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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Jan 2012 17:35:28 -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/2012/Jan/15/t13266669616rcu5mmujzbcz5z.htm/, Retrieved Fri, 03 May 2024 13:00:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161147, Retrieved Fri, 03 May 2024 13:00:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oef 2] [2012-01-15 22:35:28] [554c467d2d08ef461d24132d0b00df66] [Current]
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Dataseries X:
36,68
36,77
36,78
36,78
37
37,12
37,3
37,34
37,4
37,4
37,34
37,29
37,39
37,42
37,42
43,49
44,3
44,36
44,52
44,66
44,77
44,77
44,82
44,97
45,28
45,5
45,52
45,52
45,17
45,25
45,32
45,41
45,44
45,44
45,46
45,53
45,61
45,8
45,83
45,83
45,96
46,01
46,18
46,32
46,51
46,51
46,56
46,54
46,62
46,76
46,82
46,82
46,7
46,72
46,47
46,74
46,89
46,89
46,96
47,6
47,67
47,58
47,58
47,58
47,57
47,53
47,68
47,56
47,81
47,81
47,81
47,81
48,12
48,13
48,01




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=161147&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=161147&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161147&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
alpha0.496747147581487
beta0.0590114706957529
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.496747147581487 \tabularnewline
beta & 0.0590114706957529 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161147&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]0.496747147581487[/C][/ROW]
[ROW][C]beta[/C][C]0.0590114706957529[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161147&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161147&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
alpha0.496747147581487
beta0.0590114706957529
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1337.3934.69461805555562.69538194444445
1437.4236.05503424134891.36496575865105
1537.4236.75833228735870.661667712641346
1643.4943.19958168337130.29041831662871
1744.344.20034392610690.0996560738931294
1844.3644.34635019843080.0136498015692297
1944.5243.2529498942471.26705010575296
2044.6644.57139797700070.0886020229992823
2144.7745.3299692629272-0.559969262927233
2244.7745.4374497969304-0.667449796930377
2344.8245.1344742059104-0.314474205910393
2444.9744.9855364719553-0.0155364719553148
2545.2846.4944317571624-1.21443175716239
2645.545.27285191851530.227148081484685
2745.5245.05338031420630.466619685793702
2845.5251.2015650298769-5.68156502987691
2945.1748.9553557207326-3.78535572073263
3045.2546.8299219675288-1.57992196752879
3145.3245.23069450268430.0893054973156637
3245.4144.99151759730190.418482402698103
3345.4445.21770435779710.222295642202916
3445.4445.31275769443910.127242305560941
3545.4645.25854936848670.201450631513346
3645.5345.20783105717930.322168942820724
3745.6145.9825264579969-0.372526457996869
3845.845.63071265366540.16928734633462
3945.8345.22739035794260.602609642057374
4045.8348.0773992765422-2.24739927654223
4145.9648.320406207204-2.36040620720397
4246.0147.8835049975027-1.87350499750266
4346.1846.8406805647715-0.660680564771454
4446.3246.23482059448410.0851794055159445
4546.5146.02714927995440.482850720045597
4646.5146.04187538460.468124615399951
4746.5646.04241611347310.517583886526857
4846.5446.0668261780040.473173821995992
4946.6246.42869015221760.191309847782414
5046.7646.50792271269120.252077287308808
5146.8246.24451659712630.575483402873743
5246.8247.5267001752741-0.706700175274086
5346.748.4032623028687-1.70326230286868
5446.7248.4821816207908-1.76218162079076
5546.4748.0526291670664-1.58262916706639
5646.7447.2847392715736-0.544739271573597
5746.8946.86641083264690.0235891673531015
5846.8946.53425038312430.355749616875727
5946.9646.38922680163230.570773198367675
6047.646.30463532356081.29536467643918
6147.6746.84409924219340.825900757806608
6247.5847.19877450426540.381225495734576
6347.5847.09569335502180.484306644978219
6447.5847.6180657723565-0.0380657723564894
6547.5748.2755907772908-0.705590777290816
6647.5348.8000381665563-1.27003816655629
6747.6848.6993323408347-1.01933234083472
6847.5648.7441074329266-1.18410743292664
6947.8148.2859731396467-0.475973139646747
7047.8147.8499587213834-0.0399587213833641
7147.8147.58212116385780.227878836142231
7247.8147.6473408693450.162659130654966
7348.1247.31016385375610.809836146243889
7448.1347.35489042819060.775109571809402
7548.0147.43270764002350.577292359976497

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37.39 & 34.6946180555556 & 2.69538194444445 \tabularnewline
14 & 37.42 & 36.0550342413489 & 1.36496575865105 \tabularnewline
15 & 37.42 & 36.7583322873587 & 0.661667712641346 \tabularnewline
16 & 43.49 & 43.1995816833713 & 0.29041831662871 \tabularnewline
17 & 44.3 & 44.2003439261069 & 0.0996560738931294 \tabularnewline
18 & 44.36 & 44.3463501984308 & 0.0136498015692297 \tabularnewline
19 & 44.52 & 43.252949894247 & 1.26705010575296 \tabularnewline
20 & 44.66 & 44.5713979770007 & 0.0886020229992823 \tabularnewline
21 & 44.77 & 45.3299692629272 & -0.559969262927233 \tabularnewline
22 & 44.77 & 45.4374497969304 & -0.667449796930377 \tabularnewline
23 & 44.82 & 45.1344742059104 & -0.314474205910393 \tabularnewline
24 & 44.97 & 44.9855364719553 & -0.0155364719553148 \tabularnewline
25 & 45.28 & 46.4944317571624 & -1.21443175716239 \tabularnewline
26 & 45.5 & 45.2728519185153 & 0.227148081484685 \tabularnewline
27 & 45.52 & 45.0533803142063 & 0.466619685793702 \tabularnewline
28 & 45.52 & 51.2015650298769 & -5.68156502987691 \tabularnewline
29 & 45.17 & 48.9553557207326 & -3.78535572073263 \tabularnewline
30 & 45.25 & 46.8299219675288 & -1.57992196752879 \tabularnewline
31 & 45.32 & 45.2306945026843 & 0.0893054973156637 \tabularnewline
32 & 45.41 & 44.9915175973019 & 0.418482402698103 \tabularnewline
33 & 45.44 & 45.2177043577971 & 0.222295642202916 \tabularnewline
34 & 45.44 & 45.3127576944391 & 0.127242305560941 \tabularnewline
35 & 45.46 & 45.2585493684867 & 0.201450631513346 \tabularnewline
36 & 45.53 & 45.2078310571793 & 0.322168942820724 \tabularnewline
37 & 45.61 & 45.9825264579969 & -0.372526457996869 \tabularnewline
38 & 45.8 & 45.6307126536654 & 0.16928734633462 \tabularnewline
39 & 45.83 & 45.2273903579426 & 0.602609642057374 \tabularnewline
40 & 45.83 & 48.0773992765422 & -2.24739927654223 \tabularnewline
41 & 45.96 & 48.320406207204 & -2.36040620720397 \tabularnewline
42 & 46.01 & 47.8835049975027 & -1.87350499750266 \tabularnewline
43 & 46.18 & 46.8406805647715 & -0.660680564771454 \tabularnewline
44 & 46.32 & 46.2348205944841 & 0.0851794055159445 \tabularnewline
45 & 46.51 & 46.0271492799544 & 0.482850720045597 \tabularnewline
46 & 46.51 & 46.0418753846 & 0.468124615399951 \tabularnewline
47 & 46.56 & 46.0424161134731 & 0.517583886526857 \tabularnewline
48 & 46.54 & 46.066826178004 & 0.473173821995992 \tabularnewline
49 & 46.62 & 46.4286901522176 & 0.191309847782414 \tabularnewline
50 & 46.76 & 46.5079227126912 & 0.252077287308808 \tabularnewline
51 & 46.82 & 46.2445165971263 & 0.575483402873743 \tabularnewline
52 & 46.82 & 47.5267001752741 & -0.706700175274086 \tabularnewline
53 & 46.7 & 48.4032623028687 & -1.70326230286868 \tabularnewline
54 & 46.72 & 48.4821816207908 & -1.76218162079076 \tabularnewline
55 & 46.47 & 48.0526291670664 & -1.58262916706639 \tabularnewline
56 & 46.74 & 47.2847392715736 & -0.544739271573597 \tabularnewline
57 & 46.89 & 46.8664108326469 & 0.0235891673531015 \tabularnewline
58 & 46.89 & 46.5342503831243 & 0.355749616875727 \tabularnewline
59 & 46.96 & 46.3892268016323 & 0.570773198367675 \tabularnewline
60 & 47.6 & 46.3046353235608 & 1.29536467643918 \tabularnewline
61 & 47.67 & 46.8440992421934 & 0.825900757806608 \tabularnewline
62 & 47.58 & 47.1987745042654 & 0.381225495734576 \tabularnewline
63 & 47.58 & 47.0956933550218 & 0.484306644978219 \tabularnewline
64 & 47.58 & 47.6180657723565 & -0.0380657723564894 \tabularnewline
65 & 47.57 & 48.2755907772908 & -0.705590777290816 \tabularnewline
66 & 47.53 & 48.8000381665563 & -1.27003816655629 \tabularnewline
67 & 47.68 & 48.6993323408347 & -1.01933234083472 \tabularnewline
68 & 47.56 & 48.7441074329266 & -1.18410743292664 \tabularnewline
69 & 47.81 & 48.2859731396467 & -0.475973139646747 \tabularnewline
70 & 47.81 & 47.8499587213834 & -0.0399587213833641 \tabularnewline
71 & 47.81 & 47.5821211638578 & 0.227878836142231 \tabularnewline
72 & 47.81 & 47.647340869345 & 0.162659130654966 \tabularnewline
73 & 48.12 & 47.3101638537561 & 0.809836146243889 \tabularnewline
74 & 48.13 & 47.3548904281906 & 0.775109571809402 \tabularnewline
75 & 48.01 & 47.4327076400235 & 0.577292359976497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161147&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]37.39[/C][C]34.6946180555556[/C][C]2.69538194444445[/C][/ROW]
[ROW][C]14[/C][C]37.42[/C][C]36.0550342413489[/C][C]1.36496575865105[/C][/ROW]
[ROW][C]15[/C][C]37.42[/C][C]36.7583322873587[/C][C]0.661667712641346[/C][/ROW]
[ROW][C]16[/C][C]43.49[/C][C]43.1995816833713[/C][C]0.29041831662871[/C][/ROW]
[ROW][C]17[/C][C]44.3[/C][C]44.2003439261069[/C][C]0.0996560738931294[/C][/ROW]
[ROW][C]18[/C][C]44.36[/C][C]44.3463501984308[/C][C]0.0136498015692297[/C][/ROW]
[ROW][C]19[/C][C]44.52[/C][C]43.252949894247[/C][C]1.26705010575296[/C][/ROW]
[ROW][C]20[/C][C]44.66[/C][C]44.5713979770007[/C][C]0.0886020229992823[/C][/ROW]
[ROW][C]21[/C][C]44.77[/C][C]45.3299692629272[/C][C]-0.559969262927233[/C][/ROW]
[ROW][C]22[/C][C]44.77[/C][C]45.4374497969304[/C][C]-0.667449796930377[/C][/ROW]
[ROW][C]23[/C][C]44.82[/C][C]45.1344742059104[/C][C]-0.314474205910393[/C][/ROW]
[ROW][C]24[/C][C]44.97[/C][C]44.9855364719553[/C][C]-0.0155364719553148[/C][/ROW]
[ROW][C]25[/C][C]45.28[/C][C]46.4944317571624[/C][C]-1.21443175716239[/C][/ROW]
[ROW][C]26[/C][C]45.5[/C][C]45.2728519185153[/C][C]0.227148081484685[/C][/ROW]
[ROW][C]27[/C][C]45.52[/C][C]45.0533803142063[/C][C]0.466619685793702[/C][/ROW]
[ROW][C]28[/C][C]45.52[/C][C]51.2015650298769[/C][C]-5.68156502987691[/C][/ROW]
[ROW][C]29[/C][C]45.17[/C][C]48.9553557207326[/C][C]-3.78535572073263[/C][/ROW]
[ROW][C]30[/C][C]45.25[/C][C]46.8299219675288[/C][C]-1.57992196752879[/C][/ROW]
[ROW][C]31[/C][C]45.32[/C][C]45.2306945026843[/C][C]0.0893054973156637[/C][/ROW]
[ROW][C]32[/C][C]45.41[/C][C]44.9915175973019[/C][C]0.418482402698103[/C][/ROW]
[ROW][C]33[/C][C]45.44[/C][C]45.2177043577971[/C][C]0.222295642202916[/C][/ROW]
[ROW][C]34[/C][C]45.44[/C][C]45.3127576944391[/C][C]0.127242305560941[/C][/ROW]
[ROW][C]35[/C][C]45.46[/C][C]45.2585493684867[/C][C]0.201450631513346[/C][/ROW]
[ROW][C]36[/C][C]45.53[/C][C]45.2078310571793[/C][C]0.322168942820724[/C][/ROW]
[ROW][C]37[/C][C]45.61[/C][C]45.9825264579969[/C][C]-0.372526457996869[/C][/ROW]
[ROW][C]38[/C][C]45.8[/C][C]45.6307126536654[/C][C]0.16928734633462[/C][/ROW]
[ROW][C]39[/C][C]45.83[/C][C]45.2273903579426[/C][C]0.602609642057374[/C][/ROW]
[ROW][C]40[/C][C]45.83[/C][C]48.0773992765422[/C][C]-2.24739927654223[/C][/ROW]
[ROW][C]41[/C][C]45.96[/C][C]48.320406207204[/C][C]-2.36040620720397[/C][/ROW]
[ROW][C]42[/C][C]46.01[/C][C]47.8835049975027[/C][C]-1.87350499750266[/C][/ROW]
[ROW][C]43[/C][C]46.18[/C][C]46.8406805647715[/C][C]-0.660680564771454[/C][/ROW]
[ROW][C]44[/C][C]46.32[/C][C]46.2348205944841[/C][C]0.0851794055159445[/C][/ROW]
[ROW][C]45[/C][C]46.51[/C][C]46.0271492799544[/C][C]0.482850720045597[/C][/ROW]
[ROW][C]46[/C][C]46.51[/C][C]46.0418753846[/C][C]0.468124615399951[/C][/ROW]
[ROW][C]47[/C][C]46.56[/C][C]46.0424161134731[/C][C]0.517583886526857[/C][/ROW]
[ROW][C]48[/C][C]46.54[/C][C]46.066826178004[/C][C]0.473173821995992[/C][/ROW]
[ROW][C]49[/C][C]46.62[/C][C]46.4286901522176[/C][C]0.191309847782414[/C][/ROW]
[ROW][C]50[/C][C]46.76[/C][C]46.5079227126912[/C][C]0.252077287308808[/C][/ROW]
[ROW][C]51[/C][C]46.82[/C][C]46.2445165971263[/C][C]0.575483402873743[/C][/ROW]
[ROW][C]52[/C][C]46.82[/C][C]47.5267001752741[/C][C]-0.706700175274086[/C][/ROW]
[ROW][C]53[/C][C]46.7[/C][C]48.4032623028687[/C][C]-1.70326230286868[/C][/ROW]
[ROW][C]54[/C][C]46.72[/C][C]48.4821816207908[/C][C]-1.76218162079076[/C][/ROW]
[ROW][C]55[/C][C]46.47[/C][C]48.0526291670664[/C][C]-1.58262916706639[/C][/ROW]
[ROW][C]56[/C][C]46.74[/C][C]47.2847392715736[/C][C]-0.544739271573597[/C][/ROW]
[ROW][C]57[/C][C]46.89[/C][C]46.8664108326469[/C][C]0.0235891673531015[/C][/ROW]
[ROW][C]58[/C][C]46.89[/C][C]46.5342503831243[/C][C]0.355749616875727[/C][/ROW]
[ROW][C]59[/C][C]46.96[/C][C]46.3892268016323[/C][C]0.570773198367675[/C][/ROW]
[ROW][C]60[/C][C]47.6[/C][C]46.3046353235608[/C][C]1.29536467643918[/C][/ROW]
[ROW][C]61[/C][C]47.67[/C][C]46.8440992421934[/C][C]0.825900757806608[/C][/ROW]
[ROW][C]62[/C][C]47.58[/C][C]47.1987745042654[/C][C]0.381225495734576[/C][/ROW]
[ROW][C]63[/C][C]47.58[/C][C]47.0956933550218[/C][C]0.484306644978219[/C][/ROW]
[ROW][C]64[/C][C]47.58[/C][C]47.6180657723565[/C][C]-0.0380657723564894[/C][/ROW]
[ROW][C]65[/C][C]47.57[/C][C]48.2755907772908[/C][C]-0.705590777290816[/C][/ROW]
[ROW][C]66[/C][C]47.53[/C][C]48.8000381665563[/C][C]-1.27003816655629[/C][/ROW]
[ROW][C]67[/C][C]47.68[/C][C]48.6993323408347[/C][C]-1.01933234083472[/C][/ROW]
[ROW][C]68[/C][C]47.56[/C][C]48.7441074329266[/C][C]-1.18410743292664[/C][/ROW]
[ROW][C]69[/C][C]47.81[/C][C]48.2859731396467[/C][C]-0.475973139646747[/C][/ROW]
[ROW][C]70[/C][C]47.81[/C][C]47.8499587213834[/C][C]-0.0399587213833641[/C][/ROW]
[ROW][C]71[/C][C]47.81[/C][C]47.5821211638578[/C][C]0.227878836142231[/C][/ROW]
[ROW][C]72[/C][C]47.81[/C][C]47.647340869345[/C][C]0.162659130654966[/C][/ROW]
[ROW][C]73[/C][C]48.12[/C][C]47.3101638537561[/C][C]0.809836146243889[/C][/ROW]
[ROW][C]74[/C][C]48.13[/C][C]47.3548904281906[/C][C]0.775109571809402[/C][/ROW]
[ROW][C]75[/C][C]48.01[/C][C]47.4327076400235[/C][C]0.577292359976497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161147&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161147&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
1337.3934.69461805555562.69538194444445
1437.4236.05503424134891.36496575865105
1537.4236.75833228735870.661667712641346
1643.4943.19958168337130.29041831662871
1744.344.20034392610690.0996560738931294
1844.3644.34635019843080.0136498015692297
1944.5243.2529498942471.26705010575296
2044.6644.57139797700070.0886020229992823
2144.7745.3299692629272-0.559969262927233
2244.7745.4374497969304-0.667449796930377
2344.8245.1344742059104-0.314474205910393
2444.9744.9855364719553-0.0155364719553148
2545.2846.4944317571624-1.21443175716239
2645.545.27285191851530.227148081484685
2745.5245.05338031420630.466619685793702
2845.5251.2015650298769-5.68156502987691
2945.1748.9553557207326-3.78535572073263
3045.2546.8299219675288-1.57992196752879
3145.3245.23069450268430.0893054973156637
3245.4144.99151759730190.418482402698103
3345.4445.21770435779710.222295642202916
3445.4445.31275769443910.127242305560941
3545.4645.25854936848670.201450631513346
3645.5345.20783105717930.322168942820724
3745.6145.9825264579969-0.372526457996869
3845.845.63071265366540.16928734633462
3945.8345.22739035794260.602609642057374
4045.8348.0773992765422-2.24739927654223
4145.9648.320406207204-2.36040620720397
4246.0147.8835049975027-1.87350499750266
4346.1846.8406805647715-0.660680564771454
4446.3246.23482059448410.0851794055159445
4546.5146.02714927995440.482850720045597
4646.5146.04187538460.468124615399951
4746.5646.04241611347310.517583886526857
4846.5446.0668261780040.473173821995992
4946.6246.42869015221760.191309847782414
5046.7646.50792271269120.252077287308808
5146.8246.24451659712630.575483402873743
5246.8247.5267001752741-0.706700175274086
5346.748.4032623028687-1.70326230286868
5446.7248.4821816207908-1.76218162079076
5546.4748.0526291670664-1.58262916706639
5646.7447.2847392715736-0.544739271573597
5746.8946.86641083264690.0235891673531015
5846.8946.53425038312430.355749616875727
5946.9646.38922680163230.570773198367675
6047.646.30463532356081.29536467643918
6147.6746.84409924219340.825900757806608
6247.5847.19877450426540.381225495734576
6347.5847.09569335502180.484306644978219
6447.5847.6180657723565-0.0380657723564894
6547.5748.2755907772908-0.705590777290816
6647.5348.8000381665563-1.27003816655629
6747.6848.6993323408347-1.01933234083472
6847.5648.7441074329266-1.18410743292664
6947.8148.2859731396467-0.475973139646747
7047.8147.8499587213834-0.0399587213833641
7147.8147.58212116385780.227878836142231
7247.8147.6473408693450.162659130654966
7348.1247.31016385375610.809836146243889
7448.1347.35489042819060.775109571809402
7548.0147.43270764002350.577292359976497







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7647.674472487190845.236716462642550.1122285117391
7747.952175995026345.197684170119950.7066678199326
7848.500950666073145.431718860248551.5701824718978
7949.1524175523945.768375081199152.5364600235809
8049.645616479419945.945330417686253.3459025411536
8150.191762380638846.172867337001954.2106574242758
8250.285271935060145.944746878742554.6257969913777
8350.246905287922845.58125944460354.9125511312425
8450.234256353441745.239658221215355.228854485668
8550.205355928557344.877725227734455.5329866293801
8649.869966472049844.205041115137255.5348918289624
8749.480120759998443.473506508530855.486735011466

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 47.6744724871908 & 45.2367164626425 & 50.1122285117391 \tabularnewline
77 & 47.9521759950263 & 45.1976841701199 & 50.7066678199326 \tabularnewline
78 & 48.5009506660731 & 45.4317188602485 & 51.5701824718978 \tabularnewline
79 & 49.15241755239 & 45.7683750811991 & 52.5364600235809 \tabularnewline
80 & 49.6456164794199 & 45.9453304176862 & 53.3459025411536 \tabularnewline
81 & 50.1917623806388 & 46.1728673370019 & 54.2106574242758 \tabularnewline
82 & 50.2852719350601 & 45.9447468787425 & 54.6257969913777 \tabularnewline
83 & 50.2469052879228 & 45.581259444603 & 54.9125511312425 \tabularnewline
84 & 50.2342563534417 & 45.2396582212153 & 55.228854485668 \tabularnewline
85 & 50.2053559285573 & 44.8777252277344 & 55.5329866293801 \tabularnewline
86 & 49.8699664720498 & 44.2050411151372 & 55.5348918289624 \tabularnewline
87 & 49.4801207599984 & 43.4735065085308 & 55.486735011466 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161147&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]76[/C][C]47.6744724871908[/C][C]45.2367164626425[/C][C]50.1122285117391[/C][/ROW]
[ROW][C]77[/C][C]47.9521759950263[/C][C]45.1976841701199[/C][C]50.7066678199326[/C][/ROW]
[ROW][C]78[/C][C]48.5009506660731[/C][C]45.4317188602485[/C][C]51.5701824718978[/C][/ROW]
[ROW][C]79[/C][C]49.15241755239[/C][C]45.7683750811991[/C][C]52.5364600235809[/C][/ROW]
[ROW][C]80[/C][C]49.6456164794199[/C][C]45.9453304176862[/C][C]53.3459025411536[/C][/ROW]
[ROW][C]81[/C][C]50.1917623806388[/C][C]46.1728673370019[/C][C]54.2106574242758[/C][/ROW]
[ROW][C]82[/C][C]50.2852719350601[/C][C]45.9447468787425[/C][C]54.6257969913777[/C][/ROW]
[ROW][C]83[/C][C]50.2469052879228[/C][C]45.581259444603[/C][C]54.9125511312425[/C][/ROW]
[ROW][C]84[/C][C]50.2342563534417[/C][C]45.2396582212153[/C][C]55.228854485668[/C][/ROW]
[ROW][C]85[/C][C]50.2053559285573[/C][C]44.8777252277344[/C][C]55.5329866293801[/C][/ROW]
[ROW][C]86[/C][C]49.8699664720498[/C][C]44.2050411151372[/C][C]55.5348918289624[/C][/ROW]
[ROW][C]87[/C][C]49.4801207599984[/C][C]43.4735065085308[/C][C]55.486735011466[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161147&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161147&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
7647.674472487190845.236716462642550.1122285117391
7747.952175995026345.197684170119950.7066678199326
7848.500950666073145.431718860248551.5701824718978
7949.1524175523945.768375081199152.5364600235809
8049.645616479419945.945330417686253.3459025411536
8150.191762380638846.172867337001954.2106574242758
8250.285271935060145.944746878742554.6257969913777
8350.246905287922845.58125944460354.9125511312425
8450.234256353441745.239658221215355.228854485668
8550.205355928557344.877725227734455.5329866293801
8649.869966472049844.205041115137255.5348918289624
8749.480120759998443.473506508530855.486735011466



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')