Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 Jul 2010 14:45:56 +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/Jul/28/t1280328581gd06i6x7m8lgcyu.htm/, Retrieved Mon, 29 Apr 2024 12:07:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78149, Retrieved Mon, 29 Apr 2024 12:07:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPatrick Fieremans
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 - Sta...] [2010-07-28 14:45:56] [bffa0fb6afa860209dcefcd4361c2008] [Current]
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Dataseries X:
136
135
134
132
152
151
136
126
127
127
128
130
125
118
111
104
126
131
122
116
115
115
113
122
114
106
93
89
114
122
115
116
120
120
120
121
118
112
99
96
120
135
128
134
134
132
130
125
124
114
101
101
123
143
133
136
137
135
141
136
133
124
110
104
130
160
142
142
137
135
139
135
134
120
103
101
127
159
141
140
135
127
130
128
126
110
101
102
129
169
146
145
138
123
124
137
132
112
105
106
137
175
151
142
140
122
127
135
128
117
107
108
134
171
154
146
148
122
124
135




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78149&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78149&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78149&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.206674112244381
beta0.156145216303958
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.206674112244381 \tabularnewline
beta & 0.156145216303958 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78149&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]0.206674112244381[/C][/ROW]
[ROW][C]beta[/C][C]0.156145216303958[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78149&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78149&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
alpha0.206674112244381
beta0.156145216303958
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13125136.497707249167-11.497707249167
14118125.868466827844-7.86846682784406
15111115.829465823458-4.82946582345791
16104106.517461771267-2.51746177126746
17126127.127195352308-1.12719535230811
18131130.3363770692460.663622930753945
19122117.3261376985834.67386230141722
20116108.4338194745947.56618052540635
21115110.3614957766544.63850422334642
22115111.3559418773383.64405812266216
23113113.273838994097-0.273838994097034
24122114.9652564896567.03474351034428
25114104.1127774854359.88722251456544
26106101.8949632190544.10503678094598
279398.2124211486975-5.21242114869752
288992.1233403863731-3.12334038637309
29114111.8307866699072.16921333009276
30122117.5966650050094.40333499499071
31115110.5418781565744.45812184342579
32116105.52823531858110.4717646814189
33120107.02989266023212.9701073397680
34120110.4944931997389.5055068002625
35120112.3089172687277.6910827312734
36121123.663846534212-2.66384653421156
37118114.5959931703023.40400682969825
38112107.7550316866564.24496831334436
399997.65882511407761.34117488592241
409695.87529522178720.124704778212759
41120124.446887300445-4.44688730044543
42135133.2076489799291.79235102007070
43128126.7061949120451.29380508795455
44134127.2222128793296.77778712067129
45134131.3694334121172.63056658788315
46132130.7282574391741.271742560826
47130129.9526631786310.0473368213690435
48125132.14519310741-7.14519310740994
49124127.014338051243-3.01433805124296
50114119.134346479543-5.134346479543
51101103.923333356148-2.92333335614836
5210199.88622195722541.11377804277460
53123125.771961793655-2.77196179365495
54143140.1801027739592.81989722604084
55133132.9493904192990.0506095807014333
56136137.394194343486-1.39419434348619
57137135.9948190573891.00518094261091
58135133.3182188753441.68178112465566
59141131.0763840874449.92361591255647
60136129.2165399147636.78346008523744
61133130.4053245252632.59467547473665
62124121.8061907732392.19380922676073
63110109.4638471252840.536152874716379
64104109.946623474011-5.946623474011
65130133.486170377532-3.4861703775322
66160154.2499542315275.75004576847334
67142145.131414581241-3.13141458124142
68142148.535983295595-6.53598329559478
69137148.363336605893-11.3633366058930
70135143.435306155354-8.43530615535431
71139145.300218303875-6.3002183038752
72135136.499747085003-1.49974708500298
73134131.5127804089532.48721959104736
74120121.599293388196-1.5992933881964
75103106.460309284893-3.4603092848927
76101100.0420962280680.95790377193218
77127124.9061878618062.09381213819428
78159151.9897706621277.01022933787294
79141135.8591155984575.14088440154296
80140137.5052103373232.49478966267679
81135134.9114319980350.0885680019652568
82127134.539329979635-7.53932997963528
83130138.113277855539-8.11327785553866
84128132.699208207592-4.69920820759233
85126130.026352503398-4.02635250339841
86110115.626259796421-5.62625979642135
8710198.4619669704522.53803302954793
8810296.61515522030165.38484477969838
89129122.3208375139756.67916248602478
90169153.42060080737215.579399192628
91146138.0836704157657.9163295842352
92145138.5474224498676.45257755013265
93138135.3126717551082.68732824489229
94123129.816666734662-6.81666673466157
95124133.592182462144-9.5921824621443
96137131.0165047409615.98349525903944
97132131.8490651713880.150934828611526
98112117.160761905490-5.16076190548961
99105106.839523079279-1.83952307927935
100106106.952241870461-0.952241870460966
101137134.0579205170652.94207948293533
102175173.3226573412091.67734265879105
103151148.2918430012982.70815699870235
104142146.257365484352-4.25736548435154
105140137.3107207990502.68927920095015
106122123.797097441325-1.79709744132461
107127126.0164005045880.983599495412335
108135138.187228930160-3.1872289301603
109128132.225310477006-4.22531047700616
110117112.1402934263114.8597065736893
111107106.4340320354510.565967964548932
112108107.8239585374400.176041462560207
113134138.899016279422-4.89901627942174
114171175.614202884575-4.61420288457478
115154149.8240444858014.17595551419856
116146142.3083824973103.69161750268964
117148140.4843956529357.51560434706499
118122124.278204568723-2.27820456872307
119124128.792888611097-4.79288861109745
120135136.432504114121-1.43250411412075

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 125 & 136.497707249167 & -11.497707249167 \tabularnewline
14 & 118 & 125.868466827844 & -7.86846682784406 \tabularnewline
15 & 111 & 115.829465823458 & -4.82946582345791 \tabularnewline
16 & 104 & 106.517461771267 & -2.51746177126746 \tabularnewline
17 & 126 & 127.127195352308 & -1.12719535230811 \tabularnewline
18 & 131 & 130.336377069246 & 0.663622930753945 \tabularnewline
19 & 122 & 117.326137698583 & 4.67386230141722 \tabularnewline
20 & 116 & 108.433819474594 & 7.56618052540635 \tabularnewline
21 & 115 & 110.361495776654 & 4.63850422334642 \tabularnewline
22 & 115 & 111.355941877338 & 3.64405812266216 \tabularnewline
23 & 113 & 113.273838994097 & -0.273838994097034 \tabularnewline
24 & 122 & 114.965256489656 & 7.03474351034428 \tabularnewline
25 & 114 & 104.112777485435 & 9.88722251456544 \tabularnewline
26 & 106 & 101.894963219054 & 4.10503678094598 \tabularnewline
27 & 93 & 98.2124211486975 & -5.21242114869752 \tabularnewline
28 & 89 & 92.1233403863731 & -3.12334038637309 \tabularnewline
29 & 114 & 111.830786669907 & 2.16921333009276 \tabularnewline
30 & 122 & 117.596665005009 & 4.40333499499071 \tabularnewline
31 & 115 & 110.541878156574 & 4.45812184342579 \tabularnewline
32 & 116 & 105.528235318581 & 10.4717646814189 \tabularnewline
33 & 120 & 107.029892660232 & 12.9701073397680 \tabularnewline
34 & 120 & 110.494493199738 & 9.5055068002625 \tabularnewline
35 & 120 & 112.308917268727 & 7.6910827312734 \tabularnewline
36 & 121 & 123.663846534212 & -2.66384653421156 \tabularnewline
37 & 118 & 114.595993170302 & 3.40400682969825 \tabularnewline
38 & 112 & 107.755031686656 & 4.24496831334436 \tabularnewline
39 & 99 & 97.6588251140776 & 1.34117488592241 \tabularnewline
40 & 96 & 95.8752952217872 & 0.124704778212759 \tabularnewline
41 & 120 & 124.446887300445 & -4.44688730044543 \tabularnewline
42 & 135 & 133.207648979929 & 1.79235102007070 \tabularnewline
43 & 128 & 126.706194912045 & 1.29380508795455 \tabularnewline
44 & 134 & 127.222212879329 & 6.77778712067129 \tabularnewline
45 & 134 & 131.369433412117 & 2.63056658788315 \tabularnewline
46 & 132 & 130.728257439174 & 1.271742560826 \tabularnewline
47 & 130 & 129.952663178631 & 0.0473368213690435 \tabularnewline
48 & 125 & 132.14519310741 & -7.14519310740994 \tabularnewline
49 & 124 & 127.014338051243 & -3.01433805124296 \tabularnewline
50 & 114 & 119.134346479543 & -5.134346479543 \tabularnewline
51 & 101 & 103.923333356148 & -2.92333335614836 \tabularnewline
52 & 101 & 99.8862219572254 & 1.11377804277460 \tabularnewline
53 & 123 & 125.771961793655 & -2.77196179365495 \tabularnewline
54 & 143 & 140.180102773959 & 2.81989722604084 \tabularnewline
55 & 133 & 132.949390419299 & 0.0506095807014333 \tabularnewline
56 & 136 & 137.394194343486 & -1.39419434348619 \tabularnewline
57 & 137 & 135.994819057389 & 1.00518094261091 \tabularnewline
58 & 135 & 133.318218875344 & 1.68178112465566 \tabularnewline
59 & 141 & 131.076384087444 & 9.92361591255647 \tabularnewline
60 & 136 & 129.216539914763 & 6.78346008523744 \tabularnewline
61 & 133 & 130.405324525263 & 2.59467547473665 \tabularnewline
62 & 124 & 121.806190773239 & 2.19380922676073 \tabularnewline
63 & 110 & 109.463847125284 & 0.536152874716379 \tabularnewline
64 & 104 & 109.946623474011 & -5.946623474011 \tabularnewline
65 & 130 & 133.486170377532 & -3.4861703775322 \tabularnewline
66 & 160 & 154.249954231527 & 5.75004576847334 \tabularnewline
67 & 142 & 145.131414581241 & -3.13141458124142 \tabularnewline
68 & 142 & 148.535983295595 & -6.53598329559478 \tabularnewline
69 & 137 & 148.363336605893 & -11.3633366058930 \tabularnewline
70 & 135 & 143.435306155354 & -8.43530615535431 \tabularnewline
71 & 139 & 145.300218303875 & -6.3002183038752 \tabularnewline
72 & 135 & 136.499747085003 & -1.49974708500298 \tabularnewline
73 & 134 & 131.512780408953 & 2.48721959104736 \tabularnewline
74 & 120 & 121.599293388196 & -1.5992933881964 \tabularnewline
75 & 103 & 106.460309284893 & -3.4603092848927 \tabularnewline
76 & 101 & 100.042096228068 & 0.95790377193218 \tabularnewline
77 & 127 & 124.906187861806 & 2.09381213819428 \tabularnewline
78 & 159 & 151.989770662127 & 7.01022933787294 \tabularnewline
79 & 141 & 135.859115598457 & 5.14088440154296 \tabularnewline
80 & 140 & 137.505210337323 & 2.49478966267679 \tabularnewline
81 & 135 & 134.911431998035 & 0.0885680019652568 \tabularnewline
82 & 127 & 134.539329979635 & -7.53932997963528 \tabularnewline
83 & 130 & 138.113277855539 & -8.11327785553866 \tabularnewline
84 & 128 & 132.699208207592 & -4.69920820759233 \tabularnewline
85 & 126 & 130.026352503398 & -4.02635250339841 \tabularnewline
86 & 110 & 115.626259796421 & -5.62625979642135 \tabularnewline
87 & 101 & 98.461966970452 & 2.53803302954793 \tabularnewline
88 & 102 & 96.6151552203016 & 5.38484477969838 \tabularnewline
89 & 129 & 122.320837513975 & 6.67916248602478 \tabularnewline
90 & 169 & 153.420600807372 & 15.579399192628 \tabularnewline
91 & 146 & 138.083670415765 & 7.9163295842352 \tabularnewline
92 & 145 & 138.547422449867 & 6.45257755013265 \tabularnewline
93 & 138 & 135.312671755108 & 2.68732824489229 \tabularnewline
94 & 123 & 129.816666734662 & -6.81666673466157 \tabularnewline
95 & 124 & 133.592182462144 & -9.5921824621443 \tabularnewline
96 & 137 & 131.016504740961 & 5.98349525903944 \tabularnewline
97 & 132 & 131.849065171388 & 0.150934828611526 \tabularnewline
98 & 112 & 117.160761905490 & -5.16076190548961 \tabularnewline
99 & 105 & 106.839523079279 & -1.83952307927935 \tabularnewline
100 & 106 & 106.952241870461 & -0.952241870460966 \tabularnewline
101 & 137 & 134.057920517065 & 2.94207948293533 \tabularnewline
102 & 175 & 173.322657341209 & 1.67734265879105 \tabularnewline
103 & 151 & 148.291843001298 & 2.70815699870235 \tabularnewline
104 & 142 & 146.257365484352 & -4.25736548435154 \tabularnewline
105 & 140 & 137.310720799050 & 2.68927920095015 \tabularnewline
106 & 122 & 123.797097441325 & -1.79709744132461 \tabularnewline
107 & 127 & 126.016400504588 & 0.983599495412335 \tabularnewline
108 & 135 & 138.187228930160 & -3.1872289301603 \tabularnewline
109 & 128 & 132.225310477006 & -4.22531047700616 \tabularnewline
110 & 117 & 112.140293426311 & 4.8597065736893 \tabularnewline
111 & 107 & 106.434032035451 & 0.565967964548932 \tabularnewline
112 & 108 & 107.823958537440 & 0.176041462560207 \tabularnewline
113 & 134 & 138.899016279422 & -4.89901627942174 \tabularnewline
114 & 171 & 175.614202884575 & -4.61420288457478 \tabularnewline
115 & 154 & 149.824044485801 & 4.17595551419856 \tabularnewline
116 & 146 & 142.308382497310 & 3.69161750268964 \tabularnewline
117 & 148 & 140.484395652935 & 7.51560434706499 \tabularnewline
118 & 122 & 124.278204568723 & -2.27820456872307 \tabularnewline
119 & 124 & 128.792888611097 & -4.79288861109745 \tabularnewline
120 & 135 & 136.432504114121 & -1.43250411412075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78149&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]125[/C][C]136.497707249167[/C][C]-11.497707249167[/C][/ROW]
[ROW][C]14[/C][C]118[/C][C]125.868466827844[/C][C]-7.86846682784406[/C][/ROW]
[ROW][C]15[/C][C]111[/C][C]115.829465823458[/C][C]-4.82946582345791[/C][/ROW]
[ROW][C]16[/C][C]104[/C][C]106.517461771267[/C][C]-2.51746177126746[/C][/ROW]
[ROW][C]17[/C][C]126[/C][C]127.127195352308[/C][C]-1.12719535230811[/C][/ROW]
[ROW][C]18[/C][C]131[/C][C]130.336377069246[/C][C]0.663622930753945[/C][/ROW]
[ROW][C]19[/C][C]122[/C][C]117.326137698583[/C][C]4.67386230141722[/C][/ROW]
[ROW][C]20[/C][C]116[/C][C]108.433819474594[/C][C]7.56618052540635[/C][/ROW]
[ROW][C]21[/C][C]115[/C][C]110.361495776654[/C][C]4.63850422334642[/C][/ROW]
[ROW][C]22[/C][C]115[/C][C]111.355941877338[/C][C]3.64405812266216[/C][/ROW]
[ROW][C]23[/C][C]113[/C][C]113.273838994097[/C][C]-0.273838994097034[/C][/ROW]
[ROW][C]24[/C][C]122[/C][C]114.965256489656[/C][C]7.03474351034428[/C][/ROW]
[ROW][C]25[/C][C]114[/C][C]104.112777485435[/C][C]9.88722251456544[/C][/ROW]
[ROW][C]26[/C][C]106[/C][C]101.894963219054[/C][C]4.10503678094598[/C][/ROW]
[ROW][C]27[/C][C]93[/C][C]98.2124211486975[/C][C]-5.21242114869752[/C][/ROW]
[ROW][C]28[/C][C]89[/C][C]92.1233403863731[/C][C]-3.12334038637309[/C][/ROW]
[ROW][C]29[/C][C]114[/C][C]111.830786669907[/C][C]2.16921333009276[/C][/ROW]
[ROW][C]30[/C][C]122[/C][C]117.596665005009[/C][C]4.40333499499071[/C][/ROW]
[ROW][C]31[/C][C]115[/C][C]110.541878156574[/C][C]4.45812184342579[/C][/ROW]
[ROW][C]32[/C][C]116[/C][C]105.528235318581[/C][C]10.4717646814189[/C][/ROW]
[ROW][C]33[/C][C]120[/C][C]107.029892660232[/C][C]12.9701073397680[/C][/ROW]
[ROW][C]34[/C][C]120[/C][C]110.494493199738[/C][C]9.5055068002625[/C][/ROW]
[ROW][C]35[/C][C]120[/C][C]112.308917268727[/C][C]7.6910827312734[/C][/ROW]
[ROW][C]36[/C][C]121[/C][C]123.663846534212[/C][C]-2.66384653421156[/C][/ROW]
[ROW][C]37[/C][C]118[/C][C]114.595993170302[/C][C]3.40400682969825[/C][/ROW]
[ROW][C]38[/C][C]112[/C][C]107.755031686656[/C][C]4.24496831334436[/C][/ROW]
[ROW][C]39[/C][C]99[/C][C]97.6588251140776[/C][C]1.34117488592241[/C][/ROW]
[ROW][C]40[/C][C]96[/C][C]95.8752952217872[/C][C]0.124704778212759[/C][/ROW]
[ROW][C]41[/C][C]120[/C][C]124.446887300445[/C][C]-4.44688730044543[/C][/ROW]
[ROW][C]42[/C][C]135[/C][C]133.207648979929[/C][C]1.79235102007070[/C][/ROW]
[ROW][C]43[/C][C]128[/C][C]126.706194912045[/C][C]1.29380508795455[/C][/ROW]
[ROW][C]44[/C][C]134[/C][C]127.222212879329[/C][C]6.77778712067129[/C][/ROW]
[ROW][C]45[/C][C]134[/C][C]131.369433412117[/C][C]2.63056658788315[/C][/ROW]
[ROW][C]46[/C][C]132[/C][C]130.728257439174[/C][C]1.271742560826[/C][/ROW]
[ROW][C]47[/C][C]130[/C][C]129.952663178631[/C][C]0.0473368213690435[/C][/ROW]
[ROW][C]48[/C][C]125[/C][C]132.14519310741[/C][C]-7.14519310740994[/C][/ROW]
[ROW][C]49[/C][C]124[/C][C]127.014338051243[/C][C]-3.01433805124296[/C][/ROW]
[ROW][C]50[/C][C]114[/C][C]119.134346479543[/C][C]-5.134346479543[/C][/ROW]
[ROW][C]51[/C][C]101[/C][C]103.923333356148[/C][C]-2.92333335614836[/C][/ROW]
[ROW][C]52[/C][C]101[/C][C]99.8862219572254[/C][C]1.11377804277460[/C][/ROW]
[ROW][C]53[/C][C]123[/C][C]125.771961793655[/C][C]-2.77196179365495[/C][/ROW]
[ROW][C]54[/C][C]143[/C][C]140.180102773959[/C][C]2.81989722604084[/C][/ROW]
[ROW][C]55[/C][C]133[/C][C]132.949390419299[/C][C]0.0506095807014333[/C][/ROW]
[ROW][C]56[/C][C]136[/C][C]137.394194343486[/C][C]-1.39419434348619[/C][/ROW]
[ROW][C]57[/C][C]137[/C][C]135.994819057389[/C][C]1.00518094261091[/C][/ROW]
[ROW][C]58[/C][C]135[/C][C]133.318218875344[/C][C]1.68178112465566[/C][/ROW]
[ROW][C]59[/C][C]141[/C][C]131.076384087444[/C][C]9.92361591255647[/C][/ROW]
[ROW][C]60[/C][C]136[/C][C]129.216539914763[/C][C]6.78346008523744[/C][/ROW]
[ROW][C]61[/C][C]133[/C][C]130.405324525263[/C][C]2.59467547473665[/C][/ROW]
[ROW][C]62[/C][C]124[/C][C]121.806190773239[/C][C]2.19380922676073[/C][/ROW]
[ROW][C]63[/C][C]110[/C][C]109.463847125284[/C][C]0.536152874716379[/C][/ROW]
[ROW][C]64[/C][C]104[/C][C]109.946623474011[/C][C]-5.946623474011[/C][/ROW]
[ROW][C]65[/C][C]130[/C][C]133.486170377532[/C][C]-3.4861703775322[/C][/ROW]
[ROW][C]66[/C][C]160[/C][C]154.249954231527[/C][C]5.75004576847334[/C][/ROW]
[ROW][C]67[/C][C]142[/C][C]145.131414581241[/C][C]-3.13141458124142[/C][/ROW]
[ROW][C]68[/C][C]142[/C][C]148.535983295595[/C][C]-6.53598329559478[/C][/ROW]
[ROW][C]69[/C][C]137[/C][C]148.363336605893[/C][C]-11.3633366058930[/C][/ROW]
[ROW][C]70[/C][C]135[/C][C]143.435306155354[/C][C]-8.43530615535431[/C][/ROW]
[ROW][C]71[/C][C]139[/C][C]145.300218303875[/C][C]-6.3002183038752[/C][/ROW]
[ROW][C]72[/C][C]135[/C][C]136.499747085003[/C][C]-1.49974708500298[/C][/ROW]
[ROW][C]73[/C][C]134[/C][C]131.512780408953[/C][C]2.48721959104736[/C][/ROW]
[ROW][C]74[/C][C]120[/C][C]121.599293388196[/C][C]-1.5992933881964[/C][/ROW]
[ROW][C]75[/C][C]103[/C][C]106.460309284893[/C][C]-3.4603092848927[/C][/ROW]
[ROW][C]76[/C][C]101[/C][C]100.042096228068[/C][C]0.95790377193218[/C][/ROW]
[ROW][C]77[/C][C]127[/C][C]124.906187861806[/C][C]2.09381213819428[/C][/ROW]
[ROW][C]78[/C][C]159[/C][C]151.989770662127[/C][C]7.01022933787294[/C][/ROW]
[ROW][C]79[/C][C]141[/C][C]135.859115598457[/C][C]5.14088440154296[/C][/ROW]
[ROW][C]80[/C][C]140[/C][C]137.505210337323[/C][C]2.49478966267679[/C][/ROW]
[ROW][C]81[/C][C]135[/C][C]134.911431998035[/C][C]0.0885680019652568[/C][/ROW]
[ROW][C]82[/C][C]127[/C][C]134.539329979635[/C][C]-7.53932997963528[/C][/ROW]
[ROW][C]83[/C][C]130[/C][C]138.113277855539[/C][C]-8.11327785553866[/C][/ROW]
[ROW][C]84[/C][C]128[/C][C]132.699208207592[/C][C]-4.69920820759233[/C][/ROW]
[ROW][C]85[/C][C]126[/C][C]130.026352503398[/C][C]-4.02635250339841[/C][/ROW]
[ROW][C]86[/C][C]110[/C][C]115.626259796421[/C][C]-5.62625979642135[/C][/ROW]
[ROW][C]87[/C][C]101[/C][C]98.461966970452[/C][C]2.53803302954793[/C][/ROW]
[ROW][C]88[/C][C]102[/C][C]96.6151552203016[/C][C]5.38484477969838[/C][/ROW]
[ROW][C]89[/C][C]129[/C][C]122.320837513975[/C][C]6.67916248602478[/C][/ROW]
[ROW][C]90[/C][C]169[/C][C]153.420600807372[/C][C]15.579399192628[/C][/ROW]
[ROW][C]91[/C][C]146[/C][C]138.083670415765[/C][C]7.9163295842352[/C][/ROW]
[ROW][C]92[/C][C]145[/C][C]138.547422449867[/C][C]6.45257755013265[/C][/ROW]
[ROW][C]93[/C][C]138[/C][C]135.312671755108[/C][C]2.68732824489229[/C][/ROW]
[ROW][C]94[/C][C]123[/C][C]129.816666734662[/C][C]-6.81666673466157[/C][/ROW]
[ROW][C]95[/C][C]124[/C][C]133.592182462144[/C][C]-9.5921824621443[/C][/ROW]
[ROW][C]96[/C][C]137[/C][C]131.016504740961[/C][C]5.98349525903944[/C][/ROW]
[ROW][C]97[/C][C]132[/C][C]131.849065171388[/C][C]0.150934828611526[/C][/ROW]
[ROW][C]98[/C][C]112[/C][C]117.160761905490[/C][C]-5.16076190548961[/C][/ROW]
[ROW][C]99[/C][C]105[/C][C]106.839523079279[/C][C]-1.83952307927935[/C][/ROW]
[ROW][C]100[/C][C]106[/C][C]106.952241870461[/C][C]-0.952241870460966[/C][/ROW]
[ROW][C]101[/C][C]137[/C][C]134.057920517065[/C][C]2.94207948293533[/C][/ROW]
[ROW][C]102[/C][C]175[/C][C]173.322657341209[/C][C]1.67734265879105[/C][/ROW]
[ROW][C]103[/C][C]151[/C][C]148.291843001298[/C][C]2.70815699870235[/C][/ROW]
[ROW][C]104[/C][C]142[/C][C]146.257365484352[/C][C]-4.25736548435154[/C][/ROW]
[ROW][C]105[/C][C]140[/C][C]137.310720799050[/C][C]2.68927920095015[/C][/ROW]
[ROW][C]106[/C][C]122[/C][C]123.797097441325[/C][C]-1.79709744132461[/C][/ROW]
[ROW][C]107[/C][C]127[/C][C]126.016400504588[/C][C]0.983599495412335[/C][/ROW]
[ROW][C]108[/C][C]135[/C][C]138.187228930160[/C][C]-3.1872289301603[/C][/ROW]
[ROW][C]109[/C][C]128[/C][C]132.225310477006[/C][C]-4.22531047700616[/C][/ROW]
[ROW][C]110[/C][C]117[/C][C]112.140293426311[/C][C]4.8597065736893[/C][/ROW]
[ROW][C]111[/C][C]107[/C][C]106.434032035451[/C][C]0.565967964548932[/C][/ROW]
[ROW][C]112[/C][C]108[/C][C]107.823958537440[/C][C]0.176041462560207[/C][/ROW]
[ROW][C]113[/C][C]134[/C][C]138.899016279422[/C][C]-4.89901627942174[/C][/ROW]
[ROW][C]114[/C][C]171[/C][C]175.614202884575[/C][C]-4.61420288457478[/C][/ROW]
[ROW][C]115[/C][C]154[/C][C]149.824044485801[/C][C]4.17595551419856[/C][/ROW]
[ROW][C]116[/C][C]146[/C][C]142.308382497310[/C][C]3.69161750268964[/C][/ROW]
[ROW][C]117[/C][C]148[/C][C]140.484395652935[/C][C]7.51560434706499[/C][/ROW]
[ROW][C]118[/C][C]122[/C][C]124.278204568723[/C][C]-2.27820456872307[/C][/ROW]
[ROW][C]119[/C][C]124[/C][C]128.792888611097[/C][C]-4.79288861109745[/C][/ROW]
[ROW][C]120[/C][C]135[/C][C]136.432504114121[/C][C]-1.43250411412075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78149&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78149&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
13125136.497707249167-11.497707249167
14118125.868466827844-7.86846682784406
15111115.829465823458-4.82946582345791
16104106.517461771267-2.51746177126746
17126127.127195352308-1.12719535230811
18131130.3363770692460.663622930753945
19122117.3261376985834.67386230141722
20116108.4338194745947.56618052540635
21115110.3614957766544.63850422334642
22115111.3559418773383.64405812266216
23113113.273838994097-0.273838994097034
24122114.9652564896567.03474351034428
25114104.1127774854359.88722251456544
26106101.8949632190544.10503678094598
279398.2124211486975-5.21242114869752
288992.1233403863731-3.12334038637309
29114111.8307866699072.16921333009276
30122117.5966650050094.40333499499071
31115110.5418781565744.45812184342579
32116105.52823531858110.4717646814189
33120107.02989266023212.9701073397680
34120110.4944931997389.5055068002625
35120112.3089172687277.6910827312734
36121123.663846534212-2.66384653421156
37118114.5959931703023.40400682969825
38112107.7550316866564.24496831334436
399997.65882511407761.34117488592241
409695.87529522178720.124704778212759
41120124.446887300445-4.44688730044543
42135133.2076489799291.79235102007070
43128126.7061949120451.29380508795455
44134127.2222128793296.77778712067129
45134131.3694334121172.63056658788315
46132130.7282574391741.271742560826
47130129.9526631786310.0473368213690435
48125132.14519310741-7.14519310740994
49124127.014338051243-3.01433805124296
50114119.134346479543-5.134346479543
51101103.923333356148-2.92333335614836
5210199.88622195722541.11377804277460
53123125.771961793655-2.77196179365495
54143140.1801027739592.81989722604084
55133132.9493904192990.0506095807014333
56136137.394194343486-1.39419434348619
57137135.9948190573891.00518094261091
58135133.3182188753441.68178112465566
59141131.0763840874449.92361591255647
60136129.2165399147636.78346008523744
61133130.4053245252632.59467547473665
62124121.8061907732392.19380922676073
63110109.4638471252840.536152874716379
64104109.946623474011-5.946623474011
65130133.486170377532-3.4861703775322
66160154.2499542315275.75004576847334
67142145.131414581241-3.13141458124142
68142148.535983295595-6.53598329559478
69137148.363336605893-11.3633366058930
70135143.435306155354-8.43530615535431
71139145.300218303875-6.3002183038752
72135136.499747085003-1.49974708500298
73134131.5127804089532.48721959104736
74120121.599293388196-1.5992933881964
75103106.460309284893-3.4603092848927
76101100.0420962280680.95790377193218
77127124.9061878618062.09381213819428
78159151.9897706621277.01022933787294
79141135.8591155984575.14088440154296
80140137.5052103373232.49478966267679
81135134.9114319980350.0885680019652568
82127134.539329979635-7.53932997963528
83130138.113277855539-8.11327785553866
84128132.699208207592-4.69920820759233
85126130.026352503398-4.02635250339841
86110115.626259796421-5.62625979642135
8710198.4619669704522.53803302954793
8810296.61515522030165.38484477969838
89129122.3208375139756.67916248602478
90169153.42060080737215.579399192628
91146138.0836704157657.9163295842352
92145138.5474224498676.45257755013265
93138135.3126717551082.68732824489229
94123129.816666734662-6.81666673466157
95124133.592182462144-9.5921824621443
96137131.0165047409615.98349525903944
97132131.8490651713880.150934828611526
98112117.160761905490-5.16076190548961
99105106.839523079279-1.83952307927935
100106106.952241870461-0.952241870460966
101137134.0579205170652.94207948293533
102175173.3226573412091.67734265879105
103151148.2918430012982.70815699870235
104142146.257365484352-4.25736548435154
105140137.3107207990502.68927920095015
106122123.797097441325-1.79709744132461
107127126.0164005045880.983599495412335
108135138.187228930160-3.1872289301603
109128132.225310477006-4.22531047700616
110117112.1402934263114.8597065736893
111107106.4340320354510.565967964548932
112108107.8239585374400.176041462560207
113134138.899016279422-4.89901627942174
114171175.614202884575-4.61420288457478
115154149.8240444858014.17595551419856
116146142.3083824973103.69161750268964
117148140.4843956529357.51560434706499
118122124.278204568723-2.27820456872307
119124128.792888611097-4.79288861109745
120135136.432504114121-1.43250411412075







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121129.920542091987119.61912351386140.221960670115
122117.809395866572107.269169687027128.349622046116
123107.57117446856796.7773312182415118.365017718892
124108.47029897920597.2599351972896119.680662761120
125135.477907013571123.077610847703147.87820317944
126173.907459891797159.306299443702188.508620339891
127155.923697153213141.23034115805170.617053148375
128147.094206191856131.965590877942162.222821505770
129147.414793932782131.332818210342163.496769655222
130121.720603655513106.470496083891136.970711227135
131124.483372343429108.152042446747140.814702240111
132135.774713610729-40.0558894088902311.605316630347

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 129.920542091987 & 119.61912351386 & 140.221960670115 \tabularnewline
122 & 117.809395866572 & 107.269169687027 & 128.349622046116 \tabularnewline
123 & 107.571174468567 & 96.7773312182415 & 118.365017718892 \tabularnewline
124 & 108.470298979205 & 97.2599351972896 & 119.680662761120 \tabularnewline
125 & 135.477907013571 & 123.077610847703 & 147.87820317944 \tabularnewline
126 & 173.907459891797 & 159.306299443702 & 188.508620339891 \tabularnewline
127 & 155.923697153213 & 141.23034115805 & 170.617053148375 \tabularnewline
128 & 147.094206191856 & 131.965590877942 & 162.222821505770 \tabularnewline
129 & 147.414793932782 & 131.332818210342 & 163.496769655222 \tabularnewline
130 & 121.720603655513 & 106.470496083891 & 136.970711227135 \tabularnewline
131 & 124.483372343429 & 108.152042446747 & 140.814702240111 \tabularnewline
132 & 135.774713610729 & -40.0558894088902 & 311.605316630347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78149&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]129.920542091987[/C][C]119.61912351386[/C][C]140.221960670115[/C][/ROW]
[ROW][C]122[/C][C]117.809395866572[/C][C]107.269169687027[/C][C]128.349622046116[/C][/ROW]
[ROW][C]123[/C][C]107.571174468567[/C][C]96.7773312182415[/C][C]118.365017718892[/C][/ROW]
[ROW][C]124[/C][C]108.470298979205[/C][C]97.2599351972896[/C][C]119.680662761120[/C][/ROW]
[ROW][C]125[/C][C]135.477907013571[/C][C]123.077610847703[/C][C]147.87820317944[/C][/ROW]
[ROW][C]126[/C][C]173.907459891797[/C][C]159.306299443702[/C][C]188.508620339891[/C][/ROW]
[ROW][C]127[/C][C]155.923697153213[/C][C]141.23034115805[/C][C]170.617053148375[/C][/ROW]
[ROW][C]128[/C][C]147.094206191856[/C][C]131.965590877942[/C][C]162.222821505770[/C][/ROW]
[ROW][C]129[/C][C]147.414793932782[/C][C]131.332818210342[/C][C]163.496769655222[/C][/ROW]
[ROW][C]130[/C][C]121.720603655513[/C][C]106.470496083891[/C][C]136.970711227135[/C][/ROW]
[ROW][C]131[/C][C]124.483372343429[/C][C]108.152042446747[/C][C]140.814702240111[/C][/ROW]
[ROW][C]132[/C][C]135.774713610729[/C][C]-40.0558894088902[/C][C]311.605316630347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78149&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78149&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
121129.920542091987119.61912351386140.221960670115
122117.809395866572107.269169687027128.349622046116
123107.57117446856796.7773312182415118.365017718892
124108.47029897920597.2599351972896119.680662761120
125135.477907013571123.077610847703147.87820317944
126173.907459891797159.306299443702188.508620339891
127155.923697153213141.23034115805170.617053148375
128147.094206191856131.965590877942162.222821505770
129147.414793932782131.332818210342163.496769655222
130121.720603655513106.470496083891136.970711227135
131124.483372343429108.152042446747140.814702240111
132135.774713610729-40.0558894088902311.605316630347



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')