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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 01 Dec 2011 14:00:51 -0500
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/Dec/01/t1322766402ytdymntkw91hkoy.htm/, Retrieved Fri, 26 Apr 2024 15:33:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149951, Retrieved Fri, 26 Apr 2024 15:33:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [web server] [2010-10-19 15:51:23] [b98453cac15ba1066b407e146608df68]
- RMPD  [Classical Decomposition] [Classical Decompo...] [2011-12-01 14:47:37] [15a5dd358825f04074b70fc847ec6454]
- RMPD      [Exponential Smoothing] [Exponential smoot...] [2011-12-01 19:00:51] [614dd89c388120cee0dd25886939832b] [Current]
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Dataseries X:
548
563
581
572
519
521
531
540
548
556
551
549
564
586
604
601
545
537
552
563
575
580
575
558
564
581
597
587
536
524
537
536
533
528
516
502
506
518
534
528
478
469
490
493
508
517
514
510
527
542
565
555
499
511
526
532
549
561
557
566
588
620
626
620
573
573
574
580
590
593
597
595
612
628
629
621
569
567
573
584
589
591
595
594
611
613
611
594
543
537
544
555
561
562
555
547
565
578
580
569
507
501
509
510
517
519
512
509
519




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149951&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149951&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149951&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.933720312558662
beta0.158629503540377
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.933720312558662 \tabularnewline
beta & 0.158629503540377 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149951&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]0.933720312558662[/C][/ROW]
[ROW][C]beta[/C][C]0.158629503540377[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149951&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149951&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
alpha0.933720312558662
beta0.158629503540377
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13564552.68830128205111.3116987179485
14586587.00889071552-1.00889071552047
15604605.426063089066-1.42606308906556
16601602.200824301645-1.20082430164484
17545546.133034745739-1.13303474573854
18537538.585721565729-1.58572156572882
19552554.464188755308-2.46418875530776
20563561.8240951822831.17590481771663
21575571.4653340867613.53466591323945
22580583.582535264474-3.58253526447356
23575575.398631810933-0.398631810933239
24558573.670226766136-15.6702267661356
25564573.319487618236-9.3194876182356
26581582.660193870031-1.66019387003109
27597595.445592442641.55440755736015
28587590.463673800954-3.46367380095364
29536527.3978108917828.60218910821777
30524525.462710569782-1.46271056978173
31537537.968271479589-0.968271479589475
32536543.758239571812-7.75823957181171
33533540.682567323272-7.68256732327245
34528535.661579983682-7.66157998368169
35516517.083143507878-1.08314350787782
36502506.80513835565-4.80513835565023
37506511.731305844929-5.73130584492895
38518520.172519443126-2.17251944312579
39534527.8592221388696.14077786113126
40528522.6730168280555.32698317194513
41478465.76284693960112.2371530603986
42469464.2410391414914.75896085850928
43490481.1965500934888.80344990651213
44493495.71575802763-2.71575802762999
45508498.1554609406179.8445390593829
46517512.8994097665554.10059023344525
47514510.8798579140823.12014208591802
48510510.042716027551-0.0427160275510232
49527525.8225196634821.1774803365181
50542548.442033217303-6.44203321730345
51565559.55237608675.44762391330005
52555560.421523054159-5.42152305415925
53499499.09773939255-0.097739392550011
54511488.90043076692422.0995692330761
55526528.221192945023-2.22119294502284
56532535.955962416838-3.95596241683825
57549542.1594442689326.84055573106752
58561557.3621593518083.63784064819242
59557558.421358229552-1.42135822955174
60566556.0372382191439.96276178085679
61588585.6253474177072.37465258229315
62620613.4200993737456.57990062625458
63626643.968513884895-17.9685138848948
64620625.276023372816-5.27602337281564
65573567.4853948954035.51460510459697
66573567.8753931791275.12460682087271
67574591.095775239499-17.0957752394993
68580583.985167183731-3.98516718373071
69590590.030946198752-0.0309461987523036
70593596.741525236056-3.74152523605596
71597587.6183388832819.38166111671853
72595594.7190496794830.280950320516922
73612611.9733864260580.026613573941745
74628634.715937085943-6.7159370859431
75629646.114863664084-17.1148636640841
76621624.079303965113-3.07930396511279
77569564.3989708508834.60102914911715
78567559.1187552506887.88124474931192
79573579.057266720709-6.05726672070853
80584580.3744410505333.62555894946672
81589592.167797126251-3.16779712625123
82591593.618085137415-2.6180851374146
83595584.49466372815410.5053362718456
84594590.2887997962733.71120020372666
85611609.4846658818281.51533411817161
86613632.14636643043-19.1463664304302
87611628.384366087942-17.3843660879422
88594604.122376556496-10.1223765564957
89543534.4265822745198.57341772548091
90537529.7129996137837.28700038621696
91544544.724917385117-0.724917385116555
92555549.0046978455365.99530215446396
93561560.2533742653290.746625734670829
94562563.667764697974-1.66776469797401
95555554.714941873340.285058126660374
96547547.415549716361-0.415549716361284
97565558.9010745553016.09892544469881
98578581.440448003952-3.44044800395227
99580591.753790552366-11.7537905523661
100569573.358105178358-4.35810517835762
101507511.265057036796-4.26505703679572
102501493.5584655758327.44153442416825
103509507.2863356185881.71366438141206
104510513.752363541969-3.75236354196898
105517513.5716646993733.42833530062683
106519517.7472986074531.25270139254746
107512510.500675161661.49932483833993
108509503.3183526408895.68164735911103
109519520.861541767797-1.86154176779678

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 564 & 552.688301282051 & 11.3116987179485 \tabularnewline
14 & 586 & 587.00889071552 & -1.00889071552047 \tabularnewline
15 & 604 & 605.426063089066 & -1.42606308906556 \tabularnewline
16 & 601 & 602.200824301645 & -1.20082430164484 \tabularnewline
17 & 545 & 546.133034745739 & -1.13303474573854 \tabularnewline
18 & 537 & 538.585721565729 & -1.58572156572882 \tabularnewline
19 & 552 & 554.464188755308 & -2.46418875530776 \tabularnewline
20 & 563 & 561.824095182283 & 1.17590481771663 \tabularnewline
21 & 575 & 571.465334086761 & 3.53466591323945 \tabularnewline
22 & 580 & 583.582535264474 & -3.58253526447356 \tabularnewline
23 & 575 & 575.398631810933 & -0.398631810933239 \tabularnewline
24 & 558 & 573.670226766136 & -15.6702267661356 \tabularnewline
25 & 564 & 573.319487618236 & -9.3194876182356 \tabularnewline
26 & 581 & 582.660193870031 & -1.66019387003109 \tabularnewline
27 & 597 & 595.44559244264 & 1.55440755736015 \tabularnewline
28 & 587 & 590.463673800954 & -3.46367380095364 \tabularnewline
29 & 536 & 527.397810891782 & 8.60218910821777 \tabularnewline
30 & 524 & 525.462710569782 & -1.46271056978173 \tabularnewline
31 & 537 & 537.968271479589 & -0.968271479589475 \tabularnewline
32 & 536 & 543.758239571812 & -7.75823957181171 \tabularnewline
33 & 533 & 540.682567323272 & -7.68256732327245 \tabularnewline
34 & 528 & 535.661579983682 & -7.66157998368169 \tabularnewline
35 & 516 & 517.083143507878 & -1.08314350787782 \tabularnewline
36 & 502 & 506.80513835565 & -4.80513835565023 \tabularnewline
37 & 506 & 511.731305844929 & -5.73130584492895 \tabularnewline
38 & 518 & 520.172519443126 & -2.17251944312579 \tabularnewline
39 & 534 & 527.859222138869 & 6.14077786113126 \tabularnewline
40 & 528 & 522.673016828055 & 5.32698317194513 \tabularnewline
41 & 478 & 465.762846939601 & 12.2371530603986 \tabularnewline
42 & 469 & 464.241039141491 & 4.75896085850928 \tabularnewline
43 & 490 & 481.196550093488 & 8.80344990651213 \tabularnewline
44 & 493 & 495.71575802763 & -2.71575802762999 \tabularnewline
45 & 508 & 498.155460940617 & 9.8445390593829 \tabularnewline
46 & 517 & 512.899409766555 & 4.10059023344525 \tabularnewline
47 & 514 & 510.879857914082 & 3.12014208591802 \tabularnewline
48 & 510 & 510.042716027551 & -0.0427160275510232 \tabularnewline
49 & 527 & 525.822519663482 & 1.1774803365181 \tabularnewline
50 & 542 & 548.442033217303 & -6.44203321730345 \tabularnewline
51 & 565 & 559.5523760867 & 5.44762391330005 \tabularnewline
52 & 555 & 560.421523054159 & -5.42152305415925 \tabularnewline
53 & 499 & 499.09773939255 & -0.097739392550011 \tabularnewline
54 & 511 & 488.900430766924 & 22.0995692330761 \tabularnewline
55 & 526 & 528.221192945023 & -2.22119294502284 \tabularnewline
56 & 532 & 535.955962416838 & -3.95596241683825 \tabularnewline
57 & 549 & 542.159444268932 & 6.84055573106752 \tabularnewline
58 & 561 & 557.362159351808 & 3.63784064819242 \tabularnewline
59 & 557 & 558.421358229552 & -1.42135822955174 \tabularnewline
60 & 566 & 556.037238219143 & 9.96276178085679 \tabularnewline
61 & 588 & 585.625347417707 & 2.37465258229315 \tabularnewline
62 & 620 & 613.420099373745 & 6.57990062625458 \tabularnewline
63 & 626 & 643.968513884895 & -17.9685138848948 \tabularnewline
64 & 620 & 625.276023372816 & -5.27602337281564 \tabularnewline
65 & 573 & 567.485394895403 & 5.51460510459697 \tabularnewline
66 & 573 & 567.875393179127 & 5.12460682087271 \tabularnewline
67 & 574 & 591.095775239499 & -17.0957752394993 \tabularnewline
68 & 580 & 583.985167183731 & -3.98516718373071 \tabularnewline
69 & 590 & 590.030946198752 & -0.0309461987523036 \tabularnewline
70 & 593 & 596.741525236056 & -3.74152523605596 \tabularnewline
71 & 597 & 587.618338883281 & 9.38166111671853 \tabularnewline
72 & 595 & 594.719049679483 & 0.280950320516922 \tabularnewline
73 & 612 & 611.973386426058 & 0.026613573941745 \tabularnewline
74 & 628 & 634.715937085943 & -6.7159370859431 \tabularnewline
75 & 629 & 646.114863664084 & -17.1148636640841 \tabularnewline
76 & 621 & 624.079303965113 & -3.07930396511279 \tabularnewline
77 & 569 & 564.398970850883 & 4.60102914911715 \tabularnewline
78 & 567 & 559.118755250688 & 7.88124474931192 \tabularnewline
79 & 573 & 579.057266720709 & -6.05726672070853 \tabularnewline
80 & 584 & 580.374441050533 & 3.62555894946672 \tabularnewline
81 & 589 & 592.167797126251 & -3.16779712625123 \tabularnewline
82 & 591 & 593.618085137415 & -2.6180851374146 \tabularnewline
83 & 595 & 584.494663728154 & 10.5053362718456 \tabularnewline
84 & 594 & 590.288799796273 & 3.71120020372666 \tabularnewline
85 & 611 & 609.484665881828 & 1.51533411817161 \tabularnewline
86 & 613 & 632.14636643043 & -19.1463664304302 \tabularnewline
87 & 611 & 628.384366087942 & -17.3843660879422 \tabularnewline
88 & 594 & 604.122376556496 & -10.1223765564957 \tabularnewline
89 & 543 & 534.426582274519 & 8.57341772548091 \tabularnewline
90 & 537 & 529.712999613783 & 7.28700038621696 \tabularnewline
91 & 544 & 544.724917385117 & -0.724917385116555 \tabularnewline
92 & 555 & 549.004697845536 & 5.99530215446396 \tabularnewline
93 & 561 & 560.253374265329 & 0.746625734670829 \tabularnewline
94 & 562 & 563.667764697974 & -1.66776469797401 \tabularnewline
95 & 555 & 554.71494187334 & 0.285058126660374 \tabularnewline
96 & 547 & 547.415549716361 & -0.415549716361284 \tabularnewline
97 & 565 & 558.901074555301 & 6.09892544469881 \tabularnewline
98 & 578 & 581.440448003952 & -3.44044800395227 \tabularnewline
99 & 580 & 591.753790552366 & -11.7537905523661 \tabularnewline
100 & 569 & 573.358105178358 & -4.35810517835762 \tabularnewline
101 & 507 & 511.265057036796 & -4.26505703679572 \tabularnewline
102 & 501 & 493.558465575832 & 7.44153442416825 \tabularnewline
103 & 509 & 507.286335618588 & 1.71366438141206 \tabularnewline
104 & 510 & 513.752363541969 & -3.75236354196898 \tabularnewline
105 & 517 & 513.571664699373 & 3.42833530062683 \tabularnewline
106 & 519 & 517.747298607453 & 1.25270139254746 \tabularnewline
107 & 512 & 510.50067516166 & 1.49932483833993 \tabularnewline
108 & 509 & 503.318352640889 & 5.68164735911103 \tabularnewline
109 & 519 & 520.861541767797 & -1.86154176779678 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149951&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]564[/C][C]552.688301282051[/C][C]11.3116987179485[/C][/ROW]
[ROW][C]14[/C][C]586[/C][C]587.00889071552[/C][C]-1.00889071552047[/C][/ROW]
[ROW][C]15[/C][C]604[/C][C]605.426063089066[/C][C]-1.42606308906556[/C][/ROW]
[ROW][C]16[/C][C]601[/C][C]602.200824301645[/C][C]-1.20082430164484[/C][/ROW]
[ROW][C]17[/C][C]545[/C][C]546.133034745739[/C][C]-1.13303474573854[/C][/ROW]
[ROW][C]18[/C][C]537[/C][C]538.585721565729[/C][C]-1.58572156572882[/C][/ROW]
[ROW][C]19[/C][C]552[/C][C]554.464188755308[/C][C]-2.46418875530776[/C][/ROW]
[ROW][C]20[/C][C]563[/C][C]561.824095182283[/C][C]1.17590481771663[/C][/ROW]
[ROW][C]21[/C][C]575[/C][C]571.465334086761[/C][C]3.53466591323945[/C][/ROW]
[ROW][C]22[/C][C]580[/C][C]583.582535264474[/C][C]-3.58253526447356[/C][/ROW]
[ROW][C]23[/C][C]575[/C][C]575.398631810933[/C][C]-0.398631810933239[/C][/ROW]
[ROW][C]24[/C][C]558[/C][C]573.670226766136[/C][C]-15.6702267661356[/C][/ROW]
[ROW][C]25[/C][C]564[/C][C]573.319487618236[/C][C]-9.3194876182356[/C][/ROW]
[ROW][C]26[/C][C]581[/C][C]582.660193870031[/C][C]-1.66019387003109[/C][/ROW]
[ROW][C]27[/C][C]597[/C][C]595.44559244264[/C][C]1.55440755736015[/C][/ROW]
[ROW][C]28[/C][C]587[/C][C]590.463673800954[/C][C]-3.46367380095364[/C][/ROW]
[ROW][C]29[/C][C]536[/C][C]527.397810891782[/C][C]8.60218910821777[/C][/ROW]
[ROW][C]30[/C][C]524[/C][C]525.462710569782[/C][C]-1.46271056978173[/C][/ROW]
[ROW][C]31[/C][C]537[/C][C]537.968271479589[/C][C]-0.968271479589475[/C][/ROW]
[ROW][C]32[/C][C]536[/C][C]543.758239571812[/C][C]-7.75823957181171[/C][/ROW]
[ROW][C]33[/C][C]533[/C][C]540.682567323272[/C][C]-7.68256732327245[/C][/ROW]
[ROW][C]34[/C][C]528[/C][C]535.661579983682[/C][C]-7.66157998368169[/C][/ROW]
[ROW][C]35[/C][C]516[/C][C]517.083143507878[/C][C]-1.08314350787782[/C][/ROW]
[ROW][C]36[/C][C]502[/C][C]506.80513835565[/C][C]-4.80513835565023[/C][/ROW]
[ROW][C]37[/C][C]506[/C][C]511.731305844929[/C][C]-5.73130584492895[/C][/ROW]
[ROW][C]38[/C][C]518[/C][C]520.172519443126[/C][C]-2.17251944312579[/C][/ROW]
[ROW][C]39[/C][C]534[/C][C]527.859222138869[/C][C]6.14077786113126[/C][/ROW]
[ROW][C]40[/C][C]528[/C][C]522.673016828055[/C][C]5.32698317194513[/C][/ROW]
[ROW][C]41[/C][C]478[/C][C]465.762846939601[/C][C]12.2371530603986[/C][/ROW]
[ROW][C]42[/C][C]469[/C][C]464.241039141491[/C][C]4.75896085850928[/C][/ROW]
[ROW][C]43[/C][C]490[/C][C]481.196550093488[/C][C]8.80344990651213[/C][/ROW]
[ROW][C]44[/C][C]493[/C][C]495.71575802763[/C][C]-2.71575802762999[/C][/ROW]
[ROW][C]45[/C][C]508[/C][C]498.155460940617[/C][C]9.8445390593829[/C][/ROW]
[ROW][C]46[/C][C]517[/C][C]512.899409766555[/C][C]4.10059023344525[/C][/ROW]
[ROW][C]47[/C][C]514[/C][C]510.879857914082[/C][C]3.12014208591802[/C][/ROW]
[ROW][C]48[/C][C]510[/C][C]510.042716027551[/C][C]-0.0427160275510232[/C][/ROW]
[ROW][C]49[/C][C]527[/C][C]525.822519663482[/C][C]1.1774803365181[/C][/ROW]
[ROW][C]50[/C][C]542[/C][C]548.442033217303[/C][C]-6.44203321730345[/C][/ROW]
[ROW][C]51[/C][C]565[/C][C]559.5523760867[/C][C]5.44762391330005[/C][/ROW]
[ROW][C]52[/C][C]555[/C][C]560.421523054159[/C][C]-5.42152305415925[/C][/ROW]
[ROW][C]53[/C][C]499[/C][C]499.09773939255[/C][C]-0.097739392550011[/C][/ROW]
[ROW][C]54[/C][C]511[/C][C]488.900430766924[/C][C]22.0995692330761[/C][/ROW]
[ROW][C]55[/C][C]526[/C][C]528.221192945023[/C][C]-2.22119294502284[/C][/ROW]
[ROW][C]56[/C][C]532[/C][C]535.955962416838[/C][C]-3.95596241683825[/C][/ROW]
[ROW][C]57[/C][C]549[/C][C]542.159444268932[/C][C]6.84055573106752[/C][/ROW]
[ROW][C]58[/C][C]561[/C][C]557.362159351808[/C][C]3.63784064819242[/C][/ROW]
[ROW][C]59[/C][C]557[/C][C]558.421358229552[/C][C]-1.42135822955174[/C][/ROW]
[ROW][C]60[/C][C]566[/C][C]556.037238219143[/C][C]9.96276178085679[/C][/ROW]
[ROW][C]61[/C][C]588[/C][C]585.625347417707[/C][C]2.37465258229315[/C][/ROW]
[ROW][C]62[/C][C]620[/C][C]613.420099373745[/C][C]6.57990062625458[/C][/ROW]
[ROW][C]63[/C][C]626[/C][C]643.968513884895[/C][C]-17.9685138848948[/C][/ROW]
[ROW][C]64[/C][C]620[/C][C]625.276023372816[/C][C]-5.27602337281564[/C][/ROW]
[ROW][C]65[/C][C]573[/C][C]567.485394895403[/C][C]5.51460510459697[/C][/ROW]
[ROW][C]66[/C][C]573[/C][C]567.875393179127[/C][C]5.12460682087271[/C][/ROW]
[ROW][C]67[/C][C]574[/C][C]591.095775239499[/C][C]-17.0957752394993[/C][/ROW]
[ROW][C]68[/C][C]580[/C][C]583.985167183731[/C][C]-3.98516718373071[/C][/ROW]
[ROW][C]69[/C][C]590[/C][C]590.030946198752[/C][C]-0.0309461987523036[/C][/ROW]
[ROW][C]70[/C][C]593[/C][C]596.741525236056[/C][C]-3.74152523605596[/C][/ROW]
[ROW][C]71[/C][C]597[/C][C]587.618338883281[/C][C]9.38166111671853[/C][/ROW]
[ROW][C]72[/C][C]595[/C][C]594.719049679483[/C][C]0.280950320516922[/C][/ROW]
[ROW][C]73[/C][C]612[/C][C]611.973386426058[/C][C]0.026613573941745[/C][/ROW]
[ROW][C]74[/C][C]628[/C][C]634.715937085943[/C][C]-6.7159370859431[/C][/ROW]
[ROW][C]75[/C][C]629[/C][C]646.114863664084[/C][C]-17.1148636640841[/C][/ROW]
[ROW][C]76[/C][C]621[/C][C]624.079303965113[/C][C]-3.07930396511279[/C][/ROW]
[ROW][C]77[/C][C]569[/C][C]564.398970850883[/C][C]4.60102914911715[/C][/ROW]
[ROW][C]78[/C][C]567[/C][C]559.118755250688[/C][C]7.88124474931192[/C][/ROW]
[ROW][C]79[/C][C]573[/C][C]579.057266720709[/C][C]-6.05726672070853[/C][/ROW]
[ROW][C]80[/C][C]584[/C][C]580.374441050533[/C][C]3.62555894946672[/C][/ROW]
[ROW][C]81[/C][C]589[/C][C]592.167797126251[/C][C]-3.16779712625123[/C][/ROW]
[ROW][C]82[/C][C]591[/C][C]593.618085137415[/C][C]-2.6180851374146[/C][/ROW]
[ROW][C]83[/C][C]595[/C][C]584.494663728154[/C][C]10.5053362718456[/C][/ROW]
[ROW][C]84[/C][C]594[/C][C]590.288799796273[/C][C]3.71120020372666[/C][/ROW]
[ROW][C]85[/C][C]611[/C][C]609.484665881828[/C][C]1.51533411817161[/C][/ROW]
[ROW][C]86[/C][C]613[/C][C]632.14636643043[/C][C]-19.1463664304302[/C][/ROW]
[ROW][C]87[/C][C]611[/C][C]628.384366087942[/C][C]-17.3843660879422[/C][/ROW]
[ROW][C]88[/C][C]594[/C][C]604.122376556496[/C][C]-10.1223765564957[/C][/ROW]
[ROW][C]89[/C][C]543[/C][C]534.426582274519[/C][C]8.57341772548091[/C][/ROW]
[ROW][C]90[/C][C]537[/C][C]529.712999613783[/C][C]7.28700038621696[/C][/ROW]
[ROW][C]91[/C][C]544[/C][C]544.724917385117[/C][C]-0.724917385116555[/C][/ROW]
[ROW][C]92[/C][C]555[/C][C]549.004697845536[/C][C]5.99530215446396[/C][/ROW]
[ROW][C]93[/C][C]561[/C][C]560.253374265329[/C][C]0.746625734670829[/C][/ROW]
[ROW][C]94[/C][C]562[/C][C]563.667764697974[/C][C]-1.66776469797401[/C][/ROW]
[ROW][C]95[/C][C]555[/C][C]554.71494187334[/C][C]0.285058126660374[/C][/ROW]
[ROW][C]96[/C][C]547[/C][C]547.415549716361[/C][C]-0.415549716361284[/C][/ROW]
[ROW][C]97[/C][C]565[/C][C]558.901074555301[/C][C]6.09892544469881[/C][/ROW]
[ROW][C]98[/C][C]578[/C][C]581.440448003952[/C][C]-3.44044800395227[/C][/ROW]
[ROW][C]99[/C][C]580[/C][C]591.753790552366[/C][C]-11.7537905523661[/C][/ROW]
[ROW][C]100[/C][C]569[/C][C]573.358105178358[/C][C]-4.35810517835762[/C][/ROW]
[ROW][C]101[/C][C]507[/C][C]511.265057036796[/C][C]-4.26505703679572[/C][/ROW]
[ROW][C]102[/C][C]501[/C][C]493.558465575832[/C][C]7.44153442416825[/C][/ROW]
[ROW][C]103[/C][C]509[/C][C]507.286335618588[/C][C]1.71366438141206[/C][/ROW]
[ROW][C]104[/C][C]510[/C][C]513.752363541969[/C][C]-3.75236354196898[/C][/ROW]
[ROW][C]105[/C][C]517[/C][C]513.571664699373[/C][C]3.42833530062683[/C][/ROW]
[ROW][C]106[/C][C]519[/C][C]517.747298607453[/C][C]1.25270139254746[/C][/ROW]
[ROW][C]107[/C][C]512[/C][C]510.50067516166[/C][C]1.49932483833993[/C][/ROW]
[ROW][C]108[/C][C]509[/C][C]503.318352640889[/C][C]5.68164735911103[/C][/ROW]
[ROW][C]109[/C][C]519[/C][C]520.861541767797[/C][C]-1.86154176779678[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149951&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149951&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
13564552.68830128205111.3116987179485
14586587.00889071552-1.00889071552047
15604605.426063089066-1.42606308906556
16601602.200824301645-1.20082430164484
17545546.133034745739-1.13303474573854
18537538.585721565729-1.58572156572882
19552554.464188755308-2.46418875530776
20563561.8240951822831.17590481771663
21575571.4653340867613.53466591323945
22580583.582535264474-3.58253526447356
23575575.398631810933-0.398631810933239
24558573.670226766136-15.6702267661356
25564573.319487618236-9.3194876182356
26581582.660193870031-1.66019387003109
27597595.445592442641.55440755736015
28587590.463673800954-3.46367380095364
29536527.3978108917828.60218910821777
30524525.462710569782-1.46271056978173
31537537.968271479589-0.968271479589475
32536543.758239571812-7.75823957181171
33533540.682567323272-7.68256732327245
34528535.661579983682-7.66157998368169
35516517.083143507878-1.08314350787782
36502506.80513835565-4.80513835565023
37506511.731305844929-5.73130584492895
38518520.172519443126-2.17251944312579
39534527.8592221388696.14077786113126
40528522.6730168280555.32698317194513
41478465.76284693960112.2371530603986
42469464.2410391414914.75896085850928
43490481.1965500934888.80344990651213
44493495.71575802763-2.71575802762999
45508498.1554609406179.8445390593829
46517512.8994097665554.10059023344525
47514510.8798579140823.12014208591802
48510510.042716027551-0.0427160275510232
49527525.8225196634821.1774803365181
50542548.442033217303-6.44203321730345
51565559.55237608675.44762391330005
52555560.421523054159-5.42152305415925
53499499.09773939255-0.097739392550011
54511488.90043076692422.0995692330761
55526528.221192945023-2.22119294502284
56532535.955962416838-3.95596241683825
57549542.1594442689326.84055573106752
58561557.3621593518083.63784064819242
59557558.421358229552-1.42135822955174
60566556.0372382191439.96276178085679
61588585.6253474177072.37465258229315
62620613.4200993737456.57990062625458
63626643.968513884895-17.9685138848948
64620625.276023372816-5.27602337281564
65573567.4853948954035.51460510459697
66573567.8753931791275.12460682087271
67574591.095775239499-17.0957752394993
68580583.985167183731-3.98516718373071
69590590.030946198752-0.0309461987523036
70593596.741525236056-3.74152523605596
71597587.6183388832819.38166111671853
72595594.7190496794830.280950320516922
73612611.9733864260580.026613573941745
74628634.715937085943-6.7159370859431
75629646.114863664084-17.1148636640841
76621624.079303965113-3.07930396511279
77569564.3989708508834.60102914911715
78567559.1187552506887.88124474931192
79573579.057266720709-6.05726672070853
80584580.3744410505333.62555894946672
81589592.167797126251-3.16779712625123
82591593.618085137415-2.6180851374146
83595584.49466372815410.5053362718456
84594590.2887997962733.71120020372666
85611609.4846658818281.51533411817161
86613632.14636643043-19.1463664304302
87611628.384366087942-17.3843660879422
88594604.122376556496-10.1223765564957
89543534.4265822745198.57341772548091
90537529.7129996137837.28700038621696
91544544.724917385117-0.724917385116555
92555549.0046978455365.99530215446396
93561560.2533742653290.746625734670829
94562563.667764697974-1.66776469797401
95555554.714941873340.285058126660374
96547547.415549716361-0.415549716361284
97565558.9010745553016.09892544469881
98578581.440448003952-3.44044800395227
99580591.753790552366-11.7537905523661
100569573.358105178358-4.35810517835762
101507511.265057036796-4.26505703679572
102501493.5584655758327.44153442416825
103509507.2863356185881.71366438141206
104510513.752363541969-3.75236354196898
105517513.5716646993733.42833530062683
106519517.7472986074531.25270139254746
107512510.500675161661.49932483833993
108509503.3183526408895.68164735911103
109519520.861541767797-1.86154176779678







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
110534.089539448644520.198509910216547.980568987072
111546.327617278158525.863113632282566.792120924034
112540.401113066679513.742097154506567.060128978853
113484.033231233527451.213286182831516.853176284222
114473.366388600243434.29466823448512.438108966006
115480.945567314613435.475564249652526.415570379574
116486.374666919782434.332561236163538.416772603401
117491.654785695766432.85304660749550.456524784041
118493.458548139924427.703100625043559.213995654804
119485.846488657808412.940725717506558.752251598111
120478.107236301905397.854353938872558.360118664938
121489.569672306621401.774058050688577.365286562555

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
110 & 534.089539448644 & 520.198509910216 & 547.980568987072 \tabularnewline
111 & 546.327617278158 & 525.863113632282 & 566.792120924034 \tabularnewline
112 & 540.401113066679 & 513.742097154506 & 567.060128978853 \tabularnewline
113 & 484.033231233527 & 451.213286182831 & 516.853176284222 \tabularnewline
114 & 473.366388600243 & 434.29466823448 & 512.438108966006 \tabularnewline
115 & 480.945567314613 & 435.475564249652 & 526.415570379574 \tabularnewline
116 & 486.374666919782 & 434.332561236163 & 538.416772603401 \tabularnewline
117 & 491.654785695766 & 432.85304660749 & 550.456524784041 \tabularnewline
118 & 493.458548139924 & 427.703100625043 & 559.213995654804 \tabularnewline
119 & 485.846488657808 & 412.940725717506 & 558.752251598111 \tabularnewline
120 & 478.107236301905 & 397.854353938872 & 558.360118664938 \tabularnewline
121 & 489.569672306621 & 401.774058050688 & 577.365286562555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149951&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]534.089539448644[/C][C]520.198509910216[/C][C]547.980568987072[/C][/ROW]
[ROW][C]111[/C][C]546.327617278158[/C][C]525.863113632282[/C][C]566.792120924034[/C][/ROW]
[ROW][C]112[/C][C]540.401113066679[/C][C]513.742097154506[/C][C]567.060128978853[/C][/ROW]
[ROW][C]113[/C][C]484.033231233527[/C][C]451.213286182831[/C][C]516.853176284222[/C][/ROW]
[ROW][C]114[/C][C]473.366388600243[/C][C]434.29466823448[/C][C]512.438108966006[/C][/ROW]
[ROW][C]115[/C][C]480.945567314613[/C][C]435.475564249652[/C][C]526.415570379574[/C][/ROW]
[ROW][C]116[/C][C]486.374666919782[/C][C]434.332561236163[/C][C]538.416772603401[/C][/ROW]
[ROW][C]117[/C][C]491.654785695766[/C][C]432.85304660749[/C][C]550.456524784041[/C][/ROW]
[ROW][C]118[/C][C]493.458548139924[/C][C]427.703100625043[/C][C]559.213995654804[/C][/ROW]
[ROW][C]119[/C][C]485.846488657808[/C][C]412.940725717506[/C][C]558.752251598111[/C][/ROW]
[ROW][C]120[/C][C]478.107236301905[/C][C]397.854353938872[/C][C]558.360118664938[/C][/ROW]
[ROW][C]121[/C][C]489.569672306621[/C][C]401.774058050688[/C][C]577.365286562555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149951&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149951&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
110534.089539448644520.198509910216547.980568987072
111546.327617278158525.863113632282566.792120924034
112540.401113066679513.742097154506567.060128978853
113484.033231233527451.213286182831516.853176284222
114473.366388600243434.29466823448512.438108966006
115480.945567314613435.475564249652526.415570379574
116486.374666919782434.332561236163538.416772603401
117491.654785695766432.85304660749550.456524784041
118493.458548139924427.703100625043559.213995654804
119485.846488657808412.940725717506558.752251598111
120478.107236301905397.854353938872558.360118664938
121489.569672306621401.774058050688577.365286562555



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')