Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 04 Aug 2010 16:00:42 +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/04/t1280937623dr3wcsdzf5ci0zw.htm/, Retrieved Fri, 03 May 2024 11:15:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78348, Retrieved Fri, 03 May 2024 11:15:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBogaerts Yannik
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Tijdreeks B stap 17] [2010-08-04 14:57:12] [f713c1ac4846c73da8c41c71cf7e0185]
- RM      [Exponential Smoothing] [Tijdreeks B stap 27] [2010-08-04 16:00:42] [1596366c2ece8f787477cc7d1246d4c7] [Current]
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Dataseries X:
83
82
81
79
77
76
77
79
80
80
81
83
83
76
77
72
64
70
69
78
84
91
96
101
99
98
98
97
92
106
100
107
111
115
117
120
117
108
111
118
113
129
122
135
146
151
147
151
156
144
151
159
148
170
163
179
184
192
197
199
205
194
200
211
211
230
229
236
239
250
254
254
264
258
264
277
274
284
279
290
287
297
302
294




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78348&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78348&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.469691048112616
beta0.300455994256597
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.469691048112616 \tabularnewline
beta & 0.300455994256597 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78348&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]0.469691048112616[/C][/ROW]
[ROW][C]beta[/C][C]0.300455994256597[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78348&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
alpha0.469691048112616
beta0.300455994256597
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138386.5926816239316-3.59268162393161
147677.5833956371879-1.58339563718788
157776.7944021385840.205597861416024
167270.37469714812541.62530285187455
176461.39284671085872.60715328914131
187066.94842132694383.05157867305624
196975.018381899208-6.01838189920794
207873.72894015779974.27105984220033
218477.04176209153226.95823790846778
229181.64035108170239.3596489182977
239690.06270893524975.93729106475028
2410198.67382864157362.32617135842639
2599101.803545958472-2.80354595847177
269897.8906806257280.109319374271934
2798102.744566298714-4.74456629871405
289797.9532280513072-0.953228051307178
299291.11759495283430.882405047165733
3010698.6920006206997.30799937930114
31100107.145202148465-7.14520214846502
32107113.817987072556-6.81798707255635
33111114.817415673438-3.81741567343757
34115115.577588247146-0.577588247145613
35117116.0645718839040.935428116096247
36120118.2524460054861.74755399451405
37117116.1494953401680.850504659832467
38108113.772726932398-5.77272693239794
39111110.7348294412750.265170558725416
40118108.4591022500889.54089774991193
41113107.1588673296435.8411326703568
42129120.8026247695298.1973752304714
43122122.467137667288-0.467137667287886
44135133.8507348443551.14926515564494
45146142.7085509445633.29144905543666
46151152.054027295175-1.05402729517451
47147156.580586273897-9.58058627389698
48151156.236812945517-5.23681294551687
49156151.3689628314734.63103716852675
50144148.780340552410-4.7803405524096
51151151.075379051861-0.0753790518606365
52159155.1755109546433.82448904535673
53148150.038414410777-2.03841441077736
54170160.9288851286049.07111487139568
55163158.2303498840924.76965011590769
56179173.4912685133315.50873148666875
57184186.708376833063-2.70837683306266
58192191.2603099010620.739690098938382
59197192.6897496366534.31025036334708
60199203.716313693272-4.71631369327176
61205206.941794185064-1.94179418506357
62194197.963313758854-3.96331375885367
63200204.940765425902-4.9407654259021
64211209.9407730822061.05922691779378
65211201.1224387863399.87756121366084
66230225.9095509610254.09044903897453
67229220.2959888545458.70401114545461
68236240.057458559765-4.05745855976522
69239245.334487401686-6.33448740168612
70250250.410767879563-0.41076787956257
71254253.429951850480.570048149520062
72254257.621689750201-3.62168975020074
73264262.695913869341.30408613066021
74258254.4912839414113.5087160585891
75264265.835713240551-1.83571324055060
76277277.289958841612-0.289958841612020
77274274.137939662596-0.137939662595841
78284291.362074898671-7.36207489867076
79279281.409952410558-2.40995241055839
80290286.2093264992493.79067350075098
81287292.098119231321-5.09811923132111
82297299.204085676986-2.20408567698553
83302299.9555975862062.04440241379399
84294300.879471159033-6.87947115903336

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 83 & 86.5926816239316 & -3.59268162393161 \tabularnewline
14 & 76 & 77.5833956371879 & -1.58339563718788 \tabularnewline
15 & 77 & 76.794402138584 & 0.205597861416024 \tabularnewline
16 & 72 & 70.3746971481254 & 1.62530285187455 \tabularnewline
17 & 64 & 61.3928467108587 & 2.60715328914131 \tabularnewline
18 & 70 & 66.9484213269438 & 3.05157867305624 \tabularnewline
19 & 69 & 75.018381899208 & -6.01838189920794 \tabularnewline
20 & 78 & 73.7289401577997 & 4.27105984220033 \tabularnewline
21 & 84 & 77.0417620915322 & 6.95823790846778 \tabularnewline
22 & 91 & 81.6403510817023 & 9.3596489182977 \tabularnewline
23 & 96 & 90.0627089352497 & 5.93729106475028 \tabularnewline
24 & 101 & 98.6738286415736 & 2.32617135842639 \tabularnewline
25 & 99 & 101.803545958472 & -2.80354595847177 \tabularnewline
26 & 98 & 97.890680625728 & 0.109319374271934 \tabularnewline
27 & 98 & 102.744566298714 & -4.74456629871405 \tabularnewline
28 & 97 & 97.9532280513072 & -0.953228051307178 \tabularnewline
29 & 92 & 91.1175949528343 & 0.882405047165733 \tabularnewline
30 & 106 & 98.692000620699 & 7.30799937930114 \tabularnewline
31 & 100 & 107.145202148465 & -7.14520214846502 \tabularnewline
32 & 107 & 113.817987072556 & -6.81798707255635 \tabularnewline
33 & 111 & 114.817415673438 & -3.81741567343757 \tabularnewline
34 & 115 & 115.577588247146 & -0.577588247145613 \tabularnewline
35 & 117 & 116.064571883904 & 0.935428116096247 \tabularnewline
36 & 120 & 118.252446005486 & 1.74755399451405 \tabularnewline
37 & 117 & 116.149495340168 & 0.850504659832467 \tabularnewline
38 & 108 & 113.772726932398 & -5.77272693239794 \tabularnewline
39 & 111 & 110.734829441275 & 0.265170558725416 \tabularnewline
40 & 118 & 108.459102250088 & 9.54089774991193 \tabularnewline
41 & 113 & 107.158867329643 & 5.8411326703568 \tabularnewline
42 & 129 & 120.802624769529 & 8.1973752304714 \tabularnewline
43 & 122 & 122.467137667288 & -0.467137667287886 \tabularnewline
44 & 135 & 133.850734844355 & 1.14926515564494 \tabularnewline
45 & 146 & 142.708550944563 & 3.29144905543666 \tabularnewline
46 & 151 & 152.054027295175 & -1.05402729517451 \tabularnewline
47 & 147 & 156.580586273897 & -9.58058627389698 \tabularnewline
48 & 151 & 156.236812945517 & -5.23681294551687 \tabularnewline
49 & 156 & 151.368962831473 & 4.63103716852675 \tabularnewline
50 & 144 & 148.780340552410 & -4.7803405524096 \tabularnewline
51 & 151 & 151.075379051861 & -0.0753790518606365 \tabularnewline
52 & 159 & 155.175510954643 & 3.82448904535673 \tabularnewline
53 & 148 & 150.038414410777 & -2.03841441077736 \tabularnewline
54 & 170 & 160.928885128604 & 9.07111487139568 \tabularnewline
55 & 163 & 158.230349884092 & 4.76965011590769 \tabularnewline
56 & 179 & 173.491268513331 & 5.50873148666875 \tabularnewline
57 & 184 & 186.708376833063 & -2.70837683306266 \tabularnewline
58 & 192 & 191.260309901062 & 0.739690098938382 \tabularnewline
59 & 197 & 192.689749636653 & 4.31025036334708 \tabularnewline
60 & 199 & 203.716313693272 & -4.71631369327176 \tabularnewline
61 & 205 & 206.941794185064 & -1.94179418506357 \tabularnewline
62 & 194 & 197.963313758854 & -3.96331375885367 \tabularnewline
63 & 200 & 204.940765425902 & -4.9407654259021 \tabularnewline
64 & 211 & 209.940773082206 & 1.05922691779378 \tabularnewline
65 & 211 & 201.122438786339 & 9.87756121366084 \tabularnewline
66 & 230 & 225.909550961025 & 4.09044903897453 \tabularnewline
67 & 229 & 220.295988854545 & 8.70401114545461 \tabularnewline
68 & 236 & 240.057458559765 & -4.05745855976522 \tabularnewline
69 & 239 & 245.334487401686 & -6.33448740168612 \tabularnewline
70 & 250 & 250.410767879563 & -0.41076787956257 \tabularnewline
71 & 254 & 253.42995185048 & 0.570048149520062 \tabularnewline
72 & 254 & 257.621689750201 & -3.62168975020074 \tabularnewline
73 & 264 & 262.69591386934 & 1.30408613066021 \tabularnewline
74 & 258 & 254.491283941411 & 3.5087160585891 \tabularnewline
75 & 264 & 265.835713240551 & -1.83571324055060 \tabularnewline
76 & 277 & 277.289958841612 & -0.289958841612020 \tabularnewline
77 & 274 & 274.137939662596 & -0.137939662595841 \tabularnewline
78 & 284 & 291.362074898671 & -7.36207489867076 \tabularnewline
79 & 279 & 281.409952410558 & -2.40995241055839 \tabularnewline
80 & 290 & 286.209326499249 & 3.79067350075098 \tabularnewline
81 & 287 & 292.098119231321 & -5.09811923132111 \tabularnewline
82 & 297 & 299.204085676986 & -2.20408567698553 \tabularnewline
83 & 302 & 299.955597586206 & 2.04440241379399 \tabularnewline
84 & 294 & 300.879471159033 & -6.87947115903336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78348&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]83[/C][C]86.5926816239316[/C][C]-3.59268162393161[/C][/ROW]
[ROW][C]14[/C][C]76[/C][C]77.5833956371879[/C][C]-1.58339563718788[/C][/ROW]
[ROW][C]15[/C][C]77[/C][C]76.794402138584[/C][C]0.205597861416024[/C][/ROW]
[ROW][C]16[/C][C]72[/C][C]70.3746971481254[/C][C]1.62530285187455[/C][/ROW]
[ROW][C]17[/C][C]64[/C][C]61.3928467108587[/C][C]2.60715328914131[/C][/ROW]
[ROW][C]18[/C][C]70[/C][C]66.9484213269438[/C][C]3.05157867305624[/C][/ROW]
[ROW][C]19[/C][C]69[/C][C]75.018381899208[/C][C]-6.01838189920794[/C][/ROW]
[ROW][C]20[/C][C]78[/C][C]73.7289401577997[/C][C]4.27105984220033[/C][/ROW]
[ROW][C]21[/C][C]84[/C][C]77.0417620915322[/C][C]6.95823790846778[/C][/ROW]
[ROW][C]22[/C][C]91[/C][C]81.6403510817023[/C][C]9.3596489182977[/C][/ROW]
[ROW][C]23[/C][C]96[/C][C]90.0627089352497[/C][C]5.93729106475028[/C][/ROW]
[ROW][C]24[/C][C]101[/C][C]98.6738286415736[/C][C]2.32617135842639[/C][/ROW]
[ROW][C]25[/C][C]99[/C][C]101.803545958472[/C][C]-2.80354595847177[/C][/ROW]
[ROW][C]26[/C][C]98[/C][C]97.890680625728[/C][C]0.109319374271934[/C][/ROW]
[ROW][C]27[/C][C]98[/C][C]102.744566298714[/C][C]-4.74456629871405[/C][/ROW]
[ROW][C]28[/C][C]97[/C][C]97.9532280513072[/C][C]-0.953228051307178[/C][/ROW]
[ROW][C]29[/C][C]92[/C][C]91.1175949528343[/C][C]0.882405047165733[/C][/ROW]
[ROW][C]30[/C][C]106[/C][C]98.692000620699[/C][C]7.30799937930114[/C][/ROW]
[ROW][C]31[/C][C]100[/C][C]107.145202148465[/C][C]-7.14520214846502[/C][/ROW]
[ROW][C]32[/C][C]107[/C][C]113.817987072556[/C][C]-6.81798707255635[/C][/ROW]
[ROW][C]33[/C][C]111[/C][C]114.817415673438[/C][C]-3.81741567343757[/C][/ROW]
[ROW][C]34[/C][C]115[/C][C]115.577588247146[/C][C]-0.577588247145613[/C][/ROW]
[ROW][C]35[/C][C]117[/C][C]116.064571883904[/C][C]0.935428116096247[/C][/ROW]
[ROW][C]36[/C][C]120[/C][C]118.252446005486[/C][C]1.74755399451405[/C][/ROW]
[ROW][C]37[/C][C]117[/C][C]116.149495340168[/C][C]0.850504659832467[/C][/ROW]
[ROW][C]38[/C][C]108[/C][C]113.772726932398[/C][C]-5.77272693239794[/C][/ROW]
[ROW][C]39[/C][C]111[/C][C]110.734829441275[/C][C]0.265170558725416[/C][/ROW]
[ROW][C]40[/C][C]118[/C][C]108.459102250088[/C][C]9.54089774991193[/C][/ROW]
[ROW][C]41[/C][C]113[/C][C]107.158867329643[/C][C]5.8411326703568[/C][/ROW]
[ROW][C]42[/C][C]129[/C][C]120.802624769529[/C][C]8.1973752304714[/C][/ROW]
[ROW][C]43[/C][C]122[/C][C]122.467137667288[/C][C]-0.467137667287886[/C][/ROW]
[ROW][C]44[/C][C]135[/C][C]133.850734844355[/C][C]1.14926515564494[/C][/ROW]
[ROW][C]45[/C][C]146[/C][C]142.708550944563[/C][C]3.29144905543666[/C][/ROW]
[ROW][C]46[/C][C]151[/C][C]152.054027295175[/C][C]-1.05402729517451[/C][/ROW]
[ROW][C]47[/C][C]147[/C][C]156.580586273897[/C][C]-9.58058627389698[/C][/ROW]
[ROW][C]48[/C][C]151[/C][C]156.236812945517[/C][C]-5.23681294551687[/C][/ROW]
[ROW][C]49[/C][C]156[/C][C]151.368962831473[/C][C]4.63103716852675[/C][/ROW]
[ROW][C]50[/C][C]144[/C][C]148.780340552410[/C][C]-4.7803405524096[/C][/ROW]
[ROW][C]51[/C][C]151[/C][C]151.075379051861[/C][C]-0.0753790518606365[/C][/ROW]
[ROW][C]52[/C][C]159[/C][C]155.175510954643[/C][C]3.82448904535673[/C][/ROW]
[ROW][C]53[/C][C]148[/C][C]150.038414410777[/C][C]-2.03841441077736[/C][/ROW]
[ROW][C]54[/C][C]170[/C][C]160.928885128604[/C][C]9.07111487139568[/C][/ROW]
[ROW][C]55[/C][C]163[/C][C]158.230349884092[/C][C]4.76965011590769[/C][/ROW]
[ROW][C]56[/C][C]179[/C][C]173.491268513331[/C][C]5.50873148666875[/C][/ROW]
[ROW][C]57[/C][C]184[/C][C]186.708376833063[/C][C]-2.70837683306266[/C][/ROW]
[ROW][C]58[/C][C]192[/C][C]191.260309901062[/C][C]0.739690098938382[/C][/ROW]
[ROW][C]59[/C][C]197[/C][C]192.689749636653[/C][C]4.31025036334708[/C][/ROW]
[ROW][C]60[/C][C]199[/C][C]203.716313693272[/C][C]-4.71631369327176[/C][/ROW]
[ROW][C]61[/C][C]205[/C][C]206.941794185064[/C][C]-1.94179418506357[/C][/ROW]
[ROW][C]62[/C][C]194[/C][C]197.963313758854[/C][C]-3.96331375885367[/C][/ROW]
[ROW][C]63[/C][C]200[/C][C]204.940765425902[/C][C]-4.9407654259021[/C][/ROW]
[ROW][C]64[/C][C]211[/C][C]209.940773082206[/C][C]1.05922691779378[/C][/ROW]
[ROW][C]65[/C][C]211[/C][C]201.122438786339[/C][C]9.87756121366084[/C][/ROW]
[ROW][C]66[/C][C]230[/C][C]225.909550961025[/C][C]4.09044903897453[/C][/ROW]
[ROW][C]67[/C][C]229[/C][C]220.295988854545[/C][C]8.70401114545461[/C][/ROW]
[ROW][C]68[/C][C]236[/C][C]240.057458559765[/C][C]-4.05745855976522[/C][/ROW]
[ROW][C]69[/C][C]239[/C][C]245.334487401686[/C][C]-6.33448740168612[/C][/ROW]
[ROW][C]70[/C][C]250[/C][C]250.410767879563[/C][C]-0.41076787956257[/C][/ROW]
[ROW][C]71[/C][C]254[/C][C]253.42995185048[/C][C]0.570048149520062[/C][/ROW]
[ROW][C]72[/C][C]254[/C][C]257.621689750201[/C][C]-3.62168975020074[/C][/ROW]
[ROW][C]73[/C][C]264[/C][C]262.69591386934[/C][C]1.30408613066021[/C][/ROW]
[ROW][C]74[/C][C]258[/C][C]254.491283941411[/C][C]3.5087160585891[/C][/ROW]
[ROW][C]75[/C][C]264[/C][C]265.835713240551[/C][C]-1.83571324055060[/C][/ROW]
[ROW][C]76[/C][C]277[/C][C]277.289958841612[/C][C]-0.289958841612020[/C][/ROW]
[ROW][C]77[/C][C]274[/C][C]274.137939662596[/C][C]-0.137939662595841[/C][/ROW]
[ROW][C]78[/C][C]284[/C][C]291.362074898671[/C][C]-7.36207489867076[/C][/ROW]
[ROW][C]79[/C][C]279[/C][C]281.409952410558[/C][C]-2.40995241055839[/C][/ROW]
[ROW][C]80[/C][C]290[/C][C]286.209326499249[/C][C]3.79067350075098[/C][/ROW]
[ROW][C]81[/C][C]287[/C][C]292.098119231321[/C][C]-5.09811923132111[/C][/ROW]
[ROW][C]82[/C][C]297[/C][C]299.204085676986[/C][C]-2.20408567698553[/C][/ROW]
[ROW][C]83[/C][C]302[/C][C]299.955597586206[/C][C]2.04440241379399[/C][/ROW]
[ROW][C]84[/C][C]294[/C][C]300.879471159033[/C][C]-6.87947115903336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78348&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78348&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
138386.5926816239316-3.59268162393161
147677.5833956371879-1.58339563718788
157776.7944021385840.205597861416024
167270.37469714812541.62530285187455
176461.39284671085872.60715328914131
187066.94842132694383.05157867305624
196975.018381899208-6.01838189920794
207873.72894015779974.27105984220033
218477.04176209153226.95823790846778
229181.64035108170239.3596489182977
239690.06270893524975.93729106475028
2410198.67382864157362.32617135842639
2599101.803545958472-2.80354595847177
269897.8906806257280.109319374271934
2798102.744566298714-4.74456629871405
289797.9532280513072-0.953228051307178
299291.11759495283430.882405047165733
3010698.6920006206997.30799937930114
31100107.145202148465-7.14520214846502
32107113.817987072556-6.81798707255635
33111114.817415673438-3.81741567343757
34115115.577588247146-0.577588247145613
35117116.0645718839040.935428116096247
36120118.2524460054861.74755399451405
37117116.1494953401680.850504659832467
38108113.772726932398-5.77272693239794
39111110.7348294412750.265170558725416
40118108.4591022500889.54089774991193
41113107.1588673296435.8411326703568
42129120.8026247695298.1973752304714
43122122.467137667288-0.467137667287886
44135133.8507348443551.14926515564494
45146142.7085509445633.29144905543666
46151152.054027295175-1.05402729517451
47147156.580586273897-9.58058627389698
48151156.236812945517-5.23681294551687
49156151.3689628314734.63103716852675
50144148.780340552410-4.7803405524096
51151151.075379051861-0.0753790518606365
52159155.1755109546433.82448904535673
53148150.038414410777-2.03841441077736
54170160.9288851286049.07111487139568
55163158.2303498840924.76965011590769
56179173.4912685133315.50873148666875
57184186.708376833063-2.70837683306266
58192191.2603099010620.739690098938382
59197192.6897496366534.31025036334708
60199203.716313693272-4.71631369327176
61205206.941794185064-1.94179418506357
62194197.963313758854-3.96331375885367
63200204.940765425902-4.9407654259021
64211209.9407730822061.05922691779378
65211201.1224387863399.87756121366084
66230225.9095509610254.09044903897453
67229220.2959888545458.70401114545461
68236240.057458559765-4.05745855976522
69239245.334487401686-6.33448740168612
70250250.410767879563-0.41076787956257
71254253.429951850480.570048149520062
72254257.621689750201-3.62168975020074
73264262.695913869341.30408613066021
74258254.4912839414113.5087160585891
75264265.835713240551-1.83571324055060
76277277.289958841612-0.289958841612020
77274274.137939662596-0.137939662595841
78284291.362074898671-7.36207489867076
79279281.409952410558-2.40995241055839
80290286.2093264992493.79067350075098
81287292.098119231321-5.09811923132111
82297299.204085676986-2.20408567698553
83302299.9555975862062.04440241379399
84294300.879471159033-6.87947115903336







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85304.838545394674295.685693040981313.991397748368
86294.809316128952284.084094669302305.534537588601
87298.795162221134286.051654261088311.53867018118
88309.314039898841294.174312088511324.453767709172
89303.802434953038285.947176423893321.657693482183
90314.703407908807293.858013100900335.548802716715
91309.317360248233285.240216865131333.394503631335
92317.359030181487289.833004384508344.885055978467
93315.040740993757283.867241584663346.214240402851
94325.082604339094290.077454234522360.087754443665
95328.440034716885289.430557738399367.449511695371
96322.700419509781279.523340649142365.87749837042

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 304.838545394674 & 295.685693040981 & 313.991397748368 \tabularnewline
86 & 294.809316128952 & 284.084094669302 & 305.534537588601 \tabularnewline
87 & 298.795162221134 & 286.051654261088 & 311.53867018118 \tabularnewline
88 & 309.314039898841 & 294.174312088511 & 324.453767709172 \tabularnewline
89 & 303.802434953038 & 285.947176423893 & 321.657693482183 \tabularnewline
90 & 314.703407908807 & 293.858013100900 & 335.548802716715 \tabularnewline
91 & 309.317360248233 & 285.240216865131 & 333.394503631335 \tabularnewline
92 & 317.359030181487 & 289.833004384508 & 344.885055978467 \tabularnewline
93 & 315.040740993757 & 283.867241584663 & 346.214240402851 \tabularnewline
94 & 325.082604339094 & 290.077454234522 & 360.087754443665 \tabularnewline
95 & 328.440034716885 & 289.430557738399 & 367.449511695371 \tabularnewline
96 & 322.700419509781 & 279.523340649142 & 365.87749837042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78348&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]85[/C][C]304.838545394674[/C][C]295.685693040981[/C][C]313.991397748368[/C][/ROW]
[ROW][C]86[/C][C]294.809316128952[/C][C]284.084094669302[/C][C]305.534537588601[/C][/ROW]
[ROW][C]87[/C][C]298.795162221134[/C][C]286.051654261088[/C][C]311.53867018118[/C][/ROW]
[ROW][C]88[/C][C]309.314039898841[/C][C]294.174312088511[/C][C]324.453767709172[/C][/ROW]
[ROW][C]89[/C][C]303.802434953038[/C][C]285.947176423893[/C][C]321.657693482183[/C][/ROW]
[ROW][C]90[/C][C]314.703407908807[/C][C]293.858013100900[/C][C]335.548802716715[/C][/ROW]
[ROW][C]91[/C][C]309.317360248233[/C][C]285.240216865131[/C][C]333.394503631335[/C][/ROW]
[ROW][C]92[/C][C]317.359030181487[/C][C]289.833004384508[/C][C]344.885055978467[/C][/ROW]
[ROW][C]93[/C][C]315.040740993757[/C][C]283.867241584663[/C][C]346.214240402851[/C][/ROW]
[ROW][C]94[/C][C]325.082604339094[/C][C]290.077454234522[/C][C]360.087754443665[/C][/ROW]
[ROW][C]95[/C][C]328.440034716885[/C][C]289.430557738399[/C][C]367.449511695371[/C][/ROW]
[ROW][C]96[/C][C]322.700419509781[/C][C]279.523340649142[/C][C]365.87749837042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78348&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78348&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
85304.838545394674295.685693040981313.991397748368
86294.809316128952284.084094669302305.534537588601
87298.795162221134286.051654261088311.53867018118
88309.314039898841294.174312088511324.453767709172
89303.802434953038285.947176423893321.657693482183
90314.703407908807293.858013100900335.548802716715
91309.317360248233285.240216865131333.394503631335
92317.359030181487289.833004384508344.885055978467
93315.040740993757283.867241584663346.214240402851
94325.082604339094290.077454234522360.087754443665
95328.440034716885289.430557738399367.449511695371
96322.700419509781279.523340649142365.87749837042



Parameters (Session):
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')