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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 17:15:18 +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/t1295197995bwab2i81qci0w6z.htm/, Retrieved Sun, 19 May 2024 08:01:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117446, Retrieved Sun, 19 May 2024 08:01:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact117

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 v...] [2011-01-16 17:15:18] [3c84fba69796ffa9703fc49b6977555d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102,8
106,3
103,7
106,9
104,3
105,4
96,2
95,7
95,9
93,6
94,7
94,5
96,6
96,7
98,9
102
105,2
106,4
99,3
96,4
93,1
95,6
93,3
96,7
105,6
105,2
107
104,9
104,5
105,2
99,7
100,2
98,5
98,4
97,1
98,4
100,6
111,3
119
117,8
108,8
109,3
103,5
103,7
110
105,5
110,4
106,7
110,2
105,2
108
108,1
107,2
106
99,4
100,2
100,3
100,8
99,5
100,2
103
111
120,5
109,5
106,6
105,5
103,9
104,9
104,8
99,6
97
95,4
99,3
103,9
107,4
107,4
111
113,2
108,5
113,3
113,8
105,3
107,5
109,4
118,9
119
115
124,1
120,5
117,7
117,1
118,1
119,6
118,8
124,9
124
124,9
121,7
121,6
125,1
127,9
129
130,1
130,3
127,9
124,1
125,7
129,2
129,2
132,6
131,5
131
125,8
127,2
127,3
127,5
122
118,4
118,3
115,5

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=117446&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=117446&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117446&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
alpha0.792089098495697
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.792089098495697 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117446&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]0.792089098495697[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117446&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117446&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
alpha0.792089098495697
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1396.697.6449252136752-1.04492521367523
1496.796.67549726392570.0245027360742682
1598.998.89898486813270.00101513186729107
16102101.9497015304310.0502984695690856
17105.2105.0811216539270.118878346073132
18106.4106.2585298166440.141470183355509
1999.394.60383272738854.69616727261149
2096.498.398528216149-1.99852821614893
2193.197.5320950571806-4.43209505718056
2295.692.0422267996373.55777320036292
2393.396.0435460873106-2.74354608731063
2496.793.5078257277443.19217427225605
25105.697.66480674686257.93519325313748
26105.2104.0307784670021.16922153299844
27107107.15610202213-0.15610202213044
28104.9110.092614442731-5.19261444273108
29104.5109.085438907981-4.58543890798077
30105.2106.541305747153-1.34130574715311
3199.794.65908918573575.04091081426432
32100.297.33495210125112.86504789874886
3398.599.8149394868075-1.3149394868075
3498.498.4553168871981-0.0553168871981313
3597.198.284633930865-1.18463393086506
3698.498.21781186696630.182188133033733
37100.6100.976741030751-0.376741030750779
38111.399.352200937322611.9477990626774
39119110.7395690358698.26043096413089
40117.8119.295579644212-1.4955796442121
41108.8121.343023482929-12.5430234829292
42109.3113.170264979995-3.87026497999506
43103.5100.6118197785832.88818022141652
44103.7101.1301426391912.5698573608086
45110102.5072478720597.49275212794144
46105.5108.385991053644-2.88599105364376
47110.4105.7383646240434.66163537595726
48106.7110.586485952449-3.88648595244908
49110.2110.0064552614710.193544738528786
50105.2111.396038550367-6.19603855036718
51108107.6452266451980.35477335480212
52108.1107.9108710840860.189128915914125
53107.2108.995870199595-1.79587019959548
54106111.138975691126-5.13897569112636
5599.498.98075300087590.419246999124127
56100.297.47727797827372.72272202172627
57100.399.99898913164440.301010868355576
58100.898.0233786109452.77662138905507
5999.5101.430279581408-1.9302795814078
60100.299.27976932231740.920230677682596
61103103.355369332751-0.355369332751238
62111102.9816997479448.01830025205578
63120.5111.8518958592878.64810414071262
64109.5118.652157919295-9.15215791929545
65106.6111.925322611123-5.32532261112334
66105.5110.577719247255-5.07771924725547
67103.999.62363220869944.27636779130063
68104.9101.6542580857033.24574191429681
69104.8104.0867474451950.71325255480491
7099.6102.95237548541-3.35237548540977
7197100.525948822834-3.52594882283444
7295.497.7041785105199-2.30417851051985
7399.398.9605480057610.339451994239027
74103.9100.8782160117423.02178398825835
75107.4105.9216691543361.47833084566402
76107.4103.3419634167414.05803658325864
77111107.8744199418813.12558005811931
78113.2113.272163893365-0.072163893365385
79108.5108.2277393514780.272260648521694
80113.3106.8724772562776.42752274372337
81113.8111.2986883787782.50131162122211
82105.3110.735330121946-5.43533012194581
83107.5106.6229300100480.87706998995185
84109.4107.5427622668781.85723773312245
85118.9112.6449838044996.25501619550066
86119119.805991788761-0.805991788761162
87115121.496604732586-6.49660473258601
88124.1113.13638840777310.9636115922268
89120.5122.944807739605-2.44480773960522
90117.7123.265462414386-5.56546241438573
91117.1113.941465616223.15853438378014
92118.1116.1521355731991.94786442680051
93119.6116.2137560839053.38624391609488
94118.8114.701228711014.09877128899019
95124.9119.4531031885885.4468968114125
96124124.196433011817-0.196433011817177
97124.9128.586310425202-3.68631042520201
98121.7126.404841433083-4.70484143308323
99121.6123.824077609704-2.22407760970408
100125.1122.4782527585052.62174724149479
101127.9122.8914157259645.00858427403639
102129128.4670028348470.532997165152693
103130.1125.7873434262784.31265657372221
104130.3128.6604695060631.63953049393731
105127.9128.776916846176-0.87691684617559
106124.1124.0357285167960.0642714832035693
107125.7125.872209673035-0.172209673035312
108129.2124.9913967156144.20860328438636
109129.2132.144871798543-2.94487179854281
110132.6130.3389245597462.26107544025425
111131.5133.791565395702-2.29156539570246
112131133.399784018277-2.39978401827739
113125.8130.331696256294-4.5316962562945
114127.2127.420007809943-0.220007809943283
115127.3124.9297337645022.37026623549787
116127.5125.7085415792731.79145842072658
117122125.422132538882-3.42213253888217
118118.4118.860589920037-0.460589920036497
119118.3120.232167070165-1.93216707016535
120115.5118.868129815959-3.36812981595936

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 96.6 & 97.6449252136752 & -1.04492521367523 \tabularnewline
14 & 96.7 & 96.6754972639257 & 0.0245027360742682 \tabularnewline
15 & 98.9 & 98.8989848681327 & 0.00101513186729107 \tabularnewline
16 & 102 & 101.949701530431 & 0.0502984695690856 \tabularnewline
17 & 105.2 & 105.081121653927 & 0.118878346073132 \tabularnewline
18 & 106.4 & 106.258529816644 & 0.141470183355509 \tabularnewline
19 & 99.3 & 94.6038327273885 & 4.69616727261149 \tabularnewline
20 & 96.4 & 98.398528216149 & -1.99852821614893 \tabularnewline
21 & 93.1 & 97.5320950571806 & -4.43209505718056 \tabularnewline
22 & 95.6 & 92.042226799637 & 3.55777320036292 \tabularnewline
23 & 93.3 & 96.0435460873106 & -2.74354608731063 \tabularnewline
24 & 96.7 & 93.507825727744 & 3.19217427225605 \tabularnewline
25 & 105.6 & 97.6648067468625 & 7.93519325313748 \tabularnewline
26 & 105.2 & 104.030778467002 & 1.16922153299844 \tabularnewline
27 & 107 & 107.15610202213 & -0.15610202213044 \tabularnewline
28 & 104.9 & 110.092614442731 & -5.19261444273108 \tabularnewline
29 & 104.5 & 109.085438907981 & -4.58543890798077 \tabularnewline
30 & 105.2 & 106.541305747153 & -1.34130574715311 \tabularnewline
31 & 99.7 & 94.6590891857357 & 5.04091081426432 \tabularnewline
32 & 100.2 & 97.3349521012511 & 2.86504789874886 \tabularnewline
33 & 98.5 & 99.8149394868075 & -1.3149394868075 \tabularnewline
34 & 98.4 & 98.4553168871981 & -0.0553168871981313 \tabularnewline
35 & 97.1 & 98.284633930865 & -1.18463393086506 \tabularnewline
36 & 98.4 & 98.2178118669663 & 0.182188133033733 \tabularnewline
37 & 100.6 & 100.976741030751 & -0.376741030750779 \tabularnewline
38 & 111.3 & 99.3522009373226 & 11.9477990626774 \tabularnewline
39 & 119 & 110.739569035869 & 8.26043096413089 \tabularnewline
40 & 117.8 & 119.295579644212 & -1.4955796442121 \tabularnewline
41 & 108.8 & 121.343023482929 & -12.5430234829292 \tabularnewline
42 & 109.3 & 113.170264979995 & -3.87026497999506 \tabularnewline
43 & 103.5 & 100.611819778583 & 2.88818022141652 \tabularnewline
44 & 103.7 & 101.130142639191 & 2.5698573608086 \tabularnewline
45 & 110 & 102.507247872059 & 7.49275212794144 \tabularnewline
46 & 105.5 & 108.385991053644 & -2.88599105364376 \tabularnewline
47 & 110.4 & 105.738364624043 & 4.66163537595726 \tabularnewline
48 & 106.7 & 110.586485952449 & -3.88648595244908 \tabularnewline
49 & 110.2 & 110.006455261471 & 0.193544738528786 \tabularnewline
50 & 105.2 & 111.396038550367 & -6.19603855036718 \tabularnewline
51 & 108 & 107.645226645198 & 0.35477335480212 \tabularnewline
52 & 108.1 & 107.910871084086 & 0.189128915914125 \tabularnewline
53 & 107.2 & 108.995870199595 & -1.79587019959548 \tabularnewline
54 & 106 & 111.138975691126 & -5.13897569112636 \tabularnewline
55 & 99.4 & 98.9807530008759 & 0.419246999124127 \tabularnewline
56 & 100.2 & 97.4772779782737 & 2.72272202172627 \tabularnewline
57 & 100.3 & 99.9989891316444 & 0.301010868355576 \tabularnewline
58 & 100.8 & 98.023378610945 & 2.77662138905507 \tabularnewline
59 & 99.5 & 101.430279581408 & -1.9302795814078 \tabularnewline
60 & 100.2 & 99.2797693223174 & 0.920230677682596 \tabularnewline
61 & 103 & 103.355369332751 & -0.355369332751238 \tabularnewline
62 & 111 & 102.981699747944 & 8.01830025205578 \tabularnewline
63 & 120.5 & 111.851895859287 & 8.64810414071262 \tabularnewline
64 & 109.5 & 118.652157919295 & -9.15215791929545 \tabularnewline
65 & 106.6 & 111.925322611123 & -5.32532261112334 \tabularnewline
66 & 105.5 & 110.577719247255 & -5.07771924725547 \tabularnewline
67 & 103.9 & 99.6236322086994 & 4.27636779130063 \tabularnewline
68 & 104.9 & 101.654258085703 & 3.24574191429681 \tabularnewline
69 & 104.8 & 104.086747445195 & 0.71325255480491 \tabularnewline
70 & 99.6 & 102.95237548541 & -3.35237548540977 \tabularnewline
71 & 97 & 100.525948822834 & -3.52594882283444 \tabularnewline
72 & 95.4 & 97.7041785105199 & -2.30417851051985 \tabularnewline
73 & 99.3 & 98.960548005761 & 0.339451994239027 \tabularnewline
74 & 103.9 & 100.878216011742 & 3.02178398825835 \tabularnewline
75 & 107.4 & 105.921669154336 & 1.47833084566402 \tabularnewline
76 & 107.4 & 103.341963416741 & 4.05803658325864 \tabularnewline
77 & 111 & 107.874419941881 & 3.12558005811931 \tabularnewline
78 & 113.2 & 113.272163893365 & -0.072163893365385 \tabularnewline
79 & 108.5 & 108.227739351478 & 0.272260648521694 \tabularnewline
80 & 113.3 & 106.872477256277 & 6.42752274372337 \tabularnewline
81 & 113.8 & 111.298688378778 & 2.50131162122211 \tabularnewline
82 & 105.3 & 110.735330121946 & -5.43533012194581 \tabularnewline
83 & 107.5 & 106.622930010048 & 0.87706998995185 \tabularnewline
84 & 109.4 & 107.542762266878 & 1.85723773312245 \tabularnewline
85 & 118.9 & 112.644983804499 & 6.25501619550066 \tabularnewline
86 & 119 & 119.805991788761 & -0.805991788761162 \tabularnewline
87 & 115 & 121.496604732586 & -6.49660473258601 \tabularnewline
88 & 124.1 & 113.136388407773 & 10.9636115922268 \tabularnewline
89 & 120.5 & 122.944807739605 & -2.44480773960522 \tabularnewline
90 & 117.7 & 123.265462414386 & -5.56546241438573 \tabularnewline
91 & 117.1 & 113.94146561622 & 3.15853438378014 \tabularnewline
92 & 118.1 & 116.152135573199 & 1.94786442680051 \tabularnewline
93 & 119.6 & 116.213756083905 & 3.38624391609488 \tabularnewline
94 & 118.8 & 114.70122871101 & 4.09877128899019 \tabularnewline
95 & 124.9 & 119.453103188588 & 5.4468968114125 \tabularnewline
96 & 124 & 124.196433011817 & -0.196433011817177 \tabularnewline
97 & 124.9 & 128.586310425202 & -3.68631042520201 \tabularnewline
98 & 121.7 & 126.404841433083 & -4.70484143308323 \tabularnewline
99 & 121.6 & 123.824077609704 & -2.22407760970408 \tabularnewline
100 & 125.1 & 122.478252758505 & 2.62174724149479 \tabularnewline
101 & 127.9 & 122.891415725964 & 5.00858427403639 \tabularnewline
102 & 129 & 128.467002834847 & 0.532997165152693 \tabularnewline
103 & 130.1 & 125.787343426278 & 4.31265657372221 \tabularnewline
104 & 130.3 & 128.660469506063 & 1.63953049393731 \tabularnewline
105 & 127.9 & 128.776916846176 & -0.87691684617559 \tabularnewline
106 & 124.1 & 124.035728516796 & 0.0642714832035693 \tabularnewline
107 & 125.7 & 125.872209673035 & -0.172209673035312 \tabularnewline
108 & 129.2 & 124.991396715614 & 4.20860328438636 \tabularnewline
109 & 129.2 & 132.144871798543 & -2.94487179854281 \tabularnewline
110 & 132.6 & 130.338924559746 & 2.26107544025425 \tabularnewline
111 & 131.5 & 133.791565395702 & -2.29156539570246 \tabularnewline
112 & 131 & 133.399784018277 & -2.39978401827739 \tabularnewline
113 & 125.8 & 130.331696256294 & -4.5316962562945 \tabularnewline
114 & 127.2 & 127.420007809943 & -0.220007809943283 \tabularnewline
115 & 127.3 & 124.929733764502 & 2.37026623549787 \tabularnewline
116 & 127.5 & 125.708541579273 & 1.79145842072658 \tabularnewline
117 & 122 & 125.422132538882 & -3.42213253888217 \tabularnewline
118 & 118.4 & 118.860589920037 & -0.460589920036497 \tabularnewline
119 & 118.3 & 120.232167070165 & -1.93216707016535 \tabularnewline
120 & 115.5 & 118.868129815959 & -3.36812981595936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117446&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]96.6[/C][C]97.6449252136752[/C][C]-1.04492521367523[/C][/ROW]
[ROW][C]14[/C][C]96.7[/C][C]96.6754972639257[/C][C]0.0245027360742682[/C][/ROW]
[ROW][C]15[/C][C]98.9[/C][C]98.8989848681327[/C][C]0.00101513186729107[/C][/ROW]
[ROW][C]16[/C][C]102[/C][C]101.949701530431[/C][C]0.0502984695690856[/C][/ROW]
[ROW][C]17[/C][C]105.2[/C][C]105.081121653927[/C][C]0.118878346073132[/C][/ROW]
[ROW][C]18[/C][C]106.4[/C][C]106.258529816644[/C][C]0.141470183355509[/C][/ROW]
[ROW][C]19[/C][C]99.3[/C][C]94.6038327273885[/C][C]4.69616727261149[/C][/ROW]
[ROW][C]20[/C][C]96.4[/C][C]98.398528216149[/C][C]-1.99852821614893[/C][/ROW]
[ROW][C]21[/C][C]93.1[/C][C]97.5320950571806[/C][C]-4.43209505718056[/C][/ROW]
[ROW][C]22[/C][C]95.6[/C][C]92.042226799637[/C][C]3.55777320036292[/C][/ROW]
[ROW][C]23[/C][C]93.3[/C][C]96.0435460873106[/C][C]-2.74354608731063[/C][/ROW]
[ROW][C]24[/C][C]96.7[/C][C]93.507825727744[/C][C]3.19217427225605[/C][/ROW]
[ROW][C]25[/C][C]105.6[/C][C]97.6648067468625[/C][C]7.93519325313748[/C][/ROW]
[ROW][C]26[/C][C]105.2[/C][C]104.030778467002[/C][C]1.16922153299844[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]107.15610202213[/C][C]-0.15610202213044[/C][/ROW]
[ROW][C]28[/C][C]104.9[/C][C]110.092614442731[/C][C]-5.19261444273108[/C][/ROW]
[ROW][C]29[/C][C]104.5[/C][C]109.085438907981[/C][C]-4.58543890798077[/C][/ROW]
[ROW][C]30[/C][C]105.2[/C][C]106.541305747153[/C][C]-1.34130574715311[/C][/ROW]
[ROW][C]31[/C][C]99.7[/C][C]94.6590891857357[/C][C]5.04091081426432[/C][/ROW]
[ROW][C]32[/C][C]100.2[/C][C]97.3349521012511[/C][C]2.86504789874886[/C][/ROW]
[ROW][C]33[/C][C]98.5[/C][C]99.8149394868075[/C][C]-1.3149394868075[/C][/ROW]
[ROW][C]34[/C][C]98.4[/C][C]98.4553168871981[/C][C]-0.0553168871981313[/C][/ROW]
[ROW][C]35[/C][C]97.1[/C][C]98.284633930865[/C][C]-1.18463393086506[/C][/ROW]
[ROW][C]36[/C][C]98.4[/C][C]98.2178118669663[/C][C]0.182188133033733[/C][/ROW]
[ROW][C]37[/C][C]100.6[/C][C]100.976741030751[/C][C]-0.376741030750779[/C][/ROW]
[ROW][C]38[/C][C]111.3[/C][C]99.3522009373226[/C][C]11.9477990626774[/C][/ROW]
[ROW][C]39[/C][C]119[/C][C]110.739569035869[/C][C]8.26043096413089[/C][/ROW]
[ROW][C]40[/C][C]117.8[/C][C]119.295579644212[/C][C]-1.4955796442121[/C][/ROW]
[ROW][C]41[/C][C]108.8[/C][C]121.343023482929[/C][C]-12.5430234829292[/C][/ROW]
[ROW][C]42[/C][C]109.3[/C][C]113.170264979995[/C][C]-3.87026497999506[/C][/ROW]
[ROW][C]43[/C][C]103.5[/C][C]100.611819778583[/C][C]2.88818022141652[/C][/ROW]
[ROW][C]44[/C][C]103.7[/C][C]101.130142639191[/C][C]2.5698573608086[/C][/ROW]
[ROW][C]45[/C][C]110[/C][C]102.507247872059[/C][C]7.49275212794144[/C][/ROW]
[ROW][C]46[/C][C]105.5[/C][C]108.385991053644[/C][C]-2.88599105364376[/C][/ROW]
[ROW][C]47[/C][C]110.4[/C][C]105.738364624043[/C][C]4.66163537595726[/C][/ROW]
[ROW][C]48[/C][C]106.7[/C][C]110.586485952449[/C][C]-3.88648595244908[/C][/ROW]
[ROW][C]49[/C][C]110.2[/C][C]110.006455261471[/C][C]0.193544738528786[/C][/ROW]
[ROW][C]50[/C][C]105.2[/C][C]111.396038550367[/C][C]-6.19603855036718[/C][/ROW]
[ROW][C]51[/C][C]108[/C][C]107.645226645198[/C][C]0.35477335480212[/C][/ROW]
[ROW][C]52[/C][C]108.1[/C][C]107.910871084086[/C][C]0.189128915914125[/C][/ROW]
[ROW][C]53[/C][C]107.2[/C][C]108.995870199595[/C][C]-1.79587019959548[/C][/ROW]
[ROW][C]54[/C][C]106[/C][C]111.138975691126[/C][C]-5.13897569112636[/C][/ROW]
[ROW][C]55[/C][C]99.4[/C][C]98.9807530008759[/C][C]0.419246999124127[/C][/ROW]
[ROW][C]56[/C][C]100.2[/C][C]97.4772779782737[/C][C]2.72272202172627[/C][/ROW]
[ROW][C]57[/C][C]100.3[/C][C]99.9989891316444[/C][C]0.301010868355576[/C][/ROW]
[ROW][C]58[/C][C]100.8[/C][C]98.023378610945[/C][C]2.77662138905507[/C][/ROW]
[ROW][C]59[/C][C]99.5[/C][C]101.430279581408[/C][C]-1.9302795814078[/C][/ROW]
[ROW][C]60[/C][C]100.2[/C][C]99.2797693223174[/C][C]0.920230677682596[/C][/ROW]
[ROW][C]61[/C][C]103[/C][C]103.355369332751[/C][C]-0.355369332751238[/C][/ROW]
[ROW][C]62[/C][C]111[/C][C]102.981699747944[/C][C]8.01830025205578[/C][/ROW]
[ROW][C]63[/C][C]120.5[/C][C]111.851895859287[/C][C]8.64810414071262[/C][/ROW]
[ROW][C]64[/C][C]109.5[/C][C]118.652157919295[/C][C]-9.15215791929545[/C][/ROW]
[ROW][C]65[/C][C]106.6[/C][C]111.925322611123[/C][C]-5.32532261112334[/C][/ROW]
[ROW][C]66[/C][C]105.5[/C][C]110.577719247255[/C][C]-5.07771924725547[/C][/ROW]
[ROW][C]67[/C][C]103.9[/C][C]99.6236322086994[/C][C]4.27636779130063[/C][/ROW]
[ROW][C]68[/C][C]104.9[/C][C]101.654258085703[/C][C]3.24574191429681[/C][/ROW]
[ROW][C]69[/C][C]104.8[/C][C]104.086747445195[/C][C]0.71325255480491[/C][/ROW]
[ROW][C]70[/C][C]99.6[/C][C]102.95237548541[/C][C]-3.35237548540977[/C][/ROW]
[ROW][C]71[/C][C]97[/C][C]100.525948822834[/C][C]-3.52594882283444[/C][/ROW]
[ROW][C]72[/C][C]95.4[/C][C]97.7041785105199[/C][C]-2.30417851051985[/C][/ROW]
[ROW][C]73[/C][C]99.3[/C][C]98.960548005761[/C][C]0.339451994239027[/C][/ROW]
[ROW][C]74[/C][C]103.9[/C][C]100.878216011742[/C][C]3.02178398825835[/C][/ROW]
[ROW][C]75[/C][C]107.4[/C][C]105.921669154336[/C][C]1.47833084566402[/C][/ROW]
[ROW][C]76[/C][C]107.4[/C][C]103.341963416741[/C][C]4.05803658325864[/C][/ROW]
[ROW][C]77[/C][C]111[/C][C]107.874419941881[/C][C]3.12558005811931[/C][/ROW]
[ROW][C]78[/C][C]113.2[/C][C]113.272163893365[/C][C]-0.072163893365385[/C][/ROW]
[ROW][C]79[/C][C]108.5[/C][C]108.227739351478[/C][C]0.272260648521694[/C][/ROW]
[ROW][C]80[/C][C]113.3[/C][C]106.872477256277[/C][C]6.42752274372337[/C][/ROW]
[ROW][C]81[/C][C]113.8[/C][C]111.298688378778[/C][C]2.50131162122211[/C][/ROW]
[ROW][C]82[/C][C]105.3[/C][C]110.735330121946[/C][C]-5.43533012194581[/C][/ROW]
[ROW][C]83[/C][C]107.5[/C][C]106.622930010048[/C][C]0.87706998995185[/C][/ROW]
[ROW][C]84[/C][C]109.4[/C][C]107.542762266878[/C][C]1.85723773312245[/C][/ROW]
[ROW][C]85[/C][C]118.9[/C][C]112.644983804499[/C][C]6.25501619550066[/C][/ROW]
[ROW][C]86[/C][C]119[/C][C]119.805991788761[/C][C]-0.805991788761162[/C][/ROW]
[ROW][C]87[/C][C]115[/C][C]121.496604732586[/C][C]-6.49660473258601[/C][/ROW]
[ROW][C]88[/C][C]124.1[/C][C]113.136388407773[/C][C]10.9636115922268[/C][/ROW]
[ROW][C]89[/C][C]120.5[/C][C]122.944807739605[/C][C]-2.44480773960522[/C][/ROW]
[ROW][C]90[/C][C]117.7[/C][C]123.265462414386[/C][C]-5.56546241438573[/C][/ROW]
[ROW][C]91[/C][C]117.1[/C][C]113.94146561622[/C][C]3.15853438378014[/C][/ROW]
[ROW][C]92[/C][C]118.1[/C][C]116.152135573199[/C][C]1.94786442680051[/C][/ROW]
[ROW][C]93[/C][C]119.6[/C][C]116.213756083905[/C][C]3.38624391609488[/C][/ROW]
[ROW][C]94[/C][C]118.8[/C][C]114.70122871101[/C][C]4.09877128899019[/C][/ROW]
[ROW][C]95[/C][C]124.9[/C][C]119.453103188588[/C][C]5.4468968114125[/C][/ROW]
[ROW][C]96[/C][C]124[/C][C]124.196433011817[/C][C]-0.196433011817177[/C][/ROW]
[ROW][C]97[/C][C]124.9[/C][C]128.586310425202[/C][C]-3.68631042520201[/C][/ROW]
[ROW][C]98[/C][C]121.7[/C][C]126.404841433083[/C][C]-4.70484143308323[/C][/ROW]
[ROW][C]99[/C][C]121.6[/C][C]123.824077609704[/C][C]-2.22407760970408[/C][/ROW]
[ROW][C]100[/C][C]125.1[/C][C]122.478252758505[/C][C]2.62174724149479[/C][/ROW]
[ROW][C]101[/C][C]127.9[/C][C]122.891415725964[/C][C]5.00858427403639[/C][/ROW]
[ROW][C]102[/C][C]129[/C][C]128.467002834847[/C][C]0.532997165152693[/C][/ROW]
[ROW][C]103[/C][C]130.1[/C][C]125.787343426278[/C][C]4.31265657372221[/C][/ROW]
[ROW][C]104[/C][C]130.3[/C][C]128.660469506063[/C][C]1.63953049393731[/C][/ROW]
[ROW][C]105[/C][C]127.9[/C][C]128.776916846176[/C][C]-0.87691684617559[/C][/ROW]
[ROW][C]106[/C][C]124.1[/C][C]124.035728516796[/C][C]0.0642714832035693[/C][/ROW]
[ROW][C]107[/C][C]125.7[/C][C]125.872209673035[/C][C]-0.172209673035312[/C][/ROW]
[ROW][C]108[/C][C]129.2[/C][C]124.991396715614[/C][C]4.20860328438636[/C][/ROW]
[ROW][C]109[/C][C]129.2[/C][C]132.144871798543[/C][C]-2.94487179854281[/C][/ROW]
[ROW][C]110[/C][C]132.6[/C][C]130.338924559746[/C][C]2.26107544025425[/C][/ROW]
[ROW][C]111[/C][C]131.5[/C][C]133.791565395702[/C][C]-2.29156539570246[/C][/ROW]
[ROW][C]112[/C][C]131[/C][C]133.399784018277[/C][C]-2.39978401827739[/C][/ROW]
[ROW][C]113[/C][C]125.8[/C][C]130.331696256294[/C][C]-4.5316962562945[/C][/ROW]
[ROW][C]114[/C][C]127.2[/C][C]127.420007809943[/C][C]-0.220007809943283[/C][/ROW]
[ROW][C]115[/C][C]127.3[/C][C]124.929733764502[/C][C]2.37026623549787[/C][/ROW]
[ROW][C]116[/C][C]127.5[/C][C]125.708541579273[/C][C]1.79145842072658[/C][/ROW]
[ROW][C]117[/C][C]122[/C][C]125.422132538882[/C][C]-3.42213253888217[/C][/ROW]
[ROW][C]118[/C][C]118.4[/C][C]118.860589920037[/C][C]-0.460589920036497[/C][/ROW]
[ROW][C]119[/C][C]118.3[/C][C]120.232167070165[/C][C]-1.93216707016535[/C][/ROW]
[ROW][C]120[/C][C]115.5[/C][C]118.868129815959[/C][C]-3.36812981595936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117446&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117446&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
1396.697.6449252136752-1.04492521367523
1496.796.67549726392570.0245027360742682
1598.998.89898486813270.00101513186729107
16102101.9497015304310.0502984695690856
17105.2105.0811216539270.118878346073132
18106.4106.2585298166440.141470183355509
1999.394.60383272738854.69616727261149
2096.498.398528216149-1.99852821614893
2193.197.5320950571806-4.43209505718056
2295.692.0422267996373.55777320036292
2393.396.0435460873106-2.74354608731063
2496.793.5078257277443.19217427225605
25105.697.66480674686257.93519325313748
26105.2104.0307784670021.16922153299844
27107107.15610202213-0.15610202213044
28104.9110.092614442731-5.19261444273108
29104.5109.085438907981-4.58543890798077
30105.2106.541305747153-1.34130574715311
3199.794.65908918573575.04091081426432
32100.297.33495210125112.86504789874886
3398.599.8149394868075-1.3149394868075
3498.498.4553168871981-0.0553168871981313
3597.198.284633930865-1.18463393086506
3698.498.21781186696630.182188133033733
37100.6100.976741030751-0.376741030750779
38111.399.352200937322611.9477990626774
39119110.7395690358698.26043096413089
40117.8119.295579644212-1.4955796442121
41108.8121.343023482929-12.5430234829292
42109.3113.170264979995-3.87026497999506
43103.5100.6118197785832.88818022141652
44103.7101.1301426391912.5698573608086
45110102.5072478720597.49275212794144
46105.5108.385991053644-2.88599105364376
47110.4105.7383646240434.66163537595726
48106.7110.586485952449-3.88648595244908
49110.2110.0064552614710.193544738528786
50105.2111.396038550367-6.19603855036718
51108107.6452266451980.35477335480212
52108.1107.9108710840860.189128915914125
53107.2108.995870199595-1.79587019959548
54106111.138975691126-5.13897569112636
5599.498.98075300087590.419246999124127
56100.297.47727797827372.72272202172627
57100.399.99898913164440.301010868355576
58100.898.0233786109452.77662138905507
5999.5101.430279581408-1.9302795814078
60100.299.27976932231740.920230677682596
61103103.355369332751-0.355369332751238
62111102.9816997479448.01830025205578
63120.5111.8518958592878.64810414071262
64109.5118.652157919295-9.15215791929545
65106.6111.925322611123-5.32532261112334
66105.5110.577719247255-5.07771924725547
67103.999.62363220869944.27636779130063
68104.9101.6542580857033.24574191429681
69104.8104.0867474451950.71325255480491
7099.6102.95237548541-3.35237548540977
7197100.525948822834-3.52594882283444
7295.497.7041785105199-2.30417851051985
7399.398.9605480057610.339451994239027
74103.9100.8782160117423.02178398825835
75107.4105.9216691543361.47833084566402
76107.4103.3419634167414.05803658325864
77111107.8744199418813.12558005811931
78113.2113.272163893365-0.072163893365385
79108.5108.2277393514780.272260648521694
80113.3106.8724772562776.42752274372337
81113.8111.2986883787782.50131162122211
82105.3110.735330121946-5.43533012194581
83107.5106.6229300100480.87706998995185
84109.4107.5427622668781.85723773312245
85118.9112.6449838044996.25501619550066
86119119.805991788761-0.805991788761162
87115121.496604732586-6.49660473258601
88124.1113.13638840777310.9636115922268
89120.5122.944807739605-2.44480773960522
90117.7123.265462414386-5.56546241438573
91117.1113.941465616223.15853438378014
92118.1116.1521355731991.94786442680051
93119.6116.2137560839053.38624391609488
94118.8114.701228711014.09877128899019
95124.9119.4531031885885.4468968114125
96124124.196433011817-0.196433011817177
97124.9128.586310425202-3.68631042520201
98121.7126.404841433083-4.70484143308323
99121.6123.824077609704-2.22407760970408
100125.1122.4782527585052.62174724149479
101127.9122.8914157259645.00858427403639
102129128.4670028348470.532997165152693
103130.1125.7873434262784.31265657372221
104130.3128.6604695060631.63953049393731
105127.9128.776916846176-0.87691684617559
106124.1124.0357285167960.0642714832035693
107125.7125.872209673035-0.172209673035312
108129.2124.9913967156144.20860328438636
109129.2132.144871798543-2.94487179854281
110132.6130.3389245597462.26107544025425
111131.5133.791565395702-2.29156539570246
112131133.399784018277-2.39978401827739
113125.8130.331696256294-4.5316962562945
114127.2127.420007809943-0.220007809943283
115127.3124.9297337645022.37026623549787
116127.5125.7085415792731.79145842072658
117122125.422132538882-3.42213253888217
118118.4118.860589920037-0.460589920036497
119118.3120.232167070165-1.93216707016535
120115.5118.868129815959-3.36812981595936






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121118.532871754513110.57149365463126.494249854396
122120.141898547411109.98558519966130.298211895162
123120.857022515837108.902196695855132.811848335819
124122.257865275459108.741763028342135.773967522575
125120.647372477763105.732541619758135.562203335769
126122.221638265603106.028450219659138.414826311548
127120.444176219933103.066417484707137.821934955159
128119.225181534467100.738601044064137.71176202487
129116.43581541212396.9032575203225135.968373303924
130113.20064366666192.6753427586366133.725944574685
131114.63109213941193.1588976327161136.103286646106
132114.49895104895192.1198917188148136.878010379087

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 118.532871754513 & 110.57149365463 & 126.494249854396 \tabularnewline
122 & 120.141898547411 & 109.98558519966 & 130.298211895162 \tabularnewline
123 & 120.857022515837 & 108.902196695855 & 132.811848335819 \tabularnewline
124 & 122.257865275459 & 108.741763028342 & 135.773967522575 \tabularnewline
125 & 120.647372477763 & 105.732541619758 & 135.562203335769 \tabularnewline
126 & 122.221638265603 & 106.028450219659 & 138.414826311548 \tabularnewline
127 & 120.444176219933 & 103.066417484707 & 137.821934955159 \tabularnewline
128 & 119.225181534467 & 100.738601044064 & 137.71176202487 \tabularnewline
129 & 116.435815412123 & 96.9032575203225 & 135.968373303924 \tabularnewline
130 & 113.200643666661 & 92.6753427586366 & 133.725944574685 \tabularnewline
131 & 114.631092139411 & 93.1588976327161 & 136.103286646106 \tabularnewline
132 & 114.498951048951 & 92.1198917188148 & 136.878010379087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117446&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]118.532871754513[/C][C]110.57149365463[/C][C]126.494249854396[/C][/ROW]
[ROW][C]122[/C][C]120.141898547411[/C][C]109.98558519966[/C][C]130.298211895162[/C][/ROW]
[ROW][C]123[/C][C]120.857022515837[/C][C]108.902196695855[/C][C]132.811848335819[/C][/ROW]
[ROW][C]124[/C][C]122.257865275459[/C][C]108.741763028342[/C][C]135.773967522575[/C][/ROW]
[ROW][C]125[/C][C]120.647372477763[/C][C]105.732541619758[/C][C]135.562203335769[/C][/ROW]
[ROW][C]126[/C][C]122.221638265603[/C][C]106.028450219659[/C][C]138.414826311548[/C][/ROW]
[ROW][C]127[/C][C]120.444176219933[/C][C]103.066417484707[/C][C]137.821934955159[/C][/ROW]
[ROW][C]128[/C][C]119.225181534467[/C][C]100.738601044064[/C][C]137.71176202487[/C][/ROW]
[ROW][C]129[/C][C]116.435815412123[/C][C]96.9032575203225[/C][C]135.968373303924[/C][/ROW]
[ROW][C]130[/C][C]113.200643666661[/C][C]92.6753427586366[/C][C]133.725944574685[/C][/ROW]
[ROW][C]131[/C][C]114.631092139411[/C][C]93.1588976327161[/C][C]136.103286646106[/C][/ROW]
[ROW][C]132[/C][C]114.498951048951[/C][C]92.1198917188148[/C][C]136.878010379087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117446&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117446&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
121118.532871754513110.57149365463126.494249854396
122120.141898547411109.98558519966130.298211895162
123120.857022515837108.902196695855132.811848335819
124122.257865275459108.741763028342135.773967522575
125120.647372477763105.732541619758135.562203335769
126122.221638265603106.028450219659138.414826311548
127120.444176219933103.066417484707137.821934955159
128119.225181534467100.738601044064137.71176202487
129116.43581541212396.9032575203225135.968373303924
130113.20064366666192.6753427586366133.725944574685
131114.63109213941193.1588976327161136.103286646106
132114.49895104895192.1198917188148136.878010379087


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')