FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 31 May 2008 05:38:49 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/31/t121223418374q61ajefouybs5.htm/, Retrieved Wed, 09 Sep 2026 12:40:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13576, Retrieved Wed, 09 Sep 2026 12:40:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact484

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...] [2008-05-31 11:38:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103,6
103,7
103,8
104
104
104,1
104,2
104,3
104,4
104,5
104,7
104,7
104,9
105
105,2
105,3
105,4
105,5
105,7
105,8
105,9
106
106,1
106,2
106,6
106,8
107
107,1
107,3
107,4
107,6
107,7
107,9
108,2
108,3
108,5
108,92
109,23
109,41
109,65
109,91
110,01
110,2
110,49
110,57
110,72
110,94
111,09
111,28
111,41
111,62
111,76
111,89
112,04
112,12
112,3
112,47
112,59
112,78
112,73
112,99
113,1
113,33
113,38
113,68
113,65
113,81
113,88
114,02
114,25
114,28
114,38
114,73
114,97
115,05
115,29
115,37
115,54
115,76
115,92
116,02
116,21
116,26
116,51

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=13576&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=13576&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13576&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
alpha0.887355825989984
beta0.0349852410870049
gamma0.000576885537757277

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.887355825989984 \tabularnewline
beta & 0.0349852410870049 \tabularnewline
gamma & 0.000576885537757277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13576&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]0.887355825989984[/C][/ROW]
[ROW][C]beta[/C][C]0.0349852410870049[/C][/ROW]
[ROW][C]gamma[/C][C]0.000576885537757277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13576&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13576&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
alpha0.887355825989984
beta0.0349852410870049
gamma0.000576885537757277






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.9104.1271944444440.772805555555522
14105104.9502145707890.0497854292106865
15105.2105.233204132377-0.0332041323768379
16105.3105.341521622037-0.0415216220372798
17105.4105.445336193378-0.0453361933779775
18105.5105.544358449621-0.0443584496208302
19105.7105.730371232915-0.0303712329146464
20105.8105.815352799030-0.0153527990297135
21105.9105.909017775501-0.00901777550140537
22106106.008024220962-0.00802422096217015
23106.1106.103496529381-0.00349652938086820
24106.2106.1987112971280.00128870287225880
25106.6106.5649291612770.0350708387225751
26106.8106.7287820158770.0712179841233507
27107107.026962758075-0.0269627580747454
28107.1107.137190057582-0.0371900575823929
29107.3107.2413545211240.058645478876457
30107.4107.432380128908-0.0323801289084713
31107.6107.629129258405-0.0291292584052911
32107.7107.715358834682-0.0153588346823170
33107.9107.8091636405830.0908363594173522
34108.2108.0000209799720.199979020028181
35108.3108.2897684783000.0102315216998079
36108.5108.4072934096060.0927065903936608
37108.92108.8675998601830.0524001398166831
38109.23109.0603364931080.169663506892405
39109.41109.462427414518-0.0524274145180925
40109.65109.5658276553770.084172344623255
41109.91109.7972274162350.112772583764993
42110.01110.057494886986-0.0474948869858167
43110.2110.261580607339-0.0615806073390814
44110.49110.3387563018860.151243698114456
45110.57110.605316922304-0.0353169223036645
46110.72110.7052353425630.0147646574374249
47110.94110.8458664439570.0941335560430474
48111.09111.0556993555510.0343006444495018
49111.28111.480214817270-0.20021481726954
50111.41111.456995934128-0.0469959341281623
51111.62111.668288570797-0.0482885707969274
52111.76111.776968967715-0.0169689677150870
53111.89111.917081039623-0.0270810396231838
54112.04112.047355287642-0.00735528764214166
55112.12112.282421427464-0.162421427464082
56112.3112.262361951690.0376380483099013
57112.47112.4168076882480.0531923117517152
58112.59112.5867221343360.00327786566450072
59112.78112.7082625085650.0717374914349165
60112.73112.888619969027-0.158619969027185
61112.99113.126343579847-0.136343579847320
62113.1113.146206628359-0.0462066283589593
63113.33113.344619540014-0.0146195400138112
64113.38113.470643580129-0.0906435801289831
65113.68113.5305574147080.149442585292434
66113.65113.808130290408-0.158130290408451
67113.81113.895372642246-0.0853726422463126
68113.88113.932065151143-0.0520651511434664
69114.02113.9924977594220.0275022405778316
70114.25114.1243997134550.125600286544966
71114.28114.343072456016-0.0630724560163856
72114.38114.388189873547-0.00818987354749368
73114.73114.748469277854-0.0184692778538533
74114.97114.8656632885720.104336711427564
75115.05115.195065939976-0.145065939975581
76115.29115.1986852196830.0913147803172336
77115.37115.419077800185-0.049077800185259
78115.54115.5133108637160.0266891362842614
79115.76115.763134534343-0.00313453434252153
80115.92115.8739326968040.0460673031958976
81116.02116.02562436465-0.00562436464988991
82116.21116.1312846970270.078715302972796
83116.26116.310033091394-0.0500330913940132
84116.51116.3688210058220.141178994177665

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.9 & 104.127194444444 & 0.772805555555522 \tabularnewline
14 & 105 & 104.950214570789 & 0.0497854292106865 \tabularnewline
15 & 105.2 & 105.233204132377 & -0.0332041323768379 \tabularnewline
16 & 105.3 & 105.341521622037 & -0.0415216220372798 \tabularnewline
17 & 105.4 & 105.445336193378 & -0.0453361933779775 \tabularnewline
18 & 105.5 & 105.544358449621 & -0.0443584496208302 \tabularnewline
19 & 105.7 & 105.730371232915 & -0.0303712329146464 \tabularnewline
20 & 105.8 & 105.815352799030 & -0.0153527990297135 \tabularnewline
21 & 105.9 & 105.909017775501 & -0.00901777550140537 \tabularnewline
22 & 106 & 106.008024220962 & -0.00802422096217015 \tabularnewline
23 & 106.1 & 106.103496529381 & -0.00349652938086820 \tabularnewline
24 & 106.2 & 106.198711297128 & 0.00128870287225880 \tabularnewline
25 & 106.6 & 106.564929161277 & 0.0350708387225751 \tabularnewline
26 & 106.8 & 106.728782015877 & 0.0712179841233507 \tabularnewline
27 & 107 & 107.026962758075 & -0.0269627580747454 \tabularnewline
28 & 107.1 & 107.137190057582 & -0.0371900575823929 \tabularnewline
29 & 107.3 & 107.241354521124 & 0.058645478876457 \tabularnewline
30 & 107.4 & 107.432380128908 & -0.0323801289084713 \tabularnewline
31 & 107.6 & 107.629129258405 & -0.0291292584052911 \tabularnewline
32 & 107.7 & 107.715358834682 & -0.0153588346823170 \tabularnewline
33 & 107.9 & 107.809163640583 & 0.0908363594173522 \tabularnewline
34 & 108.2 & 108.000020979972 & 0.199979020028181 \tabularnewline
35 & 108.3 & 108.289768478300 & 0.0102315216998079 \tabularnewline
36 & 108.5 & 108.407293409606 & 0.0927065903936608 \tabularnewline
37 & 108.92 & 108.867599860183 & 0.0524001398166831 \tabularnewline
38 & 109.23 & 109.060336493108 & 0.169663506892405 \tabularnewline
39 & 109.41 & 109.462427414518 & -0.0524274145180925 \tabularnewline
40 & 109.65 & 109.565827655377 & 0.084172344623255 \tabularnewline
41 & 109.91 & 109.797227416235 & 0.112772583764993 \tabularnewline
42 & 110.01 & 110.057494886986 & -0.0474948869858167 \tabularnewline
43 & 110.2 & 110.261580607339 & -0.0615806073390814 \tabularnewline
44 & 110.49 & 110.338756301886 & 0.151243698114456 \tabularnewline
45 & 110.57 & 110.605316922304 & -0.0353169223036645 \tabularnewline
46 & 110.72 & 110.705235342563 & 0.0147646574374249 \tabularnewline
47 & 110.94 & 110.845866443957 & 0.0941335560430474 \tabularnewline
48 & 111.09 & 111.055699355551 & 0.0343006444495018 \tabularnewline
49 & 111.28 & 111.480214817270 & -0.20021481726954 \tabularnewline
50 & 111.41 & 111.456995934128 & -0.0469959341281623 \tabularnewline
51 & 111.62 & 111.668288570797 & -0.0482885707969274 \tabularnewline
52 & 111.76 & 111.776968967715 & -0.0169689677150870 \tabularnewline
53 & 111.89 & 111.917081039623 & -0.0270810396231838 \tabularnewline
54 & 112.04 & 112.047355287642 & -0.00735528764214166 \tabularnewline
55 & 112.12 & 112.282421427464 & -0.162421427464082 \tabularnewline
56 & 112.3 & 112.26236195169 & 0.0376380483099013 \tabularnewline
57 & 112.47 & 112.416807688248 & 0.0531923117517152 \tabularnewline
58 & 112.59 & 112.586722134336 & 0.00327786566450072 \tabularnewline
59 & 112.78 & 112.708262508565 & 0.0717374914349165 \tabularnewline
60 & 112.73 & 112.888619969027 & -0.158619969027185 \tabularnewline
61 & 112.99 & 113.126343579847 & -0.136343579847320 \tabularnewline
62 & 113.1 & 113.146206628359 & -0.0462066283589593 \tabularnewline
63 & 113.33 & 113.344619540014 & -0.0146195400138112 \tabularnewline
64 & 113.38 & 113.470643580129 & -0.0906435801289831 \tabularnewline
65 & 113.68 & 113.530557414708 & 0.149442585292434 \tabularnewline
66 & 113.65 & 113.808130290408 & -0.158130290408451 \tabularnewline
67 & 113.81 & 113.895372642246 & -0.0853726422463126 \tabularnewline
68 & 113.88 & 113.932065151143 & -0.0520651511434664 \tabularnewline
69 & 114.02 & 113.992497759422 & 0.0275022405778316 \tabularnewline
70 & 114.25 & 114.124399713455 & 0.125600286544966 \tabularnewline
71 & 114.28 & 114.343072456016 & -0.0630724560163856 \tabularnewline
72 & 114.38 & 114.388189873547 & -0.00818987354749368 \tabularnewline
73 & 114.73 & 114.748469277854 & -0.0184692778538533 \tabularnewline
74 & 114.97 & 114.865663288572 & 0.104336711427564 \tabularnewline
75 & 115.05 & 115.195065939976 & -0.145065939975581 \tabularnewline
76 & 115.29 & 115.198685219683 & 0.0913147803172336 \tabularnewline
77 & 115.37 & 115.419077800185 & -0.049077800185259 \tabularnewline
78 & 115.54 & 115.513310863716 & 0.0266891362842614 \tabularnewline
79 & 115.76 & 115.763134534343 & -0.00313453434252153 \tabularnewline
80 & 115.92 & 115.873932696804 & 0.0460673031958976 \tabularnewline
81 & 116.02 & 116.02562436465 & -0.00562436464988991 \tabularnewline
82 & 116.21 & 116.131284697027 & 0.078715302972796 \tabularnewline
83 & 116.26 & 116.310033091394 & -0.0500330913940132 \tabularnewline
84 & 116.51 & 116.368821005822 & 0.141178994177665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13576&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]104.9[/C][C]104.127194444444[/C][C]0.772805555555522[/C][/ROW]
[ROW][C]14[/C][C]105[/C][C]104.950214570789[/C][C]0.0497854292106865[/C][/ROW]
[ROW][C]15[/C][C]105.2[/C][C]105.233204132377[/C][C]-0.0332041323768379[/C][/ROW]
[ROW][C]16[/C][C]105.3[/C][C]105.341521622037[/C][C]-0.0415216220372798[/C][/ROW]
[ROW][C]17[/C][C]105.4[/C][C]105.445336193378[/C][C]-0.0453361933779775[/C][/ROW]
[ROW][C]18[/C][C]105.5[/C][C]105.544358449621[/C][C]-0.0443584496208302[/C][/ROW]
[ROW][C]19[/C][C]105.7[/C][C]105.730371232915[/C][C]-0.0303712329146464[/C][/ROW]
[ROW][C]20[/C][C]105.8[/C][C]105.815352799030[/C][C]-0.0153527990297135[/C][/ROW]
[ROW][C]21[/C][C]105.9[/C][C]105.909017775501[/C][C]-0.00901777550140537[/C][/ROW]
[ROW][C]22[/C][C]106[/C][C]106.008024220962[/C][C]-0.00802422096217015[/C][/ROW]
[ROW][C]23[/C][C]106.1[/C][C]106.103496529381[/C][C]-0.00349652938086820[/C][/ROW]
[ROW][C]24[/C][C]106.2[/C][C]106.198711297128[/C][C]0.00128870287225880[/C][/ROW]
[ROW][C]25[/C][C]106.6[/C][C]106.564929161277[/C][C]0.0350708387225751[/C][/ROW]
[ROW][C]26[/C][C]106.8[/C][C]106.728782015877[/C][C]0.0712179841233507[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]107.026962758075[/C][C]-0.0269627580747454[/C][/ROW]
[ROW][C]28[/C][C]107.1[/C][C]107.137190057582[/C][C]-0.0371900575823929[/C][/ROW]
[ROW][C]29[/C][C]107.3[/C][C]107.241354521124[/C][C]0.058645478876457[/C][/ROW]
[ROW][C]30[/C][C]107.4[/C][C]107.432380128908[/C][C]-0.0323801289084713[/C][/ROW]
[ROW][C]31[/C][C]107.6[/C][C]107.629129258405[/C][C]-0.0291292584052911[/C][/ROW]
[ROW][C]32[/C][C]107.7[/C][C]107.715358834682[/C][C]-0.0153588346823170[/C][/ROW]
[ROW][C]33[/C][C]107.9[/C][C]107.809163640583[/C][C]0.0908363594173522[/C][/ROW]
[ROW][C]34[/C][C]108.2[/C][C]108.000020979972[/C][C]0.199979020028181[/C][/ROW]
[ROW][C]35[/C][C]108.3[/C][C]108.289768478300[/C][C]0.0102315216998079[/C][/ROW]
[ROW][C]36[/C][C]108.5[/C][C]108.407293409606[/C][C]0.0927065903936608[/C][/ROW]
[ROW][C]37[/C][C]108.92[/C][C]108.867599860183[/C][C]0.0524001398166831[/C][/ROW]
[ROW][C]38[/C][C]109.23[/C][C]109.060336493108[/C][C]0.169663506892405[/C][/ROW]
[ROW][C]39[/C][C]109.41[/C][C]109.462427414518[/C][C]-0.0524274145180925[/C][/ROW]
[ROW][C]40[/C][C]109.65[/C][C]109.565827655377[/C][C]0.084172344623255[/C][/ROW]
[ROW][C]41[/C][C]109.91[/C][C]109.797227416235[/C][C]0.112772583764993[/C][/ROW]
[ROW][C]42[/C][C]110.01[/C][C]110.057494886986[/C][C]-0.0474948869858167[/C][/ROW]
[ROW][C]43[/C][C]110.2[/C][C]110.261580607339[/C][C]-0.0615806073390814[/C][/ROW]
[ROW][C]44[/C][C]110.49[/C][C]110.338756301886[/C][C]0.151243698114456[/C][/ROW]
[ROW][C]45[/C][C]110.57[/C][C]110.605316922304[/C][C]-0.0353169223036645[/C][/ROW]
[ROW][C]46[/C][C]110.72[/C][C]110.705235342563[/C][C]0.0147646574374249[/C][/ROW]
[ROW][C]47[/C][C]110.94[/C][C]110.845866443957[/C][C]0.0941335560430474[/C][/ROW]
[ROW][C]48[/C][C]111.09[/C][C]111.055699355551[/C][C]0.0343006444495018[/C][/ROW]
[ROW][C]49[/C][C]111.28[/C][C]111.480214817270[/C][C]-0.20021481726954[/C][/ROW]
[ROW][C]50[/C][C]111.41[/C][C]111.456995934128[/C][C]-0.0469959341281623[/C][/ROW]
[ROW][C]51[/C][C]111.62[/C][C]111.668288570797[/C][C]-0.0482885707969274[/C][/ROW]
[ROW][C]52[/C][C]111.76[/C][C]111.776968967715[/C][C]-0.0169689677150870[/C][/ROW]
[ROW][C]53[/C][C]111.89[/C][C]111.917081039623[/C][C]-0.0270810396231838[/C][/ROW]
[ROW][C]54[/C][C]112.04[/C][C]112.047355287642[/C][C]-0.00735528764214166[/C][/ROW]
[ROW][C]55[/C][C]112.12[/C][C]112.282421427464[/C][C]-0.162421427464082[/C][/ROW]
[ROW][C]56[/C][C]112.3[/C][C]112.26236195169[/C][C]0.0376380483099013[/C][/ROW]
[ROW][C]57[/C][C]112.47[/C][C]112.416807688248[/C][C]0.0531923117517152[/C][/ROW]
[ROW][C]58[/C][C]112.59[/C][C]112.586722134336[/C][C]0.00327786566450072[/C][/ROW]
[ROW][C]59[/C][C]112.78[/C][C]112.708262508565[/C][C]0.0717374914349165[/C][/ROW]
[ROW][C]60[/C][C]112.73[/C][C]112.888619969027[/C][C]-0.158619969027185[/C][/ROW]
[ROW][C]61[/C][C]112.99[/C][C]113.126343579847[/C][C]-0.136343579847320[/C][/ROW]
[ROW][C]62[/C][C]113.1[/C][C]113.146206628359[/C][C]-0.0462066283589593[/C][/ROW]
[ROW][C]63[/C][C]113.33[/C][C]113.344619540014[/C][C]-0.0146195400138112[/C][/ROW]
[ROW][C]64[/C][C]113.38[/C][C]113.470643580129[/C][C]-0.0906435801289831[/C][/ROW]
[ROW][C]65[/C][C]113.68[/C][C]113.530557414708[/C][C]0.149442585292434[/C][/ROW]
[ROW][C]66[/C][C]113.65[/C][C]113.808130290408[/C][C]-0.158130290408451[/C][/ROW]
[ROW][C]67[/C][C]113.81[/C][C]113.895372642246[/C][C]-0.0853726422463126[/C][/ROW]
[ROW][C]68[/C][C]113.88[/C][C]113.932065151143[/C][C]-0.0520651511434664[/C][/ROW]
[ROW][C]69[/C][C]114.02[/C][C]113.992497759422[/C][C]0.0275022405778316[/C][/ROW]
[ROW][C]70[/C][C]114.25[/C][C]114.124399713455[/C][C]0.125600286544966[/C][/ROW]
[ROW][C]71[/C][C]114.28[/C][C]114.343072456016[/C][C]-0.0630724560163856[/C][/ROW]
[ROW][C]72[/C][C]114.38[/C][C]114.388189873547[/C][C]-0.00818987354749368[/C][/ROW]
[ROW][C]73[/C][C]114.73[/C][C]114.748469277854[/C][C]-0.0184692778538533[/C][/ROW]
[ROW][C]74[/C][C]114.97[/C][C]114.865663288572[/C][C]0.104336711427564[/C][/ROW]
[ROW][C]75[/C][C]115.05[/C][C]115.195065939976[/C][C]-0.145065939975581[/C][/ROW]
[ROW][C]76[/C][C]115.29[/C][C]115.198685219683[/C][C]0.0913147803172336[/C][/ROW]
[ROW][C]77[/C][C]115.37[/C][C]115.419077800185[/C][C]-0.049077800185259[/C][/ROW]
[ROW][C]78[/C][C]115.54[/C][C]115.513310863716[/C][C]0.0266891362842614[/C][/ROW]
[ROW][C]79[/C][C]115.76[/C][C]115.763134534343[/C][C]-0.00313453434252153[/C][/ROW]
[ROW][C]80[/C][C]115.92[/C][C]115.873932696804[/C][C]0.0460673031958976[/C][/ROW]
[ROW][C]81[/C][C]116.02[/C][C]116.02562436465[/C][C]-0.00562436464988991[/C][/ROW]
[ROW][C]82[/C][C]116.21[/C][C]116.131284697027[/C][C]0.078715302972796[/C][/ROW]
[ROW][C]83[/C][C]116.26[/C][C]116.310033091394[/C][C]-0.0500330913940132[/C][/ROW]
[ROW][C]84[/C][C]116.51[/C][C]116.368821005822[/C][C]0.141178994177665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13576&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13576&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
13104.9104.1271944444440.772805555555522
14105104.9502145707890.0497854292106865
15105.2105.233204132377-0.0332041323768379
16105.3105.341521622037-0.0415216220372798
17105.4105.445336193378-0.0453361933779775
18105.5105.544358449621-0.0443584496208302
19105.7105.730371232915-0.0303712329146464
20105.8105.815352799030-0.0153527990297135
21105.9105.909017775501-0.00901777550140537
22106106.008024220962-0.00802422096217015
23106.1106.103496529381-0.00349652938086820
24106.2106.1987112971280.00128870287225880
25106.6106.5649291612770.0350708387225751
26106.8106.7287820158770.0712179841233507
27107107.026962758075-0.0269627580747454
28107.1107.137190057582-0.0371900575823929
29107.3107.2413545211240.058645478876457
30107.4107.432380128908-0.0323801289084713
31107.6107.629129258405-0.0291292584052911
32107.7107.715358834682-0.0153588346823170
33107.9107.8091636405830.0908363594173522
34108.2108.0000209799720.199979020028181
35108.3108.2897684783000.0102315216998079
36108.5108.4072934096060.0927065903936608
37108.92108.8675998601830.0524001398166831
38109.23109.0603364931080.169663506892405
39109.41109.462427414518-0.0524274145180925
40109.65109.5658276553770.084172344623255
41109.91109.7972274162350.112772583764993
42110.01110.057494886986-0.0474948869858167
43110.2110.261580607339-0.0615806073390814
44110.49110.3387563018860.151243698114456
45110.57110.605316922304-0.0353169223036645
46110.72110.7052353425630.0147646574374249
47110.94110.8458664439570.0941335560430474
48111.09111.0556993555510.0343006444495018
49111.28111.480214817270-0.20021481726954
50111.41111.456995934128-0.0469959341281623
51111.62111.668288570797-0.0482885707969274
52111.76111.776968967715-0.0169689677150870
53111.89111.917081039623-0.0270810396231838
54112.04112.047355287642-0.00735528764214166
55112.12112.282421427464-0.162421427464082
56112.3112.262361951690.0376380483099013
57112.47112.4168076882480.0531923117517152
58112.59112.5867221343360.00327786566450072
59112.78112.7082625085650.0717374914349165
60112.73112.888619969027-0.158619969027185
61112.99113.126343579847-0.136343579847320
62113.1113.146206628359-0.0462066283589593
63113.33113.344619540014-0.0146195400138112
64113.38113.470643580129-0.0906435801289831
65113.68113.5305574147080.149442585292434
66113.65113.808130290408-0.158130290408451
67113.81113.895372642246-0.0853726422463126
68113.88113.932065151143-0.0520651511434664
69114.02113.9924977594220.0275022405778316
70114.25114.1243997134550.125600286544966
71114.28114.343072456016-0.0630724560163856
72114.38114.388189873547-0.00818987354749368
73114.73114.748469277854-0.0184692778538533
74114.97114.8656632885720.104336711427564
75115.05115.195065939976-0.145065939975581
76115.29115.1986852196830.0913147803172336
77115.37115.419077800185-0.049077800185259
78115.54115.5133108637160.0266891362842614
79115.76115.763134534343-0.00313453434252153
80115.92115.8739326968040.0460673031958976
81116.02116.02562436465-0.00562436464988991
82116.21116.1312846970270.078715302972796
83116.26116.310033091394-0.0500330913940132
84116.51116.3688210058220.141178994177665






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85116.868376511980116.629965754023117.106787269937
86117.009274125983116.685574216604117.332974035362
87117.250144517287116.855151502630117.645137531945
88117.391075479099116.932095306168117.850055652029
89117.536166639935117.017686994605118.054646285264
90117.681214093457117.106232293045118.256195893869
91117.913784512921117.284402957392118.543166068450
92118.033896077006117.351633725510118.716158428502
93118.149804923115117.415777709017118.883832137212
94118.265734780856117.480768026473119.050701535239
95118.377455892096117.542158317358119.212753466833
96118.485036198328117.599850789270119.370221607386

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 116.868376511980 & 116.629965754023 & 117.106787269937 \tabularnewline
86 & 117.009274125983 & 116.685574216604 & 117.332974035362 \tabularnewline
87 & 117.250144517287 & 116.855151502630 & 117.645137531945 \tabularnewline
88 & 117.391075479099 & 116.932095306168 & 117.850055652029 \tabularnewline
89 & 117.536166639935 & 117.017686994605 & 118.054646285264 \tabularnewline
90 & 117.681214093457 & 117.106232293045 & 118.256195893869 \tabularnewline
91 & 117.913784512921 & 117.284402957392 & 118.543166068450 \tabularnewline
92 & 118.033896077006 & 117.351633725510 & 118.716158428502 \tabularnewline
93 & 118.149804923115 & 117.415777709017 & 118.883832137212 \tabularnewline
94 & 118.265734780856 & 117.480768026473 & 119.050701535239 \tabularnewline
95 & 118.377455892096 & 117.542158317358 & 119.212753466833 \tabularnewline
96 & 118.485036198328 & 117.599850789270 & 119.370221607386 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13576&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]116.868376511980[/C][C]116.629965754023[/C][C]117.106787269937[/C][/ROW]
[ROW][C]86[/C][C]117.009274125983[/C][C]116.685574216604[/C][C]117.332974035362[/C][/ROW]
[ROW][C]87[/C][C]117.250144517287[/C][C]116.855151502630[/C][C]117.645137531945[/C][/ROW]
[ROW][C]88[/C][C]117.391075479099[/C][C]116.932095306168[/C][C]117.850055652029[/C][/ROW]
[ROW][C]89[/C][C]117.536166639935[/C][C]117.017686994605[/C][C]118.054646285264[/C][/ROW]
[ROW][C]90[/C][C]117.681214093457[/C][C]117.106232293045[/C][C]118.256195893869[/C][/ROW]
[ROW][C]91[/C][C]117.913784512921[/C][C]117.284402957392[/C][C]118.543166068450[/C][/ROW]
[ROW][C]92[/C][C]118.033896077006[/C][C]117.351633725510[/C][C]118.716158428502[/C][/ROW]
[ROW][C]93[/C][C]118.149804923115[/C][C]117.415777709017[/C][C]118.883832137212[/C][/ROW]
[ROW][C]94[/C][C]118.265734780856[/C][C]117.480768026473[/C][C]119.050701535239[/C][/ROW]
[ROW][C]95[/C][C]118.377455892096[/C][C]117.542158317358[/C][C]119.212753466833[/C][/ROW]
[ROW][C]96[/C][C]118.485036198328[/C][C]117.599850789270[/C][C]119.370221607386[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13576&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13576&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
85116.868376511980116.629965754023117.106787269937
86117.009274125983116.685574216604117.332974035362
87117.250144517287116.855151502630117.645137531945
88117.391075479099116.932095306168117.850055652029
89117.536166639935117.017686994605118.054646285264
90117.681214093457117.106232293045118.256195893869
91117.913784512921117.284402957392118.543166068450
92118.033896077006117.351633725510118.716158428502
93118.149804923115117.415777709017118.883832137212
94118.265734780856117.480768026473119.050701535239
95118.377455892096117.542158317358119.212753466833
96118.485036198328117.599850789270119.370221607386


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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')