Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 08 Jul 2010 13:17:47 +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/Jul/08/t12785950763g99033jsflyk1j.htm/, Retrieved Wed, 08 May 2024 19:51:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77957, Retrieved Wed, 08 May 2024 19:51:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Kelly Janbroers -...] [2010-07-08 13:17:47] [413e0fefcf22560c5655fbc122c1a3c2] [Current]
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Dataseries X:
33
32
31
29
49
48
33
23
24
24
25
27
24
21
15
21
49
48
35
36
51
50
61
63
61
62
58
65
93
94
86
88
102
107
121
127
125
128
117
127
160
162
153
160
177
178
196
212
212
211
204
216
248
250
240
249
275
277
286
302
290
290
277
285
311
300
291
299
332
337
343
360
353
351
341
348
381
358
353
358
399
409
407
419
418
421
414
424
463
437
430
436
474
489
482
492
502
500
493
504
538
516
502
501
541
571
559
569
576
573
562
570
597
573
562
556
600
630
624
634




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77957&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77957&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999947806481961
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999947806481961 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77957&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]0.999947806481961[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77957&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
alpha0.999947806481961
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23233-1
33132.000052193518-1.00005219351804
42931.0000521962422-2.0000521962422
54929.000104389760419.9998956102396
64848.9989561350877-0.998956135087695
73348.000052139035-15.0000521390351
82333.0007829054919-10.0007829054919
92423.0005219760430.999478023957021
102423.99994783372575.21662742727358e-05
112523.99999999727731.00000000272274
122724.99994780648182.00005219351818
132426.9998956102398-2.99989561023976
142124.0001565751056-3.00015657510565
151521.0001565887263-6.00015658872632
162115.00031316928115.99968683071885
174920.999686855237228.0003131447628
184848.9985385651508-0.998538565150788
193548.0000521172406-13.0000521172406
203635.00067851845470.999321481545316
215135.999947841896215.0000521581038
225050.9992170945071-0.999217094507102
236150.000052152655410.9999478473446
246360.99942587402362.00057412597639
256162.9998955829983-1.99989558299827
266261.00010438158620.999895618413817
275861.99994781193-3.99994781193001
286558.00020877134836.99979122865172
299364.999634656270228.0003653437298
309492.99853856242631.00146143757365
318693.9999477302044-7.9999477302044
328886.00041754541621.99958245458383
3310287.999895634757114.0001043652429
34107101.99926928535.00073071469973
35121106.99973899427114.0002610057288
36127120.9992692771256.00073072287535
37125126.999686800753-1.99968680075277
38128125.0001043706892.9998956293109
39117127.999843424893-10.9998434248934
40127117.0005741205269.99942587947378
41160126.99947809478533.000521905215
42162159.9982775866652.00172241333536
43153161.999895523065-8.9998955230651
44160153.0004697362096.99953026379066
45177159.99963466989117.0003653301091
46178176.9991126911251.00088730887452
47196177.9999477601718.0000522398298
48212195.99906051394916.0009394860513
49212211.9991648546760.000835145323691222
50211211.999999956411-0.999999956410818
51204211.000052193516-7.00005219351576
52216204.0003653573511.9996346426496
53248215.99937369685332.0006263031472
54250247.9983297747342.0016702252662
55240249.999895525789-9.99989552578899
56249240.0005219297288.99947807027249
57275248.99953028557926.000469714421
58277274.9986429440152.00135705598507
59286276.9998955421349.00010445786558
60302285.99953025288616.0004697471144
61290301.999164879194-11.9991648791936
62290290.000626278629-0.000626278628544696
63277290.000000032688-13.0000000326877
64285277.0006785157367.99932148426382
65311284.9995824872726.0004175127302
66300310.99864294674-10.9986429467396
67291300.000574057869-9.00057405786902
68299291.0004697716247.99953022837553
69332298.99958247637533.0004175236253
70337331.9982775921135.00172240788731
71343336.9997389425116.00026105748873
72360342.99968682526617.0003131747337
73353359.999112693848-6.99911269384768
74351353.000365308315-2.00036530831466
75341351.000104406103-10.0001044061028
76348341.000521940636.99947805937029
77381347.99963467261633.0003653273844
78358380.998277594837-22.998277594837
79353358.001200361017-5.00120036101652
80358353.0002610302414.99973896975877
81399357.99973904603441.0002609539661
82409398.9978600521410.0021399478597
83407408.999477953128-1.99947795312823
84419407.00010435978911.9998956402114
85418418.99937368323-0.99937368323043
86421418.0000521608282.99994783917163
87414420.999843422168-6.99984342216834
88424414.0003653464549.99963465354608
89463423.99947808388839.0005219161117
90437462.997964425556-25.9979644255558
91430437.001356925225-7.0013569252252
92436430.0003654254495.99963457455101
93474435.99968685796538.0003131420354
94489473.99801662997115.0019833700294
95482488.99921699371-6.99921699371038
96492482.0003653137589.99963468624156
97502491.99947808388710.0005219161134
98500501.999478037579-1.99947803757897
99493500.000104359793-7.000104359793
100504493.00036536007310.9996346399268
101538503.99942589037134.000574109629
102516537.998225390422-21.9982253904219
103502516.001148164774-14.0011481647738
104501502.00073076918-1.00073076917931
105541501.0000522316639.9999477683405
106571540.99791226200530.0020877379953
107559570.998434085492-11.9984340854925
108569559.0006262404869.99937375951413
109576568.9994780975057.00052190249471
110573575.999634618134-2.99963461813377
111562573.000156561484-11.0001565614835
112570562.000574136877.99942586313011
113597569.99958248182227.0004175181781
114573596.998590753221-23.9985907532213
115562573.001252570879-11.0012525708794
116556562.000574194074-6.00057419407449
117600556.00031319107743.9996868089225
118630599.99770350155330.0022964984472
119624629.998434074597-5.9984340745965
120634624.0003130793779.99968692062293

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 32 & 33 & -1 \tabularnewline
3 & 31 & 32.000052193518 & -1.00005219351804 \tabularnewline
4 & 29 & 31.0000521962422 & -2.0000521962422 \tabularnewline
5 & 49 & 29.0001043897604 & 19.9998956102396 \tabularnewline
6 & 48 & 48.9989561350877 & -0.998956135087695 \tabularnewline
7 & 33 & 48.000052139035 & -15.0000521390351 \tabularnewline
8 & 23 & 33.0007829054919 & -10.0007829054919 \tabularnewline
9 & 24 & 23.000521976043 & 0.999478023957021 \tabularnewline
10 & 24 & 23.9999478337257 & 5.21662742727358e-05 \tabularnewline
11 & 25 & 23.9999999972773 & 1.00000000272274 \tabularnewline
12 & 27 & 24.9999478064818 & 2.00005219351818 \tabularnewline
13 & 24 & 26.9998956102398 & -2.99989561023976 \tabularnewline
14 & 21 & 24.0001565751056 & -3.00015657510565 \tabularnewline
15 & 15 & 21.0001565887263 & -6.00015658872632 \tabularnewline
16 & 21 & 15.0003131692811 & 5.99968683071885 \tabularnewline
17 & 49 & 20.9996868552372 & 28.0003131447628 \tabularnewline
18 & 48 & 48.9985385651508 & -0.998538565150788 \tabularnewline
19 & 35 & 48.0000521172406 & -13.0000521172406 \tabularnewline
20 & 36 & 35.0006785184547 & 0.999321481545316 \tabularnewline
21 & 51 & 35.9999478418962 & 15.0000521581038 \tabularnewline
22 & 50 & 50.9992170945071 & -0.999217094507102 \tabularnewline
23 & 61 & 50.0000521526554 & 10.9999478473446 \tabularnewline
24 & 63 & 60.9994258740236 & 2.00057412597639 \tabularnewline
25 & 61 & 62.9998955829983 & -1.99989558299827 \tabularnewline
26 & 62 & 61.0001043815862 & 0.999895618413817 \tabularnewline
27 & 58 & 61.99994781193 & -3.99994781193001 \tabularnewline
28 & 65 & 58.0002087713483 & 6.99979122865172 \tabularnewline
29 & 93 & 64.9996346562702 & 28.0003653437298 \tabularnewline
30 & 94 & 92.9985385624263 & 1.00146143757365 \tabularnewline
31 & 86 & 93.9999477302044 & -7.9999477302044 \tabularnewline
32 & 88 & 86.0004175454162 & 1.99958245458383 \tabularnewline
33 & 102 & 87.9998956347571 & 14.0001043652429 \tabularnewline
34 & 107 & 101.9992692853 & 5.00073071469973 \tabularnewline
35 & 121 & 106.999738994271 & 14.0002610057288 \tabularnewline
36 & 127 & 120.999269277125 & 6.00073072287535 \tabularnewline
37 & 125 & 126.999686800753 & -1.99968680075277 \tabularnewline
38 & 128 & 125.000104370689 & 2.9998956293109 \tabularnewline
39 & 117 & 127.999843424893 & -10.9998434248934 \tabularnewline
40 & 127 & 117.000574120526 & 9.99942587947378 \tabularnewline
41 & 160 & 126.999478094785 & 33.000521905215 \tabularnewline
42 & 162 & 159.998277586665 & 2.00172241333536 \tabularnewline
43 & 153 & 161.999895523065 & -8.9998955230651 \tabularnewline
44 & 160 & 153.000469736209 & 6.99953026379066 \tabularnewline
45 & 177 & 159.999634669891 & 17.0003653301091 \tabularnewline
46 & 178 & 176.999112691125 & 1.00088730887452 \tabularnewline
47 & 196 & 177.99994776017 & 18.0000522398298 \tabularnewline
48 & 212 & 195.999060513949 & 16.0009394860513 \tabularnewline
49 & 212 & 211.999164854676 & 0.000835145323691222 \tabularnewline
50 & 211 & 211.999999956411 & -0.999999956410818 \tabularnewline
51 & 204 & 211.000052193516 & -7.00005219351576 \tabularnewline
52 & 216 & 204.00036535735 & 11.9996346426496 \tabularnewline
53 & 248 & 215.999373696853 & 32.0006263031472 \tabularnewline
54 & 250 & 247.998329774734 & 2.0016702252662 \tabularnewline
55 & 240 & 249.999895525789 & -9.99989552578899 \tabularnewline
56 & 249 & 240.000521929728 & 8.99947807027249 \tabularnewline
57 & 275 & 248.999530285579 & 26.000469714421 \tabularnewline
58 & 277 & 274.998642944015 & 2.00135705598507 \tabularnewline
59 & 286 & 276.999895542134 & 9.00010445786558 \tabularnewline
60 & 302 & 285.999530252886 & 16.0004697471144 \tabularnewline
61 & 290 & 301.999164879194 & -11.9991648791936 \tabularnewline
62 & 290 & 290.000626278629 & -0.000626278628544696 \tabularnewline
63 & 277 & 290.000000032688 & -13.0000000326877 \tabularnewline
64 & 285 & 277.000678515736 & 7.99932148426382 \tabularnewline
65 & 311 & 284.99958248727 & 26.0004175127302 \tabularnewline
66 & 300 & 310.99864294674 & -10.9986429467396 \tabularnewline
67 & 291 & 300.000574057869 & -9.00057405786902 \tabularnewline
68 & 299 & 291.000469771624 & 7.99953022837553 \tabularnewline
69 & 332 & 298.999582476375 & 33.0004175236253 \tabularnewline
70 & 337 & 331.998277592113 & 5.00172240788731 \tabularnewline
71 & 343 & 336.999738942511 & 6.00026105748873 \tabularnewline
72 & 360 & 342.999686825266 & 17.0003131747337 \tabularnewline
73 & 353 & 359.999112693848 & -6.99911269384768 \tabularnewline
74 & 351 & 353.000365308315 & -2.00036530831466 \tabularnewline
75 & 341 & 351.000104406103 & -10.0001044061028 \tabularnewline
76 & 348 & 341.00052194063 & 6.99947805937029 \tabularnewline
77 & 381 & 347.999634672616 & 33.0003653273844 \tabularnewline
78 & 358 & 380.998277594837 & -22.998277594837 \tabularnewline
79 & 353 & 358.001200361017 & -5.00120036101652 \tabularnewline
80 & 358 & 353.000261030241 & 4.99973896975877 \tabularnewline
81 & 399 & 357.999739046034 & 41.0002609539661 \tabularnewline
82 & 409 & 398.99786005214 & 10.0021399478597 \tabularnewline
83 & 407 & 408.999477953128 & -1.99947795312823 \tabularnewline
84 & 419 & 407.000104359789 & 11.9998956402114 \tabularnewline
85 & 418 & 418.99937368323 & -0.99937368323043 \tabularnewline
86 & 421 & 418.000052160828 & 2.99994783917163 \tabularnewline
87 & 414 & 420.999843422168 & -6.99984342216834 \tabularnewline
88 & 424 & 414.000365346454 & 9.99963465354608 \tabularnewline
89 & 463 & 423.999478083888 & 39.0005219161117 \tabularnewline
90 & 437 & 462.997964425556 & -25.9979644255558 \tabularnewline
91 & 430 & 437.001356925225 & -7.0013569252252 \tabularnewline
92 & 436 & 430.000365425449 & 5.99963457455101 \tabularnewline
93 & 474 & 435.999686857965 & 38.0003131420354 \tabularnewline
94 & 489 & 473.998016629971 & 15.0019833700294 \tabularnewline
95 & 482 & 488.99921699371 & -6.99921699371038 \tabularnewline
96 & 492 & 482.000365313758 & 9.99963468624156 \tabularnewline
97 & 502 & 491.999478083887 & 10.0005219161134 \tabularnewline
98 & 500 & 501.999478037579 & -1.99947803757897 \tabularnewline
99 & 493 & 500.000104359793 & -7.000104359793 \tabularnewline
100 & 504 & 493.000365360073 & 10.9996346399268 \tabularnewline
101 & 538 & 503.999425890371 & 34.000574109629 \tabularnewline
102 & 516 & 537.998225390422 & -21.9982253904219 \tabularnewline
103 & 502 & 516.001148164774 & -14.0011481647738 \tabularnewline
104 & 501 & 502.00073076918 & -1.00073076917931 \tabularnewline
105 & 541 & 501.00005223166 & 39.9999477683405 \tabularnewline
106 & 571 & 540.997912262005 & 30.0020877379953 \tabularnewline
107 & 559 & 570.998434085492 & -11.9984340854925 \tabularnewline
108 & 569 & 559.000626240486 & 9.99937375951413 \tabularnewline
109 & 576 & 568.999478097505 & 7.00052190249471 \tabularnewline
110 & 573 & 575.999634618134 & -2.99963461813377 \tabularnewline
111 & 562 & 573.000156561484 & -11.0001565614835 \tabularnewline
112 & 570 & 562.00057413687 & 7.99942586313011 \tabularnewline
113 & 597 & 569.999582481822 & 27.0004175181781 \tabularnewline
114 & 573 & 596.998590753221 & -23.9985907532213 \tabularnewline
115 & 562 & 573.001252570879 & -11.0012525708794 \tabularnewline
116 & 556 & 562.000574194074 & -6.00057419407449 \tabularnewline
117 & 600 & 556.000313191077 & 43.9996868089225 \tabularnewline
118 & 630 & 599.997703501553 & 30.0022964984472 \tabularnewline
119 & 624 & 629.998434074597 & -5.9984340745965 \tabularnewline
120 & 634 & 624.000313079377 & 9.99968692062293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77957&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]2[/C][C]32[/C][C]33[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]31[/C][C]32.000052193518[/C][C]-1.00005219351804[/C][/ROW]
[ROW][C]4[/C][C]29[/C][C]31.0000521962422[/C][C]-2.0000521962422[/C][/ROW]
[ROW][C]5[/C][C]49[/C][C]29.0001043897604[/C][C]19.9998956102396[/C][/ROW]
[ROW][C]6[/C][C]48[/C][C]48.9989561350877[/C][C]-0.998956135087695[/C][/ROW]
[ROW][C]7[/C][C]33[/C][C]48.000052139035[/C][C]-15.0000521390351[/C][/ROW]
[ROW][C]8[/C][C]23[/C][C]33.0007829054919[/C][C]-10.0007829054919[/C][/ROW]
[ROW][C]9[/C][C]24[/C][C]23.000521976043[/C][C]0.999478023957021[/C][/ROW]
[ROW][C]10[/C][C]24[/C][C]23.9999478337257[/C][C]5.21662742727358e-05[/C][/ROW]
[ROW][C]11[/C][C]25[/C][C]23.9999999972773[/C][C]1.00000000272274[/C][/ROW]
[ROW][C]12[/C][C]27[/C][C]24.9999478064818[/C][C]2.00005219351818[/C][/ROW]
[ROW][C]13[/C][C]24[/C][C]26.9998956102398[/C][C]-2.99989561023976[/C][/ROW]
[ROW][C]14[/C][C]21[/C][C]24.0001565751056[/C][C]-3.00015657510565[/C][/ROW]
[ROW][C]15[/C][C]15[/C][C]21.0001565887263[/C][C]-6.00015658872632[/C][/ROW]
[ROW][C]16[/C][C]21[/C][C]15.0003131692811[/C][C]5.99968683071885[/C][/ROW]
[ROW][C]17[/C][C]49[/C][C]20.9996868552372[/C][C]28.0003131447628[/C][/ROW]
[ROW][C]18[/C][C]48[/C][C]48.9985385651508[/C][C]-0.998538565150788[/C][/ROW]
[ROW][C]19[/C][C]35[/C][C]48.0000521172406[/C][C]-13.0000521172406[/C][/ROW]
[ROW][C]20[/C][C]36[/C][C]35.0006785184547[/C][C]0.999321481545316[/C][/ROW]
[ROW][C]21[/C][C]51[/C][C]35.9999478418962[/C][C]15.0000521581038[/C][/ROW]
[ROW][C]22[/C][C]50[/C][C]50.9992170945071[/C][C]-0.999217094507102[/C][/ROW]
[ROW][C]23[/C][C]61[/C][C]50.0000521526554[/C][C]10.9999478473446[/C][/ROW]
[ROW][C]24[/C][C]63[/C][C]60.9994258740236[/C][C]2.00057412597639[/C][/ROW]
[ROW][C]25[/C][C]61[/C][C]62.9998955829983[/C][C]-1.99989558299827[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]61.0001043815862[/C][C]0.999895618413817[/C][/ROW]
[ROW][C]27[/C][C]58[/C][C]61.99994781193[/C][C]-3.99994781193001[/C][/ROW]
[ROW][C]28[/C][C]65[/C][C]58.0002087713483[/C][C]6.99979122865172[/C][/ROW]
[ROW][C]29[/C][C]93[/C][C]64.9996346562702[/C][C]28.0003653437298[/C][/ROW]
[ROW][C]30[/C][C]94[/C][C]92.9985385624263[/C][C]1.00146143757365[/C][/ROW]
[ROW][C]31[/C][C]86[/C][C]93.9999477302044[/C][C]-7.9999477302044[/C][/ROW]
[ROW][C]32[/C][C]88[/C][C]86.0004175454162[/C][C]1.99958245458383[/C][/ROW]
[ROW][C]33[/C][C]102[/C][C]87.9998956347571[/C][C]14.0001043652429[/C][/ROW]
[ROW][C]34[/C][C]107[/C][C]101.9992692853[/C][C]5.00073071469973[/C][/ROW]
[ROW][C]35[/C][C]121[/C][C]106.999738994271[/C][C]14.0002610057288[/C][/ROW]
[ROW][C]36[/C][C]127[/C][C]120.999269277125[/C][C]6.00073072287535[/C][/ROW]
[ROW][C]37[/C][C]125[/C][C]126.999686800753[/C][C]-1.99968680075277[/C][/ROW]
[ROW][C]38[/C][C]128[/C][C]125.000104370689[/C][C]2.9998956293109[/C][/ROW]
[ROW][C]39[/C][C]117[/C][C]127.999843424893[/C][C]-10.9998434248934[/C][/ROW]
[ROW][C]40[/C][C]127[/C][C]117.000574120526[/C][C]9.99942587947378[/C][/ROW]
[ROW][C]41[/C][C]160[/C][C]126.999478094785[/C][C]33.000521905215[/C][/ROW]
[ROW][C]42[/C][C]162[/C][C]159.998277586665[/C][C]2.00172241333536[/C][/ROW]
[ROW][C]43[/C][C]153[/C][C]161.999895523065[/C][C]-8.9998955230651[/C][/ROW]
[ROW][C]44[/C][C]160[/C][C]153.000469736209[/C][C]6.99953026379066[/C][/ROW]
[ROW][C]45[/C][C]177[/C][C]159.999634669891[/C][C]17.0003653301091[/C][/ROW]
[ROW][C]46[/C][C]178[/C][C]176.999112691125[/C][C]1.00088730887452[/C][/ROW]
[ROW][C]47[/C][C]196[/C][C]177.99994776017[/C][C]18.0000522398298[/C][/ROW]
[ROW][C]48[/C][C]212[/C][C]195.999060513949[/C][C]16.0009394860513[/C][/ROW]
[ROW][C]49[/C][C]212[/C][C]211.999164854676[/C][C]0.000835145323691222[/C][/ROW]
[ROW][C]50[/C][C]211[/C][C]211.999999956411[/C][C]-0.999999956410818[/C][/ROW]
[ROW][C]51[/C][C]204[/C][C]211.000052193516[/C][C]-7.00005219351576[/C][/ROW]
[ROW][C]52[/C][C]216[/C][C]204.00036535735[/C][C]11.9996346426496[/C][/ROW]
[ROW][C]53[/C][C]248[/C][C]215.999373696853[/C][C]32.0006263031472[/C][/ROW]
[ROW][C]54[/C][C]250[/C][C]247.998329774734[/C][C]2.0016702252662[/C][/ROW]
[ROW][C]55[/C][C]240[/C][C]249.999895525789[/C][C]-9.99989552578899[/C][/ROW]
[ROW][C]56[/C][C]249[/C][C]240.000521929728[/C][C]8.99947807027249[/C][/ROW]
[ROW][C]57[/C][C]275[/C][C]248.999530285579[/C][C]26.000469714421[/C][/ROW]
[ROW][C]58[/C][C]277[/C][C]274.998642944015[/C][C]2.00135705598507[/C][/ROW]
[ROW][C]59[/C][C]286[/C][C]276.999895542134[/C][C]9.00010445786558[/C][/ROW]
[ROW][C]60[/C][C]302[/C][C]285.999530252886[/C][C]16.0004697471144[/C][/ROW]
[ROW][C]61[/C][C]290[/C][C]301.999164879194[/C][C]-11.9991648791936[/C][/ROW]
[ROW][C]62[/C][C]290[/C][C]290.000626278629[/C][C]-0.000626278628544696[/C][/ROW]
[ROW][C]63[/C][C]277[/C][C]290.000000032688[/C][C]-13.0000000326877[/C][/ROW]
[ROW][C]64[/C][C]285[/C][C]277.000678515736[/C][C]7.99932148426382[/C][/ROW]
[ROW][C]65[/C][C]311[/C][C]284.99958248727[/C][C]26.0004175127302[/C][/ROW]
[ROW][C]66[/C][C]300[/C][C]310.99864294674[/C][C]-10.9986429467396[/C][/ROW]
[ROW][C]67[/C][C]291[/C][C]300.000574057869[/C][C]-9.00057405786902[/C][/ROW]
[ROW][C]68[/C][C]299[/C][C]291.000469771624[/C][C]7.99953022837553[/C][/ROW]
[ROW][C]69[/C][C]332[/C][C]298.999582476375[/C][C]33.0004175236253[/C][/ROW]
[ROW][C]70[/C][C]337[/C][C]331.998277592113[/C][C]5.00172240788731[/C][/ROW]
[ROW][C]71[/C][C]343[/C][C]336.999738942511[/C][C]6.00026105748873[/C][/ROW]
[ROW][C]72[/C][C]360[/C][C]342.999686825266[/C][C]17.0003131747337[/C][/ROW]
[ROW][C]73[/C][C]353[/C][C]359.999112693848[/C][C]-6.99911269384768[/C][/ROW]
[ROW][C]74[/C][C]351[/C][C]353.000365308315[/C][C]-2.00036530831466[/C][/ROW]
[ROW][C]75[/C][C]341[/C][C]351.000104406103[/C][C]-10.0001044061028[/C][/ROW]
[ROW][C]76[/C][C]348[/C][C]341.00052194063[/C][C]6.99947805937029[/C][/ROW]
[ROW][C]77[/C][C]381[/C][C]347.999634672616[/C][C]33.0003653273844[/C][/ROW]
[ROW][C]78[/C][C]358[/C][C]380.998277594837[/C][C]-22.998277594837[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]358.001200361017[/C][C]-5.00120036101652[/C][/ROW]
[ROW][C]80[/C][C]358[/C][C]353.000261030241[/C][C]4.99973896975877[/C][/ROW]
[ROW][C]81[/C][C]399[/C][C]357.999739046034[/C][C]41.0002609539661[/C][/ROW]
[ROW][C]82[/C][C]409[/C][C]398.99786005214[/C][C]10.0021399478597[/C][/ROW]
[ROW][C]83[/C][C]407[/C][C]408.999477953128[/C][C]-1.99947795312823[/C][/ROW]
[ROW][C]84[/C][C]419[/C][C]407.000104359789[/C][C]11.9998956402114[/C][/ROW]
[ROW][C]85[/C][C]418[/C][C]418.99937368323[/C][C]-0.99937368323043[/C][/ROW]
[ROW][C]86[/C][C]421[/C][C]418.000052160828[/C][C]2.99994783917163[/C][/ROW]
[ROW][C]87[/C][C]414[/C][C]420.999843422168[/C][C]-6.99984342216834[/C][/ROW]
[ROW][C]88[/C][C]424[/C][C]414.000365346454[/C][C]9.99963465354608[/C][/ROW]
[ROW][C]89[/C][C]463[/C][C]423.999478083888[/C][C]39.0005219161117[/C][/ROW]
[ROW][C]90[/C][C]437[/C][C]462.997964425556[/C][C]-25.9979644255558[/C][/ROW]
[ROW][C]91[/C][C]430[/C][C]437.001356925225[/C][C]-7.0013569252252[/C][/ROW]
[ROW][C]92[/C][C]436[/C][C]430.000365425449[/C][C]5.99963457455101[/C][/ROW]
[ROW][C]93[/C][C]474[/C][C]435.999686857965[/C][C]38.0003131420354[/C][/ROW]
[ROW][C]94[/C][C]489[/C][C]473.998016629971[/C][C]15.0019833700294[/C][/ROW]
[ROW][C]95[/C][C]482[/C][C]488.99921699371[/C][C]-6.99921699371038[/C][/ROW]
[ROW][C]96[/C][C]492[/C][C]482.000365313758[/C][C]9.99963468624156[/C][/ROW]
[ROW][C]97[/C][C]502[/C][C]491.999478083887[/C][C]10.0005219161134[/C][/ROW]
[ROW][C]98[/C][C]500[/C][C]501.999478037579[/C][C]-1.99947803757897[/C][/ROW]
[ROW][C]99[/C][C]493[/C][C]500.000104359793[/C][C]-7.000104359793[/C][/ROW]
[ROW][C]100[/C][C]504[/C][C]493.000365360073[/C][C]10.9996346399268[/C][/ROW]
[ROW][C]101[/C][C]538[/C][C]503.999425890371[/C][C]34.000574109629[/C][/ROW]
[ROW][C]102[/C][C]516[/C][C]537.998225390422[/C][C]-21.9982253904219[/C][/ROW]
[ROW][C]103[/C][C]502[/C][C]516.001148164774[/C][C]-14.0011481647738[/C][/ROW]
[ROW][C]104[/C][C]501[/C][C]502.00073076918[/C][C]-1.00073076917931[/C][/ROW]
[ROW][C]105[/C][C]541[/C][C]501.00005223166[/C][C]39.9999477683405[/C][/ROW]
[ROW][C]106[/C][C]571[/C][C]540.997912262005[/C][C]30.0020877379953[/C][/ROW]
[ROW][C]107[/C][C]559[/C][C]570.998434085492[/C][C]-11.9984340854925[/C][/ROW]
[ROW][C]108[/C][C]569[/C][C]559.000626240486[/C][C]9.99937375951413[/C][/ROW]
[ROW][C]109[/C][C]576[/C][C]568.999478097505[/C][C]7.00052190249471[/C][/ROW]
[ROW][C]110[/C][C]573[/C][C]575.999634618134[/C][C]-2.99963461813377[/C][/ROW]
[ROW][C]111[/C][C]562[/C][C]573.000156561484[/C][C]-11.0001565614835[/C][/ROW]
[ROW][C]112[/C][C]570[/C][C]562.00057413687[/C][C]7.99942586313011[/C][/ROW]
[ROW][C]113[/C][C]597[/C][C]569.999582481822[/C][C]27.0004175181781[/C][/ROW]
[ROW][C]114[/C][C]573[/C][C]596.998590753221[/C][C]-23.9985907532213[/C][/ROW]
[ROW][C]115[/C][C]562[/C][C]573.001252570879[/C][C]-11.0012525708794[/C][/ROW]
[ROW][C]116[/C][C]556[/C][C]562.000574194074[/C][C]-6.00057419407449[/C][/ROW]
[ROW][C]117[/C][C]600[/C][C]556.000313191077[/C][C]43.9996868089225[/C][/ROW]
[ROW][C]118[/C][C]630[/C][C]599.997703501553[/C][C]30.0022964984472[/C][/ROW]
[ROW][C]119[/C][C]624[/C][C]629.998434074597[/C][C]-5.9984340745965[/C][/ROW]
[ROW][C]120[/C][C]634[/C][C]624.000313079377[/C][C]9.99968692062293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77957&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77957&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
23233-1
33132.000052193518-1.00005219351804
42931.0000521962422-2.0000521962422
54929.000104389760419.9998956102396
64848.9989561350877-0.998956135087695
73348.000052139035-15.0000521390351
82333.0007829054919-10.0007829054919
92423.0005219760430.999478023957021
102423.99994783372575.21662742727358e-05
112523.99999999727731.00000000272274
122724.99994780648182.00005219351818
132426.9998956102398-2.99989561023976
142124.0001565751056-3.00015657510565
151521.0001565887263-6.00015658872632
162115.00031316928115.99968683071885
174920.999686855237228.0003131447628
184848.9985385651508-0.998538565150788
193548.0000521172406-13.0000521172406
203635.00067851845470.999321481545316
215135.999947841896215.0000521581038
225050.9992170945071-0.999217094507102
236150.000052152655410.9999478473446
246360.99942587402362.00057412597639
256162.9998955829983-1.99989558299827
266261.00010438158620.999895618413817
275861.99994781193-3.99994781193001
286558.00020877134836.99979122865172
299364.999634656270228.0003653437298
309492.99853856242631.00146143757365
318693.9999477302044-7.9999477302044
328886.00041754541621.99958245458383
3310287.999895634757114.0001043652429
34107101.99926928535.00073071469973
35121106.99973899427114.0002610057288
36127120.9992692771256.00073072287535
37125126.999686800753-1.99968680075277
38128125.0001043706892.9998956293109
39117127.999843424893-10.9998434248934
40127117.0005741205269.99942587947378
41160126.99947809478533.000521905215
42162159.9982775866652.00172241333536
43153161.999895523065-8.9998955230651
44160153.0004697362096.99953026379066
45177159.99963466989117.0003653301091
46178176.9991126911251.00088730887452
47196177.9999477601718.0000522398298
48212195.99906051394916.0009394860513
49212211.9991648546760.000835145323691222
50211211.999999956411-0.999999956410818
51204211.000052193516-7.00005219351576
52216204.0003653573511.9996346426496
53248215.99937369685332.0006263031472
54250247.9983297747342.0016702252662
55240249.999895525789-9.99989552578899
56249240.0005219297288.99947807027249
57275248.99953028557926.000469714421
58277274.9986429440152.00135705598507
59286276.9998955421349.00010445786558
60302285.99953025288616.0004697471144
61290301.999164879194-11.9991648791936
62290290.000626278629-0.000626278628544696
63277290.000000032688-13.0000000326877
64285277.0006785157367.99932148426382
65311284.9995824872726.0004175127302
66300310.99864294674-10.9986429467396
67291300.000574057869-9.00057405786902
68299291.0004697716247.99953022837553
69332298.99958247637533.0004175236253
70337331.9982775921135.00172240788731
71343336.9997389425116.00026105748873
72360342.99968682526617.0003131747337
73353359.999112693848-6.99911269384768
74351353.000365308315-2.00036530831466
75341351.000104406103-10.0001044061028
76348341.000521940636.99947805937029
77381347.99963467261633.0003653273844
78358380.998277594837-22.998277594837
79353358.001200361017-5.00120036101652
80358353.0002610302414.99973896975877
81399357.99973904603441.0002609539661
82409398.9978600521410.0021399478597
83407408.999477953128-1.99947795312823
84419407.00010435978911.9998956402114
85418418.99937368323-0.99937368323043
86421418.0000521608282.99994783917163
87414420.999843422168-6.99984342216834
88424414.0003653464549.99963465354608
89463423.99947808388839.0005219161117
90437462.997964425556-25.9979644255558
91430437.001356925225-7.0013569252252
92436430.0003654254495.99963457455101
93474435.99968685796538.0003131420354
94489473.99801662997115.0019833700294
95482488.99921699371-6.99921699371038
96492482.0003653137589.99963468624156
97502491.99947808388710.0005219161134
98500501.999478037579-1.99947803757897
99493500.000104359793-7.000104359793
100504493.00036536007310.9996346399268
101538503.99942589037134.000574109629
102516537.998225390422-21.9982253904219
103502516.001148164774-14.0011481647738
104501502.00073076918-1.00073076917931
105541501.0000522316639.9999477683405
106571540.99791226200530.0020877379953
107559570.998434085492-11.9984340854925
108569559.0006262404869.99937375951413
109576568.9994780975057.00052190249471
110573575.999634618134-2.99963461813377
111562573.000156561484-11.0001565614835
112570562.000574136877.99942586313011
113597569.99958248182227.0004175181781
114573596.998590753221-23.9985907532213
115562573.001252570879-11.0012525708794
116556562.000574194074-6.00057419407449
117600556.00031319107743.9996868089225
118630599.99770350155330.0022964984472
119624629.998434074597-5.9984340745965
120634624.0003130793779.99968692062293







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121633.99947808116605.147847133371662.85110902895
122633.99947808116593.198175093878674.800781068442
123633.99947808116584.028726209965683.970229952355
124633.99947808116576.298474973024691.700481189296
125633.99947808116569.487963784892698.510992377429
126633.99947808116563.330777839043704.668178323278
127633.99947808116557.668652649866710.330303512455
128633.99947808116552.398469336566715.600486825754
129633.99947808116547.448600874468720.550355287852
130633.99947808116542.766895840163725.232060322158
131633.99947808116538.313983989982729.684972172339
132633.99947808116534.05927847867733.93967768365

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 633.99947808116 & 605.147847133371 & 662.85110902895 \tabularnewline
122 & 633.99947808116 & 593.198175093878 & 674.800781068442 \tabularnewline
123 & 633.99947808116 & 584.028726209965 & 683.970229952355 \tabularnewline
124 & 633.99947808116 & 576.298474973024 & 691.700481189296 \tabularnewline
125 & 633.99947808116 & 569.487963784892 & 698.510992377429 \tabularnewline
126 & 633.99947808116 & 563.330777839043 & 704.668178323278 \tabularnewline
127 & 633.99947808116 & 557.668652649866 & 710.330303512455 \tabularnewline
128 & 633.99947808116 & 552.398469336566 & 715.600486825754 \tabularnewline
129 & 633.99947808116 & 547.448600874468 & 720.550355287852 \tabularnewline
130 & 633.99947808116 & 542.766895840163 & 725.232060322158 \tabularnewline
131 & 633.99947808116 & 538.313983989982 & 729.684972172339 \tabularnewline
132 & 633.99947808116 & 534.05927847867 & 733.93967768365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77957&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]633.99947808116[/C][C]605.147847133371[/C][C]662.85110902895[/C][/ROW]
[ROW][C]122[/C][C]633.99947808116[/C][C]593.198175093878[/C][C]674.800781068442[/C][/ROW]
[ROW][C]123[/C][C]633.99947808116[/C][C]584.028726209965[/C][C]683.970229952355[/C][/ROW]
[ROW][C]124[/C][C]633.99947808116[/C][C]576.298474973024[/C][C]691.700481189296[/C][/ROW]
[ROW][C]125[/C][C]633.99947808116[/C][C]569.487963784892[/C][C]698.510992377429[/C][/ROW]
[ROW][C]126[/C][C]633.99947808116[/C][C]563.330777839043[/C][C]704.668178323278[/C][/ROW]
[ROW][C]127[/C][C]633.99947808116[/C][C]557.668652649866[/C][C]710.330303512455[/C][/ROW]
[ROW][C]128[/C][C]633.99947808116[/C][C]552.398469336566[/C][C]715.600486825754[/C][/ROW]
[ROW][C]129[/C][C]633.99947808116[/C][C]547.448600874468[/C][C]720.550355287852[/C][/ROW]
[ROW][C]130[/C][C]633.99947808116[/C][C]542.766895840163[/C][C]725.232060322158[/C][/ROW]
[ROW][C]131[/C][C]633.99947808116[/C][C]538.313983989982[/C][C]729.684972172339[/C][/ROW]
[ROW][C]132[/C][C]633.99947808116[/C][C]534.05927847867[/C][C]733.93967768365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77957&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77957&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
121633.99947808116605.147847133371662.85110902895
122633.99947808116593.198175093878674.800781068442
123633.99947808116584.028726209965683.970229952355
124633.99947808116576.298474973024691.700481189296
125633.99947808116569.487963784892698.510992377429
126633.99947808116563.330777839043704.668178323278
127633.99947808116557.668652649866710.330303512455
128633.99947808116552.398469336566715.600486825754
129633.99947808116547.448600874468720.550355287852
130633.99947808116542.766895840163725.232060322158
131633.99947808116538.313983989982729.684972172339
132633.99947808116534.05927847867733.93967768365



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')