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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 07:58:26 -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/Dec/21/t13560947283ayg598f3jgcuvz.htm/, Retrieved Fri, 26 Apr 2024 10:22:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203588, Retrieved Fri, 26 Apr 2024 10:22:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Classical Decomposition] [Classical Decompo...] [2011-12-19 14:36:02] [920204e71d7e82687d0571379c55a021]
- RMPD    [Exponential Smoothing] [] [2012-12-21 12:33:31] [63daa42bab46576bcb233b0e49169cb8]
-   PD        [Exponential Smoothing] [] [2012-12-21 12:58:26] [7f1e2e1b7f66b13ad70fccbed4479dd6] [Current]
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Dataseries X:
127
150
130
119
129
129
131
126
131
119
127
137
124
152
134
119
131
133
131
134
136
122
131
138
131
166
134
121
140
137
134
141
139
129
136
140
133
171
136
121
143
143
143
143
147
133
140
144
143
172
145
127
153
149
145
154
149
141
149
150
145
175
152
139
153
157
161
159
155
146
162
156
141
186
159
140
159
158
157
153
161
142
152
162
146
190
154
132
155
155
150
163
160
149
171
176
156
198
157
139
160
167
162
159
169
153
161
169
156
205
167
150
174
163
163
168
168
156
170
177




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203588&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203588&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203588&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.11399538654434
beta0.00965850494570268
gamma0.391350432513914

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.11399538654434 \tabularnewline
beta & 0.00965850494570268 \tabularnewline
gamma & 0.391350432513914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203588&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]0.11399538654434[/C][/ROW]
[ROW][C]beta[/C][C]0.00965850494570268[/C][/ROW]
[ROW][C]gamma[/C][C]0.391350432513914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203588&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203588&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
alpha0.11399538654434
beta0.00965850494570268
gamma0.391350432513914







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13124122.9513888888891.04861111111114
14152150.9925348103431.00746518965721
15134132.8217661976081.1782338023923
16119117.8800950171021.11990498289779
17131129.9746743303271.02532566967253
18133132.1429342807160.85706571928381
19131133.084623690475-2.0846236904747
20134128.1470121893995.85298781060092
21136133.8290293988922.17097060110751
22122122.177037259577-0.177037259576508
23131130.3405214674560.659478532543517
24138140.433424052097-2.43342405209734
25131127.6179977058263.3820022941741
26166155.92469964768910.0753003523112
27134138.870645396162-4.87064539616247
28121123.236356061138-2.23635606113764
29140134.9289985056925.07100149430772
30137137.518014734136-0.518014734135903
31134137.299351032176-3.29935103217613
32141134.9905986690736.00940133092709
33139139.428980790049-0.428980790049138
34129126.6788301858782.32116981412224
35136135.4322693438740.567730656126258
36140144.457303142767-4.45730314276742
37133133.44038435319-0.440384353189643
38171163.6407554793997.35924452060104
39136141.100342209864-5.10034220986449
40121126.358615039778-5.35861503977773
41143140.2309748996262.76902510037414
42143140.6190158640422.38098413595813
43143139.7689860881733.23101391182669
44143141.4421133779511.55788662204893
45147143.1454558440863.854544155914
46133131.8467521877271.15324781227349
47140139.8673455730910.132654426909056
48144147.108208479618-3.10820847961776
49143137.6471826020675.35281739793328
50172171.2280432268180.771956773181614
51145143.6249022525841.37509774741562
52127129.547330394717-2.54733039471665
53153146.5769611726026.4230388273981
54149147.26965074981.73034925020008
55145146.662129668641-1.66212966864106
56154147.2138765980976.78612340190267
57149150.331862186072-1.33186218607156
58141137.5218880456753.47811195432507
59149145.4727849303633.52721506963707
60150151.999776844253-1.99977684425298
61145145.622985116503-0.622985116502804
62175176.951808965751-1.95180896575147
63152149.2618413140822.73815868591765
64139133.9956348390545.0043651609457
65153155.020847895223-2.020847895223
66157153.1388946091923.86110539080789
67161151.6153699999659.38463000003483
68159156.3852945753622.61470542463803
69155156.237913688124-1.23791368812414
70146145.1315272446620.868472755337649
71162152.8241657518169.17583424818363
72156158.107076267089-2.1070762670887
73141152.223742960846-11.2237429608461
74186181.9000071681914.09999283180861
75159156.5494034980342.45059650196563
76140142.059175341276-2.05917534127556
77159159.858468405688-0.858468405688114
78158160.165000635197-2.16500063519658
79157159.87959151707-2.8795915170702
80153160.900402449983-7.90040244998266
81161158.2032629130342.796737086966
82142148.276380821481-6.27638082148141
83152158.016360574935-6.01636057493451
84162157.619828183134.38017181686951
85146149.286670741969-3.28667074196889
86190185.161546324974.83845367503011
87154159.304523822189-5.30452382218897
88132142.339307472581-10.3393074725813
89155159.574688427074-4.57468842707351
90155158.96412600319-3.96412600318996
91150158.183430025591-8.18343002559126
92163156.8104619398326.1895380601681
93160159.3958733443750.604126655624526
94149146.0378871534192.96211284658108
95171156.89618410236814.103815897632
96176162.39530023549113.6046997645088
97156152.4626303716693.53736962833113
98198191.9475420659916.05245793400866
99157162.728123693276-5.72812369327639
100139143.984572156592-4.98457215659207
101160163.850783584317-3.85078358431656
102167163.5568465884123.44315341158784
103162162.188105880241-0.188105880240528
104159166.749583115633-7.74958311563327
105169165.8333325979533.16666740204721
106153153.611899324267-0.611899324267313
107161167.948926344231-6.9489263442305
108169170.874780639178-1.87478063917774
109156155.6694656305580.330534369442347
110205195.6400325395299.35996746047104
111167162.695660155884.30433984411977
112150145.3474108339854.65258916601468
113174166.7097827252167.29021727478428
114163170.23166280506-7.23166280505995
115163166.391899568373-3.39189956837268
116168167.9677318753970.0322681246025525
117168171.733652982087-3.73365298208722
118156157.417838294134-1.41783829413356
119170169.467211762050.5327882379502
120177175.0150948325581.98490516744235

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 124 & 122.951388888889 & 1.04861111111114 \tabularnewline
14 & 152 & 150.992534810343 & 1.00746518965721 \tabularnewline
15 & 134 & 132.821766197608 & 1.1782338023923 \tabularnewline
16 & 119 & 117.880095017102 & 1.11990498289779 \tabularnewline
17 & 131 & 129.974674330327 & 1.02532566967253 \tabularnewline
18 & 133 & 132.142934280716 & 0.85706571928381 \tabularnewline
19 & 131 & 133.084623690475 & -2.0846236904747 \tabularnewline
20 & 134 & 128.147012189399 & 5.85298781060092 \tabularnewline
21 & 136 & 133.829029398892 & 2.17097060110751 \tabularnewline
22 & 122 & 122.177037259577 & -0.177037259576508 \tabularnewline
23 & 131 & 130.340521467456 & 0.659478532543517 \tabularnewline
24 & 138 & 140.433424052097 & -2.43342405209734 \tabularnewline
25 & 131 & 127.617997705826 & 3.3820022941741 \tabularnewline
26 & 166 & 155.924699647689 & 10.0753003523112 \tabularnewline
27 & 134 & 138.870645396162 & -4.87064539616247 \tabularnewline
28 & 121 & 123.236356061138 & -2.23635606113764 \tabularnewline
29 & 140 & 134.928998505692 & 5.07100149430772 \tabularnewline
30 & 137 & 137.518014734136 & -0.518014734135903 \tabularnewline
31 & 134 & 137.299351032176 & -3.29935103217613 \tabularnewline
32 & 141 & 134.990598669073 & 6.00940133092709 \tabularnewline
33 & 139 & 139.428980790049 & -0.428980790049138 \tabularnewline
34 & 129 & 126.678830185878 & 2.32116981412224 \tabularnewline
35 & 136 & 135.432269343874 & 0.567730656126258 \tabularnewline
36 & 140 & 144.457303142767 & -4.45730314276742 \tabularnewline
37 & 133 & 133.44038435319 & -0.440384353189643 \tabularnewline
38 & 171 & 163.640755479399 & 7.35924452060104 \tabularnewline
39 & 136 & 141.100342209864 & -5.10034220986449 \tabularnewline
40 & 121 & 126.358615039778 & -5.35861503977773 \tabularnewline
41 & 143 & 140.230974899626 & 2.76902510037414 \tabularnewline
42 & 143 & 140.619015864042 & 2.38098413595813 \tabularnewline
43 & 143 & 139.768986088173 & 3.23101391182669 \tabularnewline
44 & 143 & 141.442113377951 & 1.55788662204893 \tabularnewline
45 & 147 & 143.145455844086 & 3.854544155914 \tabularnewline
46 & 133 & 131.846752187727 & 1.15324781227349 \tabularnewline
47 & 140 & 139.867345573091 & 0.132654426909056 \tabularnewline
48 & 144 & 147.108208479618 & -3.10820847961776 \tabularnewline
49 & 143 & 137.647182602067 & 5.35281739793328 \tabularnewline
50 & 172 & 171.228043226818 & 0.771956773181614 \tabularnewline
51 & 145 & 143.624902252584 & 1.37509774741562 \tabularnewline
52 & 127 & 129.547330394717 & -2.54733039471665 \tabularnewline
53 & 153 & 146.576961172602 & 6.4230388273981 \tabularnewline
54 & 149 & 147.2696507498 & 1.73034925020008 \tabularnewline
55 & 145 & 146.662129668641 & -1.66212966864106 \tabularnewline
56 & 154 & 147.213876598097 & 6.78612340190267 \tabularnewline
57 & 149 & 150.331862186072 & -1.33186218607156 \tabularnewline
58 & 141 & 137.521888045675 & 3.47811195432507 \tabularnewline
59 & 149 & 145.472784930363 & 3.52721506963707 \tabularnewline
60 & 150 & 151.999776844253 & -1.99977684425298 \tabularnewline
61 & 145 & 145.622985116503 & -0.622985116502804 \tabularnewline
62 & 175 & 176.951808965751 & -1.95180896575147 \tabularnewline
63 & 152 & 149.261841314082 & 2.73815868591765 \tabularnewline
64 & 139 & 133.995634839054 & 5.0043651609457 \tabularnewline
65 & 153 & 155.020847895223 & -2.020847895223 \tabularnewline
66 & 157 & 153.138894609192 & 3.86110539080789 \tabularnewline
67 & 161 & 151.615369999965 & 9.38463000003483 \tabularnewline
68 & 159 & 156.385294575362 & 2.61470542463803 \tabularnewline
69 & 155 & 156.237913688124 & -1.23791368812414 \tabularnewline
70 & 146 & 145.131527244662 & 0.868472755337649 \tabularnewline
71 & 162 & 152.824165751816 & 9.17583424818363 \tabularnewline
72 & 156 & 158.107076267089 & -2.1070762670887 \tabularnewline
73 & 141 & 152.223742960846 & -11.2237429608461 \tabularnewline
74 & 186 & 181.900007168191 & 4.09999283180861 \tabularnewline
75 & 159 & 156.549403498034 & 2.45059650196563 \tabularnewline
76 & 140 & 142.059175341276 & -2.05917534127556 \tabularnewline
77 & 159 & 159.858468405688 & -0.858468405688114 \tabularnewline
78 & 158 & 160.165000635197 & -2.16500063519658 \tabularnewline
79 & 157 & 159.87959151707 & -2.8795915170702 \tabularnewline
80 & 153 & 160.900402449983 & -7.90040244998266 \tabularnewline
81 & 161 & 158.203262913034 & 2.796737086966 \tabularnewline
82 & 142 & 148.276380821481 & -6.27638082148141 \tabularnewline
83 & 152 & 158.016360574935 & -6.01636057493451 \tabularnewline
84 & 162 & 157.61982818313 & 4.38017181686951 \tabularnewline
85 & 146 & 149.286670741969 & -3.28667074196889 \tabularnewline
86 & 190 & 185.16154632497 & 4.83845367503011 \tabularnewline
87 & 154 & 159.304523822189 & -5.30452382218897 \tabularnewline
88 & 132 & 142.339307472581 & -10.3393074725813 \tabularnewline
89 & 155 & 159.574688427074 & -4.57468842707351 \tabularnewline
90 & 155 & 158.96412600319 & -3.96412600318996 \tabularnewline
91 & 150 & 158.183430025591 & -8.18343002559126 \tabularnewline
92 & 163 & 156.810461939832 & 6.1895380601681 \tabularnewline
93 & 160 & 159.395873344375 & 0.604126655624526 \tabularnewline
94 & 149 & 146.037887153419 & 2.96211284658108 \tabularnewline
95 & 171 & 156.896184102368 & 14.103815897632 \tabularnewline
96 & 176 & 162.395300235491 & 13.6046997645088 \tabularnewline
97 & 156 & 152.462630371669 & 3.53736962833113 \tabularnewline
98 & 198 & 191.947542065991 & 6.05245793400866 \tabularnewline
99 & 157 & 162.728123693276 & -5.72812369327639 \tabularnewline
100 & 139 & 143.984572156592 & -4.98457215659207 \tabularnewline
101 & 160 & 163.850783584317 & -3.85078358431656 \tabularnewline
102 & 167 & 163.556846588412 & 3.44315341158784 \tabularnewline
103 & 162 & 162.188105880241 & -0.188105880240528 \tabularnewline
104 & 159 & 166.749583115633 & -7.74958311563327 \tabularnewline
105 & 169 & 165.833332597953 & 3.16666740204721 \tabularnewline
106 & 153 & 153.611899324267 & -0.611899324267313 \tabularnewline
107 & 161 & 167.948926344231 & -6.9489263442305 \tabularnewline
108 & 169 & 170.874780639178 & -1.87478063917774 \tabularnewline
109 & 156 & 155.669465630558 & 0.330534369442347 \tabularnewline
110 & 205 & 195.640032539529 & 9.35996746047104 \tabularnewline
111 & 167 & 162.69566015588 & 4.30433984411977 \tabularnewline
112 & 150 & 145.347410833985 & 4.65258916601468 \tabularnewline
113 & 174 & 166.709782725216 & 7.29021727478428 \tabularnewline
114 & 163 & 170.23166280506 & -7.23166280505995 \tabularnewline
115 & 163 & 166.391899568373 & -3.39189956837268 \tabularnewline
116 & 168 & 167.967731875397 & 0.0322681246025525 \tabularnewline
117 & 168 & 171.733652982087 & -3.73365298208722 \tabularnewline
118 & 156 & 157.417838294134 & -1.41783829413356 \tabularnewline
119 & 170 & 169.46721176205 & 0.5327882379502 \tabularnewline
120 & 177 & 175.015094832558 & 1.98490516744235 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203588&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]124[/C][C]122.951388888889[/C][C]1.04861111111114[/C][/ROW]
[ROW][C]14[/C][C]152[/C][C]150.992534810343[/C][C]1.00746518965721[/C][/ROW]
[ROW][C]15[/C][C]134[/C][C]132.821766197608[/C][C]1.1782338023923[/C][/ROW]
[ROW][C]16[/C][C]119[/C][C]117.880095017102[/C][C]1.11990498289779[/C][/ROW]
[ROW][C]17[/C][C]131[/C][C]129.974674330327[/C][C]1.02532566967253[/C][/ROW]
[ROW][C]18[/C][C]133[/C][C]132.142934280716[/C][C]0.85706571928381[/C][/ROW]
[ROW][C]19[/C][C]131[/C][C]133.084623690475[/C][C]-2.0846236904747[/C][/ROW]
[ROW][C]20[/C][C]134[/C][C]128.147012189399[/C][C]5.85298781060092[/C][/ROW]
[ROW][C]21[/C][C]136[/C][C]133.829029398892[/C][C]2.17097060110751[/C][/ROW]
[ROW][C]22[/C][C]122[/C][C]122.177037259577[/C][C]-0.177037259576508[/C][/ROW]
[ROW][C]23[/C][C]131[/C][C]130.340521467456[/C][C]0.659478532543517[/C][/ROW]
[ROW][C]24[/C][C]138[/C][C]140.433424052097[/C][C]-2.43342405209734[/C][/ROW]
[ROW][C]25[/C][C]131[/C][C]127.617997705826[/C][C]3.3820022941741[/C][/ROW]
[ROW][C]26[/C][C]166[/C][C]155.924699647689[/C][C]10.0753003523112[/C][/ROW]
[ROW][C]27[/C][C]134[/C][C]138.870645396162[/C][C]-4.87064539616247[/C][/ROW]
[ROW][C]28[/C][C]121[/C][C]123.236356061138[/C][C]-2.23635606113764[/C][/ROW]
[ROW][C]29[/C][C]140[/C][C]134.928998505692[/C][C]5.07100149430772[/C][/ROW]
[ROW][C]30[/C][C]137[/C][C]137.518014734136[/C][C]-0.518014734135903[/C][/ROW]
[ROW][C]31[/C][C]134[/C][C]137.299351032176[/C][C]-3.29935103217613[/C][/ROW]
[ROW][C]32[/C][C]141[/C][C]134.990598669073[/C][C]6.00940133092709[/C][/ROW]
[ROW][C]33[/C][C]139[/C][C]139.428980790049[/C][C]-0.428980790049138[/C][/ROW]
[ROW][C]34[/C][C]129[/C][C]126.678830185878[/C][C]2.32116981412224[/C][/ROW]
[ROW][C]35[/C][C]136[/C][C]135.432269343874[/C][C]0.567730656126258[/C][/ROW]
[ROW][C]36[/C][C]140[/C][C]144.457303142767[/C][C]-4.45730314276742[/C][/ROW]
[ROW][C]37[/C][C]133[/C][C]133.44038435319[/C][C]-0.440384353189643[/C][/ROW]
[ROW][C]38[/C][C]171[/C][C]163.640755479399[/C][C]7.35924452060104[/C][/ROW]
[ROW][C]39[/C][C]136[/C][C]141.100342209864[/C][C]-5.10034220986449[/C][/ROW]
[ROW][C]40[/C][C]121[/C][C]126.358615039778[/C][C]-5.35861503977773[/C][/ROW]
[ROW][C]41[/C][C]143[/C][C]140.230974899626[/C][C]2.76902510037414[/C][/ROW]
[ROW][C]42[/C][C]143[/C][C]140.619015864042[/C][C]2.38098413595813[/C][/ROW]
[ROW][C]43[/C][C]143[/C][C]139.768986088173[/C][C]3.23101391182669[/C][/ROW]
[ROW][C]44[/C][C]143[/C][C]141.442113377951[/C][C]1.55788662204893[/C][/ROW]
[ROW][C]45[/C][C]147[/C][C]143.145455844086[/C][C]3.854544155914[/C][/ROW]
[ROW][C]46[/C][C]133[/C][C]131.846752187727[/C][C]1.15324781227349[/C][/ROW]
[ROW][C]47[/C][C]140[/C][C]139.867345573091[/C][C]0.132654426909056[/C][/ROW]
[ROW][C]48[/C][C]144[/C][C]147.108208479618[/C][C]-3.10820847961776[/C][/ROW]
[ROW][C]49[/C][C]143[/C][C]137.647182602067[/C][C]5.35281739793328[/C][/ROW]
[ROW][C]50[/C][C]172[/C][C]171.228043226818[/C][C]0.771956773181614[/C][/ROW]
[ROW][C]51[/C][C]145[/C][C]143.624902252584[/C][C]1.37509774741562[/C][/ROW]
[ROW][C]52[/C][C]127[/C][C]129.547330394717[/C][C]-2.54733039471665[/C][/ROW]
[ROW][C]53[/C][C]153[/C][C]146.576961172602[/C][C]6.4230388273981[/C][/ROW]
[ROW][C]54[/C][C]149[/C][C]147.2696507498[/C][C]1.73034925020008[/C][/ROW]
[ROW][C]55[/C][C]145[/C][C]146.662129668641[/C][C]-1.66212966864106[/C][/ROW]
[ROW][C]56[/C][C]154[/C][C]147.213876598097[/C][C]6.78612340190267[/C][/ROW]
[ROW][C]57[/C][C]149[/C][C]150.331862186072[/C][C]-1.33186218607156[/C][/ROW]
[ROW][C]58[/C][C]141[/C][C]137.521888045675[/C][C]3.47811195432507[/C][/ROW]
[ROW][C]59[/C][C]149[/C][C]145.472784930363[/C][C]3.52721506963707[/C][/ROW]
[ROW][C]60[/C][C]150[/C][C]151.999776844253[/C][C]-1.99977684425298[/C][/ROW]
[ROW][C]61[/C][C]145[/C][C]145.622985116503[/C][C]-0.622985116502804[/C][/ROW]
[ROW][C]62[/C][C]175[/C][C]176.951808965751[/C][C]-1.95180896575147[/C][/ROW]
[ROW][C]63[/C][C]152[/C][C]149.261841314082[/C][C]2.73815868591765[/C][/ROW]
[ROW][C]64[/C][C]139[/C][C]133.995634839054[/C][C]5.0043651609457[/C][/ROW]
[ROW][C]65[/C][C]153[/C][C]155.020847895223[/C][C]-2.020847895223[/C][/ROW]
[ROW][C]66[/C][C]157[/C][C]153.138894609192[/C][C]3.86110539080789[/C][/ROW]
[ROW][C]67[/C][C]161[/C][C]151.615369999965[/C][C]9.38463000003483[/C][/ROW]
[ROW][C]68[/C][C]159[/C][C]156.385294575362[/C][C]2.61470542463803[/C][/ROW]
[ROW][C]69[/C][C]155[/C][C]156.237913688124[/C][C]-1.23791368812414[/C][/ROW]
[ROW][C]70[/C][C]146[/C][C]145.131527244662[/C][C]0.868472755337649[/C][/ROW]
[ROW][C]71[/C][C]162[/C][C]152.824165751816[/C][C]9.17583424818363[/C][/ROW]
[ROW][C]72[/C][C]156[/C][C]158.107076267089[/C][C]-2.1070762670887[/C][/ROW]
[ROW][C]73[/C][C]141[/C][C]152.223742960846[/C][C]-11.2237429608461[/C][/ROW]
[ROW][C]74[/C][C]186[/C][C]181.900007168191[/C][C]4.09999283180861[/C][/ROW]
[ROW][C]75[/C][C]159[/C][C]156.549403498034[/C][C]2.45059650196563[/C][/ROW]
[ROW][C]76[/C][C]140[/C][C]142.059175341276[/C][C]-2.05917534127556[/C][/ROW]
[ROW][C]77[/C][C]159[/C][C]159.858468405688[/C][C]-0.858468405688114[/C][/ROW]
[ROW][C]78[/C][C]158[/C][C]160.165000635197[/C][C]-2.16500063519658[/C][/ROW]
[ROW][C]79[/C][C]157[/C][C]159.87959151707[/C][C]-2.8795915170702[/C][/ROW]
[ROW][C]80[/C][C]153[/C][C]160.900402449983[/C][C]-7.90040244998266[/C][/ROW]
[ROW][C]81[/C][C]161[/C][C]158.203262913034[/C][C]2.796737086966[/C][/ROW]
[ROW][C]82[/C][C]142[/C][C]148.276380821481[/C][C]-6.27638082148141[/C][/ROW]
[ROW][C]83[/C][C]152[/C][C]158.016360574935[/C][C]-6.01636057493451[/C][/ROW]
[ROW][C]84[/C][C]162[/C][C]157.61982818313[/C][C]4.38017181686951[/C][/ROW]
[ROW][C]85[/C][C]146[/C][C]149.286670741969[/C][C]-3.28667074196889[/C][/ROW]
[ROW][C]86[/C][C]190[/C][C]185.16154632497[/C][C]4.83845367503011[/C][/ROW]
[ROW][C]87[/C][C]154[/C][C]159.304523822189[/C][C]-5.30452382218897[/C][/ROW]
[ROW][C]88[/C][C]132[/C][C]142.339307472581[/C][C]-10.3393074725813[/C][/ROW]
[ROW][C]89[/C][C]155[/C][C]159.574688427074[/C][C]-4.57468842707351[/C][/ROW]
[ROW][C]90[/C][C]155[/C][C]158.96412600319[/C][C]-3.96412600318996[/C][/ROW]
[ROW][C]91[/C][C]150[/C][C]158.183430025591[/C][C]-8.18343002559126[/C][/ROW]
[ROW][C]92[/C][C]163[/C][C]156.810461939832[/C][C]6.1895380601681[/C][/ROW]
[ROW][C]93[/C][C]160[/C][C]159.395873344375[/C][C]0.604126655624526[/C][/ROW]
[ROW][C]94[/C][C]149[/C][C]146.037887153419[/C][C]2.96211284658108[/C][/ROW]
[ROW][C]95[/C][C]171[/C][C]156.896184102368[/C][C]14.103815897632[/C][/ROW]
[ROW][C]96[/C][C]176[/C][C]162.395300235491[/C][C]13.6046997645088[/C][/ROW]
[ROW][C]97[/C][C]156[/C][C]152.462630371669[/C][C]3.53736962833113[/C][/ROW]
[ROW][C]98[/C][C]198[/C][C]191.947542065991[/C][C]6.05245793400866[/C][/ROW]
[ROW][C]99[/C][C]157[/C][C]162.728123693276[/C][C]-5.72812369327639[/C][/ROW]
[ROW][C]100[/C][C]139[/C][C]143.984572156592[/C][C]-4.98457215659207[/C][/ROW]
[ROW][C]101[/C][C]160[/C][C]163.850783584317[/C][C]-3.85078358431656[/C][/ROW]
[ROW][C]102[/C][C]167[/C][C]163.556846588412[/C][C]3.44315341158784[/C][/ROW]
[ROW][C]103[/C][C]162[/C][C]162.188105880241[/C][C]-0.188105880240528[/C][/ROW]
[ROW][C]104[/C][C]159[/C][C]166.749583115633[/C][C]-7.74958311563327[/C][/ROW]
[ROW][C]105[/C][C]169[/C][C]165.833332597953[/C][C]3.16666740204721[/C][/ROW]
[ROW][C]106[/C][C]153[/C][C]153.611899324267[/C][C]-0.611899324267313[/C][/ROW]
[ROW][C]107[/C][C]161[/C][C]167.948926344231[/C][C]-6.9489263442305[/C][/ROW]
[ROW][C]108[/C][C]169[/C][C]170.874780639178[/C][C]-1.87478063917774[/C][/ROW]
[ROW][C]109[/C][C]156[/C][C]155.669465630558[/C][C]0.330534369442347[/C][/ROW]
[ROW][C]110[/C][C]205[/C][C]195.640032539529[/C][C]9.35996746047104[/C][/ROW]
[ROW][C]111[/C][C]167[/C][C]162.69566015588[/C][C]4.30433984411977[/C][/ROW]
[ROW][C]112[/C][C]150[/C][C]145.347410833985[/C][C]4.65258916601468[/C][/ROW]
[ROW][C]113[/C][C]174[/C][C]166.709782725216[/C][C]7.29021727478428[/C][/ROW]
[ROW][C]114[/C][C]163[/C][C]170.23166280506[/C][C]-7.23166280505995[/C][/ROW]
[ROW][C]115[/C][C]163[/C][C]166.391899568373[/C][C]-3.39189956837268[/C][/ROW]
[ROW][C]116[/C][C]168[/C][C]167.967731875397[/C][C]0.0322681246025525[/C][/ROW]
[ROW][C]117[/C][C]168[/C][C]171.733652982087[/C][C]-3.73365298208722[/C][/ROW]
[ROW][C]118[/C][C]156[/C][C]157.417838294134[/C][C]-1.41783829413356[/C][/ROW]
[ROW][C]119[/C][C]170[/C][C]169.46721176205[/C][C]0.5327882379502[/C][/ROW]
[ROW][C]120[/C][C]177[/C][C]175.015094832558[/C][C]1.98490516744235[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203588&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203588&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
13124122.9513888888891.04861111111114
14152150.9925348103431.00746518965721
15134132.8217661976081.1782338023923
16119117.8800950171021.11990498289779
17131129.9746743303271.02532566967253
18133132.1429342807160.85706571928381
19131133.084623690475-2.0846236904747
20134128.1470121893995.85298781060092
21136133.8290293988922.17097060110751
22122122.177037259577-0.177037259576508
23131130.3405214674560.659478532543517
24138140.433424052097-2.43342405209734
25131127.6179977058263.3820022941741
26166155.92469964768910.0753003523112
27134138.870645396162-4.87064539616247
28121123.236356061138-2.23635606113764
29140134.9289985056925.07100149430772
30137137.518014734136-0.518014734135903
31134137.299351032176-3.29935103217613
32141134.9905986690736.00940133092709
33139139.428980790049-0.428980790049138
34129126.6788301858782.32116981412224
35136135.4322693438740.567730656126258
36140144.457303142767-4.45730314276742
37133133.44038435319-0.440384353189643
38171163.6407554793997.35924452060104
39136141.100342209864-5.10034220986449
40121126.358615039778-5.35861503977773
41143140.2309748996262.76902510037414
42143140.6190158640422.38098413595813
43143139.7689860881733.23101391182669
44143141.4421133779511.55788662204893
45147143.1454558440863.854544155914
46133131.8467521877271.15324781227349
47140139.8673455730910.132654426909056
48144147.108208479618-3.10820847961776
49143137.6471826020675.35281739793328
50172171.2280432268180.771956773181614
51145143.6249022525841.37509774741562
52127129.547330394717-2.54733039471665
53153146.5769611726026.4230388273981
54149147.26965074981.73034925020008
55145146.662129668641-1.66212966864106
56154147.2138765980976.78612340190267
57149150.331862186072-1.33186218607156
58141137.5218880456753.47811195432507
59149145.4727849303633.52721506963707
60150151.999776844253-1.99977684425298
61145145.622985116503-0.622985116502804
62175176.951808965751-1.95180896575147
63152149.2618413140822.73815868591765
64139133.9956348390545.0043651609457
65153155.020847895223-2.020847895223
66157153.1388946091923.86110539080789
67161151.6153699999659.38463000003483
68159156.3852945753622.61470542463803
69155156.237913688124-1.23791368812414
70146145.1315272446620.868472755337649
71162152.8241657518169.17583424818363
72156158.107076267089-2.1070762670887
73141152.223742960846-11.2237429608461
74186181.9000071681914.09999283180861
75159156.5494034980342.45059650196563
76140142.059175341276-2.05917534127556
77159159.858468405688-0.858468405688114
78158160.165000635197-2.16500063519658
79157159.87959151707-2.8795915170702
80153160.900402449983-7.90040244998266
81161158.2032629130342.796737086966
82142148.276380821481-6.27638082148141
83152158.016360574935-6.01636057493451
84162157.619828183134.38017181686951
85146149.286670741969-3.28667074196889
86190185.161546324974.83845367503011
87154159.304523822189-5.30452382218897
88132142.339307472581-10.3393074725813
89155159.574688427074-4.57468842707351
90155158.96412600319-3.96412600318996
91150158.183430025591-8.18343002559126
92163156.8104619398326.1895380601681
93160159.3958733443750.604126655624526
94149146.0378871534192.96211284658108
95171156.89618410236814.103815897632
96176162.39530023549113.6046997645088
97156152.4626303716693.53736962833113
98198191.9475420659916.05245793400866
99157162.728123693276-5.72812369327639
100139143.984572156592-4.98457215659207
101160163.850783584317-3.85078358431656
102167163.5568465884123.44315341158784
103162162.188105880241-0.188105880240528
104159166.749583115633-7.74958311563327
105169165.8333325979533.16666740204721
106153153.611899324267-0.611899324267313
107161167.948926344231-6.9489263442305
108169170.874780639178-1.87478063917774
109156155.6694656305580.330534369442347
110205195.6400325395299.35996746047104
111167162.695660155884.30433984411977
112150145.3474108339854.65258916601468
113174166.7097827252167.29021727478428
114163170.23166280506-7.23166280505995
115163166.391899568373-3.39189956837268
116168167.9677318753970.0322681246025525
117168171.733652982087-3.73365298208722
118156157.417838294134-1.41783829413356
119170169.467211762050.5327882379502
120177175.0150948325581.98490516744235







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121161.028430193528151.768523558998170.288336828058
122204.105800802489194.784762115473213.426839489504
123168.344782999419158.961846913122177.727719085717
124150.62519833849141.179603547465160.070793129515
125172.365228740327162.856218057464181.87423942319
126170.00620467945160.433025107167179.579384251732
127168.315611657689158.67751445351177.953708861868
128171.462530563862161.758771300523181.166289827202
129173.916084336045164.145922956314183.686245715776
130160.830081452799150.992782319169170.667380586429
131173.720210894104163.815042833523183.625378954686
132179.713048532805169.739284876621189.686812188989

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 161.028430193528 & 151.768523558998 & 170.288336828058 \tabularnewline
122 & 204.105800802489 & 194.784762115473 & 213.426839489504 \tabularnewline
123 & 168.344782999419 & 158.961846913122 & 177.727719085717 \tabularnewline
124 & 150.62519833849 & 141.179603547465 & 160.070793129515 \tabularnewline
125 & 172.365228740327 & 162.856218057464 & 181.87423942319 \tabularnewline
126 & 170.00620467945 & 160.433025107167 & 179.579384251732 \tabularnewline
127 & 168.315611657689 & 158.67751445351 & 177.953708861868 \tabularnewline
128 & 171.462530563862 & 161.758771300523 & 181.166289827202 \tabularnewline
129 & 173.916084336045 & 164.145922956314 & 183.686245715776 \tabularnewline
130 & 160.830081452799 & 150.992782319169 & 170.667380586429 \tabularnewline
131 & 173.720210894104 & 163.815042833523 & 183.625378954686 \tabularnewline
132 & 179.713048532805 & 169.739284876621 & 189.686812188989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203588&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]161.028430193528[/C][C]151.768523558998[/C][C]170.288336828058[/C][/ROW]
[ROW][C]122[/C][C]204.105800802489[/C][C]194.784762115473[/C][C]213.426839489504[/C][/ROW]
[ROW][C]123[/C][C]168.344782999419[/C][C]158.961846913122[/C][C]177.727719085717[/C][/ROW]
[ROW][C]124[/C][C]150.62519833849[/C][C]141.179603547465[/C][C]160.070793129515[/C][/ROW]
[ROW][C]125[/C][C]172.365228740327[/C][C]162.856218057464[/C][C]181.87423942319[/C][/ROW]
[ROW][C]126[/C][C]170.00620467945[/C][C]160.433025107167[/C][C]179.579384251732[/C][/ROW]
[ROW][C]127[/C][C]168.315611657689[/C][C]158.67751445351[/C][C]177.953708861868[/C][/ROW]
[ROW][C]128[/C][C]171.462530563862[/C][C]161.758771300523[/C][C]181.166289827202[/C][/ROW]
[ROW][C]129[/C][C]173.916084336045[/C][C]164.145922956314[/C][C]183.686245715776[/C][/ROW]
[ROW][C]130[/C][C]160.830081452799[/C][C]150.992782319169[/C][C]170.667380586429[/C][/ROW]
[ROW][C]131[/C][C]173.720210894104[/C][C]163.815042833523[/C][C]183.625378954686[/C][/ROW]
[ROW][C]132[/C][C]179.713048532805[/C][C]169.739284876621[/C][C]189.686812188989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203588&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203588&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
121161.028430193528151.768523558998170.288336828058
122204.105800802489194.784762115473213.426839489504
123168.344782999419158.961846913122177.727719085717
124150.62519833849141.179603547465160.070793129515
125172.365228740327162.856218057464181.87423942319
126170.00620467945160.433025107167179.579384251732
127168.315611657689158.67751445351177.953708861868
128171.462530563862161.758771300523181.166289827202
129173.916084336045164.145922956314183.686245715776
130160.830081452799150.992782319169170.667380586429
131173.720210894104163.815042833523183.625378954686
132179.713048532805169.739284876621189.686812188989



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')