Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 19:29:05 +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/2016/Nov/28/t1480361398bq9p55njnfjc6gb.htm/, Retrieved Sat, 04 May 2024 20:08:53 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 20:08:53 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
480
548
634
489
399
658
497
495
445
525
565
427
477
511
538
444
559
433
459
492
526
523
636
519
671
599
579
593
684
599
721
516
556
700
579
552
734
760
714
698
800
712
782
610
596
748
581
641
598
609
526
716
552
464
631
465
539
537
488
520
477
480
645
455
379
477
424
316
381
376
389
472




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.338127867499261
beta0
gamma0.541013145326972

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.338127867499261 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.541013145326972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.338127867499261[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.541013145326972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.338127867499261
beta0
gamma0.541013145326972







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13477501.177610177224-24.1776101772243
14511528.656498777284-17.6564987772839
15538545.285716323373-7.28571632337264
16444443.8686261645120.131373835488148
17559554.244821754354.75517824565009
18433423.691931477169.30806852283951
19459481.577913194212-22.5779131942119
20492472.34185256703319.6581474329675
21526434.20076917252391.7992308274767
22523553.988423714133-30.9884237141328
23636577.94686147607558.0531385239245
24519452.97171262430866.0282873756918
25671532.046654807384138.953345192616
26599624.616674080876-25.6166740808757
27579647.595583531225-68.5955835312245
28593513.2741821006479.7258178993601
29684676.8076503525447.19234964745579
30599520.43123839367978.5687616063212
31721602.246956300105118.753043699895
32516661.3861840054-145.3861840054
33556585.898204318138-29.8982043181381
34700627.50850604895272.4914939510476
35579732.734302763199-153.734302763199
36552523.59425228182628.4057477181738
37734617.526445448084116.473554551916
38760642.892246506695117.107753493305
39714699.90744352387614.0925564761239
40698635.05304833756862.946951662432
41800784.17673526192515.8232647380752
42712633.82689860243578.1731013975647
43782737.34552798957144.6544720104292
44610664.914551328427-54.9145513284273
45596663.647360858557-67.647360858557
46748740.0720005627967.92799943720411
47581737.956135823768-156.956135823768
48641584.16082085690956.8391791430913
49598729.416701154167-131.416701154167
50609669.047856660317-60.0478566603172
51526631.137594219328-105.137594219328
52716551.031448294088164.968551705912
53552705.810080450238-153.810080450238
54464543.00805635713-79.0080563571299
55631564.54548015291866.4545198470821
56465492.220808846623-27.2208088466234
57539491.91128870726247.0887112927384
58537611.662818652861-74.6628186528606
59488532.516516485834-44.5165164858341
60520496.82638502394123.1736149760588
61477549.376999230058-72.3769992300585
62480532.033274829351-52.0332748293509
63645484.688608706947160.311391293053
64455583.986282206008-128.986282206008
65379524.272543711351-145.272543711351
66477407.08499618867569.9150038113245
67424518.32292049811-94.3229204981099
68316383.856327446591-67.856327446591
69381387.306079717125-6.30607971712539
70376428.198250779549-52.1982507795488
71389378.26733916730610.7326608326944
72472384.24984657355687.7501534264442

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 477 & 501.177610177224 & -24.1776101772243 \tabularnewline
14 & 511 & 528.656498777284 & -17.6564987772839 \tabularnewline
15 & 538 & 545.285716323373 & -7.28571632337264 \tabularnewline
16 & 444 & 443.868626164512 & 0.131373835488148 \tabularnewline
17 & 559 & 554.24482175435 & 4.75517824565009 \tabularnewline
18 & 433 & 423.69193147716 & 9.30806852283951 \tabularnewline
19 & 459 & 481.577913194212 & -22.5779131942119 \tabularnewline
20 & 492 & 472.341852567033 & 19.6581474329675 \tabularnewline
21 & 526 & 434.200769172523 & 91.7992308274767 \tabularnewline
22 & 523 & 553.988423714133 & -30.9884237141328 \tabularnewline
23 & 636 & 577.946861476075 & 58.0531385239245 \tabularnewline
24 & 519 & 452.971712624308 & 66.0282873756918 \tabularnewline
25 & 671 & 532.046654807384 & 138.953345192616 \tabularnewline
26 & 599 & 624.616674080876 & -25.6166740808757 \tabularnewline
27 & 579 & 647.595583531225 & -68.5955835312245 \tabularnewline
28 & 593 & 513.27418210064 & 79.7258178993601 \tabularnewline
29 & 684 & 676.807650352544 & 7.19234964745579 \tabularnewline
30 & 599 & 520.431238393679 & 78.5687616063212 \tabularnewline
31 & 721 & 602.246956300105 & 118.753043699895 \tabularnewline
32 & 516 & 661.3861840054 & -145.3861840054 \tabularnewline
33 & 556 & 585.898204318138 & -29.8982043181381 \tabularnewline
34 & 700 & 627.508506048952 & 72.4914939510476 \tabularnewline
35 & 579 & 732.734302763199 & -153.734302763199 \tabularnewline
36 & 552 & 523.594252281826 & 28.4057477181738 \tabularnewline
37 & 734 & 617.526445448084 & 116.473554551916 \tabularnewline
38 & 760 & 642.892246506695 & 117.107753493305 \tabularnewline
39 & 714 & 699.907443523876 & 14.0925564761239 \tabularnewline
40 & 698 & 635.053048337568 & 62.946951662432 \tabularnewline
41 & 800 & 784.176735261925 & 15.8232647380752 \tabularnewline
42 & 712 & 633.826898602435 & 78.1731013975647 \tabularnewline
43 & 782 & 737.345527989571 & 44.6544720104292 \tabularnewline
44 & 610 & 664.914551328427 & -54.9145513284273 \tabularnewline
45 & 596 & 663.647360858557 & -67.647360858557 \tabularnewline
46 & 748 & 740.072000562796 & 7.92799943720411 \tabularnewline
47 & 581 & 737.956135823768 & -156.956135823768 \tabularnewline
48 & 641 & 584.160820856909 & 56.8391791430913 \tabularnewline
49 & 598 & 729.416701154167 & -131.416701154167 \tabularnewline
50 & 609 & 669.047856660317 & -60.0478566603172 \tabularnewline
51 & 526 & 631.137594219328 & -105.137594219328 \tabularnewline
52 & 716 & 551.031448294088 & 164.968551705912 \tabularnewline
53 & 552 & 705.810080450238 & -153.810080450238 \tabularnewline
54 & 464 & 543.00805635713 & -79.0080563571299 \tabularnewline
55 & 631 & 564.545480152918 & 66.4545198470821 \tabularnewline
56 & 465 & 492.220808846623 & -27.2208088466234 \tabularnewline
57 & 539 & 491.911288707262 & 47.0887112927384 \tabularnewline
58 & 537 & 611.662818652861 & -74.6628186528606 \tabularnewline
59 & 488 & 532.516516485834 & -44.5165164858341 \tabularnewline
60 & 520 & 496.826385023941 & 23.1736149760588 \tabularnewline
61 & 477 & 549.376999230058 & -72.3769992300585 \tabularnewline
62 & 480 & 532.033274829351 & -52.0332748293509 \tabularnewline
63 & 645 & 484.688608706947 & 160.311391293053 \tabularnewline
64 & 455 & 583.986282206008 & -128.986282206008 \tabularnewline
65 & 379 & 524.272543711351 & -145.272543711351 \tabularnewline
66 & 477 & 407.084996188675 & 69.9150038113245 \tabularnewline
67 & 424 & 518.32292049811 & -94.3229204981099 \tabularnewline
68 & 316 & 383.856327446591 & -67.856327446591 \tabularnewline
69 & 381 & 387.306079717125 & -6.30607971712539 \tabularnewline
70 & 376 & 428.198250779549 & -52.1982507795488 \tabularnewline
71 & 389 & 378.267339167306 & 10.7326608326944 \tabularnewline
72 & 472 & 384.249846573556 & 87.7501534264442 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]477[/C][C]501.177610177224[/C][C]-24.1776101772243[/C][/ROW]
[ROW][C]14[/C][C]511[/C][C]528.656498777284[/C][C]-17.6564987772839[/C][/ROW]
[ROW][C]15[/C][C]538[/C][C]545.285716323373[/C][C]-7.28571632337264[/C][/ROW]
[ROW][C]16[/C][C]444[/C][C]443.868626164512[/C][C]0.131373835488148[/C][/ROW]
[ROW][C]17[/C][C]559[/C][C]554.24482175435[/C][C]4.75517824565009[/C][/ROW]
[ROW][C]18[/C][C]433[/C][C]423.69193147716[/C][C]9.30806852283951[/C][/ROW]
[ROW][C]19[/C][C]459[/C][C]481.577913194212[/C][C]-22.5779131942119[/C][/ROW]
[ROW][C]20[/C][C]492[/C][C]472.341852567033[/C][C]19.6581474329675[/C][/ROW]
[ROW][C]21[/C][C]526[/C][C]434.200769172523[/C][C]91.7992308274767[/C][/ROW]
[ROW][C]22[/C][C]523[/C][C]553.988423714133[/C][C]-30.9884237141328[/C][/ROW]
[ROW][C]23[/C][C]636[/C][C]577.946861476075[/C][C]58.0531385239245[/C][/ROW]
[ROW][C]24[/C][C]519[/C][C]452.971712624308[/C][C]66.0282873756918[/C][/ROW]
[ROW][C]25[/C][C]671[/C][C]532.046654807384[/C][C]138.953345192616[/C][/ROW]
[ROW][C]26[/C][C]599[/C][C]624.616674080876[/C][C]-25.6166740808757[/C][/ROW]
[ROW][C]27[/C][C]579[/C][C]647.595583531225[/C][C]-68.5955835312245[/C][/ROW]
[ROW][C]28[/C][C]593[/C][C]513.27418210064[/C][C]79.7258178993601[/C][/ROW]
[ROW][C]29[/C][C]684[/C][C]676.807650352544[/C][C]7.19234964745579[/C][/ROW]
[ROW][C]30[/C][C]599[/C][C]520.431238393679[/C][C]78.5687616063212[/C][/ROW]
[ROW][C]31[/C][C]721[/C][C]602.246956300105[/C][C]118.753043699895[/C][/ROW]
[ROW][C]32[/C][C]516[/C][C]661.3861840054[/C][C]-145.3861840054[/C][/ROW]
[ROW][C]33[/C][C]556[/C][C]585.898204318138[/C][C]-29.8982043181381[/C][/ROW]
[ROW][C]34[/C][C]700[/C][C]627.508506048952[/C][C]72.4914939510476[/C][/ROW]
[ROW][C]35[/C][C]579[/C][C]732.734302763199[/C][C]-153.734302763199[/C][/ROW]
[ROW][C]36[/C][C]552[/C][C]523.594252281826[/C][C]28.4057477181738[/C][/ROW]
[ROW][C]37[/C][C]734[/C][C]617.526445448084[/C][C]116.473554551916[/C][/ROW]
[ROW][C]38[/C][C]760[/C][C]642.892246506695[/C][C]117.107753493305[/C][/ROW]
[ROW][C]39[/C][C]714[/C][C]699.907443523876[/C][C]14.0925564761239[/C][/ROW]
[ROW][C]40[/C][C]698[/C][C]635.053048337568[/C][C]62.946951662432[/C][/ROW]
[ROW][C]41[/C][C]800[/C][C]784.176735261925[/C][C]15.8232647380752[/C][/ROW]
[ROW][C]42[/C][C]712[/C][C]633.826898602435[/C][C]78.1731013975647[/C][/ROW]
[ROW][C]43[/C][C]782[/C][C]737.345527989571[/C][C]44.6544720104292[/C][/ROW]
[ROW][C]44[/C][C]610[/C][C]664.914551328427[/C][C]-54.9145513284273[/C][/ROW]
[ROW][C]45[/C][C]596[/C][C]663.647360858557[/C][C]-67.647360858557[/C][/ROW]
[ROW][C]46[/C][C]748[/C][C]740.072000562796[/C][C]7.92799943720411[/C][/ROW]
[ROW][C]47[/C][C]581[/C][C]737.956135823768[/C][C]-156.956135823768[/C][/ROW]
[ROW][C]48[/C][C]641[/C][C]584.160820856909[/C][C]56.8391791430913[/C][/ROW]
[ROW][C]49[/C][C]598[/C][C]729.416701154167[/C][C]-131.416701154167[/C][/ROW]
[ROW][C]50[/C][C]609[/C][C]669.047856660317[/C][C]-60.0478566603172[/C][/ROW]
[ROW][C]51[/C][C]526[/C][C]631.137594219328[/C][C]-105.137594219328[/C][/ROW]
[ROW][C]52[/C][C]716[/C][C]551.031448294088[/C][C]164.968551705912[/C][/ROW]
[ROW][C]53[/C][C]552[/C][C]705.810080450238[/C][C]-153.810080450238[/C][/ROW]
[ROW][C]54[/C][C]464[/C][C]543.00805635713[/C][C]-79.0080563571299[/C][/ROW]
[ROW][C]55[/C][C]631[/C][C]564.545480152918[/C][C]66.4545198470821[/C][/ROW]
[ROW][C]56[/C][C]465[/C][C]492.220808846623[/C][C]-27.2208088466234[/C][/ROW]
[ROW][C]57[/C][C]539[/C][C]491.911288707262[/C][C]47.0887112927384[/C][/ROW]
[ROW][C]58[/C][C]537[/C][C]611.662818652861[/C][C]-74.6628186528606[/C][/ROW]
[ROW][C]59[/C][C]488[/C][C]532.516516485834[/C][C]-44.5165164858341[/C][/ROW]
[ROW][C]60[/C][C]520[/C][C]496.826385023941[/C][C]23.1736149760588[/C][/ROW]
[ROW][C]61[/C][C]477[/C][C]549.376999230058[/C][C]-72.3769992300585[/C][/ROW]
[ROW][C]62[/C][C]480[/C][C]532.033274829351[/C][C]-52.0332748293509[/C][/ROW]
[ROW][C]63[/C][C]645[/C][C]484.688608706947[/C][C]160.311391293053[/C][/ROW]
[ROW][C]64[/C][C]455[/C][C]583.986282206008[/C][C]-128.986282206008[/C][/ROW]
[ROW][C]65[/C][C]379[/C][C]524.272543711351[/C][C]-145.272543711351[/C][/ROW]
[ROW][C]66[/C][C]477[/C][C]407.084996188675[/C][C]69.9150038113245[/C][/ROW]
[ROW][C]67[/C][C]424[/C][C]518.32292049811[/C][C]-94.3229204981099[/C][/ROW]
[ROW][C]68[/C][C]316[/C][C]383.856327446591[/C][C]-67.856327446591[/C][/ROW]
[ROW][C]69[/C][C]381[/C][C]387.306079717125[/C][C]-6.30607971712539[/C][/ROW]
[ROW][C]70[/C][C]376[/C][C]428.198250779549[/C][C]-52.1982507795488[/C][/ROW]
[ROW][C]71[/C][C]389[/C][C]378.267339167306[/C][C]10.7326608326944[/C][/ROW]
[ROW][C]72[/C][C]472[/C][C]384.249846573556[/C][C]87.7501534264442[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
13477501.177610177224-24.1776101772243
14511528.656498777284-17.6564987772839
15538545.285716323373-7.28571632337264
16444443.8686261645120.131373835488148
17559554.244821754354.75517824565009
18433423.691931477169.30806852283951
19459481.577913194212-22.5779131942119
20492472.34185256703319.6581474329675
21526434.20076917252391.7992308274767
22523553.988423714133-30.9884237141328
23636577.94686147607558.0531385239245
24519452.97171262430866.0282873756918
25671532.046654807384138.953345192616
26599624.616674080876-25.6166740808757
27579647.595583531225-68.5955835312245
28593513.2741821006479.7258178993601
29684676.8076503525447.19234964745579
30599520.43123839367978.5687616063212
31721602.246956300105118.753043699895
32516661.3861840054-145.3861840054
33556585.898204318138-29.8982043181381
34700627.50850604895272.4914939510476
35579732.734302763199-153.734302763199
36552523.59425228182628.4057477181738
37734617.526445448084116.473554551916
38760642.892246506695117.107753493305
39714699.90744352387614.0925564761239
40698635.05304833756862.946951662432
41800784.17673526192515.8232647380752
42712633.82689860243578.1731013975647
43782737.34552798957144.6544720104292
44610664.914551328427-54.9145513284273
45596663.647360858557-67.647360858557
46748740.0720005627967.92799943720411
47581737.956135823768-156.956135823768
48641584.16082085690956.8391791430913
49598729.416701154167-131.416701154167
50609669.047856660317-60.0478566603172
51526631.137594219328-105.137594219328
52716551.031448294088164.968551705912
53552705.810080450238-153.810080450238
54464543.00805635713-79.0080563571299
55631564.54548015291866.4545198470821
56465492.220808846623-27.2208088466234
57539491.91128870726247.0887112927384
58537611.662818652861-74.6628186528606
59488532.516516485834-44.5165164858341
60520496.82638502394123.1736149760588
61477549.376999230058-72.3769992300585
62480532.033274829351-52.0332748293509
63645484.688608706947160.311391293053
64455583.986282206008-128.986282206008
65379524.272543711351-145.272543711351
66477407.08499618867569.9150038113245
67424518.32292049811-94.3229204981099
68316383.856327446591-67.856327446591
69381387.306079717125-6.30607971712539
70376428.198250779549-52.1982507795488
71389378.26733916730610.7326608326944
72472384.24984657355687.7501534264442







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73421.178591138636308.573465781382533.783716495889
74432.607341247492306.694678189797558.520004305188
75467.77829339631326.601570260293608.955016532328
76418.693828873856274.007858315125563.379799432587
77395.375968117113244.487932116543546.264004117684
78402.4113068335240.21127407772564.61133958928
79425.723900001782248.54324212699602.904557876574
80336.653347122074174.376100398867498.930593845281
81385.080499781048199.09766577353571.063333788565
82411.021074718838207.992994639056614.04915479862
83400.818821069998193.821598396937607.816043743058
84429.631709400529212.520238845555646.743179955504

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 421.178591138636 & 308.573465781382 & 533.783716495889 \tabularnewline
74 & 432.607341247492 & 306.694678189797 & 558.520004305188 \tabularnewline
75 & 467.77829339631 & 326.601570260293 & 608.955016532328 \tabularnewline
76 & 418.693828873856 & 274.007858315125 & 563.379799432587 \tabularnewline
77 & 395.375968117113 & 244.487932116543 & 546.264004117684 \tabularnewline
78 & 402.4113068335 & 240.21127407772 & 564.61133958928 \tabularnewline
79 & 425.723900001782 & 248.54324212699 & 602.904557876574 \tabularnewline
80 & 336.653347122074 & 174.376100398867 & 498.930593845281 \tabularnewline
81 & 385.080499781048 & 199.09766577353 & 571.063333788565 \tabularnewline
82 & 411.021074718838 & 207.992994639056 & 614.04915479862 \tabularnewline
83 & 400.818821069998 & 193.821598396937 & 607.816043743058 \tabularnewline
84 & 429.631709400529 & 212.520238845555 & 646.743179955504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]421.178591138636[/C][C]308.573465781382[/C][C]533.783716495889[/C][/ROW]
[ROW][C]74[/C][C]432.607341247492[/C][C]306.694678189797[/C][C]558.520004305188[/C][/ROW]
[ROW][C]75[/C][C]467.77829339631[/C][C]326.601570260293[/C][C]608.955016532328[/C][/ROW]
[ROW][C]76[/C][C]418.693828873856[/C][C]274.007858315125[/C][C]563.379799432587[/C][/ROW]
[ROW][C]77[/C][C]395.375968117113[/C][C]244.487932116543[/C][C]546.264004117684[/C][/ROW]
[ROW][C]78[/C][C]402.4113068335[/C][C]240.21127407772[/C][C]564.61133958928[/C][/ROW]
[ROW][C]79[/C][C]425.723900001782[/C][C]248.54324212699[/C][C]602.904557876574[/C][/ROW]
[ROW][C]80[/C][C]336.653347122074[/C][C]174.376100398867[/C][C]498.930593845281[/C][/ROW]
[ROW][C]81[/C][C]385.080499781048[/C][C]199.09766577353[/C][C]571.063333788565[/C][/ROW]
[ROW][C]82[/C][C]411.021074718838[/C][C]207.992994639056[/C][C]614.04915479862[/C][/ROW]
[ROW][C]83[/C][C]400.818821069998[/C][C]193.821598396937[/C][C]607.816043743058[/C][/ROW]
[ROW][C]84[/C][C]429.631709400529[/C][C]212.520238845555[/C][C]646.743179955504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73421.178591138636308.573465781382533.783716495889
74432.607341247492306.694678189797558.520004305188
75467.77829339631326.601570260293608.955016532328
76418.693828873856274.007858315125563.379799432587
77395.375968117113244.487932116543546.264004117684
78402.4113068335240.21127407772564.61133958928
79425.723900001782248.54324212699602.904557876574
80336.653347122074174.376100398867498.930593845281
81385.080499781048199.09766577353571.063333788565
82411.021074718838207.992994639056614.04915479862
83400.818821069998193.821598396937607.816043743058
84429.631709400529212.520238845555646.743179955504



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')