Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 06 Jan 2015 12:34:40 +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/2015/Jan/06/t1420547769xci07108tzqh2h4.htm/, Retrieved Wed, 15 May 2024 12:21:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=272003, Retrieved Wed, 15 May 2024 12:21:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [] [2015-01-05 16:01:40] [a8f6a7eeade7f89f597831d453788737]
-    D  [Harrell-Davis Quantiles] [] [2015-01-05 16:10:43] [a8f6a7eeade7f89f597831d453788737]
- RM      [(Partial) Autocorrelation Function] [] [2015-01-06 09:12:41] [a8f6a7eeade7f89f597831d453788737]
- RM D      [Bootstrap Plot - Central Tendency] [] [2015-01-06 09:27:21] [a8f6a7eeade7f89f597831d453788737]
- RM D        [Blocked Bootstrap Plot - Central Tendency] [] [2015-01-06 10:19:09] [a8f6a7eeade7f89f597831d453788737]
- RM D          [Classical Decomposition] [] [2015-01-06 12:12:48] [a8f6a7eeade7f89f597831d453788737]
- RM D              [Exponential Smoothing] [] [2015-01-06 12:34:40] [12470bd120139be5e23c611c04d9c0dc] [Current]
Feedback Forum

Post a new message
Dataseries X:
383
349
317
401
285
377
380
347
414
406
487
475
566
604
764
725
585
797
740
587
719
621
677
636
591
636
748
571
475
758
554
597
521
597
658
482
567
605
653
512
653
498
520
606
601
608
732
585
800
721
689
689
777
681
836
594
662
835
702
630
857
847
820
801
900
763
897
687
682
844
687
671




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272003&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272003&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.327963874730602
beta0.503859429076574
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.327963874730602 \tabularnewline
beta & 0.503859429076574 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272003&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]0.327963874730602[/C][/ROW]
[ROW][C]beta[/C][C]0.503859429076574[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272003&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
alpha0.327963874730602
beta0.503859429076574
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33173152
4401281.98642313082119.01357686918
5285307.015791064883-22.0157910648832
6377282.15456240852994.8454375914712
7380311.29258464156968.7074153584313
8347343.2120215458043.78797845419564
9414354.46618306949859.5338169305024
10406393.84079154508812.1592084549115
11487419.68752097884467.3124790211559
12475474.7457624437290.254237556270994
13566507.85333537422858.1466646257723
14604569.55613505412334.4438649458768
15764629.17704184942134.82295815058
16725743.997847479038-18.9978474790375
17585805.231635256391-220.231635256391
18797764.07524112687832.9247588731215
19740811.385739298871-71.3857392988714
20587812.68983374871-225.68983374871
21719726.093035659168-7.09303565916809
22621710.01598271219-89.0159827121904
23677652.36147704359824.6385229564023
24636636.053002454967-0.0530024549672135
25591611.637840986131-20.6378409861312
26636577.06124054834258.938759451658
27748578.32238421892169.67761578108
28571643.940706462358-72.9407064623582
29475617.935700362764-142.935700362764
30758545.355070451244212.644929548756
31554624.531125247292-70.5311252472919
32597599.180558313361-2.18055831336073
33521595.88617592544-74.8861759254402
34597556.37220983528340.6277901647175
35658561.45630015168496.5436998483165
36482600.832412316593-118.832412316593
37567549.93615849829517.063841501705
38605546.42872704589758.5712729541031
39653566.21300123856786.7869987614334
40512609.592365321676-97.5923653216762
41653576.37504574236776.6249542576326
42498612.956810076965-114.956810076965
43520567.710329259562-47.7103292595617
44606536.6342431213369.3657568786699
45601555.41741496772345.5825850322773
46608573.93298253377534.0670174662255
47732594.301355905774137.698644094226
48585671.411542037597-86.411542037597
49800660.742375389263139.257624610737
50721747.09654391858-26.0965439185803
51689774.908125016904-85.908125016904
52689768.907548954808-79.9075489548085
53777751.67040713601225.3295928639881
54681773.132902840308-92.1329028403079
55836740.84719388793695.1528061120636
56594785.708213196946-191.708213196946
57662704.809841589113-42.8098415891128
58835665.670529413906169.329470586094
59702724.0865520207-22.0865520206995
60630716.075282451355-86.0752824513552
61857672.854279261209184.145720738791
62847748.68565841149198.3143415885091
63820812.6136637903527.38633620964811
64801847.941143204864-46.9411432048636
65900857.69425645378542.3057435462146
66763903.708050912725-140.708050912725
67897866.4482517384230.5517482615804
68687890.404085733352-203.404085733352
69682804.018802453264-122.018802453264
70844724.161626698882119.838373301118
71687743.427881879105-56.4278818791048
72671695.560595855711-24.5605958557109

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 317 & 315 & 2 \tabularnewline
4 & 401 & 281.98642313082 & 119.01357686918 \tabularnewline
5 & 285 & 307.015791064883 & -22.0157910648832 \tabularnewline
6 & 377 & 282.154562408529 & 94.8454375914712 \tabularnewline
7 & 380 & 311.292584641569 & 68.7074153584313 \tabularnewline
8 & 347 & 343.212021545804 & 3.78797845419564 \tabularnewline
9 & 414 & 354.466183069498 & 59.5338169305024 \tabularnewline
10 & 406 & 393.840791545088 & 12.1592084549115 \tabularnewline
11 & 487 & 419.687520978844 & 67.3124790211559 \tabularnewline
12 & 475 & 474.745762443729 & 0.254237556270994 \tabularnewline
13 & 566 & 507.853335374228 & 58.1466646257723 \tabularnewline
14 & 604 & 569.556135054123 & 34.4438649458768 \tabularnewline
15 & 764 & 629.17704184942 & 134.82295815058 \tabularnewline
16 & 725 & 743.997847479038 & -18.9978474790375 \tabularnewline
17 & 585 & 805.231635256391 & -220.231635256391 \tabularnewline
18 & 797 & 764.075241126878 & 32.9247588731215 \tabularnewline
19 & 740 & 811.385739298871 & -71.3857392988714 \tabularnewline
20 & 587 & 812.68983374871 & -225.68983374871 \tabularnewline
21 & 719 & 726.093035659168 & -7.09303565916809 \tabularnewline
22 & 621 & 710.01598271219 & -89.0159827121904 \tabularnewline
23 & 677 & 652.361477043598 & 24.6385229564023 \tabularnewline
24 & 636 & 636.053002454967 & -0.0530024549672135 \tabularnewline
25 & 591 & 611.637840986131 & -20.6378409861312 \tabularnewline
26 & 636 & 577.061240548342 & 58.938759451658 \tabularnewline
27 & 748 & 578.32238421892 & 169.67761578108 \tabularnewline
28 & 571 & 643.940706462358 & -72.9407064623582 \tabularnewline
29 & 475 & 617.935700362764 & -142.935700362764 \tabularnewline
30 & 758 & 545.355070451244 & 212.644929548756 \tabularnewline
31 & 554 & 624.531125247292 & -70.5311252472919 \tabularnewline
32 & 597 & 599.180558313361 & -2.18055831336073 \tabularnewline
33 & 521 & 595.88617592544 & -74.8861759254402 \tabularnewline
34 & 597 & 556.372209835283 & 40.6277901647175 \tabularnewline
35 & 658 & 561.456300151684 & 96.5436998483165 \tabularnewline
36 & 482 & 600.832412316593 & -118.832412316593 \tabularnewline
37 & 567 & 549.936158498295 & 17.063841501705 \tabularnewline
38 & 605 & 546.428727045897 & 58.5712729541031 \tabularnewline
39 & 653 & 566.213001238567 & 86.7869987614334 \tabularnewline
40 & 512 & 609.592365321676 & -97.5923653216762 \tabularnewline
41 & 653 & 576.375045742367 & 76.6249542576326 \tabularnewline
42 & 498 & 612.956810076965 & -114.956810076965 \tabularnewline
43 & 520 & 567.710329259562 & -47.7103292595617 \tabularnewline
44 & 606 & 536.63424312133 & 69.3657568786699 \tabularnewline
45 & 601 & 555.417414967723 & 45.5825850322773 \tabularnewline
46 & 608 & 573.932982533775 & 34.0670174662255 \tabularnewline
47 & 732 & 594.301355905774 & 137.698644094226 \tabularnewline
48 & 585 & 671.411542037597 & -86.411542037597 \tabularnewline
49 & 800 & 660.742375389263 & 139.257624610737 \tabularnewline
50 & 721 & 747.09654391858 & -26.0965439185803 \tabularnewline
51 & 689 & 774.908125016904 & -85.908125016904 \tabularnewline
52 & 689 & 768.907548954808 & -79.9075489548085 \tabularnewline
53 & 777 & 751.670407136012 & 25.3295928639881 \tabularnewline
54 & 681 & 773.132902840308 & -92.1329028403079 \tabularnewline
55 & 836 & 740.847193887936 & 95.1528061120636 \tabularnewline
56 & 594 & 785.708213196946 & -191.708213196946 \tabularnewline
57 & 662 & 704.809841589113 & -42.8098415891128 \tabularnewline
58 & 835 & 665.670529413906 & 169.329470586094 \tabularnewline
59 & 702 & 724.0865520207 & -22.0865520206995 \tabularnewline
60 & 630 & 716.075282451355 & -86.0752824513552 \tabularnewline
61 & 857 & 672.854279261209 & 184.145720738791 \tabularnewline
62 & 847 & 748.685658411491 & 98.3143415885091 \tabularnewline
63 & 820 & 812.613663790352 & 7.38633620964811 \tabularnewline
64 & 801 & 847.941143204864 & -46.9411432048636 \tabularnewline
65 & 900 & 857.694256453785 & 42.3057435462146 \tabularnewline
66 & 763 & 903.708050912725 & -140.708050912725 \tabularnewline
67 & 897 & 866.44825173842 & 30.5517482615804 \tabularnewline
68 & 687 & 890.404085733352 & -203.404085733352 \tabularnewline
69 & 682 & 804.018802453264 & -122.018802453264 \tabularnewline
70 & 844 & 724.161626698882 & 119.838373301118 \tabularnewline
71 & 687 & 743.427881879105 & -56.4278818791048 \tabularnewline
72 & 671 & 695.560595855711 & -24.5605958557109 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272003&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]3[/C][C]317[/C][C]315[/C][C]2[/C][/ROW]
[ROW][C]4[/C][C]401[/C][C]281.98642313082[/C][C]119.01357686918[/C][/ROW]
[ROW][C]5[/C][C]285[/C][C]307.015791064883[/C][C]-22.0157910648832[/C][/ROW]
[ROW][C]6[/C][C]377[/C][C]282.154562408529[/C][C]94.8454375914712[/C][/ROW]
[ROW][C]7[/C][C]380[/C][C]311.292584641569[/C][C]68.7074153584313[/C][/ROW]
[ROW][C]8[/C][C]347[/C][C]343.212021545804[/C][C]3.78797845419564[/C][/ROW]
[ROW][C]9[/C][C]414[/C][C]354.466183069498[/C][C]59.5338169305024[/C][/ROW]
[ROW][C]10[/C][C]406[/C][C]393.840791545088[/C][C]12.1592084549115[/C][/ROW]
[ROW][C]11[/C][C]487[/C][C]419.687520978844[/C][C]67.3124790211559[/C][/ROW]
[ROW][C]12[/C][C]475[/C][C]474.745762443729[/C][C]0.254237556270994[/C][/ROW]
[ROW][C]13[/C][C]566[/C][C]507.853335374228[/C][C]58.1466646257723[/C][/ROW]
[ROW][C]14[/C][C]604[/C][C]569.556135054123[/C][C]34.4438649458768[/C][/ROW]
[ROW][C]15[/C][C]764[/C][C]629.17704184942[/C][C]134.82295815058[/C][/ROW]
[ROW][C]16[/C][C]725[/C][C]743.997847479038[/C][C]-18.9978474790375[/C][/ROW]
[ROW][C]17[/C][C]585[/C][C]805.231635256391[/C][C]-220.231635256391[/C][/ROW]
[ROW][C]18[/C][C]797[/C][C]764.075241126878[/C][C]32.9247588731215[/C][/ROW]
[ROW][C]19[/C][C]740[/C][C]811.385739298871[/C][C]-71.3857392988714[/C][/ROW]
[ROW][C]20[/C][C]587[/C][C]812.68983374871[/C][C]-225.68983374871[/C][/ROW]
[ROW][C]21[/C][C]719[/C][C]726.093035659168[/C][C]-7.09303565916809[/C][/ROW]
[ROW][C]22[/C][C]621[/C][C]710.01598271219[/C][C]-89.0159827121904[/C][/ROW]
[ROW][C]23[/C][C]677[/C][C]652.361477043598[/C][C]24.6385229564023[/C][/ROW]
[ROW][C]24[/C][C]636[/C][C]636.053002454967[/C][C]-0.0530024549672135[/C][/ROW]
[ROW][C]25[/C][C]591[/C][C]611.637840986131[/C][C]-20.6378409861312[/C][/ROW]
[ROW][C]26[/C][C]636[/C][C]577.061240548342[/C][C]58.938759451658[/C][/ROW]
[ROW][C]27[/C][C]748[/C][C]578.32238421892[/C][C]169.67761578108[/C][/ROW]
[ROW][C]28[/C][C]571[/C][C]643.940706462358[/C][C]-72.9407064623582[/C][/ROW]
[ROW][C]29[/C][C]475[/C][C]617.935700362764[/C][C]-142.935700362764[/C][/ROW]
[ROW][C]30[/C][C]758[/C][C]545.355070451244[/C][C]212.644929548756[/C][/ROW]
[ROW][C]31[/C][C]554[/C][C]624.531125247292[/C][C]-70.5311252472919[/C][/ROW]
[ROW][C]32[/C][C]597[/C][C]599.180558313361[/C][C]-2.18055831336073[/C][/ROW]
[ROW][C]33[/C][C]521[/C][C]595.88617592544[/C][C]-74.8861759254402[/C][/ROW]
[ROW][C]34[/C][C]597[/C][C]556.372209835283[/C][C]40.6277901647175[/C][/ROW]
[ROW][C]35[/C][C]658[/C][C]561.456300151684[/C][C]96.5436998483165[/C][/ROW]
[ROW][C]36[/C][C]482[/C][C]600.832412316593[/C][C]-118.832412316593[/C][/ROW]
[ROW][C]37[/C][C]567[/C][C]549.936158498295[/C][C]17.063841501705[/C][/ROW]
[ROW][C]38[/C][C]605[/C][C]546.428727045897[/C][C]58.5712729541031[/C][/ROW]
[ROW][C]39[/C][C]653[/C][C]566.213001238567[/C][C]86.7869987614334[/C][/ROW]
[ROW][C]40[/C][C]512[/C][C]609.592365321676[/C][C]-97.5923653216762[/C][/ROW]
[ROW][C]41[/C][C]653[/C][C]576.375045742367[/C][C]76.6249542576326[/C][/ROW]
[ROW][C]42[/C][C]498[/C][C]612.956810076965[/C][C]-114.956810076965[/C][/ROW]
[ROW][C]43[/C][C]520[/C][C]567.710329259562[/C][C]-47.7103292595617[/C][/ROW]
[ROW][C]44[/C][C]606[/C][C]536.63424312133[/C][C]69.3657568786699[/C][/ROW]
[ROW][C]45[/C][C]601[/C][C]555.417414967723[/C][C]45.5825850322773[/C][/ROW]
[ROW][C]46[/C][C]608[/C][C]573.932982533775[/C][C]34.0670174662255[/C][/ROW]
[ROW][C]47[/C][C]732[/C][C]594.301355905774[/C][C]137.698644094226[/C][/ROW]
[ROW][C]48[/C][C]585[/C][C]671.411542037597[/C][C]-86.411542037597[/C][/ROW]
[ROW][C]49[/C][C]800[/C][C]660.742375389263[/C][C]139.257624610737[/C][/ROW]
[ROW][C]50[/C][C]721[/C][C]747.09654391858[/C][C]-26.0965439185803[/C][/ROW]
[ROW][C]51[/C][C]689[/C][C]774.908125016904[/C][C]-85.908125016904[/C][/ROW]
[ROW][C]52[/C][C]689[/C][C]768.907548954808[/C][C]-79.9075489548085[/C][/ROW]
[ROW][C]53[/C][C]777[/C][C]751.670407136012[/C][C]25.3295928639881[/C][/ROW]
[ROW][C]54[/C][C]681[/C][C]773.132902840308[/C][C]-92.1329028403079[/C][/ROW]
[ROW][C]55[/C][C]836[/C][C]740.847193887936[/C][C]95.1528061120636[/C][/ROW]
[ROW][C]56[/C][C]594[/C][C]785.708213196946[/C][C]-191.708213196946[/C][/ROW]
[ROW][C]57[/C][C]662[/C][C]704.809841589113[/C][C]-42.8098415891128[/C][/ROW]
[ROW][C]58[/C][C]835[/C][C]665.670529413906[/C][C]169.329470586094[/C][/ROW]
[ROW][C]59[/C][C]702[/C][C]724.0865520207[/C][C]-22.0865520206995[/C][/ROW]
[ROW][C]60[/C][C]630[/C][C]716.075282451355[/C][C]-86.0752824513552[/C][/ROW]
[ROW][C]61[/C][C]857[/C][C]672.854279261209[/C][C]184.145720738791[/C][/ROW]
[ROW][C]62[/C][C]847[/C][C]748.685658411491[/C][C]98.3143415885091[/C][/ROW]
[ROW][C]63[/C][C]820[/C][C]812.613663790352[/C][C]7.38633620964811[/C][/ROW]
[ROW][C]64[/C][C]801[/C][C]847.941143204864[/C][C]-46.9411432048636[/C][/ROW]
[ROW][C]65[/C][C]900[/C][C]857.694256453785[/C][C]42.3057435462146[/C][/ROW]
[ROW][C]66[/C][C]763[/C][C]903.708050912725[/C][C]-140.708050912725[/C][/ROW]
[ROW][C]67[/C][C]897[/C][C]866.44825173842[/C][C]30.5517482615804[/C][/ROW]
[ROW][C]68[/C][C]687[/C][C]890.404085733352[/C][C]-203.404085733352[/C][/ROW]
[ROW][C]69[/C][C]682[/C][C]804.018802453264[/C][C]-122.018802453264[/C][/ROW]
[ROW][C]70[/C][C]844[/C][C]724.161626698882[/C][C]119.838373301118[/C][/ROW]
[ROW][C]71[/C][C]687[/C][C]743.427881879105[/C][C]-56.4278818791048[/C][/ROW]
[ROW][C]72[/C][C]671[/C][C]695.560595855711[/C][C]-24.5605958557109[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272003&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272003&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
33173152
4401281.98642313082119.01357686918
5285307.015791064883-22.0157910648832
6377282.15456240852994.8454375914712
7380311.29258464156968.7074153584313
8347343.2120215458043.78797845419564
9414354.46618306949859.5338169305024
10406393.84079154508812.1592084549115
11487419.68752097884467.3124790211559
12475474.7457624437290.254237556270994
13566507.85333537422858.1466646257723
14604569.55613505412334.4438649458768
15764629.17704184942134.82295815058
16725743.997847479038-18.9978474790375
17585805.231635256391-220.231635256391
18797764.07524112687832.9247588731215
19740811.385739298871-71.3857392988714
20587812.68983374871-225.68983374871
21719726.093035659168-7.09303565916809
22621710.01598271219-89.0159827121904
23677652.36147704359824.6385229564023
24636636.053002454967-0.0530024549672135
25591611.637840986131-20.6378409861312
26636577.06124054834258.938759451658
27748578.32238421892169.67761578108
28571643.940706462358-72.9407064623582
29475617.935700362764-142.935700362764
30758545.355070451244212.644929548756
31554624.531125247292-70.5311252472919
32597599.180558313361-2.18055831336073
33521595.88617592544-74.8861759254402
34597556.37220983528340.6277901647175
35658561.45630015168496.5436998483165
36482600.832412316593-118.832412316593
37567549.93615849829517.063841501705
38605546.42872704589758.5712729541031
39653566.21300123856786.7869987614334
40512609.592365321676-97.5923653216762
41653576.37504574236776.6249542576326
42498612.956810076965-114.956810076965
43520567.710329259562-47.7103292595617
44606536.6342431213369.3657568786699
45601555.41741496772345.5825850322773
46608573.93298253377534.0670174662255
47732594.301355905774137.698644094226
48585671.411542037597-86.411542037597
49800660.742375389263139.257624610737
50721747.09654391858-26.0965439185803
51689774.908125016904-85.908125016904
52689768.907548954808-79.9075489548085
53777751.67040713601225.3295928639881
54681773.132902840308-92.1329028403079
55836740.84719388793695.1528061120636
56594785.708213196946-191.708213196946
57662704.809841589113-42.8098415891128
58835665.670529413906169.329470586094
59702724.0865520207-22.0865520206995
60630716.075282451355-86.0752824513552
61857672.854279261209184.145720738791
62847748.68565841149198.3143415885091
63820812.6136637903527.38633620964811
64801847.941143204864-46.9411432048636
65900857.69425645378542.3057435462146
66763903.708050912725-140.708050912725
67897866.4482517384230.5517482615804
68687890.404085733352-203.404085733352
69682804.018802453264-122.018802453264
70844724.161626698882119.838373301118
71687743.427881879105-56.4278818791048
72671695.560595855711-24.5605958557109







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73654.086046686829462.425161109234845.746932264424
74620.666485700478406.961792293904834.371179107052
75587.246924714128339.060786621289835.433062806966
76553.827363727777259.684448241603847.970279213951
77520.407802741426170.483592447535870.332013035317
78486.98824175507673.0036719982695900.972811511882
79453.568680768725-31.5447472761797938.68210881363
80420.149119782374-142.264042729009982.562282293758
81386.729558796024-258.4913150793161031.95043267136
82353.309997809673-379.7285007855121086.34849640486
83319.890436823322-505.59192433211145.37279797874
84286.470875836972-635.7781202322041208.71987190615

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 654.086046686829 & 462.425161109234 & 845.746932264424 \tabularnewline
74 & 620.666485700478 & 406.961792293904 & 834.371179107052 \tabularnewline
75 & 587.246924714128 & 339.060786621289 & 835.433062806966 \tabularnewline
76 & 553.827363727777 & 259.684448241603 & 847.970279213951 \tabularnewline
77 & 520.407802741426 & 170.483592447535 & 870.332013035317 \tabularnewline
78 & 486.988241755076 & 73.0036719982695 & 900.972811511882 \tabularnewline
79 & 453.568680768725 & -31.5447472761797 & 938.68210881363 \tabularnewline
80 & 420.149119782374 & -142.264042729009 & 982.562282293758 \tabularnewline
81 & 386.729558796024 & -258.491315079316 & 1031.95043267136 \tabularnewline
82 & 353.309997809673 & -379.728500785512 & 1086.34849640486 \tabularnewline
83 & 319.890436823322 & -505.5919243321 & 1145.37279797874 \tabularnewline
84 & 286.470875836972 & -635.778120232204 & 1208.71987190615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272003&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]654.086046686829[/C][C]462.425161109234[/C][C]845.746932264424[/C][/ROW]
[ROW][C]74[/C][C]620.666485700478[/C][C]406.961792293904[/C][C]834.371179107052[/C][/ROW]
[ROW][C]75[/C][C]587.246924714128[/C][C]339.060786621289[/C][C]835.433062806966[/C][/ROW]
[ROW][C]76[/C][C]553.827363727777[/C][C]259.684448241603[/C][C]847.970279213951[/C][/ROW]
[ROW][C]77[/C][C]520.407802741426[/C][C]170.483592447535[/C][C]870.332013035317[/C][/ROW]
[ROW][C]78[/C][C]486.988241755076[/C][C]73.0036719982695[/C][C]900.972811511882[/C][/ROW]
[ROW][C]79[/C][C]453.568680768725[/C][C]-31.5447472761797[/C][C]938.68210881363[/C][/ROW]
[ROW][C]80[/C][C]420.149119782374[/C][C]-142.264042729009[/C][C]982.562282293758[/C][/ROW]
[ROW][C]81[/C][C]386.729558796024[/C][C]-258.491315079316[/C][C]1031.95043267136[/C][/ROW]
[ROW][C]82[/C][C]353.309997809673[/C][C]-379.728500785512[/C][C]1086.34849640486[/C][/ROW]
[ROW][C]83[/C][C]319.890436823322[/C][C]-505.5919243321[/C][C]1145.37279797874[/C][/ROW]
[ROW][C]84[/C][C]286.470875836972[/C][C]-635.778120232204[/C][C]1208.71987190615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272003&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272003&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
73654.086046686829462.425161109234845.746932264424
74620.666485700478406.961792293904834.371179107052
75587.246924714128339.060786621289835.433062806966
76553.827363727777259.684448241603847.970279213951
77520.407802741426170.483592447535870.332013035317
78486.98824175507673.0036719982695900.972811511882
79453.568680768725-31.5447472761797938.68210881363
80420.149119782374-142.264042729009982.562282293758
81386.729558796024-258.4913150793161031.95043267136
82353.309997809673-379.7285007855121086.34849640486
83319.890436823322-505.59192433211145.37279797874
84286.470875836972-635.7781202322041208.71987190615



Parameters (Session):
par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')