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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 31 May 2010 20:29:45 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/31/t1275337831r18zpwocgzb0jaq.htm/, Retrieved Mon, 29 Apr 2024 11:22:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76792, Retrieved Mon, 29 Apr 2024 11:22:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact143

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2010-01-16 14:49:37] [b9c4c4888c8ec1a729f0d8175961f076]
- R PD    [Exponential Smoothing] [] [2010-05-31 20:29:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1
1
3
3
1
1
-2
1
1
-1
-4
-2
-1
-5
-4
-5
0
-2
-4
-6
-2
-2
-2
1
-2
0
-1
2
3
2
3
4
5
5
4
5
6
4
6
6
3
5
5
5
3
5
5
6
6
5
4
4
0
2
3
3
2
3
5
6
6
5
4
7
5
6
5
6
5
6
6
6
6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76792&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76792&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.427178567563865
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.427178567563865 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76792&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]0.427178567563865[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76792&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.427178567563865
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13-11.35890151515151-2.35890151515151
14-5-3.27377065511514-1.72622934488486
15-4-2.5945121672831-1.40548783271690
16-5-4.02823977972488-0.97176022027512
1700.514978414695782-0.514978414695782
18-2-1.91334266015361-0.0866573398463941
19-4-4.908694151791420.908694151791417
20-6-1.18718615234217-4.81281384765783
21-2-2.701450411069510.701450411069507
22-2-3.776805829251751.77680582925175
23-2-5.642792460272863.64279246027286
241-1.920002928494392.92000292849439
25-2-0.815536271769387-1.18446372823061
260-4.584105611691674.58410561169167
27-1-1.025479663819300.0254796638192989
282-1.599480158614293.59948015861429
2935.15812836103317-2.15812836103317
3022.27324033745255-0.273240337452547
313-0.2316567446170193.23165674461702
3241.204768679800592.79523132019941
3356.09918700935527-1.09918700935527
3454.870624508235190.129375491764812
3543.369768080373340.630231919626659
3655.39162698075596-0.391626980755959
3762.730309846854183.26969015314582
3844.16881973408876-0.168819734088759
3963.085819195611872.91418080438813
4065.79307399912110.206926000878902
4137.80337453365337-4.80337453365337
4254.868198296848220.131801703151781
4354.544006660579470.455993339420527
4454.544734330759360.455265669240639
4536.20876319934777-3.20876319934777
4654.782781894948780.217218105051216
4753.606351245254361.39364875474564
4865.368982776652460.631017223347541
4965.241798254231680.75820174576832
5053.637801962097961.36219803790204
5144.97482818702663-0.97482818702663
5244.47000812582455-0.470008125824545
5303.32112938065024-3.32112938065024
5423.84611122637495-1.84611122637495
5532.86270149557620.137298504423799
5632.72687273757740.273127262422599
5722.21426171745076-0.214261717450755
5834.02994278494165-1.02994278494165
5952.994636422658132.00536357734187
6064.581727729494051.41827227050595
6164.86369571074261.1363042892574
6253.767198742774951.23280125722505
6343.710250726482200.289749273517804
6474.034802804029312.96519719597069
6552.720186786268892.27981321373111
6666.48269327847014-0.482693278470141
6757.21784607675214-2.21784607675214
6866.1537556538837-0.153755653883697
6955.1796025474472-0.179602547447201
7066.542849672042-0.542849672041998
7167.45430758632294-1.45430758632294
7267.22720303786996-1.22720303786996
7366.21756336344099-0.217563363440993

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & -1 & 1.35890151515151 & -2.35890151515151 \tabularnewline
14 & -5 & -3.27377065511514 & -1.72622934488486 \tabularnewline
15 & -4 & -2.5945121672831 & -1.40548783271690 \tabularnewline
16 & -5 & -4.02823977972488 & -0.97176022027512 \tabularnewline
17 & 0 & 0.514978414695782 & -0.514978414695782 \tabularnewline
18 & -2 & -1.91334266015361 & -0.0866573398463941 \tabularnewline
19 & -4 & -4.90869415179142 & 0.908694151791417 \tabularnewline
20 & -6 & -1.18718615234217 & -4.81281384765783 \tabularnewline
21 & -2 & -2.70145041106951 & 0.701450411069507 \tabularnewline
22 & -2 & -3.77680582925175 & 1.77680582925175 \tabularnewline
23 & -2 & -5.64279246027286 & 3.64279246027286 \tabularnewline
24 & 1 & -1.92000292849439 & 2.92000292849439 \tabularnewline
25 & -2 & -0.815536271769387 & -1.18446372823061 \tabularnewline
26 & 0 & -4.58410561169167 & 4.58410561169167 \tabularnewline
27 & -1 & -1.02547966381930 & 0.0254796638192989 \tabularnewline
28 & 2 & -1.59948015861429 & 3.59948015861429 \tabularnewline
29 & 3 & 5.15812836103317 & -2.15812836103317 \tabularnewline
30 & 2 & 2.27324033745255 & -0.273240337452547 \tabularnewline
31 & 3 & -0.231656744617019 & 3.23165674461702 \tabularnewline
32 & 4 & 1.20476867980059 & 2.79523132019941 \tabularnewline
33 & 5 & 6.09918700935527 & -1.09918700935527 \tabularnewline
34 & 5 & 4.87062450823519 & 0.129375491764812 \tabularnewline
35 & 4 & 3.36976808037334 & 0.630231919626659 \tabularnewline
36 & 5 & 5.39162698075596 & -0.391626980755959 \tabularnewline
37 & 6 & 2.73030984685418 & 3.26969015314582 \tabularnewline
38 & 4 & 4.16881973408876 & -0.168819734088759 \tabularnewline
39 & 6 & 3.08581919561187 & 2.91418080438813 \tabularnewline
40 & 6 & 5.7930739991211 & 0.206926000878902 \tabularnewline
41 & 3 & 7.80337453365337 & -4.80337453365337 \tabularnewline
42 & 5 & 4.86819829684822 & 0.131801703151781 \tabularnewline
43 & 5 & 4.54400666057947 & 0.455993339420527 \tabularnewline
44 & 5 & 4.54473433075936 & 0.455265669240639 \tabularnewline
45 & 3 & 6.20876319934777 & -3.20876319934777 \tabularnewline
46 & 5 & 4.78278189494878 & 0.217218105051216 \tabularnewline
47 & 5 & 3.60635124525436 & 1.39364875474564 \tabularnewline
48 & 6 & 5.36898277665246 & 0.631017223347541 \tabularnewline
49 & 6 & 5.24179825423168 & 0.75820174576832 \tabularnewline
50 & 5 & 3.63780196209796 & 1.36219803790204 \tabularnewline
51 & 4 & 4.97482818702663 & -0.97482818702663 \tabularnewline
52 & 4 & 4.47000812582455 & -0.470008125824545 \tabularnewline
53 & 0 & 3.32112938065024 & -3.32112938065024 \tabularnewline
54 & 2 & 3.84611122637495 & -1.84611122637495 \tabularnewline
55 & 3 & 2.8627014955762 & 0.137298504423799 \tabularnewline
56 & 3 & 2.7268727375774 & 0.273127262422599 \tabularnewline
57 & 2 & 2.21426171745076 & -0.214261717450755 \tabularnewline
58 & 3 & 4.02994278494165 & -1.02994278494165 \tabularnewline
59 & 5 & 2.99463642265813 & 2.00536357734187 \tabularnewline
60 & 6 & 4.58172772949405 & 1.41827227050595 \tabularnewline
61 & 6 & 4.8636957107426 & 1.1363042892574 \tabularnewline
62 & 5 & 3.76719874277495 & 1.23280125722505 \tabularnewline
63 & 4 & 3.71025072648220 & 0.289749273517804 \tabularnewline
64 & 7 & 4.03480280402931 & 2.96519719597069 \tabularnewline
65 & 5 & 2.72018678626889 & 2.27981321373111 \tabularnewline
66 & 6 & 6.48269327847014 & -0.482693278470141 \tabularnewline
67 & 5 & 7.21784607675214 & -2.21784607675214 \tabularnewline
68 & 6 & 6.1537556538837 & -0.153755653883697 \tabularnewline
69 & 5 & 5.1796025474472 & -0.179602547447201 \tabularnewline
70 & 6 & 6.542849672042 & -0.542849672041998 \tabularnewline
71 & 6 & 7.45430758632294 & -1.45430758632294 \tabularnewline
72 & 6 & 7.22720303786996 & -1.22720303786996 \tabularnewline
73 & 6 & 6.21756336344099 & -0.217563363440993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76792&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]-1[/C][C]1.35890151515151[/C][C]-2.35890151515151[/C][/ROW]
[ROW][C]14[/C][C]-5[/C][C]-3.27377065511514[/C][C]-1.72622934488486[/C][/ROW]
[ROW][C]15[/C][C]-4[/C][C]-2.5945121672831[/C][C]-1.40548783271690[/C][/ROW]
[ROW][C]16[/C][C]-5[/C][C]-4.02823977972488[/C][C]-0.97176022027512[/C][/ROW]
[ROW][C]17[/C][C]0[/C][C]0.514978414695782[/C][C]-0.514978414695782[/C][/ROW]
[ROW][C]18[/C][C]-2[/C][C]-1.91334266015361[/C][C]-0.0866573398463941[/C][/ROW]
[ROW][C]19[/C][C]-4[/C][C]-4.90869415179142[/C][C]0.908694151791417[/C][/ROW]
[ROW][C]20[/C][C]-6[/C][C]-1.18718615234217[/C][C]-4.81281384765783[/C][/ROW]
[ROW][C]21[/C][C]-2[/C][C]-2.70145041106951[/C][C]0.701450411069507[/C][/ROW]
[ROW][C]22[/C][C]-2[/C][C]-3.77680582925175[/C][C]1.77680582925175[/C][/ROW]
[ROW][C]23[/C][C]-2[/C][C]-5.64279246027286[/C][C]3.64279246027286[/C][/ROW]
[ROW][C]24[/C][C]1[/C][C]-1.92000292849439[/C][C]2.92000292849439[/C][/ROW]
[ROW][C]25[/C][C]-2[/C][C]-0.815536271769387[/C][C]-1.18446372823061[/C][/ROW]
[ROW][C]26[/C][C]0[/C][C]-4.58410561169167[/C][C]4.58410561169167[/C][/ROW]
[ROW][C]27[/C][C]-1[/C][C]-1.02547966381930[/C][C]0.0254796638192989[/C][/ROW]
[ROW][C]28[/C][C]2[/C][C]-1.59948015861429[/C][C]3.59948015861429[/C][/ROW]
[ROW][C]29[/C][C]3[/C][C]5.15812836103317[/C][C]-2.15812836103317[/C][/ROW]
[ROW][C]30[/C][C]2[/C][C]2.27324033745255[/C][C]-0.273240337452547[/C][/ROW]
[ROW][C]31[/C][C]3[/C][C]-0.231656744617019[/C][C]3.23165674461702[/C][/ROW]
[ROW][C]32[/C][C]4[/C][C]1.20476867980059[/C][C]2.79523132019941[/C][/ROW]
[ROW][C]33[/C][C]5[/C][C]6.09918700935527[/C][C]-1.09918700935527[/C][/ROW]
[ROW][C]34[/C][C]5[/C][C]4.87062450823519[/C][C]0.129375491764812[/C][/ROW]
[ROW][C]35[/C][C]4[/C][C]3.36976808037334[/C][C]0.630231919626659[/C][/ROW]
[ROW][C]36[/C][C]5[/C][C]5.39162698075596[/C][C]-0.391626980755959[/C][/ROW]
[ROW][C]37[/C][C]6[/C][C]2.73030984685418[/C][C]3.26969015314582[/C][/ROW]
[ROW][C]38[/C][C]4[/C][C]4.16881973408876[/C][C]-0.168819734088759[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]3.08581919561187[/C][C]2.91418080438813[/C][/ROW]
[ROW][C]40[/C][C]6[/C][C]5.7930739991211[/C][C]0.206926000878902[/C][/ROW]
[ROW][C]41[/C][C]3[/C][C]7.80337453365337[/C][C]-4.80337453365337[/C][/ROW]
[ROW][C]42[/C][C]5[/C][C]4.86819829684822[/C][C]0.131801703151781[/C][/ROW]
[ROW][C]43[/C][C]5[/C][C]4.54400666057947[/C][C]0.455993339420527[/C][/ROW]
[ROW][C]44[/C][C]5[/C][C]4.54473433075936[/C][C]0.455265669240639[/C][/ROW]
[ROW][C]45[/C][C]3[/C][C]6.20876319934777[/C][C]-3.20876319934777[/C][/ROW]
[ROW][C]46[/C][C]5[/C][C]4.78278189494878[/C][C]0.217218105051216[/C][/ROW]
[ROW][C]47[/C][C]5[/C][C]3.60635124525436[/C][C]1.39364875474564[/C][/ROW]
[ROW][C]48[/C][C]6[/C][C]5.36898277665246[/C][C]0.631017223347541[/C][/ROW]
[ROW][C]49[/C][C]6[/C][C]5.24179825423168[/C][C]0.75820174576832[/C][/ROW]
[ROW][C]50[/C][C]5[/C][C]3.63780196209796[/C][C]1.36219803790204[/C][/ROW]
[ROW][C]51[/C][C]4[/C][C]4.97482818702663[/C][C]-0.97482818702663[/C][/ROW]
[ROW][C]52[/C][C]4[/C][C]4.47000812582455[/C][C]-0.470008125824545[/C][/ROW]
[ROW][C]53[/C][C]0[/C][C]3.32112938065024[/C][C]-3.32112938065024[/C][/ROW]
[ROW][C]54[/C][C]2[/C][C]3.84611122637495[/C][C]-1.84611122637495[/C][/ROW]
[ROW][C]55[/C][C]3[/C][C]2.8627014955762[/C][C]0.137298504423799[/C][/ROW]
[ROW][C]56[/C][C]3[/C][C]2.7268727375774[/C][C]0.273127262422599[/C][/ROW]
[ROW][C]57[/C][C]2[/C][C]2.21426171745076[/C][C]-0.214261717450755[/C][/ROW]
[ROW][C]58[/C][C]3[/C][C]4.02994278494165[/C][C]-1.02994278494165[/C][/ROW]
[ROW][C]59[/C][C]5[/C][C]2.99463642265813[/C][C]2.00536357734187[/C][/ROW]
[ROW][C]60[/C][C]6[/C][C]4.58172772949405[/C][C]1.41827227050595[/C][/ROW]
[ROW][C]61[/C][C]6[/C][C]4.8636957107426[/C][C]1.1363042892574[/C][/ROW]
[ROW][C]62[/C][C]5[/C][C]3.76719874277495[/C][C]1.23280125722505[/C][/ROW]
[ROW][C]63[/C][C]4[/C][C]3.71025072648220[/C][C]0.289749273517804[/C][/ROW]
[ROW][C]64[/C][C]7[/C][C]4.03480280402931[/C][C]2.96519719597069[/C][/ROW]
[ROW][C]65[/C][C]5[/C][C]2.72018678626889[/C][C]2.27981321373111[/C][/ROW]
[ROW][C]66[/C][C]6[/C][C]6.48269327847014[/C][C]-0.482693278470141[/C][/ROW]
[ROW][C]67[/C][C]5[/C][C]7.21784607675214[/C][C]-2.21784607675214[/C][/ROW]
[ROW][C]68[/C][C]6[/C][C]6.1537556538837[/C][C]-0.153755653883697[/C][/ROW]
[ROW][C]69[/C][C]5[/C][C]5.1796025474472[/C][C]-0.179602547447201[/C][/ROW]
[ROW][C]70[/C][C]6[/C][C]6.542849672042[/C][C]-0.542849672041998[/C][/ROW]
[ROW][C]71[/C][C]6[/C][C]7.45430758632294[/C][C]-1.45430758632294[/C][/ROW]
[ROW][C]72[/C][C]6[/C][C]7.22720303786996[/C][C]-1.22720303786996[/C][/ROW]
[ROW][C]73[/C][C]6[/C][C]6.21756336344099[/C][C]-0.217563363440993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76792&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13-11.35890151515151-2.35890151515151
14-5-3.27377065511514-1.72622934488486
15-4-2.5945121672831-1.40548783271690
16-5-4.02823977972488-0.97176022027512
1700.514978414695782-0.514978414695782
18-2-1.91334266015361-0.0866573398463941
19-4-4.908694151791420.908694151791417
20-6-1.18718615234217-4.81281384765783
21-2-2.701450411069510.701450411069507
22-2-3.776805829251751.77680582925175
23-2-5.642792460272863.64279246027286
241-1.920002928494392.92000292849439
25-2-0.815536271769387-1.18446372823061
260-4.584105611691674.58410561169167
27-1-1.025479663819300.0254796638192989
282-1.599480158614293.59948015861429
2935.15812836103317-2.15812836103317
3022.27324033745255-0.273240337452547
313-0.2316567446170193.23165674461702
3241.204768679800592.79523132019941
3356.09918700935527-1.09918700935527
3454.870624508235190.129375491764812
3543.369768080373340.630231919626659
3655.39162698075596-0.391626980755959
3762.730309846854183.26969015314582
3844.16881973408876-0.168819734088759
3963.085819195611872.91418080438813
4065.79307399912110.206926000878902
4137.80337453365337-4.80337453365337
4254.868198296848220.131801703151781
4354.544006660579470.455993339420527
4454.544734330759360.455265669240639
4536.20876319934777-3.20876319934777
4654.782781894948780.217218105051216
4753.606351245254361.39364875474564
4865.368982776652460.631017223347541
4965.241798254231680.75820174576832
5053.637801962097961.36219803790204
5144.97482818702663-0.97482818702663
5244.47000812582455-0.470008125824545
5303.32112938065024-3.32112938065024
5423.84611122637495-1.84611122637495
5532.86270149557620.137298504423799
5632.72687273757740.273127262422599
5722.21426171745076-0.214261717450755
5834.02994278494165-1.02994278494165
5952.994636422658132.00536357734187
6064.581727729494051.41827227050595
6164.86369571074261.1363042892574
6253.767198742774951.23280125722505
6343.710250726482200.289749273517804
6474.034802804029312.96519719597069
6552.720186786268892.27981321373111
6666.48269327847014-0.482693278470141
6757.21784607675214-2.21784607675214
6866.1537556538837-0.153755653883697
6955.1796025474472-0.179602547447201
7066.542849672042-0.542849672041998
7167.45430758632294-1.45430758632294
7267.22720303786996-1.22720303786996
7366.21756336344099-0.217563363440993






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
744.597998682339560.7877409747445368.4082563899346
753.47422400272556-0.6691251585576967.61757316400881
765.207555312006410.7559689940377279.65914162997509
772.23366796905158-2.506152620416476.97348855851963
783.43986419232116-1.571640341685038.45136872632735
793.38728050246528-1.881918314089658.65647931902021
804.45296162244616-1.061903257349469.96782650224179
813.52968398139548-2.220360637250769.27972860004171
824.76157772670089-1.2143984772713010.7375539306731
835.38282675822359-0.81084501742461911.5764985338718
845.9070615940509-0.49690971588487512.3110329039867
856-0.60758102579906512.6075810257991

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 4.59799868233956 & 0.787740974744536 & 8.4082563899346 \tabularnewline
75 & 3.47422400272556 & -0.669125158557696 & 7.61757316400881 \tabularnewline
76 & 5.20755531200641 & 0.755968994037727 & 9.65914162997509 \tabularnewline
77 & 2.23366796905158 & -2.50615262041647 & 6.97348855851963 \tabularnewline
78 & 3.43986419232116 & -1.57164034168503 & 8.45136872632735 \tabularnewline
79 & 3.38728050246528 & -1.88191831408965 & 8.65647931902021 \tabularnewline
80 & 4.45296162244616 & -1.06190325734946 & 9.96782650224179 \tabularnewline
81 & 3.52968398139548 & -2.22036063725076 & 9.27972860004171 \tabularnewline
82 & 4.76157772670089 & -1.21439847727130 & 10.7375539306731 \tabularnewline
83 & 5.38282675822359 & -0.810845017424619 & 11.5764985338718 \tabularnewline
84 & 5.9070615940509 & -0.496909715884875 & 12.3110329039867 \tabularnewline
85 & 6 & -0.607581025799065 & 12.6075810257991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76792&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]74[/C][C]4.59799868233956[/C][C]0.787740974744536[/C][C]8.4082563899346[/C][/ROW]
[ROW][C]75[/C][C]3.47422400272556[/C][C]-0.669125158557696[/C][C]7.61757316400881[/C][/ROW]
[ROW][C]76[/C][C]5.20755531200641[/C][C]0.755968994037727[/C][C]9.65914162997509[/C][/ROW]
[ROW][C]77[/C][C]2.23366796905158[/C][C]-2.50615262041647[/C][C]6.97348855851963[/C][/ROW]
[ROW][C]78[/C][C]3.43986419232116[/C][C]-1.57164034168503[/C][C]8.45136872632735[/C][/ROW]
[ROW][C]79[/C][C]3.38728050246528[/C][C]-1.88191831408965[/C][C]8.65647931902021[/C][/ROW]
[ROW][C]80[/C][C]4.45296162244616[/C][C]-1.06190325734946[/C][C]9.96782650224179[/C][/ROW]
[ROW][C]81[/C][C]3.52968398139548[/C][C]-2.22036063725076[/C][C]9.27972860004171[/C][/ROW]
[ROW][C]82[/C][C]4.76157772670089[/C][C]-1.21439847727130[/C][C]10.7375539306731[/C][/ROW]
[ROW][C]83[/C][C]5.38282675822359[/C][C]-0.810845017424619[/C][C]11.5764985338718[/C][/ROW]
[ROW][C]84[/C][C]5.9070615940509[/C][C]-0.496909715884875[/C][C]12.3110329039867[/C][/ROW]
[ROW][C]85[/C][C]6[/C][C]-0.607581025799065[/C][C]12.6075810257991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76792&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76792&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
744.597998682339560.7877409747445368.4082563899346
753.47422400272556-0.6691251585576967.61757316400881
765.207555312006410.7559689940377279.65914162997509
772.23366796905158-2.506152620416476.97348855851963
783.43986419232116-1.571640341685038.45136872632735
793.38728050246528-1.881918314089658.65647931902021
804.45296162244616-1.061903257349469.96782650224179
813.52968398139548-2.220360637250769.27972860004171
824.76157772670089-1.2143984772713010.7375539306731
835.38282675822359-0.81084501742461911.5764985338718
845.9070615940509-0.49690971588487512.3110329039867
856-0.60758102579906512.6075810257991


Figures (Output of Computation)

Input Parameters & R Code

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')