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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, 02 Jan 2012 09:19:41 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/02/t1325514036ibz9c03zsv0ogne.htm/, Retrieved Sat, 04 May 2024 13:56:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160930, Retrieved Sat, 04 May 2024 13:56:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact164

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-01-02 14:19:41] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98,6
100,1
98,8
98,3
102,8
103,6
105,2
100,1
98,2
98,4
97,4
98,4
100,3
101,1
104,1
107,3
110,1
112,6
114,3
115,3
109,9
108,2
103,2
101,8
105,6
108,2
109,8
114,6
117,2
116,5
116,1
112,1
106,8
106,9
104,5
103
105,9
107,7
107,1
112,5
114,5
114,6
113,1
112,8
111,9
112
112,4
110
112,3
109,6
111,9
110,8
110,4
110,8
114
108,4
110,5
105,1
102,3
104,3
103,4
102,4
104,5
107,3
110,1
111,8
111,8
105,7
106
106,4
107,1
111,5
109,6
109,9
109,3
111,4
112,9
115,5
118,4
116,2
113,3
113,8
114,1
117,1
115,5
115,2
114,2
115,3
118,8
118
118,1
111,8
112
114,3
115
118,5
117,6
119,1
120,6
123,6
122,7
123,8
123,1
124,5
120,7
118,7
119
122,3
118,6
118,1
118,2
120,8
119,7
119,7
117,1
114,5
116,5
116,4
114,9
115,5

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'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160930&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160930&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160930&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'Gertrude Mary Cox' @ cox.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.953684845299326
beta0.0189565168474447
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.953684845299326 \tabularnewline
beta & 0.0189565168474447 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160930&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]0.953684845299326[/C][/ROW]
[ROW][C]beta[/C][C]0.0189565168474447[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160930&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160930&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
alpha0.953684845299326
beta0.0189565168474447
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13100.396.93098188083213.36901811916792
14101.1100.7312724799840.368727520015739
15104.1103.7653132880790.334686711920625
16107.3107.1934418012520.10655819874826
17110.1110.257785139625-0.15778513962519
18112.6113.050537958068-0.450537958067983
19114.3113.5720048686590.727995131340833
20115.3109.4140181971215.88598180287852
21109.9113.44517150921-3.5451715092095
22108.2110.466675239945-2.26667523994506
23103.2107.263023920044-4.06302392004402
24101.8104.460429051434-2.66042905143406
25105.6103.9566175704321.64338242956815
26108.2105.8772796141382.32272038586207
27109.8110.86026275494-1.06026275494017
28114.6113.0032493683971.59675063160319
29117.2117.574865415443-0.374865415443409
30116.5120.232570393557-3.73257039355705
31116.1117.575825918789-1.47582591878887
32112.1111.3114038192350.788596180764884
33106.8109.893467705816-3.09346770581604
34106.9107.193717291366-0.293717291366121
35104.5105.623841527367-1.12384152736742
36103105.564110768179-2.56411076817857
37105.9105.242662476960.657337523040113
38107.7106.1060042275231.59399577247686
39107.1110.065634607699-2.96563460769934
40112.5110.2541616542842.2458383457157
41114.5115.119532403948-0.619532403948426
42114.6117.136118504881-2.53611850488106
43113.1115.540909374848-2.44090937484818
44112.8108.4083218507994.39167814920131
45111.9110.1106392348721.78936076512802
46112112.155901551624-0.155901551624012
47112.4110.5591199966771.84088000332304
48110113.31092811258-3.31092811257987
49112.3112.559611150613-0.259611150612528
50109.6112.57074852086-2.97074852085991
51111.9111.905613626695-0.00561362669519383
52110.8115.242897604104-4.44289760410419
53110.4113.411166129248-3.01116612924757
54110.8112.783741333984-1.98374133398357
55114111.5125333620182.48746663798225
56108.4109.252192096782-0.852192096782332
57110.5105.7620575315134.73794246848703
58105.1110.39605626591-5.29605626591027
59102.3103.875652513831-1.57565251383146
60104.3102.8233684588781.47663154112206
61103.4106.468093696084-3.06809369608443
62102.4103.447806412409-1.04780641240909
63104.5104.4108216682650.0891783317354395
64107.3107.2231510204450.0768489795554501
65110.1109.5505434519310.549456548068889
66111.8112.27233209165-0.472332091649704
67111.8112.591689569562-0.791689569561797
68105.7107.033390440973-1.33339044097259
69106103.2826686294262.717331370574
70106.4105.391731822721.0082681772799
71107.1104.9948579855212.10514201447884
72111.5107.6322742748863.86772572511356
73109.6113.526260838497-3.9262608384975
74109.9109.8175268705440.0824731294563321
75109.3112.115046876213-2.81504687621313
76111.4112.296910885805-0.89691088580544
77112.9113.801103019808-0.901103019808403
78115.5115.1201867852760.379813214723939
79118.4116.2481028085572.15189719144315
80116.2113.2216380808972.97836191910282
81113.3113.640959252586-0.340959252586444
82113.8112.7611928574981.03880714250168
83114.1112.3966912913531.70330870864731
84117.1114.8086265911172.29137340888263
85115.5118.932352985912-3.43235298591199
86115.2115.912469878914-0.712469878913595
87114.2117.423377067505-3.22337706750507
88115.3117.44456543409-2.1445654340905
89118.8117.8276531385270.972346861472573
90118121.123593864377-3.12359386437699
91118.1118.969425055021-0.869425055020614
92111.8113.023582327859-1.22358232785906
93112109.2348443325242.76515566747599
94114.3111.2917062820933.00829371790722
95115112.7666044543232.23339554567694
96118.5115.6584370149392.84156298506106
97117.6120.006212398457-2.40621239845657
98119.1118.0648196425291.03518035747138
99120.6121.184677434607-0.584677434607471
100123.6123.984077578794-0.384077578794489
101122.7126.443088126164-3.74308812616427
102123.8125.115580789108-1.31558078910798
103123.1124.85906000986-1.75906000986049
104124.5117.8358868462056.66411315379543
105120.7121.615959123131-0.915959123131074
106118.7120.1960451004-1.49604510040008
107119117.2783972927041.72160270729559
108122.3119.7218874566952.57811254330521
109118.6123.598679304115-4.99867930411457
110118.1119.293131448774-1.19313144877381
111118.2120.105408386567-1.90540838656734
112120.8121.476376067599-0.676376067598824
113119.7123.316339712947-3.61633971294718
114119.7122.046108376457-2.34610837645658
115117.1120.615293059399-3.51529305939889
116114.5112.3671629388552.13283706114466
117116.5111.4936291129275.00637088707269
118116.4115.5883360074380.811663992562018
119114.9114.955729720538-0.0557297205379967
120115.5115.59542665509-0.0954266550903782

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 100.3 & 96.9309818808321 & 3.36901811916792 \tabularnewline
14 & 101.1 & 100.731272479984 & 0.368727520015739 \tabularnewline
15 & 104.1 & 103.765313288079 & 0.334686711920625 \tabularnewline
16 & 107.3 & 107.193441801252 & 0.10655819874826 \tabularnewline
17 & 110.1 & 110.257785139625 & -0.15778513962519 \tabularnewline
18 & 112.6 & 113.050537958068 & -0.450537958067983 \tabularnewline
19 & 114.3 & 113.572004868659 & 0.727995131340833 \tabularnewline
20 & 115.3 & 109.414018197121 & 5.88598180287852 \tabularnewline
21 & 109.9 & 113.44517150921 & -3.5451715092095 \tabularnewline
22 & 108.2 & 110.466675239945 & -2.26667523994506 \tabularnewline
23 & 103.2 & 107.263023920044 & -4.06302392004402 \tabularnewline
24 & 101.8 & 104.460429051434 & -2.66042905143406 \tabularnewline
25 & 105.6 & 103.956617570432 & 1.64338242956815 \tabularnewline
26 & 108.2 & 105.877279614138 & 2.32272038586207 \tabularnewline
27 & 109.8 & 110.86026275494 & -1.06026275494017 \tabularnewline
28 & 114.6 & 113.003249368397 & 1.59675063160319 \tabularnewline
29 & 117.2 & 117.574865415443 & -0.374865415443409 \tabularnewline
30 & 116.5 & 120.232570393557 & -3.73257039355705 \tabularnewline
31 & 116.1 & 117.575825918789 & -1.47582591878887 \tabularnewline
32 & 112.1 & 111.311403819235 & 0.788596180764884 \tabularnewline
33 & 106.8 & 109.893467705816 & -3.09346770581604 \tabularnewline
34 & 106.9 & 107.193717291366 & -0.293717291366121 \tabularnewline
35 & 104.5 & 105.623841527367 & -1.12384152736742 \tabularnewline
36 & 103 & 105.564110768179 & -2.56411076817857 \tabularnewline
37 & 105.9 & 105.24266247696 & 0.657337523040113 \tabularnewline
38 & 107.7 & 106.106004227523 & 1.59399577247686 \tabularnewline
39 & 107.1 & 110.065634607699 & -2.96563460769934 \tabularnewline
40 & 112.5 & 110.254161654284 & 2.2458383457157 \tabularnewline
41 & 114.5 & 115.119532403948 & -0.619532403948426 \tabularnewline
42 & 114.6 & 117.136118504881 & -2.53611850488106 \tabularnewline
43 & 113.1 & 115.540909374848 & -2.44090937484818 \tabularnewline
44 & 112.8 & 108.408321850799 & 4.39167814920131 \tabularnewline
45 & 111.9 & 110.110639234872 & 1.78936076512802 \tabularnewline
46 & 112 & 112.155901551624 & -0.155901551624012 \tabularnewline
47 & 112.4 & 110.559119996677 & 1.84088000332304 \tabularnewline
48 & 110 & 113.31092811258 & -3.31092811257987 \tabularnewline
49 & 112.3 & 112.559611150613 & -0.259611150612528 \tabularnewline
50 & 109.6 & 112.57074852086 & -2.97074852085991 \tabularnewline
51 & 111.9 & 111.905613626695 & -0.00561362669519383 \tabularnewline
52 & 110.8 & 115.242897604104 & -4.44289760410419 \tabularnewline
53 & 110.4 & 113.411166129248 & -3.01116612924757 \tabularnewline
54 & 110.8 & 112.783741333984 & -1.98374133398357 \tabularnewline
55 & 114 & 111.512533362018 & 2.48746663798225 \tabularnewline
56 & 108.4 & 109.252192096782 & -0.852192096782332 \tabularnewline
57 & 110.5 & 105.762057531513 & 4.73794246848703 \tabularnewline
58 & 105.1 & 110.39605626591 & -5.29605626591027 \tabularnewline
59 & 102.3 & 103.875652513831 & -1.57565251383146 \tabularnewline
60 & 104.3 & 102.823368458878 & 1.47663154112206 \tabularnewline
61 & 103.4 & 106.468093696084 & -3.06809369608443 \tabularnewline
62 & 102.4 & 103.447806412409 & -1.04780641240909 \tabularnewline
63 & 104.5 & 104.410821668265 & 0.0891783317354395 \tabularnewline
64 & 107.3 & 107.223151020445 & 0.0768489795554501 \tabularnewline
65 & 110.1 & 109.550543451931 & 0.549456548068889 \tabularnewline
66 & 111.8 & 112.27233209165 & -0.472332091649704 \tabularnewline
67 & 111.8 & 112.591689569562 & -0.791689569561797 \tabularnewline
68 & 105.7 & 107.033390440973 & -1.33339044097259 \tabularnewline
69 & 106 & 103.282668629426 & 2.717331370574 \tabularnewline
70 & 106.4 & 105.39173182272 & 1.0082681772799 \tabularnewline
71 & 107.1 & 104.994857985521 & 2.10514201447884 \tabularnewline
72 & 111.5 & 107.632274274886 & 3.86772572511356 \tabularnewline
73 & 109.6 & 113.526260838497 & -3.9262608384975 \tabularnewline
74 & 109.9 & 109.817526870544 & 0.0824731294563321 \tabularnewline
75 & 109.3 & 112.115046876213 & -2.81504687621313 \tabularnewline
76 & 111.4 & 112.296910885805 & -0.89691088580544 \tabularnewline
77 & 112.9 & 113.801103019808 & -0.901103019808403 \tabularnewline
78 & 115.5 & 115.120186785276 & 0.379813214723939 \tabularnewline
79 & 118.4 & 116.248102808557 & 2.15189719144315 \tabularnewline
80 & 116.2 & 113.221638080897 & 2.97836191910282 \tabularnewline
81 & 113.3 & 113.640959252586 & -0.340959252586444 \tabularnewline
82 & 113.8 & 112.761192857498 & 1.03880714250168 \tabularnewline
83 & 114.1 & 112.396691291353 & 1.70330870864731 \tabularnewline
84 & 117.1 & 114.808626591117 & 2.29137340888263 \tabularnewline
85 & 115.5 & 118.932352985912 & -3.43235298591199 \tabularnewline
86 & 115.2 & 115.912469878914 & -0.712469878913595 \tabularnewline
87 & 114.2 & 117.423377067505 & -3.22337706750507 \tabularnewline
88 & 115.3 & 117.44456543409 & -2.1445654340905 \tabularnewline
89 & 118.8 & 117.827653138527 & 0.972346861472573 \tabularnewline
90 & 118 & 121.123593864377 & -3.12359386437699 \tabularnewline
91 & 118.1 & 118.969425055021 & -0.869425055020614 \tabularnewline
92 & 111.8 & 113.023582327859 & -1.22358232785906 \tabularnewline
93 & 112 & 109.234844332524 & 2.76515566747599 \tabularnewline
94 & 114.3 & 111.291706282093 & 3.00829371790722 \tabularnewline
95 & 115 & 112.766604454323 & 2.23339554567694 \tabularnewline
96 & 118.5 & 115.658437014939 & 2.84156298506106 \tabularnewline
97 & 117.6 & 120.006212398457 & -2.40621239845657 \tabularnewline
98 & 119.1 & 118.064819642529 & 1.03518035747138 \tabularnewline
99 & 120.6 & 121.184677434607 & -0.584677434607471 \tabularnewline
100 & 123.6 & 123.984077578794 & -0.384077578794489 \tabularnewline
101 & 122.7 & 126.443088126164 & -3.74308812616427 \tabularnewline
102 & 123.8 & 125.115580789108 & -1.31558078910798 \tabularnewline
103 & 123.1 & 124.85906000986 & -1.75906000986049 \tabularnewline
104 & 124.5 & 117.835886846205 & 6.66411315379543 \tabularnewline
105 & 120.7 & 121.615959123131 & -0.915959123131074 \tabularnewline
106 & 118.7 & 120.1960451004 & -1.49604510040008 \tabularnewline
107 & 119 & 117.278397292704 & 1.72160270729559 \tabularnewline
108 & 122.3 & 119.721887456695 & 2.57811254330521 \tabularnewline
109 & 118.6 & 123.598679304115 & -4.99867930411457 \tabularnewline
110 & 118.1 & 119.293131448774 & -1.19313144877381 \tabularnewline
111 & 118.2 & 120.105408386567 & -1.90540838656734 \tabularnewline
112 & 120.8 & 121.476376067599 & -0.676376067598824 \tabularnewline
113 & 119.7 & 123.316339712947 & -3.61633971294718 \tabularnewline
114 & 119.7 & 122.046108376457 & -2.34610837645658 \tabularnewline
115 & 117.1 & 120.615293059399 & -3.51529305939889 \tabularnewline
116 & 114.5 & 112.367162938855 & 2.13283706114466 \tabularnewline
117 & 116.5 & 111.493629112927 & 5.00637088707269 \tabularnewline
118 & 116.4 & 115.588336007438 & 0.811663992562018 \tabularnewline
119 & 114.9 & 114.955729720538 & -0.0557297205379967 \tabularnewline
120 & 115.5 & 115.59542665509 & -0.0954266550903782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160930&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]100.3[/C][C]96.9309818808321[/C][C]3.36901811916792[/C][/ROW]
[ROW][C]14[/C][C]101.1[/C][C]100.731272479984[/C][C]0.368727520015739[/C][/ROW]
[ROW][C]15[/C][C]104.1[/C][C]103.765313288079[/C][C]0.334686711920625[/C][/ROW]
[ROW][C]16[/C][C]107.3[/C][C]107.193441801252[/C][C]0.10655819874826[/C][/ROW]
[ROW][C]17[/C][C]110.1[/C][C]110.257785139625[/C][C]-0.15778513962519[/C][/ROW]
[ROW][C]18[/C][C]112.6[/C][C]113.050537958068[/C][C]-0.450537958067983[/C][/ROW]
[ROW][C]19[/C][C]114.3[/C][C]113.572004868659[/C][C]0.727995131340833[/C][/ROW]
[ROW][C]20[/C][C]115.3[/C][C]109.414018197121[/C][C]5.88598180287852[/C][/ROW]
[ROW][C]21[/C][C]109.9[/C][C]113.44517150921[/C][C]-3.5451715092095[/C][/ROW]
[ROW][C]22[/C][C]108.2[/C][C]110.466675239945[/C][C]-2.26667523994506[/C][/ROW]
[ROW][C]23[/C][C]103.2[/C][C]107.263023920044[/C][C]-4.06302392004402[/C][/ROW]
[ROW][C]24[/C][C]101.8[/C][C]104.460429051434[/C][C]-2.66042905143406[/C][/ROW]
[ROW][C]25[/C][C]105.6[/C][C]103.956617570432[/C][C]1.64338242956815[/C][/ROW]
[ROW][C]26[/C][C]108.2[/C][C]105.877279614138[/C][C]2.32272038586207[/C][/ROW]
[ROW][C]27[/C][C]109.8[/C][C]110.86026275494[/C][C]-1.06026275494017[/C][/ROW]
[ROW][C]28[/C][C]114.6[/C][C]113.003249368397[/C][C]1.59675063160319[/C][/ROW]
[ROW][C]29[/C][C]117.2[/C][C]117.574865415443[/C][C]-0.374865415443409[/C][/ROW]
[ROW][C]30[/C][C]116.5[/C][C]120.232570393557[/C][C]-3.73257039355705[/C][/ROW]
[ROW][C]31[/C][C]116.1[/C][C]117.575825918789[/C][C]-1.47582591878887[/C][/ROW]
[ROW][C]32[/C][C]112.1[/C][C]111.311403819235[/C][C]0.788596180764884[/C][/ROW]
[ROW][C]33[/C][C]106.8[/C][C]109.893467705816[/C][C]-3.09346770581604[/C][/ROW]
[ROW][C]34[/C][C]106.9[/C][C]107.193717291366[/C][C]-0.293717291366121[/C][/ROW]
[ROW][C]35[/C][C]104.5[/C][C]105.623841527367[/C][C]-1.12384152736742[/C][/ROW]
[ROW][C]36[/C][C]103[/C][C]105.564110768179[/C][C]-2.56411076817857[/C][/ROW]
[ROW][C]37[/C][C]105.9[/C][C]105.24266247696[/C][C]0.657337523040113[/C][/ROW]
[ROW][C]38[/C][C]107.7[/C][C]106.106004227523[/C][C]1.59399577247686[/C][/ROW]
[ROW][C]39[/C][C]107.1[/C][C]110.065634607699[/C][C]-2.96563460769934[/C][/ROW]
[ROW][C]40[/C][C]112.5[/C][C]110.254161654284[/C][C]2.2458383457157[/C][/ROW]
[ROW][C]41[/C][C]114.5[/C][C]115.119532403948[/C][C]-0.619532403948426[/C][/ROW]
[ROW][C]42[/C][C]114.6[/C][C]117.136118504881[/C][C]-2.53611850488106[/C][/ROW]
[ROW][C]43[/C][C]113.1[/C][C]115.540909374848[/C][C]-2.44090937484818[/C][/ROW]
[ROW][C]44[/C][C]112.8[/C][C]108.408321850799[/C][C]4.39167814920131[/C][/ROW]
[ROW][C]45[/C][C]111.9[/C][C]110.110639234872[/C][C]1.78936076512802[/C][/ROW]
[ROW][C]46[/C][C]112[/C][C]112.155901551624[/C][C]-0.155901551624012[/C][/ROW]
[ROW][C]47[/C][C]112.4[/C][C]110.559119996677[/C][C]1.84088000332304[/C][/ROW]
[ROW][C]48[/C][C]110[/C][C]113.31092811258[/C][C]-3.31092811257987[/C][/ROW]
[ROW][C]49[/C][C]112.3[/C][C]112.559611150613[/C][C]-0.259611150612528[/C][/ROW]
[ROW][C]50[/C][C]109.6[/C][C]112.57074852086[/C][C]-2.97074852085991[/C][/ROW]
[ROW][C]51[/C][C]111.9[/C][C]111.905613626695[/C][C]-0.00561362669519383[/C][/ROW]
[ROW][C]52[/C][C]110.8[/C][C]115.242897604104[/C][C]-4.44289760410419[/C][/ROW]
[ROW][C]53[/C][C]110.4[/C][C]113.411166129248[/C][C]-3.01116612924757[/C][/ROW]
[ROW][C]54[/C][C]110.8[/C][C]112.783741333984[/C][C]-1.98374133398357[/C][/ROW]
[ROW][C]55[/C][C]114[/C][C]111.512533362018[/C][C]2.48746663798225[/C][/ROW]
[ROW][C]56[/C][C]108.4[/C][C]109.252192096782[/C][C]-0.852192096782332[/C][/ROW]
[ROW][C]57[/C][C]110.5[/C][C]105.762057531513[/C][C]4.73794246848703[/C][/ROW]
[ROW][C]58[/C][C]105.1[/C][C]110.39605626591[/C][C]-5.29605626591027[/C][/ROW]
[ROW][C]59[/C][C]102.3[/C][C]103.875652513831[/C][C]-1.57565251383146[/C][/ROW]
[ROW][C]60[/C][C]104.3[/C][C]102.823368458878[/C][C]1.47663154112206[/C][/ROW]
[ROW][C]61[/C][C]103.4[/C][C]106.468093696084[/C][C]-3.06809369608443[/C][/ROW]
[ROW][C]62[/C][C]102.4[/C][C]103.447806412409[/C][C]-1.04780641240909[/C][/ROW]
[ROW][C]63[/C][C]104.5[/C][C]104.410821668265[/C][C]0.0891783317354395[/C][/ROW]
[ROW][C]64[/C][C]107.3[/C][C]107.223151020445[/C][C]0.0768489795554501[/C][/ROW]
[ROW][C]65[/C][C]110.1[/C][C]109.550543451931[/C][C]0.549456548068889[/C][/ROW]
[ROW][C]66[/C][C]111.8[/C][C]112.27233209165[/C][C]-0.472332091649704[/C][/ROW]
[ROW][C]67[/C][C]111.8[/C][C]112.591689569562[/C][C]-0.791689569561797[/C][/ROW]
[ROW][C]68[/C][C]105.7[/C][C]107.033390440973[/C][C]-1.33339044097259[/C][/ROW]
[ROW][C]69[/C][C]106[/C][C]103.282668629426[/C][C]2.717331370574[/C][/ROW]
[ROW][C]70[/C][C]106.4[/C][C]105.39173182272[/C][C]1.0082681772799[/C][/ROW]
[ROW][C]71[/C][C]107.1[/C][C]104.994857985521[/C][C]2.10514201447884[/C][/ROW]
[ROW][C]72[/C][C]111.5[/C][C]107.632274274886[/C][C]3.86772572511356[/C][/ROW]
[ROW][C]73[/C][C]109.6[/C][C]113.526260838497[/C][C]-3.9262608384975[/C][/ROW]
[ROW][C]74[/C][C]109.9[/C][C]109.817526870544[/C][C]0.0824731294563321[/C][/ROW]
[ROW][C]75[/C][C]109.3[/C][C]112.115046876213[/C][C]-2.81504687621313[/C][/ROW]
[ROW][C]76[/C][C]111.4[/C][C]112.296910885805[/C][C]-0.89691088580544[/C][/ROW]
[ROW][C]77[/C][C]112.9[/C][C]113.801103019808[/C][C]-0.901103019808403[/C][/ROW]
[ROW][C]78[/C][C]115.5[/C][C]115.120186785276[/C][C]0.379813214723939[/C][/ROW]
[ROW][C]79[/C][C]118.4[/C][C]116.248102808557[/C][C]2.15189719144315[/C][/ROW]
[ROW][C]80[/C][C]116.2[/C][C]113.221638080897[/C][C]2.97836191910282[/C][/ROW]
[ROW][C]81[/C][C]113.3[/C][C]113.640959252586[/C][C]-0.340959252586444[/C][/ROW]
[ROW][C]82[/C][C]113.8[/C][C]112.761192857498[/C][C]1.03880714250168[/C][/ROW]
[ROW][C]83[/C][C]114.1[/C][C]112.396691291353[/C][C]1.70330870864731[/C][/ROW]
[ROW][C]84[/C][C]117.1[/C][C]114.808626591117[/C][C]2.29137340888263[/C][/ROW]
[ROW][C]85[/C][C]115.5[/C][C]118.932352985912[/C][C]-3.43235298591199[/C][/ROW]
[ROW][C]86[/C][C]115.2[/C][C]115.912469878914[/C][C]-0.712469878913595[/C][/ROW]
[ROW][C]87[/C][C]114.2[/C][C]117.423377067505[/C][C]-3.22337706750507[/C][/ROW]
[ROW][C]88[/C][C]115.3[/C][C]117.44456543409[/C][C]-2.1445654340905[/C][/ROW]
[ROW][C]89[/C][C]118.8[/C][C]117.827653138527[/C][C]0.972346861472573[/C][/ROW]
[ROW][C]90[/C][C]118[/C][C]121.123593864377[/C][C]-3.12359386437699[/C][/ROW]
[ROW][C]91[/C][C]118.1[/C][C]118.969425055021[/C][C]-0.869425055020614[/C][/ROW]
[ROW][C]92[/C][C]111.8[/C][C]113.023582327859[/C][C]-1.22358232785906[/C][/ROW]
[ROW][C]93[/C][C]112[/C][C]109.234844332524[/C][C]2.76515566747599[/C][/ROW]
[ROW][C]94[/C][C]114.3[/C][C]111.291706282093[/C][C]3.00829371790722[/C][/ROW]
[ROW][C]95[/C][C]115[/C][C]112.766604454323[/C][C]2.23339554567694[/C][/ROW]
[ROW][C]96[/C][C]118.5[/C][C]115.658437014939[/C][C]2.84156298506106[/C][/ROW]
[ROW][C]97[/C][C]117.6[/C][C]120.006212398457[/C][C]-2.40621239845657[/C][/ROW]
[ROW][C]98[/C][C]119.1[/C][C]118.064819642529[/C][C]1.03518035747138[/C][/ROW]
[ROW][C]99[/C][C]120.6[/C][C]121.184677434607[/C][C]-0.584677434607471[/C][/ROW]
[ROW][C]100[/C][C]123.6[/C][C]123.984077578794[/C][C]-0.384077578794489[/C][/ROW]
[ROW][C]101[/C][C]122.7[/C][C]126.443088126164[/C][C]-3.74308812616427[/C][/ROW]
[ROW][C]102[/C][C]123.8[/C][C]125.115580789108[/C][C]-1.31558078910798[/C][/ROW]
[ROW][C]103[/C][C]123.1[/C][C]124.85906000986[/C][C]-1.75906000986049[/C][/ROW]
[ROW][C]104[/C][C]124.5[/C][C]117.835886846205[/C][C]6.66411315379543[/C][/ROW]
[ROW][C]105[/C][C]120.7[/C][C]121.615959123131[/C][C]-0.915959123131074[/C][/ROW]
[ROW][C]106[/C][C]118.7[/C][C]120.1960451004[/C][C]-1.49604510040008[/C][/ROW]
[ROW][C]107[/C][C]119[/C][C]117.278397292704[/C][C]1.72160270729559[/C][/ROW]
[ROW][C]108[/C][C]122.3[/C][C]119.721887456695[/C][C]2.57811254330521[/C][/ROW]
[ROW][C]109[/C][C]118.6[/C][C]123.598679304115[/C][C]-4.99867930411457[/C][/ROW]
[ROW][C]110[/C][C]118.1[/C][C]119.293131448774[/C][C]-1.19313144877381[/C][/ROW]
[ROW][C]111[/C][C]118.2[/C][C]120.105408386567[/C][C]-1.90540838656734[/C][/ROW]
[ROW][C]112[/C][C]120.8[/C][C]121.476376067599[/C][C]-0.676376067598824[/C][/ROW]
[ROW][C]113[/C][C]119.7[/C][C]123.316339712947[/C][C]-3.61633971294718[/C][/ROW]
[ROW][C]114[/C][C]119.7[/C][C]122.046108376457[/C][C]-2.34610837645658[/C][/ROW]
[ROW][C]115[/C][C]117.1[/C][C]120.615293059399[/C][C]-3.51529305939889[/C][/ROW]
[ROW][C]116[/C][C]114.5[/C][C]112.367162938855[/C][C]2.13283706114466[/C][/ROW]
[ROW][C]117[/C][C]116.5[/C][C]111.493629112927[/C][C]5.00637088707269[/C][/ROW]
[ROW][C]118[/C][C]116.4[/C][C]115.588336007438[/C][C]0.811663992562018[/C][/ROW]
[ROW][C]119[/C][C]114.9[/C][C]114.955729720538[/C][C]-0.0557297205379967[/C][/ROW]
[ROW][C]120[/C][C]115.5[/C][C]115.59542665509[/C][C]-0.0954266550903782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160930&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160930&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
13100.396.93098188083213.36901811916792
14101.1100.7312724799840.368727520015739
15104.1103.7653132880790.334686711920625
16107.3107.1934418012520.10655819874826
17110.1110.257785139625-0.15778513962519
18112.6113.050537958068-0.450537958067983
19114.3113.5720048686590.727995131340833
20115.3109.4140181971215.88598180287852
21109.9113.44517150921-3.5451715092095
22108.2110.466675239945-2.26667523994506
23103.2107.263023920044-4.06302392004402
24101.8104.460429051434-2.66042905143406
25105.6103.9566175704321.64338242956815
26108.2105.8772796141382.32272038586207
27109.8110.86026275494-1.06026275494017
28114.6113.0032493683971.59675063160319
29117.2117.574865415443-0.374865415443409
30116.5120.232570393557-3.73257039355705
31116.1117.575825918789-1.47582591878887
32112.1111.3114038192350.788596180764884
33106.8109.893467705816-3.09346770581604
34106.9107.193717291366-0.293717291366121
35104.5105.623841527367-1.12384152736742
36103105.564110768179-2.56411076817857
37105.9105.242662476960.657337523040113
38107.7106.1060042275231.59399577247686
39107.1110.065634607699-2.96563460769934
40112.5110.2541616542842.2458383457157
41114.5115.119532403948-0.619532403948426
42114.6117.136118504881-2.53611850488106
43113.1115.540909374848-2.44090937484818
44112.8108.4083218507994.39167814920131
45111.9110.1106392348721.78936076512802
46112112.155901551624-0.155901551624012
47112.4110.5591199966771.84088000332304
48110113.31092811258-3.31092811257987
49112.3112.559611150613-0.259611150612528
50109.6112.57074852086-2.97074852085991
51111.9111.905613626695-0.00561362669519383
52110.8115.242897604104-4.44289760410419
53110.4113.411166129248-3.01116612924757
54110.8112.783741333984-1.98374133398357
55114111.5125333620182.48746663798225
56108.4109.252192096782-0.852192096782332
57110.5105.7620575315134.73794246848703
58105.1110.39605626591-5.29605626591027
59102.3103.875652513831-1.57565251383146
60104.3102.8233684588781.47663154112206
61103.4106.468093696084-3.06809369608443
62102.4103.447806412409-1.04780641240909
63104.5104.4108216682650.0891783317354395
64107.3107.2231510204450.0768489795554501
65110.1109.5505434519310.549456548068889
66111.8112.27233209165-0.472332091649704
67111.8112.591689569562-0.791689569561797
68105.7107.033390440973-1.33339044097259
69106103.2826686294262.717331370574
70106.4105.391731822721.0082681772799
71107.1104.9948579855212.10514201447884
72111.5107.6322742748863.86772572511356
73109.6113.526260838497-3.9262608384975
74109.9109.8175268705440.0824731294563321
75109.3112.115046876213-2.81504687621313
76111.4112.296910885805-0.89691088580544
77112.9113.801103019808-0.901103019808403
78115.5115.1201867852760.379813214723939
79118.4116.2481028085572.15189719144315
80116.2113.2216380808972.97836191910282
81113.3113.640959252586-0.340959252586444
82113.8112.7611928574981.03880714250168
83114.1112.3966912913531.70330870864731
84117.1114.8086265911172.29137340888263
85115.5118.932352985912-3.43235298591199
86115.2115.912469878914-0.712469878913595
87114.2117.423377067505-3.22337706750507
88115.3117.44456543409-2.1445654340905
89118.8117.8276531385270.972346861472573
90118121.123593864377-3.12359386437699
91118.1118.969425055021-0.869425055020614
92111.8113.023582327859-1.22358232785906
93112109.2348443325242.76515566747599
94114.3111.2917062820933.00829371790722
95115112.7666044543232.23339554567694
96118.5115.6584370149392.84156298506106
97117.6120.006212398457-2.40621239845657
98119.1118.0648196425291.03518035747138
99120.6121.184677434607-0.584677434607471
100123.6123.984077578794-0.384077578794489
101122.7126.443088126164-3.74308812616427
102123.8125.115580789108-1.31558078910798
103123.1124.85906000986-1.75906000986049
104124.5117.8358868462056.66411315379543
105120.7121.615959123131-0.915959123131074
106118.7120.1960451004-1.49604510040008
107119117.2783972927041.72160270729559
108122.3119.7218874566952.57811254330521
109118.6123.598679304115-4.99867930411457
110118.1119.293131448774-1.19313144877381
111118.2120.105408386567-1.90540838656734
112120.8121.476376067599-0.676376067598824
113119.7123.316339712947-3.61633971294718
114119.7122.046108376457-2.34610837645658
115117.1120.615293059399-3.51529305939889
116114.5112.3671629388552.13283706114466
117116.5111.4936291129275.00637088707269
118116.4115.5883360074380.811663992562018
119114.9114.955729720538-0.0557297205379967
120115.5115.59542665509-0.0954266550903782






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121116.346953704968111.588215574882121.105691835054
122116.889568780573110.244904585137123.53423297601
123118.720936551996110.501456441786126.940416662205
124121.944860107114112.244527116047131.645193098181
125124.286467484373113.265770864291135.307164104455
126126.644156903966114.36727325257138.921040555362
127127.513552480857114.160935006051140.866169955663
128122.602571982206108.788000769928136.417143194484
129119.716251085959105.279616757073134.152885414845
130118.824131982263103.579633139483134.068630825042
131117.339976334718101.392307716344133.287644953092
132118.03939815883191.4827160906476144.596080227014

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 116.346953704968 & 111.588215574882 & 121.105691835054 \tabularnewline
122 & 116.889568780573 & 110.244904585137 & 123.53423297601 \tabularnewline
123 & 118.720936551996 & 110.501456441786 & 126.940416662205 \tabularnewline
124 & 121.944860107114 & 112.244527116047 & 131.645193098181 \tabularnewline
125 & 124.286467484373 & 113.265770864291 & 135.307164104455 \tabularnewline
126 & 126.644156903966 & 114.36727325257 & 138.921040555362 \tabularnewline
127 & 127.513552480857 & 114.160935006051 & 140.866169955663 \tabularnewline
128 & 122.602571982206 & 108.788000769928 & 136.417143194484 \tabularnewline
129 & 119.716251085959 & 105.279616757073 & 134.152885414845 \tabularnewline
130 & 118.824131982263 & 103.579633139483 & 134.068630825042 \tabularnewline
131 & 117.339976334718 & 101.392307716344 & 133.287644953092 \tabularnewline
132 & 118.039398158831 & 91.4827160906476 & 144.596080227014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160930&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]116.346953704968[/C][C]111.588215574882[/C][C]121.105691835054[/C][/ROW]
[ROW][C]122[/C][C]116.889568780573[/C][C]110.244904585137[/C][C]123.53423297601[/C][/ROW]
[ROW][C]123[/C][C]118.720936551996[/C][C]110.501456441786[/C][C]126.940416662205[/C][/ROW]
[ROW][C]124[/C][C]121.944860107114[/C][C]112.244527116047[/C][C]131.645193098181[/C][/ROW]
[ROW][C]125[/C][C]124.286467484373[/C][C]113.265770864291[/C][C]135.307164104455[/C][/ROW]
[ROW][C]126[/C][C]126.644156903966[/C][C]114.36727325257[/C][C]138.921040555362[/C][/ROW]
[ROW][C]127[/C][C]127.513552480857[/C][C]114.160935006051[/C][C]140.866169955663[/C][/ROW]
[ROW][C]128[/C][C]122.602571982206[/C][C]108.788000769928[/C][C]136.417143194484[/C][/ROW]
[ROW][C]129[/C][C]119.716251085959[/C][C]105.279616757073[/C][C]134.152885414845[/C][/ROW]
[ROW][C]130[/C][C]118.824131982263[/C][C]103.579633139483[/C][C]134.068630825042[/C][/ROW]
[ROW][C]131[/C][C]117.339976334718[/C][C]101.392307716344[/C][C]133.287644953092[/C][/ROW]
[ROW][C]132[/C][C]118.039398158831[/C][C]91.4827160906476[/C][C]144.596080227014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160930&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160930&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
121116.346953704968111.588215574882121.105691835054
122116.889568780573110.244904585137123.53423297601
123118.720936551996110.501456441786126.940416662205
124121.944860107114112.244527116047131.645193098181
125124.286467484373113.265770864291135.307164104455
126126.644156903966114.36727325257138.921040555362
127127.513552480857114.160935006051140.866169955663
128122.602571982206108.788000769928136.417143194484
129119.716251085959105.279616757073134.152885414845
130118.824131982263103.579633139483134.068630825042
131117.339976334718101.392307716344133.287644953092
132118.03939815883191.4827160906476144.596080227014


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')