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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 computationThu, 14 Aug 2014 16:31:10 +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/2014/Aug/14/t1408030495wxdjedeogc65xyp.htm/, Retrieved Wed, 15 May 2024 01:16:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235563, Retrieved Wed, 15 May 2024 01:16:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBoeykens Brice
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B Stap 27] [2014-08-14 15:31:10] [7314f5de623f4497f735e8af2050bf2f] [Current]
- RMP     [(Partial) Autocorrelation Function] [Tijdreeks B Stap 18] [2014-08-17 11:26:29] [2064a7ed2562130dd70fccaf2dd61d5a]
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Dataseries X:
330
310
310
380
330
250
370
380
430
360
440
480
260
340
270
400
330
340
360
480
490
420
430
450
300
320
260
330
260
330
350
500
570
450
420
360
280
360
260
370
200
320
390
480
570
450
460
320
310
410
230
450
230
310
430
540
450
430
480
320
310
380
210
450
120
210
410
660
510
510
450
290
320
380
260
530
180
260
460
620
540
610
460
290
330
440
350
450
240
280
540
540
600
590
410
270
370
350
340
420
210
180
580
560
610
560
410
330




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235563&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235563&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235563&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0621818484263268
beta0.0413548826237257
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0621818484263268 \tabularnewline
beta & 0.0413548826237257 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235563&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]0.0621818484263268[/C][/ROW]
[ROW][C]beta[/C][C]0.0413548826237257[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235563&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235563&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
alpha0.0621818484263268
beta0.0413548826237257
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13260249.81837606837610.1816239316237
14340329.28594560325710.7140543967432
15270255.89750741971514.1024925802848
16400384.42270013700515.5772998629947
17330315.99632314941914.0036768505811
18340331.2581061519028.74189384809773
19360385.38184840941-25.3818484094095
20480398.15177662339681.8482233766039
21490456.54994350036633.4500564996339
22420392.44130715822527.5586928417747
23430476.370536081098-46.3705360810979
24450512.666799328098-62.6667993280979
25300297.7537600876952.24623991230533
26320377.417054424325-57.4170544243246
27260302.98447477009-42.9844747700897
28330429.210832901407-99.2108329014075
29260351.743602613011-91.7436026130111
30330354.79595433381-24.79595433381
31350374.046868591788-24.0468685917883
32500486.68003124665613.3199687533439
33570494.46999840848675.530001591514
34450426.60284583330523.397154166695
35420440.080331056081-20.080331056081
36360461.935243521944-101.935243521944
37280304.562873751858-24.5628737518583
38360325.64269462270834.3573053772923
39260269.724836541944-9.7248365419436
40370344.64765619904125.3523438009589
41200281.607630664686-81.6076306646855
42320347.779772578055-27.7797725780554
43390367.24477771064222.755222289358
44480517.648955873495-37.6489558734945
45570580.297687988813-10.297687988813
46450457.668181433124-7.66818143312446
47460427.82580762526532.1741923747351
48320375.685169737476-55.6851697374764
49310293.38905047304116.6109495269594
50410372.03055132598637.9694486740135
51230274.75056091236-44.7505609123602
52450380.05565403218869.9443459678118
53230219.25832674792310.7416732520772
54310341.670030492784-31.670030492784
55430408.29213282493821.7078671750617
56540501.98672165221938.0132783477807
57450595.189025870483-145.189025870483
58430466.489088414747-36.4890884147473
59480471.9967279183478.00327208165317
60320335.672086097654-15.6720860976542
61310323.482654979905-13.4826549799053
62380420.023869382048-40.0238693820478
63210239.857823496529-29.8578234965291
64450453.230276837902-3.23027683790224
65120231.751641642103-111.751641642103
66210305.847191140932-95.8471911409322
67410417.447539380591-7.44753938059068
68660523.455866961094136.544133038906
69510450.06309516617859.936904833822
70510435.67506734135174.3249326586489
71450489.700057274042-39.700057274042
72290327.984269889004-37.9842698890037
73320316.1816541664113.81834583358909
74380388.673274051768-8.67327405176781
75260219.83661717676940.1633828232308
76530462.56102497247867.4389750275216
77180143.91126617524936.0887338247507
78260242.70329823325117.2967017667488
79460445.12090538328514.8790946167152
80620688.491926356715-68.4919263567147
81540530.9151072420559.08489275794489
82610527.13671684878782.8632831512133
83460475.05824434994-15.0582443499399
84290316.847506428989-26.8475064289892
85330345.332964929556-15.3329649295564
86440405.2619228817234.7380771182804
87350285.37927047546164.6207295245388
88450555.721622522133-105.721622522133
89240196.97590173311643.0240982668841
90280278.6658225467941.33417745320594
91540477.87267030579262.1273296942084
92540646.165412757358-106.165412757358
93600559.07265316057840.9273468394224
94590626.620600161497-36.6206001614974
95410475.128158497779-65.1281584977787
96270302.467386332254-32.4673863322544
97370341.10707422612728.8929257738729
98350450.562477696649-100.562477696649
99340349.762017833659-9.76201783365877
100420455.008623769627-35.0086237696268
101210239.617905323569-29.6179053235693
102180276.967947465653-96.967947465653
103580526.09702273833853.902977261662
104560535.05113567493724.9488643250634
105610593.39549205251916.6045079474809
106560585.980508872118-25.980508872118
107410407.7175245420092.2824754579907
108330269.35442563386860.6455743661319

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 260 & 249.818376068376 & 10.1816239316237 \tabularnewline
14 & 340 & 329.285945603257 & 10.7140543967432 \tabularnewline
15 & 270 & 255.897507419715 & 14.1024925802848 \tabularnewline
16 & 400 & 384.422700137005 & 15.5772998629947 \tabularnewline
17 & 330 & 315.996323149419 & 14.0036768505811 \tabularnewline
18 & 340 & 331.258106151902 & 8.74189384809773 \tabularnewline
19 & 360 & 385.38184840941 & -25.3818484094095 \tabularnewline
20 & 480 & 398.151776623396 & 81.8482233766039 \tabularnewline
21 & 490 & 456.549943500366 & 33.4500564996339 \tabularnewline
22 & 420 & 392.441307158225 & 27.5586928417747 \tabularnewline
23 & 430 & 476.370536081098 & -46.3705360810979 \tabularnewline
24 & 450 & 512.666799328098 & -62.6667993280979 \tabularnewline
25 & 300 & 297.753760087695 & 2.24623991230533 \tabularnewline
26 & 320 & 377.417054424325 & -57.4170544243246 \tabularnewline
27 & 260 & 302.98447477009 & -42.9844747700897 \tabularnewline
28 & 330 & 429.210832901407 & -99.2108329014075 \tabularnewline
29 & 260 & 351.743602613011 & -91.7436026130111 \tabularnewline
30 & 330 & 354.79595433381 & -24.79595433381 \tabularnewline
31 & 350 & 374.046868591788 & -24.0468685917883 \tabularnewline
32 & 500 & 486.680031246656 & 13.3199687533439 \tabularnewline
33 & 570 & 494.469998408486 & 75.530001591514 \tabularnewline
34 & 450 & 426.602845833305 & 23.397154166695 \tabularnewline
35 & 420 & 440.080331056081 & -20.080331056081 \tabularnewline
36 & 360 & 461.935243521944 & -101.935243521944 \tabularnewline
37 & 280 & 304.562873751858 & -24.5628737518583 \tabularnewline
38 & 360 & 325.642694622708 & 34.3573053772923 \tabularnewline
39 & 260 & 269.724836541944 & -9.7248365419436 \tabularnewline
40 & 370 & 344.647656199041 & 25.3523438009589 \tabularnewline
41 & 200 & 281.607630664686 & -81.6076306646855 \tabularnewline
42 & 320 & 347.779772578055 & -27.7797725780554 \tabularnewline
43 & 390 & 367.244777710642 & 22.755222289358 \tabularnewline
44 & 480 & 517.648955873495 & -37.6489558734945 \tabularnewline
45 & 570 & 580.297687988813 & -10.297687988813 \tabularnewline
46 & 450 & 457.668181433124 & -7.66818143312446 \tabularnewline
47 & 460 & 427.825807625265 & 32.1741923747351 \tabularnewline
48 & 320 & 375.685169737476 & -55.6851697374764 \tabularnewline
49 & 310 & 293.389050473041 & 16.6109495269594 \tabularnewline
50 & 410 & 372.030551325986 & 37.9694486740135 \tabularnewline
51 & 230 & 274.75056091236 & -44.7505609123602 \tabularnewline
52 & 450 & 380.055654032188 & 69.9443459678118 \tabularnewline
53 & 230 & 219.258326747923 & 10.7416732520772 \tabularnewline
54 & 310 & 341.670030492784 & -31.670030492784 \tabularnewline
55 & 430 & 408.292132824938 & 21.7078671750617 \tabularnewline
56 & 540 & 501.986721652219 & 38.0132783477807 \tabularnewline
57 & 450 & 595.189025870483 & -145.189025870483 \tabularnewline
58 & 430 & 466.489088414747 & -36.4890884147473 \tabularnewline
59 & 480 & 471.996727918347 & 8.00327208165317 \tabularnewline
60 & 320 & 335.672086097654 & -15.6720860976542 \tabularnewline
61 & 310 & 323.482654979905 & -13.4826549799053 \tabularnewline
62 & 380 & 420.023869382048 & -40.0238693820478 \tabularnewline
63 & 210 & 239.857823496529 & -29.8578234965291 \tabularnewline
64 & 450 & 453.230276837902 & -3.23027683790224 \tabularnewline
65 & 120 & 231.751641642103 & -111.751641642103 \tabularnewline
66 & 210 & 305.847191140932 & -95.8471911409322 \tabularnewline
67 & 410 & 417.447539380591 & -7.44753938059068 \tabularnewline
68 & 660 & 523.455866961094 & 136.544133038906 \tabularnewline
69 & 510 & 450.063095166178 & 59.936904833822 \tabularnewline
70 & 510 & 435.675067341351 & 74.3249326586489 \tabularnewline
71 & 450 & 489.700057274042 & -39.700057274042 \tabularnewline
72 & 290 & 327.984269889004 & -37.9842698890037 \tabularnewline
73 & 320 & 316.181654166411 & 3.81834583358909 \tabularnewline
74 & 380 & 388.673274051768 & -8.67327405176781 \tabularnewline
75 & 260 & 219.836617176769 & 40.1633828232308 \tabularnewline
76 & 530 & 462.561024972478 & 67.4389750275216 \tabularnewline
77 & 180 & 143.911266175249 & 36.0887338247507 \tabularnewline
78 & 260 & 242.703298233251 & 17.2967017667488 \tabularnewline
79 & 460 & 445.120905383285 & 14.8790946167152 \tabularnewline
80 & 620 & 688.491926356715 & -68.4919263567147 \tabularnewline
81 & 540 & 530.915107242055 & 9.08489275794489 \tabularnewline
82 & 610 & 527.136716848787 & 82.8632831512133 \tabularnewline
83 & 460 & 475.05824434994 & -15.0582443499399 \tabularnewline
84 & 290 & 316.847506428989 & -26.8475064289892 \tabularnewline
85 & 330 & 345.332964929556 & -15.3329649295564 \tabularnewline
86 & 440 & 405.26192288172 & 34.7380771182804 \tabularnewline
87 & 350 & 285.379270475461 & 64.6207295245388 \tabularnewline
88 & 450 & 555.721622522133 & -105.721622522133 \tabularnewline
89 & 240 & 196.975901733116 & 43.0240982668841 \tabularnewline
90 & 280 & 278.665822546794 & 1.33417745320594 \tabularnewline
91 & 540 & 477.872670305792 & 62.1273296942084 \tabularnewline
92 & 540 & 646.165412757358 & -106.165412757358 \tabularnewline
93 & 600 & 559.072653160578 & 40.9273468394224 \tabularnewline
94 & 590 & 626.620600161497 & -36.6206001614974 \tabularnewline
95 & 410 & 475.128158497779 & -65.1281584977787 \tabularnewline
96 & 270 & 302.467386332254 & -32.4673863322544 \tabularnewline
97 & 370 & 341.107074226127 & 28.8929257738729 \tabularnewline
98 & 350 & 450.562477696649 & -100.562477696649 \tabularnewline
99 & 340 & 349.762017833659 & -9.76201783365877 \tabularnewline
100 & 420 & 455.008623769627 & -35.0086237696268 \tabularnewline
101 & 210 & 239.617905323569 & -29.6179053235693 \tabularnewline
102 & 180 & 276.967947465653 & -96.967947465653 \tabularnewline
103 & 580 & 526.097022738338 & 53.902977261662 \tabularnewline
104 & 560 & 535.051135674937 & 24.9488643250634 \tabularnewline
105 & 610 & 593.395492052519 & 16.6045079474809 \tabularnewline
106 & 560 & 585.980508872118 & -25.980508872118 \tabularnewline
107 & 410 & 407.717524542009 & 2.2824754579907 \tabularnewline
108 & 330 & 269.354425633868 & 60.6455743661319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235563&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]260[/C][C]249.818376068376[/C][C]10.1816239316237[/C][/ROW]
[ROW][C]14[/C][C]340[/C][C]329.285945603257[/C][C]10.7140543967432[/C][/ROW]
[ROW][C]15[/C][C]270[/C][C]255.897507419715[/C][C]14.1024925802848[/C][/ROW]
[ROW][C]16[/C][C]400[/C][C]384.422700137005[/C][C]15.5772998629947[/C][/ROW]
[ROW][C]17[/C][C]330[/C][C]315.996323149419[/C][C]14.0036768505811[/C][/ROW]
[ROW][C]18[/C][C]340[/C][C]331.258106151902[/C][C]8.74189384809773[/C][/ROW]
[ROW][C]19[/C][C]360[/C][C]385.38184840941[/C][C]-25.3818484094095[/C][/ROW]
[ROW][C]20[/C][C]480[/C][C]398.151776623396[/C][C]81.8482233766039[/C][/ROW]
[ROW][C]21[/C][C]490[/C][C]456.549943500366[/C][C]33.4500564996339[/C][/ROW]
[ROW][C]22[/C][C]420[/C][C]392.441307158225[/C][C]27.5586928417747[/C][/ROW]
[ROW][C]23[/C][C]430[/C][C]476.370536081098[/C][C]-46.3705360810979[/C][/ROW]
[ROW][C]24[/C][C]450[/C][C]512.666799328098[/C][C]-62.6667993280979[/C][/ROW]
[ROW][C]25[/C][C]300[/C][C]297.753760087695[/C][C]2.24623991230533[/C][/ROW]
[ROW][C]26[/C][C]320[/C][C]377.417054424325[/C][C]-57.4170544243246[/C][/ROW]
[ROW][C]27[/C][C]260[/C][C]302.98447477009[/C][C]-42.9844747700897[/C][/ROW]
[ROW][C]28[/C][C]330[/C][C]429.210832901407[/C][C]-99.2108329014075[/C][/ROW]
[ROW][C]29[/C][C]260[/C][C]351.743602613011[/C][C]-91.7436026130111[/C][/ROW]
[ROW][C]30[/C][C]330[/C][C]354.79595433381[/C][C]-24.79595433381[/C][/ROW]
[ROW][C]31[/C][C]350[/C][C]374.046868591788[/C][C]-24.0468685917883[/C][/ROW]
[ROW][C]32[/C][C]500[/C][C]486.680031246656[/C][C]13.3199687533439[/C][/ROW]
[ROW][C]33[/C][C]570[/C][C]494.469998408486[/C][C]75.530001591514[/C][/ROW]
[ROW][C]34[/C][C]450[/C][C]426.602845833305[/C][C]23.397154166695[/C][/ROW]
[ROW][C]35[/C][C]420[/C][C]440.080331056081[/C][C]-20.080331056081[/C][/ROW]
[ROW][C]36[/C][C]360[/C][C]461.935243521944[/C][C]-101.935243521944[/C][/ROW]
[ROW][C]37[/C][C]280[/C][C]304.562873751858[/C][C]-24.5628737518583[/C][/ROW]
[ROW][C]38[/C][C]360[/C][C]325.642694622708[/C][C]34.3573053772923[/C][/ROW]
[ROW][C]39[/C][C]260[/C][C]269.724836541944[/C][C]-9.7248365419436[/C][/ROW]
[ROW][C]40[/C][C]370[/C][C]344.647656199041[/C][C]25.3523438009589[/C][/ROW]
[ROW][C]41[/C][C]200[/C][C]281.607630664686[/C][C]-81.6076306646855[/C][/ROW]
[ROW][C]42[/C][C]320[/C][C]347.779772578055[/C][C]-27.7797725780554[/C][/ROW]
[ROW][C]43[/C][C]390[/C][C]367.244777710642[/C][C]22.755222289358[/C][/ROW]
[ROW][C]44[/C][C]480[/C][C]517.648955873495[/C][C]-37.6489558734945[/C][/ROW]
[ROW][C]45[/C][C]570[/C][C]580.297687988813[/C][C]-10.297687988813[/C][/ROW]
[ROW][C]46[/C][C]450[/C][C]457.668181433124[/C][C]-7.66818143312446[/C][/ROW]
[ROW][C]47[/C][C]460[/C][C]427.825807625265[/C][C]32.1741923747351[/C][/ROW]
[ROW][C]48[/C][C]320[/C][C]375.685169737476[/C][C]-55.6851697374764[/C][/ROW]
[ROW][C]49[/C][C]310[/C][C]293.389050473041[/C][C]16.6109495269594[/C][/ROW]
[ROW][C]50[/C][C]410[/C][C]372.030551325986[/C][C]37.9694486740135[/C][/ROW]
[ROW][C]51[/C][C]230[/C][C]274.75056091236[/C][C]-44.7505609123602[/C][/ROW]
[ROW][C]52[/C][C]450[/C][C]380.055654032188[/C][C]69.9443459678118[/C][/ROW]
[ROW][C]53[/C][C]230[/C][C]219.258326747923[/C][C]10.7416732520772[/C][/ROW]
[ROW][C]54[/C][C]310[/C][C]341.670030492784[/C][C]-31.670030492784[/C][/ROW]
[ROW][C]55[/C][C]430[/C][C]408.292132824938[/C][C]21.7078671750617[/C][/ROW]
[ROW][C]56[/C][C]540[/C][C]501.986721652219[/C][C]38.0132783477807[/C][/ROW]
[ROW][C]57[/C][C]450[/C][C]595.189025870483[/C][C]-145.189025870483[/C][/ROW]
[ROW][C]58[/C][C]430[/C][C]466.489088414747[/C][C]-36.4890884147473[/C][/ROW]
[ROW][C]59[/C][C]480[/C][C]471.996727918347[/C][C]8.00327208165317[/C][/ROW]
[ROW][C]60[/C][C]320[/C][C]335.672086097654[/C][C]-15.6720860976542[/C][/ROW]
[ROW][C]61[/C][C]310[/C][C]323.482654979905[/C][C]-13.4826549799053[/C][/ROW]
[ROW][C]62[/C][C]380[/C][C]420.023869382048[/C][C]-40.0238693820478[/C][/ROW]
[ROW][C]63[/C][C]210[/C][C]239.857823496529[/C][C]-29.8578234965291[/C][/ROW]
[ROW][C]64[/C][C]450[/C][C]453.230276837902[/C][C]-3.23027683790224[/C][/ROW]
[ROW][C]65[/C][C]120[/C][C]231.751641642103[/C][C]-111.751641642103[/C][/ROW]
[ROW][C]66[/C][C]210[/C][C]305.847191140932[/C][C]-95.8471911409322[/C][/ROW]
[ROW][C]67[/C][C]410[/C][C]417.447539380591[/C][C]-7.44753938059068[/C][/ROW]
[ROW][C]68[/C][C]660[/C][C]523.455866961094[/C][C]136.544133038906[/C][/ROW]
[ROW][C]69[/C][C]510[/C][C]450.063095166178[/C][C]59.936904833822[/C][/ROW]
[ROW][C]70[/C][C]510[/C][C]435.675067341351[/C][C]74.3249326586489[/C][/ROW]
[ROW][C]71[/C][C]450[/C][C]489.700057274042[/C][C]-39.700057274042[/C][/ROW]
[ROW][C]72[/C][C]290[/C][C]327.984269889004[/C][C]-37.9842698890037[/C][/ROW]
[ROW][C]73[/C][C]320[/C][C]316.181654166411[/C][C]3.81834583358909[/C][/ROW]
[ROW][C]74[/C][C]380[/C][C]388.673274051768[/C][C]-8.67327405176781[/C][/ROW]
[ROW][C]75[/C][C]260[/C][C]219.836617176769[/C][C]40.1633828232308[/C][/ROW]
[ROW][C]76[/C][C]530[/C][C]462.561024972478[/C][C]67.4389750275216[/C][/ROW]
[ROW][C]77[/C][C]180[/C][C]143.911266175249[/C][C]36.0887338247507[/C][/ROW]
[ROW][C]78[/C][C]260[/C][C]242.703298233251[/C][C]17.2967017667488[/C][/ROW]
[ROW][C]79[/C][C]460[/C][C]445.120905383285[/C][C]14.8790946167152[/C][/ROW]
[ROW][C]80[/C][C]620[/C][C]688.491926356715[/C][C]-68.4919263567147[/C][/ROW]
[ROW][C]81[/C][C]540[/C][C]530.915107242055[/C][C]9.08489275794489[/C][/ROW]
[ROW][C]82[/C][C]610[/C][C]527.136716848787[/C][C]82.8632831512133[/C][/ROW]
[ROW][C]83[/C][C]460[/C][C]475.05824434994[/C][C]-15.0582443499399[/C][/ROW]
[ROW][C]84[/C][C]290[/C][C]316.847506428989[/C][C]-26.8475064289892[/C][/ROW]
[ROW][C]85[/C][C]330[/C][C]345.332964929556[/C][C]-15.3329649295564[/C][/ROW]
[ROW][C]86[/C][C]440[/C][C]405.26192288172[/C][C]34.7380771182804[/C][/ROW]
[ROW][C]87[/C][C]350[/C][C]285.379270475461[/C][C]64.6207295245388[/C][/ROW]
[ROW][C]88[/C][C]450[/C][C]555.721622522133[/C][C]-105.721622522133[/C][/ROW]
[ROW][C]89[/C][C]240[/C][C]196.975901733116[/C][C]43.0240982668841[/C][/ROW]
[ROW][C]90[/C][C]280[/C][C]278.665822546794[/C][C]1.33417745320594[/C][/ROW]
[ROW][C]91[/C][C]540[/C][C]477.872670305792[/C][C]62.1273296942084[/C][/ROW]
[ROW][C]92[/C][C]540[/C][C]646.165412757358[/C][C]-106.165412757358[/C][/ROW]
[ROW][C]93[/C][C]600[/C][C]559.072653160578[/C][C]40.9273468394224[/C][/ROW]
[ROW][C]94[/C][C]590[/C][C]626.620600161497[/C][C]-36.6206001614974[/C][/ROW]
[ROW][C]95[/C][C]410[/C][C]475.128158497779[/C][C]-65.1281584977787[/C][/ROW]
[ROW][C]96[/C][C]270[/C][C]302.467386332254[/C][C]-32.4673863322544[/C][/ROW]
[ROW][C]97[/C][C]370[/C][C]341.107074226127[/C][C]28.8929257738729[/C][/ROW]
[ROW][C]98[/C][C]350[/C][C]450.562477696649[/C][C]-100.562477696649[/C][/ROW]
[ROW][C]99[/C][C]340[/C][C]349.762017833659[/C][C]-9.76201783365877[/C][/ROW]
[ROW][C]100[/C][C]420[/C][C]455.008623769627[/C][C]-35.0086237696268[/C][/ROW]
[ROW][C]101[/C][C]210[/C][C]239.617905323569[/C][C]-29.6179053235693[/C][/ROW]
[ROW][C]102[/C][C]180[/C][C]276.967947465653[/C][C]-96.967947465653[/C][/ROW]
[ROW][C]103[/C][C]580[/C][C]526.097022738338[/C][C]53.902977261662[/C][/ROW]
[ROW][C]104[/C][C]560[/C][C]535.051135674937[/C][C]24.9488643250634[/C][/ROW]
[ROW][C]105[/C][C]610[/C][C]593.395492052519[/C][C]16.6045079474809[/C][/ROW]
[ROW][C]106[/C][C]560[/C][C]585.980508872118[/C][C]-25.980508872118[/C][/ROW]
[ROW][C]107[/C][C]410[/C][C]407.717524542009[/C][C]2.2824754579907[/C][/ROW]
[ROW][C]108[/C][C]330[/C][C]269.354425633868[/C][C]60.6455743661319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235563&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235563&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
13260249.81837606837610.1816239316237
14340329.28594560325710.7140543967432
15270255.89750741971514.1024925802848
16400384.42270013700515.5772998629947
17330315.99632314941914.0036768505811
18340331.2581061519028.74189384809773
19360385.38184840941-25.3818484094095
20480398.15177662339681.8482233766039
21490456.54994350036633.4500564996339
22420392.44130715822527.5586928417747
23430476.370536081098-46.3705360810979
24450512.666799328098-62.6667993280979
25300297.7537600876952.24623991230533
26320377.417054424325-57.4170544243246
27260302.98447477009-42.9844747700897
28330429.210832901407-99.2108329014075
29260351.743602613011-91.7436026130111
30330354.79595433381-24.79595433381
31350374.046868591788-24.0468685917883
32500486.68003124665613.3199687533439
33570494.46999840848675.530001591514
34450426.60284583330523.397154166695
35420440.080331056081-20.080331056081
36360461.935243521944-101.935243521944
37280304.562873751858-24.5628737518583
38360325.64269462270834.3573053772923
39260269.724836541944-9.7248365419436
40370344.64765619904125.3523438009589
41200281.607630664686-81.6076306646855
42320347.779772578055-27.7797725780554
43390367.24477771064222.755222289358
44480517.648955873495-37.6489558734945
45570580.297687988813-10.297687988813
46450457.668181433124-7.66818143312446
47460427.82580762526532.1741923747351
48320375.685169737476-55.6851697374764
49310293.38905047304116.6109495269594
50410372.03055132598637.9694486740135
51230274.75056091236-44.7505609123602
52450380.05565403218869.9443459678118
53230219.25832674792310.7416732520772
54310341.670030492784-31.670030492784
55430408.29213282493821.7078671750617
56540501.98672165221938.0132783477807
57450595.189025870483-145.189025870483
58430466.489088414747-36.4890884147473
59480471.9967279183478.00327208165317
60320335.672086097654-15.6720860976542
61310323.482654979905-13.4826549799053
62380420.023869382048-40.0238693820478
63210239.857823496529-29.8578234965291
64450453.230276837902-3.23027683790224
65120231.751641642103-111.751641642103
66210305.847191140932-95.8471911409322
67410417.447539380591-7.44753938059068
68660523.455866961094136.544133038906
69510450.06309516617859.936904833822
70510435.67506734135174.3249326586489
71450489.700057274042-39.700057274042
72290327.984269889004-37.9842698890037
73320316.1816541664113.81834583358909
74380388.673274051768-8.67327405176781
75260219.83661717676940.1633828232308
76530462.56102497247867.4389750275216
77180143.91126617524936.0887338247507
78260242.70329823325117.2967017667488
79460445.12090538328514.8790946167152
80620688.491926356715-68.4919263567147
81540530.9151072420559.08489275794489
82610527.13671684878782.8632831512133
83460475.05824434994-15.0582443499399
84290316.847506428989-26.8475064289892
85330345.332964929556-15.3329649295564
86440405.2619228817234.7380771182804
87350285.37927047546164.6207295245388
88450555.721622522133-105.721622522133
89240196.97590173311643.0240982668841
90280278.6658225467941.33417745320594
91540477.87267030579262.1273296942084
92540646.165412757358-106.165412757358
93600559.07265316057840.9273468394224
94590626.620600161497-36.6206001614974
95410475.128158497779-65.1281584977787
96270302.467386332254-32.4673863322544
97370341.10707422612728.8929257738729
98350450.562477696649-100.562477696649
99340349.762017833659-9.76201783365877
100420455.008623769627-35.0086237696268
101210239.617905323569-29.6179053235693
102180276.967947465653-96.967947465653
103580526.09702273833853.902977261662
104560535.05113567493724.9488643250634
105610593.39549205251916.6045079474809
106560585.980508872118-25.980508872118
107410407.7175245420092.2824754579907
108330269.35442563386860.6455743661319







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109371.044396592986269.947312137907472.141481048065
110356.938791091307255.629978355278458.247603827337
111347.445643886045245.90844899794448.98283877415
112429.547480558178327.764697726191531.330263390165
113221.404137875716119.358023220417323.450252531016
114197.52490843126595.1971945712121299.852622291318
115594.513601324821491.885512693132697.141689956509
116573.164101732204470.216370597556676.111832866852
117622.269313063565518.982196224231725.556429902898
118573.97984058123470.333136696119677.62654446634
119423.999732968438319.972800484626528.026665452249
120340.384630547414235.956406179495444.812854915332

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 371.044396592986 & 269.947312137907 & 472.141481048065 \tabularnewline
110 & 356.938791091307 & 255.629978355278 & 458.247603827337 \tabularnewline
111 & 347.445643886045 & 245.90844899794 & 448.98283877415 \tabularnewline
112 & 429.547480558178 & 327.764697726191 & 531.330263390165 \tabularnewline
113 & 221.404137875716 & 119.358023220417 & 323.450252531016 \tabularnewline
114 & 197.524908431265 & 95.1971945712121 & 299.852622291318 \tabularnewline
115 & 594.513601324821 & 491.885512693132 & 697.141689956509 \tabularnewline
116 & 573.164101732204 & 470.216370597556 & 676.111832866852 \tabularnewline
117 & 622.269313063565 & 518.982196224231 & 725.556429902898 \tabularnewline
118 & 573.97984058123 & 470.333136696119 & 677.62654446634 \tabularnewline
119 & 423.999732968438 & 319.972800484626 & 528.026665452249 \tabularnewline
120 & 340.384630547414 & 235.956406179495 & 444.812854915332 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235563&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]371.044396592986[/C][C]269.947312137907[/C][C]472.141481048065[/C][/ROW]
[ROW][C]110[/C][C]356.938791091307[/C][C]255.629978355278[/C][C]458.247603827337[/C][/ROW]
[ROW][C]111[/C][C]347.445643886045[/C][C]245.90844899794[/C][C]448.98283877415[/C][/ROW]
[ROW][C]112[/C][C]429.547480558178[/C][C]327.764697726191[/C][C]531.330263390165[/C][/ROW]
[ROW][C]113[/C][C]221.404137875716[/C][C]119.358023220417[/C][C]323.450252531016[/C][/ROW]
[ROW][C]114[/C][C]197.524908431265[/C][C]95.1971945712121[/C][C]299.852622291318[/C][/ROW]
[ROW][C]115[/C][C]594.513601324821[/C][C]491.885512693132[/C][C]697.141689956509[/C][/ROW]
[ROW][C]116[/C][C]573.164101732204[/C][C]470.216370597556[/C][C]676.111832866852[/C][/ROW]
[ROW][C]117[/C][C]622.269313063565[/C][C]518.982196224231[/C][C]725.556429902898[/C][/ROW]
[ROW][C]118[/C][C]573.97984058123[/C][C]470.333136696119[/C][C]677.62654446634[/C][/ROW]
[ROW][C]119[/C][C]423.999732968438[/C][C]319.972800484626[/C][C]528.026665452249[/C][/ROW]
[ROW][C]120[/C][C]340.384630547414[/C][C]235.956406179495[/C][C]444.812854915332[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235563&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235563&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
109371.044396592986269.947312137907472.141481048065
110356.938791091307255.629978355278458.247603827337
111347.445643886045245.90844899794448.98283877415
112429.547480558178327.764697726191531.330263390165
113221.404137875716119.358023220417323.450252531016
114197.52490843126595.1971945712121299.852622291318
115594.513601324821491.885512693132697.141689956509
116573.164101732204470.216370597556676.111832866852
117622.269313063565518.982196224231725.556429902898
118573.97984058123470.333136696119677.62654446634
119423.999732968438319.972800484626528.026665452249
120340.384630547414235.956406179495444.812854915332



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')