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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 12:40:52 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/27/t1211913763f0as1va93eeyt1w.htm/, Retrieved Sun, 19 May 2024 22:24:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13373, Retrieved Sun, 19 May 2024 22:24:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2008-05-27 18:40:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   PD    [Exponential Smoothing] [Exponential smoot...] [2008-05-30 13:34:24] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
44,13
44,13
44,14
44,14
44,14
44,14
44,15
44,17
44,19
44,26
44,27
44,29
44,29
44,29
44,29
44,32
44,33
44,34
44,34
44,34
44,37
44,47
44,51
44,51
44,51
44,52
44,7
44,84
44,9
44,91
44,94
44,94
44,95
45,28
45,34
45,34
45,34
45,36
45,44
45,62
45,75
45,77
45,77
45,77
46,09
46,25
46,28
46,29
46,29
46,29
46,3
46,34
46,34
46,35
46,42
46,52
46,59
46,66
46,67
46,72
46,72
46,72
46,76
46,89
47,02
47,02
47,04
47,18
47,22
47,8
47,88
47,91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 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 & 10 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13373&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]10 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=13373&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13373&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 time10 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0554345114806499
gamma0.226961583618481

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0554345114806499 \tabularnewline
gamma & 0.226961583618481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13373&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]0.0554345114806499[/C][/ROW]
[ROW][C]gamma[/C][C]0.226961583618481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13373&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13373&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
beta0.0554345114806499
gamma0.226961583618481







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1344.2944.13608214556460.153917854435385
1444.2944.3119882486531-0.0219882486530594
1544.2944.3111790454529-0.0211790454528895
1644.3244.3383445236373-0.0183445236372748
1744.3344.34482465423-0.0148246542299972
1844.3444.3535834613256-0.0135834613256378
1944.3444.3536578284509-0.0136578284509383
2044.3444.3524791104286-0.0124791104285720
2144.3744.373880698356-0.00388069835599936
2244.4744.46158458198080.00841541801923285
2344.5144.49538470239590.0146152976041023
2444.5144.49412828605120.0158717139488331
2544.5144.6017747283616-0.0917747283616066
2644.5244.5223338901019-0.00233389010188034
2744.744.53261581332030.167384186679712
2844.8444.75043780609780.0895621939021751
2944.944.87266821862450.0273317813754801
3044.9144.9337466748532-0.0237466748532142
3144.9444.93313591473890.00686408526105708
3244.9444.9630723152294-0.0230723152294203
3344.9544.9841863840214-0.0341863840214316
3445.2845.0509771468290.229022853170967
3545.3445.32610470743840.0138952925615925
3645.3445.3440000690773-0.00400006907727857
3745.3445.4525612249642-0.112561224964246
3845.3645.370575491329-0.0105754913289928
3945.4445.39039920554030.0496007944597423
4045.6245.50220174937420.117798250625754
4145.7545.66561116381390.0843888361860508
4245.7745.7998275020901-0.0298275020901144
4345.7745.8086933990125-0.0386933990124589
4445.7745.8061034374659-0.0361034374659184
4546.0945.82690961489470.263090385105308
4646.2546.22173049187890.0282695081211273
4746.2846.314035460906-0.0340354609060398
4846.2946.2983734682822-0.0083734682821941
4946.2946.4189795289091-0.128979528909142
5046.2946.3344920667427-0.0444920667426629
5146.346.3324471881525-0.0324471881525383
5246.3446.3702769810044-0.0302769810043699
5346.3446.3850689182122-0.0450689182122161
5446.3546.3821305842786-0.0321305842786401
5546.4246.38075427433670.0392457256632852
5646.5246.45245135038180.0675486496182529
5746.5946.57933503994310.0106649600569284
5846.6646.7107800096162-0.050780009616247
5946.6746.7079647570146-0.0379647570145636
6046.7246.67173644392850.0482635560714684
6146.7246.836453112982-0.116453112982015
6246.7246.7519460283806-0.031946028380581
6346.7646.75060457823660.00939542176342911
6446.8946.82103533354810.0689646664518975
6547.0246.93107810058290.0889218994171372
6647.0247.06553479511-0.0455347951100009
6747.0447.0532779655913-0.0132779655912998
6847.1847.07207840945030.107921590549658
6947.2247.2415122454647-0.0215122454646774
7047.847.34199343860110.458006561398875
7147.8847.87637051143350.0036294885664816
7247.9147.9112640024059-0.00126400240590385

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 44.29 & 44.1360821455646 & 0.153917854435385 \tabularnewline
14 & 44.29 & 44.3119882486531 & -0.0219882486530594 \tabularnewline
15 & 44.29 & 44.3111790454529 & -0.0211790454528895 \tabularnewline
16 & 44.32 & 44.3383445236373 & -0.0183445236372748 \tabularnewline
17 & 44.33 & 44.34482465423 & -0.0148246542299972 \tabularnewline
18 & 44.34 & 44.3535834613256 & -0.0135834613256378 \tabularnewline
19 & 44.34 & 44.3536578284509 & -0.0136578284509383 \tabularnewline
20 & 44.34 & 44.3524791104286 & -0.0124791104285720 \tabularnewline
21 & 44.37 & 44.373880698356 & -0.00388069835599936 \tabularnewline
22 & 44.47 & 44.4615845819808 & 0.00841541801923285 \tabularnewline
23 & 44.51 & 44.4953847023959 & 0.0146152976041023 \tabularnewline
24 & 44.51 & 44.4941282860512 & 0.0158717139488331 \tabularnewline
25 & 44.51 & 44.6017747283616 & -0.0917747283616066 \tabularnewline
26 & 44.52 & 44.5223338901019 & -0.00233389010188034 \tabularnewline
27 & 44.7 & 44.5326158133203 & 0.167384186679712 \tabularnewline
28 & 44.84 & 44.7504378060978 & 0.0895621939021751 \tabularnewline
29 & 44.9 & 44.8726682186245 & 0.0273317813754801 \tabularnewline
30 & 44.91 & 44.9337466748532 & -0.0237466748532142 \tabularnewline
31 & 44.94 & 44.9331359147389 & 0.00686408526105708 \tabularnewline
32 & 44.94 & 44.9630723152294 & -0.0230723152294203 \tabularnewline
33 & 44.95 & 44.9841863840214 & -0.0341863840214316 \tabularnewline
34 & 45.28 & 45.050977146829 & 0.229022853170967 \tabularnewline
35 & 45.34 & 45.3261047074384 & 0.0138952925615925 \tabularnewline
36 & 45.34 & 45.3440000690773 & -0.00400006907727857 \tabularnewline
37 & 45.34 & 45.4525612249642 & -0.112561224964246 \tabularnewline
38 & 45.36 & 45.370575491329 & -0.0105754913289928 \tabularnewline
39 & 45.44 & 45.3903992055403 & 0.0496007944597423 \tabularnewline
40 & 45.62 & 45.5022017493742 & 0.117798250625754 \tabularnewline
41 & 45.75 & 45.6656111638139 & 0.0843888361860508 \tabularnewline
42 & 45.77 & 45.7998275020901 & -0.0298275020901144 \tabularnewline
43 & 45.77 & 45.8086933990125 & -0.0386933990124589 \tabularnewline
44 & 45.77 & 45.8061034374659 & -0.0361034374659184 \tabularnewline
45 & 46.09 & 45.8269096148947 & 0.263090385105308 \tabularnewline
46 & 46.25 & 46.2217304918789 & 0.0282695081211273 \tabularnewline
47 & 46.28 & 46.314035460906 & -0.0340354609060398 \tabularnewline
48 & 46.29 & 46.2983734682822 & -0.0083734682821941 \tabularnewline
49 & 46.29 & 46.4189795289091 & -0.128979528909142 \tabularnewline
50 & 46.29 & 46.3344920667427 & -0.0444920667426629 \tabularnewline
51 & 46.3 & 46.3324471881525 & -0.0324471881525383 \tabularnewline
52 & 46.34 & 46.3702769810044 & -0.0302769810043699 \tabularnewline
53 & 46.34 & 46.3850689182122 & -0.0450689182122161 \tabularnewline
54 & 46.35 & 46.3821305842786 & -0.0321305842786401 \tabularnewline
55 & 46.42 & 46.3807542743367 & 0.0392457256632852 \tabularnewline
56 & 46.52 & 46.4524513503818 & 0.0675486496182529 \tabularnewline
57 & 46.59 & 46.5793350399431 & 0.0106649600569284 \tabularnewline
58 & 46.66 & 46.7107800096162 & -0.050780009616247 \tabularnewline
59 & 46.67 & 46.7079647570146 & -0.0379647570145636 \tabularnewline
60 & 46.72 & 46.6717364439285 & 0.0482635560714684 \tabularnewline
61 & 46.72 & 46.836453112982 & -0.116453112982015 \tabularnewline
62 & 46.72 & 46.7519460283806 & -0.031946028380581 \tabularnewline
63 & 46.76 & 46.7506045782366 & 0.00939542176342911 \tabularnewline
64 & 46.89 & 46.8210353335481 & 0.0689646664518975 \tabularnewline
65 & 47.02 & 46.9310781005829 & 0.0889218994171372 \tabularnewline
66 & 47.02 & 47.06553479511 & -0.0455347951100009 \tabularnewline
67 & 47.04 & 47.0532779655913 & -0.0132779655912998 \tabularnewline
68 & 47.18 & 47.0720784094503 & 0.107921590549658 \tabularnewline
69 & 47.22 & 47.2415122454647 & -0.0215122454646774 \tabularnewline
70 & 47.8 & 47.3419934386011 & 0.458006561398875 \tabularnewline
71 & 47.88 & 47.8763705114335 & 0.0036294885664816 \tabularnewline
72 & 47.91 & 47.9112640024059 & -0.00126400240590385 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13373&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]44.29[/C][C]44.1360821455646[/C][C]0.153917854435385[/C][/ROW]
[ROW][C]14[/C][C]44.29[/C][C]44.3119882486531[/C][C]-0.0219882486530594[/C][/ROW]
[ROW][C]15[/C][C]44.29[/C][C]44.3111790454529[/C][C]-0.0211790454528895[/C][/ROW]
[ROW][C]16[/C][C]44.32[/C][C]44.3383445236373[/C][C]-0.0183445236372748[/C][/ROW]
[ROW][C]17[/C][C]44.33[/C][C]44.34482465423[/C][C]-0.0148246542299972[/C][/ROW]
[ROW][C]18[/C][C]44.34[/C][C]44.3535834613256[/C][C]-0.0135834613256378[/C][/ROW]
[ROW][C]19[/C][C]44.34[/C][C]44.3536578284509[/C][C]-0.0136578284509383[/C][/ROW]
[ROW][C]20[/C][C]44.34[/C][C]44.3524791104286[/C][C]-0.0124791104285720[/C][/ROW]
[ROW][C]21[/C][C]44.37[/C][C]44.373880698356[/C][C]-0.00388069835599936[/C][/ROW]
[ROW][C]22[/C][C]44.47[/C][C]44.4615845819808[/C][C]0.00841541801923285[/C][/ROW]
[ROW][C]23[/C][C]44.51[/C][C]44.4953847023959[/C][C]0.0146152976041023[/C][/ROW]
[ROW][C]24[/C][C]44.51[/C][C]44.4941282860512[/C][C]0.0158717139488331[/C][/ROW]
[ROW][C]25[/C][C]44.51[/C][C]44.6017747283616[/C][C]-0.0917747283616066[/C][/ROW]
[ROW][C]26[/C][C]44.52[/C][C]44.5223338901019[/C][C]-0.00233389010188034[/C][/ROW]
[ROW][C]27[/C][C]44.7[/C][C]44.5326158133203[/C][C]0.167384186679712[/C][/ROW]
[ROW][C]28[/C][C]44.84[/C][C]44.7504378060978[/C][C]0.0895621939021751[/C][/ROW]
[ROW][C]29[/C][C]44.9[/C][C]44.8726682186245[/C][C]0.0273317813754801[/C][/ROW]
[ROW][C]30[/C][C]44.91[/C][C]44.9337466748532[/C][C]-0.0237466748532142[/C][/ROW]
[ROW][C]31[/C][C]44.94[/C][C]44.9331359147389[/C][C]0.00686408526105708[/C][/ROW]
[ROW][C]32[/C][C]44.94[/C][C]44.9630723152294[/C][C]-0.0230723152294203[/C][/ROW]
[ROW][C]33[/C][C]44.95[/C][C]44.9841863840214[/C][C]-0.0341863840214316[/C][/ROW]
[ROW][C]34[/C][C]45.28[/C][C]45.050977146829[/C][C]0.229022853170967[/C][/ROW]
[ROW][C]35[/C][C]45.34[/C][C]45.3261047074384[/C][C]0.0138952925615925[/C][/ROW]
[ROW][C]36[/C][C]45.34[/C][C]45.3440000690773[/C][C]-0.00400006907727857[/C][/ROW]
[ROW][C]37[/C][C]45.34[/C][C]45.4525612249642[/C][C]-0.112561224964246[/C][/ROW]
[ROW][C]38[/C][C]45.36[/C][C]45.370575491329[/C][C]-0.0105754913289928[/C][/ROW]
[ROW][C]39[/C][C]45.44[/C][C]45.3903992055403[/C][C]0.0496007944597423[/C][/ROW]
[ROW][C]40[/C][C]45.62[/C][C]45.5022017493742[/C][C]0.117798250625754[/C][/ROW]
[ROW][C]41[/C][C]45.75[/C][C]45.6656111638139[/C][C]0.0843888361860508[/C][/ROW]
[ROW][C]42[/C][C]45.77[/C][C]45.7998275020901[/C][C]-0.0298275020901144[/C][/ROW]
[ROW][C]43[/C][C]45.77[/C][C]45.8086933990125[/C][C]-0.0386933990124589[/C][/ROW]
[ROW][C]44[/C][C]45.77[/C][C]45.8061034374659[/C][C]-0.0361034374659184[/C][/ROW]
[ROW][C]45[/C][C]46.09[/C][C]45.8269096148947[/C][C]0.263090385105308[/C][/ROW]
[ROW][C]46[/C][C]46.25[/C][C]46.2217304918789[/C][C]0.0282695081211273[/C][/ROW]
[ROW][C]47[/C][C]46.28[/C][C]46.314035460906[/C][C]-0.0340354609060398[/C][/ROW]
[ROW][C]48[/C][C]46.29[/C][C]46.2983734682822[/C][C]-0.0083734682821941[/C][/ROW]
[ROW][C]49[/C][C]46.29[/C][C]46.4189795289091[/C][C]-0.128979528909142[/C][/ROW]
[ROW][C]50[/C][C]46.29[/C][C]46.3344920667427[/C][C]-0.0444920667426629[/C][/ROW]
[ROW][C]51[/C][C]46.3[/C][C]46.3324471881525[/C][C]-0.0324471881525383[/C][/ROW]
[ROW][C]52[/C][C]46.34[/C][C]46.3702769810044[/C][C]-0.0302769810043699[/C][/ROW]
[ROW][C]53[/C][C]46.34[/C][C]46.3850689182122[/C][C]-0.0450689182122161[/C][/ROW]
[ROW][C]54[/C][C]46.35[/C][C]46.3821305842786[/C][C]-0.0321305842786401[/C][/ROW]
[ROW][C]55[/C][C]46.42[/C][C]46.3807542743367[/C][C]0.0392457256632852[/C][/ROW]
[ROW][C]56[/C][C]46.52[/C][C]46.4524513503818[/C][C]0.0675486496182529[/C][/ROW]
[ROW][C]57[/C][C]46.59[/C][C]46.5793350399431[/C][C]0.0106649600569284[/C][/ROW]
[ROW][C]58[/C][C]46.66[/C][C]46.7107800096162[/C][C]-0.050780009616247[/C][/ROW]
[ROW][C]59[/C][C]46.67[/C][C]46.7079647570146[/C][C]-0.0379647570145636[/C][/ROW]
[ROW][C]60[/C][C]46.72[/C][C]46.6717364439285[/C][C]0.0482635560714684[/C][/ROW]
[ROW][C]61[/C][C]46.72[/C][C]46.836453112982[/C][C]-0.116453112982015[/C][/ROW]
[ROW][C]62[/C][C]46.72[/C][C]46.7519460283806[/C][C]-0.031946028380581[/C][/ROW]
[ROW][C]63[/C][C]46.76[/C][C]46.7506045782366[/C][C]0.00939542176342911[/C][/ROW]
[ROW][C]64[/C][C]46.89[/C][C]46.8210353335481[/C][C]0.0689646664518975[/C][/ROW]
[ROW][C]65[/C][C]47.02[/C][C]46.9310781005829[/C][C]0.0889218994171372[/C][/ROW]
[ROW][C]66[/C][C]47.02[/C][C]47.06553479511[/C][C]-0.0455347951100009[/C][/ROW]
[ROW][C]67[/C][C]47.04[/C][C]47.0532779655913[/C][C]-0.0132779655912998[/C][/ROW]
[ROW][C]68[/C][C]47.18[/C][C]47.0720784094503[/C][C]0.107921590549658[/C][/ROW]
[ROW][C]69[/C][C]47.22[/C][C]47.2415122454647[/C][C]-0.0215122454646774[/C][/ROW]
[ROW][C]70[/C][C]47.8[/C][C]47.3419934386011[/C][C]0.458006561398875[/C][/ROW]
[ROW][C]71[/C][C]47.88[/C][C]47.8763705114335[/C][C]0.0036294885664816[/C][/ROW]
[ROW][C]72[/C][C]47.91[/C][C]47.9112640024059[/C][C]-0.00126400240590385[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13373&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13373&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
1344.2944.13608214556460.153917854435385
1444.2944.3119882486531-0.0219882486530594
1544.2944.3111790454529-0.0211790454528895
1644.3244.3383445236373-0.0183445236372748
1744.3344.34482465423-0.0148246542299972
1844.3444.3535834613256-0.0135834613256378
1944.3444.3536578284509-0.0136578284509383
2044.3444.3524791104286-0.0124791104285720
2144.3744.373880698356-0.00388069835599936
2244.4744.46158458198080.00841541801923285
2344.5144.49538470239590.0146152976041023
2444.5144.49412828605120.0158717139488331
2544.5144.6017747283616-0.0917747283616066
2644.5244.5223338901019-0.00233389010188034
2744.744.53261581332030.167384186679712
2844.8444.75043780609780.0895621939021751
2944.944.87266821862450.0273317813754801
3044.9144.9337466748532-0.0237466748532142
3144.9444.93313591473890.00686408526105708
3244.9444.9630723152294-0.0230723152294203
3344.9544.9841863840214-0.0341863840214316
3445.2845.0509771468290.229022853170967
3545.3445.32610470743840.0138952925615925
3645.3445.3440000690773-0.00400006907727857
3745.3445.4525612249642-0.112561224964246
3845.3645.370575491329-0.0105754913289928
3945.4445.39039920554030.0496007944597423
4045.6245.50220174937420.117798250625754
4145.7545.66561116381390.0843888361860508
4245.7745.7998275020901-0.0298275020901144
4345.7745.8086933990125-0.0386933990124589
4445.7745.8061034374659-0.0361034374659184
4546.0945.82690961489470.263090385105308
4646.2546.22173049187890.0282695081211273
4746.2846.314035460906-0.0340354609060398
4846.2946.2983734682822-0.0083734682821941
4946.2946.4189795289091-0.128979528909142
5046.2946.3344920667427-0.0444920667426629
5146.346.3324471881525-0.0324471881525383
5246.3446.3702769810044-0.0302769810043699
5346.3446.3850689182122-0.0450689182122161
5446.3546.3821305842786-0.0321305842786401
5546.4246.38075427433670.0392457256632852
5646.5246.45245135038180.0675486496182529
5746.5946.57933503994310.0106649600569284
5846.6646.7107800096162-0.050780009616247
5946.6746.7079647570146-0.0379647570145636
6046.7246.67173644392850.0482635560714684
6146.7246.836453112982-0.116453112982015
6246.7246.7519460283806-0.031946028380581
6346.7646.75060457823660.00939542176342911
6446.8946.82103533354810.0689646664518975
6547.0246.93107810058290.0889218994171372
6647.0247.06553479511-0.0455347951100009
6747.0447.0532779655913-0.0132779655912998
6847.1847.07207840945030.107921590549658
6947.2247.2415122454647-0.0215122454646774
7047.847.34199343860110.458006561398875
7147.8847.87637051143350.0036294885664816
7247.9147.9112640024059-0.00126400240590385







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7348.056147148656447.873995977882548.2382983194303
7448.122193898812147.857404257119048.3869835405052
7548.188649129091947.855477196040148.5218210621437
7648.285930480504447.890704042676348.6811569183325
7748.358706256116747.905209266227748.8122032460058
7848.431002688486147.921415665529148.9405897114432
7948.493247931209647.929025586500649.0574702759186
8048.55498604492447.936975747877549.1729963419704
8148.640895355441347.969282536184549.3125081746982
8248.790370412535448.064490215829549.5162506092412
8348.866751242560848.087666863255949.6458356218657
8448.896893152813446.540607025665451.2531792799615

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 48.0561471486564 & 47.8739959778825 & 48.2382983194303 \tabularnewline
74 & 48.1221938988121 & 47.8574042571190 & 48.3869835405052 \tabularnewline
75 & 48.1886491290919 & 47.8554771960401 & 48.5218210621437 \tabularnewline
76 & 48.2859304805044 & 47.8907040426763 & 48.6811569183325 \tabularnewline
77 & 48.3587062561167 & 47.9052092662277 & 48.8122032460058 \tabularnewline
78 & 48.4310026884861 & 47.9214156655291 & 48.9405897114432 \tabularnewline
79 & 48.4932479312096 & 47.9290255865006 & 49.0574702759186 \tabularnewline
80 & 48.554986044924 & 47.9369757478775 & 49.1729963419704 \tabularnewline
81 & 48.6408953554413 & 47.9692825361845 & 49.3125081746982 \tabularnewline
82 & 48.7903704125354 & 48.0644902158295 & 49.5162506092412 \tabularnewline
83 & 48.8667512425608 & 48.0876668632559 & 49.6458356218657 \tabularnewline
84 & 48.8968931528134 & 46.5406070256654 & 51.2531792799615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13373&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]48.0561471486564[/C][C]47.8739959778825[/C][C]48.2382983194303[/C][/ROW]
[ROW][C]74[/C][C]48.1221938988121[/C][C]47.8574042571190[/C][C]48.3869835405052[/C][/ROW]
[ROW][C]75[/C][C]48.1886491290919[/C][C]47.8554771960401[/C][C]48.5218210621437[/C][/ROW]
[ROW][C]76[/C][C]48.2859304805044[/C][C]47.8907040426763[/C][C]48.6811569183325[/C][/ROW]
[ROW][C]77[/C][C]48.3587062561167[/C][C]47.9052092662277[/C][C]48.8122032460058[/C][/ROW]
[ROW][C]78[/C][C]48.4310026884861[/C][C]47.9214156655291[/C][C]48.9405897114432[/C][/ROW]
[ROW][C]79[/C][C]48.4932479312096[/C][C]47.9290255865006[/C][C]49.0574702759186[/C][/ROW]
[ROW][C]80[/C][C]48.554986044924[/C][C]47.9369757478775[/C][C]49.1729963419704[/C][/ROW]
[ROW][C]81[/C][C]48.6408953554413[/C][C]47.9692825361845[/C][C]49.3125081746982[/C][/ROW]
[ROW][C]82[/C][C]48.7903704125354[/C][C]48.0644902158295[/C][C]49.5162506092412[/C][/ROW]
[ROW][C]83[/C][C]48.8667512425608[/C][C]48.0876668632559[/C][C]49.6458356218657[/C][/ROW]
[ROW][C]84[/C][C]48.8968931528134[/C][C]46.5406070256654[/C][C]51.2531792799615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13373&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13373&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
7348.056147148656447.873995977882548.2382983194303
7448.122193898812147.857404257119048.3869835405052
7548.188649129091947.855477196040148.5218210621437
7648.285930480504447.890704042676348.6811569183325
7748.358706256116747.905209266227748.8122032460058
7848.431002688486147.921415665529148.9405897114432
7948.493247931209647.929025586500649.0574702759186
8048.55498604492447.936975747877549.1729963419704
8148.640895355441347.969282536184549.3125081746982
8248.790370412535448.064490215829549.5162506092412
8348.866751242560848.087666863255949.6458356218657
8448.896893152813446.540607025665451.2531792799615



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')