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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 14:37:00 +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/2011/May/19/t1305815674ex6mrylvmlw4lg0.htm/, Retrieved Sat, 11 May 2024 14:56:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122047, Retrieved Sat, 11 May 2024 14:56:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords KDGP2W102
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Datareeks-exponen...] [2011-05-19 14:37:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
5.81    
5.76    
5.99    
6.12    
6.03    
6.25    
5.80    
5.67    
5.89    
5.91    
5.86    
6.07    
6.27    
6.68    
6.77    
6.71    
6.62
6.50
5.89
6.05
6.43
6.47
6.62
6.77
6.70
6.95
6.73
7.07
7.28
7.32
6.76
6.93
6.99
7.16
7.28
7.08
7.34
7.87
6.28
6.30
6.36
6.28
5.89
6.04
5.96
6.10
6.26
6.02
6.25
6.41
6.22
6.57
6.18
6.26
6.10
6.02
6.06
6.35
6.21
6.48
6.74
6.53
6.80
6.75
6.56
6.66
6.18
6.40
6.43
6.54
6.44
6.64
6.82
6.97
7.00
6.91
6.74
6.98
6.37
6.56
6.63
6.87
6.68
6.75
6.84
7.15
7.09
6.97
7.15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122047&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122047&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122047&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.747355048775388
beta0.0237084331610309
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.747355048775388 \tabularnewline
beta & 0.0237084331610309 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122047&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]0.747355048775388[/C][/ROW]
[ROW][C]beta[/C][C]0.0237084331610309[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122047&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122047&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
alpha0.747355048775388
beta0.0237084331610309
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35.995.710.28
46.125.874220626479120.245779373520885
56.036.017221165627150.012778834372849
66.255.98631399875030.263686001249696
75.86.14759572113559-0.347595721135595
85.675.84587404654151-0.175874046541509
95.895.669373187529620.220626812470379
105.915.7931084493830.116891550617004
115.865.841387796196020.0186122038039809
126.075.816547359492830.253452640507168
136.275.97170693913730.298293060862697
146.686.165663573888930.514336426111071
156.776.530194638670660.239805361329338
166.716.693802545547130.0161974544528691
176.626.69058295076879-0.0705829507687863
186.56.62125694972623-0.121256949726231
195.896.51191097424355-0.62191097424355
206.056.017379283349690.0326207166503059
216.436.012593150220670.417406849779331
226.476.302774748581230.167225251418769
236.626.408944866515980.21105513348402
246.776.551611073222250.21838892677775
256.76.70362777717224-0.00362777717224194
266.956.689654897317660.260345102682343
276.736.87757643718208-0.147576437182083
287.076.758020904323270.311979095676734
297.286.987444357316540.29255564268346
307.327.207535276099320.112464723900678
316.767.2950270568849-0.535027056884906
326.936.889132646635750.0408673533642459
336.996.914359944438940.0756400555610552
347.166.966915033979580.19308496602042
357.287.110664368909130.169335631090873
367.087.23966491170327-0.159664911703271
377.347.11995619633620.220043803663798
387.877.28792357839180.582076421608201
396.287.73677145459763-1.45677145459763
406.36.6360641010529-0.336064101052899
416.366.3669684552111-0.00696845521109868
426.286.34370063042866-0.0637006304286558
435.896.27690504098203-0.386905040982032
446.045.961705581199660.0782944188003416
455.965.99556255521052-0.0355625552105243
466.15.943697825552890.15630217444711
476.266.037993628686720.222006371313278
486.026.18532744098824-0.165327440988238
496.256.040255999461730.209744000538274
506.416.179212467071550.230787532928451
516.226.33798516081268-0.117985160812681
526.576.234010287109140.335989712890864
536.186.47526910039816-0.295269100398162
546.266.23952169232440.020478307675603
556.16.24011255110735-0.14011255110735
566.026.1182024201307-0.098202420130697
576.066.025874026041770.0341259739582327
586.356.033046590441410.316953409558588
596.216.25720764291018-0.0472076429101804
606.486.20837464009440.271625359905596
616.746.402635917429020.337364082570978
626.536.652004986091-0.122004986090999
636.86.555900502389540.244099497610455
646.756.737731158523790.0122688414762138
656.566.74651939024106-0.18651939024106
666.666.603437367667240.0565626323327626
676.186.64302613356184-0.463026133561836
686.46.286093429154020.113906570845978
696.436.362352561116850.067647438883145
706.546.405238316330880.134761683669121
716.446.5006700319195-0.0606700319195008
726.646.448969879099740.191030120900264
736.826.588763895857360.231236104142642
746.976.762703241199230.207296758800766
7576.922424407855920.0775755921440808
766.916.98657233790162-0.0765723379016245
776.746.93416027822437-0.194160278224367
786.986.790428026022340.189571973977659
796.376.93683896312427-0.566838963124274
806.566.507898764820350.0521012351796468
816.636.542449810451820.087550189548181
826.876.605045079400690.264954920599312
836.686.8049193045963-0.124919304596299
846.756.711205661862860.0387943381371354
856.846.740531618607480.0994683813925157
867.156.816965070084160.333034929915841
877.097.073856579269340.0161434207306641
886.977.09420365824349-0.12420365824349
897.157.007460922087510.142539077912489

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5.99 & 5.71 & 0.28 \tabularnewline
4 & 6.12 & 5.87422062647912 & 0.245779373520885 \tabularnewline
5 & 6.03 & 6.01722116562715 & 0.012778834372849 \tabularnewline
6 & 6.25 & 5.9863139987503 & 0.263686001249696 \tabularnewline
7 & 5.8 & 6.14759572113559 & -0.347595721135595 \tabularnewline
8 & 5.67 & 5.84587404654151 & -0.175874046541509 \tabularnewline
9 & 5.89 & 5.66937318752962 & 0.220626812470379 \tabularnewline
10 & 5.91 & 5.793108449383 & 0.116891550617004 \tabularnewline
11 & 5.86 & 5.84138779619602 & 0.0186122038039809 \tabularnewline
12 & 6.07 & 5.81654735949283 & 0.253452640507168 \tabularnewline
13 & 6.27 & 5.9717069391373 & 0.298293060862697 \tabularnewline
14 & 6.68 & 6.16566357388893 & 0.514336426111071 \tabularnewline
15 & 6.77 & 6.53019463867066 & 0.239805361329338 \tabularnewline
16 & 6.71 & 6.69380254554713 & 0.0161974544528691 \tabularnewline
17 & 6.62 & 6.69058295076879 & -0.0705829507687863 \tabularnewline
18 & 6.5 & 6.62125694972623 & -0.121256949726231 \tabularnewline
19 & 5.89 & 6.51191097424355 & -0.62191097424355 \tabularnewline
20 & 6.05 & 6.01737928334969 & 0.0326207166503059 \tabularnewline
21 & 6.43 & 6.01259315022067 & 0.417406849779331 \tabularnewline
22 & 6.47 & 6.30277474858123 & 0.167225251418769 \tabularnewline
23 & 6.62 & 6.40894486651598 & 0.21105513348402 \tabularnewline
24 & 6.77 & 6.55161107322225 & 0.21838892677775 \tabularnewline
25 & 6.7 & 6.70362777717224 & -0.00362777717224194 \tabularnewline
26 & 6.95 & 6.68965489731766 & 0.260345102682343 \tabularnewline
27 & 6.73 & 6.87757643718208 & -0.147576437182083 \tabularnewline
28 & 7.07 & 6.75802090432327 & 0.311979095676734 \tabularnewline
29 & 7.28 & 6.98744435731654 & 0.29255564268346 \tabularnewline
30 & 7.32 & 7.20753527609932 & 0.112464723900678 \tabularnewline
31 & 6.76 & 7.2950270568849 & -0.535027056884906 \tabularnewline
32 & 6.93 & 6.88913264663575 & 0.0408673533642459 \tabularnewline
33 & 6.99 & 6.91435994443894 & 0.0756400555610552 \tabularnewline
34 & 7.16 & 6.96691503397958 & 0.19308496602042 \tabularnewline
35 & 7.28 & 7.11066436890913 & 0.169335631090873 \tabularnewline
36 & 7.08 & 7.23966491170327 & -0.159664911703271 \tabularnewline
37 & 7.34 & 7.1199561963362 & 0.220043803663798 \tabularnewline
38 & 7.87 & 7.2879235783918 & 0.582076421608201 \tabularnewline
39 & 6.28 & 7.73677145459763 & -1.45677145459763 \tabularnewline
40 & 6.3 & 6.6360641010529 & -0.336064101052899 \tabularnewline
41 & 6.36 & 6.3669684552111 & -0.00696845521109868 \tabularnewline
42 & 6.28 & 6.34370063042866 & -0.0637006304286558 \tabularnewline
43 & 5.89 & 6.27690504098203 & -0.386905040982032 \tabularnewline
44 & 6.04 & 5.96170558119966 & 0.0782944188003416 \tabularnewline
45 & 5.96 & 5.99556255521052 & -0.0355625552105243 \tabularnewline
46 & 6.1 & 5.94369782555289 & 0.15630217444711 \tabularnewline
47 & 6.26 & 6.03799362868672 & 0.222006371313278 \tabularnewline
48 & 6.02 & 6.18532744098824 & -0.165327440988238 \tabularnewline
49 & 6.25 & 6.04025599946173 & 0.209744000538274 \tabularnewline
50 & 6.41 & 6.17921246707155 & 0.230787532928451 \tabularnewline
51 & 6.22 & 6.33798516081268 & -0.117985160812681 \tabularnewline
52 & 6.57 & 6.23401028710914 & 0.335989712890864 \tabularnewline
53 & 6.18 & 6.47526910039816 & -0.295269100398162 \tabularnewline
54 & 6.26 & 6.2395216923244 & 0.020478307675603 \tabularnewline
55 & 6.1 & 6.24011255110735 & -0.14011255110735 \tabularnewline
56 & 6.02 & 6.1182024201307 & -0.098202420130697 \tabularnewline
57 & 6.06 & 6.02587402604177 & 0.0341259739582327 \tabularnewline
58 & 6.35 & 6.03304659044141 & 0.316953409558588 \tabularnewline
59 & 6.21 & 6.25720764291018 & -0.0472076429101804 \tabularnewline
60 & 6.48 & 6.2083746400944 & 0.271625359905596 \tabularnewline
61 & 6.74 & 6.40263591742902 & 0.337364082570978 \tabularnewline
62 & 6.53 & 6.652004986091 & -0.122004986090999 \tabularnewline
63 & 6.8 & 6.55590050238954 & 0.244099497610455 \tabularnewline
64 & 6.75 & 6.73773115852379 & 0.0122688414762138 \tabularnewline
65 & 6.56 & 6.74651939024106 & -0.18651939024106 \tabularnewline
66 & 6.66 & 6.60343736766724 & 0.0565626323327626 \tabularnewline
67 & 6.18 & 6.64302613356184 & -0.463026133561836 \tabularnewline
68 & 6.4 & 6.28609342915402 & 0.113906570845978 \tabularnewline
69 & 6.43 & 6.36235256111685 & 0.067647438883145 \tabularnewline
70 & 6.54 & 6.40523831633088 & 0.134761683669121 \tabularnewline
71 & 6.44 & 6.5006700319195 & -0.0606700319195008 \tabularnewline
72 & 6.64 & 6.44896987909974 & 0.191030120900264 \tabularnewline
73 & 6.82 & 6.58876389585736 & 0.231236104142642 \tabularnewline
74 & 6.97 & 6.76270324119923 & 0.207296758800766 \tabularnewline
75 & 7 & 6.92242440785592 & 0.0775755921440808 \tabularnewline
76 & 6.91 & 6.98657233790162 & -0.0765723379016245 \tabularnewline
77 & 6.74 & 6.93416027822437 & -0.194160278224367 \tabularnewline
78 & 6.98 & 6.79042802602234 & 0.189571973977659 \tabularnewline
79 & 6.37 & 6.93683896312427 & -0.566838963124274 \tabularnewline
80 & 6.56 & 6.50789876482035 & 0.0521012351796468 \tabularnewline
81 & 6.63 & 6.54244981045182 & 0.087550189548181 \tabularnewline
82 & 6.87 & 6.60504507940069 & 0.264954920599312 \tabularnewline
83 & 6.68 & 6.8049193045963 & -0.124919304596299 \tabularnewline
84 & 6.75 & 6.71120566186286 & 0.0387943381371354 \tabularnewline
85 & 6.84 & 6.74053161860748 & 0.0994683813925157 \tabularnewline
86 & 7.15 & 6.81696507008416 & 0.333034929915841 \tabularnewline
87 & 7.09 & 7.07385657926934 & 0.0161434207306641 \tabularnewline
88 & 6.97 & 7.09420365824349 & -0.12420365824349 \tabularnewline
89 & 7.15 & 7.00746092208751 & 0.142539077912489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122047&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]5.99[/C][C]5.71[/C][C]0.28[/C][/ROW]
[ROW][C]4[/C][C]6.12[/C][C]5.87422062647912[/C][C]0.245779373520885[/C][/ROW]
[ROW][C]5[/C][C]6.03[/C][C]6.01722116562715[/C][C]0.012778834372849[/C][/ROW]
[ROW][C]6[/C][C]6.25[/C][C]5.9863139987503[/C][C]0.263686001249696[/C][/ROW]
[ROW][C]7[/C][C]5.8[/C][C]6.14759572113559[/C][C]-0.347595721135595[/C][/ROW]
[ROW][C]8[/C][C]5.67[/C][C]5.84587404654151[/C][C]-0.175874046541509[/C][/ROW]
[ROW][C]9[/C][C]5.89[/C][C]5.66937318752962[/C][C]0.220626812470379[/C][/ROW]
[ROW][C]10[/C][C]5.91[/C][C]5.793108449383[/C][C]0.116891550617004[/C][/ROW]
[ROW][C]11[/C][C]5.86[/C][C]5.84138779619602[/C][C]0.0186122038039809[/C][/ROW]
[ROW][C]12[/C][C]6.07[/C][C]5.81654735949283[/C][C]0.253452640507168[/C][/ROW]
[ROW][C]13[/C][C]6.27[/C][C]5.9717069391373[/C][C]0.298293060862697[/C][/ROW]
[ROW][C]14[/C][C]6.68[/C][C]6.16566357388893[/C][C]0.514336426111071[/C][/ROW]
[ROW][C]15[/C][C]6.77[/C][C]6.53019463867066[/C][C]0.239805361329338[/C][/ROW]
[ROW][C]16[/C][C]6.71[/C][C]6.69380254554713[/C][C]0.0161974544528691[/C][/ROW]
[ROW][C]17[/C][C]6.62[/C][C]6.69058295076879[/C][C]-0.0705829507687863[/C][/ROW]
[ROW][C]18[/C][C]6.5[/C][C]6.62125694972623[/C][C]-0.121256949726231[/C][/ROW]
[ROW][C]19[/C][C]5.89[/C][C]6.51191097424355[/C][C]-0.62191097424355[/C][/ROW]
[ROW][C]20[/C][C]6.05[/C][C]6.01737928334969[/C][C]0.0326207166503059[/C][/ROW]
[ROW][C]21[/C][C]6.43[/C][C]6.01259315022067[/C][C]0.417406849779331[/C][/ROW]
[ROW][C]22[/C][C]6.47[/C][C]6.30277474858123[/C][C]0.167225251418769[/C][/ROW]
[ROW][C]23[/C][C]6.62[/C][C]6.40894486651598[/C][C]0.21105513348402[/C][/ROW]
[ROW][C]24[/C][C]6.77[/C][C]6.55161107322225[/C][C]0.21838892677775[/C][/ROW]
[ROW][C]25[/C][C]6.7[/C][C]6.70362777717224[/C][C]-0.00362777717224194[/C][/ROW]
[ROW][C]26[/C][C]6.95[/C][C]6.68965489731766[/C][C]0.260345102682343[/C][/ROW]
[ROW][C]27[/C][C]6.73[/C][C]6.87757643718208[/C][C]-0.147576437182083[/C][/ROW]
[ROW][C]28[/C][C]7.07[/C][C]6.75802090432327[/C][C]0.311979095676734[/C][/ROW]
[ROW][C]29[/C][C]7.28[/C][C]6.98744435731654[/C][C]0.29255564268346[/C][/ROW]
[ROW][C]30[/C][C]7.32[/C][C]7.20753527609932[/C][C]0.112464723900678[/C][/ROW]
[ROW][C]31[/C][C]6.76[/C][C]7.2950270568849[/C][C]-0.535027056884906[/C][/ROW]
[ROW][C]32[/C][C]6.93[/C][C]6.88913264663575[/C][C]0.0408673533642459[/C][/ROW]
[ROW][C]33[/C][C]6.99[/C][C]6.91435994443894[/C][C]0.0756400555610552[/C][/ROW]
[ROW][C]34[/C][C]7.16[/C][C]6.96691503397958[/C][C]0.19308496602042[/C][/ROW]
[ROW][C]35[/C][C]7.28[/C][C]7.11066436890913[/C][C]0.169335631090873[/C][/ROW]
[ROW][C]36[/C][C]7.08[/C][C]7.23966491170327[/C][C]-0.159664911703271[/C][/ROW]
[ROW][C]37[/C][C]7.34[/C][C]7.1199561963362[/C][C]0.220043803663798[/C][/ROW]
[ROW][C]38[/C][C]7.87[/C][C]7.2879235783918[/C][C]0.582076421608201[/C][/ROW]
[ROW][C]39[/C][C]6.28[/C][C]7.73677145459763[/C][C]-1.45677145459763[/C][/ROW]
[ROW][C]40[/C][C]6.3[/C][C]6.6360641010529[/C][C]-0.336064101052899[/C][/ROW]
[ROW][C]41[/C][C]6.36[/C][C]6.3669684552111[/C][C]-0.00696845521109868[/C][/ROW]
[ROW][C]42[/C][C]6.28[/C][C]6.34370063042866[/C][C]-0.0637006304286558[/C][/ROW]
[ROW][C]43[/C][C]5.89[/C][C]6.27690504098203[/C][C]-0.386905040982032[/C][/ROW]
[ROW][C]44[/C][C]6.04[/C][C]5.96170558119966[/C][C]0.0782944188003416[/C][/ROW]
[ROW][C]45[/C][C]5.96[/C][C]5.99556255521052[/C][C]-0.0355625552105243[/C][/ROW]
[ROW][C]46[/C][C]6.1[/C][C]5.94369782555289[/C][C]0.15630217444711[/C][/ROW]
[ROW][C]47[/C][C]6.26[/C][C]6.03799362868672[/C][C]0.222006371313278[/C][/ROW]
[ROW][C]48[/C][C]6.02[/C][C]6.18532744098824[/C][C]-0.165327440988238[/C][/ROW]
[ROW][C]49[/C][C]6.25[/C][C]6.04025599946173[/C][C]0.209744000538274[/C][/ROW]
[ROW][C]50[/C][C]6.41[/C][C]6.17921246707155[/C][C]0.230787532928451[/C][/ROW]
[ROW][C]51[/C][C]6.22[/C][C]6.33798516081268[/C][C]-0.117985160812681[/C][/ROW]
[ROW][C]52[/C][C]6.57[/C][C]6.23401028710914[/C][C]0.335989712890864[/C][/ROW]
[ROW][C]53[/C][C]6.18[/C][C]6.47526910039816[/C][C]-0.295269100398162[/C][/ROW]
[ROW][C]54[/C][C]6.26[/C][C]6.2395216923244[/C][C]0.020478307675603[/C][/ROW]
[ROW][C]55[/C][C]6.1[/C][C]6.24011255110735[/C][C]-0.14011255110735[/C][/ROW]
[ROW][C]56[/C][C]6.02[/C][C]6.1182024201307[/C][C]-0.098202420130697[/C][/ROW]
[ROW][C]57[/C][C]6.06[/C][C]6.02587402604177[/C][C]0.0341259739582327[/C][/ROW]
[ROW][C]58[/C][C]6.35[/C][C]6.03304659044141[/C][C]0.316953409558588[/C][/ROW]
[ROW][C]59[/C][C]6.21[/C][C]6.25720764291018[/C][C]-0.0472076429101804[/C][/ROW]
[ROW][C]60[/C][C]6.48[/C][C]6.2083746400944[/C][C]0.271625359905596[/C][/ROW]
[ROW][C]61[/C][C]6.74[/C][C]6.40263591742902[/C][C]0.337364082570978[/C][/ROW]
[ROW][C]62[/C][C]6.53[/C][C]6.652004986091[/C][C]-0.122004986090999[/C][/ROW]
[ROW][C]63[/C][C]6.8[/C][C]6.55590050238954[/C][C]0.244099497610455[/C][/ROW]
[ROW][C]64[/C][C]6.75[/C][C]6.73773115852379[/C][C]0.0122688414762138[/C][/ROW]
[ROW][C]65[/C][C]6.56[/C][C]6.74651939024106[/C][C]-0.18651939024106[/C][/ROW]
[ROW][C]66[/C][C]6.66[/C][C]6.60343736766724[/C][C]0.0565626323327626[/C][/ROW]
[ROW][C]67[/C][C]6.18[/C][C]6.64302613356184[/C][C]-0.463026133561836[/C][/ROW]
[ROW][C]68[/C][C]6.4[/C][C]6.28609342915402[/C][C]0.113906570845978[/C][/ROW]
[ROW][C]69[/C][C]6.43[/C][C]6.36235256111685[/C][C]0.067647438883145[/C][/ROW]
[ROW][C]70[/C][C]6.54[/C][C]6.40523831633088[/C][C]0.134761683669121[/C][/ROW]
[ROW][C]71[/C][C]6.44[/C][C]6.5006700319195[/C][C]-0.0606700319195008[/C][/ROW]
[ROW][C]72[/C][C]6.64[/C][C]6.44896987909974[/C][C]0.191030120900264[/C][/ROW]
[ROW][C]73[/C][C]6.82[/C][C]6.58876389585736[/C][C]0.231236104142642[/C][/ROW]
[ROW][C]74[/C][C]6.97[/C][C]6.76270324119923[/C][C]0.207296758800766[/C][/ROW]
[ROW][C]75[/C][C]7[/C][C]6.92242440785592[/C][C]0.0775755921440808[/C][/ROW]
[ROW][C]76[/C][C]6.91[/C][C]6.98657233790162[/C][C]-0.0765723379016245[/C][/ROW]
[ROW][C]77[/C][C]6.74[/C][C]6.93416027822437[/C][C]-0.194160278224367[/C][/ROW]
[ROW][C]78[/C][C]6.98[/C][C]6.79042802602234[/C][C]0.189571973977659[/C][/ROW]
[ROW][C]79[/C][C]6.37[/C][C]6.93683896312427[/C][C]-0.566838963124274[/C][/ROW]
[ROW][C]80[/C][C]6.56[/C][C]6.50789876482035[/C][C]0.0521012351796468[/C][/ROW]
[ROW][C]81[/C][C]6.63[/C][C]6.54244981045182[/C][C]0.087550189548181[/C][/ROW]
[ROW][C]82[/C][C]6.87[/C][C]6.60504507940069[/C][C]0.264954920599312[/C][/ROW]
[ROW][C]83[/C][C]6.68[/C][C]6.8049193045963[/C][C]-0.124919304596299[/C][/ROW]
[ROW][C]84[/C][C]6.75[/C][C]6.71120566186286[/C][C]0.0387943381371354[/C][/ROW]
[ROW][C]85[/C][C]6.84[/C][C]6.74053161860748[/C][C]0.0994683813925157[/C][/ROW]
[ROW][C]86[/C][C]7.15[/C][C]6.81696507008416[/C][C]0.333034929915841[/C][/ROW]
[ROW][C]87[/C][C]7.09[/C][C]7.07385657926934[/C][C]0.0161434207306641[/C][/ROW]
[ROW][C]88[/C][C]6.97[/C][C]7.09420365824349[/C][C]-0.12420365824349[/C][/ROW]
[ROW][C]89[/C][C]7.15[/C][C]7.00746092208751[/C][C]0.142539077912489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122047&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122047&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
35.995.710.28
46.125.874220626479120.245779373520885
56.036.017221165627150.012778834372849
66.255.98631399875030.263686001249696
75.86.14759572113559-0.347595721135595
85.675.84587404654151-0.175874046541509
95.895.669373187529620.220626812470379
105.915.7931084493830.116891550617004
115.865.841387796196020.0186122038039809
126.075.816547359492830.253452640507168
136.275.97170693913730.298293060862697
146.686.165663573888930.514336426111071
156.776.530194638670660.239805361329338
166.716.693802545547130.0161974544528691
176.626.69058295076879-0.0705829507687863
186.56.62125694972623-0.121256949726231
195.896.51191097424355-0.62191097424355
206.056.017379283349690.0326207166503059
216.436.012593150220670.417406849779331
226.476.302774748581230.167225251418769
236.626.408944866515980.21105513348402
246.776.551611073222250.21838892677775
256.76.70362777717224-0.00362777717224194
266.956.689654897317660.260345102682343
276.736.87757643718208-0.147576437182083
287.076.758020904323270.311979095676734
297.286.987444357316540.29255564268346
307.327.207535276099320.112464723900678
316.767.2950270568849-0.535027056884906
326.936.889132646635750.0408673533642459
336.996.914359944438940.0756400555610552
347.166.966915033979580.19308496602042
357.287.110664368909130.169335631090873
367.087.23966491170327-0.159664911703271
377.347.11995619633620.220043803663798
387.877.28792357839180.582076421608201
396.287.73677145459763-1.45677145459763
406.36.6360641010529-0.336064101052899
416.366.3669684552111-0.00696845521109868
426.286.34370063042866-0.0637006304286558
435.896.27690504098203-0.386905040982032
446.045.961705581199660.0782944188003416
455.965.99556255521052-0.0355625552105243
466.15.943697825552890.15630217444711
476.266.037993628686720.222006371313278
486.026.18532744098824-0.165327440988238
496.256.040255999461730.209744000538274
506.416.179212467071550.230787532928451
516.226.33798516081268-0.117985160812681
526.576.234010287109140.335989712890864
536.186.47526910039816-0.295269100398162
546.266.23952169232440.020478307675603
556.16.24011255110735-0.14011255110735
566.026.1182024201307-0.098202420130697
576.066.025874026041770.0341259739582327
586.356.033046590441410.316953409558588
596.216.25720764291018-0.0472076429101804
606.486.20837464009440.271625359905596
616.746.402635917429020.337364082570978
626.536.652004986091-0.122004986090999
636.86.555900502389540.244099497610455
646.756.737731158523790.0122688414762138
656.566.74651939024106-0.18651939024106
666.666.603437367667240.0565626323327626
676.186.64302613356184-0.463026133561836
686.46.286093429154020.113906570845978
696.436.362352561116850.067647438883145
706.546.405238316330880.134761683669121
716.446.5006700319195-0.0606700319195008
726.646.448969879099740.191030120900264
736.826.588763895857360.231236104142642
746.976.762703241199230.207296758800766
7576.922424407855920.0775755921440808
766.916.98657233790162-0.0765723379016245
776.746.93416027822437-0.194160278224367
786.986.790428026022340.189571973977659
796.376.93683896312427-0.566838963124274
806.566.507898764820350.0521012351796468
816.636.542449810451820.087550189548181
826.876.605045079400690.264954920599312
836.686.8049193045963-0.124919304596299
846.756.711205661862860.0387943381371354
856.846.740531618607480.0994683813925157
867.156.816965070084160.333034929915841
877.097.073856579269340.0161434207306641
886.977.09420365824349-0.12420365824349
897.157.007460922087510.142539077912489







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
907.12259531188256.570553179596217.67463744416878
917.131202402151796.436125078243467.82627972606012
927.139809492421096.321352066686337.95826691815585
937.148416582690386.218275688585378.0785574767954
947.157023672959686.123006064729168.1910412811902
957.165630763228976.033307971815618.29795355464234
967.174237853498275.947762861972768.40071284502378
977.182844943767565.865407366778918.50028252075622
987.191452034036865.785554153781088.59734991429264
997.200059124306165.707694055478718.6924241931336
1007.208666214575455.631438561828878.78589386732204
1017.217273304844755.556484061146118.87806254854339

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
90 & 7.1225953118825 & 6.57055317959621 & 7.67463744416878 \tabularnewline
91 & 7.13120240215179 & 6.43612507824346 & 7.82627972606012 \tabularnewline
92 & 7.13980949242109 & 6.32135206668633 & 7.95826691815585 \tabularnewline
93 & 7.14841658269038 & 6.21827568858537 & 8.0785574767954 \tabularnewline
94 & 7.15702367295968 & 6.12300606472916 & 8.1910412811902 \tabularnewline
95 & 7.16563076322897 & 6.03330797181561 & 8.29795355464234 \tabularnewline
96 & 7.17423785349827 & 5.94776286197276 & 8.40071284502378 \tabularnewline
97 & 7.18284494376756 & 5.86540736677891 & 8.50028252075622 \tabularnewline
98 & 7.19145203403686 & 5.78555415378108 & 8.59734991429264 \tabularnewline
99 & 7.20005912430616 & 5.70769405547871 & 8.6924241931336 \tabularnewline
100 & 7.20866621457545 & 5.63143856182887 & 8.78589386732204 \tabularnewline
101 & 7.21727330484475 & 5.55648406114611 & 8.87806254854339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122047&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]90[/C][C]7.1225953118825[/C][C]6.57055317959621[/C][C]7.67463744416878[/C][/ROW]
[ROW][C]91[/C][C]7.13120240215179[/C][C]6.43612507824346[/C][C]7.82627972606012[/C][/ROW]
[ROW][C]92[/C][C]7.13980949242109[/C][C]6.32135206668633[/C][C]7.95826691815585[/C][/ROW]
[ROW][C]93[/C][C]7.14841658269038[/C][C]6.21827568858537[/C][C]8.0785574767954[/C][/ROW]
[ROW][C]94[/C][C]7.15702367295968[/C][C]6.12300606472916[/C][C]8.1910412811902[/C][/ROW]
[ROW][C]95[/C][C]7.16563076322897[/C][C]6.03330797181561[/C][C]8.29795355464234[/C][/ROW]
[ROW][C]96[/C][C]7.17423785349827[/C][C]5.94776286197276[/C][C]8.40071284502378[/C][/ROW]
[ROW][C]97[/C][C]7.18284494376756[/C][C]5.86540736677891[/C][C]8.50028252075622[/C][/ROW]
[ROW][C]98[/C][C]7.19145203403686[/C][C]5.78555415378108[/C][C]8.59734991429264[/C][/ROW]
[ROW][C]99[/C][C]7.20005912430616[/C][C]5.70769405547871[/C][C]8.6924241931336[/C][/ROW]
[ROW][C]100[/C][C]7.20866621457545[/C][C]5.63143856182887[/C][C]8.78589386732204[/C][/ROW]
[ROW][C]101[/C][C]7.21727330484475[/C][C]5.55648406114611[/C][C]8.87806254854339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122047&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122047&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
907.12259531188256.570553179596217.67463744416878
917.131202402151796.436125078243467.82627972606012
927.139809492421096.321352066686337.95826691815585
937.148416582690386.218275688585378.0785574767954
947.157023672959686.123006064729168.1910412811902
957.165630763228976.033307971815618.29795355464234
967.174237853498275.947762861972768.40071284502378
977.182844943767565.865407366778918.50028252075622
987.191452034036865.785554153781088.59734991429264
997.200059124306165.707694055478718.6924241931336
1007.208666214575455.631438561828878.78589386732204
1017.217273304844755.556484061146118.87806254854339



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')