Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 11 May 2014 11:49:36 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/11/t1399823397z10xe2ldw1ag4qk.htm/, Retrieved Tue, 14 May 2024 22:44:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234792, Retrieved Tue, 14 May 2024 22:44:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oefening 1] [2014-05-11 15:49:36] [4e14f87d0dfb5763171576624afe788b] [Current]
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Dataseries X:
254
200
165
123
162
145
145
161
155
173
160
47
232
143
161
159
243
192
157
143
221
227
132
41
273
182
188
162
140
186
178
236
202
184
119
16
340
151
240
235
174
309
174
207
209
171
117
10
339
139
186
155
153
222
102
107
188
162
185
24
394
209
248
254
202
258
215
309
240
258
276
48
455
345
311
346
310
297
300
274
292
304
186
14
321
206
160
217
204
246
234
175
364
328
158
40
556
193
221
278
230
253
240
252
228
306
206
48
557
279
399
364
306
471
293
333
316
329
265
61
679
428
394
352
387
590
177
199
203
255
261
115




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234792&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234792&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.362348627852405
beta0
gamma0.765301978638003

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.362348627852405 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.765301978638003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234792&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]0.362348627852405[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.765301978638003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234792&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
alpha0.362348627852405
beta0
gamma0.765301978638003







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13232215.74065170940216.2593482905983
14143134.8977928303638.10220716963713
15161155.8492050589455.15079494105461
16159152.7311771162746.26882288372582
17243239.9349317311973.06506826880269
18192193.477810257427-1.47781025742711
19157162.541249649844-5.5412496498441
20143181.840640687391-38.8406406873907
21221166.32404307416254.6759569258384
22227204.81805628751222.1819437124884
23132196.99624173292-64.9962417329196
244157.1271979701882-16.1271979701882
25273243.77527975919129.2247202408092
26182163.64975454566118.3502454543391
27188186.8742524456691.1257475543311
28162182.843347109172-20.8433471091718
29140258.659625150827-118.659625150827
30186165.87882214201820.1211778579823
31178140.78568365325437.214316346746
32236159.32753050290576.6724694970947
33202231.302662039948-29.3026620399481
34184223.510194083648-39.5101940836478
35119150.791724749882-31.7917247498818
361646.8021830357525-30.8021830357525
37340250.26435230674889.7356476932518
38151186.758179985168-35.7581799851683
39240181.97108056149758.0289194385028
40235187.83813430455547.161865695445
41174240.562069482239-66.5620694822389
42309234.38320115411174.616798845889
43174237.377856916262-63.3778569162625
44207238.725683065161-31.7256830651607
45209219.707467647128-10.7074676471283
46171213.671709518381-42.6717095183814
47117143.574250460511-26.5742504605115
481041.9581456526026-31.9581456526026
49339303.82341543723535.1765845627648
50139159.307373494151-20.3073734941514
51186205.886568540422-19.886568540422
52155178.217974923785-23.2179749237851
53153149.9430622405343.05693775946577
54222237.885248468718-15.8852484687179
55102140.745791298077-38.7457912980766
56107166.465142322496-59.4651423224961
57188147.65237394623240.3476260537684
58162144.5179413664117.4820586335899
59185104.07261098357880.9273890164219
602438.7822591849105-14.7822591849105
61394339.63265805479154.3673419452088
62209174.99441906683334.0055809331673
63248241.4591896983876.54081030161274
64254221.74080803054632.2591919694536
65202226.390019175034-24.3900191750344
66258295.143129821459-37.1431298214594
67215179.14505832700235.8549416729982
68309221.78492512506787.2150748749332
69240304.829749605321-64.8297496053206
70258252.4261371102085.57386288979208
71276238.62694669864137.3730533013593
7248110.848829339921-62.8488293399212
73455428.02709131845126.9729086815491
74345243.526062015872101.473937984128
75311321.035204972528-10.0352049725277
76346307.86099061198438.1390093880164
77310286.99616520141723.0038347985832
78297366.698908647233-69.6989086472332
79300274.52705180923825.4729481907616
80274338.468549721153-64.468549721153
81292292.353776569249-0.353776569248794
82304297.6696156335736.33038436642721
83186299.662422910992-113.662422910992
841468.248944501476-54.248944501476
85321432.375998954681-111.375998954681
86206234.100626431171-28.1006264311708
87160210.242604010787-50.2426040107873
88217206.00811079107210.9918892089282
89204167.92066114209536.079338857905
90246207.12274082805138.8772591719494
91234200.73678123636133.2632187636389
92175223.609994666834-48.6099946668345
93364214.529290835475149.470709164525
94328277.39566956682350.6043304331768
95158236.875087655664-78.8750876556642
964047.0602837436337-7.06028374363368
97556400.408318789095155.591681210905
98193339.506355618291-146.506355618291
99221261.938986377194-40.9389863771943
100278290.957825224674-12.9578252246736
101230256.434800899247-26.4348008992471
102253274.350341343696-21.3503413436956
103240243.401364887236-3.40136488723579
104252213.03542780522538.9645721947749
105228332.349810889855-104.349810889855
106306254.99828926240251.0017107375978
107206151.43627799289654.5637220071041
1084845.01817042938272.98182957061729
109557481.37843645088475.6215635491159
110279244.07682056036634.9231794396338
111399283.766633200839115.233366799161
112364383.029000640738-19.0290006407376
113306339.729385942654-33.7293859426543
114471357.482938702976113.517061297024
115293384.162006679697-91.1620066796967
116333342.67052322961-9.67052322961013
117316374.425221058632-58.4252210586323
118329389.525310440773-60.5253104407728
119265247.28988282016117.7101171798388
12061102.346172321898-41.3461723218977
121679558.092136901737120.907863098263
122428317.339306690062110.660693309938
123394423.663542247532-29.6635422475318
124352404.903234481384-52.9032344813843
125387342.15561051110144.8443894888989
126590460.23591916362129.76408083638
127177392.9195352337-215.9195352337
128199345.989838784783-146.989838784783
129203304.194980505351-101.194980505351
130255302.772671321031-47.7726713210312
131261203.33670951967857.663290480322
13211544.050751951204370.9492480487957

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 232 & 215.740651709402 & 16.2593482905983 \tabularnewline
14 & 143 & 134.897792830363 & 8.10220716963713 \tabularnewline
15 & 161 & 155.849205058945 & 5.15079494105461 \tabularnewline
16 & 159 & 152.731177116274 & 6.26882288372582 \tabularnewline
17 & 243 & 239.934931731197 & 3.06506826880269 \tabularnewline
18 & 192 & 193.477810257427 & -1.47781025742711 \tabularnewline
19 & 157 & 162.541249649844 & -5.5412496498441 \tabularnewline
20 & 143 & 181.840640687391 & -38.8406406873907 \tabularnewline
21 & 221 & 166.324043074162 & 54.6759569258384 \tabularnewline
22 & 227 & 204.818056287512 & 22.1819437124884 \tabularnewline
23 & 132 & 196.99624173292 & -64.9962417329196 \tabularnewline
24 & 41 & 57.1271979701882 & -16.1271979701882 \tabularnewline
25 & 273 & 243.775279759191 & 29.2247202408092 \tabularnewline
26 & 182 & 163.649754545661 & 18.3502454543391 \tabularnewline
27 & 188 & 186.874252445669 & 1.1257475543311 \tabularnewline
28 & 162 & 182.843347109172 & -20.8433471091718 \tabularnewline
29 & 140 & 258.659625150827 & -118.659625150827 \tabularnewline
30 & 186 & 165.878822142018 & 20.1211778579823 \tabularnewline
31 & 178 & 140.785683653254 & 37.214316346746 \tabularnewline
32 & 236 & 159.327530502905 & 76.6724694970947 \tabularnewline
33 & 202 & 231.302662039948 & -29.3026620399481 \tabularnewline
34 & 184 & 223.510194083648 & -39.5101940836478 \tabularnewline
35 & 119 & 150.791724749882 & -31.7917247498818 \tabularnewline
36 & 16 & 46.8021830357525 & -30.8021830357525 \tabularnewline
37 & 340 & 250.264352306748 & 89.7356476932518 \tabularnewline
38 & 151 & 186.758179985168 & -35.7581799851683 \tabularnewline
39 & 240 & 181.971080561497 & 58.0289194385028 \tabularnewline
40 & 235 & 187.838134304555 & 47.161865695445 \tabularnewline
41 & 174 & 240.562069482239 & -66.5620694822389 \tabularnewline
42 & 309 & 234.383201154111 & 74.616798845889 \tabularnewline
43 & 174 & 237.377856916262 & -63.3778569162625 \tabularnewline
44 & 207 & 238.725683065161 & -31.7256830651607 \tabularnewline
45 & 209 & 219.707467647128 & -10.7074676471283 \tabularnewline
46 & 171 & 213.671709518381 & -42.6717095183814 \tabularnewline
47 & 117 & 143.574250460511 & -26.5742504605115 \tabularnewline
48 & 10 & 41.9581456526026 & -31.9581456526026 \tabularnewline
49 & 339 & 303.823415437235 & 35.1765845627648 \tabularnewline
50 & 139 & 159.307373494151 & -20.3073734941514 \tabularnewline
51 & 186 & 205.886568540422 & -19.886568540422 \tabularnewline
52 & 155 & 178.217974923785 & -23.2179749237851 \tabularnewline
53 & 153 & 149.943062240534 & 3.05693775946577 \tabularnewline
54 & 222 & 237.885248468718 & -15.8852484687179 \tabularnewline
55 & 102 & 140.745791298077 & -38.7457912980766 \tabularnewline
56 & 107 & 166.465142322496 & -59.4651423224961 \tabularnewline
57 & 188 & 147.652373946232 & 40.3476260537684 \tabularnewline
58 & 162 & 144.51794136641 & 17.4820586335899 \tabularnewline
59 & 185 & 104.072610983578 & 80.9273890164219 \tabularnewline
60 & 24 & 38.7822591849105 & -14.7822591849105 \tabularnewline
61 & 394 & 339.632658054791 & 54.3673419452088 \tabularnewline
62 & 209 & 174.994419066833 & 34.0055809331673 \tabularnewline
63 & 248 & 241.459189698387 & 6.54081030161274 \tabularnewline
64 & 254 & 221.740808030546 & 32.2591919694536 \tabularnewline
65 & 202 & 226.390019175034 & -24.3900191750344 \tabularnewline
66 & 258 & 295.143129821459 & -37.1431298214594 \tabularnewline
67 & 215 & 179.145058327002 & 35.8549416729982 \tabularnewline
68 & 309 & 221.784925125067 & 87.2150748749332 \tabularnewline
69 & 240 & 304.829749605321 & -64.8297496053206 \tabularnewline
70 & 258 & 252.426137110208 & 5.57386288979208 \tabularnewline
71 & 276 & 238.626946698641 & 37.3730533013593 \tabularnewline
72 & 48 & 110.848829339921 & -62.8488293399212 \tabularnewline
73 & 455 & 428.027091318451 & 26.9729086815491 \tabularnewline
74 & 345 & 243.526062015872 & 101.473937984128 \tabularnewline
75 & 311 & 321.035204972528 & -10.0352049725277 \tabularnewline
76 & 346 & 307.860990611984 & 38.1390093880164 \tabularnewline
77 & 310 & 286.996165201417 & 23.0038347985832 \tabularnewline
78 & 297 & 366.698908647233 & -69.6989086472332 \tabularnewline
79 & 300 & 274.527051809238 & 25.4729481907616 \tabularnewline
80 & 274 & 338.468549721153 & -64.468549721153 \tabularnewline
81 & 292 & 292.353776569249 & -0.353776569248794 \tabularnewline
82 & 304 & 297.669615633573 & 6.33038436642721 \tabularnewline
83 & 186 & 299.662422910992 & -113.662422910992 \tabularnewline
84 & 14 & 68.248944501476 & -54.248944501476 \tabularnewline
85 & 321 & 432.375998954681 & -111.375998954681 \tabularnewline
86 & 206 & 234.100626431171 & -28.1006264311708 \tabularnewline
87 & 160 & 210.242604010787 & -50.2426040107873 \tabularnewline
88 & 217 & 206.008110791072 & 10.9918892089282 \tabularnewline
89 & 204 & 167.920661142095 & 36.079338857905 \tabularnewline
90 & 246 & 207.122740828051 & 38.8772591719494 \tabularnewline
91 & 234 & 200.736781236361 & 33.2632187636389 \tabularnewline
92 & 175 & 223.609994666834 & -48.6099946668345 \tabularnewline
93 & 364 & 214.529290835475 & 149.470709164525 \tabularnewline
94 & 328 & 277.395669566823 & 50.6043304331768 \tabularnewline
95 & 158 & 236.875087655664 & -78.8750876556642 \tabularnewline
96 & 40 & 47.0602837436337 & -7.06028374363368 \tabularnewline
97 & 556 & 400.408318789095 & 155.591681210905 \tabularnewline
98 & 193 & 339.506355618291 & -146.506355618291 \tabularnewline
99 & 221 & 261.938986377194 & -40.9389863771943 \tabularnewline
100 & 278 & 290.957825224674 & -12.9578252246736 \tabularnewline
101 & 230 & 256.434800899247 & -26.4348008992471 \tabularnewline
102 & 253 & 274.350341343696 & -21.3503413436956 \tabularnewline
103 & 240 & 243.401364887236 & -3.40136488723579 \tabularnewline
104 & 252 & 213.035427805225 & 38.9645721947749 \tabularnewline
105 & 228 & 332.349810889855 & -104.349810889855 \tabularnewline
106 & 306 & 254.998289262402 & 51.0017107375978 \tabularnewline
107 & 206 & 151.436277992896 & 54.5637220071041 \tabularnewline
108 & 48 & 45.0181704293827 & 2.98182957061729 \tabularnewline
109 & 557 & 481.378436450884 & 75.6215635491159 \tabularnewline
110 & 279 & 244.076820560366 & 34.9231794396338 \tabularnewline
111 & 399 & 283.766633200839 & 115.233366799161 \tabularnewline
112 & 364 & 383.029000640738 & -19.0290006407376 \tabularnewline
113 & 306 & 339.729385942654 & -33.7293859426543 \tabularnewline
114 & 471 & 357.482938702976 & 113.517061297024 \tabularnewline
115 & 293 & 384.162006679697 & -91.1620066796967 \tabularnewline
116 & 333 & 342.67052322961 & -9.67052322961013 \tabularnewline
117 & 316 & 374.425221058632 & -58.4252210586323 \tabularnewline
118 & 329 & 389.525310440773 & -60.5253104407728 \tabularnewline
119 & 265 & 247.289882820161 & 17.7101171798388 \tabularnewline
120 & 61 & 102.346172321898 & -41.3461723218977 \tabularnewline
121 & 679 & 558.092136901737 & 120.907863098263 \tabularnewline
122 & 428 & 317.339306690062 & 110.660693309938 \tabularnewline
123 & 394 & 423.663542247532 & -29.6635422475318 \tabularnewline
124 & 352 & 404.903234481384 & -52.9032344813843 \tabularnewline
125 & 387 & 342.155610511101 & 44.8443894888989 \tabularnewline
126 & 590 & 460.23591916362 & 129.76408083638 \tabularnewline
127 & 177 & 392.9195352337 & -215.9195352337 \tabularnewline
128 & 199 & 345.989838784783 & -146.989838784783 \tabularnewline
129 & 203 & 304.194980505351 & -101.194980505351 \tabularnewline
130 & 255 & 302.772671321031 & -47.7726713210312 \tabularnewline
131 & 261 & 203.336709519678 & 57.663290480322 \tabularnewline
132 & 115 & 44.0507519512043 & 70.9492480487957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234792&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]232[/C][C]215.740651709402[/C][C]16.2593482905983[/C][/ROW]
[ROW][C]14[/C][C]143[/C][C]134.897792830363[/C][C]8.10220716963713[/C][/ROW]
[ROW][C]15[/C][C]161[/C][C]155.849205058945[/C][C]5.15079494105461[/C][/ROW]
[ROW][C]16[/C][C]159[/C][C]152.731177116274[/C][C]6.26882288372582[/C][/ROW]
[ROW][C]17[/C][C]243[/C][C]239.934931731197[/C][C]3.06506826880269[/C][/ROW]
[ROW][C]18[/C][C]192[/C][C]193.477810257427[/C][C]-1.47781025742711[/C][/ROW]
[ROW][C]19[/C][C]157[/C][C]162.541249649844[/C][C]-5.5412496498441[/C][/ROW]
[ROW][C]20[/C][C]143[/C][C]181.840640687391[/C][C]-38.8406406873907[/C][/ROW]
[ROW][C]21[/C][C]221[/C][C]166.324043074162[/C][C]54.6759569258384[/C][/ROW]
[ROW][C]22[/C][C]227[/C][C]204.818056287512[/C][C]22.1819437124884[/C][/ROW]
[ROW][C]23[/C][C]132[/C][C]196.99624173292[/C][C]-64.9962417329196[/C][/ROW]
[ROW][C]24[/C][C]41[/C][C]57.1271979701882[/C][C]-16.1271979701882[/C][/ROW]
[ROW][C]25[/C][C]273[/C][C]243.775279759191[/C][C]29.2247202408092[/C][/ROW]
[ROW][C]26[/C][C]182[/C][C]163.649754545661[/C][C]18.3502454543391[/C][/ROW]
[ROW][C]27[/C][C]188[/C][C]186.874252445669[/C][C]1.1257475543311[/C][/ROW]
[ROW][C]28[/C][C]162[/C][C]182.843347109172[/C][C]-20.8433471091718[/C][/ROW]
[ROW][C]29[/C][C]140[/C][C]258.659625150827[/C][C]-118.659625150827[/C][/ROW]
[ROW][C]30[/C][C]186[/C][C]165.878822142018[/C][C]20.1211778579823[/C][/ROW]
[ROW][C]31[/C][C]178[/C][C]140.785683653254[/C][C]37.214316346746[/C][/ROW]
[ROW][C]32[/C][C]236[/C][C]159.327530502905[/C][C]76.6724694970947[/C][/ROW]
[ROW][C]33[/C][C]202[/C][C]231.302662039948[/C][C]-29.3026620399481[/C][/ROW]
[ROW][C]34[/C][C]184[/C][C]223.510194083648[/C][C]-39.5101940836478[/C][/ROW]
[ROW][C]35[/C][C]119[/C][C]150.791724749882[/C][C]-31.7917247498818[/C][/ROW]
[ROW][C]36[/C][C]16[/C][C]46.8021830357525[/C][C]-30.8021830357525[/C][/ROW]
[ROW][C]37[/C][C]340[/C][C]250.264352306748[/C][C]89.7356476932518[/C][/ROW]
[ROW][C]38[/C][C]151[/C][C]186.758179985168[/C][C]-35.7581799851683[/C][/ROW]
[ROW][C]39[/C][C]240[/C][C]181.971080561497[/C][C]58.0289194385028[/C][/ROW]
[ROW][C]40[/C][C]235[/C][C]187.838134304555[/C][C]47.161865695445[/C][/ROW]
[ROW][C]41[/C][C]174[/C][C]240.562069482239[/C][C]-66.5620694822389[/C][/ROW]
[ROW][C]42[/C][C]309[/C][C]234.383201154111[/C][C]74.616798845889[/C][/ROW]
[ROW][C]43[/C][C]174[/C][C]237.377856916262[/C][C]-63.3778569162625[/C][/ROW]
[ROW][C]44[/C][C]207[/C][C]238.725683065161[/C][C]-31.7256830651607[/C][/ROW]
[ROW][C]45[/C][C]209[/C][C]219.707467647128[/C][C]-10.7074676471283[/C][/ROW]
[ROW][C]46[/C][C]171[/C][C]213.671709518381[/C][C]-42.6717095183814[/C][/ROW]
[ROW][C]47[/C][C]117[/C][C]143.574250460511[/C][C]-26.5742504605115[/C][/ROW]
[ROW][C]48[/C][C]10[/C][C]41.9581456526026[/C][C]-31.9581456526026[/C][/ROW]
[ROW][C]49[/C][C]339[/C][C]303.823415437235[/C][C]35.1765845627648[/C][/ROW]
[ROW][C]50[/C][C]139[/C][C]159.307373494151[/C][C]-20.3073734941514[/C][/ROW]
[ROW][C]51[/C][C]186[/C][C]205.886568540422[/C][C]-19.886568540422[/C][/ROW]
[ROW][C]52[/C][C]155[/C][C]178.217974923785[/C][C]-23.2179749237851[/C][/ROW]
[ROW][C]53[/C][C]153[/C][C]149.943062240534[/C][C]3.05693775946577[/C][/ROW]
[ROW][C]54[/C][C]222[/C][C]237.885248468718[/C][C]-15.8852484687179[/C][/ROW]
[ROW][C]55[/C][C]102[/C][C]140.745791298077[/C][C]-38.7457912980766[/C][/ROW]
[ROW][C]56[/C][C]107[/C][C]166.465142322496[/C][C]-59.4651423224961[/C][/ROW]
[ROW][C]57[/C][C]188[/C][C]147.652373946232[/C][C]40.3476260537684[/C][/ROW]
[ROW][C]58[/C][C]162[/C][C]144.51794136641[/C][C]17.4820586335899[/C][/ROW]
[ROW][C]59[/C][C]185[/C][C]104.072610983578[/C][C]80.9273890164219[/C][/ROW]
[ROW][C]60[/C][C]24[/C][C]38.7822591849105[/C][C]-14.7822591849105[/C][/ROW]
[ROW][C]61[/C][C]394[/C][C]339.632658054791[/C][C]54.3673419452088[/C][/ROW]
[ROW][C]62[/C][C]209[/C][C]174.994419066833[/C][C]34.0055809331673[/C][/ROW]
[ROW][C]63[/C][C]248[/C][C]241.459189698387[/C][C]6.54081030161274[/C][/ROW]
[ROW][C]64[/C][C]254[/C][C]221.740808030546[/C][C]32.2591919694536[/C][/ROW]
[ROW][C]65[/C][C]202[/C][C]226.390019175034[/C][C]-24.3900191750344[/C][/ROW]
[ROW][C]66[/C][C]258[/C][C]295.143129821459[/C][C]-37.1431298214594[/C][/ROW]
[ROW][C]67[/C][C]215[/C][C]179.145058327002[/C][C]35.8549416729982[/C][/ROW]
[ROW][C]68[/C][C]309[/C][C]221.784925125067[/C][C]87.2150748749332[/C][/ROW]
[ROW][C]69[/C][C]240[/C][C]304.829749605321[/C][C]-64.8297496053206[/C][/ROW]
[ROW][C]70[/C][C]258[/C][C]252.426137110208[/C][C]5.57386288979208[/C][/ROW]
[ROW][C]71[/C][C]276[/C][C]238.626946698641[/C][C]37.3730533013593[/C][/ROW]
[ROW][C]72[/C][C]48[/C][C]110.848829339921[/C][C]-62.8488293399212[/C][/ROW]
[ROW][C]73[/C][C]455[/C][C]428.027091318451[/C][C]26.9729086815491[/C][/ROW]
[ROW][C]74[/C][C]345[/C][C]243.526062015872[/C][C]101.473937984128[/C][/ROW]
[ROW][C]75[/C][C]311[/C][C]321.035204972528[/C][C]-10.0352049725277[/C][/ROW]
[ROW][C]76[/C][C]346[/C][C]307.860990611984[/C][C]38.1390093880164[/C][/ROW]
[ROW][C]77[/C][C]310[/C][C]286.996165201417[/C][C]23.0038347985832[/C][/ROW]
[ROW][C]78[/C][C]297[/C][C]366.698908647233[/C][C]-69.6989086472332[/C][/ROW]
[ROW][C]79[/C][C]300[/C][C]274.527051809238[/C][C]25.4729481907616[/C][/ROW]
[ROW][C]80[/C][C]274[/C][C]338.468549721153[/C][C]-64.468549721153[/C][/ROW]
[ROW][C]81[/C][C]292[/C][C]292.353776569249[/C][C]-0.353776569248794[/C][/ROW]
[ROW][C]82[/C][C]304[/C][C]297.669615633573[/C][C]6.33038436642721[/C][/ROW]
[ROW][C]83[/C][C]186[/C][C]299.662422910992[/C][C]-113.662422910992[/C][/ROW]
[ROW][C]84[/C][C]14[/C][C]68.248944501476[/C][C]-54.248944501476[/C][/ROW]
[ROW][C]85[/C][C]321[/C][C]432.375998954681[/C][C]-111.375998954681[/C][/ROW]
[ROW][C]86[/C][C]206[/C][C]234.100626431171[/C][C]-28.1006264311708[/C][/ROW]
[ROW][C]87[/C][C]160[/C][C]210.242604010787[/C][C]-50.2426040107873[/C][/ROW]
[ROW][C]88[/C][C]217[/C][C]206.008110791072[/C][C]10.9918892089282[/C][/ROW]
[ROW][C]89[/C][C]204[/C][C]167.920661142095[/C][C]36.079338857905[/C][/ROW]
[ROW][C]90[/C][C]246[/C][C]207.122740828051[/C][C]38.8772591719494[/C][/ROW]
[ROW][C]91[/C][C]234[/C][C]200.736781236361[/C][C]33.2632187636389[/C][/ROW]
[ROW][C]92[/C][C]175[/C][C]223.609994666834[/C][C]-48.6099946668345[/C][/ROW]
[ROW][C]93[/C][C]364[/C][C]214.529290835475[/C][C]149.470709164525[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]277.395669566823[/C][C]50.6043304331768[/C][/ROW]
[ROW][C]95[/C][C]158[/C][C]236.875087655664[/C][C]-78.8750876556642[/C][/ROW]
[ROW][C]96[/C][C]40[/C][C]47.0602837436337[/C][C]-7.06028374363368[/C][/ROW]
[ROW][C]97[/C][C]556[/C][C]400.408318789095[/C][C]155.591681210905[/C][/ROW]
[ROW][C]98[/C][C]193[/C][C]339.506355618291[/C][C]-146.506355618291[/C][/ROW]
[ROW][C]99[/C][C]221[/C][C]261.938986377194[/C][C]-40.9389863771943[/C][/ROW]
[ROW][C]100[/C][C]278[/C][C]290.957825224674[/C][C]-12.9578252246736[/C][/ROW]
[ROW][C]101[/C][C]230[/C][C]256.434800899247[/C][C]-26.4348008992471[/C][/ROW]
[ROW][C]102[/C][C]253[/C][C]274.350341343696[/C][C]-21.3503413436956[/C][/ROW]
[ROW][C]103[/C][C]240[/C][C]243.401364887236[/C][C]-3.40136488723579[/C][/ROW]
[ROW][C]104[/C][C]252[/C][C]213.035427805225[/C][C]38.9645721947749[/C][/ROW]
[ROW][C]105[/C][C]228[/C][C]332.349810889855[/C][C]-104.349810889855[/C][/ROW]
[ROW][C]106[/C][C]306[/C][C]254.998289262402[/C][C]51.0017107375978[/C][/ROW]
[ROW][C]107[/C][C]206[/C][C]151.436277992896[/C][C]54.5637220071041[/C][/ROW]
[ROW][C]108[/C][C]48[/C][C]45.0181704293827[/C][C]2.98182957061729[/C][/ROW]
[ROW][C]109[/C][C]557[/C][C]481.378436450884[/C][C]75.6215635491159[/C][/ROW]
[ROW][C]110[/C][C]279[/C][C]244.076820560366[/C][C]34.9231794396338[/C][/ROW]
[ROW][C]111[/C][C]399[/C][C]283.766633200839[/C][C]115.233366799161[/C][/ROW]
[ROW][C]112[/C][C]364[/C][C]383.029000640738[/C][C]-19.0290006407376[/C][/ROW]
[ROW][C]113[/C][C]306[/C][C]339.729385942654[/C][C]-33.7293859426543[/C][/ROW]
[ROW][C]114[/C][C]471[/C][C]357.482938702976[/C][C]113.517061297024[/C][/ROW]
[ROW][C]115[/C][C]293[/C][C]384.162006679697[/C][C]-91.1620066796967[/C][/ROW]
[ROW][C]116[/C][C]333[/C][C]342.67052322961[/C][C]-9.67052322961013[/C][/ROW]
[ROW][C]117[/C][C]316[/C][C]374.425221058632[/C][C]-58.4252210586323[/C][/ROW]
[ROW][C]118[/C][C]329[/C][C]389.525310440773[/C][C]-60.5253104407728[/C][/ROW]
[ROW][C]119[/C][C]265[/C][C]247.289882820161[/C][C]17.7101171798388[/C][/ROW]
[ROW][C]120[/C][C]61[/C][C]102.346172321898[/C][C]-41.3461723218977[/C][/ROW]
[ROW][C]121[/C][C]679[/C][C]558.092136901737[/C][C]120.907863098263[/C][/ROW]
[ROW][C]122[/C][C]428[/C][C]317.339306690062[/C][C]110.660693309938[/C][/ROW]
[ROW][C]123[/C][C]394[/C][C]423.663542247532[/C][C]-29.6635422475318[/C][/ROW]
[ROW][C]124[/C][C]352[/C][C]404.903234481384[/C][C]-52.9032344813843[/C][/ROW]
[ROW][C]125[/C][C]387[/C][C]342.155610511101[/C][C]44.8443894888989[/C][/ROW]
[ROW][C]126[/C][C]590[/C][C]460.23591916362[/C][C]129.76408083638[/C][/ROW]
[ROW][C]127[/C][C]177[/C][C]392.9195352337[/C][C]-215.9195352337[/C][/ROW]
[ROW][C]128[/C][C]199[/C][C]345.989838784783[/C][C]-146.989838784783[/C][/ROW]
[ROW][C]129[/C][C]203[/C][C]304.194980505351[/C][C]-101.194980505351[/C][/ROW]
[ROW][C]130[/C][C]255[/C][C]302.772671321031[/C][C]-47.7726713210312[/C][/ROW]
[ROW][C]131[/C][C]261[/C][C]203.336709519678[/C][C]57.663290480322[/C][/ROW]
[ROW][C]132[/C][C]115[/C][C]44.0507519512043[/C][C]70.9492480487957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234792&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
13232215.74065170940216.2593482905983
14143134.8977928303638.10220716963713
15161155.8492050589455.15079494105461
16159152.7311771162746.26882288372582
17243239.9349317311973.06506826880269
18192193.477810257427-1.47781025742711
19157162.541249649844-5.5412496498441
20143181.840640687391-38.8406406873907
21221166.32404307416254.6759569258384
22227204.81805628751222.1819437124884
23132196.99624173292-64.9962417329196
244157.1271979701882-16.1271979701882
25273243.77527975919129.2247202408092
26182163.64975454566118.3502454543391
27188186.8742524456691.1257475543311
28162182.843347109172-20.8433471091718
29140258.659625150827-118.659625150827
30186165.87882214201820.1211778579823
31178140.78568365325437.214316346746
32236159.32753050290576.6724694970947
33202231.302662039948-29.3026620399481
34184223.510194083648-39.5101940836478
35119150.791724749882-31.7917247498818
361646.8021830357525-30.8021830357525
37340250.26435230674889.7356476932518
38151186.758179985168-35.7581799851683
39240181.97108056149758.0289194385028
40235187.83813430455547.161865695445
41174240.562069482239-66.5620694822389
42309234.38320115411174.616798845889
43174237.377856916262-63.3778569162625
44207238.725683065161-31.7256830651607
45209219.707467647128-10.7074676471283
46171213.671709518381-42.6717095183814
47117143.574250460511-26.5742504605115
481041.9581456526026-31.9581456526026
49339303.82341543723535.1765845627648
50139159.307373494151-20.3073734941514
51186205.886568540422-19.886568540422
52155178.217974923785-23.2179749237851
53153149.9430622405343.05693775946577
54222237.885248468718-15.8852484687179
55102140.745791298077-38.7457912980766
56107166.465142322496-59.4651423224961
57188147.65237394623240.3476260537684
58162144.5179413664117.4820586335899
59185104.07261098357880.9273890164219
602438.7822591849105-14.7822591849105
61394339.63265805479154.3673419452088
62209174.99441906683334.0055809331673
63248241.4591896983876.54081030161274
64254221.74080803054632.2591919694536
65202226.390019175034-24.3900191750344
66258295.143129821459-37.1431298214594
67215179.14505832700235.8549416729982
68309221.78492512506787.2150748749332
69240304.829749605321-64.8297496053206
70258252.4261371102085.57386288979208
71276238.62694669864137.3730533013593
7248110.848829339921-62.8488293399212
73455428.02709131845126.9729086815491
74345243.526062015872101.473937984128
75311321.035204972528-10.0352049725277
76346307.86099061198438.1390093880164
77310286.99616520141723.0038347985832
78297366.698908647233-69.6989086472332
79300274.52705180923825.4729481907616
80274338.468549721153-64.468549721153
81292292.353776569249-0.353776569248794
82304297.6696156335736.33038436642721
83186299.662422910992-113.662422910992
841468.248944501476-54.248944501476
85321432.375998954681-111.375998954681
86206234.100626431171-28.1006264311708
87160210.242604010787-50.2426040107873
88217206.00811079107210.9918892089282
89204167.92066114209536.079338857905
90246207.12274082805138.8772591719494
91234200.73678123636133.2632187636389
92175223.609994666834-48.6099946668345
93364214.529290835475149.470709164525
94328277.39566956682350.6043304331768
95158236.875087655664-78.8750876556642
964047.0602837436337-7.06028374363368
97556400.408318789095155.591681210905
98193339.506355618291-146.506355618291
99221261.938986377194-40.9389863771943
100278290.957825224674-12.9578252246736
101230256.434800899247-26.4348008992471
102253274.350341343696-21.3503413436956
103240243.401364887236-3.40136488723579
104252213.03542780522538.9645721947749
105228332.349810889855-104.349810889855
106306254.99828926240251.0017107375978
107206151.43627799289654.5637220071041
1084845.01817042938272.98182957061729
109557481.37843645088475.6215635491159
110279244.07682056036634.9231794396338
111399283.766633200839115.233366799161
112364383.029000640738-19.0290006407376
113306339.729385942654-33.7293859426543
114471357.482938702976113.517061297024
115293384.162006679697-91.1620066796967
116333342.67052322961-9.67052322961013
117316374.425221058632-58.4252210586323
118329389.525310440773-60.5253104407728
119265247.28988282016117.7101171798388
12061102.346172321898-41.3461723218977
121679558.092136901737120.907863098263
122428317.339306690062110.660693309938
123394423.663542247532-29.6635422475318
124352404.903234481384-52.9032344813843
125387342.15561051110144.8443894888989
126590460.23591916362129.76408083638
127177392.9195352337-215.9195352337
128199345.989838784783-146.989838784783
129203304.194980505351-101.194980505351
130255302.772671321031-47.7726713210312
131261203.33670951967857.663290480322
13211544.050751951204370.9492480487957







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133619.666105048287497.494938417516741.837271679058
134330.101900145906200.157685647647460.046114644166
135327.850739766646190.5729054043465.128574128992
136308.498102308036164.259034324145452.737170291928
137312.620328269191161.740860950049463.499795588332
138455.891791460627298.652106316724613.13147660453
139172.8633984941879.51094669195675336.215850296417
140237.80925564030468.5646739384192407.053837342189
141271.6236648552496.6852946756476446.562035034832
142332.939083544462152.486490637799513.391676451126
143302.265796160414116.462558265096488.069034055732
144128.569116655788-62.4349360185731319.573169330149

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 619.666105048287 & 497.494938417516 & 741.837271679058 \tabularnewline
134 & 330.101900145906 & 200.157685647647 & 460.046114644166 \tabularnewline
135 & 327.850739766646 & 190.5729054043 & 465.128574128992 \tabularnewline
136 & 308.498102308036 & 164.259034324145 & 452.737170291928 \tabularnewline
137 & 312.620328269191 & 161.740860950049 & 463.499795588332 \tabularnewline
138 & 455.891791460627 & 298.652106316724 & 613.13147660453 \tabularnewline
139 & 172.863398494187 & 9.51094669195675 & 336.215850296417 \tabularnewline
140 & 237.809255640304 & 68.5646739384192 & 407.053837342189 \tabularnewline
141 & 271.62366485524 & 96.6852946756476 & 446.562035034832 \tabularnewline
142 & 332.939083544462 & 152.486490637799 & 513.391676451126 \tabularnewline
143 & 302.265796160414 & 116.462558265096 & 488.069034055732 \tabularnewline
144 & 128.569116655788 & -62.4349360185731 & 319.573169330149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234792&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]133[/C][C]619.666105048287[/C][C]497.494938417516[/C][C]741.837271679058[/C][/ROW]
[ROW][C]134[/C][C]330.101900145906[/C][C]200.157685647647[/C][C]460.046114644166[/C][/ROW]
[ROW][C]135[/C][C]327.850739766646[/C][C]190.5729054043[/C][C]465.128574128992[/C][/ROW]
[ROW][C]136[/C][C]308.498102308036[/C][C]164.259034324145[/C][C]452.737170291928[/C][/ROW]
[ROW][C]137[/C][C]312.620328269191[/C][C]161.740860950049[/C][C]463.499795588332[/C][/ROW]
[ROW][C]138[/C][C]455.891791460627[/C][C]298.652106316724[/C][C]613.13147660453[/C][/ROW]
[ROW][C]139[/C][C]172.863398494187[/C][C]9.51094669195675[/C][C]336.215850296417[/C][/ROW]
[ROW][C]140[/C][C]237.809255640304[/C][C]68.5646739384192[/C][C]407.053837342189[/C][/ROW]
[ROW][C]141[/C][C]271.62366485524[/C][C]96.6852946756476[/C][C]446.562035034832[/C][/ROW]
[ROW][C]142[/C][C]332.939083544462[/C][C]152.486490637799[/C][C]513.391676451126[/C][/ROW]
[ROW][C]143[/C][C]302.265796160414[/C][C]116.462558265096[/C][C]488.069034055732[/C][/ROW]
[ROW][C]144[/C][C]128.569116655788[/C][C]-62.4349360185731[/C][C]319.573169330149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234792&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234792&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
133619.666105048287497.494938417516741.837271679058
134330.101900145906200.157685647647460.046114644166
135327.850739766646190.5729054043465.128574128992
136308.498102308036164.259034324145452.737170291928
137312.620328269191161.740860950049463.499795588332
138455.891791460627298.652106316724613.13147660453
139172.8633984941879.51094669195675336.215850296417
140237.80925564030468.5646739384192407.053837342189
141271.6236648552496.6852946756476446.562035034832
142332.939083544462152.486490637799513.391676451126
143302.265796160414116.462558265096488.069034055732
144128.569116655788-62.4349360185731319.573169330149



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')