Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 14:23:08 +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/2011/May/19/t1305814777q64bk2rqxgygeln.htm/, Retrieved Sat, 11 May 2024 05:09:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122037, Retrieved Sat, 11 May 2024 05:09:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2010-01-16 14:49:37] [b9c4c4888c8ec1a729f0d8175961f076]
- R     [Exponential Smoothing] [] [2011-05-18 14:28:26] [74be16979710d4c4e7c6647856088456]
-   P     [Exponential Smoothing] [] [2011-05-18 14:41:08] [74be16979710d4c4e7c6647856088456]
-   PD        [Exponential Smoothing] [] [2011-05-19 14:23:08] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
30790
30800
31025
30835
31110
31270
31090
30755
31460
32135
32680
32700
32515
32275
32200
31835
31985
31875
31795
32260
33255
33160
32195
33130
33950
34210
33855
33735
34175
34265
33915
33660
33720
33810
33590
33545
33660
33165
33800
33880
33975
33930
33905
33890
33640
34395
34245
33940
34295
33745
33535
33715
33600
34120
34330
34130
33755
32910
32910
32850
32780
32565
31905
31975
31380
31355
31440
30310
31410
31300
31070
31075
31815




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=122037&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=122037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122037&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
alpha0.881100620755513
beta0.0267387813206933
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.881100620755513 \tabularnewline
beta & 0.0267387813206933 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122037&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]0.881100620755513[/C][/ROW]
[ROW][C]beta[/C][C]0.0267387813206933[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122037&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
alpha0.881100620755513
beta0.0267387813206933
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133251532055.3766025641459.623397435891
143227532222.891416743152.108583256886
153220032152.155663643347.8443363566985
163183531808.789871313626.2101286864054
173198532056.9796641921-71.9796641920693
183187531981.7502272917-106.75022729173
193179532092.1194376148-297.119437614838
203226031448.3792162767811.620783723261
213325532863.5887848533391.411215146742
223316033907.5645831395-747.564583139458
233219533812.8758082572-1617.87580825716
243313032404.6971689743725.3028310257
253395032934.91476653851015.08523346148
263421033548.7725819275661.227418072456
273385534033.9538569078-178.953856907829
283373533502.5695378428232.430462157194
293417533940.029744796234.970255204033
303426534157.5957337773107.404266222708
313391534465.5430650265-550.543065026504
323366033755.8903486605-95.8903486604904
333372034325.6987745448-605.698774544828
343381034336.3754933537-526.37549335372
353359034318.9868820909-728.986882090918
363354533979.442925989-434.442925989046
373366033501.7712817191158.228718280901
383316533277.9001721621-112.900172162139
393380032922.1833689154877.816631084643
403388033336.8138214624543.186178537573
413397534021.6846282736-46.684628273586
423393033942.5827088857-12.5827088857113
433390534030.4189738699-125.418973869855
443389033723.2560802956166.74391970443
453364034443.8981610928-803.898161092802
463439534264.7456199613130.254380038728
473424534792.6663919014-547.666391901395
483394034643.0197186921-703.0197186921
493429533987.9602289324307.039771067561
503374533855.2625387277-110.262538727693
513353533612.0204754608-77.0204754607548
523371533115.415575171599.584424828994
533360033751.0319242677-151.031924267707
543412033552.7741438355567.225856164521
553433034120.4538755588209.546124441207
563413034133.4484960053-3.4484960053378
573375534574.9971061925-819.99710619248
583291034478.6225611835-1568.62256118354
593291033374.9252882213-464.925288221333
603285033227.5276239975-377.527623997521
613278032934.840502046-154.840502046041
623256532290.1667711452274.833228854844
633190532343.8619143012-438.861914301157
643197531554.0380022025420.961997797469
653138031883.9657387138-503.965738713814
663135531392.7667319746-37.7667319745924
673144031303.2344358661136.765564133904
683031031143.4376687478-833.437668747774
693141030653.7015411162756.298458883797
703130031791.4340804147-491.434080414667
713107031727.6984356857-657.698435685656
723107531375.9193781966-300.919378196639
733181531134.0936646679680.906335332125

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 32515 & 32055.3766025641 & 459.623397435891 \tabularnewline
14 & 32275 & 32222.8914167431 & 52.108583256886 \tabularnewline
15 & 32200 & 32152.1556636433 & 47.8443363566985 \tabularnewline
16 & 31835 & 31808.7898713136 & 26.2101286864054 \tabularnewline
17 & 31985 & 32056.9796641921 & -71.9796641920693 \tabularnewline
18 & 31875 & 31981.7502272917 & -106.75022729173 \tabularnewline
19 & 31795 & 32092.1194376148 & -297.119437614838 \tabularnewline
20 & 32260 & 31448.3792162767 & 811.620783723261 \tabularnewline
21 & 33255 & 32863.5887848533 & 391.411215146742 \tabularnewline
22 & 33160 & 33907.5645831395 & -747.564583139458 \tabularnewline
23 & 32195 & 33812.8758082572 & -1617.87580825716 \tabularnewline
24 & 33130 & 32404.6971689743 & 725.3028310257 \tabularnewline
25 & 33950 & 32934.9147665385 & 1015.08523346148 \tabularnewline
26 & 34210 & 33548.7725819275 & 661.227418072456 \tabularnewline
27 & 33855 & 34033.9538569078 & -178.953856907829 \tabularnewline
28 & 33735 & 33502.5695378428 & 232.430462157194 \tabularnewline
29 & 34175 & 33940.029744796 & 234.970255204033 \tabularnewline
30 & 34265 & 34157.5957337773 & 107.404266222708 \tabularnewline
31 & 33915 & 34465.5430650265 & -550.543065026504 \tabularnewline
32 & 33660 & 33755.8903486605 & -95.8903486604904 \tabularnewline
33 & 33720 & 34325.6987745448 & -605.698774544828 \tabularnewline
34 & 33810 & 34336.3754933537 & -526.37549335372 \tabularnewline
35 & 33590 & 34318.9868820909 & -728.986882090918 \tabularnewline
36 & 33545 & 33979.442925989 & -434.442925989046 \tabularnewline
37 & 33660 & 33501.7712817191 & 158.228718280901 \tabularnewline
38 & 33165 & 33277.9001721621 & -112.900172162139 \tabularnewline
39 & 33800 & 32922.1833689154 & 877.816631084643 \tabularnewline
40 & 33880 & 33336.8138214624 & 543.186178537573 \tabularnewline
41 & 33975 & 34021.6846282736 & -46.684628273586 \tabularnewline
42 & 33930 & 33942.5827088857 & -12.5827088857113 \tabularnewline
43 & 33905 & 34030.4189738699 & -125.418973869855 \tabularnewline
44 & 33890 & 33723.2560802956 & 166.74391970443 \tabularnewline
45 & 33640 & 34443.8981610928 & -803.898161092802 \tabularnewline
46 & 34395 & 34264.7456199613 & 130.254380038728 \tabularnewline
47 & 34245 & 34792.6663919014 & -547.666391901395 \tabularnewline
48 & 33940 & 34643.0197186921 & -703.0197186921 \tabularnewline
49 & 34295 & 33987.9602289324 & 307.039771067561 \tabularnewline
50 & 33745 & 33855.2625387277 & -110.262538727693 \tabularnewline
51 & 33535 & 33612.0204754608 & -77.0204754607548 \tabularnewline
52 & 33715 & 33115.415575171 & 599.584424828994 \tabularnewline
53 & 33600 & 33751.0319242677 & -151.031924267707 \tabularnewline
54 & 34120 & 33552.7741438355 & 567.225856164521 \tabularnewline
55 & 34330 & 34120.4538755588 & 209.546124441207 \tabularnewline
56 & 34130 & 34133.4484960053 & -3.4484960053378 \tabularnewline
57 & 33755 & 34574.9971061925 & -819.99710619248 \tabularnewline
58 & 32910 & 34478.6225611835 & -1568.62256118354 \tabularnewline
59 & 32910 & 33374.9252882213 & -464.925288221333 \tabularnewline
60 & 32850 & 33227.5276239975 & -377.527623997521 \tabularnewline
61 & 32780 & 32934.840502046 & -154.840502046041 \tabularnewline
62 & 32565 & 32290.1667711452 & 274.833228854844 \tabularnewline
63 & 31905 & 32343.8619143012 & -438.861914301157 \tabularnewline
64 & 31975 & 31554.0380022025 & 420.961997797469 \tabularnewline
65 & 31380 & 31883.9657387138 & -503.965738713814 \tabularnewline
66 & 31355 & 31392.7667319746 & -37.7667319745924 \tabularnewline
67 & 31440 & 31303.2344358661 & 136.765564133904 \tabularnewline
68 & 30310 & 31143.4376687478 & -833.437668747774 \tabularnewline
69 & 31410 & 30653.7015411162 & 756.298458883797 \tabularnewline
70 & 31300 & 31791.4340804147 & -491.434080414667 \tabularnewline
71 & 31070 & 31727.6984356857 & -657.698435685656 \tabularnewline
72 & 31075 & 31375.9193781966 & -300.919378196639 \tabularnewline
73 & 31815 & 31134.0936646679 & 680.906335332125 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122037&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]32515[/C][C]32055.3766025641[/C][C]459.623397435891[/C][/ROW]
[ROW][C]14[/C][C]32275[/C][C]32222.8914167431[/C][C]52.108583256886[/C][/ROW]
[ROW][C]15[/C][C]32200[/C][C]32152.1556636433[/C][C]47.8443363566985[/C][/ROW]
[ROW][C]16[/C][C]31835[/C][C]31808.7898713136[/C][C]26.2101286864054[/C][/ROW]
[ROW][C]17[/C][C]31985[/C][C]32056.9796641921[/C][C]-71.9796641920693[/C][/ROW]
[ROW][C]18[/C][C]31875[/C][C]31981.7502272917[/C][C]-106.75022729173[/C][/ROW]
[ROW][C]19[/C][C]31795[/C][C]32092.1194376148[/C][C]-297.119437614838[/C][/ROW]
[ROW][C]20[/C][C]32260[/C][C]31448.3792162767[/C][C]811.620783723261[/C][/ROW]
[ROW][C]21[/C][C]33255[/C][C]32863.5887848533[/C][C]391.411215146742[/C][/ROW]
[ROW][C]22[/C][C]33160[/C][C]33907.5645831395[/C][C]-747.564583139458[/C][/ROW]
[ROW][C]23[/C][C]32195[/C][C]33812.8758082572[/C][C]-1617.87580825716[/C][/ROW]
[ROW][C]24[/C][C]33130[/C][C]32404.6971689743[/C][C]725.3028310257[/C][/ROW]
[ROW][C]25[/C][C]33950[/C][C]32934.9147665385[/C][C]1015.08523346148[/C][/ROW]
[ROW][C]26[/C][C]34210[/C][C]33548.7725819275[/C][C]661.227418072456[/C][/ROW]
[ROW][C]27[/C][C]33855[/C][C]34033.9538569078[/C][C]-178.953856907829[/C][/ROW]
[ROW][C]28[/C][C]33735[/C][C]33502.5695378428[/C][C]232.430462157194[/C][/ROW]
[ROW][C]29[/C][C]34175[/C][C]33940.029744796[/C][C]234.970255204033[/C][/ROW]
[ROW][C]30[/C][C]34265[/C][C]34157.5957337773[/C][C]107.404266222708[/C][/ROW]
[ROW][C]31[/C][C]33915[/C][C]34465.5430650265[/C][C]-550.543065026504[/C][/ROW]
[ROW][C]32[/C][C]33660[/C][C]33755.8903486605[/C][C]-95.8903486604904[/C][/ROW]
[ROW][C]33[/C][C]33720[/C][C]34325.6987745448[/C][C]-605.698774544828[/C][/ROW]
[ROW][C]34[/C][C]33810[/C][C]34336.3754933537[/C][C]-526.37549335372[/C][/ROW]
[ROW][C]35[/C][C]33590[/C][C]34318.9868820909[/C][C]-728.986882090918[/C][/ROW]
[ROW][C]36[/C][C]33545[/C][C]33979.442925989[/C][C]-434.442925989046[/C][/ROW]
[ROW][C]37[/C][C]33660[/C][C]33501.7712817191[/C][C]158.228718280901[/C][/ROW]
[ROW][C]38[/C][C]33165[/C][C]33277.9001721621[/C][C]-112.900172162139[/C][/ROW]
[ROW][C]39[/C][C]33800[/C][C]32922.1833689154[/C][C]877.816631084643[/C][/ROW]
[ROW][C]40[/C][C]33880[/C][C]33336.8138214624[/C][C]543.186178537573[/C][/ROW]
[ROW][C]41[/C][C]33975[/C][C]34021.6846282736[/C][C]-46.684628273586[/C][/ROW]
[ROW][C]42[/C][C]33930[/C][C]33942.5827088857[/C][C]-12.5827088857113[/C][/ROW]
[ROW][C]43[/C][C]33905[/C][C]34030.4189738699[/C][C]-125.418973869855[/C][/ROW]
[ROW][C]44[/C][C]33890[/C][C]33723.2560802956[/C][C]166.74391970443[/C][/ROW]
[ROW][C]45[/C][C]33640[/C][C]34443.8981610928[/C][C]-803.898161092802[/C][/ROW]
[ROW][C]46[/C][C]34395[/C][C]34264.7456199613[/C][C]130.254380038728[/C][/ROW]
[ROW][C]47[/C][C]34245[/C][C]34792.6663919014[/C][C]-547.666391901395[/C][/ROW]
[ROW][C]48[/C][C]33940[/C][C]34643.0197186921[/C][C]-703.0197186921[/C][/ROW]
[ROW][C]49[/C][C]34295[/C][C]33987.9602289324[/C][C]307.039771067561[/C][/ROW]
[ROW][C]50[/C][C]33745[/C][C]33855.2625387277[/C][C]-110.262538727693[/C][/ROW]
[ROW][C]51[/C][C]33535[/C][C]33612.0204754608[/C][C]-77.0204754607548[/C][/ROW]
[ROW][C]52[/C][C]33715[/C][C]33115.415575171[/C][C]599.584424828994[/C][/ROW]
[ROW][C]53[/C][C]33600[/C][C]33751.0319242677[/C][C]-151.031924267707[/C][/ROW]
[ROW][C]54[/C][C]34120[/C][C]33552.7741438355[/C][C]567.225856164521[/C][/ROW]
[ROW][C]55[/C][C]34330[/C][C]34120.4538755588[/C][C]209.546124441207[/C][/ROW]
[ROW][C]56[/C][C]34130[/C][C]34133.4484960053[/C][C]-3.4484960053378[/C][/ROW]
[ROW][C]57[/C][C]33755[/C][C]34574.9971061925[/C][C]-819.99710619248[/C][/ROW]
[ROW][C]58[/C][C]32910[/C][C]34478.6225611835[/C][C]-1568.62256118354[/C][/ROW]
[ROW][C]59[/C][C]32910[/C][C]33374.9252882213[/C][C]-464.925288221333[/C][/ROW]
[ROW][C]60[/C][C]32850[/C][C]33227.5276239975[/C][C]-377.527623997521[/C][/ROW]
[ROW][C]61[/C][C]32780[/C][C]32934.840502046[/C][C]-154.840502046041[/C][/ROW]
[ROW][C]62[/C][C]32565[/C][C]32290.1667711452[/C][C]274.833228854844[/C][/ROW]
[ROW][C]63[/C][C]31905[/C][C]32343.8619143012[/C][C]-438.861914301157[/C][/ROW]
[ROW][C]64[/C][C]31975[/C][C]31554.0380022025[/C][C]420.961997797469[/C][/ROW]
[ROW][C]65[/C][C]31380[/C][C]31883.9657387138[/C][C]-503.965738713814[/C][/ROW]
[ROW][C]66[/C][C]31355[/C][C]31392.7667319746[/C][C]-37.7667319745924[/C][/ROW]
[ROW][C]67[/C][C]31440[/C][C]31303.2344358661[/C][C]136.765564133904[/C][/ROW]
[ROW][C]68[/C][C]30310[/C][C]31143.4376687478[/C][C]-833.437668747774[/C][/ROW]
[ROW][C]69[/C][C]31410[/C][C]30653.7015411162[/C][C]756.298458883797[/C][/ROW]
[ROW][C]70[/C][C]31300[/C][C]31791.4340804147[/C][C]-491.434080414667[/C][/ROW]
[ROW][C]71[/C][C]31070[/C][C]31727.6984356857[/C][C]-657.698435685656[/C][/ROW]
[ROW][C]72[/C][C]31075[/C][C]31375.9193781966[/C][C]-300.919378196639[/C][/ROW]
[ROW][C]73[/C][C]31815[/C][C]31134.0936646679[/C][C]680.906335332125[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122037&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122037&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
133251532055.3766025641459.623397435891
143227532222.891416743152.108583256886
153220032152.155663643347.8443363566985
163183531808.789871313626.2101286864054
173198532056.9796641921-71.9796641920693
183187531981.7502272917-106.75022729173
193179532092.1194376148-297.119437614838
203226031448.3792162767811.620783723261
213325532863.5887848533391.411215146742
223316033907.5645831395-747.564583139458
233219533812.8758082572-1617.87580825716
243313032404.6971689743725.3028310257
253395032934.91476653851015.08523346148
263421033548.7725819275661.227418072456
273385534033.9538569078-178.953856907829
283373533502.5695378428232.430462157194
293417533940.029744796234.970255204033
303426534157.5957337773107.404266222708
313391534465.5430650265-550.543065026504
323366033755.8903486605-95.8903486604904
333372034325.6987745448-605.698774544828
343381034336.3754933537-526.37549335372
353359034318.9868820909-728.986882090918
363354533979.442925989-434.442925989046
373366033501.7712817191158.228718280901
383316533277.9001721621-112.900172162139
393380032922.1833689154877.816631084643
403388033336.8138214624543.186178537573
413397534021.6846282736-46.684628273586
423393033942.5827088857-12.5827088857113
433390534030.4189738699-125.418973869855
443389033723.2560802956166.74391970443
453364034443.8981610928-803.898161092802
463439534264.7456199613130.254380038728
473424534792.6663919014-547.666391901395
483394034643.0197186921-703.0197186921
493429533987.9602289324307.039771067561
503374533855.2625387277-110.262538727693
513353533612.0204754608-77.0204754607548
523371533115.415575171599.584424828994
533360033751.0319242677-151.031924267707
543412033552.7741438355567.225856164521
553433034120.4538755588209.546124441207
563413034133.4484960053-3.4484960053378
573375534574.9971061925-819.99710619248
583291034478.6225611835-1568.62256118354
593291033374.9252882213-464.925288221333
603285033227.5276239975-377.527623997521
613278032934.840502046-154.840502046041
623256532290.1667711452274.833228854844
633190532343.8619143012-438.861914301157
643197531554.0380022025420.961997797469
653138031883.9657387138-503.965738713814
663135531392.7667319746-37.7667319745924
673144031303.2344358661136.765564133904
683031031143.4376687478-833.437668747774
693141030653.7015411162756.298458883797
703130031791.4340804147-491.434080414667
713107031727.6984356857-657.698435685656
723107531375.9193781966-300.919378196639
733181531134.0936646679680.906335332125







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7431253.459230886230180.956036176132325.9624255963
7530950.240086960829503.986315678532396.493858243
7630629.768952550928874.004926639532385.5329784622
7730449.334542828928418.395831987632480.2732536703
7830440.005108329928155.504926277232724.5052903827
7930387.784926855827864.558553376432911.0113003351
8029972.189280053427220.975055282132723.4035048247
8130405.511566470127434.359747493533376.6633854467
8230710.393711284727525.485783633533895.3016389359
8331053.349451878827659.510511603534447.1883921541
8431332.442027112727733.479290507834931.4047637175
8531488.536883871527687.47315094635289.600616797

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 31253.4592308862 & 30180.9560361761 & 32325.9624255963 \tabularnewline
75 & 30950.2400869608 & 29503.9863156785 & 32396.493858243 \tabularnewline
76 & 30629.7689525509 & 28874.0049266395 & 32385.5329784622 \tabularnewline
77 & 30449.3345428289 & 28418.3958319876 & 32480.2732536703 \tabularnewline
78 & 30440.0051083299 & 28155.5049262772 & 32724.5052903827 \tabularnewline
79 & 30387.7849268558 & 27864.5585533764 & 32911.0113003351 \tabularnewline
80 & 29972.1892800534 & 27220.9750552821 & 32723.4035048247 \tabularnewline
81 & 30405.5115664701 & 27434.3597474935 & 33376.6633854467 \tabularnewline
82 & 30710.3937112847 & 27525.4857836335 & 33895.3016389359 \tabularnewline
83 & 31053.3494518788 & 27659.5105116035 & 34447.1883921541 \tabularnewline
84 & 31332.4420271127 & 27733.4792905078 & 34931.4047637175 \tabularnewline
85 & 31488.5368838715 & 27687.473150946 & 35289.600616797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122037&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]31253.4592308862[/C][C]30180.9560361761[/C][C]32325.9624255963[/C][/ROW]
[ROW][C]75[/C][C]30950.2400869608[/C][C]29503.9863156785[/C][C]32396.493858243[/C][/ROW]
[ROW][C]76[/C][C]30629.7689525509[/C][C]28874.0049266395[/C][C]32385.5329784622[/C][/ROW]
[ROW][C]77[/C][C]30449.3345428289[/C][C]28418.3958319876[/C][C]32480.2732536703[/C][/ROW]
[ROW][C]78[/C][C]30440.0051083299[/C][C]28155.5049262772[/C][C]32724.5052903827[/C][/ROW]
[ROW][C]79[/C][C]30387.7849268558[/C][C]27864.5585533764[/C][C]32911.0113003351[/C][/ROW]
[ROW][C]80[/C][C]29972.1892800534[/C][C]27220.9750552821[/C][C]32723.4035048247[/C][/ROW]
[ROW][C]81[/C][C]30405.5115664701[/C][C]27434.3597474935[/C][C]33376.6633854467[/C][/ROW]
[ROW][C]82[/C][C]30710.3937112847[/C][C]27525.4857836335[/C][C]33895.3016389359[/C][/ROW]
[ROW][C]83[/C][C]31053.3494518788[/C][C]27659.5105116035[/C][C]34447.1883921541[/C][/ROW]
[ROW][C]84[/C][C]31332.4420271127[/C][C]27733.4792905078[/C][C]34931.4047637175[/C][/ROW]
[ROW][C]85[/C][C]31488.5368838715[/C][C]27687.473150946[/C][C]35289.600616797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122037&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122037&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
7431253.459230886230180.956036176132325.9624255963
7530950.240086960829503.986315678532396.493858243
7630629.768952550928874.004926639532385.5329784622
7730449.334542828928418.395831987632480.2732536703
7830440.005108329928155.504926277232724.5052903827
7930387.784926855827864.558553376432911.0113003351
8029972.189280053427220.975055282132723.4035048247
8130405.511566470127434.359747493533376.6633854467
8230710.393711284727525.485783633533895.3016389359
8331053.349451878827659.510511603534447.1883921541
8431332.442027112727733.479290507834931.4047637175
8531488.536883871527687.47315094635289.600616797



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