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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 computationTue, 28 Dec 2010 23:08:22 +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/29/t1293577613hhe2fr0ymfs2usl.htm/, Retrieved Fri, 03 May 2024 14:47:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116584, Retrieved Fri, 03 May 2024 14:47:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Paper Exponential...] [2010-12-28 23:08:22] [a2e464febd5f86100a78930292e787b9] [Current]
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Dataseries X:
1203
1319
1328
1260
1286
1274
1389
1255
1244
1336
1214
1239
1174
1061
1116
1123
1086
1074
965
1035
1016
941
1003
998
891
828
833
887
842
793
778
699
686
727
641
619
627
593
535
536
504
487
477
435
433
393
389
377
339
370
350
341
367
396
408
405
391
396
368
356




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=116584&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=116584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116584&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
alpha0.79903298900027
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.79903298900027 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116584&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]0.79903298900027[/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=116584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116584&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
alpha0.79903298900027
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
213191203116
313281295.6878267240332.3121732759687
412601321.50631911782-61.5063191178233
512861272.3607411107013.6392588892954
612741283.25895890877-9.25895890876677
713891275.86074529686113.139254703136
812551366.26274215557-111.262742155574
912441277.36014072664-33.3601407266392
1013361250.7042877683685.295712231637
1112141318.85837566171-104.858375661715
1212391235.073074335023.9269256649784
1311741238.21081748669-64.2108174866912
1410611186.90425606415-125.904256064150
1511161086.3026020133629.6973979866432
1611231110.0318026921512.968197307845
1710861120.39382014899-34.3938201489877
1810741092.91202323220-18.9120232322043
199651077.80069278093-112.800692780934
201035987.66921806688347.3307819331169
2110161025.48807422662-9.4880742266214
229411017.90678991747-76.9067899174677
231003956.45572769529846.5442723047024
24998993.6461367157664.35386328423351
25891997.125017109466-106.125017109466
26828912.327627480785-84.3276274807846
27833844.947071239512-11.9470712395118
28887835.40096719720651.5990328027945
29842876.630296607145-34.6302966071454
30793848.959547199172-55.959547199172
31778804.246022937516-26.2460229375159
32699783.274584780383-84.274584780383
33686715.936411406557-29.936411406557
34727692.01623112043434.983768879566
35641719.969416534768-78.9694165347682
36619656.870247601385-37.870247601385
37627626.610670466270.389329533730006
38593626.921757607312-33.9217576073123
39535599.817154234199-64.817154234199
40536548.026109747956-12.0261097479555
41504538.416851330001-34.4168513300014
42487510.916651739812-23.9166517398124
43477491.806458013272-14.8064580132716
44435479.97560961042-44.9756096104202
45433444.038613831297-11.0386138312969
46393435.218397227256-42.218397227256
47389401.484505099961-12.4845050999609
48377391.50897367375-14.5089736737501
49339379.915825071887-40.9158250718873
50370347.22273106728522.777268932715
51350365.422520343855-15.4225203438552
52341353.099417815587-12.0994178155871
53367343.43158383323523.5684161667646
54396362.26352584896833.7364741510324
55408389.22008162819718.7799183718026
56405404.2258559380.774144062000119
57391404.844422581777-13.8444225817766
58396393.7822722252772.21772777472319
59368395.554309877903-27.5543098779028
60356373.537507296322-17.5375072963225

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1319 & 1203 & 116 \tabularnewline
3 & 1328 & 1295.68782672403 & 32.3121732759687 \tabularnewline
4 & 1260 & 1321.50631911782 & -61.5063191178233 \tabularnewline
5 & 1286 & 1272.36074111070 & 13.6392588892954 \tabularnewline
6 & 1274 & 1283.25895890877 & -9.25895890876677 \tabularnewline
7 & 1389 & 1275.86074529686 & 113.139254703136 \tabularnewline
8 & 1255 & 1366.26274215557 & -111.262742155574 \tabularnewline
9 & 1244 & 1277.36014072664 & -33.3601407266392 \tabularnewline
10 & 1336 & 1250.70428776836 & 85.295712231637 \tabularnewline
11 & 1214 & 1318.85837566171 & -104.858375661715 \tabularnewline
12 & 1239 & 1235.07307433502 & 3.9269256649784 \tabularnewline
13 & 1174 & 1238.21081748669 & -64.2108174866912 \tabularnewline
14 & 1061 & 1186.90425606415 & -125.904256064150 \tabularnewline
15 & 1116 & 1086.30260201336 & 29.6973979866432 \tabularnewline
16 & 1123 & 1110.03180269215 & 12.968197307845 \tabularnewline
17 & 1086 & 1120.39382014899 & -34.3938201489877 \tabularnewline
18 & 1074 & 1092.91202323220 & -18.9120232322043 \tabularnewline
19 & 965 & 1077.80069278093 & -112.800692780934 \tabularnewline
20 & 1035 & 987.669218066883 & 47.3307819331169 \tabularnewline
21 & 1016 & 1025.48807422662 & -9.4880742266214 \tabularnewline
22 & 941 & 1017.90678991747 & -76.9067899174677 \tabularnewline
23 & 1003 & 956.455727695298 & 46.5442723047024 \tabularnewline
24 & 998 & 993.646136715766 & 4.35386328423351 \tabularnewline
25 & 891 & 997.125017109466 & -106.125017109466 \tabularnewline
26 & 828 & 912.327627480785 & -84.3276274807846 \tabularnewline
27 & 833 & 844.947071239512 & -11.9470712395118 \tabularnewline
28 & 887 & 835.400967197206 & 51.5990328027945 \tabularnewline
29 & 842 & 876.630296607145 & -34.6302966071454 \tabularnewline
30 & 793 & 848.959547199172 & -55.959547199172 \tabularnewline
31 & 778 & 804.246022937516 & -26.2460229375159 \tabularnewline
32 & 699 & 783.274584780383 & -84.274584780383 \tabularnewline
33 & 686 & 715.936411406557 & -29.936411406557 \tabularnewline
34 & 727 & 692.016231120434 & 34.983768879566 \tabularnewline
35 & 641 & 719.969416534768 & -78.9694165347682 \tabularnewline
36 & 619 & 656.870247601385 & -37.870247601385 \tabularnewline
37 & 627 & 626.61067046627 & 0.389329533730006 \tabularnewline
38 & 593 & 626.921757607312 & -33.9217576073123 \tabularnewline
39 & 535 & 599.817154234199 & -64.817154234199 \tabularnewline
40 & 536 & 548.026109747956 & -12.0261097479555 \tabularnewline
41 & 504 & 538.416851330001 & -34.4168513300014 \tabularnewline
42 & 487 & 510.916651739812 & -23.9166517398124 \tabularnewline
43 & 477 & 491.806458013272 & -14.8064580132716 \tabularnewline
44 & 435 & 479.97560961042 & -44.9756096104202 \tabularnewline
45 & 433 & 444.038613831297 & -11.0386138312969 \tabularnewline
46 & 393 & 435.218397227256 & -42.218397227256 \tabularnewline
47 & 389 & 401.484505099961 & -12.4845050999609 \tabularnewline
48 & 377 & 391.50897367375 & -14.5089736737501 \tabularnewline
49 & 339 & 379.915825071887 & -40.9158250718873 \tabularnewline
50 & 370 & 347.222731067285 & 22.777268932715 \tabularnewline
51 & 350 & 365.422520343855 & -15.4225203438552 \tabularnewline
52 & 341 & 353.099417815587 & -12.0994178155871 \tabularnewline
53 & 367 & 343.431583833235 & 23.5684161667646 \tabularnewline
54 & 396 & 362.263525848968 & 33.7364741510324 \tabularnewline
55 & 408 & 389.220081628197 & 18.7799183718026 \tabularnewline
56 & 405 & 404.225855938 & 0.774144062000119 \tabularnewline
57 & 391 & 404.844422581777 & -13.8444225817766 \tabularnewline
58 & 396 & 393.782272225277 & 2.21772777472319 \tabularnewline
59 & 368 & 395.554309877903 & -27.5543098779028 \tabularnewline
60 & 356 & 373.537507296322 & -17.5375072963225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116584&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]1319[/C][C]1203[/C][C]116[/C][/ROW]
[ROW][C]3[/C][C]1328[/C][C]1295.68782672403[/C][C]32.3121732759687[/C][/ROW]
[ROW][C]4[/C][C]1260[/C][C]1321.50631911782[/C][C]-61.5063191178233[/C][/ROW]
[ROW][C]5[/C][C]1286[/C][C]1272.36074111070[/C][C]13.6392588892954[/C][/ROW]
[ROW][C]6[/C][C]1274[/C][C]1283.25895890877[/C][C]-9.25895890876677[/C][/ROW]
[ROW][C]7[/C][C]1389[/C][C]1275.86074529686[/C][C]113.139254703136[/C][/ROW]
[ROW][C]8[/C][C]1255[/C][C]1366.26274215557[/C][C]-111.262742155574[/C][/ROW]
[ROW][C]9[/C][C]1244[/C][C]1277.36014072664[/C][C]-33.3601407266392[/C][/ROW]
[ROW][C]10[/C][C]1336[/C][C]1250.70428776836[/C][C]85.295712231637[/C][/ROW]
[ROW][C]11[/C][C]1214[/C][C]1318.85837566171[/C][C]-104.858375661715[/C][/ROW]
[ROW][C]12[/C][C]1239[/C][C]1235.07307433502[/C][C]3.9269256649784[/C][/ROW]
[ROW][C]13[/C][C]1174[/C][C]1238.21081748669[/C][C]-64.2108174866912[/C][/ROW]
[ROW][C]14[/C][C]1061[/C][C]1186.90425606415[/C][C]-125.904256064150[/C][/ROW]
[ROW][C]15[/C][C]1116[/C][C]1086.30260201336[/C][C]29.6973979866432[/C][/ROW]
[ROW][C]16[/C][C]1123[/C][C]1110.03180269215[/C][C]12.968197307845[/C][/ROW]
[ROW][C]17[/C][C]1086[/C][C]1120.39382014899[/C][C]-34.3938201489877[/C][/ROW]
[ROW][C]18[/C][C]1074[/C][C]1092.91202323220[/C][C]-18.9120232322043[/C][/ROW]
[ROW][C]19[/C][C]965[/C][C]1077.80069278093[/C][C]-112.800692780934[/C][/ROW]
[ROW][C]20[/C][C]1035[/C][C]987.669218066883[/C][C]47.3307819331169[/C][/ROW]
[ROW][C]21[/C][C]1016[/C][C]1025.48807422662[/C][C]-9.4880742266214[/C][/ROW]
[ROW][C]22[/C][C]941[/C][C]1017.90678991747[/C][C]-76.9067899174677[/C][/ROW]
[ROW][C]23[/C][C]1003[/C][C]956.455727695298[/C][C]46.5442723047024[/C][/ROW]
[ROW][C]24[/C][C]998[/C][C]993.646136715766[/C][C]4.35386328423351[/C][/ROW]
[ROW][C]25[/C][C]891[/C][C]997.125017109466[/C][C]-106.125017109466[/C][/ROW]
[ROW][C]26[/C][C]828[/C][C]912.327627480785[/C][C]-84.3276274807846[/C][/ROW]
[ROW][C]27[/C][C]833[/C][C]844.947071239512[/C][C]-11.9470712395118[/C][/ROW]
[ROW][C]28[/C][C]887[/C][C]835.400967197206[/C][C]51.5990328027945[/C][/ROW]
[ROW][C]29[/C][C]842[/C][C]876.630296607145[/C][C]-34.6302966071454[/C][/ROW]
[ROW][C]30[/C][C]793[/C][C]848.959547199172[/C][C]-55.959547199172[/C][/ROW]
[ROW][C]31[/C][C]778[/C][C]804.246022937516[/C][C]-26.2460229375159[/C][/ROW]
[ROW][C]32[/C][C]699[/C][C]783.274584780383[/C][C]-84.274584780383[/C][/ROW]
[ROW][C]33[/C][C]686[/C][C]715.936411406557[/C][C]-29.936411406557[/C][/ROW]
[ROW][C]34[/C][C]727[/C][C]692.016231120434[/C][C]34.983768879566[/C][/ROW]
[ROW][C]35[/C][C]641[/C][C]719.969416534768[/C][C]-78.9694165347682[/C][/ROW]
[ROW][C]36[/C][C]619[/C][C]656.870247601385[/C][C]-37.870247601385[/C][/ROW]
[ROW][C]37[/C][C]627[/C][C]626.61067046627[/C][C]0.389329533730006[/C][/ROW]
[ROW][C]38[/C][C]593[/C][C]626.921757607312[/C][C]-33.9217576073123[/C][/ROW]
[ROW][C]39[/C][C]535[/C][C]599.817154234199[/C][C]-64.817154234199[/C][/ROW]
[ROW][C]40[/C][C]536[/C][C]548.026109747956[/C][C]-12.0261097479555[/C][/ROW]
[ROW][C]41[/C][C]504[/C][C]538.416851330001[/C][C]-34.4168513300014[/C][/ROW]
[ROW][C]42[/C][C]487[/C][C]510.916651739812[/C][C]-23.9166517398124[/C][/ROW]
[ROW][C]43[/C][C]477[/C][C]491.806458013272[/C][C]-14.8064580132716[/C][/ROW]
[ROW][C]44[/C][C]435[/C][C]479.97560961042[/C][C]-44.9756096104202[/C][/ROW]
[ROW][C]45[/C][C]433[/C][C]444.038613831297[/C][C]-11.0386138312969[/C][/ROW]
[ROW][C]46[/C][C]393[/C][C]435.218397227256[/C][C]-42.218397227256[/C][/ROW]
[ROW][C]47[/C][C]389[/C][C]401.484505099961[/C][C]-12.4845050999609[/C][/ROW]
[ROW][C]48[/C][C]377[/C][C]391.50897367375[/C][C]-14.5089736737501[/C][/ROW]
[ROW][C]49[/C][C]339[/C][C]379.915825071887[/C][C]-40.9158250718873[/C][/ROW]
[ROW][C]50[/C][C]370[/C][C]347.222731067285[/C][C]22.777268932715[/C][/ROW]
[ROW][C]51[/C][C]350[/C][C]365.422520343855[/C][C]-15.4225203438552[/C][/ROW]
[ROW][C]52[/C][C]341[/C][C]353.099417815587[/C][C]-12.0994178155871[/C][/ROW]
[ROW][C]53[/C][C]367[/C][C]343.431583833235[/C][C]23.5684161667646[/C][/ROW]
[ROW][C]54[/C][C]396[/C][C]362.263525848968[/C][C]33.7364741510324[/C][/ROW]
[ROW][C]55[/C][C]408[/C][C]389.220081628197[/C][C]18.7799183718026[/C][/ROW]
[ROW][C]56[/C][C]405[/C][C]404.225855938[/C][C]0.774144062000119[/C][/ROW]
[ROW][C]57[/C][C]391[/C][C]404.844422581777[/C][C]-13.8444225817766[/C][/ROW]
[ROW][C]58[/C][C]396[/C][C]393.782272225277[/C][C]2.21772777472319[/C][/ROW]
[ROW][C]59[/C][C]368[/C][C]395.554309877903[/C][C]-27.5543098779028[/C][/ROW]
[ROW][C]60[/C][C]356[/C][C]373.537507296322[/C][C]-17.5375072963225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116584&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116584&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
213191203116
313281295.6878267240332.3121732759687
412601321.50631911782-61.5063191178233
512861272.3607411107013.6392588892954
612741283.25895890877-9.25895890876677
713891275.86074529686113.139254703136
812551366.26274215557-111.262742155574
912441277.36014072664-33.3601407266392
1013361250.7042877683685.295712231637
1112141318.85837566171-104.858375661715
1212391235.073074335023.9269256649784
1311741238.21081748669-64.2108174866912
1410611186.90425606415-125.904256064150
1511161086.3026020133629.6973979866432
1611231110.0318026921512.968197307845
1710861120.39382014899-34.3938201489877
1810741092.91202323220-18.9120232322043
199651077.80069278093-112.800692780934
201035987.66921806688347.3307819331169
2110161025.48807422662-9.4880742266214
229411017.90678991747-76.9067899174677
231003956.45572769529846.5442723047024
24998993.6461367157664.35386328423351
25891997.125017109466-106.125017109466
26828912.327627480785-84.3276274807846
27833844.947071239512-11.9470712395118
28887835.40096719720651.5990328027945
29842876.630296607145-34.6302966071454
30793848.959547199172-55.959547199172
31778804.246022937516-26.2460229375159
32699783.274584780383-84.274584780383
33686715.936411406557-29.936411406557
34727692.01623112043434.983768879566
35641719.969416534768-78.9694165347682
36619656.870247601385-37.870247601385
37627626.610670466270.389329533730006
38593626.921757607312-33.9217576073123
39535599.817154234199-64.817154234199
40536548.026109747956-12.0261097479555
41504538.416851330001-34.4168513300014
42487510.916651739812-23.9166517398124
43477491.806458013272-14.8064580132716
44435479.97560961042-44.9756096104202
45433444.038613831297-11.0386138312969
46393435.218397227256-42.218397227256
47389401.484505099961-12.4845050999609
48377391.50897367375-14.5089736737501
49339379.915825071887-40.9158250718873
50370347.22273106728522.777268932715
51350365.422520343855-15.4225203438552
52341353.099417815587-12.0994178155871
53367343.43158383323523.5684161667646
54396362.26352584896833.7364741510324
55408389.22008162819718.7799183718026
56405404.2258559380.774144062000119
57391404.844422581777-13.8444225817766
58396393.7822722252772.21772777472319
59368395.554309877903-27.5543098779028
60356373.537507296322-17.5375072963225







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61359.524460421728259.615045741503459.433875101953
62359.524460421728231.638313208750487.410607634706
63359.524460421728208.766899562533510.282021280923
64359.524460421728188.934842732232530.114078111224
65359.524460421728171.179582151352547.869338692104
66359.524460421728154.959632853748564.089287989707
67359.524460421728139.934514875144579.114405968312
68359.524460421728125.873610450267593.175310393189
69359.524460421728112.612137522241606.436783321215
70359.524460421728100.027503393606619.02141744985
71359.52446042172888.0255723685921631.023348474864
72359.52446042172876.5321960021442642.516724841312

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 359.524460421728 & 259.615045741503 & 459.433875101953 \tabularnewline
62 & 359.524460421728 & 231.638313208750 & 487.410607634706 \tabularnewline
63 & 359.524460421728 & 208.766899562533 & 510.282021280923 \tabularnewline
64 & 359.524460421728 & 188.934842732232 & 530.114078111224 \tabularnewline
65 & 359.524460421728 & 171.179582151352 & 547.869338692104 \tabularnewline
66 & 359.524460421728 & 154.959632853748 & 564.089287989707 \tabularnewline
67 & 359.524460421728 & 139.934514875144 & 579.114405968312 \tabularnewline
68 & 359.524460421728 & 125.873610450267 & 593.175310393189 \tabularnewline
69 & 359.524460421728 & 112.612137522241 & 606.436783321215 \tabularnewline
70 & 359.524460421728 & 100.027503393606 & 619.02141744985 \tabularnewline
71 & 359.524460421728 & 88.0255723685921 & 631.023348474864 \tabularnewline
72 & 359.524460421728 & 76.5321960021442 & 642.516724841312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116584&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]61[/C][C]359.524460421728[/C][C]259.615045741503[/C][C]459.433875101953[/C][/ROW]
[ROW][C]62[/C][C]359.524460421728[/C][C]231.638313208750[/C][C]487.410607634706[/C][/ROW]
[ROW][C]63[/C][C]359.524460421728[/C][C]208.766899562533[/C][C]510.282021280923[/C][/ROW]
[ROW][C]64[/C][C]359.524460421728[/C][C]188.934842732232[/C][C]530.114078111224[/C][/ROW]
[ROW][C]65[/C][C]359.524460421728[/C][C]171.179582151352[/C][C]547.869338692104[/C][/ROW]
[ROW][C]66[/C][C]359.524460421728[/C][C]154.959632853748[/C][C]564.089287989707[/C][/ROW]
[ROW][C]67[/C][C]359.524460421728[/C][C]139.934514875144[/C][C]579.114405968312[/C][/ROW]
[ROW][C]68[/C][C]359.524460421728[/C][C]125.873610450267[/C][C]593.175310393189[/C][/ROW]
[ROW][C]69[/C][C]359.524460421728[/C][C]112.612137522241[/C][C]606.436783321215[/C][/ROW]
[ROW][C]70[/C][C]359.524460421728[/C][C]100.027503393606[/C][C]619.02141744985[/C][/ROW]
[ROW][C]71[/C][C]359.524460421728[/C][C]88.0255723685921[/C][C]631.023348474864[/C][/ROW]
[ROW][C]72[/C][C]359.524460421728[/C][C]76.5321960021442[/C][C]642.516724841312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116584&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116584&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
61359.524460421728259.615045741503459.433875101953
62359.524460421728231.638313208750487.410607634706
63359.524460421728208.766899562533510.282021280923
64359.524460421728188.934842732232530.114078111224
65359.524460421728171.179582151352547.869338692104
66359.524460421728154.959632853748564.089287989707
67359.524460421728139.934514875144579.114405968312
68359.524460421728125.873610450267593.175310393189
69359.524460421728112.612137522241606.436783321215
70359.524460421728100.027503393606619.02141744985
71359.52446042172888.0255723685921631.023348474864
72359.52446042172876.5321960021442642.516724841312



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; 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')