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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 computationFri, 28 Nov 2014 16:30:33 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/28/t1417192246ge2fcpxne7j6rix.htm/, Retrieved Sun, 19 May 2024 15:21:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260961, Retrieved Sun, 19 May 2024 15:21:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2014-11-28 16:17:29] [4df2cd86c9043e1a56e9383f8c504201]
- RMP     [Exponential Smoothing] [] [2014-11-28 16:30:33] [062c419fa600f620f2df94d64c8876ba] [Current]
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Dataseries X:
53
47
49
44
48
51
47
44
33
47
41
36
46
24
17
22
30
24
18
24
24
28
19
22
26
14
16
21
15
23
29
17
24
18
22
8
26
22
34
25
20
35
38
24
14
25
31
17
32
27
30
19
36
27
28
38
26
25
30
27
30
50
48
34
41
26
39
33
38
28
36
20
39
22
32
32
31
28
44
40
32
35
32
31
41
23
36
36
42
36
64
30
25
51
38
27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260961&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260961&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260961&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.287589349722968
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.287589349722968 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260961&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]0.287589349722968[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260961&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260961&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
alpha0.287589349722968
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24753-6
34951.2744639016622-2.27446390166219
44450.6203523072148-6.6203523072148
54848.7164094922459-0.716409492245944
65148.51037775223562.48962224776443
74749.226366595526-2.22636659552597
84448.5860872740737-4.58608727407372
93347.2671774171501-14.2671774171501
104743.16408914136973.83591085863033
114144.2672562507984-3.26725625079844
123643.327628150253-7.32762815025301
134641.220280335514.77971966448997
142442.5948768056788-18.5948768056788
151737.2471882769549-20.2471882769549
162231.4243125666669-9.42431256666694
173028.71398064403321.2860193559668
182429.0838261143468-5.08382611434684
191827.6217718680172-9.62177186801719
202424.8546527533114-0.854652753311374
212424.6088637237476-0.608863723747611
222824.43376100136513.56623899863487
231925.4593733559392-6.45937335593922
242223.6017263728868-1.60172637288679
252623.14108692687422.85891307312585
261423.9632798784889-9.96327987848891
271621.0979466971263-5.09794669712635
282119.63183152157741.36816847842258
291520.0253022045984-5.02530220459844
302318.58007881141664.41992118858343
312919.85120107186819.14879892813195
321722.4822982063557-5.48229820635571
332420.90564763020253.09435236979753
341821.7955504160463-3.79555041604627
352220.70399054005481.29600945994522
36821.0767090578752-13.0767090578752
372617.31598680340448.68401319659555
382219.8134165115992.18658348840096
393420.442254635143313.5577453648567
402524.3413178083320.658682191668007
412024.5307477915079-4.53074779150789
423523.227752980389411.7722470196106
433826.613325845537311.3866741544627
442429.8880120611266-5.88801206112659
451428.1946825013062-14.1946825013062
462524.11244299123150.88755700876845
473124.36769493422536.63230506577467
481726.2750752352558-9.27507523525582
493223.6076623797178.39233762028301
502726.02120929858980.978790701410215
513026.30269907992323.69730092007676
521927.3660034472582-8.36600344725824
533624.960029956081111.0399700439189
542728.1350077619728-1.13500776197281
552827.80859161777650.191408382223472
563827.863638629951710.1363613700483
572630.7787482049209-4.77874820492091
582529.4044311161779-4.4044311161779
593028.13776363557671.86223636442331
602728.6733229806517-1.67332298065165
613028.19209311276951.80790688723045
625028.712027878827821.2879721211722
634834.834221938076413.1657780619236
643438.6205594895019-4.62055948950194
654137.29173579055983.70826420944022
662638.3581930831537-12.3581930831537
673934.80410837061864.19589162938139
683336.0108021158204-3.01080211582045
693835.14492749318712.85507250681289
702835.9660159388334-7.96601593883336
713633.67507459510152.32492540489853
722034.3436983804506-14.3436983804506
733930.21860349059458.78139650940555
742232.7440396023939-10.7440396023939
753229.65416823974362.34583176025635
763230.32880447023531.67119552976474
773130.80942250590020.190577494099767
782830.8642305635002-2.86423056350022
794430.040508358286513.9594916417135
804034.05510948199015.94489051800988
813235.7647966802388-3.76479668023882
823534.68208125112980.317918748870248
833234.7735112973821-2.77351129738209
843133.9758789869187-2.97587898691867
854133.12004788421657.87995211578352
862335.3862381890428-12.3862381890428
873631.82408800274224.17591199725782
883633.02503581853392.97496418146611
894233.88060383293098.11939616706914
903636.2156556967614-0.215655696761431
916436.153635415165827.8463645848342
923044.1619532982669-14.1619532982669
932540.0891263584113-15.0891263584113
945135.749654321108115.2503456788919
953840.1354913179511-2.13549131795109
962739.5213467584825-12.5213467584825

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 47 & 53 & -6 \tabularnewline
3 & 49 & 51.2744639016622 & -2.27446390166219 \tabularnewline
4 & 44 & 50.6203523072148 & -6.6203523072148 \tabularnewline
5 & 48 & 48.7164094922459 & -0.716409492245944 \tabularnewline
6 & 51 & 48.5103777522356 & 2.48962224776443 \tabularnewline
7 & 47 & 49.226366595526 & -2.22636659552597 \tabularnewline
8 & 44 & 48.5860872740737 & -4.58608727407372 \tabularnewline
9 & 33 & 47.2671774171501 & -14.2671774171501 \tabularnewline
10 & 47 & 43.1640891413697 & 3.83591085863033 \tabularnewline
11 & 41 & 44.2672562507984 & -3.26725625079844 \tabularnewline
12 & 36 & 43.327628150253 & -7.32762815025301 \tabularnewline
13 & 46 & 41.22028033551 & 4.77971966448997 \tabularnewline
14 & 24 & 42.5948768056788 & -18.5948768056788 \tabularnewline
15 & 17 & 37.2471882769549 & -20.2471882769549 \tabularnewline
16 & 22 & 31.4243125666669 & -9.42431256666694 \tabularnewline
17 & 30 & 28.7139806440332 & 1.2860193559668 \tabularnewline
18 & 24 & 29.0838261143468 & -5.08382611434684 \tabularnewline
19 & 18 & 27.6217718680172 & -9.62177186801719 \tabularnewline
20 & 24 & 24.8546527533114 & -0.854652753311374 \tabularnewline
21 & 24 & 24.6088637237476 & -0.608863723747611 \tabularnewline
22 & 28 & 24.4337610013651 & 3.56623899863487 \tabularnewline
23 & 19 & 25.4593733559392 & -6.45937335593922 \tabularnewline
24 & 22 & 23.6017263728868 & -1.60172637288679 \tabularnewline
25 & 26 & 23.1410869268742 & 2.85891307312585 \tabularnewline
26 & 14 & 23.9632798784889 & -9.96327987848891 \tabularnewline
27 & 16 & 21.0979466971263 & -5.09794669712635 \tabularnewline
28 & 21 & 19.6318315215774 & 1.36816847842258 \tabularnewline
29 & 15 & 20.0253022045984 & -5.02530220459844 \tabularnewline
30 & 23 & 18.5800788114166 & 4.41992118858343 \tabularnewline
31 & 29 & 19.8512010718681 & 9.14879892813195 \tabularnewline
32 & 17 & 22.4822982063557 & -5.48229820635571 \tabularnewline
33 & 24 & 20.9056476302025 & 3.09435236979753 \tabularnewline
34 & 18 & 21.7955504160463 & -3.79555041604627 \tabularnewline
35 & 22 & 20.7039905400548 & 1.29600945994522 \tabularnewline
36 & 8 & 21.0767090578752 & -13.0767090578752 \tabularnewline
37 & 26 & 17.3159868034044 & 8.68401319659555 \tabularnewline
38 & 22 & 19.813416511599 & 2.18658348840096 \tabularnewline
39 & 34 & 20.4422546351433 & 13.5577453648567 \tabularnewline
40 & 25 & 24.341317808332 & 0.658682191668007 \tabularnewline
41 & 20 & 24.5307477915079 & -4.53074779150789 \tabularnewline
42 & 35 & 23.2277529803894 & 11.7722470196106 \tabularnewline
43 & 38 & 26.6133258455373 & 11.3866741544627 \tabularnewline
44 & 24 & 29.8880120611266 & -5.88801206112659 \tabularnewline
45 & 14 & 28.1946825013062 & -14.1946825013062 \tabularnewline
46 & 25 & 24.1124429912315 & 0.88755700876845 \tabularnewline
47 & 31 & 24.3676949342253 & 6.63230506577467 \tabularnewline
48 & 17 & 26.2750752352558 & -9.27507523525582 \tabularnewline
49 & 32 & 23.607662379717 & 8.39233762028301 \tabularnewline
50 & 27 & 26.0212092985898 & 0.978790701410215 \tabularnewline
51 & 30 & 26.3026990799232 & 3.69730092007676 \tabularnewline
52 & 19 & 27.3660034472582 & -8.36600344725824 \tabularnewline
53 & 36 & 24.9600299560811 & 11.0399700439189 \tabularnewline
54 & 27 & 28.1350077619728 & -1.13500776197281 \tabularnewline
55 & 28 & 27.8085916177765 & 0.191408382223472 \tabularnewline
56 & 38 & 27.8636386299517 & 10.1363613700483 \tabularnewline
57 & 26 & 30.7787482049209 & -4.77874820492091 \tabularnewline
58 & 25 & 29.4044311161779 & -4.4044311161779 \tabularnewline
59 & 30 & 28.1377636355767 & 1.86223636442331 \tabularnewline
60 & 27 & 28.6733229806517 & -1.67332298065165 \tabularnewline
61 & 30 & 28.1920931127695 & 1.80790688723045 \tabularnewline
62 & 50 & 28.7120278788278 & 21.2879721211722 \tabularnewline
63 & 48 & 34.8342219380764 & 13.1657780619236 \tabularnewline
64 & 34 & 38.6205594895019 & -4.62055948950194 \tabularnewline
65 & 41 & 37.2917357905598 & 3.70826420944022 \tabularnewline
66 & 26 & 38.3581930831537 & -12.3581930831537 \tabularnewline
67 & 39 & 34.8041083706186 & 4.19589162938139 \tabularnewline
68 & 33 & 36.0108021158204 & -3.01080211582045 \tabularnewline
69 & 38 & 35.1449274931871 & 2.85507250681289 \tabularnewline
70 & 28 & 35.9660159388334 & -7.96601593883336 \tabularnewline
71 & 36 & 33.6750745951015 & 2.32492540489853 \tabularnewline
72 & 20 & 34.3436983804506 & -14.3436983804506 \tabularnewline
73 & 39 & 30.2186034905945 & 8.78139650940555 \tabularnewline
74 & 22 & 32.7440396023939 & -10.7440396023939 \tabularnewline
75 & 32 & 29.6541682397436 & 2.34583176025635 \tabularnewline
76 & 32 & 30.3288044702353 & 1.67119552976474 \tabularnewline
77 & 31 & 30.8094225059002 & 0.190577494099767 \tabularnewline
78 & 28 & 30.8642305635002 & -2.86423056350022 \tabularnewline
79 & 44 & 30.0405083582865 & 13.9594916417135 \tabularnewline
80 & 40 & 34.0551094819901 & 5.94489051800988 \tabularnewline
81 & 32 & 35.7647966802388 & -3.76479668023882 \tabularnewline
82 & 35 & 34.6820812511298 & 0.317918748870248 \tabularnewline
83 & 32 & 34.7735112973821 & -2.77351129738209 \tabularnewline
84 & 31 & 33.9758789869187 & -2.97587898691867 \tabularnewline
85 & 41 & 33.1200478842165 & 7.87995211578352 \tabularnewline
86 & 23 & 35.3862381890428 & -12.3862381890428 \tabularnewline
87 & 36 & 31.8240880027422 & 4.17591199725782 \tabularnewline
88 & 36 & 33.0250358185339 & 2.97496418146611 \tabularnewline
89 & 42 & 33.8806038329309 & 8.11939616706914 \tabularnewline
90 & 36 & 36.2156556967614 & -0.215655696761431 \tabularnewline
91 & 64 & 36.1536354151658 & 27.8463645848342 \tabularnewline
92 & 30 & 44.1619532982669 & -14.1619532982669 \tabularnewline
93 & 25 & 40.0891263584113 & -15.0891263584113 \tabularnewline
94 & 51 & 35.7496543211081 & 15.2503456788919 \tabularnewline
95 & 38 & 40.1354913179511 & -2.13549131795109 \tabularnewline
96 & 27 & 39.5213467584825 & -12.5213467584825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260961&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]47[/C][C]53[/C][C]-6[/C][/ROW]
[ROW][C]3[/C][C]49[/C][C]51.2744639016622[/C][C]-2.27446390166219[/C][/ROW]
[ROW][C]4[/C][C]44[/C][C]50.6203523072148[/C][C]-6.6203523072148[/C][/ROW]
[ROW][C]5[/C][C]48[/C][C]48.7164094922459[/C][C]-0.716409492245944[/C][/ROW]
[ROW][C]6[/C][C]51[/C][C]48.5103777522356[/C][C]2.48962224776443[/C][/ROW]
[ROW][C]7[/C][C]47[/C][C]49.226366595526[/C][C]-2.22636659552597[/C][/ROW]
[ROW][C]8[/C][C]44[/C][C]48.5860872740737[/C][C]-4.58608727407372[/C][/ROW]
[ROW][C]9[/C][C]33[/C][C]47.2671774171501[/C][C]-14.2671774171501[/C][/ROW]
[ROW][C]10[/C][C]47[/C][C]43.1640891413697[/C][C]3.83591085863033[/C][/ROW]
[ROW][C]11[/C][C]41[/C][C]44.2672562507984[/C][C]-3.26725625079844[/C][/ROW]
[ROW][C]12[/C][C]36[/C][C]43.327628150253[/C][C]-7.32762815025301[/C][/ROW]
[ROW][C]13[/C][C]46[/C][C]41.22028033551[/C][C]4.77971966448997[/C][/ROW]
[ROW][C]14[/C][C]24[/C][C]42.5948768056788[/C][C]-18.5948768056788[/C][/ROW]
[ROW][C]15[/C][C]17[/C][C]37.2471882769549[/C][C]-20.2471882769549[/C][/ROW]
[ROW][C]16[/C][C]22[/C][C]31.4243125666669[/C][C]-9.42431256666694[/C][/ROW]
[ROW][C]17[/C][C]30[/C][C]28.7139806440332[/C][C]1.2860193559668[/C][/ROW]
[ROW][C]18[/C][C]24[/C][C]29.0838261143468[/C][C]-5.08382611434684[/C][/ROW]
[ROW][C]19[/C][C]18[/C][C]27.6217718680172[/C][C]-9.62177186801719[/C][/ROW]
[ROW][C]20[/C][C]24[/C][C]24.8546527533114[/C][C]-0.854652753311374[/C][/ROW]
[ROW][C]21[/C][C]24[/C][C]24.6088637237476[/C][C]-0.608863723747611[/C][/ROW]
[ROW][C]22[/C][C]28[/C][C]24.4337610013651[/C][C]3.56623899863487[/C][/ROW]
[ROW][C]23[/C][C]19[/C][C]25.4593733559392[/C][C]-6.45937335593922[/C][/ROW]
[ROW][C]24[/C][C]22[/C][C]23.6017263728868[/C][C]-1.60172637288679[/C][/ROW]
[ROW][C]25[/C][C]26[/C][C]23.1410869268742[/C][C]2.85891307312585[/C][/ROW]
[ROW][C]26[/C][C]14[/C][C]23.9632798784889[/C][C]-9.96327987848891[/C][/ROW]
[ROW][C]27[/C][C]16[/C][C]21.0979466971263[/C][C]-5.09794669712635[/C][/ROW]
[ROW][C]28[/C][C]21[/C][C]19.6318315215774[/C][C]1.36816847842258[/C][/ROW]
[ROW][C]29[/C][C]15[/C][C]20.0253022045984[/C][C]-5.02530220459844[/C][/ROW]
[ROW][C]30[/C][C]23[/C][C]18.5800788114166[/C][C]4.41992118858343[/C][/ROW]
[ROW][C]31[/C][C]29[/C][C]19.8512010718681[/C][C]9.14879892813195[/C][/ROW]
[ROW][C]32[/C][C]17[/C][C]22.4822982063557[/C][C]-5.48229820635571[/C][/ROW]
[ROW][C]33[/C][C]24[/C][C]20.9056476302025[/C][C]3.09435236979753[/C][/ROW]
[ROW][C]34[/C][C]18[/C][C]21.7955504160463[/C][C]-3.79555041604627[/C][/ROW]
[ROW][C]35[/C][C]22[/C][C]20.7039905400548[/C][C]1.29600945994522[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]21.0767090578752[/C][C]-13.0767090578752[/C][/ROW]
[ROW][C]37[/C][C]26[/C][C]17.3159868034044[/C][C]8.68401319659555[/C][/ROW]
[ROW][C]38[/C][C]22[/C][C]19.813416511599[/C][C]2.18658348840096[/C][/ROW]
[ROW][C]39[/C][C]34[/C][C]20.4422546351433[/C][C]13.5577453648567[/C][/ROW]
[ROW][C]40[/C][C]25[/C][C]24.341317808332[/C][C]0.658682191668007[/C][/ROW]
[ROW][C]41[/C][C]20[/C][C]24.5307477915079[/C][C]-4.53074779150789[/C][/ROW]
[ROW][C]42[/C][C]35[/C][C]23.2277529803894[/C][C]11.7722470196106[/C][/ROW]
[ROW][C]43[/C][C]38[/C][C]26.6133258455373[/C][C]11.3866741544627[/C][/ROW]
[ROW][C]44[/C][C]24[/C][C]29.8880120611266[/C][C]-5.88801206112659[/C][/ROW]
[ROW][C]45[/C][C]14[/C][C]28.1946825013062[/C][C]-14.1946825013062[/C][/ROW]
[ROW][C]46[/C][C]25[/C][C]24.1124429912315[/C][C]0.88755700876845[/C][/ROW]
[ROW][C]47[/C][C]31[/C][C]24.3676949342253[/C][C]6.63230506577467[/C][/ROW]
[ROW][C]48[/C][C]17[/C][C]26.2750752352558[/C][C]-9.27507523525582[/C][/ROW]
[ROW][C]49[/C][C]32[/C][C]23.607662379717[/C][C]8.39233762028301[/C][/ROW]
[ROW][C]50[/C][C]27[/C][C]26.0212092985898[/C][C]0.978790701410215[/C][/ROW]
[ROW][C]51[/C][C]30[/C][C]26.3026990799232[/C][C]3.69730092007676[/C][/ROW]
[ROW][C]52[/C][C]19[/C][C]27.3660034472582[/C][C]-8.36600344725824[/C][/ROW]
[ROW][C]53[/C][C]36[/C][C]24.9600299560811[/C][C]11.0399700439189[/C][/ROW]
[ROW][C]54[/C][C]27[/C][C]28.1350077619728[/C][C]-1.13500776197281[/C][/ROW]
[ROW][C]55[/C][C]28[/C][C]27.8085916177765[/C][C]0.191408382223472[/C][/ROW]
[ROW][C]56[/C][C]38[/C][C]27.8636386299517[/C][C]10.1363613700483[/C][/ROW]
[ROW][C]57[/C][C]26[/C][C]30.7787482049209[/C][C]-4.77874820492091[/C][/ROW]
[ROW][C]58[/C][C]25[/C][C]29.4044311161779[/C][C]-4.4044311161779[/C][/ROW]
[ROW][C]59[/C][C]30[/C][C]28.1377636355767[/C][C]1.86223636442331[/C][/ROW]
[ROW][C]60[/C][C]27[/C][C]28.6733229806517[/C][C]-1.67332298065165[/C][/ROW]
[ROW][C]61[/C][C]30[/C][C]28.1920931127695[/C][C]1.80790688723045[/C][/ROW]
[ROW][C]62[/C][C]50[/C][C]28.7120278788278[/C][C]21.2879721211722[/C][/ROW]
[ROW][C]63[/C][C]48[/C][C]34.8342219380764[/C][C]13.1657780619236[/C][/ROW]
[ROW][C]64[/C][C]34[/C][C]38.6205594895019[/C][C]-4.62055948950194[/C][/ROW]
[ROW][C]65[/C][C]41[/C][C]37.2917357905598[/C][C]3.70826420944022[/C][/ROW]
[ROW][C]66[/C][C]26[/C][C]38.3581930831537[/C][C]-12.3581930831537[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]34.8041083706186[/C][C]4.19589162938139[/C][/ROW]
[ROW][C]68[/C][C]33[/C][C]36.0108021158204[/C][C]-3.01080211582045[/C][/ROW]
[ROW][C]69[/C][C]38[/C][C]35.1449274931871[/C][C]2.85507250681289[/C][/ROW]
[ROW][C]70[/C][C]28[/C][C]35.9660159388334[/C][C]-7.96601593883336[/C][/ROW]
[ROW][C]71[/C][C]36[/C][C]33.6750745951015[/C][C]2.32492540489853[/C][/ROW]
[ROW][C]72[/C][C]20[/C][C]34.3436983804506[/C][C]-14.3436983804506[/C][/ROW]
[ROW][C]73[/C][C]39[/C][C]30.2186034905945[/C][C]8.78139650940555[/C][/ROW]
[ROW][C]74[/C][C]22[/C][C]32.7440396023939[/C][C]-10.7440396023939[/C][/ROW]
[ROW][C]75[/C][C]32[/C][C]29.6541682397436[/C][C]2.34583176025635[/C][/ROW]
[ROW][C]76[/C][C]32[/C][C]30.3288044702353[/C][C]1.67119552976474[/C][/ROW]
[ROW][C]77[/C][C]31[/C][C]30.8094225059002[/C][C]0.190577494099767[/C][/ROW]
[ROW][C]78[/C][C]28[/C][C]30.8642305635002[/C][C]-2.86423056350022[/C][/ROW]
[ROW][C]79[/C][C]44[/C][C]30.0405083582865[/C][C]13.9594916417135[/C][/ROW]
[ROW][C]80[/C][C]40[/C][C]34.0551094819901[/C][C]5.94489051800988[/C][/ROW]
[ROW][C]81[/C][C]32[/C][C]35.7647966802388[/C][C]-3.76479668023882[/C][/ROW]
[ROW][C]82[/C][C]35[/C][C]34.6820812511298[/C][C]0.317918748870248[/C][/ROW]
[ROW][C]83[/C][C]32[/C][C]34.7735112973821[/C][C]-2.77351129738209[/C][/ROW]
[ROW][C]84[/C][C]31[/C][C]33.9758789869187[/C][C]-2.97587898691867[/C][/ROW]
[ROW][C]85[/C][C]41[/C][C]33.1200478842165[/C][C]7.87995211578352[/C][/ROW]
[ROW][C]86[/C][C]23[/C][C]35.3862381890428[/C][C]-12.3862381890428[/C][/ROW]
[ROW][C]87[/C][C]36[/C][C]31.8240880027422[/C][C]4.17591199725782[/C][/ROW]
[ROW][C]88[/C][C]36[/C][C]33.0250358185339[/C][C]2.97496418146611[/C][/ROW]
[ROW][C]89[/C][C]42[/C][C]33.8806038329309[/C][C]8.11939616706914[/C][/ROW]
[ROW][C]90[/C][C]36[/C][C]36.2156556967614[/C][C]-0.215655696761431[/C][/ROW]
[ROW][C]91[/C][C]64[/C][C]36.1536354151658[/C][C]27.8463645848342[/C][/ROW]
[ROW][C]92[/C][C]30[/C][C]44.1619532982669[/C][C]-14.1619532982669[/C][/ROW]
[ROW][C]93[/C][C]25[/C][C]40.0891263584113[/C][C]-15.0891263584113[/C][/ROW]
[ROW][C]94[/C][C]51[/C][C]35.7496543211081[/C][C]15.2503456788919[/C][/ROW]
[ROW][C]95[/C][C]38[/C][C]40.1354913179511[/C][C]-2.13549131795109[/C][/ROW]
[ROW][C]96[/C][C]27[/C][C]39.5213467584825[/C][C]-12.5213467584825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260961&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260961&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
24753-6
34951.2744639016622-2.27446390166219
44450.6203523072148-6.6203523072148
54848.7164094922459-0.716409492245944
65148.51037775223562.48962224776443
74749.226366595526-2.22636659552597
84448.5860872740737-4.58608727407372
93347.2671774171501-14.2671774171501
104743.16408914136973.83591085863033
114144.2672562507984-3.26725625079844
123643.327628150253-7.32762815025301
134641.220280335514.77971966448997
142442.5948768056788-18.5948768056788
151737.2471882769549-20.2471882769549
162231.4243125666669-9.42431256666694
173028.71398064403321.2860193559668
182429.0838261143468-5.08382611434684
191827.6217718680172-9.62177186801719
202424.8546527533114-0.854652753311374
212424.6088637237476-0.608863723747611
222824.43376100136513.56623899863487
231925.4593733559392-6.45937335593922
242223.6017263728868-1.60172637288679
252623.14108692687422.85891307312585
261423.9632798784889-9.96327987848891
271621.0979466971263-5.09794669712635
282119.63183152157741.36816847842258
291520.0253022045984-5.02530220459844
302318.58007881141664.41992118858343
312919.85120107186819.14879892813195
321722.4822982063557-5.48229820635571
332420.90564763020253.09435236979753
341821.7955504160463-3.79555041604627
352220.70399054005481.29600945994522
36821.0767090578752-13.0767090578752
372617.31598680340448.68401319659555
382219.8134165115992.18658348840096
393420.442254635143313.5577453648567
402524.3413178083320.658682191668007
412024.5307477915079-4.53074779150789
423523.227752980389411.7722470196106
433826.613325845537311.3866741544627
442429.8880120611266-5.88801206112659
451428.1946825013062-14.1946825013062
462524.11244299123150.88755700876845
473124.36769493422536.63230506577467
481726.2750752352558-9.27507523525582
493223.6076623797178.39233762028301
502726.02120929858980.978790701410215
513026.30269907992323.69730092007676
521927.3660034472582-8.36600344725824
533624.960029956081111.0399700439189
542728.1350077619728-1.13500776197281
552827.80859161777650.191408382223472
563827.863638629951710.1363613700483
572630.7787482049209-4.77874820492091
582529.4044311161779-4.4044311161779
593028.13776363557671.86223636442331
602728.6733229806517-1.67332298065165
613028.19209311276951.80790688723045
625028.712027878827821.2879721211722
634834.834221938076413.1657780619236
643438.6205594895019-4.62055948950194
654137.29173579055983.70826420944022
662638.3581930831537-12.3581930831537
673934.80410837061864.19589162938139
683336.0108021158204-3.01080211582045
693835.14492749318712.85507250681289
702835.9660159388334-7.96601593883336
713633.67507459510152.32492540489853
722034.3436983804506-14.3436983804506
733930.21860349059458.78139650940555
742232.7440396023939-10.7440396023939
753229.65416823974362.34583176025635
763230.32880447023531.67119552976474
773130.80942250590020.190577494099767
782830.8642305635002-2.86423056350022
794430.040508358286513.9594916417135
804034.05510948199015.94489051800988
813235.7647966802388-3.76479668023882
823534.68208125112980.317918748870248
833234.7735112973821-2.77351129738209
843133.9758789869187-2.97587898691867
854133.12004788421657.87995211578352
862335.3862381890428-12.3862381890428
873631.82408800274224.17591199725782
883633.02503581853392.97496418146611
894233.88060383293098.11939616706914
903636.2156556967614-0.215655696761431
916436.153635415165827.8463645848342
923044.1619532982669-14.1619532982669
932540.0891263584113-15.0891263584113
945135.749654321108115.2503456788919
953840.1354913179511-2.13549131795109
962739.5213467584825-12.5213467584825







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9735.920340786554719.30982385977152.5308577133384
9835.920340786554718.636560073737753.2041214993717
9935.920340786554717.988556745848753.8521248272608
10035.920340786554717.363167455567754.4775141175418
10135.920340786554716.758177933941455.082503639168
10235.920340786554716.171713281235655.6689682918739
10335.920340786554715.602169326070856.2385122470387
10435.920340786554715.048160865631256.7925207074782
10535.920340786554714.508481974084157.3321995990254
10635.920340786554713.982075108544757.8586064645647
10735.920340786554713.468006740564658.3726748325449
10835.920340786554712.965447903630958.8752336694785

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 35.9203407865547 & 19.309823859771 & 52.5308577133384 \tabularnewline
98 & 35.9203407865547 & 18.6365600737377 & 53.2041214993717 \tabularnewline
99 & 35.9203407865547 & 17.9885567458487 & 53.8521248272608 \tabularnewline
100 & 35.9203407865547 & 17.3631674555677 & 54.4775141175418 \tabularnewline
101 & 35.9203407865547 & 16.7581779339414 & 55.082503639168 \tabularnewline
102 & 35.9203407865547 & 16.1717132812356 & 55.6689682918739 \tabularnewline
103 & 35.9203407865547 & 15.6021693260708 & 56.2385122470387 \tabularnewline
104 & 35.9203407865547 & 15.0481608656312 & 56.7925207074782 \tabularnewline
105 & 35.9203407865547 & 14.5084819740841 & 57.3321995990254 \tabularnewline
106 & 35.9203407865547 & 13.9820751085447 & 57.8586064645647 \tabularnewline
107 & 35.9203407865547 & 13.4680067405646 & 58.3726748325449 \tabularnewline
108 & 35.9203407865547 & 12.9654479036309 & 58.8752336694785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260961&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]35.9203407865547[/C][C]19.309823859771[/C][C]52.5308577133384[/C][/ROW]
[ROW][C]98[/C][C]35.9203407865547[/C][C]18.6365600737377[/C][C]53.2041214993717[/C][/ROW]
[ROW][C]99[/C][C]35.9203407865547[/C][C]17.9885567458487[/C][C]53.8521248272608[/C][/ROW]
[ROW][C]100[/C][C]35.9203407865547[/C][C]17.3631674555677[/C][C]54.4775141175418[/C][/ROW]
[ROW][C]101[/C][C]35.9203407865547[/C][C]16.7581779339414[/C][C]55.082503639168[/C][/ROW]
[ROW][C]102[/C][C]35.9203407865547[/C][C]16.1717132812356[/C][C]55.6689682918739[/C][/ROW]
[ROW][C]103[/C][C]35.9203407865547[/C][C]15.6021693260708[/C][C]56.2385122470387[/C][/ROW]
[ROW][C]104[/C][C]35.9203407865547[/C][C]15.0481608656312[/C][C]56.7925207074782[/C][/ROW]
[ROW][C]105[/C][C]35.9203407865547[/C][C]14.5084819740841[/C][C]57.3321995990254[/C][/ROW]
[ROW][C]106[/C][C]35.9203407865547[/C][C]13.9820751085447[/C][C]57.8586064645647[/C][/ROW]
[ROW][C]107[/C][C]35.9203407865547[/C][C]13.4680067405646[/C][C]58.3726748325449[/C][/ROW]
[ROW][C]108[/C][C]35.9203407865547[/C][C]12.9654479036309[/C][C]58.8752336694785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260961&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260961&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
9735.920340786554719.30982385977152.5308577133384
9835.920340786554718.636560073737753.2041214993717
9935.920340786554717.988556745848753.8521248272608
10035.920340786554717.363167455567754.4775141175418
10135.920340786554716.758177933941455.082503639168
10235.920340786554716.171713281235655.6689682918739
10335.920340786554715.602169326070856.2385122470387
10435.920340786554715.048160865631256.7925207074782
10535.920340786554714.508481974084157.3321995990254
10635.920340786554713.982075108544757.8586064645647
10735.920340786554713.468006740564658.3726748325449
10835.920340786554712.965447903630958.8752336694785



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