Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 10 Aug 2016 23:07:50 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/10/t14708670150vlty9u23z3mq35.htm/, Retrieved Tue, 30 Apr 2024 04:20:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296268, Retrieved Tue, 30 Apr 2024 04:20:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-10 22:07:50] [409a9d71664281dd1fd3bb0995266dd0] [Current]
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Dataseries X:
700
700
620
680
700
670
660
730
680
680
650
800
660
710
660
590
660
710
620
700
690
680
640
810
620
700
720
620
630
680
670
720
660
630
620
810
540
690
720
620
650
690
660
700
630
590
570
760
500
660
750
680
710
620
640
720
680
580
530
740
480
640
690
600
640
580
690
690
720
550
510
680
450
560
730
650
680
580
750
670
670
590
480
810
350
570
710
650
710
510
800
680
660
620
580
830
480
550
720
620
730
520
870
660
650
620
560
820




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296268&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296268&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296268&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0466491042254684
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0466491042254684 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296268&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]0.0466491042254684[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296268&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296268&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
alpha0.0466491042254684
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
27007000
3620700-80
4680696.268071661962-16.2680716619625
5700695.5091806914564.49081930854379
6670695.718673389438-25.7186733894382
7660694.518920313954-34.5189203139536
8730692.90864360247737.0913563975226
9680694.638922152929-14.6389221529294
10680693.956029547669-13.9560295476689
11650693.304993270726-43.304993270726
12800691.284854126157108.715145873843
13660696.356318296913-36.3563182969126
14710694.66032861542615.3396713845743
15660695.375910544629-35.3759105446291
16590693.725656006562-103.725656006562
17660688.886947068657-28.8869470686567
18710687.53939686409522.4606031359046
19620688.587163880749-68.587163880749
20700685.38763412434714.6123658756533
21690686.0692879030613.93071209693926
22680686.252652101351-6.25265210135126
23640685.96097148179-45.9609714817898
24810683.816933332832126.183066667168
25620689.703260361278-69.703260361278
26700686.4516657038313.5483342961702
27720687.08368336249332.9163166375067
28620688.619200048035-68.6192000480348
29630685.418175833126-55.4181758331258
30680682.832967572701-2.83296757270102
31670682.700812173135-12.7008121731348
32720682.10833066232237.8916693376779
33660683.875943094532-23.8759430945324
34630682.762151736634-52.7621517366342
35620680.300844621112-60.300844621112
36810677.487864235498132.512135764502
37540683.669436667916-143.669436667916
38690676.9673861427813.0326138572203
39720677.57534590493542.4246540950645
40620679.554418015546-59.5544180155456
41650676.776257762451-26.7762577624513
42690675.52716932332314.4728306766772
43660676.202313909997-16.2023139099967
44700675.44649047971624.5535095202844
45630676.591889704428-46.5918897044285
46590674.418419785545-84.4184197855451
47570670.48037612242-100.48037612242
48760665.79305658407194.2069434159291
49500670.187726106243-170.187726106243
50660662.248621133218-2.24862113321763
51750662.14372497161187.8562750283894
52680666.24214150227113.7578584977286
53710666.88393327725143.1160667227488
54620668.895259167593-48.8952591675929
55640666.614339126553-26.6143391265526
56720665.37280404674654.6271959532538
57680667.92111380431512.0788861956854
58580668.484583025385-88.4845830253847
59530664.356856489486-134.356856489486
60740658.08922948770281.910770512298
61480661.910293558519-181.910293558519
62640653.424341314622-13.4243413146216
63690652.79810781747837.2018921825223
64600654.533542763285-54.5335427632848
65640651.989601843136-11.9896018431363
66580651.430297657134-71.4302976571339
67690648.0981382568741.90186174313
68690650.05282257256639.9471774274335
69720651.91632261589268.0836773841079
70550655.092365178236-105.092365178236
71510650.189900481736-140.189900481736
72680643.65016720280536.3498327971947
73450645.34585434154-195.34585434154
74560636.233145222348-76.2331452223483
75730632.67693728543697.3230627145643
76650637.21697098154912.7830290184509
77680637.81328783454842.1867121654519
78580639.781260167284-59.7812601672841
79750636.992517931011113.007482068989
80670642.26421574030527.7357842596954
81670643.5580652310126.4419347689897
82590644.791557801972-54.791557801972
83480642.235580711392-162.235580711392
84810634.667436197707175.332563802293
85350642.846543240639-292.846543240639
86570629.185514322938-59.1855143229378
87710626.42456309664983.5754369033508
88650630.32328236344319.6767176365574
89710631.24118361528578.7588163847146
90510634.91521184949-124.91521184949
91800629.088029112577170.911970887423
92680637.06091945588542.9390805441154
93660639.06398909953320.9360109004672
94620640.040635254094-20.0406352540942
95580639.105757571381-59.1057575713814
96830636.348526926109193.651473073891
97480645.382194676948-165.382194676948
98550637.667263440426-87.6672634404265
99720633.57766413103286.4223358689676
100620637.609188684392-17.6091886843923
101730636.78773580612893.2122641938719
102520641.1360044336-121.1360044336
103870635.48511833732234.51488166268
104660646.42502749442613.5749725055742
105650647.0582878016962.94171219830378
106620647.195516040636-27.1955160406362
107560645.926869578391-85.9268695783912
108820641.918458083661178.081541916339

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 700 & 700 & 0 \tabularnewline
3 & 620 & 700 & -80 \tabularnewline
4 & 680 & 696.268071661962 & -16.2680716619625 \tabularnewline
5 & 700 & 695.509180691456 & 4.49081930854379 \tabularnewline
6 & 670 & 695.718673389438 & -25.7186733894382 \tabularnewline
7 & 660 & 694.518920313954 & -34.5189203139536 \tabularnewline
8 & 730 & 692.908643602477 & 37.0913563975226 \tabularnewline
9 & 680 & 694.638922152929 & -14.6389221529294 \tabularnewline
10 & 680 & 693.956029547669 & -13.9560295476689 \tabularnewline
11 & 650 & 693.304993270726 & -43.304993270726 \tabularnewline
12 & 800 & 691.284854126157 & 108.715145873843 \tabularnewline
13 & 660 & 696.356318296913 & -36.3563182969126 \tabularnewline
14 & 710 & 694.660328615426 & 15.3396713845743 \tabularnewline
15 & 660 & 695.375910544629 & -35.3759105446291 \tabularnewline
16 & 590 & 693.725656006562 & -103.725656006562 \tabularnewline
17 & 660 & 688.886947068657 & -28.8869470686567 \tabularnewline
18 & 710 & 687.539396864095 & 22.4606031359046 \tabularnewline
19 & 620 & 688.587163880749 & -68.587163880749 \tabularnewline
20 & 700 & 685.387634124347 & 14.6123658756533 \tabularnewline
21 & 690 & 686.069287903061 & 3.93071209693926 \tabularnewline
22 & 680 & 686.252652101351 & -6.25265210135126 \tabularnewline
23 & 640 & 685.96097148179 & -45.9609714817898 \tabularnewline
24 & 810 & 683.816933332832 & 126.183066667168 \tabularnewline
25 & 620 & 689.703260361278 & -69.703260361278 \tabularnewline
26 & 700 & 686.45166570383 & 13.5483342961702 \tabularnewline
27 & 720 & 687.083683362493 & 32.9163166375067 \tabularnewline
28 & 620 & 688.619200048035 & -68.6192000480348 \tabularnewline
29 & 630 & 685.418175833126 & -55.4181758331258 \tabularnewline
30 & 680 & 682.832967572701 & -2.83296757270102 \tabularnewline
31 & 670 & 682.700812173135 & -12.7008121731348 \tabularnewline
32 & 720 & 682.108330662322 & 37.8916693376779 \tabularnewline
33 & 660 & 683.875943094532 & -23.8759430945324 \tabularnewline
34 & 630 & 682.762151736634 & -52.7621517366342 \tabularnewline
35 & 620 & 680.300844621112 & -60.300844621112 \tabularnewline
36 & 810 & 677.487864235498 & 132.512135764502 \tabularnewline
37 & 540 & 683.669436667916 & -143.669436667916 \tabularnewline
38 & 690 & 676.96738614278 & 13.0326138572203 \tabularnewline
39 & 720 & 677.575345904935 & 42.4246540950645 \tabularnewline
40 & 620 & 679.554418015546 & -59.5544180155456 \tabularnewline
41 & 650 & 676.776257762451 & -26.7762577624513 \tabularnewline
42 & 690 & 675.527169323323 & 14.4728306766772 \tabularnewline
43 & 660 & 676.202313909997 & -16.2023139099967 \tabularnewline
44 & 700 & 675.446490479716 & 24.5535095202844 \tabularnewline
45 & 630 & 676.591889704428 & -46.5918897044285 \tabularnewline
46 & 590 & 674.418419785545 & -84.4184197855451 \tabularnewline
47 & 570 & 670.48037612242 & -100.48037612242 \tabularnewline
48 & 760 & 665.793056584071 & 94.2069434159291 \tabularnewline
49 & 500 & 670.187726106243 & -170.187726106243 \tabularnewline
50 & 660 & 662.248621133218 & -2.24862113321763 \tabularnewline
51 & 750 & 662.143724971611 & 87.8562750283894 \tabularnewline
52 & 680 & 666.242141502271 & 13.7578584977286 \tabularnewline
53 & 710 & 666.883933277251 & 43.1160667227488 \tabularnewline
54 & 620 & 668.895259167593 & -48.8952591675929 \tabularnewline
55 & 640 & 666.614339126553 & -26.6143391265526 \tabularnewline
56 & 720 & 665.372804046746 & 54.6271959532538 \tabularnewline
57 & 680 & 667.921113804315 & 12.0788861956854 \tabularnewline
58 & 580 & 668.484583025385 & -88.4845830253847 \tabularnewline
59 & 530 & 664.356856489486 & -134.356856489486 \tabularnewline
60 & 740 & 658.089229487702 & 81.910770512298 \tabularnewline
61 & 480 & 661.910293558519 & -181.910293558519 \tabularnewline
62 & 640 & 653.424341314622 & -13.4243413146216 \tabularnewline
63 & 690 & 652.798107817478 & 37.2018921825223 \tabularnewline
64 & 600 & 654.533542763285 & -54.5335427632848 \tabularnewline
65 & 640 & 651.989601843136 & -11.9896018431363 \tabularnewline
66 & 580 & 651.430297657134 & -71.4302976571339 \tabularnewline
67 & 690 & 648.09813825687 & 41.90186174313 \tabularnewline
68 & 690 & 650.052822572566 & 39.9471774274335 \tabularnewline
69 & 720 & 651.916322615892 & 68.0836773841079 \tabularnewline
70 & 550 & 655.092365178236 & -105.092365178236 \tabularnewline
71 & 510 & 650.189900481736 & -140.189900481736 \tabularnewline
72 & 680 & 643.650167202805 & 36.3498327971947 \tabularnewline
73 & 450 & 645.34585434154 & -195.34585434154 \tabularnewline
74 & 560 & 636.233145222348 & -76.2331452223483 \tabularnewline
75 & 730 & 632.676937285436 & 97.3230627145643 \tabularnewline
76 & 650 & 637.216970981549 & 12.7830290184509 \tabularnewline
77 & 680 & 637.813287834548 & 42.1867121654519 \tabularnewline
78 & 580 & 639.781260167284 & -59.7812601672841 \tabularnewline
79 & 750 & 636.992517931011 & 113.007482068989 \tabularnewline
80 & 670 & 642.264215740305 & 27.7357842596954 \tabularnewline
81 & 670 & 643.55806523101 & 26.4419347689897 \tabularnewline
82 & 590 & 644.791557801972 & -54.791557801972 \tabularnewline
83 & 480 & 642.235580711392 & -162.235580711392 \tabularnewline
84 & 810 & 634.667436197707 & 175.332563802293 \tabularnewline
85 & 350 & 642.846543240639 & -292.846543240639 \tabularnewline
86 & 570 & 629.185514322938 & -59.1855143229378 \tabularnewline
87 & 710 & 626.424563096649 & 83.5754369033508 \tabularnewline
88 & 650 & 630.323282363443 & 19.6767176365574 \tabularnewline
89 & 710 & 631.241183615285 & 78.7588163847146 \tabularnewline
90 & 510 & 634.91521184949 & -124.91521184949 \tabularnewline
91 & 800 & 629.088029112577 & 170.911970887423 \tabularnewline
92 & 680 & 637.060919455885 & 42.9390805441154 \tabularnewline
93 & 660 & 639.063989099533 & 20.9360109004672 \tabularnewline
94 & 620 & 640.040635254094 & -20.0406352540942 \tabularnewline
95 & 580 & 639.105757571381 & -59.1057575713814 \tabularnewline
96 & 830 & 636.348526926109 & 193.651473073891 \tabularnewline
97 & 480 & 645.382194676948 & -165.382194676948 \tabularnewline
98 & 550 & 637.667263440426 & -87.6672634404265 \tabularnewline
99 & 720 & 633.577664131032 & 86.4223358689676 \tabularnewline
100 & 620 & 637.609188684392 & -17.6091886843923 \tabularnewline
101 & 730 & 636.787735806128 & 93.2122641938719 \tabularnewline
102 & 520 & 641.1360044336 & -121.1360044336 \tabularnewline
103 & 870 & 635.48511833732 & 234.51488166268 \tabularnewline
104 & 660 & 646.425027494426 & 13.5749725055742 \tabularnewline
105 & 650 & 647.058287801696 & 2.94171219830378 \tabularnewline
106 & 620 & 647.195516040636 & -27.1955160406362 \tabularnewline
107 & 560 & 645.926869578391 & -85.9268695783912 \tabularnewline
108 & 820 & 641.918458083661 & 178.081541916339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296268&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]2[/C][C]700[/C][C]700[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]620[/C][C]700[/C][C]-80[/C][/ROW]
[ROW][C]4[/C][C]680[/C][C]696.268071661962[/C][C]-16.2680716619625[/C][/ROW]
[ROW][C]5[/C][C]700[/C][C]695.509180691456[/C][C]4.49081930854379[/C][/ROW]
[ROW][C]6[/C][C]670[/C][C]695.718673389438[/C][C]-25.7186733894382[/C][/ROW]
[ROW][C]7[/C][C]660[/C][C]694.518920313954[/C][C]-34.5189203139536[/C][/ROW]
[ROW][C]8[/C][C]730[/C][C]692.908643602477[/C][C]37.0913563975226[/C][/ROW]
[ROW][C]9[/C][C]680[/C][C]694.638922152929[/C][C]-14.6389221529294[/C][/ROW]
[ROW][C]10[/C][C]680[/C][C]693.956029547669[/C][C]-13.9560295476689[/C][/ROW]
[ROW][C]11[/C][C]650[/C][C]693.304993270726[/C][C]-43.304993270726[/C][/ROW]
[ROW][C]12[/C][C]800[/C][C]691.284854126157[/C][C]108.715145873843[/C][/ROW]
[ROW][C]13[/C][C]660[/C][C]696.356318296913[/C][C]-36.3563182969126[/C][/ROW]
[ROW][C]14[/C][C]710[/C][C]694.660328615426[/C][C]15.3396713845743[/C][/ROW]
[ROW][C]15[/C][C]660[/C][C]695.375910544629[/C][C]-35.3759105446291[/C][/ROW]
[ROW][C]16[/C][C]590[/C][C]693.725656006562[/C][C]-103.725656006562[/C][/ROW]
[ROW][C]17[/C][C]660[/C][C]688.886947068657[/C][C]-28.8869470686567[/C][/ROW]
[ROW][C]18[/C][C]710[/C][C]687.539396864095[/C][C]22.4606031359046[/C][/ROW]
[ROW][C]19[/C][C]620[/C][C]688.587163880749[/C][C]-68.587163880749[/C][/ROW]
[ROW][C]20[/C][C]700[/C][C]685.387634124347[/C][C]14.6123658756533[/C][/ROW]
[ROW][C]21[/C][C]690[/C][C]686.069287903061[/C][C]3.93071209693926[/C][/ROW]
[ROW][C]22[/C][C]680[/C][C]686.252652101351[/C][C]-6.25265210135126[/C][/ROW]
[ROW][C]23[/C][C]640[/C][C]685.96097148179[/C][C]-45.9609714817898[/C][/ROW]
[ROW][C]24[/C][C]810[/C][C]683.816933332832[/C][C]126.183066667168[/C][/ROW]
[ROW][C]25[/C][C]620[/C][C]689.703260361278[/C][C]-69.703260361278[/C][/ROW]
[ROW][C]26[/C][C]700[/C][C]686.45166570383[/C][C]13.5483342961702[/C][/ROW]
[ROW][C]27[/C][C]720[/C][C]687.083683362493[/C][C]32.9163166375067[/C][/ROW]
[ROW][C]28[/C][C]620[/C][C]688.619200048035[/C][C]-68.6192000480348[/C][/ROW]
[ROW][C]29[/C][C]630[/C][C]685.418175833126[/C][C]-55.4181758331258[/C][/ROW]
[ROW][C]30[/C][C]680[/C][C]682.832967572701[/C][C]-2.83296757270102[/C][/ROW]
[ROW][C]31[/C][C]670[/C][C]682.700812173135[/C][C]-12.7008121731348[/C][/ROW]
[ROW][C]32[/C][C]720[/C][C]682.108330662322[/C][C]37.8916693376779[/C][/ROW]
[ROW][C]33[/C][C]660[/C][C]683.875943094532[/C][C]-23.8759430945324[/C][/ROW]
[ROW][C]34[/C][C]630[/C][C]682.762151736634[/C][C]-52.7621517366342[/C][/ROW]
[ROW][C]35[/C][C]620[/C][C]680.300844621112[/C][C]-60.300844621112[/C][/ROW]
[ROW][C]36[/C][C]810[/C][C]677.487864235498[/C][C]132.512135764502[/C][/ROW]
[ROW][C]37[/C][C]540[/C][C]683.669436667916[/C][C]-143.669436667916[/C][/ROW]
[ROW][C]38[/C][C]690[/C][C]676.96738614278[/C][C]13.0326138572203[/C][/ROW]
[ROW][C]39[/C][C]720[/C][C]677.575345904935[/C][C]42.4246540950645[/C][/ROW]
[ROW][C]40[/C][C]620[/C][C]679.554418015546[/C][C]-59.5544180155456[/C][/ROW]
[ROW][C]41[/C][C]650[/C][C]676.776257762451[/C][C]-26.7762577624513[/C][/ROW]
[ROW][C]42[/C][C]690[/C][C]675.527169323323[/C][C]14.4728306766772[/C][/ROW]
[ROW][C]43[/C][C]660[/C][C]676.202313909997[/C][C]-16.2023139099967[/C][/ROW]
[ROW][C]44[/C][C]700[/C][C]675.446490479716[/C][C]24.5535095202844[/C][/ROW]
[ROW][C]45[/C][C]630[/C][C]676.591889704428[/C][C]-46.5918897044285[/C][/ROW]
[ROW][C]46[/C][C]590[/C][C]674.418419785545[/C][C]-84.4184197855451[/C][/ROW]
[ROW][C]47[/C][C]570[/C][C]670.48037612242[/C][C]-100.48037612242[/C][/ROW]
[ROW][C]48[/C][C]760[/C][C]665.793056584071[/C][C]94.2069434159291[/C][/ROW]
[ROW][C]49[/C][C]500[/C][C]670.187726106243[/C][C]-170.187726106243[/C][/ROW]
[ROW][C]50[/C][C]660[/C][C]662.248621133218[/C][C]-2.24862113321763[/C][/ROW]
[ROW][C]51[/C][C]750[/C][C]662.143724971611[/C][C]87.8562750283894[/C][/ROW]
[ROW][C]52[/C][C]680[/C][C]666.242141502271[/C][C]13.7578584977286[/C][/ROW]
[ROW][C]53[/C][C]710[/C][C]666.883933277251[/C][C]43.1160667227488[/C][/ROW]
[ROW][C]54[/C][C]620[/C][C]668.895259167593[/C][C]-48.8952591675929[/C][/ROW]
[ROW][C]55[/C][C]640[/C][C]666.614339126553[/C][C]-26.6143391265526[/C][/ROW]
[ROW][C]56[/C][C]720[/C][C]665.372804046746[/C][C]54.6271959532538[/C][/ROW]
[ROW][C]57[/C][C]680[/C][C]667.921113804315[/C][C]12.0788861956854[/C][/ROW]
[ROW][C]58[/C][C]580[/C][C]668.484583025385[/C][C]-88.4845830253847[/C][/ROW]
[ROW][C]59[/C][C]530[/C][C]664.356856489486[/C][C]-134.356856489486[/C][/ROW]
[ROW][C]60[/C][C]740[/C][C]658.089229487702[/C][C]81.910770512298[/C][/ROW]
[ROW][C]61[/C][C]480[/C][C]661.910293558519[/C][C]-181.910293558519[/C][/ROW]
[ROW][C]62[/C][C]640[/C][C]653.424341314622[/C][C]-13.4243413146216[/C][/ROW]
[ROW][C]63[/C][C]690[/C][C]652.798107817478[/C][C]37.2018921825223[/C][/ROW]
[ROW][C]64[/C][C]600[/C][C]654.533542763285[/C][C]-54.5335427632848[/C][/ROW]
[ROW][C]65[/C][C]640[/C][C]651.989601843136[/C][C]-11.9896018431363[/C][/ROW]
[ROW][C]66[/C][C]580[/C][C]651.430297657134[/C][C]-71.4302976571339[/C][/ROW]
[ROW][C]67[/C][C]690[/C][C]648.09813825687[/C][C]41.90186174313[/C][/ROW]
[ROW][C]68[/C][C]690[/C][C]650.052822572566[/C][C]39.9471774274335[/C][/ROW]
[ROW][C]69[/C][C]720[/C][C]651.916322615892[/C][C]68.0836773841079[/C][/ROW]
[ROW][C]70[/C][C]550[/C][C]655.092365178236[/C][C]-105.092365178236[/C][/ROW]
[ROW][C]71[/C][C]510[/C][C]650.189900481736[/C][C]-140.189900481736[/C][/ROW]
[ROW][C]72[/C][C]680[/C][C]643.650167202805[/C][C]36.3498327971947[/C][/ROW]
[ROW][C]73[/C][C]450[/C][C]645.34585434154[/C][C]-195.34585434154[/C][/ROW]
[ROW][C]74[/C][C]560[/C][C]636.233145222348[/C][C]-76.2331452223483[/C][/ROW]
[ROW][C]75[/C][C]730[/C][C]632.676937285436[/C][C]97.3230627145643[/C][/ROW]
[ROW][C]76[/C][C]650[/C][C]637.216970981549[/C][C]12.7830290184509[/C][/ROW]
[ROW][C]77[/C][C]680[/C][C]637.813287834548[/C][C]42.1867121654519[/C][/ROW]
[ROW][C]78[/C][C]580[/C][C]639.781260167284[/C][C]-59.7812601672841[/C][/ROW]
[ROW][C]79[/C][C]750[/C][C]636.992517931011[/C][C]113.007482068989[/C][/ROW]
[ROW][C]80[/C][C]670[/C][C]642.264215740305[/C][C]27.7357842596954[/C][/ROW]
[ROW][C]81[/C][C]670[/C][C]643.55806523101[/C][C]26.4419347689897[/C][/ROW]
[ROW][C]82[/C][C]590[/C][C]644.791557801972[/C][C]-54.791557801972[/C][/ROW]
[ROW][C]83[/C][C]480[/C][C]642.235580711392[/C][C]-162.235580711392[/C][/ROW]
[ROW][C]84[/C][C]810[/C][C]634.667436197707[/C][C]175.332563802293[/C][/ROW]
[ROW][C]85[/C][C]350[/C][C]642.846543240639[/C][C]-292.846543240639[/C][/ROW]
[ROW][C]86[/C][C]570[/C][C]629.185514322938[/C][C]-59.1855143229378[/C][/ROW]
[ROW][C]87[/C][C]710[/C][C]626.424563096649[/C][C]83.5754369033508[/C][/ROW]
[ROW][C]88[/C][C]650[/C][C]630.323282363443[/C][C]19.6767176365574[/C][/ROW]
[ROW][C]89[/C][C]710[/C][C]631.241183615285[/C][C]78.7588163847146[/C][/ROW]
[ROW][C]90[/C][C]510[/C][C]634.91521184949[/C][C]-124.91521184949[/C][/ROW]
[ROW][C]91[/C][C]800[/C][C]629.088029112577[/C][C]170.911970887423[/C][/ROW]
[ROW][C]92[/C][C]680[/C][C]637.060919455885[/C][C]42.9390805441154[/C][/ROW]
[ROW][C]93[/C][C]660[/C][C]639.063989099533[/C][C]20.9360109004672[/C][/ROW]
[ROW][C]94[/C][C]620[/C][C]640.040635254094[/C][C]-20.0406352540942[/C][/ROW]
[ROW][C]95[/C][C]580[/C][C]639.105757571381[/C][C]-59.1057575713814[/C][/ROW]
[ROW][C]96[/C][C]830[/C][C]636.348526926109[/C][C]193.651473073891[/C][/ROW]
[ROW][C]97[/C][C]480[/C][C]645.382194676948[/C][C]-165.382194676948[/C][/ROW]
[ROW][C]98[/C][C]550[/C][C]637.667263440426[/C][C]-87.6672634404265[/C][/ROW]
[ROW][C]99[/C][C]720[/C][C]633.577664131032[/C][C]86.4223358689676[/C][/ROW]
[ROW][C]100[/C][C]620[/C][C]637.609188684392[/C][C]-17.6091886843923[/C][/ROW]
[ROW][C]101[/C][C]730[/C][C]636.787735806128[/C][C]93.2122641938719[/C][/ROW]
[ROW][C]102[/C][C]520[/C][C]641.1360044336[/C][C]-121.1360044336[/C][/ROW]
[ROW][C]103[/C][C]870[/C][C]635.48511833732[/C][C]234.51488166268[/C][/ROW]
[ROW][C]104[/C][C]660[/C][C]646.425027494426[/C][C]13.5749725055742[/C][/ROW]
[ROW][C]105[/C][C]650[/C][C]647.058287801696[/C][C]2.94171219830378[/C][/ROW]
[ROW][C]106[/C][C]620[/C][C]647.195516040636[/C][C]-27.1955160406362[/C][/ROW]
[ROW][C]107[/C][C]560[/C][C]645.926869578391[/C][C]-85.9268695783912[/C][/ROW]
[ROW][C]108[/C][C]820[/C][C]641.918458083661[/C][C]178.081541916339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296268&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296268&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
27007000
3620700-80
4680696.268071661962-16.2680716619625
5700695.5091806914564.49081930854379
6670695.718673389438-25.7186733894382
7660694.518920313954-34.5189203139536
8730692.90864360247737.0913563975226
9680694.638922152929-14.6389221529294
10680693.956029547669-13.9560295476689
11650693.304993270726-43.304993270726
12800691.284854126157108.715145873843
13660696.356318296913-36.3563182969126
14710694.66032861542615.3396713845743
15660695.375910544629-35.3759105446291
16590693.725656006562-103.725656006562
17660688.886947068657-28.8869470686567
18710687.53939686409522.4606031359046
19620688.587163880749-68.587163880749
20700685.38763412434714.6123658756533
21690686.0692879030613.93071209693926
22680686.252652101351-6.25265210135126
23640685.96097148179-45.9609714817898
24810683.816933332832126.183066667168
25620689.703260361278-69.703260361278
26700686.4516657038313.5483342961702
27720687.08368336249332.9163166375067
28620688.619200048035-68.6192000480348
29630685.418175833126-55.4181758331258
30680682.832967572701-2.83296757270102
31670682.700812173135-12.7008121731348
32720682.10833066232237.8916693376779
33660683.875943094532-23.8759430945324
34630682.762151736634-52.7621517366342
35620680.300844621112-60.300844621112
36810677.487864235498132.512135764502
37540683.669436667916-143.669436667916
38690676.9673861427813.0326138572203
39720677.57534590493542.4246540950645
40620679.554418015546-59.5544180155456
41650676.776257762451-26.7762577624513
42690675.52716932332314.4728306766772
43660676.202313909997-16.2023139099967
44700675.44649047971624.5535095202844
45630676.591889704428-46.5918897044285
46590674.418419785545-84.4184197855451
47570670.48037612242-100.48037612242
48760665.79305658407194.2069434159291
49500670.187726106243-170.187726106243
50660662.248621133218-2.24862113321763
51750662.14372497161187.8562750283894
52680666.24214150227113.7578584977286
53710666.88393327725143.1160667227488
54620668.895259167593-48.8952591675929
55640666.614339126553-26.6143391265526
56720665.37280404674654.6271959532538
57680667.92111380431512.0788861956854
58580668.484583025385-88.4845830253847
59530664.356856489486-134.356856489486
60740658.08922948770281.910770512298
61480661.910293558519-181.910293558519
62640653.424341314622-13.4243413146216
63690652.79810781747837.2018921825223
64600654.533542763285-54.5335427632848
65640651.989601843136-11.9896018431363
66580651.430297657134-71.4302976571339
67690648.0981382568741.90186174313
68690650.05282257256639.9471774274335
69720651.91632261589268.0836773841079
70550655.092365178236-105.092365178236
71510650.189900481736-140.189900481736
72680643.65016720280536.3498327971947
73450645.34585434154-195.34585434154
74560636.233145222348-76.2331452223483
75730632.67693728543697.3230627145643
76650637.21697098154912.7830290184509
77680637.81328783454842.1867121654519
78580639.781260167284-59.7812601672841
79750636.992517931011113.007482068989
80670642.26421574030527.7357842596954
81670643.5580652310126.4419347689897
82590644.791557801972-54.791557801972
83480642.235580711392-162.235580711392
84810634.667436197707175.332563802293
85350642.846543240639-292.846543240639
86570629.185514322938-59.1855143229378
87710626.42456309664983.5754369033508
88650630.32328236344319.6767176365574
89710631.24118361528578.7588163847146
90510634.91521184949-124.91521184949
91800629.088029112577170.911970887423
92680637.06091945588542.9390805441154
93660639.06398909953320.9360109004672
94620640.040635254094-20.0406352540942
95580639.105757571381-59.1057575713814
96830636.348526926109193.651473073891
97480645.382194676948-165.382194676948
98550637.667263440426-87.6672634404265
99720633.57766413103286.4223358689676
100620637.609188684392-17.6091886843923
101730636.78773580612893.2122641938719
102520641.1360044336-121.1360044336
103870635.48511833732234.51488166268
104660646.42502749442613.5749725055742
105650647.0582878016962.94171219830378
106620647.195516040636-27.1955160406362
107560645.926869578391-85.9268695783912
108820641.918458083661178.081541916339







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109650.225802493148480.615808618178819.835796368119
110650.225802493148480.431361454435820.020243531861
111650.225802493148480.247114437761820.204490548535
112650.225802493148480.063066918017820.388538068279
113650.225802493148479.879218248575820.572386737721
114650.225802493148479.695567786294820.756037200002
115650.225802493148479.512114891491820.939490094805
116650.225802493148479.328858927917821.122746058379
117650.225802493148479.145799262732821.305805723564
118650.225802493148478.962935266476821.48866971982
119650.225802493148478.780266313048821.671338673248
120650.225802493148478.597791779677821.85381320662

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 650.225802493148 & 480.615808618178 & 819.835796368119 \tabularnewline
110 & 650.225802493148 & 480.431361454435 & 820.020243531861 \tabularnewline
111 & 650.225802493148 & 480.247114437761 & 820.204490548535 \tabularnewline
112 & 650.225802493148 & 480.063066918017 & 820.388538068279 \tabularnewline
113 & 650.225802493148 & 479.879218248575 & 820.572386737721 \tabularnewline
114 & 650.225802493148 & 479.695567786294 & 820.756037200002 \tabularnewline
115 & 650.225802493148 & 479.512114891491 & 820.939490094805 \tabularnewline
116 & 650.225802493148 & 479.328858927917 & 821.122746058379 \tabularnewline
117 & 650.225802493148 & 479.145799262732 & 821.305805723564 \tabularnewline
118 & 650.225802493148 & 478.962935266476 & 821.48866971982 \tabularnewline
119 & 650.225802493148 & 478.780266313048 & 821.671338673248 \tabularnewline
120 & 650.225802493148 & 478.597791779677 & 821.85381320662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296268&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]650.225802493148[/C][C]480.615808618178[/C][C]819.835796368119[/C][/ROW]
[ROW][C]110[/C][C]650.225802493148[/C][C]480.431361454435[/C][C]820.020243531861[/C][/ROW]
[ROW][C]111[/C][C]650.225802493148[/C][C]480.247114437761[/C][C]820.204490548535[/C][/ROW]
[ROW][C]112[/C][C]650.225802493148[/C][C]480.063066918017[/C][C]820.388538068279[/C][/ROW]
[ROW][C]113[/C][C]650.225802493148[/C][C]479.879218248575[/C][C]820.572386737721[/C][/ROW]
[ROW][C]114[/C][C]650.225802493148[/C][C]479.695567786294[/C][C]820.756037200002[/C][/ROW]
[ROW][C]115[/C][C]650.225802493148[/C][C]479.512114891491[/C][C]820.939490094805[/C][/ROW]
[ROW][C]116[/C][C]650.225802493148[/C][C]479.328858927917[/C][C]821.122746058379[/C][/ROW]
[ROW][C]117[/C][C]650.225802493148[/C][C]479.145799262732[/C][C]821.305805723564[/C][/ROW]
[ROW][C]118[/C][C]650.225802493148[/C][C]478.962935266476[/C][C]821.48866971982[/C][/ROW]
[ROW][C]119[/C][C]650.225802493148[/C][C]478.780266313048[/C][C]821.671338673248[/C][/ROW]
[ROW][C]120[/C][C]650.225802493148[/C][C]478.597791779677[/C][C]821.85381320662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296268&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296268&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
109650.225802493148480.615808618178819.835796368119
110650.225802493148480.431361454435820.020243531861
111650.225802493148480.247114437761820.204490548535
112650.225802493148480.063066918017820.388538068279
113650.225802493148479.879218248575820.572386737721
114650.225802493148479.695567786294820.756037200002
115650.225802493148479.512114891491820.939490094805
116650.225802493148479.328858927917821.122746058379
117650.225802493148479.145799262732821.305805723564
118650.225802493148478.962935266476821.48866971982
119650.225802493148478.780266313048821.671338673248
120650.225802493148478.597791779677821.85381320662



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')