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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 computationSun, 16 Jan 2011 15:15:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jan/16/t1295190889q75olqunhqh68kc.htm/, Retrieved Thu, 16 May 2024 16:00:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117425, Retrieved Thu, 16 May 2024 16:00:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact111

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [10/2 eigen reeks ...] [2011-01-16 15:15:54] [c6c4f641f0c0971fe864266cb6b6a9b0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100,4
97,7
97
96,5
98,4
106,3
103,1
102,4
95
98,1
106,1
99,1
101,2
95,5
99,8
97,1
97,5
96,8
97,7
100,9
94,3
99,5
100,8
97
99,2
101
102,3
97
91,2
97,6
95,7
100,5
94,4
102,9
105,1
98,8
100,7
99,6
107,7
102,9
101,6
102,7
110,5
109,8
94,3
102,5
105
102,3
107,7
100,3
99,5
95
97,7
96,3
97,8
106,4
96,1
106,2
114,7
111,9
121
117,7
115,4
114,3
109,5
108,1
108,2
99,1
101,2
98,1
95,5
97,9
98,2
98,7
95,6
95,8
94,4
96,5
103,3
104,3
104,5
102,3
103,8
103,1
102,2
106,3
102,1
94
102,6
102,6
106,7
107,9
109,3
105,9
109,1
108,5
111,7
109,8
109,1
108,5
108,5
106,2
117,1
109,8
115,2
115,9
119,2
121
118,6
117,6
114,6
110,6
102,5
101,6
107,4
105,8
102,8
104
100,4
100,6

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'Herman Ole Andreas Wold' @ www.yougetit.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117425&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117425&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117425&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'Herman Ole Andreas Wold' @ www.yougetit.org






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.645519343176284
beta0
gamma0.630222883115812

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.645519343176284 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.630222883115812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117425&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]0.645519343176284[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.630222883115812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117425&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117425&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
alpha0.645519343176284
beta0
gamma0.630222883115812






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13101.2102.525-1.32500000000003
1495.596.0715808096854-0.571580809685358
1599.899.9086749469057-0.108674946905722
1697.196.92375043928670.17624956071333
1797.597.41441687934740.0855831206526005
1896.896.8923897119053-0.0923897119053265
1997.7101.167977638487-3.46797763848723
20100.998.10205826386822.7979417361318
2194.392.29757771501542.00242228498456
2299.596.36290730590753.1370926940925
23100.8106.214855260675-5.41485526067517
249795.96718872213681.03281127786325
2599.298.87310823901860.326891760981354
2610193.65433235275977.3456676472403
27102.3102.70557752661-0.40557752661033
289799.59264931476-2.59264931475998
2991.298.2756829235404-7.07568292354041
3097.693.091160547964.50883945204001
3195.799.5828184106473-3.88281841064732
32100.597.648929095252.85107090474993
3394.491.70102395796062.69897604203936
34102.996.46947990884986.43052009115019
35105.1106.53687820285-1.43687820285
3698.8100.29749325132-1.49749325132005
37100.7101.412348544547-0.712348544546884
3899.697.09073025691812.50926974308186
39107.7101.2883447412016.4116552587989
40102.9102.087476337930.812523662070177
41101.6101.967097095834-0.36709709583387
42102.7103.701100037914-1.00110003791352
43110.5104.7612737277385.73872627226244
44109.8110.542640755584-0.742640755584318
4594.3102.240946958373-7.9409469583727
46102.5100.9747605403631.52523945963662
47105106.118114193257-1.11811419325703
48102.3100.0709560635862.2290439364139
49107.7103.7667659522363.93323404776383
50100.3103.163676482069-2.86367648206925
5199.5104.764750280781-5.26475028078139
529596.7756800451205-1.7756800451205
5397.794.72103581989582.9789641801042
5496.398.4733486269165-2.17334862691654
5597.8100.282502652167-2.48250265216697
56106.499.30895818444467.09104181555536
5796.194.4559432974131.64405670258699
58106.2101.4918254359054.7081745640951
59114.7108.0992952457386.60070475426187
60111.9107.7825452763584.11745472364193
61121113.0780800311737.92191996882654
62117.7113.5313222836154.16867771638482
63115.4119.135512485183-3.73551248518277
64114.3112.9130594730671.38694052693265
65109.5113.962144182978-4.46214418297819
66108.1111.760041540663-3.6600415406631
67108.2112.540440960346-4.34044096034586
6899.1112.506308649066-13.4063086490663
69101.293.2049911570537.99500884294704
7098.1105.025065261446-6.92506526144575
7195.5104.54584843191-9.0458484319095
7297.993.57418314660924.32581685339082
7398.299.8541441523693-1.6541441523693
7498.793.28737062716045.41262937283958
7595.697.9287451960203-2.32874519602026
7695.893.75875301412922.04124698587081
7794.493.92350902104240.476490978957571
7896.595.08858209601251.41141790398754
79103.398.9907042156114.30929578438892
80104.3102.5148129308291.78518706917117
81104.597.80099308805086.69900691194917
82102.3105.451301144575-3.15130114457507
83103.8106.934335225665-3.13433522566451
84103.1102.765920444360.334079555639818
85102.2105.133203630046-2.93320363004567
86106.399.31950254895256.98049745104753
87102.1103.243529109843-1.14352910984277
8894100.814881051026-6.81488105102643
89102.694.91326576224757.68673423775253
90102.6100.9415547078461.65844529215403
91106.7105.6505289819181.04947101808204
92107.9106.5064672703441.393532729656
93109.3102.6375832792266.66241672077385
94105.9108.063694896898-2.16369489689808
95109.1110.188038131494-1.08803813149372
96108.5108.1153978864040.384602113595903
97111.7109.7853773453081.91462265469212
98109.8109.3157807832120.484219216788134
99109.1107.2314117531911.86858824680893
100108.5105.4801533576863.01984664231378
101108.5109.166732300793-0.666732300792702
102106.2108.455966281895-2.25596628189453
103117.1110.5020662056596.59793379434106
104109.8115.016508554146-5.21650855414576
105115.2108.0577933363037.14220666369683
106115.9111.8218492301824.07815076981788
107119.2118.215728260520.984271739479709
108121117.8097946354433.19020536455668
109118.6121.632654638014-3.0326546380138
110117.6117.649940153837-0.0499401538369852
111114.6115.530031480746-0.930031480745939
112110.6112.229403139543-1.62940313954277
113102.5112.091212966017-9.59121296601667
114101.6105.264484283663-3.6644842836628
115107.4108.379335996946-0.979335996946219
116105.8105.3631361854160.436863814583987
117102.8104.814741677478-2.0147416774781
118104101.9832946246322.01670537536775
119100.4106.355292566911-5.95529256691141
120100.6101.962545538909-1.36254553890876

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101.2 & 102.525 & -1.32500000000003 \tabularnewline
14 & 95.5 & 96.0715808096854 & -0.571580809685358 \tabularnewline
15 & 99.8 & 99.9086749469057 & -0.108674946905722 \tabularnewline
16 & 97.1 & 96.9237504392867 & 0.17624956071333 \tabularnewline
17 & 97.5 & 97.4144168793474 & 0.0855831206526005 \tabularnewline
18 & 96.8 & 96.8923897119053 & -0.0923897119053265 \tabularnewline
19 & 97.7 & 101.167977638487 & -3.46797763848723 \tabularnewline
20 & 100.9 & 98.1020582638682 & 2.7979417361318 \tabularnewline
21 & 94.3 & 92.2975777150154 & 2.00242228498456 \tabularnewline
22 & 99.5 & 96.3629073059075 & 3.1370926940925 \tabularnewline
23 & 100.8 & 106.214855260675 & -5.41485526067517 \tabularnewline
24 & 97 & 95.9671887221368 & 1.03281127786325 \tabularnewline
25 & 99.2 & 98.8731082390186 & 0.326891760981354 \tabularnewline
26 & 101 & 93.6543323527597 & 7.3456676472403 \tabularnewline
27 & 102.3 & 102.70557752661 & -0.40557752661033 \tabularnewline
28 & 97 & 99.59264931476 & -2.59264931475998 \tabularnewline
29 & 91.2 & 98.2756829235404 & -7.07568292354041 \tabularnewline
30 & 97.6 & 93.09116054796 & 4.50883945204001 \tabularnewline
31 & 95.7 & 99.5828184106473 & -3.88281841064732 \tabularnewline
32 & 100.5 & 97.64892909525 & 2.85107090474993 \tabularnewline
33 & 94.4 & 91.7010239579606 & 2.69897604203936 \tabularnewline
34 & 102.9 & 96.4694799088498 & 6.43052009115019 \tabularnewline
35 & 105.1 & 106.53687820285 & -1.43687820285 \tabularnewline
36 & 98.8 & 100.29749325132 & -1.49749325132005 \tabularnewline
37 & 100.7 & 101.412348544547 & -0.712348544546884 \tabularnewline
38 & 99.6 & 97.0907302569181 & 2.50926974308186 \tabularnewline
39 & 107.7 & 101.288344741201 & 6.4116552587989 \tabularnewline
40 & 102.9 & 102.08747633793 & 0.812523662070177 \tabularnewline
41 & 101.6 & 101.967097095834 & -0.36709709583387 \tabularnewline
42 & 102.7 & 103.701100037914 & -1.00110003791352 \tabularnewline
43 & 110.5 & 104.761273727738 & 5.73872627226244 \tabularnewline
44 & 109.8 & 110.542640755584 & -0.742640755584318 \tabularnewline
45 & 94.3 & 102.240946958373 & -7.9409469583727 \tabularnewline
46 & 102.5 & 100.974760540363 & 1.52523945963662 \tabularnewline
47 & 105 & 106.118114193257 & -1.11811419325703 \tabularnewline
48 & 102.3 & 100.070956063586 & 2.2290439364139 \tabularnewline
49 & 107.7 & 103.766765952236 & 3.93323404776383 \tabularnewline
50 & 100.3 & 103.163676482069 & -2.86367648206925 \tabularnewline
51 & 99.5 & 104.764750280781 & -5.26475028078139 \tabularnewline
52 & 95 & 96.7756800451205 & -1.7756800451205 \tabularnewline
53 & 97.7 & 94.7210358198958 & 2.9789641801042 \tabularnewline
54 & 96.3 & 98.4733486269165 & -2.17334862691654 \tabularnewline
55 & 97.8 & 100.282502652167 & -2.48250265216697 \tabularnewline
56 & 106.4 & 99.3089581844446 & 7.09104181555536 \tabularnewline
57 & 96.1 & 94.455943297413 & 1.64405670258699 \tabularnewline
58 & 106.2 & 101.491825435905 & 4.7081745640951 \tabularnewline
59 & 114.7 & 108.099295245738 & 6.60070475426187 \tabularnewline
60 & 111.9 & 107.782545276358 & 4.11745472364193 \tabularnewline
61 & 121 & 113.078080031173 & 7.92191996882654 \tabularnewline
62 & 117.7 & 113.531322283615 & 4.16867771638482 \tabularnewline
63 & 115.4 & 119.135512485183 & -3.73551248518277 \tabularnewline
64 & 114.3 & 112.913059473067 & 1.38694052693265 \tabularnewline
65 & 109.5 & 113.962144182978 & -4.46214418297819 \tabularnewline
66 & 108.1 & 111.760041540663 & -3.6600415406631 \tabularnewline
67 & 108.2 & 112.540440960346 & -4.34044096034586 \tabularnewline
68 & 99.1 & 112.506308649066 & -13.4063086490663 \tabularnewline
69 & 101.2 & 93.204991157053 & 7.99500884294704 \tabularnewline
70 & 98.1 & 105.025065261446 & -6.92506526144575 \tabularnewline
71 & 95.5 & 104.54584843191 & -9.0458484319095 \tabularnewline
72 & 97.9 & 93.5741831466092 & 4.32581685339082 \tabularnewline
73 & 98.2 & 99.8541441523693 & -1.6541441523693 \tabularnewline
74 & 98.7 & 93.2873706271604 & 5.41262937283958 \tabularnewline
75 & 95.6 & 97.9287451960203 & -2.32874519602026 \tabularnewline
76 & 95.8 & 93.7587530141292 & 2.04124698587081 \tabularnewline
77 & 94.4 & 93.9235090210424 & 0.476490978957571 \tabularnewline
78 & 96.5 & 95.0885820960125 & 1.41141790398754 \tabularnewline
79 & 103.3 & 98.990704215611 & 4.30929578438892 \tabularnewline
80 & 104.3 & 102.514812930829 & 1.78518706917117 \tabularnewline
81 & 104.5 & 97.8009930880508 & 6.69900691194917 \tabularnewline
82 & 102.3 & 105.451301144575 & -3.15130114457507 \tabularnewline
83 & 103.8 & 106.934335225665 & -3.13433522566451 \tabularnewline
84 & 103.1 & 102.76592044436 & 0.334079555639818 \tabularnewline
85 & 102.2 & 105.133203630046 & -2.93320363004567 \tabularnewline
86 & 106.3 & 99.3195025489525 & 6.98049745104753 \tabularnewline
87 & 102.1 & 103.243529109843 & -1.14352910984277 \tabularnewline
88 & 94 & 100.814881051026 & -6.81488105102643 \tabularnewline
89 & 102.6 & 94.9132657622475 & 7.68673423775253 \tabularnewline
90 & 102.6 & 100.941554707846 & 1.65844529215403 \tabularnewline
91 & 106.7 & 105.650528981918 & 1.04947101808204 \tabularnewline
92 & 107.9 & 106.506467270344 & 1.393532729656 \tabularnewline
93 & 109.3 & 102.637583279226 & 6.66241672077385 \tabularnewline
94 & 105.9 & 108.063694896898 & -2.16369489689808 \tabularnewline
95 & 109.1 & 110.188038131494 & -1.08803813149372 \tabularnewline
96 & 108.5 & 108.115397886404 & 0.384602113595903 \tabularnewline
97 & 111.7 & 109.785377345308 & 1.91462265469212 \tabularnewline
98 & 109.8 & 109.315780783212 & 0.484219216788134 \tabularnewline
99 & 109.1 & 107.231411753191 & 1.86858824680893 \tabularnewline
100 & 108.5 & 105.480153357686 & 3.01984664231378 \tabularnewline
101 & 108.5 & 109.166732300793 & -0.666732300792702 \tabularnewline
102 & 106.2 & 108.455966281895 & -2.25596628189453 \tabularnewline
103 & 117.1 & 110.502066205659 & 6.59793379434106 \tabularnewline
104 & 109.8 & 115.016508554146 & -5.21650855414576 \tabularnewline
105 & 115.2 & 108.057793336303 & 7.14220666369683 \tabularnewline
106 & 115.9 & 111.821849230182 & 4.07815076981788 \tabularnewline
107 & 119.2 & 118.21572826052 & 0.984271739479709 \tabularnewline
108 & 121 & 117.809794635443 & 3.19020536455668 \tabularnewline
109 & 118.6 & 121.632654638014 & -3.0326546380138 \tabularnewline
110 & 117.6 & 117.649940153837 & -0.0499401538369852 \tabularnewline
111 & 114.6 & 115.530031480746 & -0.930031480745939 \tabularnewline
112 & 110.6 & 112.229403139543 & -1.62940313954277 \tabularnewline
113 & 102.5 & 112.091212966017 & -9.59121296601667 \tabularnewline
114 & 101.6 & 105.264484283663 & -3.6644842836628 \tabularnewline
115 & 107.4 & 108.379335996946 & -0.979335996946219 \tabularnewline
116 & 105.8 & 105.363136185416 & 0.436863814583987 \tabularnewline
117 & 102.8 & 104.814741677478 & -2.0147416774781 \tabularnewline
118 & 104 & 101.983294624632 & 2.01670537536775 \tabularnewline
119 & 100.4 & 106.355292566911 & -5.95529256691141 \tabularnewline
120 & 100.6 & 101.962545538909 & -1.36254553890876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117425&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]101.2[/C][C]102.525[/C][C]-1.32500000000003[/C][/ROW]
[ROW][C]14[/C][C]95.5[/C][C]96.0715808096854[/C][C]-0.571580809685358[/C][/ROW]
[ROW][C]15[/C][C]99.8[/C][C]99.9086749469057[/C][C]-0.108674946905722[/C][/ROW]
[ROW][C]16[/C][C]97.1[/C][C]96.9237504392867[/C][C]0.17624956071333[/C][/ROW]
[ROW][C]17[/C][C]97.5[/C][C]97.4144168793474[/C][C]0.0855831206526005[/C][/ROW]
[ROW][C]18[/C][C]96.8[/C][C]96.8923897119053[/C][C]-0.0923897119053265[/C][/ROW]
[ROW][C]19[/C][C]97.7[/C][C]101.167977638487[/C][C]-3.46797763848723[/C][/ROW]
[ROW][C]20[/C][C]100.9[/C][C]98.1020582638682[/C][C]2.7979417361318[/C][/ROW]
[ROW][C]21[/C][C]94.3[/C][C]92.2975777150154[/C][C]2.00242228498456[/C][/ROW]
[ROW][C]22[/C][C]99.5[/C][C]96.3629073059075[/C][C]3.1370926940925[/C][/ROW]
[ROW][C]23[/C][C]100.8[/C][C]106.214855260675[/C][C]-5.41485526067517[/C][/ROW]
[ROW][C]24[/C][C]97[/C][C]95.9671887221368[/C][C]1.03281127786325[/C][/ROW]
[ROW][C]25[/C][C]99.2[/C][C]98.8731082390186[/C][C]0.326891760981354[/C][/ROW]
[ROW][C]26[/C][C]101[/C][C]93.6543323527597[/C][C]7.3456676472403[/C][/ROW]
[ROW][C]27[/C][C]102.3[/C][C]102.70557752661[/C][C]-0.40557752661033[/C][/ROW]
[ROW][C]28[/C][C]97[/C][C]99.59264931476[/C][C]-2.59264931475998[/C][/ROW]
[ROW][C]29[/C][C]91.2[/C][C]98.2756829235404[/C][C]-7.07568292354041[/C][/ROW]
[ROW][C]30[/C][C]97.6[/C][C]93.09116054796[/C][C]4.50883945204001[/C][/ROW]
[ROW][C]31[/C][C]95.7[/C][C]99.5828184106473[/C][C]-3.88281841064732[/C][/ROW]
[ROW][C]32[/C][C]100.5[/C][C]97.64892909525[/C][C]2.85107090474993[/C][/ROW]
[ROW][C]33[/C][C]94.4[/C][C]91.7010239579606[/C][C]2.69897604203936[/C][/ROW]
[ROW][C]34[/C][C]102.9[/C][C]96.4694799088498[/C][C]6.43052009115019[/C][/ROW]
[ROW][C]35[/C][C]105.1[/C][C]106.53687820285[/C][C]-1.43687820285[/C][/ROW]
[ROW][C]36[/C][C]98.8[/C][C]100.29749325132[/C][C]-1.49749325132005[/C][/ROW]
[ROW][C]37[/C][C]100.7[/C][C]101.412348544547[/C][C]-0.712348544546884[/C][/ROW]
[ROW][C]38[/C][C]99.6[/C][C]97.0907302569181[/C][C]2.50926974308186[/C][/ROW]
[ROW][C]39[/C][C]107.7[/C][C]101.288344741201[/C][C]6.4116552587989[/C][/ROW]
[ROW][C]40[/C][C]102.9[/C][C]102.08747633793[/C][C]0.812523662070177[/C][/ROW]
[ROW][C]41[/C][C]101.6[/C][C]101.967097095834[/C][C]-0.36709709583387[/C][/ROW]
[ROW][C]42[/C][C]102.7[/C][C]103.701100037914[/C][C]-1.00110003791352[/C][/ROW]
[ROW][C]43[/C][C]110.5[/C][C]104.761273727738[/C][C]5.73872627226244[/C][/ROW]
[ROW][C]44[/C][C]109.8[/C][C]110.542640755584[/C][C]-0.742640755584318[/C][/ROW]
[ROW][C]45[/C][C]94.3[/C][C]102.240946958373[/C][C]-7.9409469583727[/C][/ROW]
[ROW][C]46[/C][C]102.5[/C][C]100.974760540363[/C][C]1.52523945963662[/C][/ROW]
[ROW][C]47[/C][C]105[/C][C]106.118114193257[/C][C]-1.11811419325703[/C][/ROW]
[ROW][C]48[/C][C]102.3[/C][C]100.070956063586[/C][C]2.2290439364139[/C][/ROW]
[ROW][C]49[/C][C]107.7[/C][C]103.766765952236[/C][C]3.93323404776383[/C][/ROW]
[ROW][C]50[/C][C]100.3[/C][C]103.163676482069[/C][C]-2.86367648206925[/C][/ROW]
[ROW][C]51[/C][C]99.5[/C][C]104.764750280781[/C][C]-5.26475028078139[/C][/ROW]
[ROW][C]52[/C][C]95[/C][C]96.7756800451205[/C][C]-1.7756800451205[/C][/ROW]
[ROW][C]53[/C][C]97.7[/C][C]94.7210358198958[/C][C]2.9789641801042[/C][/ROW]
[ROW][C]54[/C][C]96.3[/C][C]98.4733486269165[/C][C]-2.17334862691654[/C][/ROW]
[ROW][C]55[/C][C]97.8[/C][C]100.282502652167[/C][C]-2.48250265216697[/C][/ROW]
[ROW][C]56[/C][C]106.4[/C][C]99.3089581844446[/C][C]7.09104181555536[/C][/ROW]
[ROW][C]57[/C][C]96.1[/C][C]94.455943297413[/C][C]1.64405670258699[/C][/ROW]
[ROW][C]58[/C][C]106.2[/C][C]101.491825435905[/C][C]4.7081745640951[/C][/ROW]
[ROW][C]59[/C][C]114.7[/C][C]108.099295245738[/C][C]6.60070475426187[/C][/ROW]
[ROW][C]60[/C][C]111.9[/C][C]107.782545276358[/C][C]4.11745472364193[/C][/ROW]
[ROW][C]61[/C][C]121[/C][C]113.078080031173[/C][C]7.92191996882654[/C][/ROW]
[ROW][C]62[/C][C]117.7[/C][C]113.531322283615[/C][C]4.16867771638482[/C][/ROW]
[ROW][C]63[/C][C]115.4[/C][C]119.135512485183[/C][C]-3.73551248518277[/C][/ROW]
[ROW][C]64[/C][C]114.3[/C][C]112.913059473067[/C][C]1.38694052693265[/C][/ROW]
[ROW][C]65[/C][C]109.5[/C][C]113.962144182978[/C][C]-4.46214418297819[/C][/ROW]
[ROW][C]66[/C][C]108.1[/C][C]111.760041540663[/C][C]-3.6600415406631[/C][/ROW]
[ROW][C]67[/C][C]108.2[/C][C]112.540440960346[/C][C]-4.34044096034586[/C][/ROW]
[ROW][C]68[/C][C]99.1[/C][C]112.506308649066[/C][C]-13.4063086490663[/C][/ROW]
[ROW][C]69[/C][C]101.2[/C][C]93.204991157053[/C][C]7.99500884294704[/C][/ROW]
[ROW][C]70[/C][C]98.1[/C][C]105.025065261446[/C][C]-6.92506526144575[/C][/ROW]
[ROW][C]71[/C][C]95.5[/C][C]104.54584843191[/C][C]-9.0458484319095[/C][/ROW]
[ROW][C]72[/C][C]97.9[/C][C]93.5741831466092[/C][C]4.32581685339082[/C][/ROW]
[ROW][C]73[/C][C]98.2[/C][C]99.8541441523693[/C][C]-1.6541441523693[/C][/ROW]
[ROW][C]74[/C][C]98.7[/C][C]93.2873706271604[/C][C]5.41262937283958[/C][/ROW]
[ROW][C]75[/C][C]95.6[/C][C]97.9287451960203[/C][C]-2.32874519602026[/C][/ROW]
[ROW][C]76[/C][C]95.8[/C][C]93.7587530141292[/C][C]2.04124698587081[/C][/ROW]
[ROW][C]77[/C][C]94.4[/C][C]93.9235090210424[/C][C]0.476490978957571[/C][/ROW]
[ROW][C]78[/C][C]96.5[/C][C]95.0885820960125[/C][C]1.41141790398754[/C][/ROW]
[ROW][C]79[/C][C]103.3[/C][C]98.990704215611[/C][C]4.30929578438892[/C][/ROW]
[ROW][C]80[/C][C]104.3[/C][C]102.514812930829[/C][C]1.78518706917117[/C][/ROW]
[ROW][C]81[/C][C]104.5[/C][C]97.8009930880508[/C][C]6.69900691194917[/C][/ROW]
[ROW][C]82[/C][C]102.3[/C][C]105.451301144575[/C][C]-3.15130114457507[/C][/ROW]
[ROW][C]83[/C][C]103.8[/C][C]106.934335225665[/C][C]-3.13433522566451[/C][/ROW]
[ROW][C]84[/C][C]103.1[/C][C]102.76592044436[/C][C]0.334079555639818[/C][/ROW]
[ROW][C]85[/C][C]102.2[/C][C]105.133203630046[/C][C]-2.93320363004567[/C][/ROW]
[ROW][C]86[/C][C]106.3[/C][C]99.3195025489525[/C][C]6.98049745104753[/C][/ROW]
[ROW][C]87[/C][C]102.1[/C][C]103.243529109843[/C][C]-1.14352910984277[/C][/ROW]
[ROW][C]88[/C][C]94[/C][C]100.814881051026[/C][C]-6.81488105102643[/C][/ROW]
[ROW][C]89[/C][C]102.6[/C][C]94.9132657622475[/C][C]7.68673423775253[/C][/ROW]
[ROW][C]90[/C][C]102.6[/C][C]100.941554707846[/C][C]1.65844529215403[/C][/ROW]
[ROW][C]91[/C][C]106.7[/C][C]105.650528981918[/C][C]1.04947101808204[/C][/ROW]
[ROW][C]92[/C][C]107.9[/C][C]106.506467270344[/C][C]1.393532729656[/C][/ROW]
[ROW][C]93[/C][C]109.3[/C][C]102.637583279226[/C][C]6.66241672077385[/C][/ROW]
[ROW][C]94[/C][C]105.9[/C][C]108.063694896898[/C][C]-2.16369489689808[/C][/ROW]
[ROW][C]95[/C][C]109.1[/C][C]110.188038131494[/C][C]-1.08803813149372[/C][/ROW]
[ROW][C]96[/C][C]108.5[/C][C]108.115397886404[/C][C]0.384602113595903[/C][/ROW]
[ROW][C]97[/C][C]111.7[/C][C]109.785377345308[/C][C]1.91462265469212[/C][/ROW]
[ROW][C]98[/C][C]109.8[/C][C]109.315780783212[/C][C]0.484219216788134[/C][/ROW]
[ROW][C]99[/C][C]109.1[/C][C]107.231411753191[/C][C]1.86858824680893[/C][/ROW]
[ROW][C]100[/C][C]108.5[/C][C]105.480153357686[/C][C]3.01984664231378[/C][/ROW]
[ROW][C]101[/C][C]108.5[/C][C]109.166732300793[/C][C]-0.666732300792702[/C][/ROW]
[ROW][C]102[/C][C]106.2[/C][C]108.455966281895[/C][C]-2.25596628189453[/C][/ROW]
[ROW][C]103[/C][C]117.1[/C][C]110.502066205659[/C][C]6.59793379434106[/C][/ROW]
[ROW][C]104[/C][C]109.8[/C][C]115.016508554146[/C][C]-5.21650855414576[/C][/ROW]
[ROW][C]105[/C][C]115.2[/C][C]108.057793336303[/C][C]7.14220666369683[/C][/ROW]
[ROW][C]106[/C][C]115.9[/C][C]111.821849230182[/C][C]4.07815076981788[/C][/ROW]
[ROW][C]107[/C][C]119.2[/C][C]118.21572826052[/C][C]0.984271739479709[/C][/ROW]
[ROW][C]108[/C][C]121[/C][C]117.809794635443[/C][C]3.19020536455668[/C][/ROW]
[ROW][C]109[/C][C]118.6[/C][C]121.632654638014[/C][C]-3.0326546380138[/C][/ROW]
[ROW][C]110[/C][C]117.6[/C][C]117.649940153837[/C][C]-0.0499401538369852[/C][/ROW]
[ROW][C]111[/C][C]114.6[/C][C]115.530031480746[/C][C]-0.930031480745939[/C][/ROW]
[ROW][C]112[/C][C]110.6[/C][C]112.229403139543[/C][C]-1.62940313954277[/C][/ROW]
[ROW][C]113[/C][C]102.5[/C][C]112.091212966017[/C][C]-9.59121296601667[/C][/ROW]
[ROW][C]114[/C][C]101.6[/C][C]105.264484283663[/C][C]-3.6644842836628[/C][/ROW]
[ROW][C]115[/C][C]107.4[/C][C]108.379335996946[/C][C]-0.979335996946219[/C][/ROW]
[ROW][C]116[/C][C]105.8[/C][C]105.363136185416[/C][C]0.436863814583987[/C][/ROW]
[ROW][C]117[/C][C]102.8[/C][C]104.814741677478[/C][C]-2.0147416774781[/C][/ROW]
[ROW][C]118[/C][C]104[/C][C]101.983294624632[/C][C]2.01670537536775[/C][/ROW]
[ROW][C]119[/C][C]100.4[/C][C]106.355292566911[/C][C]-5.95529256691141[/C][/ROW]
[ROW][C]120[/C][C]100.6[/C][C]101.962545538909[/C][C]-1.36254553890876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117425&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117425&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
13101.2102.525-1.32500000000003
1495.596.0715808096854-0.571580809685358
1599.899.9086749469057-0.108674946905722
1697.196.92375043928670.17624956071333
1797.597.41441687934740.0855831206526005
1896.896.8923897119053-0.0923897119053265
1997.7101.167977638487-3.46797763848723
20100.998.10205826386822.7979417361318
2194.392.29757771501542.00242228498456
2299.596.36290730590753.1370926940925
23100.8106.214855260675-5.41485526067517
249795.96718872213681.03281127786325
2599.298.87310823901860.326891760981354
2610193.65433235275977.3456676472403
27102.3102.70557752661-0.40557752661033
289799.59264931476-2.59264931475998
2991.298.2756829235404-7.07568292354041
3097.693.091160547964.50883945204001
3195.799.5828184106473-3.88281841064732
32100.597.648929095252.85107090474993
3394.491.70102395796062.69897604203936
34102.996.46947990884986.43052009115019
35105.1106.53687820285-1.43687820285
3698.8100.29749325132-1.49749325132005
37100.7101.412348544547-0.712348544546884
3899.697.09073025691812.50926974308186
39107.7101.2883447412016.4116552587989
40102.9102.087476337930.812523662070177
41101.6101.967097095834-0.36709709583387
42102.7103.701100037914-1.00110003791352
43110.5104.7612737277385.73872627226244
44109.8110.542640755584-0.742640755584318
4594.3102.240946958373-7.9409469583727
46102.5100.9747605403631.52523945963662
47105106.118114193257-1.11811419325703
48102.3100.0709560635862.2290439364139
49107.7103.7667659522363.93323404776383
50100.3103.163676482069-2.86367648206925
5199.5104.764750280781-5.26475028078139
529596.7756800451205-1.7756800451205
5397.794.72103581989582.9789641801042
5496.398.4733486269165-2.17334862691654
5597.8100.282502652167-2.48250265216697
56106.499.30895818444467.09104181555536
5796.194.4559432974131.64405670258699
58106.2101.4918254359054.7081745640951
59114.7108.0992952457386.60070475426187
60111.9107.7825452763584.11745472364193
61121113.0780800311737.92191996882654
62117.7113.5313222836154.16867771638482
63115.4119.135512485183-3.73551248518277
64114.3112.9130594730671.38694052693265
65109.5113.962144182978-4.46214418297819
66108.1111.760041540663-3.6600415406631
67108.2112.540440960346-4.34044096034586
6899.1112.506308649066-13.4063086490663
69101.293.2049911570537.99500884294704
7098.1105.025065261446-6.92506526144575
7195.5104.54584843191-9.0458484319095
7297.993.57418314660924.32581685339082
7398.299.8541441523693-1.6541441523693
7498.793.28737062716045.41262937283958
7595.697.9287451960203-2.32874519602026
7695.893.75875301412922.04124698587081
7794.493.92350902104240.476490978957571
7896.595.08858209601251.41141790398754
79103.398.9907042156114.30929578438892
80104.3102.5148129308291.78518706917117
81104.597.80099308805086.69900691194917
82102.3105.451301144575-3.15130114457507
83103.8106.934335225665-3.13433522566451
84103.1102.765920444360.334079555639818
85102.2105.133203630046-2.93320363004567
86106.399.31950254895256.98049745104753
87102.1103.243529109843-1.14352910984277
8894100.814881051026-6.81488105102643
89102.694.91326576224757.68673423775253
90102.6100.9415547078461.65844529215403
91106.7105.6505289819181.04947101808204
92107.9106.5064672703441.393532729656
93109.3102.6375832792266.66241672077385
94105.9108.063694896898-2.16369489689808
95109.1110.188038131494-1.08803813149372
96108.5108.1153978864040.384602113595903
97111.7109.7853773453081.91462265469212
98109.8109.3157807832120.484219216788134
99109.1107.2314117531911.86858824680893
100108.5105.4801533576863.01984664231378
101108.5109.166732300793-0.666732300792702
102106.2108.455966281895-2.25596628189453
103117.1110.5020662056596.59793379434106
104109.8115.016508554146-5.21650855414576
105115.2108.0577933363037.14220666369683
106115.9111.8218492301824.07815076981788
107119.2118.215728260520.984271739479709
108121117.8097946354433.19020536455668
109118.6121.632654638014-3.0326546380138
110117.6117.649940153837-0.0499401538369852
111114.6115.530031480746-0.930031480745939
112110.6112.229403139543-1.62940313954277
113102.5112.091212966017-9.59121296601667
114101.6105.264484283663-3.6644842836628
115107.4108.379335996946-0.979335996946219
116105.8105.3631361854160.436863814583987
117102.8104.814741677478-2.0147416774781
118104101.9832946246322.01670537536775
119100.4106.355292566911-5.95529256691141
120100.6101.962545538909-1.36254553890876






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121101.4563185087993.287596187126109.625040830454
122100.0975851035690.3747628114492109.820407395671
12397.81329976020886.7526251750177108.873974345398
12494.95678382707282.7034670828193107.210100571325
12594.091722079866380.7519687016926107.43147545804
12694.78034887508380.436211774999109.124485975167
127100.86056309462785.5779089370035116.14321725225
12898.792925230171882.6261454934083114.959704966935
12997.41483354693280.4098338111915114.419833282673
13096.784573833498978.980774661186114.588373005812
13198.073790584774879.5055242703458116.642056899204
13298.551328154971879.2488474108014117.853808899142

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 101.45631850879 & 93.287596187126 & 109.625040830454 \tabularnewline
122 & 100.09758510356 & 90.3747628114492 & 109.820407395671 \tabularnewline
123 & 97.813299760208 & 86.7526251750177 & 108.873974345398 \tabularnewline
124 & 94.956783827072 & 82.7034670828193 & 107.210100571325 \tabularnewline
125 & 94.0917220798663 & 80.7519687016926 & 107.43147545804 \tabularnewline
126 & 94.780348875083 & 80.436211774999 & 109.124485975167 \tabularnewline
127 & 100.860563094627 & 85.5779089370035 & 116.14321725225 \tabularnewline
128 & 98.7929252301718 & 82.6261454934083 & 114.959704966935 \tabularnewline
129 & 97.414833546932 & 80.4098338111915 & 114.419833282673 \tabularnewline
130 & 96.7845738334989 & 78.980774661186 & 114.588373005812 \tabularnewline
131 & 98.0737905847748 & 79.5055242703458 & 116.642056899204 \tabularnewline
132 & 98.5513281549718 & 79.2488474108014 & 117.853808899142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117425&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]121[/C][C]101.45631850879[/C][C]93.287596187126[/C][C]109.625040830454[/C][/ROW]
[ROW][C]122[/C][C]100.09758510356[/C][C]90.3747628114492[/C][C]109.820407395671[/C][/ROW]
[ROW][C]123[/C][C]97.813299760208[/C][C]86.7526251750177[/C][C]108.873974345398[/C][/ROW]
[ROW][C]124[/C][C]94.956783827072[/C][C]82.7034670828193[/C][C]107.210100571325[/C][/ROW]
[ROW][C]125[/C][C]94.0917220798663[/C][C]80.7519687016926[/C][C]107.43147545804[/C][/ROW]
[ROW][C]126[/C][C]94.780348875083[/C][C]80.436211774999[/C][C]109.124485975167[/C][/ROW]
[ROW][C]127[/C][C]100.860563094627[/C][C]85.5779089370035[/C][C]116.14321725225[/C][/ROW]
[ROW][C]128[/C][C]98.7929252301718[/C][C]82.6261454934083[/C][C]114.959704966935[/C][/ROW]
[ROW][C]129[/C][C]97.414833546932[/C][C]80.4098338111915[/C][C]114.419833282673[/C][/ROW]
[ROW][C]130[/C][C]96.7845738334989[/C][C]78.980774661186[/C][C]114.588373005812[/C][/ROW]
[ROW][C]131[/C][C]98.0737905847748[/C][C]79.5055242703458[/C][C]116.642056899204[/C][/ROW]
[ROW][C]132[/C][C]98.5513281549718[/C][C]79.2488474108014[/C][C]117.853808899142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117425&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117425&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
121101.4563185087993.287596187126109.625040830454
122100.0975851035690.3747628114492109.820407395671
12397.81329976020886.7526251750177108.873974345398
12494.95678382707282.7034670828193107.210100571325
12594.091722079866380.7519687016926107.43147545804
12694.78034887508380.436211774999109.124485975167
127100.86056309462785.5779089370035116.14321725225
12898.792925230171882.6261454934083114.959704966935
12997.41483354693280.4098338111915114.419833282673
13096.784573833498978.980774661186114.588373005812
13198.073790584774879.5055242703458116.642056899204
13298.551328154971879.2488474108014117.853808899142


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')