Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Aug 2010 15:29:15 +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/13/t12817133790zip2ss6juwhsvo.htm/, Retrieved Thu, 16 May 2024 06:14:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78756, Retrieved Thu, 16 May 2024 06:14:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsReuben Vermoet
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 - sta...] [2010-08-13 15:29:15] [2c3906e099e396db093769aeca236bf5] [Current]
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Dataseries X:
210
209
208
206
226
225
210
200
201
201
202
204
197
196
187
196
221
218
200
191
194
192
199
196
182
178
169
177
207
213
191
182
188
189
194
195
171
165
156
170
201
208
189
175
184
187
193
199
179
188
171
182
212
216
192
182
183
183
187
190
167
167
158
171
201
208
181
169
173
180
181
192
169
168
156
161
195
208
176
164
170
175
170
175
148
151
143
139
166
186
149
142
138
137
130
138
118
113
99
93
125
146
109
97
97
94
92
103
78
72
57
40
70
89
53
46
43
38
29
34




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78756&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78756&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.113784222520231
beta0.171310491544316
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.113784222520231 \tabularnewline
beta & 0.171310491544316 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78756&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]0.113784222520231[/C][/ROW]
[ROW][C]beta[/C][C]0.171310491544316[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78756&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
alpha0.113784222520231
beta0.171310491544316
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32082080
4206207-1
5226205.8667233463920.1332766536102
6225207.53052665390117.4694733460994
7210209.2317536784960.768246321504307
8200209.047619559445-9.04761955944534
9201207.570234671978-6.57023467197789
10201206.246667251226-5.24666725122609
11202204.971430620551-2.97143062055133
12204203.8971596143380.102840385662120
13197203.174696753514-6.17469675351367
14196201.617589358997-5.61758935899741
15187200.014371522755-13.0143715227546
16196197.315834838771-1.31583483877122
17221195.92275823607925.0772417639212
18218198.02161374154919.9783862584507
19200199.9297272550180.0702727449822191
20191199.573981337151-8.57398133715074
21194198.0675279489-4.06752794890016
22192196.994551847505-4.99455184750499
23199195.7187390948373.28126090516312
24196195.4485430140360.551456985963938
25182194.878487553954-12.8784875539545
26178192.529283264720-14.5292832647204
27169189.709033416174-20.7090334161736
28177185.781956094471-8.78195609447053
29207183.0408103187523.9591896812501
30213184.49211321337428.5078867866265
31191187.0166740903203.98332590967979
32182186.828371581037-4.82837158103661
33188185.5433202233682.45667977663160
34189185.1350794317083.86492056829152
35194184.9624109214949.03758907850568
36195185.5544750584029.44552494159836
37171186.377072104361-15.3770721043614
38165184.075512726154-19.0755127261544
39156180.98130103994-24.9813010399400
40170176.728157533014-6.72815753301447
41201174.42078562150026.5792143784997
42208176.42136063182731.5786393681727
43189179.6063357794509.39366422054977
44175180.450116130771-5.45011613077128
45184179.4986724624454.501327537555
46187179.7672878917127.23271210828793
47193180.48767493312812.5123250668722
48199182.05269426438516.9473057356153
49179184.452688612138-5.4526886121381
50188184.1976308615483.80236913845209
51171185.069770079898-14.0697700798982
52182183.634087808782-1.63408780878163
53212183.58153763238528.4184623676149
54216187.50243843194328.4975615680574
55192191.9878262276210.0121737723792421
56182193.232263616200-11.2322636161996
57183192.978317314319-9.97831731431887
58183192.672548654837-9.67254865483696
59187192.213030156427-5.21303015642684
60190192.159319872079-2.15931987207907
61167192.410983244430-25.4109832444302
62167189.521652337837-22.5216523378369
63158186.522079945827-28.5220799458273
64171182.283788885768-11.2837888857681
65201179.78699489426621.2130051057339
66208181.40131638172126.5986836182789
67181184.146916118982-3.14691611898203
68169183.446594871146-14.4465948711457
69173181.178949206756-8.17894920675616
70180179.4650351275210.534964872479264
71181178.7530547528122.24694524718845
72192178.27966915940213.7203308405978
73169179.379216428855-10.3792164288551
74168177.534299288157-9.53429928815686
75156175.599673715542-19.5996737155419
76161172.137722050047-11.1377220500465
77195169.42150569625425.578494303746
78208171.38160251176236.6183974882377
79176175.3116477174800.688352282520299
80164175.166838323780-11.1668383237804
81170173.455426457595-3.45542645759534
82175172.5540969330262.44590306697356
83170172.371922197232-2.37192219723195
84175171.5953204295313.40467957046872
85148171.542370284688-23.5423702846881
86151167.964372992394-16.9643729923941
87143164.804171136206-21.8041711362058
88139160.668260307724-21.6682603077236
89166156.1254469163059.87455308369456
90186155.36418706825830.6358129317418
91149157.562397503018-8.5623975030175
92142155.133568095981-13.1335680959811
93138151.928606425941-13.9286064259412
94137148.361679536717-11.3616795367167
95130144.865361672413-14.8653616724135
96138140.680618022316-2.68061802231563
97118137.830054192974-19.8300541929741
98113132.641619137428-19.6416191374277
9999127.091762110641-28.0917621106413
10093120.032835398327-27.0328353983267
101125112.56746215751112.4325378424886
102146109.83496611454136.1650338854593
103109110.507798113161-1.50779811316109
10497106.864665561865-9.86466556186487
10597102.078367031523-5.0783670315234
1069497.7376840387952-3.73768403879524
1079293.4766930694786-1.4766930694786
10810389.444182861833113.5558171381669
1097887.3863709721254-9.38637097212543
1107282.5351368560166-10.5351368560166
1115777.3478358777625-20.3478358777625
1124070.6473757818176-30.6473757818176
1137062.17759868505957.82240131494055
1148958.237552884371830.7624471156282
1155357.5073572402528-4.50735724025282
1164652.6761549786559-6.67615497865594
1174347.4680432617241-4.46804326172409
1183842.4240867943552-4.42408679435516
1192937.2988956724757-8.29889567247572
1203431.57104678296662.42895321703341

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 208 & 208 & 0 \tabularnewline
4 & 206 & 207 & -1 \tabularnewline
5 & 226 & 205.86672334639 & 20.1332766536102 \tabularnewline
6 & 225 & 207.530526653901 & 17.4694733460994 \tabularnewline
7 & 210 & 209.231753678496 & 0.768246321504307 \tabularnewline
8 & 200 & 209.047619559445 & -9.04761955944534 \tabularnewline
9 & 201 & 207.570234671978 & -6.57023467197789 \tabularnewline
10 & 201 & 206.246667251226 & -5.24666725122609 \tabularnewline
11 & 202 & 204.971430620551 & -2.97143062055133 \tabularnewline
12 & 204 & 203.897159614338 & 0.102840385662120 \tabularnewline
13 & 197 & 203.174696753514 & -6.17469675351367 \tabularnewline
14 & 196 & 201.617589358997 & -5.61758935899741 \tabularnewline
15 & 187 & 200.014371522755 & -13.0143715227546 \tabularnewline
16 & 196 & 197.315834838771 & -1.31583483877122 \tabularnewline
17 & 221 & 195.922758236079 & 25.0772417639212 \tabularnewline
18 & 218 & 198.021613741549 & 19.9783862584507 \tabularnewline
19 & 200 & 199.929727255018 & 0.0702727449822191 \tabularnewline
20 & 191 & 199.573981337151 & -8.57398133715074 \tabularnewline
21 & 194 & 198.0675279489 & -4.06752794890016 \tabularnewline
22 & 192 & 196.994551847505 & -4.99455184750499 \tabularnewline
23 & 199 & 195.718739094837 & 3.28126090516312 \tabularnewline
24 & 196 & 195.448543014036 & 0.551456985963938 \tabularnewline
25 & 182 & 194.878487553954 & -12.8784875539545 \tabularnewline
26 & 178 & 192.529283264720 & -14.5292832647204 \tabularnewline
27 & 169 & 189.709033416174 & -20.7090334161736 \tabularnewline
28 & 177 & 185.781956094471 & -8.78195609447053 \tabularnewline
29 & 207 & 183.04081031875 & 23.9591896812501 \tabularnewline
30 & 213 & 184.492113213374 & 28.5078867866265 \tabularnewline
31 & 191 & 187.016674090320 & 3.98332590967979 \tabularnewline
32 & 182 & 186.828371581037 & -4.82837158103661 \tabularnewline
33 & 188 & 185.543320223368 & 2.45667977663160 \tabularnewline
34 & 189 & 185.135079431708 & 3.86492056829152 \tabularnewline
35 & 194 & 184.962410921494 & 9.03758907850568 \tabularnewline
36 & 195 & 185.554475058402 & 9.44552494159836 \tabularnewline
37 & 171 & 186.377072104361 & -15.3770721043614 \tabularnewline
38 & 165 & 184.075512726154 & -19.0755127261544 \tabularnewline
39 & 156 & 180.98130103994 & -24.9813010399400 \tabularnewline
40 & 170 & 176.728157533014 & -6.72815753301447 \tabularnewline
41 & 201 & 174.420785621500 & 26.5792143784997 \tabularnewline
42 & 208 & 176.421360631827 & 31.5786393681727 \tabularnewline
43 & 189 & 179.606335779450 & 9.39366422054977 \tabularnewline
44 & 175 & 180.450116130771 & -5.45011613077128 \tabularnewline
45 & 184 & 179.498672462445 & 4.501327537555 \tabularnewline
46 & 187 & 179.767287891712 & 7.23271210828793 \tabularnewline
47 & 193 & 180.487674933128 & 12.5123250668722 \tabularnewline
48 & 199 & 182.052694264385 & 16.9473057356153 \tabularnewline
49 & 179 & 184.452688612138 & -5.4526886121381 \tabularnewline
50 & 188 & 184.197630861548 & 3.80236913845209 \tabularnewline
51 & 171 & 185.069770079898 & -14.0697700798982 \tabularnewline
52 & 182 & 183.634087808782 & -1.63408780878163 \tabularnewline
53 & 212 & 183.581537632385 & 28.4184623676149 \tabularnewline
54 & 216 & 187.502438431943 & 28.4975615680574 \tabularnewline
55 & 192 & 191.987826227621 & 0.0121737723792421 \tabularnewline
56 & 182 & 193.232263616200 & -11.2322636161996 \tabularnewline
57 & 183 & 192.978317314319 & -9.97831731431887 \tabularnewline
58 & 183 & 192.672548654837 & -9.67254865483696 \tabularnewline
59 & 187 & 192.213030156427 & -5.21303015642684 \tabularnewline
60 & 190 & 192.159319872079 & -2.15931987207907 \tabularnewline
61 & 167 & 192.410983244430 & -25.4109832444302 \tabularnewline
62 & 167 & 189.521652337837 & -22.5216523378369 \tabularnewline
63 & 158 & 186.522079945827 & -28.5220799458273 \tabularnewline
64 & 171 & 182.283788885768 & -11.2837888857681 \tabularnewline
65 & 201 & 179.786994894266 & 21.2130051057339 \tabularnewline
66 & 208 & 181.401316381721 & 26.5986836182789 \tabularnewline
67 & 181 & 184.146916118982 & -3.14691611898203 \tabularnewline
68 & 169 & 183.446594871146 & -14.4465948711457 \tabularnewline
69 & 173 & 181.178949206756 & -8.17894920675616 \tabularnewline
70 & 180 & 179.465035127521 & 0.534964872479264 \tabularnewline
71 & 181 & 178.753054752812 & 2.24694524718845 \tabularnewline
72 & 192 & 178.279669159402 & 13.7203308405978 \tabularnewline
73 & 169 & 179.379216428855 & -10.3792164288551 \tabularnewline
74 & 168 & 177.534299288157 & -9.53429928815686 \tabularnewline
75 & 156 & 175.599673715542 & -19.5996737155419 \tabularnewline
76 & 161 & 172.137722050047 & -11.1377220500465 \tabularnewline
77 & 195 & 169.421505696254 & 25.578494303746 \tabularnewline
78 & 208 & 171.381602511762 & 36.6183974882377 \tabularnewline
79 & 176 & 175.311647717480 & 0.688352282520299 \tabularnewline
80 & 164 & 175.166838323780 & -11.1668383237804 \tabularnewline
81 & 170 & 173.455426457595 & -3.45542645759534 \tabularnewline
82 & 175 & 172.554096933026 & 2.44590306697356 \tabularnewline
83 & 170 & 172.371922197232 & -2.37192219723195 \tabularnewline
84 & 175 & 171.595320429531 & 3.40467957046872 \tabularnewline
85 & 148 & 171.542370284688 & -23.5423702846881 \tabularnewline
86 & 151 & 167.964372992394 & -16.9643729923941 \tabularnewline
87 & 143 & 164.804171136206 & -21.8041711362058 \tabularnewline
88 & 139 & 160.668260307724 & -21.6682603077236 \tabularnewline
89 & 166 & 156.125446916305 & 9.87455308369456 \tabularnewline
90 & 186 & 155.364187068258 & 30.6358129317418 \tabularnewline
91 & 149 & 157.562397503018 & -8.5623975030175 \tabularnewline
92 & 142 & 155.133568095981 & -13.1335680959811 \tabularnewline
93 & 138 & 151.928606425941 & -13.9286064259412 \tabularnewline
94 & 137 & 148.361679536717 & -11.3616795367167 \tabularnewline
95 & 130 & 144.865361672413 & -14.8653616724135 \tabularnewline
96 & 138 & 140.680618022316 & -2.68061802231563 \tabularnewline
97 & 118 & 137.830054192974 & -19.8300541929741 \tabularnewline
98 & 113 & 132.641619137428 & -19.6416191374277 \tabularnewline
99 & 99 & 127.091762110641 & -28.0917621106413 \tabularnewline
100 & 93 & 120.032835398327 & -27.0328353983267 \tabularnewline
101 & 125 & 112.567462157511 & 12.4325378424886 \tabularnewline
102 & 146 & 109.834966114541 & 36.1650338854593 \tabularnewline
103 & 109 & 110.507798113161 & -1.50779811316109 \tabularnewline
104 & 97 & 106.864665561865 & -9.86466556186487 \tabularnewline
105 & 97 & 102.078367031523 & -5.0783670315234 \tabularnewline
106 & 94 & 97.7376840387952 & -3.73768403879524 \tabularnewline
107 & 92 & 93.4766930694786 & -1.4766930694786 \tabularnewline
108 & 103 & 89.4441828618331 & 13.5558171381669 \tabularnewline
109 & 78 & 87.3863709721254 & -9.38637097212543 \tabularnewline
110 & 72 & 82.5351368560166 & -10.5351368560166 \tabularnewline
111 & 57 & 77.3478358777625 & -20.3478358777625 \tabularnewline
112 & 40 & 70.6473757818176 & -30.6473757818176 \tabularnewline
113 & 70 & 62.1775986850595 & 7.82240131494055 \tabularnewline
114 & 89 & 58.2375528843718 & 30.7624471156282 \tabularnewline
115 & 53 & 57.5073572402528 & -4.50735724025282 \tabularnewline
116 & 46 & 52.6761549786559 & -6.67615497865594 \tabularnewline
117 & 43 & 47.4680432617241 & -4.46804326172409 \tabularnewline
118 & 38 & 42.4240867943552 & -4.42408679435516 \tabularnewline
119 & 29 & 37.2988956724757 & -8.29889567247572 \tabularnewline
120 & 34 & 31.5710467829666 & 2.42895321703341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78756&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]3[/C][C]208[/C][C]208[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]206[/C][C]207[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]226[/C][C]205.86672334639[/C][C]20.1332766536102[/C][/ROW]
[ROW][C]6[/C][C]225[/C][C]207.530526653901[/C][C]17.4694733460994[/C][/ROW]
[ROW][C]7[/C][C]210[/C][C]209.231753678496[/C][C]0.768246321504307[/C][/ROW]
[ROW][C]8[/C][C]200[/C][C]209.047619559445[/C][C]-9.04761955944534[/C][/ROW]
[ROW][C]9[/C][C]201[/C][C]207.570234671978[/C][C]-6.57023467197789[/C][/ROW]
[ROW][C]10[/C][C]201[/C][C]206.246667251226[/C][C]-5.24666725122609[/C][/ROW]
[ROW][C]11[/C][C]202[/C][C]204.971430620551[/C][C]-2.97143062055133[/C][/ROW]
[ROW][C]12[/C][C]204[/C][C]203.897159614338[/C][C]0.102840385662120[/C][/ROW]
[ROW][C]13[/C][C]197[/C][C]203.174696753514[/C][C]-6.17469675351367[/C][/ROW]
[ROW][C]14[/C][C]196[/C][C]201.617589358997[/C][C]-5.61758935899741[/C][/ROW]
[ROW][C]15[/C][C]187[/C][C]200.014371522755[/C][C]-13.0143715227546[/C][/ROW]
[ROW][C]16[/C][C]196[/C][C]197.315834838771[/C][C]-1.31583483877122[/C][/ROW]
[ROW][C]17[/C][C]221[/C][C]195.922758236079[/C][C]25.0772417639212[/C][/ROW]
[ROW][C]18[/C][C]218[/C][C]198.021613741549[/C][C]19.9783862584507[/C][/ROW]
[ROW][C]19[/C][C]200[/C][C]199.929727255018[/C][C]0.0702727449822191[/C][/ROW]
[ROW][C]20[/C][C]191[/C][C]199.573981337151[/C][C]-8.57398133715074[/C][/ROW]
[ROW][C]21[/C][C]194[/C][C]198.0675279489[/C][C]-4.06752794890016[/C][/ROW]
[ROW][C]22[/C][C]192[/C][C]196.994551847505[/C][C]-4.99455184750499[/C][/ROW]
[ROW][C]23[/C][C]199[/C][C]195.718739094837[/C][C]3.28126090516312[/C][/ROW]
[ROW][C]24[/C][C]196[/C][C]195.448543014036[/C][C]0.551456985963938[/C][/ROW]
[ROW][C]25[/C][C]182[/C][C]194.878487553954[/C][C]-12.8784875539545[/C][/ROW]
[ROW][C]26[/C][C]178[/C][C]192.529283264720[/C][C]-14.5292832647204[/C][/ROW]
[ROW][C]27[/C][C]169[/C][C]189.709033416174[/C][C]-20.7090334161736[/C][/ROW]
[ROW][C]28[/C][C]177[/C][C]185.781956094471[/C][C]-8.78195609447053[/C][/ROW]
[ROW][C]29[/C][C]207[/C][C]183.04081031875[/C][C]23.9591896812501[/C][/ROW]
[ROW][C]30[/C][C]213[/C][C]184.492113213374[/C][C]28.5078867866265[/C][/ROW]
[ROW][C]31[/C][C]191[/C][C]187.016674090320[/C][C]3.98332590967979[/C][/ROW]
[ROW][C]32[/C][C]182[/C][C]186.828371581037[/C][C]-4.82837158103661[/C][/ROW]
[ROW][C]33[/C][C]188[/C][C]185.543320223368[/C][C]2.45667977663160[/C][/ROW]
[ROW][C]34[/C][C]189[/C][C]185.135079431708[/C][C]3.86492056829152[/C][/ROW]
[ROW][C]35[/C][C]194[/C][C]184.962410921494[/C][C]9.03758907850568[/C][/ROW]
[ROW][C]36[/C][C]195[/C][C]185.554475058402[/C][C]9.44552494159836[/C][/ROW]
[ROW][C]37[/C][C]171[/C][C]186.377072104361[/C][C]-15.3770721043614[/C][/ROW]
[ROW][C]38[/C][C]165[/C][C]184.075512726154[/C][C]-19.0755127261544[/C][/ROW]
[ROW][C]39[/C][C]156[/C][C]180.98130103994[/C][C]-24.9813010399400[/C][/ROW]
[ROW][C]40[/C][C]170[/C][C]176.728157533014[/C][C]-6.72815753301447[/C][/ROW]
[ROW][C]41[/C][C]201[/C][C]174.420785621500[/C][C]26.5792143784997[/C][/ROW]
[ROW][C]42[/C][C]208[/C][C]176.421360631827[/C][C]31.5786393681727[/C][/ROW]
[ROW][C]43[/C][C]189[/C][C]179.606335779450[/C][C]9.39366422054977[/C][/ROW]
[ROW][C]44[/C][C]175[/C][C]180.450116130771[/C][C]-5.45011613077128[/C][/ROW]
[ROW][C]45[/C][C]184[/C][C]179.498672462445[/C][C]4.501327537555[/C][/ROW]
[ROW][C]46[/C][C]187[/C][C]179.767287891712[/C][C]7.23271210828793[/C][/ROW]
[ROW][C]47[/C][C]193[/C][C]180.487674933128[/C][C]12.5123250668722[/C][/ROW]
[ROW][C]48[/C][C]199[/C][C]182.052694264385[/C][C]16.9473057356153[/C][/ROW]
[ROW][C]49[/C][C]179[/C][C]184.452688612138[/C][C]-5.4526886121381[/C][/ROW]
[ROW][C]50[/C][C]188[/C][C]184.197630861548[/C][C]3.80236913845209[/C][/ROW]
[ROW][C]51[/C][C]171[/C][C]185.069770079898[/C][C]-14.0697700798982[/C][/ROW]
[ROW][C]52[/C][C]182[/C][C]183.634087808782[/C][C]-1.63408780878163[/C][/ROW]
[ROW][C]53[/C][C]212[/C][C]183.581537632385[/C][C]28.4184623676149[/C][/ROW]
[ROW][C]54[/C][C]216[/C][C]187.502438431943[/C][C]28.4975615680574[/C][/ROW]
[ROW][C]55[/C][C]192[/C][C]191.987826227621[/C][C]0.0121737723792421[/C][/ROW]
[ROW][C]56[/C][C]182[/C][C]193.232263616200[/C][C]-11.2322636161996[/C][/ROW]
[ROW][C]57[/C][C]183[/C][C]192.978317314319[/C][C]-9.97831731431887[/C][/ROW]
[ROW][C]58[/C][C]183[/C][C]192.672548654837[/C][C]-9.67254865483696[/C][/ROW]
[ROW][C]59[/C][C]187[/C][C]192.213030156427[/C][C]-5.21303015642684[/C][/ROW]
[ROW][C]60[/C][C]190[/C][C]192.159319872079[/C][C]-2.15931987207907[/C][/ROW]
[ROW][C]61[/C][C]167[/C][C]192.410983244430[/C][C]-25.4109832444302[/C][/ROW]
[ROW][C]62[/C][C]167[/C][C]189.521652337837[/C][C]-22.5216523378369[/C][/ROW]
[ROW][C]63[/C][C]158[/C][C]186.522079945827[/C][C]-28.5220799458273[/C][/ROW]
[ROW][C]64[/C][C]171[/C][C]182.283788885768[/C][C]-11.2837888857681[/C][/ROW]
[ROW][C]65[/C][C]201[/C][C]179.786994894266[/C][C]21.2130051057339[/C][/ROW]
[ROW][C]66[/C][C]208[/C][C]181.401316381721[/C][C]26.5986836182789[/C][/ROW]
[ROW][C]67[/C][C]181[/C][C]184.146916118982[/C][C]-3.14691611898203[/C][/ROW]
[ROW][C]68[/C][C]169[/C][C]183.446594871146[/C][C]-14.4465948711457[/C][/ROW]
[ROW][C]69[/C][C]173[/C][C]181.178949206756[/C][C]-8.17894920675616[/C][/ROW]
[ROW][C]70[/C][C]180[/C][C]179.465035127521[/C][C]0.534964872479264[/C][/ROW]
[ROW][C]71[/C][C]181[/C][C]178.753054752812[/C][C]2.24694524718845[/C][/ROW]
[ROW][C]72[/C][C]192[/C][C]178.279669159402[/C][C]13.7203308405978[/C][/ROW]
[ROW][C]73[/C][C]169[/C][C]179.379216428855[/C][C]-10.3792164288551[/C][/ROW]
[ROW][C]74[/C][C]168[/C][C]177.534299288157[/C][C]-9.53429928815686[/C][/ROW]
[ROW][C]75[/C][C]156[/C][C]175.599673715542[/C][C]-19.5996737155419[/C][/ROW]
[ROW][C]76[/C][C]161[/C][C]172.137722050047[/C][C]-11.1377220500465[/C][/ROW]
[ROW][C]77[/C][C]195[/C][C]169.421505696254[/C][C]25.578494303746[/C][/ROW]
[ROW][C]78[/C][C]208[/C][C]171.381602511762[/C][C]36.6183974882377[/C][/ROW]
[ROW][C]79[/C][C]176[/C][C]175.311647717480[/C][C]0.688352282520299[/C][/ROW]
[ROW][C]80[/C][C]164[/C][C]175.166838323780[/C][C]-11.1668383237804[/C][/ROW]
[ROW][C]81[/C][C]170[/C][C]173.455426457595[/C][C]-3.45542645759534[/C][/ROW]
[ROW][C]82[/C][C]175[/C][C]172.554096933026[/C][C]2.44590306697356[/C][/ROW]
[ROW][C]83[/C][C]170[/C][C]172.371922197232[/C][C]-2.37192219723195[/C][/ROW]
[ROW][C]84[/C][C]175[/C][C]171.595320429531[/C][C]3.40467957046872[/C][/ROW]
[ROW][C]85[/C][C]148[/C][C]171.542370284688[/C][C]-23.5423702846881[/C][/ROW]
[ROW][C]86[/C][C]151[/C][C]167.964372992394[/C][C]-16.9643729923941[/C][/ROW]
[ROW][C]87[/C][C]143[/C][C]164.804171136206[/C][C]-21.8041711362058[/C][/ROW]
[ROW][C]88[/C][C]139[/C][C]160.668260307724[/C][C]-21.6682603077236[/C][/ROW]
[ROW][C]89[/C][C]166[/C][C]156.125446916305[/C][C]9.87455308369456[/C][/ROW]
[ROW][C]90[/C][C]186[/C][C]155.364187068258[/C][C]30.6358129317418[/C][/ROW]
[ROW][C]91[/C][C]149[/C][C]157.562397503018[/C][C]-8.5623975030175[/C][/ROW]
[ROW][C]92[/C][C]142[/C][C]155.133568095981[/C][C]-13.1335680959811[/C][/ROW]
[ROW][C]93[/C][C]138[/C][C]151.928606425941[/C][C]-13.9286064259412[/C][/ROW]
[ROW][C]94[/C][C]137[/C][C]148.361679536717[/C][C]-11.3616795367167[/C][/ROW]
[ROW][C]95[/C][C]130[/C][C]144.865361672413[/C][C]-14.8653616724135[/C][/ROW]
[ROW][C]96[/C][C]138[/C][C]140.680618022316[/C][C]-2.68061802231563[/C][/ROW]
[ROW][C]97[/C][C]118[/C][C]137.830054192974[/C][C]-19.8300541929741[/C][/ROW]
[ROW][C]98[/C][C]113[/C][C]132.641619137428[/C][C]-19.6416191374277[/C][/ROW]
[ROW][C]99[/C][C]99[/C][C]127.091762110641[/C][C]-28.0917621106413[/C][/ROW]
[ROW][C]100[/C][C]93[/C][C]120.032835398327[/C][C]-27.0328353983267[/C][/ROW]
[ROW][C]101[/C][C]125[/C][C]112.567462157511[/C][C]12.4325378424886[/C][/ROW]
[ROW][C]102[/C][C]146[/C][C]109.834966114541[/C][C]36.1650338854593[/C][/ROW]
[ROW][C]103[/C][C]109[/C][C]110.507798113161[/C][C]-1.50779811316109[/C][/ROW]
[ROW][C]104[/C][C]97[/C][C]106.864665561865[/C][C]-9.86466556186487[/C][/ROW]
[ROW][C]105[/C][C]97[/C][C]102.078367031523[/C][C]-5.0783670315234[/C][/ROW]
[ROW][C]106[/C][C]94[/C][C]97.7376840387952[/C][C]-3.73768403879524[/C][/ROW]
[ROW][C]107[/C][C]92[/C][C]93.4766930694786[/C][C]-1.4766930694786[/C][/ROW]
[ROW][C]108[/C][C]103[/C][C]89.4441828618331[/C][C]13.5558171381669[/C][/ROW]
[ROW][C]109[/C][C]78[/C][C]87.3863709721254[/C][C]-9.38637097212543[/C][/ROW]
[ROW][C]110[/C][C]72[/C][C]82.5351368560166[/C][C]-10.5351368560166[/C][/ROW]
[ROW][C]111[/C][C]57[/C][C]77.3478358777625[/C][C]-20.3478358777625[/C][/ROW]
[ROW][C]112[/C][C]40[/C][C]70.6473757818176[/C][C]-30.6473757818176[/C][/ROW]
[ROW][C]113[/C][C]70[/C][C]62.1775986850595[/C][C]7.82240131494055[/C][/ROW]
[ROW][C]114[/C][C]89[/C][C]58.2375528843718[/C][C]30.7624471156282[/C][/ROW]
[ROW][C]115[/C][C]53[/C][C]57.5073572402528[/C][C]-4.50735724025282[/C][/ROW]
[ROW][C]116[/C][C]46[/C][C]52.6761549786559[/C][C]-6.67615497865594[/C][/ROW]
[ROW][C]117[/C][C]43[/C][C]47.4680432617241[/C][C]-4.46804326172409[/C][/ROW]
[ROW][C]118[/C][C]38[/C][C]42.4240867943552[/C][C]-4.42408679435516[/C][/ROW]
[ROW][C]119[/C][C]29[/C][C]37.2988956724757[/C][C]-8.29889567247572[/C][/ROW]
[ROW][C]120[/C][C]34[/C][C]31.5710467829666[/C][C]2.42895321703341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78756&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78756&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
32082080
4206207-1
5226205.8667233463920.1332766536102
6225207.53052665390117.4694733460994
7210209.2317536784960.768246321504307
8200209.047619559445-9.04761955944534
9201207.570234671978-6.57023467197789
10201206.246667251226-5.24666725122609
11202204.971430620551-2.97143062055133
12204203.8971596143380.102840385662120
13197203.174696753514-6.17469675351367
14196201.617589358997-5.61758935899741
15187200.014371522755-13.0143715227546
16196197.315834838771-1.31583483877122
17221195.92275823607925.0772417639212
18218198.02161374154919.9783862584507
19200199.9297272550180.0702727449822191
20191199.573981337151-8.57398133715074
21194198.0675279489-4.06752794890016
22192196.994551847505-4.99455184750499
23199195.7187390948373.28126090516312
24196195.4485430140360.551456985963938
25182194.878487553954-12.8784875539545
26178192.529283264720-14.5292832647204
27169189.709033416174-20.7090334161736
28177185.781956094471-8.78195609447053
29207183.0408103187523.9591896812501
30213184.49211321337428.5078867866265
31191187.0166740903203.98332590967979
32182186.828371581037-4.82837158103661
33188185.5433202233682.45667977663160
34189185.1350794317083.86492056829152
35194184.9624109214949.03758907850568
36195185.5544750584029.44552494159836
37171186.377072104361-15.3770721043614
38165184.075512726154-19.0755127261544
39156180.98130103994-24.9813010399400
40170176.728157533014-6.72815753301447
41201174.42078562150026.5792143784997
42208176.42136063182731.5786393681727
43189179.6063357794509.39366422054977
44175180.450116130771-5.45011613077128
45184179.4986724624454.501327537555
46187179.7672878917127.23271210828793
47193180.48767493312812.5123250668722
48199182.05269426438516.9473057356153
49179184.452688612138-5.4526886121381
50188184.1976308615483.80236913845209
51171185.069770079898-14.0697700798982
52182183.634087808782-1.63408780878163
53212183.58153763238528.4184623676149
54216187.50243843194328.4975615680574
55192191.9878262276210.0121737723792421
56182193.232263616200-11.2322636161996
57183192.978317314319-9.97831731431887
58183192.672548654837-9.67254865483696
59187192.213030156427-5.21303015642684
60190192.159319872079-2.15931987207907
61167192.410983244430-25.4109832444302
62167189.521652337837-22.5216523378369
63158186.522079945827-28.5220799458273
64171182.283788885768-11.2837888857681
65201179.78699489426621.2130051057339
66208181.40131638172126.5986836182789
67181184.146916118982-3.14691611898203
68169183.446594871146-14.4465948711457
69173181.178949206756-8.17894920675616
70180179.4650351275210.534964872479264
71181178.7530547528122.24694524718845
72192178.27966915940213.7203308405978
73169179.379216428855-10.3792164288551
74168177.534299288157-9.53429928815686
75156175.599673715542-19.5996737155419
76161172.137722050047-11.1377220500465
77195169.42150569625425.578494303746
78208171.38160251176236.6183974882377
79176175.3116477174800.688352282520299
80164175.166838323780-11.1668383237804
81170173.455426457595-3.45542645759534
82175172.5540969330262.44590306697356
83170172.371922197232-2.37192219723195
84175171.5953204295313.40467957046872
85148171.542370284688-23.5423702846881
86151167.964372992394-16.9643729923941
87143164.804171136206-21.8041711362058
88139160.668260307724-21.6682603077236
89166156.1254469163059.87455308369456
90186155.36418706825830.6358129317418
91149157.562397503018-8.5623975030175
92142155.133568095981-13.1335680959811
93138151.928606425941-13.9286064259412
94137148.361679536717-11.3616795367167
95130144.865361672413-14.8653616724135
96138140.680618022316-2.68061802231563
97118137.830054192974-19.8300541929741
98113132.641619137428-19.6416191374277
9999127.091762110641-28.0917621106413
10093120.032835398327-27.0328353983267
101125112.56746215751112.4325378424886
102146109.83496611454136.1650338854593
103109110.507798113161-1.50779811316109
10497106.864665561865-9.86466556186487
10597102.078367031523-5.0783670315234
1069497.7376840387952-3.73768403879524
1079293.4766930694786-1.4766930694786
10810389.444182861833113.5558171381669
1097887.3863709721254-9.38637097212543
1107282.5351368560166-10.5351368560166
1115777.3478358777625-20.3478358777625
1124070.6473757818176-30.6473757818176
1137062.17759868505957.82240131494055
1148958.237552884371830.7624471156282
1155357.5073572402528-4.50735724025282
1164652.6761549786559-6.67615497865594
1174347.4680432617241-4.46804326172409
1183842.4240867943552-4.42408679435516
1192937.2988956724757-8.29889567247572
1203431.57104678296662.42895321703341







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12127.1112040418685-2.8384884307794457.0608965145164
12222.3749847474322-7.8395301116386252.589499606503
12317.6387654529959-12.920211547873048.1977424538649
12412.9025461585596-18.088875358629743.893967675749
1258.16632686412337-23.352713921669439.6853676499161
1263.43010756968709-28.717643136680635.5778582760548
127-1.30611172474919-34.188229431202531.5760059817041
128-6.04233101918546-39.767676490230927.68301445186
129-10.7785503136217-45.457871086349723.9007704591063
130-15.5147696080580-51.259480799341820.2299415832257
131-20.2509889024943-57.172091550586816.6701137455982
132-24.9872081969306-63.194370405133113.2199540112720

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 27.1112040418685 & -2.83848843077944 & 57.0608965145164 \tabularnewline
122 & 22.3749847474322 & -7.83953011163862 & 52.589499606503 \tabularnewline
123 & 17.6387654529959 & -12.9202115478730 & 48.1977424538649 \tabularnewline
124 & 12.9025461585596 & -18.0888753586297 & 43.893967675749 \tabularnewline
125 & 8.16632686412337 & -23.3527139216694 & 39.6853676499161 \tabularnewline
126 & 3.43010756968709 & -28.7176431366806 & 35.5778582760548 \tabularnewline
127 & -1.30611172474919 & -34.1882294312025 & 31.5760059817041 \tabularnewline
128 & -6.04233101918546 & -39.7676764902309 & 27.68301445186 \tabularnewline
129 & -10.7785503136217 & -45.4578710863497 & 23.9007704591063 \tabularnewline
130 & -15.5147696080580 & -51.2594807993418 & 20.2299415832257 \tabularnewline
131 & -20.2509889024943 & -57.1720915505868 & 16.6701137455982 \tabularnewline
132 & -24.9872081969306 & -63.1943704051331 & 13.2199540112720 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78756&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]27.1112040418685[/C][C]-2.83848843077944[/C][C]57.0608965145164[/C][/ROW]
[ROW][C]122[/C][C]22.3749847474322[/C][C]-7.83953011163862[/C][C]52.589499606503[/C][/ROW]
[ROW][C]123[/C][C]17.6387654529959[/C][C]-12.9202115478730[/C][C]48.1977424538649[/C][/ROW]
[ROW][C]124[/C][C]12.9025461585596[/C][C]-18.0888753586297[/C][C]43.893967675749[/C][/ROW]
[ROW][C]125[/C][C]8.16632686412337[/C][C]-23.3527139216694[/C][C]39.6853676499161[/C][/ROW]
[ROW][C]126[/C][C]3.43010756968709[/C][C]-28.7176431366806[/C][C]35.5778582760548[/C][/ROW]
[ROW][C]127[/C][C]-1.30611172474919[/C][C]-34.1882294312025[/C][C]31.5760059817041[/C][/ROW]
[ROW][C]128[/C][C]-6.04233101918546[/C][C]-39.7676764902309[/C][C]27.68301445186[/C][/ROW]
[ROW][C]129[/C][C]-10.7785503136217[/C][C]-45.4578710863497[/C][C]23.9007704591063[/C][/ROW]
[ROW][C]130[/C][C]-15.5147696080580[/C][C]-51.2594807993418[/C][C]20.2299415832257[/C][/ROW]
[ROW][C]131[/C][C]-20.2509889024943[/C][C]-57.1720915505868[/C][C]16.6701137455982[/C][/ROW]
[ROW][C]132[/C][C]-24.9872081969306[/C][C]-63.1943704051331[/C][C]13.2199540112720[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78756&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78756&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
12127.1112040418685-2.8384884307794457.0608965145164
12222.3749847474322-7.8395301116386252.589499606503
12317.6387654529959-12.920211547873048.1977424538649
12412.9025461585596-18.088875358629743.893967675749
1258.16632686412337-23.352713921669439.6853676499161
1263.43010756968709-28.717643136680635.5778582760548
127-1.30611172474919-34.188229431202531.5760059817041
128-6.04233101918546-39.767676490230927.68301445186
129-10.7785503136217-45.457871086349723.9007704591063
130-15.5147696080580-51.259480799341820.2299415832257
131-20.2509889024943-57.172091550586816.6701137455982
132-24.9872081969306-63.194370405133113.2199540112720



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')