Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Aug 2010 14:20:22 +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/16/t1281968478dc0cvsounltxsx0.htm/, Retrieved Thu, 16 May 2024 04:07:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79001, Retrieved Thu, 16 May 2024 04:07:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJeroen_Kinne
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential_Smoot...] [2010-08-16 14:20:22] [6fe3b5976049c9b6736c06f51fce3033] [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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79001&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79001&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.124791631525621
beta0.0903911823166393
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.124791631525621 \tabularnewline
beta & 0.0903911823166393 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79001&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]0.124791631525621[/C][/ROW]
[ROW][C]beta[/C][C]0.0903911823166393[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79001&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
alpha0.124791631525621
beta0.0903911823166393
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132828.7814054374197-0.781405437419746
142929.4996210015149-0.499621001514875
152525.0751391320068-0.0751391320067611
162827.48421870194200.515781298057966
175553.0885562974241.91144370257596
185350.80919476501922.19080523498079
194237.63996100340244.36003899659757
203228.32682261777093.67317738222907
213730.78919256731536.21080743268472
224132.49842234355618.5015776564439
233735.3690130880351.63098691196502
243838.4449775716736-0.444977571673597
253935.13593308337443.86406691662564
263237.2471740287663-5.24717402876632
273631.75292923961074.24707076038930
283936.33769003008892.66230996991113
298372.25836704559910.7416329544010
308371.141481359444111.8585186405559
316657.25833154375388.74166845624622
325344.15419723892968.84580276107038
337251.527489087505720.4725109124943
347758.644130420186718.3558695798133
356955.232603417589313.7673965824107
367259.23743729398512.7625627060150
378162.363640461465918.6363595385341
387154.748892659417216.2511073405828
396363.8486403153705-0.848640315370545
406669.4028479886932-3.40284798869324
41114145.936784916613-31.9367849166129
42116140.301520865075-24.3015208650754
43109107.7194219404631.28057805953746
449784.871548280509712.1284517194903
45111112.196601480667-1.19660148066666
46120115.3197864863984.68021351360176
47110100.5091321717979.49086782820338
48106103.0023076243482.99769237565154
49115111.6151439069723.38485609302802
5011094.108700003878815.8912999961212
5110384.83495336609918.1650466339010
5211291.393647089650820.6063529103492
53163166.495244554399-3.49524455439897
54166172.614676298980-6.61467629898044
55156161.279978360779-5.27997836077907
56140140.462656150105-0.462656150105460
57166160.7247897865335.27521021346718
58176173.4874663192852.51253368071482
59163157.3405032062095.65949679379102
60162151.56479153887810.4352084611216
61171165.0848614573695.91513854263061
62167155.22505358599811.7749464140016
63163142.69740530820820.3025946917918
64168153.30411743571914.6958825642812
65222225.738019612001-3.73801961200067
66216229.909230344462-13.9092303444623
67197214.720204210965-17.7202042109653
68178190.210088540833-12.2100885408333
69204222.047100034280-18.0471000342803
70220231.616305991051-11.6163059910511
71196211.21750758362-15.2175075836199
72195205.135795250163-10.1357952501627
73213212.8941663937890.105833606210808
74218204.67105396464213.3289460353577
75216196.66238952055219.3376104794482
76225201.49931227307323.5006877269274
77280269.15639009319510.8436099068049
78272263.8769733358968.12302666410437
79252243.1229428033878.87705719661264
80230221.8259581666758.17404183332474
81248257.536031178919-9.53603117891947
82259277.802840768603-18.8028407686027
83240247.255624673105-7.25562467310519
84237246.344461665583-9.34446166558308
85252267.536872966414-15.5368729664141
86250269.242449940353-19.2424499403534
87255260.480463680905-5.4804636809053
88255265.746466884705-10.7464668847052
89313325.740518194468-12.7405181944683
90291311.916455303031-20.9164553030314
91271283.436620072139-12.4366200721386
92247254.309660286664-7.30966028666396
93268272.464183474588-4.46418347458797
94283284.370560790463-1.37056079046289
95259262.656050995746-3.65605099574577
96259258.5915861673050.40841383269526
97267275.497912500129-8.49791250012868
98270273.299518289933-3.29951828993308
99279277.8327484972631.16725150273680
100269278.235774979787-9.23577497978715
101334340.411527037191-6.41152703719052
102326317.2207229347818.77927706521916
103301297.2623783374083.73762166259178
104276271.7660736866914.23392631330893
105301295.570494472625.42950552738017
106313312.6284742282030.371525771796712
107291286.3236242155274.67637578447273
108287286.6111606989010.388839301098983
109289296.411979002331-7.41197900233067
110298299.032979654439-1.03297965443949
111320308.50426102737911.4957389726211
112312299.98112342008812.0188765799124
113385375.3772975953489.6227024046521
114380366.61770374416113.3822962558390
115351339.83677411009511.1632258899053
116322312.6378395135149.36216048648572
117350341.8790566346348.1209433653662
118363356.9699972653056.03000273469485
119344332.37530147953611.6246985204639
120345329.70185570165015.2981442983503

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 28 & 28.7814054374197 & -0.781405437419746 \tabularnewline
14 & 29 & 29.4996210015149 & -0.499621001514875 \tabularnewline
15 & 25 & 25.0751391320068 & -0.0751391320067611 \tabularnewline
16 & 28 & 27.4842187019420 & 0.515781298057966 \tabularnewline
17 & 55 & 53.088556297424 & 1.91144370257596 \tabularnewline
18 & 53 & 50.8091947650192 & 2.19080523498079 \tabularnewline
19 & 42 & 37.6399610034024 & 4.36003899659757 \tabularnewline
20 & 32 & 28.3268226177709 & 3.67317738222907 \tabularnewline
21 & 37 & 30.7891925673153 & 6.21080743268472 \tabularnewline
22 & 41 & 32.4984223435561 & 8.5015776564439 \tabularnewline
23 & 37 & 35.369013088035 & 1.63098691196502 \tabularnewline
24 & 38 & 38.4449775716736 & -0.444977571673597 \tabularnewline
25 & 39 & 35.1359330833744 & 3.86406691662564 \tabularnewline
26 & 32 & 37.2471740287663 & -5.24717402876632 \tabularnewline
27 & 36 & 31.7529292396107 & 4.24707076038930 \tabularnewline
28 & 39 & 36.3376900300889 & 2.66230996991113 \tabularnewline
29 & 83 & 72.258367045599 & 10.7416329544010 \tabularnewline
30 & 83 & 71.1414813594441 & 11.8585186405559 \tabularnewline
31 & 66 & 57.2583315437538 & 8.74166845624622 \tabularnewline
32 & 53 & 44.1541972389296 & 8.84580276107038 \tabularnewline
33 & 72 & 51.5274890875057 & 20.4725109124943 \tabularnewline
34 & 77 & 58.6441304201867 & 18.3558695798133 \tabularnewline
35 & 69 & 55.2326034175893 & 13.7673965824107 \tabularnewline
36 & 72 & 59.237437293985 & 12.7625627060150 \tabularnewline
37 & 81 & 62.3636404614659 & 18.6363595385341 \tabularnewline
38 & 71 & 54.7488926594172 & 16.2511073405828 \tabularnewline
39 & 63 & 63.8486403153705 & -0.848640315370545 \tabularnewline
40 & 66 & 69.4028479886932 & -3.40284798869324 \tabularnewline
41 & 114 & 145.936784916613 & -31.9367849166129 \tabularnewline
42 & 116 & 140.301520865075 & -24.3015208650754 \tabularnewline
43 & 109 & 107.719421940463 & 1.28057805953746 \tabularnewline
44 & 97 & 84.8715482805097 & 12.1284517194903 \tabularnewline
45 & 111 & 112.196601480667 & -1.19660148066666 \tabularnewline
46 & 120 & 115.319786486398 & 4.68021351360176 \tabularnewline
47 & 110 & 100.509132171797 & 9.49086782820338 \tabularnewline
48 & 106 & 103.002307624348 & 2.99769237565154 \tabularnewline
49 & 115 & 111.615143906972 & 3.38485609302802 \tabularnewline
50 & 110 & 94.1087000038788 & 15.8912999961212 \tabularnewline
51 & 103 & 84.834953366099 & 18.1650466339010 \tabularnewline
52 & 112 & 91.3936470896508 & 20.6063529103492 \tabularnewline
53 & 163 & 166.495244554399 & -3.49524455439897 \tabularnewline
54 & 166 & 172.614676298980 & -6.61467629898044 \tabularnewline
55 & 156 & 161.279978360779 & -5.27997836077907 \tabularnewline
56 & 140 & 140.462656150105 & -0.462656150105460 \tabularnewline
57 & 166 & 160.724789786533 & 5.27521021346718 \tabularnewline
58 & 176 & 173.487466319285 & 2.51253368071482 \tabularnewline
59 & 163 & 157.340503206209 & 5.65949679379102 \tabularnewline
60 & 162 & 151.564791538878 & 10.4352084611216 \tabularnewline
61 & 171 & 165.084861457369 & 5.91513854263061 \tabularnewline
62 & 167 & 155.225053585998 & 11.7749464140016 \tabularnewline
63 & 163 & 142.697405308208 & 20.3025946917918 \tabularnewline
64 & 168 & 153.304117435719 & 14.6958825642812 \tabularnewline
65 & 222 & 225.738019612001 & -3.73801961200067 \tabularnewline
66 & 216 & 229.909230344462 & -13.9092303444623 \tabularnewline
67 & 197 & 214.720204210965 & -17.7202042109653 \tabularnewline
68 & 178 & 190.210088540833 & -12.2100885408333 \tabularnewline
69 & 204 & 222.047100034280 & -18.0471000342803 \tabularnewline
70 & 220 & 231.616305991051 & -11.6163059910511 \tabularnewline
71 & 196 & 211.21750758362 & -15.2175075836199 \tabularnewline
72 & 195 & 205.135795250163 & -10.1357952501627 \tabularnewline
73 & 213 & 212.894166393789 & 0.105833606210808 \tabularnewline
74 & 218 & 204.671053964642 & 13.3289460353577 \tabularnewline
75 & 216 & 196.662389520552 & 19.3376104794482 \tabularnewline
76 & 225 & 201.499312273073 & 23.5006877269274 \tabularnewline
77 & 280 & 269.156390093195 & 10.8436099068049 \tabularnewline
78 & 272 & 263.876973335896 & 8.12302666410437 \tabularnewline
79 & 252 & 243.122942803387 & 8.87705719661264 \tabularnewline
80 & 230 & 221.825958166675 & 8.17404183332474 \tabularnewline
81 & 248 & 257.536031178919 & -9.53603117891947 \tabularnewline
82 & 259 & 277.802840768603 & -18.8028407686027 \tabularnewline
83 & 240 & 247.255624673105 & -7.25562467310519 \tabularnewline
84 & 237 & 246.344461665583 & -9.34446166558308 \tabularnewline
85 & 252 & 267.536872966414 & -15.5368729664141 \tabularnewline
86 & 250 & 269.242449940353 & -19.2424499403534 \tabularnewline
87 & 255 & 260.480463680905 & -5.4804636809053 \tabularnewline
88 & 255 & 265.746466884705 & -10.7464668847052 \tabularnewline
89 & 313 & 325.740518194468 & -12.7405181944683 \tabularnewline
90 & 291 & 311.916455303031 & -20.9164553030314 \tabularnewline
91 & 271 & 283.436620072139 & -12.4366200721386 \tabularnewline
92 & 247 & 254.309660286664 & -7.30966028666396 \tabularnewline
93 & 268 & 272.464183474588 & -4.46418347458797 \tabularnewline
94 & 283 & 284.370560790463 & -1.37056079046289 \tabularnewline
95 & 259 & 262.656050995746 & -3.65605099574577 \tabularnewline
96 & 259 & 258.591586167305 & 0.40841383269526 \tabularnewline
97 & 267 & 275.497912500129 & -8.49791250012868 \tabularnewline
98 & 270 & 273.299518289933 & -3.29951828993308 \tabularnewline
99 & 279 & 277.832748497263 & 1.16725150273680 \tabularnewline
100 & 269 & 278.235774979787 & -9.23577497978715 \tabularnewline
101 & 334 & 340.411527037191 & -6.41152703719052 \tabularnewline
102 & 326 & 317.220722934781 & 8.77927706521916 \tabularnewline
103 & 301 & 297.262378337408 & 3.73762166259178 \tabularnewline
104 & 276 & 271.766073686691 & 4.23392631330893 \tabularnewline
105 & 301 & 295.57049447262 & 5.42950552738017 \tabularnewline
106 & 313 & 312.628474228203 & 0.371525771796712 \tabularnewline
107 & 291 & 286.323624215527 & 4.67637578447273 \tabularnewline
108 & 287 & 286.611160698901 & 0.388839301098983 \tabularnewline
109 & 289 & 296.411979002331 & -7.41197900233067 \tabularnewline
110 & 298 & 299.032979654439 & -1.03297965443949 \tabularnewline
111 & 320 & 308.504261027379 & 11.4957389726211 \tabularnewline
112 & 312 & 299.981123420088 & 12.0188765799124 \tabularnewline
113 & 385 & 375.377297595348 & 9.6227024046521 \tabularnewline
114 & 380 & 366.617703744161 & 13.3822962558390 \tabularnewline
115 & 351 & 339.836774110095 & 11.1632258899053 \tabularnewline
116 & 322 & 312.637839513514 & 9.36216048648572 \tabularnewline
117 & 350 & 341.879056634634 & 8.1209433653662 \tabularnewline
118 & 363 & 356.969997265305 & 6.03000273469485 \tabularnewline
119 & 344 & 332.375301479536 & 11.6246985204639 \tabularnewline
120 & 345 & 329.701855701650 & 15.2981442983503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79001&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]28.7814054374197[/C][C]-0.781405437419746[/C][/ROW]
[ROW][C]14[/C][C]29[/C][C]29.4996210015149[/C][C]-0.499621001514875[/C][/ROW]
[ROW][C]15[/C][C]25[/C][C]25.0751391320068[/C][C]-0.0751391320067611[/C][/ROW]
[ROW][C]16[/C][C]28[/C][C]27.4842187019420[/C][C]0.515781298057966[/C][/ROW]
[ROW][C]17[/C][C]55[/C][C]53.088556297424[/C][C]1.91144370257596[/C][/ROW]
[ROW][C]18[/C][C]53[/C][C]50.8091947650192[/C][C]2.19080523498079[/C][/ROW]
[ROW][C]19[/C][C]42[/C][C]37.6399610034024[/C][C]4.36003899659757[/C][/ROW]
[ROW][C]20[/C][C]32[/C][C]28.3268226177709[/C][C]3.67317738222907[/C][/ROW]
[ROW][C]21[/C][C]37[/C][C]30.7891925673153[/C][C]6.21080743268472[/C][/ROW]
[ROW][C]22[/C][C]41[/C][C]32.4984223435561[/C][C]8.5015776564439[/C][/ROW]
[ROW][C]23[/C][C]37[/C][C]35.369013088035[/C][C]1.63098691196502[/C][/ROW]
[ROW][C]24[/C][C]38[/C][C]38.4449775716736[/C][C]-0.444977571673597[/C][/ROW]
[ROW][C]25[/C][C]39[/C][C]35.1359330833744[/C][C]3.86406691662564[/C][/ROW]
[ROW][C]26[/C][C]32[/C][C]37.2471740287663[/C][C]-5.24717402876632[/C][/ROW]
[ROW][C]27[/C][C]36[/C][C]31.7529292396107[/C][C]4.24707076038930[/C][/ROW]
[ROW][C]28[/C][C]39[/C][C]36.3376900300889[/C][C]2.66230996991113[/C][/ROW]
[ROW][C]29[/C][C]83[/C][C]72.258367045599[/C][C]10.7416329544010[/C][/ROW]
[ROW][C]30[/C][C]83[/C][C]71.1414813594441[/C][C]11.8585186405559[/C][/ROW]
[ROW][C]31[/C][C]66[/C][C]57.2583315437538[/C][C]8.74166845624622[/C][/ROW]
[ROW][C]32[/C][C]53[/C][C]44.1541972389296[/C][C]8.84580276107038[/C][/ROW]
[ROW][C]33[/C][C]72[/C][C]51.5274890875057[/C][C]20.4725109124943[/C][/ROW]
[ROW][C]34[/C][C]77[/C][C]58.6441304201867[/C][C]18.3558695798133[/C][/ROW]
[ROW][C]35[/C][C]69[/C][C]55.2326034175893[/C][C]13.7673965824107[/C][/ROW]
[ROW][C]36[/C][C]72[/C][C]59.237437293985[/C][C]12.7625627060150[/C][/ROW]
[ROW][C]37[/C][C]81[/C][C]62.3636404614659[/C][C]18.6363595385341[/C][/ROW]
[ROW][C]38[/C][C]71[/C][C]54.7488926594172[/C][C]16.2511073405828[/C][/ROW]
[ROW][C]39[/C][C]63[/C][C]63.8486403153705[/C][C]-0.848640315370545[/C][/ROW]
[ROW][C]40[/C][C]66[/C][C]69.4028479886932[/C][C]-3.40284798869324[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]145.936784916613[/C][C]-31.9367849166129[/C][/ROW]
[ROW][C]42[/C][C]116[/C][C]140.301520865075[/C][C]-24.3015208650754[/C][/ROW]
[ROW][C]43[/C][C]109[/C][C]107.719421940463[/C][C]1.28057805953746[/C][/ROW]
[ROW][C]44[/C][C]97[/C][C]84.8715482805097[/C][C]12.1284517194903[/C][/ROW]
[ROW][C]45[/C][C]111[/C][C]112.196601480667[/C][C]-1.19660148066666[/C][/ROW]
[ROW][C]46[/C][C]120[/C][C]115.319786486398[/C][C]4.68021351360176[/C][/ROW]
[ROW][C]47[/C][C]110[/C][C]100.509132171797[/C][C]9.49086782820338[/C][/ROW]
[ROW][C]48[/C][C]106[/C][C]103.002307624348[/C][C]2.99769237565154[/C][/ROW]
[ROW][C]49[/C][C]115[/C][C]111.615143906972[/C][C]3.38485609302802[/C][/ROW]
[ROW][C]50[/C][C]110[/C][C]94.1087000038788[/C][C]15.8912999961212[/C][/ROW]
[ROW][C]51[/C][C]103[/C][C]84.834953366099[/C][C]18.1650466339010[/C][/ROW]
[ROW][C]52[/C][C]112[/C][C]91.3936470896508[/C][C]20.6063529103492[/C][/ROW]
[ROW][C]53[/C][C]163[/C][C]166.495244554399[/C][C]-3.49524455439897[/C][/ROW]
[ROW][C]54[/C][C]166[/C][C]172.614676298980[/C][C]-6.61467629898044[/C][/ROW]
[ROW][C]55[/C][C]156[/C][C]161.279978360779[/C][C]-5.27997836077907[/C][/ROW]
[ROW][C]56[/C][C]140[/C][C]140.462656150105[/C][C]-0.462656150105460[/C][/ROW]
[ROW][C]57[/C][C]166[/C][C]160.724789786533[/C][C]5.27521021346718[/C][/ROW]
[ROW][C]58[/C][C]176[/C][C]173.487466319285[/C][C]2.51253368071482[/C][/ROW]
[ROW][C]59[/C][C]163[/C][C]157.340503206209[/C][C]5.65949679379102[/C][/ROW]
[ROW][C]60[/C][C]162[/C][C]151.564791538878[/C][C]10.4352084611216[/C][/ROW]
[ROW][C]61[/C][C]171[/C][C]165.084861457369[/C][C]5.91513854263061[/C][/ROW]
[ROW][C]62[/C][C]167[/C][C]155.225053585998[/C][C]11.7749464140016[/C][/ROW]
[ROW][C]63[/C][C]163[/C][C]142.697405308208[/C][C]20.3025946917918[/C][/ROW]
[ROW][C]64[/C][C]168[/C][C]153.304117435719[/C][C]14.6958825642812[/C][/ROW]
[ROW][C]65[/C][C]222[/C][C]225.738019612001[/C][C]-3.73801961200067[/C][/ROW]
[ROW][C]66[/C][C]216[/C][C]229.909230344462[/C][C]-13.9092303444623[/C][/ROW]
[ROW][C]67[/C][C]197[/C][C]214.720204210965[/C][C]-17.7202042109653[/C][/ROW]
[ROW][C]68[/C][C]178[/C][C]190.210088540833[/C][C]-12.2100885408333[/C][/ROW]
[ROW][C]69[/C][C]204[/C][C]222.047100034280[/C][C]-18.0471000342803[/C][/ROW]
[ROW][C]70[/C][C]220[/C][C]231.616305991051[/C][C]-11.6163059910511[/C][/ROW]
[ROW][C]71[/C][C]196[/C][C]211.21750758362[/C][C]-15.2175075836199[/C][/ROW]
[ROW][C]72[/C][C]195[/C][C]205.135795250163[/C][C]-10.1357952501627[/C][/ROW]
[ROW][C]73[/C][C]213[/C][C]212.894166393789[/C][C]0.105833606210808[/C][/ROW]
[ROW][C]74[/C][C]218[/C][C]204.671053964642[/C][C]13.3289460353577[/C][/ROW]
[ROW][C]75[/C][C]216[/C][C]196.662389520552[/C][C]19.3376104794482[/C][/ROW]
[ROW][C]76[/C][C]225[/C][C]201.499312273073[/C][C]23.5006877269274[/C][/ROW]
[ROW][C]77[/C][C]280[/C][C]269.156390093195[/C][C]10.8436099068049[/C][/ROW]
[ROW][C]78[/C][C]272[/C][C]263.876973335896[/C][C]8.12302666410437[/C][/ROW]
[ROW][C]79[/C][C]252[/C][C]243.122942803387[/C][C]8.87705719661264[/C][/ROW]
[ROW][C]80[/C][C]230[/C][C]221.825958166675[/C][C]8.17404183332474[/C][/ROW]
[ROW][C]81[/C][C]248[/C][C]257.536031178919[/C][C]-9.53603117891947[/C][/ROW]
[ROW][C]82[/C][C]259[/C][C]277.802840768603[/C][C]-18.8028407686027[/C][/ROW]
[ROW][C]83[/C][C]240[/C][C]247.255624673105[/C][C]-7.25562467310519[/C][/ROW]
[ROW][C]84[/C][C]237[/C][C]246.344461665583[/C][C]-9.34446166558308[/C][/ROW]
[ROW][C]85[/C][C]252[/C][C]267.536872966414[/C][C]-15.5368729664141[/C][/ROW]
[ROW][C]86[/C][C]250[/C][C]269.242449940353[/C][C]-19.2424499403534[/C][/ROW]
[ROW][C]87[/C][C]255[/C][C]260.480463680905[/C][C]-5.4804636809053[/C][/ROW]
[ROW][C]88[/C][C]255[/C][C]265.746466884705[/C][C]-10.7464668847052[/C][/ROW]
[ROW][C]89[/C][C]313[/C][C]325.740518194468[/C][C]-12.7405181944683[/C][/ROW]
[ROW][C]90[/C][C]291[/C][C]311.916455303031[/C][C]-20.9164553030314[/C][/ROW]
[ROW][C]91[/C][C]271[/C][C]283.436620072139[/C][C]-12.4366200721386[/C][/ROW]
[ROW][C]92[/C][C]247[/C][C]254.309660286664[/C][C]-7.30966028666396[/C][/ROW]
[ROW][C]93[/C][C]268[/C][C]272.464183474588[/C][C]-4.46418347458797[/C][/ROW]
[ROW][C]94[/C][C]283[/C][C]284.370560790463[/C][C]-1.37056079046289[/C][/ROW]
[ROW][C]95[/C][C]259[/C][C]262.656050995746[/C][C]-3.65605099574577[/C][/ROW]
[ROW][C]96[/C][C]259[/C][C]258.591586167305[/C][C]0.40841383269526[/C][/ROW]
[ROW][C]97[/C][C]267[/C][C]275.497912500129[/C][C]-8.49791250012868[/C][/ROW]
[ROW][C]98[/C][C]270[/C][C]273.299518289933[/C][C]-3.29951828993308[/C][/ROW]
[ROW][C]99[/C][C]279[/C][C]277.832748497263[/C][C]1.16725150273680[/C][/ROW]
[ROW][C]100[/C][C]269[/C][C]278.235774979787[/C][C]-9.23577497978715[/C][/ROW]
[ROW][C]101[/C][C]334[/C][C]340.411527037191[/C][C]-6.41152703719052[/C][/ROW]
[ROW][C]102[/C][C]326[/C][C]317.220722934781[/C][C]8.77927706521916[/C][/ROW]
[ROW][C]103[/C][C]301[/C][C]297.262378337408[/C][C]3.73762166259178[/C][/ROW]
[ROW][C]104[/C][C]276[/C][C]271.766073686691[/C][C]4.23392631330893[/C][/ROW]
[ROW][C]105[/C][C]301[/C][C]295.57049447262[/C][C]5.42950552738017[/C][/ROW]
[ROW][C]106[/C][C]313[/C][C]312.628474228203[/C][C]0.371525771796712[/C][/ROW]
[ROW][C]107[/C][C]291[/C][C]286.323624215527[/C][C]4.67637578447273[/C][/ROW]
[ROW][C]108[/C][C]287[/C][C]286.611160698901[/C][C]0.388839301098983[/C][/ROW]
[ROW][C]109[/C][C]289[/C][C]296.411979002331[/C][C]-7.41197900233067[/C][/ROW]
[ROW][C]110[/C][C]298[/C][C]299.032979654439[/C][C]-1.03297965443949[/C][/ROW]
[ROW][C]111[/C][C]320[/C][C]308.504261027379[/C][C]11.4957389726211[/C][/ROW]
[ROW][C]112[/C][C]312[/C][C]299.981123420088[/C][C]12.0188765799124[/C][/ROW]
[ROW][C]113[/C][C]385[/C][C]375.377297595348[/C][C]9.6227024046521[/C][/ROW]
[ROW][C]114[/C][C]380[/C][C]366.617703744161[/C][C]13.3822962558390[/C][/ROW]
[ROW][C]115[/C][C]351[/C][C]339.836774110095[/C][C]11.1632258899053[/C][/ROW]
[ROW][C]116[/C][C]322[/C][C]312.637839513514[/C][C]9.36216048648572[/C][/ROW]
[ROW][C]117[/C][C]350[/C][C]341.879056634634[/C][C]8.1209433653662[/C][/ROW]
[ROW][C]118[/C][C]363[/C][C]356.969997265305[/C][C]6.03000273469485[/C][/ROW]
[ROW][C]119[/C][C]344[/C][C]332.375301479536[/C][C]11.6246985204639[/C][/ROW]
[ROW][C]120[/C][C]345[/C][C]329.701855701650[/C][C]15.2981442983503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79001&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
132828.7814054374197-0.781405437419746
142929.4996210015149-0.499621001514875
152525.0751391320068-0.0751391320067611
162827.48421870194200.515781298057966
175553.0885562974241.91144370257596
185350.80919476501922.19080523498079
194237.63996100340244.36003899659757
203228.32682261777093.67317738222907
213730.78919256731536.21080743268472
224132.49842234355618.5015776564439
233735.3690130880351.63098691196502
243838.4449775716736-0.444977571673597
253935.13593308337443.86406691662564
263237.2471740287663-5.24717402876632
273631.75292923961074.24707076038930
283936.33769003008892.66230996991113
298372.25836704559910.7416329544010
308371.141481359444111.8585186405559
316657.25833154375388.74166845624622
325344.15419723892968.84580276107038
337251.527489087505720.4725109124943
347758.644130420186718.3558695798133
356955.232603417589313.7673965824107
367259.23743729398512.7625627060150
378162.363640461465918.6363595385341
387154.748892659417216.2511073405828
396363.8486403153705-0.848640315370545
406669.4028479886932-3.40284798869324
41114145.936784916613-31.9367849166129
42116140.301520865075-24.3015208650754
43109107.7194219404631.28057805953746
449784.871548280509712.1284517194903
45111112.196601480667-1.19660148066666
46120115.3197864863984.68021351360176
47110100.5091321717979.49086782820338
48106103.0023076243482.99769237565154
49115111.6151439069723.38485609302802
5011094.108700003878815.8912999961212
5110384.83495336609918.1650466339010
5211291.393647089650820.6063529103492
53163166.495244554399-3.49524455439897
54166172.614676298980-6.61467629898044
55156161.279978360779-5.27997836077907
56140140.462656150105-0.462656150105460
57166160.7247897865335.27521021346718
58176173.4874663192852.51253368071482
59163157.3405032062095.65949679379102
60162151.56479153887810.4352084611216
61171165.0848614573695.91513854263061
62167155.22505358599811.7749464140016
63163142.69740530820820.3025946917918
64168153.30411743571914.6958825642812
65222225.738019612001-3.73801961200067
66216229.909230344462-13.9092303444623
67197214.720204210965-17.7202042109653
68178190.210088540833-12.2100885408333
69204222.047100034280-18.0471000342803
70220231.616305991051-11.6163059910511
71196211.21750758362-15.2175075836199
72195205.135795250163-10.1357952501627
73213212.8941663937890.105833606210808
74218204.67105396464213.3289460353577
75216196.66238952055219.3376104794482
76225201.49931227307323.5006877269274
77280269.15639009319510.8436099068049
78272263.8769733358968.12302666410437
79252243.1229428033878.87705719661264
80230221.8259581666758.17404183332474
81248257.536031178919-9.53603117891947
82259277.802840768603-18.8028407686027
83240247.255624673105-7.25562467310519
84237246.344461665583-9.34446166558308
85252267.536872966414-15.5368729664141
86250269.242449940353-19.2424499403534
87255260.480463680905-5.4804636809053
88255265.746466884705-10.7464668847052
89313325.740518194468-12.7405181944683
90291311.916455303031-20.9164553030314
91271283.436620072139-12.4366200721386
92247254.309660286664-7.30966028666396
93268272.464183474588-4.46418347458797
94283284.370560790463-1.37056079046289
95259262.656050995746-3.65605099574577
96259258.5915861673050.40841383269526
97267275.497912500129-8.49791250012868
98270273.299518289933-3.29951828993308
99279277.8327484972631.16725150273680
100269278.235774979787-9.23577497978715
101334340.411527037191-6.41152703719052
102326317.2207229347818.77927706521916
103301297.2623783374083.73762166259178
104276271.7660736866914.23392631330893
105301295.570494472625.42950552738017
106313312.6284742282030.371525771796712
107291286.3236242155274.67637578447273
108287286.6111606989010.388839301098983
109289296.411979002331-7.41197900233067
110298299.032979654439-1.03297965443949
111320308.50426102737911.4957389726211
112312299.98112342008812.0188765799124
113385375.3772975953489.6227024046521
114380366.61770374416113.3822962558390
115351339.83677411009511.1632258899053
116322312.6378395135149.36216048648572
117350341.8790566346348.1209433653662
118363356.9699972653056.03000273469485
119344332.37530147953611.6246985204639
120345329.70185570165015.2981442983503







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121335.636009681172314.261896244569357.010123117774
122347.004585361403325.424263598509368.584907124297
123371.717489459965349.853301219648393.581677700281
124361.26754001249339.187271515152383.347808509828
125444.974623900517422.121586314335467.8276614867
126437.671737480202414.513484180969460.829990779434
127402.894824386870379.669632770995426.120016002746
128368.356574187279345.101706443548391.611441931009
129399.218236369251375.215519815881423.22095292262
130413.09177712158388.451803952472437.731750290688
131389.625832274864364.893737164886414.357927384841
132388.234357368062372.560490417341403.908224318783

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 335.636009681172 & 314.261896244569 & 357.010123117774 \tabularnewline
122 & 347.004585361403 & 325.424263598509 & 368.584907124297 \tabularnewline
123 & 371.717489459965 & 349.853301219648 & 393.581677700281 \tabularnewline
124 & 361.26754001249 & 339.187271515152 & 383.347808509828 \tabularnewline
125 & 444.974623900517 & 422.121586314335 & 467.8276614867 \tabularnewline
126 & 437.671737480202 & 414.513484180969 & 460.829990779434 \tabularnewline
127 & 402.894824386870 & 379.669632770995 & 426.120016002746 \tabularnewline
128 & 368.356574187279 & 345.101706443548 & 391.611441931009 \tabularnewline
129 & 399.218236369251 & 375.215519815881 & 423.22095292262 \tabularnewline
130 & 413.09177712158 & 388.451803952472 & 437.731750290688 \tabularnewline
131 & 389.625832274864 & 364.893737164886 & 414.357927384841 \tabularnewline
132 & 388.234357368062 & 372.560490417341 & 403.908224318783 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79001&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]335.636009681172[/C][C]314.261896244569[/C][C]357.010123117774[/C][/ROW]
[ROW][C]122[/C][C]347.004585361403[/C][C]325.424263598509[/C][C]368.584907124297[/C][/ROW]
[ROW][C]123[/C][C]371.717489459965[/C][C]349.853301219648[/C][C]393.581677700281[/C][/ROW]
[ROW][C]124[/C][C]361.26754001249[/C][C]339.187271515152[/C][C]383.347808509828[/C][/ROW]
[ROW][C]125[/C][C]444.974623900517[/C][C]422.121586314335[/C][C]467.8276614867[/C][/ROW]
[ROW][C]126[/C][C]437.671737480202[/C][C]414.513484180969[/C][C]460.829990779434[/C][/ROW]
[ROW][C]127[/C][C]402.894824386870[/C][C]379.669632770995[/C][C]426.120016002746[/C][/ROW]
[ROW][C]128[/C][C]368.356574187279[/C][C]345.101706443548[/C][C]391.611441931009[/C][/ROW]
[ROW][C]129[/C][C]399.218236369251[/C][C]375.215519815881[/C][C]423.22095292262[/C][/ROW]
[ROW][C]130[/C][C]413.09177712158[/C][C]388.451803952472[/C][C]437.731750290688[/C][/ROW]
[ROW][C]131[/C][C]389.625832274864[/C][C]364.893737164886[/C][C]414.357927384841[/C][/ROW]
[ROW][C]132[/C][C]388.234357368062[/C][C]372.560490417341[/C][C]403.908224318783[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79001&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79001&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
121335.636009681172314.261896244569357.010123117774
122347.004585361403325.424263598509368.584907124297
123371.717489459965349.853301219648393.581677700281
124361.26754001249339.187271515152383.347808509828
125444.974623900517422.121586314335467.8276614867
126437.671737480202414.513484180969460.829990779434
127402.894824386870379.669632770995426.120016002746
128368.356574187279345.101706443548391.611441931009
129399.218236369251375.215519815881423.22095292262
130413.09177712158388.451803952472437.731750290688
131389.625832274864364.893737164886414.357927384841
132388.234357368062372.560490417341403.908224318783



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')