Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 13:52:18 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/26/t1480168362soehttyjko6y8zc.htm/, Retrieved Sat, 04 May 2024 02:43:21 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 02:43:21 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
467
475
470
442
433
427
410
406
429
425
431
408
454
459
441
420
416
400
401
398
442
458
476
447
511
514
513
511
498
490
495
486
530
539
555
548
615
634
645
634
630
635
642
637
675
679
676
660
716
730
717
694
670
641
626
604
630
634
635
619
674
664
653
635
614
595
580
570
608
617
591
565




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999928063237351
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999928063237351 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.999928063237351[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.999928063237351
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24754678
3470474.999424505899-4.99942450589879
4442470.000359642414-28.000359642414
5433442.002014255226-9.00201425522567
6427433.000647575763-6.00064757576286
7410427.00043166716-17.0004316671605
8406410.001222956018-4.00122295601778
9429406.00028783502622.9997121649739
10425428.998345475165-3.99834547516502
11431425.0002876280295.99971237197059
12408430.999568400115-22.9995684001152
13454408.00165451449345.9983454855069
14459453.9966910279395.0033089720614
15441458.99964007815-17.99964007815
16420441.001294835836-21.0012948358361
17416420.001510765162-4.00151076516192
18400416.00028785573-16.0002878557302
19401400.001151008910.998848991090199
20398400.999928146037-2.99992814603718
21442398.00021580511943.999784194881
22458441.99683479796816.0031652020323
23476457.99884878410318.0011512158968
24447475.998705055458-28.9987050554576
25511447.00208607296363.9979139270373
26514510.9953961972563.00460380274421
27513513.999783858529-0.99978385852944
28511513.000071921214-2.00007192121416
29498511.000143878699-13.0001438786991
30490498.000935188265-8.00093518826458
31495490.0005755613764.99942443862437
32486494.999640357591-8.99964035759075
33530486.00064740499243.9993525950077
34539529.9968348290169.00316517098429
35555538.99935234144416.000647658556
36548554.998848965207-6.99884896520712
37615548.00050347453766.9994965254632
38634614.99518027312119.0048197268791
39645633.99863285479411.0013671452059
40634644.999208597263-10.9992085972629
41630634.000791247458-4.00079124745821
42635630.000287803974.99971219602958
43642634.999640336897.00035966310952
44637641.999496416788-4.99949641678847
45675637.00035964758737.9996403524129
46679674.9972664288914.00273357110882
47676678.999712056305-2.99971205630516
48660676.000215789574-16.0002157895742
49716660.00115100372655.9988489962743
50730715.99597162409114.0040283759089
51717729.998992595535-12.9989925955346
52694717.000935105445-23.000935105445
53670694.001654612809-24.0016546128094
54641670.001726601331-29.0017266013311
55626641.002086290323-15.0020862903229
56604626.001079201521-22.0010792015207
57630604.00158268641225.9984173135875
58634629.9981297580244.00187024197555
59635633.999712118411.00028788158977
60619634.999928042528-15.999928042528
61674619.00115098302654.998849016974
62664673.996043560852-9.99604356085229
63653664.000719083013-11.0007190830131
64635653.000791356118-18.0007913561176
65614635.001294918655-21.0012949186553
66595614.001510765168-19.001510765168
67580595.00136690717-15.0013669071699
68570580.001079149771-10.0010791497706
69608570.00071944525737.9992805547429
70617607.9972664547749.00273354522619
71591616.999352372494-25.9993523724938
72565591.001870309241-26.0018703092406

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 475 & 467 & 8 \tabularnewline
3 & 470 & 474.999424505899 & -4.99942450589879 \tabularnewline
4 & 442 & 470.000359642414 & -28.000359642414 \tabularnewline
5 & 433 & 442.002014255226 & -9.00201425522567 \tabularnewline
6 & 427 & 433.000647575763 & -6.00064757576286 \tabularnewline
7 & 410 & 427.00043166716 & -17.0004316671605 \tabularnewline
8 & 406 & 410.001222956018 & -4.00122295601778 \tabularnewline
9 & 429 & 406.000287835026 & 22.9997121649739 \tabularnewline
10 & 425 & 428.998345475165 & -3.99834547516502 \tabularnewline
11 & 431 & 425.000287628029 & 5.99971237197059 \tabularnewline
12 & 408 & 430.999568400115 & -22.9995684001152 \tabularnewline
13 & 454 & 408.001654514493 & 45.9983454855069 \tabularnewline
14 & 459 & 453.996691027939 & 5.0033089720614 \tabularnewline
15 & 441 & 458.99964007815 & -17.99964007815 \tabularnewline
16 & 420 & 441.001294835836 & -21.0012948358361 \tabularnewline
17 & 416 & 420.001510765162 & -4.00151076516192 \tabularnewline
18 & 400 & 416.00028785573 & -16.0002878557302 \tabularnewline
19 & 401 & 400.00115100891 & 0.998848991090199 \tabularnewline
20 & 398 & 400.999928146037 & -2.99992814603718 \tabularnewline
21 & 442 & 398.000215805119 & 43.999784194881 \tabularnewline
22 & 458 & 441.996834797968 & 16.0031652020323 \tabularnewline
23 & 476 & 457.998848784103 & 18.0011512158968 \tabularnewline
24 & 447 & 475.998705055458 & -28.9987050554576 \tabularnewline
25 & 511 & 447.002086072963 & 63.9979139270373 \tabularnewline
26 & 514 & 510.995396197256 & 3.00460380274421 \tabularnewline
27 & 513 & 513.999783858529 & -0.99978385852944 \tabularnewline
28 & 511 & 513.000071921214 & -2.00007192121416 \tabularnewline
29 & 498 & 511.000143878699 & -13.0001438786991 \tabularnewline
30 & 490 & 498.000935188265 & -8.00093518826458 \tabularnewline
31 & 495 & 490.000575561376 & 4.99942443862437 \tabularnewline
32 & 486 & 494.999640357591 & -8.99964035759075 \tabularnewline
33 & 530 & 486.000647404992 & 43.9993525950077 \tabularnewline
34 & 539 & 529.996834829016 & 9.00316517098429 \tabularnewline
35 & 555 & 538.999352341444 & 16.000647658556 \tabularnewline
36 & 548 & 554.998848965207 & -6.99884896520712 \tabularnewline
37 & 615 & 548.000503474537 & 66.9994965254632 \tabularnewline
38 & 634 & 614.995180273121 & 19.0048197268791 \tabularnewline
39 & 645 & 633.998632854794 & 11.0013671452059 \tabularnewline
40 & 634 & 644.999208597263 & -10.9992085972629 \tabularnewline
41 & 630 & 634.000791247458 & -4.00079124745821 \tabularnewline
42 & 635 & 630.00028780397 & 4.99971219602958 \tabularnewline
43 & 642 & 634.99964033689 & 7.00035966310952 \tabularnewline
44 & 637 & 641.999496416788 & -4.99949641678847 \tabularnewline
45 & 675 & 637.000359647587 & 37.9996403524129 \tabularnewline
46 & 679 & 674.997266428891 & 4.00273357110882 \tabularnewline
47 & 676 & 678.999712056305 & -2.99971205630516 \tabularnewline
48 & 660 & 676.000215789574 & -16.0002157895742 \tabularnewline
49 & 716 & 660.001151003726 & 55.9988489962743 \tabularnewline
50 & 730 & 715.995971624091 & 14.0040283759089 \tabularnewline
51 & 717 & 729.998992595535 & -12.9989925955346 \tabularnewline
52 & 694 & 717.000935105445 & -23.000935105445 \tabularnewline
53 & 670 & 694.001654612809 & -24.0016546128094 \tabularnewline
54 & 641 & 670.001726601331 & -29.0017266013311 \tabularnewline
55 & 626 & 641.002086290323 & -15.0020862903229 \tabularnewline
56 & 604 & 626.001079201521 & -22.0010792015207 \tabularnewline
57 & 630 & 604.001582686412 & 25.9984173135875 \tabularnewline
58 & 634 & 629.998129758024 & 4.00187024197555 \tabularnewline
59 & 635 & 633.99971211841 & 1.00028788158977 \tabularnewline
60 & 619 & 634.999928042528 & -15.999928042528 \tabularnewline
61 & 674 & 619.001150983026 & 54.998849016974 \tabularnewline
62 & 664 & 673.996043560852 & -9.99604356085229 \tabularnewline
63 & 653 & 664.000719083013 & -11.0007190830131 \tabularnewline
64 & 635 & 653.000791356118 & -18.0007913561176 \tabularnewline
65 & 614 & 635.001294918655 & -21.0012949186553 \tabularnewline
66 & 595 & 614.001510765168 & -19.001510765168 \tabularnewline
67 & 580 & 595.00136690717 & -15.0013669071699 \tabularnewline
68 & 570 & 580.001079149771 & -10.0010791497706 \tabularnewline
69 & 608 & 570.000719445257 & 37.9992805547429 \tabularnewline
70 & 617 & 607.997266454774 & 9.00273354522619 \tabularnewline
71 & 591 & 616.999352372494 & -25.9993523724938 \tabularnewline
72 & 565 & 591.001870309241 & -26.0018703092406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]475[/C][C]467[/C][C]8[/C][/ROW]
[ROW][C]3[/C][C]470[/C][C]474.999424505899[/C][C]-4.99942450589879[/C][/ROW]
[ROW][C]4[/C][C]442[/C][C]470.000359642414[/C][C]-28.000359642414[/C][/ROW]
[ROW][C]5[/C][C]433[/C][C]442.002014255226[/C][C]-9.00201425522567[/C][/ROW]
[ROW][C]6[/C][C]427[/C][C]433.000647575763[/C][C]-6.00064757576286[/C][/ROW]
[ROW][C]7[/C][C]410[/C][C]427.00043166716[/C][C]-17.0004316671605[/C][/ROW]
[ROW][C]8[/C][C]406[/C][C]410.001222956018[/C][C]-4.00122295601778[/C][/ROW]
[ROW][C]9[/C][C]429[/C][C]406.000287835026[/C][C]22.9997121649739[/C][/ROW]
[ROW][C]10[/C][C]425[/C][C]428.998345475165[/C][C]-3.99834547516502[/C][/ROW]
[ROW][C]11[/C][C]431[/C][C]425.000287628029[/C][C]5.99971237197059[/C][/ROW]
[ROW][C]12[/C][C]408[/C][C]430.999568400115[/C][C]-22.9995684001152[/C][/ROW]
[ROW][C]13[/C][C]454[/C][C]408.001654514493[/C][C]45.9983454855069[/C][/ROW]
[ROW][C]14[/C][C]459[/C][C]453.996691027939[/C][C]5.0033089720614[/C][/ROW]
[ROW][C]15[/C][C]441[/C][C]458.99964007815[/C][C]-17.99964007815[/C][/ROW]
[ROW][C]16[/C][C]420[/C][C]441.001294835836[/C][C]-21.0012948358361[/C][/ROW]
[ROW][C]17[/C][C]416[/C][C]420.001510765162[/C][C]-4.00151076516192[/C][/ROW]
[ROW][C]18[/C][C]400[/C][C]416.00028785573[/C][C]-16.0002878557302[/C][/ROW]
[ROW][C]19[/C][C]401[/C][C]400.00115100891[/C][C]0.998848991090199[/C][/ROW]
[ROW][C]20[/C][C]398[/C][C]400.999928146037[/C][C]-2.99992814603718[/C][/ROW]
[ROW][C]21[/C][C]442[/C][C]398.000215805119[/C][C]43.999784194881[/C][/ROW]
[ROW][C]22[/C][C]458[/C][C]441.996834797968[/C][C]16.0031652020323[/C][/ROW]
[ROW][C]23[/C][C]476[/C][C]457.998848784103[/C][C]18.0011512158968[/C][/ROW]
[ROW][C]24[/C][C]447[/C][C]475.998705055458[/C][C]-28.9987050554576[/C][/ROW]
[ROW][C]25[/C][C]511[/C][C]447.002086072963[/C][C]63.9979139270373[/C][/ROW]
[ROW][C]26[/C][C]514[/C][C]510.995396197256[/C][C]3.00460380274421[/C][/ROW]
[ROW][C]27[/C][C]513[/C][C]513.999783858529[/C][C]-0.99978385852944[/C][/ROW]
[ROW][C]28[/C][C]511[/C][C]513.000071921214[/C][C]-2.00007192121416[/C][/ROW]
[ROW][C]29[/C][C]498[/C][C]511.000143878699[/C][C]-13.0001438786991[/C][/ROW]
[ROW][C]30[/C][C]490[/C][C]498.000935188265[/C][C]-8.00093518826458[/C][/ROW]
[ROW][C]31[/C][C]495[/C][C]490.000575561376[/C][C]4.99942443862437[/C][/ROW]
[ROW][C]32[/C][C]486[/C][C]494.999640357591[/C][C]-8.99964035759075[/C][/ROW]
[ROW][C]33[/C][C]530[/C][C]486.000647404992[/C][C]43.9993525950077[/C][/ROW]
[ROW][C]34[/C][C]539[/C][C]529.996834829016[/C][C]9.00316517098429[/C][/ROW]
[ROW][C]35[/C][C]555[/C][C]538.999352341444[/C][C]16.000647658556[/C][/ROW]
[ROW][C]36[/C][C]548[/C][C]554.998848965207[/C][C]-6.99884896520712[/C][/ROW]
[ROW][C]37[/C][C]615[/C][C]548.000503474537[/C][C]66.9994965254632[/C][/ROW]
[ROW][C]38[/C][C]634[/C][C]614.995180273121[/C][C]19.0048197268791[/C][/ROW]
[ROW][C]39[/C][C]645[/C][C]633.998632854794[/C][C]11.0013671452059[/C][/ROW]
[ROW][C]40[/C][C]634[/C][C]644.999208597263[/C][C]-10.9992085972629[/C][/ROW]
[ROW][C]41[/C][C]630[/C][C]634.000791247458[/C][C]-4.00079124745821[/C][/ROW]
[ROW][C]42[/C][C]635[/C][C]630.00028780397[/C][C]4.99971219602958[/C][/ROW]
[ROW][C]43[/C][C]642[/C][C]634.99964033689[/C][C]7.00035966310952[/C][/ROW]
[ROW][C]44[/C][C]637[/C][C]641.999496416788[/C][C]-4.99949641678847[/C][/ROW]
[ROW][C]45[/C][C]675[/C][C]637.000359647587[/C][C]37.9996403524129[/C][/ROW]
[ROW][C]46[/C][C]679[/C][C]674.997266428891[/C][C]4.00273357110882[/C][/ROW]
[ROW][C]47[/C][C]676[/C][C]678.999712056305[/C][C]-2.99971205630516[/C][/ROW]
[ROW][C]48[/C][C]660[/C][C]676.000215789574[/C][C]-16.0002157895742[/C][/ROW]
[ROW][C]49[/C][C]716[/C][C]660.001151003726[/C][C]55.9988489962743[/C][/ROW]
[ROW][C]50[/C][C]730[/C][C]715.995971624091[/C][C]14.0040283759089[/C][/ROW]
[ROW][C]51[/C][C]717[/C][C]729.998992595535[/C][C]-12.9989925955346[/C][/ROW]
[ROW][C]52[/C][C]694[/C][C]717.000935105445[/C][C]-23.000935105445[/C][/ROW]
[ROW][C]53[/C][C]670[/C][C]694.001654612809[/C][C]-24.0016546128094[/C][/ROW]
[ROW][C]54[/C][C]641[/C][C]670.001726601331[/C][C]-29.0017266013311[/C][/ROW]
[ROW][C]55[/C][C]626[/C][C]641.002086290323[/C][C]-15.0020862903229[/C][/ROW]
[ROW][C]56[/C][C]604[/C][C]626.001079201521[/C][C]-22.0010792015207[/C][/ROW]
[ROW][C]57[/C][C]630[/C][C]604.001582686412[/C][C]25.9984173135875[/C][/ROW]
[ROW][C]58[/C][C]634[/C][C]629.998129758024[/C][C]4.00187024197555[/C][/ROW]
[ROW][C]59[/C][C]635[/C][C]633.99971211841[/C][C]1.00028788158977[/C][/ROW]
[ROW][C]60[/C][C]619[/C][C]634.999928042528[/C][C]-15.999928042528[/C][/ROW]
[ROW][C]61[/C][C]674[/C][C]619.001150983026[/C][C]54.998849016974[/C][/ROW]
[ROW][C]62[/C][C]664[/C][C]673.996043560852[/C][C]-9.99604356085229[/C][/ROW]
[ROW][C]63[/C][C]653[/C][C]664.000719083013[/C][C]-11.0007190830131[/C][/ROW]
[ROW][C]64[/C][C]635[/C][C]653.000791356118[/C][C]-18.0007913561176[/C][/ROW]
[ROW][C]65[/C][C]614[/C][C]635.001294918655[/C][C]-21.0012949186553[/C][/ROW]
[ROW][C]66[/C][C]595[/C][C]614.001510765168[/C][C]-19.001510765168[/C][/ROW]
[ROW][C]67[/C][C]580[/C][C]595.00136690717[/C][C]-15.0013669071699[/C][/ROW]
[ROW][C]68[/C][C]570[/C][C]580.001079149771[/C][C]-10.0010791497706[/C][/ROW]
[ROW][C]69[/C][C]608[/C][C]570.000719445257[/C][C]37.9992805547429[/C][/ROW]
[ROW][C]70[/C][C]617[/C][C]607.997266454774[/C][C]9.00273354522619[/C][/ROW]
[ROW][C]71[/C][C]591[/C][C]616.999352372494[/C][C]-25.9993523724938[/C][/ROW]
[ROW][C]72[/C][C]565[/C][C]591.001870309241[/C][C]-26.0018703092406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
24754678
3470474.999424505899-4.99942450589879
4442470.000359642414-28.000359642414
5433442.002014255226-9.00201425522567
6427433.000647575763-6.00064757576286
7410427.00043166716-17.0004316671605
8406410.001222956018-4.00122295601778
9429406.00028783502622.9997121649739
10425428.998345475165-3.99834547516502
11431425.0002876280295.99971237197059
12408430.999568400115-22.9995684001152
13454408.00165451449345.9983454855069
14459453.9966910279395.0033089720614
15441458.99964007815-17.99964007815
16420441.001294835836-21.0012948358361
17416420.001510765162-4.00151076516192
18400416.00028785573-16.0002878557302
19401400.001151008910.998848991090199
20398400.999928146037-2.99992814603718
21442398.00021580511943.999784194881
22458441.99683479796816.0031652020323
23476457.99884878410318.0011512158968
24447475.998705055458-28.9987050554576
25511447.00208607296363.9979139270373
26514510.9953961972563.00460380274421
27513513.999783858529-0.99978385852944
28511513.000071921214-2.00007192121416
29498511.000143878699-13.0001438786991
30490498.000935188265-8.00093518826458
31495490.0005755613764.99942443862437
32486494.999640357591-8.99964035759075
33530486.00064740499243.9993525950077
34539529.9968348290169.00316517098429
35555538.99935234144416.000647658556
36548554.998848965207-6.99884896520712
37615548.00050347453766.9994965254632
38634614.99518027312119.0048197268791
39645633.99863285479411.0013671452059
40634644.999208597263-10.9992085972629
41630634.000791247458-4.00079124745821
42635630.000287803974.99971219602958
43642634.999640336897.00035966310952
44637641.999496416788-4.99949641678847
45675637.00035964758737.9996403524129
46679674.9972664288914.00273357110882
47676678.999712056305-2.99971205630516
48660676.000215789574-16.0002157895742
49716660.00115100372655.9988489962743
50730715.99597162409114.0040283759089
51717729.998992595535-12.9989925955346
52694717.000935105445-23.000935105445
53670694.001654612809-24.0016546128094
54641670.001726601331-29.0017266013311
55626641.002086290323-15.0020862903229
56604626.001079201521-22.0010792015207
57630604.00158268641225.9984173135875
58634629.9981297580244.00187024197555
59635633.999712118411.00028788158977
60619634.999928042528-15.999928042528
61674619.00115098302654.998849016974
62664673.996043560852-9.99604356085229
63653664.000719083013-11.0007190830131
64635653.000791356118-18.0007913561176
65614635.001294918655-21.0012949186553
66595614.001510765168-19.001510765168
67580595.00136690717-15.0013669071699
68570580.001079149771-10.0010791497706
69608570.00071944525737.9992805547429
70617607.9972664547749.00273354522619
71591616.999352372494-25.9993523724938
72565591.001870309241-26.0018703092406







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73565.001870490373519.821207862609610.182533118137
74565.001870490373501.109062807385628.894678173361
75565.001870490373486.750420205111643.253320775634
76565.001870490373474.64542041691655.358320563836
77565.001870490373463.980651590531666.023089390214
78565.001870490373454.338935113883675.664805866863
79565.001870490373445.472443719085684.53129726166
80565.001870490373437.219702476193692.784038504553
81565.001870490373429.468549640718700.535191340028
82565.001870490373422.137320448499707.866420532246
83565.001870490373415.164364315188714.839376665557
84565.001870490373408.501784691898721.501956288847

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 565.001870490373 & 519.821207862609 & 610.182533118137 \tabularnewline
74 & 565.001870490373 & 501.109062807385 & 628.894678173361 \tabularnewline
75 & 565.001870490373 & 486.750420205111 & 643.253320775634 \tabularnewline
76 & 565.001870490373 & 474.64542041691 & 655.358320563836 \tabularnewline
77 & 565.001870490373 & 463.980651590531 & 666.023089390214 \tabularnewline
78 & 565.001870490373 & 454.338935113883 & 675.664805866863 \tabularnewline
79 & 565.001870490373 & 445.472443719085 & 684.53129726166 \tabularnewline
80 & 565.001870490373 & 437.219702476193 & 692.784038504553 \tabularnewline
81 & 565.001870490373 & 429.468549640718 & 700.535191340028 \tabularnewline
82 & 565.001870490373 & 422.137320448499 & 707.866420532246 \tabularnewline
83 & 565.001870490373 & 415.164364315188 & 714.839376665557 \tabularnewline
84 & 565.001870490373 & 408.501784691898 & 721.501956288847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]565.001870490373[/C][C]519.821207862609[/C][C]610.182533118137[/C][/ROW]
[ROW][C]74[/C][C]565.001870490373[/C][C]501.109062807385[/C][C]628.894678173361[/C][/ROW]
[ROW][C]75[/C][C]565.001870490373[/C][C]486.750420205111[/C][C]643.253320775634[/C][/ROW]
[ROW][C]76[/C][C]565.001870490373[/C][C]474.64542041691[/C][C]655.358320563836[/C][/ROW]
[ROW][C]77[/C][C]565.001870490373[/C][C]463.980651590531[/C][C]666.023089390214[/C][/ROW]
[ROW][C]78[/C][C]565.001870490373[/C][C]454.338935113883[/C][C]675.664805866863[/C][/ROW]
[ROW][C]79[/C][C]565.001870490373[/C][C]445.472443719085[/C][C]684.53129726166[/C][/ROW]
[ROW][C]80[/C][C]565.001870490373[/C][C]437.219702476193[/C][C]692.784038504553[/C][/ROW]
[ROW][C]81[/C][C]565.001870490373[/C][C]429.468549640718[/C][C]700.535191340028[/C][/ROW]
[ROW][C]82[/C][C]565.001870490373[/C][C]422.137320448499[/C][C]707.866420532246[/C][/ROW]
[ROW][C]83[/C][C]565.001870490373[/C][C]415.164364315188[/C][C]714.839376665557[/C][/ROW]
[ROW][C]84[/C][C]565.001870490373[/C][C]408.501784691898[/C][C]721.501956288847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73565.001870490373519.821207862609610.182533118137
74565.001870490373501.109062807385628.894678173361
75565.001870490373486.750420205111643.253320775634
76565.001870490373474.64542041691655.358320563836
77565.001870490373463.980651590531666.023089390214
78565.001870490373454.338935113883675.664805866863
79565.001870490373445.472443719085684.53129726166
80565.001870490373437.219702476193692.784038504553
81565.001870490373429.468549640718700.535191340028
82565.001870490373422.137320448499707.866420532246
83565.001870490373415.164364315188714.839376665557
84565.001870490373408.501784691898721.501956288847



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
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')