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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 30 May 2008 07:34:24 -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/30/t12121545329ifzmz8fbwidxro.htm/, Retrieved Tue, 14 May 2024 20:23:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13548, Retrieved Tue, 14 May 2024 20:23:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233
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] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [Exponential smoot...] [2008-05-30 13:34:24] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13548&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13548&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0784142333807304
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0784142333807304 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13548&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]0.0784142333807304[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13548&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
beta0.0784142333807304
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
344.1444.130.00999999999999801
444.1444.1407841423338-0.000784142333806415
544.1444.1407226544138-0.000722654413841894
644.1444.140665988022-0.000665988021978592
744.1544.14061376508180.00938623491820323
844.1744.15134977949720.0186502205027637
944.1944.17281222224030.0171877777596521
1044.2644.19415998865690.0658400113431128
1144.2744.26932278267210.000677217327869073
1244.2944.27937588614970.0106241138502625
1344.2944.3002089678927-0.0102089678926518
1444.2944.2994084395017-0.00940843950174042
1544.2944.2986706839309-0.00867068393090165
1644.3244.29799077889760.0220092211024294
1744.3344.32971661509760.000283384902374451
1844.3444.33973883650750.000261163492510263
1944.3444.3497593154426-0.00975931544255104
2044.3444.3489940462038-0.00899404620380295
2144.3744.34828878496570.0217112150342516
2244.4744.37999125324840.090008746751586
2344.5144.48704922012250.0229507798774975
2444.5144.5288488879321-0.0188488879320872
2544.5144.5273708668348-0.0173708668348098
2644.5244.5260087436288-0.00600874362879722
2744.744.53553757260360.164462427396430
2844.8444.72843376776780.111566232232207
2944.944.87718214833950.0228178516605411
3044.9144.9389713926848-0.0289713926848165
3144.9444.9466996231375-0.00669962313745742
3244.9444.9761742773252-0.0361742773251947
3344.9544.9733376991006-0.0233376991006367
3445.2844.98150769131680.298492308683201
3545.3445.33491373687220.00508626312777238
3645.3445.3953125722962-0.0553125722961667
3745.3445.3909752793433-0.0509752793432483
3845.3645.3869780918922-0.0269780918921825
3945.4445.40486262549840.0351373745016161
4045.6245.48761789578290.132382104217065
4145.7545.67799853699840.0720014630015555
4245.7745.813644476522-0.0436444765219974
4345.7745.8302221283542-0.0602221283542264
4445.7745.8254998563268-0.0554998563267759
4546.0945.82114787764020.268852122359831
4646.2546.16222971070780.0877702892922017
4746.2846.3291121506563-0.0491121506562493
4846.2946.3552610590129-0.0652610590128617
4946.2946.3601436631008-0.070143663100751
5046.2946.3546434015322-0.0646434015321944
5146.346.3495744387579-0.0495744387579222
5246.3446.3556870971474-0.0156870971474348
5346.3446.3944570054507-0.0544570054506579
5446.3546.390186801116-0.040186801116036
5546.4246.39703558391450.0229644160855074
5646.5246.46883632099690.0511636790031247
5746.5946.57284828166280.0171517183371606
5846.6646.64419322050740.0158067794925785
5946.6746.7154326970035-0.0454326970035339
6046.7246.7218701268976-0.00187012689759314
6146.7246.7717234823306-0.0517234823305941
6246.7246.7676676251159-0.0476676251158565
6346.7646.7639298048353-0.00392980483531602
6446.8946.80362165220180.0863783477981812
6547.0246.94039494412510.0796050558748931
6647.0247.0766371135548-0.0566371135547712
6747.0447.0721959577145-0.0321959577144781
6847.1847.08967133637230.0903286636276661
6947.2247.236754389283-0.0167543892830011
7047.847.27544060669160.524559393308387
7147.8847.8965735293805-0.016573529380544
7247.9147.9752739287798-0.0652739287797672

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 44.14 & 44.13 & 0.00999999999999801 \tabularnewline
4 & 44.14 & 44.1407841423338 & -0.000784142333806415 \tabularnewline
5 & 44.14 & 44.1407226544138 & -0.000722654413841894 \tabularnewline
6 & 44.14 & 44.140665988022 & -0.000665988021978592 \tabularnewline
7 & 44.15 & 44.1406137650818 & 0.00938623491820323 \tabularnewline
8 & 44.17 & 44.1513497794972 & 0.0186502205027637 \tabularnewline
9 & 44.19 & 44.1728122222403 & 0.0171877777596521 \tabularnewline
10 & 44.26 & 44.1941599886569 & 0.0658400113431128 \tabularnewline
11 & 44.27 & 44.2693227826721 & 0.000677217327869073 \tabularnewline
12 & 44.29 & 44.2793758861497 & 0.0106241138502625 \tabularnewline
13 & 44.29 & 44.3002089678927 & -0.0102089678926518 \tabularnewline
14 & 44.29 & 44.2994084395017 & -0.00940843950174042 \tabularnewline
15 & 44.29 & 44.2986706839309 & -0.00867068393090165 \tabularnewline
16 & 44.32 & 44.2979907788976 & 0.0220092211024294 \tabularnewline
17 & 44.33 & 44.3297166150976 & 0.000283384902374451 \tabularnewline
18 & 44.34 & 44.3397388365075 & 0.000261163492510263 \tabularnewline
19 & 44.34 & 44.3497593154426 & -0.00975931544255104 \tabularnewline
20 & 44.34 & 44.3489940462038 & -0.00899404620380295 \tabularnewline
21 & 44.37 & 44.3482887849657 & 0.0217112150342516 \tabularnewline
22 & 44.47 & 44.3799912532484 & 0.090008746751586 \tabularnewline
23 & 44.51 & 44.4870492201225 & 0.0229507798774975 \tabularnewline
24 & 44.51 & 44.5288488879321 & -0.0188488879320872 \tabularnewline
25 & 44.51 & 44.5273708668348 & -0.0173708668348098 \tabularnewline
26 & 44.52 & 44.5260087436288 & -0.00600874362879722 \tabularnewline
27 & 44.7 & 44.5355375726036 & 0.164462427396430 \tabularnewline
28 & 44.84 & 44.7284337677678 & 0.111566232232207 \tabularnewline
29 & 44.9 & 44.8771821483395 & 0.0228178516605411 \tabularnewline
30 & 44.91 & 44.9389713926848 & -0.0289713926848165 \tabularnewline
31 & 44.94 & 44.9466996231375 & -0.00669962313745742 \tabularnewline
32 & 44.94 & 44.9761742773252 & -0.0361742773251947 \tabularnewline
33 & 44.95 & 44.9733376991006 & -0.0233376991006367 \tabularnewline
34 & 45.28 & 44.9815076913168 & 0.298492308683201 \tabularnewline
35 & 45.34 & 45.3349137368722 & 0.00508626312777238 \tabularnewline
36 & 45.34 & 45.3953125722962 & -0.0553125722961667 \tabularnewline
37 & 45.34 & 45.3909752793433 & -0.0509752793432483 \tabularnewline
38 & 45.36 & 45.3869780918922 & -0.0269780918921825 \tabularnewline
39 & 45.44 & 45.4048626254984 & 0.0351373745016161 \tabularnewline
40 & 45.62 & 45.4876178957829 & 0.132382104217065 \tabularnewline
41 & 45.75 & 45.6779985369984 & 0.0720014630015555 \tabularnewline
42 & 45.77 & 45.813644476522 & -0.0436444765219974 \tabularnewline
43 & 45.77 & 45.8302221283542 & -0.0602221283542264 \tabularnewline
44 & 45.77 & 45.8254998563268 & -0.0554998563267759 \tabularnewline
45 & 46.09 & 45.8211478776402 & 0.268852122359831 \tabularnewline
46 & 46.25 & 46.1622297107078 & 0.0877702892922017 \tabularnewline
47 & 46.28 & 46.3291121506563 & -0.0491121506562493 \tabularnewline
48 & 46.29 & 46.3552610590129 & -0.0652610590128617 \tabularnewline
49 & 46.29 & 46.3601436631008 & -0.070143663100751 \tabularnewline
50 & 46.29 & 46.3546434015322 & -0.0646434015321944 \tabularnewline
51 & 46.3 & 46.3495744387579 & -0.0495744387579222 \tabularnewline
52 & 46.34 & 46.3556870971474 & -0.0156870971474348 \tabularnewline
53 & 46.34 & 46.3944570054507 & -0.0544570054506579 \tabularnewline
54 & 46.35 & 46.390186801116 & -0.040186801116036 \tabularnewline
55 & 46.42 & 46.3970355839145 & 0.0229644160855074 \tabularnewline
56 & 46.52 & 46.4688363209969 & 0.0511636790031247 \tabularnewline
57 & 46.59 & 46.5728482816628 & 0.0171517183371606 \tabularnewline
58 & 46.66 & 46.6441932205074 & 0.0158067794925785 \tabularnewline
59 & 46.67 & 46.7154326970035 & -0.0454326970035339 \tabularnewline
60 & 46.72 & 46.7218701268976 & -0.00187012689759314 \tabularnewline
61 & 46.72 & 46.7717234823306 & -0.0517234823305941 \tabularnewline
62 & 46.72 & 46.7676676251159 & -0.0476676251158565 \tabularnewline
63 & 46.76 & 46.7639298048353 & -0.00392980483531602 \tabularnewline
64 & 46.89 & 46.8036216522018 & 0.0863783477981812 \tabularnewline
65 & 47.02 & 46.9403949441251 & 0.0796050558748931 \tabularnewline
66 & 47.02 & 47.0766371135548 & -0.0566371135547712 \tabularnewline
67 & 47.04 & 47.0721959577145 & -0.0321959577144781 \tabularnewline
68 & 47.18 & 47.0896713363723 & 0.0903286636276661 \tabularnewline
69 & 47.22 & 47.236754389283 & -0.0167543892830011 \tabularnewline
70 & 47.8 & 47.2754406066916 & 0.524559393308387 \tabularnewline
71 & 47.88 & 47.8965735293805 & -0.016573529380544 \tabularnewline
72 & 47.91 & 47.9752739287798 & -0.0652739287797672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13548&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]44.14[/C][C]44.13[/C][C]0.00999999999999801[/C][/ROW]
[ROW][C]4[/C][C]44.14[/C][C]44.1407841423338[/C][C]-0.000784142333806415[/C][/ROW]
[ROW][C]5[/C][C]44.14[/C][C]44.1407226544138[/C][C]-0.000722654413841894[/C][/ROW]
[ROW][C]6[/C][C]44.14[/C][C]44.140665988022[/C][C]-0.000665988021978592[/C][/ROW]
[ROW][C]7[/C][C]44.15[/C][C]44.1406137650818[/C][C]0.00938623491820323[/C][/ROW]
[ROW][C]8[/C][C]44.17[/C][C]44.1513497794972[/C][C]0.0186502205027637[/C][/ROW]
[ROW][C]9[/C][C]44.19[/C][C]44.1728122222403[/C][C]0.0171877777596521[/C][/ROW]
[ROW][C]10[/C][C]44.26[/C][C]44.1941599886569[/C][C]0.0658400113431128[/C][/ROW]
[ROW][C]11[/C][C]44.27[/C][C]44.2693227826721[/C][C]0.000677217327869073[/C][/ROW]
[ROW][C]12[/C][C]44.29[/C][C]44.2793758861497[/C][C]0.0106241138502625[/C][/ROW]
[ROW][C]13[/C][C]44.29[/C][C]44.3002089678927[/C][C]-0.0102089678926518[/C][/ROW]
[ROW][C]14[/C][C]44.29[/C][C]44.2994084395017[/C][C]-0.00940843950174042[/C][/ROW]
[ROW][C]15[/C][C]44.29[/C][C]44.2986706839309[/C][C]-0.00867068393090165[/C][/ROW]
[ROW][C]16[/C][C]44.32[/C][C]44.2979907788976[/C][C]0.0220092211024294[/C][/ROW]
[ROW][C]17[/C][C]44.33[/C][C]44.3297166150976[/C][C]0.000283384902374451[/C][/ROW]
[ROW][C]18[/C][C]44.34[/C][C]44.3397388365075[/C][C]0.000261163492510263[/C][/ROW]
[ROW][C]19[/C][C]44.34[/C][C]44.3497593154426[/C][C]-0.00975931544255104[/C][/ROW]
[ROW][C]20[/C][C]44.34[/C][C]44.3489940462038[/C][C]-0.00899404620380295[/C][/ROW]
[ROW][C]21[/C][C]44.37[/C][C]44.3482887849657[/C][C]0.0217112150342516[/C][/ROW]
[ROW][C]22[/C][C]44.47[/C][C]44.3799912532484[/C][C]0.090008746751586[/C][/ROW]
[ROW][C]23[/C][C]44.51[/C][C]44.4870492201225[/C][C]0.0229507798774975[/C][/ROW]
[ROW][C]24[/C][C]44.51[/C][C]44.5288488879321[/C][C]-0.0188488879320872[/C][/ROW]
[ROW][C]25[/C][C]44.51[/C][C]44.5273708668348[/C][C]-0.0173708668348098[/C][/ROW]
[ROW][C]26[/C][C]44.52[/C][C]44.5260087436288[/C][C]-0.00600874362879722[/C][/ROW]
[ROW][C]27[/C][C]44.7[/C][C]44.5355375726036[/C][C]0.164462427396430[/C][/ROW]
[ROW][C]28[/C][C]44.84[/C][C]44.7284337677678[/C][C]0.111566232232207[/C][/ROW]
[ROW][C]29[/C][C]44.9[/C][C]44.8771821483395[/C][C]0.0228178516605411[/C][/ROW]
[ROW][C]30[/C][C]44.91[/C][C]44.9389713926848[/C][C]-0.0289713926848165[/C][/ROW]
[ROW][C]31[/C][C]44.94[/C][C]44.9466996231375[/C][C]-0.00669962313745742[/C][/ROW]
[ROW][C]32[/C][C]44.94[/C][C]44.9761742773252[/C][C]-0.0361742773251947[/C][/ROW]
[ROW][C]33[/C][C]44.95[/C][C]44.9733376991006[/C][C]-0.0233376991006367[/C][/ROW]
[ROW][C]34[/C][C]45.28[/C][C]44.9815076913168[/C][C]0.298492308683201[/C][/ROW]
[ROW][C]35[/C][C]45.34[/C][C]45.3349137368722[/C][C]0.00508626312777238[/C][/ROW]
[ROW][C]36[/C][C]45.34[/C][C]45.3953125722962[/C][C]-0.0553125722961667[/C][/ROW]
[ROW][C]37[/C][C]45.34[/C][C]45.3909752793433[/C][C]-0.0509752793432483[/C][/ROW]
[ROW][C]38[/C][C]45.36[/C][C]45.3869780918922[/C][C]-0.0269780918921825[/C][/ROW]
[ROW][C]39[/C][C]45.44[/C][C]45.4048626254984[/C][C]0.0351373745016161[/C][/ROW]
[ROW][C]40[/C][C]45.62[/C][C]45.4876178957829[/C][C]0.132382104217065[/C][/ROW]
[ROW][C]41[/C][C]45.75[/C][C]45.6779985369984[/C][C]0.0720014630015555[/C][/ROW]
[ROW][C]42[/C][C]45.77[/C][C]45.813644476522[/C][C]-0.0436444765219974[/C][/ROW]
[ROW][C]43[/C][C]45.77[/C][C]45.8302221283542[/C][C]-0.0602221283542264[/C][/ROW]
[ROW][C]44[/C][C]45.77[/C][C]45.8254998563268[/C][C]-0.0554998563267759[/C][/ROW]
[ROW][C]45[/C][C]46.09[/C][C]45.8211478776402[/C][C]0.268852122359831[/C][/ROW]
[ROW][C]46[/C][C]46.25[/C][C]46.1622297107078[/C][C]0.0877702892922017[/C][/ROW]
[ROW][C]47[/C][C]46.28[/C][C]46.3291121506563[/C][C]-0.0491121506562493[/C][/ROW]
[ROW][C]48[/C][C]46.29[/C][C]46.3552610590129[/C][C]-0.0652610590128617[/C][/ROW]
[ROW][C]49[/C][C]46.29[/C][C]46.3601436631008[/C][C]-0.070143663100751[/C][/ROW]
[ROW][C]50[/C][C]46.29[/C][C]46.3546434015322[/C][C]-0.0646434015321944[/C][/ROW]
[ROW][C]51[/C][C]46.3[/C][C]46.3495744387579[/C][C]-0.0495744387579222[/C][/ROW]
[ROW][C]52[/C][C]46.34[/C][C]46.3556870971474[/C][C]-0.0156870971474348[/C][/ROW]
[ROW][C]53[/C][C]46.34[/C][C]46.3944570054507[/C][C]-0.0544570054506579[/C][/ROW]
[ROW][C]54[/C][C]46.35[/C][C]46.390186801116[/C][C]-0.040186801116036[/C][/ROW]
[ROW][C]55[/C][C]46.42[/C][C]46.3970355839145[/C][C]0.0229644160855074[/C][/ROW]
[ROW][C]56[/C][C]46.52[/C][C]46.4688363209969[/C][C]0.0511636790031247[/C][/ROW]
[ROW][C]57[/C][C]46.59[/C][C]46.5728482816628[/C][C]0.0171517183371606[/C][/ROW]
[ROW][C]58[/C][C]46.66[/C][C]46.6441932205074[/C][C]0.0158067794925785[/C][/ROW]
[ROW][C]59[/C][C]46.67[/C][C]46.7154326970035[/C][C]-0.0454326970035339[/C][/ROW]
[ROW][C]60[/C][C]46.72[/C][C]46.7218701268976[/C][C]-0.00187012689759314[/C][/ROW]
[ROW][C]61[/C][C]46.72[/C][C]46.7717234823306[/C][C]-0.0517234823305941[/C][/ROW]
[ROW][C]62[/C][C]46.72[/C][C]46.7676676251159[/C][C]-0.0476676251158565[/C][/ROW]
[ROW][C]63[/C][C]46.76[/C][C]46.7639298048353[/C][C]-0.00392980483531602[/C][/ROW]
[ROW][C]64[/C][C]46.89[/C][C]46.8036216522018[/C][C]0.0863783477981812[/C][/ROW]
[ROW][C]65[/C][C]47.02[/C][C]46.9403949441251[/C][C]0.0796050558748931[/C][/ROW]
[ROW][C]66[/C][C]47.02[/C][C]47.0766371135548[/C][C]-0.0566371135547712[/C][/ROW]
[ROW][C]67[/C][C]47.04[/C][C]47.0721959577145[/C][C]-0.0321959577144781[/C][/ROW]
[ROW][C]68[/C][C]47.18[/C][C]47.0896713363723[/C][C]0.0903286636276661[/C][/ROW]
[ROW][C]69[/C][C]47.22[/C][C]47.236754389283[/C][C]-0.0167543892830011[/C][/ROW]
[ROW][C]70[/C][C]47.8[/C][C]47.2754406066916[/C][C]0.524559393308387[/C][/ROW]
[ROW][C]71[/C][C]47.88[/C][C]47.8965735293805[/C][C]-0.016573529380544[/C][/ROW]
[ROW][C]72[/C][C]47.91[/C][C]47.9752739287798[/C][C]-0.0652739287797672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13548&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13548&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
344.1444.130.00999999999999801
444.1444.1407841423338-0.000784142333806415
544.1444.1407226544138-0.000722654413841894
644.1444.140665988022-0.000665988021978592
744.1544.14061376508180.00938623491820323
844.1744.15134977949720.0186502205027637
944.1944.17281222224030.0171877777596521
1044.2644.19415998865690.0658400113431128
1144.2744.26932278267210.000677217327869073
1244.2944.27937588614970.0106241138502625
1344.2944.3002089678927-0.0102089678926518
1444.2944.2994084395017-0.00940843950174042
1544.2944.2986706839309-0.00867068393090165
1644.3244.29799077889760.0220092211024294
1744.3344.32971661509760.000283384902374451
1844.3444.33973883650750.000261163492510263
1944.3444.3497593154426-0.00975931544255104
2044.3444.3489940462038-0.00899404620380295
2144.3744.34828878496570.0217112150342516
2244.4744.37999125324840.090008746751586
2344.5144.48704922012250.0229507798774975
2444.5144.5288488879321-0.0188488879320872
2544.5144.5273708668348-0.0173708668348098
2644.5244.5260087436288-0.00600874362879722
2744.744.53553757260360.164462427396430
2844.8444.72843376776780.111566232232207
2944.944.87718214833950.0228178516605411
3044.9144.9389713926848-0.0289713926848165
3144.9444.9466996231375-0.00669962313745742
3244.9444.9761742773252-0.0361742773251947
3344.9544.9733376991006-0.0233376991006367
3445.2844.98150769131680.298492308683201
3545.3445.33491373687220.00508626312777238
3645.3445.3953125722962-0.0553125722961667
3745.3445.3909752793433-0.0509752793432483
3845.3645.3869780918922-0.0269780918921825
3945.4445.40486262549840.0351373745016161
4045.6245.48761789578290.132382104217065
4145.7545.67799853699840.0720014630015555
4245.7745.813644476522-0.0436444765219974
4345.7745.8302221283542-0.0602221283542264
4445.7745.8254998563268-0.0554998563267759
4546.0945.82114787764020.268852122359831
4646.2546.16222971070780.0877702892922017
4746.2846.3291121506563-0.0491121506562493
4846.2946.3552610590129-0.0652610590128617
4946.2946.3601436631008-0.070143663100751
5046.2946.3546434015322-0.0646434015321944
5146.346.3495744387579-0.0495744387579222
5246.3446.3556870971474-0.0156870971474348
5346.3446.3944570054507-0.0544570054506579
5446.3546.390186801116-0.040186801116036
5546.4246.39703558391450.0229644160855074
5646.5246.46883632099690.0511636790031247
5746.5946.57284828166280.0171517183371606
5846.6646.64419322050740.0158067794925785
5946.6746.7154326970035-0.0454326970035339
6046.7246.7218701268976-0.00187012689759314
6146.7246.7717234823306-0.0517234823305941
6246.7246.7676676251159-0.0476676251158565
6346.7646.7639298048353-0.00392980483531602
6446.8946.80362165220180.0863783477981812
6547.0246.94039494412510.0796050558748931
6647.0247.0766371135548-0.0566371135547712
6747.0447.0721959577145-0.0321959577144781
6847.1847.08967133637230.0903286636276661
6947.2247.236754389283-0.0167543892830011
7047.847.27544060669160.524559393308387
7147.8847.8965735293805-0.016573529380544
7247.9147.9752739287798-0.0652739287797672







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7348.000155523694747.819243948028848.1810670993607
7448.090311047389547.824243238682748.3563788560962
7548.180466571084247.841952569210248.5189805729583
7648.27062209477947.86499857756348.676245611995
7748.360777618473747.8906598766348.8308953603175
7848.450933142168547.917608684167548.9842576001694
7948.541088665863247.945097236192949.1370800955335
8048.63124418955847.972665721176249.2898226579398
8148.721399713252748.000014303479749.4427851230258
8248.811555236947548.026939277960649.5961711959344
8348.901710760642248.05329814427549.7501233770095
8448.99186628433748.078989134562449.9047434341116

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 48.0001555236947 & 47.8192439480288 & 48.1810670993607 \tabularnewline
74 & 48.0903110473895 & 47.8242432386827 & 48.3563788560962 \tabularnewline
75 & 48.1804665710842 & 47.8419525692102 & 48.5189805729583 \tabularnewline
76 & 48.270622094779 & 47.864998577563 & 48.676245611995 \tabularnewline
77 & 48.3607776184737 & 47.89065987663 & 48.8308953603175 \tabularnewline
78 & 48.4509331421685 & 47.9176086841675 & 48.9842576001694 \tabularnewline
79 & 48.5410886658632 & 47.9450972361929 & 49.1370800955335 \tabularnewline
80 & 48.631244189558 & 47.9726657211762 & 49.2898226579398 \tabularnewline
81 & 48.7213997132527 & 48.0000143034797 & 49.4427851230258 \tabularnewline
82 & 48.8115552369475 & 48.0269392779606 & 49.5961711959344 \tabularnewline
83 & 48.9017107606422 & 48.053298144275 & 49.7501233770095 \tabularnewline
84 & 48.991866284337 & 48.0789891345624 & 49.9047434341116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13548&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]48.0001555236947[/C][C]47.8192439480288[/C][C]48.1810670993607[/C][/ROW]
[ROW][C]74[/C][C]48.0903110473895[/C][C]47.8242432386827[/C][C]48.3563788560962[/C][/ROW]
[ROW][C]75[/C][C]48.1804665710842[/C][C]47.8419525692102[/C][C]48.5189805729583[/C][/ROW]
[ROW][C]76[/C][C]48.270622094779[/C][C]47.864998577563[/C][C]48.676245611995[/C][/ROW]
[ROW][C]77[/C][C]48.3607776184737[/C][C]47.89065987663[/C][C]48.8308953603175[/C][/ROW]
[ROW][C]78[/C][C]48.4509331421685[/C][C]47.9176086841675[/C][C]48.9842576001694[/C][/ROW]
[ROW][C]79[/C][C]48.5410886658632[/C][C]47.9450972361929[/C][C]49.1370800955335[/C][/ROW]
[ROW][C]80[/C][C]48.631244189558[/C][C]47.9726657211762[/C][C]49.2898226579398[/C][/ROW]
[ROW][C]81[/C][C]48.7213997132527[/C][C]48.0000143034797[/C][C]49.4427851230258[/C][/ROW]
[ROW][C]82[/C][C]48.8115552369475[/C][C]48.0269392779606[/C][C]49.5961711959344[/C][/ROW]
[ROW][C]83[/C][C]48.9017107606422[/C][C]48.053298144275[/C][C]49.7501233770095[/C][/ROW]
[ROW][C]84[/C][C]48.991866284337[/C][C]48.0789891345624[/C][C]49.9047434341116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13548&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13548&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
7348.000155523694747.819243948028848.1810670993607
7448.090311047389547.824243238682748.3563788560962
7548.180466571084247.841952569210248.5189805729583
7648.27062209477947.86499857756348.676245611995
7748.360777618473747.8906598766348.8308953603175
7848.450933142168547.917608684167548.9842576001694
7948.541088665863247.945097236192949.1370800955335
8048.63124418955847.972665721176249.2898226579398
8148.721399713252748.000014303479749.4427851230258
8248.811555236947548.026939277960649.5961711959344
8348.901710760642248.05329814427549.7501233770095
8448.99186628433748.078989134562449.9047434341116



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')