Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 16:57:16 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/18/t1313701145qoi7yqxrd03rk4z.htm/, Retrieved Thu, 31 Oct 2024 22:57:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124162, Retrieved Thu, 31 Oct 2024 22:57:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmattias debbaut
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks B - Exp...] [2011-08-18 20:57:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
510
460
570
520
470
500
520
500
580
460
530
610
460
380
570
480
530
530
580
420
580
460
520
640
380
360
610
440
520
540
580
360
500
530
470
660
410
360
610
360
540
560
580
480
560
560
390
630
380
440
620
310
500
660
420
550
570
560
290
560
320
440
610
250
510
670
350
590
500
530
300
620
280
450
620
320
560
680
370
670
510
480
280
570
240
460
600
320
570
680
390
700
570
450
270
640
230
490
590
310
570
660
370
600
540
510
330
590




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=124162&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=124162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124162&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
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124162&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124162&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13460455.6652551607834.33474483921748
14380376.9948400072563.00515999274393
15570569.1303769403540.86962305964596
16480479.2239961564810.776003843518765
17530529.5268359474010.47316405259869
18530528.6155101392041.38448986079629
19580512.74396132142567.2560386785754
20420498.196903041666-78.1969030416662
21580581.644919518678-1.64491951867819
22460462.779827051894-2.77982705189396
23520532.278748330859-12.2787483308587
24640608.07366816911331.9263318308873
25380459.496892605483-79.4968926054835
26360379.584351660372-19.5843516603717
27610569.37647065526440.6235293447356
28440479.474874787038-39.4748747870384
29520529.420121377896-9.42012137789561
30540529.42006850212910.5799314978713
31580579.3653001088610.63469989113878
32360419.540347817165-59.5403478171652
33500579.365184327988-79.3651843279882
34530459.49647957583970.5035204241611
35470519.430751073329-49.4307510733286
36660639.29932201650220.7006779834978
37410379.5839344879330.4160655120696
38360359.6057967047070.394203295293039
39610609.331983459290.668016540710028
40360439.518108026399-79.5181080263992
41540519.43043932159320.5695606784068
42560539.40847915014520.5915208498546
43580579.3646047894280.635395210571573
44480359.605580758367120.394419241633
45560499.45214547820360.547854521797
46560529.41922117651130.5807788234889
47390469.484922687032-79.4849226870325
48630659.276633881528-29.2766338815285
49380409.550595153141-29.5505951531414
50440359.60536457530580.3946354246955
51620609.33125110630210.6687488936977
52310359.605292461611-49.6052924616115
53500539.407884592321-39.4078845923211
54660559.385898277979100.614101722021
55420579.363907944868-159.363907944868
56550479.47353087350770.5264691264929
57570559.38572987425510.6142701257447
58560559.3856737191540.614326280846058
59290389.572126510671-99.5721265106712
60560629.308756550412-69.3087565504119
61320379.583021380442-59.5830213804417
62440439.5171384968880.482861503112076
63610619.319542017023-9.31954201702308
64250309.659739888524-59.6597398885237
65510499.45114316587510.548856834125
66670659.27544269925110.7245573007494
67350419.53887589563-69.5388758956296
68590549.39609175287840.6039082471219
69500569.374074179988-69.3740741799882
70530559.384999056221-29.3849990562209
71300289.6814882188410.3185117811604
72620559.38488646830360.6151135316966
73280319.648474376506-39.6484743765055
74450439.51660801647910.4833919835206
75620609.32978157242710.6702184275731
76320249.72529516462370.2747048353773
77560509.43955081646350.5604491835367
78680669.26365618971910.7363438102814
79370349.61530755359720.3846924464034
80670589.35145904539580.6485409546054
81510499.45033867153710.5496613284625
82480529.417305611068-49.4173056110677
83280299.670142766334-19.670142766334
84570619.318232582114-49.3182325821141
85240279.692076820418-39.6920768204183
86460449.50507810486210.4949218951383
87600619.318045108475-19.3180451084747
88320319.6479910164380.352008983562484
89570559.3839278040410.6160721959603
90680679.2518437444490.74815625555118
91390369.59287765125320.4071223487474
92700669.2627108444130.7372891555905
93570509.43872842641160.5612715735894
94450479.471695950013-29.471695950013
95270279.691794369056-9.69179436905569
96640569.37252383709970.6274761629005
97230239.735775271364-9.73577527136368
98490459.49352280351730.5064771964834
99590599.339316950076-9.33931695007618
100310319.647603370252-9.64760337025172
101570569.3722358933770.627764106623317
102660679.251019694006-19.2510196940059
103370389.570398333917-19.5703983339167
104600699.228849298563-99.2288492985629
105540569.372005348054-29.372005348054
106510449.50416922520760.4958307747929
107330269.70247421615460.2975257838461
108590639.294688929578-49.2946889295781

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 460 & 455.665255160783 & 4.33474483921748 \tabularnewline
14 & 380 & 376.994840007256 & 3.00515999274393 \tabularnewline
15 & 570 & 569.130376940354 & 0.86962305964596 \tabularnewline
16 & 480 & 479.223996156481 & 0.776003843518765 \tabularnewline
17 & 530 & 529.526835947401 & 0.47316405259869 \tabularnewline
18 & 530 & 528.615510139204 & 1.38448986079629 \tabularnewline
19 & 580 & 512.743961321425 & 67.2560386785754 \tabularnewline
20 & 420 & 498.196903041666 & -78.1969030416662 \tabularnewline
21 & 580 & 581.644919518678 & -1.64491951867819 \tabularnewline
22 & 460 & 462.779827051894 & -2.77982705189396 \tabularnewline
23 & 520 & 532.278748330859 & -12.2787483308587 \tabularnewline
24 & 640 & 608.073668169113 & 31.9263318308873 \tabularnewline
25 & 380 & 459.496892605483 & -79.4968926054835 \tabularnewline
26 & 360 & 379.584351660372 & -19.5843516603717 \tabularnewline
27 & 610 & 569.376470655264 & 40.6235293447356 \tabularnewline
28 & 440 & 479.474874787038 & -39.4748747870384 \tabularnewline
29 & 520 & 529.420121377896 & -9.42012137789561 \tabularnewline
30 & 540 & 529.420068502129 & 10.5799314978713 \tabularnewline
31 & 580 & 579.365300108861 & 0.63469989113878 \tabularnewline
32 & 360 & 419.540347817165 & -59.5403478171652 \tabularnewline
33 & 500 & 579.365184327988 & -79.3651843279882 \tabularnewline
34 & 530 & 459.496479575839 & 70.5035204241611 \tabularnewline
35 & 470 & 519.430751073329 & -49.4307510733286 \tabularnewline
36 & 660 & 639.299322016502 & 20.7006779834978 \tabularnewline
37 & 410 & 379.58393448793 & 30.4160655120696 \tabularnewline
38 & 360 & 359.605796704707 & 0.394203295293039 \tabularnewline
39 & 610 & 609.33198345929 & 0.668016540710028 \tabularnewline
40 & 360 & 439.518108026399 & -79.5181080263992 \tabularnewline
41 & 540 & 519.430439321593 & 20.5695606784068 \tabularnewline
42 & 560 & 539.408479150145 & 20.5915208498546 \tabularnewline
43 & 580 & 579.364604789428 & 0.635395210571573 \tabularnewline
44 & 480 & 359.605580758367 & 120.394419241633 \tabularnewline
45 & 560 & 499.452145478203 & 60.547854521797 \tabularnewline
46 & 560 & 529.419221176511 & 30.5807788234889 \tabularnewline
47 & 390 & 469.484922687032 & -79.4849226870325 \tabularnewline
48 & 630 & 659.276633881528 & -29.2766338815285 \tabularnewline
49 & 380 & 409.550595153141 & -29.5505951531414 \tabularnewline
50 & 440 & 359.605364575305 & 80.3946354246955 \tabularnewline
51 & 620 & 609.331251106302 & 10.6687488936977 \tabularnewline
52 & 310 & 359.605292461611 & -49.6052924616115 \tabularnewline
53 & 500 & 539.407884592321 & -39.4078845923211 \tabularnewline
54 & 660 & 559.385898277979 & 100.614101722021 \tabularnewline
55 & 420 & 579.363907944868 & -159.363907944868 \tabularnewline
56 & 550 & 479.473530873507 & 70.5264691264929 \tabularnewline
57 & 570 & 559.385729874255 & 10.6142701257447 \tabularnewline
58 & 560 & 559.385673719154 & 0.614326280846058 \tabularnewline
59 & 290 & 389.572126510671 & -99.5721265106712 \tabularnewline
60 & 560 & 629.308756550412 & -69.3087565504119 \tabularnewline
61 & 320 & 379.583021380442 & -59.5830213804417 \tabularnewline
62 & 440 & 439.517138496888 & 0.482861503112076 \tabularnewline
63 & 610 & 619.319542017023 & -9.31954201702308 \tabularnewline
64 & 250 & 309.659739888524 & -59.6597398885237 \tabularnewline
65 & 510 & 499.451143165875 & 10.548856834125 \tabularnewline
66 & 670 & 659.275442699251 & 10.7245573007494 \tabularnewline
67 & 350 & 419.53887589563 & -69.5388758956296 \tabularnewline
68 & 590 & 549.396091752878 & 40.6039082471219 \tabularnewline
69 & 500 & 569.374074179988 & -69.3740741799882 \tabularnewline
70 & 530 & 559.384999056221 & -29.3849990562209 \tabularnewline
71 & 300 & 289.68148821884 & 10.3185117811604 \tabularnewline
72 & 620 & 559.384886468303 & 60.6151135316966 \tabularnewline
73 & 280 & 319.648474376506 & -39.6484743765055 \tabularnewline
74 & 450 & 439.516608016479 & 10.4833919835206 \tabularnewline
75 & 620 & 609.329781572427 & 10.6702184275731 \tabularnewline
76 & 320 & 249.725295164623 & 70.2747048353773 \tabularnewline
77 & 560 & 509.439550816463 & 50.5604491835367 \tabularnewline
78 & 680 & 669.263656189719 & 10.7363438102814 \tabularnewline
79 & 370 & 349.615307553597 & 20.3846924464034 \tabularnewline
80 & 670 & 589.351459045395 & 80.6485409546054 \tabularnewline
81 & 510 & 499.450338671537 & 10.5496613284625 \tabularnewline
82 & 480 & 529.417305611068 & -49.4173056110677 \tabularnewline
83 & 280 & 299.670142766334 & -19.670142766334 \tabularnewline
84 & 570 & 619.318232582114 & -49.3182325821141 \tabularnewline
85 & 240 & 279.692076820418 & -39.6920768204183 \tabularnewline
86 & 460 & 449.505078104862 & 10.4949218951383 \tabularnewline
87 & 600 & 619.318045108475 & -19.3180451084747 \tabularnewline
88 & 320 & 319.647991016438 & 0.352008983562484 \tabularnewline
89 & 570 & 559.38392780404 & 10.6160721959603 \tabularnewline
90 & 680 & 679.251843744449 & 0.74815625555118 \tabularnewline
91 & 390 & 369.592877651253 & 20.4071223487474 \tabularnewline
92 & 700 & 669.26271084441 & 30.7372891555905 \tabularnewline
93 & 570 & 509.438728426411 & 60.5612715735894 \tabularnewline
94 & 450 & 479.471695950013 & -29.471695950013 \tabularnewline
95 & 270 & 279.691794369056 & -9.69179436905569 \tabularnewline
96 & 640 & 569.372523837099 & 70.6274761629005 \tabularnewline
97 & 230 & 239.735775271364 & -9.73577527136368 \tabularnewline
98 & 490 & 459.493522803517 & 30.5064771964834 \tabularnewline
99 & 590 & 599.339316950076 & -9.33931695007618 \tabularnewline
100 & 310 & 319.647603370252 & -9.64760337025172 \tabularnewline
101 & 570 & 569.372235893377 & 0.627764106623317 \tabularnewline
102 & 660 & 679.251019694006 & -19.2510196940059 \tabularnewline
103 & 370 & 389.570398333917 & -19.5703983339167 \tabularnewline
104 & 600 & 699.228849298563 & -99.2288492985629 \tabularnewline
105 & 540 & 569.372005348054 & -29.372005348054 \tabularnewline
106 & 510 & 449.504169225207 & 60.4958307747929 \tabularnewline
107 & 330 & 269.702474216154 & 60.2975257838461 \tabularnewline
108 & 590 & 639.294688929578 & -49.2946889295781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124162&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]460[/C][C]455.665255160783[/C][C]4.33474483921748[/C][/ROW]
[ROW][C]14[/C][C]380[/C][C]376.994840007256[/C][C]3.00515999274393[/C][/ROW]
[ROW][C]15[/C][C]570[/C][C]569.130376940354[/C][C]0.86962305964596[/C][/ROW]
[ROW][C]16[/C][C]480[/C][C]479.223996156481[/C][C]0.776003843518765[/C][/ROW]
[ROW][C]17[/C][C]530[/C][C]529.526835947401[/C][C]0.47316405259869[/C][/ROW]
[ROW][C]18[/C][C]530[/C][C]528.615510139204[/C][C]1.38448986079629[/C][/ROW]
[ROW][C]19[/C][C]580[/C][C]512.743961321425[/C][C]67.2560386785754[/C][/ROW]
[ROW][C]20[/C][C]420[/C][C]498.196903041666[/C][C]-78.1969030416662[/C][/ROW]
[ROW][C]21[/C][C]580[/C][C]581.644919518678[/C][C]-1.64491951867819[/C][/ROW]
[ROW][C]22[/C][C]460[/C][C]462.779827051894[/C][C]-2.77982705189396[/C][/ROW]
[ROW][C]23[/C][C]520[/C][C]532.278748330859[/C][C]-12.2787483308587[/C][/ROW]
[ROW][C]24[/C][C]640[/C][C]608.073668169113[/C][C]31.9263318308873[/C][/ROW]
[ROW][C]25[/C][C]380[/C][C]459.496892605483[/C][C]-79.4968926054835[/C][/ROW]
[ROW][C]26[/C][C]360[/C][C]379.584351660372[/C][C]-19.5843516603717[/C][/ROW]
[ROW][C]27[/C][C]610[/C][C]569.376470655264[/C][C]40.6235293447356[/C][/ROW]
[ROW][C]28[/C][C]440[/C][C]479.474874787038[/C][C]-39.4748747870384[/C][/ROW]
[ROW][C]29[/C][C]520[/C][C]529.420121377896[/C][C]-9.42012137789561[/C][/ROW]
[ROW][C]30[/C][C]540[/C][C]529.420068502129[/C][C]10.5799314978713[/C][/ROW]
[ROW][C]31[/C][C]580[/C][C]579.365300108861[/C][C]0.63469989113878[/C][/ROW]
[ROW][C]32[/C][C]360[/C][C]419.540347817165[/C][C]-59.5403478171652[/C][/ROW]
[ROW][C]33[/C][C]500[/C][C]579.365184327988[/C][C]-79.3651843279882[/C][/ROW]
[ROW][C]34[/C][C]530[/C][C]459.496479575839[/C][C]70.5035204241611[/C][/ROW]
[ROW][C]35[/C][C]470[/C][C]519.430751073329[/C][C]-49.4307510733286[/C][/ROW]
[ROW][C]36[/C][C]660[/C][C]639.299322016502[/C][C]20.7006779834978[/C][/ROW]
[ROW][C]37[/C][C]410[/C][C]379.58393448793[/C][C]30.4160655120696[/C][/ROW]
[ROW][C]38[/C][C]360[/C][C]359.605796704707[/C][C]0.394203295293039[/C][/ROW]
[ROW][C]39[/C][C]610[/C][C]609.33198345929[/C][C]0.668016540710028[/C][/ROW]
[ROW][C]40[/C][C]360[/C][C]439.518108026399[/C][C]-79.5181080263992[/C][/ROW]
[ROW][C]41[/C][C]540[/C][C]519.430439321593[/C][C]20.5695606784068[/C][/ROW]
[ROW][C]42[/C][C]560[/C][C]539.408479150145[/C][C]20.5915208498546[/C][/ROW]
[ROW][C]43[/C][C]580[/C][C]579.364604789428[/C][C]0.635395210571573[/C][/ROW]
[ROW][C]44[/C][C]480[/C][C]359.605580758367[/C][C]120.394419241633[/C][/ROW]
[ROW][C]45[/C][C]560[/C][C]499.452145478203[/C][C]60.547854521797[/C][/ROW]
[ROW][C]46[/C][C]560[/C][C]529.419221176511[/C][C]30.5807788234889[/C][/ROW]
[ROW][C]47[/C][C]390[/C][C]469.484922687032[/C][C]-79.4849226870325[/C][/ROW]
[ROW][C]48[/C][C]630[/C][C]659.276633881528[/C][C]-29.2766338815285[/C][/ROW]
[ROW][C]49[/C][C]380[/C][C]409.550595153141[/C][C]-29.5505951531414[/C][/ROW]
[ROW][C]50[/C][C]440[/C][C]359.605364575305[/C][C]80.3946354246955[/C][/ROW]
[ROW][C]51[/C][C]620[/C][C]609.331251106302[/C][C]10.6687488936977[/C][/ROW]
[ROW][C]52[/C][C]310[/C][C]359.605292461611[/C][C]-49.6052924616115[/C][/ROW]
[ROW][C]53[/C][C]500[/C][C]539.407884592321[/C][C]-39.4078845923211[/C][/ROW]
[ROW][C]54[/C][C]660[/C][C]559.385898277979[/C][C]100.614101722021[/C][/ROW]
[ROW][C]55[/C][C]420[/C][C]579.363907944868[/C][C]-159.363907944868[/C][/ROW]
[ROW][C]56[/C][C]550[/C][C]479.473530873507[/C][C]70.5264691264929[/C][/ROW]
[ROW][C]57[/C][C]570[/C][C]559.385729874255[/C][C]10.6142701257447[/C][/ROW]
[ROW][C]58[/C][C]560[/C][C]559.385673719154[/C][C]0.614326280846058[/C][/ROW]
[ROW][C]59[/C][C]290[/C][C]389.572126510671[/C][C]-99.5721265106712[/C][/ROW]
[ROW][C]60[/C][C]560[/C][C]629.308756550412[/C][C]-69.3087565504119[/C][/ROW]
[ROW][C]61[/C][C]320[/C][C]379.583021380442[/C][C]-59.5830213804417[/C][/ROW]
[ROW][C]62[/C][C]440[/C][C]439.517138496888[/C][C]0.482861503112076[/C][/ROW]
[ROW][C]63[/C][C]610[/C][C]619.319542017023[/C][C]-9.31954201702308[/C][/ROW]
[ROW][C]64[/C][C]250[/C][C]309.659739888524[/C][C]-59.6597398885237[/C][/ROW]
[ROW][C]65[/C][C]510[/C][C]499.451143165875[/C][C]10.548856834125[/C][/ROW]
[ROW][C]66[/C][C]670[/C][C]659.275442699251[/C][C]10.7245573007494[/C][/ROW]
[ROW][C]67[/C][C]350[/C][C]419.53887589563[/C][C]-69.5388758956296[/C][/ROW]
[ROW][C]68[/C][C]590[/C][C]549.396091752878[/C][C]40.6039082471219[/C][/ROW]
[ROW][C]69[/C][C]500[/C][C]569.374074179988[/C][C]-69.3740741799882[/C][/ROW]
[ROW][C]70[/C][C]530[/C][C]559.384999056221[/C][C]-29.3849990562209[/C][/ROW]
[ROW][C]71[/C][C]300[/C][C]289.68148821884[/C][C]10.3185117811604[/C][/ROW]
[ROW][C]72[/C][C]620[/C][C]559.384886468303[/C][C]60.6151135316966[/C][/ROW]
[ROW][C]73[/C][C]280[/C][C]319.648474376506[/C][C]-39.6484743765055[/C][/ROW]
[ROW][C]74[/C][C]450[/C][C]439.516608016479[/C][C]10.4833919835206[/C][/ROW]
[ROW][C]75[/C][C]620[/C][C]609.329781572427[/C][C]10.6702184275731[/C][/ROW]
[ROW][C]76[/C][C]320[/C][C]249.725295164623[/C][C]70.2747048353773[/C][/ROW]
[ROW][C]77[/C][C]560[/C][C]509.439550816463[/C][C]50.5604491835367[/C][/ROW]
[ROW][C]78[/C][C]680[/C][C]669.263656189719[/C][C]10.7363438102814[/C][/ROW]
[ROW][C]79[/C][C]370[/C][C]349.615307553597[/C][C]20.3846924464034[/C][/ROW]
[ROW][C]80[/C][C]670[/C][C]589.351459045395[/C][C]80.6485409546054[/C][/ROW]
[ROW][C]81[/C][C]510[/C][C]499.450338671537[/C][C]10.5496613284625[/C][/ROW]
[ROW][C]82[/C][C]480[/C][C]529.417305611068[/C][C]-49.4173056110677[/C][/ROW]
[ROW][C]83[/C][C]280[/C][C]299.670142766334[/C][C]-19.670142766334[/C][/ROW]
[ROW][C]84[/C][C]570[/C][C]619.318232582114[/C][C]-49.3182325821141[/C][/ROW]
[ROW][C]85[/C][C]240[/C][C]279.692076820418[/C][C]-39.6920768204183[/C][/ROW]
[ROW][C]86[/C][C]460[/C][C]449.505078104862[/C][C]10.4949218951383[/C][/ROW]
[ROW][C]87[/C][C]600[/C][C]619.318045108475[/C][C]-19.3180451084747[/C][/ROW]
[ROW][C]88[/C][C]320[/C][C]319.647991016438[/C][C]0.352008983562484[/C][/ROW]
[ROW][C]89[/C][C]570[/C][C]559.38392780404[/C][C]10.6160721959603[/C][/ROW]
[ROW][C]90[/C][C]680[/C][C]679.251843744449[/C][C]0.74815625555118[/C][/ROW]
[ROW][C]91[/C][C]390[/C][C]369.592877651253[/C][C]20.4071223487474[/C][/ROW]
[ROW][C]92[/C][C]700[/C][C]669.26271084441[/C][C]30.7372891555905[/C][/ROW]
[ROW][C]93[/C][C]570[/C][C]509.438728426411[/C][C]60.5612715735894[/C][/ROW]
[ROW][C]94[/C][C]450[/C][C]479.471695950013[/C][C]-29.471695950013[/C][/ROW]
[ROW][C]95[/C][C]270[/C][C]279.691794369056[/C][C]-9.69179436905569[/C][/ROW]
[ROW][C]96[/C][C]640[/C][C]569.372523837099[/C][C]70.6274761629005[/C][/ROW]
[ROW][C]97[/C][C]230[/C][C]239.735775271364[/C][C]-9.73577527136368[/C][/ROW]
[ROW][C]98[/C][C]490[/C][C]459.493522803517[/C][C]30.5064771964834[/C][/ROW]
[ROW][C]99[/C][C]590[/C][C]599.339316950076[/C][C]-9.33931695007618[/C][/ROW]
[ROW][C]100[/C][C]310[/C][C]319.647603370252[/C][C]-9.64760337025172[/C][/ROW]
[ROW][C]101[/C][C]570[/C][C]569.372235893377[/C][C]0.627764106623317[/C][/ROW]
[ROW][C]102[/C][C]660[/C][C]679.251019694006[/C][C]-19.2510196940059[/C][/ROW]
[ROW][C]103[/C][C]370[/C][C]389.570398333917[/C][C]-19.5703983339167[/C][/ROW]
[ROW][C]104[/C][C]600[/C][C]699.228849298563[/C][C]-99.2288492985629[/C][/ROW]
[ROW][C]105[/C][C]540[/C][C]569.372005348054[/C][C]-29.372005348054[/C][/ROW]
[ROW][C]106[/C][C]510[/C][C]449.504169225207[/C][C]60.4958307747929[/C][/ROW]
[ROW][C]107[/C][C]330[/C][C]269.702474216154[/C][C]60.2975257838461[/C][/ROW]
[ROW][C]108[/C][C]590[/C][C]639.294688929578[/C][C]-49.2946889295781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124162&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124162&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
13460455.6652551607834.33474483921748
14380376.9948400072563.00515999274393
15570569.1303769403540.86962305964596
16480479.2239961564810.776003843518765
17530529.5268359474010.47316405259869
18530528.6155101392041.38448986079629
19580512.74396132142567.2560386785754
20420498.196903041666-78.1969030416662
21580581.644919518678-1.64491951867819
22460462.779827051894-2.77982705189396
23520532.278748330859-12.2787483308587
24640608.07366816911331.9263318308873
25380459.496892605483-79.4968926054835
26360379.584351660372-19.5843516603717
27610569.37647065526440.6235293447356
28440479.474874787038-39.4748747870384
29520529.420121377896-9.42012137789561
30540529.42006850212910.5799314978713
31580579.3653001088610.63469989113878
32360419.540347817165-59.5403478171652
33500579.365184327988-79.3651843279882
34530459.49647957583970.5035204241611
35470519.430751073329-49.4307510733286
36660639.29932201650220.7006779834978
37410379.5839344879330.4160655120696
38360359.6057967047070.394203295293039
39610609.331983459290.668016540710028
40360439.518108026399-79.5181080263992
41540519.43043932159320.5695606784068
42560539.40847915014520.5915208498546
43580579.3646047894280.635395210571573
44480359.605580758367120.394419241633
45560499.45214547820360.547854521797
46560529.41922117651130.5807788234889
47390469.484922687032-79.4849226870325
48630659.276633881528-29.2766338815285
49380409.550595153141-29.5505951531414
50440359.60536457530580.3946354246955
51620609.33125110630210.6687488936977
52310359.605292461611-49.6052924616115
53500539.407884592321-39.4078845923211
54660559.385898277979100.614101722021
55420579.363907944868-159.363907944868
56550479.47353087350770.5264691264929
57570559.38572987425510.6142701257447
58560559.3856737191540.614326280846058
59290389.572126510671-99.5721265106712
60560629.308756550412-69.3087565504119
61320379.583021380442-59.5830213804417
62440439.5171384968880.482861503112076
63610619.319542017023-9.31954201702308
64250309.659739888524-59.6597398885237
65510499.45114316587510.548856834125
66670659.27544269925110.7245573007494
67350419.53887589563-69.5388758956296
68590549.39609175287840.6039082471219
69500569.374074179988-69.3740741799882
70530559.384999056221-29.3849990562209
71300289.6814882188410.3185117811604
72620559.38488646830360.6151135316966
73280319.648474376506-39.6484743765055
74450439.51660801647910.4833919835206
75620609.32978157242710.6702184275731
76320249.72529516462370.2747048353773
77560509.43955081646350.5604491835367
78680669.26365618971910.7363438102814
79370349.61530755359720.3846924464034
80670589.35145904539580.6485409546054
81510499.45033867153710.5496613284625
82480529.417305611068-49.4173056110677
83280299.670142766334-19.670142766334
84570619.318232582114-49.3182325821141
85240279.692076820418-39.6920768204183
86460449.50507810486210.4949218951383
87600619.318045108475-19.3180451084747
88320319.6479910164380.352008983562484
89570559.3839278040410.6160721959603
90680679.2518437444490.74815625555118
91390369.59287765125320.4071223487474
92700669.2627108444130.7372891555905
93570509.43872842641160.5612715735894
94450479.471695950013-29.471695950013
95270279.691794369056-9.69179436905569
96640569.37252383709970.6274761629005
97230239.735775271364-9.73577527136368
98490459.49352280351730.5064771964834
99590599.339316950076-9.33931695007618
100310319.647603370252-9.64760337025172
101570569.3722358933770.627764106623317
102660679.251019694006-19.2510196940059
103370389.570398333917-19.5703983339167
104600699.228849298563-99.2288492985629
105540569.372005348054-29.372005348054
106510449.50416922520760.4958307747929
107330269.70247421615460.2975257838461
108590639.294688929578-49.2946889295781







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109229.746505553802135.324899619658324.168111487946
110489.459897008422395.038291074278583.881502942566
111589.349612167213494.928006233069683.771218101357
112309.658239404675215.236633470531404.079845338819
113569.371543749031474.949937814887663.793149683175
114659.272246949031564.850641014887753.693852883175
115369.591979736832275.170373802688464.013585670976
116599.338284709897504.916678775753693.759890644041
117539.404401500486444.982795566342633.82600743463
118509.437438599112415.015832664968603.859044533256
119329.635956218219235.214350284075424.057562152363
120589.349074004907-1767.199225154482945.89737316429

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 229.746505553802 & 135.324899619658 & 324.168111487946 \tabularnewline
110 & 489.459897008422 & 395.038291074278 & 583.881502942566 \tabularnewline
111 & 589.349612167213 & 494.928006233069 & 683.771218101357 \tabularnewline
112 & 309.658239404675 & 215.236633470531 & 404.079845338819 \tabularnewline
113 & 569.371543749031 & 474.949937814887 & 663.793149683175 \tabularnewline
114 & 659.272246949031 & 564.850641014887 & 753.693852883175 \tabularnewline
115 & 369.591979736832 & 275.170373802688 & 464.013585670976 \tabularnewline
116 & 599.338284709897 & 504.916678775753 & 693.759890644041 \tabularnewline
117 & 539.404401500486 & 444.982795566342 & 633.82600743463 \tabularnewline
118 & 509.437438599112 & 415.015832664968 & 603.859044533256 \tabularnewline
119 & 329.635956218219 & 235.214350284075 & 424.057562152363 \tabularnewline
120 & 589.349074004907 & -1767.19922515448 & 2945.89737316429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124162&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]229.746505553802[/C][C]135.324899619658[/C][C]324.168111487946[/C][/ROW]
[ROW][C]110[/C][C]489.459897008422[/C][C]395.038291074278[/C][C]583.881502942566[/C][/ROW]
[ROW][C]111[/C][C]589.349612167213[/C][C]494.928006233069[/C][C]683.771218101357[/C][/ROW]
[ROW][C]112[/C][C]309.658239404675[/C][C]215.236633470531[/C][C]404.079845338819[/C][/ROW]
[ROW][C]113[/C][C]569.371543749031[/C][C]474.949937814887[/C][C]663.793149683175[/C][/ROW]
[ROW][C]114[/C][C]659.272246949031[/C][C]564.850641014887[/C][C]753.693852883175[/C][/ROW]
[ROW][C]115[/C][C]369.591979736832[/C][C]275.170373802688[/C][C]464.013585670976[/C][/ROW]
[ROW][C]116[/C][C]599.338284709897[/C][C]504.916678775753[/C][C]693.759890644041[/C][/ROW]
[ROW][C]117[/C][C]539.404401500486[/C][C]444.982795566342[/C][C]633.82600743463[/C][/ROW]
[ROW][C]118[/C][C]509.437438599112[/C][C]415.015832664968[/C][C]603.859044533256[/C][/ROW]
[ROW][C]119[/C][C]329.635956218219[/C][C]235.214350284075[/C][C]424.057562152363[/C][/ROW]
[ROW][C]120[/C][C]589.349074004907[/C][C]-1767.19922515448[/C][C]2945.89737316429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124162&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124162&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
109229.746505553802135.324899619658324.168111487946
110489.459897008422395.038291074278583.881502942566
111589.349612167213494.928006233069683.771218101357
112309.658239404675215.236633470531404.079845338819
113569.371543749031474.949937814887663.793149683175
114659.272246949031564.850641014887753.693852883175
115369.591979736832275.170373802688464.013585670976
116599.338284709897504.916678775753693.759890644041
117539.404401500486444.982795566342633.82600743463
118509.437438599112415.015832664968603.859044533256
119329.635956218219235.214350284075424.057562152363
120589.349074004907-1767.199225154482945.89737316429



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')