Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 May 2010 15:27:14 +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/May/28/t127506050844ypym524i49at8.htm/, Retrieved Sun, 28 Apr 2024 00:53:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76642, Retrieved Sun, 28 Apr 2024 00:53:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact213
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-05-28 15:27:14] [5c964c3d7ddd2ed48ce2db94081575d2] [Current]
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Dataseries X:
2550
2867
3458
2961
3163
2880
3331
3062
3534
3622
4464
5411
2564
2820
3508
3088
3299
2939
3320
3418
3604
3495
4163
4882
2211
3260
2992
2425
2707
3244
3965
3315
3333
3583
4021
4904
2252
2952
3573
3048
3059
2731
3563
3092
3478
3478
4308
5029
2075
3264
3308
3688
3136
2824
3644
4694
2914
3686
4358
5587
2265
3685
3754
3708
3210
3517
3905
3670
4221
4404
5086
5725
2367
3819
4067
4022
3937
4365
4290




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76642&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76642&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76642&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0219538867872071
beta0.849748700445273
gamma0.31528236748219

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0219538867872071 \tabularnewline
beta & 0.849748700445273 \tabularnewline
gamma & 0.31528236748219 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76642&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]0.0219538867872071[/C][/ROW]
[ROW][C]beta[/C][C]0.849748700445273[/C][/ROW]
[ROW][C]gamma[/C][C]0.31528236748219[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76642&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76642&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
alpha0.0219538867872071
beta0.849748700445273
gamma0.31528236748219







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325642540.4360262156723.5639737843312
1428202786.8909846354733.1090153645282
1535083455.5698982385652.4301017614375
1630883050.5697308132437.4302691867629
1732993283.3981959532715.6018040467293
1829392961.14590175454-22.1459017545403
1933203366.75875814298-46.7587581429775
2034183100.59931681039317.400683189611
2136043599.568379451714.43162054829372
2234953694.90035916793-199.900359167934
2341634546.02210889468-383.022108894679
2448825493.2020492742-611.202049274198
2522112599.88516127479-388.885161274794
2632602829.75306104031430.246938959695
2729923514.04923030427-522.049230304274
2824253070.94469955403-645.944699554028
2927073249.40172859017-542.401728590168
3032442870.35214456770373.647855432297
3139653232.17887781673732.821122183275
3233153080.69145459866234.308545401342
3333333443.40913219231-110.409132192313
3435833446.36955696997136.630443030027
3540214185.26716669707-164.267166697068
3649044995.02349954517-91.0234995451665
3722522332.71711674191-80.7171167419096
3829522791.13887019654160.861129803455
3935733144.28423347904428.715766520959
4030482716.65581452568331.34418547432
4130592963.7953380331595.2046619668545
4227312920.88139677717-189.881396777173
4335633399.23070619969163.769293800309
4430923106.31236676567-14.3123667656746
4534783367.92849927736110.07150072264
4634783470.472162212197.52783778780577
4743084130.19080414777177.809195852225
4850295002.9438100443726.0561899556269
4920752341.88088511256-266.880885112562
5032642893.34757275042370.652427249584
5133083364.69995854097-56.6999585409685
5236882896.39343174623791.60656825377
5331363106.5965199780829.4034800219247
5428242987.66349368554-163.663493685535
5536443624.4788930947419.5211069052552
5646943273.897667484181420.10233251582
5729143673.86917067579-759.869170675788
5836863763.76039016466-77.760390164658
5943584570.98991837248-212.989918372482
6055875498.1726415829588.8273584170529
6122652496.17060320570-231.170603205705
6236853347.35915372792337.640846272082
6337543747.338986838116.66101316189406
6437083539.20744667407168.792553325934
6532103504.03572867123-294.035728671233
6635173298.69945035517218.300549644833
6739054100.03008792936-195.030087929355
6836704190.1011634476-520.1011634476
6942213806.95905597092414.040944029085
7044044159.40935432775244.590645672249
7150865015.0592087368770.9407912631259
7257256160.50026357569-435.500263575693
7323672694.56000863673-327.560008636734
7438193825.67730976688-6.67730976687517
7540674131.41753902044-64.4175390204364
7640223939.8592312912482.1407687087567
7739373725.88583305532211.11416694468
7843653679.12360994954685.876390050455
7942904429.40676732055-139.406767320545

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2564 & 2540.43602621567 & 23.5639737843312 \tabularnewline
14 & 2820 & 2786.89098463547 & 33.1090153645282 \tabularnewline
15 & 3508 & 3455.56989823856 & 52.4301017614375 \tabularnewline
16 & 3088 & 3050.56973081324 & 37.4302691867629 \tabularnewline
17 & 3299 & 3283.39819595327 & 15.6018040467293 \tabularnewline
18 & 2939 & 2961.14590175454 & -22.1459017545403 \tabularnewline
19 & 3320 & 3366.75875814298 & -46.7587581429775 \tabularnewline
20 & 3418 & 3100.59931681039 & 317.400683189611 \tabularnewline
21 & 3604 & 3599.56837945171 & 4.43162054829372 \tabularnewline
22 & 3495 & 3694.90035916793 & -199.900359167934 \tabularnewline
23 & 4163 & 4546.02210889468 & -383.022108894679 \tabularnewline
24 & 4882 & 5493.2020492742 & -611.202049274198 \tabularnewline
25 & 2211 & 2599.88516127479 & -388.885161274794 \tabularnewline
26 & 3260 & 2829.75306104031 & 430.246938959695 \tabularnewline
27 & 2992 & 3514.04923030427 & -522.049230304274 \tabularnewline
28 & 2425 & 3070.94469955403 & -645.944699554028 \tabularnewline
29 & 2707 & 3249.40172859017 & -542.401728590168 \tabularnewline
30 & 3244 & 2870.35214456770 & 373.647855432297 \tabularnewline
31 & 3965 & 3232.17887781673 & 732.821122183275 \tabularnewline
32 & 3315 & 3080.69145459866 & 234.308545401342 \tabularnewline
33 & 3333 & 3443.40913219231 & -110.409132192313 \tabularnewline
34 & 3583 & 3446.36955696997 & 136.630443030027 \tabularnewline
35 & 4021 & 4185.26716669707 & -164.267166697068 \tabularnewline
36 & 4904 & 4995.02349954517 & -91.0234995451665 \tabularnewline
37 & 2252 & 2332.71711674191 & -80.7171167419096 \tabularnewline
38 & 2952 & 2791.13887019654 & 160.861129803455 \tabularnewline
39 & 3573 & 3144.28423347904 & 428.715766520959 \tabularnewline
40 & 3048 & 2716.65581452568 & 331.34418547432 \tabularnewline
41 & 3059 & 2963.79533803315 & 95.2046619668545 \tabularnewline
42 & 2731 & 2920.88139677717 & -189.881396777173 \tabularnewline
43 & 3563 & 3399.23070619969 & 163.769293800309 \tabularnewline
44 & 3092 & 3106.31236676567 & -14.3123667656746 \tabularnewline
45 & 3478 & 3367.92849927736 & 110.07150072264 \tabularnewline
46 & 3478 & 3470.47216221219 & 7.52783778780577 \tabularnewline
47 & 4308 & 4130.19080414777 & 177.809195852225 \tabularnewline
48 & 5029 & 5002.94381004437 & 26.0561899556269 \tabularnewline
49 & 2075 & 2341.88088511256 & -266.880885112562 \tabularnewline
50 & 3264 & 2893.34757275042 & 370.652427249584 \tabularnewline
51 & 3308 & 3364.69995854097 & -56.6999585409685 \tabularnewline
52 & 3688 & 2896.39343174623 & 791.60656825377 \tabularnewline
53 & 3136 & 3106.59651997808 & 29.4034800219247 \tabularnewline
54 & 2824 & 2987.66349368554 & -163.663493685535 \tabularnewline
55 & 3644 & 3624.47889309474 & 19.5211069052552 \tabularnewline
56 & 4694 & 3273.89766748418 & 1420.10233251582 \tabularnewline
57 & 2914 & 3673.86917067579 & -759.869170675788 \tabularnewline
58 & 3686 & 3763.76039016466 & -77.760390164658 \tabularnewline
59 & 4358 & 4570.98991837248 & -212.989918372482 \tabularnewline
60 & 5587 & 5498.17264158295 & 88.8273584170529 \tabularnewline
61 & 2265 & 2496.17060320570 & -231.170603205705 \tabularnewline
62 & 3685 & 3347.35915372792 & 337.640846272082 \tabularnewline
63 & 3754 & 3747.33898683811 & 6.66101316189406 \tabularnewline
64 & 3708 & 3539.20744667407 & 168.792553325934 \tabularnewline
65 & 3210 & 3504.03572867123 & -294.035728671233 \tabularnewline
66 & 3517 & 3298.69945035517 & 218.300549644833 \tabularnewline
67 & 3905 & 4100.03008792936 & -195.030087929355 \tabularnewline
68 & 3670 & 4190.1011634476 & -520.1011634476 \tabularnewline
69 & 4221 & 3806.95905597092 & 414.040944029085 \tabularnewline
70 & 4404 & 4159.40935432775 & 244.590645672249 \tabularnewline
71 & 5086 & 5015.05920873687 & 70.9407912631259 \tabularnewline
72 & 5725 & 6160.50026357569 & -435.500263575693 \tabularnewline
73 & 2367 & 2694.56000863673 & -327.560008636734 \tabularnewline
74 & 3819 & 3825.67730976688 & -6.67730976687517 \tabularnewline
75 & 4067 & 4131.41753902044 & -64.4175390204364 \tabularnewline
76 & 4022 & 3939.85923129124 & 82.1407687087567 \tabularnewline
77 & 3937 & 3725.88583305532 & 211.11416694468 \tabularnewline
78 & 4365 & 3679.12360994954 & 685.876390050455 \tabularnewline
79 & 4290 & 4429.40676732055 & -139.406767320545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76642&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]2564[/C][C]2540.43602621567[/C][C]23.5639737843312[/C][/ROW]
[ROW][C]14[/C][C]2820[/C][C]2786.89098463547[/C][C]33.1090153645282[/C][/ROW]
[ROW][C]15[/C][C]3508[/C][C]3455.56989823856[/C][C]52.4301017614375[/C][/ROW]
[ROW][C]16[/C][C]3088[/C][C]3050.56973081324[/C][C]37.4302691867629[/C][/ROW]
[ROW][C]17[/C][C]3299[/C][C]3283.39819595327[/C][C]15.6018040467293[/C][/ROW]
[ROW][C]18[/C][C]2939[/C][C]2961.14590175454[/C][C]-22.1459017545403[/C][/ROW]
[ROW][C]19[/C][C]3320[/C][C]3366.75875814298[/C][C]-46.7587581429775[/C][/ROW]
[ROW][C]20[/C][C]3418[/C][C]3100.59931681039[/C][C]317.400683189611[/C][/ROW]
[ROW][C]21[/C][C]3604[/C][C]3599.56837945171[/C][C]4.43162054829372[/C][/ROW]
[ROW][C]22[/C][C]3495[/C][C]3694.90035916793[/C][C]-199.900359167934[/C][/ROW]
[ROW][C]23[/C][C]4163[/C][C]4546.02210889468[/C][C]-383.022108894679[/C][/ROW]
[ROW][C]24[/C][C]4882[/C][C]5493.2020492742[/C][C]-611.202049274198[/C][/ROW]
[ROW][C]25[/C][C]2211[/C][C]2599.88516127479[/C][C]-388.885161274794[/C][/ROW]
[ROW][C]26[/C][C]3260[/C][C]2829.75306104031[/C][C]430.246938959695[/C][/ROW]
[ROW][C]27[/C][C]2992[/C][C]3514.04923030427[/C][C]-522.049230304274[/C][/ROW]
[ROW][C]28[/C][C]2425[/C][C]3070.94469955403[/C][C]-645.944699554028[/C][/ROW]
[ROW][C]29[/C][C]2707[/C][C]3249.40172859017[/C][C]-542.401728590168[/C][/ROW]
[ROW][C]30[/C][C]3244[/C][C]2870.35214456770[/C][C]373.647855432297[/C][/ROW]
[ROW][C]31[/C][C]3965[/C][C]3232.17887781673[/C][C]732.821122183275[/C][/ROW]
[ROW][C]32[/C][C]3315[/C][C]3080.69145459866[/C][C]234.308545401342[/C][/ROW]
[ROW][C]33[/C][C]3333[/C][C]3443.40913219231[/C][C]-110.409132192313[/C][/ROW]
[ROW][C]34[/C][C]3583[/C][C]3446.36955696997[/C][C]136.630443030027[/C][/ROW]
[ROW][C]35[/C][C]4021[/C][C]4185.26716669707[/C][C]-164.267166697068[/C][/ROW]
[ROW][C]36[/C][C]4904[/C][C]4995.02349954517[/C][C]-91.0234995451665[/C][/ROW]
[ROW][C]37[/C][C]2252[/C][C]2332.71711674191[/C][C]-80.7171167419096[/C][/ROW]
[ROW][C]38[/C][C]2952[/C][C]2791.13887019654[/C][C]160.861129803455[/C][/ROW]
[ROW][C]39[/C][C]3573[/C][C]3144.28423347904[/C][C]428.715766520959[/C][/ROW]
[ROW][C]40[/C][C]3048[/C][C]2716.65581452568[/C][C]331.34418547432[/C][/ROW]
[ROW][C]41[/C][C]3059[/C][C]2963.79533803315[/C][C]95.2046619668545[/C][/ROW]
[ROW][C]42[/C][C]2731[/C][C]2920.88139677717[/C][C]-189.881396777173[/C][/ROW]
[ROW][C]43[/C][C]3563[/C][C]3399.23070619969[/C][C]163.769293800309[/C][/ROW]
[ROW][C]44[/C][C]3092[/C][C]3106.31236676567[/C][C]-14.3123667656746[/C][/ROW]
[ROW][C]45[/C][C]3478[/C][C]3367.92849927736[/C][C]110.07150072264[/C][/ROW]
[ROW][C]46[/C][C]3478[/C][C]3470.47216221219[/C][C]7.52783778780577[/C][/ROW]
[ROW][C]47[/C][C]4308[/C][C]4130.19080414777[/C][C]177.809195852225[/C][/ROW]
[ROW][C]48[/C][C]5029[/C][C]5002.94381004437[/C][C]26.0561899556269[/C][/ROW]
[ROW][C]49[/C][C]2075[/C][C]2341.88088511256[/C][C]-266.880885112562[/C][/ROW]
[ROW][C]50[/C][C]3264[/C][C]2893.34757275042[/C][C]370.652427249584[/C][/ROW]
[ROW][C]51[/C][C]3308[/C][C]3364.69995854097[/C][C]-56.6999585409685[/C][/ROW]
[ROW][C]52[/C][C]3688[/C][C]2896.39343174623[/C][C]791.60656825377[/C][/ROW]
[ROW][C]53[/C][C]3136[/C][C]3106.59651997808[/C][C]29.4034800219247[/C][/ROW]
[ROW][C]54[/C][C]2824[/C][C]2987.66349368554[/C][C]-163.663493685535[/C][/ROW]
[ROW][C]55[/C][C]3644[/C][C]3624.47889309474[/C][C]19.5211069052552[/C][/ROW]
[ROW][C]56[/C][C]4694[/C][C]3273.89766748418[/C][C]1420.10233251582[/C][/ROW]
[ROW][C]57[/C][C]2914[/C][C]3673.86917067579[/C][C]-759.869170675788[/C][/ROW]
[ROW][C]58[/C][C]3686[/C][C]3763.76039016466[/C][C]-77.760390164658[/C][/ROW]
[ROW][C]59[/C][C]4358[/C][C]4570.98991837248[/C][C]-212.989918372482[/C][/ROW]
[ROW][C]60[/C][C]5587[/C][C]5498.17264158295[/C][C]88.8273584170529[/C][/ROW]
[ROW][C]61[/C][C]2265[/C][C]2496.17060320570[/C][C]-231.170603205705[/C][/ROW]
[ROW][C]62[/C][C]3685[/C][C]3347.35915372792[/C][C]337.640846272082[/C][/ROW]
[ROW][C]63[/C][C]3754[/C][C]3747.33898683811[/C][C]6.66101316189406[/C][/ROW]
[ROW][C]64[/C][C]3708[/C][C]3539.20744667407[/C][C]168.792553325934[/C][/ROW]
[ROW][C]65[/C][C]3210[/C][C]3504.03572867123[/C][C]-294.035728671233[/C][/ROW]
[ROW][C]66[/C][C]3517[/C][C]3298.69945035517[/C][C]218.300549644833[/C][/ROW]
[ROW][C]67[/C][C]3905[/C][C]4100.03008792936[/C][C]-195.030087929355[/C][/ROW]
[ROW][C]68[/C][C]3670[/C][C]4190.1011634476[/C][C]-520.1011634476[/C][/ROW]
[ROW][C]69[/C][C]4221[/C][C]3806.95905597092[/C][C]414.040944029085[/C][/ROW]
[ROW][C]70[/C][C]4404[/C][C]4159.40935432775[/C][C]244.590645672249[/C][/ROW]
[ROW][C]71[/C][C]5086[/C][C]5015.05920873687[/C][C]70.9407912631259[/C][/ROW]
[ROW][C]72[/C][C]5725[/C][C]6160.50026357569[/C][C]-435.500263575693[/C][/ROW]
[ROW][C]73[/C][C]2367[/C][C]2694.56000863673[/C][C]-327.560008636734[/C][/ROW]
[ROW][C]74[/C][C]3819[/C][C]3825.67730976688[/C][C]-6.67730976687517[/C][/ROW]
[ROW][C]75[/C][C]4067[/C][C]4131.41753902044[/C][C]-64.4175390204364[/C][/ROW]
[ROW][C]76[/C][C]4022[/C][C]3939.85923129124[/C][C]82.1407687087567[/C][/ROW]
[ROW][C]77[/C][C]3937[/C][C]3725.88583305532[/C][C]211.11416694468[/C][/ROW]
[ROW][C]78[/C][C]4365[/C][C]3679.12360994954[/C][C]685.876390050455[/C][/ROW]
[ROW][C]79[/C][C]4290[/C][C]4429.40676732055[/C][C]-139.406767320545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76642&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76642&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
1325642540.4360262156723.5639737843312
1428202786.8909846354733.1090153645282
1535083455.5698982385652.4301017614375
1630883050.5697308132437.4302691867629
1732993283.3981959532715.6018040467293
1829392961.14590175454-22.1459017545403
1933203366.75875814298-46.7587581429775
2034183100.59931681039317.400683189611
2136043599.568379451714.43162054829372
2234953694.90035916793-199.900359167934
2341634546.02210889468-383.022108894679
2448825493.2020492742-611.202049274198
2522112599.88516127479-388.885161274794
2632602829.75306104031430.246938959695
2729923514.04923030427-522.049230304274
2824253070.94469955403-645.944699554028
2927073249.40172859017-542.401728590168
3032442870.35214456770373.647855432297
3139653232.17887781673732.821122183275
3233153080.69145459866234.308545401342
3333333443.40913219231-110.409132192313
3435833446.36955696997136.630443030027
3540214185.26716669707-164.267166697068
3649044995.02349954517-91.0234995451665
3722522332.71711674191-80.7171167419096
3829522791.13887019654160.861129803455
3935733144.28423347904428.715766520959
4030482716.65581452568331.34418547432
4130592963.7953380331595.2046619668545
4227312920.88139677717-189.881396777173
4335633399.23070619969163.769293800309
4430923106.31236676567-14.3123667656746
4534783367.92849927736110.07150072264
4634783470.472162212197.52783778780577
4743084130.19080414777177.809195852225
4850295002.9438100443726.0561899556269
4920752341.88088511256-266.880885112562
5032642893.34757275042370.652427249584
5133083364.69995854097-56.6999585409685
5236882896.39343174623791.60656825377
5331363106.5965199780829.4034800219247
5428242987.66349368554-163.663493685535
5536443624.4788930947419.5211069052552
5646943273.897667484181420.10233251582
5729143673.86917067579-759.869170675788
5836863763.76039016466-77.760390164658
5943584570.98991837248-212.989918372482
6055875498.1726415829588.8273584170529
6122652496.17060320570-231.170603205705
6236853347.35915372792337.640846272082
6337543747.338986838116.66101316189406
6437083539.20744667407168.792553325934
6532103504.03572867123-294.035728671233
6635173298.69945035517218.300549644833
6739054100.03008792936-195.030087929355
6836704190.1011634476-520.1011634476
6942213806.95905597092414.040944029085
7044044159.40935432775244.590645672249
7150865015.0592087368770.9407912631259
7257256160.50026357569-435.500263575693
7323672694.56000863673-327.560008636734
7438193825.67730976688-6.67730976687517
7540674131.41753902044-64.4175390204364
7640223939.8592312912482.1407687087567
7739373725.88583305532211.11416694468
7843653679.12360994954685.876390050455
7942904429.40676732055-139.406767320545







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
804422.695235934884191.146011141114654.24446072865
814343.325221246944110.125783009334576.52465948454
824668.346783570594430.889424595684905.8041425455
835544.8396805935296.08007436695793.59928681909
846629.075019322796356.606151705446901.54388694014
852859.887054687802615.759142603113104.01496677250
864241.301544290763969.004975761374513.59811282014
874575.151674628034278.0080729424872.29527631407
884428.691913070644114.49053088674742.89329525458
894244.567645489173914.141749755144574.9935412232
904357.916900517633997.350647224944718.48315381033
914886.560187859834536.789101489625236.33127423003

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
80 & 4422.69523593488 & 4191.14601114111 & 4654.24446072865 \tabularnewline
81 & 4343.32522124694 & 4110.12578300933 & 4576.52465948454 \tabularnewline
82 & 4668.34678357059 & 4430.88942459568 & 4905.8041425455 \tabularnewline
83 & 5544.839680593 & 5296.0800743669 & 5793.59928681909 \tabularnewline
84 & 6629.07501932279 & 6356.60615170544 & 6901.54388694014 \tabularnewline
85 & 2859.88705468780 & 2615.75914260311 & 3104.01496677250 \tabularnewline
86 & 4241.30154429076 & 3969.00497576137 & 4513.59811282014 \tabularnewline
87 & 4575.15167462803 & 4278.008072942 & 4872.29527631407 \tabularnewline
88 & 4428.69191307064 & 4114.4905308867 & 4742.89329525458 \tabularnewline
89 & 4244.56764548917 & 3914.14174975514 & 4574.9935412232 \tabularnewline
90 & 4357.91690051763 & 3997.35064722494 & 4718.48315381033 \tabularnewline
91 & 4886.56018785983 & 4536.78910148962 & 5236.33127423003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76642&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]80[/C][C]4422.69523593488[/C][C]4191.14601114111[/C][C]4654.24446072865[/C][/ROW]
[ROW][C]81[/C][C]4343.32522124694[/C][C]4110.12578300933[/C][C]4576.52465948454[/C][/ROW]
[ROW][C]82[/C][C]4668.34678357059[/C][C]4430.88942459568[/C][C]4905.8041425455[/C][/ROW]
[ROW][C]83[/C][C]5544.839680593[/C][C]5296.0800743669[/C][C]5793.59928681909[/C][/ROW]
[ROW][C]84[/C][C]6629.07501932279[/C][C]6356.60615170544[/C][C]6901.54388694014[/C][/ROW]
[ROW][C]85[/C][C]2859.88705468780[/C][C]2615.75914260311[/C][C]3104.01496677250[/C][/ROW]
[ROW][C]86[/C][C]4241.30154429076[/C][C]3969.00497576137[/C][C]4513.59811282014[/C][/ROW]
[ROW][C]87[/C][C]4575.15167462803[/C][C]4278.008072942[/C][C]4872.29527631407[/C][/ROW]
[ROW][C]88[/C][C]4428.69191307064[/C][C]4114.4905308867[/C][C]4742.89329525458[/C][/ROW]
[ROW][C]89[/C][C]4244.56764548917[/C][C]3914.14174975514[/C][C]4574.9935412232[/C][/ROW]
[ROW][C]90[/C][C]4357.91690051763[/C][C]3997.35064722494[/C][C]4718.48315381033[/C][/ROW]
[ROW][C]91[/C][C]4886.56018785983[/C][C]4536.78910148962[/C][C]5236.33127423003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76642&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76642&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
804422.695235934884191.146011141114654.24446072865
814343.325221246944110.125783009334576.52465948454
824668.346783570594430.889424595684905.8041425455
835544.8396805935296.08007436695793.59928681909
846629.075019322796356.606151705446901.54388694014
852859.887054687802615.759142603113104.01496677250
864241.301544290763969.004975761374513.59811282014
874575.151674628034278.0080729424872.29527631407
884428.691913070644114.49053088674742.89329525458
894244.567645489173914.141749755144574.9935412232
904357.916900517633997.350647224944718.48315381033
914886.560187859834536.789101489625236.33127423003



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