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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 computationFri, 09 Dec 2011 08:50:20 -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/09/t132343869029dxqysybgxbwiy.htm/, Retrieved Thu, 02 May 2024 15:44:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153365, Retrieved Thu, 02 May 2024 15:44:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Decomposition by Loess] [HPC Retail Sales] [2008-03-06 11:35:25] [74be16979710d4c4e7c6647856088456]
- RMPD  [Exponential Smoothing] [paper] [2011-12-06 14:39:17] [7e261c986c934df955dd3ac53e9d45c6]
- R P       [Exponential Smoothing] [paper Smoothin (3)] [2011-12-09 13:50:20] [13dfa60174f50d862e8699db2153bfc5] [Current]
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Dataseries X:
617
614
647
580
614
636
388
356
639
753
611
639
630
586
695
552
619
681
421
307
754
690
644
643
608
651
691
627
634
731
475
337
803
722
590
724
627
696
825
677
656
785
412
352
839
729
696
641
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
706
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858
775
785
1006
789
734
906
532
387
991
841
892
782
811
792
978
773
796
946
594
438
1023
868
791
760
779
852
1001
734
996
869
599
426
1138




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153365&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153365&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.148875008151242
beta0.00245473669165473
gamma0.366056540292939

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.148875008151242 \tabularnewline
beta & 0.00245473669165473 \tabularnewline
gamma & 0.366056540292939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153365&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]0.148875008151242[/C][/ROW]
[ROW][C]beta[/C][C]0.00245473669165473[/C][/ROW]
[ROW][C]gamma[/C][C]0.366056540292939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153365&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
alpha0.148875008151242
beta0.00245473669165473
gamma0.366056540292939







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13630622.5971556111677.4028443888327
14586581.8441567921764.15584320782409
15695688.8835217316416.11647826835872
16552546.8815547012655.11844529873485
17619616.5087136237772.49128637622334
18681678.1525506452572.84744935474339
19421393.83579934644527.1642006535546
20307366.112192997443-59.1121929974433
21754641.598115400468112.401884599532
22690776.087460839425-86.0874608394249
23644621.44723819704622.5527618029536
24643652.310556260995-9.31055626099544
25608641.767506733403-33.767506733403
26651593.11215073979857.8878492602016
27691712.030917145274-21.0309171452735
28627562.09208146264664.9079185373538
29634642.574418845687-8.5744188456872
30731705.01140486563225.9885951343684
31475419.6164003890255.3835996109798
32337365.623816805575-28.6238168055751
33803720.51944616348282.480553836518
34722791.4061122015-69.4061122015
35590666.506029371062-76.5060293710624
36724673.31699270253250.6830072974684
37627663.13559094086-36.1355909408603
38696641.64105632366954.3589436763314
39825739.5457055077385.4542944922697
40677623.33395174548953.6660482545109
41656682.422460214116-26.4224602141163
42785757.56462902435127.4353709756485
43412463.732912376803-51.7329123768027
44352365.331490495871-13.3314904958709
45839768.83221938481670.1677806151845
46729790.553225332901-61.5532253329008
47696660.78872309624235.2112769037579
48641726.846563253107-85.8465632531065
49695668.0531080136826.9468919863192
50638684.385757816045-46.3857578160449
51762778.104056985306-16.1040569853059
52635637.190939658401-2.19093965840102
53721662.4712126663558.5287873336499
54854767.08896331850586.9110366814948
55418453.034143253764-35.0341432537637
56367367.631183634147-0.631183634147135
57824808.73388190018215.266118099818
58687780.615801855966-93.6158018559664
59601675.577503589146-74.5775035891464
60676686.632075846258-10.6320758462579
61740674.12792374674365.8720762532572
62691673.17488638349717.825113616503
63683787.967758523234-104.967758523234
64594637.840555780448-43.8405557804483
65729675.22406442604953.7759355739513
66731786.546647710782-55.5466477107823
67386426.171484358408-40.1714843584076
68331353.351230470417-22.3512304704171
69706775.060851848366-69.060851848366
70715703.91715787717611.0828421228241
71657623.66235434752433.3376456524758
72653669.82687962768-16.8268796276795
73642679.630089728489-37.6300897284889
74643649.334634087946-6.33463408794591
75718718.003367461543-0.00336746154266621
76654605.74375946540148.2562405345985
77632686.451099274401-54.451099274401
78731745.227182696241-14.2271826962408
79392403.745161134142-11.7451611341419
80344341.4772081844592.5227918155411
81792750.56688364755441.4331163524456
82852720.16097531153131.83902468847
83649661.471675151065-12.4716751510647
84629685.978020038318-56.9780200383183
85685683.3399112044791.66008879552123
86617668.148069025357-51.1480690253574
87715733.660243694049-18.6602436940485
88715631.71548467853783.2845153214633
89629686.481595047169-57.4815950471688
90916759.293201142028156.706798857972
91531423.87318474272107.12681525728
92357377.921723369814-20.9217233698141
93917835.0646875576581.9353124423495
94828836.838047988683-8.83804798868266
95708703.6113303020634.38866969793685
96858717.45813648827140.54186351173
97775765.4068164856239.59318351437707
98785730.91718887560454.0828111243965
991006834.437798904381171.562201095619
100789779.5154392753029.48456072469787
101734778.990293191557-44.990293191557
102906943.964861495937-37.9648614959368
103532514.68153971134217.3184602886583
104387405.937518050068-18.9375180500682
105991941.60247494316849.3975250568323
106841906.886561570359-65.886561570359
107892759.427697219592132.572302780408
108782839.230688707677-57.2306887076767
109811816.07751781631-5.07751781630941
110792791.7656719804060.234328019594159
111978928.4859775675649.514022432441
112773801.653357524608-28.6533575246083
113796778.00234065491217.9976593450883
114946959.584054243603-13.5840542436027
115594537.48324698834856.516753011652
116438417.77819245945920.2218075405409
11710231013.653361996099.34663800391206
118868932.715411210144-64.7154112101445
119791842.131704356192-51.1317043561918
120760835.252368613981-75.252368613981
121779825.655241848995-46.6552418489947
122852796.64015093646355.3598490635368
1231001959.26193362951641.738066370484
124734804.475579753578-70.4755797535781
125996789.04630361056206.953696389439
126869996.115445703673-127.115445703673
127599568.69216322849130.3078367715092
128426431.317596990674-5.31759699067442
12911381024.70112078835113.298879211653

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 630 & 622.597155611167 & 7.4028443888327 \tabularnewline
14 & 586 & 581.844156792176 & 4.15584320782409 \tabularnewline
15 & 695 & 688.883521731641 & 6.11647826835872 \tabularnewline
16 & 552 & 546.881554701265 & 5.11844529873485 \tabularnewline
17 & 619 & 616.508713623777 & 2.49128637622334 \tabularnewline
18 & 681 & 678.152550645257 & 2.84744935474339 \tabularnewline
19 & 421 & 393.835799346445 & 27.1642006535546 \tabularnewline
20 & 307 & 366.112192997443 & -59.1121929974433 \tabularnewline
21 & 754 & 641.598115400468 & 112.401884599532 \tabularnewline
22 & 690 & 776.087460839425 & -86.0874608394249 \tabularnewline
23 & 644 & 621.447238197046 & 22.5527618029536 \tabularnewline
24 & 643 & 652.310556260995 & -9.31055626099544 \tabularnewline
25 & 608 & 641.767506733403 & -33.767506733403 \tabularnewline
26 & 651 & 593.112150739798 & 57.8878492602016 \tabularnewline
27 & 691 & 712.030917145274 & -21.0309171452735 \tabularnewline
28 & 627 & 562.092081462646 & 64.9079185373538 \tabularnewline
29 & 634 & 642.574418845687 & -8.5744188456872 \tabularnewline
30 & 731 & 705.011404865632 & 25.9885951343684 \tabularnewline
31 & 475 & 419.61640038902 & 55.3835996109798 \tabularnewline
32 & 337 & 365.623816805575 & -28.6238168055751 \tabularnewline
33 & 803 & 720.519446163482 & 82.480553836518 \tabularnewline
34 & 722 & 791.4061122015 & -69.4061122015 \tabularnewline
35 & 590 & 666.506029371062 & -76.5060293710624 \tabularnewline
36 & 724 & 673.316992702532 & 50.6830072974684 \tabularnewline
37 & 627 & 663.13559094086 & -36.1355909408603 \tabularnewline
38 & 696 & 641.641056323669 & 54.3589436763314 \tabularnewline
39 & 825 & 739.54570550773 & 85.4542944922697 \tabularnewline
40 & 677 & 623.333951745489 & 53.6660482545109 \tabularnewline
41 & 656 & 682.422460214116 & -26.4224602141163 \tabularnewline
42 & 785 & 757.564629024351 & 27.4353709756485 \tabularnewline
43 & 412 & 463.732912376803 & -51.7329123768027 \tabularnewline
44 & 352 & 365.331490495871 & -13.3314904958709 \tabularnewline
45 & 839 & 768.832219384816 & 70.1677806151845 \tabularnewline
46 & 729 & 790.553225332901 & -61.5532253329008 \tabularnewline
47 & 696 & 660.788723096242 & 35.2112769037579 \tabularnewline
48 & 641 & 726.846563253107 & -85.8465632531065 \tabularnewline
49 & 695 & 668.05310801368 & 26.9468919863192 \tabularnewline
50 & 638 & 684.385757816045 & -46.3857578160449 \tabularnewline
51 & 762 & 778.104056985306 & -16.1040569853059 \tabularnewline
52 & 635 & 637.190939658401 & -2.19093965840102 \tabularnewline
53 & 721 & 662.47121266635 & 58.5287873336499 \tabularnewline
54 & 854 & 767.088963318505 & 86.9110366814948 \tabularnewline
55 & 418 & 453.034143253764 & -35.0341432537637 \tabularnewline
56 & 367 & 367.631183634147 & -0.631183634147135 \tabularnewline
57 & 824 & 808.733881900182 & 15.266118099818 \tabularnewline
58 & 687 & 780.615801855966 & -93.6158018559664 \tabularnewline
59 & 601 & 675.577503589146 & -74.5775035891464 \tabularnewline
60 & 676 & 686.632075846258 & -10.6320758462579 \tabularnewline
61 & 740 & 674.127923746743 & 65.8720762532572 \tabularnewline
62 & 691 & 673.174886383497 & 17.825113616503 \tabularnewline
63 & 683 & 787.967758523234 & -104.967758523234 \tabularnewline
64 & 594 & 637.840555780448 & -43.8405557804483 \tabularnewline
65 & 729 & 675.224064426049 & 53.7759355739513 \tabularnewline
66 & 731 & 786.546647710782 & -55.5466477107823 \tabularnewline
67 & 386 & 426.171484358408 & -40.1714843584076 \tabularnewline
68 & 331 & 353.351230470417 & -22.3512304704171 \tabularnewline
69 & 706 & 775.060851848366 & -69.060851848366 \tabularnewline
70 & 715 & 703.917157877176 & 11.0828421228241 \tabularnewline
71 & 657 & 623.662354347524 & 33.3376456524758 \tabularnewline
72 & 653 & 669.82687962768 & -16.8268796276795 \tabularnewline
73 & 642 & 679.630089728489 & -37.6300897284889 \tabularnewline
74 & 643 & 649.334634087946 & -6.33463408794591 \tabularnewline
75 & 718 & 718.003367461543 & -0.00336746154266621 \tabularnewline
76 & 654 & 605.743759465401 & 48.2562405345985 \tabularnewline
77 & 632 & 686.451099274401 & -54.451099274401 \tabularnewline
78 & 731 & 745.227182696241 & -14.2271826962408 \tabularnewline
79 & 392 & 403.745161134142 & -11.7451611341419 \tabularnewline
80 & 344 & 341.477208184459 & 2.5227918155411 \tabularnewline
81 & 792 & 750.566883647554 & 41.4331163524456 \tabularnewline
82 & 852 & 720.16097531153 & 131.83902468847 \tabularnewline
83 & 649 & 661.471675151065 & -12.4716751510647 \tabularnewline
84 & 629 & 685.978020038318 & -56.9780200383183 \tabularnewline
85 & 685 & 683.339911204479 & 1.66008879552123 \tabularnewline
86 & 617 & 668.148069025357 & -51.1480690253574 \tabularnewline
87 & 715 & 733.660243694049 & -18.6602436940485 \tabularnewline
88 & 715 & 631.715484678537 & 83.2845153214633 \tabularnewline
89 & 629 & 686.481595047169 & -57.4815950471688 \tabularnewline
90 & 916 & 759.293201142028 & 156.706798857972 \tabularnewline
91 & 531 & 423.87318474272 & 107.12681525728 \tabularnewline
92 & 357 & 377.921723369814 & -20.9217233698141 \tabularnewline
93 & 917 & 835.06468755765 & 81.9353124423495 \tabularnewline
94 & 828 & 836.838047988683 & -8.83804798868266 \tabularnewline
95 & 708 & 703.611330302063 & 4.38866969793685 \tabularnewline
96 & 858 & 717.45813648827 & 140.54186351173 \tabularnewline
97 & 775 & 765.406816485623 & 9.59318351437707 \tabularnewline
98 & 785 & 730.917188875604 & 54.0828111243965 \tabularnewline
99 & 1006 & 834.437798904381 & 171.562201095619 \tabularnewline
100 & 789 & 779.515439275302 & 9.48456072469787 \tabularnewline
101 & 734 & 778.990293191557 & -44.990293191557 \tabularnewline
102 & 906 & 943.964861495937 & -37.9648614959368 \tabularnewline
103 & 532 & 514.681539711342 & 17.3184602886583 \tabularnewline
104 & 387 & 405.937518050068 & -18.9375180500682 \tabularnewline
105 & 991 & 941.602474943168 & 49.3975250568323 \tabularnewline
106 & 841 & 906.886561570359 & -65.886561570359 \tabularnewline
107 & 892 & 759.427697219592 & 132.572302780408 \tabularnewline
108 & 782 & 839.230688707677 & -57.2306887076767 \tabularnewline
109 & 811 & 816.07751781631 & -5.07751781630941 \tabularnewline
110 & 792 & 791.765671980406 & 0.234328019594159 \tabularnewline
111 & 978 & 928.48597756756 & 49.514022432441 \tabularnewline
112 & 773 & 801.653357524608 & -28.6533575246083 \tabularnewline
113 & 796 & 778.002340654912 & 17.9976593450883 \tabularnewline
114 & 946 & 959.584054243603 & -13.5840542436027 \tabularnewline
115 & 594 & 537.483246988348 & 56.516753011652 \tabularnewline
116 & 438 & 417.778192459459 & 20.2218075405409 \tabularnewline
117 & 1023 & 1013.65336199609 & 9.34663800391206 \tabularnewline
118 & 868 & 932.715411210144 & -64.7154112101445 \tabularnewline
119 & 791 & 842.131704356192 & -51.1317043561918 \tabularnewline
120 & 760 & 835.252368613981 & -75.252368613981 \tabularnewline
121 & 779 & 825.655241848995 & -46.6552418489947 \tabularnewline
122 & 852 & 796.640150936463 & 55.3598490635368 \tabularnewline
123 & 1001 & 959.261933629516 & 41.738066370484 \tabularnewline
124 & 734 & 804.475579753578 & -70.4755797535781 \tabularnewline
125 & 996 & 789.04630361056 & 206.953696389439 \tabularnewline
126 & 869 & 996.115445703673 & -127.115445703673 \tabularnewline
127 & 599 & 568.692163228491 & 30.3078367715092 \tabularnewline
128 & 426 & 431.317596990674 & -5.31759699067442 \tabularnewline
129 & 1138 & 1024.70112078835 & 113.298879211653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153365&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]630[/C][C]622.597155611167[/C][C]7.4028443888327[/C][/ROW]
[ROW][C]14[/C][C]586[/C][C]581.844156792176[/C][C]4.15584320782409[/C][/ROW]
[ROW][C]15[/C][C]695[/C][C]688.883521731641[/C][C]6.11647826835872[/C][/ROW]
[ROW][C]16[/C][C]552[/C][C]546.881554701265[/C][C]5.11844529873485[/C][/ROW]
[ROW][C]17[/C][C]619[/C][C]616.508713623777[/C][C]2.49128637622334[/C][/ROW]
[ROW][C]18[/C][C]681[/C][C]678.152550645257[/C][C]2.84744935474339[/C][/ROW]
[ROW][C]19[/C][C]421[/C][C]393.835799346445[/C][C]27.1642006535546[/C][/ROW]
[ROW][C]20[/C][C]307[/C][C]366.112192997443[/C][C]-59.1121929974433[/C][/ROW]
[ROW][C]21[/C][C]754[/C][C]641.598115400468[/C][C]112.401884599532[/C][/ROW]
[ROW][C]22[/C][C]690[/C][C]776.087460839425[/C][C]-86.0874608394249[/C][/ROW]
[ROW][C]23[/C][C]644[/C][C]621.447238197046[/C][C]22.5527618029536[/C][/ROW]
[ROW][C]24[/C][C]643[/C][C]652.310556260995[/C][C]-9.31055626099544[/C][/ROW]
[ROW][C]25[/C][C]608[/C][C]641.767506733403[/C][C]-33.767506733403[/C][/ROW]
[ROW][C]26[/C][C]651[/C][C]593.112150739798[/C][C]57.8878492602016[/C][/ROW]
[ROW][C]27[/C][C]691[/C][C]712.030917145274[/C][C]-21.0309171452735[/C][/ROW]
[ROW][C]28[/C][C]627[/C][C]562.092081462646[/C][C]64.9079185373538[/C][/ROW]
[ROW][C]29[/C][C]634[/C][C]642.574418845687[/C][C]-8.5744188456872[/C][/ROW]
[ROW][C]30[/C][C]731[/C][C]705.011404865632[/C][C]25.9885951343684[/C][/ROW]
[ROW][C]31[/C][C]475[/C][C]419.61640038902[/C][C]55.3835996109798[/C][/ROW]
[ROW][C]32[/C][C]337[/C][C]365.623816805575[/C][C]-28.6238168055751[/C][/ROW]
[ROW][C]33[/C][C]803[/C][C]720.519446163482[/C][C]82.480553836518[/C][/ROW]
[ROW][C]34[/C][C]722[/C][C]791.4061122015[/C][C]-69.4061122015[/C][/ROW]
[ROW][C]35[/C][C]590[/C][C]666.506029371062[/C][C]-76.5060293710624[/C][/ROW]
[ROW][C]36[/C][C]724[/C][C]673.316992702532[/C][C]50.6830072974684[/C][/ROW]
[ROW][C]37[/C][C]627[/C][C]663.13559094086[/C][C]-36.1355909408603[/C][/ROW]
[ROW][C]38[/C][C]696[/C][C]641.641056323669[/C][C]54.3589436763314[/C][/ROW]
[ROW][C]39[/C][C]825[/C][C]739.54570550773[/C][C]85.4542944922697[/C][/ROW]
[ROW][C]40[/C][C]677[/C][C]623.333951745489[/C][C]53.6660482545109[/C][/ROW]
[ROW][C]41[/C][C]656[/C][C]682.422460214116[/C][C]-26.4224602141163[/C][/ROW]
[ROW][C]42[/C][C]785[/C][C]757.564629024351[/C][C]27.4353709756485[/C][/ROW]
[ROW][C]43[/C][C]412[/C][C]463.732912376803[/C][C]-51.7329123768027[/C][/ROW]
[ROW][C]44[/C][C]352[/C][C]365.331490495871[/C][C]-13.3314904958709[/C][/ROW]
[ROW][C]45[/C][C]839[/C][C]768.832219384816[/C][C]70.1677806151845[/C][/ROW]
[ROW][C]46[/C][C]729[/C][C]790.553225332901[/C][C]-61.5532253329008[/C][/ROW]
[ROW][C]47[/C][C]696[/C][C]660.788723096242[/C][C]35.2112769037579[/C][/ROW]
[ROW][C]48[/C][C]641[/C][C]726.846563253107[/C][C]-85.8465632531065[/C][/ROW]
[ROW][C]49[/C][C]695[/C][C]668.05310801368[/C][C]26.9468919863192[/C][/ROW]
[ROW][C]50[/C][C]638[/C][C]684.385757816045[/C][C]-46.3857578160449[/C][/ROW]
[ROW][C]51[/C][C]762[/C][C]778.104056985306[/C][C]-16.1040569853059[/C][/ROW]
[ROW][C]52[/C][C]635[/C][C]637.190939658401[/C][C]-2.19093965840102[/C][/ROW]
[ROW][C]53[/C][C]721[/C][C]662.47121266635[/C][C]58.5287873336499[/C][/ROW]
[ROW][C]54[/C][C]854[/C][C]767.088963318505[/C][C]86.9110366814948[/C][/ROW]
[ROW][C]55[/C][C]418[/C][C]453.034143253764[/C][C]-35.0341432537637[/C][/ROW]
[ROW][C]56[/C][C]367[/C][C]367.631183634147[/C][C]-0.631183634147135[/C][/ROW]
[ROW][C]57[/C][C]824[/C][C]808.733881900182[/C][C]15.266118099818[/C][/ROW]
[ROW][C]58[/C][C]687[/C][C]780.615801855966[/C][C]-93.6158018559664[/C][/ROW]
[ROW][C]59[/C][C]601[/C][C]675.577503589146[/C][C]-74.5775035891464[/C][/ROW]
[ROW][C]60[/C][C]676[/C][C]686.632075846258[/C][C]-10.6320758462579[/C][/ROW]
[ROW][C]61[/C][C]740[/C][C]674.127923746743[/C][C]65.8720762532572[/C][/ROW]
[ROW][C]62[/C][C]691[/C][C]673.174886383497[/C][C]17.825113616503[/C][/ROW]
[ROW][C]63[/C][C]683[/C][C]787.967758523234[/C][C]-104.967758523234[/C][/ROW]
[ROW][C]64[/C][C]594[/C][C]637.840555780448[/C][C]-43.8405557804483[/C][/ROW]
[ROW][C]65[/C][C]729[/C][C]675.224064426049[/C][C]53.7759355739513[/C][/ROW]
[ROW][C]66[/C][C]731[/C][C]786.546647710782[/C][C]-55.5466477107823[/C][/ROW]
[ROW][C]67[/C][C]386[/C][C]426.171484358408[/C][C]-40.1714843584076[/C][/ROW]
[ROW][C]68[/C][C]331[/C][C]353.351230470417[/C][C]-22.3512304704171[/C][/ROW]
[ROW][C]69[/C][C]706[/C][C]775.060851848366[/C][C]-69.060851848366[/C][/ROW]
[ROW][C]70[/C][C]715[/C][C]703.917157877176[/C][C]11.0828421228241[/C][/ROW]
[ROW][C]71[/C][C]657[/C][C]623.662354347524[/C][C]33.3376456524758[/C][/ROW]
[ROW][C]72[/C][C]653[/C][C]669.82687962768[/C][C]-16.8268796276795[/C][/ROW]
[ROW][C]73[/C][C]642[/C][C]679.630089728489[/C][C]-37.6300897284889[/C][/ROW]
[ROW][C]74[/C][C]643[/C][C]649.334634087946[/C][C]-6.33463408794591[/C][/ROW]
[ROW][C]75[/C][C]718[/C][C]718.003367461543[/C][C]-0.00336746154266621[/C][/ROW]
[ROW][C]76[/C][C]654[/C][C]605.743759465401[/C][C]48.2562405345985[/C][/ROW]
[ROW][C]77[/C][C]632[/C][C]686.451099274401[/C][C]-54.451099274401[/C][/ROW]
[ROW][C]78[/C][C]731[/C][C]745.227182696241[/C][C]-14.2271826962408[/C][/ROW]
[ROW][C]79[/C][C]392[/C][C]403.745161134142[/C][C]-11.7451611341419[/C][/ROW]
[ROW][C]80[/C][C]344[/C][C]341.477208184459[/C][C]2.5227918155411[/C][/ROW]
[ROW][C]81[/C][C]792[/C][C]750.566883647554[/C][C]41.4331163524456[/C][/ROW]
[ROW][C]82[/C][C]852[/C][C]720.16097531153[/C][C]131.83902468847[/C][/ROW]
[ROW][C]83[/C][C]649[/C][C]661.471675151065[/C][C]-12.4716751510647[/C][/ROW]
[ROW][C]84[/C][C]629[/C][C]685.978020038318[/C][C]-56.9780200383183[/C][/ROW]
[ROW][C]85[/C][C]685[/C][C]683.339911204479[/C][C]1.66008879552123[/C][/ROW]
[ROW][C]86[/C][C]617[/C][C]668.148069025357[/C][C]-51.1480690253574[/C][/ROW]
[ROW][C]87[/C][C]715[/C][C]733.660243694049[/C][C]-18.6602436940485[/C][/ROW]
[ROW][C]88[/C][C]715[/C][C]631.715484678537[/C][C]83.2845153214633[/C][/ROW]
[ROW][C]89[/C][C]629[/C][C]686.481595047169[/C][C]-57.4815950471688[/C][/ROW]
[ROW][C]90[/C][C]916[/C][C]759.293201142028[/C][C]156.706798857972[/C][/ROW]
[ROW][C]91[/C][C]531[/C][C]423.87318474272[/C][C]107.12681525728[/C][/ROW]
[ROW][C]92[/C][C]357[/C][C]377.921723369814[/C][C]-20.9217233698141[/C][/ROW]
[ROW][C]93[/C][C]917[/C][C]835.06468755765[/C][C]81.9353124423495[/C][/ROW]
[ROW][C]94[/C][C]828[/C][C]836.838047988683[/C][C]-8.83804798868266[/C][/ROW]
[ROW][C]95[/C][C]708[/C][C]703.611330302063[/C][C]4.38866969793685[/C][/ROW]
[ROW][C]96[/C][C]858[/C][C]717.45813648827[/C][C]140.54186351173[/C][/ROW]
[ROW][C]97[/C][C]775[/C][C]765.406816485623[/C][C]9.59318351437707[/C][/ROW]
[ROW][C]98[/C][C]785[/C][C]730.917188875604[/C][C]54.0828111243965[/C][/ROW]
[ROW][C]99[/C][C]1006[/C][C]834.437798904381[/C][C]171.562201095619[/C][/ROW]
[ROW][C]100[/C][C]789[/C][C]779.515439275302[/C][C]9.48456072469787[/C][/ROW]
[ROW][C]101[/C][C]734[/C][C]778.990293191557[/C][C]-44.990293191557[/C][/ROW]
[ROW][C]102[/C][C]906[/C][C]943.964861495937[/C][C]-37.9648614959368[/C][/ROW]
[ROW][C]103[/C][C]532[/C][C]514.681539711342[/C][C]17.3184602886583[/C][/ROW]
[ROW][C]104[/C][C]387[/C][C]405.937518050068[/C][C]-18.9375180500682[/C][/ROW]
[ROW][C]105[/C][C]991[/C][C]941.602474943168[/C][C]49.3975250568323[/C][/ROW]
[ROW][C]106[/C][C]841[/C][C]906.886561570359[/C][C]-65.886561570359[/C][/ROW]
[ROW][C]107[/C][C]892[/C][C]759.427697219592[/C][C]132.572302780408[/C][/ROW]
[ROW][C]108[/C][C]782[/C][C]839.230688707677[/C][C]-57.2306887076767[/C][/ROW]
[ROW][C]109[/C][C]811[/C][C]816.07751781631[/C][C]-5.07751781630941[/C][/ROW]
[ROW][C]110[/C][C]792[/C][C]791.765671980406[/C][C]0.234328019594159[/C][/ROW]
[ROW][C]111[/C][C]978[/C][C]928.48597756756[/C][C]49.514022432441[/C][/ROW]
[ROW][C]112[/C][C]773[/C][C]801.653357524608[/C][C]-28.6533575246083[/C][/ROW]
[ROW][C]113[/C][C]796[/C][C]778.002340654912[/C][C]17.9976593450883[/C][/ROW]
[ROW][C]114[/C][C]946[/C][C]959.584054243603[/C][C]-13.5840542436027[/C][/ROW]
[ROW][C]115[/C][C]594[/C][C]537.483246988348[/C][C]56.516753011652[/C][/ROW]
[ROW][C]116[/C][C]438[/C][C]417.778192459459[/C][C]20.2218075405409[/C][/ROW]
[ROW][C]117[/C][C]1023[/C][C]1013.65336199609[/C][C]9.34663800391206[/C][/ROW]
[ROW][C]118[/C][C]868[/C][C]932.715411210144[/C][C]-64.7154112101445[/C][/ROW]
[ROW][C]119[/C][C]791[/C][C]842.131704356192[/C][C]-51.1317043561918[/C][/ROW]
[ROW][C]120[/C][C]760[/C][C]835.252368613981[/C][C]-75.252368613981[/C][/ROW]
[ROW][C]121[/C][C]779[/C][C]825.655241848995[/C][C]-46.6552418489947[/C][/ROW]
[ROW][C]122[/C][C]852[/C][C]796.640150936463[/C][C]55.3598490635368[/C][/ROW]
[ROW][C]123[/C][C]1001[/C][C]959.261933629516[/C][C]41.738066370484[/C][/ROW]
[ROW][C]124[/C][C]734[/C][C]804.475579753578[/C][C]-70.4755797535781[/C][/ROW]
[ROW][C]125[/C][C]996[/C][C]789.04630361056[/C][C]206.953696389439[/C][/ROW]
[ROW][C]126[/C][C]869[/C][C]996.115445703673[/C][C]-127.115445703673[/C][/ROW]
[ROW][C]127[/C][C]599[/C][C]568.692163228491[/C][C]30.3078367715092[/C][/ROW]
[ROW][C]128[/C][C]426[/C][C]431.317596990674[/C][C]-5.31759699067442[/C][/ROW]
[ROW][C]129[/C][C]1138[/C][C]1024.70112078835[/C][C]113.298879211653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153365&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153365&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
13630622.5971556111677.4028443888327
14586581.8441567921764.15584320782409
15695688.8835217316416.11647826835872
16552546.8815547012655.11844529873485
17619616.5087136237772.49128637622334
18681678.1525506452572.84744935474339
19421393.83579934644527.1642006535546
20307366.112192997443-59.1121929974433
21754641.598115400468112.401884599532
22690776.087460839425-86.0874608394249
23644621.44723819704622.5527618029536
24643652.310556260995-9.31055626099544
25608641.767506733403-33.767506733403
26651593.11215073979857.8878492602016
27691712.030917145274-21.0309171452735
28627562.09208146264664.9079185373538
29634642.574418845687-8.5744188456872
30731705.01140486563225.9885951343684
31475419.6164003890255.3835996109798
32337365.623816805575-28.6238168055751
33803720.51944616348282.480553836518
34722791.4061122015-69.4061122015
35590666.506029371062-76.5060293710624
36724673.31699270253250.6830072974684
37627663.13559094086-36.1355909408603
38696641.64105632366954.3589436763314
39825739.5457055077385.4542944922697
40677623.33395174548953.6660482545109
41656682.422460214116-26.4224602141163
42785757.56462902435127.4353709756485
43412463.732912376803-51.7329123768027
44352365.331490495871-13.3314904958709
45839768.83221938481670.1677806151845
46729790.553225332901-61.5532253329008
47696660.78872309624235.2112769037579
48641726.846563253107-85.8465632531065
49695668.0531080136826.9468919863192
50638684.385757816045-46.3857578160449
51762778.104056985306-16.1040569853059
52635637.190939658401-2.19093965840102
53721662.4712126663558.5287873336499
54854767.08896331850586.9110366814948
55418453.034143253764-35.0341432537637
56367367.631183634147-0.631183634147135
57824808.73388190018215.266118099818
58687780.615801855966-93.6158018559664
59601675.577503589146-74.5775035891464
60676686.632075846258-10.6320758462579
61740674.12792374674365.8720762532572
62691673.17488638349717.825113616503
63683787.967758523234-104.967758523234
64594637.840555780448-43.8405557804483
65729675.22406442604953.7759355739513
66731786.546647710782-55.5466477107823
67386426.171484358408-40.1714843584076
68331353.351230470417-22.3512304704171
69706775.060851848366-69.060851848366
70715703.91715787717611.0828421228241
71657623.66235434752433.3376456524758
72653669.82687962768-16.8268796276795
73642679.630089728489-37.6300897284889
74643649.334634087946-6.33463408794591
75718718.003367461543-0.00336746154266621
76654605.74375946540148.2562405345985
77632686.451099274401-54.451099274401
78731745.227182696241-14.2271826962408
79392403.745161134142-11.7451611341419
80344341.4772081844592.5227918155411
81792750.56688364755441.4331163524456
82852720.16097531153131.83902468847
83649661.471675151065-12.4716751510647
84629685.978020038318-56.9780200383183
85685683.3399112044791.66008879552123
86617668.148069025357-51.1480690253574
87715733.660243694049-18.6602436940485
88715631.71548467853783.2845153214633
89629686.481595047169-57.4815950471688
90916759.293201142028156.706798857972
91531423.87318474272107.12681525728
92357377.921723369814-20.9217233698141
93917835.0646875576581.9353124423495
94828836.838047988683-8.83804798868266
95708703.6113303020634.38866969793685
96858717.45813648827140.54186351173
97775765.4068164856239.59318351437707
98785730.91718887560454.0828111243965
991006834.437798904381171.562201095619
100789779.5154392753029.48456072469787
101734778.990293191557-44.990293191557
102906943.964861495937-37.9648614959368
103532514.68153971134217.3184602886583
104387405.937518050068-18.9375180500682
105991941.60247494316849.3975250568323
106841906.886561570359-65.886561570359
107892759.427697219592132.572302780408
108782839.230688707677-57.2306887076767
109811816.07751781631-5.07751781630941
110792791.7656719804060.234328019594159
111978928.4859775675649.514022432441
112773801.653357524608-28.6533575246083
113796778.00234065491217.9976593450883
114946959.584054243603-13.5840542436027
115594537.48324698834856.516753011652
116438417.77819245945920.2218075405409
11710231013.653361996099.34663800391206
118868932.715411210144-64.7154112101445
119791842.131704356192-51.1317043561918
120760835.252368613981-75.252368613981
121779825.655241848995-46.6552418489947
122852796.64015093646355.3598490635368
1231001959.26193362951641.738066370484
124734804.475579753578-70.4755797535781
125996789.04630361056206.953696389439
126869996.115445703673-127.115445703673
127599568.69216322849130.3078367715092
128426431.317596990674-5.31759699067442
12911381024.70112078835113.298879211653







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
130933.478961807411878.696118849487988.261804765335
131853.999454762674796.86617874393911.132730781419
132846.582434285923786.841672953041906.323195618804
133857.572538775262795.064200816093920.080876734432
134867.750906572797802.541223254005932.96058989159
1351026.12919030151954.065699634771098.19268096825
136820.315549731638752.453506388079888.177593075198
137904.341765387895831.293907732564977.389623043227
138977.339613681664899.2381878669191055.44103949641
139602.562796442921536.984841946268668.140750939574
140444.336205877929382.048214317885506.624197437973
1411097.6187750373996.5742078129371198.66334226165

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
130 & 933.478961807411 & 878.696118849487 & 988.261804765335 \tabularnewline
131 & 853.999454762674 & 796.86617874393 & 911.132730781419 \tabularnewline
132 & 846.582434285923 & 786.841672953041 & 906.323195618804 \tabularnewline
133 & 857.572538775262 & 795.064200816093 & 920.080876734432 \tabularnewline
134 & 867.750906572797 & 802.541223254005 & 932.96058989159 \tabularnewline
135 & 1026.12919030151 & 954.06569963477 & 1098.19268096825 \tabularnewline
136 & 820.315549731638 & 752.453506388079 & 888.177593075198 \tabularnewline
137 & 904.341765387895 & 831.293907732564 & 977.389623043227 \tabularnewline
138 & 977.339613681664 & 899.238187866919 & 1055.44103949641 \tabularnewline
139 & 602.562796442921 & 536.984841946268 & 668.140750939574 \tabularnewline
140 & 444.336205877929 & 382.048214317885 & 506.624197437973 \tabularnewline
141 & 1097.6187750373 & 996.574207812937 & 1198.66334226165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153365&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]130[/C][C]933.478961807411[/C][C]878.696118849487[/C][C]988.261804765335[/C][/ROW]
[ROW][C]131[/C][C]853.999454762674[/C][C]796.86617874393[/C][C]911.132730781419[/C][/ROW]
[ROW][C]132[/C][C]846.582434285923[/C][C]786.841672953041[/C][C]906.323195618804[/C][/ROW]
[ROW][C]133[/C][C]857.572538775262[/C][C]795.064200816093[/C][C]920.080876734432[/C][/ROW]
[ROW][C]134[/C][C]867.750906572797[/C][C]802.541223254005[/C][C]932.96058989159[/C][/ROW]
[ROW][C]135[/C][C]1026.12919030151[/C][C]954.06569963477[/C][C]1098.19268096825[/C][/ROW]
[ROW][C]136[/C][C]820.315549731638[/C][C]752.453506388079[/C][C]888.177593075198[/C][/ROW]
[ROW][C]137[/C][C]904.341765387895[/C][C]831.293907732564[/C][C]977.389623043227[/C][/ROW]
[ROW][C]138[/C][C]977.339613681664[/C][C]899.238187866919[/C][C]1055.44103949641[/C][/ROW]
[ROW][C]139[/C][C]602.562796442921[/C][C]536.984841946268[/C][C]668.140750939574[/C][/ROW]
[ROW][C]140[/C][C]444.336205877929[/C][C]382.048214317885[/C][C]506.624197437973[/C][/ROW]
[ROW][C]141[/C][C]1097.6187750373[/C][C]996.574207812937[/C][C]1198.66334226165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153365&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153365&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
130933.478961807411878.696118849487988.261804765335
131853.999454762674796.86617874393911.132730781419
132846.582434285923786.841672953041906.323195618804
133857.572538775262795.064200816093920.080876734432
134867.750906572797802.541223254005932.96058989159
1351026.12919030151954.065699634771098.19268096825
136820.315549731638752.453506388079888.177593075198
137904.341765387895831.293907732564977.389623043227
138977.339613681664899.2381878669191055.44103949641
139602.562796442921536.984841946268668.140750939574
140444.336205877929382.048214317885506.624197437973
1411097.6187750373996.5742078129371198.66334226165



Parameters (Session):
par1 = 12 ;
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')