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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 13:19:16 +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/t1295183822c0a9jvw2amd5wle.htm/, Retrieved Tue, 07 May 2024 05:55:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117397, Retrieved Tue, 07 May 2024 05:55:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact156

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [opgave 6bis deel 1.2] [2010-11-17 09:49:18] [4fbbbfaec2662edf81d9d4e1604b565e]
- R PD  [(Partial) Autocorrelation Function] [Autocorrelatie ei...] [2011-01-16 10:14:11] [4fbbbfaec2662edf81d9d4e1604b565e]
- RMP       [Exponential Smoothing] [oef 10.2 eigen wa...] [2011-01-16 13:19:16] [63c073ae7ca4ef34c1cc2bde848eb699] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
89,3
88,1
93,6
79,7
83,8
62,3
62,3
77,6
80,3
97
94
75,1
74
77,6
75,1
85
75,4
63,2
64,7
77
82,6
97,6
99
75,3
71,6
76,8
83,9
79,7
77,5
73,1
65,6
85,2
98,3
98
100,6
84,1
76,7
82,4
95,5
79,9
82,4
83,6
73,1
91,1
118,6
102,9
111,8
93,9
91,6
92
91,1
97,5
94,7
96,7
78,7
103,5
113,8
106,1
120,3
114,2
106,3
98,8
113,1
97,7
116,3
107,2
94,5
123,5
126,6
126,5
141,4
124,3
124,9
108,9
126,7
107,7
121,8
118,3
122,8
149,5
147
139,3
162,1
142,2
141,4
124,7
114
126,6
121,9
125,1
122,1
135,9
148,4
137,5
145,3
139,9
128,2
115,4
124,7
111,5
121,1
122,5
127,4
143,7
157,8
148,8
162,9
153,9

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' @ www.wessa.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117397&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117397&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' @ www.wessa.org






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.731350595836053
beta0.015292862227736
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.731350595836053 \tabularnewline
beta & 0.015292862227736 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117397&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]0.731350595836053[/C][/ROW]
[ROW][C]beta[/C][C]0.015292862227736[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117397&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
alpha0.731350595836053
beta0.015292862227736
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
393.686.96.7
479.790.6749847662469-10.9749847662469
583.881.40060979085942.39939020914062
662.381.9344277678502-19.6344277678502
762.366.1341996829024-3.83419968290244
877.661.846594430963215.7534055690368
980.372.0605890318888.23941096811195
109776.871372434078420.1286275659216
119490.6024689849423.39753101505802
1275.192.1352675993852-17.0352675993852
137478.5339967777313-4.53399677773135
1477.674.02482758758823.5751724124118
1575.175.4862904316792-0.386290431679242
168574.046214620698810.9537853793012
1775.481.0222220089975-5.62222200899748
1863.275.8124750906152-12.6124750906152
1964.765.349338895827-0.649338895826986
207763.62818699071113.371813009289
2182.672.310969178183810.2890308218162
2297.678.854233864051118.7457661359489
239991.79199793049027.20800206950977
2475.396.3722288671173-21.0722288671173
2571.680.0340148962004-8.43401489620045
2676.872.84443647673953.95556352326049
2783.974.76022439483679.1397756051633
2879.780.5697122155095-0.869712215509466
2977.579.049027907034-1.54902790703399
3073.177.014200647072-3.91420064707197
3165.673.2058247368685-7.60582473686847
3285.266.612510428889418.5874895711106
3398.379.383582881364418.9164171186356
349892.60678629780455.39321370219554
35100.696.00010693412424.59989306587578
3684.198.8646792963343-14.7646792963343
3776.787.4018253960065-10.7018253960065
3882.478.79064815068453.60935184931554
3995.580.686327504126414.8136724958736
4079.990.9419761273838-11.0419761273838
4182.482.16458236172710.235417638272921
4283.681.637550261431.96244973856993
4373.182.3955330257254-9.29553302572538
4491.174.816018019773216.2839819802268
45118.686.126223837585132.4737761624149
46102.9109.640046404788-6.74004640478756
47111.8104.3994328015447.40056719845596
4893.9109.583336611196-15.6833366111963
4991.697.7094042169086-6.1094042169086
509292.7690426949368-0.769042694936829
5191.191.725756439159-0.625756439159062
5297.590.78026393412926.71973606587082
5394.795.2820582604291-0.582058260429122
5496.794.43717095755572.26282904244434
5578.795.6982021632108-16.9982021632108
56103.582.68255128165920.817448718341
57113.897.556230791637416.2437692083626
58106.1109.266624592303-3.16662459230274
59120.3106.74579838632713.5542016136732
60114.2116.605354596551-2.40535459655094
61106.3114.765977309598-8.46597730959843
6298.8108.399472742024-9.59947274202383
63113.1101.09662085019312.0033791498073
6497.7109.727278681949-12.0272786819493
65116.3100.64858216640315.6514178335972
66107.2111.987769244218-4.78776924421778
6794.5108.325196137739-13.8251961377391
68123.597.898468357218125.6015316427819
69126.6116.59284032531910.0071596746815
70126.5123.9941835788622.50581642113758
71141.4125.93744113754815.4625588624521
72124.3137.529560122966-13.229560122966
73124.9127.989715519552-3.08971551955231
74108.9125.831095558628-16.9310955586278
75126.7113.36020917045213.3397908295477
76107.7123.177151720956-15.4771517209558
77121.8111.74570283178510.054297168215
78118.3119.099146022922-0.799146022921832
79122.8118.5059790654854.29402093451512
80149.5121.68572903331927.8142709666807
81147142.3781150297014.62188497029899
82139.3146.160428921942-6.86042892194237
83162.1141.46841562509320.6315843749067
84142.2157.113455431684-14.9134554316841
85141.4146.595810491043-5.1958104910434
86124.7143.1270587169-18.4270587168995
87114129.775529264618-15.7755292646176
88126.6118.186756935058.41324306495022
89121.9124.38255510635-2.48255510635032
90125.1122.581938794642.51806120536048
91122.1124.46668931634-2.3666893163398
92135.9122.75250452959113.1474954704087
93148.4132.53167545608615.8683245439136
94137.5144.478204732342-6.9782047323422
95145.3139.6378638702555.66213612974516
96139.9144.105371673136-4.2053716731362
97128.2141.309237021397-13.1092370213969
98115.4131.854635615895-16.4546356158954
99124.7119.769339006024.93066099398028
100111.5123.379338515196-11.8793385151957
101121.1114.5624710721136.53752892788745
102122.5119.2879092325153.21209076748457
103127.4121.617211661895.78278833811028
104143.7125.89127256302217.8087274369781
105157.8139.15969190258918.6403080974108
106148.8153.244769733887-4.44476973388669
107162.9150.39684986059612.5031501394042
108153.9160.083642066154-6.18364206615405

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 93.6 & 86.9 & 6.7 \tabularnewline
4 & 79.7 & 90.6749847662469 & -10.9749847662469 \tabularnewline
5 & 83.8 & 81.4006097908594 & 2.39939020914062 \tabularnewline
6 & 62.3 & 81.9344277678502 & -19.6344277678502 \tabularnewline
7 & 62.3 & 66.1341996829024 & -3.83419968290244 \tabularnewline
8 & 77.6 & 61.8465944309632 & 15.7534055690368 \tabularnewline
9 & 80.3 & 72.060589031888 & 8.23941096811195 \tabularnewline
10 & 97 & 76.8713724340784 & 20.1286275659216 \tabularnewline
11 & 94 & 90.602468984942 & 3.39753101505802 \tabularnewline
12 & 75.1 & 92.1352675993852 & -17.0352675993852 \tabularnewline
13 & 74 & 78.5339967777313 & -4.53399677773135 \tabularnewline
14 & 77.6 & 74.0248275875882 & 3.5751724124118 \tabularnewline
15 & 75.1 & 75.4862904316792 & -0.386290431679242 \tabularnewline
16 & 85 & 74.0462146206988 & 10.9537853793012 \tabularnewline
17 & 75.4 & 81.0222220089975 & -5.62222200899748 \tabularnewline
18 & 63.2 & 75.8124750906152 & -12.6124750906152 \tabularnewline
19 & 64.7 & 65.349338895827 & -0.649338895826986 \tabularnewline
20 & 77 & 63.628186990711 & 13.371813009289 \tabularnewline
21 & 82.6 & 72.3109691781838 & 10.2890308218162 \tabularnewline
22 & 97.6 & 78.8542338640511 & 18.7457661359489 \tabularnewline
23 & 99 & 91.7919979304902 & 7.20800206950977 \tabularnewline
24 & 75.3 & 96.3722288671173 & -21.0722288671173 \tabularnewline
25 & 71.6 & 80.0340148962004 & -8.43401489620045 \tabularnewline
26 & 76.8 & 72.8444364767395 & 3.95556352326049 \tabularnewline
27 & 83.9 & 74.7602243948367 & 9.1397756051633 \tabularnewline
28 & 79.7 & 80.5697122155095 & -0.869712215509466 \tabularnewline
29 & 77.5 & 79.049027907034 & -1.54902790703399 \tabularnewline
30 & 73.1 & 77.014200647072 & -3.91420064707197 \tabularnewline
31 & 65.6 & 73.2058247368685 & -7.60582473686847 \tabularnewline
32 & 85.2 & 66.6125104288894 & 18.5874895711106 \tabularnewline
33 & 98.3 & 79.3835828813644 & 18.9164171186356 \tabularnewline
34 & 98 & 92.6067862978045 & 5.39321370219554 \tabularnewline
35 & 100.6 & 96.0001069341242 & 4.59989306587578 \tabularnewline
36 & 84.1 & 98.8646792963343 & -14.7646792963343 \tabularnewline
37 & 76.7 & 87.4018253960065 & -10.7018253960065 \tabularnewline
38 & 82.4 & 78.7906481506845 & 3.60935184931554 \tabularnewline
39 & 95.5 & 80.6863275041264 & 14.8136724958736 \tabularnewline
40 & 79.9 & 90.9419761273838 & -11.0419761273838 \tabularnewline
41 & 82.4 & 82.1645823617271 & 0.235417638272921 \tabularnewline
42 & 83.6 & 81.63755026143 & 1.96244973856993 \tabularnewline
43 & 73.1 & 82.3955330257254 & -9.29553302572538 \tabularnewline
44 & 91.1 & 74.8160180197732 & 16.2839819802268 \tabularnewline
45 & 118.6 & 86.1262238375851 & 32.4737761624149 \tabularnewline
46 & 102.9 & 109.640046404788 & -6.74004640478756 \tabularnewline
47 & 111.8 & 104.399432801544 & 7.40056719845596 \tabularnewline
48 & 93.9 & 109.583336611196 & -15.6833366111963 \tabularnewline
49 & 91.6 & 97.7094042169086 & -6.1094042169086 \tabularnewline
50 & 92 & 92.7690426949368 & -0.769042694936829 \tabularnewline
51 & 91.1 & 91.725756439159 & -0.625756439159062 \tabularnewline
52 & 97.5 & 90.7802639341292 & 6.71973606587082 \tabularnewline
53 & 94.7 & 95.2820582604291 & -0.582058260429122 \tabularnewline
54 & 96.7 & 94.4371709575557 & 2.26282904244434 \tabularnewline
55 & 78.7 & 95.6982021632108 & -16.9982021632108 \tabularnewline
56 & 103.5 & 82.682551281659 & 20.817448718341 \tabularnewline
57 & 113.8 & 97.5562307916374 & 16.2437692083626 \tabularnewline
58 & 106.1 & 109.266624592303 & -3.16662459230274 \tabularnewline
59 & 120.3 & 106.745798386327 & 13.5542016136732 \tabularnewline
60 & 114.2 & 116.605354596551 & -2.40535459655094 \tabularnewline
61 & 106.3 & 114.765977309598 & -8.46597730959843 \tabularnewline
62 & 98.8 & 108.399472742024 & -9.59947274202383 \tabularnewline
63 & 113.1 & 101.096620850193 & 12.0033791498073 \tabularnewline
64 & 97.7 & 109.727278681949 & -12.0272786819493 \tabularnewline
65 & 116.3 & 100.648582166403 & 15.6514178335972 \tabularnewline
66 & 107.2 & 111.987769244218 & -4.78776924421778 \tabularnewline
67 & 94.5 & 108.325196137739 & -13.8251961377391 \tabularnewline
68 & 123.5 & 97.8984683572181 & 25.6015316427819 \tabularnewline
69 & 126.6 & 116.592840325319 & 10.0071596746815 \tabularnewline
70 & 126.5 & 123.994183578862 & 2.50581642113758 \tabularnewline
71 & 141.4 & 125.937441137548 & 15.4625588624521 \tabularnewline
72 & 124.3 & 137.529560122966 & -13.229560122966 \tabularnewline
73 & 124.9 & 127.989715519552 & -3.08971551955231 \tabularnewline
74 & 108.9 & 125.831095558628 & -16.9310955586278 \tabularnewline
75 & 126.7 & 113.360209170452 & 13.3397908295477 \tabularnewline
76 & 107.7 & 123.177151720956 & -15.4771517209558 \tabularnewline
77 & 121.8 & 111.745702831785 & 10.054297168215 \tabularnewline
78 & 118.3 & 119.099146022922 & -0.799146022921832 \tabularnewline
79 & 122.8 & 118.505979065485 & 4.29402093451512 \tabularnewline
80 & 149.5 & 121.685729033319 & 27.8142709666807 \tabularnewline
81 & 147 & 142.378115029701 & 4.62188497029899 \tabularnewline
82 & 139.3 & 146.160428921942 & -6.86042892194237 \tabularnewline
83 & 162.1 & 141.468415625093 & 20.6315843749067 \tabularnewline
84 & 142.2 & 157.113455431684 & -14.9134554316841 \tabularnewline
85 & 141.4 & 146.595810491043 & -5.1958104910434 \tabularnewline
86 & 124.7 & 143.1270587169 & -18.4270587168995 \tabularnewline
87 & 114 & 129.775529264618 & -15.7755292646176 \tabularnewline
88 & 126.6 & 118.18675693505 & 8.41324306495022 \tabularnewline
89 & 121.9 & 124.38255510635 & -2.48255510635032 \tabularnewline
90 & 125.1 & 122.58193879464 & 2.51806120536048 \tabularnewline
91 & 122.1 & 124.46668931634 & -2.3666893163398 \tabularnewline
92 & 135.9 & 122.752504529591 & 13.1474954704087 \tabularnewline
93 & 148.4 & 132.531675456086 & 15.8683245439136 \tabularnewline
94 & 137.5 & 144.478204732342 & -6.9782047323422 \tabularnewline
95 & 145.3 & 139.637863870255 & 5.66213612974516 \tabularnewline
96 & 139.9 & 144.105371673136 & -4.2053716731362 \tabularnewline
97 & 128.2 & 141.309237021397 & -13.1092370213969 \tabularnewline
98 & 115.4 & 131.854635615895 & -16.4546356158954 \tabularnewline
99 & 124.7 & 119.76933900602 & 4.93066099398028 \tabularnewline
100 & 111.5 & 123.379338515196 & -11.8793385151957 \tabularnewline
101 & 121.1 & 114.562471072113 & 6.53752892788745 \tabularnewline
102 & 122.5 & 119.287909232515 & 3.21209076748457 \tabularnewline
103 & 127.4 & 121.61721166189 & 5.78278833811028 \tabularnewline
104 & 143.7 & 125.891272563022 & 17.8087274369781 \tabularnewline
105 & 157.8 & 139.159691902589 & 18.6403080974108 \tabularnewline
106 & 148.8 & 153.244769733887 & -4.44476973388669 \tabularnewline
107 & 162.9 & 150.396849860596 & 12.5031501394042 \tabularnewline
108 & 153.9 & 160.083642066154 & -6.18364206615405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117397&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]93.6[/C][C]86.9[/C][C]6.7[/C][/ROW]
[ROW][C]4[/C][C]79.7[/C][C]90.6749847662469[/C][C]-10.9749847662469[/C][/ROW]
[ROW][C]5[/C][C]83.8[/C][C]81.4006097908594[/C][C]2.39939020914062[/C][/ROW]
[ROW][C]6[/C][C]62.3[/C][C]81.9344277678502[/C][C]-19.6344277678502[/C][/ROW]
[ROW][C]7[/C][C]62.3[/C][C]66.1341996829024[/C][C]-3.83419968290244[/C][/ROW]
[ROW][C]8[/C][C]77.6[/C][C]61.8465944309632[/C][C]15.7534055690368[/C][/ROW]
[ROW][C]9[/C][C]80.3[/C][C]72.060589031888[/C][C]8.23941096811195[/C][/ROW]
[ROW][C]10[/C][C]97[/C][C]76.8713724340784[/C][C]20.1286275659216[/C][/ROW]
[ROW][C]11[/C][C]94[/C][C]90.602468984942[/C][C]3.39753101505802[/C][/ROW]
[ROW][C]12[/C][C]75.1[/C][C]92.1352675993852[/C][C]-17.0352675993852[/C][/ROW]
[ROW][C]13[/C][C]74[/C][C]78.5339967777313[/C][C]-4.53399677773135[/C][/ROW]
[ROW][C]14[/C][C]77.6[/C][C]74.0248275875882[/C][C]3.5751724124118[/C][/ROW]
[ROW][C]15[/C][C]75.1[/C][C]75.4862904316792[/C][C]-0.386290431679242[/C][/ROW]
[ROW][C]16[/C][C]85[/C][C]74.0462146206988[/C][C]10.9537853793012[/C][/ROW]
[ROW][C]17[/C][C]75.4[/C][C]81.0222220089975[/C][C]-5.62222200899748[/C][/ROW]
[ROW][C]18[/C][C]63.2[/C][C]75.8124750906152[/C][C]-12.6124750906152[/C][/ROW]
[ROW][C]19[/C][C]64.7[/C][C]65.349338895827[/C][C]-0.649338895826986[/C][/ROW]
[ROW][C]20[/C][C]77[/C][C]63.628186990711[/C][C]13.371813009289[/C][/ROW]
[ROW][C]21[/C][C]82.6[/C][C]72.3109691781838[/C][C]10.2890308218162[/C][/ROW]
[ROW][C]22[/C][C]97.6[/C][C]78.8542338640511[/C][C]18.7457661359489[/C][/ROW]
[ROW][C]23[/C][C]99[/C][C]91.7919979304902[/C][C]7.20800206950977[/C][/ROW]
[ROW][C]24[/C][C]75.3[/C][C]96.3722288671173[/C][C]-21.0722288671173[/C][/ROW]
[ROW][C]25[/C][C]71.6[/C][C]80.0340148962004[/C][C]-8.43401489620045[/C][/ROW]
[ROW][C]26[/C][C]76.8[/C][C]72.8444364767395[/C][C]3.95556352326049[/C][/ROW]
[ROW][C]27[/C][C]83.9[/C][C]74.7602243948367[/C][C]9.1397756051633[/C][/ROW]
[ROW][C]28[/C][C]79.7[/C][C]80.5697122155095[/C][C]-0.869712215509466[/C][/ROW]
[ROW][C]29[/C][C]77.5[/C][C]79.049027907034[/C][C]-1.54902790703399[/C][/ROW]
[ROW][C]30[/C][C]73.1[/C][C]77.014200647072[/C][C]-3.91420064707197[/C][/ROW]
[ROW][C]31[/C][C]65.6[/C][C]73.2058247368685[/C][C]-7.60582473686847[/C][/ROW]
[ROW][C]32[/C][C]85.2[/C][C]66.6125104288894[/C][C]18.5874895711106[/C][/ROW]
[ROW][C]33[/C][C]98.3[/C][C]79.3835828813644[/C][C]18.9164171186356[/C][/ROW]
[ROW][C]34[/C][C]98[/C][C]92.6067862978045[/C][C]5.39321370219554[/C][/ROW]
[ROW][C]35[/C][C]100.6[/C][C]96.0001069341242[/C][C]4.59989306587578[/C][/ROW]
[ROW][C]36[/C][C]84.1[/C][C]98.8646792963343[/C][C]-14.7646792963343[/C][/ROW]
[ROW][C]37[/C][C]76.7[/C][C]87.4018253960065[/C][C]-10.7018253960065[/C][/ROW]
[ROW][C]38[/C][C]82.4[/C][C]78.7906481506845[/C][C]3.60935184931554[/C][/ROW]
[ROW][C]39[/C][C]95.5[/C][C]80.6863275041264[/C][C]14.8136724958736[/C][/ROW]
[ROW][C]40[/C][C]79.9[/C][C]90.9419761273838[/C][C]-11.0419761273838[/C][/ROW]
[ROW][C]41[/C][C]82.4[/C][C]82.1645823617271[/C][C]0.235417638272921[/C][/ROW]
[ROW][C]42[/C][C]83.6[/C][C]81.63755026143[/C][C]1.96244973856993[/C][/ROW]
[ROW][C]43[/C][C]73.1[/C][C]82.3955330257254[/C][C]-9.29553302572538[/C][/ROW]
[ROW][C]44[/C][C]91.1[/C][C]74.8160180197732[/C][C]16.2839819802268[/C][/ROW]
[ROW][C]45[/C][C]118.6[/C][C]86.1262238375851[/C][C]32.4737761624149[/C][/ROW]
[ROW][C]46[/C][C]102.9[/C][C]109.640046404788[/C][C]-6.74004640478756[/C][/ROW]
[ROW][C]47[/C][C]111.8[/C][C]104.399432801544[/C][C]7.40056719845596[/C][/ROW]
[ROW][C]48[/C][C]93.9[/C][C]109.583336611196[/C][C]-15.6833366111963[/C][/ROW]
[ROW][C]49[/C][C]91.6[/C][C]97.7094042169086[/C][C]-6.1094042169086[/C][/ROW]
[ROW][C]50[/C][C]92[/C][C]92.7690426949368[/C][C]-0.769042694936829[/C][/ROW]
[ROW][C]51[/C][C]91.1[/C][C]91.725756439159[/C][C]-0.625756439159062[/C][/ROW]
[ROW][C]52[/C][C]97.5[/C][C]90.7802639341292[/C][C]6.71973606587082[/C][/ROW]
[ROW][C]53[/C][C]94.7[/C][C]95.2820582604291[/C][C]-0.582058260429122[/C][/ROW]
[ROW][C]54[/C][C]96.7[/C][C]94.4371709575557[/C][C]2.26282904244434[/C][/ROW]
[ROW][C]55[/C][C]78.7[/C][C]95.6982021632108[/C][C]-16.9982021632108[/C][/ROW]
[ROW][C]56[/C][C]103.5[/C][C]82.682551281659[/C][C]20.817448718341[/C][/ROW]
[ROW][C]57[/C][C]113.8[/C][C]97.5562307916374[/C][C]16.2437692083626[/C][/ROW]
[ROW][C]58[/C][C]106.1[/C][C]109.266624592303[/C][C]-3.16662459230274[/C][/ROW]
[ROW][C]59[/C][C]120.3[/C][C]106.745798386327[/C][C]13.5542016136732[/C][/ROW]
[ROW][C]60[/C][C]114.2[/C][C]116.605354596551[/C][C]-2.40535459655094[/C][/ROW]
[ROW][C]61[/C][C]106.3[/C][C]114.765977309598[/C][C]-8.46597730959843[/C][/ROW]
[ROW][C]62[/C][C]98.8[/C][C]108.399472742024[/C][C]-9.59947274202383[/C][/ROW]
[ROW][C]63[/C][C]113.1[/C][C]101.096620850193[/C][C]12.0033791498073[/C][/ROW]
[ROW][C]64[/C][C]97.7[/C][C]109.727278681949[/C][C]-12.0272786819493[/C][/ROW]
[ROW][C]65[/C][C]116.3[/C][C]100.648582166403[/C][C]15.6514178335972[/C][/ROW]
[ROW][C]66[/C][C]107.2[/C][C]111.987769244218[/C][C]-4.78776924421778[/C][/ROW]
[ROW][C]67[/C][C]94.5[/C][C]108.325196137739[/C][C]-13.8251961377391[/C][/ROW]
[ROW][C]68[/C][C]123.5[/C][C]97.8984683572181[/C][C]25.6015316427819[/C][/ROW]
[ROW][C]69[/C][C]126.6[/C][C]116.592840325319[/C][C]10.0071596746815[/C][/ROW]
[ROW][C]70[/C][C]126.5[/C][C]123.994183578862[/C][C]2.50581642113758[/C][/ROW]
[ROW][C]71[/C][C]141.4[/C][C]125.937441137548[/C][C]15.4625588624521[/C][/ROW]
[ROW][C]72[/C][C]124.3[/C][C]137.529560122966[/C][C]-13.229560122966[/C][/ROW]
[ROW][C]73[/C][C]124.9[/C][C]127.989715519552[/C][C]-3.08971551955231[/C][/ROW]
[ROW][C]74[/C][C]108.9[/C][C]125.831095558628[/C][C]-16.9310955586278[/C][/ROW]
[ROW][C]75[/C][C]126.7[/C][C]113.360209170452[/C][C]13.3397908295477[/C][/ROW]
[ROW][C]76[/C][C]107.7[/C][C]123.177151720956[/C][C]-15.4771517209558[/C][/ROW]
[ROW][C]77[/C][C]121.8[/C][C]111.745702831785[/C][C]10.054297168215[/C][/ROW]
[ROW][C]78[/C][C]118.3[/C][C]119.099146022922[/C][C]-0.799146022921832[/C][/ROW]
[ROW][C]79[/C][C]122.8[/C][C]118.505979065485[/C][C]4.29402093451512[/C][/ROW]
[ROW][C]80[/C][C]149.5[/C][C]121.685729033319[/C][C]27.8142709666807[/C][/ROW]
[ROW][C]81[/C][C]147[/C][C]142.378115029701[/C][C]4.62188497029899[/C][/ROW]
[ROW][C]82[/C][C]139.3[/C][C]146.160428921942[/C][C]-6.86042892194237[/C][/ROW]
[ROW][C]83[/C][C]162.1[/C][C]141.468415625093[/C][C]20.6315843749067[/C][/ROW]
[ROW][C]84[/C][C]142.2[/C][C]157.113455431684[/C][C]-14.9134554316841[/C][/ROW]
[ROW][C]85[/C][C]141.4[/C][C]146.595810491043[/C][C]-5.1958104910434[/C][/ROW]
[ROW][C]86[/C][C]124.7[/C][C]143.1270587169[/C][C]-18.4270587168995[/C][/ROW]
[ROW][C]87[/C][C]114[/C][C]129.775529264618[/C][C]-15.7755292646176[/C][/ROW]
[ROW][C]88[/C][C]126.6[/C][C]118.18675693505[/C][C]8.41324306495022[/C][/ROW]
[ROW][C]89[/C][C]121.9[/C][C]124.38255510635[/C][C]-2.48255510635032[/C][/ROW]
[ROW][C]90[/C][C]125.1[/C][C]122.58193879464[/C][C]2.51806120536048[/C][/ROW]
[ROW][C]91[/C][C]122.1[/C][C]124.46668931634[/C][C]-2.3666893163398[/C][/ROW]
[ROW][C]92[/C][C]135.9[/C][C]122.752504529591[/C][C]13.1474954704087[/C][/ROW]
[ROW][C]93[/C][C]148.4[/C][C]132.531675456086[/C][C]15.8683245439136[/C][/ROW]
[ROW][C]94[/C][C]137.5[/C][C]144.478204732342[/C][C]-6.9782047323422[/C][/ROW]
[ROW][C]95[/C][C]145.3[/C][C]139.637863870255[/C][C]5.66213612974516[/C][/ROW]
[ROW][C]96[/C][C]139.9[/C][C]144.105371673136[/C][C]-4.2053716731362[/C][/ROW]
[ROW][C]97[/C][C]128.2[/C][C]141.309237021397[/C][C]-13.1092370213969[/C][/ROW]
[ROW][C]98[/C][C]115.4[/C][C]131.854635615895[/C][C]-16.4546356158954[/C][/ROW]
[ROW][C]99[/C][C]124.7[/C][C]119.76933900602[/C][C]4.93066099398028[/C][/ROW]
[ROW][C]100[/C][C]111.5[/C][C]123.379338515196[/C][C]-11.8793385151957[/C][/ROW]
[ROW][C]101[/C][C]121.1[/C][C]114.562471072113[/C][C]6.53752892788745[/C][/ROW]
[ROW][C]102[/C][C]122.5[/C][C]119.287909232515[/C][C]3.21209076748457[/C][/ROW]
[ROW][C]103[/C][C]127.4[/C][C]121.61721166189[/C][C]5.78278833811028[/C][/ROW]
[ROW][C]104[/C][C]143.7[/C][C]125.891272563022[/C][C]17.8087274369781[/C][/ROW]
[ROW][C]105[/C][C]157.8[/C][C]139.159691902589[/C][C]18.6403080974108[/C][/ROW]
[ROW][C]106[/C][C]148.8[/C][C]153.244769733887[/C][C]-4.44476973388669[/C][/ROW]
[ROW][C]107[/C][C]162.9[/C][C]150.396849860596[/C][C]12.5031501394042[/C][/ROW]
[ROW][C]108[/C][C]153.9[/C][C]160.083642066154[/C][C]-6.18364206615405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117397&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
393.686.96.7
479.790.6749847662469-10.9749847662469
583.881.40060979085942.39939020914062
662.381.9344277678502-19.6344277678502
762.366.1341996829024-3.83419968290244
877.661.846594430963215.7534055690368
980.372.0605890318888.23941096811195
109776.871372434078420.1286275659216
119490.6024689849423.39753101505802
1275.192.1352675993852-17.0352675993852
137478.5339967777313-4.53399677773135
1477.674.02482758758823.5751724124118
1575.175.4862904316792-0.386290431679242
168574.046214620698810.9537853793012
1775.481.0222220089975-5.62222200899748
1863.275.8124750906152-12.6124750906152
1964.765.349338895827-0.649338895826986
207763.62818699071113.371813009289
2182.672.310969178183810.2890308218162
2297.678.854233864051118.7457661359489
239991.79199793049027.20800206950977
2475.396.3722288671173-21.0722288671173
2571.680.0340148962004-8.43401489620045
2676.872.84443647673953.95556352326049
2783.974.76022439483679.1397756051633
2879.780.5697122155095-0.869712215509466
2977.579.049027907034-1.54902790703399
3073.177.014200647072-3.91420064707197
3165.673.2058247368685-7.60582473686847
3285.266.612510428889418.5874895711106
3398.379.383582881364418.9164171186356
349892.60678629780455.39321370219554
35100.696.00010693412424.59989306587578
3684.198.8646792963343-14.7646792963343
3776.787.4018253960065-10.7018253960065
3882.478.79064815068453.60935184931554
3995.580.686327504126414.8136724958736
4079.990.9419761273838-11.0419761273838
4182.482.16458236172710.235417638272921
4283.681.637550261431.96244973856993
4373.182.3955330257254-9.29553302572538
4491.174.816018019773216.2839819802268
45118.686.126223837585132.4737761624149
46102.9109.640046404788-6.74004640478756
47111.8104.3994328015447.40056719845596
4893.9109.583336611196-15.6833366111963
4991.697.7094042169086-6.1094042169086
509292.7690426949368-0.769042694936829
5191.191.725756439159-0.625756439159062
5297.590.78026393412926.71973606587082
5394.795.2820582604291-0.582058260429122
5496.794.43717095755572.26282904244434
5578.795.6982021632108-16.9982021632108
56103.582.68255128165920.817448718341
57113.897.556230791637416.2437692083626
58106.1109.266624592303-3.16662459230274
59120.3106.74579838632713.5542016136732
60114.2116.605354596551-2.40535459655094
61106.3114.765977309598-8.46597730959843
6298.8108.399472742024-9.59947274202383
63113.1101.09662085019312.0033791498073
6497.7109.727278681949-12.0272786819493
65116.3100.64858216640315.6514178335972
66107.2111.987769244218-4.78776924421778
6794.5108.325196137739-13.8251961377391
68123.597.898468357218125.6015316427819
69126.6116.59284032531910.0071596746815
70126.5123.9941835788622.50581642113758
71141.4125.93744113754815.4625588624521
72124.3137.529560122966-13.229560122966
73124.9127.989715519552-3.08971551955231
74108.9125.831095558628-16.9310955586278
75126.7113.36020917045213.3397908295477
76107.7123.177151720956-15.4771517209558
77121.8111.74570283178510.054297168215
78118.3119.099146022922-0.799146022921832
79122.8118.5059790654854.29402093451512
80149.5121.68572903331927.8142709666807
81147142.3781150297014.62188497029899
82139.3146.160428921942-6.86042892194237
83162.1141.46841562509320.6315843749067
84142.2157.113455431684-14.9134554316841
85141.4146.595810491043-5.1958104910434
86124.7143.1270587169-18.4270587168995
87114129.775529264618-15.7755292646176
88126.6118.186756935058.41324306495022
89121.9124.38255510635-2.48255510635032
90125.1122.581938794642.51806120536048
91122.1124.46668931634-2.3666893163398
92135.9122.75250452959113.1474954704087
93148.4132.53167545608615.8683245439136
94137.5144.478204732342-6.9782047323422
95145.3139.6378638702555.66213612974516
96139.9144.105371673136-4.2053716731362
97128.2141.309237021397-13.1092370213969
98115.4131.854635615895-16.4546356158954
99124.7119.769339006024.93066099398028
100111.5123.379338515196-11.8793385151957
101121.1114.5624710721136.53752892788745
102122.5119.2879092325153.21209076748457
103127.4121.617211661895.78278833811028
104143.7125.89127256302217.8087274369781
105157.8139.15969190258918.6403080974108
106148.8153.244769733887-4.44476973388669
107162.9150.39684986059612.5031501394042
108153.9160.083642066154-6.18364206615405






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109156.034677060112132.773109212627179.296244907597
110156.508122363589127.535017526592185.481227200585
111156.981567667065123.116596609688190.846538724442
112157.455012970542119.200310048516195.709715892567
113157.928458274018115.627934977412200.228981570625
114158.401903577495112.307353295223204.496453859767
115158.875348880971109.179498412428208.571199349515
116159.348794184448106.203901580995212.493686787901
117159.822239487924103.351458474094216.293020501755
118160.295684791401100.600446926937219.990922655865
119160.76913009487897.9341722254992223.604087964256
120161.24257539835495.3394950224593227.145655774249

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 156.034677060112 & 132.773109212627 & 179.296244907597 \tabularnewline
110 & 156.508122363589 & 127.535017526592 & 185.481227200585 \tabularnewline
111 & 156.981567667065 & 123.116596609688 & 190.846538724442 \tabularnewline
112 & 157.455012970542 & 119.200310048516 & 195.709715892567 \tabularnewline
113 & 157.928458274018 & 115.627934977412 & 200.228981570625 \tabularnewline
114 & 158.401903577495 & 112.307353295223 & 204.496453859767 \tabularnewline
115 & 158.875348880971 & 109.179498412428 & 208.571199349515 \tabularnewline
116 & 159.348794184448 & 106.203901580995 & 212.493686787901 \tabularnewline
117 & 159.822239487924 & 103.351458474094 & 216.293020501755 \tabularnewline
118 & 160.295684791401 & 100.600446926937 & 219.990922655865 \tabularnewline
119 & 160.769130094878 & 97.9341722254992 & 223.604087964256 \tabularnewline
120 & 161.242575398354 & 95.3394950224593 & 227.145655774249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117397&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]156.034677060112[/C][C]132.773109212627[/C][C]179.296244907597[/C][/ROW]
[ROW][C]110[/C][C]156.508122363589[/C][C]127.535017526592[/C][C]185.481227200585[/C][/ROW]
[ROW][C]111[/C][C]156.981567667065[/C][C]123.116596609688[/C][C]190.846538724442[/C][/ROW]
[ROW][C]112[/C][C]157.455012970542[/C][C]119.200310048516[/C][C]195.709715892567[/C][/ROW]
[ROW][C]113[/C][C]157.928458274018[/C][C]115.627934977412[/C][C]200.228981570625[/C][/ROW]
[ROW][C]114[/C][C]158.401903577495[/C][C]112.307353295223[/C][C]204.496453859767[/C][/ROW]
[ROW][C]115[/C][C]158.875348880971[/C][C]109.179498412428[/C][C]208.571199349515[/C][/ROW]
[ROW][C]116[/C][C]159.348794184448[/C][C]106.203901580995[/C][C]212.493686787901[/C][/ROW]
[ROW][C]117[/C][C]159.822239487924[/C][C]103.351458474094[/C][C]216.293020501755[/C][/ROW]
[ROW][C]118[/C][C]160.295684791401[/C][C]100.600446926937[/C][C]219.990922655865[/C][/ROW]
[ROW][C]119[/C][C]160.769130094878[/C][C]97.9341722254992[/C][C]223.604087964256[/C][/ROW]
[ROW][C]120[/C][C]161.242575398354[/C][C]95.3394950224593[/C][C]227.145655774249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117397&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117397&T=3

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:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109156.034677060112132.773109212627179.296244907597
110156.508122363589127.535017526592185.481227200585
111156.981567667065123.116596609688190.846538724442
112157.455012970542119.200310048516195.709715892567
113157.928458274018115.627934977412200.228981570625
114158.401903577495112.307353295223204.496453859767
115158.875348880971109.179498412428208.571199349515
116159.348794184448106.203901580995212.493686787901
117159.822239487924103.351458474094216.293020501755
118160.295684791401100.600446926937219.990922655865
119160.76913009487897.9341722254992223.604087964256
120161.24257539835495.3394950224593227.145655774249


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')