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 12:20:14 +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/t12819611841umy7yd4oejoziy.htm/, Retrieved Thu, 16 May 2024 19:30:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78971, Retrieved Thu, 16 May 2024 19:30:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Aantal bezoekers] [2010-08-16 12:20:14] [5e78ed906b09bab42b8ec3dd93b6358a] [Current]
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Dataseries X:
556
555
554
552
572
571
556
546
547
547
548
550
555
549
555
550
566
573
543
535
542
541
535
536
548
546
548
548
561
563
527
527
541
534
522
527
539
533
532
519
538
542
503
502
522
511
492
500
509
511
505
493
518
518
474
471
483
461
439
446
461
449
441
424
447
448
404
403
411
386
359
370
385
369
368
352
378
383
334
323
330
303
275
284
301
281
284
272
297
300
240
236
247
218
192
201
223
197
195
175
197
204
142
142
151
127
100
114
139
112
123
108
132
140
76
71
81
57
38
46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78971&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78971&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.312700997165616
beta0.158746465680972
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.312700997165616 \tabularnewline
beta & 0.158746465680972 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78971&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]0.312700997165616[/C][/ROW]
[ROW][C]beta[/C][C]0.158746465680972[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78971&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
alpha0.312700997165616
beta0.158746465680972
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13555556.096125968013-1.09612596801264
14549550.206838318706-1.20683831870599
15555555.909186031654-0.909186031654144
16550550.436065507093-0.436065507092508
17566566.440247225086-0.440247225086296
18573573.766014542637-0.766014542637436
19543550.225015114608-7.22501511460837
20535537.330053349687-2.33005334968720
21542536.6047280020035.3952719979975
22541537.4184025855073.58159741449333
23535539.109847151401-4.10984715140148
24536539.004461470953-3.00446147095295
25548541.5657069316396.43429306836106
26546537.8152689377338.18473106226702
27548546.7753467402641.22465325973565
28548542.6824894474845.31751055251561
29561560.9425504645390.0574495354612736
30563568.79555489801-5.79555489801044
31527539.90321780154-12.9032178015398
32527528.78717895982-1.78717895982038
33541533.5864776915737.41352230842665
34534534.030031809365-0.0300318093646865
35522529.406827228539-7.40682722853853
36527528.875073865166-1.8750738651662
37539538.0462919207910.953708079208923
38533533.498495593853-0.498495593853477
39532534.147861080172-2.14786108017165
40519530.908081947645-11.9080819476446
41538537.8418594691210.158140530879336
42542539.6953019868832.30469801311654
43503508.300312948131-5.30031294813119
44502506.150266856587-4.15026685658694
45522514.841278725737.15872127427008
46511509.2291197227821.77088027721834
47492499.454474038915-7.45447403891473
48500501.341235430462-1.34123543046184
49509510.936593504713-1.9365935047133
50511503.5556926946397.44430730536124
51505504.7224571997590.277542800241463
52493495.230095705913-2.23009570591250
53518512.3055081893275.69449181067341
54518517.2135282654740.786471734525662
55474481.725044855555-7.72504485555481
56471479.376457379085-8.37645737908474
57483493.150719195499-10.150719195499
58461477.835306271544-16.8353062715440
59439454.961426817135-15.9614268171351
60446454.966726298304-8.96672629830408
61461457.6649757482683.33502425173208
62449455.441866952845-6.44186695284452
63441444.42357547944-3.42357547943982
64424429.696144133860-5.69614413385955
65447443.9173378412723.0826621587276
66448440.4064896894457.59351031055508
67404403.5881191122040.411880887795746
68403400.0688968229092.93110317709068
69411410.9580522531380.0419477468622063
70386394.209388588765-8.20938858876485
71359375.020366169593-16.0203661695929
72370375.931993643433-5.9319936434328
73385383.4274373523471.57256264765283
74369373.170317363881-4.17031736388128
75368363.7471369205174.25286307948346
76352350.4840115893171.51598841068346
77378367.40936974605910.5906302539411
78383368.16718842694914.8328115730511
79334335.211434335291-1.21143433529147
80323332.266994940328-9.26699494032829
81330334.233761039406-4.23376103940632
82303312.879468444041-9.8794684440407
83275290.078212639396-15.0782126393955
84284293.336608130076-9.33660813007629
85301299.1344144423371.86558555766288
86281285.645488727339-4.64548872733883
87284279.6064483397054.39355166029526
88272265.7032184676726.29678153232817
89297282.20714796361814.7928520363818
90300284.61749479234315.3825052076568
91240250.715508243537-10.7155082435370
92236238.813634439328-2.8136344393275
93247241.6188081902925.38119180970767
94218223.721025347817-5.72102534781669
95192202.998784772789-10.9987847727890
96201206.224278226510-5.22427822650963
97223214.3439276798298.65607232017149
98197202.023412541456-5.02341254145594
99195199.753519815179-4.75351981517909
100175186.183052349202-11.1830523492015
101197192.6350373004884.36496269951246
102204188.57102078939415.4289792106057
103142153.54340498258-11.5434049825801
104142144.302293384114-2.30229338411394
105151145.1671743418045.83282565819627
106127127.096249244895-0.0962492448953896
107100110.522622860485-10.5226228604849
108114109.1339995098184.86600049018212
109139117.04143035189221.9585696481085
110112107.2690458402144.73095415978588
111123105.65045340779817.3495465922016
11210899.9957570241458.00424297585492
113132113.6730714323418.3269285676599
114140120.63178663317619.3682133668242
1157690.8084882621225-14.8084882621225
1167186.612711818103-15.6127118181030
1178184.7881741440841-3.78817414408411
1185768.9266573814876-11.9266573814876
1193850.9446403466986-12.9446403466986
1204649.5255992797587-3.52559927975867

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 555 & 556.096125968013 & -1.09612596801264 \tabularnewline
14 & 549 & 550.206838318706 & -1.20683831870599 \tabularnewline
15 & 555 & 555.909186031654 & -0.909186031654144 \tabularnewline
16 & 550 & 550.436065507093 & -0.436065507092508 \tabularnewline
17 & 566 & 566.440247225086 & -0.440247225086296 \tabularnewline
18 & 573 & 573.766014542637 & -0.766014542637436 \tabularnewline
19 & 543 & 550.225015114608 & -7.22501511460837 \tabularnewline
20 & 535 & 537.330053349687 & -2.33005334968720 \tabularnewline
21 & 542 & 536.604728002003 & 5.3952719979975 \tabularnewline
22 & 541 & 537.418402585507 & 3.58159741449333 \tabularnewline
23 & 535 & 539.109847151401 & -4.10984715140148 \tabularnewline
24 & 536 & 539.004461470953 & -3.00446147095295 \tabularnewline
25 & 548 & 541.565706931639 & 6.43429306836106 \tabularnewline
26 & 546 & 537.815268937733 & 8.18473106226702 \tabularnewline
27 & 548 & 546.775346740264 & 1.22465325973565 \tabularnewline
28 & 548 & 542.682489447484 & 5.31751055251561 \tabularnewline
29 & 561 & 560.942550464539 & 0.0574495354612736 \tabularnewline
30 & 563 & 568.79555489801 & -5.79555489801044 \tabularnewline
31 & 527 & 539.90321780154 & -12.9032178015398 \tabularnewline
32 & 527 & 528.78717895982 & -1.78717895982038 \tabularnewline
33 & 541 & 533.586477691573 & 7.41352230842665 \tabularnewline
34 & 534 & 534.030031809365 & -0.0300318093646865 \tabularnewline
35 & 522 & 529.406827228539 & -7.40682722853853 \tabularnewline
36 & 527 & 528.875073865166 & -1.8750738651662 \tabularnewline
37 & 539 & 538.046291920791 & 0.953708079208923 \tabularnewline
38 & 533 & 533.498495593853 & -0.498495593853477 \tabularnewline
39 & 532 & 534.147861080172 & -2.14786108017165 \tabularnewline
40 & 519 & 530.908081947645 & -11.9080819476446 \tabularnewline
41 & 538 & 537.841859469121 & 0.158140530879336 \tabularnewline
42 & 542 & 539.695301986883 & 2.30469801311654 \tabularnewline
43 & 503 & 508.300312948131 & -5.30031294813119 \tabularnewline
44 & 502 & 506.150266856587 & -4.15026685658694 \tabularnewline
45 & 522 & 514.84127872573 & 7.15872127427008 \tabularnewline
46 & 511 & 509.229119722782 & 1.77088027721834 \tabularnewline
47 & 492 & 499.454474038915 & -7.45447403891473 \tabularnewline
48 & 500 & 501.341235430462 & -1.34123543046184 \tabularnewline
49 & 509 & 510.936593504713 & -1.9365935047133 \tabularnewline
50 & 511 & 503.555692694639 & 7.44430730536124 \tabularnewline
51 & 505 & 504.722457199759 & 0.277542800241463 \tabularnewline
52 & 493 & 495.230095705913 & -2.23009570591250 \tabularnewline
53 & 518 & 512.305508189327 & 5.69449181067341 \tabularnewline
54 & 518 & 517.213528265474 & 0.786471734525662 \tabularnewline
55 & 474 & 481.725044855555 & -7.72504485555481 \tabularnewline
56 & 471 & 479.376457379085 & -8.37645737908474 \tabularnewline
57 & 483 & 493.150719195499 & -10.150719195499 \tabularnewline
58 & 461 & 477.835306271544 & -16.8353062715440 \tabularnewline
59 & 439 & 454.961426817135 & -15.9614268171351 \tabularnewline
60 & 446 & 454.966726298304 & -8.96672629830408 \tabularnewline
61 & 461 & 457.664975748268 & 3.33502425173208 \tabularnewline
62 & 449 & 455.441866952845 & -6.44186695284452 \tabularnewline
63 & 441 & 444.42357547944 & -3.42357547943982 \tabularnewline
64 & 424 & 429.696144133860 & -5.69614413385955 \tabularnewline
65 & 447 & 443.917337841272 & 3.0826621587276 \tabularnewline
66 & 448 & 440.406489689445 & 7.59351031055508 \tabularnewline
67 & 404 & 403.588119112204 & 0.411880887795746 \tabularnewline
68 & 403 & 400.068896822909 & 2.93110317709068 \tabularnewline
69 & 411 & 410.958052253138 & 0.0419477468622063 \tabularnewline
70 & 386 & 394.209388588765 & -8.20938858876485 \tabularnewline
71 & 359 & 375.020366169593 & -16.0203661695929 \tabularnewline
72 & 370 & 375.931993643433 & -5.9319936434328 \tabularnewline
73 & 385 & 383.427437352347 & 1.57256264765283 \tabularnewline
74 & 369 & 373.170317363881 & -4.17031736388128 \tabularnewline
75 & 368 & 363.747136920517 & 4.25286307948346 \tabularnewline
76 & 352 & 350.484011589317 & 1.51598841068346 \tabularnewline
77 & 378 & 367.409369746059 & 10.5906302539411 \tabularnewline
78 & 383 & 368.167188426949 & 14.8328115730511 \tabularnewline
79 & 334 & 335.211434335291 & -1.21143433529147 \tabularnewline
80 & 323 & 332.266994940328 & -9.26699494032829 \tabularnewline
81 & 330 & 334.233761039406 & -4.23376103940632 \tabularnewline
82 & 303 & 312.879468444041 & -9.8794684440407 \tabularnewline
83 & 275 & 290.078212639396 & -15.0782126393955 \tabularnewline
84 & 284 & 293.336608130076 & -9.33660813007629 \tabularnewline
85 & 301 & 299.134414442337 & 1.86558555766288 \tabularnewline
86 & 281 & 285.645488727339 & -4.64548872733883 \tabularnewline
87 & 284 & 279.606448339705 & 4.39355166029526 \tabularnewline
88 & 272 & 265.703218467672 & 6.29678153232817 \tabularnewline
89 & 297 & 282.207147963618 & 14.7928520363818 \tabularnewline
90 & 300 & 284.617494792343 & 15.3825052076568 \tabularnewline
91 & 240 & 250.715508243537 & -10.7155082435370 \tabularnewline
92 & 236 & 238.813634439328 & -2.8136344393275 \tabularnewline
93 & 247 & 241.618808190292 & 5.38119180970767 \tabularnewline
94 & 218 & 223.721025347817 & -5.72102534781669 \tabularnewline
95 & 192 & 202.998784772789 & -10.9987847727890 \tabularnewline
96 & 201 & 206.224278226510 & -5.22427822650963 \tabularnewline
97 & 223 & 214.343927679829 & 8.65607232017149 \tabularnewline
98 & 197 & 202.023412541456 & -5.02341254145594 \tabularnewline
99 & 195 & 199.753519815179 & -4.75351981517909 \tabularnewline
100 & 175 & 186.183052349202 & -11.1830523492015 \tabularnewline
101 & 197 & 192.635037300488 & 4.36496269951246 \tabularnewline
102 & 204 & 188.571020789394 & 15.4289792106057 \tabularnewline
103 & 142 & 153.54340498258 & -11.5434049825801 \tabularnewline
104 & 142 & 144.302293384114 & -2.30229338411394 \tabularnewline
105 & 151 & 145.167174341804 & 5.83282565819627 \tabularnewline
106 & 127 & 127.096249244895 & -0.0962492448953896 \tabularnewline
107 & 100 & 110.522622860485 & -10.5226228604849 \tabularnewline
108 & 114 & 109.133999509818 & 4.86600049018212 \tabularnewline
109 & 139 & 117.041430351892 & 21.9585696481085 \tabularnewline
110 & 112 & 107.269045840214 & 4.73095415978588 \tabularnewline
111 & 123 & 105.650453407798 & 17.3495465922016 \tabularnewline
112 & 108 & 99.995757024145 & 8.00424297585492 \tabularnewline
113 & 132 & 113.67307143234 & 18.3269285676599 \tabularnewline
114 & 140 & 120.631786633176 & 19.3682133668242 \tabularnewline
115 & 76 & 90.8084882621225 & -14.8084882621225 \tabularnewline
116 & 71 & 86.612711818103 & -15.6127118181030 \tabularnewline
117 & 81 & 84.7881741440841 & -3.78817414408411 \tabularnewline
118 & 57 & 68.9266573814876 & -11.9266573814876 \tabularnewline
119 & 38 & 50.9446403466986 & -12.9446403466986 \tabularnewline
120 & 46 & 49.5255992797587 & -3.52559927975867 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78971&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]555[/C][C]556.096125968013[/C][C]-1.09612596801264[/C][/ROW]
[ROW][C]14[/C][C]549[/C][C]550.206838318706[/C][C]-1.20683831870599[/C][/ROW]
[ROW][C]15[/C][C]555[/C][C]555.909186031654[/C][C]-0.909186031654144[/C][/ROW]
[ROW][C]16[/C][C]550[/C][C]550.436065507093[/C][C]-0.436065507092508[/C][/ROW]
[ROW][C]17[/C][C]566[/C][C]566.440247225086[/C][C]-0.440247225086296[/C][/ROW]
[ROW][C]18[/C][C]573[/C][C]573.766014542637[/C][C]-0.766014542637436[/C][/ROW]
[ROW][C]19[/C][C]543[/C][C]550.225015114608[/C][C]-7.22501511460837[/C][/ROW]
[ROW][C]20[/C][C]535[/C][C]537.330053349687[/C][C]-2.33005334968720[/C][/ROW]
[ROW][C]21[/C][C]542[/C][C]536.604728002003[/C][C]5.3952719979975[/C][/ROW]
[ROW][C]22[/C][C]541[/C][C]537.418402585507[/C][C]3.58159741449333[/C][/ROW]
[ROW][C]23[/C][C]535[/C][C]539.109847151401[/C][C]-4.10984715140148[/C][/ROW]
[ROW][C]24[/C][C]536[/C][C]539.004461470953[/C][C]-3.00446147095295[/C][/ROW]
[ROW][C]25[/C][C]548[/C][C]541.565706931639[/C][C]6.43429306836106[/C][/ROW]
[ROW][C]26[/C][C]546[/C][C]537.815268937733[/C][C]8.18473106226702[/C][/ROW]
[ROW][C]27[/C][C]548[/C][C]546.775346740264[/C][C]1.22465325973565[/C][/ROW]
[ROW][C]28[/C][C]548[/C][C]542.682489447484[/C][C]5.31751055251561[/C][/ROW]
[ROW][C]29[/C][C]561[/C][C]560.942550464539[/C][C]0.0574495354612736[/C][/ROW]
[ROW][C]30[/C][C]563[/C][C]568.79555489801[/C][C]-5.79555489801044[/C][/ROW]
[ROW][C]31[/C][C]527[/C][C]539.90321780154[/C][C]-12.9032178015398[/C][/ROW]
[ROW][C]32[/C][C]527[/C][C]528.78717895982[/C][C]-1.78717895982038[/C][/ROW]
[ROW][C]33[/C][C]541[/C][C]533.586477691573[/C][C]7.41352230842665[/C][/ROW]
[ROW][C]34[/C][C]534[/C][C]534.030031809365[/C][C]-0.0300318093646865[/C][/ROW]
[ROW][C]35[/C][C]522[/C][C]529.406827228539[/C][C]-7.40682722853853[/C][/ROW]
[ROW][C]36[/C][C]527[/C][C]528.875073865166[/C][C]-1.8750738651662[/C][/ROW]
[ROW][C]37[/C][C]539[/C][C]538.046291920791[/C][C]0.953708079208923[/C][/ROW]
[ROW][C]38[/C][C]533[/C][C]533.498495593853[/C][C]-0.498495593853477[/C][/ROW]
[ROW][C]39[/C][C]532[/C][C]534.147861080172[/C][C]-2.14786108017165[/C][/ROW]
[ROW][C]40[/C][C]519[/C][C]530.908081947645[/C][C]-11.9080819476446[/C][/ROW]
[ROW][C]41[/C][C]538[/C][C]537.841859469121[/C][C]0.158140530879336[/C][/ROW]
[ROW][C]42[/C][C]542[/C][C]539.695301986883[/C][C]2.30469801311654[/C][/ROW]
[ROW][C]43[/C][C]503[/C][C]508.300312948131[/C][C]-5.30031294813119[/C][/ROW]
[ROW][C]44[/C][C]502[/C][C]506.150266856587[/C][C]-4.15026685658694[/C][/ROW]
[ROW][C]45[/C][C]522[/C][C]514.84127872573[/C][C]7.15872127427008[/C][/ROW]
[ROW][C]46[/C][C]511[/C][C]509.229119722782[/C][C]1.77088027721834[/C][/ROW]
[ROW][C]47[/C][C]492[/C][C]499.454474038915[/C][C]-7.45447403891473[/C][/ROW]
[ROW][C]48[/C][C]500[/C][C]501.341235430462[/C][C]-1.34123543046184[/C][/ROW]
[ROW][C]49[/C][C]509[/C][C]510.936593504713[/C][C]-1.9365935047133[/C][/ROW]
[ROW][C]50[/C][C]511[/C][C]503.555692694639[/C][C]7.44430730536124[/C][/ROW]
[ROW][C]51[/C][C]505[/C][C]504.722457199759[/C][C]0.277542800241463[/C][/ROW]
[ROW][C]52[/C][C]493[/C][C]495.230095705913[/C][C]-2.23009570591250[/C][/ROW]
[ROW][C]53[/C][C]518[/C][C]512.305508189327[/C][C]5.69449181067341[/C][/ROW]
[ROW][C]54[/C][C]518[/C][C]517.213528265474[/C][C]0.786471734525662[/C][/ROW]
[ROW][C]55[/C][C]474[/C][C]481.725044855555[/C][C]-7.72504485555481[/C][/ROW]
[ROW][C]56[/C][C]471[/C][C]479.376457379085[/C][C]-8.37645737908474[/C][/ROW]
[ROW][C]57[/C][C]483[/C][C]493.150719195499[/C][C]-10.150719195499[/C][/ROW]
[ROW][C]58[/C][C]461[/C][C]477.835306271544[/C][C]-16.8353062715440[/C][/ROW]
[ROW][C]59[/C][C]439[/C][C]454.961426817135[/C][C]-15.9614268171351[/C][/ROW]
[ROW][C]60[/C][C]446[/C][C]454.966726298304[/C][C]-8.96672629830408[/C][/ROW]
[ROW][C]61[/C][C]461[/C][C]457.664975748268[/C][C]3.33502425173208[/C][/ROW]
[ROW][C]62[/C][C]449[/C][C]455.441866952845[/C][C]-6.44186695284452[/C][/ROW]
[ROW][C]63[/C][C]441[/C][C]444.42357547944[/C][C]-3.42357547943982[/C][/ROW]
[ROW][C]64[/C][C]424[/C][C]429.696144133860[/C][C]-5.69614413385955[/C][/ROW]
[ROW][C]65[/C][C]447[/C][C]443.917337841272[/C][C]3.0826621587276[/C][/ROW]
[ROW][C]66[/C][C]448[/C][C]440.406489689445[/C][C]7.59351031055508[/C][/ROW]
[ROW][C]67[/C][C]404[/C][C]403.588119112204[/C][C]0.411880887795746[/C][/ROW]
[ROW][C]68[/C][C]403[/C][C]400.068896822909[/C][C]2.93110317709068[/C][/ROW]
[ROW][C]69[/C][C]411[/C][C]410.958052253138[/C][C]0.0419477468622063[/C][/ROW]
[ROW][C]70[/C][C]386[/C][C]394.209388588765[/C][C]-8.20938858876485[/C][/ROW]
[ROW][C]71[/C][C]359[/C][C]375.020366169593[/C][C]-16.0203661695929[/C][/ROW]
[ROW][C]72[/C][C]370[/C][C]375.931993643433[/C][C]-5.9319936434328[/C][/ROW]
[ROW][C]73[/C][C]385[/C][C]383.427437352347[/C][C]1.57256264765283[/C][/ROW]
[ROW][C]74[/C][C]369[/C][C]373.170317363881[/C][C]-4.17031736388128[/C][/ROW]
[ROW][C]75[/C][C]368[/C][C]363.747136920517[/C][C]4.25286307948346[/C][/ROW]
[ROW][C]76[/C][C]352[/C][C]350.484011589317[/C][C]1.51598841068346[/C][/ROW]
[ROW][C]77[/C][C]378[/C][C]367.409369746059[/C][C]10.5906302539411[/C][/ROW]
[ROW][C]78[/C][C]383[/C][C]368.167188426949[/C][C]14.8328115730511[/C][/ROW]
[ROW][C]79[/C][C]334[/C][C]335.211434335291[/C][C]-1.21143433529147[/C][/ROW]
[ROW][C]80[/C][C]323[/C][C]332.266994940328[/C][C]-9.26699494032829[/C][/ROW]
[ROW][C]81[/C][C]330[/C][C]334.233761039406[/C][C]-4.23376103940632[/C][/ROW]
[ROW][C]82[/C][C]303[/C][C]312.879468444041[/C][C]-9.8794684440407[/C][/ROW]
[ROW][C]83[/C][C]275[/C][C]290.078212639396[/C][C]-15.0782126393955[/C][/ROW]
[ROW][C]84[/C][C]284[/C][C]293.336608130076[/C][C]-9.33660813007629[/C][/ROW]
[ROW][C]85[/C][C]301[/C][C]299.134414442337[/C][C]1.86558555766288[/C][/ROW]
[ROW][C]86[/C][C]281[/C][C]285.645488727339[/C][C]-4.64548872733883[/C][/ROW]
[ROW][C]87[/C][C]284[/C][C]279.606448339705[/C][C]4.39355166029526[/C][/ROW]
[ROW][C]88[/C][C]272[/C][C]265.703218467672[/C][C]6.29678153232817[/C][/ROW]
[ROW][C]89[/C][C]297[/C][C]282.207147963618[/C][C]14.7928520363818[/C][/ROW]
[ROW][C]90[/C][C]300[/C][C]284.617494792343[/C][C]15.3825052076568[/C][/ROW]
[ROW][C]91[/C][C]240[/C][C]250.715508243537[/C][C]-10.7155082435370[/C][/ROW]
[ROW][C]92[/C][C]236[/C][C]238.813634439328[/C][C]-2.8136344393275[/C][/ROW]
[ROW][C]93[/C][C]247[/C][C]241.618808190292[/C][C]5.38119180970767[/C][/ROW]
[ROW][C]94[/C][C]218[/C][C]223.721025347817[/C][C]-5.72102534781669[/C][/ROW]
[ROW][C]95[/C][C]192[/C][C]202.998784772789[/C][C]-10.9987847727890[/C][/ROW]
[ROW][C]96[/C][C]201[/C][C]206.224278226510[/C][C]-5.22427822650963[/C][/ROW]
[ROW][C]97[/C][C]223[/C][C]214.343927679829[/C][C]8.65607232017149[/C][/ROW]
[ROW][C]98[/C][C]197[/C][C]202.023412541456[/C][C]-5.02341254145594[/C][/ROW]
[ROW][C]99[/C][C]195[/C][C]199.753519815179[/C][C]-4.75351981517909[/C][/ROW]
[ROW][C]100[/C][C]175[/C][C]186.183052349202[/C][C]-11.1830523492015[/C][/ROW]
[ROW][C]101[/C][C]197[/C][C]192.635037300488[/C][C]4.36496269951246[/C][/ROW]
[ROW][C]102[/C][C]204[/C][C]188.571020789394[/C][C]15.4289792106057[/C][/ROW]
[ROW][C]103[/C][C]142[/C][C]153.54340498258[/C][C]-11.5434049825801[/C][/ROW]
[ROW][C]104[/C][C]142[/C][C]144.302293384114[/C][C]-2.30229338411394[/C][/ROW]
[ROW][C]105[/C][C]151[/C][C]145.167174341804[/C][C]5.83282565819627[/C][/ROW]
[ROW][C]106[/C][C]127[/C][C]127.096249244895[/C][C]-0.0962492448953896[/C][/ROW]
[ROW][C]107[/C][C]100[/C][C]110.522622860485[/C][C]-10.5226228604849[/C][/ROW]
[ROW][C]108[/C][C]114[/C][C]109.133999509818[/C][C]4.86600049018212[/C][/ROW]
[ROW][C]109[/C][C]139[/C][C]117.041430351892[/C][C]21.9585696481085[/C][/ROW]
[ROW][C]110[/C][C]112[/C][C]107.269045840214[/C][C]4.73095415978588[/C][/ROW]
[ROW][C]111[/C][C]123[/C][C]105.650453407798[/C][C]17.3495465922016[/C][/ROW]
[ROW][C]112[/C][C]108[/C][C]99.995757024145[/C][C]8.00424297585492[/C][/ROW]
[ROW][C]113[/C][C]132[/C][C]113.67307143234[/C][C]18.3269285676599[/C][/ROW]
[ROW][C]114[/C][C]140[/C][C]120.631786633176[/C][C]19.3682133668242[/C][/ROW]
[ROW][C]115[/C][C]76[/C][C]90.8084882621225[/C][C]-14.8084882621225[/C][/ROW]
[ROW][C]116[/C][C]71[/C][C]86.612711818103[/C][C]-15.6127118181030[/C][/ROW]
[ROW][C]117[/C][C]81[/C][C]84.7881741440841[/C][C]-3.78817414408411[/C][/ROW]
[ROW][C]118[/C][C]57[/C][C]68.9266573814876[/C][C]-11.9266573814876[/C][/ROW]
[ROW][C]119[/C][C]38[/C][C]50.9446403466986[/C][C]-12.9446403466986[/C][/ROW]
[ROW][C]120[/C][C]46[/C][C]49.5255992797587[/C][C]-3.52559927975867[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78971&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78971&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
13555556.096125968013-1.09612596801264
14549550.206838318706-1.20683831870599
15555555.909186031654-0.909186031654144
16550550.436065507093-0.436065507092508
17566566.440247225086-0.440247225086296
18573573.766014542637-0.766014542637436
19543550.225015114608-7.22501511460837
20535537.330053349687-2.33005334968720
21542536.6047280020035.3952719979975
22541537.4184025855073.58159741449333
23535539.109847151401-4.10984715140148
24536539.004461470953-3.00446147095295
25548541.5657069316396.43429306836106
26546537.8152689377338.18473106226702
27548546.7753467402641.22465325973565
28548542.6824894474845.31751055251561
29561560.9425504645390.0574495354612736
30563568.79555489801-5.79555489801044
31527539.90321780154-12.9032178015398
32527528.78717895982-1.78717895982038
33541533.5864776915737.41352230842665
34534534.030031809365-0.0300318093646865
35522529.406827228539-7.40682722853853
36527528.875073865166-1.8750738651662
37539538.0462919207910.953708079208923
38533533.498495593853-0.498495593853477
39532534.147861080172-2.14786108017165
40519530.908081947645-11.9080819476446
41538537.8418594691210.158140530879336
42542539.6953019868832.30469801311654
43503508.300312948131-5.30031294813119
44502506.150266856587-4.15026685658694
45522514.841278725737.15872127427008
46511509.2291197227821.77088027721834
47492499.454474038915-7.45447403891473
48500501.341235430462-1.34123543046184
49509510.936593504713-1.9365935047133
50511503.5556926946397.44430730536124
51505504.7224571997590.277542800241463
52493495.230095705913-2.23009570591250
53518512.3055081893275.69449181067341
54518517.2135282654740.786471734525662
55474481.725044855555-7.72504485555481
56471479.376457379085-8.37645737908474
57483493.150719195499-10.150719195499
58461477.835306271544-16.8353062715440
59439454.961426817135-15.9614268171351
60446454.966726298304-8.96672629830408
61461457.6649757482683.33502425173208
62449455.441866952845-6.44186695284452
63441444.42357547944-3.42357547943982
64424429.696144133860-5.69614413385955
65447443.9173378412723.0826621587276
66448440.4064896894457.59351031055508
67404403.5881191122040.411880887795746
68403400.0688968229092.93110317709068
69411410.9580522531380.0419477468622063
70386394.209388588765-8.20938858876485
71359375.020366169593-16.0203661695929
72370375.931993643433-5.9319936434328
73385383.4274373523471.57256264765283
74369373.170317363881-4.17031736388128
75368363.7471369205174.25286307948346
76352350.4840115893171.51598841068346
77378367.40936974605910.5906302539411
78383368.16718842694914.8328115730511
79334335.211434335291-1.21143433529147
80323332.266994940328-9.26699494032829
81330334.233761039406-4.23376103940632
82303312.879468444041-9.8794684440407
83275290.078212639396-15.0782126393955
84284293.336608130076-9.33660813007629
85301299.1344144423371.86558555766288
86281285.645488727339-4.64548872733883
87284279.6064483397054.39355166029526
88272265.7032184676726.29678153232817
89297282.20714796361814.7928520363818
90300284.61749479234315.3825052076568
91240250.715508243537-10.7155082435370
92236238.813634439328-2.8136344393275
93247241.6188081902925.38119180970767
94218223.721025347817-5.72102534781669
95192202.998784772789-10.9987847727890
96201206.224278226510-5.22427822650963
97223214.3439276798298.65607232017149
98197202.023412541456-5.02341254145594
99195199.753519815179-4.75351981517909
100175186.183052349202-11.1830523492015
101197192.6350373004884.36496269951246
102204188.57102078939415.4289792106057
103142153.54340498258-11.5434049825801
104142144.302293384114-2.30229338411394
105151145.1671743418045.83282565819627
106127127.096249244895-0.0962492448953896
107100110.522622860485-10.5226228604849
108114109.1339995098184.86600049018212
109139117.04143035189221.9585696481085
110112107.2690458402144.73095415978588
111123105.65045340779817.3495465922016
11210899.9957570241458.00424297585492
113132113.6730714323418.3269285676599
114140120.63178663317619.3682133668242
1157690.8084882621225-14.8084882621225
1167186.612711818103-15.6127118181030
1178184.7881741440841-3.78817414408411
1185768.9266573814876-11.9266573814876
1193850.9446403466986-12.9446403466986
1204649.5255992797587-3.52559927975867







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12151.022895070708634.930370425497867.1154197159195
12235.683022751407818.850967149054752.5150783537609
12331.380663373630712.938361366365349.8229653808961
12420.87741969725471.5937341839944640.161105210515
12516.3552363945071-6.5336914196687539.244164208683
1267.4764579354967-18.297697872339133.2506137433325
127-1.39573003629813-22.510980873607419.7195208010111
128-7.5376989378109-30.784025796257715.7086279206359
129-16.8539920080947-45.634801567326811.9268175511373
130-19.5597083221400-46.35584889814347.23643225386336
131-20.4147863808383-45.43067590178074.60110314010403
132-35.6448778254921-66.1727852380443-5.11697041293999

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 51.0228950707086 & 34.9303704254978 & 67.1154197159195 \tabularnewline
122 & 35.6830227514078 & 18.8509671490547 & 52.5150783537609 \tabularnewline
123 & 31.3806633736307 & 12.9383613663653 & 49.8229653808961 \tabularnewline
124 & 20.8774196972547 & 1.59373418399446 & 40.161105210515 \tabularnewline
125 & 16.3552363945071 & -6.53369141966875 & 39.244164208683 \tabularnewline
126 & 7.4764579354967 & -18.2976978723391 & 33.2506137433325 \tabularnewline
127 & -1.39573003629813 & -22.5109808736074 & 19.7195208010111 \tabularnewline
128 & -7.5376989378109 & -30.7840257962577 & 15.7086279206359 \tabularnewline
129 & -16.8539920080947 & -45.6348015673268 & 11.9268175511373 \tabularnewline
130 & -19.5597083221400 & -46.3558488981434 & 7.23643225386336 \tabularnewline
131 & -20.4147863808383 & -45.4306759017807 & 4.60110314010403 \tabularnewline
132 & -35.6448778254921 & -66.1727852380443 & -5.11697041293999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78971&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]51.0228950707086[/C][C]34.9303704254978[/C][C]67.1154197159195[/C][/ROW]
[ROW][C]122[/C][C]35.6830227514078[/C][C]18.8509671490547[/C][C]52.5150783537609[/C][/ROW]
[ROW][C]123[/C][C]31.3806633736307[/C][C]12.9383613663653[/C][C]49.8229653808961[/C][/ROW]
[ROW][C]124[/C][C]20.8774196972547[/C][C]1.59373418399446[/C][C]40.161105210515[/C][/ROW]
[ROW][C]125[/C][C]16.3552363945071[/C][C]-6.53369141966875[/C][C]39.244164208683[/C][/ROW]
[ROW][C]126[/C][C]7.4764579354967[/C][C]-18.2976978723391[/C][C]33.2506137433325[/C][/ROW]
[ROW][C]127[/C][C]-1.39573003629813[/C][C]-22.5109808736074[/C][C]19.7195208010111[/C][/ROW]
[ROW][C]128[/C][C]-7.5376989378109[/C][C]-30.7840257962577[/C][C]15.7086279206359[/C][/ROW]
[ROW][C]129[/C][C]-16.8539920080947[/C][C]-45.6348015673268[/C][C]11.9268175511373[/C][/ROW]
[ROW][C]130[/C][C]-19.5597083221400[/C][C]-46.3558488981434[/C][C]7.23643225386336[/C][/ROW]
[ROW][C]131[/C][C]-20.4147863808383[/C][C]-45.4306759017807[/C][C]4.60110314010403[/C][/ROW]
[ROW][C]132[/C][C]-35.6448778254921[/C][C]-66.1727852380443[/C][C]-5.11697041293999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78971&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78971&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
12151.022895070708634.930370425497867.1154197159195
12235.683022751407818.850967149054752.5150783537609
12331.380663373630712.938361366365349.8229653808961
12420.87741969725471.5937341839944640.161105210515
12516.3552363945071-6.5336914196687539.244164208683
1267.4764579354967-18.297697872339133.2506137433325
127-1.39573003629813-22.510980873607419.7195208010111
128-7.5376989378109-30.784025796257715.7086279206359
129-16.8539920080947-45.634801567326811.9268175511373
130-19.5597083221400-46.35584889814347.23643225386336
131-20.4147863808383-45.43067590178074.60110314010403
132-35.6448778254921-66.1727852380443-5.11697041293999



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')