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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 May 2011 13:56:00 +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/2011/May/29/t1306677170mmvscje9jnycfb3.htm/, Retrieved Tue, 07 May 2024 17:41:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122555, Retrieved Tue, 07 May 2024 17:41:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2011-05-29 13:56:00] [aa971e749556000e4c6ae2b60b566045] [Current]
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Dataseries X:
476
475
470
461
455
456
517
525
523
519
509
512
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
577
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556




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=122555&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=122555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122555&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
alpha0.896019100477419
beta0.149965314457529
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.896019100477419 \tabularnewline
beta & 0.149965314457529 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122555&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]0.896019100477419[/C][/ROW]
[ROW][C]beta[/C][C]0.149965314457529[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122555&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
alpha0.896019100477419
beta0.149965314457529
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13519495.15261712648723.8473828735126
14517517.285341877365-0.285341877364772
15510512.543885898163-2.54388589816313
16509511.77398259048-2.77398259047987
17501504.039839483569-3.03983948356949
18507509.798531759515-2.79853175951524
19569568.259671133850.74032886614998
20580579.6272287292630.372771270736848
21578579.810609693414-1.81060969341377
22565575.267047567444-10.2670475674438
23547555.059916434488-8.05991643448772
24555549.8074036399145.19259636008599
25562563.870693221883-1.87069322188279
26561556.0625142409954.93748575900509
27555551.9038921140553.09610788594466
28544553.618642200399-9.61864220039945
29537535.9692387993131.03076120068749
30543543.183176255541-0.183176255541412
31594606.001986407741-12.0019864077411
32611602.0892780513188.91072194868218
33613606.5044698514346.49553014856622
34611606.228267273014.77173272698951
35594598.804345495192-4.80434549519202
36595598.594921159887-3.59492115988689
37591603.94776852926-12.9477685292593
38589584.5231107928414.47688920715916
39584577.1981862077346.80181379226588
40573579.132619056229-6.13261905622869
41567564.1850691148772.81493088512309
42569572.34002679714-3.34002679713979
43621632.664381004718-11.6643810047181
44629630.341379251068-1.34137925106791
45628622.5474249390595.45257506094106
46612618.258537483585-6.25853748358486
47595595.884560743539-0.884560743539168
48597595.8146358103821.18536418961776
49593601.58976680362-8.58976680362014
50590585.5771878865044.42281211349575
51580576.2052941087983.7947058912016
52574571.5710389704952.42896102950533
53573563.7988116031779.20118839682266
54573576.500238726862-3.50023872686211
55620635.617675603752-15.6176756037519
56626629.6454873794-3.64548737939992
57620619.033258403120.966741596879956
58588607.604795019858-19.6047950198581
59566570.691464189829-4.69146418982916
60577563.1431821525913.8568178474098
61561576.565347258292-15.5653472582917
62549552.509894888093-3.50989488809262
63532532.45165269515-0.451652695150301
64526519.655930344026.34406965597975
65511512.607365407336-1.60736540733615
66499508.389266012661-9.38926601266144
67555546.1179856665768.88201433342363
68565558.2744713187326.72552868126752
69542555.404035729895-13.4040357298946
70527526.1488369563530.85116304364658
71510508.951774781211.04822521878958
72514507.2966562130746.7033437869265
73517509.34597718477.6540228153002
74508508.962377934173-0.962377934172878
75493493.950882115909-0.950882115908826
76490483.3912287904086.60877120959174
77469477.913011507385-8.91301150738468
78478466.79064670977611.2093532902241
79528526.077374270031.92262572996981
80534534.053007923467-0.0530079234665664
81518525.160939996395-7.1609399963952
82506505.9824128376250.0175871623750368
83502490.95133898467311.0486610153267
84516502.52555943169313.4744405683071
85528515.37920973847712.6207902615226
86533523.7120648858639.2879351141371
87536523.84772346449412.1522765355063
88537533.4612658466233.53873415337728
89524530.12959350431-6.12959350430958
90536531.811868849584.18813115042008
91587597.663629278294-10.6636292782937
92597601.212283981931-4.21228398193148
93581592.438111859684-11.4381118596835
94564573.873529788956-9.87352978895626
95558553.2343028233144.76569717668644
96575562.35024867671412.6497513232858
97580576.8472504050733.1527495949274
98575576.989648381008-1.98964838100778
99563566.087652129082-3.08765212908213
100552558.459977641041-6.45997764104072
101537541.206802761931-4.20680276193082
102545542.4363518804732.56364811952699
103601602.243509146296-1.24350914629565
104604612.4278443106-8.42784431060045
105586595.76513711945-9.76513711945017
106564575.800839572587-11.8008395725869
107549551.792750259015-2.79275025901529
108551550.6826099404560.317390059544437
109556547.3505191396238.64948086037668

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 519 & 495.152617126487 & 23.8473828735126 \tabularnewline
14 & 517 & 517.285341877365 & -0.285341877364772 \tabularnewline
15 & 510 & 512.543885898163 & -2.54388589816313 \tabularnewline
16 & 509 & 511.77398259048 & -2.77398259047987 \tabularnewline
17 & 501 & 504.039839483569 & -3.03983948356949 \tabularnewline
18 & 507 & 509.798531759515 & -2.79853175951524 \tabularnewline
19 & 569 & 568.25967113385 & 0.74032886614998 \tabularnewline
20 & 580 & 579.627228729263 & 0.372771270736848 \tabularnewline
21 & 578 & 579.810609693414 & -1.81060969341377 \tabularnewline
22 & 565 & 575.267047567444 & -10.2670475674438 \tabularnewline
23 & 547 & 555.059916434488 & -8.05991643448772 \tabularnewline
24 & 555 & 549.807403639914 & 5.19259636008599 \tabularnewline
25 & 562 & 563.870693221883 & -1.87069322188279 \tabularnewline
26 & 561 & 556.062514240995 & 4.93748575900509 \tabularnewline
27 & 555 & 551.903892114055 & 3.09610788594466 \tabularnewline
28 & 544 & 553.618642200399 & -9.61864220039945 \tabularnewline
29 & 537 & 535.969238799313 & 1.03076120068749 \tabularnewline
30 & 543 & 543.183176255541 & -0.183176255541412 \tabularnewline
31 & 594 & 606.001986407741 & -12.0019864077411 \tabularnewline
32 & 611 & 602.089278051318 & 8.91072194868218 \tabularnewline
33 & 613 & 606.504469851434 & 6.49553014856622 \tabularnewline
34 & 611 & 606.22826727301 & 4.77173272698951 \tabularnewline
35 & 594 & 598.804345495192 & -4.80434549519202 \tabularnewline
36 & 595 & 598.594921159887 & -3.59492115988689 \tabularnewline
37 & 591 & 603.94776852926 & -12.9477685292593 \tabularnewline
38 & 589 & 584.523110792841 & 4.47688920715916 \tabularnewline
39 & 584 & 577.198186207734 & 6.80181379226588 \tabularnewline
40 & 573 & 579.132619056229 & -6.13261905622869 \tabularnewline
41 & 567 & 564.185069114877 & 2.81493088512309 \tabularnewline
42 & 569 & 572.34002679714 & -3.34002679713979 \tabularnewline
43 & 621 & 632.664381004718 & -11.6643810047181 \tabularnewline
44 & 629 & 630.341379251068 & -1.34137925106791 \tabularnewline
45 & 628 & 622.547424939059 & 5.45257506094106 \tabularnewline
46 & 612 & 618.258537483585 & -6.25853748358486 \tabularnewline
47 & 595 & 595.884560743539 & -0.884560743539168 \tabularnewline
48 & 597 & 595.814635810382 & 1.18536418961776 \tabularnewline
49 & 593 & 601.58976680362 & -8.58976680362014 \tabularnewline
50 & 590 & 585.577187886504 & 4.42281211349575 \tabularnewline
51 & 580 & 576.205294108798 & 3.7947058912016 \tabularnewline
52 & 574 & 571.571038970495 & 2.42896102950533 \tabularnewline
53 & 573 & 563.798811603177 & 9.20118839682266 \tabularnewline
54 & 573 & 576.500238726862 & -3.50023872686211 \tabularnewline
55 & 620 & 635.617675603752 & -15.6176756037519 \tabularnewline
56 & 626 & 629.6454873794 & -3.64548737939992 \tabularnewline
57 & 620 & 619.03325840312 & 0.966741596879956 \tabularnewline
58 & 588 & 607.604795019858 & -19.6047950198581 \tabularnewline
59 & 566 & 570.691464189829 & -4.69146418982916 \tabularnewline
60 & 577 & 563.14318215259 & 13.8568178474098 \tabularnewline
61 & 561 & 576.565347258292 & -15.5653472582917 \tabularnewline
62 & 549 & 552.509894888093 & -3.50989488809262 \tabularnewline
63 & 532 & 532.45165269515 & -0.451652695150301 \tabularnewline
64 & 526 & 519.65593034402 & 6.34406965597975 \tabularnewline
65 & 511 & 512.607365407336 & -1.60736540733615 \tabularnewline
66 & 499 & 508.389266012661 & -9.38926601266144 \tabularnewline
67 & 555 & 546.117985666576 & 8.88201433342363 \tabularnewline
68 & 565 & 558.274471318732 & 6.72552868126752 \tabularnewline
69 & 542 & 555.404035729895 & -13.4040357298946 \tabularnewline
70 & 527 & 526.148836956353 & 0.85116304364658 \tabularnewline
71 & 510 & 508.95177478121 & 1.04822521878958 \tabularnewline
72 & 514 & 507.296656213074 & 6.7033437869265 \tabularnewline
73 & 517 & 509.3459771847 & 7.6540228153002 \tabularnewline
74 & 508 & 508.962377934173 & -0.962377934172878 \tabularnewline
75 & 493 & 493.950882115909 & -0.950882115908826 \tabularnewline
76 & 490 & 483.391228790408 & 6.60877120959174 \tabularnewline
77 & 469 & 477.913011507385 & -8.91301150738468 \tabularnewline
78 & 478 & 466.790646709776 & 11.2093532902241 \tabularnewline
79 & 528 & 526.07737427003 & 1.92262572996981 \tabularnewline
80 & 534 & 534.053007923467 & -0.0530079234665664 \tabularnewline
81 & 518 & 525.160939996395 & -7.1609399963952 \tabularnewline
82 & 506 & 505.982412837625 & 0.0175871623750368 \tabularnewline
83 & 502 & 490.951338984673 & 11.0486610153267 \tabularnewline
84 & 516 & 502.525559431693 & 13.4744405683071 \tabularnewline
85 & 528 & 515.379209738477 & 12.6207902615226 \tabularnewline
86 & 533 & 523.712064885863 & 9.2879351141371 \tabularnewline
87 & 536 & 523.847723464494 & 12.1522765355063 \tabularnewline
88 & 537 & 533.461265846623 & 3.53873415337728 \tabularnewline
89 & 524 & 530.12959350431 & -6.12959350430958 \tabularnewline
90 & 536 & 531.81186884958 & 4.18813115042008 \tabularnewline
91 & 587 & 597.663629278294 & -10.6636292782937 \tabularnewline
92 & 597 & 601.212283981931 & -4.21228398193148 \tabularnewline
93 & 581 & 592.438111859684 & -11.4381118596835 \tabularnewline
94 & 564 & 573.873529788956 & -9.87352978895626 \tabularnewline
95 & 558 & 553.234302823314 & 4.76569717668644 \tabularnewline
96 & 575 & 562.350248676714 & 12.6497513232858 \tabularnewline
97 & 580 & 576.847250405073 & 3.1527495949274 \tabularnewline
98 & 575 & 576.989648381008 & -1.98964838100778 \tabularnewline
99 & 563 & 566.087652129082 & -3.08765212908213 \tabularnewline
100 & 552 & 558.459977641041 & -6.45997764104072 \tabularnewline
101 & 537 & 541.206802761931 & -4.20680276193082 \tabularnewline
102 & 545 & 542.436351880473 & 2.56364811952699 \tabularnewline
103 & 601 & 602.243509146296 & -1.24350914629565 \tabularnewline
104 & 604 & 612.4278443106 & -8.42784431060045 \tabularnewline
105 & 586 & 595.76513711945 & -9.76513711945017 \tabularnewline
106 & 564 & 575.800839572587 & -11.8008395725869 \tabularnewline
107 & 549 & 551.792750259015 & -2.79275025901529 \tabularnewline
108 & 551 & 550.682609940456 & 0.317390059544437 \tabularnewline
109 & 556 & 547.350519139623 & 8.64948086037668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122555&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]519[/C][C]495.152617126487[/C][C]23.8473828735126[/C][/ROW]
[ROW][C]14[/C][C]517[/C][C]517.285341877365[/C][C]-0.285341877364772[/C][/ROW]
[ROW][C]15[/C][C]510[/C][C]512.543885898163[/C][C]-2.54388589816313[/C][/ROW]
[ROW][C]16[/C][C]509[/C][C]511.77398259048[/C][C]-2.77398259047987[/C][/ROW]
[ROW][C]17[/C][C]501[/C][C]504.039839483569[/C][C]-3.03983948356949[/C][/ROW]
[ROW][C]18[/C][C]507[/C][C]509.798531759515[/C][C]-2.79853175951524[/C][/ROW]
[ROW][C]19[/C][C]569[/C][C]568.25967113385[/C][C]0.74032886614998[/C][/ROW]
[ROW][C]20[/C][C]580[/C][C]579.627228729263[/C][C]0.372771270736848[/C][/ROW]
[ROW][C]21[/C][C]578[/C][C]579.810609693414[/C][C]-1.81060969341377[/C][/ROW]
[ROW][C]22[/C][C]565[/C][C]575.267047567444[/C][C]-10.2670475674438[/C][/ROW]
[ROW][C]23[/C][C]547[/C][C]555.059916434488[/C][C]-8.05991643448772[/C][/ROW]
[ROW][C]24[/C][C]555[/C][C]549.807403639914[/C][C]5.19259636008599[/C][/ROW]
[ROW][C]25[/C][C]562[/C][C]563.870693221883[/C][C]-1.87069322188279[/C][/ROW]
[ROW][C]26[/C][C]561[/C][C]556.062514240995[/C][C]4.93748575900509[/C][/ROW]
[ROW][C]27[/C][C]555[/C][C]551.903892114055[/C][C]3.09610788594466[/C][/ROW]
[ROW][C]28[/C][C]544[/C][C]553.618642200399[/C][C]-9.61864220039945[/C][/ROW]
[ROW][C]29[/C][C]537[/C][C]535.969238799313[/C][C]1.03076120068749[/C][/ROW]
[ROW][C]30[/C][C]543[/C][C]543.183176255541[/C][C]-0.183176255541412[/C][/ROW]
[ROW][C]31[/C][C]594[/C][C]606.001986407741[/C][C]-12.0019864077411[/C][/ROW]
[ROW][C]32[/C][C]611[/C][C]602.089278051318[/C][C]8.91072194868218[/C][/ROW]
[ROW][C]33[/C][C]613[/C][C]606.504469851434[/C][C]6.49553014856622[/C][/ROW]
[ROW][C]34[/C][C]611[/C][C]606.22826727301[/C][C]4.77173272698951[/C][/ROW]
[ROW][C]35[/C][C]594[/C][C]598.804345495192[/C][C]-4.80434549519202[/C][/ROW]
[ROW][C]36[/C][C]595[/C][C]598.594921159887[/C][C]-3.59492115988689[/C][/ROW]
[ROW][C]37[/C][C]591[/C][C]603.94776852926[/C][C]-12.9477685292593[/C][/ROW]
[ROW][C]38[/C][C]589[/C][C]584.523110792841[/C][C]4.47688920715916[/C][/ROW]
[ROW][C]39[/C][C]584[/C][C]577.198186207734[/C][C]6.80181379226588[/C][/ROW]
[ROW][C]40[/C][C]573[/C][C]579.132619056229[/C][C]-6.13261905622869[/C][/ROW]
[ROW][C]41[/C][C]567[/C][C]564.185069114877[/C][C]2.81493088512309[/C][/ROW]
[ROW][C]42[/C][C]569[/C][C]572.34002679714[/C][C]-3.34002679713979[/C][/ROW]
[ROW][C]43[/C][C]621[/C][C]632.664381004718[/C][C]-11.6643810047181[/C][/ROW]
[ROW][C]44[/C][C]629[/C][C]630.341379251068[/C][C]-1.34137925106791[/C][/ROW]
[ROW][C]45[/C][C]628[/C][C]622.547424939059[/C][C]5.45257506094106[/C][/ROW]
[ROW][C]46[/C][C]612[/C][C]618.258537483585[/C][C]-6.25853748358486[/C][/ROW]
[ROW][C]47[/C][C]595[/C][C]595.884560743539[/C][C]-0.884560743539168[/C][/ROW]
[ROW][C]48[/C][C]597[/C][C]595.814635810382[/C][C]1.18536418961776[/C][/ROW]
[ROW][C]49[/C][C]593[/C][C]601.58976680362[/C][C]-8.58976680362014[/C][/ROW]
[ROW][C]50[/C][C]590[/C][C]585.577187886504[/C][C]4.42281211349575[/C][/ROW]
[ROW][C]51[/C][C]580[/C][C]576.205294108798[/C][C]3.7947058912016[/C][/ROW]
[ROW][C]52[/C][C]574[/C][C]571.571038970495[/C][C]2.42896102950533[/C][/ROW]
[ROW][C]53[/C][C]573[/C][C]563.798811603177[/C][C]9.20118839682266[/C][/ROW]
[ROW][C]54[/C][C]573[/C][C]576.500238726862[/C][C]-3.50023872686211[/C][/ROW]
[ROW][C]55[/C][C]620[/C][C]635.617675603752[/C][C]-15.6176756037519[/C][/ROW]
[ROW][C]56[/C][C]626[/C][C]629.6454873794[/C][C]-3.64548737939992[/C][/ROW]
[ROW][C]57[/C][C]620[/C][C]619.03325840312[/C][C]0.966741596879956[/C][/ROW]
[ROW][C]58[/C][C]588[/C][C]607.604795019858[/C][C]-19.6047950198581[/C][/ROW]
[ROW][C]59[/C][C]566[/C][C]570.691464189829[/C][C]-4.69146418982916[/C][/ROW]
[ROW][C]60[/C][C]577[/C][C]563.14318215259[/C][C]13.8568178474098[/C][/ROW]
[ROW][C]61[/C][C]561[/C][C]576.565347258292[/C][C]-15.5653472582917[/C][/ROW]
[ROW][C]62[/C][C]549[/C][C]552.509894888093[/C][C]-3.50989488809262[/C][/ROW]
[ROW][C]63[/C][C]532[/C][C]532.45165269515[/C][C]-0.451652695150301[/C][/ROW]
[ROW][C]64[/C][C]526[/C][C]519.65593034402[/C][C]6.34406965597975[/C][/ROW]
[ROW][C]65[/C][C]511[/C][C]512.607365407336[/C][C]-1.60736540733615[/C][/ROW]
[ROW][C]66[/C][C]499[/C][C]508.389266012661[/C][C]-9.38926601266144[/C][/ROW]
[ROW][C]67[/C][C]555[/C][C]546.117985666576[/C][C]8.88201433342363[/C][/ROW]
[ROW][C]68[/C][C]565[/C][C]558.274471318732[/C][C]6.72552868126752[/C][/ROW]
[ROW][C]69[/C][C]542[/C][C]555.404035729895[/C][C]-13.4040357298946[/C][/ROW]
[ROW][C]70[/C][C]527[/C][C]526.148836956353[/C][C]0.85116304364658[/C][/ROW]
[ROW][C]71[/C][C]510[/C][C]508.95177478121[/C][C]1.04822521878958[/C][/ROW]
[ROW][C]72[/C][C]514[/C][C]507.296656213074[/C][C]6.7033437869265[/C][/ROW]
[ROW][C]73[/C][C]517[/C][C]509.3459771847[/C][C]7.6540228153002[/C][/ROW]
[ROW][C]74[/C][C]508[/C][C]508.962377934173[/C][C]-0.962377934172878[/C][/ROW]
[ROW][C]75[/C][C]493[/C][C]493.950882115909[/C][C]-0.950882115908826[/C][/ROW]
[ROW][C]76[/C][C]490[/C][C]483.391228790408[/C][C]6.60877120959174[/C][/ROW]
[ROW][C]77[/C][C]469[/C][C]477.913011507385[/C][C]-8.91301150738468[/C][/ROW]
[ROW][C]78[/C][C]478[/C][C]466.790646709776[/C][C]11.2093532902241[/C][/ROW]
[ROW][C]79[/C][C]528[/C][C]526.07737427003[/C][C]1.92262572996981[/C][/ROW]
[ROW][C]80[/C][C]534[/C][C]534.053007923467[/C][C]-0.0530079234665664[/C][/ROW]
[ROW][C]81[/C][C]518[/C][C]525.160939996395[/C][C]-7.1609399963952[/C][/ROW]
[ROW][C]82[/C][C]506[/C][C]505.982412837625[/C][C]0.0175871623750368[/C][/ROW]
[ROW][C]83[/C][C]502[/C][C]490.951338984673[/C][C]11.0486610153267[/C][/ROW]
[ROW][C]84[/C][C]516[/C][C]502.525559431693[/C][C]13.4744405683071[/C][/ROW]
[ROW][C]85[/C][C]528[/C][C]515.379209738477[/C][C]12.6207902615226[/C][/ROW]
[ROW][C]86[/C][C]533[/C][C]523.712064885863[/C][C]9.2879351141371[/C][/ROW]
[ROW][C]87[/C][C]536[/C][C]523.847723464494[/C][C]12.1522765355063[/C][/ROW]
[ROW][C]88[/C][C]537[/C][C]533.461265846623[/C][C]3.53873415337728[/C][/ROW]
[ROW][C]89[/C][C]524[/C][C]530.12959350431[/C][C]-6.12959350430958[/C][/ROW]
[ROW][C]90[/C][C]536[/C][C]531.81186884958[/C][C]4.18813115042008[/C][/ROW]
[ROW][C]91[/C][C]587[/C][C]597.663629278294[/C][C]-10.6636292782937[/C][/ROW]
[ROW][C]92[/C][C]597[/C][C]601.212283981931[/C][C]-4.21228398193148[/C][/ROW]
[ROW][C]93[/C][C]581[/C][C]592.438111859684[/C][C]-11.4381118596835[/C][/ROW]
[ROW][C]94[/C][C]564[/C][C]573.873529788956[/C][C]-9.87352978895626[/C][/ROW]
[ROW][C]95[/C][C]558[/C][C]553.234302823314[/C][C]4.76569717668644[/C][/ROW]
[ROW][C]96[/C][C]575[/C][C]562.350248676714[/C][C]12.6497513232858[/C][/ROW]
[ROW][C]97[/C][C]580[/C][C]576.847250405073[/C][C]3.1527495949274[/C][/ROW]
[ROW][C]98[/C][C]575[/C][C]576.989648381008[/C][C]-1.98964838100778[/C][/ROW]
[ROW][C]99[/C][C]563[/C][C]566.087652129082[/C][C]-3.08765212908213[/C][/ROW]
[ROW][C]100[/C][C]552[/C][C]558.459977641041[/C][C]-6.45997764104072[/C][/ROW]
[ROW][C]101[/C][C]537[/C][C]541.206802761931[/C][C]-4.20680276193082[/C][/ROW]
[ROW][C]102[/C][C]545[/C][C]542.436351880473[/C][C]2.56364811952699[/C][/ROW]
[ROW][C]103[/C][C]601[/C][C]602.243509146296[/C][C]-1.24350914629565[/C][/ROW]
[ROW][C]104[/C][C]604[/C][C]612.4278443106[/C][C]-8.42784431060045[/C][/ROW]
[ROW][C]105[/C][C]586[/C][C]595.76513711945[/C][C]-9.76513711945017[/C][/ROW]
[ROW][C]106[/C][C]564[/C][C]575.800839572587[/C][C]-11.8008395725869[/C][/ROW]
[ROW][C]107[/C][C]549[/C][C]551.792750259015[/C][C]-2.79275025901529[/C][/ROW]
[ROW][C]108[/C][C]551[/C][C]550.682609940456[/C][C]0.317390059544437[/C][/ROW]
[ROW][C]109[/C][C]556[/C][C]547.350519139623[/C][C]8.64948086037668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122555&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122555&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
13519495.15261712648723.8473828735126
14517517.285341877365-0.285341877364772
15510512.543885898163-2.54388589816313
16509511.77398259048-2.77398259047987
17501504.039839483569-3.03983948356949
18507509.798531759515-2.79853175951524
19569568.259671133850.74032886614998
20580579.6272287292630.372771270736848
21578579.810609693414-1.81060969341377
22565575.267047567444-10.2670475674438
23547555.059916434488-8.05991643448772
24555549.8074036399145.19259636008599
25562563.870693221883-1.87069322188279
26561556.0625142409954.93748575900509
27555551.9038921140553.09610788594466
28544553.618642200399-9.61864220039945
29537535.9692387993131.03076120068749
30543543.183176255541-0.183176255541412
31594606.001986407741-12.0019864077411
32611602.0892780513188.91072194868218
33613606.5044698514346.49553014856622
34611606.228267273014.77173272698951
35594598.804345495192-4.80434549519202
36595598.594921159887-3.59492115988689
37591603.94776852926-12.9477685292593
38589584.5231107928414.47688920715916
39584577.1981862077346.80181379226588
40573579.132619056229-6.13261905622869
41567564.1850691148772.81493088512309
42569572.34002679714-3.34002679713979
43621632.664381004718-11.6643810047181
44629630.341379251068-1.34137925106791
45628622.5474249390595.45257506094106
46612618.258537483585-6.25853748358486
47595595.884560743539-0.884560743539168
48597595.8146358103821.18536418961776
49593601.58976680362-8.58976680362014
50590585.5771878865044.42281211349575
51580576.2052941087983.7947058912016
52574571.5710389704952.42896102950533
53573563.7988116031779.20118839682266
54573576.500238726862-3.50023872686211
55620635.617675603752-15.6176756037519
56626629.6454873794-3.64548737939992
57620619.033258403120.966741596879956
58588607.604795019858-19.6047950198581
59566570.691464189829-4.69146418982916
60577563.1431821525913.8568178474098
61561576.565347258292-15.5653472582917
62549552.509894888093-3.50989488809262
63532532.45165269515-0.451652695150301
64526519.655930344026.34406965597975
65511512.607365407336-1.60736540733615
66499508.389266012661-9.38926601266144
67555546.1179856665768.88201433342363
68565558.2744713187326.72552868126752
69542555.404035729895-13.4040357298946
70527526.1488369563530.85116304364658
71510508.951774781211.04822521878958
72514507.2966562130746.7033437869265
73517509.34597718477.6540228153002
74508508.962377934173-0.962377934172878
75493493.950882115909-0.950882115908826
76490483.3912287904086.60877120959174
77469477.913011507385-8.91301150738468
78478466.79064670977611.2093532902241
79528526.077374270031.92262572996981
80534534.053007923467-0.0530079234665664
81518525.160939996395-7.1609399963952
82506505.9824128376250.0175871623750368
83502490.95133898467311.0486610153267
84516502.52555943169313.4744405683071
85528515.37920973847712.6207902615226
86533523.7120648858639.2879351141371
87536523.84772346449412.1522765355063
88537533.4612658466233.53873415337728
89524530.12959350431-6.12959350430958
90536531.811868849584.18813115042008
91587597.663629278294-10.6636292782937
92597601.212283981931-4.21228398193148
93581592.438111859684-11.4381118596835
94564573.873529788956-9.87352978895626
95558553.2343028233144.76569717668644
96575562.35024867671412.6497513232858
97580576.8472504050733.1527495949274
98575576.989648381008-1.98964838100778
99563566.087652129082-3.08765212908213
100552558.459977641041-6.45997764104072
101537541.206802761931-4.20680276193082
102545542.4363518804732.56364811952699
103601602.243509146296-1.24350914629565
104604612.4278443106-8.42784431060045
105586595.76513711945-9.76513711945017
106564575.800839572587-11.8008395725869
107549551.792750259015-2.79275025901529
108551550.6826099404560.317390059544437
109556547.3505191396238.64948086037668







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
110547.139995750804532.051174650631562.228816850977
111533.845816089555512.421395963215555.270236215894
112524.853108568665497.47066666358552.23555047375
113511.02146025158478.087713288261543.955207214899
114513.811713301297474.370722208903553.252704393691
115564.409407826634514.420059079258614.398756574011
116571.17868902913513.591608022507628.765770035754
117560.379162514143496.73682117116624.021503857127
118548.654016850196479.086521267024618.221512433369
119537.255806517171461.765465835619612.746147198723
120540.084730482562456.593869518811623.575591446313
121538.488961909698448.073347236991628.904576582405

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
110 & 547.139995750804 & 532.051174650631 & 562.228816850977 \tabularnewline
111 & 533.845816089555 & 512.421395963215 & 555.270236215894 \tabularnewline
112 & 524.853108568665 & 497.47066666358 & 552.23555047375 \tabularnewline
113 & 511.02146025158 & 478.087713288261 & 543.955207214899 \tabularnewline
114 & 513.811713301297 & 474.370722208903 & 553.252704393691 \tabularnewline
115 & 564.409407826634 & 514.420059079258 & 614.398756574011 \tabularnewline
116 & 571.17868902913 & 513.591608022507 & 628.765770035754 \tabularnewline
117 & 560.379162514143 & 496.73682117116 & 624.021503857127 \tabularnewline
118 & 548.654016850196 & 479.086521267024 & 618.221512433369 \tabularnewline
119 & 537.255806517171 & 461.765465835619 & 612.746147198723 \tabularnewline
120 & 540.084730482562 & 456.593869518811 & 623.575591446313 \tabularnewline
121 & 538.488961909698 & 448.073347236991 & 628.904576582405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122555&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]110[/C][C]547.139995750804[/C][C]532.051174650631[/C][C]562.228816850977[/C][/ROW]
[ROW][C]111[/C][C]533.845816089555[/C][C]512.421395963215[/C][C]555.270236215894[/C][/ROW]
[ROW][C]112[/C][C]524.853108568665[/C][C]497.47066666358[/C][C]552.23555047375[/C][/ROW]
[ROW][C]113[/C][C]511.02146025158[/C][C]478.087713288261[/C][C]543.955207214899[/C][/ROW]
[ROW][C]114[/C][C]513.811713301297[/C][C]474.370722208903[/C][C]553.252704393691[/C][/ROW]
[ROW][C]115[/C][C]564.409407826634[/C][C]514.420059079258[/C][C]614.398756574011[/C][/ROW]
[ROW][C]116[/C][C]571.17868902913[/C][C]513.591608022507[/C][C]628.765770035754[/C][/ROW]
[ROW][C]117[/C][C]560.379162514143[/C][C]496.73682117116[/C][C]624.021503857127[/C][/ROW]
[ROW][C]118[/C][C]548.654016850196[/C][C]479.086521267024[/C][C]618.221512433369[/C][/ROW]
[ROW][C]119[/C][C]537.255806517171[/C][C]461.765465835619[/C][C]612.746147198723[/C][/ROW]
[ROW][C]120[/C][C]540.084730482562[/C][C]456.593869518811[/C][C]623.575591446313[/C][/ROW]
[ROW][C]121[/C][C]538.488961909698[/C][C]448.073347236991[/C][C]628.904576582405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122555&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122555&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
110547.139995750804532.051174650631562.228816850977
111533.845816089555512.421395963215555.270236215894
112524.853108568665497.47066666358552.23555047375
113511.02146025158478.087713288261543.955207214899
114513.811713301297474.370722208903553.252704393691
115564.409407826634514.420059079258614.398756574011
116571.17868902913513.591608022507628.765770035754
117560.379162514143496.73682117116624.021503857127
118548.654016850196479.086521267024618.221512433369
119537.255806517171461.765465835619612.746147198723
120540.084730482562456.593869518811623.575591446313
121538.488961909698448.073347236991628.904576582405



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')