Free Statistics

of Irreproducible Research!

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, 07 Dec 2011 11:06:51 -0500
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/Dec/07/t1323274038ets7cxtnloegqq6.htm/, Retrieved Fri, 03 May 2024 00:52:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152536, Retrieved Fri, 03 May 2024 00:52:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
- RM D  [Classical Decomposition] [Klassieke decompo...] [2010-12-19 00:01:25] [b8e188bcc949964bed729335b3416734]
- RMP       [Exponential Smoothing] [paper] [2011-12-07 16:06:51] [9c3f7eb531442757fa35fbfef7e48a65] [Current]
Feedback Forum

Post a new message
Dataseries X:
4143
4429
5219
4929
5761
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5657
4248
3830
4736
4839
4411
4570
4104
4801
3953
3828
4440
4026
4109
4785
3224
3552
3940
3913
3681
4309
3830
4143
4087
3818
3380
3430
3458
3970
5260
5024
5634
6549
4676




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152536&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152536&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152536&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.378097190398073
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.378097190398073 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152536&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]0.378097190398073[/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=152536&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152536&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
alpha0.378097190398073
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
244294143286
352194251.13579645385967.864203546151
449294617.08253250152311.917467498482
557614735.017650598781025.98234940122
655925122.93869430539469.061305694607
741635300.28945611298-1137.28945611298
849624870.2835080873191.7164919126935
952084904.96125599266303.038744007336
1047555019.5393536836-264.539353683598
1144914919.51776730611-428.517767306107
1257324757.49640345201974.503596547987
1357315125.95347533962605.046524660375
1450405354.71986637383-314.719866373831
1561025235.72516913543866.274830864571
1649045563.26124879789-659.261248797889
1753695313.9964228890855.0035771109178
1855785334.79312085656243.206879143436
1946195426.74895854618-807.748958546181
2047315121.3413467729-390.3413467729
2150114973.7543802618737.2456197381334
2252994987.83684443949311.16315556051
2341465105.48675931232-959.486759312317
2446254742.70751139218-117.707511392177
2547364698.2026320460537.7973679539546
2642194712.49371067388-493.493710673878
2751164525.90512518897590.094874811035
2842054749.01833942332-544.01833942332
2941214543.32653376234-422.326533762337
3051034383.64605791624719.35394208376
3143004655.63176231989-355.631762319888
3245784521.1683921704256.8316078295766
3338094542.65626341659-733.656263416591
3456574265.262891500831391.73710849917
3542484791.4747819971-543.474781997104
3638304585.98849387179-755.988493871794
3747364300.1513683656435.848631634402
3848394464.94451142541374.05548857459
3944114606.37384070844-195.373840708441
4045704532.503540459337.4964595407009
4141044546.68084646151-442.680846461513
4248014379.30446217137421.695537828626
4339534538.74636022778-585.746360227782
4438284317.27730713976-489.27730713976
4544404132.28293198468307.717068015319
4640264248.62989083881-222.629890838806
4741094164.45415461402-55.4541546140235
4847854143.48709455856641.512905441439
4932244386.04132171007-1162.04132171007
5035523946.67676284503-394.676762845031
5139403797.45058769792142.549412302082
5239133851.3481199822361.6518800177682
5336813874.65852259971-193.658522599709
5443093801.43677930812507.563220691883
5538303993.34500700112-163.345007001115
5641433931.58471878844211.41528121156
5740874011.5202426217575.4797573782507
5838184040.05892681839-222.058926818394
5933803956.09907048555-576.099070485548
6034303738.27763054402-308.27763054402
6134583621.71872457275-163.718724572751
6239703559.81713479624410.182865203762
6352603714.906123679211545.09387632079
6450244299.10177721737724.89822278263
6556344573.183758576041060.81624142396
6665494974.275398987081574.72460101292
6746765569.67434628079-893.674346280794

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4429 & 4143 & 286 \tabularnewline
3 & 5219 & 4251.13579645385 & 967.864203546151 \tabularnewline
4 & 4929 & 4617.08253250152 & 311.917467498482 \tabularnewline
5 & 5761 & 4735.01765059878 & 1025.98234940122 \tabularnewline
6 & 5592 & 5122.93869430539 & 469.061305694607 \tabularnewline
7 & 4163 & 5300.28945611298 & -1137.28945611298 \tabularnewline
8 & 4962 & 4870.28350808731 & 91.7164919126935 \tabularnewline
9 & 5208 & 4904.96125599266 & 303.038744007336 \tabularnewline
10 & 4755 & 5019.5393536836 & -264.539353683598 \tabularnewline
11 & 4491 & 4919.51776730611 & -428.517767306107 \tabularnewline
12 & 5732 & 4757.49640345201 & 974.503596547987 \tabularnewline
13 & 5731 & 5125.95347533962 & 605.046524660375 \tabularnewline
14 & 5040 & 5354.71986637383 & -314.719866373831 \tabularnewline
15 & 6102 & 5235.72516913543 & 866.274830864571 \tabularnewline
16 & 4904 & 5563.26124879789 & -659.261248797889 \tabularnewline
17 & 5369 & 5313.99642288908 & 55.0035771109178 \tabularnewline
18 & 5578 & 5334.79312085656 & 243.206879143436 \tabularnewline
19 & 4619 & 5426.74895854618 & -807.748958546181 \tabularnewline
20 & 4731 & 5121.3413467729 & -390.3413467729 \tabularnewline
21 & 5011 & 4973.75438026187 & 37.2456197381334 \tabularnewline
22 & 5299 & 4987.83684443949 & 311.16315556051 \tabularnewline
23 & 4146 & 5105.48675931232 & -959.486759312317 \tabularnewline
24 & 4625 & 4742.70751139218 & -117.707511392177 \tabularnewline
25 & 4736 & 4698.20263204605 & 37.7973679539546 \tabularnewline
26 & 4219 & 4712.49371067388 & -493.493710673878 \tabularnewline
27 & 5116 & 4525.90512518897 & 590.094874811035 \tabularnewline
28 & 4205 & 4749.01833942332 & -544.01833942332 \tabularnewline
29 & 4121 & 4543.32653376234 & -422.326533762337 \tabularnewline
30 & 5103 & 4383.64605791624 & 719.35394208376 \tabularnewline
31 & 4300 & 4655.63176231989 & -355.631762319888 \tabularnewline
32 & 4578 & 4521.16839217042 & 56.8316078295766 \tabularnewline
33 & 3809 & 4542.65626341659 & -733.656263416591 \tabularnewline
34 & 5657 & 4265.26289150083 & 1391.73710849917 \tabularnewline
35 & 4248 & 4791.4747819971 & -543.474781997104 \tabularnewline
36 & 3830 & 4585.98849387179 & -755.988493871794 \tabularnewline
37 & 4736 & 4300.1513683656 & 435.848631634402 \tabularnewline
38 & 4839 & 4464.94451142541 & 374.05548857459 \tabularnewline
39 & 4411 & 4606.37384070844 & -195.373840708441 \tabularnewline
40 & 4570 & 4532.5035404593 & 37.4964595407009 \tabularnewline
41 & 4104 & 4546.68084646151 & -442.680846461513 \tabularnewline
42 & 4801 & 4379.30446217137 & 421.695537828626 \tabularnewline
43 & 3953 & 4538.74636022778 & -585.746360227782 \tabularnewline
44 & 3828 & 4317.27730713976 & -489.27730713976 \tabularnewline
45 & 4440 & 4132.28293198468 & 307.717068015319 \tabularnewline
46 & 4026 & 4248.62989083881 & -222.629890838806 \tabularnewline
47 & 4109 & 4164.45415461402 & -55.4541546140235 \tabularnewline
48 & 4785 & 4143.48709455856 & 641.512905441439 \tabularnewline
49 & 3224 & 4386.04132171007 & -1162.04132171007 \tabularnewline
50 & 3552 & 3946.67676284503 & -394.676762845031 \tabularnewline
51 & 3940 & 3797.45058769792 & 142.549412302082 \tabularnewline
52 & 3913 & 3851.34811998223 & 61.6518800177682 \tabularnewline
53 & 3681 & 3874.65852259971 & -193.658522599709 \tabularnewline
54 & 4309 & 3801.43677930812 & 507.563220691883 \tabularnewline
55 & 3830 & 3993.34500700112 & -163.345007001115 \tabularnewline
56 & 4143 & 3931.58471878844 & 211.41528121156 \tabularnewline
57 & 4087 & 4011.52024262175 & 75.4797573782507 \tabularnewline
58 & 3818 & 4040.05892681839 & -222.058926818394 \tabularnewline
59 & 3380 & 3956.09907048555 & -576.099070485548 \tabularnewline
60 & 3430 & 3738.27763054402 & -308.27763054402 \tabularnewline
61 & 3458 & 3621.71872457275 & -163.718724572751 \tabularnewline
62 & 3970 & 3559.81713479624 & 410.182865203762 \tabularnewline
63 & 5260 & 3714.90612367921 & 1545.09387632079 \tabularnewline
64 & 5024 & 4299.10177721737 & 724.89822278263 \tabularnewline
65 & 5634 & 4573.18375857604 & 1060.81624142396 \tabularnewline
66 & 6549 & 4974.27539898708 & 1574.72460101292 \tabularnewline
67 & 4676 & 5569.67434628079 & -893.674346280794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152536&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]4429[/C][C]4143[/C][C]286[/C][/ROW]
[ROW][C]3[/C][C]5219[/C][C]4251.13579645385[/C][C]967.864203546151[/C][/ROW]
[ROW][C]4[/C][C]4929[/C][C]4617.08253250152[/C][C]311.917467498482[/C][/ROW]
[ROW][C]5[/C][C]5761[/C][C]4735.01765059878[/C][C]1025.98234940122[/C][/ROW]
[ROW][C]6[/C][C]5592[/C][C]5122.93869430539[/C][C]469.061305694607[/C][/ROW]
[ROW][C]7[/C][C]4163[/C][C]5300.28945611298[/C][C]-1137.28945611298[/C][/ROW]
[ROW][C]8[/C][C]4962[/C][C]4870.28350808731[/C][C]91.7164919126935[/C][/ROW]
[ROW][C]9[/C][C]5208[/C][C]4904.96125599266[/C][C]303.038744007336[/C][/ROW]
[ROW][C]10[/C][C]4755[/C][C]5019.5393536836[/C][C]-264.539353683598[/C][/ROW]
[ROW][C]11[/C][C]4491[/C][C]4919.51776730611[/C][C]-428.517767306107[/C][/ROW]
[ROW][C]12[/C][C]5732[/C][C]4757.49640345201[/C][C]974.503596547987[/C][/ROW]
[ROW][C]13[/C][C]5731[/C][C]5125.95347533962[/C][C]605.046524660375[/C][/ROW]
[ROW][C]14[/C][C]5040[/C][C]5354.71986637383[/C][C]-314.719866373831[/C][/ROW]
[ROW][C]15[/C][C]6102[/C][C]5235.72516913543[/C][C]866.274830864571[/C][/ROW]
[ROW][C]16[/C][C]4904[/C][C]5563.26124879789[/C][C]-659.261248797889[/C][/ROW]
[ROW][C]17[/C][C]5369[/C][C]5313.99642288908[/C][C]55.0035771109178[/C][/ROW]
[ROW][C]18[/C][C]5578[/C][C]5334.79312085656[/C][C]243.206879143436[/C][/ROW]
[ROW][C]19[/C][C]4619[/C][C]5426.74895854618[/C][C]-807.748958546181[/C][/ROW]
[ROW][C]20[/C][C]4731[/C][C]5121.3413467729[/C][C]-390.3413467729[/C][/ROW]
[ROW][C]21[/C][C]5011[/C][C]4973.75438026187[/C][C]37.2456197381334[/C][/ROW]
[ROW][C]22[/C][C]5299[/C][C]4987.83684443949[/C][C]311.16315556051[/C][/ROW]
[ROW][C]23[/C][C]4146[/C][C]5105.48675931232[/C][C]-959.486759312317[/C][/ROW]
[ROW][C]24[/C][C]4625[/C][C]4742.70751139218[/C][C]-117.707511392177[/C][/ROW]
[ROW][C]25[/C][C]4736[/C][C]4698.20263204605[/C][C]37.7973679539546[/C][/ROW]
[ROW][C]26[/C][C]4219[/C][C]4712.49371067388[/C][C]-493.493710673878[/C][/ROW]
[ROW][C]27[/C][C]5116[/C][C]4525.90512518897[/C][C]590.094874811035[/C][/ROW]
[ROW][C]28[/C][C]4205[/C][C]4749.01833942332[/C][C]-544.01833942332[/C][/ROW]
[ROW][C]29[/C][C]4121[/C][C]4543.32653376234[/C][C]-422.326533762337[/C][/ROW]
[ROW][C]30[/C][C]5103[/C][C]4383.64605791624[/C][C]719.35394208376[/C][/ROW]
[ROW][C]31[/C][C]4300[/C][C]4655.63176231989[/C][C]-355.631762319888[/C][/ROW]
[ROW][C]32[/C][C]4578[/C][C]4521.16839217042[/C][C]56.8316078295766[/C][/ROW]
[ROW][C]33[/C][C]3809[/C][C]4542.65626341659[/C][C]-733.656263416591[/C][/ROW]
[ROW][C]34[/C][C]5657[/C][C]4265.26289150083[/C][C]1391.73710849917[/C][/ROW]
[ROW][C]35[/C][C]4248[/C][C]4791.4747819971[/C][C]-543.474781997104[/C][/ROW]
[ROW][C]36[/C][C]3830[/C][C]4585.98849387179[/C][C]-755.988493871794[/C][/ROW]
[ROW][C]37[/C][C]4736[/C][C]4300.1513683656[/C][C]435.848631634402[/C][/ROW]
[ROW][C]38[/C][C]4839[/C][C]4464.94451142541[/C][C]374.05548857459[/C][/ROW]
[ROW][C]39[/C][C]4411[/C][C]4606.37384070844[/C][C]-195.373840708441[/C][/ROW]
[ROW][C]40[/C][C]4570[/C][C]4532.5035404593[/C][C]37.4964595407009[/C][/ROW]
[ROW][C]41[/C][C]4104[/C][C]4546.68084646151[/C][C]-442.680846461513[/C][/ROW]
[ROW][C]42[/C][C]4801[/C][C]4379.30446217137[/C][C]421.695537828626[/C][/ROW]
[ROW][C]43[/C][C]3953[/C][C]4538.74636022778[/C][C]-585.746360227782[/C][/ROW]
[ROW][C]44[/C][C]3828[/C][C]4317.27730713976[/C][C]-489.27730713976[/C][/ROW]
[ROW][C]45[/C][C]4440[/C][C]4132.28293198468[/C][C]307.717068015319[/C][/ROW]
[ROW][C]46[/C][C]4026[/C][C]4248.62989083881[/C][C]-222.629890838806[/C][/ROW]
[ROW][C]47[/C][C]4109[/C][C]4164.45415461402[/C][C]-55.4541546140235[/C][/ROW]
[ROW][C]48[/C][C]4785[/C][C]4143.48709455856[/C][C]641.512905441439[/C][/ROW]
[ROW][C]49[/C][C]3224[/C][C]4386.04132171007[/C][C]-1162.04132171007[/C][/ROW]
[ROW][C]50[/C][C]3552[/C][C]3946.67676284503[/C][C]-394.676762845031[/C][/ROW]
[ROW][C]51[/C][C]3940[/C][C]3797.45058769792[/C][C]142.549412302082[/C][/ROW]
[ROW][C]52[/C][C]3913[/C][C]3851.34811998223[/C][C]61.6518800177682[/C][/ROW]
[ROW][C]53[/C][C]3681[/C][C]3874.65852259971[/C][C]-193.658522599709[/C][/ROW]
[ROW][C]54[/C][C]4309[/C][C]3801.43677930812[/C][C]507.563220691883[/C][/ROW]
[ROW][C]55[/C][C]3830[/C][C]3993.34500700112[/C][C]-163.345007001115[/C][/ROW]
[ROW][C]56[/C][C]4143[/C][C]3931.58471878844[/C][C]211.41528121156[/C][/ROW]
[ROW][C]57[/C][C]4087[/C][C]4011.52024262175[/C][C]75.4797573782507[/C][/ROW]
[ROW][C]58[/C][C]3818[/C][C]4040.05892681839[/C][C]-222.058926818394[/C][/ROW]
[ROW][C]59[/C][C]3380[/C][C]3956.09907048555[/C][C]-576.099070485548[/C][/ROW]
[ROW][C]60[/C][C]3430[/C][C]3738.27763054402[/C][C]-308.27763054402[/C][/ROW]
[ROW][C]61[/C][C]3458[/C][C]3621.71872457275[/C][C]-163.718724572751[/C][/ROW]
[ROW][C]62[/C][C]3970[/C][C]3559.81713479624[/C][C]410.182865203762[/C][/ROW]
[ROW][C]63[/C][C]5260[/C][C]3714.90612367921[/C][C]1545.09387632079[/C][/ROW]
[ROW][C]64[/C][C]5024[/C][C]4299.10177721737[/C][C]724.89822278263[/C][/ROW]
[ROW][C]65[/C][C]5634[/C][C]4573.18375857604[/C][C]1060.81624142396[/C][/ROW]
[ROW][C]66[/C][C]6549[/C][C]4974.27539898708[/C][C]1574.72460101292[/C][/ROW]
[ROW][C]67[/C][C]4676[/C][C]5569.67434628079[/C][C]-893.674346280794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152536&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152536&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
244294143286
352194251.13579645385967.864203546151
449294617.08253250152311.917467498482
557614735.017650598781025.98234940122
655925122.93869430539469.061305694607
741635300.28945611298-1137.28945611298
849624870.2835080873191.7164919126935
952084904.96125599266303.038744007336
1047555019.5393536836-264.539353683598
1144914919.51776730611-428.517767306107
1257324757.49640345201974.503596547987
1357315125.95347533962605.046524660375
1450405354.71986637383-314.719866373831
1561025235.72516913543866.274830864571
1649045563.26124879789-659.261248797889
1753695313.9964228890855.0035771109178
1855785334.79312085656243.206879143436
1946195426.74895854618-807.748958546181
2047315121.3413467729-390.3413467729
2150114973.7543802618737.2456197381334
2252994987.83684443949311.16315556051
2341465105.48675931232-959.486759312317
2446254742.70751139218-117.707511392177
2547364698.2026320460537.7973679539546
2642194712.49371067388-493.493710673878
2751164525.90512518897590.094874811035
2842054749.01833942332-544.01833942332
2941214543.32653376234-422.326533762337
3051034383.64605791624719.35394208376
3143004655.63176231989-355.631762319888
3245784521.1683921704256.8316078295766
3338094542.65626341659-733.656263416591
3456574265.262891500831391.73710849917
3542484791.4747819971-543.474781997104
3638304585.98849387179-755.988493871794
3747364300.1513683656435.848631634402
3848394464.94451142541374.05548857459
3944114606.37384070844-195.373840708441
4045704532.503540459337.4964595407009
4141044546.68084646151-442.680846461513
4248014379.30446217137421.695537828626
4339534538.74636022778-585.746360227782
4438284317.27730713976-489.27730713976
4544404132.28293198468307.717068015319
4640264248.62989083881-222.629890838806
4741094164.45415461402-55.4541546140235
4847854143.48709455856641.512905441439
4932244386.04132171007-1162.04132171007
5035523946.67676284503-394.676762845031
5139403797.45058769792142.549412302082
5239133851.3481199822361.6518800177682
5336813874.65852259971-193.658522599709
5443093801.43677930812507.563220691883
5538303993.34500700112-163.345007001115
5641433931.58471878844211.41528121156
5740874011.5202426217575.4797573782507
5838184040.05892681839-222.058926818394
5933803956.09907048555-576.099070485548
6034303738.27763054402-308.27763054402
6134583621.71872457275-163.718724572751
6239703559.81713479624410.182865203762
6352603714.906123679211545.09387632079
6450244299.10177721737724.89822278263
6556344573.183758576041060.81624142396
6665494974.275398987081574.72460101292
6746765569.67434628079-893.674346280794







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
685231.778586821194010.409228195436453.14794544695
695231.778586821193926.022501610056537.53467203233
705231.778586821193846.767829483216616.78934415917
715231.778586821193771.809189259066691.74798438332
725231.778586821193700.515550731726763.04162291066
735231.778586821193632.396728236466831.16044540592
745231.778586821193567.062943401596896.4942302408
755231.778586821193504.198192940216959.35898070217
765231.778586821193443.542064098887020.0151095435
775231.778586821193384.876936739647078.68023690275
785231.778586821193328.018741423157135.53843221923
795231.778586821193272.810135613777190.74703802861

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
68 & 5231.77858682119 & 4010.40922819543 & 6453.14794544695 \tabularnewline
69 & 5231.77858682119 & 3926.02250161005 & 6537.53467203233 \tabularnewline
70 & 5231.77858682119 & 3846.76782948321 & 6616.78934415917 \tabularnewline
71 & 5231.77858682119 & 3771.80918925906 & 6691.74798438332 \tabularnewline
72 & 5231.77858682119 & 3700.51555073172 & 6763.04162291066 \tabularnewline
73 & 5231.77858682119 & 3632.39672823646 & 6831.16044540592 \tabularnewline
74 & 5231.77858682119 & 3567.06294340159 & 6896.4942302408 \tabularnewline
75 & 5231.77858682119 & 3504.19819294021 & 6959.35898070217 \tabularnewline
76 & 5231.77858682119 & 3443.54206409888 & 7020.0151095435 \tabularnewline
77 & 5231.77858682119 & 3384.87693673964 & 7078.68023690275 \tabularnewline
78 & 5231.77858682119 & 3328.01874142315 & 7135.53843221923 \tabularnewline
79 & 5231.77858682119 & 3272.81013561377 & 7190.74703802861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152536&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]68[/C][C]5231.77858682119[/C][C]4010.40922819543[/C][C]6453.14794544695[/C][/ROW]
[ROW][C]69[/C][C]5231.77858682119[/C][C]3926.02250161005[/C][C]6537.53467203233[/C][/ROW]
[ROW][C]70[/C][C]5231.77858682119[/C][C]3846.76782948321[/C][C]6616.78934415917[/C][/ROW]
[ROW][C]71[/C][C]5231.77858682119[/C][C]3771.80918925906[/C][C]6691.74798438332[/C][/ROW]
[ROW][C]72[/C][C]5231.77858682119[/C][C]3700.51555073172[/C][C]6763.04162291066[/C][/ROW]
[ROW][C]73[/C][C]5231.77858682119[/C][C]3632.39672823646[/C][C]6831.16044540592[/C][/ROW]
[ROW][C]74[/C][C]5231.77858682119[/C][C]3567.06294340159[/C][C]6896.4942302408[/C][/ROW]
[ROW][C]75[/C][C]5231.77858682119[/C][C]3504.19819294021[/C][C]6959.35898070217[/C][/ROW]
[ROW][C]76[/C][C]5231.77858682119[/C][C]3443.54206409888[/C][C]7020.0151095435[/C][/ROW]
[ROW][C]77[/C][C]5231.77858682119[/C][C]3384.87693673964[/C][C]7078.68023690275[/C][/ROW]
[ROW][C]78[/C][C]5231.77858682119[/C][C]3328.01874142315[/C][C]7135.53843221923[/C][/ROW]
[ROW][C]79[/C][C]5231.77858682119[/C][C]3272.81013561377[/C][C]7190.74703802861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152536&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152536&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
685231.778586821194010.409228195436453.14794544695
695231.778586821193926.022501610056537.53467203233
705231.778586821193846.767829483216616.78934415917
715231.778586821193771.809189259066691.74798438332
725231.778586821193700.515550731726763.04162291066
735231.778586821193632.396728236466831.16044540592
745231.778586821193567.062943401596896.4942302408
755231.778586821193504.198192940216959.35898070217
765231.778586821193443.542064098887020.0151095435
775231.778586821193384.876936739647078.68023690275
785231.778586821193328.018741423157135.53843221923
795231.778586821193272.810135613777190.74703802861



Parameters (Session):
par1 = 12 ; par2 = Single ; 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')