Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 15 Jan 2011 20:31:01 +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/Jan/15/t1295123605yk2wyjx8eyclgf3.htm/, Retrieved Thu, 16 May 2024 09:05:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117362, Retrieved Thu, 16 May 2024 09:05:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oef 2] [2011-01-15 20:31:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2834
4683
4120
3849
8435
12854
15883
10520
12562
5060
4520
2150
2905
4820
3950
4053
8700
13520
15400
11100
11950
4900
4633
2300
2945
3960
3900
3767
8820
11980
14085
11600
9814
4930
4360
2640
3050
5485
4366
4790
10100
14830
17930
13580
12490
6400
4980
4930
5856
5120
5100
5623
12035
19846
17030
15860
14890
8053
6080
5987
5682
4980
5450
6035
13240
18400
17689
16490
14062
9556
7555
4328




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117362&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117362&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117362&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'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0537548879628944
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0537548879628944 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117362&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0537548879628944[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117362&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117362&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
alpha1
beta0.0537548879628944
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
341206532-2412
438495839.3432102335-1990.3432102335
584355461.352533959692973.64746604031
61285410207.20062033782646.79937966217
71588314768.47902445181114.52097554817
81052017857.3899746247-7337.38997462472
91256212099.9693985987462.030601401299
10506014166.8058018125-9106.80580181246
1145206175.27047623619-1655.27047623619
1221505546.29159723783-3396.29159723783
1329052993.72432293899-88.7243229389887
1448203743.954956899821076.04504310018
1539505716.7976376347-1766.7976376347
1640534751.82362857054-698.823628570538
1787004817.258442710913882.74155728909
18135209672.974780111863847.02521988814
191540014699.7711897974700.228810202629
201110016617.4119110382-5517.41191103821
211195012020.8240519152-70.824051915206
22490012867.0169129394-7967.01691293943
2346335388.75081138588-755.750811385883
2423005081.12551119197-2781.12551119197
2529452598.6264209271346.373579072903
2639603262.24569386347697.754306136533
2739004314.75339841546-414.753398415463
2837674232.45837595141-465.458375951411
2988204074.437713100754745.56228689925
30119809382.534882153962597.46511784604
311408512682.16132855131402.8386714487
321160014862.570764165-3262.57076416504
33981412202.1916382663-2388.19163826633
34493010287.8146643174-5357.8146643174
3543605115.80593731107-755.80593731107
3626404505.17767382922-1865.17767382922
3730502684.91525694164365.084743058359
3854853114.54034640172370.4596535983
3943665676.96413950144-1310.96413950144
4047904487.49340905917302.506590940829
41101004927.754616963235172.24538303677
421483010515.7880880454314.21191195503
431793015477.69806602032452.3019339797
441358018709.5212817326-5129.52128173257
451249014083.7844399298-1593.78443992975
46640012908.1107359243-6508.11073592432
4749806468.2679724646-1488.2679724646
4849304968.266294346-38.2662943460009
4958564916.20929398068939.790706019324
5051205892.72763809131-772.727638091314
5151005115.18975047988-15.1897504798844
5256235094.37322714465528.626772855347
53120355645.789500093686389.21049990632
541984612401.24079468757444.75920531251
551703020612.4329916798-3582.43299167979
561586017603.8597075775-1743.85970757747
571489016340.1187243736-1450.11872437364
58805315292.167754812-7239.16775481204
5960808066.02710320752-1986.02710320752
6059875986.268438783330.73156121667489
6156825893.30776377457-211.307763774566
6249805576.94893860717-596.948938607175
6354504842.86001529278607.139984707223
6460355345.4967571485689.503242851493
65132405967.560926718047272.43907328196
661840013563.49007431934836.50992568071
671768918983.4761235057-1294.47612350568
681649018202.891704516-1712.89170451599
691406216911.8154028472-2849.81540284717
70955614330.6238951522-4774.62389515218
7175559567.96452260332-2012.96452260332
7243287458.7578402175-3130.7578402175

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4120 & 6532 & -2412 \tabularnewline
4 & 3849 & 5839.3432102335 & -1990.3432102335 \tabularnewline
5 & 8435 & 5461.35253395969 & 2973.64746604031 \tabularnewline
6 & 12854 & 10207.2006203378 & 2646.79937966217 \tabularnewline
7 & 15883 & 14768.4790244518 & 1114.52097554817 \tabularnewline
8 & 10520 & 17857.3899746247 & -7337.38997462472 \tabularnewline
9 & 12562 & 12099.9693985987 & 462.030601401299 \tabularnewline
10 & 5060 & 14166.8058018125 & -9106.80580181246 \tabularnewline
11 & 4520 & 6175.27047623619 & -1655.27047623619 \tabularnewline
12 & 2150 & 5546.29159723783 & -3396.29159723783 \tabularnewline
13 & 2905 & 2993.72432293899 & -88.7243229389887 \tabularnewline
14 & 4820 & 3743.95495689982 & 1076.04504310018 \tabularnewline
15 & 3950 & 5716.7976376347 & -1766.7976376347 \tabularnewline
16 & 4053 & 4751.82362857054 & -698.823628570538 \tabularnewline
17 & 8700 & 4817.25844271091 & 3882.74155728909 \tabularnewline
18 & 13520 & 9672.97478011186 & 3847.02521988814 \tabularnewline
19 & 15400 & 14699.7711897974 & 700.228810202629 \tabularnewline
20 & 11100 & 16617.4119110382 & -5517.41191103821 \tabularnewline
21 & 11950 & 12020.8240519152 & -70.824051915206 \tabularnewline
22 & 4900 & 12867.0169129394 & -7967.01691293943 \tabularnewline
23 & 4633 & 5388.75081138588 & -755.750811385883 \tabularnewline
24 & 2300 & 5081.12551119197 & -2781.12551119197 \tabularnewline
25 & 2945 & 2598.6264209271 & 346.373579072903 \tabularnewline
26 & 3960 & 3262.24569386347 & 697.754306136533 \tabularnewline
27 & 3900 & 4314.75339841546 & -414.753398415463 \tabularnewline
28 & 3767 & 4232.45837595141 & -465.458375951411 \tabularnewline
29 & 8820 & 4074.43771310075 & 4745.56228689925 \tabularnewline
30 & 11980 & 9382.53488215396 & 2597.46511784604 \tabularnewline
31 & 14085 & 12682.1613285513 & 1402.8386714487 \tabularnewline
32 & 11600 & 14862.570764165 & -3262.57076416504 \tabularnewline
33 & 9814 & 12202.1916382663 & -2388.19163826633 \tabularnewline
34 & 4930 & 10287.8146643174 & -5357.8146643174 \tabularnewline
35 & 4360 & 5115.80593731107 & -755.80593731107 \tabularnewline
36 & 2640 & 4505.17767382922 & -1865.17767382922 \tabularnewline
37 & 3050 & 2684.91525694164 & 365.084743058359 \tabularnewline
38 & 5485 & 3114.5403464017 & 2370.4596535983 \tabularnewline
39 & 4366 & 5676.96413950144 & -1310.96413950144 \tabularnewline
40 & 4790 & 4487.49340905917 & 302.506590940829 \tabularnewline
41 & 10100 & 4927.75461696323 & 5172.24538303677 \tabularnewline
42 & 14830 & 10515.788088045 & 4314.21191195503 \tabularnewline
43 & 17930 & 15477.6980660203 & 2452.3019339797 \tabularnewline
44 & 13580 & 18709.5212817326 & -5129.52128173257 \tabularnewline
45 & 12490 & 14083.7844399298 & -1593.78443992975 \tabularnewline
46 & 6400 & 12908.1107359243 & -6508.11073592432 \tabularnewline
47 & 4980 & 6468.2679724646 & -1488.2679724646 \tabularnewline
48 & 4930 & 4968.266294346 & -38.2662943460009 \tabularnewline
49 & 5856 & 4916.20929398068 & 939.790706019324 \tabularnewline
50 & 5120 & 5892.72763809131 & -772.727638091314 \tabularnewline
51 & 5100 & 5115.18975047988 & -15.1897504798844 \tabularnewline
52 & 5623 & 5094.37322714465 & 528.626772855347 \tabularnewline
53 & 12035 & 5645.78950009368 & 6389.21049990632 \tabularnewline
54 & 19846 & 12401.2407946875 & 7444.75920531251 \tabularnewline
55 & 17030 & 20612.4329916798 & -3582.43299167979 \tabularnewline
56 & 15860 & 17603.8597075775 & -1743.85970757747 \tabularnewline
57 & 14890 & 16340.1187243736 & -1450.11872437364 \tabularnewline
58 & 8053 & 15292.167754812 & -7239.16775481204 \tabularnewline
59 & 6080 & 8066.02710320752 & -1986.02710320752 \tabularnewline
60 & 5987 & 5986.26843878333 & 0.73156121667489 \tabularnewline
61 & 5682 & 5893.30776377457 & -211.307763774566 \tabularnewline
62 & 4980 & 5576.94893860717 & -596.948938607175 \tabularnewline
63 & 5450 & 4842.86001529278 & 607.139984707223 \tabularnewline
64 & 6035 & 5345.4967571485 & 689.503242851493 \tabularnewline
65 & 13240 & 5967.56092671804 & 7272.43907328196 \tabularnewline
66 & 18400 & 13563.4900743193 & 4836.50992568071 \tabularnewline
67 & 17689 & 18983.4761235057 & -1294.47612350568 \tabularnewline
68 & 16490 & 18202.891704516 & -1712.89170451599 \tabularnewline
69 & 14062 & 16911.8154028472 & -2849.81540284717 \tabularnewline
70 & 9556 & 14330.6238951522 & -4774.62389515218 \tabularnewline
71 & 7555 & 9567.96452260332 & -2012.96452260332 \tabularnewline
72 & 4328 & 7458.7578402175 & -3130.7578402175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117362&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]4120[/C][C]6532[/C][C]-2412[/C][/ROW]
[ROW][C]4[/C][C]3849[/C][C]5839.3432102335[/C][C]-1990.3432102335[/C][/ROW]
[ROW][C]5[/C][C]8435[/C][C]5461.35253395969[/C][C]2973.64746604031[/C][/ROW]
[ROW][C]6[/C][C]12854[/C][C]10207.2006203378[/C][C]2646.79937966217[/C][/ROW]
[ROW][C]7[/C][C]15883[/C][C]14768.4790244518[/C][C]1114.52097554817[/C][/ROW]
[ROW][C]8[/C][C]10520[/C][C]17857.3899746247[/C][C]-7337.38997462472[/C][/ROW]
[ROW][C]9[/C][C]12562[/C][C]12099.9693985987[/C][C]462.030601401299[/C][/ROW]
[ROW][C]10[/C][C]5060[/C][C]14166.8058018125[/C][C]-9106.80580181246[/C][/ROW]
[ROW][C]11[/C][C]4520[/C][C]6175.27047623619[/C][C]-1655.27047623619[/C][/ROW]
[ROW][C]12[/C][C]2150[/C][C]5546.29159723783[/C][C]-3396.29159723783[/C][/ROW]
[ROW][C]13[/C][C]2905[/C][C]2993.72432293899[/C][C]-88.7243229389887[/C][/ROW]
[ROW][C]14[/C][C]4820[/C][C]3743.95495689982[/C][C]1076.04504310018[/C][/ROW]
[ROW][C]15[/C][C]3950[/C][C]5716.7976376347[/C][C]-1766.7976376347[/C][/ROW]
[ROW][C]16[/C][C]4053[/C][C]4751.82362857054[/C][C]-698.823628570538[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]4817.25844271091[/C][C]3882.74155728909[/C][/ROW]
[ROW][C]18[/C][C]13520[/C][C]9672.97478011186[/C][C]3847.02521988814[/C][/ROW]
[ROW][C]19[/C][C]15400[/C][C]14699.7711897974[/C][C]700.228810202629[/C][/ROW]
[ROW][C]20[/C][C]11100[/C][C]16617.4119110382[/C][C]-5517.41191103821[/C][/ROW]
[ROW][C]21[/C][C]11950[/C][C]12020.8240519152[/C][C]-70.824051915206[/C][/ROW]
[ROW][C]22[/C][C]4900[/C][C]12867.0169129394[/C][C]-7967.01691293943[/C][/ROW]
[ROW][C]23[/C][C]4633[/C][C]5388.75081138588[/C][C]-755.750811385883[/C][/ROW]
[ROW][C]24[/C][C]2300[/C][C]5081.12551119197[/C][C]-2781.12551119197[/C][/ROW]
[ROW][C]25[/C][C]2945[/C][C]2598.6264209271[/C][C]346.373579072903[/C][/ROW]
[ROW][C]26[/C][C]3960[/C][C]3262.24569386347[/C][C]697.754306136533[/C][/ROW]
[ROW][C]27[/C][C]3900[/C][C]4314.75339841546[/C][C]-414.753398415463[/C][/ROW]
[ROW][C]28[/C][C]3767[/C][C]4232.45837595141[/C][C]-465.458375951411[/C][/ROW]
[ROW][C]29[/C][C]8820[/C][C]4074.43771310075[/C][C]4745.56228689925[/C][/ROW]
[ROW][C]30[/C][C]11980[/C][C]9382.53488215396[/C][C]2597.46511784604[/C][/ROW]
[ROW][C]31[/C][C]14085[/C][C]12682.1613285513[/C][C]1402.8386714487[/C][/ROW]
[ROW][C]32[/C][C]11600[/C][C]14862.570764165[/C][C]-3262.57076416504[/C][/ROW]
[ROW][C]33[/C][C]9814[/C][C]12202.1916382663[/C][C]-2388.19163826633[/C][/ROW]
[ROW][C]34[/C][C]4930[/C][C]10287.8146643174[/C][C]-5357.8146643174[/C][/ROW]
[ROW][C]35[/C][C]4360[/C][C]5115.80593731107[/C][C]-755.80593731107[/C][/ROW]
[ROW][C]36[/C][C]2640[/C][C]4505.17767382922[/C][C]-1865.17767382922[/C][/ROW]
[ROW][C]37[/C][C]3050[/C][C]2684.91525694164[/C][C]365.084743058359[/C][/ROW]
[ROW][C]38[/C][C]5485[/C][C]3114.5403464017[/C][C]2370.4596535983[/C][/ROW]
[ROW][C]39[/C][C]4366[/C][C]5676.96413950144[/C][C]-1310.96413950144[/C][/ROW]
[ROW][C]40[/C][C]4790[/C][C]4487.49340905917[/C][C]302.506590940829[/C][/ROW]
[ROW][C]41[/C][C]10100[/C][C]4927.75461696323[/C][C]5172.24538303677[/C][/ROW]
[ROW][C]42[/C][C]14830[/C][C]10515.788088045[/C][C]4314.21191195503[/C][/ROW]
[ROW][C]43[/C][C]17930[/C][C]15477.6980660203[/C][C]2452.3019339797[/C][/ROW]
[ROW][C]44[/C][C]13580[/C][C]18709.5212817326[/C][C]-5129.52128173257[/C][/ROW]
[ROW][C]45[/C][C]12490[/C][C]14083.7844399298[/C][C]-1593.78443992975[/C][/ROW]
[ROW][C]46[/C][C]6400[/C][C]12908.1107359243[/C][C]-6508.11073592432[/C][/ROW]
[ROW][C]47[/C][C]4980[/C][C]6468.2679724646[/C][C]-1488.2679724646[/C][/ROW]
[ROW][C]48[/C][C]4930[/C][C]4968.266294346[/C][C]-38.2662943460009[/C][/ROW]
[ROW][C]49[/C][C]5856[/C][C]4916.20929398068[/C][C]939.790706019324[/C][/ROW]
[ROW][C]50[/C][C]5120[/C][C]5892.72763809131[/C][C]-772.727638091314[/C][/ROW]
[ROW][C]51[/C][C]5100[/C][C]5115.18975047988[/C][C]-15.1897504798844[/C][/ROW]
[ROW][C]52[/C][C]5623[/C][C]5094.37322714465[/C][C]528.626772855347[/C][/ROW]
[ROW][C]53[/C][C]12035[/C][C]5645.78950009368[/C][C]6389.21049990632[/C][/ROW]
[ROW][C]54[/C][C]19846[/C][C]12401.2407946875[/C][C]7444.75920531251[/C][/ROW]
[ROW][C]55[/C][C]17030[/C][C]20612.4329916798[/C][C]-3582.43299167979[/C][/ROW]
[ROW][C]56[/C][C]15860[/C][C]17603.8597075775[/C][C]-1743.85970757747[/C][/ROW]
[ROW][C]57[/C][C]14890[/C][C]16340.1187243736[/C][C]-1450.11872437364[/C][/ROW]
[ROW][C]58[/C][C]8053[/C][C]15292.167754812[/C][C]-7239.16775481204[/C][/ROW]
[ROW][C]59[/C][C]6080[/C][C]8066.02710320752[/C][C]-1986.02710320752[/C][/ROW]
[ROW][C]60[/C][C]5987[/C][C]5986.26843878333[/C][C]0.73156121667489[/C][/ROW]
[ROW][C]61[/C][C]5682[/C][C]5893.30776377457[/C][C]-211.307763774566[/C][/ROW]
[ROW][C]62[/C][C]4980[/C][C]5576.94893860717[/C][C]-596.948938607175[/C][/ROW]
[ROW][C]63[/C][C]5450[/C][C]4842.86001529278[/C][C]607.139984707223[/C][/ROW]
[ROW][C]64[/C][C]6035[/C][C]5345.4967571485[/C][C]689.503242851493[/C][/ROW]
[ROW][C]65[/C][C]13240[/C][C]5967.56092671804[/C][C]7272.43907328196[/C][/ROW]
[ROW][C]66[/C][C]18400[/C][C]13563.4900743193[/C][C]4836.50992568071[/C][/ROW]
[ROW][C]67[/C][C]17689[/C][C]18983.4761235057[/C][C]-1294.47612350568[/C][/ROW]
[ROW][C]68[/C][C]16490[/C][C]18202.891704516[/C][C]-1712.89170451599[/C][/ROW]
[ROW][C]69[/C][C]14062[/C][C]16911.8154028472[/C][C]-2849.81540284717[/C][/ROW]
[ROW][C]70[/C][C]9556[/C][C]14330.6238951522[/C][C]-4774.62389515218[/C][/ROW]
[ROW][C]71[/C][C]7555[/C][C]9567.96452260332[/C][C]-2012.96452260332[/C][/ROW]
[ROW][C]72[/C][C]4328[/C][C]7458.7578402175[/C][C]-3130.7578402175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117362&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117362&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
341206532-2412
438495839.3432102335-1990.3432102335
584355461.352533959692973.64746604031
61285410207.20062033782646.79937966217
71588314768.47902445181114.52097554817
81052017857.3899746247-7337.38997462472
91256212099.9693985987462.030601401299
10506014166.8058018125-9106.80580181246
1145206175.27047623619-1655.27047623619
1221505546.29159723783-3396.29159723783
1329052993.72432293899-88.7243229389887
1448203743.954956899821076.04504310018
1539505716.7976376347-1766.7976376347
1640534751.82362857054-698.823628570538
1787004817.258442710913882.74155728909
18135209672.974780111863847.02521988814
191540014699.7711897974700.228810202629
201110016617.4119110382-5517.41191103821
211195012020.8240519152-70.824051915206
22490012867.0169129394-7967.01691293943
2346335388.75081138588-755.750811385883
2423005081.12551119197-2781.12551119197
2529452598.6264209271346.373579072903
2639603262.24569386347697.754306136533
2739004314.75339841546-414.753398415463
2837674232.45837595141-465.458375951411
2988204074.437713100754745.56228689925
30119809382.534882153962597.46511784604
311408512682.16132855131402.8386714487
321160014862.570764165-3262.57076416504
33981412202.1916382663-2388.19163826633
34493010287.8146643174-5357.8146643174
3543605115.80593731107-755.80593731107
3626404505.17767382922-1865.17767382922
3730502684.91525694164365.084743058359
3854853114.54034640172370.4596535983
3943665676.96413950144-1310.96413950144
4047904487.49340905917302.506590940829
41101004927.754616963235172.24538303677
421483010515.7880880454314.21191195503
431793015477.69806602032452.3019339797
441358018709.5212817326-5129.52128173257
451249014083.7844399298-1593.78443992975
46640012908.1107359243-6508.11073592432
4749806468.2679724646-1488.2679724646
4849304968.266294346-38.2662943460009
4958564916.20929398068939.790706019324
5051205892.72763809131-772.727638091314
5151005115.18975047988-15.1897504798844
5256235094.37322714465528.626772855347
53120355645.789500093686389.21049990632
541984612401.24079468757444.75920531251
551703020612.4329916798-3582.43299167979
561586017603.8597075775-1743.85970757747
571489016340.1187243736-1450.11872437364
58805315292.167754812-7239.16775481204
5960808066.02710320752-1986.02710320752
6059875986.268438783330.73156121667489
6156825893.30776377457-211.307763774566
6249805576.94893860717-596.948938607175
6354504842.86001529278607.139984707223
6460355345.4967571485689.503242851493
65132405967.560926718047272.43907328196
661840013563.49007431934836.50992568071
671768918983.4761235057-1294.47612350568
681649018202.891704516-1712.89170451599
691406216911.8154028472-2849.81540284717
70955614330.6238951522-4774.62389515218
7175559567.96452260332-2012.96452260332
7243287458.7578402175-3130.7578402175







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734063.46430327765-2636.7088412895410763.6374478448
743798.9286065553-5934.5560687840613532.4132818947
753534.39290983296-8705.0781527232315773.8639723891
763269.85721311061-11233.368106897417773.0825331186
773005.32151638826-13626.480638455719637.1236712322
782740.78581966591-15937.650603479621419.2222428114
792476.25012294356-18197.511464809723150.0117106968
802211.71442622122-20425.369671707224848.7985241497
811947.17872949887-22634.174012757726528.5314717555
821682.64303277652-24833.009652994528198.2957185475
831418.10733605417-27028.471038396129864.6857105045
841153.57163933183-29225.472039504731532.6153181684

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4063.46430327765 & -2636.70884128954 & 10763.6374478448 \tabularnewline
74 & 3798.9286065553 & -5934.55606878406 & 13532.4132818947 \tabularnewline
75 & 3534.39290983296 & -8705.07815272323 & 15773.8639723891 \tabularnewline
76 & 3269.85721311061 & -11233.3681068974 & 17773.0825331186 \tabularnewline
77 & 3005.32151638826 & -13626.4806384557 & 19637.1236712322 \tabularnewline
78 & 2740.78581966591 & -15937.6506034796 & 21419.2222428114 \tabularnewline
79 & 2476.25012294356 & -18197.5114648097 & 23150.0117106968 \tabularnewline
80 & 2211.71442622122 & -20425.3696717072 & 24848.7985241497 \tabularnewline
81 & 1947.17872949887 & -22634.1740127577 & 26528.5314717555 \tabularnewline
82 & 1682.64303277652 & -24833.0096529945 & 28198.2957185475 \tabularnewline
83 & 1418.10733605417 & -27028.4710383961 & 29864.6857105045 \tabularnewline
84 & 1153.57163933183 & -29225.4720395047 & 31532.6153181684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117362&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]73[/C][C]4063.46430327765[/C][C]-2636.70884128954[/C][C]10763.6374478448[/C][/ROW]
[ROW][C]74[/C][C]3798.9286065553[/C][C]-5934.55606878406[/C][C]13532.4132818947[/C][/ROW]
[ROW][C]75[/C][C]3534.39290983296[/C][C]-8705.07815272323[/C][C]15773.8639723891[/C][/ROW]
[ROW][C]76[/C][C]3269.85721311061[/C][C]-11233.3681068974[/C][C]17773.0825331186[/C][/ROW]
[ROW][C]77[/C][C]3005.32151638826[/C][C]-13626.4806384557[/C][C]19637.1236712322[/C][/ROW]
[ROW][C]78[/C][C]2740.78581966591[/C][C]-15937.6506034796[/C][C]21419.2222428114[/C][/ROW]
[ROW][C]79[/C][C]2476.25012294356[/C][C]-18197.5114648097[/C][C]23150.0117106968[/C][/ROW]
[ROW][C]80[/C][C]2211.71442622122[/C][C]-20425.3696717072[/C][C]24848.7985241497[/C][/ROW]
[ROW][C]81[/C][C]1947.17872949887[/C][C]-22634.1740127577[/C][C]26528.5314717555[/C][/ROW]
[ROW][C]82[/C][C]1682.64303277652[/C][C]-24833.0096529945[/C][C]28198.2957185475[/C][/ROW]
[ROW][C]83[/C][C]1418.10733605417[/C][C]-27028.4710383961[/C][C]29864.6857105045[/C][/ROW]
[ROW][C]84[/C][C]1153.57163933183[/C][C]-29225.4720395047[/C][C]31532.6153181684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117362&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117362&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
734063.46430327765-2636.7088412895410763.6374478448
743798.9286065553-5934.5560687840613532.4132818947
753534.39290983296-8705.0781527232315773.8639723891
763269.85721311061-11233.368106897417773.0825331186
773005.32151638826-13626.480638455719637.1236712322
782740.78581966591-15937.650603479621419.2222428114
792476.25012294356-18197.511464809723150.0117106968
802211.71442622122-20425.369671707224848.7985241497
811947.17872949887-22634.174012757726528.5314717555
821682.64303277652-24833.009652994528198.2957185475
831418.10733605417-27028.471038396129864.6857105045
841153.57163933183-29225.472039504731532.6153181684



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')