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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Aug 2013 08:21:39 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/21/t1377087754h0y0ocxtboinb01.htm/, Retrieved Sat, 27 Apr 2024 17:07:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211334, Retrieved Sat, 27 Apr 2024 17:07:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJoris Claus
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2013-08-21 12:21:39] [5b48cba8ffed7710e2defc0d8d22bd89] [Current]
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Dataseries X:
580
610
550
515
555
580
585
545
580
605
625
600
590
605
475
535
560
610
585
560
590
625
620
615
560
665
495
555
545
605
610
610
550
600
660
590
555
650
530
565
580
630
605
595
565
585
685
585
520
670
525
565
575
610
605
575
565
575
720
580
565
675
525
575
560
585
550
560
605
585
685
585
555
660
530
575
580
615
570
550
635
580
690
575
590
685
540
580
615
605
565
555
625
605
685
540
610
680
560
575
590
625
520
590
625
560
715
575




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211334&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211334&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma0.809499765629382

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.809499765629382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211334&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.809499765629382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211334&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
beta0
gamma0.809499765629382







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13590589.0811965811970.918803418803122
14605603.8378982128981.16210178710162
15475473.1779331779341.82206682206646
16535532.3096348096352.69036519036501
17560557.0663364413372.93366355866328
18610607.0313714063722.9686285936283
19585584.704739704740.29526029526005
20560544.87810800310815.1218919968918
21590583.5931429681436.40685703185682
22625611.26651126651113.7334887334886
23620630.606546231546-10.6065462315464
24615604.52991452991510.4700854700852
25560594.405387313797-34.4053873137968
26665609.35903891761455.640961082386
27495479.23331542377715.7666845762232
28555539.06790438111215.9320956188876
29545564.021555984929-19.0215559849295
30605614.014895137574-9.01489513757394
31610589.52417242497220.475827575028
32610561.69969561088448.3003043891157
33550593.359911814272-43.3599118142716
34600626.964186757964-26.9641867579636
35660626.60096912339233.3990308766082
36590617.585865844488-27.5858658444878
37555571.13465392731-16.1346539273096
38650658.980803453618-8.98080345361848
39530496.57686247340133.4231375265987
40565556.5453516310068.45464836899373
41580553.20403045364226.7959695463577
42630611.29775921695418.7022407830462
43605610.679769628444-5.67976962844421
44595605.379200274121-10.3792002741206
45565562.8404929433272.15950705667251
46585609.717103477425-24.7171034774245
47685658.21789637067426.782103629326
48585599.835533489111-14.8355334891107
49520562.654074935061-42.6540749350606
50670656.2912647431713.7087352568299
51525528.213304048201-3.21330404820094
52565567.969807084605-2.96980708460489
53575579.47578110165-4.47578110165034
54610631.017638327993-21.0176383279934
55605610.662417025809-5.66241702580919
56575601.557659665219-26.5576596652189
57565569.169032979998-4.16903297999829
58575594.289033585832-19.2890335858316
59720684.47842256209535.5215774379053
60580592.406592187108-12.4065921871081
61565532.7060308524132.2939691475897
62675671.9689023010693.03109769893149
63525530.192554754706-5.19255475470572
64575570.1461685260724.85383147392781
65560580.433056929275-20.4330569292754
66585618.584284607819-33.584284607819
67550610.65911135094-60.6591113509402
68560584.639659970979-24.6396599709788
69605570.37462134020834.6253786597921
70585583.2549849993031.74501500069698
71685717.813550753284-32.8135507532844
72585586.943878299804-1.94387829980417
73555563.428410889046-8.42841088904606
74660679.002994758373-19.0029947583728
75530530.569602478173-0.569602478173124
76575578.655763547041-3.65576354704069
77580568.47292171435511.5270782856454
78615595.97823366937819.0217663306215
79570566.1359945094873.86400549051314
80550569.274280579703-19.2742805797031
81635602.98427683055832.0157231694424
82580589.247993813806-9.24799381380637
83690695.831408689452-5.83140868945225
84575589.95072885212-14.9507288521201
85590561.18603383015528.8139661698455
86685668.20049453563316.799505464367
87540534.688928986015.3110710139905
88580580.276843392934-0.276843392934211
89615582.38450846539532.6154915346045
90605615.956768636293-10.9567686362928
91565573.844325628867-8.8443256288673
92555558.252174548178-3.25217454817789
93625633.481416813096-8.48141681309585
94605586.34216456940718.6578354305925
95685695.691304302471-10.6913043024709
96540582.42853693076-42.4285369307598
97610589.09135227191720.9086477280832
98680686.380109852147-6.38010985214703
99560543.56865930749516.4313406925048
100575584.633158311657-9.63315831165733
101590613.367160798964-23.3671607989644
102625611.66768657357813.3323134264222
103520571.265265685569-51.2652656855687
104590560.19995959406129.8000404059386
105625631.196131471109-6.19613147110908
106560606.026097558043-46.0260975580431
107715691.61711555576823.3828844442323
108575552.66306580973222.3369341902685

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 590 & 589.081196581197 & 0.918803418803122 \tabularnewline
14 & 605 & 603.837898212898 & 1.16210178710162 \tabularnewline
15 & 475 & 473.177933177934 & 1.82206682206646 \tabularnewline
16 & 535 & 532.309634809635 & 2.69036519036501 \tabularnewline
17 & 560 & 557.066336441337 & 2.93366355866328 \tabularnewline
18 & 610 & 607.031371406372 & 2.9686285936283 \tabularnewline
19 & 585 & 584.70473970474 & 0.29526029526005 \tabularnewline
20 & 560 & 544.878108003108 & 15.1218919968918 \tabularnewline
21 & 590 & 583.593142968143 & 6.40685703185682 \tabularnewline
22 & 625 & 611.266511266511 & 13.7334887334886 \tabularnewline
23 & 620 & 630.606546231546 & -10.6065462315464 \tabularnewline
24 & 615 & 604.529914529915 & 10.4700854700852 \tabularnewline
25 & 560 & 594.405387313797 & -34.4053873137968 \tabularnewline
26 & 665 & 609.359038917614 & 55.640961082386 \tabularnewline
27 & 495 & 479.233315423777 & 15.7666845762232 \tabularnewline
28 & 555 & 539.067904381112 & 15.9320956188876 \tabularnewline
29 & 545 & 564.021555984929 & -19.0215559849295 \tabularnewline
30 & 605 & 614.014895137574 & -9.01489513757394 \tabularnewline
31 & 610 & 589.524172424972 & 20.475827575028 \tabularnewline
32 & 610 & 561.699695610884 & 48.3003043891157 \tabularnewline
33 & 550 & 593.359911814272 & -43.3599118142716 \tabularnewline
34 & 600 & 626.964186757964 & -26.9641867579636 \tabularnewline
35 & 660 & 626.600969123392 & 33.3990308766082 \tabularnewline
36 & 590 & 617.585865844488 & -27.5858658444878 \tabularnewline
37 & 555 & 571.13465392731 & -16.1346539273096 \tabularnewline
38 & 650 & 658.980803453618 & -8.98080345361848 \tabularnewline
39 & 530 & 496.576862473401 & 33.4231375265987 \tabularnewline
40 & 565 & 556.545351631006 & 8.45464836899373 \tabularnewline
41 & 580 & 553.204030453642 & 26.7959695463577 \tabularnewline
42 & 630 & 611.297759216954 & 18.7022407830462 \tabularnewline
43 & 605 & 610.679769628444 & -5.67976962844421 \tabularnewline
44 & 595 & 605.379200274121 & -10.3792002741206 \tabularnewline
45 & 565 & 562.840492943327 & 2.15950705667251 \tabularnewline
46 & 585 & 609.717103477425 & -24.7171034774245 \tabularnewline
47 & 685 & 658.217896370674 & 26.782103629326 \tabularnewline
48 & 585 & 599.835533489111 & -14.8355334891107 \tabularnewline
49 & 520 & 562.654074935061 & -42.6540749350606 \tabularnewline
50 & 670 & 656.29126474317 & 13.7087352568299 \tabularnewline
51 & 525 & 528.213304048201 & -3.21330404820094 \tabularnewline
52 & 565 & 567.969807084605 & -2.96980708460489 \tabularnewline
53 & 575 & 579.47578110165 & -4.47578110165034 \tabularnewline
54 & 610 & 631.017638327993 & -21.0176383279934 \tabularnewline
55 & 605 & 610.662417025809 & -5.66241702580919 \tabularnewline
56 & 575 & 601.557659665219 & -26.5576596652189 \tabularnewline
57 & 565 & 569.169032979998 & -4.16903297999829 \tabularnewline
58 & 575 & 594.289033585832 & -19.2890335858316 \tabularnewline
59 & 720 & 684.478422562095 & 35.5215774379053 \tabularnewline
60 & 580 & 592.406592187108 & -12.4065921871081 \tabularnewline
61 & 565 & 532.70603085241 & 32.2939691475897 \tabularnewline
62 & 675 & 671.968902301069 & 3.03109769893149 \tabularnewline
63 & 525 & 530.192554754706 & -5.19255475470572 \tabularnewline
64 & 575 & 570.146168526072 & 4.85383147392781 \tabularnewline
65 & 560 & 580.433056929275 & -20.4330569292754 \tabularnewline
66 & 585 & 618.584284607819 & -33.584284607819 \tabularnewline
67 & 550 & 610.65911135094 & -60.6591113509402 \tabularnewline
68 & 560 & 584.639659970979 & -24.6396599709788 \tabularnewline
69 & 605 & 570.374621340208 & 34.6253786597921 \tabularnewline
70 & 585 & 583.254984999303 & 1.74501500069698 \tabularnewline
71 & 685 & 717.813550753284 & -32.8135507532844 \tabularnewline
72 & 585 & 586.943878299804 & -1.94387829980417 \tabularnewline
73 & 555 & 563.428410889046 & -8.42841088904606 \tabularnewline
74 & 660 & 679.002994758373 & -19.0029947583728 \tabularnewline
75 & 530 & 530.569602478173 & -0.569602478173124 \tabularnewline
76 & 575 & 578.655763547041 & -3.65576354704069 \tabularnewline
77 & 580 & 568.472921714355 & 11.5270782856454 \tabularnewline
78 & 615 & 595.978233669378 & 19.0217663306215 \tabularnewline
79 & 570 & 566.135994509487 & 3.86400549051314 \tabularnewline
80 & 550 & 569.274280579703 & -19.2742805797031 \tabularnewline
81 & 635 & 602.984276830558 & 32.0157231694424 \tabularnewline
82 & 580 & 589.247993813806 & -9.24799381380637 \tabularnewline
83 & 690 & 695.831408689452 & -5.83140868945225 \tabularnewline
84 & 575 & 589.95072885212 & -14.9507288521201 \tabularnewline
85 & 590 & 561.186033830155 & 28.8139661698455 \tabularnewline
86 & 685 & 668.200494535633 & 16.799505464367 \tabularnewline
87 & 540 & 534.68892898601 & 5.3110710139905 \tabularnewline
88 & 580 & 580.276843392934 & -0.276843392934211 \tabularnewline
89 & 615 & 582.384508465395 & 32.6154915346045 \tabularnewline
90 & 605 & 615.956768636293 & -10.9567686362928 \tabularnewline
91 & 565 & 573.844325628867 & -8.8443256288673 \tabularnewline
92 & 555 & 558.252174548178 & -3.25217454817789 \tabularnewline
93 & 625 & 633.481416813096 & -8.48141681309585 \tabularnewline
94 & 605 & 586.342164569407 & 18.6578354305925 \tabularnewline
95 & 685 & 695.691304302471 & -10.6913043024709 \tabularnewline
96 & 540 & 582.42853693076 & -42.4285369307598 \tabularnewline
97 & 610 & 589.091352271917 & 20.9086477280832 \tabularnewline
98 & 680 & 686.380109852147 & -6.38010985214703 \tabularnewline
99 & 560 & 543.568659307495 & 16.4313406925048 \tabularnewline
100 & 575 & 584.633158311657 & -9.63315831165733 \tabularnewline
101 & 590 & 613.367160798964 & -23.3671607989644 \tabularnewline
102 & 625 & 611.667686573578 & 13.3323134264222 \tabularnewline
103 & 520 & 571.265265685569 & -51.2652656855687 \tabularnewline
104 & 590 & 560.199959594061 & 29.8000404059386 \tabularnewline
105 & 625 & 631.196131471109 & -6.19613147110908 \tabularnewline
106 & 560 & 606.026097558043 & -46.0260975580431 \tabularnewline
107 & 715 & 691.617115555768 & 23.3828844442323 \tabularnewline
108 & 575 & 552.663065809732 & 22.3369341902685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211334&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]590[/C][C]589.081196581197[/C][C]0.918803418803122[/C][/ROW]
[ROW][C]14[/C][C]605[/C][C]603.837898212898[/C][C]1.16210178710162[/C][/ROW]
[ROW][C]15[/C][C]475[/C][C]473.177933177934[/C][C]1.82206682206646[/C][/ROW]
[ROW][C]16[/C][C]535[/C][C]532.309634809635[/C][C]2.69036519036501[/C][/ROW]
[ROW][C]17[/C][C]560[/C][C]557.066336441337[/C][C]2.93366355866328[/C][/ROW]
[ROW][C]18[/C][C]610[/C][C]607.031371406372[/C][C]2.9686285936283[/C][/ROW]
[ROW][C]19[/C][C]585[/C][C]584.70473970474[/C][C]0.29526029526005[/C][/ROW]
[ROW][C]20[/C][C]560[/C][C]544.878108003108[/C][C]15.1218919968918[/C][/ROW]
[ROW][C]21[/C][C]590[/C][C]583.593142968143[/C][C]6.40685703185682[/C][/ROW]
[ROW][C]22[/C][C]625[/C][C]611.266511266511[/C][C]13.7334887334886[/C][/ROW]
[ROW][C]23[/C][C]620[/C][C]630.606546231546[/C][C]-10.6065462315464[/C][/ROW]
[ROW][C]24[/C][C]615[/C][C]604.529914529915[/C][C]10.4700854700852[/C][/ROW]
[ROW][C]25[/C][C]560[/C][C]594.405387313797[/C][C]-34.4053873137968[/C][/ROW]
[ROW][C]26[/C][C]665[/C][C]609.359038917614[/C][C]55.640961082386[/C][/ROW]
[ROW][C]27[/C][C]495[/C][C]479.233315423777[/C][C]15.7666845762232[/C][/ROW]
[ROW][C]28[/C][C]555[/C][C]539.067904381112[/C][C]15.9320956188876[/C][/ROW]
[ROW][C]29[/C][C]545[/C][C]564.021555984929[/C][C]-19.0215559849295[/C][/ROW]
[ROW][C]30[/C][C]605[/C][C]614.014895137574[/C][C]-9.01489513757394[/C][/ROW]
[ROW][C]31[/C][C]610[/C][C]589.524172424972[/C][C]20.475827575028[/C][/ROW]
[ROW][C]32[/C][C]610[/C][C]561.699695610884[/C][C]48.3003043891157[/C][/ROW]
[ROW][C]33[/C][C]550[/C][C]593.359911814272[/C][C]-43.3599118142716[/C][/ROW]
[ROW][C]34[/C][C]600[/C][C]626.964186757964[/C][C]-26.9641867579636[/C][/ROW]
[ROW][C]35[/C][C]660[/C][C]626.600969123392[/C][C]33.3990308766082[/C][/ROW]
[ROW][C]36[/C][C]590[/C][C]617.585865844488[/C][C]-27.5858658444878[/C][/ROW]
[ROW][C]37[/C][C]555[/C][C]571.13465392731[/C][C]-16.1346539273096[/C][/ROW]
[ROW][C]38[/C][C]650[/C][C]658.980803453618[/C][C]-8.98080345361848[/C][/ROW]
[ROW][C]39[/C][C]530[/C][C]496.576862473401[/C][C]33.4231375265987[/C][/ROW]
[ROW][C]40[/C][C]565[/C][C]556.545351631006[/C][C]8.45464836899373[/C][/ROW]
[ROW][C]41[/C][C]580[/C][C]553.204030453642[/C][C]26.7959695463577[/C][/ROW]
[ROW][C]42[/C][C]630[/C][C]611.297759216954[/C][C]18.7022407830462[/C][/ROW]
[ROW][C]43[/C][C]605[/C][C]610.679769628444[/C][C]-5.67976962844421[/C][/ROW]
[ROW][C]44[/C][C]595[/C][C]605.379200274121[/C][C]-10.3792002741206[/C][/ROW]
[ROW][C]45[/C][C]565[/C][C]562.840492943327[/C][C]2.15950705667251[/C][/ROW]
[ROW][C]46[/C][C]585[/C][C]609.717103477425[/C][C]-24.7171034774245[/C][/ROW]
[ROW][C]47[/C][C]685[/C][C]658.217896370674[/C][C]26.782103629326[/C][/ROW]
[ROW][C]48[/C][C]585[/C][C]599.835533489111[/C][C]-14.8355334891107[/C][/ROW]
[ROW][C]49[/C][C]520[/C][C]562.654074935061[/C][C]-42.6540749350606[/C][/ROW]
[ROW][C]50[/C][C]670[/C][C]656.29126474317[/C][C]13.7087352568299[/C][/ROW]
[ROW][C]51[/C][C]525[/C][C]528.213304048201[/C][C]-3.21330404820094[/C][/ROW]
[ROW][C]52[/C][C]565[/C][C]567.969807084605[/C][C]-2.96980708460489[/C][/ROW]
[ROW][C]53[/C][C]575[/C][C]579.47578110165[/C][C]-4.47578110165034[/C][/ROW]
[ROW][C]54[/C][C]610[/C][C]631.017638327993[/C][C]-21.0176383279934[/C][/ROW]
[ROW][C]55[/C][C]605[/C][C]610.662417025809[/C][C]-5.66241702580919[/C][/ROW]
[ROW][C]56[/C][C]575[/C][C]601.557659665219[/C][C]-26.5576596652189[/C][/ROW]
[ROW][C]57[/C][C]565[/C][C]569.169032979998[/C][C]-4.16903297999829[/C][/ROW]
[ROW][C]58[/C][C]575[/C][C]594.289033585832[/C][C]-19.2890335858316[/C][/ROW]
[ROW][C]59[/C][C]720[/C][C]684.478422562095[/C][C]35.5215774379053[/C][/ROW]
[ROW][C]60[/C][C]580[/C][C]592.406592187108[/C][C]-12.4065921871081[/C][/ROW]
[ROW][C]61[/C][C]565[/C][C]532.70603085241[/C][C]32.2939691475897[/C][/ROW]
[ROW][C]62[/C][C]675[/C][C]671.968902301069[/C][C]3.03109769893149[/C][/ROW]
[ROW][C]63[/C][C]525[/C][C]530.192554754706[/C][C]-5.19255475470572[/C][/ROW]
[ROW][C]64[/C][C]575[/C][C]570.146168526072[/C][C]4.85383147392781[/C][/ROW]
[ROW][C]65[/C][C]560[/C][C]580.433056929275[/C][C]-20.4330569292754[/C][/ROW]
[ROW][C]66[/C][C]585[/C][C]618.584284607819[/C][C]-33.584284607819[/C][/ROW]
[ROW][C]67[/C][C]550[/C][C]610.65911135094[/C][C]-60.6591113509402[/C][/ROW]
[ROW][C]68[/C][C]560[/C][C]584.639659970979[/C][C]-24.6396599709788[/C][/ROW]
[ROW][C]69[/C][C]605[/C][C]570.374621340208[/C][C]34.6253786597921[/C][/ROW]
[ROW][C]70[/C][C]585[/C][C]583.254984999303[/C][C]1.74501500069698[/C][/ROW]
[ROW][C]71[/C][C]685[/C][C]717.813550753284[/C][C]-32.8135507532844[/C][/ROW]
[ROW][C]72[/C][C]585[/C][C]586.943878299804[/C][C]-1.94387829980417[/C][/ROW]
[ROW][C]73[/C][C]555[/C][C]563.428410889046[/C][C]-8.42841088904606[/C][/ROW]
[ROW][C]74[/C][C]660[/C][C]679.002994758373[/C][C]-19.0029947583728[/C][/ROW]
[ROW][C]75[/C][C]530[/C][C]530.569602478173[/C][C]-0.569602478173124[/C][/ROW]
[ROW][C]76[/C][C]575[/C][C]578.655763547041[/C][C]-3.65576354704069[/C][/ROW]
[ROW][C]77[/C][C]580[/C][C]568.472921714355[/C][C]11.5270782856454[/C][/ROW]
[ROW][C]78[/C][C]615[/C][C]595.978233669378[/C][C]19.0217663306215[/C][/ROW]
[ROW][C]79[/C][C]570[/C][C]566.135994509487[/C][C]3.86400549051314[/C][/ROW]
[ROW][C]80[/C][C]550[/C][C]569.274280579703[/C][C]-19.2742805797031[/C][/ROW]
[ROW][C]81[/C][C]635[/C][C]602.984276830558[/C][C]32.0157231694424[/C][/ROW]
[ROW][C]82[/C][C]580[/C][C]589.247993813806[/C][C]-9.24799381380637[/C][/ROW]
[ROW][C]83[/C][C]690[/C][C]695.831408689452[/C][C]-5.83140868945225[/C][/ROW]
[ROW][C]84[/C][C]575[/C][C]589.95072885212[/C][C]-14.9507288521201[/C][/ROW]
[ROW][C]85[/C][C]590[/C][C]561.186033830155[/C][C]28.8139661698455[/C][/ROW]
[ROW][C]86[/C][C]685[/C][C]668.200494535633[/C][C]16.799505464367[/C][/ROW]
[ROW][C]87[/C][C]540[/C][C]534.68892898601[/C][C]5.3110710139905[/C][/ROW]
[ROW][C]88[/C][C]580[/C][C]580.276843392934[/C][C]-0.276843392934211[/C][/ROW]
[ROW][C]89[/C][C]615[/C][C]582.384508465395[/C][C]32.6154915346045[/C][/ROW]
[ROW][C]90[/C][C]605[/C][C]615.956768636293[/C][C]-10.9567686362928[/C][/ROW]
[ROW][C]91[/C][C]565[/C][C]573.844325628867[/C][C]-8.8443256288673[/C][/ROW]
[ROW][C]92[/C][C]555[/C][C]558.252174548178[/C][C]-3.25217454817789[/C][/ROW]
[ROW][C]93[/C][C]625[/C][C]633.481416813096[/C][C]-8.48141681309585[/C][/ROW]
[ROW][C]94[/C][C]605[/C][C]586.342164569407[/C][C]18.6578354305925[/C][/ROW]
[ROW][C]95[/C][C]685[/C][C]695.691304302471[/C][C]-10.6913043024709[/C][/ROW]
[ROW][C]96[/C][C]540[/C][C]582.42853693076[/C][C]-42.4285369307598[/C][/ROW]
[ROW][C]97[/C][C]610[/C][C]589.091352271917[/C][C]20.9086477280832[/C][/ROW]
[ROW][C]98[/C][C]680[/C][C]686.380109852147[/C][C]-6.38010985214703[/C][/ROW]
[ROW][C]99[/C][C]560[/C][C]543.568659307495[/C][C]16.4313406925048[/C][/ROW]
[ROW][C]100[/C][C]575[/C][C]584.633158311657[/C][C]-9.63315831165733[/C][/ROW]
[ROW][C]101[/C][C]590[/C][C]613.367160798964[/C][C]-23.3671607989644[/C][/ROW]
[ROW][C]102[/C][C]625[/C][C]611.667686573578[/C][C]13.3323134264222[/C][/ROW]
[ROW][C]103[/C][C]520[/C][C]571.265265685569[/C][C]-51.2652656855687[/C][/ROW]
[ROW][C]104[/C][C]590[/C][C]560.199959594061[/C][C]29.8000404059386[/C][/ROW]
[ROW][C]105[/C][C]625[/C][C]631.196131471109[/C][C]-6.19613147110908[/C][/ROW]
[ROW][C]106[/C][C]560[/C][C]606.026097558043[/C][C]-46.0260975580431[/C][/ROW]
[ROW][C]107[/C][C]715[/C][C]691.617115555768[/C][C]23.3828844442323[/C][/ROW]
[ROW][C]108[/C][C]575[/C][C]552.663065809732[/C][C]22.3369341902685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211334&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
13590589.0811965811970.918803418803122
14605603.8378982128981.16210178710162
15475473.1779331779341.82206682206646
16535532.3096348096352.69036519036501
17560557.0663364413372.93366355866328
18610607.0313714063722.9686285936283
19585584.704739704740.29526029526005
20560544.87810800310815.1218919968918
21590583.5931429681436.40685703185682
22625611.26651126651113.7334887334886
23620630.606546231546-10.6065462315464
24615604.52991452991510.4700854700852
25560594.405387313797-34.4053873137968
26665609.35903891761455.640961082386
27495479.23331542377715.7666845762232
28555539.06790438111215.9320956188876
29545564.021555984929-19.0215559849295
30605614.014895137574-9.01489513757394
31610589.52417242497220.475827575028
32610561.69969561088448.3003043891157
33550593.359911814272-43.3599118142716
34600626.964186757964-26.9641867579636
35660626.60096912339233.3990308766082
36590617.585865844488-27.5858658444878
37555571.13465392731-16.1346539273096
38650658.980803453618-8.98080345361848
39530496.57686247340133.4231375265987
40565556.5453516310068.45464836899373
41580553.20403045364226.7959695463577
42630611.29775921695418.7022407830462
43605610.679769628444-5.67976962844421
44595605.379200274121-10.3792002741206
45565562.8404929433272.15950705667251
46585609.717103477425-24.7171034774245
47685658.21789637067426.782103629326
48585599.835533489111-14.8355334891107
49520562.654074935061-42.6540749350606
50670656.2912647431713.7087352568299
51525528.213304048201-3.21330404820094
52565567.969807084605-2.96980708460489
53575579.47578110165-4.47578110165034
54610631.017638327993-21.0176383279934
55605610.662417025809-5.66241702580919
56575601.557659665219-26.5576596652189
57565569.169032979998-4.16903297999829
58575594.289033585832-19.2890335858316
59720684.47842256209535.5215774379053
60580592.406592187108-12.4065921871081
61565532.7060308524132.2939691475897
62675671.9689023010693.03109769893149
63525530.192554754706-5.19255475470572
64575570.1461685260724.85383147392781
65560580.433056929275-20.4330569292754
66585618.584284607819-33.584284607819
67550610.65911135094-60.6591113509402
68560584.639659970979-24.6396599709788
69605570.37462134020834.6253786597921
70585583.2549849993031.74501500069698
71685717.813550753284-32.8135507532844
72585586.943878299804-1.94387829980417
73555563.428410889046-8.42841088904606
74660679.002994758373-19.0029947583728
75530530.569602478173-0.569602478173124
76575578.655763547041-3.65576354704069
77580568.47292171435511.5270782856454
78615595.97823366937819.0217663306215
79570566.1359945094873.86400549051314
80550569.274280579703-19.2742805797031
81635602.98427683055832.0157231694424
82580589.247993813806-9.24799381380637
83690695.831408689452-5.83140868945225
84575589.95072885212-14.9507288521201
85590561.18603383015528.8139661698455
86685668.20049453563316.799505464367
87540534.688928986015.3110710139905
88580580.276843392934-0.276843392934211
89615582.38450846539532.6154915346045
90605615.956768636293-10.9567686362928
91565573.844325628867-8.8443256288673
92555558.252174548178-3.25217454817789
93625633.481416813096-8.48141681309585
94605586.34216456940718.6578354305925
95685695.691304302471-10.6913043024709
96540582.42853693076-42.4285369307598
97610589.09135227191720.9086477280832
98680686.380109852147-6.38010985214703
99560543.56865930749516.4313406925048
100575584.633158311657-9.63315831165733
101590613.367160798964-23.3671607989644
102625611.66768657357813.3323134264222
103520571.265265685569-51.2652656855687
104590560.19995959406129.8000404059386
105625631.196131471109-6.19613147110908
106560606.026097558043-46.0260975580431
107715691.61711555576823.3828844442323
108575552.66306580973222.3369341902685







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109610.597317287847566.846196823004654.348437752689
110685.795832002564642.044711537721729.546952467406
111561.450245327474517.699124862631605.201365792316
112581.415538496519537.664418031677625.166658961362
113599.031869189198555.280748724355642.782989654041
114627.040610747983583.289490283141670.791731212826
115534.346464708592490.59534424375578.097585173435
116588.903504898834545.152384433992632.654625363677
117630.760784077857587.009663613014674.511904542699
118573.348401952391529.597281487549617.099522417234
119715.125974613532671.374854148689758.877095078375
120575.325228382052531.57410791721619.076348846895

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 610.597317287847 & 566.846196823004 & 654.348437752689 \tabularnewline
110 & 685.795832002564 & 642.044711537721 & 729.546952467406 \tabularnewline
111 & 561.450245327474 & 517.699124862631 & 605.201365792316 \tabularnewline
112 & 581.415538496519 & 537.664418031677 & 625.166658961362 \tabularnewline
113 & 599.031869189198 & 555.280748724355 & 642.782989654041 \tabularnewline
114 & 627.040610747983 & 583.289490283141 & 670.791731212826 \tabularnewline
115 & 534.346464708592 & 490.59534424375 & 578.097585173435 \tabularnewline
116 & 588.903504898834 & 545.152384433992 & 632.654625363677 \tabularnewline
117 & 630.760784077857 & 587.009663613014 & 674.511904542699 \tabularnewline
118 & 573.348401952391 & 529.597281487549 & 617.099522417234 \tabularnewline
119 & 715.125974613532 & 671.374854148689 & 758.877095078375 \tabularnewline
120 & 575.325228382052 & 531.57410791721 & 619.076348846895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211334&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]109[/C][C]610.597317287847[/C][C]566.846196823004[/C][C]654.348437752689[/C][/ROW]
[ROW][C]110[/C][C]685.795832002564[/C][C]642.044711537721[/C][C]729.546952467406[/C][/ROW]
[ROW][C]111[/C][C]561.450245327474[/C][C]517.699124862631[/C][C]605.201365792316[/C][/ROW]
[ROW][C]112[/C][C]581.415538496519[/C][C]537.664418031677[/C][C]625.166658961362[/C][/ROW]
[ROW][C]113[/C][C]599.031869189198[/C][C]555.280748724355[/C][C]642.782989654041[/C][/ROW]
[ROW][C]114[/C][C]627.040610747983[/C][C]583.289490283141[/C][C]670.791731212826[/C][/ROW]
[ROW][C]115[/C][C]534.346464708592[/C][C]490.59534424375[/C][C]578.097585173435[/C][/ROW]
[ROW][C]116[/C][C]588.903504898834[/C][C]545.152384433992[/C][C]632.654625363677[/C][/ROW]
[ROW][C]117[/C][C]630.760784077857[/C][C]587.009663613014[/C][C]674.511904542699[/C][/ROW]
[ROW][C]118[/C][C]573.348401952391[/C][C]529.597281487549[/C][C]617.099522417234[/C][/ROW]
[ROW][C]119[/C][C]715.125974613532[/C][C]671.374854148689[/C][C]758.877095078375[/C][/ROW]
[ROW][C]120[/C][C]575.325228382052[/C][C]531.57410791721[/C][C]619.076348846895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211334&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211334&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
109610.597317287847566.846196823004654.348437752689
110685.795832002564642.044711537721729.546952467406
111561.450245327474517.699124862631605.201365792316
112581.415538496519537.664418031677625.166658961362
113599.031869189198555.280748724355642.782989654041
114627.040610747983583.289490283141670.791731212826
115534.346464708592490.59534424375578.097585173435
116588.903504898834545.152384433992632.654625363677
117630.760784077857587.009663613014674.511904542699
118573.348401952391529.597281487549617.099522417234
119715.125974613532671.374854148689758.877095078375
120575.325228382052531.57410791721619.076348846895



Parameters (Session):
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')