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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, 12 Aug 2008 11:56:58 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Aug/12/t1218564013okbgbp8ivq6y3r8.htm/, Retrieved Wed, 15 May 2024 17:39:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14010, Retrieved Wed, 15 May 2024 17:39:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact291
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [sven van roy - tw...] [2008-08-12 17:56:58] [9ed44c8445a965e8d6beecda46dd06a5] [Current]
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Dataseries X:
0.22
0.22
0.2
0.21
0.21
0.19
0.19
0.18
0.18
0.19
0.18
0.17
0.17
0.17
0.18
0.2
0.2
0.2
0.22
0.23
0.25
0.25
0.27
0.29
0.3
0.31
0.33
0.31
0.33
0.33
0.35
0.37
0.47
0.45
0.45
0.4
0.34
0.35
0.34
0.35
0.36
0.37
0.36
0.35
0.36
0.33
0.3
0.28
0.28
0.28
0.3
0.32
0.32
0.3
0.3
0.31
0.33
0.34
0.31
0.33
0.35
0.38
0.4
0.32
0.29
0.3
0.3
0.32
0.32
0.32
0.32
0.32
0.33
0.31
0.33
0.35
0.37
0.37
0.38
0.42
0.42
0.49
0.45
0.41
0.4
0.42
0.47
0.49
0.47
0.52
0.56
0.57
0.61
0.52
0.5
0.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14010&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14010&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14010&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.83737132434265
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.83737132434265 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14010&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]0.83737132434265[/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=14010&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14010&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
alpha0.83737132434265
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.170.1348918306620010.0351081693379985
140.170.1613890291115550.00861097088844537
150.180.1739103369366710.00608966306332939
160.20.1934902033118950.00650979668810495
170.20.1928883390353340.00711166096466626
180.20.1907194862214530.00928051377854672
190.220.2082127168981110.0117872831018890
200.230.217119785405480.0128802145945200
210.250.2356492586613150.0143507413386849
220.250.2372968824076100.0127031175923895
230.270.2578053458855420.0121946541144582
240.290.2767154736218160.0132845263781843
250.30.2632695485641770.0367304514358226
260.310.281451800201670.0285481997983298
270.330.3141092844321970.0158907155678029
280.310.353827019841738-0.0438270198417379
290.330.3076299754370680.0223700245629319
300.330.3135843872477040.0164156127522964
310.350.3437670918265480.00623290817345185
320.370.347583024287940.0224169757120602
330.470.3788898265614820.0911101734385179
340.450.4356539616260640.0143460383739363
350.450.465059653523729-0.0150596535237292
360.40.467182926739026-0.0671829267390257
370.340.380628044534449-0.0406280445344492
380.350.3301215907457790.0198784092542206
390.340.354137170417545-0.0141371704175446
400.350.358765416588651-0.0087654165886506
410.360.352626220476090.0073737795239101
420.370.3437332729951580.0262667270048416
430.360.382092491501809-0.0220924915018093
440.350.364675206780122-0.0146752067801224
450.360.372599752807644-0.0125997528076440
460.330.337340719319497-0.00734071931949676
470.30.340424742763661-0.0404247427636607
480.280.309817961589425-0.0298179615894248
490.280.2658870048129660.0141129951870344
500.280.2721500793045940.00784992069540646
510.30.2801238025363170.0198761974636835
520.320.3118766385349030.00812336146509651
530.320.322143195592592-0.00214319559259202
540.30.309446099328076-0.00944609932807572
550.30.308314099477698-0.00831409947769773
560.310.3031982026667920.00680179733320813
570.330.3269782059737480.00302179402625158
580.340.3076555163551380.0323444836448624
590.310.337909363988388-0.0279093639883883
600.330.3193027011062740.0106972988937265
610.350.3142910899354690.0357089100645311
620.380.3360754067884970.0439245932115032
630.40.3770844701729980.0229155298270017
640.320.413669055208418-0.0936690552084178
650.290.337111311878162-0.0471113118781621
660.30.2863780365618860.0136219634381139
670.30.304664249982951-0.00466424998295129
680.320.3050533462607210.0149466537392786
690.320.33546157062212-0.0154615706221201
700.320.3054017294766620.0145982705233380
710.320.311117616849220.00888238315077972
720.320.329853826495010-0.00985382649500954
730.330.3114611948290650.0185388051709350
740.310.319991437024553-0.00999143702455285
750.330.3121421363393670.0178578636606329
760.350.3229020997266870.0270979002733129
770.370.3547019111222370.0152980888777633
780.370.3656219400360560.00437805996394414
790.380.3740836480654450.00591635193455547
800.420.3883726500739590.0316273499260407
810.420.431510554189102-0.0115105541891018
820.490.4056357524006480.084364247599352
830.450.465159441092324-0.0151594410923237
840.410.464074201691166-0.0540742016911657
850.40.411377434924934-0.0113774349249343
860.420.3876307848302030.0323692151697968
870.470.4213094904287340.0486905095712662
880.490.4579082960431780.0320917039568217
890.470.494619389743961-0.0246193897439614
900.520.4692982033025010.0507017966974992
910.560.5187160101496510.0412839898503494
920.570.572487699832381-0.00248769983238140
930.610.583436739306150.0265632606938496
940.520.60181635141335-0.0818163514133499
950.50.503511218308032-0.00351121830803225
960.50.505386933158921-0.00538693315892069

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.17 & 0.134891830662001 & 0.0351081693379985 \tabularnewline
14 & 0.17 & 0.161389029111555 & 0.00861097088844537 \tabularnewline
15 & 0.18 & 0.173910336936671 & 0.00608966306332939 \tabularnewline
16 & 0.2 & 0.193490203311895 & 0.00650979668810495 \tabularnewline
17 & 0.2 & 0.192888339035334 & 0.00711166096466626 \tabularnewline
18 & 0.2 & 0.190719486221453 & 0.00928051377854672 \tabularnewline
19 & 0.22 & 0.208212716898111 & 0.0117872831018890 \tabularnewline
20 & 0.23 & 0.21711978540548 & 0.0128802145945200 \tabularnewline
21 & 0.25 & 0.235649258661315 & 0.0143507413386849 \tabularnewline
22 & 0.25 & 0.237296882407610 & 0.0127031175923895 \tabularnewline
23 & 0.27 & 0.257805345885542 & 0.0121946541144582 \tabularnewline
24 & 0.29 & 0.276715473621816 & 0.0132845263781843 \tabularnewline
25 & 0.3 & 0.263269548564177 & 0.0367304514358226 \tabularnewline
26 & 0.31 & 0.28145180020167 & 0.0285481997983298 \tabularnewline
27 & 0.33 & 0.314109284432197 & 0.0158907155678029 \tabularnewline
28 & 0.31 & 0.353827019841738 & -0.0438270198417379 \tabularnewline
29 & 0.33 & 0.307629975437068 & 0.0223700245629319 \tabularnewline
30 & 0.33 & 0.313584387247704 & 0.0164156127522964 \tabularnewline
31 & 0.35 & 0.343767091826548 & 0.00623290817345185 \tabularnewline
32 & 0.37 & 0.34758302428794 & 0.0224169757120602 \tabularnewline
33 & 0.47 & 0.378889826561482 & 0.0911101734385179 \tabularnewline
34 & 0.45 & 0.435653961626064 & 0.0143460383739363 \tabularnewline
35 & 0.45 & 0.465059653523729 & -0.0150596535237292 \tabularnewline
36 & 0.4 & 0.467182926739026 & -0.0671829267390257 \tabularnewline
37 & 0.34 & 0.380628044534449 & -0.0406280445344492 \tabularnewline
38 & 0.35 & 0.330121590745779 & 0.0198784092542206 \tabularnewline
39 & 0.34 & 0.354137170417545 & -0.0141371704175446 \tabularnewline
40 & 0.35 & 0.358765416588651 & -0.0087654165886506 \tabularnewline
41 & 0.36 & 0.35262622047609 & 0.0073737795239101 \tabularnewline
42 & 0.37 & 0.343733272995158 & 0.0262667270048416 \tabularnewline
43 & 0.36 & 0.382092491501809 & -0.0220924915018093 \tabularnewline
44 & 0.35 & 0.364675206780122 & -0.0146752067801224 \tabularnewline
45 & 0.36 & 0.372599752807644 & -0.0125997528076440 \tabularnewline
46 & 0.33 & 0.337340719319497 & -0.00734071931949676 \tabularnewline
47 & 0.3 & 0.340424742763661 & -0.0404247427636607 \tabularnewline
48 & 0.28 & 0.309817961589425 & -0.0298179615894248 \tabularnewline
49 & 0.28 & 0.265887004812966 & 0.0141129951870344 \tabularnewline
50 & 0.28 & 0.272150079304594 & 0.00784992069540646 \tabularnewline
51 & 0.3 & 0.280123802536317 & 0.0198761974636835 \tabularnewline
52 & 0.32 & 0.311876638534903 & 0.00812336146509651 \tabularnewline
53 & 0.32 & 0.322143195592592 & -0.00214319559259202 \tabularnewline
54 & 0.3 & 0.309446099328076 & -0.00944609932807572 \tabularnewline
55 & 0.3 & 0.308314099477698 & -0.00831409947769773 \tabularnewline
56 & 0.31 & 0.303198202666792 & 0.00680179733320813 \tabularnewline
57 & 0.33 & 0.326978205973748 & 0.00302179402625158 \tabularnewline
58 & 0.34 & 0.307655516355138 & 0.0323444836448624 \tabularnewline
59 & 0.31 & 0.337909363988388 & -0.0279093639883883 \tabularnewline
60 & 0.33 & 0.319302701106274 & 0.0106972988937265 \tabularnewline
61 & 0.35 & 0.314291089935469 & 0.0357089100645311 \tabularnewline
62 & 0.38 & 0.336075406788497 & 0.0439245932115032 \tabularnewline
63 & 0.4 & 0.377084470172998 & 0.0229155298270017 \tabularnewline
64 & 0.32 & 0.413669055208418 & -0.0936690552084178 \tabularnewline
65 & 0.29 & 0.337111311878162 & -0.0471113118781621 \tabularnewline
66 & 0.3 & 0.286378036561886 & 0.0136219634381139 \tabularnewline
67 & 0.3 & 0.304664249982951 & -0.00466424998295129 \tabularnewline
68 & 0.32 & 0.305053346260721 & 0.0149466537392786 \tabularnewline
69 & 0.32 & 0.33546157062212 & -0.0154615706221201 \tabularnewline
70 & 0.32 & 0.305401729476662 & 0.0145982705233380 \tabularnewline
71 & 0.32 & 0.31111761684922 & 0.00888238315077972 \tabularnewline
72 & 0.32 & 0.329853826495010 & -0.00985382649500954 \tabularnewline
73 & 0.33 & 0.311461194829065 & 0.0185388051709350 \tabularnewline
74 & 0.31 & 0.319991437024553 & -0.00999143702455285 \tabularnewline
75 & 0.33 & 0.312142136339367 & 0.0178578636606329 \tabularnewline
76 & 0.35 & 0.322902099726687 & 0.0270979002733129 \tabularnewline
77 & 0.37 & 0.354701911122237 & 0.0152980888777633 \tabularnewline
78 & 0.37 & 0.365621940036056 & 0.00437805996394414 \tabularnewline
79 & 0.38 & 0.374083648065445 & 0.00591635193455547 \tabularnewline
80 & 0.42 & 0.388372650073959 & 0.0316273499260407 \tabularnewline
81 & 0.42 & 0.431510554189102 & -0.0115105541891018 \tabularnewline
82 & 0.49 & 0.405635752400648 & 0.084364247599352 \tabularnewline
83 & 0.45 & 0.465159441092324 & -0.0151594410923237 \tabularnewline
84 & 0.41 & 0.464074201691166 & -0.0540742016911657 \tabularnewline
85 & 0.4 & 0.411377434924934 & -0.0113774349249343 \tabularnewline
86 & 0.42 & 0.387630784830203 & 0.0323692151697968 \tabularnewline
87 & 0.47 & 0.421309490428734 & 0.0486905095712662 \tabularnewline
88 & 0.49 & 0.457908296043178 & 0.0320917039568217 \tabularnewline
89 & 0.47 & 0.494619389743961 & -0.0246193897439614 \tabularnewline
90 & 0.52 & 0.469298203302501 & 0.0507017966974992 \tabularnewline
91 & 0.56 & 0.518716010149651 & 0.0412839898503494 \tabularnewline
92 & 0.57 & 0.572487699832381 & -0.00248769983238140 \tabularnewline
93 & 0.61 & 0.58343673930615 & 0.0265632606938496 \tabularnewline
94 & 0.52 & 0.60181635141335 & -0.0818163514133499 \tabularnewline
95 & 0.5 & 0.503511218308032 & -0.00351121830803225 \tabularnewline
96 & 0.5 & 0.505386933158921 & -0.00538693315892069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14010&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]0.17[/C][C]0.134891830662001[/C][C]0.0351081693379985[/C][/ROW]
[ROW][C]14[/C][C]0.17[/C][C]0.161389029111555[/C][C]0.00861097088844537[/C][/ROW]
[ROW][C]15[/C][C]0.18[/C][C]0.173910336936671[/C][C]0.00608966306332939[/C][/ROW]
[ROW][C]16[/C][C]0.2[/C][C]0.193490203311895[/C][C]0.00650979668810495[/C][/ROW]
[ROW][C]17[/C][C]0.2[/C][C]0.192888339035334[/C][C]0.00711166096466626[/C][/ROW]
[ROW][C]18[/C][C]0.2[/C][C]0.190719486221453[/C][C]0.00928051377854672[/C][/ROW]
[ROW][C]19[/C][C]0.22[/C][C]0.208212716898111[/C][C]0.0117872831018890[/C][/ROW]
[ROW][C]20[/C][C]0.23[/C][C]0.21711978540548[/C][C]0.0128802145945200[/C][/ROW]
[ROW][C]21[/C][C]0.25[/C][C]0.235649258661315[/C][C]0.0143507413386849[/C][/ROW]
[ROW][C]22[/C][C]0.25[/C][C]0.237296882407610[/C][C]0.0127031175923895[/C][/ROW]
[ROW][C]23[/C][C]0.27[/C][C]0.257805345885542[/C][C]0.0121946541144582[/C][/ROW]
[ROW][C]24[/C][C]0.29[/C][C]0.276715473621816[/C][C]0.0132845263781843[/C][/ROW]
[ROW][C]25[/C][C]0.3[/C][C]0.263269548564177[/C][C]0.0367304514358226[/C][/ROW]
[ROW][C]26[/C][C]0.31[/C][C]0.28145180020167[/C][C]0.0285481997983298[/C][/ROW]
[ROW][C]27[/C][C]0.33[/C][C]0.314109284432197[/C][C]0.0158907155678029[/C][/ROW]
[ROW][C]28[/C][C]0.31[/C][C]0.353827019841738[/C][C]-0.0438270198417379[/C][/ROW]
[ROW][C]29[/C][C]0.33[/C][C]0.307629975437068[/C][C]0.0223700245629319[/C][/ROW]
[ROW][C]30[/C][C]0.33[/C][C]0.313584387247704[/C][C]0.0164156127522964[/C][/ROW]
[ROW][C]31[/C][C]0.35[/C][C]0.343767091826548[/C][C]0.00623290817345185[/C][/ROW]
[ROW][C]32[/C][C]0.37[/C][C]0.34758302428794[/C][C]0.0224169757120602[/C][/ROW]
[ROW][C]33[/C][C]0.47[/C][C]0.378889826561482[/C][C]0.0911101734385179[/C][/ROW]
[ROW][C]34[/C][C]0.45[/C][C]0.435653961626064[/C][C]0.0143460383739363[/C][/ROW]
[ROW][C]35[/C][C]0.45[/C][C]0.465059653523729[/C][C]-0.0150596535237292[/C][/ROW]
[ROW][C]36[/C][C]0.4[/C][C]0.467182926739026[/C][C]-0.0671829267390257[/C][/ROW]
[ROW][C]37[/C][C]0.34[/C][C]0.380628044534449[/C][C]-0.0406280445344492[/C][/ROW]
[ROW][C]38[/C][C]0.35[/C][C]0.330121590745779[/C][C]0.0198784092542206[/C][/ROW]
[ROW][C]39[/C][C]0.34[/C][C]0.354137170417545[/C][C]-0.0141371704175446[/C][/ROW]
[ROW][C]40[/C][C]0.35[/C][C]0.358765416588651[/C][C]-0.0087654165886506[/C][/ROW]
[ROW][C]41[/C][C]0.36[/C][C]0.35262622047609[/C][C]0.0073737795239101[/C][/ROW]
[ROW][C]42[/C][C]0.37[/C][C]0.343733272995158[/C][C]0.0262667270048416[/C][/ROW]
[ROW][C]43[/C][C]0.36[/C][C]0.382092491501809[/C][C]-0.0220924915018093[/C][/ROW]
[ROW][C]44[/C][C]0.35[/C][C]0.364675206780122[/C][C]-0.0146752067801224[/C][/ROW]
[ROW][C]45[/C][C]0.36[/C][C]0.372599752807644[/C][C]-0.0125997528076440[/C][/ROW]
[ROW][C]46[/C][C]0.33[/C][C]0.337340719319497[/C][C]-0.00734071931949676[/C][/ROW]
[ROW][C]47[/C][C]0.3[/C][C]0.340424742763661[/C][C]-0.0404247427636607[/C][/ROW]
[ROW][C]48[/C][C]0.28[/C][C]0.309817961589425[/C][C]-0.0298179615894248[/C][/ROW]
[ROW][C]49[/C][C]0.28[/C][C]0.265887004812966[/C][C]0.0141129951870344[/C][/ROW]
[ROW][C]50[/C][C]0.28[/C][C]0.272150079304594[/C][C]0.00784992069540646[/C][/ROW]
[ROW][C]51[/C][C]0.3[/C][C]0.280123802536317[/C][C]0.0198761974636835[/C][/ROW]
[ROW][C]52[/C][C]0.32[/C][C]0.311876638534903[/C][C]0.00812336146509651[/C][/ROW]
[ROW][C]53[/C][C]0.32[/C][C]0.322143195592592[/C][C]-0.00214319559259202[/C][/ROW]
[ROW][C]54[/C][C]0.3[/C][C]0.309446099328076[/C][C]-0.00944609932807572[/C][/ROW]
[ROW][C]55[/C][C]0.3[/C][C]0.308314099477698[/C][C]-0.00831409947769773[/C][/ROW]
[ROW][C]56[/C][C]0.31[/C][C]0.303198202666792[/C][C]0.00680179733320813[/C][/ROW]
[ROW][C]57[/C][C]0.33[/C][C]0.326978205973748[/C][C]0.00302179402625158[/C][/ROW]
[ROW][C]58[/C][C]0.34[/C][C]0.307655516355138[/C][C]0.0323444836448624[/C][/ROW]
[ROW][C]59[/C][C]0.31[/C][C]0.337909363988388[/C][C]-0.0279093639883883[/C][/ROW]
[ROW][C]60[/C][C]0.33[/C][C]0.319302701106274[/C][C]0.0106972988937265[/C][/ROW]
[ROW][C]61[/C][C]0.35[/C][C]0.314291089935469[/C][C]0.0357089100645311[/C][/ROW]
[ROW][C]62[/C][C]0.38[/C][C]0.336075406788497[/C][C]0.0439245932115032[/C][/ROW]
[ROW][C]63[/C][C]0.4[/C][C]0.377084470172998[/C][C]0.0229155298270017[/C][/ROW]
[ROW][C]64[/C][C]0.32[/C][C]0.413669055208418[/C][C]-0.0936690552084178[/C][/ROW]
[ROW][C]65[/C][C]0.29[/C][C]0.337111311878162[/C][C]-0.0471113118781621[/C][/ROW]
[ROW][C]66[/C][C]0.3[/C][C]0.286378036561886[/C][C]0.0136219634381139[/C][/ROW]
[ROW][C]67[/C][C]0.3[/C][C]0.304664249982951[/C][C]-0.00466424998295129[/C][/ROW]
[ROW][C]68[/C][C]0.32[/C][C]0.305053346260721[/C][C]0.0149466537392786[/C][/ROW]
[ROW][C]69[/C][C]0.32[/C][C]0.33546157062212[/C][C]-0.0154615706221201[/C][/ROW]
[ROW][C]70[/C][C]0.32[/C][C]0.305401729476662[/C][C]0.0145982705233380[/C][/ROW]
[ROW][C]71[/C][C]0.32[/C][C]0.31111761684922[/C][C]0.00888238315077972[/C][/ROW]
[ROW][C]72[/C][C]0.32[/C][C]0.329853826495010[/C][C]-0.00985382649500954[/C][/ROW]
[ROW][C]73[/C][C]0.33[/C][C]0.311461194829065[/C][C]0.0185388051709350[/C][/ROW]
[ROW][C]74[/C][C]0.31[/C][C]0.319991437024553[/C][C]-0.00999143702455285[/C][/ROW]
[ROW][C]75[/C][C]0.33[/C][C]0.312142136339367[/C][C]0.0178578636606329[/C][/ROW]
[ROW][C]76[/C][C]0.35[/C][C]0.322902099726687[/C][C]0.0270979002733129[/C][/ROW]
[ROW][C]77[/C][C]0.37[/C][C]0.354701911122237[/C][C]0.0152980888777633[/C][/ROW]
[ROW][C]78[/C][C]0.37[/C][C]0.365621940036056[/C][C]0.00437805996394414[/C][/ROW]
[ROW][C]79[/C][C]0.38[/C][C]0.374083648065445[/C][C]0.00591635193455547[/C][/ROW]
[ROW][C]80[/C][C]0.42[/C][C]0.388372650073959[/C][C]0.0316273499260407[/C][/ROW]
[ROW][C]81[/C][C]0.42[/C][C]0.431510554189102[/C][C]-0.0115105541891018[/C][/ROW]
[ROW][C]82[/C][C]0.49[/C][C]0.405635752400648[/C][C]0.084364247599352[/C][/ROW]
[ROW][C]83[/C][C]0.45[/C][C]0.465159441092324[/C][C]-0.0151594410923237[/C][/ROW]
[ROW][C]84[/C][C]0.41[/C][C]0.464074201691166[/C][C]-0.0540742016911657[/C][/ROW]
[ROW][C]85[/C][C]0.4[/C][C]0.411377434924934[/C][C]-0.0113774349249343[/C][/ROW]
[ROW][C]86[/C][C]0.42[/C][C]0.387630784830203[/C][C]0.0323692151697968[/C][/ROW]
[ROW][C]87[/C][C]0.47[/C][C]0.421309490428734[/C][C]0.0486905095712662[/C][/ROW]
[ROW][C]88[/C][C]0.49[/C][C]0.457908296043178[/C][C]0.0320917039568217[/C][/ROW]
[ROW][C]89[/C][C]0.47[/C][C]0.494619389743961[/C][C]-0.0246193897439614[/C][/ROW]
[ROW][C]90[/C][C]0.52[/C][C]0.469298203302501[/C][C]0.0507017966974992[/C][/ROW]
[ROW][C]91[/C][C]0.56[/C][C]0.518716010149651[/C][C]0.0412839898503494[/C][/ROW]
[ROW][C]92[/C][C]0.57[/C][C]0.572487699832381[/C][C]-0.00248769983238140[/C][/ROW]
[ROW][C]93[/C][C]0.61[/C][C]0.58343673930615[/C][C]0.0265632606938496[/C][/ROW]
[ROW][C]94[/C][C]0.52[/C][C]0.60181635141335[/C][C]-0.0818163514133499[/C][/ROW]
[ROW][C]95[/C][C]0.5[/C][C]0.503511218308032[/C][C]-0.00351121830803225[/C][/ROW]
[ROW][C]96[/C][C]0.5[/C][C]0.505386933158921[/C][C]-0.00538693315892069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14010&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14010&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
130.170.1348918306620010.0351081693379985
140.170.1613890291115550.00861097088844537
150.180.1739103369366710.00608966306332939
160.20.1934902033118950.00650979668810495
170.20.1928883390353340.00711166096466626
180.20.1907194862214530.00928051377854672
190.220.2082127168981110.0117872831018890
200.230.217119785405480.0128802145945200
210.250.2356492586613150.0143507413386849
220.250.2372968824076100.0127031175923895
230.270.2578053458855420.0121946541144582
240.290.2767154736218160.0132845263781843
250.30.2632695485641770.0367304514358226
260.310.281451800201670.0285481997983298
270.330.3141092844321970.0158907155678029
280.310.353827019841738-0.0438270198417379
290.330.3076299754370680.0223700245629319
300.330.3135843872477040.0164156127522964
310.350.3437670918265480.00623290817345185
320.370.347583024287940.0224169757120602
330.470.3788898265614820.0911101734385179
340.450.4356539616260640.0143460383739363
350.450.465059653523729-0.0150596535237292
360.40.467182926739026-0.0671829267390257
370.340.380628044534449-0.0406280445344492
380.350.3301215907457790.0198784092542206
390.340.354137170417545-0.0141371704175446
400.350.358765416588651-0.0087654165886506
410.360.352626220476090.0073737795239101
420.370.3437332729951580.0262667270048416
430.360.382092491501809-0.0220924915018093
440.350.364675206780122-0.0146752067801224
450.360.372599752807644-0.0125997528076440
460.330.337340719319497-0.00734071931949676
470.30.340424742763661-0.0404247427636607
480.280.309817961589425-0.0298179615894248
490.280.2658870048129660.0141129951870344
500.280.2721500793045940.00784992069540646
510.30.2801238025363170.0198761974636835
520.320.3118766385349030.00812336146509651
530.320.322143195592592-0.00214319559259202
540.30.309446099328076-0.00944609932807572
550.30.308314099477698-0.00831409947769773
560.310.3031982026667920.00680179733320813
570.330.3269782059737480.00302179402625158
580.340.3076555163551380.0323444836448624
590.310.337909363988388-0.0279093639883883
600.330.3193027011062740.0106972988937265
610.350.3142910899354690.0357089100645311
620.380.3360754067884970.0439245932115032
630.40.3770844701729980.0229155298270017
640.320.413669055208418-0.0936690552084178
650.290.337111311878162-0.0471113118781621
660.30.2863780365618860.0136219634381139
670.30.304664249982951-0.00466424998295129
680.320.3050533462607210.0149466537392786
690.320.33546157062212-0.0154615706221201
700.320.3054017294766620.0145982705233380
710.320.311117616849220.00888238315077972
720.320.329853826495010-0.00985382649500954
730.330.3114611948290650.0185388051709350
740.310.319991437024553-0.00999143702455285
750.330.3121421363393670.0178578636606329
760.350.3229020997266870.0270979002733129
770.370.3547019111222370.0152980888777633
780.370.3656219400360560.00437805996394414
790.380.3740836480654450.00591635193455547
800.420.3883726500739590.0316273499260407
810.420.431510554189102-0.0115105541891018
820.490.4056357524006480.084364247599352
830.450.465159441092324-0.0151594410923237
840.410.464074201691166-0.0540742016911657
850.40.411377434924934-0.0113774349249343
860.420.3876307848302030.0323692151697968
870.470.4213094904287340.0486905095712662
880.490.4579082960431780.0320917039568217
890.470.494619389743961-0.0246193897439614
900.520.4692982033025010.0507017966974992
910.560.5187160101496510.0412839898503494
920.570.572487699832381-0.00248769983238140
930.610.583436739306150.0265632606938496
940.520.60181635141335-0.0818163514133499
950.50.503511218308032-0.00351121830803225
960.50.505386933158921-0.00538693315892069







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
970.5002448078502970.4414042103074170.559085405393177
980.4909288840867530.4135370743468590.568320693826647
990.500898565432360.4099738329729710.591823297891749
1000.4932657482390460.3897861928033690.596745303674722
1010.4937101255593840.3778648686358460.609555382482922
1020.5009158770982680.3740788541510790.627752900045456
1030.5057424653063850.3672800782699620.644204852342808
1040.5166535438102590.3658665183254240.667440569295094
1050.5326045776766360.3791604608754590.686048694477813
1060.5123493312687630.3557616674612970.668936995076228
1070.4955372180625690.3300914955306550.660982940594482
1080.5NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 0.500244807850297 & 0.441404210307417 & 0.559085405393177 \tabularnewline
98 & 0.490928884086753 & 0.413537074346859 & 0.568320693826647 \tabularnewline
99 & 0.50089856543236 & 0.409973832972971 & 0.591823297891749 \tabularnewline
100 & 0.493265748239046 & 0.389786192803369 & 0.596745303674722 \tabularnewline
101 & 0.493710125559384 & 0.377864868635846 & 0.609555382482922 \tabularnewline
102 & 0.500915877098268 & 0.374078854151079 & 0.627752900045456 \tabularnewline
103 & 0.505742465306385 & 0.367280078269962 & 0.644204852342808 \tabularnewline
104 & 0.516653543810259 & 0.365866518325424 & 0.667440569295094 \tabularnewline
105 & 0.532604577676636 & 0.379160460875459 & 0.686048694477813 \tabularnewline
106 & 0.512349331268763 & 0.355761667461297 & 0.668936995076228 \tabularnewline
107 & 0.495537218062569 & 0.330091495530655 & 0.660982940594482 \tabularnewline
108 & 0.5 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14010&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]97[/C][C]0.500244807850297[/C][C]0.441404210307417[/C][C]0.559085405393177[/C][/ROW]
[ROW][C]98[/C][C]0.490928884086753[/C][C]0.413537074346859[/C][C]0.568320693826647[/C][/ROW]
[ROW][C]99[/C][C]0.50089856543236[/C][C]0.409973832972971[/C][C]0.591823297891749[/C][/ROW]
[ROW][C]100[/C][C]0.493265748239046[/C][C]0.389786192803369[/C][C]0.596745303674722[/C][/ROW]
[ROW][C]101[/C][C]0.493710125559384[/C][C]0.377864868635846[/C][C]0.609555382482922[/C][/ROW]
[ROW][C]102[/C][C]0.500915877098268[/C][C]0.374078854151079[/C][C]0.627752900045456[/C][/ROW]
[ROW][C]103[/C][C]0.505742465306385[/C][C]0.367280078269962[/C][C]0.644204852342808[/C][/ROW]
[ROW][C]104[/C][C]0.516653543810259[/C][C]0.365866518325424[/C][C]0.667440569295094[/C][/ROW]
[ROW][C]105[/C][C]0.532604577676636[/C][C]0.379160460875459[/C][C]0.686048694477813[/C][/ROW]
[ROW][C]106[/C][C]0.512349331268763[/C][C]0.355761667461297[/C][C]0.668936995076228[/C][/ROW]
[ROW][C]107[/C][C]0.495537218062569[/C][C]0.330091495530655[/C][C]0.660982940594482[/C][/ROW]
[ROW][C]108[/C][C]0.5[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14010&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14010&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
970.5002448078502970.4414042103074170.559085405393177
980.4909288840867530.4135370743468590.568320693826647
990.500898565432360.4099738329729710.591823297891749
1000.4932657482390460.3897861928033690.596745303674722
1010.4937101255593840.3778648686358460.609555382482922
1020.5009158770982680.3740788541510790.627752900045456
1030.5057424653063850.3672800782699620.644204852342808
1040.5166535438102590.3658665183254240.667440569295094
1050.5326045776766360.3791604608754590.686048694477813
1060.5123493312687630.3557616674612970.668936995076228
1070.4955372180625690.3300914955306550.660982940594482
1080.5NANA



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')