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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 computationTue, 16 Aug 2011 12:57:48 -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/16/t1313513909lf44cfftxobi7vb.htm/, Retrieved Tue, 14 May 2024 05:00:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123892, Retrieved Tue, 14 May 2024 05:00:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmattias debbaut
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks B - Exp...] [2011-08-16 16:57:48] [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=123892&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=123892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123892&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
alpha0.135920858403689
beta0.40536946367675
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.135920858403689 \tabularnewline
beta & 0.40536946367675 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123892&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]0.135920858403689[/C][/ROW]
[ROW][C]beta[/C][C]0.40536946367675[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123892&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
alpha0.135920858403689
beta0.40536946367675
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3570410160
4520390.563043820364129.436956179636
5470374.10367131921895.8963286807821
6500358.369139722992141.630860277008
7520356.654485495725163.345514504275
8500366.891343898492133.108656101508
9580380.352425311572199.647574688428
10460413.85774876282346.142251237177
11530429.040850275033100.959149724967
12610457.237375622351152.762624377649
13460500.892014068894-40.8920140688939
14380515.971872866211-135.971872866211
15570510.63659488795859.3634051120417
16480535.122270286972-55.1222702869723
17530541.009818441275-11.0098184412747
18530552.286548118424-22.2865481184242
19580560.80258710180519.1974128981948
20420576.01490390908-156.01490390908
21580558.81607722108221.1839227789177
22460566.869462447296-106.869462447296
23520551.629410306071-31.6294103060708
24640544.87332815534395.126671844657
25380560.587346604679-180.587346604679
26360528.876047486791-168.876047486791
27610489.451797789075120.548202210925
28440496.008325346078-56.0083253460777
29520475.48118214294144.5188178570588
30540471.07067972982268.9293202701776
31580473.775952852988106.224047147012
32360487.403107394164-127.403107394164
33500462.2557810506437.7442189493601
34530461.63505828814568.3649417118554
35470468.9431133195011.05688668049908
36660467.160832250722192.839167749278
37410502.070847825867-92.0708478258667
38360493.182714707427-133.182714707427
39610471.368498098696138.631501901304
40360494.137844569359-134.137844569359
41540472.44139816516467.5586018348355
42560481.88206091626178.1179390837387
43580497.06211298449482.9378870155055
44480517.467021935885-37.4670219358845
45560519.44202813215840.5579718678423
46560534.25692830842325.7430716915766
47390548.476570559427-158.476570559427
48630528.925152592484101.074847407516
49380550.221224823179-170.221224823179
50440525.263624822305-85.2636248223049
51620507.15566543213112.84433456787
52310522.192225757648-212.192225757648
53500481.35813542413518.6418645758652
54660472.926345336725187.073654663275
55420497.695363920852-77.6953639208519
56550482.1958782024867.8041217975198
57570490.20869020283679.791309797164
58560504.24716587650855.7528341234919
59290518.090190182056-228.090190182056
60560480.78567593054279.214324069458
61320489.61481898288-169.61481898288
62440455.277425952598-15.2774259525982
63610441.075945723633168.924054276367
64250461.218694301608-211.218694301608
65510418.05435160718291.9456483928185
66670421.162403158895248.837596841105
67350459.305838107129-109.305838107129
68590442.747558790297147.252441209703
69500469.17424040094430.8257595990564
70530481.47455030921648.5254496907837
71300498.854280544979-198.854280544979
72620471.653439440825148.346560559175
73280499.818058039158-219.818058039158
74450465.829853907814-15.8298539078143
75620458.695705676194161.304294323806
76320484.525353625076-164.525353625076
77560457.002910972739102.997089027261
78680471.517299022481208.482700977519
79370511.85639635458-141.85639635458
80670496.761075645095173.238924354905
81510534.038928326002-24.0389283260022
82480543.17810507577-63.17810507577
83280543.516453636723-263.516453636723
84570502.10536872260567.8946312773948
85240509.480832583402-269.480832583402
86460456.1520342862563.84796571374369
87600440.18633673174159.81366326826
88320454.225070334058-134.225070334058
89570420.902251725246149.097748274754
90680434.303926233278245.696073766722
91390474.372730991147-84.3727309911467
92700464.929517780437235.070482219563
93570511.8572526478558.1427473521501
94450537.940376631361-87.9403766313611
95270539.322403581296-269.322403581296
96640501.211659370929138.788340629071
97230526.218660795189-296.218660795189
98490475.7780323853914.2219676146099
99590468.316364997422121.683635002578
100310482.165524743118-172.165524743118
101570446.588449883832123.411550116168
102660457.986214773525202.013785226475
103370491.198251898214-121.198251898214
104600473.801230152312126.198769847688
105540496.98394467226143.0160553277395
106510511.230498964777-1.23049896477738
107330519.395225380874-189.395225380874
108590491.54911119325698.4508888067441

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 570 & 410 & 160 \tabularnewline
4 & 520 & 390.563043820364 & 129.436956179636 \tabularnewline
5 & 470 & 374.103671319218 & 95.8963286807821 \tabularnewline
6 & 500 & 358.369139722992 & 141.630860277008 \tabularnewline
7 & 520 & 356.654485495725 & 163.345514504275 \tabularnewline
8 & 500 & 366.891343898492 & 133.108656101508 \tabularnewline
9 & 580 & 380.352425311572 & 199.647574688428 \tabularnewline
10 & 460 & 413.857748762823 & 46.142251237177 \tabularnewline
11 & 530 & 429.040850275033 & 100.959149724967 \tabularnewline
12 & 610 & 457.237375622351 & 152.762624377649 \tabularnewline
13 & 460 & 500.892014068894 & -40.8920140688939 \tabularnewline
14 & 380 & 515.971872866211 & -135.971872866211 \tabularnewline
15 & 570 & 510.636594887958 & 59.3634051120417 \tabularnewline
16 & 480 & 535.122270286972 & -55.1222702869723 \tabularnewline
17 & 530 & 541.009818441275 & -11.0098184412747 \tabularnewline
18 & 530 & 552.286548118424 & -22.2865481184242 \tabularnewline
19 & 580 & 560.802587101805 & 19.1974128981948 \tabularnewline
20 & 420 & 576.01490390908 & -156.01490390908 \tabularnewline
21 & 580 & 558.816077221082 & 21.1839227789177 \tabularnewline
22 & 460 & 566.869462447296 & -106.869462447296 \tabularnewline
23 & 520 & 551.629410306071 & -31.6294103060708 \tabularnewline
24 & 640 & 544.873328155343 & 95.126671844657 \tabularnewline
25 & 380 & 560.587346604679 & -180.587346604679 \tabularnewline
26 & 360 & 528.876047486791 & -168.876047486791 \tabularnewline
27 & 610 & 489.451797789075 & 120.548202210925 \tabularnewline
28 & 440 & 496.008325346078 & -56.0083253460777 \tabularnewline
29 & 520 & 475.481182142941 & 44.5188178570588 \tabularnewline
30 & 540 & 471.070679729822 & 68.9293202701776 \tabularnewline
31 & 580 & 473.775952852988 & 106.224047147012 \tabularnewline
32 & 360 & 487.403107394164 & -127.403107394164 \tabularnewline
33 & 500 & 462.25578105064 & 37.7442189493601 \tabularnewline
34 & 530 & 461.635058288145 & 68.3649417118554 \tabularnewline
35 & 470 & 468.943113319501 & 1.05688668049908 \tabularnewline
36 & 660 & 467.160832250722 & 192.839167749278 \tabularnewline
37 & 410 & 502.070847825867 & -92.0708478258667 \tabularnewline
38 & 360 & 493.182714707427 & -133.182714707427 \tabularnewline
39 & 610 & 471.368498098696 & 138.631501901304 \tabularnewline
40 & 360 & 494.137844569359 & -134.137844569359 \tabularnewline
41 & 540 & 472.441398165164 & 67.5586018348355 \tabularnewline
42 & 560 & 481.882060916261 & 78.1179390837387 \tabularnewline
43 & 580 & 497.062112984494 & 82.9378870155055 \tabularnewline
44 & 480 & 517.467021935885 & -37.4670219358845 \tabularnewline
45 & 560 & 519.442028132158 & 40.5579718678423 \tabularnewline
46 & 560 & 534.256928308423 & 25.7430716915766 \tabularnewline
47 & 390 & 548.476570559427 & -158.476570559427 \tabularnewline
48 & 630 & 528.925152592484 & 101.074847407516 \tabularnewline
49 & 380 & 550.221224823179 & -170.221224823179 \tabularnewline
50 & 440 & 525.263624822305 & -85.2636248223049 \tabularnewline
51 & 620 & 507.15566543213 & 112.84433456787 \tabularnewline
52 & 310 & 522.192225757648 & -212.192225757648 \tabularnewline
53 & 500 & 481.358135424135 & 18.6418645758652 \tabularnewline
54 & 660 & 472.926345336725 & 187.073654663275 \tabularnewline
55 & 420 & 497.695363920852 & -77.6953639208519 \tabularnewline
56 & 550 & 482.19587820248 & 67.8041217975198 \tabularnewline
57 & 570 & 490.208690202836 & 79.791309797164 \tabularnewline
58 & 560 & 504.247165876508 & 55.7528341234919 \tabularnewline
59 & 290 & 518.090190182056 & -228.090190182056 \tabularnewline
60 & 560 & 480.785675930542 & 79.214324069458 \tabularnewline
61 & 320 & 489.61481898288 & -169.61481898288 \tabularnewline
62 & 440 & 455.277425952598 & -15.2774259525982 \tabularnewline
63 & 610 & 441.075945723633 & 168.924054276367 \tabularnewline
64 & 250 & 461.218694301608 & -211.218694301608 \tabularnewline
65 & 510 & 418.054351607182 & 91.9456483928185 \tabularnewline
66 & 670 & 421.162403158895 & 248.837596841105 \tabularnewline
67 & 350 & 459.305838107129 & -109.305838107129 \tabularnewline
68 & 590 & 442.747558790297 & 147.252441209703 \tabularnewline
69 & 500 & 469.174240400944 & 30.8257595990564 \tabularnewline
70 & 530 & 481.474550309216 & 48.5254496907837 \tabularnewline
71 & 300 & 498.854280544979 & -198.854280544979 \tabularnewline
72 & 620 & 471.653439440825 & 148.346560559175 \tabularnewline
73 & 280 & 499.818058039158 & -219.818058039158 \tabularnewline
74 & 450 & 465.829853907814 & -15.8298539078143 \tabularnewline
75 & 620 & 458.695705676194 & 161.304294323806 \tabularnewline
76 & 320 & 484.525353625076 & -164.525353625076 \tabularnewline
77 & 560 & 457.002910972739 & 102.997089027261 \tabularnewline
78 & 680 & 471.517299022481 & 208.482700977519 \tabularnewline
79 & 370 & 511.85639635458 & -141.85639635458 \tabularnewline
80 & 670 & 496.761075645095 & 173.238924354905 \tabularnewline
81 & 510 & 534.038928326002 & -24.0389283260022 \tabularnewline
82 & 480 & 543.17810507577 & -63.17810507577 \tabularnewline
83 & 280 & 543.516453636723 & -263.516453636723 \tabularnewline
84 & 570 & 502.105368722605 & 67.8946312773948 \tabularnewline
85 & 240 & 509.480832583402 & -269.480832583402 \tabularnewline
86 & 460 & 456.152034286256 & 3.84796571374369 \tabularnewline
87 & 600 & 440.18633673174 & 159.81366326826 \tabularnewline
88 & 320 & 454.225070334058 & -134.225070334058 \tabularnewline
89 & 570 & 420.902251725246 & 149.097748274754 \tabularnewline
90 & 680 & 434.303926233278 & 245.696073766722 \tabularnewline
91 & 390 & 474.372730991147 & -84.3727309911467 \tabularnewline
92 & 700 & 464.929517780437 & 235.070482219563 \tabularnewline
93 & 570 & 511.85725264785 & 58.1427473521501 \tabularnewline
94 & 450 & 537.940376631361 & -87.9403766313611 \tabularnewline
95 & 270 & 539.322403581296 & -269.322403581296 \tabularnewline
96 & 640 & 501.211659370929 & 138.788340629071 \tabularnewline
97 & 230 & 526.218660795189 & -296.218660795189 \tabularnewline
98 & 490 & 475.77803238539 & 14.2219676146099 \tabularnewline
99 & 590 & 468.316364997422 & 121.683635002578 \tabularnewline
100 & 310 & 482.165524743118 & -172.165524743118 \tabularnewline
101 & 570 & 446.588449883832 & 123.411550116168 \tabularnewline
102 & 660 & 457.986214773525 & 202.013785226475 \tabularnewline
103 & 370 & 491.198251898214 & -121.198251898214 \tabularnewline
104 & 600 & 473.801230152312 & 126.198769847688 \tabularnewline
105 & 540 & 496.983944672261 & 43.0160553277395 \tabularnewline
106 & 510 & 511.230498964777 & -1.23049896477738 \tabularnewline
107 & 330 & 519.395225380874 & -189.395225380874 \tabularnewline
108 & 590 & 491.549111193256 & 98.4508888067441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123892&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]3[/C][C]570[/C][C]410[/C][C]160[/C][/ROW]
[ROW][C]4[/C][C]520[/C][C]390.563043820364[/C][C]129.436956179636[/C][/ROW]
[ROW][C]5[/C][C]470[/C][C]374.103671319218[/C][C]95.8963286807821[/C][/ROW]
[ROW][C]6[/C][C]500[/C][C]358.369139722992[/C][C]141.630860277008[/C][/ROW]
[ROW][C]7[/C][C]520[/C][C]356.654485495725[/C][C]163.345514504275[/C][/ROW]
[ROW][C]8[/C][C]500[/C][C]366.891343898492[/C][C]133.108656101508[/C][/ROW]
[ROW][C]9[/C][C]580[/C][C]380.352425311572[/C][C]199.647574688428[/C][/ROW]
[ROW][C]10[/C][C]460[/C][C]413.857748762823[/C][C]46.142251237177[/C][/ROW]
[ROW][C]11[/C][C]530[/C][C]429.040850275033[/C][C]100.959149724967[/C][/ROW]
[ROW][C]12[/C][C]610[/C][C]457.237375622351[/C][C]152.762624377649[/C][/ROW]
[ROW][C]13[/C][C]460[/C][C]500.892014068894[/C][C]-40.8920140688939[/C][/ROW]
[ROW][C]14[/C][C]380[/C][C]515.971872866211[/C][C]-135.971872866211[/C][/ROW]
[ROW][C]15[/C][C]570[/C][C]510.636594887958[/C][C]59.3634051120417[/C][/ROW]
[ROW][C]16[/C][C]480[/C][C]535.122270286972[/C][C]-55.1222702869723[/C][/ROW]
[ROW][C]17[/C][C]530[/C][C]541.009818441275[/C][C]-11.0098184412747[/C][/ROW]
[ROW][C]18[/C][C]530[/C][C]552.286548118424[/C][C]-22.2865481184242[/C][/ROW]
[ROW][C]19[/C][C]580[/C][C]560.802587101805[/C][C]19.1974128981948[/C][/ROW]
[ROW][C]20[/C][C]420[/C][C]576.01490390908[/C][C]-156.01490390908[/C][/ROW]
[ROW][C]21[/C][C]580[/C][C]558.816077221082[/C][C]21.1839227789177[/C][/ROW]
[ROW][C]22[/C][C]460[/C][C]566.869462447296[/C][C]-106.869462447296[/C][/ROW]
[ROW][C]23[/C][C]520[/C][C]551.629410306071[/C][C]-31.6294103060708[/C][/ROW]
[ROW][C]24[/C][C]640[/C][C]544.873328155343[/C][C]95.126671844657[/C][/ROW]
[ROW][C]25[/C][C]380[/C][C]560.587346604679[/C][C]-180.587346604679[/C][/ROW]
[ROW][C]26[/C][C]360[/C][C]528.876047486791[/C][C]-168.876047486791[/C][/ROW]
[ROW][C]27[/C][C]610[/C][C]489.451797789075[/C][C]120.548202210925[/C][/ROW]
[ROW][C]28[/C][C]440[/C][C]496.008325346078[/C][C]-56.0083253460777[/C][/ROW]
[ROW][C]29[/C][C]520[/C][C]475.481182142941[/C][C]44.5188178570588[/C][/ROW]
[ROW][C]30[/C][C]540[/C][C]471.070679729822[/C][C]68.9293202701776[/C][/ROW]
[ROW][C]31[/C][C]580[/C][C]473.775952852988[/C][C]106.224047147012[/C][/ROW]
[ROW][C]32[/C][C]360[/C][C]487.403107394164[/C][C]-127.403107394164[/C][/ROW]
[ROW][C]33[/C][C]500[/C][C]462.25578105064[/C][C]37.7442189493601[/C][/ROW]
[ROW][C]34[/C][C]530[/C][C]461.635058288145[/C][C]68.3649417118554[/C][/ROW]
[ROW][C]35[/C][C]470[/C][C]468.943113319501[/C][C]1.05688668049908[/C][/ROW]
[ROW][C]36[/C][C]660[/C][C]467.160832250722[/C][C]192.839167749278[/C][/ROW]
[ROW][C]37[/C][C]410[/C][C]502.070847825867[/C][C]-92.0708478258667[/C][/ROW]
[ROW][C]38[/C][C]360[/C][C]493.182714707427[/C][C]-133.182714707427[/C][/ROW]
[ROW][C]39[/C][C]610[/C][C]471.368498098696[/C][C]138.631501901304[/C][/ROW]
[ROW][C]40[/C][C]360[/C][C]494.137844569359[/C][C]-134.137844569359[/C][/ROW]
[ROW][C]41[/C][C]540[/C][C]472.441398165164[/C][C]67.5586018348355[/C][/ROW]
[ROW][C]42[/C][C]560[/C][C]481.882060916261[/C][C]78.1179390837387[/C][/ROW]
[ROW][C]43[/C][C]580[/C][C]497.062112984494[/C][C]82.9378870155055[/C][/ROW]
[ROW][C]44[/C][C]480[/C][C]517.467021935885[/C][C]-37.4670219358845[/C][/ROW]
[ROW][C]45[/C][C]560[/C][C]519.442028132158[/C][C]40.5579718678423[/C][/ROW]
[ROW][C]46[/C][C]560[/C][C]534.256928308423[/C][C]25.7430716915766[/C][/ROW]
[ROW][C]47[/C][C]390[/C][C]548.476570559427[/C][C]-158.476570559427[/C][/ROW]
[ROW][C]48[/C][C]630[/C][C]528.925152592484[/C][C]101.074847407516[/C][/ROW]
[ROW][C]49[/C][C]380[/C][C]550.221224823179[/C][C]-170.221224823179[/C][/ROW]
[ROW][C]50[/C][C]440[/C][C]525.263624822305[/C][C]-85.2636248223049[/C][/ROW]
[ROW][C]51[/C][C]620[/C][C]507.15566543213[/C][C]112.84433456787[/C][/ROW]
[ROW][C]52[/C][C]310[/C][C]522.192225757648[/C][C]-212.192225757648[/C][/ROW]
[ROW][C]53[/C][C]500[/C][C]481.358135424135[/C][C]18.6418645758652[/C][/ROW]
[ROW][C]54[/C][C]660[/C][C]472.926345336725[/C][C]187.073654663275[/C][/ROW]
[ROW][C]55[/C][C]420[/C][C]497.695363920852[/C][C]-77.6953639208519[/C][/ROW]
[ROW][C]56[/C][C]550[/C][C]482.19587820248[/C][C]67.8041217975198[/C][/ROW]
[ROW][C]57[/C][C]570[/C][C]490.208690202836[/C][C]79.791309797164[/C][/ROW]
[ROW][C]58[/C][C]560[/C][C]504.247165876508[/C][C]55.7528341234919[/C][/ROW]
[ROW][C]59[/C][C]290[/C][C]518.090190182056[/C][C]-228.090190182056[/C][/ROW]
[ROW][C]60[/C][C]560[/C][C]480.785675930542[/C][C]79.214324069458[/C][/ROW]
[ROW][C]61[/C][C]320[/C][C]489.61481898288[/C][C]-169.61481898288[/C][/ROW]
[ROW][C]62[/C][C]440[/C][C]455.277425952598[/C][C]-15.2774259525982[/C][/ROW]
[ROW][C]63[/C][C]610[/C][C]441.075945723633[/C][C]168.924054276367[/C][/ROW]
[ROW][C]64[/C][C]250[/C][C]461.218694301608[/C][C]-211.218694301608[/C][/ROW]
[ROW][C]65[/C][C]510[/C][C]418.054351607182[/C][C]91.9456483928185[/C][/ROW]
[ROW][C]66[/C][C]670[/C][C]421.162403158895[/C][C]248.837596841105[/C][/ROW]
[ROW][C]67[/C][C]350[/C][C]459.305838107129[/C][C]-109.305838107129[/C][/ROW]
[ROW][C]68[/C][C]590[/C][C]442.747558790297[/C][C]147.252441209703[/C][/ROW]
[ROW][C]69[/C][C]500[/C][C]469.174240400944[/C][C]30.8257595990564[/C][/ROW]
[ROW][C]70[/C][C]530[/C][C]481.474550309216[/C][C]48.5254496907837[/C][/ROW]
[ROW][C]71[/C][C]300[/C][C]498.854280544979[/C][C]-198.854280544979[/C][/ROW]
[ROW][C]72[/C][C]620[/C][C]471.653439440825[/C][C]148.346560559175[/C][/ROW]
[ROW][C]73[/C][C]280[/C][C]499.818058039158[/C][C]-219.818058039158[/C][/ROW]
[ROW][C]74[/C][C]450[/C][C]465.829853907814[/C][C]-15.8298539078143[/C][/ROW]
[ROW][C]75[/C][C]620[/C][C]458.695705676194[/C][C]161.304294323806[/C][/ROW]
[ROW][C]76[/C][C]320[/C][C]484.525353625076[/C][C]-164.525353625076[/C][/ROW]
[ROW][C]77[/C][C]560[/C][C]457.002910972739[/C][C]102.997089027261[/C][/ROW]
[ROW][C]78[/C][C]680[/C][C]471.517299022481[/C][C]208.482700977519[/C][/ROW]
[ROW][C]79[/C][C]370[/C][C]511.85639635458[/C][C]-141.85639635458[/C][/ROW]
[ROW][C]80[/C][C]670[/C][C]496.761075645095[/C][C]173.238924354905[/C][/ROW]
[ROW][C]81[/C][C]510[/C][C]534.038928326002[/C][C]-24.0389283260022[/C][/ROW]
[ROW][C]82[/C][C]480[/C][C]543.17810507577[/C][C]-63.17810507577[/C][/ROW]
[ROW][C]83[/C][C]280[/C][C]543.516453636723[/C][C]-263.516453636723[/C][/ROW]
[ROW][C]84[/C][C]570[/C][C]502.105368722605[/C][C]67.8946312773948[/C][/ROW]
[ROW][C]85[/C][C]240[/C][C]509.480832583402[/C][C]-269.480832583402[/C][/ROW]
[ROW][C]86[/C][C]460[/C][C]456.152034286256[/C][C]3.84796571374369[/C][/ROW]
[ROW][C]87[/C][C]600[/C][C]440.18633673174[/C][C]159.81366326826[/C][/ROW]
[ROW][C]88[/C][C]320[/C][C]454.225070334058[/C][C]-134.225070334058[/C][/ROW]
[ROW][C]89[/C][C]570[/C][C]420.902251725246[/C][C]149.097748274754[/C][/ROW]
[ROW][C]90[/C][C]680[/C][C]434.303926233278[/C][C]245.696073766722[/C][/ROW]
[ROW][C]91[/C][C]390[/C][C]474.372730991147[/C][C]-84.3727309911467[/C][/ROW]
[ROW][C]92[/C][C]700[/C][C]464.929517780437[/C][C]235.070482219563[/C][/ROW]
[ROW][C]93[/C][C]570[/C][C]511.85725264785[/C][C]58.1427473521501[/C][/ROW]
[ROW][C]94[/C][C]450[/C][C]537.940376631361[/C][C]-87.9403766313611[/C][/ROW]
[ROW][C]95[/C][C]270[/C][C]539.322403581296[/C][C]-269.322403581296[/C][/ROW]
[ROW][C]96[/C][C]640[/C][C]501.211659370929[/C][C]138.788340629071[/C][/ROW]
[ROW][C]97[/C][C]230[/C][C]526.218660795189[/C][C]-296.218660795189[/C][/ROW]
[ROW][C]98[/C][C]490[/C][C]475.77803238539[/C][C]14.2219676146099[/C][/ROW]
[ROW][C]99[/C][C]590[/C][C]468.316364997422[/C][C]121.683635002578[/C][/ROW]
[ROW][C]100[/C][C]310[/C][C]482.165524743118[/C][C]-172.165524743118[/C][/ROW]
[ROW][C]101[/C][C]570[/C][C]446.588449883832[/C][C]123.411550116168[/C][/ROW]
[ROW][C]102[/C][C]660[/C][C]457.986214773525[/C][C]202.013785226475[/C][/ROW]
[ROW][C]103[/C][C]370[/C][C]491.198251898214[/C][C]-121.198251898214[/C][/ROW]
[ROW][C]104[/C][C]600[/C][C]473.801230152312[/C][C]126.198769847688[/C][/ROW]
[ROW][C]105[/C][C]540[/C][C]496.983944672261[/C][C]43.0160553277395[/C][/ROW]
[ROW][C]106[/C][C]510[/C][C]511.230498964777[/C][C]-1.23049896477738[/C][/ROW]
[ROW][C]107[/C][C]330[/C][C]519.395225380874[/C][C]-189.395225380874[/C][/ROW]
[ROW][C]108[/C][C]590[/C][C]491.549111193256[/C][C]98.4508888067441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123892&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123892&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
3570410160
4520390.563043820364129.436956179636
5470374.10367131921895.8963286807821
6500358.369139722992141.630860277008
7520356.654485495725163.345514504275
8500366.891343898492133.108656101508
9580380.352425311572199.647574688428
10460413.85774876282346.142251237177
11530429.040850275033100.959149724967
12610457.237375622351152.762624377649
13460500.892014068894-40.8920140688939
14380515.971872866211-135.971872866211
15570510.63659488795859.3634051120417
16480535.122270286972-55.1222702869723
17530541.009818441275-11.0098184412747
18530552.286548118424-22.2865481184242
19580560.80258710180519.1974128981948
20420576.01490390908-156.01490390908
21580558.81607722108221.1839227789177
22460566.869462447296-106.869462447296
23520551.629410306071-31.6294103060708
24640544.87332815534395.126671844657
25380560.587346604679-180.587346604679
26360528.876047486791-168.876047486791
27610489.451797789075120.548202210925
28440496.008325346078-56.0083253460777
29520475.48118214294144.5188178570588
30540471.07067972982268.9293202701776
31580473.775952852988106.224047147012
32360487.403107394164-127.403107394164
33500462.2557810506437.7442189493601
34530461.63505828814568.3649417118554
35470468.9431133195011.05688668049908
36660467.160832250722192.839167749278
37410502.070847825867-92.0708478258667
38360493.182714707427-133.182714707427
39610471.368498098696138.631501901304
40360494.137844569359-134.137844569359
41540472.44139816516467.5586018348355
42560481.88206091626178.1179390837387
43580497.06211298449482.9378870155055
44480517.467021935885-37.4670219358845
45560519.44202813215840.5579718678423
46560534.25692830842325.7430716915766
47390548.476570559427-158.476570559427
48630528.925152592484101.074847407516
49380550.221224823179-170.221224823179
50440525.263624822305-85.2636248223049
51620507.15566543213112.84433456787
52310522.192225757648-212.192225757648
53500481.35813542413518.6418645758652
54660472.926345336725187.073654663275
55420497.695363920852-77.6953639208519
56550482.1958782024867.8041217975198
57570490.20869020283679.791309797164
58560504.24716587650855.7528341234919
59290518.090190182056-228.090190182056
60560480.78567593054279.214324069458
61320489.61481898288-169.61481898288
62440455.277425952598-15.2774259525982
63610441.075945723633168.924054276367
64250461.218694301608-211.218694301608
65510418.05435160718291.9456483928185
66670421.162403158895248.837596841105
67350459.305838107129-109.305838107129
68590442.747558790297147.252441209703
69500469.17424040094430.8257595990564
70530481.47455030921648.5254496907837
71300498.854280544979-198.854280544979
72620471.653439440825148.346560559175
73280499.818058039158-219.818058039158
74450465.829853907814-15.8298539078143
75620458.695705676194161.304294323806
76320484.525353625076-164.525353625076
77560457.002910972739102.997089027261
78680471.517299022481208.482700977519
79370511.85639635458-141.85639635458
80670496.761075645095173.238924354905
81510534.038928326002-24.0389283260022
82480543.17810507577-63.17810507577
83280543.516453636723-263.516453636723
84570502.10536872260567.8946312773948
85240509.480832583402-269.480832583402
86460456.1520342862563.84796571374369
87600440.18633673174159.81366326826
88320454.225070334058-134.225070334058
89570420.902251725246149.097748274754
90680434.303926233278245.696073766722
91390474.372730991147-84.3727309911467
92700464.929517780437235.070482219563
93570511.8572526478558.1427473521501
94450537.940376631361-87.9403766313611
95270539.322403581296-269.322403581296
96640501.211659370929138.788340629071
97230526.218660795189-296.218660795189
98490475.7780323853914.2219676146099
99590468.316364997422121.683635002578
100310482.165524743118-172.165524743118
101570446.588449883832123.411550116168
102660457.986214773525202.013785226475
103370491.198251898214-121.198251898214
104600473.801230152312126.198769847688
105540496.98394467226143.0160553277395
106510511.230498964777-1.23049896477738
107330519.395225380874-189.395225380874
108590491.54911119325698.4508888067441







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109508.251751296681242.746906060265773.756596533098
110511.572862082888241.267509158497781.878215007279
111514.893972869094236.802274195942792.985671542247
112518.215083655301228.852239934243807.577927376359
113521.536194441508217.101346708638825.971042174378
114524.857305227714201.419271343914848.295339111515
115528.178416013921181.835209930577874.521622097264
116531.499526800127158.49423762201904.504815978244
117534.820637586334131.610822285159938.030452887508
118538.14174837254101.429886924444974.853609820637
119541.46285915874768.19947011843961014.72624819905
120544.78396994495432.15436007748031057.41357981243

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 508.251751296681 & 242.746906060265 & 773.756596533098 \tabularnewline
110 & 511.572862082888 & 241.267509158497 & 781.878215007279 \tabularnewline
111 & 514.893972869094 & 236.802274195942 & 792.985671542247 \tabularnewline
112 & 518.215083655301 & 228.852239934243 & 807.577927376359 \tabularnewline
113 & 521.536194441508 & 217.101346708638 & 825.971042174378 \tabularnewline
114 & 524.857305227714 & 201.419271343914 & 848.295339111515 \tabularnewline
115 & 528.178416013921 & 181.835209930577 & 874.521622097264 \tabularnewline
116 & 531.499526800127 & 158.49423762201 & 904.504815978244 \tabularnewline
117 & 534.820637586334 & 131.610822285159 & 938.030452887508 \tabularnewline
118 & 538.14174837254 & 101.429886924444 & 974.853609820637 \tabularnewline
119 & 541.462859158747 & 68.1994701184396 & 1014.72624819905 \tabularnewline
120 & 544.783969944954 & 32.1543600774803 & 1057.41357981243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123892&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]508.251751296681[/C][C]242.746906060265[/C][C]773.756596533098[/C][/ROW]
[ROW][C]110[/C][C]511.572862082888[/C][C]241.267509158497[/C][C]781.878215007279[/C][/ROW]
[ROW][C]111[/C][C]514.893972869094[/C][C]236.802274195942[/C][C]792.985671542247[/C][/ROW]
[ROW][C]112[/C][C]518.215083655301[/C][C]228.852239934243[/C][C]807.577927376359[/C][/ROW]
[ROW][C]113[/C][C]521.536194441508[/C][C]217.101346708638[/C][C]825.971042174378[/C][/ROW]
[ROW][C]114[/C][C]524.857305227714[/C][C]201.419271343914[/C][C]848.295339111515[/C][/ROW]
[ROW][C]115[/C][C]528.178416013921[/C][C]181.835209930577[/C][C]874.521622097264[/C][/ROW]
[ROW][C]116[/C][C]531.499526800127[/C][C]158.49423762201[/C][C]904.504815978244[/C][/ROW]
[ROW][C]117[/C][C]534.820637586334[/C][C]131.610822285159[/C][C]938.030452887508[/C][/ROW]
[ROW][C]118[/C][C]538.14174837254[/C][C]101.429886924444[/C][C]974.853609820637[/C][/ROW]
[ROW][C]119[/C][C]541.462859158747[/C][C]68.1994701184396[/C][C]1014.72624819905[/C][/ROW]
[ROW][C]120[/C][C]544.783969944954[/C][C]32.1543600774803[/C][C]1057.41357981243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123892&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123892&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
109508.251751296681242.746906060265773.756596533098
110511.572862082888241.267509158497781.878215007279
111514.893972869094236.802274195942792.985671542247
112518.215083655301228.852239934243807.577927376359
113521.536194441508217.101346708638825.971042174378
114524.857305227714201.419271343914848.295339111515
115528.178416013921181.835209930577874.521622097264
116531.499526800127158.49423762201904.504815978244
117534.820637586334131.610822285159938.030452887508
118538.14174837254101.429886924444974.853609820637
119541.46285915874768.19947011843961014.72624819905
120544.78396994495432.15436007748031057.41357981243



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')