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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 23 May 2013 13:43:26 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/23/t1369331158o9c7bkp2kzux9h3.htm/, Retrieved Mon, 29 Apr 2024 17:02:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210373, Retrieved Mon, 29 Apr 2024 17:02:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [joggingschoenen] [2013-05-23 17:43:26] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
85,3
85,65
85,15
84,94
85,15
85,15
85,15
85,14
85,37
85,61
85,59
85,54
85,54
85,5
85,78
86,16
86,38
86,49
86,49
86
85,9
85,66
85,64
85,6
85,6
85,57
85,81
86,29
86,37
86,41
86,41
86,38
86,62
87,08
87,19
87,21
87,21
87,24
87,16
87,05
87,04
86,98
86,98
86,94
86,96
86,98
86,86
86,82
86,82
86,84
86,91
86,85
86,61
86,65
86,65
86,36
86,33
86,43
86,36
86,29
86,29
86,44
86,51
86,72
86,93
86,79
86,79
86,8
86,41
86,26
86,19
86,28




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210373&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210373&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210373&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 time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999926608669377
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999926608669377 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210373&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]0.999926608669377[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210373&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210373&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
alpha0.999926608669377
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
285.6585.30.350000000000009
385.1585.6499743130343-0.499974313034286
484.9485.1500366937801-0.210036693780125
585.1584.94001541487240.209984585127572
685.1585.14998458895191.54110481105363e-05
785.1585.1499999988691.13104192678293e-09
885.1485.1499999999999-0.00999999999991985
985.3785.14000073391330.229999266086693
1085.6185.36998312004780.240016879952179
1185.5985.6099823848418-0.0199823848418106
1285.5485.5900014665338-0.0500014665338142
1385.5485.5400036696742-3.66967415743602e-06
1485.585.5400000002693-0.0400000002693304
1585.7885.50000293565320.279997064346759
1686.1685.77997945064290.380020549357113
1786.3886.15997210978620.220027890213785
1886.4986.37998385186040.110016148139636
1986.4986.48999192576858.07423150206432e-06
208686.4899999994074-0.489999999407416
2185.986.000035961752-0.100035961751956
2285.6685.9000073417724-0.240007341772355
2385.6485.6600176144582-0.020017614458169
2485.685.6400014691194-0.0400014691193604
2585.685.600002935761-2.93576104581916e-06
2685.5785.6000000002155-0.0300000002154661
2785.8185.57000220173990.239997798260077
2886.2985.80998238624220.480017613757767
2986.3786.28996477086860.080035229131397
3086.4186.3699941261080.0400058738919569
3186.4186.40999706391572.93608431434222e-06
3286.3886.4099999997845-0.0299999997845219
3386.6286.38000220173990.239997798260106
3487.0886.61998238624220.460017613757756
3587.1987.07996623869520.110033761304777
3687.2187.18999192447580.0200080755241459
3787.2187.20999853158071.46841928483354e-06
3887.2487.20999999989220.0300000001077763
3987.1687.2399977982601-0.0799977982600666
4087.0587.1600058711449-0.110005871144864
4187.0487.0500080734773-0.0100080734772519
4286.9887.0400007345058-0.0600007345058344
4386.9886.9800044035337-4.40353373676317e-06
4486.9486.9800000003232-0.0400000003231895
4586.9686.94000293565320.0199970643467537
4686.9886.95999853238880.0200014676111664
4786.8686.9799985320657-0.119998532065679
4886.8286.8600088068519-0.0400088068519437
4986.8286.8200029362996-2.9362995661586e-06
5086.8486.82000000021550.0199999997845168
5186.9186.83999853217340.0700014678265859
5286.8586.9099948624991-0.0599948624991384
5386.6186.8500044031028-0.240004403102787
5486.6586.61001761424250.0399823857575115
5586.6586.64999706563952.93436049503271e-06
5686.3686.6499999997847-0.289999999784655
5786.3386.3600212834859-0.0300212834858655
5886.4386.33000220330190.0999977966980623
5986.3686.4299926610286-0.0699926610286496
6086.2986.3600051368545-0.0700051368545189
6186.2986.2900051377702-5.13777014532479e-06
6286.4486.29000000037710.149999999622921
6386.5186.43998899130040.0700110086995664
6486.7286.50999486179890.210005138201083
6586.9386.71998458744350.210015412556544
6686.7986.9299845866894-0.139984586689422
6786.7986.7900102736551-1.02736550786631e-05
6886.886.7900000007540.00999999924599138
6986.4186.7999992660867-0.389999266086747
7086.2686.4100286225651-0.150028622565074
7186.1986.2600110108002-0.0700110108002434
7286.2886.19000513820120.0899948617987576

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 85.65 & 85.3 & 0.350000000000009 \tabularnewline
3 & 85.15 & 85.6499743130343 & -0.499974313034286 \tabularnewline
4 & 84.94 & 85.1500366937801 & -0.210036693780125 \tabularnewline
5 & 85.15 & 84.9400154148724 & 0.209984585127572 \tabularnewline
6 & 85.15 & 85.1499845889519 & 1.54110481105363e-05 \tabularnewline
7 & 85.15 & 85.149999998869 & 1.13104192678293e-09 \tabularnewline
8 & 85.14 & 85.1499999999999 & -0.00999999999991985 \tabularnewline
9 & 85.37 & 85.1400007339133 & 0.229999266086693 \tabularnewline
10 & 85.61 & 85.3699831200478 & 0.240016879952179 \tabularnewline
11 & 85.59 & 85.6099823848418 & -0.0199823848418106 \tabularnewline
12 & 85.54 & 85.5900014665338 & -0.0500014665338142 \tabularnewline
13 & 85.54 & 85.5400036696742 & -3.66967415743602e-06 \tabularnewline
14 & 85.5 & 85.5400000002693 & -0.0400000002693304 \tabularnewline
15 & 85.78 & 85.5000029356532 & 0.279997064346759 \tabularnewline
16 & 86.16 & 85.7799794506429 & 0.380020549357113 \tabularnewline
17 & 86.38 & 86.1599721097862 & 0.220027890213785 \tabularnewline
18 & 86.49 & 86.3799838518604 & 0.110016148139636 \tabularnewline
19 & 86.49 & 86.4899919257685 & 8.07423150206432e-06 \tabularnewline
20 & 86 & 86.4899999994074 & -0.489999999407416 \tabularnewline
21 & 85.9 & 86.000035961752 & -0.100035961751956 \tabularnewline
22 & 85.66 & 85.9000073417724 & -0.240007341772355 \tabularnewline
23 & 85.64 & 85.6600176144582 & -0.020017614458169 \tabularnewline
24 & 85.6 & 85.6400014691194 & -0.0400014691193604 \tabularnewline
25 & 85.6 & 85.600002935761 & -2.93576104581916e-06 \tabularnewline
26 & 85.57 & 85.6000000002155 & -0.0300000002154661 \tabularnewline
27 & 85.81 & 85.5700022017399 & 0.239997798260077 \tabularnewline
28 & 86.29 & 85.8099823862422 & 0.480017613757767 \tabularnewline
29 & 86.37 & 86.2899647708686 & 0.080035229131397 \tabularnewline
30 & 86.41 & 86.369994126108 & 0.0400058738919569 \tabularnewline
31 & 86.41 & 86.4099970639157 & 2.93608431434222e-06 \tabularnewline
32 & 86.38 & 86.4099999997845 & -0.0299999997845219 \tabularnewline
33 & 86.62 & 86.3800022017399 & 0.239997798260106 \tabularnewline
34 & 87.08 & 86.6199823862422 & 0.460017613757756 \tabularnewline
35 & 87.19 & 87.0799662386952 & 0.110033761304777 \tabularnewline
36 & 87.21 & 87.1899919244758 & 0.0200080755241459 \tabularnewline
37 & 87.21 & 87.2099985315807 & 1.46841928483354e-06 \tabularnewline
38 & 87.24 & 87.2099999998922 & 0.0300000001077763 \tabularnewline
39 & 87.16 & 87.2399977982601 & -0.0799977982600666 \tabularnewline
40 & 87.05 & 87.1600058711449 & -0.110005871144864 \tabularnewline
41 & 87.04 & 87.0500080734773 & -0.0100080734772519 \tabularnewline
42 & 86.98 & 87.0400007345058 & -0.0600007345058344 \tabularnewline
43 & 86.98 & 86.9800044035337 & -4.40353373676317e-06 \tabularnewline
44 & 86.94 & 86.9800000003232 & -0.0400000003231895 \tabularnewline
45 & 86.96 & 86.9400029356532 & 0.0199970643467537 \tabularnewline
46 & 86.98 & 86.9599985323888 & 0.0200014676111664 \tabularnewline
47 & 86.86 & 86.9799985320657 & -0.119998532065679 \tabularnewline
48 & 86.82 & 86.8600088068519 & -0.0400088068519437 \tabularnewline
49 & 86.82 & 86.8200029362996 & -2.9362995661586e-06 \tabularnewline
50 & 86.84 & 86.8200000002155 & 0.0199999997845168 \tabularnewline
51 & 86.91 & 86.8399985321734 & 0.0700014678265859 \tabularnewline
52 & 86.85 & 86.9099948624991 & -0.0599948624991384 \tabularnewline
53 & 86.61 & 86.8500044031028 & -0.240004403102787 \tabularnewline
54 & 86.65 & 86.6100176142425 & 0.0399823857575115 \tabularnewline
55 & 86.65 & 86.6499970656395 & 2.93436049503271e-06 \tabularnewline
56 & 86.36 & 86.6499999997847 & -0.289999999784655 \tabularnewline
57 & 86.33 & 86.3600212834859 & -0.0300212834858655 \tabularnewline
58 & 86.43 & 86.3300022033019 & 0.0999977966980623 \tabularnewline
59 & 86.36 & 86.4299926610286 & -0.0699926610286496 \tabularnewline
60 & 86.29 & 86.3600051368545 & -0.0700051368545189 \tabularnewline
61 & 86.29 & 86.2900051377702 & -5.13777014532479e-06 \tabularnewline
62 & 86.44 & 86.2900000003771 & 0.149999999622921 \tabularnewline
63 & 86.51 & 86.4399889913004 & 0.0700110086995664 \tabularnewline
64 & 86.72 & 86.5099948617989 & 0.210005138201083 \tabularnewline
65 & 86.93 & 86.7199845874435 & 0.210015412556544 \tabularnewline
66 & 86.79 & 86.9299845866894 & -0.139984586689422 \tabularnewline
67 & 86.79 & 86.7900102736551 & -1.02736550786631e-05 \tabularnewline
68 & 86.8 & 86.790000000754 & 0.00999999924599138 \tabularnewline
69 & 86.41 & 86.7999992660867 & -0.389999266086747 \tabularnewline
70 & 86.26 & 86.4100286225651 & -0.150028622565074 \tabularnewline
71 & 86.19 & 86.2600110108002 & -0.0700110108002434 \tabularnewline
72 & 86.28 & 86.1900051382012 & 0.0899948617987576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210373&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]85.65[/C][C]85.3[/C][C]0.350000000000009[/C][/ROW]
[ROW][C]3[/C][C]85.15[/C][C]85.6499743130343[/C][C]-0.499974313034286[/C][/ROW]
[ROW][C]4[/C][C]84.94[/C][C]85.1500366937801[/C][C]-0.210036693780125[/C][/ROW]
[ROW][C]5[/C][C]85.15[/C][C]84.9400154148724[/C][C]0.209984585127572[/C][/ROW]
[ROW][C]6[/C][C]85.15[/C][C]85.1499845889519[/C][C]1.54110481105363e-05[/C][/ROW]
[ROW][C]7[/C][C]85.15[/C][C]85.149999998869[/C][C]1.13104192678293e-09[/C][/ROW]
[ROW][C]8[/C][C]85.14[/C][C]85.1499999999999[/C][C]-0.00999999999991985[/C][/ROW]
[ROW][C]9[/C][C]85.37[/C][C]85.1400007339133[/C][C]0.229999266086693[/C][/ROW]
[ROW][C]10[/C][C]85.61[/C][C]85.3699831200478[/C][C]0.240016879952179[/C][/ROW]
[ROW][C]11[/C][C]85.59[/C][C]85.6099823848418[/C][C]-0.0199823848418106[/C][/ROW]
[ROW][C]12[/C][C]85.54[/C][C]85.5900014665338[/C][C]-0.0500014665338142[/C][/ROW]
[ROW][C]13[/C][C]85.54[/C][C]85.5400036696742[/C][C]-3.66967415743602e-06[/C][/ROW]
[ROW][C]14[/C][C]85.5[/C][C]85.5400000002693[/C][C]-0.0400000002693304[/C][/ROW]
[ROW][C]15[/C][C]85.78[/C][C]85.5000029356532[/C][C]0.279997064346759[/C][/ROW]
[ROW][C]16[/C][C]86.16[/C][C]85.7799794506429[/C][C]0.380020549357113[/C][/ROW]
[ROW][C]17[/C][C]86.38[/C][C]86.1599721097862[/C][C]0.220027890213785[/C][/ROW]
[ROW][C]18[/C][C]86.49[/C][C]86.3799838518604[/C][C]0.110016148139636[/C][/ROW]
[ROW][C]19[/C][C]86.49[/C][C]86.4899919257685[/C][C]8.07423150206432e-06[/C][/ROW]
[ROW][C]20[/C][C]86[/C][C]86.4899999994074[/C][C]-0.489999999407416[/C][/ROW]
[ROW][C]21[/C][C]85.9[/C][C]86.000035961752[/C][C]-0.100035961751956[/C][/ROW]
[ROW][C]22[/C][C]85.66[/C][C]85.9000073417724[/C][C]-0.240007341772355[/C][/ROW]
[ROW][C]23[/C][C]85.64[/C][C]85.6600176144582[/C][C]-0.020017614458169[/C][/ROW]
[ROW][C]24[/C][C]85.6[/C][C]85.6400014691194[/C][C]-0.0400014691193604[/C][/ROW]
[ROW][C]25[/C][C]85.6[/C][C]85.600002935761[/C][C]-2.93576104581916e-06[/C][/ROW]
[ROW][C]26[/C][C]85.57[/C][C]85.6000000002155[/C][C]-0.0300000002154661[/C][/ROW]
[ROW][C]27[/C][C]85.81[/C][C]85.5700022017399[/C][C]0.239997798260077[/C][/ROW]
[ROW][C]28[/C][C]86.29[/C][C]85.8099823862422[/C][C]0.480017613757767[/C][/ROW]
[ROW][C]29[/C][C]86.37[/C][C]86.2899647708686[/C][C]0.080035229131397[/C][/ROW]
[ROW][C]30[/C][C]86.41[/C][C]86.369994126108[/C][C]0.0400058738919569[/C][/ROW]
[ROW][C]31[/C][C]86.41[/C][C]86.4099970639157[/C][C]2.93608431434222e-06[/C][/ROW]
[ROW][C]32[/C][C]86.38[/C][C]86.4099999997845[/C][C]-0.0299999997845219[/C][/ROW]
[ROW][C]33[/C][C]86.62[/C][C]86.3800022017399[/C][C]0.239997798260106[/C][/ROW]
[ROW][C]34[/C][C]87.08[/C][C]86.6199823862422[/C][C]0.460017613757756[/C][/ROW]
[ROW][C]35[/C][C]87.19[/C][C]87.0799662386952[/C][C]0.110033761304777[/C][/ROW]
[ROW][C]36[/C][C]87.21[/C][C]87.1899919244758[/C][C]0.0200080755241459[/C][/ROW]
[ROW][C]37[/C][C]87.21[/C][C]87.2099985315807[/C][C]1.46841928483354e-06[/C][/ROW]
[ROW][C]38[/C][C]87.24[/C][C]87.2099999998922[/C][C]0.0300000001077763[/C][/ROW]
[ROW][C]39[/C][C]87.16[/C][C]87.2399977982601[/C][C]-0.0799977982600666[/C][/ROW]
[ROW][C]40[/C][C]87.05[/C][C]87.1600058711449[/C][C]-0.110005871144864[/C][/ROW]
[ROW][C]41[/C][C]87.04[/C][C]87.0500080734773[/C][C]-0.0100080734772519[/C][/ROW]
[ROW][C]42[/C][C]86.98[/C][C]87.0400007345058[/C][C]-0.0600007345058344[/C][/ROW]
[ROW][C]43[/C][C]86.98[/C][C]86.9800044035337[/C][C]-4.40353373676317e-06[/C][/ROW]
[ROW][C]44[/C][C]86.94[/C][C]86.9800000003232[/C][C]-0.0400000003231895[/C][/ROW]
[ROW][C]45[/C][C]86.96[/C][C]86.9400029356532[/C][C]0.0199970643467537[/C][/ROW]
[ROW][C]46[/C][C]86.98[/C][C]86.9599985323888[/C][C]0.0200014676111664[/C][/ROW]
[ROW][C]47[/C][C]86.86[/C][C]86.9799985320657[/C][C]-0.119998532065679[/C][/ROW]
[ROW][C]48[/C][C]86.82[/C][C]86.8600088068519[/C][C]-0.0400088068519437[/C][/ROW]
[ROW][C]49[/C][C]86.82[/C][C]86.8200029362996[/C][C]-2.9362995661586e-06[/C][/ROW]
[ROW][C]50[/C][C]86.84[/C][C]86.8200000002155[/C][C]0.0199999997845168[/C][/ROW]
[ROW][C]51[/C][C]86.91[/C][C]86.8399985321734[/C][C]0.0700014678265859[/C][/ROW]
[ROW][C]52[/C][C]86.85[/C][C]86.9099948624991[/C][C]-0.0599948624991384[/C][/ROW]
[ROW][C]53[/C][C]86.61[/C][C]86.8500044031028[/C][C]-0.240004403102787[/C][/ROW]
[ROW][C]54[/C][C]86.65[/C][C]86.6100176142425[/C][C]0.0399823857575115[/C][/ROW]
[ROW][C]55[/C][C]86.65[/C][C]86.6499970656395[/C][C]2.93436049503271e-06[/C][/ROW]
[ROW][C]56[/C][C]86.36[/C][C]86.6499999997847[/C][C]-0.289999999784655[/C][/ROW]
[ROW][C]57[/C][C]86.33[/C][C]86.3600212834859[/C][C]-0.0300212834858655[/C][/ROW]
[ROW][C]58[/C][C]86.43[/C][C]86.3300022033019[/C][C]0.0999977966980623[/C][/ROW]
[ROW][C]59[/C][C]86.36[/C][C]86.4299926610286[/C][C]-0.0699926610286496[/C][/ROW]
[ROW][C]60[/C][C]86.29[/C][C]86.3600051368545[/C][C]-0.0700051368545189[/C][/ROW]
[ROW][C]61[/C][C]86.29[/C][C]86.2900051377702[/C][C]-5.13777014532479e-06[/C][/ROW]
[ROW][C]62[/C][C]86.44[/C][C]86.2900000003771[/C][C]0.149999999622921[/C][/ROW]
[ROW][C]63[/C][C]86.51[/C][C]86.4399889913004[/C][C]0.0700110086995664[/C][/ROW]
[ROW][C]64[/C][C]86.72[/C][C]86.5099948617989[/C][C]0.210005138201083[/C][/ROW]
[ROW][C]65[/C][C]86.93[/C][C]86.7199845874435[/C][C]0.210015412556544[/C][/ROW]
[ROW][C]66[/C][C]86.79[/C][C]86.9299845866894[/C][C]-0.139984586689422[/C][/ROW]
[ROW][C]67[/C][C]86.79[/C][C]86.7900102736551[/C][C]-1.02736550786631e-05[/C][/ROW]
[ROW][C]68[/C][C]86.8[/C][C]86.790000000754[/C][C]0.00999999924599138[/C][/ROW]
[ROW][C]69[/C][C]86.41[/C][C]86.7999992660867[/C][C]-0.389999266086747[/C][/ROW]
[ROW][C]70[/C][C]86.26[/C][C]86.4100286225651[/C][C]-0.150028622565074[/C][/ROW]
[ROW][C]71[/C][C]86.19[/C][C]86.2600110108002[/C][C]-0.0700110108002434[/C][/ROW]
[ROW][C]72[/C][C]86.28[/C][C]86.1900051382012[/C][C]0.0899948617987576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210373&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210373&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
285.6585.30.350000000000009
385.1585.6499743130343-0.499974313034286
484.9485.1500366937801-0.210036693780125
585.1584.94001541487240.209984585127572
685.1585.14998458895191.54110481105363e-05
785.1585.1499999988691.13104192678293e-09
885.1485.1499999999999-0.00999999999991985
985.3785.14000073391330.229999266086693
1085.6185.36998312004780.240016879952179
1185.5985.6099823848418-0.0199823848418106
1285.5485.5900014665338-0.0500014665338142
1385.5485.5400036696742-3.66967415743602e-06
1485.585.5400000002693-0.0400000002693304
1585.7885.50000293565320.279997064346759
1686.1685.77997945064290.380020549357113
1786.3886.15997210978620.220027890213785
1886.4986.37998385186040.110016148139636
1986.4986.48999192576858.07423150206432e-06
208686.4899999994074-0.489999999407416
2185.986.000035961752-0.100035961751956
2285.6685.9000073417724-0.240007341772355
2385.6485.6600176144582-0.020017614458169
2485.685.6400014691194-0.0400014691193604
2585.685.600002935761-2.93576104581916e-06
2685.5785.6000000002155-0.0300000002154661
2785.8185.57000220173990.239997798260077
2886.2985.80998238624220.480017613757767
2986.3786.28996477086860.080035229131397
3086.4186.3699941261080.0400058738919569
3186.4186.40999706391572.93608431434222e-06
3286.3886.4099999997845-0.0299999997845219
3386.6286.38000220173990.239997798260106
3487.0886.61998238624220.460017613757756
3587.1987.07996623869520.110033761304777
3687.2187.18999192447580.0200080755241459
3787.2187.20999853158071.46841928483354e-06
3887.2487.20999999989220.0300000001077763
3987.1687.2399977982601-0.0799977982600666
4087.0587.1600058711449-0.110005871144864
4187.0487.0500080734773-0.0100080734772519
4286.9887.0400007345058-0.0600007345058344
4386.9886.9800044035337-4.40353373676317e-06
4486.9486.9800000003232-0.0400000003231895
4586.9686.94000293565320.0199970643467537
4686.9886.95999853238880.0200014676111664
4786.8686.9799985320657-0.119998532065679
4886.8286.8600088068519-0.0400088068519437
4986.8286.8200029362996-2.9362995661586e-06
5086.8486.82000000021550.0199999997845168
5186.9186.83999853217340.0700014678265859
5286.8586.9099948624991-0.0599948624991384
5386.6186.8500044031028-0.240004403102787
5486.6586.61001761424250.0399823857575115
5586.6586.64999706563952.93436049503271e-06
5686.3686.6499999997847-0.289999999784655
5786.3386.3600212834859-0.0300212834858655
5886.4386.33000220330190.0999977966980623
5986.3686.4299926610286-0.0699926610286496
6086.2986.3600051368545-0.0700051368545189
6186.2986.2900051377702-5.13777014532479e-06
6286.4486.29000000037710.149999999622921
6386.5186.43998899130040.0700110086995664
6486.7286.50999486179890.210005138201083
6586.9386.71998458744350.210015412556544
6686.7986.9299845866894-0.139984586689422
6786.7986.7900102736551-1.02736550786631e-05
6886.886.7900000007540.00999999924599138
6986.4186.7999992660867-0.389999266086747
7086.2686.4100286225651-0.150028622565074
7186.1986.2600110108002-0.0700110108002434
7286.2886.19000513820120.0899948617987576







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7386.279993395157385.926876096593686.6331106937211
7486.279993395157385.780628447285186.7793583430296
7586.279993395157385.66840621757686.8915805727386
7686.279993395157385.573797671295886.9861891190189
7786.279993395157385.490445470697687.0695413196171
7886.279993395157385.415089094302587.1448976960122
7986.279993395157385.345791610607787.2141951797069
8086.279993395157385.281290987593487.2786958027213
8186.279993395157385.220710607846787.339276182468
8286.279993395157385.163412207732587.3965745825822
8386.279993395157385.108913947498387.4510728428164
8486.279993395157385.056841484171787.503145306143

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 86.2799933951573 & 85.9268760965936 & 86.6331106937211 \tabularnewline
74 & 86.2799933951573 & 85.7806284472851 & 86.7793583430296 \tabularnewline
75 & 86.2799933951573 & 85.668406217576 & 86.8915805727386 \tabularnewline
76 & 86.2799933951573 & 85.5737976712958 & 86.9861891190189 \tabularnewline
77 & 86.2799933951573 & 85.4904454706976 & 87.0695413196171 \tabularnewline
78 & 86.2799933951573 & 85.4150890943025 & 87.1448976960122 \tabularnewline
79 & 86.2799933951573 & 85.3457916106077 & 87.2141951797069 \tabularnewline
80 & 86.2799933951573 & 85.2812909875934 & 87.2786958027213 \tabularnewline
81 & 86.2799933951573 & 85.2207106078467 & 87.339276182468 \tabularnewline
82 & 86.2799933951573 & 85.1634122077325 & 87.3965745825822 \tabularnewline
83 & 86.2799933951573 & 85.1089139474983 & 87.4510728428164 \tabularnewline
84 & 86.2799933951573 & 85.0568414841717 & 87.503145306143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210373&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]86.2799933951573[/C][C]85.9268760965936[/C][C]86.6331106937211[/C][/ROW]
[ROW][C]74[/C][C]86.2799933951573[/C][C]85.7806284472851[/C][C]86.7793583430296[/C][/ROW]
[ROW][C]75[/C][C]86.2799933951573[/C][C]85.668406217576[/C][C]86.8915805727386[/C][/ROW]
[ROW][C]76[/C][C]86.2799933951573[/C][C]85.5737976712958[/C][C]86.9861891190189[/C][/ROW]
[ROW][C]77[/C][C]86.2799933951573[/C][C]85.4904454706976[/C][C]87.0695413196171[/C][/ROW]
[ROW][C]78[/C][C]86.2799933951573[/C][C]85.4150890943025[/C][C]87.1448976960122[/C][/ROW]
[ROW][C]79[/C][C]86.2799933951573[/C][C]85.3457916106077[/C][C]87.2141951797069[/C][/ROW]
[ROW][C]80[/C][C]86.2799933951573[/C][C]85.2812909875934[/C][C]87.2786958027213[/C][/ROW]
[ROW][C]81[/C][C]86.2799933951573[/C][C]85.2207106078467[/C][C]87.339276182468[/C][/ROW]
[ROW][C]82[/C][C]86.2799933951573[/C][C]85.1634122077325[/C][C]87.3965745825822[/C][/ROW]
[ROW][C]83[/C][C]86.2799933951573[/C][C]85.1089139474983[/C][C]87.4510728428164[/C][/ROW]
[ROW][C]84[/C][C]86.2799933951573[/C][C]85.0568414841717[/C][C]87.503145306143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210373&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210373&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
7386.279993395157385.926876096593686.6331106937211
7486.279993395157385.780628447285186.7793583430296
7586.279993395157385.66840621757686.8915805727386
7686.279993395157385.573797671295886.9861891190189
7786.279993395157385.490445470697687.0695413196171
7886.279993395157385.415089094302587.1448976960122
7986.279993395157385.345791610607787.2141951797069
8086.279993395157385.281290987593487.2786958027213
8186.279993395157385.220710607846787.339276182468
8286.279993395157385.163412207732587.3965745825822
8386.279993395157385.108913947498387.4510728428164
8486.279993395157385.056841484171787.503145306143



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')