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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 computationMon, 18 Jan 2010 08:56:11 -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/18/t12638302246qiwwyg1q05azt1.htm/, Retrieved Sun, 05 May 2024 06:44:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72275, Retrieved Sun, 05 May 2024 06:44:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact188

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 oefening 2] [2010-01-18 15:56:11] [d41d8cd98f00b204e9800998ecf8427e] [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 time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72275&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72275&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'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.152389418657338
beta0.0403497841851909
gamma0.289315718348342

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.152389418657338 \tabularnewline
beta & 0.0403497841851909 \tabularnewline
gamma & 0.289315718348342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72275&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]0.152389418657338[/C][/ROW]
[ROW][C]beta[/C][C]0.0403497841851909[/C][/ROW]
[ROW][C]gamma[/C][C]0.289315718348342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72275&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
alpha0.152389418657338
beta0.0403497841851909
gamma0.289315718348342






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.799.85415776648042.84584223351962
1475.473.86407647569961.53592352430037
1587.285.81492771850641.38507228149356
1683.782.36839556526891.33160443473115
17105.8103.8646666592061.93533334079383
18111.5109.2594124506232.24058754937664
1999.7103.552937819575-3.85293781957476
20111.2111.592282860904-0.392282860904231
21101.5101.0236809424440.476319057555585
22110.9101.5660285983229.33397140167772
23116.3111.7685035443994.5314964556013
24164.9161.5795830816823.32041691831793
25118.1110.9488295039867.15117049601382
2683.782.45722314037251.24277685962748
278495.7097150921302-11.7097150921302
28107.289.961800944224317.2381990557757
29113.7116.677877146881-2.97787714688113
30120.7122.089478988153-1.38947898815346
31111.2113.617386421764-2.41738642176409
32112.4123.875711719721-11.4757117197207
33112.5110.8873899599131.61261004008730
34130.4114.05002803767916.3499719623206
35130.7125.0369648498725.66303515012832
36174.3180.148818447016-5.84881844701641
37132.2124.0534716617328.14652833826754
3891.891.16561781126430.634382188735714
39104.2102.1178049529492.08219504705104
40104.8105.946193936461-1.14619393646073
41131.4126.6780957362894.72190426371127
42141.2134.3487235300086.85127646999155
43132.7125.9960731957316.70392680426896
44135.7136.595426964986-0.8954269649862
45136.9127.4670688204989.4329311795017
46151.2136.59821418901214.6017858109880
47144145.803742351963-1.80374235196251
48201.5204.568736053253-3.06873605325254
49149.6144.8459132696674.75408673033252
50108.7104.5508479468364.14915205316417
51122.8118.2295141879504.57048581205039
52126.7122.2299405179044.47005948209616
53139.9149.170215243516-9.27021524351608
54162.5156.4931271346526.00687286534759
55142.7146.699640439811-3.99964043981112
56151.6154.930791018806-3.33079101880574
57148.1147.1384134805550.961586519445149
58159157.2950524533721.70494754662803
59157.8160.765946370615-2.9659463706154
60226.7225.1159375387791.58406246122121
61153.7161.762691979094-8.06269197909418
62122.3115.4083064882516.89169351174898
63117.6130.795358567693-13.1953585676933
64166132.12724126968133.8727587303188
65154.5162.577769569462-8.07776956946228
66183.9175.160680901118.73931909889018
67164.4161.8576686840002.54233131599972
68173.3172.3378599158490.9621400841514
69160.2165.534649711094-5.33464971109444
70166.4176.118688701466-9.71868870146588
71170.3176.877063656989-6.57706365698888
72238.4248.438145850133-10.0381458501329
73166.8174.649207746374-7.84920774637393
74122.5128.014099723703-5.51409972370283
75141.8137.1046771186954.69532288130526
76140.5153.763910712417-13.2639107124170
77173.8167.0174645087366.78253549126444
78188.8186.6558867666212.1441132333795
79168169.776545813552-1.77654581355222
80187.4179.2750991790898.1249008209109
81177.7171.3525719276436.34742807235699
82183.8182.9560115532450.84398844675485
83196.1186.1022521741739.99774782582668
84264.6264.70569713596-0.105697135960042
85193.7186.9693504150606.7306495849397
86141.3138.8371268420742.46287315792557
87170.1153.03942281651317.0605771834873
88163.7168.661514288136-4.96151428813573
89190.1190.946882434901-0.846882434900749
90230.7210.64899439838520.0510056016149
91195.9193.2531897909382.64681020906161
92210.3207.9084504928582.39154950714226
93204.7197.5543789522177.14562104778307
94210.3209.5043064146330.79569358536736
95221.2215.8761728773745.32382712262589
96288.2302.03938884432-13.8393888443202
97203.2213.908324541505-10.7083245415054
98162.4156.1294982000616.27050179993947
99149.2176.639134446847-27.439134446847
100195.3180.50630074410814.793699255892
101213.7209.0547078561304.6452921438696
102227.9237.096744304260-9.19674430425965
103212.1208.8575315796313.24246842036882
104226.8224.4435079901242.35649200987592
105212.6214.325818835862-1.72581883586176
106220.9223.761351406124-2.86135140612356
107228.1230.891271727254-2.79127172725376
108311.6315.294264877466-3.69426487746625

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102.7 & 99.8541577664804 & 2.84584223351962 \tabularnewline
14 & 75.4 & 73.8640764756996 & 1.53592352430037 \tabularnewline
15 & 87.2 & 85.8149277185064 & 1.38507228149356 \tabularnewline
16 & 83.7 & 82.3683955652689 & 1.33160443473115 \tabularnewline
17 & 105.8 & 103.864666659206 & 1.93533334079383 \tabularnewline
18 & 111.5 & 109.259412450623 & 2.24058754937664 \tabularnewline
19 & 99.7 & 103.552937819575 & -3.85293781957476 \tabularnewline
20 & 111.2 & 111.592282860904 & -0.392282860904231 \tabularnewline
21 & 101.5 & 101.023680942444 & 0.476319057555585 \tabularnewline
22 & 110.9 & 101.566028598322 & 9.33397140167772 \tabularnewline
23 & 116.3 & 111.768503544399 & 4.5314964556013 \tabularnewline
24 & 164.9 & 161.579583081682 & 3.32041691831793 \tabularnewline
25 & 118.1 & 110.948829503986 & 7.15117049601382 \tabularnewline
26 & 83.7 & 82.4572231403725 & 1.24277685962748 \tabularnewline
27 & 84 & 95.7097150921302 & -11.7097150921302 \tabularnewline
28 & 107.2 & 89.9618009442243 & 17.2381990557757 \tabularnewline
29 & 113.7 & 116.677877146881 & -2.97787714688113 \tabularnewline
30 & 120.7 & 122.089478988153 & -1.38947898815346 \tabularnewline
31 & 111.2 & 113.617386421764 & -2.41738642176409 \tabularnewline
32 & 112.4 & 123.875711719721 & -11.4757117197207 \tabularnewline
33 & 112.5 & 110.887389959913 & 1.61261004008730 \tabularnewline
34 & 130.4 & 114.050028037679 & 16.3499719623206 \tabularnewline
35 & 130.7 & 125.036964849872 & 5.66303515012832 \tabularnewline
36 & 174.3 & 180.148818447016 & -5.84881844701641 \tabularnewline
37 & 132.2 & 124.053471661732 & 8.14652833826754 \tabularnewline
38 & 91.8 & 91.1656178112643 & 0.634382188735714 \tabularnewline
39 & 104.2 & 102.117804952949 & 2.08219504705104 \tabularnewline
40 & 104.8 & 105.946193936461 & -1.14619393646073 \tabularnewline
41 & 131.4 & 126.678095736289 & 4.72190426371127 \tabularnewline
42 & 141.2 & 134.348723530008 & 6.85127646999155 \tabularnewline
43 & 132.7 & 125.996073195731 & 6.70392680426896 \tabularnewline
44 & 135.7 & 136.595426964986 & -0.8954269649862 \tabularnewline
45 & 136.9 & 127.467068820498 & 9.4329311795017 \tabularnewline
46 & 151.2 & 136.598214189012 & 14.6017858109880 \tabularnewline
47 & 144 & 145.803742351963 & -1.80374235196251 \tabularnewline
48 & 201.5 & 204.568736053253 & -3.06873605325254 \tabularnewline
49 & 149.6 & 144.845913269667 & 4.75408673033252 \tabularnewline
50 & 108.7 & 104.550847946836 & 4.14915205316417 \tabularnewline
51 & 122.8 & 118.229514187950 & 4.57048581205039 \tabularnewline
52 & 126.7 & 122.229940517904 & 4.47005948209616 \tabularnewline
53 & 139.9 & 149.170215243516 & -9.27021524351608 \tabularnewline
54 & 162.5 & 156.493127134652 & 6.00687286534759 \tabularnewline
55 & 142.7 & 146.699640439811 & -3.99964043981112 \tabularnewline
56 & 151.6 & 154.930791018806 & -3.33079101880574 \tabularnewline
57 & 148.1 & 147.138413480555 & 0.961586519445149 \tabularnewline
58 & 159 & 157.295052453372 & 1.70494754662803 \tabularnewline
59 & 157.8 & 160.765946370615 & -2.9659463706154 \tabularnewline
60 & 226.7 & 225.115937538779 & 1.58406246122121 \tabularnewline
61 & 153.7 & 161.762691979094 & -8.06269197909418 \tabularnewline
62 & 122.3 & 115.408306488251 & 6.89169351174898 \tabularnewline
63 & 117.6 & 130.795358567693 & -13.1953585676933 \tabularnewline
64 & 166 & 132.127241269681 & 33.8727587303188 \tabularnewline
65 & 154.5 & 162.577769569462 & -8.07776956946228 \tabularnewline
66 & 183.9 & 175.16068090111 & 8.73931909889018 \tabularnewline
67 & 164.4 & 161.857668684000 & 2.54233131599972 \tabularnewline
68 & 173.3 & 172.337859915849 & 0.9621400841514 \tabularnewline
69 & 160.2 & 165.534649711094 & -5.33464971109444 \tabularnewline
70 & 166.4 & 176.118688701466 & -9.71868870146588 \tabularnewline
71 & 170.3 & 176.877063656989 & -6.57706365698888 \tabularnewline
72 & 238.4 & 248.438145850133 & -10.0381458501329 \tabularnewline
73 & 166.8 & 174.649207746374 & -7.84920774637393 \tabularnewline
74 & 122.5 & 128.014099723703 & -5.51409972370283 \tabularnewline
75 & 141.8 & 137.104677118695 & 4.69532288130526 \tabularnewline
76 & 140.5 & 153.763910712417 & -13.2639107124170 \tabularnewline
77 & 173.8 & 167.017464508736 & 6.78253549126444 \tabularnewline
78 & 188.8 & 186.655886766621 & 2.1441132333795 \tabularnewline
79 & 168 & 169.776545813552 & -1.77654581355222 \tabularnewline
80 & 187.4 & 179.275099179089 & 8.1249008209109 \tabularnewline
81 & 177.7 & 171.352571927643 & 6.34742807235699 \tabularnewline
82 & 183.8 & 182.956011553245 & 0.84398844675485 \tabularnewline
83 & 196.1 & 186.102252174173 & 9.99774782582668 \tabularnewline
84 & 264.6 & 264.70569713596 & -0.105697135960042 \tabularnewline
85 & 193.7 & 186.969350415060 & 6.7306495849397 \tabularnewline
86 & 141.3 & 138.837126842074 & 2.46287315792557 \tabularnewline
87 & 170.1 & 153.039422816513 & 17.0605771834873 \tabularnewline
88 & 163.7 & 168.661514288136 & -4.96151428813573 \tabularnewline
89 & 190.1 & 190.946882434901 & -0.846882434900749 \tabularnewline
90 & 230.7 & 210.648994398385 & 20.0510056016149 \tabularnewline
91 & 195.9 & 193.253189790938 & 2.64681020906161 \tabularnewline
92 & 210.3 & 207.908450492858 & 2.39154950714226 \tabularnewline
93 & 204.7 & 197.554378952217 & 7.14562104778307 \tabularnewline
94 & 210.3 & 209.504306414633 & 0.79569358536736 \tabularnewline
95 & 221.2 & 215.876172877374 & 5.32382712262589 \tabularnewline
96 & 288.2 & 302.03938884432 & -13.8393888443202 \tabularnewline
97 & 203.2 & 213.908324541505 & -10.7083245415054 \tabularnewline
98 & 162.4 & 156.129498200061 & 6.27050179993947 \tabularnewline
99 & 149.2 & 176.639134446847 & -27.439134446847 \tabularnewline
100 & 195.3 & 180.506300744108 & 14.793699255892 \tabularnewline
101 & 213.7 & 209.054707856130 & 4.6452921438696 \tabularnewline
102 & 227.9 & 237.096744304260 & -9.19674430425965 \tabularnewline
103 & 212.1 & 208.857531579631 & 3.24246842036882 \tabularnewline
104 & 226.8 & 224.443507990124 & 2.35649200987592 \tabularnewline
105 & 212.6 & 214.325818835862 & -1.72581883586176 \tabularnewline
106 & 220.9 & 223.761351406124 & -2.86135140612356 \tabularnewline
107 & 228.1 & 230.891271727254 & -2.79127172725376 \tabularnewline
108 & 311.6 & 315.294264877466 & -3.69426487746625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72275&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]102.7[/C][C]99.8541577664804[/C][C]2.84584223351962[/C][/ROW]
[ROW][C]14[/C][C]75.4[/C][C]73.8640764756996[/C][C]1.53592352430037[/C][/ROW]
[ROW][C]15[/C][C]87.2[/C][C]85.8149277185064[/C][C]1.38507228149356[/C][/ROW]
[ROW][C]16[/C][C]83.7[/C][C]82.3683955652689[/C][C]1.33160443473115[/C][/ROW]
[ROW][C]17[/C][C]105.8[/C][C]103.864666659206[/C][C]1.93533334079383[/C][/ROW]
[ROW][C]18[/C][C]111.5[/C][C]109.259412450623[/C][C]2.24058754937664[/C][/ROW]
[ROW][C]19[/C][C]99.7[/C][C]103.552937819575[/C][C]-3.85293781957476[/C][/ROW]
[ROW][C]20[/C][C]111.2[/C][C]111.592282860904[/C][C]-0.392282860904231[/C][/ROW]
[ROW][C]21[/C][C]101.5[/C][C]101.023680942444[/C][C]0.476319057555585[/C][/ROW]
[ROW][C]22[/C][C]110.9[/C][C]101.566028598322[/C][C]9.33397140167772[/C][/ROW]
[ROW][C]23[/C][C]116.3[/C][C]111.768503544399[/C][C]4.5314964556013[/C][/ROW]
[ROW][C]24[/C][C]164.9[/C][C]161.579583081682[/C][C]3.32041691831793[/C][/ROW]
[ROW][C]25[/C][C]118.1[/C][C]110.948829503986[/C][C]7.15117049601382[/C][/ROW]
[ROW][C]26[/C][C]83.7[/C][C]82.4572231403725[/C][C]1.24277685962748[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]95.7097150921302[/C][C]-11.7097150921302[/C][/ROW]
[ROW][C]28[/C][C]107.2[/C][C]89.9618009442243[/C][C]17.2381990557757[/C][/ROW]
[ROW][C]29[/C][C]113.7[/C][C]116.677877146881[/C][C]-2.97787714688113[/C][/ROW]
[ROW][C]30[/C][C]120.7[/C][C]122.089478988153[/C][C]-1.38947898815346[/C][/ROW]
[ROW][C]31[/C][C]111.2[/C][C]113.617386421764[/C][C]-2.41738642176409[/C][/ROW]
[ROW][C]32[/C][C]112.4[/C][C]123.875711719721[/C][C]-11.4757117197207[/C][/ROW]
[ROW][C]33[/C][C]112.5[/C][C]110.887389959913[/C][C]1.61261004008730[/C][/ROW]
[ROW][C]34[/C][C]130.4[/C][C]114.050028037679[/C][C]16.3499719623206[/C][/ROW]
[ROW][C]35[/C][C]130.7[/C][C]125.036964849872[/C][C]5.66303515012832[/C][/ROW]
[ROW][C]36[/C][C]174.3[/C][C]180.148818447016[/C][C]-5.84881844701641[/C][/ROW]
[ROW][C]37[/C][C]132.2[/C][C]124.053471661732[/C][C]8.14652833826754[/C][/ROW]
[ROW][C]38[/C][C]91.8[/C][C]91.1656178112643[/C][C]0.634382188735714[/C][/ROW]
[ROW][C]39[/C][C]104.2[/C][C]102.117804952949[/C][C]2.08219504705104[/C][/ROW]
[ROW][C]40[/C][C]104.8[/C][C]105.946193936461[/C][C]-1.14619393646073[/C][/ROW]
[ROW][C]41[/C][C]131.4[/C][C]126.678095736289[/C][C]4.72190426371127[/C][/ROW]
[ROW][C]42[/C][C]141.2[/C][C]134.348723530008[/C][C]6.85127646999155[/C][/ROW]
[ROW][C]43[/C][C]132.7[/C][C]125.996073195731[/C][C]6.70392680426896[/C][/ROW]
[ROW][C]44[/C][C]135.7[/C][C]136.595426964986[/C][C]-0.8954269649862[/C][/ROW]
[ROW][C]45[/C][C]136.9[/C][C]127.467068820498[/C][C]9.4329311795017[/C][/ROW]
[ROW][C]46[/C][C]151.2[/C][C]136.598214189012[/C][C]14.6017858109880[/C][/ROW]
[ROW][C]47[/C][C]144[/C][C]145.803742351963[/C][C]-1.80374235196251[/C][/ROW]
[ROW][C]48[/C][C]201.5[/C][C]204.568736053253[/C][C]-3.06873605325254[/C][/ROW]
[ROW][C]49[/C][C]149.6[/C][C]144.845913269667[/C][C]4.75408673033252[/C][/ROW]
[ROW][C]50[/C][C]108.7[/C][C]104.550847946836[/C][C]4.14915205316417[/C][/ROW]
[ROW][C]51[/C][C]122.8[/C][C]118.229514187950[/C][C]4.57048581205039[/C][/ROW]
[ROW][C]52[/C][C]126.7[/C][C]122.229940517904[/C][C]4.47005948209616[/C][/ROW]
[ROW][C]53[/C][C]139.9[/C][C]149.170215243516[/C][C]-9.27021524351608[/C][/ROW]
[ROW][C]54[/C][C]162.5[/C][C]156.493127134652[/C][C]6.00687286534759[/C][/ROW]
[ROW][C]55[/C][C]142.7[/C][C]146.699640439811[/C][C]-3.99964043981112[/C][/ROW]
[ROW][C]56[/C][C]151.6[/C][C]154.930791018806[/C][C]-3.33079101880574[/C][/ROW]
[ROW][C]57[/C][C]148.1[/C][C]147.138413480555[/C][C]0.961586519445149[/C][/ROW]
[ROW][C]58[/C][C]159[/C][C]157.295052453372[/C][C]1.70494754662803[/C][/ROW]
[ROW][C]59[/C][C]157.8[/C][C]160.765946370615[/C][C]-2.9659463706154[/C][/ROW]
[ROW][C]60[/C][C]226.7[/C][C]225.115937538779[/C][C]1.58406246122121[/C][/ROW]
[ROW][C]61[/C][C]153.7[/C][C]161.762691979094[/C][C]-8.06269197909418[/C][/ROW]
[ROW][C]62[/C][C]122.3[/C][C]115.408306488251[/C][C]6.89169351174898[/C][/ROW]
[ROW][C]63[/C][C]117.6[/C][C]130.795358567693[/C][C]-13.1953585676933[/C][/ROW]
[ROW][C]64[/C][C]166[/C][C]132.127241269681[/C][C]33.8727587303188[/C][/ROW]
[ROW][C]65[/C][C]154.5[/C][C]162.577769569462[/C][C]-8.07776956946228[/C][/ROW]
[ROW][C]66[/C][C]183.9[/C][C]175.16068090111[/C][C]8.73931909889018[/C][/ROW]
[ROW][C]67[/C][C]164.4[/C][C]161.857668684000[/C][C]2.54233131599972[/C][/ROW]
[ROW][C]68[/C][C]173.3[/C][C]172.337859915849[/C][C]0.9621400841514[/C][/ROW]
[ROW][C]69[/C][C]160.2[/C][C]165.534649711094[/C][C]-5.33464971109444[/C][/ROW]
[ROW][C]70[/C][C]166.4[/C][C]176.118688701466[/C][C]-9.71868870146588[/C][/ROW]
[ROW][C]71[/C][C]170.3[/C][C]176.877063656989[/C][C]-6.57706365698888[/C][/ROW]
[ROW][C]72[/C][C]238.4[/C][C]248.438145850133[/C][C]-10.0381458501329[/C][/ROW]
[ROW][C]73[/C][C]166.8[/C][C]174.649207746374[/C][C]-7.84920774637393[/C][/ROW]
[ROW][C]74[/C][C]122.5[/C][C]128.014099723703[/C][C]-5.51409972370283[/C][/ROW]
[ROW][C]75[/C][C]141.8[/C][C]137.104677118695[/C][C]4.69532288130526[/C][/ROW]
[ROW][C]76[/C][C]140.5[/C][C]153.763910712417[/C][C]-13.2639107124170[/C][/ROW]
[ROW][C]77[/C][C]173.8[/C][C]167.017464508736[/C][C]6.78253549126444[/C][/ROW]
[ROW][C]78[/C][C]188.8[/C][C]186.655886766621[/C][C]2.1441132333795[/C][/ROW]
[ROW][C]79[/C][C]168[/C][C]169.776545813552[/C][C]-1.77654581355222[/C][/ROW]
[ROW][C]80[/C][C]187.4[/C][C]179.275099179089[/C][C]8.1249008209109[/C][/ROW]
[ROW][C]81[/C][C]177.7[/C][C]171.352571927643[/C][C]6.34742807235699[/C][/ROW]
[ROW][C]82[/C][C]183.8[/C][C]182.956011553245[/C][C]0.84398844675485[/C][/ROW]
[ROW][C]83[/C][C]196.1[/C][C]186.102252174173[/C][C]9.99774782582668[/C][/ROW]
[ROW][C]84[/C][C]264.6[/C][C]264.70569713596[/C][C]-0.105697135960042[/C][/ROW]
[ROW][C]85[/C][C]193.7[/C][C]186.969350415060[/C][C]6.7306495849397[/C][/ROW]
[ROW][C]86[/C][C]141.3[/C][C]138.837126842074[/C][C]2.46287315792557[/C][/ROW]
[ROW][C]87[/C][C]170.1[/C][C]153.039422816513[/C][C]17.0605771834873[/C][/ROW]
[ROW][C]88[/C][C]163.7[/C][C]168.661514288136[/C][C]-4.96151428813573[/C][/ROW]
[ROW][C]89[/C][C]190.1[/C][C]190.946882434901[/C][C]-0.846882434900749[/C][/ROW]
[ROW][C]90[/C][C]230.7[/C][C]210.648994398385[/C][C]20.0510056016149[/C][/ROW]
[ROW][C]91[/C][C]195.9[/C][C]193.253189790938[/C][C]2.64681020906161[/C][/ROW]
[ROW][C]92[/C][C]210.3[/C][C]207.908450492858[/C][C]2.39154950714226[/C][/ROW]
[ROW][C]93[/C][C]204.7[/C][C]197.554378952217[/C][C]7.14562104778307[/C][/ROW]
[ROW][C]94[/C][C]210.3[/C][C]209.504306414633[/C][C]0.79569358536736[/C][/ROW]
[ROW][C]95[/C][C]221.2[/C][C]215.876172877374[/C][C]5.32382712262589[/C][/ROW]
[ROW][C]96[/C][C]288.2[/C][C]302.03938884432[/C][C]-13.8393888443202[/C][/ROW]
[ROW][C]97[/C][C]203.2[/C][C]213.908324541505[/C][C]-10.7083245415054[/C][/ROW]
[ROW][C]98[/C][C]162.4[/C][C]156.129498200061[/C][C]6.27050179993947[/C][/ROW]
[ROW][C]99[/C][C]149.2[/C][C]176.639134446847[/C][C]-27.439134446847[/C][/ROW]
[ROW][C]100[/C][C]195.3[/C][C]180.506300744108[/C][C]14.793699255892[/C][/ROW]
[ROW][C]101[/C][C]213.7[/C][C]209.054707856130[/C][C]4.6452921438696[/C][/ROW]
[ROW][C]102[/C][C]227.9[/C][C]237.096744304260[/C][C]-9.19674430425965[/C][/ROW]
[ROW][C]103[/C][C]212.1[/C][C]208.857531579631[/C][C]3.24246842036882[/C][/ROW]
[ROW][C]104[/C][C]226.8[/C][C]224.443507990124[/C][C]2.35649200987592[/C][/ROW]
[ROW][C]105[/C][C]212.6[/C][C]214.325818835862[/C][C]-1.72581883586176[/C][/ROW]
[ROW][C]106[/C][C]220.9[/C][C]223.761351406124[/C][C]-2.86135140612356[/C][/ROW]
[ROW][C]107[/C][C]228.1[/C][C]230.891271727254[/C][C]-2.79127172725376[/C][/ROW]
[ROW][C]108[/C][C]311.6[/C][C]315.294264877466[/C][C]-3.69426487746625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72275&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72275&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
13102.799.85415776648042.84584223351962
1475.473.86407647569961.53592352430037
1587.285.81492771850641.38507228149356
1683.782.36839556526891.33160443473115
17105.8103.8646666592061.93533334079383
18111.5109.2594124506232.24058754937664
1999.7103.552937819575-3.85293781957476
20111.2111.592282860904-0.392282860904231
21101.5101.0236809424440.476319057555585
22110.9101.5660285983229.33397140167772
23116.3111.7685035443994.5314964556013
24164.9161.5795830816823.32041691831793
25118.1110.9488295039867.15117049601382
2683.782.45722314037251.24277685962748
278495.7097150921302-11.7097150921302
28107.289.961800944224317.2381990557757
29113.7116.677877146881-2.97787714688113
30120.7122.089478988153-1.38947898815346
31111.2113.617386421764-2.41738642176409
32112.4123.875711719721-11.4757117197207
33112.5110.8873899599131.61261004008730
34130.4114.05002803767916.3499719623206
35130.7125.0369648498725.66303515012832
36174.3180.148818447016-5.84881844701641
37132.2124.0534716617328.14652833826754
3891.891.16561781126430.634382188735714
39104.2102.1178049529492.08219504705104
40104.8105.946193936461-1.14619393646073
41131.4126.6780957362894.72190426371127
42141.2134.3487235300086.85127646999155
43132.7125.9960731957316.70392680426896
44135.7136.595426964986-0.8954269649862
45136.9127.4670688204989.4329311795017
46151.2136.59821418901214.6017858109880
47144145.803742351963-1.80374235196251
48201.5204.568736053253-3.06873605325254
49149.6144.8459132696674.75408673033252
50108.7104.5508479468364.14915205316417
51122.8118.2295141879504.57048581205039
52126.7122.2299405179044.47005948209616
53139.9149.170215243516-9.27021524351608
54162.5156.4931271346526.00687286534759
55142.7146.699640439811-3.99964043981112
56151.6154.930791018806-3.33079101880574
57148.1147.1384134805550.961586519445149
58159157.2950524533721.70494754662803
59157.8160.765946370615-2.9659463706154
60226.7225.1159375387791.58406246122121
61153.7161.762691979094-8.06269197909418
62122.3115.4083064882516.89169351174898
63117.6130.795358567693-13.1953585676933
64166132.12724126968133.8727587303188
65154.5162.577769569462-8.07776956946228
66183.9175.160680901118.73931909889018
67164.4161.8576686840002.54233131599972
68173.3172.3378599158490.9621400841514
69160.2165.534649711094-5.33464971109444
70166.4176.118688701466-9.71868870146588
71170.3176.877063656989-6.57706365698888
72238.4248.438145850133-10.0381458501329
73166.8174.649207746374-7.84920774637393
74122.5128.014099723703-5.51409972370283
75141.8137.1046771186954.69532288130526
76140.5153.763910712417-13.2639107124170
77173.8167.0174645087366.78253549126444
78188.8186.6558867666212.1441132333795
79168169.776545813552-1.77654581355222
80187.4179.2750991790898.1249008209109
81177.7171.3525719276436.34742807235699
82183.8182.9560115532450.84398844675485
83196.1186.1022521741739.99774782582668
84264.6264.70569713596-0.105697135960042
85193.7186.9693504150606.7306495849397
86141.3138.8371268420742.46287315792557
87170.1153.03942281651317.0605771834873
88163.7168.661514288136-4.96151428813573
89190.1190.946882434901-0.846882434900749
90230.7210.64899439838520.0510056016149
91195.9193.2531897909382.64681020906161
92210.3207.9084504928582.39154950714226
93204.7197.5543789522177.14562104778307
94210.3209.5043064146330.79569358536736
95221.2215.8761728773745.32382712262589
96288.2302.03938884432-13.8393888443202
97203.2213.908324541505-10.7083245415054
98162.4156.1294982000616.27050179993947
99149.2176.639134446847-27.439134446847
100195.3180.50630074410814.793699255892
101213.7209.0547078561304.6452921438696
102227.9237.096744304260-9.19674430425965
103212.1208.8575315796313.24246842036882
104226.8224.4435079901242.35649200987592
105212.6214.325818835862-1.72581883586176
106220.9223.761351406124-2.86135140612356
107228.1230.891271727254-2.79127172725376
108311.6315.294264877466-3.69426487746625






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109223.972630086684217.537735902683230.407524270686
110168.283969247903161.569803264235174.998135231571
111179.897323263878172.595500523373187.199146004382
112199.781434347138191.714430661169207.848438033106
113225.147416182435216.111379710796234.183452654075
114250.501208821895240.383009309149260.619408334642
115224.851043074167214.913794158129234.788291990204
116240.616902366314229.736149297275251.497655435353
117228.211020791761217.233978052832239.188063530690
118238.125826675523226.317468962718249.934184388328
119246.102538660923233.500227836307258.70484948554
120336.558436973491319.414273267573353.702600679409

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 223.972630086684 & 217.537735902683 & 230.407524270686 \tabularnewline
110 & 168.283969247903 & 161.569803264235 & 174.998135231571 \tabularnewline
111 & 179.897323263878 & 172.595500523373 & 187.199146004382 \tabularnewline
112 & 199.781434347138 & 191.714430661169 & 207.848438033106 \tabularnewline
113 & 225.147416182435 & 216.111379710796 & 234.183452654075 \tabularnewline
114 & 250.501208821895 & 240.383009309149 & 260.619408334642 \tabularnewline
115 & 224.851043074167 & 214.913794158129 & 234.788291990204 \tabularnewline
116 & 240.616902366314 & 229.736149297275 & 251.497655435353 \tabularnewline
117 & 228.211020791761 & 217.233978052832 & 239.188063530690 \tabularnewline
118 & 238.125826675523 & 226.317468962718 & 249.934184388328 \tabularnewline
119 & 246.102538660923 & 233.500227836307 & 258.70484948554 \tabularnewline
120 & 336.558436973491 & 319.414273267573 & 353.702600679409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72275&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]223.972630086684[/C][C]217.537735902683[/C][C]230.407524270686[/C][/ROW]
[ROW][C]110[/C][C]168.283969247903[/C][C]161.569803264235[/C][C]174.998135231571[/C][/ROW]
[ROW][C]111[/C][C]179.897323263878[/C][C]172.595500523373[/C][C]187.199146004382[/C][/ROW]
[ROW][C]112[/C][C]199.781434347138[/C][C]191.714430661169[/C][C]207.848438033106[/C][/ROW]
[ROW][C]113[/C][C]225.147416182435[/C][C]216.111379710796[/C][C]234.183452654075[/C][/ROW]
[ROW][C]114[/C][C]250.501208821895[/C][C]240.383009309149[/C][C]260.619408334642[/C][/ROW]
[ROW][C]115[/C][C]224.851043074167[/C][C]214.913794158129[/C][C]234.788291990204[/C][/ROW]
[ROW][C]116[/C][C]240.616902366314[/C][C]229.736149297275[/C][C]251.497655435353[/C][/ROW]
[ROW][C]117[/C][C]228.211020791761[/C][C]217.233978052832[/C][C]239.188063530690[/C][/ROW]
[ROW][C]118[/C][C]238.125826675523[/C][C]226.317468962718[/C][C]249.934184388328[/C][/ROW]
[ROW][C]119[/C][C]246.102538660923[/C][C]233.500227836307[/C][C]258.70484948554[/C][/ROW]
[ROW][C]120[/C][C]336.558436973491[/C][C]319.414273267573[/C][C]353.702600679409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72275&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72275&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
109223.972630086684217.537735902683230.407524270686
110168.283969247903161.569803264235174.998135231571
111179.897323263878172.595500523373187.199146004382
112199.781434347138191.714430661169207.848438033106
113225.147416182435216.111379710796234.183452654075
114250.501208821895240.383009309149260.619408334642
115224.851043074167214.913794158129234.788291990204
116240.616902366314229.736149297275251.497655435353
117228.211020791761217.233978052832239.188063530690
118238.125826675523226.317468962718249.934184388328
119246.102538660923233.500227836307258.70484948554
120336.558436973491319.414273267573353.702600679409


Figures (Output of Computation)

Input Parameters & R Code

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