Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 14 Aug 2010 10:04:53 +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/2010/Aug/14/t1281780295axbpinaedqnaqc2.htm/, Retrieved Mon, 06 May 2024 02:42:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78767, Retrieved Mon, 06 May 2024 02:42:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJacobs Jeff
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A -Stap 32] [2010-08-14 10:04:53] [03859715711bd3369851d387eaa83ba4] [Current]
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Dataseries X:
130
129
128
126
146
145
130
120
121
121
122
124
123
125
120
124
146
149
138
133
135
149
146
141
139
141
138
139
166
179
167
154
151
162
148
143
145
143
148
139
169
186
174
161
151
158
144
135
139
137
149
136
169
185
177
164
145
147
142
126
130
136
139
120
151
166
156
150
141
141
130
110
110
123
133
108
136
148
146
142
132
128
116
90
94
112
130
106
124
139
140
129
113
110
102
78
79
94
121
99
126
137
141
119
96
96
88
64
66
92
120
101
135
146
149
134
101
100
91
70




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78767&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78767&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78767&T=0

As an alternative you can also use a 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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0791399017664453
beta0.566472187949833
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0791399017664453 \tabularnewline
beta & 0.566472187949833 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78767&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]0.0791399017664453[/C][/ROW]
[ROW][C]beta[/C][C]0.566472187949833[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78767&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78767&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0791399017664453
beta0.566472187949833
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13123123.276442307692-0.276442307692349
14125124.9646366639710.0353633360290075
15120119.4290926461850.570907353815045
16124122.3365256219171.66347437808288
17146142.9883320547393.01166794526083
18149145.3401824677293.65981753227146
19138134.4490656870083.55093431299221
20133126.333522249026.66647775097978
21135129.8050711655215.19492883447887
22149132.30972004603716.6902799539635
23146137.1390110367838.86098896321678
24141142.495935745696-1.49593574569636
25139143.3782527994-4.37825279940037
26141147.002878135421-6.00287813542059
27138143.185850174811-5.1858501748107
28139148.088937454503-9.08893745450308
29166170.094402311978-4.09440231197826
30179173.125270633885.87472936612002
31167163.05300778783.94699221219969
32154158.59937570586-4.59937570585984
33151160.080788699166-9.08078869916619
34162171.657813834142-9.65781383414182
35148165.627582953401-17.6275829534015
36143156.598773996173-13.5987739961728
37145150.574333937181-5.57433393718148
38143149.259898986482-6.25989898648169
39148142.8150265856185.18497341438209
40139142.04971996595-3.04971996594961
41169166.5081949620942.49180503790561
42186176.9115329206749.08846707932588
43174163.1335646340610.8664353659399
44161149.48286576565211.5171342343484
45151146.9608337838434.03916621615659
46158158.480836698389-0.480836698388572
47144145.685262734181-1.68526273418064
48135142.190234103142-7.1902341031417
49139144.911787570036-5.91178757003632
50137143.773644487554-6.7736444875541
51149148.6385165606760.361483439323592
52136140.503515057763-4.50351505776274
53169170.479767868892-1.47976786889225
54185186.995212738657-1.99521273865719
55177173.832269617593.16773038240993
56164159.681287859264.31871214074042
57145148.890491093191-3.89049109319132
58147154.452240451531-7.45224045153097
59142138.5148995861073.48510041389281
60126129.110591936456-3.1105919364561
61130132.266018324703-2.26601832470334
62136129.7199333099096.28006669009096
63139141.870716395263-2.87071639526283
64120128.537421602323-8.5374216023232
65151160.335522998079-9.33552299807911
66166174.759077135043-8.75907713504265
67156164.516428546165-8.51642854616486
68150148.6780872497811.32191275021859
69141128.13367867982312.8663213201768
70141130.53598713654510.4640128634553
71130125.6857926056264.31420739437417
72110109.9080548433760.0919451566242344
73110113.872899699601-3.87289969960085
74123118.775593413694.22440658631007
75133121.95114284641511.0488571535854
76108104.7392633040733.26073669592736
77136137.503112304349-1.50311230434946
78148154.195462198873-6.19546219887343
79146145.612185074260.387814925740059
80142141.1704846524820.829515347518281
81132132.828042550505-0.828042550504676
82128132.930614025063-4.93061402506288
83116121.505053755462-5.50505375546159
8490100.927978890333-10.9279788903328
859499.7414824027497-5.74148240274971
86112111.2408551171830.759144882817367
87130119.55925088938810.4407491106124
8810694.232937137048911.7670628629511
89124122.7699415753781.23005842462219
90139134.9669301833164.03306981668436
91140133.3232996823126.67670031768796
92129130.135863923285-1.13586392328509
93113120.373212526736-7.3732125267355
94110116.148191486384-6.14819148638428
95102104.010994923377-2.01099492337667
967878.7870260431467-0.787026043146724
977983.7040876445314-4.70408764453141
9894101.843201351779-7.84320135177886
99121118.582036759632.41796324037026
1009993.66830945560835.33169054439168
101126111.53057043858114.4694295614192
102137127.487689477029.51231052298024
103141129.08892333612611.9110766638744
104119119.732940866378-0.732940866377803
10596104.887998510694-8.88799851069437
10696102.232808955541-6.23280895554109
1078894.4565400634072-6.45654006340723
1086470.3664040880459-6.3664040880459
1096671.3432707304009-5.34327073040092
1109286.62088226519475.37911773480531
111120114.5277588926585.47224110734193
11210193.34833816879377.65166183120631
113135120.72224241519514.2777575848052
114146133.00424838161212.9957516183878
115149138.15112299675410.8488770032456
116134118.08112147251715.9188785274825
11710198.80426010874322.19573989125684
118100101.728109586083-1.72810958608258
1199196.5610802243557-5.56108022435569
1207075.123720550656-5.12372055065605

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 123 & 123.276442307692 & -0.276442307692349 \tabularnewline
14 & 125 & 124.964636663971 & 0.0353633360290075 \tabularnewline
15 & 120 & 119.429092646185 & 0.570907353815045 \tabularnewline
16 & 124 & 122.336525621917 & 1.66347437808288 \tabularnewline
17 & 146 & 142.988332054739 & 3.01166794526083 \tabularnewline
18 & 149 & 145.340182467729 & 3.65981753227146 \tabularnewline
19 & 138 & 134.449065687008 & 3.55093431299221 \tabularnewline
20 & 133 & 126.33352224902 & 6.66647775097978 \tabularnewline
21 & 135 & 129.805071165521 & 5.19492883447887 \tabularnewline
22 & 149 & 132.309720046037 & 16.6902799539635 \tabularnewline
23 & 146 & 137.139011036783 & 8.86098896321678 \tabularnewline
24 & 141 & 142.495935745696 & -1.49593574569636 \tabularnewline
25 & 139 & 143.3782527994 & -4.37825279940037 \tabularnewline
26 & 141 & 147.002878135421 & -6.00287813542059 \tabularnewline
27 & 138 & 143.185850174811 & -5.1858501748107 \tabularnewline
28 & 139 & 148.088937454503 & -9.08893745450308 \tabularnewline
29 & 166 & 170.094402311978 & -4.09440231197826 \tabularnewline
30 & 179 & 173.12527063388 & 5.87472936612002 \tabularnewline
31 & 167 & 163.0530077878 & 3.94699221219969 \tabularnewline
32 & 154 & 158.59937570586 & -4.59937570585984 \tabularnewline
33 & 151 & 160.080788699166 & -9.08078869916619 \tabularnewline
34 & 162 & 171.657813834142 & -9.65781383414182 \tabularnewline
35 & 148 & 165.627582953401 & -17.6275829534015 \tabularnewline
36 & 143 & 156.598773996173 & -13.5987739961728 \tabularnewline
37 & 145 & 150.574333937181 & -5.57433393718148 \tabularnewline
38 & 143 & 149.259898986482 & -6.25989898648169 \tabularnewline
39 & 148 & 142.815026585618 & 5.18497341438209 \tabularnewline
40 & 139 & 142.04971996595 & -3.04971996594961 \tabularnewline
41 & 169 & 166.508194962094 & 2.49180503790561 \tabularnewline
42 & 186 & 176.911532920674 & 9.08846707932588 \tabularnewline
43 & 174 & 163.13356463406 & 10.8664353659399 \tabularnewline
44 & 161 & 149.482865765652 & 11.5171342343484 \tabularnewline
45 & 151 & 146.960833783843 & 4.03916621615659 \tabularnewline
46 & 158 & 158.480836698389 & -0.480836698388572 \tabularnewline
47 & 144 & 145.685262734181 & -1.68526273418064 \tabularnewline
48 & 135 & 142.190234103142 & -7.1902341031417 \tabularnewline
49 & 139 & 144.911787570036 & -5.91178757003632 \tabularnewline
50 & 137 & 143.773644487554 & -6.7736444875541 \tabularnewline
51 & 149 & 148.638516560676 & 0.361483439323592 \tabularnewline
52 & 136 & 140.503515057763 & -4.50351505776274 \tabularnewline
53 & 169 & 170.479767868892 & -1.47976786889225 \tabularnewline
54 & 185 & 186.995212738657 & -1.99521273865719 \tabularnewline
55 & 177 & 173.83226961759 & 3.16773038240993 \tabularnewline
56 & 164 & 159.68128785926 & 4.31871214074042 \tabularnewline
57 & 145 & 148.890491093191 & -3.89049109319132 \tabularnewline
58 & 147 & 154.452240451531 & -7.45224045153097 \tabularnewline
59 & 142 & 138.514899586107 & 3.48510041389281 \tabularnewline
60 & 126 & 129.110591936456 & -3.1105919364561 \tabularnewline
61 & 130 & 132.266018324703 & -2.26601832470334 \tabularnewline
62 & 136 & 129.719933309909 & 6.28006669009096 \tabularnewline
63 & 139 & 141.870716395263 & -2.87071639526283 \tabularnewline
64 & 120 & 128.537421602323 & -8.5374216023232 \tabularnewline
65 & 151 & 160.335522998079 & -9.33552299807911 \tabularnewline
66 & 166 & 174.759077135043 & -8.75907713504265 \tabularnewline
67 & 156 & 164.516428546165 & -8.51642854616486 \tabularnewline
68 & 150 & 148.678087249781 & 1.32191275021859 \tabularnewline
69 & 141 & 128.133678679823 & 12.8663213201768 \tabularnewline
70 & 141 & 130.535987136545 & 10.4640128634553 \tabularnewline
71 & 130 & 125.685792605626 & 4.31420739437417 \tabularnewline
72 & 110 & 109.908054843376 & 0.0919451566242344 \tabularnewline
73 & 110 & 113.872899699601 & -3.87289969960085 \tabularnewline
74 & 123 & 118.77559341369 & 4.22440658631007 \tabularnewline
75 & 133 & 121.951142846415 & 11.0488571535854 \tabularnewline
76 & 108 & 104.739263304073 & 3.26073669592736 \tabularnewline
77 & 136 & 137.503112304349 & -1.50311230434946 \tabularnewline
78 & 148 & 154.195462198873 & -6.19546219887343 \tabularnewline
79 & 146 & 145.61218507426 & 0.387814925740059 \tabularnewline
80 & 142 & 141.170484652482 & 0.829515347518281 \tabularnewline
81 & 132 & 132.828042550505 & -0.828042550504676 \tabularnewline
82 & 128 & 132.930614025063 & -4.93061402506288 \tabularnewline
83 & 116 & 121.505053755462 & -5.50505375546159 \tabularnewline
84 & 90 & 100.927978890333 & -10.9279788903328 \tabularnewline
85 & 94 & 99.7414824027497 & -5.74148240274971 \tabularnewline
86 & 112 & 111.240855117183 & 0.759144882817367 \tabularnewline
87 & 130 & 119.559250889388 & 10.4407491106124 \tabularnewline
88 & 106 & 94.2329371370489 & 11.7670628629511 \tabularnewline
89 & 124 & 122.769941575378 & 1.23005842462219 \tabularnewline
90 & 139 & 134.966930183316 & 4.03306981668436 \tabularnewline
91 & 140 & 133.323299682312 & 6.67670031768796 \tabularnewline
92 & 129 & 130.135863923285 & -1.13586392328509 \tabularnewline
93 & 113 & 120.373212526736 & -7.3732125267355 \tabularnewline
94 & 110 & 116.148191486384 & -6.14819148638428 \tabularnewline
95 & 102 & 104.010994923377 & -2.01099492337667 \tabularnewline
96 & 78 & 78.7870260431467 & -0.787026043146724 \tabularnewline
97 & 79 & 83.7040876445314 & -4.70408764453141 \tabularnewline
98 & 94 & 101.843201351779 & -7.84320135177886 \tabularnewline
99 & 121 & 118.58203675963 & 2.41796324037026 \tabularnewline
100 & 99 & 93.6683094556083 & 5.33169054439168 \tabularnewline
101 & 126 & 111.530570438581 & 14.4694295614192 \tabularnewline
102 & 137 & 127.48768947702 & 9.51231052298024 \tabularnewline
103 & 141 & 129.088923336126 & 11.9110766638744 \tabularnewline
104 & 119 & 119.732940866378 & -0.732940866377803 \tabularnewline
105 & 96 & 104.887998510694 & -8.88799851069437 \tabularnewline
106 & 96 & 102.232808955541 & -6.23280895554109 \tabularnewline
107 & 88 & 94.4565400634072 & -6.45654006340723 \tabularnewline
108 & 64 & 70.3664040880459 & -6.3664040880459 \tabularnewline
109 & 66 & 71.3432707304009 & -5.34327073040092 \tabularnewline
110 & 92 & 86.6208822651947 & 5.37911773480531 \tabularnewline
111 & 120 & 114.527758892658 & 5.47224110734193 \tabularnewline
112 & 101 & 93.3483381687937 & 7.65166183120631 \tabularnewline
113 & 135 & 120.722242415195 & 14.2777575848052 \tabularnewline
114 & 146 & 133.004248381612 & 12.9957516183878 \tabularnewline
115 & 149 & 138.151122996754 & 10.8488770032456 \tabularnewline
116 & 134 & 118.081121472517 & 15.9188785274825 \tabularnewline
117 & 101 & 98.8042601087432 & 2.19573989125684 \tabularnewline
118 & 100 & 101.728109586083 & -1.72810958608258 \tabularnewline
119 & 91 & 96.5610802243557 & -5.56108022435569 \tabularnewline
120 & 70 & 75.123720550656 & -5.12372055065605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78767&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]123[/C][C]123.276442307692[/C][C]-0.276442307692349[/C][/ROW]
[ROW][C]14[/C][C]125[/C][C]124.964636663971[/C][C]0.0353633360290075[/C][/ROW]
[ROW][C]15[/C][C]120[/C][C]119.429092646185[/C][C]0.570907353815045[/C][/ROW]
[ROW][C]16[/C][C]124[/C][C]122.336525621917[/C][C]1.66347437808288[/C][/ROW]
[ROW][C]17[/C][C]146[/C][C]142.988332054739[/C][C]3.01166794526083[/C][/ROW]
[ROW][C]18[/C][C]149[/C][C]145.340182467729[/C][C]3.65981753227146[/C][/ROW]
[ROW][C]19[/C][C]138[/C][C]134.449065687008[/C][C]3.55093431299221[/C][/ROW]
[ROW][C]20[/C][C]133[/C][C]126.33352224902[/C][C]6.66647775097978[/C][/ROW]
[ROW][C]21[/C][C]135[/C][C]129.805071165521[/C][C]5.19492883447887[/C][/ROW]
[ROW][C]22[/C][C]149[/C][C]132.309720046037[/C][C]16.6902799539635[/C][/ROW]
[ROW][C]23[/C][C]146[/C][C]137.139011036783[/C][C]8.86098896321678[/C][/ROW]
[ROW][C]24[/C][C]141[/C][C]142.495935745696[/C][C]-1.49593574569636[/C][/ROW]
[ROW][C]25[/C][C]139[/C][C]143.3782527994[/C][C]-4.37825279940037[/C][/ROW]
[ROW][C]26[/C][C]141[/C][C]147.002878135421[/C][C]-6.00287813542059[/C][/ROW]
[ROW][C]27[/C][C]138[/C][C]143.185850174811[/C][C]-5.1858501748107[/C][/ROW]
[ROW][C]28[/C][C]139[/C][C]148.088937454503[/C][C]-9.08893745450308[/C][/ROW]
[ROW][C]29[/C][C]166[/C][C]170.094402311978[/C][C]-4.09440231197826[/C][/ROW]
[ROW][C]30[/C][C]179[/C][C]173.12527063388[/C][C]5.87472936612002[/C][/ROW]
[ROW][C]31[/C][C]167[/C][C]163.0530077878[/C][C]3.94699221219969[/C][/ROW]
[ROW][C]32[/C][C]154[/C][C]158.59937570586[/C][C]-4.59937570585984[/C][/ROW]
[ROW][C]33[/C][C]151[/C][C]160.080788699166[/C][C]-9.08078869916619[/C][/ROW]
[ROW][C]34[/C][C]162[/C][C]171.657813834142[/C][C]-9.65781383414182[/C][/ROW]
[ROW][C]35[/C][C]148[/C][C]165.627582953401[/C][C]-17.6275829534015[/C][/ROW]
[ROW][C]36[/C][C]143[/C][C]156.598773996173[/C][C]-13.5987739961728[/C][/ROW]
[ROW][C]37[/C][C]145[/C][C]150.574333937181[/C][C]-5.57433393718148[/C][/ROW]
[ROW][C]38[/C][C]143[/C][C]149.259898986482[/C][C]-6.25989898648169[/C][/ROW]
[ROW][C]39[/C][C]148[/C][C]142.815026585618[/C][C]5.18497341438209[/C][/ROW]
[ROW][C]40[/C][C]139[/C][C]142.04971996595[/C][C]-3.04971996594961[/C][/ROW]
[ROW][C]41[/C][C]169[/C][C]166.508194962094[/C][C]2.49180503790561[/C][/ROW]
[ROW][C]42[/C][C]186[/C][C]176.911532920674[/C][C]9.08846707932588[/C][/ROW]
[ROW][C]43[/C][C]174[/C][C]163.13356463406[/C][C]10.8664353659399[/C][/ROW]
[ROW][C]44[/C][C]161[/C][C]149.482865765652[/C][C]11.5171342343484[/C][/ROW]
[ROW][C]45[/C][C]151[/C][C]146.960833783843[/C][C]4.03916621615659[/C][/ROW]
[ROW][C]46[/C][C]158[/C][C]158.480836698389[/C][C]-0.480836698388572[/C][/ROW]
[ROW][C]47[/C][C]144[/C][C]145.685262734181[/C][C]-1.68526273418064[/C][/ROW]
[ROW][C]48[/C][C]135[/C][C]142.190234103142[/C][C]-7.1902341031417[/C][/ROW]
[ROW][C]49[/C][C]139[/C][C]144.911787570036[/C][C]-5.91178757003632[/C][/ROW]
[ROW][C]50[/C][C]137[/C][C]143.773644487554[/C][C]-6.7736444875541[/C][/ROW]
[ROW][C]51[/C][C]149[/C][C]148.638516560676[/C][C]0.361483439323592[/C][/ROW]
[ROW][C]52[/C][C]136[/C][C]140.503515057763[/C][C]-4.50351505776274[/C][/ROW]
[ROW][C]53[/C][C]169[/C][C]170.479767868892[/C][C]-1.47976786889225[/C][/ROW]
[ROW][C]54[/C][C]185[/C][C]186.995212738657[/C][C]-1.99521273865719[/C][/ROW]
[ROW][C]55[/C][C]177[/C][C]173.83226961759[/C][C]3.16773038240993[/C][/ROW]
[ROW][C]56[/C][C]164[/C][C]159.68128785926[/C][C]4.31871214074042[/C][/ROW]
[ROW][C]57[/C][C]145[/C][C]148.890491093191[/C][C]-3.89049109319132[/C][/ROW]
[ROW][C]58[/C][C]147[/C][C]154.452240451531[/C][C]-7.45224045153097[/C][/ROW]
[ROW][C]59[/C][C]142[/C][C]138.514899586107[/C][C]3.48510041389281[/C][/ROW]
[ROW][C]60[/C][C]126[/C][C]129.110591936456[/C][C]-3.1105919364561[/C][/ROW]
[ROW][C]61[/C][C]130[/C][C]132.266018324703[/C][C]-2.26601832470334[/C][/ROW]
[ROW][C]62[/C][C]136[/C][C]129.719933309909[/C][C]6.28006669009096[/C][/ROW]
[ROW][C]63[/C][C]139[/C][C]141.870716395263[/C][C]-2.87071639526283[/C][/ROW]
[ROW][C]64[/C][C]120[/C][C]128.537421602323[/C][C]-8.5374216023232[/C][/ROW]
[ROW][C]65[/C][C]151[/C][C]160.335522998079[/C][C]-9.33552299807911[/C][/ROW]
[ROW][C]66[/C][C]166[/C][C]174.759077135043[/C][C]-8.75907713504265[/C][/ROW]
[ROW][C]67[/C][C]156[/C][C]164.516428546165[/C][C]-8.51642854616486[/C][/ROW]
[ROW][C]68[/C][C]150[/C][C]148.678087249781[/C][C]1.32191275021859[/C][/ROW]
[ROW][C]69[/C][C]141[/C][C]128.133678679823[/C][C]12.8663213201768[/C][/ROW]
[ROW][C]70[/C][C]141[/C][C]130.535987136545[/C][C]10.4640128634553[/C][/ROW]
[ROW][C]71[/C][C]130[/C][C]125.685792605626[/C][C]4.31420739437417[/C][/ROW]
[ROW][C]72[/C][C]110[/C][C]109.908054843376[/C][C]0.0919451566242344[/C][/ROW]
[ROW][C]73[/C][C]110[/C][C]113.872899699601[/C][C]-3.87289969960085[/C][/ROW]
[ROW][C]74[/C][C]123[/C][C]118.77559341369[/C][C]4.22440658631007[/C][/ROW]
[ROW][C]75[/C][C]133[/C][C]121.951142846415[/C][C]11.0488571535854[/C][/ROW]
[ROW][C]76[/C][C]108[/C][C]104.739263304073[/C][C]3.26073669592736[/C][/ROW]
[ROW][C]77[/C][C]136[/C][C]137.503112304349[/C][C]-1.50311230434946[/C][/ROW]
[ROW][C]78[/C][C]148[/C][C]154.195462198873[/C][C]-6.19546219887343[/C][/ROW]
[ROW][C]79[/C][C]146[/C][C]145.61218507426[/C][C]0.387814925740059[/C][/ROW]
[ROW][C]80[/C][C]142[/C][C]141.170484652482[/C][C]0.829515347518281[/C][/ROW]
[ROW][C]81[/C][C]132[/C][C]132.828042550505[/C][C]-0.828042550504676[/C][/ROW]
[ROW][C]82[/C][C]128[/C][C]132.930614025063[/C][C]-4.93061402506288[/C][/ROW]
[ROW][C]83[/C][C]116[/C][C]121.505053755462[/C][C]-5.50505375546159[/C][/ROW]
[ROW][C]84[/C][C]90[/C][C]100.927978890333[/C][C]-10.9279788903328[/C][/ROW]
[ROW][C]85[/C][C]94[/C][C]99.7414824027497[/C][C]-5.74148240274971[/C][/ROW]
[ROW][C]86[/C][C]112[/C][C]111.240855117183[/C][C]0.759144882817367[/C][/ROW]
[ROW][C]87[/C][C]130[/C][C]119.559250889388[/C][C]10.4407491106124[/C][/ROW]
[ROW][C]88[/C][C]106[/C][C]94.2329371370489[/C][C]11.7670628629511[/C][/ROW]
[ROW][C]89[/C][C]124[/C][C]122.769941575378[/C][C]1.23005842462219[/C][/ROW]
[ROW][C]90[/C][C]139[/C][C]134.966930183316[/C][C]4.03306981668436[/C][/ROW]
[ROW][C]91[/C][C]140[/C][C]133.323299682312[/C][C]6.67670031768796[/C][/ROW]
[ROW][C]92[/C][C]129[/C][C]130.135863923285[/C][C]-1.13586392328509[/C][/ROW]
[ROW][C]93[/C][C]113[/C][C]120.373212526736[/C][C]-7.3732125267355[/C][/ROW]
[ROW][C]94[/C][C]110[/C][C]116.148191486384[/C][C]-6.14819148638428[/C][/ROW]
[ROW][C]95[/C][C]102[/C][C]104.010994923377[/C][C]-2.01099492337667[/C][/ROW]
[ROW][C]96[/C][C]78[/C][C]78.7870260431467[/C][C]-0.787026043146724[/C][/ROW]
[ROW][C]97[/C][C]79[/C][C]83.7040876445314[/C][C]-4.70408764453141[/C][/ROW]
[ROW][C]98[/C][C]94[/C][C]101.843201351779[/C][C]-7.84320135177886[/C][/ROW]
[ROW][C]99[/C][C]121[/C][C]118.58203675963[/C][C]2.41796324037026[/C][/ROW]
[ROW][C]100[/C][C]99[/C][C]93.6683094556083[/C][C]5.33169054439168[/C][/ROW]
[ROW][C]101[/C][C]126[/C][C]111.530570438581[/C][C]14.4694295614192[/C][/ROW]
[ROW][C]102[/C][C]137[/C][C]127.48768947702[/C][C]9.51231052298024[/C][/ROW]
[ROW][C]103[/C][C]141[/C][C]129.088923336126[/C][C]11.9110766638744[/C][/ROW]
[ROW][C]104[/C][C]119[/C][C]119.732940866378[/C][C]-0.732940866377803[/C][/ROW]
[ROW][C]105[/C][C]96[/C][C]104.887998510694[/C][C]-8.88799851069437[/C][/ROW]
[ROW][C]106[/C][C]96[/C][C]102.232808955541[/C][C]-6.23280895554109[/C][/ROW]
[ROW][C]107[/C][C]88[/C][C]94.4565400634072[/C][C]-6.45654006340723[/C][/ROW]
[ROW][C]108[/C][C]64[/C][C]70.3664040880459[/C][C]-6.3664040880459[/C][/ROW]
[ROW][C]109[/C][C]66[/C][C]71.3432707304009[/C][C]-5.34327073040092[/C][/ROW]
[ROW][C]110[/C][C]92[/C][C]86.6208822651947[/C][C]5.37911773480531[/C][/ROW]
[ROW][C]111[/C][C]120[/C][C]114.527758892658[/C][C]5.47224110734193[/C][/ROW]
[ROW][C]112[/C][C]101[/C][C]93.3483381687937[/C][C]7.65166183120631[/C][/ROW]
[ROW][C]113[/C][C]135[/C][C]120.722242415195[/C][C]14.2777575848052[/C][/ROW]
[ROW][C]114[/C][C]146[/C][C]133.004248381612[/C][C]12.9957516183878[/C][/ROW]
[ROW][C]115[/C][C]149[/C][C]138.151122996754[/C][C]10.8488770032456[/C][/ROW]
[ROW][C]116[/C][C]134[/C][C]118.081121472517[/C][C]15.9188785274825[/C][/ROW]
[ROW][C]117[/C][C]101[/C][C]98.8042601087432[/C][C]2.19573989125684[/C][/ROW]
[ROW][C]118[/C][C]100[/C][C]101.728109586083[/C][C]-1.72810958608258[/C][/ROW]
[ROW][C]119[/C][C]91[/C][C]96.5610802243557[/C][C]-5.56108022435569[/C][/ROW]
[ROW][C]120[/C][C]70[/C][C]75.123720550656[/C][C]-5.12372055065605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78767&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78767&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13123123.276442307692-0.276442307692349
14125124.9646366639710.0353633360290075
15120119.4290926461850.570907353815045
16124122.3365256219171.66347437808288
17146142.9883320547393.01166794526083
18149145.3401824677293.65981753227146
19138134.4490656870083.55093431299221
20133126.333522249026.66647775097978
21135129.8050711655215.19492883447887
22149132.30972004603716.6902799539635
23146137.1390110367838.86098896321678
24141142.495935745696-1.49593574569636
25139143.3782527994-4.37825279940037
26141147.002878135421-6.00287813542059
27138143.185850174811-5.1858501748107
28139148.088937454503-9.08893745450308
29166170.094402311978-4.09440231197826
30179173.125270633885.87472936612002
31167163.05300778783.94699221219969
32154158.59937570586-4.59937570585984
33151160.080788699166-9.08078869916619
34162171.657813834142-9.65781383414182
35148165.627582953401-17.6275829534015
36143156.598773996173-13.5987739961728
37145150.574333937181-5.57433393718148
38143149.259898986482-6.25989898648169
39148142.8150265856185.18497341438209
40139142.04971996595-3.04971996594961
41169166.5081949620942.49180503790561
42186176.9115329206749.08846707932588
43174163.1335646340610.8664353659399
44161149.48286576565211.5171342343484
45151146.9608337838434.03916621615659
46158158.480836698389-0.480836698388572
47144145.685262734181-1.68526273418064
48135142.190234103142-7.1902341031417
49139144.911787570036-5.91178757003632
50137143.773644487554-6.7736444875541
51149148.6385165606760.361483439323592
52136140.503515057763-4.50351505776274
53169170.479767868892-1.47976786889225
54185186.995212738657-1.99521273865719
55177173.832269617593.16773038240993
56164159.681287859264.31871214074042
57145148.890491093191-3.89049109319132
58147154.452240451531-7.45224045153097
59142138.5148995861073.48510041389281
60126129.110591936456-3.1105919364561
61130132.266018324703-2.26601832470334
62136129.7199333099096.28006669009096
63139141.870716395263-2.87071639526283
64120128.537421602323-8.5374216023232
65151160.335522998079-9.33552299807911
66166174.759077135043-8.75907713504265
67156164.516428546165-8.51642854616486
68150148.6780872497811.32191275021859
69141128.13367867982312.8663213201768
70141130.53598713654510.4640128634553
71130125.6857926056264.31420739437417
72110109.9080548433760.0919451566242344
73110113.872899699601-3.87289969960085
74123118.775593413694.22440658631007
75133121.95114284641511.0488571535854
76108104.7392633040733.26073669592736
77136137.503112304349-1.50311230434946
78148154.195462198873-6.19546219887343
79146145.612185074260.387814925740059
80142141.1704846524820.829515347518281
81132132.828042550505-0.828042550504676
82128132.930614025063-4.93061402506288
83116121.505053755462-5.50505375546159
8490100.927978890333-10.9279788903328
859499.7414824027497-5.74148240274971
86112111.2408551171830.759144882817367
87130119.55925088938810.4407491106124
8810694.232937137048911.7670628629511
89124122.7699415753781.23005842462219
90139134.9669301833164.03306981668436
91140133.3232996823126.67670031768796
92129130.135863923285-1.13586392328509
93113120.373212526736-7.3732125267355
94110116.148191486384-6.14819148638428
95102104.010994923377-2.01099492337667
967878.7870260431467-0.787026043146724
977983.7040876445314-4.70408764453141
9894101.843201351779-7.84320135177886
99121118.582036759632.41796324037026
1009993.66830945560835.33169054439168
101126111.53057043858114.4694295614192
102137127.487689477029.51231052298024
103141129.08892333612611.9110766638744
104119119.732940866378-0.732940866377803
10596104.887998510694-8.88799851069437
10696102.232808955541-6.23280895554109
1078894.4565400634072-6.45654006340723
1086470.3664040880459-6.3664040880459
1096671.3432707304009-5.34327073040092
1109286.62088226519475.37911773480531
111120114.5277588926585.47224110734193
11210193.34833816879377.65166183120631
113135120.72224241519514.2777575848052
114146133.00424838161212.9957516183878
115149138.15112299675410.8488770032456
116134118.08112147251715.9188785274825
11710198.80426010874322.19573989125684
118100101.728109586083-1.72810958608258
1199196.5610802243557-5.56108022435569
1207075.123720550656-5.12372055065605







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12179.695712995719265.862459543035393.5289664484032
122108.06416919531994.1250216746646122.003316715974
123138.184106796005124.050728851806152.317484740205
124120.886241658021106.447207942657135.325275373385
125155.720959719386140.845846974394170.596072464377
126167.017055834475151.561590660107182.472521008843
127169.900448660009153.712115009281186.088782310737
128153.896240904136136.819637463057170.972844345215
129120.264428859434102.145783825656138.383073893213
130118.84471364267199.5352324810767138.154194804265
131109.80581145461589.1638188737672130.447804035462
13288.98160296839266.8736437498751111.089562186909

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 79.6957129957192 & 65.8624595430353 & 93.5289664484032 \tabularnewline
122 & 108.064169195319 & 94.1250216746646 & 122.003316715974 \tabularnewline
123 & 138.184106796005 & 124.050728851806 & 152.317484740205 \tabularnewline
124 & 120.886241658021 & 106.447207942657 & 135.325275373385 \tabularnewline
125 & 155.720959719386 & 140.845846974394 & 170.596072464377 \tabularnewline
126 & 167.017055834475 & 151.561590660107 & 182.472521008843 \tabularnewline
127 & 169.900448660009 & 153.712115009281 & 186.088782310737 \tabularnewline
128 & 153.896240904136 & 136.819637463057 & 170.972844345215 \tabularnewline
129 & 120.264428859434 & 102.145783825656 & 138.383073893213 \tabularnewline
130 & 118.844713642671 & 99.5352324810767 & 138.154194804265 \tabularnewline
131 & 109.805811454615 & 89.1638188737672 & 130.447804035462 \tabularnewline
132 & 88.981602968392 & 66.8736437498751 & 111.089562186909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78767&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]79.6957129957192[/C][C]65.8624595430353[/C][C]93.5289664484032[/C][/ROW]
[ROW][C]122[/C][C]108.064169195319[/C][C]94.1250216746646[/C][C]122.003316715974[/C][/ROW]
[ROW][C]123[/C][C]138.184106796005[/C][C]124.050728851806[/C][C]152.317484740205[/C][/ROW]
[ROW][C]124[/C][C]120.886241658021[/C][C]106.447207942657[/C][C]135.325275373385[/C][/ROW]
[ROW][C]125[/C][C]155.720959719386[/C][C]140.845846974394[/C][C]170.596072464377[/C][/ROW]
[ROW][C]126[/C][C]167.017055834475[/C][C]151.561590660107[/C][C]182.472521008843[/C][/ROW]
[ROW][C]127[/C][C]169.900448660009[/C][C]153.712115009281[/C][C]186.088782310737[/C][/ROW]
[ROW][C]128[/C][C]153.896240904136[/C][C]136.819637463057[/C][C]170.972844345215[/C][/ROW]
[ROW][C]129[/C][C]120.264428859434[/C][C]102.145783825656[/C][C]138.383073893213[/C][/ROW]
[ROW][C]130[/C][C]118.844713642671[/C][C]99.5352324810767[/C][C]138.154194804265[/C][/ROW]
[ROW][C]131[/C][C]109.805811454615[/C][C]89.1638188737672[/C][C]130.447804035462[/C][/ROW]
[ROW][C]132[/C][C]88.981602968392[/C][C]66.8736437498751[/C][C]111.089562186909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78767&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78767&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12179.695712995719265.862459543035393.5289664484032
122108.06416919531994.1250216746646122.003316715974
123138.184106796005124.050728851806152.317484740205
124120.886241658021106.447207942657135.325275373385
125155.720959719386140.845846974394170.596072464377
126167.017055834475151.561590660107182.472521008843
127169.900448660009153.712115009281186.088782310737
128153.896240904136136.819637463057170.972844345215
129120.264428859434102.145783825656138.383073893213
130118.84471364267199.5352324810767138.154194804265
131109.80581145461589.1638188737672130.447804035462
13288.98160296839266.8736437498751111.089562186909



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')