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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Sep 2015 08:24:18 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Sep/03/t14412650758c7ssu7k7qq4fg4.htm/, Retrieved Fri, 01 Nov 2024 00:32:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280486, Retrieved Fri, 01 Nov 2024 00:32:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-09-03 07:24:18] [3e99441ea7f7f69c8fa4628f6be951c3] [Current]
- RMPD    [Multiple Regression] [] [2015-09-03 07:28:12] [82473208b72870f966ef7d4d2162cc96]
- RMPD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2015-09-03 07:35:44] [82473208b72870f966ef7d4d2162cc96]
- RMPD    [Paired and Unpaired Two Samples Tests about the Mean] [] [2015-09-03 07:39:27] [82473208b72870f966ef7d4d2162cc96]
- RMPD    [Two-Way ANOVA] [] [2015-09-03 07:43:28] [82473208b72870f966ef7d4d2162cc96]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [] [2015-09-03 07:45:03] [82473208b72870f966ef7d4d2162cc96]
- RMPD    [Notched Boxplots] [] [2015-09-03 07:49:47] [82473208b72870f966ef7d4d2162cc96]
- RM D      [Kendall tau Correlation Matrix] [] [2015-09-03 07:52:24] [82473208b72870f966ef7d4d2162cc96]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
67
72
74
62
56
66
65
59
61
69
74
69
66
68
58
64
66
57
68
62
59
73
61
61
57
58
57
67
81
79
76
78
74
67
84
85
79
82
87
90
87
93
92
82
80
79
77
72
65
73
76
77
76
76
76
75
78
73
80
77
83
84
85
81
84
83
83
88
92
92
89
82
73
81
91
80
81
82
84
87
85
74
81
82
86
85
82
86
88
86
83
81
81
81
82
86
85
87
89
90
90
92
86
86
82
80
79
77
79
76
78
78
77
72
75
79
81
86
88
97
94
96
94
91
92
93
93
87
84
80
78
75
73
81
76
77
71
71
78
67
76
68
82
64
71
81
69
63
70
77
75
76
68

Tables (Output of Computation)





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=280486&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=280486&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280486&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.572095490251119
beta0
gamma0.62569921923147

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.572095490251119 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.62569921923147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280486&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]0.572095490251119[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.62569921923147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280486&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280486&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
alpha0.572095490251119
beta0
gamma0.62569921923147






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136667.2150106837607-1.21501068376068
146868.161371254937-0.161371254936967
155857.91884752502740.0811524749725976
166463.77340386061130.22659613938869
176666.1695011940266-0.16950119402658
185757.8389930292945-0.838993029294507
196863.04213827151244.95786172848762
206259.97830464496482.02169535503521
215963.8597034775381-4.8597034775381
227369.55428507137693.44571492862308
236175.9170257466958-14.9170257466958
246162.2328586263474-1.23285862634735
255758.3437020956432-1.34370209564317
265859.4985398029035-1.49853980290352
275748.55596116346268.44403883653735
286759.23382808853727.76617191146284
298165.837231810569415.1627681894306
307966.098996394379612.9010036056204
317680.7147788442654-4.7147788442654
327871.33114339864146.66885660135864
337476.0287398184778-2.02873981847779
346785.5665916727225-18.5665916727225
358474.41975968014389.58024031985623
368578.41416030427096.58583969572915
377978.96836864625610.0316313537438901
388280.86857224444551.13142775555447
398774.09260739388112.907392606119
409087.14244711837442.85755288162555
418792.9180131498315-5.91801314983149
429380.513994039760212.4860059602398
439290.17591711200231.82408288799769
448287.580984038159-5.58098403815903
458082.9418116016233-2.94181160162329
467987.5294627279413-8.52946272794134
477789.6608461609643-12.6608461609643
487280.1295021323577-8.1295021323577
496570.510309196894-5.51030919689403
507369.53445255696373.46554744303629
517667.24671820233218.75328179766785
527775.22927062695631.77072937304368
537678.0335040140385-2.0335040140385
547672.77927826184683.22072173815324
557674.28595587409611.71404412590385
567569.64544107369035.35455892630974
577871.96905420574226.03094579425778
587380.1939443559736-7.1939443559736
598081.9832372191393-1.98323721913934
607779.7737249773661-2.7737249773661
618373.91980945225089.08019054774918
628483.69430344406080.30569655593915
638581.01456809265453.98543190734553
648184.3999498786578-3.39994987865782
658483.22751737220020.772482627799803
668380.9853477920542.01465220794604
678381.39864132797651.60135867202347
688877.668369364267210.3316306357328
699283.02043826970948.97956173029057
709289.39139258955782.60860741044216
718998.1837933267032-9.18379332670324
728291.6432305973923-9.64323059739233
737385.0330635118287-12.0330635118287
748180.37948128258980.620518717410178
759178.865064838077612.1349351619224
768084.9353821267249-4.93538212672495
778184.0016608222911-3.00166082229109
788279.93289867902172.06710132097827
798480.26554310401973.73445689598034
808780.09304581906366.90695418093642
818583.12387049256751.87612950743249
827483.7252270358129-9.72522703581288
838182.3042050233882-1.30420502338819
848280.1485097141921.85149028580797
858679.47456789581426.52543210418575
868588.826081317013-3.82608131701302
878287.850649350795-5.85064935079504
888679.06109633309766.93890366690242
898885.43833399048022.56166600951984
908685.90943396983230.0905660301677216
918385.5577284460466-2.55772844604658
928182.6349031959302-1.63490319593022
938179.43201921426721.56798078573283
948176.75094365846354.24905634153647
958285.5791865174845-3.57918651748452
968682.9668888950633.03311110493701
978584.22034594649810.779654053501886
988787.5132164465206-0.513216446520588
998987.89100266369711.10899733630286
1009086.50730088541733.49269911458272
1019089.74102096088380.258979039116213
1029288.23315299245773.76684700754228
1038689.2755781510526-3.27557815105264
1048686.1891511093707-0.189151109370698
1058284.6709139888065-2.67091398880646
1068080.2826157249487-0.282615724948684
1077984.4223794642721-5.42237946427214
1087782.5259728453525-5.5259728453525
1097978.27947706413760.720522935862363
1107681.192366394358-5.192366394358
1117879.3275627639153-1.32756276391527
1127877.1881271049260.811872895074004
1137778.0223639368263-1.02236393682631
1147276.7206403082642-4.72064030826415
1157571.02187673483553.97812326516453
1167972.91161804841836.08838195158165
1178174.32026328565186.67973671434819
1188675.92087194516510.079128054835
1198884.61242470761063.38757529238939
1209787.72841743241079.27158256758933
1219493.61997013718040.380029862819569
1229694.75495077862771.24504922137227
1239497.6077242506644-3.60772425066438
1249194.7366299594544-3.73662995945442
1259292.4775911362457-0.477591136245735
1269390.49735483826172.50264516173829
1279391.26000307036691.73999692963309
1288792.4343220436096-5.43432204360964
1298487.409209328642-3.40920932864201
1308084.1481288533978-4.14812885339785
1317882.9087389910159-4.90873899101585
1327582.8538289983173-7.85382899831731
1337376.567390945154-3.567390945154
1348175.67566981005785.32433018994224
1357679.562902298986-3.562902298986
1367776.6829372919010.317062708099002
1377177.6155712452101-6.61557124521009
1387172.9217512365581-1.92175123655812
1397870.949031172317.05096882769004
1406773.2408845158788-6.24088451587878
1417668.29654374942367.70345625057637
1426871.1951311795748-3.19513117957479
1438270.297301597237111.7026984027629
1446478.9572030461012-14.9572030461012
1457169.7546055914481.24539440855196
1468173.99692238059157.0030776194085
1476976.4650953633101-7.46509536331014
1486372.3915232615532-9.39152326155325
1497065.91377889416794.08622110583212
1507768.59912713222938.40087286777069
1517574.93428550768480.0657144923152089
1527669.67115194477386.32884805522616
1536875.6513495667451-7.65134956674507

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 66 & 67.2150106837607 & -1.21501068376068 \tabularnewline
14 & 68 & 68.161371254937 & -0.161371254936967 \tabularnewline
15 & 58 & 57.9188475250274 & 0.0811524749725976 \tabularnewline
16 & 64 & 63.7734038606113 & 0.22659613938869 \tabularnewline
17 & 66 & 66.1695011940266 & -0.16950119402658 \tabularnewline
18 & 57 & 57.8389930292945 & -0.838993029294507 \tabularnewline
19 & 68 & 63.0421382715124 & 4.95786172848762 \tabularnewline
20 & 62 & 59.9783046449648 & 2.02169535503521 \tabularnewline
21 & 59 & 63.8597034775381 & -4.8597034775381 \tabularnewline
22 & 73 & 69.5542850713769 & 3.44571492862308 \tabularnewline
23 & 61 & 75.9170257466958 & -14.9170257466958 \tabularnewline
24 & 61 & 62.2328586263474 & -1.23285862634735 \tabularnewline
25 & 57 & 58.3437020956432 & -1.34370209564317 \tabularnewline
26 & 58 & 59.4985398029035 & -1.49853980290352 \tabularnewline
27 & 57 & 48.5559611634626 & 8.44403883653735 \tabularnewline
28 & 67 & 59.2338280885372 & 7.76617191146284 \tabularnewline
29 & 81 & 65.8372318105694 & 15.1627681894306 \tabularnewline
30 & 79 & 66.0989963943796 & 12.9010036056204 \tabularnewline
31 & 76 & 80.7147788442654 & -4.7147788442654 \tabularnewline
32 & 78 & 71.3311433986414 & 6.66885660135864 \tabularnewline
33 & 74 & 76.0287398184778 & -2.02873981847779 \tabularnewline
34 & 67 & 85.5665916727225 & -18.5665916727225 \tabularnewline
35 & 84 & 74.4197596801438 & 9.58024031985623 \tabularnewline
36 & 85 & 78.4141603042709 & 6.58583969572915 \tabularnewline
37 & 79 & 78.9683686462561 & 0.0316313537438901 \tabularnewline
38 & 82 & 80.8685722444455 & 1.13142775555447 \tabularnewline
39 & 87 & 74.092607393881 & 12.907392606119 \tabularnewline
40 & 90 & 87.1424471183744 & 2.85755288162555 \tabularnewline
41 & 87 & 92.9180131498315 & -5.91801314983149 \tabularnewline
42 & 93 & 80.5139940397602 & 12.4860059602398 \tabularnewline
43 & 92 & 90.1759171120023 & 1.82408288799769 \tabularnewline
44 & 82 & 87.580984038159 & -5.58098403815903 \tabularnewline
45 & 80 & 82.9418116016233 & -2.94181160162329 \tabularnewline
46 & 79 & 87.5294627279413 & -8.52946272794134 \tabularnewline
47 & 77 & 89.6608461609643 & -12.6608461609643 \tabularnewline
48 & 72 & 80.1295021323577 & -8.1295021323577 \tabularnewline
49 & 65 & 70.510309196894 & -5.51030919689403 \tabularnewline
50 & 73 & 69.5344525569637 & 3.46554744303629 \tabularnewline
51 & 76 & 67.2467182023321 & 8.75328179766785 \tabularnewline
52 & 77 & 75.2292706269563 & 1.77072937304368 \tabularnewline
53 & 76 & 78.0335040140385 & -2.0335040140385 \tabularnewline
54 & 76 & 72.7792782618468 & 3.22072173815324 \tabularnewline
55 & 76 & 74.2859558740961 & 1.71404412590385 \tabularnewline
56 & 75 & 69.6454410736903 & 5.35455892630974 \tabularnewline
57 & 78 & 71.9690542057422 & 6.03094579425778 \tabularnewline
58 & 73 & 80.1939443559736 & -7.1939443559736 \tabularnewline
59 & 80 & 81.9832372191393 & -1.98323721913934 \tabularnewline
60 & 77 & 79.7737249773661 & -2.7737249773661 \tabularnewline
61 & 83 & 73.9198094522508 & 9.08019054774918 \tabularnewline
62 & 84 & 83.6943034440608 & 0.30569655593915 \tabularnewline
63 & 85 & 81.0145680926545 & 3.98543190734553 \tabularnewline
64 & 81 & 84.3999498786578 & -3.39994987865782 \tabularnewline
65 & 84 & 83.2275173722002 & 0.772482627799803 \tabularnewline
66 & 83 & 80.985347792054 & 2.01465220794604 \tabularnewline
67 & 83 & 81.3986413279765 & 1.60135867202347 \tabularnewline
68 & 88 & 77.6683693642672 & 10.3316306357328 \tabularnewline
69 & 92 & 83.0204382697094 & 8.97956173029057 \tabularnewline
70 & 92 & 89.3913925895578 & 2.60860741044216 \tabularnewline
71 & 89 & 98.1837933267032 & -9.18379332670324 \tabularnewline
72 & 82 & 91.6432305973923 & -9.64323059739233 \tabularnewline
73 & 73 & 85.0330635118287 & -12.0330635118287 \tabularnewline
74 & 81 & 80.3794812825898 & 0.620518717410178 \tabularnewline
75 & 91 & 78.8650648380776 & 12.1349351619224 \tabularnewline
76 & 80 & 84.9353821267249 & -4.93538212672495 \tabularnewline
77 & 81 & 84.0016608222911 & -3.00166082229109 \tabularnewline
78 & 82 & 79.9328986790217 & 2.06710132097827 \tabularnewline
79 & 84 & 80.2655431040197 & 3.73445689598034 \tabularnewline
80 & 87 & 80.0930458190636 & 6.90695418093642 \tabularnewline
81 & 85 & 83.1238704925675 & 1.87612950743249 \tabularnewline
82 & 74 & 83.7252270358129 & -9.72522703581288 \tabularnewline
83 & 81 & 82.3042050233882 & -1.30420502338819 \tabularnewline
84 & 82 & 80.148509714192 & 1.85149028580797 \tabularnewline
85 & 86 & 79.4745678958142 & 6.52543210418575 \tabularnewline
86 & 85 & 88.826081317013 & -3.82608131701302 \tabularnewline
87 & 82 & 87.850649350795 & -5.85064935079504 \tabularnewline
88 & 86 & 79.0610963330976 & 6.93890366690242 \tabularnewline
89 & 88 & 85.4383339904802 & 2.56166600951984 \tabularnewline
90 & 86 & 85.9094339698323 & 0.0905660301677216 \tabularnewline
91 & 83 & 85.5577284460466 & -2.55772844604658 \tabularnewline
92 & 81 & 82.6349031959302 & -1.63490319593022 \tabularnewline
93 & 81 & 79.4320192142672 & 1.56798078573283 \tabularnewline
94 & 81 & 76.7509436584635 & 4.24905634153647 \tabularnewline
95 & 82 & 85.5791865174845 & -3.57918651748452 \tabularnewline
96 & 86 & 82.966888895063 & 3.03311110493701 \tabularnewline
97 & 85 & 84.2203459464981 & 0.779654053501886 \tabularnewline
98 & 87 & 87.5132164465206 & -0.513216446520588 \tabularnewline
99 & 89 & 87.8910026636971 & 1.10899733630286 \tabularnewline
100 & 90 & 86.5073008854173 & 3.49269911458272 \tabularnewline
101 & 90 & 89.7410209608838 & 0.258979039116213 \tabularnewline
102 & 92 & 88.2331529924577 & 3.76684700754228 \tabularnewline
103 & 86 & 89.2755781510526 & -3.27557815105264 \tabularnewline
104 & 86 & 86.1891511093707 & -0.189151109370698 \tabularnewline
105 & 82 & 84.6709139888065 & -2.67091398880646 \tabularnewline
106 & 80 & 80.2826157249487 & -0.282615724948684 \tabularnewline
107 & 79 & 84.4223794642721 & -5.42237946427214 \tabularnewline
108 & 77 & 82.5259728453525 & -5.5259728453525 \tabularnewline
109 & 79 & 78.2794770641376 & 0.720522935862363 \tabularnewline
110 & 76 & 81.192366394358 & -5.192366394358 \tabularnewline
111 & 78 & 79.3275627639153 & -1.32756276391527 \tabularnewline
112 & 78 & 77.188127104926 & 0.811872895074004 \tabularnewline
113 & 77 & 78.0223639368263 & -1.02236393682631 \tabularnewline
114 & 72 & 76.7206403082642 & -4.72064030826415 \tabularnewline
115 & 75 & 71.0218767348355 & 3.97812326516453 \tabularnewline
116 & 79 & 72.9116180484183 & 6.08838195158165 \tabularnewline
117 & 81 & 74.3202632856518 & 6.67973671434819 \tabularnewline
118 & 86 & 75.920871945165 & 10.079128054835 \tabularnewline
119 & 88 & 84.6124247076106 & 3.38757529238939 \tabularnewline
120 & 97 & 87.7284174324107 & 9.27158256758933 \tabularnewline
121 & 94 & 93.6199701371804 & 0.380029862819569 \tabularnewline
122 & 96 & 94.7549507786277 & 1.24504922137227 \tabularnewline
123 & 94 & 97.6077242506644 & -3.60772425066438 \tabularnewline
124 & 91 & 94.7366299594544 & -3.73662995945442 \tabularnewline
125 & 92 & 92.4775911362457 & -0.477591136245735 \tabularnewline
126 & 93 & 90.4973548382617 & 2.50264516173829 \tabularnewline
127 & 93 & 91.2600030703669 & 1.73999692963309 \tabularnewline
128 & 87 & 92.4343220436096 & -5.43432204360964 \tabularnewline
129 & 84 & 87.409209328642 & -3.40920932864201 \tabularnewline
130 & 80 & 84.1481288533978 & -4.14812885339785 \tabularnewline
131 & 78 & 82.9087389910159 & -4.90873899101585 \tabularnewline
132 & 75 & 82.8538289983173 & -7.85382899831731 \tabularnewline
133 & 73 & 76.567390945154 & -3.567390945154 \tabularnewline
134 & 81 & 75.6756698100578 & 5.32433018994224 \tabularnewline
135 & 76 & 79.562902298986 & -3.562902298986 \tabularnewline
136 & 77 & 76.682937291901 & 0.317062708099002 \tabularnewline
137 & 71 & 77.6155712452101 & -6.61557124521009 \tabularnewline
138 & 71 & 72.9217512365581 & -1.92175123655812 \tabularnewline
139 & 78 & 70.94903117231 & 7.05096882769004 \tabularnewline
140 & 67 & 73.2408845158788 & -6.24088451587878 \tabularnewline
141 & 76 & 68.2965437494236 & 7.70345625057637 \tabularnewline
142 & 68 & 71.1951311795748 & -3.19513117957479 \tabularnewline
143 & 82 & 70.2973015972371 & 11.7026984027629 \tabularnewline
144 & 64 & 78.9572030461012 & -14.9572030461012 \tabularnewline
145 & 71 & 69.754605591448 & 1.24539440855196 \tabularnewline
146 & 81 & 73.9969223805915 & 7.0030776194085 \tabularnewline
147 & 69 & 76.4650953633101 & -7.46509536331014 \tabularnewline
148 & 63 & 72.3915232615532 & -9.39152326155325 \tabularnewline
149 & 70 & 65.9137788941679 & 4.08622110583212 \tabularnewline
150 & 77 & 68.5991271322293 & 8.40087286777069 \tabularnewline
151 & 75 & 74.9342855076848 & 0.0657144923152089 \tabularnewline
152 & 76 & 69.6711519447738 & 6.32884805522616 \tabularnewline
153 & 68 & 75.6513495667451 & -7.65134956674507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280486&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]66[/C][C]67.2150106837607[/C][C]-1.21501068376068[/C][/ROW]
[ROW][C]14[/C][C]68[/C][C]68.161371254937[/C][C]-0.161371254936967[/C][/ROW]
[ROW][C]15[/C][C]58[/C][C]57.9188475250274[/C][C]0.0811524749725976[/C][/ROW]
[ROW][C]16[/C][C]64[/C][C]63.7734038606113[/C][C]0.22659613938869[/C][/ROW]
[ROW][C]17[/C][C]66[/C][C]66.1695011940266[/C][C]-0.16950119402658[/C][/ROW]
[ROW][C]18[/C][C]57[/C][C]57.8389930292945[/C][C]-0.838993029294507[/C][/ROW]
[ROW][C]19[/C][C]68[/C][C]63.0421382715124[/C][C]4.95786172848762[/C][/ROW]
[ROW][C]20[/C][C]62[/C][C]59.9783046449648[/C][C]2.02169535503521[/C][/ROW]
[ROW][C]21[/C][C]59[/C][C]63.8597034775381[/C][C]-4.8597034775381[/C][/ROW]
[ROW][C]22[/C][C]73[/C][C]69.5542850713769[/C][C]3.44571492862308[/C][/ROW]
[ROW][C]23[/C][C]61[/C][C]75.9170257466958[/C][C]-14.9170257466958[/C][/ROW]
[ROW][C]24[/C][C]61[/C][C]62.2328586263474[/C][C]-1.23285862634735[/C][/ROW]
[ROW][C]25[/C][C]57[/C][C]58.3437020956432[/C][C]-1.34370209564317[/C][/ROW]
[ROW][C]26[/C][C]58[/C][C]59.4985398029035[/C][C]-1.49853980290352[/C][/ROW]
[ROW][C]27[/C][C]57[/C][C]48.5559611634626[/C][C]8.44403883653735[/C][/ROW]
[ROW][C]28[/C][C]67[/C][C]59.2338280885372[/C][C]7.76617191146284[/C][/ROW]
[ROW][C]29[/C][C]81[/C][C]65.8372318105694[/C][C]15.1627681894306[/C][/ROW]
[ROW][C]30[/C][C]79[/C][C]66.0989963943796[/C][C]12.9010036056204[/C][/ROW]
[ROW][C]31[/C][C]76[/C][C]80.7147788442654[/C][C]-4.7147788442654[/C][/ROW]
[ROW][C]32[/C][C]78[/C][C]71.3311433986414[/C][C]6.66885660135864[/C][/ROW]
[ROW][C]33[/C][C]74[/C][C]76.0287398184778[/C][C]-2.02873981847779[/C][/ROW]
[ROW][C]34[/C][C]67[/C][C]85.5665916727225[/C][C]-18.5665916727225[/C][/ROW]
[ROW][C]35[/C][C]84[/C][C]74.4197596801438[/C][C]9.58024031985623[/C][/ROW]
[ROW][C]36[/C][C]85[/C][C]78.4141603042709[/C][C]6.58583969572915[/C][/ROW]
[ROW][C]37[/C][C]79[/C][C]78.9683686462561[/C][C]0.0316313537438901[/C][/ROW]
[ROW][C]38[/C][C]82[/C][C]80.8685722444455[/C][C]1.13142775555447[/C][/ROW]
[ROW][C]39[/C][C]87[/C][C]74.092607393881[/C][C]12.907392606119[/C][/ROW]
[ROW][C]40[/C][C]90[/C][C]87.1424471183744[/C][C]2.85755288162555[/C][/ROW]
[ROW][C]41[/C][C]87[/C][C]92.9180131498315[/C][C]-5.91801314983149[/C][/ROW]
[ROW][C]42[/C][C]93[/C][C]80.5139940397602[/C][C]12.4860059602398[/C][/ROW]
[ROW][C]43[/C][C]92[/C][C]90.1759171120023[/C][C]1.82408288799769[/C][/ROW]
[ROW][C]44[/C][C]82[/C][C]87.580984038159[/C][C]-5.58098403815903[/C][/ROW]
[ROW][C]45[/C][C]80[/C][C]82.9418116016233[/C][C]-2.94181160162329[/C][/ROW]
[ROW][C]46[/C][C]79[/C][C]87.5294627279413[/C][C]-8.52946272794134[/C][/ROW]
[ROW][C]47[/C][C]77[/C][C]89.6608461609643[/C][C]-12.6608461609643[/C][/ROW]
[ROW][C]48[/C][C]72[/C][C]80.1295021323577[/C][C]-8.1295021323577[/C][/ROW]
[ROW][C]49[/C][C]65[/C][C]70.510309196894[/C][C]-5.51030919689403[/C][/ROW]
[ROW][C]50[/C][C]73[/C][C]69.5344525569637[/C][C]3.46554744303629[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]67.2467182023321[/C][C]8.75328179766785[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]75.2292706269563[/C][C]1.77072937304368[/C][/ROW]
[ROW][C]53[/C][C]76[/C][C]78.0335040140385[/C][C]-2.0335040140385[/C][/ROW]
[ROW][C]54[/C][C]76[/C][C]72.7792782618468[/C][C]3.22072173815324[/C][/ROW]
[ROW][C]55[/C][C]76[/C][C]74.2859558740961[/C][C]1.71404412590385[/C][/ROW]
[ROW][C]56[/C][C]75[/C][C]69.6454410736903[/C][C]5.35455892630974[/C][/ROW]
[ROW][C]57[/C][C]78[/C][C]71.9690542057422[/C][C]6.03094579425778[/C][/ROW]
[ROW][C]58[/C][C]73[/C][C]80.1939443559736[/C][C]-7.1939443559736[/C][/ROW]
[ROW][C]59[/C][C]80[/C][C]81.9832372191393[/C][C]-1.98323721913934[/C][/ROW]
[ROW][C]60[/C][C]77[/C][C]79.7737249773661[/C][C]-2.7737249773661[/C][/ROW]
[ROW][C]61[/C][C]83[/C][C]73.9198094522508[/C][C]9.08019054774918[/C][/ROW]
[ROW][C]62[/C][C]84[/C][C]83.6943034440608[/C][C]0.30569655593915[/C][/ROW]
[ROW][C]63[/C][C]85[/C][C]81.0145680926545[/C][C]3.98543190734553[/C][/ROW]
[ROW][C]64[/C][C]81[/C][C]84.3999498786578[/C][C]-3.39994987865782[/C][/ROW]
[ROW][C]65[/C][C]84[/C][C]83.2275173722002[/C][C]0.772482627799803[/C][/ROW]
[ROW][C]66[/C][C]83[/C][C]80.985347792054[/C][C]2.01465220794604[/C][/ROW]
[ROW][C]67[/C][C]83[/C][C]81.3986413279765[/C][C]1.60135867202347[/C][/ROW]
[ROW][C]68[/C][C]88[/C][C]77.6683693642672[/C][C]10.3316306357328[/C][/ROW]
[ROW][C]69[/C][C]92[/C][C]83.0204382697094[/C][C]8.97956173029057[/C][/ROW]
[ROW][C]70[/C][C]92[/C][C]89.3913925895578[/C][C]2.60860741044216[/C][/ROW]
[ROW][C]71[/C][C]89[/C][C]98.1837933267032[/C][C]-9.18379332670324[/C][/ROW]
[ROW][C]72[/C][C]82[/C][C]91.6432305973923[/C][C]-9.64323059739233[/C][/ROW]
[ROW][C]73[/C][C]73[/C][C]85.0330635118287[/C][C]-12.0330635118287[/C][/ROW]
[ROW][C]74[/C][C]81[/C][C]80.3794812825898[/C][C]0.620518717410178[/C][/ROW]
[ROW][C]75[/C][C]91[/C][C]78.8650648380776[/C][C]12.1349351619224[/C][/ROW]
[ROW][C]76[/C][C]80[/C][C]84.9353821267249[/C][C]-4.93538212672495[/C][/ROW]
[ROW][C]77[/C][C]81[/C][C]84.0016608222911[/C][C]-3.00166082229109[/C][/ROW]
[ROW][C]78[/C][C]82[/C][C]79.9328986790217[/C][C]2.06710132097827[/C][/ROW]
[ROW][C]79[/C][C]84[/C][C]80.2655431040197[/C][C]3.73445689598034[/C][/ROW]
[ROW][C]80[/C][C]87[/C][C]80.0930458190636[/C][C]6.90695418093642[/C][/ROW]
[ROW][C]81[/C][C]85[/C][C]83.1238704925675[/C][C]1.87612950743249[/C][/ROW]
[ROW][C]82[/C][C]74[/C][C]83.7252270358129[/C][C]-9.72522703581288[/C][/ROW]
[ROW][C]83[/C][C]81[/C][C]82.3042050233882[/C][C]-1.30420502338819[/C][/ROW]
[ROW][C]84[/C][C]82[/C][C]80.148509714192[/C][C]1.85149028580797[/C][/ROW]
[ROW][C]85[/C][C]86[/C][C]79.4745678958142[/C][C]6.52543210418575[/C][/ROW]
[ROW][C]86[/C][C]85[/C][C]88.826081317013[/C][C]-3.82608131701302[/C][/ROW]
[ROW][C]87[/C][C]82[/C][C]87.850649350795[/C][C]-5.85064935079504[/C][/ROW]
[ROW][C]88[/C][C]86[/C][C]79.0610963330976[/C][C]6.93890366690242[/C][/ROW]
[ROW][C]89[/C][C]88[/C][C]85.4383339904802[/C][C]2.56166600951984[/C][/ROW]
[ROW][C]90[/C][C]86[/C][C]85.9094339698323[/C][C]0.0905660301677216[/C][/ROW]
[ROW][C]91[/C][C]83[/C][C]85.5577284460466[/C][C]-2.55772844604658[/C][/ROW]
[ROW][C]92[/C][C]81[/C][C]82.6349031959302[/C][C]-1.63490319593022[/C][/ROW]
[ROW][C]93[/C][C]81[/C][C]79.4320192142672[/C][C]1.56798078573283[/C][/ROW]
[ROW][C]94[/C][C]81[/C][C]76.7509436584635[/C][C]4.24905634153647[/C][/ROW]
[ROW][C]95[/C][C]82[/C][C]85.5791865174845[/C][C]-3.57918651748452[/C][/ROW]
[ROW][C]96[/C][C]86[/C][C]82.966888895063[/C][C]3.03311110493701[/C][/ROW]
[ROW][C]97[/C][C]85[/C][C]84.2203459464981[/C][C]0.779654053501886[/C][/ROW]
[ROW][C]98[/C][C]87[/C][C]87.5132164465206[/C][C]-0.513216446520588[/C][/ROW]
[ROW][C]99[/C][C]89[/C][C]87.8910026636971[/C][C]1.10899733630286[/C][/ROW]
[ROW][C]100[/C][C]90[/C][C]86.5073008854173[/C][C]3.49269911458272[/C][/ROW]
[ROW][C]101[/C][C]90[/C][C]89.7410209608838[/C][C]0.258979039116213[/C][/ROW]
[ROW][C]102[/C][C]92[/C][C]88.2331529924577[/C][C]3.76684700754228[/C][/ROW]
[ROW][C]103[/C][C]86[/C][C]89.2755781510526[/C][C]-3.27557815105264[/C][/ROW]
[ROW][C]104[/C][C]86[/C][C]86.1891511093707[/C][C]-0.189151109370698[/C][/ROW]
[ROW][C]105[/C][C]82[/C][C]84.6709139888065[/C][C]-2.67091398880646[/C][/ROW]
[ROW][C]106[/C][C]80[/C][C]80.2826157249487[/C][C]-0.282615724948684[/C][/ROW]
[ROW][C]107[/C][C]79[/C][C]84.4223794642721[/C][C]-5.42237946427214[/C][/ROW]
[ROW][C]108[/C][C]77[/C][C]82.5259728453525[/C][C]-5.5259728453525[/C][/ROW]
[ROW][C]109[/C][C]79[/C][C]78.2794770641376[/C][C]0.720522935862363[/C][/ROW]
[ROW][C]110[/C][C]76[/C][C]81.192366394358[/C][C]-5.192366394358[/C][/ROW]
[ROW][C]111[/C][C]78[/C][C]79.3275627639153[/C][C]-1.32756276391527[/C][/ROW]
[ROW][C]112[/C][C]78[/C][C]77.188127104926[/C][C]0.811872895074004[/C][/ROW]
[ROW][C]113[/C][C]77[/C][C]78.0223639368263[/C][C]-1.02236393682631[/C][/ROW]
[ROW][C]114[/C][C]72[/C][C]76.7206403082642[/C][C]-4.72064030826415[/C][/ROW]
[ROW][C]115[/C][C]75[/C][C]71.0218767348355[/C][C]3.97812326516453[/C][/ROW]
[ROW][C]116[/C][C]79[/C][C]72.9116180484183[/C][C]6.08838195158165[/C][/ROW]
[ROW][C]117[/C][C]81[/C][C]74.3202632856518[/C][C]6.67973671434819[/C][/ROW]
[ROW][C]118[/C][C]86[/C][C]75.920871945165[/C][C]10.079128054835[/C][/ROW]
[ROW][C]119[/C][C]88[/C][C]84.6124247076106[/C][C]3.38757529238939[/C][/ROW]
[ROW][C]120[/C][C]97[/C][C]87.7284174324107[/C][C]9.27158256758933[/C][/ROW]
[ROW][C]121[/C][C]94[/C][C]93.6199701371804[/C][C]0.380029862819569[/C][/ROW]
[ROW][C]122[/C][C]96[/C][C]94.7549507786277[/C][C]1.24504922137227[/C][/ROW]
[ROW][C]123[/C][C]94[/C][C]97.6077242506644[/C][C]-3.60772425066438[/C][/ROW]
[ROW][C]124[/C][C]91[/C][C]94.7366299594544[/C][C]-3.73662995945442[/C][/ROW]
[ROW][C]125[/C][C]92[/C][C]92.4775911362457[/C][C]-0.477591136245735[/C][/ROW]
[ROW][C]126[/C][C]93[/C][C]90.4973548382617[/C][C]2.50264516173829[/C][/ROW]
[ROW][C]127[/C][C]93[/C][C]91.2600030703669[/C][C]1.73999692963309[/C][/ROW]
[ROW][C]128[/C][C]87[/C][C]92.4343220436096[/C][C]-5.43432204360964[/C][/ROW]
[ROW][C]129[/C][C]84[/C][C]87.409209328642[/C][C]-3.40920932864201[/C][/ROW]
[ROW][C]130[/C][C]80[/C][C]84.1481288533978[/C][C]-4.14812885339785[/C][/ROW]
[ROW][C]131[/C][C]78[/C][C]82.9087389910159[/C][C]-4.90873899101585[/C][/ROW]
[ROW][C]132[/C][C]75[/C][C]82.8538289983173[/C][C]-7.85382899831731[/C][/ROW]
[ROW][C]133[/C][C]73[/C][C]76.567390945154[/C][C]-3.567390945154[/C][/ROW]
[ROW][C]134[/C][C]81[/C][C]75.6756698100578[/C][C]5.32433018994224[/C][/ROW]
[ROW][C]135[/C][C]76[/C][C]79.562902298986[/C][C]-3.562902298986[/C][/ROW]
[ROW][C]136[/C][C]77[/C][C]76.682937291901[/C][C]0.317062708099002[/C][/ROW]
[ROW][C]137[/C][C]71[/C][C]77.6155712452101[/C][C]-6.61557124521009[/C][/ROW]
[ROW][C]138[/C][C]71[/C][C]72.9217512365581[/C][C]-1.92175123655812[/C][/ROW]
[ROW][C]139[/C][C]78[/C][C]70.94903117231[/C][C]7.05096882769004[/C][/ROW]
[ROW][C]140[/C][C]67[/C][C]73.2408845158788[/C][C]-6.24088451587878[/C][/ROW]
[ROW][C]141[/C][C]76[/C][C]68.2965437494236[/C][C]7.70345625057637[/C][/ROW]
[ROW][C]142[/C][C]68[/C][C]71.1951311795748[/C][C]-3.19513117957479[/C][/ROW]
[ROW][C]143[/C][C]82[/C][C]70.2973015972371[/C][C]11.7026984027629[/C][/ROW]
[ROW][C]144[/C][C]64[/C][C]78.9572030461012[/C][C]-14.9572030461012[/C][/ROW]
[ROW][C]145[/C][C]71[/C][C]69.754605591448[/C][C]1.24539440855196[/C][/ROW]
[ROW][C]146[/C][C]81[/C][C]73.9969223805915[/C][C]7.0030776194085[/C][/ROW]
[ROW][C]147[/C][C]69[/C][C]76.4650953633101[/C][C]-7.46509536331014[/C][/ROW]
[ROW][C]148[/C][C]63[/C][C]72.3915232615532[/C][C]-9.39152326155325[/C][/ROW]
[ROW][C]149[/C][C]70[/C][C]65.9137788941679[/C][C]4.08622110583212[/C][/ROW]
[ROW][C]150[/C][C]77[/C][C]68.5991271322293[/C][C]8.40087286777069[/C][/ROW]
[ROW][C]151[/C][C]75[/C][C]74.9342855076848[/C][C]0.0657144923152089[/C][/ROW]
[ROW][C]152[/C][C]76[/C][C]69.6711519447738[/C][C]6.32884805522616[/C][/ROW]
[ROW][C]153[/C][C]68[/C][C]75.6513495667451[/C][C]-7.65134956674507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280486&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280486&T=2

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136667.2150106837607-1.21501068376068
146868.161371254937-0.161371254936967
155857.91884752502740.0811524749725976
166463.77340386061130.22659613938869
176666.1695011940266-0.16950119402658
185757.8389930292945-0.838993029294507
196863.04213827151244.95786172848762
206259.97830464496482.02169535503521
215963.8597034775381-4.8597034775381
227369.55428507137693.44571492862308
236175.9170257466958-14.9170257466958
246162.2328586263474-1.23285862634735
255758.3437020956432-1.34370209564317
265859.4985398029035-1.49853980290352
275748.55596116346268.44403883653735
286759.23382808853727.76617191146284
298165.837231810569415.1627681894306
307966.098996394379612.9010036056204
317680.7147788442654-4.7147788442654
327871.33114339864146.66885660135864
337476.0287398184778-2.02873981847779
346785.5665916727225-18.5665916727225
358474.41975968014389.58024031985623
368578.41416030427096.58583969572915
377978.96836864625610.0316313537438901
388280.86857224444551.13142775555447
398774.09260739388112.907392606119
409087.14244711837442.85755288162555
418792.9180131498315-5.91801314983149
429380.513994039760212.4860059602398
439290.17591711200231.82408288799769
448287.580984038159-5.58098403815903
458082.9418116016233-2.94181160162329
467987.5294627279413-8.52946272794134
477789.6608461609643-12.6608461609643
487280.1295021323577-8.1295021323577
496570.510309196894-5.51030919689403
507369.53445255696373.46554744303629
517667.24671820233218.75328179766785
527775.22927062695631.77072937304368
537678.0335040140385-2.0335040140385
547672.77927826184683.22072173815324
557674.28595587409611.71404412590385
567569.64544107369035.35455892630974
577871.96905420574226.03094579425778
587380.1939443559736-7.1939443559736
598081.9832372191393-1.98323721913934
607779.7737249773661-2.7737249773661
618373.91980945225089.08019054774918
628483.69430344406080.30569655593915
638581.01456809265453.98543190734553
648184.3999498786578-3.39994987865782
658483.22751737220020.772482627799803
668380.9853477920542.01465220794604
678381.39864132797651.60135867202347
688877.668369364267210.3316306357328
699283.02043826970948.97956173029057
709289.39139258955782.60860741044216
718998.1837933267032-9.18379332670324
728291.6432305973923-9.64323059739233
737385.0330635118287-12.0330635118287
748180.37948128258980.620518717410178
759178.865064838077612.1349351619224
768084.9353821267249-4.93538212672495
778184.0016608222911-3.00166082229109
788279.93289867902172.06710132097827
798480.26554310401973.73445689598034
808780.09304581906366.90695418093642
818583.12387049256751.87612950743249
827483.7252270358129-9.72522703581288
838182.3042050233882-1.30420502338819
848280.1485097141921.85149028580797
858679.47456789581426.52543210418575
868588.826081317013-3.82608131701302
878287.850649350795-5.85064935079504
888679.06109633309766.93890366690242
898885.43833399048022.56166600951984
908685.90943396983230.0905660301677216
918385.5577284460466-2.55772844604658
928182.6349031959302-1.63490319593022
938179.43201921426721.56798078573283
948176.75094365846354.24905634153647
958285.5791865174845-3.57918651748452
968682.9668888950633.03311110493701
978584.22034594649810.779654053501886
988787.5132164465206-0.513216446520588
998987.89100266369711.10899733630286
1009086.50730088541733.49269911458272
1019089.74102096088380.258979039116213
1029288.23315299245773.76684700754228
1038689.2755781510526-3.27557815105264
1048686.1891511093707-0.189151109370698
1058284.6709139888065-2.67091398880646
1068080.2826157249487-0.282615724948684
1077984.4223794642721-5.42237946427214
1087782.5259728453525-5.5259728453525
1097978.27947706413760.720522935862363
1107681.192366394358-5.192366394358
1117879.3275627639153-1.32756276391527
1127877.1881271049260.811872895074004
1137778.0223639368263-1.02236393682631
1147276.7206403082642-4.72064030826415
1157571.02187673483553.97812326516453
1167972.91161804841836.08838195158165
1178174.32026328565186.67973671434819
1188675.92087194516510.079128054835
1198884.61242470761063.38757529238939
1209787.72841743241079.27158256758933
1219493.61997013718040.380029862819569
1229694.75495077862771.24504922137227
1239497.6077242506644-3.60772425066438
1249194.7366299594544-3.73662995945442
1259292.4775911362457-0.477591136245735
1269390.49735483826172.50264516173829
1279391.26000307036691.73999692963309
1288792.4343220436096-5.43432204360964
1298487.409209328642-3.40920932864201
1308084.1481288533978-4.14812885339785
1317882.9087389910159-4.90873899101585
1327582.8538289983173-7.85382899831731
1337376.567390945154-3.567390945154
1348175.67566981005785.32433018994224
1357679.562902298986-3.562902298986
1367776.6829372919010.317062708099002
1377177.6155712452101-6.61557124521009
1387172.9217512365581-1.92175123655812
1397870.949031172317.05096882769004
1406773.2408845158788-6.24088451587878
1417668.29654374942367.70345625057637
1426871.1951311795748-3.19513117957479
1438270.297301597237111.7026984027629
1446478.9572030461012-14.9572030461012
1457169.7546055914481.24539440855196
1468173.99692238059157.0030776194085
1476976.4650953633101-7.46509536331014
1486372.3915232615532-9.39152326155325
1497065.91377889416794.08622110583212
1507768.59912713222938.40087286777069
1517574.93428550768480.0657144923152089
1527669.67115194477386.32884805522616
1536875.6513495667451-7.65134956674507






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
15466.8475392934554.945675323855578.7494032630445
15571.766367556196758.05444268203885.4782924303554
15666.593298870409251.283844224393481.9027535164249
15770.285725452475953.53037050660187.0410803983508
15875.357117042590757.271088258855593.4431458263258
15969.945159245617850.619866105022589.270452386213
16069.626553659231449.136812988013190.1162943304498
16172.130182172377150.538702589504193.72166175525
16273.633024525215950.993357823131796.2726912273001
16372.930430135820149.28900407508396.5718561965572
16469.306589967357244.704160331462793.9090196032518
16567.923030790413942.39575005405393.4503115267748

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
154 & 66.84753929345 & 54.9456753238555 & 78.7494032630445 \tabularnewline
155 & 71.7663675561967 & 58.054442682038 & 85.4782924303554 \tabularnewline
156 & 66.5932988704092 & 51.2838442243934 & 81.9027535164249 \tabularnewline
157 & 70.2857254524759 & 53.530370506601 & 87.0410803983508 \tabularnewline
158 & 75.3571170425907 & 57.2710882588555 & 93.4431458263258 \tabularnewline
159 & 69.9451592456178 & 50.6198661050225 & 89.270452386213 \tabularnewline
160 & 69.6265536592314 & 49.1368129880131 & 90.1162943304498 \tabularnewline
161 & 72.1301821723771 & 50.5387025895041 & 93.72166175525 \tabularnewline
162 & 73.6330245252159 & 50.9933578231317 & 96.2726912273001 \tabularnewline
163 & 72.9304301358201 & 49.289004075083 & 96.5718561965572 \tabularnewline
164 & 69.3065899673572 & 44.7041603314627 & 93.9090196032518 \tabularnewline
165 & 67.9230307904139 & 42.395750054053 & 93.4503115267748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280486&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]154[/C][C]66.84753929345[/C][C]54.9456753238555[/C][C]78.7494032630445[/C][/ROW]
[ROW][C]155[/C][C]71.7663675561967[/C][C]58.054442682038[/C][C]85.4782924303554[/C][/ROW]
[ROW][C]156[/C][C]66.5932988704092[/C][C]51.2838442243934[/C][C]81.9027535164249[/C][/ROW]
[ROW][C]157[/C][C]70.2857254524759[/C][C]53.530370506601[/C][C]87.0410803983508[/C][/ROW]
[ROW][C]158[/C][C]75.3571170425907[/C][C]57.2710882588555[/C][C]93.4431458263258[/C][/ROW]
[ROW][C]159[/C][C]69.9451592456178[/C][C]50.6198661050225[/C][C]89.270452386213[/C][/ROW]
[ROW][C]160[/C][C]69.6265536592314[/C][C]49.1368129880131[/C][C]90.1162943304498[/C][/ROW]
[ROW][C]161[/C][C]72.1301821723771[/C][C]50.5387025895041[/C][C]93.72166175525[/C][/ROW]
[ROW][C]162[/C][C]73.6330245252159[/C][C]50.9933578231317[/C][C]96.2726912273001[/C][/ROW]
[ROW][C]163[/C][C]72.9304301358201[/C][C]49.289004075083[/C][C]96.5718561965572[/C][/ROW]
[ROW][C]164[/C][C]69.3065899673572[/C][C]44.7041603314627[/C][C]93.9090196032518[/C][/ROW]
[ROW][C]165[/C][C]67.9230307904139[/C][C]42.395750054053[/C][C]93.4503115267748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280486&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280486&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
15466.8475392934554.945675323855578.7494032630445
15571.766367556196758.05444268203885.4782924303554
15666.593298870409251.283844224393481.9027535164249
15770.285725452475953.53037050660187.0410803983508
15875.357117042590757.271088258855593.4431458263258
15969.945159245617850.619866105022589.270452386213
16069.626553659231449.136812988013190.1162943304498
16172.130182172377150.538702589504193.72166175525
16273.633024525215950.993357823131796.2726912273001
16372.930430135820149.28900407508396.5718561965572
16469.306589967357244.704160331462793.9090196032518
16567.923030790413942.39575005405393.4503115267748


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')