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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 11:49:16 +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/2014/Nov/28/t1417175374opmpx16r22tbcpe.htm/, Retrieved Sun, 19 May 2024 14:58:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260858, Retrieved Sun, 19 May 2024 14:58:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 11:49:16] [5cf6a598f846f655ef95f65053f7ffc6] [Current]
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Dataseries X:
70,38
70,38
70,29
70,42
70,29
70,59
70,64
70,64
70,68
70,78
70,9
71,04
71,15
71,15
71,15
71,07
71,17
71,24
71,23
71,23
71,23
71,24
71,28
71,52
71,52
71,52
71,6
71,61
71,78
71,66
71,86
71,86
71,82
71,8
72,22
72,51
72,56
72,56
72,78
72,88
73,05
73,02
73,08
73,08
73,24
73,82
74
74,37
74,38
74,38
74,36
74,42
74,59
75,07
75,19
75,19
75,21
75,18
75,86
75,93
76,01
73,23
73,23
73,2
73,24
73,36
73,4
73,49
73,49
73,57
73,82
74,08
74,08




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260858&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260858&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260858&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00371607839979814
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00371607839979814 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260858&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]0.00371607839979814[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260858&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260858&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
beta0.00371607839979814
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
370.2970.38-0.0899999999999892
470.4270.2896655529440.130334447055972
570.2970.4201498859675-0.130149885967469
670.5970.28966623878750.300333761212499
770.6470.59078230259030.0492176974097305
870.6470.6409651994125-0.000965199412490847
970.6870.64096161265580.039038387344192
1070.7870.68110668236380.098893317636211
1170.970.78147417768530.118525822314666
1271.0470.90191462893350.138085371066552
1371.1571.04242776499820.107572235001797
1471.1571.1528275118571-0.00282751185710595
1571.1571.1528170046014-0.00281700460136847
1671.0771.1528065363914-0.0828065363914305
1771.1771.07249882081020.0975011791898339
1871.2471.17286114283610.0671388571638687
1971.2371.243110636093-0.0131106360930033
2071.2371.2330619159414-0.0030619159414158
2171.2371.2330505376217-0.00305053762173202
2271.2471.23303920158480.00696079841522135
2371.2871.24306506845740.0369349315426035
2471.5271.28320232155870.236797678441292
2571.5271.5240822802967-0.00408228029668578
2671.5271.524067110223-0.00406711022304762
2771.671.52405199652260.0759480034773929
2871.6171.60433422525780.00566577474216956
2971.7871.6143552797210.165644720279033
3071.6671.784970828488-0.124970828488046
3171.8671.66450642709170.195493572908319
3271.8671.8652328965353-0.0052328965352757
3371.8271.8652134506815-0.0452134506815014
3471.871.825045433954-0.025045433954034
3572.2271.80495236315790.415047636842104
3672.5172.22649471271610.283505287283944
3772.5672.51754824059040.0424517594096301
3872.5672.5677059946565-0.00770599465653277
3972.7872.56767735857620.212322641423754
4072.8872.78846636615780.0915336338421611
4173.0572.88880651231740.161193487682596
4273.0273.0594055199552-0.0394055199551673
4373.0873.02925908595360.0507409140463722
4473.0873.0894476431683-0.0094476431683006
4573.2473.08941253498560.150587465014397
4673.8273.24997212981160.570027870188383
477473.83209039806730.167909601932692
4874.3774.01271436331220.357285636687834
4974.3874.3840420647492-0.0040420647492283
5074.3874.3940270441197-0.0140270441197146
5174.3674.3939749185241-0.0339749185240521
5274.4274.37384866506320.046151334936809
5374.5974.43402016704210.155979832957925
5475.0774.60459980033010.465400199669858
5575.1975.08632926395940.103670736040627
5675.1975.2067145125423-0.0167145125422792
5775.2175.20665240010330.00334759989674183
5875.1875.2266648400469-0.0466648400469154
5975.8675.19649142984280.663508570157205
6075.9375.87895707970840.0510429202915788
6176.0175.9491467592020.0608532407980107
6273.2376.0293728946157-2.79937289461569
6373.2373.238970205469-0.00897020546901217
6473.273.2389368714822-0.0389368714822353
6573.2473.20879217901520.0312078209848323
6673.3673.24890814972460.111091850275372
6773.473.36932097574980.0306790242501762
6873.4973.40943498140920.0805650185908178
6973.4973.4997343673345-0.00973436733454491
7073.5773.49969819366230.0703018063376533
7173.8273.57995944068630.240040559313655
7274.0873.83085145022390.249148549776109
7374.0874.091777305768-0.0117773057680495

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 70.29 & 70.38 & -0.0899999999999892 \tabularnewline
4 & 70.42 & 70.289665552944 & 0.130334447055972 \tabularnewline
5 & 70.29 & 70.4201498859675 & -0.130149885967469 \tabularnewline
6 & 70.59 & 70.2896662387875 & 0.300333761212499 \tabularnewline
7 & 70.64 & 70.5907823025903 & 0.0492176974097305 \tabularnewline
8 & 70.64 & 70.6409651994125 & -0.000965199412490847 \tabularnewline
9 & 70.68 & 70.6409616126558 & 0.039038387344192 \tabularnewline
10 & 70.78 & 70.6811066823638 & 0.098893317636211 \tabularnewline
11 & 70.9 & 70.7814741776853 & 0.118525822314666 \tabularnewline
12 & 71.04 & 70.9019146289335 & 0.138085371066552 \tabularnewline
13 & 71.15 & 71.0424277649982 & 0.107572235001797 \tabularnewline
14 & 71.15 & 71.1528275118571 & -0.00282751185710595 \tabularnewline
15 & 71.15 & 71.1528170046014 & -0.00281700460136847 \tabularnewline
16 & 71.07 & 71.1528065363914 & -0.0828065363914305 \tabularnewline
17 & 71.17 & 71.0724988208102 & 0.0975011791898339 \tabularnewline
18 & 71.24 & 71.1728611428361 & 0.0671388571638687 \tabularnewline
19 & 71.23 & 71.243110636093 & -0.0131106360930033 \tabularnewline
20 & 71.23 & 71.2330619159414 & -0.0030619159414158 \tabularnewline
21 & 71.23 & 71.2330505376217 & -0.00305053762173202 \tabularnewline
22 & 71.24 & 71.2330392015848 & 0.00696079841522135 \tabularnewline
23 & 71.28 & 71.2430650684574 & 0.0369349315426035 \tabularnewline
24 & 71.52 & 71.2832023215587 & 0.236797678441292 \tabularnewline
25 & 71.52 & 71.5240822802967 & -0.00408228029668578 \tabularnewline
26 & 71.52 & 71.524067110223 & -0.00406711022304762 \tabularnewline
27 & 71.6 & 71.5240519965226 & 0.0759480034773929 \tabularnewline
28 & 71.61 & 71.6043342252578 & 0.00566577474216956 \tabularnewline
29 & 71.78 & 71.614355279721 & 0.165644720279033 \tabularnewline
30 & 71.66 & 71.784970828488 & -0.124970828488046 \tabularnewline
31 & 71.86 & 71.6645064270917 & 0.195493572908319 \tabularnewline
32 & 71.86 & 71.8652328965353 & -0.0052328965352757 \tabularnewline
33 & 71.82 & 71.8652134506815 & -0.0452134506815014 \tabularnewline
34 & 71.8 & 71.825045433954 & -0.025045433954034 \tabularnewline
35 & 72.22 & 71.8049523631579 & 0.415047636842104 \tabularnewline
36 & 72.51 & 72.2264947127161 & 0.283505287283944 \tabularnewline
37 & 72.56 & 72.5175482405904 & 0.0424517594096301 \tabularnewline
38 & 72.56 & 72.5677059946565 & -0.00770599465653277 \tabularnewline
39 & 72.78 & 72.5676773585762 & 0.212322641423754 \tabularnewline
40 & 72.88 & 72.7884663661578 & 0.0915336338421611 \tabularnewline
41 & 73.05 & 72.8888065123174 & 0.161193487682596 \tabularnewline
42 & 73.02 & 73.0594055199552 & -0.0394055199551673 \tabularnewline
43 & 73.08 & 73.0292590859536 & 0.0507409140463722 \tabularnewline
44 & 73.08 & 73.0894476431683 & -0.0094476431683006 \tabularnewline
45 & 73.24 & 73.0894125349856 & 0.150587465014397 \tabularnewline
46 & 73.82 & 73.2499721298116 & 0.570027870188383 \tabularnewline
47 & 74 & 73.8320903980673 & 0.167909601932692 \tabularnewline
48 & 74.37 & 74.0127143633122 & 0.357285636687834 \tabularnewline
49 & 74.38 & 74.3840420647492 & -0.0040420647492283 \tabularnewline
50 & 74.38 & 74.3940270441197 & -0.0140270441197146 \tabularnewline
51 & 74.36 & 74.3939749185241 & -0.0339749185240521 \tabularnewline
52 & 74.42 & 74.3738486650632 & 0.046151334936809 \tabularnewline
53 & 74.59 & 74.4340201670421 & 0.155979832957925 \tabularnewline
54 & 75.07 & 74.6045998003301 & 0.465400199669858 \tabularnewline
55 & 75.19 & 75.0863292639594 & 0.103670736040627 \tabularnewline
56 & 75.19 & 75.2067145125423 & -0.0167145125422792 \tabularnewline
57 & 75.21 & 75.2066524001033 & 0.00334759989674183 \tabularnewline
58 & 75.18 & 75.2266648400469 & -0.0466648400469154 \tabularnewline
59 & 75.86 & 75.1964914298428 & 0.663508570157205 \tabularnewline
60 & 75.93 & 75.8789570797084 & 0.0510429202915788 \tabularnewline
61 & 76.01 & 75.949146759202 & 0.0608532407980107 \tabularnewline
62 & 73.23 & 76.0293728946157 & -2.79937289461569 \tabularnewline
63 & 73.23 & 73.238970205469 & -0.00897020546901217 \tabularnewline
64 & 73.2 & 73.2389368714822 & -0.0389368714822353 \tabularnewline
65 & 73.24 & 73.2087921790152 & 0.0312078209848323 \tabularnewline
66 & 73.36 & 73.2489081497246 & 0.111091850275372 \tabularnewline
67 & 73.4 & 73.3693209757498 & 0.0306790242501762 \tabularnewline
68 & 73.49 & 73.4094349814092 & 0.0805650185908178 \tabularnewline
69 & 73.49 & 73.4997343673345 & -0.00973436733454491 \tabularnewline
70 & 73.57 & 73.4996981936623 & 0.0703018063376533 \tabularnewline
71 & 73.82 & 73.5799594406863 & 0.240040559313655 \tabularnewline
72 & 74.08 & 73.8308514502239 & 0.249148549776109 \tabularnewline
73 & 74.08 & 74.091777305768 & -0.0117773057680495 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260858&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]70.29[/C][C]70.38[/C][C]-0.0899999999999892[/C][/ROW]
[ROW][C]4[/C][C]70.42[/C][C]70.289665552944[/C][C]0.130334447055972[/C][/ROW]
[ROW][C]5[/C][C]70.29[/C][C]70.4201498859675[/C][C]-0.130149885967469[/C][/ROW]
[ROW][C]6[/C][C]70.59[/C][C]70.2896662387875[/C][C]0.300333761212499[/C][/ROW]
[ROW][C]7[/C][C]70.64[/C][C]70.5907823025903[/C][C]0.0492176974097305[/C][/ROW]
[ROW][C]8[/C][C]70.64[/C][C]70.6409651994125[/C][C]-0.000965199412490847[/C][/ROW]
[ROW][C]9[/C][C]70.68[/C][C]70.6409616126558[/C][C]0.039038387344192[/C][/ROW]
[ROW][C]10[/C][C]70.78[/C][C]70.6811066823638[/C][C]0.098893317636211[/C][/ROW]
[ROW][C]11[/C][C]70.9[/C][C]70.7814741776853[/C][C]0.118525822314666[/C][/ROW]
[ROW][C]12[/C][C]71.04[/C][C]70.9019146289335[/C][C]0.138085371066552[/C][/ROW]
[ROW][C]13[/C][C]71.15[/C][C]71.0424277649982[/C][C]0.107572235001797[/C][/ROW]
[ROW][C]14[/C][C]71.15[/C][C]71.1528275118571[/C][C]-0.00282751185710595[/C][/ROW]
[ROW][C]15[/C][C]71.15[/C][C]71.1528170046014[/C][C]-0.00281700460136847[/C][/ROW]
[ROW][C]16[/C][C]71.07[/C][C]71.1528065363914[/C][C]-0.0828065363914305[/C][/ROW]
[ROW][C]17[/C][C]71.17[/C][C]71.0724988208102[/C][C]0.0975011791898339[/C][/ROW]
[ROW][C]18[/C][C]71.24[/C][C]71.1728611428361[/C][C]0.0671388571638687[/C][/ROW]
[ROW][C]19[/C][C]71.23[/C][C]71.243110636093[/C][C]-0.0131106360930033[/C][/ROW]
[ROW][C]20[/C][C]71.23[/C][C]71.2330619159414[/C][C]-0.0030619159414158[/C][/ROW]
[ROW][C]21[/C][C]71.23[/C][C]71.2330505376217[/C][C]-0.00305053762173202[/C][/ROW]
[ROW][C]22[/C][C]71.24[/C][C]71.2330392015848[/C][C]0.00696079841522135[/C][/ROW]
[ROW][C]23[/C][C]71.28[/C][C]71.2430650684574[/C][C]0.0369349315426035[/C][/ROW]
[ROW][C]24[/C][C]71.52[/C][C]71.2832023215587[/C][C]0.236797678441292[/C][/ROW]
[ROW][C]25[/C][C]71.52[/C][C]71.5240822802967[/C][C]-0.00408228029668578[/C][/ROW]
[ROW][C]26[/C][C]71.52[/C][C]71.524067110223[/C][C]-0.00406711022304762[/C][/ROW]
[ROW][C]27[/C][C]71.6[/C][C]71.5240519965226[/C][C]0.0759480034773929[/C][/ROW]
[ROW][C]28[/C][C]71.61[/C][C]71.6043342252578[/C][C]0.00566577474216956[/C][/ROW]
[ROW][C]29[/C][C]71.78[/C][C]71.614355279721[/C][C]0.165644720279033[/C][/ROW]
[ROW][C]30[/C][C]71.66[/C][C]71.784970828488[/C][C]-0.124970828488046[/C][/ROW]
[ROW][C]31[/C][C]71.86[/C][C]71.6645064270917[/C][C]0.195493572908319[/C][/ROW]
[ROW][C]32[/C][C]71.86[/C][C]71.8652328965353[/C][C]-0.0052328965352757[/C][/ROW]
[ROW][C]33[/C][C]71.82[/C][C]71.8652134506815[/C][C]-0.0452134506815014[/C][/ROW]
[ROW][C]34[/C][C]71.8[/C][C]71.825045433954[/C][C]-0.025045433954034[/C][/ROW]
[ROW][C]35[/C][C]72.22[/C][C]71.8049523631579[/C][C]0.415047636842104[/C][/ROW]
[ROW][C]36[/C][C]72.51[/C][C]72.2264947127161[/C][C]0.283505287283944[/C][/ROW]
[ROW][C]37[/C][C]72.56[/C][C]72.5175482405904[/C][C]0.0424517594096301[/C][/ROW]
[ROW][C]38[/C][C]72.56[/C][C]72.5677059946565[/C][C]-0.00770599465653277[/C][/ROW]
[ROW][C]39[/C][C]72.78[/C][C]72.5676773585762[/C][C]0.212322641423754[/C][/ROW]
[ROW][C]40[/C][C]72.88[/C][C]72.7884663661578[/C][C]0.0915336338421611[/C][/ROW]
[ROW][C]41[/C][C]73.05[/C][C]72.8888065123174[/C][C]0.161193487682596[/C][/ROW]
[ROW][C]42[/C][C]73.02[/C][C]73.0594055199552[/C][C]-0.0394055199551673[/C][/ROW]
[ROW][C]43[/C][C]73.08[/C][C]73.0292590859536[/C][C]0.0507409140463722[/C][/ROW]
[ROW][C]44[/C][C]73.08[/C][C]73.0894476431683[/C][C]-0.0094476431683006[/C][/ROW]
[ROW][C]45[/C][C]73.24[/C][C]73.0894125349856[/C][C]0.150587465014397[/C][/ROW]
[ROW][C]46[/C][C]73.82[/C][C]73.2499721298116[/C][C]0.570027870188383[/C][/ROW]
[ROW][C]47[/C][C]74[/C][C]73.8320903980673[/C][C]0.167909601932692[/C][/ROW]
[ROW][C]48[/C][C]74.37[/C][C]74.0127143633122[/C][C]0.357285636687834[/C][/ROW]
[ROW][C]49[/C][C]74.38[/C][C]74.3840420647492[/C][C]-0.0040420647492283[/C][/ROW]
[ROW][C]50[/C][C]74.38[/C][C]74.3940270441197[/C][C]-0.0140270441197146[/C][/ROW]
[ROW][C]51[/C][C]74.36[/C][C]74.3939749185241[/C][C]-0.0339749185240521[/C][/ROW]
[ROW][C]52[/C][C]74.42[/C][C]74.3738486650632[/C][C]0.046151334936809[/C][/ROW]
[ROW][C]53[/C][C]74.59[/C][C]74.4340201670421[/C][C]0.155979832957925[/C][/ROW]
[ROW][C]54[/C][C]75.07[/C][C]74.6045998003301[/C][C]0.465400199669858[/C][/ROW]
[ROW][C]55[/C][C]75.19[/C][C]75.0863292639594[/C][C]0.103670736040627[/C][/ROW]
[ROW][C]56[/C][C]75.19[/C][C]75.2067145125423[/C][C]-0.0167145125422792[/C][/ROW]
[ROW][C]57[/C][C]75.21[/C][C]75.2066524001033[/C][C]0.00334759989674183[/C][/ROW]
[ROW][C]58[/C][C]75.18[/C][C]75.2266648400469[/C][C]-0.0466648400469154[/C][/ROW]
[ROW][C]59[/C][C]75.86[/C][C]75.1964914298428[/C][C]0.663508570157205[/C][/ROW]
[ROW][C]60[/C][C]75.93[/C][C]75.8789570797084[/C][C]0.0510429202915788[/C][/ROW]
[ROW][C]61[/C][C]76.01[/C][C]75.949146759202[/C][C]0.0608532407980107[/C][/ROW]
[ROW][C]62[/C][C]73.23[/C][C]76.0293728946157[/C][C]-2.79937289461569[/C][/ROW]
[ROW][C]63[/C][C]73.23[/C][C]73.238970205469[/C][C]-0.00897020546901217[/C][/ROW]
[ROW][C]64[/C][C]73.2[/C][C]73.2389368714822[/C][C]-0.0389368714822353[/C][/ROW]
[ROW][C]65[/C][C]73.24[/C][C]73.2087921790152[/C][C]0.0312078209848323[/C][/ROW]
[ROW][C]66[/C][C]73.36[/C][C]73.2489081497246[/C][C]0.111091850275372[/C][/ROW]
[ROW][C]67[/C][C]73.4[/C][C]73.3693209757498[/C][C]0.0306790242501762[/C][/ROW]
[ROW][C]68[/C][C]73.49[/C][C]73.4094349814092[/C][C]0.0805650185908178[/C][/ROW]
[ROW][C]69[/C][C]73.49[/C][C]73.4997343673345[/C][C]-0.00973436733454491[/C][/ROW]
[ROW][C]70[/C][C]73.57[/C][C]73.4996981936623[/C][C]0.0703018063376533[/C][/ROW]
[ROW][C]71[/C][C]73.82[/C][C]73.5799594406863[/C][C]0.240040559313655[/C][/ROW]
[ROW][C]72[/C][C]74.08[/C][C]73.8308514502239[/C][C]0.249148549776109[/C][/ROW]
[ROW][C]73[/C][C]74.08[/C][C]74.091777305768[/C][C]-0.0117773057680495[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260858&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260858&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
370.2970.38-0.0899999999999892
470.4270.2896655529440.130334447055972
570.2970.4201498859675-0.130149885967469
670.5970.28966623878750.300333761212499
770.6470.59078230259030.0492176974097305
870.6470.6409651994125-0.000965199412490847
970.6870.64096161265580.039038387344192
1070.7870.68110668236380.098893317636211
1170.970.78147417768530.118525822314666
1271.0470.90191462893350.138085371066552
1371.1571.04242776499820.107572235001797
1471.1571.1528275118571-0.00282751185710595
1571.1571.1528170046014-0.00281700460136847
1671.0771.1528065363914-0.0828065363914305
1771.1771.07249882081020.0975011791898339
1871.2471.17286114283610.0671388571638687
1971.2371.243110636093-0.0131106360930033
2071.2371.2330619159414-0.0030619159414158
2171.2371.2330505376217-0.00305053762173202
2271.2471.23303920158480.00696079841522135
2371.2871.24306506845740.0369349315426035
2471.5271.28320232155870.236797678441292
2571.5271.5240822802967-0.00408228029668578
2671.5271.524067110223-0.00406711022304762
2771.671.52405199652260.0759480034773929
2871.6171.60433422525780.00566577474216956
2971.7871.6143552797210.165644720279033
3071.6671.784970828488-0.124970828488046
3171.8671.66450642709170.195493572908319
3271.8671.8652328965353-0.0052328965352757
3371.8271.8652134506815-0.0452134506815014
3471.871.825045433954-0.025045433954034
3572.2271.80495236315790.415047636842104
3672.5172.22649471271610.283505287283944
3772.5672.51754824059040.0424517594096301
3872.5672.5677059946565-0.00770599465653277
3972.7872.56767735857620.212322641423754
4072.8872.78846636615780.0915336338421611
4173.0572.88880651231740.161193487682596
4273.0273.0594055199552-0.0394055199551673
4373.0873.02925908595360.0507409140463722
4473.0873.0894476431683-0.0094476431683006
4573.2473.08941253498560.150587465014397
4673.8273.24997212981160.570027870188383
477473.83209039806730.167909601932692
4874.3774.01271436331220.357285636687834
4974.3874.3840420647492-0.0040420647492283
5074.3874.3940270441197-0.0140270441197146
5174.3674.3939749185241-0.0339749185240521
5274.4274.37384866506320.046151334936809
5374.5974.43402016704210.155979832957925
5475.0774.60459980033010.465400199669858
5575.1975.08632926395940.103670736040627
5675.1975.2067145125423-0.0167145125422792
5775.2175.20665240010330.00334759989674183
5875.1875.2266648400469-0.0466648400469154
5975.8675.19649142984280.663508570157205
6075.9375.87895707970840.0510429202915788
6176.0175.9491467592020.0608532407980107
6273.2376.0293728946157-2.79937289461569
6373.2373.238970205469-0.00897020546901217
6473.273.2389368714822-0.0389368714822353
6573.2473.20879217901520.0312078209848323
6673.3673.24890814972460.111091850275372
6773.473.36932097574980.0306790242501762
6873.4973.40943498140920.0805650185908178
6973.4973.4997343673345-0.00973436733454491
7073.5773.49969819366230.0703018063376533
7173.8273.57995944068630.240040559313655
7274.0873.83085145022390.249148549776109
7374.0874.091777305768-0.0117773057680495







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7474.091733540376573.360326595739674.8231404850134
7574.10346708075373.067177786000975.1397563755051
7674.115200621129472.843653167851675.3867480744073
7774.126934161505972.655953820408475.5979145026035
7874.138667701882472.491014525098775.7863208786661
7974.150401242258972.342147614633475.9586548698844
8074.162134782635472.205387862071976.1188817031988
8174.173868323011972.078156569554276.2695800764696
8274.185601863388371.958665922721776.4125378040549
8374.197335403764871.845616654304476.5490541532252
8474.209068944141371.738029748489676.680108139793
8574.220802484517871.635146020840476.8064589481951

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 74.0917335403765 & 73.3603265957396 & 74.8231404850134 \tabularnewline
75 & 74.103467080753 & 73.0671777860009 & 75.1397563755051 \tabularnewline
76 & 74.1152006211294 & 72.8436531678516 & 75.3867480744073 \tabularnewline
77 & 74.1269341615059 & 72.6559538204084 & 75.5979145026035 \tabularnewline
78 & 74.1386677018824 & 72.4910145250987 & 75.7863208786661 \tabularnewline
79 & 74.1504012422589 & 72.3421476146334 & 75.9586548698844 \tabularnewline
80 & 74.1621347826354 & 72.2053878620719 & 76.1188817031988 \tabularnewline
81 & 74.1738683230119 & 72.0781565695542 & 76.2695800764696 \tabularnewline
82 & 74.1856018633883 & 71.9586659227217 & 76.4125378040549 \tabularnewline
83 & 74.1973354037648 & 71.8456166543044 & 76.5490541532252 \tabularnewline
84 & 74.2090689441413 & 71.7380297484896 & 76.680108139793 \tabularnewline
85 & 74.2208024845178 & 71.6351460208404 & 76.8064589481951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260858&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]74.0917335403765[/C][C]73.3603265957396[/C][C]74.8231404850134[/C][/ROW]
[ROW][C]75[/C][C]74.103467080753[/C][C]73.0671777860009[/C][C]75.1397563755051[/C][/ROW]
[ROW][C]76[/C][C]74.1152006211294[/C][C]72.8436531678516[/C][C]75.3867480744073[/C][/ROW]
[ROW][C]77[/C][C]74.1269341615059[/C][C]72.6559538204084[/C][C]75.5979145026035[/C][/ROW]
[ROW][C]78[/C][C]74.1386677018824[/C][C]72.4910145250987[/C][C]75.7863208786661[/C][/ROW]
[ROW][C]79[/C][C]74.1504012422589[/C][C]72.3421476146334[/C][C]75.9586548698844[/C][/ROW]
[ROW][C]80[/C][C]74.1621347826354[/C][C]72.2053878620719[/C][C]76.1188817031988[/C][/ROW]
[ROW][C]81[/C][C]74.1738683230119[/C][C]72.0781565695542[/C][C]76.2695800764696[/C][/ROW]
[ROW][C]82[/C][C]74.1856018633883[/C][C]71.9586659227217[/C][C]76.4125378040549[/C][/ROW]
[ROW][C]83[/C][C]74.1973354037648[/C][C]71.8456166543044[/C][C]76.5490541532252[/C][/ROW]
[ROW][C]84[/C][C]74.2090689441413[/C][C]71.7380297484896[/C][C]76.680108139793[/C][/ROW]
[ROW][C]85[/C][C]74.2208024845178[/C][C]71.6351460208404[/C][C]76.8064589481951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260858&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260858&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
7474.091733540376573.360326595739674.8231404850134
7574.10346708075373.067177786000975.1397563755051
7674.115200621129472.843653167851675.3867480744073
7774.126934161505972.655953820408475.5979145026035
7874.138667701882472.491014525098775.7863208786661
7974.150401242258972.342147614633475.9586548698844
8074.162134782635472.205387862071976.1188817031988
8174.173868323011972.078156569554276.2695800764696
8274.185601863388371.958665922721776.4125378040549
8374.197335403764871.845616654304476.5490541532252
8474.209068944141371.738029748489676.680108139793
8574.220802484517871.635146020840476.8064589481951



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')