Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 05 Aug 2010 13:42:52 +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/05/t128101586740z6c0le8djopyn.htm/, Retrieved Sun, 05 May 2024 09:17:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78409, Retrieved Sun, 05 May 2024 09:17:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMathias Goossenaerts
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 - Sta...] [2010-08-05 13:42:52] [f7fc4e1bbbe57039ee5ebdd2c8b864c0] [Current]
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Dataseries X:
36
35
34
32
52
51
36
26
27
27
28
30
28
29
25
28
55
53
42
32
37
41
37
38
39
32
36
39
83
83
66
53
72
77
69
72
81
71
63
66
114
116
109
97
111
120
110
106
115
110
103
112
163
166
156
140
166
176
163
162
171
167
163
168
222
216
197
178
204
220
196
195
213
218
216
225
280
272
252
230
248
259
240
237
252
250
255
255
313
291
271
247
268
283
259
259
267
270
279
269
334
326
301
276
301
313
291
287
289
298
320
312
385
380
351
322
350
363
344
345




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78409&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]1 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=78409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78409&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.601667916362739
beta0.0534961536760316
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.601667916362739 \tabularnewline
beta & 0.0534961536760316 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78409&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]0.601667916362739[/C][/ROW]
[ROW][C]beta[/C][C]0.0534961536760316[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78409&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
alpha0.601667916362739
beta0.0534961536760316
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132828.6610576923077-0.661057692307701
142929.0120022848353-0.0120022848352548
152524.58640970874050.413590291259538
162827.09686139512530.90313860487474
175553.97259451139451.02740548860555
185352.20616404223710.793835957762909
194238.61642008072093.38357991927913
203231.69374898630310.306251013696908
213733.97107176463573.02892823536429
224136.90070060924864.09929939075144
233741.1062812553989-4.10628125539889
243840.9926587481785-2.99265874817853
253937.06442222084371.93557777915627
263239.5188411962294-7.51884119622937
273630.78715218943915.21284781056087
283936.57563977987992.42436022012006
298364.660579892360818.3394201076392
308374.01885263683628.98114736316384
316667.4519113967683-1.45191139676832
325357.3036239330653-4.30362393306527
337258.653027325727213.3469726742728
347769.31032648273977.68967351726033
356973.6164079359505-4.61640793595049
367274.8318646627762-2.83186466277621
378174.16103748594096.83896251405915
387177.1550821602728-6.15508216027283
396375.7146734558376-12.7146734558376
406670.428280962221-4.42828096222098
41114101.33139864425512.6686013557446
42116103.96920816414112.0307918358593
4310995.598663545122913.4013364548771
449794.24659588126762.75340411873236
45111108.0953552643682.90464473563188
46120111.1028203035198.89717969648059
47110112.158841656803-2.15884165680269
48106116.568208733904-10.568208733904
49115115.85029392439-0.850293924389959
50110109.5499429774550.450057022545423
51103110.191266184242-7.19126618424195
52112112.427175337348-0.427175337347634
53163153.5749586397649.42504136023553
54166154.92985395516511.0701460448349
55156147.4190230245748.58097697542607
56140139.6619056671390.338094332861033
57166152.77657227729013.2234277227102
58176165.37054439156710.6294556084333
59163164.111616664646-1.11161666464602
60162166.881815760854-4.88181576085424
61171174.719676939564-3.71967693956404
62167168.382023717026-1.38202371702567
63163165.989431415208-2.98943141520823
64168174.695221143629-6.69522114362937
65222217.041844311054.95815568894989
66216217.266348439443-1.26634843944308
67197201.846347553377-4.8463475533766
68178182.79966987299-4.79966987298999
69204197.8630161610366.13698383896426
70220204.83921509951315.1607849004873
71196201.454821641072-5.4548216410721
72195199.795292596558-4.79529259655803
73213207.8361442890165.16385571098436
74218207.74853859749810.2514614025021
75216212.0635537090843.93644629091582
76225224.0316042879780.968395712021987
77280276.4490793193613.55092068063914
78272274.120166637217-2.12016663721715
79252257.505631495046-5.50563149504649
80230238.804865984211-8.80486598421086
81248256.40990835776-8.40990835775995
82259258.3550328356790.644967164320974
83240237.6847149800322.3152850199684
84237240.872652118435-3.8726521184347
85252253.375102955871-1.37510295587134
86250251.108730943252-1.10873094325166
87255245.4365188139869.56348118601386
88255259.152332045134-4.1523320451343
89313308.8971376402974.10286235970273
90291304.038705444525-13.0387054445246
91271278.552233324085-7.55223332408542
92247256.285965185278-9.2859651852782
93268272.723447776690-4.72344777668951
94283279.5766784316843.42332156831594
95259260.416008828737-1.41600882873661
96259257.9466537797991.05334622020098
97267273.618887948337-6.61888794833737
98270267.3459361925732.65406380742729
99279267.35220713447611.6477928655236
100269276.089168638958-7.08916863895843
101334326.4912882168547.50871178314645
102326316.0996392761839.9003607238173
103301306.584272393367-5.58427239336697
104276284.858772003442-8.85877200344248
105301303.431739945875-2.43173994587499
106313315.043760152929-2.04376015292894
107291290.6249166719270.375083328072833
108287290.233331739831-3.23333173983139
109289300.148841420857-11.1488414208574
110298294.5768000768053.42319992319545
111320298.38580638476521.6141936152353
112312305.7339662881526.26603371184842
113385370.49441732609514.5055826739048
114380365.99856990382614.0014300961735
115351353.647997782839-2.64799778283901
116322333.344670072757-11.3446700727569
117350353.861881279653-3.86188127965318
118363365.601779590946-2.60177959094551
119344342.6265392158381.37346078416221
120345342.2462757041662.75372429583427

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 28 & 28.6610576923077 & -0.661057692307701 \tabularnewline
14 & 29 & 29.0120022848353 & -0.0120022848352548 \tabularnewline
15 & 25 & 24.5864097087405 & 0.413590291259538 \tabularnewline
16 & 28 & 27.0968613951253 & 0.90313860487474 \tabularnewline
17 & 55 & 53.9725945113945 & 1.02740548860555 \tabularnewline
18 & 53 & 52.2061640422371 & 0.793835957762909 \tabularnewline
19 & 42 & 38.6164200807209 & 3.38357991927913 \tabularnewline
20 & 32 & 31.6937489863031 & 0.306251013696908 \tabularnewline
21 & 37 & 33.9710717646357 & 3.02892823536429 \tabularnewline
22 & 41 & 36.9007006092486 & 4.09929939075144 \tabularnewline
23 & 37 & 41.1062812553989 & -4.10628125539889 \tabularnewline
24 & 38 & 40.9926587481785 & -2.99265874817853 \tabularnewline
25 & 39 & 37.0644222208437 & 1.93557777915627 \tabularnewline
26 & 32 & 39.5188411962294 & -7.51884119622937 \tabularnewline
27 & 36 & 30.7871521894391 & 5.21284781056087 \tabularnewline
28 & 39 & 36.5756397798799 & 2.42436022012006 \tabularnewline
29 & 83 & 64.6605798923608 & 18.3394201076392 \tabularnewline
30 & 83 & 74.0188526368362 & 8.98114736316384 \tabularnewline
31 & 66 & 67.4519113967683 & -1.45191139676832 \tabularnewline
32 & 53 & 57.3036239330653 & -4.30362393306527 \tabularnewline
33 & 72 & 58.6530273257272 & 13.3469726742728 \tabularnewline
34 & 77 & 69.3103264827397 & 7.68967351726033 \tabularnewline
35 & 69 & 73.6164079359505 & -4.61640793595049 \tabularnewline
36 & 72 & 74.8318646627762 & -2.83186466277621 \tabularnewline
37 & 81 & 74.1610374859409 & 6.83896251405915 \tabularnewline
38 & 71 & 77.1550821602728 & -6.15508216027283 \tabularnewline
39 & 63 & 75.7146734558376 & -12.7146734558376 \tabularnewline
40 & 66 & 70.428280962221 & -4.42828096222098 \tabularnewline
41 & 114 & 101.331398644255 & 12.6686013557446 \tabularnewline
42 & 116 & 103.969208164141 & 12.0307918358593 \tabularnewline
43 & 109 & 95.5986635451229 & 13.4013364548771 \tabularnewline
44 & 97 & 94.2465958812676 & 2.75340411873236 \tabularnewline
45 & 111 & 108.095355264368 & 2.90464473563188 \tabularnewline
46 & 120 & 111.102820303519 & 8.89717969648059 \tabularnewline
47 & 110 & 112.158841656803 & -2.15884165680269 \tabularnewline
48 & 106 & 116.568208733904 & -10.568208733904 \tabularnewline
49 & 115 & 115.85029392439 & -0.850293924389959 \tabularnewline
50 & 110 & 109.549942977455 & 0.450057022545423 \tabularnewline
51 & 103 & 110.191266184242 & -7.19126618424195 \tabularnewline
52 & 112 & 112.427175337348 & -0.427175337347634 \tabularnewline
53 & 163 & 153.574958639764 & 9.42504136023553 \tabularnewline
54 & 166 & 154.929853955165 & 11.0701460448349 \tabularnewline
55 & 156 & 147.419023024574 & 8.58097697542607 \tabularnewline
56 & 140 & 139.661905667139 & 0.338094332861033 \tabularnewline
57 & 166 & 152.776572277290 & 13.2234277227102 \tabularnewline
58 & 176 & 165.370544391567 & 10.6294556084333 \tabularnewline
59 & 163 & 164.111616664646 & -1.11161666464602 \tabularnewline
60 & 162 & 166.881815760854 & -4.88181576085424 \tabularnewline
61 & 171 & 174.719676939564 & -3.71967693956404 \tabularnewline
62 & 167 & 168.382023717026 & -1.38202371702567 \tabularnewline
63 & 163 & 165.989431415208 & -2.98943141520823 \tabularnewline
64 & 168 & 174.695221143629 & -6.69522114362937 \tabularnewline
65 & 222 & 217.04184431105 & 4.95815568894989 \tabularnewline
66 & 216 & 217.266348439443 & -1.26634843944308 \tabularnewline
67 & 197 & 201.846347553377 & -4.8463475533766 \tabularnewline
68 & 178 & 182.79966987299 & -4.79966987298999 \tabularnewline
69 & 204 & 197.863016161036 & 6.13698383896426 \tabularnewline
70 & 220 & 204.839215099513 & 15.1607849004873 \tabularnewline
71 & 196 & 201.454821641072 & -5.4548216410721 \tabularnewline
72 & 195 & 199.795292596558 & -4.79529259655803 \tabularnewline
73 & 213 & 207.836144289016 & 5.16385571098436 \tabularnewline
74 & 218 & 207.748538597498 & 10.2514614025021 \tabularnewline
75 & 216 & 212.063553709084 & 3.93644629091582 \tabularnewline
76 & 225 & 224.031604287978 & 0.968395712021987 \tabularnewline
77 & 280 & 276.449079319361 & 3.55092068063914 \tabularnewline
78 & 272 & 274.120166637217 & -2.12016663721715 \tabularnewline
79 & 252 & 257.505631495046 & -5.50563149504649 \tabularnewline
80 & 230 & 238.804865984211 & -8.80486598421086 \tabularnewline
81 & 248 & 256.40990835776 & -8.40990835775995 \tabularnewline
82 & 259 & 258.355032835679 & 0.644967164320974 \tabularnewline
83 & 240 & 237.684714980032 & 2.3152850199684 \tabularnewline
84 & 237 & 240.872652118435 & -3.8726521184347 \tabularnewline
85 & 252 & 253.375102955871 & -1.37510295587134 \tabularnewline
86 & 250 & 251.108730943252 & -1.10873094325166 \tabularnewline
87 & 255 & 245.436518813986 & 9.56348118601386 \tabularnewline
88 & 255 & 259.152332045134 & -4.1523320451343 \tabularnewline
89 & 313 & 308.897137640297 & 4.10286235970273 \tabularnewline
90 & 291 & 304.038705444525 & -13.0387054445246 \tabularnewline
91 & 271 & 278.552233324085 & -7.55223332408542 \tabularnewline
92 & 247 & 256.285965185278 & -9.2859651852782 \tabularnewline
93 & 268 & 272.723447776690 & -4.72344777668951 \tabularnewline
94 & 283 & 279.576678431684 & 3.42332156831594 \tabularnewline
95 & 259 & 260.416008828737 & -1.41600882873661 \tabularnewline
96 & 259 & 257.946653779799 & 1.05334622020098 \tabularnewline
97 & 267 & 273.618887948337 & -6.61888794833737 \tabularnewline
98 & 270 & 267.345936192573 & 2.65406380742729 \tabularnewline
99 & 279 & 267.352207134476 & 11.6477928655236 \tabularnewline
100 & 269 & 276.089168638958 & -7.08916863895843 \tabularnewline
101 & 334 & 326.491288216854 & 7.50871178314645 \tabularnewline
102 & 326 & 316.099639276183 & 9.9003607238173 \tabularnewline
103 & 301 & 306.584272393367 & -5.58427239336697 \tabularnewline
104 & 276 & 284.858772003442 & -8.85877200344248 \tabularnewline
105 & 301 & 303.431739945875 & -2.43173994587499 \tabularnewline
106 & 313 & 315.043760152929 & -2.04376015292894 \tabularnewline
107 & 291 & 290.624916671927 & 0.375083328072833 \tabularnewline
108 & 287 & 290.233331739831 & -3.23333173983139 \tabularnewline
109 & 289 & 300.148841420857 & -11.1488414208574 \tabularnewline
110 & 298 & 294.576800076805 & 3.42319992319545 \tabularnewline
111 & 320 & 298.385806384765 & 21.6141936152353 \tabularnewline
112 & 312 & 305.733966288152 & 6.26603371184842 \tabularnewline
113 & 385 & 370.494417326095 & 14.5055826739048 \tabularnewline
114 & 380 & 365.998569903826 & 14.0014300961735 \tabularnewline
115 & 351 & 353.647997782839 & -2.64799778283901 \tabularnewline
116 & 322 & 333.344670072757 & -11.3446700727569 \tabularnewline
117 & 350 & 353.861881279653 & -3.86188127965318 \tabularnewline
118 & 363 & 365.601779590946 & -2.60177959094551 \tabularnewline
119 & 344 & 342.626539215838 & 1.37346078416221 \tabularnewline
120 & 345 & 342.246275704166 & 2.75372429583427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78409&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]28[/C][C]28.6610576923077[/C][C]-0.661057692307701[/C][/ROW]
[ROW][C]14[/C][C]29[/C][C]29.0120022848353[/C][C]-0.0120022848352548[/C][/ROW]
[ROW][C]15[/C][C]25[/C][C]24.5864097087405[/C][C]0.413590291259538[/C][/ROW]
[ROW][C]16[/C][C]28[/C][C]27.0968613951253[/C][C]0.90313860487474[/C][/ROW]
[ROW][C]17[/C][C]55[/C][C]53.9725945113945[/C][C]1.02740548860555[/C][/ROW]
[ROW][C]18[/C][C]53[/C][C]52.2061640422371[/C][C]0.793835957762909[/C][/ROW]
[ROW][C]19[/C][C]42[/C][C]38.6164200807209[/C][C]3.38357991927913[/C][/ROW]
[ROW][C]20[/C][C]32[/C][C]31.6937489863031[/C][C]0.306251013696908[/C][/ROW]
[ROW][C]21[/C][C]37[/C][C]33.9710717646357[/C][C]3.02892823536429[/C][/ROW]
[ROW][C]22[/C][C]41[/C][C]36.9007006092486[/C][C]4.09929939075144[/C][/ROW]
[ROW][C]23[/C][C]37[/C][C]41.1062812553989[/C][C]-4.10628125539889[/C][/ROW]
[ROW][C]24[/C][C]38[/C][C]40.9926587481785[/C][C]-2.99265874817853[/C][/ROW]
[ROW][C]25[/C][C]39[/C][C]37.0644222208437[/C][C]1.93557777915627[/C][/ROW]
[ROW][C]26[/C][C]32[/C][C]39.5188411962294[/C][C]-7.51884119622937[/C][/ROW]
[ROW][C]27[/C][C]36[/C][C]30.7871521894391[/C][C]5.21284781056087[/C][/ROW]
[ROW][C]28[/C][C]39[/C][C]36.5756397798799[/C][C]2.42436022012006[/C][/ROW]
[ROW][C]29[/C][C]83[/C][C]64.6605798923608[/C][C]18.3394201076392[/C][/ROW]
[ROW][C]30[/C][C]83[/C][C]74.0188526368362[/C][C]8.98114736316384[/C][/ROW]
[ROW][C]31[/C][C]66[/C][C]67.4519113967683[/C][C]-1.45191139676832[/C][/ROW]
[ROW][C]32[/C][C]53[/C][C]57.3036239330653[/C][C]-4.30362393306527[/C][/ROW]
[ROW][C]33[/C][C]72[/C][C]58.6530273257272[/C][C]13.3469726742728[/C][/ROW]
[ROW][C]34[/C][C]77[/C][C]69.3103264827397[/C][C]7.68967351726033[/C][/ROW]
[ROW][C]35[/C][C]69[/C][C]73.6164079359505[/C][C]-4.61640793595049[/C][/ROW]
[ROW][C]36[/C][C]72[/C][C]74.8318646627762[/C][C]-2.83186466277621[/C][/ROW]
[ROW][C]37[/C][C]81[/C][C]74.1610374859409[/C][C]6.83896251405915[/C][/ROW]
[ROW][C]38[/C][C]71[/C][C]77.1550821602728[/C][C]-6.15508216027283[/C][/ROW]
[ROW][C]39[/C][C]63[/C][C]75.7146734558376[/C][C]-12.7146734558376[/C][/ROW]
[ROW][C]40[/C][C]66[/C][C]70.428280962221[/C][C]-4.42828096222098[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]101.331398644255[/C][C]12.6686013557446[/C][/ROW]
[ROW][C]42[/C][C]116[/C][C]103.969208164141[/C][C]12.0307918358593[/C][/ROW]
[ROW][C]43[/C][C]109[/C][C]95.5986635451229[/C][C]13.4013364548771[/C][/ROW]
[ROW][C]44[/C][C]97[/C][C]94.2465958812676[/C][C]2.75340411873236[/C][/ROW]
[ROW][C]45[/C][C]111[/C][C]108.095355264368[/C][C]2.90464473563188[/C][/ROW]
[ROW][C]46[/C][C]120[/C][C]111.102820303519[/C][C]8.89717969648059[/C][/ROW]
[ROW][C]47[/C][C]110[/C][C]112.158841656803[/C][C]-2.15884165680269[/C][/ROW]
[ROW][C]48[/C][C]106[/C][C]116.568208733904[/C][C]-10.568208733904[/C][/ROW]
[ROW][C]49[/C][C]115[/C][C]115.85029392439[/C][C]-0.850293924389959[/C][/ROW]
[ROW][C]50[/C][C]110[/C][C]109.549942977455[/C][C]0.450057022545423[/C][/ROW]
[ROW][C]51[/C][C]103[/C][C]110.191266184242[/C][C]-7.19126618424195[/C][/ROW]
[ROW][C]52[/C][C]112[/C][C]112.427175337348[/C][C]-0.427175337347634[/C][/ROW]
[ROW][C]53[/C][C]163[/C][C]153.574958639764[/C][C]9.42504136023553[/C][/ROW]
[ROW][C]54[/C][C]166[/C][C]154.929853955165[/C][C]11.0701460448349[/C][/ROW]
[ROW][C]55[/C][C]156[/C][C]147.419023024574[/C][C]8.58097697542607[/C][/ROW]
[ROW][C]56[/C][C]140[/C][C]139.661905667139[/C][C]0.338094332861033[/C][/ROW]
[ROW][C]57[/C][C]166[/C][C]152.776572277290[/C][C]13.2234277227102[/C][/ROW]
[ROW][C]58[/C][C]176[/C][C]165.370544391567[/C][C]10.6294556084333[/C][/ROW]
[ROW][C]59[/C][C]163[/C][C]164.111616664646[/C][C]-1.11161666464602[/C][/ROW]
[ROW][C]60[/C][C]162[/C][C]166.881815760854[/C][C]-4.88181576085424[/C][/ROW]
[ROW][C]61[/C][C]171[/C][C]174.719676939564[/C][C]-3.71967693956404[/C][/ROW]
[ROW][C]62[/C][C]167[/C][C]168.382023717026[/C][C]-1.38202371702567[/C][/ROW]
[ROW][C]63[/C][C]163[/C][C]165.989431415208[/C][C]-2.98943141520823[/C][/ROW]
[ROW][C]64[/C][C]168[/C][C]174.695221143629[/C][C]-6.69522114362937[/C][/ROW]
[ROW][C]65[/C][C]222[/C][C]217.04184431105[/C][C]4.95815568894989[/C][/ROW]
[ROW][C]66[/C][C]216[/C][C]217.266348439443[/C][C]-1.26634843944308[/C][/ROW]
[ROW][C]67[/C][C]197[/C][C]201.846347553377[/C][C]-4.8463475533766[/C][/ROW]
[ROW][C]68[/C][C]178[/C][C]182.79966987299[/C][C]-4.79966987298999[/C][/ROW]
[ROW][C]69[/C][C]204[/C][C]197.863016161036[/C][C]6.13698383896426[/C][/ROW]
[ROW][C]70[/C][C]220[/C][C]204.839215099513[/C][C]15.1607849004873[/C][/ROW]
[ROW][C]71[/C][C]196[/C][C]201.454821641072[/C][C]-5.4548216410721[/C][/ROW]
[ROW][C]72[/C][C]195[/C][C]199.795292596558[/C][C]-4.79529259655803[/C][/ROW]
[ROW][C]73[/C][C]213[/C][C]207.836144289016[/C][C]5.16385571098436[/C][/ROW]
[ROW][C]74[/C][C]218[/C][C]207.748538597498[/C][C]10.2514614025021[/C][/ROW]
[ROW][C]75[/C][C]216[/C][C]212.063553709084[/C][C]3.93644629091582[/C][/ROW]
[ROW][C]76[/C][C]225[/C][C]224.031604287978[/C][C]0.968395712021987[/C][/ROW]
[ROW][C]77[/C][C]280[/C][C]276.449079319361[/C][C]3.55092068063914[/C][/ROW]
[ROW][C]78[/C][C]272[/C][C]274.120166637217[/C][C]-2.12016663721715[/C][/ROW]
[ROW][C]79[/C][C]252[/C][C]257.505631495046[/C][C]-5.50563149504649[/C][/ROW]
[ROW][C]80[/C][C]230[/C][C]238.804865984211[/C][C]-8.80486598421086[/C][/ROW]
[ROW][C]81[/C][C]248[/C][C]256.40990835776[/C][C]-8.40990835775995[/C][/ROW]
[ROW][C]82[/C][C]259[/C][C]258.355032835679[/C][C]0.644967164320974[/C][/ROW]
[ROW][C]83[/C][C]240[/C][C]237.684714980032[/C][C]2.3152850199684[/C][/ROW]
[ROW][C]84[/C][C]237[/C][C]240.872652118435[/C][C]-3.8726521184347[/C][/ROW]
[ROW][C]85[/C][C]252[/C][C]253.375102955871[/C][C]-1.37510295587134[/C][/ROW]
[ROW][C]86[/C][C]250[/C][C]251.108730943252[/C][C]-1.10873094325166[/C][/ROW]
[ROW][C]87[/C][C]255[/C][C]245.436518813986[/C][C]9.56348118601386[/C][/ROW]
[ROW][C]88[/C][C]255[/C][C]259.152332045134[/C][C]-4.1523320451343[/C][/ROW]
[ROW][C]89[/C][C]313[/C][C]308.897137640297[/C][C]4.10286235970273[/C][/ROW]
[ROW][C]90[/C][C]291[/C][C]304.038705444525[/C][C]-13.0387054445246[/C][/ROW]
[ROW][C]91[/C][C]271[/C][C]278.552233324085[/C][C]-7.55223332408542[/C][/ROW]
[ROW][C]92[/C][C]247[/C][C]256.285965185278[/C][C]-9.2859651852782[/C][/ROW]
[ROW][C]93[/C][C]268[/C][C]272.723447776690[/C][C]-4.72344777668951[/C][/ROW]
[ROW][C]94[/C][C]283[/C][C]279.576678431684[/C][C]3.42332156831594[/C][/ROW]
[ROW][C]95[/C][C]259[/C][C]260.416008828737[/C][C]-1.41600882873661[/C][/ROW]
[ROW][C]96[/C][C]259[/C][C]257.946653779799[/C][C]1.05334622020098[/C][/ROW]
[ROW][C]97[/C][C]267[/C][C]273.618887948337[/C][C]-6.61888794833737[/C][/ROW]
[ROW][C]98[/C][C]270[/C][C]267.345936192573[/C][C]2.65406380742729[/C][/ROW]
[ROW][C]99[/C][C]279[/C][C]267.352207134476[/C][C]11.6477928655236[/C][/ROW]
[ROW][C]100[/C][C]269[/C][C]276.089168638958[/C][C]-7.08916863895843[/C][/ROW]
[ROW][C]101[/C][C]334[/C][C]326.491288216854[/C][C]7.50871178314645[/C][/ROW]
[ROW][C]102[/C][C]326[/C][C]316.099639276183[/C][C]9.9003607238173[/C][/ROW]
[ROW][C]103[/C][C]301[/C][C]306.584272393367[/C][C]-5.58427239336697[/C][/ROW]
[ROW][C]104[/C][C]276[/C][C]284.858772003442[/C][C]-8.85877200344248[/C][/ROW]
[ROW][C]105[/C][C]301[/C][C]303.431739945875[/C][C]-2.43173994587499[/C][/ROW]
[ROW][C]106[/C][C]313[/C][C]315.043760152929[/C][C]-2.04376015292894[/C][/ROW]
[ROW][C]107[/C][C]291[/C][C]290.624916671927[/C][C]0.375083328072833[/C][/ROW]
[ROW][C]108[/C][C]287[/C][C]290.233331739831[/C][C]-3.23333173983139[/C][/ROW]
[ROW][C]109[/C][C]289[/C][C]300.148841420857[/C][C]-11.1488414208574[/C][/ROW]
[ROW][C]110[/C][C]298[/C][C]294.576800076805[/C][C]3.42319992319545[/C][/ROW]
[ROW][C]111[/C][C]320[/C][C]298.385806384765[/C][C]21.6141936152353[/C][/ROW]
[ROW][C]112[/C][C]312[/C][C]305.733966288152[/C][C]6.26603371184842[/C][/ROW]
[ROW][C]113[/C][C]385[/C][C]370.494417326095[/C][C]14.5055826739048[/C][/ROW]
[ROW][C]114[/C][C]380[/C][C]365.998569903826[/C][C]14.0014300961735[/C][/ROW]
[ROW][C]115[/C][C]351[/C][C]353.647997782839[/C][C]-2.64799778283901[/C][/ROW]
[ROW][C]116[/C][C]322[/C][C]333.344670072757[/C][C]-11.3446700727569[/C][/ROW]
[ROW][C]117[/C][C]350[/C][C]353.861881279653[/C][C]-3.86188127965318[/C][/ROW]
[ROW][C]118[/C][C]363[/C][C]365.601779590946[/C][C]-2.60177959094551[/C][/ROW]
[ROW][C]119[/C][C]344[/C][C]342.626539215838[/C][C]1.37346078416221[/C][/ROW]
[ROW][C]120[/C][C]345[/C][C]342.246275704166[/C][C]2.75372429583427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78409&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
132828.6610576923077-0.661057692307701
142929.0120022848353-0.0120022848352548
152524.58640970874050.413590291259538
162827.09686139512530.90313860487474
175553.97259451139451.02740548860555
185352.20616404223710.793835957762909
194238.61642008072093.38357991927913
203231.69374898630310.306251013696908
213733.97107176463573.02892823536429
224136.90070060924864.09929939075144
233741.1062812553989-4.10628125539889
243840.9926587481785-2.99265874817853
253937.06442222084371.93557777915627
263239.5188411962294-7.51884119622937
273630.78715218943915.21284781056087
283936.57563977987992.42436022012006
298364.660579892360818.3394201076392
308374.01885263683628.98114736316384
316667.4519113967683-1.45191139676832
325357.3036239330653-4.30362393306527
337258.653027325727213.3469726742728
347769.31032648273977.68967351726033
356973.6164079359505-4.61640793595049
367274.8318646627762-2.83186466277621
378174.16103748594096.83896251405915
387177.1550821602728-6.15508216027283
396375.7146734558376-12.7146734558376
406670.428280962221-4.42828096222098
41114101.33139864425512.6686013557446
42116103.96920816414112.0307918358593
4310995.598663545122913.4013364548771
449794.24659588126762.75340411873236
45111108.0953552643682.90464473563188
46120111.1028203035198.89717969648059
47110112.158841656803-2.15884165680269
48106116.568208733904-10.568208733904
49115115.85029392439-0.850293924389959
50110109.5499429774550.450057022545423
51103110.191266184242-7.19126618424195
52112112.427175337348-0.427175337347634
53163153.5749586397649.42504136023553
54166154.92985395516511.0701460448349
55156147.4190230245748.58097697542607
56140139.6619056671390.338094332861033
57166152.77657227729013.2234277227102
58176165.37054439156710.6294556084333
59163164.111616664646-1.11161666464602
60162166.881815760854-4.88181576085424
61171174.719676939564-3.71967693956404
62167168.382023717026-1.38202371702567
63163165.989431415208-2.98943141520823
64168174.695221143629-6.69522114362937
65222217.041844311054.95815568894989
66216217.266348439443-1.26634843944308
67197201.846347553377-4.8463475533766
68178182.79966987299-4.79966987298999
69204197.8630161610366.13698383896426
70220204.83921509951315.1607849004873
71196201.454821641072-5.4548216410721
72195199.795292596558-4.79529259655803
73213207.8361442890165.16385571098436
74218207.74853859749810.2514614025021
75216212.0635537090843.93644629091582
76225224.0316042879780.968395712021987
77280276.4490793193613.55092068063914
78272274.120166637217-2.12016663721715
79252257.505631495046-5.50563149504649
80230238.804865984211-8.80486598421086
81248256.40990835776-8.40990835775995
82259258.3550328356790.644967164320974
83240237.6847149800322.3152850199684
84237240.872652118435-3.8726521184347
85252253.375102955871-1.37510295587134
86250251.108730943252-1.10873094325166
87255245.4365188139869.56348118601386
88255259.152332045134-4.1523320451343
89313308.8971376402974.10286235970273
90291304.038705444525-13.0387054445246
91271278.552233324085-7.55223332408542
92247256.285965185278-9.2859651852782
93268272.723447776690-4.72344777668951
94283279.5766784316843.42332156831594
95259260.416008828737-1.41600882873661
96259257.9466537797991.05334622020098
97267273.618887948337-6.61888794833737
98270267.3459361925732.65406380742729
99279267.35220713447611.6477928655236
100269276.089168638958-7.08916863895843
101334326.4912882168547.50871178314645
102326316.0996392761839.9003607238173
103301306.584272393367-5.58427239336697
104276284.858772003442-8.85877200344248
105301303.431739945875-2.43173994587499
106313315.043760152929-2.04376015292894
107291290.6249166719270.375083328072833
108287290.233331739831-3.23333173983139
109289300.148841420857-11.1488414208574
110298294.5768000768053.42319992319545
111320298.38580638476521.6141936152353
112312305.7339662881526.26603371184842
113385370.49441732609514.5055826739048
114380365.99856990382614.0014300961735
115351353.647997782839-2.64799778283901
116322333.344670072757-11.3446700727569
117350353.861881279653-3.86188127965318
118363365.601779590946-2.60177959094551
119344342.6265392158381.37346078416221
120345342.2462757041662.75372429583427







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121353.651685569883339.688594721905367.614776417862
122361.991584982937345.459781017536378.523388948339
123372.276364865005353.308218648937391.244511081073
124361.099945830178339.7729215597382.426970100656
125425.764370218070402.124177852895449.404562583244
126412.265237017782386.337554205881438.192919829682
127384.332867497281356.129958788011412.535776206552
128361.71823756373331.242991236539392.19348389092
129391.966603668744359.215138880941424.718068456546
130406.581109077463371.544535994063441.617682160862
131386.887583162421349.55323390625424.221932418592
132386.319389504836346.671704058641425.967074951032

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 353.651685569883 & 339.688594721905 & 367.614776417862 \tabularnewline
122 & 361.991584982937 & 345.459781017536 & 378.523388948339 \tabularnewline
123 & 372.276364865005 & 353.308218648937 & 391.244511081073 \tabularnewline
124 & 361.099945830178 & 339.7729215597 & 382.426970100656 \tabularnewline
125 & 425.764370218070 & 402.124177852895 & 449.404562583244 \tabularnewline
126 & 412.265237017782 & 386.337554205881 & 438.192919829682 \tabularnewline
127 & 384.332867497281 & 356.129958788011 & 412.535776206552 \tabularnewline
128 & 361.71823756373 & 331.242991236539 & 392.19348389092 \tabularnewline
129 & 391.966603668744 & 359.215138880941 & 424.718068456546 \tabularnewline
130 & 406.581109077463 & 371.544535994063 & 441.617682160862 \tabularnewline
131 & 386.887583162421 & 349.55323390625 & 424.221932418592 \tabularnewline
132 & 386.319389504836 & 346.671704058641 & 425.967074951032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78409&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]353.651685569883[/C][C]339.688594721905[/C][C]367.614776417862[/C][/ROW]
[ROW][C]122[/C][C]361.991584982937[/C][C]345.459781017536[/C][C]378.523388948339[/C][/ROW]
[ROW][C]123[/C][C]372.276364865005[/C][C]353.308218648937[/C][C]391.244511081073[/C][/ROW]
[ROW][C]124[/C][C]361.099945830178[/C][C]339.7729215597[/C][C]382.426970100656[/C][/ROW]
[ROW][C]125[/C][C]425.764370218070[/C][C]402.124177852895[/C][C]449.404562583244[/C][/ROW]
[ROW][C]126[/C][C]412.265237017782[/C][C]386.337554205881[/C][C]438.192919829682[/C][/ROW]
[ROW][C]127[/C][C]384.332867497281[/C][C]356.129958788011[/C][C]412.535776206552[/C][/ROW]
[ROW][C]128[/C][C]361.71823756373[/C][C]331.242991236539[/C][C]392.19348389092[/C][/ROW]
[ROW][C]129[/C][C]391.966603668744[/C][C]359.215138880941[/C][C]424.718068456546[/C][/ROW]
[ROW][C]130[/C][C]406.581109077463[/C][C]371.544535994063[/C][C]441.617682160862[/C][/ROW]
[ROW][C]131[/C][C]386.887583162421[/C][C]349.55323390625[/C][C]424.221932418592[/C][/ROW]
[ROW][C]132[/C][C]386.319389504836[/C][C]346.671704058641[/C][C]425.967074951032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78409&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78409&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
121353.651685569883339.688594721905367.614776417862
122361.991584982937345.459781017536378.523388948339
123372.276364865005353.308218648937391.244511081073
124361.099945830178339.7729215597382.426970100656
125425.764370218070402.124177852895449.404562583244
126412.265237017782386.337554205881438.192919829682
127384.332867497281356.129958788011412.535776206552
128361.71823756373331.242991236539392.19348389092
129391.966603668744359.215138880941424.718068456546
130406.581109077463371.544535994063441.617682160862
131386.887583162421349.55323390625424.221932418592
132386.319389504836346.671704058641425.967074951032



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')