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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 16 Jan 2010 02:10:15 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/16/t126363306356qv88hyz32h22v.htm/, Retrieved Fri, 03 May 2024 09:53:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72220, Retrieved Fri, 03 May 2024 09:53:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact147

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oef 2] [2010-01-16 09:10:15] [bd31152a03695b5eaed3983221abfe73] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102,5
77,7
82,8
77,3
103,1
99,7
99,5
107,2
96,7
97,1
105,2
151,2
102,7
75,4
87,2
83,7
105,8
111,5
99,7
111,2
101,5
110,9
116,3
164,9
118,1
83,7
84
107,2
113,7
120,7
111,2
112,4
112,5
130,4
130,7
174,3
132,2
91,8
104,2
104,8
131,4
141,2
132,7
135,7
136,9
151,2
144
201,5
149,6
108,7
122,8
126,7
139,9
162,5
142,7
151,6
148,1
159
157,8
226,7
153,7
122,3
117,6
166
154,5
183,9
164,4
173,3
160,2
166,4
170,3
238,4
166,8
122,5
141,8
140,5
173,8
188,8
168
187,4
177,7
183,8
196,1
264,6
193,7
141,3
170,1
163,7
190,1
230,7
195,9
210,3
204,7
210,3
221,2
288,2
203,2
162,4
149,2
195,3
213,7
227,9
212,1
226,8
212,6
220,9
228,1
311,6

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72220&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72220&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72220&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' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.779753800673534
beta0.0793509153332443
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.779753800673534 \tabularnewline
beta & 0.0793509153332443 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72220&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]0.779753800673534[/C][/ROW]
[ROW][C]beta[/C][C]0.0793509153332443[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72220&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72220&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
alpha0.779753800673534
beta0.0793509153332443
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
382.852.929.9
477.353.264676556897524.0353234431025
5103.150.543515155465452.5564848445346
699.773.313727045184126.3862729548159
799.577.310245694224122.1897543057759
8107.279.407485780731527.7925142192685
996.787.5931381708599.10686182914098
1097.181.772061679900515.3279383200995
11105.281.750296808249223.4497031917508
12151.289.51244006851161.687559931489
13102.7130.907564503555-28.2075645035545
1475.4100.461304136446-25.0613041364463
1587.270.917704660009316.2822953399907
1683.774.61938764600059.08061235399953
17105.873.26738637590732.532613624093
18111.592.215100949831619.2848990501684
1999.7102.026097007533-2.32609700753298
20111.294.84191141303516.3580885869651
21101.5103.238933830329-1.73893383032922
22110.997.417139135832613.4828608641674
23116.3104.29883763804712.0011623619529
24164.9110.76773815571454.1322618442861
25118.1153.43791281633-35.3379128163299
2683.7124.156874437090-40.4568744370903
278488.381070435679-4.38107043567891
28107.280.46443658555126.7355634144489
29113.798.465357248997815.2346427510022
30120.7108.44102230844712.2589776915533
31111.2116.854915393813-5.65491539381316
32112.4110.9504890203831.44951097961687
33112.5110.6754534133421.82454658665755
34130.4110.80574556622019.5942544337803
35130.7126.0044133327974.69558666720341
36174.3129.87632384781944.4236761521807
37132.2167.475041569822-35.2750415698216
3891.8140.745767044656-48.9457670446562
39104.2100.3282132789643.8717867210365
40104.8101.3349114243993.4650885756007
41131.4102.23888465188729.1611153481135
42141.2124.98375245387116.2162475461295
43132.7138.638177372251-5.93817737225129
44135.7134.6501854161431.04981458385743
45136.9136.1760631611230.723936838876767
46151.2137.49262949259813.7073705074020
47144149.781209853091-5.78120985309053
48201.5146.51578800130454.984211998696
49149.6194.034537698370-44.4345376983697
50108.7161.281788974127-52.5817889741272
51122.8118.9227351415963.87726485840433
52126.7120.8277456927095.87225430729127
53139.9124.65169775609715.2483022439030
54162.5136.73013499781825.7698650021823
55142.7158.607289998823-15.9072899988232
56151.6147.0022744965454.59772550345537
57148.1151.670603250397-3.57060325039677
58159149.7487184728499.25128152715087
59157.8158.397162520648-0.597162520647913
60226.7159.32929595146667.3707040485338
61153.7217.428138585300-63.7281385852997
62122.3169.359034232662-47.0590342326617
63117.6131.375988300761-13.7759883007609
64166118.49314598251147.5068540174887
65154.5156.335280411047-1.83528041104654
66183.9155.58914151908828.310858480912
67164.4180.101280095595-15.7012800955952
68173.3169.3232825446953.97671745530485
69160.2174.135334496716-13.9353344967155
70166.4164.1181584966832.28184150331720
71170.3166.8875741857963.41242581420397
72238.4170.74970832992467.6502916700761
73166.8228.88736869856-62.08736869856
74122.5182.019990413152-59.5199904131522
75141.8133.4717846330088.3282153669924
76140.5138.3437766573352.15622334266513
77173.8138.53654898948635.2634510105144
78188.8166.72670496370722.0732950362925
79168185.997553667658-17.9975536676583
80187.4172.90942196256714.4905780374328
81177.7186.050627033477-8.35062703347731
82183.8180.8646274564202.93537254357975
83196.1184.66055270669711.439447293303
84264.6195.79536896024868.804631039752
85193.7255.918135242085-62.2181352420852
86141.3210.025705577425-68.7257055774252
87170.1154.80662668306715.2933733169331
88163.7166.048008785723-2.34800878572329
89190.1163.38817503157326.7118249684268
90230.7185.04062930210345.659370697897
91195.9224.292640390243-28.3926403902434
92210.3204.0455431046596.25445689534143
93204.7211.201640987912-6.50164098791174
94210.3208.0088393743402.29116062566044
95221.2211.8140219174809.3859780825195
96288.2221.73216501456666.467834985434
97203.2280.272745622270-77.0727456222696
98162.4222.118200182675-59.7182001826750
99149.2173.800912971491-24.6009129714909
100195.3151.34430266888843.955697331112
101213.7185.06469244381428.6353075561856
102227.9208.61073617554719.2892638244528
103212.1226.062674126053-13.9626741260532
104226.8216.72235809820110.0776419017989
105212.6226.751115669478-14.1511156694778
106220.9217.0118187916973.88818120830285
107228.1221.5793102313156.5206897686846
108311.6228.60297254444182.9970274555593

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 82.8 & 52.9 & 29.9 \tabularnewline
4 & 77.3 & 53.2646765568975 & 24.0353234431025 \tabularnewline
5 & 103.1 & 50.5435151554654 & 52.5564848445346 \tabularnewline
6 & 99.7 & 73.3137270451841 & 26.3862729548159 \tabularnewline
7 & 99.5 & 77.3102456942241 & 22.1897543057759 \tabularnewline
8 & 107.2 & 79.4074857807315 & 27.7925142192685 \tabularnewline
9 & 96.7 & 87.593138170859 & 9.10686182914098 \tabularnewline
10 & 97.1 & 81.7720616799005 & 15.3279383200995 \tabularnewline
11 & 105.2 & 81.7502968082492 & 23.4497031917508 \tabularnewline
12 & 151.2 & 89.512440068511 & 61.687559931489 \tabularnewline
13 & 102.7 & 130.907564503555 & -28.2075645035545 \tabularnewline
14 & 75.4 & 100.461304136446 & -25.0613041364463 \tabularnewline
15 & 87.2 & 70.9177046600093 & 16.2822953399907 \tabularnewline
16 & 83.7 & 74.6193876460005 & 9.08061235399953 \tabularnewline
17 & 105.8 & 73.267386375907 & 32.532613624093 \tabularnewline
18 & 111.5 & 92.2151009498316 & 19.2848990501684 \tabularnewline
19 & 99.7 & 102.026097007533 & -2.32609700753298 \tabularnewline
20 & 111.2 & 94.841911413035 & 16.3580885869651 \tabularnewline
21 & 101.5 & 103.238933830329 & -1.73893383032922 \tabularnewline
22 & 110.9 & 97.4171391358326 & 13.4828608641674 \tabularnewline
23 & 116.3 & 104.298837638047 & 12.0011623619529 \tabularnewline
24 & 164.9 & 110.767738155714 & 54.1322618442861 \tabularnewline
25 & 118.1 & 153.43791281633 & -35.3379128163299 \tabularnewline
26 & 83.7 & 124.156874437090 & -40.4568744370903 \tabularnewline
27 & 84 & 88.381070435679 & -4.38107043567891 \tabularnewline
28 & 107.2 & 80.464436585551 & 26.7355634144489 \tabularnewline
29 & 113.7 & 98.4653572489978 & 15.2346427510022 \tabularnewline
30 & 120.7 & 108.441022308447 & 12.2589776915533 \tabularnewline
31 & 111.2 & 116.854915393813 & -5.65491539381316 \tabularnewline
32 & 112.4 & 110.950489020383 & 1.44951097961687 \tabularnewline
33 & 112.5 & 110.675453413342 & 1.82454658665755 \tabularnewline
34 & 130.4 & 110.805745566220 & 19.5942544337803 \tabularnewline
35 & 130.7 & 126.004413332797 & 4.69558666720341 \tabularnewline
36 & 174.3 & 129.876323847819 & 44.4236761521807 \tabularnewline
37 & 132.2 & 167.475041569822 & -35.2750415698216 \tabularnewline
38 & 91.8 & 140.745767044656 & -48.9457670446562 \tabularnewline
39 & 104.2 & 100.328213278964 & 3.8717867210365 \tabularnewline
40 & 104.8 & 101.334911424399 & 3.4650885756007 \tabularnewline
41 & 131.4 & 102.238884651887 & 29.1611153481135 \tabularnewline
42 & 141.2 & 124.983752453871 & 16.2162475461295 \tabularnewline
43 & 132.7 & 138.638177372251 & -5.93817737225129 \tabularnewline
44 & 135.7 & 134.650185416143 & 1.04981458385743 \tabularnewline
45 & 136.9 & 136.176063161123 & 0.723936838876767 \tabularnewline
46 & 151.2 & 137.492629492598 & 13.7073705074020 \tabularnewline
47 & 144 & 149.781209853091 & -5.78120985309053 \tabularnewline
48 & 201.5 & 146.515788001304 & 54.984211998696 \tabularnewline
49 & 149.6 & 194.034537698370 & -44.4345376983697 \tabularnewline
50 & 108.7 & 161.281788974127 & -52.5817889741272 \tabularnewline
51 & 122.8 & 118.922735141596 & 3.87726485840433 \tabularnewline
52 & 126.7 & 120.827745692709 & 5.87225430729127 \tabularnewline
53 & 139.9 & 124.651697756097 & 15.2483022439030 \tabularnewline
54 & 162.5 & 136.730134997818 & 25.7698650021823 \tabularnewline
55 & 142.7 & 158.607289998823 & -15.9072899988232 \tabularnewline
56 & 151.6 & 147.002274496545 & 4.59772550345537 \tabularnewline
57 & 148.1 & 151.670603250397 & -3.57060325039677 \tabularnewline
58 & 159 & 149.748718472849 & 9.25128152715087 \tabularnewline
59 & 157.8 & 158.397162520648 & -0.597162520647913 \tabularnewline
60 & 226.7 & 159.329295951466 & 67.3707040485338 \tabularnewline
61 & 153.7 & 217.428138585300 & -63.7281385852997 \tabularnewline
62 & 122.3 & 169.359034232662 & -47.0590342326617 \tabularnewline
63 & 117.6 & 131.375988300761 & -13.7759883007609 \tabularnewline
64 & 166 & 118.493145982511 & 47.5068540174887 \tabularnewline
65 & 154.5 & 156.335280411047 & -1.83528041104654 \tabularnewline
66 & 183.9 & 155.589141519088 & 28.310858480912 \tabularnewline
67 & 164.4 & 180.101280095595 & -15.7012800955952 \tabularnewline
68 & 173.3 & 169.323282544695 & 3.97671745530485 \tabularnewline
69 & 160.2 & 174.135334496716 & -13.9353344967155 \tabularnewline
70 & 166.4 & 164.118158496683 & 2.28184150331720 \tabularnewline
71 & 170.3 & 166.887574185796 & 3.41242581420397 \tabularnewline
72 & 238.4 & 170.749708329924 & 67.6502916700761 \tabularnewline
73 & 166.8 & 228.88736869856 & -62.08736869856 \tabularnewline
74 & 122.5 & 182.019990413152 & -59.5199904131522 \tabularnewline
75 & 141.8 & 133.471784633008 & 8.3282153669924 \tabularnewline
76 & 140.5 & 138.343776657335 & 2.15622334266513 \tabularnewline
77 & 173.8 & 138.536548989486 & 35.2634510105144 \tabularnewline
78 & 188.8 & 166.726704963707 & 22.0732950362925 \tabularnewline
79 & 168 & 185.997553667658 & -17.9975536676583 \tabularnewline
80 & 187.4 & 172.909421962567 & 14.4905780374328 \tabularnewline
81 & 177.7 & 186.050627033477 & -8.35062703347731 \tabularnewline
82 & 183.8 & 180.864627456420 & 2.93537254357975 \tabularnewline
83 & 196.1 & 184.660552706697 & 11.439447293303 \tabularnewline
84 & 264.6 & 195.795368960248 & 68.804631039752 \tabularnewline
85 & 193.7 & 255.918135242085 & -62.2181352420852 \tabularnewline
86 & 141.3 & 210.025705577425 & -68.7257055774252 \tabularnewline
87 & 170.1 & 154.806626683067 & 15.2933733169331 \tabularnewline
88 & 163.7 & 166.048008785723 & -2.34800878572329 \tabularnewline
89 & 190.1 & 163.388175031573 & 26.7118249684268 \tabularnewline
90 & 230.7 & 185.040629302103 & 45.659370697897 \tabularnewline
91 & 195.9 & 224.292640390243 & -28.3926403902434 \tabularnewline
92 & 210.3 & 204.045543104659 & 6.25445689534143 \tabularnewline
93 & 204.7 & 211.201640987912 & -6.50164098791174 \tabularnewline
94 & 210.3 & 208.008839374340 & 2.29116062566044 \tabularnewline
95 & 221.2 & 211.814021917480 & 9.3859780825195 \tabularnewline
96 & 288.2 & 221.732165014566 & 66.467834985434 \tabularnewline
97 & 203.2 & 280.272745622270 & -77.0727456222696 \tabularnewline
98 & 162.4 & 222.118200182675 & -59.7182001826750 \tabularnewline
99 & 149.2 & 173.800912971491 & -24.6009129714909 \tabularnewline
100 & 195.3 & 151.344302668888 & 43.955697331112 \tabularnewline
101 & 213.7 & 185.064692443814 & 28.6353075561856 \tabularnewline
102 & 227.9 & 208.610736175547 & 19.2892638244528 \tabularnewline
103 & 212.1 & 226.062674126053 & -13.9626741260532 \tabularnewline
104 & 226.8 & 216.722358098201 & 10.0776419017989 \tabularnewline
105 & 212.6 & 226.751115669478 & -14.1511156694778 \tabularnewline
106 & 220.9 & 217.011818791697 & 3.88818120830285 \tabularnewline
107 & 228.1 & 221.579310231315 & 6.5206897686846 \tabularnewline
108 & 311.6 & 228.602972544441 & 82.9970274555593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72220&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]82.8[/C][C]52.9[/C][C]29.9[/C][/ROW]
[ROW][C]4[/C][C]77.3[/C][C]53.2646765568975[/C][C]24.0353234431025[/C][/ROW]
[ROW][C]5[/C][C]103.1[/C][C]50.5435151554654[/C][C]52.5564848445346[/C][/ROW]
[ROW][C]6[/C][C]99.7[/C][C]73.3137270451841[/C][C]26.3862729548159[/C][/ROW]
[ROW][C]7[/C][C]99.5[/C][C]77.3102456942241[/C][C]22.1897543057759[/C][/ROW]
[ROW][C]8[/C][C]107.2[/C][C]79.4074857807315[/C][C]27.7925142192685[/C][/ROW]
[ROW][C]9[/C][C]96.7[/C][C]87.593138170859[/C][C]9.10686182914098[/C][/ROW]
[ROW][C]10[/C][C]97.1[/C][C]81.7720616799005[/C][C]15.3279383200995[/C][/ROW]
[ROW][C]11[/C][C]105.2[/C][C]81.7502968082492[/C][C]23.4497031917508[/C][/ROW]
[ROW][C]12[/C][C]151.2[/C][C]89.512440068511[/C][C]61.687559931489[/C][/ROW]
[ROW][C]13[/C][C]102.7[/C][C]130.907564503555[/C][C]-28.2075645035545[/C][/ROW]
[ROW][C]14[/C][C]75.4[/C][C]100.461304136446[/C][C]-25.0613041364463[/C][/ROW]
[ROW][C]15[/C][C]87.2[/C][C]70.9177046600093[/C][C]16.2822953399907[/C][/ROW]
[ROW][C]16[/C][C]83.7[/C][C]74.6193876460005[/C][C]9.08061235399953[/C][/ROW]
[ROW][C]17[/C][C]105.8[/C][C]73.267386375907[/C][C]32.532613624093[/C][/ROW]
[ROW][C]18[/C][C]111.5[/C][C]92.2151009498316[/C][C]19.2848990501684[/C][/ROW]
[ROW][C]19[/C][C]99.7[/C][C]102.026097007533[/C][C]-2.32609700753298[/C][/ROW]
[ROW][C]20[/C][C]111.2[/C][C]94.841911413035[/C][C]16.3580885869651[/C][/ROW]
[ROW][C]21[/C][C]101.5[/C][C]103.238933830329[/C][C]-1.73893383032922[/C][/ROW]
[ROW][C]22[/C][C]110.9[/C][C]97.4171391358326[/C][C]13.4828608641674[/C][/ROW]
[ROW][C]23[/C][C]116.3[/C][C]104.298837638047[/C][C]12.0011623619529[/C][/ROW]
[ROW][C]24[/C][C]164.9[/C][C]110.767738155714[/C][C]54.1322618442861[/C][/ROW]
[ROW][C]25[/C][C]118.1[/C][C]153.43791281633[/C][C]-35.3379128163299[/C][/ROW]
[ROW][C]26[/C][C]83.7[/C][C]124.156874437090[/C][C]-40.4568744370903[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]88.381070435679[/C][C]-4.38107043567891[/C][/ROW]
[ROW][C]28[/C][C]107.2[/C][C]80.464436585551[/C][C]26.7355634144489[/C][/ROW]
[ROW][C]29[/C][C]113.7[/C][C]98.4653572489978[/C][C]15.2346427510022[/C][/ROW]
[ROW][C]30[/C][C]120.7[/C][C]108.441022308447[/C][C]12.2589776915533[/C][/ROW]
[ROW][C]31[/C][C]111.2[/C][C]116.854915393813[/C][C]-5.65491539381316[/C][/ROW]
[ROW][C]32[/C][C]112.4[/C][C]110.950489020383[/C][C]1.44951097961687[/C][/ROW]
[ROW][C]33[/C][C]112.5[/C][C]110.675453413342[/C][C]1.82454658665755[/C][/ROW]
[ROW][C]34[/C][C]130.4[/C][C]110.805745566220[/C][C]19.5942544337803[/C][/ROW]
[ROW][C]35[/C][C]130.7[/C][C]126.004413332797[/C][C]4.69558666720341[/C][/ROW]
[ROW][C]36[/C][C]174.3[/C][C]129.876323847819[/C][C]44.4236761521807[/C][/ROW]
[ROW][C]37[/C][C]132.2[/C][C]167.475041569822[/C][C]-35.2750415698216[/C][/ROW]
[ROW][C]38[/C][C]91.8[/C][C]140.745767044656[/C][C]-48.9457670446562[/C][/ROW]
[ROW][C]39[/C][C]104.2[/C][C]100.328213278964[/C][C]3.8717867210365[/C][/ROW]
[ROW][C]40[/C][C]104.8[/C][C]101.334911424399[/C][C]3.4650885756007[/C][/ROW]
[ROW][C]41[/C][C]131.4[/C][C]102.238884651887[/C][C]29.1611153481135[/C][/ROW]
[ROW][C]42[/C][C]141.2[/C][C]124.983752453871[/C][C]16.2162475461295[/C][/ROW]
[ROW][C]43[/C][C]132.7[/C][C]138.638177372251[/C][C]-5.93817737225129[/C][/ROW]
[ROW][C]44[/C][C]135.7[/C][C]134.650185416143[/C][C]1.04981458385743[/C][/ROW]
[ROW][C]45[/C][C]136.9[/C][C]136.176063161123[/C][C]0.723936838876767[/C][/ROW]
[ROW][C]46[/C][C]151.2[/C][C]137.492629492598[/C][C]13.7073705074020[/C][/ROW]
[ROW][C]47[/C][C]144[/C][C]149.781209853091[/C][C]-5.78120985309053[/C][/ROW]
[ROW][C]48[/C][C]201.5[/C][C]146.515788001304[/C][C]54.984211998696[/C][/ROW]
[ROW][C]49[/C][C]149.6[/C][C]194.034537698370[/C][C]-44.4345376983697[/C][/ROW]
[ROW][C]50[/C][C]108.7[/C][C]161.281788974127[/C][C]-52.5817889741272[/C][/ROW]
[ROW][C]51[/C][C]122.8[/C][C]118.922735141596[/C][C]3.87726485840433[/C][/ROW]
[ROW][C]52[/C][C]126.7[/C][C]120.827745692709[/C][C]5.87225430729127[/C][/ROW]
[ROW][C]53[/C][C]139.9[/C][C]124.651697756097[/C][C]15.2483022439030[/C][/ROW]
[ROW][C]54[/C][C]162.5[/C][C]136.730134997818[/C][C]25.7698650021823[/C][/ROW]
[ROW][C]55[/C][C]142.7[/C][C]158.607289998823[/C][C]-15.9072899988232[/C][/ROW]
[ROW][C]56[/C][C]151.6[/C][C]147.002274496545[/C][C]4.59772550345537[/C][/ROW]
[ROW][C]57[/C][C]148.1[/C][C]151.670603250397[/C][C]-3.57060325039677[/C][/ROW]
[ROW][C]58[/C][C]159[/C][C]149.748718472849[/C][C]9.25128152715087[/C][/ROW]
[ROW][C]59[/C][C]157.8[/C][C]158.397162520648[/C][C]-0.597162520647913[/C][/ROW]
[ROW][C]60[/C][C]226.7[/C][C]159.329295951466[/C][C]67.3707040485338[/C][/ROW]
[ROW][C]61[/C][C]153.7[/C][C]217.428138585300[/C][C]-63.7281385852997[/C][/ROW]
[ROW][C]62[/C][C]122.3[/C][C]169.359034232662[/C][C]-47.0590342326617[/C][/ROW]
[ROW][C]63[/C][C]117.6[/C][C]131.375988300761[/C][C]-13.7759883007609[/C][/ROW]
[ROW][C]64[/C][C]166[/C][C]118.493145982511[/C][C]47.5068540174887[/C][/ROW]
[ROW][C]65[/C][C]154.5[/C][C]156.335280411047[/C][C]-1.83528041104654[/C][/ROW]
[ROW][C]66[/C][C]183.9[/C][C]155.589141519088[/C][C]28.310858480912[/C][/ROW]
[ROW][C]67[/C][C]164.4[/C][C]180.101280095595[/C][C]-15.7012800955952[/C][/ROW]
[ROW][C]68[/C][C]173.3[/C][C]169.323282544695[/C][C]3.97671745530485[/C][/ROW]
[ROW][C]69[/C][C]160.2[/C][C]174.135334496716[/C][C]-13.9353344967155[/C][/ROW]
[ROW][C]70[/C][C]166.4[/C][C]164.118158496683[/C][C]2.28184150331720[/C][/ROW]
[ROW][C]71[/C][C]170.3[/C][C]166.887574185796[/C][C]3.41242581420397[/C][/ROW]
[ROW][C]72[/C][C]238.4[/C][C]170.749708329924[/C][C]67.6502916700761[/C][/ROW]
[ROW][C]73[/C][C]166.8[/C][C]228.88736869856[/C][C]-62.08736869856[/C][/ROW]
[ROW][C]74[/C][C]122.5[/C][C]182.019990413152[/C][C]-59.5199904131522[/C][/ROW]
[ROW][C]75[/C][C]141.8[/C][C]133.471784633008[/C][C]8.3282153669924[/C][/ROW]
[ROW][C]76[/C][C]140.5[/C][C]138.343776657335[/C][C]2.15622334266513[/C][/ROW]
[ROW][C]77[/C][C]173.8[/C][C]138.536548989486[/C][C]35.2634510105144[/C][/ROW]
[ROW][C]78[/C][C]188.8[/C][C]166.726704963707[/C][C]22.0732950362925[/C][/ROW]
[ROW][C]79[/C][C]168[/C][C]185.997553667658[/C][C]-17.9975536676583[/C][/ROW]
[ROW][C]80[/C][C]187.4[/C][C]172.909421962567[/C][C]14.4905780374328[/C][/ROW]
[ROW][C]81[/C][C]177.7[/C][C]186.050627033477[/C][C]-8.35062703347731[/C][/ROW]
[ROW][C]82[/C][C]183.8[/C][C]180.864627456420[/C][C]2.93537254357975[/C][/ROW]
[ROW][C]83[/C][C]196.1[/C][C]184.660552706697[/C][C]11.439447293303[/C][/ROW]
[ROW][C]84[/C][C]264.6[/C][C]195.795368960248[/C][C]68.804631039752[/C][/ROW]
[ROW][C]85[/C][C]193.7[/C][C]255.918135242085[/C][C]-62.2181352420852[/C][/ROW]
[ROW][C]86[/C][C]141.3[/C][C]210.025705577425[/C][C]-68.7257055774252[/C][/ROW]
[ROW][C]87[/C][C]170.1[/C][C]154.806626683067[/C][C]15.2933733169331[/C][/ROW]
[ROW][C]88[/C][C]163.7[/C][C]166.048008785723[/C][C]-2.34800878572329[/C][/ROW]
[ROW][C]89[/C][C]190.1[/C][C]163.388175031573[/C][C]26.7118249684268[/C][/ROW]
[ROW][C]90[/C][C]230.7[/C][C]185.040629302103[/C][C]45.659370697897[/C][/ROW]
[ROW][C]91[/C][C]195.9[/C][C]224.292640390243[/C][C]-28.3926403902434[/C][/ROW]
[ROW][C]92[/C][C]210.3[/C][C]204.045543104659[/C][C]6.25445689534143[/C][/ROW]
[ROW][C]93[/C][C]204.7[/C][C]211.201640987912[/C][C]-6.50164098791174[/C][/ROW]
[ROW][C]94[/C][C]210.3[/C][C]208.008839374340[/C][C]2.29116062566044[/C][/ROW]
[ROW][C]95[/C][C]221.2[/C][C]211.814021917480[/C][C]9.3859780825195[/C][/ROW]
[ROW][C]96[/C][C]288.2[/C][C]221.732165014566[/C][C]66.467834985434[/C][/ROW]
[ROW][C]97[/C][C]203.2[/C][C]280.272745622270[/C][C]-77.0727456222696[/C][/ROW]
[ROW][C]98[/C][C]162.4[/C][C]222.118200182675[/C][C]-59.7182001826750[/C][/ROW]
[ROW][C]99[/C][C]149.2[/C][C]173.800912971491[/C][C]-24.6009129714909[/C][/ROW]
[ROW][C]100[/C][C]195.3[/C][C]151.344302668888[/C][C]43.955697331112[/C][/ROW]
[ROW][C]101[/C][C]213.7[/C][C]185.064692443814[/C][C]28.6353075561856[/C][/ROW]
[ROW][C]102[/C][C]227.9[/C][C]208.610736175547[/C][C]19.2892638244528[/C][/ROW]
[ROW][C]103[/C][C]212.1[/C][C]226.062674126053[/C][C]-13.9626741260532[/C][/ROW]
[ROW][C]104[/C][C]226.8[/C][C]216.722358098201[/C][C]10.0776419017989[/C][/ROW]
[ROW][C]105[/C][C]212.6[/C][C]226.751115669478[/C][C]-14.1511156694778[/C][/ROW]
[ROW][C]106[/C][C]220.9[/C][C]217.011818791697[/C][C]3.88818120830285[/C][/ROW]
[ROW][C]107[/C][C]228.1[/C][C]221.579310231315[/C][C]6.5206897686846[/C][/ROW]
[ROW][C]108[/C][C]311.6[/C][C]228.602972544441[/C][C]82.9970274555593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72220&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72220&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
382.852.929.9
477.353.264676556897524.0353234431025
5103.150.543515155465452.5564848445346
699.773.313727045184126.3862729548159
799.577.310245694224122.1897543057759
8107.279.407485780731527.7925142192685
996.787.5931381708599.10686182914098
1097.181.772061679900515.3279383200995
11105.281.750296808249223.4497031917508
12151.289.51244006851161.687559931489
13102.7130.907564503555-28.2075645035545
1475.4100.461304136446-25.0613041364463
1587.270.917704660009316.2822953399907
1683.774.61938764600059.08061235399953
17105.873.26738637590732.532613624093
18111.592.215100949831619.2848990501684
1999.7102.026097007533-2.32609700753298
20111.294.84191141303516.3580885869651
21101.5103.238933830329-1.73893383032922
22110.997.417139135832613.4828608641674
23116.3104.29883763804712.0011623619529
24164.9110.76773815571454.1322618442861
25118.1153.43791281633-35.3379128163299
2683.7124.156874437090-40.4568744370903
278488.381070435679-4.38107043567891
28107.280.46443658555126.7355634144489
29113.798.465357248997815.2346427510022
30120.7108.44102230844712.2589776915533
31111.2116.854915393813-5.65491539381316
32112.4110.9504890203831.44951097961687
33112.5110.6754534133421.82454658665755
34130.4110.80574556622019.5942544337803
35130.7126.0044133327974.69558666720341
36174.3129.87632384781944.4236761521807
37132.2167.475041569822-35.2750415698216
3891.8140.745767044656-48.9457670446562
39104.2100.3282132789643.8717867210365
40104.8101.3349114243993.4650885756007
41131.4102.23888465188729.1611153481135
42141.2124.98375245387116.2162475461295
43132.7138.638177372251-5.93817737225129
44135.7134.6501854161431.04981458385743
45136.9136.1760631611230.723936838876767
46151.2137.49262949259813.7073705074020
47144149.781209853091-5.78120985309053
48201.5146.51578800130454.984211998696
49149.6194.034537698370-44.4345376983697
50108.7161.281788974127-52.5817889741272
51122.8118.9227351415963.87726485840433
52126.7120.8277456927095.87225430729127
53139.9124.65169775609715.2483022439030
54162.5136.73013499781825.7698650021823
55142.7158.607289998823-15.9072899988232
56151.6147.0022744965454.59772550345537
57148.1151.670603250397-3.57060325039677
58159149.7487184728499.25128152715087
59157.8158.397162520648-0.597162520647913
60226.7159.32929595146667.3707040485338
61153.7217.428138585300-63.7281385852997
62122.3169.359034232662-47.0590342326617
63117.6131.375988300761-13.7759883007609
64166118.49314598251147.5068540174887
65154.5156.335280411047-1.83528041104654
66183.9155.58914151908828.310858480912
67164.4180.101280095595-15.7012800955952
68173.3169.3232825446953.97671745530485
69160.2174.135334496716-13.9353344967155
70166.4164.1181584966832.28184150331720
71170.3166.8875741857963.41242581420397
72238.4170.74970832992467.6502916700761
73166.8228.88736869856-62.08736869856
74122.5182.019990413152-59.5199904131522
75141.8133.4717846330088.3282153669924
76140.5138.3437766573352.15622334266513
77173.8138.53654898948635.2634510105144
78188.8166.72670496370722.0732950362925
79168185.997553667658-17.9975536676583
80187.4172.90942196256714.4905780374328
81177.7186.050627033477-8.35062703347731
82183.8180.8646274564202.93537254357975
83196.1184.66055270669711.439447293303
84264.6195.79536896024868.804631039752
85193.7255.918135242085-62.2181352420852
86141.3210.025705577425-68.7257055774252
87170.1154.80662668306715.2933733169331
88163.7166.048008785723-2.34800878572329
89190.1163.38817503157326.7118249684268
90230.7185.04062930210345.659370697897
91195.9224.292640390243-28.3926403902434
92210.3204.0455431046596.25445689534143
93204.7211.201640987912-6.50164098791174
94210.3208.0088393743402.29116062566044
95221.2211.8140219174809.3859780825195
96288.2221.73216501456666.467834985434
97203.2280.272745622270-77.0727456222696
98162.4222.118200182675-59.7182001826750
99149.2173.800912971491-24.6009129714909
100195.3151.34430266888843.955697331112
101213.7185.06469244381428.6353075561856
102227.9208.61073617554719.2892638244528
103212.1226.062674126053-13.9626741260532
104226.8216.72235809820110.0776419017989
105212.6226.751115669478-14.1511156694778
106220.9217.0118187916973.88818120830285
107228.1221.5793102313156.5206897686846
108311.6228.60297254444182.9970274555593






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109300.394722665652237.78616821994363.003277111363
110307.469225183785225.637721172808389.300729194761
111314.543727701917215.063998818754414.023456585081
112321.618230220050205.216731985719438.019728454382
113328.692732738183195.705193781353461.680271695013
114335.767235256316186.317042516501485.217427996131
115342.841737774449176.925053745310508.758421803588
116349.916240292582167.448005311602532.384475273562
117356.990742810715157.831746541346556.149739080084
118364.065245328848148.039074311124580.091416346571
119371.139747846981138.043903702881604.23559199108
120378.214250365114127.827714695670628.600786034557

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 300.394722665652 & 237.78616821994 & 363.003277111363 \tabularnewline
110 & 307.469225183785 & 225.637721172808 & 389.300729194761 \tabularnewline
111 & 314.543727701917 & 215.063998818754 & 414.023456585081 \tabularnewline
112 & 321.618230220050 & 205.216731985719 & 438.019728454382 \tabularnewline
113 & 328.692732738183 & 195.705193781353 & 461.680271695013 \tabularnewline
114 & 335.767235256316 & 186.317042516501 & 485.217427996131 \tabularnewline
115 & 342.841737774449 & 176.925053745310 & 508.758421803588 \tabularnewline
116 & 349.916240292582 & 167.448005311602 & 532.384475273562 \tabularnewline
117 & 356.990742810715 & 157.831746541346 & 556.149739080084 \tabularnewline
118 & 364.065245328848 & 148.039074311124 & 580.091416346571 \tabularnewline
119 & 371.139747846981 & 138.043903702881 & 604.23559199108 \tabularnewline
120 & 378.214250365114 & 127.827714695670 & 628.600786034557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72220&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]109[/C][C]300.394722665652[/C][C]237.78616821994[/C][C]363.003277111363[/C][/ROW]
[ROW][C]110[/C][C]307.469225183785[/C][C]225.637721172808[/C][C]389.300729194761[/C][/ROW]
[ROW][C]111[/C][C]314.543727701917[/C][C]215.063998818754[/C][C]414.023456585081[/C][/ROW]
[ROW][C]112[/C][C]321.618230220050[/C][C]205.216731985719[/C][C]438.019728454382[/C][/ROW]
[ROW][C]113[/C][C]328.692732738183[/C][C]195.705193781353[/C][C]461.680271695013[/C][/ROW]
[ROW][C]114[/C][C]335.767235256316[/C][C]186.317042516501[/C][C]485.217427996131[/C][/ROW]
[ROW][C]115[/C][C]342.841737774449[/C][C]176.925053745310[/C][C]508.758421803588[/C][/ROW]
[ROW][C]116[/C][C]349.916240292582[/C][C]167.448005311602[/C][C]532.384475273562[/C][/ROW]
[ROW][C]117[/C][C]356.990742810715[/C][C]157.831746541346[/C][C]556.149739080084[/C][/ROW]
[ROW][C]118[/C][C]364.065245328848[/C][C]148.039074311124[/C][C]580.091416346571[/C][/ROW]
[ROW][C]119[/C][C]371.139747846981[/C][C]138.043903702881[/C][C]604.23559199108[/C][/ROW]
[ROW][C]120[/C][C]378.214250365114[/C][C]127.827714695670[/C][C]628.600786034557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72220&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72220&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
109300.394722665652237.78616821994363.003277111363
110307.469225183785225.637721172808389.300729194761
111314.543727701917215.063998818754414.023456585081
112321.618230220050205.216731985719438.019728454382
113328.692732738183195.705193781353461.680271695013
114335.767235256316186.317042516501485.217427996131
115342.841737774449176.925053745310508.758421803588
116349.916240292582167.448005311602532.384475273562
117356.990742810715157.831746541346556.149739080084
118364.065245328848148.039074311124580.091416346571
119371.139747846981138.043903702881604.23559199108
120378.214250365114127.827714695670628.600786034557


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')