Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Jul 2010 12:07:44 +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/21/t1279714102s54q1z5kd99ega0.htm/, Retrieved Mon, 29 Apr 2024 05:07:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78050, Retrieved Mon, 29 Apr 2024 05:07:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan de Walle Mathias
Estimated Impact237
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks 1 - sta...] [2010-07-21 12:07:44] [589929edeb20bd59f78e9be1ffd92c80] [Current]
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Dataseries X:
268
267
266
264
284
283
268
258
259
259
260
262
255
259
258
258
288
289
271
268
274
284
284
279
273
280
276
271
298
297
278
270
280
289
288
293
285
283
275
268
295
290
267
252
268
278
280
278
261
263
259
265
294
285
255
231
246
258
265
260
238
241
239
233
265
255
224
194
210
222
230
225
206
204
207
195
230
221
195
162
182
203
211
206
187
181
189
174
213
201
177
140
165
192
197
196
176
164
177
165
208
195
164
123
147
173
176
170
157
145
148
135
175
168
140
109
129
150
150
152




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=78050&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=78050&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78050&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
alpha0.384345027192648
beta0.0463295896458016
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.384345027192648 \tabularnewline
beta & 0.0463295896458016 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78050&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]0.384345027192648[/C][/ROW]
[ROW][C]beta[/C][C]0.0463295896458016[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78050&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78050&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
alpha0.384345027192648
beta0.0463295896458016
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13255255.300480769231-0.300480769230774
14259259.140160602771-0.140160602770720
15258257.5389629186330.461037081367351
16258256.5520420533921.44795794660831
17288285.5952224467372.40477755326299
18289286.3823058166242.61769418337627
19271272.589501396703-1.58950139670253
20268263.4430454118674.55695458813261
21274267.5317595141676.46824048583335
22284271.38691054421312.6130894557874
23284278.3283992938675.67160070613261
24279283.202952988042-4.20295298804217
25273275.064105179402-2.06410517940202
26280278.8275860241011.17241397589942
27276278.627311992736-2.62731199273571
28271277.532321219691-6.53232121969137
29298304.426609492209-6.42660949220902
30297302.122437581545-5.1224375815454
31278282.798707335886-4.79870733588564
32270276.179896530020-6.17989653001956
33280277.1044530471722.89554695282754
34289283.0917516553605.90824834463962
35288282.7855036731485.21449632685193
36293280.99971171010412.0002882898957
37285280.2884734081714.71152659182911
38283288.652546358686-5.65254635868632
39275283.372116210301-8.37211621030099
40268277.445008662307-9.44500866230715
41295303.013045551913-8.01304555191268
42290300.601949404772-10.6019494047719
43267278.973825638867-11.9738256388671
44252268.221517178735-16.2215171787346
45268270.169721432029-2.16972143202929
46278275.2705517637882.72944823621174
47280272.4643902782697.53560972173085
48278274.9386986787033.06130132129698
49261265.335555713253-4.33555571325303
50263262.7117501298840.288249870115692
51259257.0161194473561.98388055264411
52265253.56896141140711.4310385885930
53294287.5741340118106.42586598818963
54285288.907732897365-3.90773289736535
55255268.916139130245-13.9161391302451
56231254.675857420555-23.6758574205552
57246262.151002638017-16.1510026380166
58258264.386358525733-6.38635852573339
59265260.3651615083434.63483849165698
60260258.2479322217481.75206777825224
61238242.842356635871-4.84235663587134
62241242.116085761908-1.11608576190832
63239236.1452749785542.85472502144555
64233238.085164094791-5.08516409479051
65265261.6030129661253.39698703387535
66255254.2986679116790.701332088320754
67224228.887013983715-4.88701398371543
68194211.239383769247-17.2393837692469
69210225.06665251076-15.0666525107600
70222232.995315831967-10.9953158319673
71230233.170765275649-3.17076527564896
72225225.322529550495-0.322529550495176
73206204.0665918776891.93340812231122
74204207.366191926987-3.3661919269868
75207202.0626890506564.93731094934387
76195199.039336776433-4.03933677643295
77230227.3244045554562.67559544454357
78221217.2135392213753.78646077862476
79195188.7324179675836.26758203241738
80162167.151100073264-5.15110007326351
81182186.561240636430-4.5612406364302
82203200.8203578487812.17964215121935
83211210.8975732568330.102426743167342
84206206.140000263964-0.140000263963572
85187186.4254434466380.574556553362072
86181185.998201458894-4.9982014588941
87189185.2086271475203.79137285248038
88174176.227006727094-2.22700672709428
89213209.3836725773483.61632742265240
90201200.3759904717980.62400952820218
91177172.2083069099134.79169309008699
92140143.004884997966-3.004884997966
93165163.6163942079191.38360579208063
94192184.4296304412557.57036955874486
95197195.5150762182771.48492378172259
96196191.3794042863354.62059571366467
97176174.2590456868481.74095431315203
98164171.194542581722-7.19454258172203
99177175.2783872495461.72161275045426
100165162.0653908627892.93460913721137
101208201.1646577401126.83534225988757
102195191.9705540383103.02944596169044
103164167.754677086213-3.75467708621264
104123130.775750848478-7.7757508484776
105147152.479697645337-5.47969764533687
106173174.566057446934-1.56605744693428
107176178.332827999186-2.33282799918561
108170174.531733210713-4.53173321071338
109157151.8293046125665.17069538743374
110145144.3513418418310.648658158168786
111148156.848136911331-8.84813691133064
112135140.040466144071-5.04046614407090
113175178.055018767335-3.05501876733521
114168162.1193323504665.88066764953408
115140134.2762469439085.72375305609182
11610998.087110013701310.9128899862987
117129128.3426955959650.657304404034704
118150155.261688528099-5.2616885280986
119150157.134643979543-7.1346439795426
120152150.0473728365661.95262716343359

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 255 & 255.300480769231 & -0.300480769230774 \tabularnewline
14 & 259 & 259.140160602771 & -0.140160602770720 \tabularnewline
15 & 258 & 257.538962918633 & 0.461037081367351 \tabularnewline
16 & 258 & 256.552042053392 & 1.44795794660831 \tabularnewline
17 & 288 & 285.595222446737 & 2.40477755326299 \tabularnewline
18 & 289 & 286.382305816624 & 2.61769418337627 \tabularnewline
19 & 271 & 272.589501396703 & -1.58950139670253 \tabularnewline
20 & 268 & 263.443045411867 & 4.55695458813261 \tabularnewline
21 & 274 & 267.531759514167 & 6.46824048583335 \tabularnewline
22 & 284 & 271.386910544213 & 12.6130894557874 \tabularnewline
23 & 284 & 278.328399293867 & 5.67160070613261 \tabularnewline
24 & 279 & 283.202952988042 & -4.20295298804217 \tabularnewline
25 & 273 & 275.064105179402 & -2.06410517940202 \tabularnewline
26 & 280 & 278.827586024101 & 1.17241397589942 \tabularnewline
27 & 276 & 278.627311992736 & -2.62731199273571 \tabularnewline
28 & 271 & 277.532321219691 & -6.53232121969137 \tabularnewline
29 & 298 & 304.426609492209 & -6.42660949220902 \tabularnewline
30 & 297 & 302.122437581545 & -5.1224375815454 \tabularnewline
31 & 278 & 282.798707335886 & -4.79870733588564 \tabularnewline
32 & 270 & 276.179896530020 & -6.17989653001956 \tabularnewline
33 & 280 & 277.104453047172 & 2.89554695282754 \tabularnewline
34 & 289 & 283.091751655360 & 5.90824834463962 \tabularnewline
35 & 288 & 282.785503673148 & 5.21449632685193 \tabularnewline
36 & 293 & 280.999711710104 & 12.0002882898957 \tabularnewline
37 & 285 & 280.288473408171 & 4.71152659182911 \tabularnewline
38 & 283 & 288.652546358686 & -5.65254635868632 \tabularnewline
39 & 275 & 283.372116210301 & -8.37211621030099 \tabularnewline
40 & 268 & 277.445008662307 & -9.44500866230715 \tabularnewline
41 & 295 & 303.013045551913 & -8.01304555191268 \tabularnewline
42 & 290 & 300.601949404772 & -10.6019494047719 \tabularnewline
43 & 267 & 278.973825638867 & -11.9738256388671 \tabularnewline
44 & 252 & 268.221517178735 & -16.2215171787346 \tabularnewline
45 & 268 & 270.169721432029 & -2.16972143202929 \tabularnewline
46 & 278 & 275.270551763788 & 2.72944823621174 \tabularnewline
47 & 280 & 272.464390278269 & 7.53560972173085 \tabularnewline
48 & 278 & 274.938698678703 & 3.06130132129698 \tabularnewline
49 & 261 & 265.335555713253 & -4.33555571325303 \tabularnewline
50 & 263 & 262.711750129884 & 0.288249870115692 \tabularnewline
51 & 259 & 257.016119447356 & 1.98388055264411 \tabularnewline
52 & 265 & 253.568961411407 & 11.4310385885930 \tabularnewline
53 & 294 & 287.574134011810 & 6.42586598818963 \tabularnewline
54 & 285 & 288.907732897365 & -3.90773289736535 \tabularnewline
55 & 255 & 268.916139130245 & -13.9161391302451 \tabularnewline
56 & 231 & 254.675857420555 & -23.6758574205552 \tabularnewline
57 & 246 & 262.151002638017 & -16.1510026380166 \tabularnewline
58 & 258 & 264.386358525733 & -6.38635852573339 \tabularnewline
59 & 265 & 260.365161508343 & 4.63483849165698 \tabularnewline
60 & 260 & 258.247932221748 & 1.75206777825224 \tabularnewline
61 & 238 & 242.842356635871 & -4.84235663587134 \tabularnewline
62 & 241 & 242.116085761908 & -1.11608576190832 \tabularnewline
63 & 239 & 236.145274978554 & 2.85472502144555 \tabularnewline
64 & 233 & 238.085164094791 & -5.08516409479051 \tabularnewline
65 & 265 & 261.603012966125 & 3.39698703387535 \tabularnewline
66 & 255 & 254.298667911679 & 0.701332088320754 \tabularnewline
67 & 224 & 228.887013983715 & -4.88701398371543 \tabularnewline
68 & 194 & 211.239383769247 & -17.2393837692469 \tabularnewline
69 & 210 & 225.06665251076 & -15.0666525107600 \tabularnewline
70 & 222 & 232.995315831967 & -10.9953158319673 \tabularnewline
71 & 230 & 233.170765275649 & -3.17076527564896 \tabularnewline
72 & 225 & 225.322529550495 & -0.322529550495176 \tabularnewline
73 & 206 & 204.066591877689 & 1.93340812231122 \tabularnewline
74 & 204 & 207.366191926987 & -3.3661919269868 \tabularnewline
75 & 207 & 202.062689050656 & 4.93731094934387 \tabularnewline
76 & 195 & 199.039336776433 & -4.03933677643295 \tabularnewline
77 & 230 & 227.324404555456 & 2.67559544454357 \tabularnewline
78 & 221 & 217.213539221375 & 3.78646077862476 \tabularnewline
79 & 195 & 188.732417967583 & 6.26758203241738 \tabularnewline
80 & 162 & 167.151100073264 & -5.15110007326351 \tabularnewline
81 & 182 & 186.561240636430 & -4.5612406364302 \tabularnewline
82 & 203 & 200.820357848781 & 2.17964215121935 \tabularnewline
83 & 211 & 210.897573256833 & 0.102426743167342 \tabularnewline
84 & 206 & 206.140000263964 & -0.140000263963572 \tabularnewline
85 & 187 & 186.425443446638 & 0.574556553362072 \tabularnewline
86 & 181 & 185.998201458894 & -4.9982014588941 \tabularnewline
87 & 189 & 185.208627147520 & 3.79137285248038 \tabularnewline
88 & 174 & 176.227006727094 & -2.22700672709428 \tabularnewline
89 & 213 & 209.383672577348 & 3.61632742265240 \tabularnewline
90 & 201 & 200.375990471798 & 0.62400952820218 \tabularnewline
91 & 177 & 172.208306909913 & 4.79169309008699 \tabularnewline
92 & 140 & 143.004884997966 & -3.004884997966 \tabularnewline
93 & 165 & 163.616394207919 & 1.38360579208063 \tabularnewline
94 & 192 & 184.429630441255 & 7.57036955874486 \tabularnewline
95 & 197 & 195.515076218277 & 1.48492378172259 \tabularnewline
96 & 196 & 191.379404286335 & 4.62059571366467 \tabularnewline
97 & 176 & 174.259045686848 & 1.74095431315203 \tabularnewline
98 & 164 & 171.194542581722 & -7.19454258172203 \tabularnewline
99 & 177 & 175.278387249546 & 1.72161275045426 \tabularnewline
100 & 165 & 162.065390862789 & 2.93460913721137 \tabularnewline
101 & 208 & 201.164657740112 & 6.83534225988757 \tabularnewline
102 & 195 & 191.970554038310 & 3.02944596169044 \tabularnewline
103 & 164 & 167.754677086213 & -3.75467708621264 \tabularnewline
104 & 123 & 130.775750848478 & -7.7757508484776 \tabularnewline
105 & 147 & 152.479697645337 & -5.47969764533687 \tabularnewline
106 & 173 & 174.566057446934 & -1.56605744693428 \tabularnewline
107 & 176 & 178.332827999186 & -2.33282799918561 \tabularnewline
108 & 170 & 174.531733210713 & -4.53173321071338 \tabularnewline
109 & 157 & 151.829304612566 & 5.17069538743374 \tabularnewline
110 & 145 & 144.351341841831 & 0.648658158168786 \tabularnewline
111 & 148 & 156.848136911331 & -8.84813691133064 \tabularnewline
112 & 135 & 140.040466144071 & -5.04046614407090 \tabularnewline
113 & 175 & 178.055018767335 & -3.05501876733521 \tabularnewline
114 & 168 & 162.119332350466 & 5.88066764953408 \tabularnewline
115 & 140 & 134.276246943908 & 5.72375305609182 \tabularnewline
116 & 109 & 98.0871100137013 & 10.9128899862987 \tabularnewline
117 & 129 & 128.342695595965 & 0.657304404034704 \tabularnewline
118 & 150 & 155.261688528099 & -5.2616885280986 \tabularnewline
119 & 150 & 157.134643979543 & -7.1346439795426 \tabularnewline
120 & 152 & 150.047372836566 & 1.95262716343359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78050&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]255[/C][C]255.300480769231[/C][C]-0.300480769230774[/C][/ROW]
[ROW][C]14[/C][C]259[/C][C]259.140160602771[/C][C]-0.140160602770720[/C][/ROW]
[ROW][C]15[/C][C]258[/C][C]257.538962918633[/C][C]0.461037081367351[/C][/ROW]
[ROW][C]16[/C][C]258[/C][C]256.552042053392[/C][C]1.44795794660831[/C][/ROW]
[ROW][C]17[/C][C]288[/C][C]285.595222446737[/C][C]2.40477755326299[/C][/ROW]
[ROW][C]18[/C][C]289[/C][C]286.382305816624[/C][C]2.61769418337627[/C][/ROW]
[ROW][C]19[/C][C]271[/C][C]272.589501396703[/C][C]-1.58950139670253[/C][/ROW]
[ROW][C]20[/C][C]268[/C][C]263.443045411867[/C][C]4.55695458813261[/C][/ROW]
[ROW][C]21[/C][C]274[/C][C]267.531759514167[/C][C]6.46824048583335[/C][/ROW]
[ROW][C]22[/C][C]284[/C][C]271.386910544213[/C][C]12.6130894557874[/C][/ROW]
[ROW][C]23[/C][C]284[/C][C]278.328399293867[/C][C]5.67160070613261[/C][/ROW]
[ROW][C]24[/C][C]279[/C][C]283.202952988042[/C][C]-4.20295298804217[/C][/ROW]
[ROW][C]25[/C][C]273[/C][C]275.064105179402[/C][C]-2.06410517940202[/C][/ROW]
[ROW][C]26[/C][C]280[/C][C]278.827586024101[/C][C]1.17241397589942[/C][/ROW]
[ROW][C]27[/C][C]276[/C][C]278.627311992736[/C][C]-2.62731199273571[/C][/ROW]
[ROW][C]28[/C][C]271[/C][C]277.532321219691[/C][C]-6.53232121969137[/C][/ROW]
[ROW][C]29[/C][C]298[/C][C]304.426609492209[/C][C]-6.42660949220902[/C][/ROW]
[ROW][C]30[/C][C]297[/C][C]302.122437581545[/C][C]-5.1224375815454[/C][/ROW]
[ROW][C]31[/C][C]278[/C][C]282.798707335886[/C][C]-4.79870733588564[/C][/ROW]
[ROW][C]32[/C][C]270[/C][C]276.179896530020[/C][C]-6.17989653001956[/C][/ROW]
[ROW][C]33[/C][C]280[/C][C]277.104453047172[/C][C]2.89554695282754[/C][/ROW]
[ROW][C]34[/C][C]289[/C][C]283.091751655360[/C][C]5.90824834463962[/C][/ROW]
[ROW][C]35[/C][C]288[/C][C]282.785503673148[/C][C]5.21449632685193[/C][/ROW]
[ROW][C]36[/C][C]293[/C][C]280.999711710104[/C][C]12.0002882898957[/C][/ROW]
[ROW][C]37[/C][C]285[/C][C]280.288473408171[/C][C]4.71152659182911[/C][/ROW]
[ROW][C]38[/C][C]283[/C][C]288.652546358686[/C][C]-5.65254635868632[/C][/ROW]
[ROW][C]39[/C][C]275[/C][C]283.372116210301[/C][C]-8.37211621030099[/C][/ROW]
[ROW][C]40[/C][C]268[/C][C]277.445008662307[/C][C]-9.44500866230715[/C][/ROW]
[ROW][C]41[/C][C]295[/C][C]303.013045551913[/C][C]-8.01304555191268[/C][/ROW]
[ROW][C]42[/C][C]290[/C][C]300.601949404772[/C][C]-10.6019494047719[/C][/ROW]
[ROW][C]43[/C][C]267[/C][C]278.973825638867[/C][C]-11.9738256388671[/C][/ROW]
[ROW][C]44[/C][C]252[/C][C]268.221517178735[/C][C]-16.2215171787346[/C][/ROW]
[ROW][C]45[/C][C]268[/C][C]270.169721432029[/C][C]-2.16972143202929[/C][/ROW]
[ROW][C]46[/C][C]278[/C][C]275.270551763788[/C][C]2.72944823621174[/C][/ROW]
[ROW][C]47[/C][C]280[/C][C]272.464390278269[/C][C]7.53560972173085[/C][/ROW]
[ROW][C]48[/C][C]278[/C][C]274.938698678703[/C][C]3.06130132129698[/C][/ROW]
[ROW][C]49[/C][C]261[/C][C]265.335555713253[/C][C]-4.33555571325303[/C][/ROW]
[ROW][C]50[/C][C]263[/C][C]262.711750129884[/C][C]0.288249870115692[/C][/ROW]
[ROW][C]51[/C][C]259[/C][C]257.016119447356[/C][C]1.98388055264411[/C][/ROW]
[ROW][C]52[/C][C]265[/C][C]253.568961411407[/C][C]11.4310385885930[/C][/ROW]
[ROW][C]53[/C][C]294[/C][C]287.574134011810[/C][C]6.42586598818963[/C][/ROW]
[ROW][C]54[/C][C]285[/C][C]288.907732897365[/C][C]-3.90773289736535[/C][/ROW]
[ROW][C]55[/C][C]255[/C][C]268.916139130245[/C][C]-13.9161391302451[/C][/ROW]
[ROW][C]56[/C][C]231[/C][C]254.675857420555[/C][C]-23.6758574205552[/C][/ROW]
[ROW][C]57[/C][C]246[/C][C]262.151002638017[/C][C]-16.1510026380166[/C][/ROW]
[ROW][C]58[/C][C]258[/C][C]264.386358525733[/C][C]-6.38635852573339[/C][/ROW]
[ROW][C]59[/C][C]265[/C][C]260.365161508343[/C][C]4.63483849165698[/C][/ROW]
[ROW][C]60[/C][C]260[/C][C]258.247932221748[/C][C]1.75206777825224[/C][/ROW]
[ROW][C]61[/C][C]238[/C][C]242.842356635871[/C][C]-4.84235663587134[/C][/ROW]
[ROW][C]62[/C][C]241[/C][C]242.116085761908[/C][C]-1.11608576190832[/C][/ROW]
[ROW][C]63[/C][C]239[/C][C]236.145274978554[/C][C]2.85472502144555[/C][/ROW]
[ROW][C]64[/C][C]233[/C][C]238.085164094791[/C][C]-5.08516409479051[/C][/ROW]
[ROW][C]65[/C][C]265[/C][C]261.603012966125[/C][C]3.39698703387535[/C][/ROW]
[ROW][C]66[/C][C]255[/C][C]254.298667911679[/C][C]0.701332088320754[/C][/ROW]
[ROW][C]67[/C][C]224[/C][C]228.887013983715[/C][C]-4.88701398371543[/C][/ROW]
[ROW][C]68[/C][C]194[/C][C]211.239383769247[/C][C]-17.2393837692469[/C][/ROW]
[ROW][C]69[/C][C]210[/C][C]225.06665251076[/C][C]-15.0666525107600[/C][/ROW]
[ROW][C]70[/C][C]222[/C][C]232.995315831967[/C][C]-10.9953158319673[/C][/ROW]
[ROW][C]71[/C][C]230[/C][C]233.170765275649[/C][C]-3.17076527564896[/C][/ROW]
[ROW][C]72[/C][C]225[/C][C]225.322529550495[/C][C]-0.322529550495176[/C][/ROW]
[ROW][C]73[/C][C]206[/C][C]204.066591877689[/C][C]1.93340812231122[/C][/ROW]
[ROW][C]74[/C][C]204[/C][C]207.366191926987[/C][C]-3.3661919269868[/C][/ROW]
[ROW][C]75[/C][C]207[/C][C]202.062689050656[/C][C]4.93731094934387[/C][/ROW]
[ROW][C]76[/C][C]195[/C][C]199.039336776433[/C][C]-4.03933677643295[/C][/ROW]
[ROW][C]77[/C][C]230[/C][C]227.324404555456[/C][C]2.67559544454357[/C][/ROW]
[ROW][C]78[/C][C]221[/C][C]217.213539221375[/C][C]3.78646077862476[/C][/ROW]
[ROW][C]79[/C][C]195[/C][C]188.732417967583[/C][C]6.26758203241738[/C][/ROW]
[ROW][C]80[/C][C]162[/C][C]167.151100073264[/C][C]-5.15110007326351[/C][/ROW]
[ROW][C]81[/C][C]182[/C][C]186.561240636430[/C][C]-4.5612406364302[/C][/ROW]
[ROW][C]82[/C][C]203[/C][C]200.820357848781[/C][C]2.17964215121935[/C][/ROW]
[ROW][C]83[/C][C]211[/C][C]210.897573256833[/C][C]0.102426743167342[/C][/ROW]
[ROW][C]84[/C][C]206[/C][C]206.140000263964[/C][C]-0.140000263963572[/C][/ROW]
[ROW][C]85[/C][C]187[/C][C]186.425443446638[/C][C]0.574556553362072[/C][/ROW]
[ROW][C]86[/C][C]181[/C][C]185.998201458894[/C][C]-4.9982014588941[/C][/ROW]
[ROW][C]87[/C][C]189[/C][C]185.208627147520[/C][C]3.79137285248038[/C][/ROW]
[ROW][C]88[/C][C]174[/C][C]176.227006727094[/C][C]-2.22700672709428[/C][/ROW]
[ROW][C]89[/C][C]213[/C][C]209.383672577348[/C][C]3.61632742265240[/C][/ROW]
[ROW][C]90[/C][C]201[/C][C]200.375990471798[/C][C]0.62400952820218[/C][/ROW]
[ROW][C]91[/C][C]177[/C][C]172.208306909913[/C][C]4.79169309008699[/C][/ROW]
[ROW][C]92[/C][C]140[/C][C]143.004884997966[/C][C]-3.004884997966[/C][/ROW]
[ROW][C]93[/C][C]165[/C][C]163.616394207919[/C][C]1.38360579208063[/C][/ROW]
[ROW][C]94[/C][C]192[/C][C]184.429630441255[/C][C]7.57036955874486[/C][/ROW]
[ROW][C]95[/C][C]197[/C][C]195.515076218277[/C][C]1.48492378172259[/C][/ROW]
[ROW][C]96[/C][C]196[/C][C]191.379404286335[/C][C]4.62059571366467[/C][/ROW]
[ROW][C]97[/C][C]176[/C][C]174.259045686848[/C][C]1.74095431315203[/C][/ROW]
[ROW][C]98[/C][C]164[/C][C]171.194542581722[/C][C]-7.19454258172203[/C][/ROW]
[ROW][C]99[/C][C]177[/C][C]175.278387249546[/C][C]1.72161275045426[/C][/ROW]
[ROW][C]100[/C][C]165[/C][C]162.065390862789[/C][C]2.93460913721137[/C][/ROW]
[ROW][C]101[/C][C]208[/C][C]201.164657740112[/C][C]6.83534225988757[/C][/ROW]
[ROW][C]102[/C][C]195[/C][C]191.970554038310[/C][C]3.02944596169044[/C][/ROW]
[ROW][C]103[/C][C]164[/C][C]167.754677086213[/C][C]-3.75467708621264[/C][/ROW]
[ROW][C]104[/C][C]123[/C][C]130.775750848478[/C][C]-7.7757508484776[/C][/ROW]
[ROW][C]105[/C][C]147[/C][C]152.479697645337[/C][C]-5.47969764533687[/C][/ROW]
[ROW][C]106[/C][C]173[/C][C]174.566057446934[/C][C]-1.56605744693428[/C][/ROW]
[ROW][C]107[/C][C]176[/C][C]178.332827999186[/C][C]-2.33282799918561[/C][/ROW]
[ROW][C]108[/C][C]170[/C][C]174.531733210713[/C][C]-4.53173321071338[/C][/ROW]
[ROW][C]109[/C][C]157[/C][C]151.829304612566[/C][C]5.17069538743374[/C][/ROW]
[ROW][C]110[/C][C]145[/C][C]144.351341841831[/C][C]0.648658158168786[/C][/ROW]
[ROW][C]111[/C][C]148[/C][C]156.848136911331[/C][C]-8.84813691133064[/C][/ROW]
[ROW][C]112[/C][C]135[/C][C]140.040466144071[/C][C]-5.04046614407090[/C][/ROW]
[ROW][C]113[/C][C]175[/C][C]178.055018767335[/C][C]-3.05501876733521[/C][/ROW]
[ROW][C]114[/C][C]168[/C][C]162.119332350466[/C][C]5.88066764953408[/C][/ROW]
[ROW][C]115[/C][C]140[/C][C]134.276246943908[/C][C]5.72375305609182[/C][/ROW]
[ROW][C]116[/C][C]109[/C][C]98.0871100137013[/C][C]10.9128899862987[/C][/ROW]
[ROW][C]117[/C][C]129[/C][C]128.342695595965[/C][C]0.657304404034704[/C][/ROW]
[ROW][C]118[/C][C]150[/C][C]155.261688528099[/C][C]-5.2616885280986[/C][/ROW]
[ROW][C]119[/C][C]150[/C][C]157.134643979543[/C][C]-7.1346439795426[/C][/ROW]
[ROW][C]120[/C][C]152[/C][C]150.047372836566[/C][C]1.95262716343359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78050&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78050&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
13255255.300480769231-0.300480769230774
14259259.140160602771-0.140160602770720
15258257.5389629186330.461037081367351
16258256.5520420533921.44795794660831
17288285.5952224467372.40477755326299
18289286.3823058166242.61769418337627
19271272.589501396703-1.58950139670253
20268263.4430454118674.55695458813261
21274267.5317595141676.46824048583335
22284271.38691054421312.6130894557874
23284278.3283992938675.67160070613261
24279283.202952988042-4.20295298804217
25273275.064105179402-2.06410517940202
26280278.8275860241011.17241397589942
27276278.627311992736-2.62731199273571
28271277.532321219691-6.53232121969137
29298304.426609492209-6.42660949220902
30297302.122437581545-5.1224375815454
31278282.798707335886-4.79870733588564
32270276.179896530020-6.17989653001956
33280277.1044530471722.89554695282754
34289283.0917516553605.90824834463962
35288282.7855036731485.21449632685193
36293280.99971171010412.0002882898957
37285280.2884734081714.71152659182911
38283288.652546358686-5.65254635868632
39275283.372116210301-8.37211621030099
40268277.445008662307-9.44500866230715
41295303.013045551913-8.01304555191268
42290300.601949404772-10.6019494047719
43267278.973825638867-11.9738256388671
44252268.221517178735-16.2215171787346
45268270.169721432029-2.16972143202929
46278275.2705517637882.72944823621174
47280272.4643902782697.53560972173085
48278274.9386986787033.06130132129698
49261265.335555713253-4.33555571325303
50263262.7117501298840.288249870115692
51259257.0161194473561.98388055264411
52265253.56896141140711.4310385885930
53294287.5741340118106.42586598818963
54285288.907732897365-3.90773289736535
55255268.916139130245-13.9161391302451
56231254.675857420555-23.6758574205552
57246262.151002638017-16.1510026380166
58258264.386358525733-6.38635852573339
59265260.3651615083434.63483849165698
60260258.2479322217481.75206777825224
61238242.842356635871-4.84235663587134
62241242.116085761908-1.11608576190832
63239236.1452749785542.85472502144555
64233238.085164094791-5.08516409479051
65265261.6030129661253.39698703387535
66255254.2986679116790.701332088320754
67224228.887013983715-4.88701398371543
68194211.239383769247-17.2393837692469
69210225.06665251076-15.0666525107600
70222232.995315831967-10.9953158319673
71230233.170765275649-3.17076527564896
72225225.322529550495-0.322529550495176
73206204.0665918776891.93340812231122
74204207.366191926987-3.3661919269868
75207202.0626890506564.93731094934387
76195199.039336776433-4.03933677643295
77230227.3244045554562.67559544454357
78221217.2135392213753.78646077862476
79195188.7324179675836.26758203241738
80162167.151100073264-5.15110007326351
81182186.561240636430-4.5612406364302
82203200.8203578487812.17964215121935
83211210.8975732568330.102426743167342
84206206.140000263964-0.140000263963572
85187186.4254434466380.574556553362072
86181185.998201458894-4.9982014588941
87189185.2086271475203.79137285248038
88174176.227006727094-2.22700672709428
89213209.3836725773483.61632742265240
90201200.3759904717980.62400952820218
91177172.2083069099134.79169309008699
92140143.004884997966-3.004884997966
93165163.6163942079191.38360579208063
94192184.4296304412557.57036955874486
95197195.5150762182771.48492378172259
96196191.3794042863354.62059571366467
97176174.2590456868481.74095431315203
98164171.194542581722-7.19454258172203
99177175.2783872495461.72161275045426
100165162.0653908627892.93460913721137
101208201.1646577401126.83534225988757
102195191.9705540383103.02944596169044
103164167.754677086213-3.75467708621264
104123130.775750848478-7.7757508484776
105147152.479697645337-5.47969764533687
106173174.566057446934-1.56605744693428
107176178.332827999186-2.33282799918561
108170174.531733210713-4.53173321071338
109157151.8293046125665.17069538743374
110145144.3513418418310.648658158168786
111148156.848136911331-8.84813691133064
112135140.040466144071-5.04046614407090
113175178.055018767335-3.05501876733521
114168162.1193323504665.88066764953408
115140134.2762469439085.72375305609182
11610998.087110013701310.9128899862987
117129128.3426955959650.657304404034704
118150155.261688528099-5.2616885280986
119150157.134643979543-7.1346439795426
120152150.0473728365661.95262716343359







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121135.839133055065123.164581818624148.513684291507
122123.526361022718109.865300191828137.187421853608
123129.852084587366115.190687049300144.513482125432
124118.871903596675103.195739996269134.548067197082
125160.218379079257143.512600517709176.924157640805
126151.184867259427133.434339208654168.9353953102
127121.106950396081102.296352229679139.917548562483
12885.93269427813366.0465940775685105.818794478697
129105.50580058695084.5287118600039126.482889313896
130128.342138073199106.258563042390150.425713104008
131130.992029179503107.786491969899154.197566389106
132132.276316187401107.933388332629156.619244042172

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 135.839133055065 & 123.164581818624 & 148.513684291507 \tabularnewline
122 & 123.526361022718 & 109.865300191828 & 137.187421853608 \tabularnewline
123 & 129.852084587366 & 115.190687049300 & 144.513482125432 \tabularnewline
124 & 118.871903596675 & 103.195739996269 & 134.548067197082 \tabularnewline
125 & 160.218379079257 & 143.512600517709 & 176.924157640805 \tabularnewline
126 & 151.184867259427 & 133.434339208654 & 168.9353953102 \tabularnewline
127 & 121.106950396081 & 102.296352229679 & 139.917548562483 \tabularnewline
128 & 85.932694278133 & 66.0465940775685 & 105.818794478697 \tabularnewline
129 & 105.505800586950 & 84.5287118600039 & 126.482889313896 \tabularnewline
130 & 128.342138073199 & 106.258563042390 & 150.425713104008 \tabularnewline
131 & 130.992029179503 & 107.786491969899 & 154.197566389106 \tabularnewline
132 & 132.276316187401 & 107.933388332629 & 156.619244042172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78050&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]135.839133055065[/C][C]123.164581818624[/C][C]148.513684291507[/C][/ROW]
[ROW][C]122[/C][C]123.526361022718[/C][C]109.865300191828[/C][C]137.187421853608[/C][/ROW]
[ROW][C]123[/C][C]129.852084587366[/C][C]115.190687049300[/C][C]144.513482125432[/C][/ROW]
[ROW][C]124[/C][C]118.871903596675[/C][C]103.195739996269[/C][C]134.548067197082[/C][/ROW]
[ROW][C]125[/C][C]160.218379079257[/C][C]143.512600517709[/C][C]176.924157640805[/C][/ROW]
[ROW][C]126[/C][C]151.184867259427[/C][C]133.434339208654[/C][C]168.9353953102[/C][/ROW]
[ROW][C]127[/C][C]121.106950396081[/C][C]102.296352229679[/C][C]139.917548562483[/C][/ROW]
[ROW][C]128[/C][C]85.932694278133[/C][C]66.0465940775685[/C][C]105.818794478697[/C][/ROW]
[ROW][C]129[/C][C]105.505800586950[/C][C]84.5287118600039[/C][C]126.482889313896[/C][/ROW]
[ROW][C]130[/C][C]128.342138073199[/C][C]106.258563042390[/C][C]150.425713104008[/C][/ROW]
[ROW][C]131[/C][C]130.992029179503[/C][C]107.786491969899[/C][C]154.197566389106[/C][/ROW]
[ROW][C]132[/C][C]132.276316187401[/C][C]107.933388332629[/C][C]156.619244042172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78050&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78050&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
121135.839133055065123.164581818624148.513684291507
122123.526361022718109.865300191828137.187421853608
123129.852084587366115.190687049300144.513482125432
124118.871903596675103.195739996269134.548067197082
125160.218379079257143.512600517709176.924157640805
126151.184867259427133.434339208654168.9353953102
127121.106950396081102.296352229679139.917548562483
12885.93269427813366.0465940775685105.818794478697
129105.50580058695084.5287118600039126.482889313896
130128.342138073199106.258563042390150.425713104008
131130.992029179503107.786491969899154.197566389106
132132.276316187401107.933388332629156.619244042172



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')