Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Dec 2012 03:54:52 -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/2012/Dec/18/t13558209012tls1gjo89rlt3f.htm/, Retrieved Fri, 19 Apr 2024 05:19:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201283, Retrieved Fri, 19 Apr 2024 05:19:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
-  MPD  [Multiple Regression] [] [2012-11-10 21:11:43] [391561951b5d7f721cfaa4f5575ab127]
- RMP     [Exponential Smoothing] [] [2012-11-10 22:13:06] [391561951b5d7f721cfaa4f5575ab127]
- R P       [Exponential Smoothing] [] [2012-11-10 22:23:12] [391561951b5d7f721cfaa4f5575ab127]
-               [Exponential Smoothing] [] [2012-12-18 08:54:52] [7338cd26db379c04f0557b08db763c32] [Current]
Feedback Forum

Post a new message
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
1091
830
909




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201283&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201283&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.151461747160508
beta0.0130427200103942
gamma0.411395508330862

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.151461747160508 \tabularnewline
beta & 0.0130427200103942 \tabularnewline
gamma & 0.411395508330862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201283&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]0.151461747160508[/C][/ROW]
[ROW][C]beta[/C][C]0.0130427200103942[/C][/ROW]
[ROW][C]gamma[/C][C]0.411395508330862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201283&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
alpha0.151461747160508
beta0.0130427200103942
gamma0.411395508330862







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13630622.7414529914537.25854700854688
14586581.5941120069414.40588799305851
15695689.6067393507035.39326064929708
16552546.362903457075.63709654292973
17619616.5838019734982.41619802650212
18681678.5299640408862.47003595911406
19421396.98915998535424.0108400146464
20307370.425063183991-63.4250631839909
21754644.034143876249109.965856123751
22690775.122550745969-85.122550745969
23644622.28603601275521.7139639872448
24643652.632395147972-9.63239514797181
25608642.579133375207-34.5791333752071
26651594.06608296717356.9339170328266
27691710.450060607724-19.4500606077236
28627563.55014039910163.4498596008993
29634641.538910897884-7.53891089788351
30731702.11219940840728.8878005915932
31475432.26058218656142.739417813439
32337378.215937474415-41.2159374744148
33803715.96619957087387.0338004291269
34722775.68278256634-53.6827825663403
35590665.169212499472-75.1692124994725
36724669.97356432433854.0264356756625
37627661.054035023088-34.0540350230882
38696644.76775401539951.2322459846011
39825733.81381538602191.1861846139793
40677633.0188736435343.9811263564699
41656683.648028497491-27.6480284974909
42785754.22209743288930.7779025671114
43412489.826411863353-77.8264118633532
44352388.309204917751-36.3092049177511
45839771.67846940021267.3215305997882
46729779.354215312366-50.3542153123658
47696661.9176263177734.0823736822305
48641728.658895299873-87.6588952998731
49695667.54124756584527.4587524341553
50638690.47480935382-52.4748093538202
51762777.686524115126-15.6865241151263
52635643.940752951343-8.94075295134348
53721661.15993800945959.8400619905406
54854765.16386388841888.8361361115821
55418471.547506030353-53.5475060303531
56367388.14645827814-21.1464582781402
57824809.96397645959314.0360235404074
58687768.360685353665-81.3606853536647
59601675.512577999539-74.5125779995392
60676682.902553571871-6.90255357187129
61740673.95647583708566.0435241629153
62691674.66103362190616.3389663780938
63683785.104047552285-102.104047552285
64594640.419870478895-46.4198704788954
65729675.6943995537853.30560044622
66731788.539443135078-57.5394431350778
67386422.468403530654-36.4684035306544
68331352.418228055126-21.4182280551265
69706785.92904463628-79.9290446362796
70715696.05926173547718.9407382645231
71657620.25886149439836.7411385056021
72653667.786239567656-14.7862395676563
73642682.779966428273-40.7799664282727
74643649.41223045958-6.41223045958031
75718714.4761907636153.52380923638486
76654604.85130097095449.148699029046
77632689.224460638992-57.2244606389916
78731746.22675557852-15.2267555785204
79392393.596287588733-1.59628758873299
80344333.82681837431610.1731816256845
81792751.50482159370840.4951784062916
82852714.434072433297137.565927566703
83649663.094470687955-14.0944706879545
84629685.114118839537-56.1141188395374
85685684.8719412349280.128058765071501
86617669.875978017188-52.8759780171881
87715731.457707393615-16.4577073936148
88715634.78059470987180.2194052901291
89629686.835157080812-57.8351570808125
90916758.513145180141157.486854819859
91531437.24899177825793.7510082217433
92357396.666509563253-39.6665095632533
93917817.91917394868899.080826051312
94828824.2620881863093.73791181369131
95708700.1001972673247.89980273267633
96858711.21604366433146.78395633567
97775762.17260222198212.8273977780181
98785731.45643375736253.5435662426377
991006822.939183480501183.060816519499
100789791.693616137035-2.69361613703518
101734784.297090177805-50.2970901778048
102906933.597160961274-27.5971609612737
103532562.999720612548-30.999720612548
104387457.650880734783-70.6508807347831
105991923.28661547587367.7133845241267
106841892.175259918581-51.1752599185813
107892761.619959853569130.380040146431
108782840.482166819464-58.4821668194642
109811813.893999338186-2.89399933818572
110792795.286421503453-3.28642150345263
111978923.53822696192254.4617730380776
112773807.880844284195-34.8808442841949
113796778.83802331430917.1619766856908
114946946.259515887327-0.259515887327211
115594578.64865868839315.3513413116068
116438466.603936191577-28.6039361915771
1171023987.11742555601635.8825744439844
118868909.828202733059-41.8282027330587
119791844.230794034079-53.2307940340789
120760829.155303797136-69.1553037971361
121779820.135716782185-41.135716782185
122852795.30361417460356.6963858253969
1231001952.62265448108148.3773455189191
124734804.666657762128-70.6666577621279
125996788.111416132637207.888583867363
126869978.456292529227-109.456292529227
127599599.657276192243-0.657276192242989
128426469.713577600937-43.7135776009368
12911381010.28978539866127.710214601344
1301091919.802676095642171.197323904358
131830882.93223228537-52.9322322853702
132909862.78576584876546.2142341512351

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 630 & 622.741452991453 & 7.25854700854688 \tabularnewline
14 & 586 & 581.594112006941 & 4.40588799305851 \tabularnewline
15 & 695 & 689.606739350703 & 5.39326064929708 \tabularnewline
16 & 552 & 546.36290345707 & 5.63709654292973 \tabularnewline
17 & 619 & 616.583801973498 & 2.41619802650212 \tabularnewline
18 & 681 & 678.529964040886 & 2.47003595911406 \tabularnewline
19 & 421 & 396.989159985354 & 24.0108400146464 \tabularnewline
20 & 307 & 370.425063183991 & -63.4250631839909 \tabularnewline
21 & 754 & 644.034143876249 & 109.965856123751 \tabularnewline
22 & 690 & 775.122550745969 & -85.122550745969 \tabularnewline
23 & 644 & 622.286036012755 & 21.7139639872448 \tabularnewline
24 & 643 & 652.632395147972 & -9.63239514797181 \tabularnewline
25 & 608 & 642.579133375207 & -34.5791333752071 \tabularnewline
26 & 651 & 594.066082967173 & 56.9339170328266 \tabularnewline
27 & 691 & 710.450060607724 & -19.4500606077236 \tabularnewline
28 & 627 & 563.550140399101 & 63.4498596008993 \tabularnewline
29 & 634 & 641.538910897884 & -7.53891089788351 \tabularnewline
30 & 731 & 702.112199408407 & 28.8878005915932 \tabularnewline
31 & 475 & 432.260582186561 & 42.739417813439 \tabularnewline
32 & 337 & 378.215937474415 & -41.2159374744148 \tabularnewline
33 & 803 & 715.966199570873 & 87.0338004291269 \tabularnewline
34 & 722 & 775.68278256634 & -53.6827825663403 \tabularnewline
35 & 590 & 665.169212499472 & -75.1692124994725 \tabularnewline
36 & 724 & 669.973564324338 & 54.0264356756625 \tabularnewline
37 & 627 & 661.054035023088 & -34.0540350230882 \tabularnewline
38 & 696 & 644.767754015399 & 51.2322459846011 \tabularnewline
39 & 825 & 733.813815386021 & 91.1861846139793 \tabularnewline
40 & 677 & 633.01887364353 & 43.9811263564699 \tabularnewline
41 & 656 & 683.648028497491 & -27.6480284974909 \tabularnewline
42 & 785 & 754.222097432889 & 30.7779025671114 \tabularnewline
43 & 412 & 489.826411863353 & -77.8264118633532 \tabularnewline
44 & 352 & 388.309204917751 & -36.3092049177511 \tabularnewline
45 & 839 & 771.678469400212 & 67.3215305997882 \tabularnewline
46 & 729 & 779.354215312366 & -50.3542153123658 \tabularnewline
47 & 696 & 661.91762631777 & 34.0823736822305 \tabularnewline
48 & 641 & 728.658895299873 & -87.6588952998731 \tabularnewline
49 & 695 & 667.541247565845 & 27.4587524341553 \tabularnewline
50 & 638 & 690.47480935382 & -52.4748093538202 \tabularnewline
51 & 762 & 777.686524115126 & -15.6865241151263 \tabularnewline
52 & 635 & 643.940752951343 & -8.94075295134348 \tabularnewline
53 & 721 & 661.159938009459 & 59.8400619905406 \tabularnewline
54 & 854 & 765.163863888418 & 88.8361361115821 \tabularnewline
55 & 418 & 471.547506030353 & -53.5475060303531 \tabularnewline
56 & 367 & 388.14645827814 & -21.1464582781402 \tabularnewline
57 & 824 & 809.963976459593 & 14.0360235404074 \tabularnewline
58 & 687 & 768.360685353665 & -81.3606853536647 \tabularnewline
59 & 601 & 675.512577999539 & -74.5125779995392 \tabularnewline
60 & 676 & 682.902553571871 & -6.90255357187129 \tabularnewline
61 & 740 & 673.956475837085 & 66.0435241629153 \tabularnewline
62 & 691 & 674.661033621906 & 16.3389663780938 \tabularnewline
63 & 683 & 785.104047552285 & -102.104047552285 \tabularnewline
64 & 594 & 640.419870478895 & -46.4198704788954 \tabularnewline
65 & 729 & 675.69439955378 & 53.30560044622 \tabularnewline
66 & 731 & 788.539443135078 & -57.5394431350778 \tabularnewline
67 & 386 & 422.468403530654 & -36.4684035306544 \tabularnewline
68 & 331 & 352.418228055126 & -21.4182280551265 \tabularnewline
69 & 706 & 785.92904463628 & -79.9290446362796 \tabularnewline
70 & 715 & 696.059261735477 & 18.9407382645231 \tabularnewline
71 & 657 & 620.258861494398 & 36.7411385056021 \tabularnewline
72 & 653 & 667.786239567656 & -14.7862395676563 \tabularnewline
73 & 642 & 682.779966428273 & -40.7799664282727 \tabularnewline
74 & 643 & 649.41223045958 & -6.41223045958031 \tabularnewline
75 & 718 & 714.476190763615 & 3.52380923638486 \tabularnewline
76 & 654 & 604.851300970954 & 49.148699029046 \tabularnewline
77 & 632 & 689.224460638992 & -57.2244606389916 \tabularnewline
78 & 731 & 746.22675557852 & -15.2267555785204 \tabularnewline
79 & 392 & 393.596287588733 & -1.59628758873299 \tabularnewline
80 & 344 & 333.826818374316 & 10.1731816256845 \tabularnewline
81 & 792 & 751.504821593708 & 40.4951784062916 \tabularnewline
82 & 852 & 714.434072433297 & 137.565927566703 \tabularnewline
83 & 649 & 663.094470687955 & -14.0944706879545 \tabularnewline
84 & 629 & 685.114118839537 & -56.1141188395374 \tabularnewline
85 & 685 & 684.871941234928 & 0.128058765071501 \tabularnewline
86 & 617 & 669.875978017188 & -52.8759780171881 \tabularnewline
87 & 715 & 731.457707393615 & -16.4577073936148 \tabularnewline
88 & 715 & 634.780594709871 & 80.2194052901291 \tabularnewline
89 & 629 & 686.835157080812 & -57.8351570808125 \tabularnewline
90 & 916 & 758.513145180141 & 157.486854819859 \tabularnewline
91 & 531 & 437.248991778257 & 93.7510082217433 \tabularnewline
92 & 357 & 396.666509563253 & -39.6665095632533 \tabularnewline
93 & 917 & 817.919173948688 & 99.080826051312 \tabularnewline
94 & 828 & 824.262088186309 & 3.73791181369131 \tabularnewline
95 & 708 & 700.100197267324 & 7.89980273267633 \tabularnewline
96 & 858 & 711.21604366433 & 146.78395633567 \tabularnewline
97 & 775 & 762.172602221982 & 12.8273977780181 \tabularnewline
98 & 785 & 731.456433757362 & 53.5435662426377 \tabularnewline
99 & 1006 & 822.939183480501 & 183.060816519499 \tabularnewline
100 & 789 & 791.693616137035 & -2.69361613703518 \tabularnewline
101 & 734 & 784.297090177805 & -50.2970901778048 \tabularnewline
102 & 906 & 933.597160961274 & -27.5971609612737 \tabularnewline
103 & 532 & 562.999720612548 & -30.999720612548 \tabularnewline
104 & 387 & 457.650880734783 & -70.6508807347831 \tabularnewline
105 & 991 & 923.286615475873 & 67.7133845241267 \tabularnewline
106 & 841 & 892.175259918581 & -51.1752599185813 \tabularnewline
107 & 892 & 761.619959853569 & 130.380040146431 \tabularnewline
108 & 782 & 840.482166819464 & -58.4821668194642 \tabularnewline
109 & 811 & 813.893999338186 & -2.89399933818572 \tabularnewline
110 & 792 & 795.286421503453 & -3.28642150345263 \tabularnewline
111 & 978 & 923.538226961922 & 54.4617730380776 \tabularnewline
112 & 773 & 807.880844284195 & -34.8808442841949 \tabularnewline
113 & 796 & 778.838023314309 & 17.1619766856908 \tabularnewline
114 & 946 & 946.259515887327 & -0.259515887327211 \tabularnewline
115 & 594 & 578.648658688393 & 15.3513413116068 \tabularnewline
116 & 438 & 466.603936191577 & -28.6039361915771 \tabularnewline
117 & 1023 & 987.117425556016 & 35.8825744439844 \tabularnewline
118 & 868 & 909.828202733059 & -41.8282027330587 \tabularnewline
119 & 791 & 844.230794034079 & -53.2307940340789 \tabularnewline
120 & 760 & 829.155303797136 & -69.1553037971361 \tabularnewline
121 & 779 & 820.135716782185 & -41.135716782185 \tabularnewline
122 & 852 & 795.303614174603 & 56.6963858253969 \tabularnewline
123 & 1001 & 952.622654481081 & 48.3773455189191 \tabularnewline
124 & 734 & 804.666657762128 & -70.6666577621279 \tabularnewline
125 & 996 & 788.111416132637 & 207.888583867363 \tabularnewline
126 & 869 & 978.456292529227 & -109.456292529227 \tabularnewline
127 & 599 & 599.657276192243 & -0.657276192242989 \tabularnewline
128 & 426 & 469.713577600937 & -43.7135776009368 \tabularnewline
129 & 1138 & 1010.28978539866 & 127.710214601344 \tabularnewline
130 & 1091 & 919.802676095642 & 171.197323904358 \tabularnewline
131 & 830 & 882.93223228537 & -52.9322322853702 \tabularnewline
132 & 909 & 862.785765848765 & 46.2142341512351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201283&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]622.741452991453[/C][C]7.25854700854688[/C][/ROW]
[ROW][C]14[/C][C]586[/C][C]581.594112006941[/C][C]4.40588799305851[/C][/ROW]
[ROW][C]15[/C][C]695[/C][C]689.606739350703[/C][C]5.39326064929708[/C][/ROW]
[ROW][C]16[/C][C]552[/C][C]546.36290345707[/C][C]5.63709654292973[/C][/ROW]
[ROW][C]17[/C][C]619[/C][C]616.583801973498[/C][C]2.41619802650212[/C][/ROW]
[ROW][C]18[/C][C]681[/C][C]678.529964040886[/C][C]2.47003595911406[/C][/ROW]
[ROW][C]19[/C][C]421[/C][C]396.989159985354[/C][C]24.0108400146464[/C][/ROW]
[ROW][C]20[/C][C]307[/C][C]370.425063183991[/C][C]-63.4250631839909[/C][/ROW]
[ROW][C]21[/C][C]754[/C][C]644.034143876249[/C][C]109.965856123751[/C][/ROW]
[ROW][C]22[/C][C]690[/C][C]775.122550745969[/C][C]-85.122550745969[/C][/ROW]
[ROW][C]23[/C][C]644[/C][C]622.286036012755[/C][C]21.7139639872448[/C][/ROW]
[ROW][C]24[/C][C]643[/C][C]652.632395147972[/C][C]-9.63239514797181[/C][/ROW]
[ROW][C]25[/C][C]608[/C][C]642.579133375207[/C][C]-34.5791333752071[/C][/ROW]
[ROW][C]26[/C][C]651[/C][C]594.066082967173[/C][C]56.9339170328266[/C][/ROW]
[ROW][C]27[/C][C]691[/C][C]710.450060607724[/C][C]-19.4500606077236[/C][/ROW]
[ROW][C]28[/C][C]627[/C][C]563.550140399101[/C][C]63.4498596008993[/C][/ROW]
[ROW][C]29[/C][C]634[/C][C]641.538910897884[/C][C]-7.53891089788351[/C][/ROW]
[ROW][C]30[/C][C]731[/C][C]702.112199408407[/C][C]28.8878005915932[/C][/ROW]
[ROW][C]31[/C][C]475[/C][C]432.260582186561[/C][C]42.739417813439[/C][/ROW]
[ROW][C]32[/C][C]337[/C][C]378.215937474415[/C][C]-41.2159374744148[/C][/ROW]
[ROW][C]33[/C][C]803[/C][C]715.966199570873[/C][C]87.0338004291269[/C][/ROW]
[ROW][C]34[/C][C]722[/C][C]775.68278256634[/C][C]-53.6827825663403[/C][/ROW]
[ROW][C]35[/C][C]590[/C][C]665.169212499472[/C][C]-75.1692124994725[/C][/ROW]
[ROW][C]36[/C][C]724[/C][C]669.973564324338[/C][C]54.0264356756625[/C][/ROW]
[ROW][C]37[/C][C]627[/C][C]661.054035023088[/C][C]-34.0540350230882[/C][/ROW]
[ROW][C]38[/C][C]696[/C][C]644.767754015399[/C][C]51.2322459846011[/C][/ROW]
[ROW][C]39[/C][C]825[/C][C]733.813815386021[/C][C]91.1861846139793[/C][/ROW]
[ROW][C]40[/C][C]677[/C][C]633.01887364353[/C][C]43.9811263564699[/C][/ROW]
[ROW][C]41[/C][C]656[/C][C]683.648028497491[/C][C]-27.6480284974909[/C][/ROW]
[ROW][C]42[/C][C]785[/C][C]754.222097432889[/C][C]30.7779025671114[/C][/ROW]
[ROW][C]43[/C][C]412[/C][C]489.826411863353[/C][C]-77.8264118633532[/C][/ROW]
[ROW][C]44[/C][C]352[/C][C]388.309204917751[/C][C]-36.3092049177511[/C][/ROW]
[ROW][C]45[/C][C]839[/C][C]771.678469400212[/C][C]67.3215305997882[/C][/ROW]
[ROW][C]46[/C][C]729[/C][C]779.354215312366[/C][C]-50.3542153123658[/C][/ROW]
[ROW][C]47[/C][C]696[/C][C]661.91762631777[/C][C]34.0823736822305[/C][/ROW]
[ROW][C]48[/C][C]641[/C][C]728.658895299873[/C][C]-87.6588952998731[/C][/ROW]
[ROW][C]49[/C][C]695[/C][C]667.541247565845[/C][C]27.4587524341553[/C][/ROW]
[ROW][C]50[/C][C]638[/C][C]690.47480935382[/C][C]-52.4748093538202[/C][/ROW]
[ROW][C]51[/C][C]762[/C][C]777.686524115126[/C][C]-15.6865241151263[/C][/ROW]
[ROW][C]52[/C][C]635[/C][C]643.940752951343[/C][C]-8.94075295134348[/C][/ROW]
[ROW][C]53[/C][C]721[/C][C]661.159938009459[/C][C]59.8400619905406[/C][/ROW]
[ROW][C]54[/C][C]854[/C][C]765.163863888418[/C][C]88.8361361115821[/C][/ROW]
[ROW][C]55[/C][C]418[/C][C]471.547506030353[/C][C]-53.5475060303531[/C][/ROW]
[ROW][C]56[/C][C]367[/C][C]388.14645827814[/C][C]-21.1464582781402[/C][/ROW]
[ROW][C]57[/C][C]824[/C][C]809.963976459593[/C][C]14.0360235404074[/C][/ROW]
[ROW][C]58[/C][C]687[/C][C]768.360685353665[/C][C]-81.3606853536647[/C][/ROW]
[ROW][C]59[/C][C]601[/C][C]675.512577999539[/C][C]-74.5125779995392[/C][/ROW]
[ROW][C]60[/C][C]676[/C][C]682.902553571871[/C][C]-6.90255357187129[/C][/ROW]
[ROW][C]61[/C][C]740[/C][C]673.956475837085[/C][C]66.0435241629153[/C][/ROW]
[ROW][C]62[/C][C]691[/C][C]674.661033621906[/C][C]16.3389663780938[/C][/ROW]
[ROW][C]63[/C][C]683[/C][C]785.104047552285[/C][C]-102.104047552285[/C][/ROW]
[ROW][C]64[/C][C]594[/C][C]640.419870478895[/C][C]-46.4198704788954[/C][/ROW]
[ROW][C]65[/C][C]729[/C][C]675.69439955378[/C][C]53.30560044622[/C][/ROW]
[ROW][C]66[/C][C]731[/C][C]788.539443135078[/C][C]-57.5394431350778[/C][/ROW]
[ROW][C]67[/C][C]386[/C][C]422.468403530654[/C][C]-36.4684035306544[/C][/ROW]
[ROW][C]68[/C][C]331[/C][C]352.418228055126[/C][C]-21.4182280551265[/C][/ROW]
[ROW][C]69[/C][C]706[/C][C]785.92904463628[/C][C]-79.9290446362796[/C][/ROW]
[ROW][C]70[/C][C]715[/C][C]696.059261735477[/C][C]18.9407382645231[/C][/ROW]
[ROW][C]71[/C][C]657[/C][C]620.258861494398[/C][C]36.7411385056021[/C][/ROW]
[ROW][C]72[/C][C]653[/C][C]667.786239567656[/C][C]-14.7862395676563[/C][/ROW]
[ROW][C]73[/C][C]642[/C][C]682.779966428273[/C][C]-40.7799664282727[/C][/ROW]
[ROW][C]74[/C][C]643[/C][C]649.41223045958[/C][C]-6.41223045958031[/C][/ROW]
[ROW][C]75[/C][C]718[/C][C]714.476190763615[/C][C]3.52380923638486[/C][/ROW]
[ROW][C]76[/C][C]654[/C][C]604.851300970954[/C][C]49.148699029046[/C][/ROW]
[ROW][C]77[/C][C]632[/C][C]689.224460638992[/C][C]-57.2244606389916[/C][/ROW]
[ROW][C]78[/C][C]731[/C][C]746.22675557852[/C][C]-15.2267555785204[/C][/ROW]
[ROW][C]79[/C][C]392[/C][C]393.596287588733[/C][C]-1.59628758873299[/C][/ROW]
[ROW][C]80[/C][C]344[/C][C]333.826818374316[/C][C]10.1731816256845[/C][/ROW]
[ROW][C]81[/C][C]792[/C][C]751.504821593708[/C][C]40.4951784062916[/C][/ROW]
[ROW][C]82[/C][C]852[/C][C]714.434072433297[/C][C]137.565927566703[/C][/ROW]
[ROW][C]83[/C][C]649[/C][C]663.094470687955[/C][C]-14.0944706879545[/C][/ROW]
[ROW][C]84[/C][C]629[/C][C]685.114118839537[/C][C]-56.1141188395374[/C][/ROW]
[ROW][C]85[/C][C]685[/C][C]684.871941234928[/C][C]0.128058765071501[/C][/ROW]
[ROW][C]86[/C][C]617[/C][C]669.875978017188[/C][C]-52.8759780171881[/C][/ROW]
[ROW][C]87[/C][C]715[/C][C]731.457707393615[/C][C]-16.4577073936148[/C][/ROW]
[ROW][C]88[/C][C]715[/C][C]634.780594709871[/C][C]80.2194052901291[/C][/ROW]
[ROW][C]89[/C][C]629[/C][C]686.835157080812[/C][C]-57.8351570808125[/C][/ROW]
[ROW][C]90[/C][C]916[/C][C]758.513145180141[/C][C]157.486854819859[/C][/ROW]
[ROW][C]91[/C][C]531[/C][C]437.248991778257[/C][C]93.7510082217433[/C][/ROW]
[ROW][C]92[/C][C]357[/C][C]396.666509563253[/C][C]-39.6665095632533[/C][/ROW]
[ROW][C]93[/C][C]917[/C][C]817.919173948688[/C][C]99.080826051312[/C][/ROW]
[ROW][C]94[/C][C]828[/C][C]824.262088186309[/C][C]3.73791181369131[/C][/ROW]
[ROW][C]95[/C][C]708[/C][C]700.100197267324[/C][C]7.89980273267633[/C][/ROW]
[ROW][C]96[/C][C]858[/C][C]711.21604366433[/C][C]146.78395633567[/C][/ROW]
[ROW][C]97[/C][C]775[/C][C]762.172602221982[/C][C]12.8273977780181[/C][/ROW]
[ROW][C]98[/C][C]785[/C][C]731.456433757362[/C][C]53.5435662426377[/C][/ROW]
[ROW][C]99[/C][C]1006[/C][C]822.939183480501[/C][C]183.060816519499[/C][/ROW]
[ROW][C]100[/C][C]789[/C][C]791.693616137035[/C][C]-2.69361613703518[/C][/ROW]
[ROW][C]101[/C][C]734[/C][C]784.297090177805[/C][C]-50.2970901778048[/C][/ROW]
[ROW][C]102[/C][C]906[/C][C]933.597160961274[/C][C]-27.5971609612737[/C][/ROW]
[ROW][C]103[/C][C]532[/C][C]562.999720612548[/C][C]-30.999720612548[/C][/ROW]
[ROW][C]104[/C][C]387[/C][C]457.650880734783[/C][C]-70.6508807347831[/C][/ROW]
[ROW][C]105[/C][C]991[/C][C]923.286615475873[/C][C]67.7133845241267[/C][/ROW]
[ROW][C]106[/C][C]841[/C][C]892.175259918581[/C][C]-51.1752599185813[/C][/ROW]
[ROW][C]107[/C][C]892[/C][C]761.619959853569[/C][C]130.380040146431[/C][/ROW]
[ROW][C]108[/C][C]782[/C][C]840.482166819464[/C][C]-58.4821668194642[/C][/ROW]
[ROW][C]109[/C][C]811[/C][C]813.893999338186[/C][C]-2.89399933818572[/C][/ROW]
[ROW][C]110[/C][C]792[/C][C]795.286421503453[/C][C]-3.28642150345263[/C][/ROW]
[ROW][C]111[/C][C]978[/C][C]923.538226961922[/C][C]54.4617730380776[/C][/ROW]
[ROW][C]112[/C][C]773[/C][C]807.880844284195[/C][C]-34.8808442841949[/C][/ROW]
[ROW][C]113[/C][C]796[/C][C]778.838023314309[/C][C]17.1619766856908[/C][/ROW]
[ROW][C]114[/C][C]946[/C][C]946.259515887327[/C][C]-0.259515887327211[/C][/ROW]
[ROW][C]115[/C][C]594[/C][C]578.648658688393[/C][C]15.3513413116068[/C][/ROW]
[ROW][C]116[/C][C]438[/C][C]466.603936191577[/C][C]-28.6039361915771[/C][/ROW]
[ROW][C]117[/C][C]1023[/C][C]987.117425556016[/C][C]35.8825744439844[/C][/ROW]
[ROW][C]118[/C][C]868[/C][C]909.828202733059[/C][C]-41.8282027330587[/C][/ROW]
[ROW][C]119[/C][C]791[/C][C]844.230794034079[/C][C]-53.2307940340789[/C][/ROW]
[ROW][C]120[/C][C]760[/C][C]829.155303797136[/C][C]-69.1553037971361[/C][/ROW]
[ROW][C]121[/C][C]779[/C][C]820.135716782185[/C][C]-41.135716782185[/C][/ROW]
[ROW][C]122[/C][C]852[/C][C]795.303614174603[/C][C]56.6963858253969[/C][/ROW]
[ROW][C]123[/C][C]1001[/C][C]952.622654481081[/C][C]48.3773455189191[/C][/ROW]
[ROW][C]124[/C][C]734[/C][C]804.666657762128[/C][C]-70.6666577621279[/C][/ROW]
[ROW][C]125[/C][C]996[/C][C]788.111416132637[/C][C]207.888583867363[/C][/ROW]
[ROW][C]126[/C][C]869[/C][C]978.456292529227[/C][C]-109.456292529227[/C][/ROW]
[ROW][C]127[/C][C]599[/C][C]599.657276192243[/C][C]-0.657276192242989[/C][/ROW]
[ROW][C]128[/C][C]426[/C][C]469.713577600937[/C][C]-43.7135776009368[/C][/ROW]
[ROW][C]129[/C][C]1138[/C][C]1010.28978539866[/C][C]127.710214601344[/C][/ROW]
[ROW][C]130[/C][C]1091[/C][C]919.802676095642[/C][C]171.197323904358[/C][/ROW]
[ROW][C]131[/C][C]830[/C][C]882.93223228537[/C][C]-52.9322322853702[/C][/ROW]
[ROW][C]132[/C][C]909[/C][C]862.785765848765[/C][C]46.2142341512351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201283&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
13630622.7414529914537.25854700854688
14586581.5941120069414.40588799305851
15695689.6067393507035.39326064929708
16552546.362903457075.63709654292973
17619616.5838019734982.41619802650212
18681678.5299640408862.47003595911406
19421396.98915998535424.0108400146464
20307370.425063183991-63.4250631839909
21754644.034143876249109.965856123751
22690775.122550745969-85.122550745969
23644622.28603601275521.7139639872448
24643652.632395147972-9.63239514797181
25608642.579133375207-34.5791333752071
26651594.06608296717356.9339170328266
27691710.450060607724-19.4500606077236
28627563.55014039910163.4498596008993
29634641.538910897884-7.53891089788351
30731702.11219940840728.8878005915932
31475432.26058218656142.739417813439
32337378.215937474415-41.2159374744148
33803715.96619957087387.0338004291269
34722775.68278256634-53.6827825663403
35590665.169212499472-75.1692124994725
36724669.97356432433854.0264356756625
37627661.054035023088-34.0540350230882
38696644.76775401539951.2322459846011
39825733.81381538602191.1861846139793
40677633.0188736435343.9811263564699
41656683.648028497491-27.6480284974909
42785754.22209743288930.7779025671114
43412489.826411863353-77.8264118633532
44352388.309204917751-36.3092049177511
45839771.67846940021267.3215305997882
46729779.354215312366-50.3542153123658
47696661.9176263177734.0823736822305
48641728.658895299873-87.6588952998731
49695667.54124756584527.4587524341553
50638690.47480935382-52.4748093538202
51762777.686524115126-15.6865241151263
52635643.940752951343-8.94075295134348
53721661.15993800945959.8400619905406
54854765.16386388841888.8361361115821
55418471.547506030353-53.5475060303531
56367388.14645827814-21.1464582781402
57824809.96397645959314.0360235404074
58687768.360685353665-81.3606853536647
59601675.512577999539-74.5125779995392
60676682.902553571871-6.90255357187129
61740673.95647583708566.0435241629153
62691674.66103362190616.3389663780938
63683785.104047552285-102.104047552285
64594640.419870478895-46.4198704788954
65729675.6943995537853.30560044622
66731788.539443135078-57.5394431350778
67386422.468403530654-36.4684035306544
68331352.418228055126-21.4182280551265
69706785.92904463628-79.9290446362796
70715696.05926173547718.9407382645231
71657620.25886149439836.7411385056021
72653667.786239567656-14.7862395676563
73642682.779966428273-40.7799664282727
74643649.41223045958-6.41223045958031
75718714.4761907636153.52380923638486
76654604.85130097095449.148699029046
77632689.224460638992-57.2244606389916
78731746.22675557852-15.2267555785204
79392393.596287588733-1.59628758873299
80344333.82681837431610.1731816256845
81792751.50482159370840.4951784062916
82852714.434072433297137.565927566703
83649663.094470687955-14.0944706879545
84629685.114118839537-56.1141188395374
85685684.8719412349280.128058765071501
86617669.875978017188-52.8759780171881
87715731.457707393615-16.4577073936148
88715634.78059470987180.2194052901291
89629686.835157080812-57.8351570808125
90916758.513145180141157.486854819859
91531437.24899177825793.7510082217433
92357396.666509563253-39.6665095632533
93917817.91917394868899.080826051312
94828824.2620881863093.73791181369131
95708700.1001972673247.89980273267633
96858711.21604366433146.78395633567
97775762.17260222198212.8273977780181
98785731.45643375736253.5435662426377
991006822.939183480501183.060816519499
100789791.693616137035-2.69361613703518
101734784.297090177805-50.2970901778048
102906933.597160961274-27.5971609612737
103532562.999720612548-30.999720612548
104387457.650880734783-70.6508807347831
105991923.28661547587367.7133845241267
106841892.175259918581-51.1752599185813
107892761.619959853569130.380040146431
108782840.482166819464-58.4821668194642
109811813.893999338186-2.89399933818572
110792795.286421503453-3.28642150345263
111978923.53822696192254.4617730380776
112773807.880844284195-34.8808442841949
113796778.83802331430917.1619766856908
114946946.259515887327-0.259515887327211
115594578.64865868839315.3513413116068
116438466.603936191577-28.6039361915771
1171023987.11742555601635.8825744439844
118868909.828202733059-41.8282027330587
119791844.230794034079-53.2307940340789
120760829.155303797136-69.1553037971361
121779820.135716782185-41.135716782185
122852795.30361417460356.6963858253969
1231001952.62265448108148.3773455189191
124734804.666657762128-70.6666577621279
125996788.111416132637207.888583867363
126869978.456292529227-109.456292529227
127599599.657276192243-0.657276192242989
128426469.713577600937-43.7135776009368
12911381010.28978539866127.710214601344
1301091919.802676095642171.197323904358
131830882.93223228537-52.9322322853702
132909862.78576584876546.2142341512351







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133881.692180534123757.5933071837661005.79105388448
134897.994247727917772.4430440133641023.54545144247
1351044.46188121841917.4379646289561171.48579780787
136848.166521496448719.649742582394976.683300410502
137940.23799284931810.2084339586841070.26755173994
138988.588751398412857.0267251323671120.15077766446
139664.837821201911531.723868615359797.951773788463
140520.454230926883385.769119499474655.139342354292
1411128.07003080752991.7947522087071264.34530940634
1421033.74532374268895.8610914131991171.62955607217
143892.691535825937753.1797823967321032.20328925514
144915.26409972274774.1064742909261056.42172515455

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 881.692180534123 & 757.593307183766 & 1005.79105388448 \tabularnewline
134 & 897.994247727917 & 772.443044013364 & 1023.54545144247 \tabularnewline
135 & 1044.46188121841 & 917.437964628956 & 1171.48579780787 \tabularnewline
136 & 848.166521496448 & 719.649742582394 & 976.683300410502 \tabularnewline
137 & 940.23799284931 & 810.208433958684 & 1070.26755173994 \tabularnewline
138 & 988.588751398412 & 857.026725132367 & 1120.15077766446 \tabularnewline
139 & 664.837821201911 & 531.723868615359 & 797.951773788463 \tabularnewline
140 & 520.454230926883 & 385.769119499474 & 655.139342354292 \tabularnewline
141 & 1128.07003080752 & 991.794752208707 & 1264.34530940634 \tabularnewline
142 & 1033.74532374268 & 895.861091413199 & 1171.62955607217 \tabularnewline
143 & 892.691535825937 & 753.179782396732 & 1032.20328925514 \tabularnewline
144 & 915.26409972274 & 774.106474290926 & 1056.42172515455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201283&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]133[/C][C]881.692180534123[/C][C]757.593307183766[/C][C]1005.79105388448[/C][/ROW]
[ROW][C]134[/C][C]897.994247727917[/C][C]772.443044013364[/C][C]1023.54545144247[/C][/ROW]
[ROW][C]135[/C][C]1044.46188121841[/C][C]917.437964628956[/C][C]1171.48579780787[/C][/ROW]
[ROW][C]136[/C][C]848.166521496448[/C][C]719.649742582394[/C][C]976.683300410502[/C][/ROW]
[ROW][C]137[/C][C]940.23799284931[/C][C]810.208433958684[/C][C]1070.26755173994[/C][/ROW]
[ROW][C]138[/C][C]988.588751398412[/C][C]857.026725132367[/C][C]1120.15077766446[/C][/ROW]
[ROW][C]139[/C][C]664.837821201911[/C][C]531.723868615359[/C][C]797.951773788463[/C][/ROW]
[ROW][C]140[/C][C]520.454230926883[/C][C]385.769119499474[/C][C]655.139342354292[/C][/ROW]
[ROW][C]141[/C][C]1128.07003080752[/C][C]991.794752208707[/C][C]1264.34530940634[/C][/ROW]
[ROW][C]142[/C][C]1033.74532374268[/C][C]895.861091413199[/C][C]1171.62955607217[/C][/ROW]
[ROW][C]143[/C][C]892.691535825937[/C][C]753.179782396732[/C][C]1032.20328925514[/C][/ROW]
[ROW][C]144[/C][C]915.26409972274[/C][C]774.106474290926[/C][C]1056.42172515455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201283&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
133881.692180534123757.5933071837661005.79105388448
134897.994247727917772.4430440133641023.54545144247
1351044.46188121841917.4379646289561171.48579780787
136848.166521496448719.649742582394976.683300410502
137940.23799284931810.2084339586841070.26755173994
138988.588751398412857.0267251323671120.15077766446
139664.837821201911531.723868615359797.951773788463
140520.454230926883385.769119499474655.139342354292
1411128.07003080752991.7947522087071264.34530940634
1421033.74532374268895.8610914131991171.62955607217
143892.691535825937753.1797823967321032.20328925514
144915.26409972274774.1064742909261056.42172515455



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')