Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 08:11:30 +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/19/t1282205671ezre51xbd1wix6c.htm/, Retrieved Fri, 03 May 2024 10:01:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79244, Retrieved Fri, 03 May 2024 10:01:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDeGroodtOlivierStap32
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-08-19 08:11:30] [461523bf9c5715e033e9a40193969321] [Current]
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Dataseries X:
356
355
354
352
372
371
356
346
347
347
348
350
353
351
348
351
370
370
351
335
330
328
332
334
343
334
336
343
365
364
351
326
320
312
315
316
319
311
315
322
336
339
317
295
291
283
285
289
296
283
285
289
306
306
283
258
255
248
244
249
258
252
246
249
267
284
261
235
229
218
218
229
237
231
229
233
245
256
224
194
192
178
170
187
192
182
178
186
204
224
194
173
178
168
152
163
172
170
156
155
178
194
164
135
139
135
109
121
131
135
119
121
151
169
135
105
112
105
82
81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79244&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79244&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79244&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.394255067360942
beta0.0506505428827482
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.394255067360942 \tabularnewline
beta & 0.0506505428827482 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79244&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]0.394255067360942[/C][/ROW]
[ROW][C]beta[/C][C]0.0506505428827482[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79244&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79244&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
alpha0.394255067360942
beta0.0506505428827482
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13353354.266826923077-1.26682692307702
14351351.77310789547-0.773107895469991
15348348.958601724499-0.958601724499317
16351352.385154463424-1.38515446342416
17370371.574209484372-1.57420948437181
18370371.532292849008-1.53229284900789
19351348.5179700129832.48202998701692
20335339.052545199361-4.05254519936085
21330338.054904785334-8.05490478533432
22328334.193463551106-6.19346355110633
23332331.7755595714570.224440428542948
24334332.8924286608771.1075713391233
25343334.7372199481038.26278005189664
26334336.051098365042-2.05109836504221
27336332.3462893443083.65371065569212
28343337.1509051086365.84909489136436
29365359.0400605450655.95993945493524
30364362.1068423435751.89315765642471
31351343.0560113099917.94398869000895
32326332.07611158047-6.07611158047024
33320328.106257753623-8.10625775362303
34312325.601100391939-13.6011003919389
35315324.251357482428-9.25135748242838
36316322.079119501867-6.07911950186696
37319325.193062421669-6.19306242166863
38311314.039709508571-3.03970950857058
39315312.8606902894232.13930971057744
40322317.827742856044.17225714396022
41336338.519109055059-2.51910905505946
42339335.0063994574853.99360054251525
43317319.717732058076-2.71773205807608
44295295.097676960794-0.0976769607942742
45291291.430372033698-0.430372033697552
46283287.951551494658-4.95155149465756
47285292.148049717865-7.14804971786498
48289292.269897930646-3.2698979306461
49296296.02174771171-0.0217477117101339
50283288.934208233543-5.93420823354262
51285289.415995742938-4.41599574293753
52289292.563941969522-3.56394196952164
53306305.5314337813220.468566218678347
54306306.580755203655-0.580755203655372
55283284.771006847854-1.77100684785427
56258261.47793112752-3.47793112752038
57255255.575557494987-0.575557494987322
58248248.597058045054-0.5970580450537
59244252.5630183444-8.56301834440029
60249253.831121596759-4.83112159675903
61258258.258767929918-0.258767929918179
62252246.815372275295.18462772470986
63246252.141534601518-6.14153460151755
64249254.631915831188-5.63191583118808
65267268.692084203824-1.69208420382387
66284267.67610491616.3238950839999
67261251.5698524017249.43014759827642
68235231.6423470201543.35765297984597
69229230.312955724817-1.3129557248169
70218223.135904703611-5.13590470361112
71218220.501619602301-2.50161960230079
72229226.5556370324062.44436296759437
73237236.9022453987320.0977546012675816
74231229.1847246866011.8152753133995
75229226.542458725372.45754127462953
76233233.124206542766-0.124206542765933
77245252.244773348025-7.24477334802484
78256260.344246535748-4.34424653574797
79224231.892435056846-7.89243505684581
80194201.089925355788-7.08992535578821
81192192.236590192334-0.236590192333523
82178182.613928346868-4.61392834686816
83170181.237321969951-11.2373219699507
84187186.1249851250350.87501487496462
85192193.681822020319-1.68182202031889
86182185.517934988619-3.51793498861932
87178180.270434384907-2.27043438490685
88186182.4382203269093.56177967309071
89204197.7863120789686.21368792103152
90224212.30513985374111.6948601462593
91194187.7041275193726.2958724806279
92173162.94147304483510.0585269551654
93178165.30274349024712.6972565097533
94168158.6884131838449.31158681615554
95152159.628653803024-7.62865380302372
96163174.18683087324-11.1868308732401
97172176.109358694816-4.10935869481574
98170166.4976365828963.50236341710428
99156165.535231026364-9.53523102636419
100155168.988235429744-13.9882354297436
101178179.289631672999-1.28963167299938
102194194.286701332168-0.286701332168064
103164161.5684970109982.43150298900227
104135137.361344428722-2.36134442872228
105139135.9762396586993.02376034130072
106135122.85588486482912.1441151351708
107109114.066615289534-5.06661528953421
108121126.94591931635-5.94591931634969
109131134.792880989432-3.79288098943215
110135129.4940487362565.50595126374353
111119121.041476007907-2.04147600790745
112121124.518555924663-3.51855592466282
113151146.6158721913614.38412780863933
114169164.5467518227684.45324817723156
115135135.527869839099-0.527869839098742
116105107.375664811775-2.37566481177504
117112109.371566442112.62843355789015
118105101.7367187459183.26328125408168
1198278.96023721112843.03976278887157
1208194.604180611327-13.6041806113271

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 353 & 354.266826923077 & -1.26682692307702 \tabularnewline
14 & 351 & 351.77310789547 & -0.773107895469991 \tabularnewline
15 & 348 & 348.958601724499 & -0.958601724499317 \tabularnewline
16 & 351 & 352.385154463424 & -1.38515446342416 \tabularnewline
17 & 370 & 371.574209484372 & -1.57420948437181 \tabularnewline
18 & 370 & 371.532292849008 & -1.53229284900789 \tabularnewline
19 & 351 & 348.517970012983 & 2.48202998701692 \tabularnewline
20 & 335 & 339.052545199361 & -4.05254519936085 \tabularnewline
21 & 330 & 338.054904785334 & -8.05490478533432 \tabularnewline
22 & 328 & 334.193463551106 & -6.19346355110633 \tabularnewline
23 & 332 & 331.775559571457 & 0.224440428542948 \tabularnewline
24 & 334 & 332.892428660877 & 1.1075713391233 \tabularnewline
25 & 343 & 334.737219948103 & 8.26278005189664 \tabularnewline
26 & 334 & 336.051098365042 & -2.05109836504221 \tabularnewline
27 & 336 & 332.346289344308 & 3.65371065569212 \tabularnewline
28 & 343 & 337.150905108636 & 5.84909489136436 \tabularnewline
29 & 365 & 359.040060545065 & 5.95993945493524 \tabularnewline
30 & 364 & 362.106842343575 & 1.89315765642471 \tabularnewline
31 & 351 & 343.056011309991 & 7.94398869000895 \tabularnewline
32 & 326 & 332.07611158047 & -6.07611158047024 \tabularnewline
33 & 320 & 328.106257753623 & -8.10625775362303 \tabularnewline
34 & 312 & 325.601100391939 & -13.6011003919389 \tabularnewline
35 & 315 & 324.251357482428 & -9.25135748242838 \tabularnewline
36 & 316 & 322.079119501867 & -6.07911950186696 \tabularnewline
37 & 319 & 325.193062421669 & -6.19306242166863 \tabularnewline
38 & 311 & 314.039709508571 & -3.03970950857058 \tabularnewline
39 & 315 & 312.860690289423 & 2.13930971057744 \tabularnewline
40 & 322 & 317.82774285604 & 4.17225714396022 \tabularnewline
41 & 336 & 338.519109055059 & -2.51910905505946 \tabularnewline
42 & 339 & 335.006399457485 & 3.99360054251525 \tabularnewline
43 & 317 & 319.717732058076 & -2.71773205807608 \tabularnewline
44 & 295 & 295.097676960794 & -0.0976769607942742 \tabularnewline
45 & 291 & 291.430372033698 & -0.430372033697552 \tabularnewline
46 & 283 & 287.951551494658 & -4.95155149465756 \tabularnewline
47 & 285 & 292.148049717865 & -7.14804971786498 \tabularnewline
48 & 289 & 292.269897930646 & -3.2698979306461 \tabularnewline
49 & 296 & 296.02174771171 & -0.0217477117101339 \tabularnewline
50 & 283 & 288.934208233543 & -5.93420823354262 \tabularnewline
51 & 285 & 289.415995742938 & -4.41599574293753 \tabularnewline
52 & 289 & 292.563941969522 & -3.56394196952164 \tabularnewline
53 & 306 & 305.531433781322 & 0.468566218678347 \tabularnewline
54 & 306 & 306.580755203655 & -0.580755203655372 \tabularnewline
55 & 283 & 284.771006847854 & -1.77100684785427 \tabularnewline
56 & 258 & 261.47793112752 & -3.47793112752038 \tabularnewline
57 & 255 & 255.575557494987 & -0.575557494987322 \tabularnewline
58 & 248 & 248.597058045054 & -0.5970580450537 \tabularnewline
59 & 244 & 252.5630183444 & -8.56301834440029 \tabularnewline
60 & 249 & 253.831121596759 & -4.83112159675903 \tabularnewline
61 & 258 & 258.258767929918 & -0.258767929918179 \tabularnewline
62 & 252 & 246.81537227529 & 5.18462772470986 \tabularnewline
63 & 246 & 252.141534601518 & -6.14153460151755 \tabularnewline
64 & 249 & 254.631915831188 & -5.63191583118808 \tabularnewline
65 & 267 & 268.692084203824 & -1.69208420382387 \tabularnewline
66 & 284 & 267.676104916 & 16.3238950839999 \tabularnewline
67 & 261 & 251.569852401724 & 9.43014759827642 \tabularnewline
68 & 235 & 231.642347020154 & 3.35765297984597 \tabularnewline
69 & 229 & 230.312955724817 & -1.3129557248169 \tabularnewline
70 & 218 & 223.135904703611 & -5.13590470361112 \tabularnewline
71 & 218 & 220.501619602301 & -2.50161960230079 \tabularnewline
72 & 229 & 226.555637032406 & 2.44436296759437 \tabularnewline
73 & 237 & 236.902245398732 & 0.0977546012675816 \tabularnewline
74 & 231 & 229.184724686601 & 1.8152753133995 \tabularnewline
75 & 229 & 226.54245872537 & 2.45754127462953 \tabularnewline
76 & 233 & 233.124206542766 & -0.124206542765933 \tabularnewline
77 & 245 & 252.244773348025 & -7.24477334802484 \tabularnewline
78 & 256 & 260.344246535748 & -4.34424653574797 \tabularnewline
79 & 224 & 231.892435056846 & -7.89243505684581 \tabularnewline
80 & 194 & 201.089925355788 & -7.08992535578821 \tabularnewline
81 & 192 & 192.236590192334 & -0.236590192333523 \tabularnewline
82 & 178 & 182.613928346868 & -4.61392834686816 \tabularnewline
83 & 170 & 181.237321969951 & -11.2373219699507 \tabularnewline
84 & 187 & 186.124985125035 & 0.87501487496462 \tabularnewline
85 & 192 & 193.681822020319 & -1.68182202031889 \tabularnewline
86 & 182 & 185.517934988619 & -3.51793498861932 \tabularnewline
87 & 178 & 180.270434384907 & -2.27043438490685 \tabularnewline
88 & 186 & 182.438220326909 & 3.56177967309071 \tabularnewline
89 & 204 & 197.786312078968 & 6.21368792103152 \tabularnewline
90 & 224 & 212.305139853741 & 11.6948601462593 \tabularnewline
91 & 194 & 187.704127519372 & 6.2958724806279 \tabularnewline
92 & 173 & 162.941473044835 & 10.0585269551654 \tabularnewline
93 & 178 & 165.302743490247 & 12.6972565097533 \tabularnewline
94 & 168 & 158.688413183844 & 9.31158681615554 \tabularnewline
95 & 152 & 159.628653803024 & -7.62865380302372 \tabularnewline
96 & 163 & 174.18683087324 & -11.1868308732401 \tabularnewline
97 & 172 & 176.109358694816 & -4.10935869481574 \tabularnewline
98 & 170 & 166.497636582896 & 3.50236341710428 \tabularnewline
99 & 156 & 165.535231026364 & -9.53523102636419 \tabularnewline
100 & 155 & 168.988235429744 & -13.9882354297436 \tabularnewline
101 & 178 & 179.289631672999 & -1.28963167299938 \tabularnewline
102 & 194 & 194.286701332168 & -0.286701332168064 \tabularnewline
103 & 164 & 161.568497010998 & 2.43150298900227 \tabularnewline
104 & 135 & 137.361344428722 & -2.36134442872228 \tabularnewline
105 & 139 & 135.976239658699 & 3.02376034130072 \tabularnewline
106 & 135 & 122.855884864829 & 12.1441151351708 \tabularnewline
107 & 109 & 114.066615289534 & -5.06661528953421 \tabularnewline
108 & 121 & 126.94591931635 & -5.94591931634969 \tabularnewline
109 & 131 & 134.792880989432 & -3.79288098943215 \tabularnewline
110 & 135 & 129.494048736256 & 5.50595126374353 \tabularnewline
111 & 119 & 121.041476007907 & -2.04147600790745 \tabularnewline
112 & 121 & 124.518555924663 & -3.51855592466282 \tabularnewline
113 & 151 & 146.615872191361 & 4.38412780863933 \tabularnewline
114 & 169 & 164.546751822768 & 4.45324817723156 \tabularnewline
115 & 135 & 135.527869839099 & -0.527869839098742 \tabularnewline
116 & 105 & 107.375664811775 & -2.37566481177504 \tabularnewline
117 & 112 & 109.37156644211 & 2.62843355789015 \tabularnewline
118 & 105 & 101.736718745918 & 3.26328125408168 \tabularnewline
119 & 82 & 78.9602372111284 & 3.03976278887157 \tabularnewline
120 & 81 & 94.604180611327 & -13.6041806113271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79244&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]353[/C][C]354.266826923077[/C][C]-1.26682692307702[/C][/ROW]
[ROW][C]14[/C][C]351[/C][C]351.77310789547[/C][C]-0.773107895469991[/C][/ROW]
[ROW][C]15[/C][C]348[/C][C]348.958601724499[/C][C]-0.958601724499317[/C][/ROW]
[ROW][C]16[/C][C]351[/C][C]352.385154463424[/C][C]-1.38515446342416[/C][/ROW]
[ROW][C]17[/C][C]370[/C][C]371.574209484372[/C][C]-1.57420948437181[/C][/ROW]
[ROW][C]18[/C][C]370[/C][C]371.532292849008[/C][C]-1.53229284900789[/C][/ROW]
[ROW][C]19[/C][C]351[/C][C]348.517970012983[/C][C]2.48202998701692[/C][/ROW]
[ROW][C]20[/C][C]335[/C][C]339.052545199361[/C][C]-4.05254519936085[/C][/ROW]
[ROW][C]21[/C][C]330[/C][C]338.054904785334[/C][C]-8.05490478533432[/C][/ROW]
[ROW][C]22[/C][C]328[/C][C]334.193463551106[/C][C]-6.19346355110633[/C][/ROW]
[ROW][C]23[/C][C]332[/C][C]331.775559571457[/C][C]0.224440428542948[/C][/ROW]
[ROW][C]24[/C][C]334[/C][C]332.892428660877[/C][C]1.1075713391233[/C][/ROW]
[ROW][C]25[/C][C]343[/C][C]334.737219948103[/C][C]8.26278005189664[/C][/ROW]
[ROW][C]26[/C][C]334[/C][C]336.051098365042[/C][C]-2.05109836504221[/C][/ROW]
[ROW][C]27[/C][C]336[/C][C]332.346289344308[/C][C]3.65371065569212[/C][/ROW]
[ROW][C]28[/C][C]343[/C][C]337.150905108636[/C][C]5.84909489136436[/C][/ROW]
[ROW][C]29[/C][C]365[/C][C]359.040060545065[/C][C]5.95993945493524[/C][/ROW]
[ROW][C]30[/C][C]364[/C][C]362.106842343575[/C][C]1.89315765642471[/C][/ROW]
[ROW][C]31[/C][C]351[/C][C]343.056011309991[/C][C]7.94398869000895[/C][/ROW]
[ROW][C]32[/C][C]326[/C][C]332.07611158047[/C][C]-6.07611158047024[/C][/ROW]
[ROW][C]33[/C][C]320[/C][C]328.106257753623[/C][C]-8.10625775362303[/C][/ROW]
[ROW][C]34[/C][C]312[/C][C]325.601100391939[/C][C]-13.6011003919389[/C][/ROW]
[ROW][C]35[/C][C]315[/C][C]324.251357482428[/C][C]-9.25135748242838[/C][/ROW]
[ROW][C]36[/C][C]316[/C][C]322.079119501867[/C][C]-6.07911950186696[/C][/ROW]
[ROW][C]37[/C][C]319[/C][C]325.193062421669[/C][C]-6.19306242166863[/C][/ROW]
[ROW][C]38[/C][C]311[/C][C]314.039709508571[/C][C]-3.03970950857058[/C][/ROW]
[ROW][C]39[/C][C]315[/C][C]312.860690289423[/C][C]2.13930971057744[/C][/ROW]
[ROW][C]40[/C][C]322[/C][C]317.82774285604[/C][C]4.17225714396022[/C][/ROW]
[ROW][C]41[/C][C]336[/C][C]338.519109055059[/C][C]-2.51910905505946[/C][/ROW]
[ROW][C]42[/C][C]339[/C][C]335.006399457485[/C][C]3.99360054251525[/C][/ROW]
[ROW][C]43[/C][C]317[/C][C]319.717732058076[/C][C]-2.71773205807608[/C][/ROW]
[ROW][C]44[/C][C]295[/C][C]295.097676960794[/C][C]-0.0976769607942742[/C][/ROW]
[ROW][C]45[/C][C]291[/C][C]291.430372033698[/C][C]-0.430372033697552[/C][/ROW]
[ROW][C]46[/C][C]283[/C][C]287.951551494658[/C][C]-4.95155149465756[/C][/ROW]
[ROW][C]47[/C][C]285[/C][C]292.148049717865[/C][C]-7.14804971786498[/C][/ROW]
[ROW][C]48[/C][C]289[/C][C]292.269897930646[/C][C]-3.2698979306461[/C][/ROW]
[ROW][C]49[/C][C]296[/C][C]296.02174771171[/C][C]-0.0217477117101339[/C][/ROW]
[ROW][C]50[/C][C]283[/C][C]288.934208233543[/C][C]-5.93420823354262[/C][/ROW]
[ROW][C]51[/C][C]285[/C][C]289.415995742938[/C][C]-4.41599574293753[/C][/ROW]
[ROW][C]52[/C][C]289[/C][C]292.563941969522[/C][C]-3.56394196952164[/C][/ROW]
[ROW][C]53[/C][C]306[/C][C]305.531433781322[/C][C]0.468566218678347[/C][/ROW]
[ROW][C]54[/C][C]306[/C][C]306.580755203655[/C][C]-0.580755203655372[/C][/ROW]
[ROW][C]55[/C][C]283[/C][C]284.771006847854[/C][C]-1.77100684785427[/C][/ROW]
[ROW][C]56[/C][C]258[/C][C]261.47793112752[/C][C]-3.47793112752038[/C][/ROW]
[ROW][C]57[/C][C]255[/C][C]255.575557494987[/C][C]-0.575557494987322[/C][/ROW]
[ROW][C]58[/C][C]248[/C][C]248.597058045054[/C][C]-0.5970580450537[/C][/ROW]
[ROW][C]59[/C][C]244[/C][C]252.5630183444[/C][C]-8.56301834440029[/C][/ROW]
[ROW][C]60[/C][C]249[/C][C]253.831121596759[/C][C]-4.83112159675903[/C][/ROW]
[ROW][C]61[/C][C]258[/C][C]258.258767929918[/C][C]-0.258767929918179[/C][/ROW]
[ROW][C]62[/C][C]252[/C][C]246.81537227529[/C][C]5.18462772470986[/C][/ROW]
[ROW][C]63[/C][C]246[/C][C]252.141534601518[/C][C]-6.14153460151755[/C][/ROW]
[ROW][C]64[/C][C]249[/C][C]254.631915831188[/C][C]-5.63191583118808[/C][/ROW]
[ROW][C]65[/C][C]267[/C][C]268.692084203824[/C][C]-1.69208420382387[/C][/ROW]
[ROW][C]66[/C][C]284[/C][C]267.676104916[/C][C]16.3238950839999[/C][/ROW]
[ROW][C]67[/C][C]261[/C][C]251.569852401724[/C][C]9.43014759827642[/C][/ROW]
[ROW][C]68[/C][C]235[/C][C]231.642347020154[/C][C]3.35765297984597[/C][/ROW]
[ROW][C]69[/C][C]229[/C][C]230.312955724817[/C][C]-1.3129557248169[/C][/ROW]
[ROW][C]70[/C][C]218[/C][C]223.135904703611[/C][C]-5.13590470361112[/C][/ROW]
[ROW][C]71[/C][C]218[/C][C]220.501619602301[/C][C]-2.50161960230079[/C][/ROW]
[ROW][C]72[/C][C]229[/C][C]226.555637032406[/C][C]2.44436296759437[/C][/ROW]
[ROW][C]73[/C][C]237[/C][C]236.902245398732[/C][C]0.0977546012675816[/C][/ROW]
[ROW][C]74[/C][C]231[/C][C]229.184724686601[/C][C]1.8152753133995[/C][/ROW]
[ROW][C]75[/C][C]229[/C][C]226.54245872537[/C][C]2.45754127462953[/C][/ROW]
[ROW][C]76[/C][C]233[/C][C]233.124206542766[/C][C]-0.124206542765933[/C][/ROW]
[ROW][C]77[/C][C]245[/C][C]252.244773348025[/C][C]-7.24477334802484[/C][/ROW]
[ROW][C]78[/C][C]256[/C][C]260.344246535748[/C][C]-4.34424653574797[/C][/ROW]
[ROW][C]79[/C][C]224[/C][C]231.892435056846[/C][C]-7.89243505684581[/C][/ROW]
[ROW][C]80[/C][C]194[/C][C]201.089925355788[/C][C]-7.08992535578821[/C][/ROW]
[ROW][C]81[/C][C]192[/C][C]192.236590192334[/C][C]-0.236590192333523[/C][/ROW]
[ROW][C]82[/C][C]178[/C][C]182.613928346868[/C][C]-4.61392834686816[/C][/ROW]
[ROW][C]83[/C][C]170[/C][C]181.237321969951[/C][C]-11.2373219699507[/C][/ROW]
[ROW][C]84[/C][C]187[/C][C]186.124985125035[/C][C]0.87501487496462[/C][/ROW]
[ROW][C]85[/C][C]192[/C][C]193.681822020319[/C][C]-1.68182202031889[/C][/ROW]
[ROW][C]86[/C][C]182[/C][C]185.517934988619[/C][C]-3.51793498861932[/C][/ROW]
[ROW][C]87[/C][C]178[/C][C]180.270434384907[/C][C]-2.27043438490685[/C][/ROW]
[ROW][C]88[/C][C]186[/C][C]182.438220326909[/C][C]3.56177967309071[/C][/ROW]
[ROW][C]89[/C][C]204[/C][C]197.786312078968[/C][C]6.21368792103152[/C][/ROW]
[ROW][C]90[/C][C]224[/C][C]212.305139853741[/C][C]11.6948601462593[/C][/ROW]
[ROW][C]91[/C][C]194[/C][C]187.704127519372[/C][C]6.2958724806279[/C][/ROW]
[ROW][C]92[/C][C]173[/C][C]162.941473044835[/C][C]10.0585269551654[/C][/ROW]
[ROW][C]93[/C][C]178[/C][C]165.302743490247[/C][C]12.6972565097533[/C][/ROW]
[ROW][C]94[/C][C]168[/C][C]158.688413183844[/C][C]9.31158681615554[/C][/ROW]
[ROW][C]95[/C][C]152[/C][C]159.628653803024[/C][C]-7.62865380302372[/C][/ROW]
[ROW][C]96[/C][C]163[/C][C]174.18683087324[/C][C]-11.1868308732401[/C][/ROW]
[ROW][C]97[/C][C]172[/C][C]176.109358694816[/C][C]-4.10935869481574[/C][/ROW]
[ROW][C]98[/C][C]170[/C][C]166.497636582896[/C][C]3.50236341710428[/C][/ROW]
[ROW][C]99[/C][C]156[/C][C]165.535231026364[/C][C]-9.53523102636419[/C][/ROW]
[ROW][C]100[/C][C]155[/C][C]168.988235429744[/C][C]-13.9882354297436[/C][/ROW]
[ROW][C]101[/C][C]178[/C][C]179.289631672999[/C][C]-1.28963167299938[/C][/ROW]
[ROW][C]102[/C][C]194[/C][C]194.286701332168[/C][C]-0.286701332168064[/C][/ROW]
[ROW][C]103[/C][C]164[/C][C]161.568497010998[/C][C]2.43150298900227[/C][/ROW]
[ROW][C]104[/C][C]135[/C][C]137.361344428722[/C][C]-2.36134442872228[/C][/ROW]
[ROW][C]105[/C][C]139[/C][C]135.976239658699[/C][C]3.02376034130072[/C][/ROW]
[ROW][C]106[/C][C]135[/C][C]122.855884864829[/C][C]12.1441151351708[/C][/ROW]
[ROW][C]107[/C][C]109[/C][C]114.066615289534[/C][C]-5.06661528953421[/C][/ROW]
[ROW][C]108[/C][C]121[/C][C]126.94591931635[/C][C]-5.94591931634969[/C][/ROW]
[ROW][C]109[/C][C]131[/C][C]134.792880989432[/C][C]-3.79288098943215[/C][/ROW]
[ROW][C]110[/C][C]135[/C][C]129.494048736256[/C][C]5.50595126374353[/C][/ROW]
[ROW][C]111[/C][C]119[/C][C]121.041476007907[/C][C]-2.04147600790745[/C][/ROW]
[ROW][C]112[/C][C]121[/C][C]124.518555924663[/C][C]-3.51855592466282[/C][/ROW]
[ROW][C]113[/C][C]151[/C][C]146.615872191361[/C][C]4.38412780863933[/C][/ROW]
[ROW][C]114[/C][C]169[/C][C]164.546751822768[/C][C]4.45324817723156[/C][/ROW]
[ROW][C]115[/C][C]135[/C][C]135.527869839099[/C][C]-0.527869839098742[/C][/ROW]
[ROW][C]116[/C][C]105[/C][C]107.375664811775[/C][C]-2.37566481177504[/C][/ROW]
[ROW][C]117[/C][C]112[/C][C]109.37156644211[/C][C]2.62843355789015[/C][/ROW]
[ROW][C]118[/C][C]105[/C][C]101.736718745918[/C][C]3.26328125408168[/C][/ROW]
[ROW][C]119[/C][C]82[/C][C]78.9602372111284[/C][C]3.03976278887157[/C][/ROW]
[ROW][C]120[/C][C]81[/C][C]94.604180611327[/C][C]-13.6041806113271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79244&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79244&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
13353354.266826923077-1.26682692307702
14351351.77310789547-0.773107895469991
15348348.958601724499-0.958601724499317
16351352.385154463424-1.38515446342416
17370371.574209484372-1.57420948437181
18370371.532292849008-1.53229284900789
19351348.5179700129832.48202998701692
20335339.052545199361-4.05254519936085
21330338.054904785334-8.05490478533432
22328334.193463551106-6.19346355110633
23332331.7755595714570.224440428542948
24334332.8924286608771.1075713391233
25343334.7372199481038.26278005189664
26334336.051098365042-2.05109836504221
27336332.3462893443083.65371065569212
28343337.1509051086365.84909489136436
29365359.0400605450655.95993945493524
30364362.1068423435751.89315765642471
31351343.0560113099917.94398869000895
32326332.07611158047-6.07611158047024
33320328.106257753623-8.10625775362303
34312325.601100391939-13.6011003919389
35315324.251357482428-9.25135748242838
36316322.079119501867-6.07911950186696
37319325.193062421669-6.19306242166863
38311314.039709508571-3.03970950857058
39315312.8606902894232.13930971057744
40322317.827742856044.17225714396022
41336338.519109055059-2.51910905505946
42339335.0063994574853.99360054251525
43317319.717732058076-2.71773205807608
44295295.097676960794-0.0976769607942742
45291291.430372033698-0.430372033697552
46283287.951551494658-4.95155149465756
47285292.148049717865-7.14804971786498
48289292.269897930646-3.2698979306461
49296296.02174771171-0.0217477117101339
50283288.934208233543-5.93420823354262
51285289.415995742938-4.41599574293753
52289292.563941969522-3.56394196952164
53306305.5314337813220.468566218678347
54306306.580755203655-0.580755203655372
55283284.771006847854-1.77100684785427
56258261.47793112752-3.47793112752038
57255255.575557494987-0.575557494987322
58248248.597058045054-0.5970580450537
59244252.5630183444-8.56301834440029
60249253.831121596759-4.83112159675903
61258258.258767929918-0.258767929918179
62252246.815372275295.18462772470986
63246252.141534601518-6.14153460151755
64249254.631915831188-5.63191583118808
65267268.692084203824-1.69208420382387
66284267.67610491616.3238950839999
67261251.5698524017249.43014759827642
68235231.6423470201543.35765297984597
69229230.312955724817-1.3129557248169
70218223.135904703611-5.13590470361112
71218220.501619602301-2.50161960230079
72229226.5556370324062.44436296759437
73237236.9022453987320.0977546012675816
74231229.1847246866011.8152753133995
75229226.542458725372.45754127462953
76233233.124206542766-0.124206542765933
77245252.244773348025-7.24477334802484
78256260.344246535748-4.34424653574797
79224231.892435056846-7.89243505684581
80194201.089925355788-7.08992535578821
81192192.236590192334-0.236590192333523
82178182.613928346868-4.61392834686816
83170181.237321969951-11.2373219699507
84187186.1249851250350.87501487496462
85192193.681822020319-1.68182202031889
86182185.517934988619-3.51793498861932
87178180.270434384907-2.27043438490685
88186182.4382203269093.56177967309071
89204197.7863120789686.21368792103152
90224212.30513985374111.6948601462593
91194187.7041275193726.2958724806279
92173162.94147304483510.0585269551654
93178165.30274349024712.6972565097533
94168158.6884131838449.31158681615554
95152159.628653803024-7.62865380302372
96163174.18683087324-11.1868308732401
97172176.109358694816-4.10935869481574
98170166.4976365828963.50236341710428
99156165.535231026364-9.53523102636419
100155168.988235429744-13.9882354297436
101178179.289631672999-1.28963167299938
102194194.286701332168-0.286701332168064
103164161.5684970109982.43150298900227
104135137.361344428722-2.36134442872228
105139135.9762396586993.02376034130072
106135122.85588486482912.1441151351708
107109114.066615289534-5.06661528953421
108121126.94591931635-5.94591931634969
109131134.792880989432-3.79288098943215
110135129.4940487362565.50595126374353
111119121.041476007907-2.04147600790745
112121124.518555924663-3.51855592466282
113151146.6158721913614.38412780863933
114169164.5467518227684.45324817723156
115135135.527869839099-0.527869839098742
116105107.375664811775-2.37566481177504
117112109.371566442112.62843355789015
118105101.7367187459183.26328125408168
1198278.96023721112843.03976278887157
1208194.604180611327-13.6041806113271







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121100.68438910884389.421329585523111.947448632163
122102.53774393827790.3466498747216114.728838001833
12387.25676059034674.1213780582324100.39214312246
12490.598890194958976.5026430904347104.695137299483
125118.89560955574103.821735727905133.969483383574
126135.077530190373119.009178790416151.145881590329
127101.13435389273684.054655732427118.214052053044
12871.930221282434353.822340042701490.0381025221672
12977.80063773694258.647807367567696.9534681063165
13069.368274467565949.15382649204689.5827224430859
13144.958869261400423.666252616336366.2514859064644
13249.0507213496426.663516649533471.4379260497466

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 100.684389108843 & 89.421329585523 & 111.947448632163 \tabularnewline
122 & 102.537743938277 & 90.3466498747216 & 114.728838001833 \tabularnewline
123 & 87.256760590346 & 74.1213780582324 & 100.39214312246 \tabularnewline
124 & 90.5988901949589 & 76.5026430904347 & 104.695137299483 \tabularnewline
125 & 118.89560955574 & 103.821735727905 & 133.969483383574 \tabularnewline
126 & 135.077530190373 & 119.009178790416 & 151.145881590329 \tabularnewline
127 & 101.134353892736 & 84.054655732427 & 118.214052053044 \tabularnewline
128 & 71.9302212824343 & 53.8223400427014 & 90.0381025221672 \tabularnewline
129 & 77.800637736942 & 58.6478073675676 & 96.9534681063165 \tabularnewline
130 & 69.3682744675659 & 49.153826492046 & 89.5827224430859 \tabularnewline
131 & 44.9588692614004 & 23.6662526163363 & 66.2514859064644 \tabularnewline
132 & 49.05072134964 & 26.6635166495334 & 71.4379260497466 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79244&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]100.684389108843[/C][C]89.421329585523[/C][C]111.947448632163[/C][/ROW]
[ROW][C]122[/C][C]102.537743938277[/C][C]90.3466498747216[/C][C]114.728838001833[/C][/ROW]
[ROW][C]123[/C][C]87.256760590346[/C][C]74.1213780582324[/C][C]100.39214312246[/C][/ROW]
[ROW][C]124[/C][C]90.5988901949589[/C][C]76.5026430904347[/C][C]104.695137299483[/C][/ROW]
[ROW][C]125[/C][C]118.89560955574[/C][C]103.821735727905[/C][C]133.969483383574[/C][/ROW]
[ROW][C]126[/C][C]135.077530190373[/C][C]119.009178790416[/C][C]151.145881590329[/C][/ROW]
[ROW][C]127[/C][C]101.134353892736[/C][C]84.054655732427[/C][C]118.214052053044[/C][/ROW]
[ROW][C]128[/C][C]71.9302212824343[/C][C]53.8223400427014[/C][C]90.0381025221672[/C][/ROW]
[ROW][C]129[/C][C]77.800637736942[/C][C]58.6478073675676[/C][C]96.9534681063165[/C][/ROW]
[ROW][C]130[/C][C]69.3682744675659[/C][C]49.153826492046[/C][C]89.5827224430859[/C][/ROW]
[ROW][C]131[/C][C]44.9588692614004[/C][C]23.6662526163363[/C][C]66.2514859064644[/C][/ROW]
[ROW][C]132[/C][C]49.05072134964[/C][C]26.6635166495334[/C][C]71.4379260497466[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79244&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79244&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
121100.68438910884389.421329585523111.947448632163
122102.53774393827790.3466498747216114.728838001833
12387.25676059034674.1213780582324100.39214312246
12490.598890194958976.5026430904347104.695137299483
125118.89560955574103.821735727905133.969483383574
126135.077530190373119.009178790416151.145881590329
127101.13435389273684.054655732427118.214052053044
12871.930221282434353.822340042701490.0381025221672
12977.80063773694258.647807367567696.9534681063165
13069.368274467565949.15382649204689.5827224430859
13144.958869261400423.666252616336366.2514859064644
13249.0507213496426.663516649533471.4379260497466



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')