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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 computationSat, 25 May 2013 09:31:10 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/25/t1369488703kihhkvi42ih4t4e.htm/, Retrieved Thu, 02 May 2024 21:14:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210508, Retrieved Thu, 02 May 2024 21:14:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2013-05-25 13:31:10] [15971d651321f956bb80618182636bf1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15,13
15,25
15,33
15,36
15,4
15,4
15,41
15,47
15,54
15,55
15,59
15,65
15,75
15,86
15,89
15,94
15,93
15,95
15,99
15,99
16,06
16,08
16,07
16,11
16,15
16,18
16,3
16,42
16,49
16,5
16,58
16,64
16,66
16,81
16,91
16,92
16,95
17,11
17,16
17,16
17,27
17,34
17,39
17,43
17,45
17,5
17,56
17,65
17,62
17,7
17,72
17,71
17,74
17,75
17,78
17,8
17,86
17,88
17,89
17,94
17,98
18,1
18,14
18,19
18,23
18,24
18,27
18,3
18,34
18,36
18,36
18,4
18,43
18,47
18,56
18,58
18,61
18,61
18,69
18,74
18,75
18,81
18,85
18,88

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210508&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210508&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210508&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.95488598009163
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.95488598009163 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210508&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]0.95488598009163[/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=210508&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210508&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
alpha0.95488598009163
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.7515.46941773504270.280582264957271
1415.8615.84701837953940.0129816204606428
1515.8915.8915909203427-0.00159092034266983
1615.9415.9418316795719-0.00183167957191621
1715.9315.9335092078552-0.003509207855247
1815.9515.9565015545663-0.00650155456628454
1915.9915.9558032180220.0341967819779541
2015.9916.042717152457-0.052717152456955
2116.0616.05913818942540.00086181057463719
2216.0816.06797102702050.0120289729795111
2316.0716.1187172314334-0.0487172314334288
2416.1116.1327077369087-0.0227077369086786
2516.1516.2221092046088-0.0721092046087612
2616.1816.2508571687156-0.0708571687155555
2716.316.21471579925070.0852842007492605
2816.4216.34790153201280.0720984679872316
2916.4916.41009824166210.0799017583379289
3016.516.5126035537878-0.0126035537877733
3116.5816.50791456930150.0720854306985004
3216.6416.62708680623590.0129131937641418
3316.6616.7085945030842-0.0485945030842281
3416.8116.67070599572650.139294004273456
3516.9116.84023528880270.0697647111972515
3616.9216.9685359330438-0.0485359330438477
3716.9517.0310457195661-0.0810457195660774
3817.1117.05131681520150.0586831847985323
3917.1617.14591587801390.0140841219860732
4017.1617.2105187923732-0.0505187923732358
4117.2717.15598203698330.114017963016689
4217.3417.28689114815780.0531088518421683
4317.3917.34877067905780.0412293209421826
4417.4317.4358093519106-0.00580935191062437
4517.4517.4966642929224-0.0466642929224008
4617.517.46909532204840.0309046779516358
4717.5617.53198842111620.0280115788837634
4817.6517.61508256706680.0349174329331881
4917.6217.7558141555956-0.135814155595583
5017.717.7300913720881-0.0300913720881333
5117.7217.7379088121331-0.0179088121330544
5217.7117.7690476250755-0.0590476250754648
5317.7417.713789721370.0262102786300424
5417.7517.7581046509252-0.00810465092522961
5517.7817.76099633284680.0190036671531999
5617.817.8246899368746-0.0246899368745908
5717.8617.8656729413862-0.00567294138618735
5817.8817.8807454854954-0.000745485495372122
5917.8917.9132857678911-0.0232857678911387
6017.9417.9477083474275-0.00770834742753124
6117.9818.0400347876155-0.0600347876155141
6218.118.09144223993240.00855776006764231
6318.1418.13671479866790.00328520133211185
6418.1918.1862355407040.00376445929603264
6518.2318.19480234251030.0351976574897499
6618.2418.2461511097213-0.00615110972132271
6718.2718.25213116595150.0178688340484925
6818.318.3127699396359-0.0127699396358878
6918.3418.3659931155065-0.0259931155065125
7018.3618.3618845075783-0.00188450757833536
7118.3618.3923202710073-0.0323202710073254
7218.418.4188186902379-0.0188186902378966
7318.4318.4981753637779-0.0681753637778719
7418.4718.5449039796092-0.0749039796091573
7518.5618.51024222693350.04975777306651
7618.5818.6041605974309-0.0241605974308747
7718.6118.58748023200450.0225197679955365
7818.6118.6248576511732-0.0148576511732124
7918.6918.62360758925730.0663924107426688
8018.7418.72919860778490.0108013922150789
8118.7518.8043331673526-0.0543331673526382
8218.8118.77425067745960.0357493225404397
8318.8518.83924937800890.0107506219911464
8418.8818.9074846996973-0.0274846996973217

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.75 & 15.4694177350427 & 0.280582264957271 \tabularnewline
14 & 15.86 & 15.8470183795394 & 0.0129816204606428 \tabularnewline
15 & 15.89 & 15.8915909203427 & -0.00159092034266983 \tabularnewline
16 & 15.94 & 15.9418316795719 & -0.00183167957191621 \tabularnewline
17 & 15.93 & 15.9335092078552 & -0.003509207855247 \tabularnewline
18 & 15.95 & 15.9565015545663 & -0.00650155456628454 \tabularnewline
19 & 15.99 & 15.955803218022 & 0.0341967819779541 \tabularnewline
20 & 15.99 & 16.042717152457 & -0.052717152456955 \tabularnewline
21 & 16.06 & 16.0591381894254 & 0.00086181057463719 \tabularnewline
22 & 16.08 & 16.0679710270205 & 0.0120289729795111 \tabularnewline
23 & 16.07 & 16.1187172314334 & -0.0487172314334288 \tabularnewline
24 & 16.11 & 16.1327077369087 & -0.0227077369086786 \tabularnewline
25 & 16.15 & 16.2221092046088 & -0.0721092046087612 \tabularnewline
26 & 16.18 & 16.2508571687156 & -0.0708571687155555 \tabularnewline
27 & 16.3 & 16.2147157992507 & 0.0852842007492605 \tabularnewline
28 & 16.42 & 16.3479015320128 & 0.0720984679872316 \tabularnewline
29 & 16.49 & 16.4100982416621 & 0.0799017583379289 \tabularnewline
30 & 16.5 & 16.5126035537878 & -0.0126035537877733 \tabularnewline
31 & 16.58 & 16.5079145693015 & 0.0720854306985004 \tabularnewline
32 & 16.64 & 16.6270868062359 & 0.0129131937641418 \tabularnewline
33 & 16.66 & 16.7085945030842 & -0.0485945030842281 \tabularnewline
34 & 16.81 & 16.6707059957265 & 0.139294004273456 \tabularnewline
35 & 16.91 & 16.8402352888027 & 0.0697647111972515 \tabularnewline
36 & 16.92 & 16.9685359330438 & -0.0485359330438477 \tabularnewline
37 & 16.95 & 17.0310457195661 & -0.0810457195660774 \tabularnewline
38 & 17.11 & 17.0513168152015 & 0.0586831847985323 \tabularnewline
39 & 17.16 & 17.1459158780139 & 0.0140841219860732 \tabularnewline
40 & 17.16 & 17.2105187923732 & -0.0505187923732358 \tabularnewline
41 & 17.27 & 17.1559820369833 & 0.114017963016689 \tabularnewline
42 & 17.34 & 17.2868911481578 & 0.0531088518421683 \tabularnewline
43 & 17.39 & 17.3487706790578 & 0.0412293209421826 \tabularnewline
44 & 17.43 & 17.4358093519106 & -0.00580935191062437 \tabularnewline
45 & 17.45 & 17.4966642929224 & -0.0466642929224008 \tabularnewline
46 & 17.5 & 17.4690953220484 & 0.0309046779516358 \tabularnewline
47 & 17.56 & 17.5319884211162 & 0.0280115788837634 \tabularnewline
48 & 17.65 & 17.6150825670668 & 0.0349174329331881 \tabularnewline
49 & 17.62 & 17.7558141555956 & -0.135814155595583 \tabularnewline
50 & 17.7 & 17.7300913720881 & -0.0300913720881333 \tabularnewline
51 & 17.72 & 17.7379088121331 & -0.0179088121330544 \tabularnewline
52 & 17.71 & 17.7690476250755 & -0.0590476250754648 \tabularnewline
53 & 17.74 & 17.71378972137 & 0.0262102786300424 \tabularnewline
54 & 17.75 & 17.7581046509252 & -0.00810465092522961 \tabularnewline
55 & 17.78 & 17.7609963328468 & 0.0190036671531999 \tabularnewline
56 & 17.8 & 17.8246899368746 & -0.0246899368745908 \tabularnewline
57 & 17.86 & 17.8656729413862 & -0.00567294138618735 \tabularnewline
58 & 17.88 & 17.8807454854954 & -0.000745485495372122 \tabularnewline
59 & 17.89 & 17.9132857678911 & -0.0232857678911387 \tabularnewline
60 & 17.94 & 17.9477083474275 & -0.00770834742753124 \tabularnewline
61 & 17.98 & 18.0400347876155 & -0.0600347876155141 \tabularnewline
62 & 18.1 & 18.0914422399324 & 0.00855776006764231 \tabularnewline
63 & 18.14 & 18.1367147986679 & 0.00328520133211185 \tabularnewline
64 & 18.19 & 18.186235540704 & 0.00376445929603264 \tabularnewline
65 & 18.23 & 18.1948023425103 & 0.0351976574897499 \tabularnewline
66 & 18.24 & 18.2461511097213 & -0.00615110972132271 \tabularnewline
67 & 18.27 & 18.2521311659515 & 0.0178688340484925 \tabularnewline
68 & 18.3 & 18.3127699396359 & -0.0127699396358878 \tabularnewline
69 & 18.34 & 18.3659931155065 & -0.0259931155065125 \tabularnewline
70 & 18.36 & 18.3618845075783 & -0.00188450757833536 \tabularnewline
71 & 18.36 & 18.3923202710073 & -0.0323202710073254 \tabularnewline
72 & 18.4 & 18.4188186902379 & -0.0188186902378966 \tabularnewline
73 & 18.43 & 18.4981753637779 & -0.0681753637778719 \tabularnewline
74 & 18.47 & 18.5449039796092 & -0.0749039796091573 \tabularnewline
75 & 18.56 & 18.5102422269335 & 0.04975777306651 \tabularnewline
76 & 18.58 & 18.6041605974309 & -0.0241605974308747 \tabularnewline
77 & 18.61 & 18.5874802320045 & 0.0225197679955365 \tabularnewline
78 & 18.61 & 18.6248576511732 & -0.0148576511732124 \tabularnewline
79 & 18.69 & 18.6236075892573 & 0.0663924107426688 \tabularnewline
80 & 18.74 & 18.7291986077849 & 0.0108013922150789 \tabularnewline
81 & 18.75 & 18.8043331673526 & -0.0543331673526382 \tabularnewline
82 & 18.81 & 18.7742506774596 & 0.0357493225404397 \tabularnewline
83 & 18.85 & 18.8392493780089 & 0.0107506219911464 \tabularnewline
84 & 18.88 & 18.9074846996973 & -0.0274846996973217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210508&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]15.75[/C][C]15.4694177350427[/C][C]0.280582264957271[/C][/ROW]
[ROW][C]14[/C][C]15.86[/C][C]15.8470183795394[/C][C]0.0129816204606428[/C][/ROW]
[ROW][C]15[/C][C]15.89[/C][C]15.8915909203427[/C][C]-0.00159092034266983[/C][/ROW]
[ROW][C]16[/C][C]15.94[/C][C]15.9418316795719[/C][C]-0.00183167957191621[/C][/ROW]
[ROW][C]17[/C][C]15.93[/C][C]15.9335092078552[/C][C]-0.003509207855247[/C][/ROW]
[ROW][C]18[/C][C]15.95[/C][C]15.9565015545663[/C][C]-0.00650155456628454[/C][/ROW]
[ROW][C]19[/C][C]15.99[/C][C]15.955803218022[/C][C]0.0341967819779541[/C][/ROW]
[ROW][C]20[/C][C]15.99[/C][C]16.042717152457[/C][C]-0.052717152456955[/C][/ROW]
[ROW][C]21[/C][C]16.06[/C][C]16.0591381894254[/C][C]0.00086181057463719[/C][/ROW]
[ROW][C]22[/C][C]16.08[/C][C]16.0679710270205[/C][C]0.0120289729795111[/C][/ROW]
[ROW][C]23[/C][C]16.07[/C][C]16.1187172314334[/C][C]-0.0487172314334288[/C][/ROW]
[ROW][C]24[/C][C]16.11[/C][C]16.1327077369087[/C][C]-0.0227077369086786[/C][/ROW]
[ROW][C]25[/C][C]16.15[/C][C]16.2221092046088[/C][C]-0.0721092046087612[/C][/ROW]
[ROW][C]26[/C][C]16.18[/C][C]16.2508571687156[/C][C]-0.0708571687155555[/C][/ROW]
[ROW][C]27[/C][C]16.3[/C][C]16.2147157992507[/C][C]0.0852842007492605[/C][/ROW]
[ROW][C]28[/C][C]16.42[/C][C]16.3479015320128[/C][C]0.0720984679872316[/C][/ROW]
[ROW][C]29[/C][C]16.49[/C][C]16.4100982416621[/C][C]0.0799017583379289[/C][/ROW]
[ROW][C]30[/C][C]16.5[/C][C]16.5126035537878[/C][C]-0.0126035537877733[/C][/ROW]
[ROW][C]31[/C][C]16.58[/C][C]16.5079145693015[/C][C]0.0720854306985004[/C][/ROW]
[ROW][C]32[/C][C]16.64[/C][C]16.6270868062359[/C][C]0.0129131937641418[/C][/ROW]
[ROW][C]33[/C][C]16.66[/C][C]16.7085945030842[/C][C]-0.0485945030842281[/C][/ROW]
[ROW][C]34[/C][C]16.81[/C][C]16.6707059957265[/C][C]0.139294004273456[/C][/ROW]
[ROW][C]35[/C][C]16.91[/C][C]16.8402352888027[/C][C]0.0697647111972515[/C][/ROW]
[ROW][C]36[/C][C]16.92[/C][C]16.9685359330438[/C][C]-0.0485359330438477[/C][/ROW]
[ROW][C]37[/C][C]16.95[/C][C]17.0310457195661[/C][C]-0.0810457195660774[/C][/ROW]
[ROW][C]38[/C][C]17.11[/C][C]17.0513168152015[/C][C]0.0586831847985323[/C][/ROW]
[ROW][C]39[/C][C]17.16[/C][C]17.1459158780139[/C][C]0.0140841219860732[/C][/ROW]
[ROW][C]40[/C][C]17.16[/C][C]17.2105187923732[/C][C]-0.0505187923732358[/C][/ROW]
[ROW][C]41[/C][C]17.27[/C][C]17.1559820369833[/C][C]0.114017963016689[/C][/ROW]
[ROW][C]42[/C][C]17.34[/C][C]17.2868911481578[/C][C]0.0531088518421683[/C][/ROW]
[ROW][C]43[/C][C]17.39[/C][C]17.3487706790578[/C][C]0.0412293209421826[/C][/ROW]
[ROW][C]44[/C][C]17.43[/C][C]17.4358093519106[/C][C]-0.00580935191062437[/C][/ROW]
[ROW][C]45[/C][C]17.45[/C][C]17.4966642929224[/C][C]-0.0466642929224008[/C][/ROW]
[ROW][C]46[/C][C]17.5[/C][C]17.4690953220484[/C][C]0.0309046779516358[/C][/ROW]
[ROW][C]47[/C][C]17.56[/C][C]17.5319884211162[/C][C]0.0280115788837634[/C][/ROW]
[ROW][C]48[/C][C]17.65[/C][C]17.6150825670668[/C][C]0.0349174329331881[/C][/ROW]
[ROW][C]49[/C][C]17.62[/C][C]17.7558141555956[/C][C]-0.135814155595583[/C][/ROW]
[ROW][C]50[/C][C]17.7[/C][C]17.7300913720881[/C][C]-0.0300913720881333[/C][/ROW]
[ROW][C]51[/C][C]17.72[/C][C]17.7379088121331[/C][C]-0.0179088121330544[/C][/ROW]
[ROW][C]52[/C][C]17.71[/C][C]17.7690476250755[/C][C]-0.0590476250754648[/C][/ROW]
[ROW][C]53[/C][C]17.74[/C][C]17.71378972137[/C][C]0.0262102786300424[/C][/ROW]
[ROW][C]54[/C][C]17.75[/C][C]17.7581046509252[/C][C]-0.00810465092522961[/C][/ROW]
[ROW][C]55[/C][C]17.78[/C][C]17.7609963328468[/C][C]0.0190036671531999[/C][/ROW]
[ROW][C]56[/C][C]17.8[/C][C]17.8246899368746[/C][C]-0.0246899368745908[/C][/ROW]
[ROW][C]57[/C][C]17.86[/C][C]17.8656729413862[/C][C]-0.00567294138618735[/C][/ROW]
[ROW][C]58[/C][C]17.88[/C][C]17.8807454854954[/C][C]-0.000745485495372122[/C][/ROW]
[ROW][C]59[/C][C]17.89[/C][C]17.9132857678911[/C][C]-0.0232857678911387[/C][/ROW]
[ROW][C]60[/C][C]17.94[/C][C]17.9477083474275[/C][C]-0.00770834742753124[/C][/ROW]
[ROW][C]61[/C][C]17.98[/C][C]18.0400347876155[/C][C]-0.0600347876155141[/C][/ROW]
[ROW][C]62[/C][C]18.1[/C][C]18.0914422399324[/C][C]0.00855776006764231[/C][/ROW]
[ROW][C]63[/C][C]18.14[/C][C]18.1367147986679[/C][C]0.00328520133211185[/C][/ROW]
[ROW][C]64[/C][C]18.19[/C][C]18.186235540704[/C][C]0.00376445929603264[/C][/ROW]
[ROW][C]65[/C][C]18.23[/C][C]18.1948023425103[/C][C]0.0351976574897499[/C][/ROW]
[ROW][C]66[/C][C]18.24[/C][C]18.2461511097213[/C][C]-0.00615110972132271[/C][/ROW]
[ROW][C]67[/C][C]18.27[/C][C]18.2521311659515[/C][C]0.0178688340484925[/C][/ROW]
[ROW][C]68[/C][C]18.3[/C][C]18.3127699396359[/C][C]-0.0127699396358878[/C][/ROW]
[ROW][C]69[/C][C]18.34[/C][C]18.3659931155065[/C][C]-0.0259931155065125[/C][/ROW]
[ROW][C]70[/C][C]18.36[/C][C]18.3618845075783[/C][C]-0.00188450757833536[/C][/ROW]
[ROW][C]71[/C][C]18.36[/C][C]18.3923202710073[/C][C]-0.0323202710073254[/C][/ROW]
[ROW][C]72[/C][C]18.4[/C][C]18.4188186902379[/C][C]-0.0188186902378966[/C][/ROW]
[ROW][C]73[/C][C]18.43[/C][C]18.4981753637779[/C][C]-0.0681753637778719[/C][/ROW]
[ROW][C]74[/C][C]18.47[/C][C]18.5449039796092[/C][C]-0.0749039796091573[/C][/ROW]
[ROW][C]75[/C][C]18.56[/C][C]18.5102422269335[/C][C]0.04975777306651[/C][/ROW]
[ROW][C]76[/C][C]18.58[/C][C]18.6041605974309[/C][C]-0.0241605974308747[/C][/ROW]
[ROW][C]77[/C][C]18.61[/C][C]18.5874802320045[/C][C]0.0225197679955365[/C][/ROW]
[ROW][C]78[/C][C]18.61[/C][C]18.6248576511732[/C][C]-0.0148576511732124[/C][/ROW]
[ROW][C]79[/C][C]18.69[/C][C]18.6236075892573[/C][C]0.0663924107426688[/C][/ROW]
[ROW][C]80[/C][C]18.74[/C][C]18.7291986077849[/C][C]0.0108013922150789[/C][/ROW]
[ROW][C]81[/C][C]18.75[/C][C]18.8043331673526[/C][C]-0.0543331673526382[/C][/ROW]
[ROW][C]82[/C][C]18.81[/C][C]18.7742506774596[/C][C]0.0357493225404397[/C][/ROW]
[ROW][C]83[/C][C]18.85[/C][C]18.8392493780089[/C][C]0.0107506219911464[/C][/ROW]
[ROW][C]84[/C][C]18.88[/C][C]18.9074846996973[/C][C]-0.0274846996973217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210508&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210508&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
1315.7515.46941773504270.280582264957271
1415.8615.84701837953940.0129816204606428
1515.8915.8915909203427-0.00159092034266983
1615.9415.9418316795719-0.00183167957191621
1715.9315.9335092078552-0.003509207855247
1815.9515.9565015545663-0.00650155456628454
1915.9915.9558032180220.0341967819779541
2015.9916.042717152457-0.052717152456955
2116.0616.05913818942540.00086181057463719
2216.0816.06797102702050.0120289729795111
2316.0716.1187172314334-0.0487172314334288
2416.1116.1327077369087-0.0227077369086786
2516.1516.2221092046088-0.0721092046087612
2616.1816.2508571687156-0.0708571687155555
2716.316.21471579925070.0852842007492605
2816.4216.34790153201280.0720984679872316
2916.4916.41009824166210.0799017583379289
3016.516.5126035537878-0.0126035537877733
3116.5816.50791456930150.0720854306985004
3216.6416.62708680623590.0129131937641418
3316.6616.7085945030842-0.0485945030842281
3416.8116.67070599572650.139294004273456
3516.9116.84023528880270.0697647111972515
3616.9216.9685359330438-0.0485359330438477
3716.9517.0310457195661-0.0810457195660774
3817.1117.05131681520150.0586831847985323
3917.1617.14591587801390.0140841219860732
4017.1617.2105187923732-0.0505187923732358
4117.2717.15598203698330.114017963016689
4217.3417.28689114815780.0531088518421683
4317.3917.34877067905780.0412293209421826
4417.4317.4358093519106-0.00580935191062437
4517.4517.4966642929224-0.0466642929224008
4617.517.46909532204840.0309046779516358
4717.5617.53198842111620.0280115788837634
4817.6517.61508256706680.0349174329331881
4917.6217.7558141555956-0.135814155595583
5017.717.7300913720881-0.0300913720881333
5117.7217.7379088121331-0.0179088121330544
5217.7117.7690476250755-0.0590476250754648
5317.7417.713789721370.0262102786300424
5417.7517.7581046509252-0.00810465092522961
5517.7817.76099633284680.0190036671531999
5617.817.8246899368746-0.0246899368745908
5717.8617.8656729413862-0.00567294138618735
5817.8817.8807454854954-0.000745485495372122
5917.8917.9132857678911-0.0232857678911387
6017.9417.9477083474275-0.00770834742753124
6117.9818.0400347876155-0.0600347876155141
6218.118.09144223993240.00855776006764231
6318.1418.13671479866790.00328520133211185
6418.1918.1862355407040.00376445929603264
6518.2318.19480234251030.0351976574897499
6618.2418.2461511097213-0.00615110972132271
6718.2718.25213116595150.0178688340484925
6818.318.3127699396359-0.0127699396358878
6918.3418.3659931155065-0.0259931155065125
7018.3618.3618845075783-0.00188450757833536
7118.3618.3923202710073-0.0323202710073254
7218.418.4188186902379-0.0188186902378966
7318.4318.4981753637779-0.0681753637778719
7418.4718.5449039796092-0.0749039796091573
7518.5618.51024222693350.04975777306651
7618.5818.6041605974309-0.0241605974308747
7718.6118.58748023200450.0225197679955365
7818.6118.6248576511732-0.0148576511732124
7918.6918.62360758925730.0663924107426688
8018.7418.72919860778490.0108013922150789
8118.7518.8043331673526-0.0543331673526382
8218.8118.77425067745960.0357493225404397
8318.8518.83924937800890.0107506219911464
8418.8818.9074846996973-0.0274846996973217






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8518.976339644348518.862184582967319.0904947057297
8619.087864404330318.930024349792319.2457044588683
8719.130351404428518.938529644468519.3221731643886
8819.173422020185918.952791803824319.3940522365475
8919.18191820945218.935829206956219.4280072119479
9019.196105572254418.926955238933119.4652559055758
9119.212708390051818.922322428434119.5030943516694
9219.252394292060118.942223191726419.5625653923939
9319.314276271819118.985508547947319.6430439956909
9419.340139744927518.993772423955319.6865070658997
9519.369874126710919.006759233302419.7329890201194
9619.426118881118919.046995509915419.8052422523224

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 18.9763396443485 & 18.8621845829673 & 19.0904947057297 \tabularnewline
86 & 19.0878644043303 & 18.9300243497923 & 19.2457044588683 \tabularnewline
87 & 19.1303514044285 & 18.9385296444685 & 19.3221731643886 \tabularnewline
88 & 19.1734220201859 & 18.9527918038243 & 19.3940522365475 \tabularnewline
89 & 19.181918209452 & 18.9358292069562 & 19.4280072119479 \tabularnewline
90 & 19.1961055722544 & 18.9269552389331 & 19.4652559055758 \tabularnewline
91 & 19.2127083900518 & 18.9223224284341 & 19.5030943516694 \tabularnewline
92 & 19.2523942920601 & 18.9422231917264 & 19.5625653923939 \tabularnewline
93 & 19.3142762718191 & 18.9855085479473 & 19.6430439956909 \tabularnewline
94 & 19.3401397449275 & 18.9937724239553 & 19.6865070658997 \tabularnewline
95 & 19.3698741267109 & 19.0067592333024 & 19.7329890201194 \tabularnewline
96 & 19.4261188811189 & 19.0469955099154 & 19.8052422523224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210508&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]85[/C][C]18.9763396443485[/C][C]18.8621845829673[/C][C]19.0904947057297[/C][/ROW]
[ROW][C]86[/C][C]19.0878644043303[/C][C]18.9300243497923[/C][C]19.2457044588683[/C][/ROW]
[ROW][C]87[/C][C]19.1303514044285[/C][C]18.9385296444685[/C][C]19.3221731643886[/C][/ROW]
[ROW][C]88[/C][C]19.1734220201859[/C][C]18.9527918038243[/C][C]19.3940522365475[/C][/ROW]
[ROW][C]89[/C][C]19.181918209452[/C][C]18.9358292069562[/C][C]19.4280072119479[/C][/ROW]
[ROW][C]90[/C][C]19.1961055722544[/C][C]18.9269552389331[/C][C]19.4652559055758[/C][/ROW]
[ROW][C]91[/C][C]19.2127083900518[/C][C]18.9223224284341[/C][C]19.5030943516694[/C][/ROW]
[ROW][C]92[/C][C]19.2523942920601[/C][C]18.9422231917264[/C][C]19.5625653923939[/C][/ROW]
[ROW][C]93[/C][C]19.3142762718191[/C][C]18.9855085479473[/C][C]19.6430439956909[/C][/ROW]
[ROW][C]94[/C][C]19.3401397449275[/C][C]18.9937724239553[/C][C]19.6865070658997[/C][/ROW]
[ROW][C]95[/C][C]19.3698741267109[/C][C]19.0067592333024[/C][C]19.7329890201194[/C][/ROW]
[ROW][C]96[/C][C]19.4261188811189[/C][C]19.0469955099154[/C][C]19.8052422523224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210508&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210508&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
8518.976339644348518.862184582967319.0904947057297
8619.087864404330318.930024349792319.2457044588683
8719.130351404428518.938529644468519.3221731643886
8819.173422020185918.952791803824319.3940522365475
8919.18191820945218.935829206956219.4280072119479
9019.196105572254418.926955238933119.4652559055758
9119.212708390051818.922322428434119.5030943516694
9219.252394292060118.942223191726419.5625653923939
9319.314276271819118.985508547947319.6430439956909
9419.340139744927518.993772423955319.6865070658997
9519.369874126710919.006759233302419.7329890201194
9619.426118881118919.046995509915419.8052422523224


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')