.504328904[/C][/ROW]
[ROW][C]7[/C][C]207617[/C][C]203350.617122679[/C][C]4266.38287732139[/C][/ROW]
[ROW][C]8[/C][C]212071[/C][C]206781.040330757[/C][C]5289.95966924325[/C][/ROW]
[ROW][C]9[/C][C]214239[/C][C]211034.479588549[/C][C]3204.52041145149[/C][/ROW]
[ROW][C]10[/C][C]215883[/C][C]213611.102809272[/C][C]2271.89719072802[/C][/ROW]
[ROW][C]11[/C][C]223484[/C][C]215437.842010498[/C][C]8046.15798950236[/C][/ROW]
[ROW][C]12[/C][C]221529[/C][C]221907.427112616[/C][C]-378.427112616191[/C][/ROW]
[ROW][C]13[/C][C]225247[/C][C]221603.149417198[/C][C]3643.85058280238[/C][/ROW]
[ROW][C]14[/C][C]226699[/C][C]224533.019980962[/C][C]2165.98001903755[/C][/ROW]
[ROW][C]15[/C][C]231406[/C][C]226274.595535523[/C][C]5131.40446447671[/C][/ROW]
[ROW][C]16[/C][C]232324[/C][C]230400.547066631[/C][C]1923.45293336883[/C][/ROW]
[ROW][C]17[/C][C]237192[/C][C]231947.116554651[/C][C]5244.88344534926[/C][/ROW]
[ROW][C]18[/C][C]236727[/C][C]236164.311872547[/C][C]562.68812745341[/C][/ROW]
[ROW][C]19[/C][C]240698[/C][C]236616.746280529[/C][C]4081.25371947122[/C][/ROW]
[ROW][C]20[/C][C]240688[/C][C]239898.31473791[/C][C]789.685262090003[/C][/ROW]
[ROW][C]21[/C][C]245283[/C][C]240533.268216781[/C][C]4749.73178321903[/C][/ROW]
[ROW][C]22[/C][C]243556[/C][C]244352.332424054[/C][C]-796.332424054039[/C][/ROW]
[ROW][C]23[/C][C]247826[/C][C]243712.034235314[/C][C]4113.96576468591[/C][/ROW]
[ROW][C]24[/C][C]245798[/C][C]247019.905104437[/C][C]-1221.90510443729[/C][/ROW]
[ROW][C]25[/C][C]250479[/C][C]246037.421405983[/C][C]4441.57859401655[/C][/ROW]
[ROW][C]26[/C][C]249216[/C][C]249608.712292793[/C][C]-392.712292792799[/C][/ROW]
[ROW][C]27[/C][C]251896[/C][C]249292.948470831[/C][C]2603.05152916868[/C][/ROW]
[ROW][C]28[/C][C]247616[/C][C]251385.955271733[/C][C]-3769.95527173285[/C][/ROW]
[ROW][C]29[/C][C]249994[/C][C]248354.689107996[/C][C]1639.31089200359[/C][/ROW]
[ROW][C]30[/C][C]246552[/C][C]249672.791653147[/C][C]-3120.79165314703[/C][/ROW]
[ROW][C]31[/C][C]248771[/C][C]247163.491287388[/C][C]1607.50871261233[/C][/ROW]
[ROW][C]32[/C][C]247551[/C][C]248456.023006528[/C][C]-905.02300652754[/C][/ROW]
[ROW][C]33[/C][C]249745[/C][C]247728.331185444[/C][C]2016.66881455577[/C][/ROW]
[ROW][C]34[/C][C]245742[/C][C]249349.851734205[/C][C]-3607.85173420541[/C][/ROW]
[ROW][C]35[/C][C]249019[/C][C]246448.92636576[/C][C]2570.07363424011[/C][/ROW]
[ROW][C]36[/C][C]245841[/C][C]248515.416996086[/C][C]-2674.41699608567[/C][/ROW]
[ROW][C]37[/C][C]248771[/C][C]246365.028154939[/C][C]2405.97184506094[/C][/ROW]
[ROW][C]38[/C][C]244723[/C][C]248299.571277909[/C][C]-3576.57127790918[/C][/ROW]
[ROW][C]39[/C][C]246878[/C][C]245423.797239366[/C][C]1454.20276063384[/C][/ROW]
[ROW][C]40[/C][C]246014[/C][C]246593.061940349[/C][C]-579.061940349027[/C][/ROW]
[ROW][C]41[/C][C]248496[/C][C]246127.462022056[/C][C]2368.5379779441[/C][/ROW]
[ROW][C]42[/C][C]244351[/C][C]248031.906110266[/C][C]-3680.90611026561[/C][/ROW]
[ROW][C]43[/C][C]248016[/C][C]245072.240719114[/C][C]2943.75928088641[/C][/ROW]
[ROW][C]44[/C][C]246509[/C][C]247439.196626852[/C][C]-930.196626851597[/C][/ROW]
[ROW][C]45[/C][C]249426[/C][C]246691.263731801[/C][C]2734.73626819864[/C][/ROW]
[ROW][C]46[/C][C]247840[/C][C]248890.152821730[/C][C]-1050.15282173027[/C][/ROW]
[ROW][C]47[/C][C]251035[/C][C]248045.768078195[/C][C]2989.23192180545[/C][/ROW]
[ROW][C]48[/C][C]250161[/C][C]250449.286668473[/C][C]-288.286668473418[/C][/ROW]
[ROW][C]49[/C][C]254278[/C][C]250217.487201209[/C][C]4060.51279879137[/C][/ROW]
[ROW][C]50[/C][C]250801[/C][C]253482.378736311[/C][C]-2681.37873631096[/C][/ROW]
[ROW][C]51[/C][C]253985[/C][C]251326.392245838[/C][C]2658.60775416158[/C][/ROW]
[ROW][C]52[/C][C]249174[/C][C]253464.069525000[/C][C]-4290.06952499962[/C][/ROW]
[ROW][C]53[/C][C]251287[/C][C]250014.600856574[/C][C]1272.39914342592[/C][/ROW]
[ROW][C]54[/C][C]247947[/C][C]251037.684737477[/C][C]-3090.68473747684[/C][/ROW]
[ROW][C]55[/C][C]249992[/C][C]248552.592105812[/C][C]1439.40789418822[/C][/ROW]
[ROW][C]56[/C][C]243805[/C][C]249709.960862461[/C][C]-5904.96086246081[/C][/ROW]
[ROW][C]57[/C][C]255812[/C][C]244962.024409534[/C][C]10849.9755904664[/C][/ROW]
[ROW][C]58[/C][C]250417[/C][C]253686.044063387[/C][C]-3269.04406338738[/C][/ROW]
[ROW][C]59[/C][C]253033[/C][C]251057.540024782[/C][C]1975.45997521753[/C][/ROW]
[ROW][C]60[/C][C]248705[/C][C]252645.926238696[/C][C]-3940.92623869638[/C][/ROW]
[ROW][C]61[/C][C]253950[/C][C]249477.189343935[/C][C]4472.81065606538[/C][/ROW]
[ROW][C]62[/C][C]251484[/C][C]253073.59264882[/C][C]-1589.59264882017[/C][/ROW]
[ROW][C]63[/C][C]251093[/C][C]251795.466500581[/C][C]-702.4665005813[/C][/ROW]
[ROW][C]64[/C][C]245996[/C][C]251230.642044881[/C][C]-5234.64204488116[/C][/ROW]
[ROW][C]65[/C][C]252721[/C][C]247021.681416384[/C][C]5699.3185836164[/C][/ROW]
[ROW][C]66[/C][C]248019[/C][C]251604.269360704[/C][C]-3585.26936070414[/C][/ROW]
[ROW][C]67[/C][C]250464[/C][C]248721.501551104[/C][C]1742.4984488959[/C][/ROW]
[ROW][C]68[/C][C]245571[/C][C]250122.572971793[/C][C]-4551.57297179327[/C][/ROW]
[ROW][C]69[/C][C]252690[/C][C]246462.840124397[/C][C]6227.1598756027[/C][/ROW]
[ROW][C]70[/C][C]250183[/C][C]251469.843567814[/C][C]-1286.84356781357[/C][/ROW]
[ROW][C]71[/C][C]253639[/C][C]250435.145518640[/C][C]3203.85448136041[/C][/ROW]
[ROW][C]72[/C][C]254436[/C][C]253011.233292333[/C][C]1424.76670766668[/C][/ROW]
[ROW][C]73[/C][C]265280[/C][C]254156.829672362[/C][C]11123.1703276378[/C][/ROW]
[ROW][C]74[/C][C]268705[/C][C]263100.513991499[/C][C]5604.48600850062[/C][/ROW]
[ROW][C]75[/C][C]270643[/C][C]267606.850957904[/C][C]3036.14904209587[/C][/ROW]
[ROW][C]76[/C][C]271480[/C][C]270048.093677247[/C][C]1431.906322753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107019&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107019&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
21905301864484082
3194207189730.1685108974476.83148910289
4190855193329.804802452-2474.80480245178
5200779191339.9159261119439.08407388927
6204428198929.4956710965498.504328904
7207617203350.6171226794266.38287732139
8212071206781.0403307575289.95966924325
9214239211034.4795885493204.52041145149
10215883213611.1028092722271.89719072802
11223484215437.8420104988046.15798950236
12221529221907.427112616-378.427112616191
13225247221603.1494171983643.85058280238
14226699224533.0199809622165.98001903755
15231406226274.5955355235131.40446447671
16232324230400.5470666311923.45293336883
17237192231947.1165546515244.88344534926
18236727236164.311872547562.68812745341
19240698236616.7462805294081.25371947122
20240688239898.31473791789.685262090003
21245283240533.2682167814749.73178321903
22243556244352.332424054-796.332424054039
23247826243712.0342353144113.96576468591
24245798247019.905104437-1221.90510443729
25250479246037.4214059834441.57859401655
26249216249608.712292793-392.712292792799
27251896249292.9484708312603.05152916868
28247616251385.955271733-3769.95527173285
29249994248354.6891079961639.31089200359
30246552249672.791653147-3120.79165314703
31248771247163.4912873881607.50871261233
32247551248456.023006528-905.02300652754
33249745247728.3311854442016.66881455577
34245742249349.851734205-3607.85173420541
35249019246448.926365762570.07363424011
36245841248515.416996086-2674.41699608567
37248771246365.0281549392405.97184506094
38244723248299.571277909-3576.57127790918
39246878245423.7972393661454.20276063384
40246014246593.061940349-579.061940349027
41248496246127.4620220562368.5379779441
42244351248031.906110266-3680.90611026561
43248016245072.2407191142943.75928088641
44246509247439.196626852-930.196626851597
45249426246691.2637318012734.73626819864
46247840248890.152821730-1050.15282173027
47251035248045.7680781952989.23192180545
48250161250449.286668473-288.286668473418
49254278250217.4872012094060.51279879137
50250801253482.378736311-2681.37873631096
51253985251326.3922458382658.60775416158
52249174253464.069525000-4290.06952499962
53251287250014.6008565741272.39914342592
54247947251037.684737477-3090.68473747684
55249992248552.5921058121439.40789418822
56243805249709.960862461-5904.96086246081
57255812244962.02440953410849.9755904664
58250417253686.044063387-3269.04406338738
59253033251057.5400247821975.45997521753
60248705252645.926238696-3940.92623869638
61253950249477.1893439354472.81065606538
62251484253073.59264882-1589.59264882017
63251093251795.466500581-702.4665005813
64245996251230.642044881-5234.64204488116
65252721247021.6814163845699.3185836164
66248019251604.269360704-3585.26936070414
67250464248721.5015511041742.4984488959
68245571250122.572971793-4551.57297179327
69252690246462.8401243976227.1598756027
70250183251469.843567814-1286.84356781357
71253639250435.1455186403203.85448136041
72254436253011.2332923331424.76670766668
73265280254156.82967236211123.1703276378
74268705263100.5139914995604.48600850062
75270643267606.8509579043036.14904209587
76271480270048.0936772471431.906322753







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
77271199.430728470263944.709273618278454.152183323
78271199.430728470261890.430795471280508.430661470
79271199.430728470260213.804841993282185.056614948
80271199.430728470258761.164270369283637.697186572

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 271199.430728470 & 263944.709273618 & 278454.152183323 \tabularnewline
78 & 271199.430728470 & 261890.430795471 & 280508.430661470 \tabularnewline
79 & 271199.430728470 & 260213.804841993 & 282185.056614948 \tabularnewline
80 & 271199.430728470 & 258761.164270369 & 283637.697186572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107019&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]271199.430728470[/C][C]263944.709273618[/C][C]278454.152183323[/C][/ROW]
[ROW][C]78[/C][C]271199.430728470[/C][C]261890.430795471[/C][C]280508.430661470[/C][/ROW]
[ROW][C]79[/C][C]271199.430728470[/C][C]260213.804841993[/C][C]282185.056614948[/C][/ROW]
[ROW][C]80[/C][C]271199.430728470[/C][C]258761.164270369[/C][C]283637.697186572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107019&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107019&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
77271199.430728470263944.709273618278454.152183323
78271199.430728470261890.430795471280508.430661470
79271199.430728470260213.804841993282185.056614948
80271199.430728470258761.164270369283637.697186572



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