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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 20:43:25 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1428003869q6971lgflisq7ys.htm/, Retrieved Thu, 09 May 2024 05:00:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278644, Retrieved Thu, 09 May 2024 05:00:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Vooruitzichten we...] [2015-04-02 19:43:25] [181905e06b04c65545707bd953ef5b1f] [Current]
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Dataseries X:
24
24
31
25
28
24
25
16
17
11
12
39
19
14
15
7
12
12
14
9
8
4
7
3
5
0
-2
6
11
9
17
21
21
41
57
65
68
73
71
71
70
69
65
57
57
57
55
65
65
64
60
43
47
40
31
27
24
23
17
16
15
8
5
6
5
12
8
17
22
24
36
31
34
47
33
35
31
35
39
46
40
50
62
57
59
52
63
56
55
54
48
39
40
38
34
32




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=278644&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=278644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278644&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
alpha0.94792451851306
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.94792451851306 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278644&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]0.94792451851306[/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=278644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278644&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
alpha0.94792451851306
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
224240
331247
42530.6354716295914-5.63547162959142
52825.2934698985172.70653010148304
62427.8590561418064-3.85905614180637
72524.20096220666970.799037793330299
81624.9583897221861-8.95838972218606
91716.46651245813050.533487541869505
101116.9722183793899-5.97221837938986
111211.31100614765190.688993852348119
123911.964120313397427.0358796866026
131937.5920935478972-18.5920935478972
141419.968192223357-5.96819222335698
151514.31079648363790.689203516362072
16714.964109395043-7.96410939504295
17127.414734831361534.58526516863847
181211.76122010859790.238779891402144
191411.98756542218582.01243457781417
20913.8952015003994-4.89520150039936
2189.25491997510889-1.25491997510889
2248.06535056193137-4.06535056193137
2374.211705087925782.78829491207422
2436.85479819992615-3.85479819992615
2553.200740472296151.79925952770385
2604.90630269377486-4.90630269377486
27-20.255498075098998-2.255498075099
286-1.882543851746357.88254385174635
29115.589512733578395.41048726642161
30910.7182462705221-1.71824627052214
31179.089478501850587.91052149814942
322116.58805578417114.41194421582892
332120.77024588066720.229754119332814
344120.988035443612120.0119645563879
355739.957867310226517.0421326897735
366556.11252273461578.88747726538428
376864.53718034220093.46281965779912
387367.81967199901775.18032800098233
397172.7302319250886-1.73023192508857
407171.0901026605831-0.0901026605830566
417071.0046921394331-1.00469213943312
426970.0523198269071-1.05231982690712
436569.0548000616645-4.05480006166445
445765.2111556655445-8.21115566554445
455757.4275998848474-0.427599884847446
465757.0222674698872-0.022267469887197
475557.0011595892159-2.00115958921587
486555.10421134914069.89578865085938
496564.48467204131350.515327958686498
506464.9731640484277-0.973164048427719
516064.0506779863877-4.05067798638765
524360.2109410064897-17.2109410064897
534743.89626803975633.10373196024372
544046.8383716637639-6.8383716637639
553140.3561114969772-9.35611149697716
562731.4872240110506-4.48722401105059
572427.2336743509152-3.23367435091522
582324.1683951487959-1.16839514879588
591723.0608447399405-6.06084473994055
601617.31562140805-1.31562140805
611516.0685116182787-1.06851161827873
62815.0556432569963-7.05564325699625
6358.36742601980816-3.36742601980816
6465.175360331353160.824639668646839
6555.95705649220199-0.957056492201986
66125.049839177641626.95016082235838
67811.638067028764-3.63806702876402
68178.189454092204658.81054590779535
692216.54118657968885.45881342031123
702421.71572966278992.28427033721008
713623.881045522343412.1189544776566
723135.3688996104577-4.36889961045772
733431.22751255078272.77248744921731
744733.855621381165513.1443786188345
753346.3155001545775-13.3155001545775
763533.69341108178911.30658891821095
773134.9319587529787-3.93195875297866
783531.20475864524823.79524135475184
793934.80236097909214.19763902090785
804638.78140592687797.21859407312215
814045.6240882379834-5.62408823798339
825040.2928771029189.70712289708197
836249.494496901281612.5055030987184
845761.3487699048978-4.34876990489781
855957.22646428667351.77353571332652
865258.9076422737942-6.90764227379424
876352.359718797347410.6402812026526
885662.4459022332154-6.44590223321542
895556.3356734624124-1.33567346241244
905455.0695558386645-1.06955583866446
914854.0556976352756-6.05569763527562
923948.3153533700963-9.3153533700963
934039.48510151196880.514898488031243
943839.9731864133189-1.97318641331888
953438.1027546325371-4.10275463253706
963234.2136529229121-2.21365292291215

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 24 & 24 & 0 \tabularnewline
3 & 31 & 24 & 7 \tabularnewline
4 & 25 & 30.6354716295914 & -5.63547162959142 \tabularnewline
5 & 28 & 25.293469898517 & 2.70653010148304 \tabularnewline
6 & 24 & 27.8590561418064 & -3.85905614180637 \tabularnewline
7 & 25 & 24.2009622066697 & 0.799037793330299 \tabularnewline
8 & 16 & 24.9583897221861 & -8.95838972218606 \tabularnewline
9 & 17 & 16.4665124581305 & 0.533487541869505 \tabularnewline
10 & 11 & 16.9722183793899 & -5.97221837938986 \tabularnewline
11 & 12 & 11.3110061476519 & 0.688993852348119 \tabularnewline
12 & 39 & 11.9641203133974 & 27.0358796866026 \tabularnewline
13 & 19 & 37.5920935478972 & -18.5920935478972 \tabularnewline
14 & 14 & 19.968192223357 & -5.96819222335698 \tabularnewline
15 & 15 & 14.3107964836379 & 0.689203516362072 \tabularnewline
16 & 7 & 14.964109395043 & -7.96410939504295 \tabularnewline
17 & 12 & 7.41473483136153 & 4.58526516863847 \tabularnewline
18 & 12 & 11.7612201085979 & 0.238779891402144 \tabularnewline
19 & 14 & 11.9875654221858 & 2.01243457781417 \tabularnewline
20 & 9 & 13.8952015003994 & -4.89520150039936 \tabularnewline
21 & 8 & 9.25491997510889 & -1.25491997510889 \tabularnewline
22 & 4 & 8.06535056193137 & -4.06535056193137 \tabularnewline
23 & 7 & 4.21170508792578 & 2.78829491207422 \tabularnewline
24 & 3 & 6.85479819992615 & -3.85479819992615 \tabularnewline
25 & 5 & 3.20074047229615 & 1.79925952770385 \tabularnewline
26 & 0 & 4.90630269377486 & -4.90630269377486 \tabularnewline
27 & -2 & 0.255498075098998 & -2.255498075099 \tabularnewline
28 & 6 & -1.88254385174635 & 7.88254385174635 \tabularnewline
29 & 11 & 5.58951273357839 & 5.41048726642161 \tabularnewline
30 & 9 & 10.7182462705221 & -1.71824627052214 \tabularnewline
31 & 17 & 9.08947850185058 & 7.91052149814942 \tabularnewline
32 & 21 & 16.5880557841711 & 4.41194421582892 \tabularnewline
33 & 21 & 20.7702458806672 & 0.229754119332814 \tabularnewline
34 & 41 & 20.9880354436121 & 20.0119645563879 \tabularnewline
35 & 57 & 39.9578673102265 & 17.0421326897735 \tabularnewline
36 & 65 & 56.1125227346157 & 8.88747726538428 \tabularnewline
37 & 68 & 64.5371803422009 & 3.46281965779912 \tabularnewline
38 & 73 & 67.8196719990177 & 5.18032800098233 \tabularnewline
39 & 71 & 72.7302319250886 & -1.73023192508857 \tabularnewline
40 & 71 & 71.0901026605831 & -0.0901026605830566 \tabularnewline
41 & 70 & 71.0046921394331 & -1.00469213943312 \tabularnewline
42 & 69 & 70.0523198269071 & -1.05231982690712 \tabularnewline
43 & 65 & 69.0548000616645 & -4.05480006166445 \tabularnewline
44 & 57 & 65.2111556655445 & -8.21115566554445 \tabularnewline
45 & 57 & 57.4275998848474 & -0.427599884847446 \tabularnewline
46 & 57 & 57.0222674698872 & -0.022267469887197 \tabularnewline
47 & 55 & 57.0011595892159 & -2.00115958921587 \tabularnewline
48 & 65 & 55.1042113491406 & 9.89578865085938 \tabularnewline
49 & 65 & 64.4846720413135 & 0.515327958686498 \tabularnewline
50 & 64 & 64.9731640484277 & -0.973164048427719 \tabularnewline
51 & 60 & 64.0506779863877 & -4.05067798638765 \tabularnewline
52 & 43 & 60.2109410064897 & -17.2109410064897 \tabularnewline
53 & 47 & 43.8962680397563 & 3.10373196024372 \tabularnewline
54 & 40 & 46.8383716637639 & -6.8383716637639 \tabularnewline
55 & 31 & 40.3561114969772 & -9.35611149697716 \tabularnewline
56 & 27 & 31.4872240110506 & -4.48722401105059 \tabularnewline
57 & 24 & 27.2336743509152 & -3.23367435091522 \tabularnewline
58 & 23 & 24.1683951487959 & -1.16839514879588 \tabularnewline
59 & 17 & 23.0608447399405 & -6.06084473994055 \tabularnewline
60 & 16 & 17.31562140805 & -1.31562140805 \tabularnewline
61 & 15 & 16.0685116182787 & -1.06851161827873 \tabularnewline
62 & 8 & 15.0556432569963 & -7.05564325699625 \tabularnewline
63 & 5 & 8.36742601980816 & -3.36742601980816 \tabularnewline
64 & 6 & 5.17536033135316 & 0.824639668646839 \tabularnewline
65 & 5 & 5.95705649220199 & -0.957056492201986 \tabularnewline
66 & 12 & 5.04983917764162 & 6.95016082235838 \tabularnewline
67 & 8 & 11.638067028764 & -3.63806702876402 \tabularnewline
68 & 17 & 8.18945409220465 & 8.81054590779535 \tabularnewline
69 & 22 & 16.5411865796888 & 5.45881342031123 \tabularnewline
70 & 24 & 21.7157296627899 & 2.28427033721008 \tabularnewline
71 & 36 & 23.8810455223434 & 12.1189544776566 \tabularnewline
72 & 31 & 35.3688996104577 & -4.36889961045772 \tabularnewline
73 & 34 & 31.2275125507827 & 2.77248744921731 \tabularnewline
74 & 47 & 33.8556213811655 & 13.1443786188345 \tabularnewline
75 & 33 & 46.3155001545775 & -13.3155001545775 \tabularnewline
76 & 35 & 33.6934110817891 & 1.30658891821095 \tabularnewline
77 & 31 & 34.9319587529787 & -3.93195875297866 \tabularnewline
78 & 35 & 31.2047586452482 & 3.79524135475184 \tabularnewline
79 & 39 & 34.8023609790921 & 4.19763902090785 \tabularnewline
80 & 46 & 38.7814059268779 & 7.21859407312215 \tabularnewline
81 & 40 & 45.6240882379834 & -5.62408823798339 \tabularnewline
82 & 50 & 40.292877102918 & 9.70712289708197 \tabularnewline
83 & 62 & 49.4944969012816 & 12.5055030987184 \tabularnewline
84 & 57 & 61.3487699048978 & -4.34876990489781 \tabularnewline
85 & 59 & 57.2264642866735 & 1.77353571332652 \tabularnewline
86 & 52 & 58.9076422737942 & -6.90764227379424 \tabularnewline
87 & 63 & 52.3597187973474 & 10.6402812026526 \tabularnewline
88 & 56 & 62.4459022332154 & -6.44590223321542 \tabularnewline
89 & 55 & 56.3356734624124 & -1.33567346241244 \tabularnewline
90 & 54 & 55.0695558386645 & -1.06955583866446 \tabularnewline
91 & 48 & 54.0556976352756 & -6.05569763527562 \tabularnewline
92 & 39 & 48.3153533700963 & -9.3153533700963 \tabularnewline
93 & 40 & 39.4851015119688 & 0.514898488031243 \tabularnewline
94 & 38 & 39.9731864133189 & -1.97318641331888 \tabularnewline
95 & 34 & 38.1027546325371 & -4.10275463253706 \tabularnewline
96 & 32 & 34.2136529229121 & -2.21365292291215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278644&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]24[/C][C]24[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]31[/C][C]24[/C][C]7[/C][/ROW]
[ROW][C]4[/C][C]25[/C][C]30.6354716295914[/C][C]-5.63547162959142[/C][/ROW]
[ROW][C]5[/C][C]28[/C][C]25.293469898517[/C][C]2.70653010148304[/C][/ROW]
[ROW][C]6[/C][C]24[/C][C]27.8590561418064[/C][C]-3.85905614180637[/C][/ROW]
[ROW][C]7[/C][C]25[/C][C]24.2009622066697[/C][C]0.799037793330299[/C][/ROW]
[ROW][C]8[/C][C]16[/C][C]24.9583897221861[/C][C]-8.95838972218606[/C][/ROW]
[ROW][C]9[/C][C]17[/C][C]16.4665124581305[/C][C]0.533487541869505[/C][/ROW]
[ROW][C]10[/C][C]11[/C][C]16.9722183793899[/C][C]-5.97221837938986[/C][/ROW]
[ROW][C]11[/C][C]12[/C][C]11.3110061476519[/C][C]0.688993852348119[/C][/ROW]
[ROW][C]12[/C][C]39[/C][C]11.9641203133974[/C][C]27.0358796866026[/C][/ROW]
[ROW][C]13[/C][C]19[/C][C]37.5920935478972[/C][C]-18.5920935478972[/C][/ROW]
[ROW][C]14[/C][C]14[/C][C]19.968192223357[/C][C]-5.96819222335698[/C][/ROW]
[ROW][C]15[/C][C]15[/C][C]14.3107964836379[/C][C]0.689203516362072[/C][/ROW]
[ROW][C]16[/C][C]7[/C][C]14.964109395043[/C][C]-7.96410939504295[/C][/ROW]
[ROW][C]17[/C][C]12[/C][C]7.41473483136153[/C][C]4.58526516863847[/C][/ROW]
[ROW][C]18[/C][C]12[/C][C]11.7612201085979[/C][C]0.238779891402144[/C][/ROW]
[ROW][C]19[/C][C]14[/C][C]11.9875654221858[/C][C]2.01243457781417[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]13.8952015003994[/C][C]-4.89520150039936[/C][/ROW]
[ROW][C]21[/C][C]8[/C][C]9.25491997510889[/C][C]-1.25491997510889[/C][/ROW]
[ROW][C]22[/C][C]4[/C][C]8.06535056193137[/C][C]-4.06535056193137[/C][/ROW]
[ROW][C]23[/C][C]7[/C][C]4.21170508792578[/C][C]2.78829491207422[/C][/ROW]
[ROW][C]24[/C][C]3[/C][C]6.85479819992615[/C][C]-3.85479819992615[/C][/ROW]
[ROW][C]25[/C][C]5[/C][C]3.20074047229615[/C][C]1.79925952770385[/C][/ROW]
[ROW][C]26[/C][C]0[/C][C]4.90630269377486[/C][C]-4.90630269377486[/C][/ROW]
[ROW][C]27[/C][C]-2[/C][C]0.255498075098998[/C][C]-2.255498075099[/C][/ROW]
[ROW][C]28[/C][C]6[/C][C]-1.88254385174635[/C][C]7.88254385174635[/C][/ROW]
[ROW][C]29[/C][C]11[/C][C]5.58951273357839[/C][C]5.41048726642161[/C][/ROW]
[ROW][C]30[/C][C]9[/C][C]10.7182462705221[/C][C]-1.71824627052214[/C][/ROW]
[ROW][C]31[/C][C]17[/C][C]9.08947850185058[/C][C]7.91052149814942[/C][/ROW]
[ROW][C]32[/C][C]21[/C][C]16.5880557841711[/C][C]4.41194421582892[/C][/ROW]
[ROW][C]33[/C][C]21[/C][C]20.7702458806672[/C][C]0.229754119332814[/C][/ROW]
[ROW][C]34[/C][C]41[/C][C]20.9880354436121[/C][C]20.0119645563879[/C][/ROW]
[ROW][C]35[/C][C]57[/C][C]39.9578673102265[/C][C]17.0421326897735[/C][/ROW]
[ROW][C]36[/C][C]65[/C][C]56.1125227346157[/C][C]8.88747726538428[/C][/ROW]
[ROW][C]37[/C][C]68[/C][C]64.5371803422009[/C][C]3.46281965779912[/C][/ROW]
[ROW][C]38[/C][C]73[/C][C]67.8196719990177[/C][C]5.18032800098233[/C][/ROW]
[ROW][C]39[/C][C]71[/C][C]72.7302319250886[/C][C]-1.73023192508857[/C][/ROW]
[ROW][C]40[/C][C]71[/C][C]71.0901026605831[/C][C]-0.0901026605830566[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]71.0046921394331[/C][C]-1.00469213943312[/C][/ROW]
[ROW][C]42[/C][C]69[/C][C]70.0523198269071[/C][C]-1.05231982690712[/C][/ROW]
[ROW][C]43[/C][C]65[/C][C]69.0548000616645[/C][C]-4.05480006166445[/C][/ROW]
[ROW][C]44[/C][C]57[/C][C]65.2111556655445[/C][C]-8.21115566554445[/C][/ROW]
[ROW][C]45[/C][C]57[/C][C]57.4275998848474[/C][C]-0.427599884847446[/C][/ROW]
[ROW][C]46[/C][C]57[/C][C]57.0222674698872[/C][C]-0.022267469887197[/C][/ROW]
[ROW][C]47[/C][C]55[/C][C]57.0011595892159[/C][C]-2.00115958921587[/C][/ROW]
[ROW][C]48[/C][C]65[/C][C]55.1042113491406[/C][C]9.89578865085938[/C][/ROW]
[ROW][C]49[/C][C]65[/C][C]64.4846720413135[/C][C]0.515327958686498[/C][/ROW]
[ROW][C]50[/C][C]64[/C][C]64.9731640484277[/C][C]-0.973164048427719[/C][/ROW]
[ROW][C]51[/C][C]60[/C][C]64.0506779863877[/C][C]-4.05067798638765[/C][/ROW]
[ROW][C]52[/C][C]43[/C][C]60.2109410064897[/C][C]-17.2109410064897[/C][/ROW]
[ROW][C]53[/C][C]47[/C][C]43.8962680397563[/C][C]3.10373196024372[/C][/ROW]
[ROW][C]54[/C][C]40[/C][C]46.8383716637639[/C][C]-6.8383716637639[/C][/ROW]
[ROW][C]55[/C][C]31[/C][C]40.3561114969772[/C][C]-9.35611149697716[/C][/ROW]
[ROW][C]56[/C][C]27[/C][C]31.4872240110506[/C][C]-4.48722401105059[/C][/ROW]
[ROW][C]57[/C][C]24[/C][C]27.2336743509152[/C][C]-3.23367435091522[/C][/ROW]
[ROW][C]58[/C][C]23[/C][C]24.1683951487959[/C][C]-1.16839514879588[/C][/ROW]
[ROW][C]59[/C][C]17[/C][C]23.0608447399405[/C][C]-6.06084473994055[/C][/ROW]
[ROW][C]60[/C][C]16[/C][C]17.31562140805[/C][C]-1.31562140805[/C][/ROW]
[ROW][C]61[/C][C]15[/C][C]16.0685116182787[/C][C]-1.06851161827873[/C][/ROW]
[ROW][C]62[/C][C]8[/C][C]15.0556432569963[/C][C]-7.05564325699625[/C][/ROW]
[ROW][C]63[/C][C]5[/C][C]8.36742601980816[/C][C]-3.36742601980816[/C][/ROW]
[ROW][C]64[/C][C]6[/C][C]5.17536033135316[/C][C]0.824639668646839[/C][/ROW]
[ROW][C]65[/C][C]5[/C][C]5.95705649220199[/C][C]-0.957056492201986[/C][/ROW]
[ROW][C]66[/C][C]12[/C][C]5.04983917764162[/C][C]6.95016082235838[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]11.638067028764[/C][C]-3.63806702876402[/C][/ROW]
[ROW][C]68[/C][C]17[/C][C]8.18945409220465[/C][C]8.81054590779535[/C][/ROW]
[ROW][C]69[/C][C]22[/C][C]16.5411865796888[/C][C]5.45881342031123[/C][/ROW]
[ROW][C]70[/C][C]24[/C][C]21.7157296627899[/C][C]2.28427033721008[/C][/ROW]
[ROW][C]71[/C][C]36[/C][C]23.8810455223434[/C][C]12.1189544776566[/C][/ROW]
[ROW][C]72[/C][C]31[/C][C]35.3688996104577[/C][C]-4.36889961045772[/C][/ROW]
[ROW][C]73[/C][C]34[/C][C]31.2275125507827[/C][C]2.77248744921731[/C][/ROW]
[ROW][C]74[/C][C]47[/C][C]33.8556213811655[/C][C]13.1443786188345[/C][/ROW]
[ROW][C]75[/C][C]33[/C][C]46.3155001545775[/C][C]-13.3155001545775[/C][/ROW]
[ROW][C]76[/C][C]35[/C][C]33.6934110817891[/C][C]1.30658891821095[/C][/ROW]
[ROW][C]77[/C][C]31[/C][C]34.9319587529787[/C][C]-3.93195875297866[/C][/ROW]
[ROW][C]78[/C][C]35[/C][C]31.2047586452482[/C][C]3.79524135475184[/C][/ROW]
[ROW][C]79[/C][C]39[/C][C]34.8023609790921[/C][C]4.19763902090785[/C][/ROW]
[ROW][C]80[/C][C]46[/C][C]38.7814059268779[/C][C]7.21859407312215[/C][/ROW]
[ROW][C]81[/C][C]40[/C][C]45.6240882379834[/C][C]-5.62408823798339[/C][/ROW]
[ROW][C]82[/C][C]50[/C][C]40.292877102918[/C][C]9.70712289708197[/C][/ROW]
[ROW][C]83[/C][C]62[/C][C]49.4944969012816[/C][C]12.5055030987184[/C][/ROW]
[ROW][C]84[/C][C]57[/C][C]61.3487699048978[/C][C]-4.34876990489781[/C][/ROW]
[ROW][C]85[/C][C]59[/C][C]57.2264642866735[/C][C]1.77353571332652[/C][/ROW]
[ROW][C]86[/C][C]52[/C][C]58.9076422737942[/C][C]-6.90764227379424[/C][/ROW]
[ROW][C]87[/C][C]63[/C][C]52.3597187973474[/C][C]10.6402812026526[/C][/ROW]
[ROW][C]88[/C][C]56[/C][C]62.4459022332154[/C][C]-6.44590223321542[/C][/ROW]
[ROW][C]89[/C][C]55[/C][C]56.3356734624124[/C][C]-1.33567346241244[/C][/ROW]
[ROW][C]90[/C][C]54[/C][C]55.0695558386645[/C][C]-1.06955583866446[/C][/ROW]
[ROW][C]91[/C][C]48[/C][C]54.0556976352756[/C][C]-6.05569763527562[/C][/ROW]
[ROW][C]92[/C][C]39[/C][C]48.3153533700963[/C][C]-9.3153533700963[/C][/ROW]
[ROW][C]93[/C][C]40[/C][C]39.4851015119688[/C][C]0.514898488031243[/C][/ROW]
[ROW][C]94[/C][C]38[/C][C]39.9731864133189[/C][C]-1.97318641331888[/C][/ROW]
[ROW][C]95[/C][C]34[/C][C]38.1027546325371[/C][C]-4.10275463253706[/C][/ROW]
[ROW][C]96[/C][C]32[/C][C]34.2136529229121[/C][C]-2.21365292291215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278644&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
224240
331247
42530.6354716295914-5.63547162959142
52825.2934698985172.70653010148304
62427.8590561418064-3.85905614180637
72524.20096220666970.799037793330299
81624.9583897221861-8.95838972218606
91716.46651245813050.533487541869505
101116.9722183793899-5.97221837938986
111211.31100614765190.688993852348119
123911.964120313397427.0358796866026
131937.5920935478972-18.5920935478972
141419.968192223357-5.96819222335698
151514.31079648363790.689203516362072
16714.964109395043-7.96410939504295
17127.414734831361534.58526516863847
181211.76122010859790.238779891402144
191411.98756542218582.01243457781417
20913.8952015003994-4.89520150039936
2189.25491997510889-1.25491997510889
2248.06535056193137-4.06535056193137
2374.211705087925782.78829491207422
2436.85479819992615-3.85479819992615
2553.200740472296151.79925952770385
2604.90630269377486-4.90630269377486
27-20.255498075098998-2.255498075099
286-1.882543851746357.88254385174635
29115.589512733578395.41048726642161
30910.7182462705221-1.71824627052214
31179.089478501850587.91052149814942
322116.58805578417114.41194421582892
332120.77024588066720.229754119332814
344120.988035443612120.0119645563879
355739.957867310226517.0421326897735
366556.11252273461578.88747726538428
376864.53718034220093.46281965779912
387367.81967199901775.18032800098233
397172.7302319250886-1.73023192508857
407171.0901026605831-0.0901026605830566
417071.0046921394331-1.00469213943312
426970.0523198269071-1.05231982690712
436569.0548000616645-4.05480006166445
445765.2111556655445-8.21115566554445
455757.4275998848474-0.427599884847446
465757.0222674698872-0.022267469887197
475557.0011595892159-2.00115958921587
486555.10421134914069.89578865085938
496564.48467204131350.515327958686498
506464.9731640484277-0.973164048427719
516064.0506779863877-4.05067798638765
524360.2109410064897-17.2109410064897
534743.89626803975633.10373196024372
544046.8383716637639-6.8383716637639
553140.3561114969772-9.35611149697716
562731.4872240110506-4.48722401105059
572427.2336743509152-3.23367435091522
582324.1683951487959-1.16839514879588
591723.0608447399405-6.06084473994055
601617.31562140805-1.31562140805
611516.0685116182787-1.06851161827873
62815.0556432569963-7.05564325699625
6358.36742601980816-3.36742601980816
6465.175360331353160.824639668646839
6555.95705649220199-0.957056492201986
66125.049839177641626.95016082235838
67811.638067028764-3.63806702876402
68178.189454092204658.81054590779535
692216.54118657968885.45881342031123
702421.71572966278992.28427033721008
713623.881045522343412.1189544776566
723135.3688996104577-4.36889961045772
733431.22751255078272.77248744921731
744733.855621381165513.1443786188345
753346.3155001545775-13.3155001545775
763533.69341108178911.30658891821095
773134.9319587529787-3.93195875297866
783531.20475864524823.79524135475184
793934.80236097909214.19763902090785
804638.78140592687797.21859407312215
814045.6240882379834-5.62408823798339
825040.2928771029189.70712289708197
836249.494496901281612.5055030987184
845761.3487699048978-4.34876990489781
855957.22646428667351.77353571332652
865258.9076422737942-6.90764227379424
876352.359718797347410.6402812026526
885662.4459022332154-6.44590223321542
895556.3356734624124-1.33567346241244
905455.0695558386645-1.06955583866446
914854.0556976352756-6.05569763527562
923948.3153533700963-9.3153533700963
934039.48510151196880.514898488031243
943839.9731864133189-1.97318641331888
953438.1027546325371-4.10275463253706
963234.2136529229121-2.21365292291215







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9732.115277041805618.190843032164346.039711051447
9832.115277041805612.929039515094851.3015145685164
9932.11527704180568.8272209105207255.4033331730905
10032.11527704180565.3467244788375258.8838296047737
10132.11527704180562.2693852933773961.9611687902339
10232.1152770418056-0.51904694692449764.7496010305358
10332.1152770418056-3.0872931789029367.3178472625142
10432.1152770418056-5.4805046110131769.7110586946244
10532.1152770418056-7.730232693030771.960786776642
10632.1152770418056-9.8595546311319974.0901087147433
10732.1152770418056-11.885954099083676.1165081826948
10832.1152770418056-13.823053248448478.0536073320596

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 32.1152770418056 & 18.1908430321643 & 46.039711051447 \tabularnewline
98 & 32.1152770418056 & 12.9290395150948 & 51.3015145685164 \tabularnewline
99 & 32.1152770418056 & 8.82722091052072 & 55.4033331730905 \tabularnewline
100 & 32.1152770418056 & 5.34672447883752 & 58.8838296047737 \tabularnewline
101 & 32.1152770418056 & 2.26938529337739 & 61.9611687902339 \tabularnewline
102 & 32.1152770418056 & -0.519046946924497 & 64.7496010305358 \tabularnewline
103 & 32.1152770418056 & -3.08729317890293 & 67.3178472625142 \tabularnewline
104 & 32.1152770418056 & -5.48050461101317 & 69.7110586946244 \tabularnewline
105 & 32.1152770418056 & -7.7302326930307 & 71.960786776642 \tabularnewline
106 & 32.1152770418056 & -9.85955463113199 & 74.0901087147433 \tabularnewline
107 & 32.1152770418056 & -11.8859540990836 & 76.1165081826948 \tabularnewline
108 & 32.1152770418056 & -13.8230532484484 & 78.0536073320596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278644&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]32.1152770418056[/C][C]18.1908430321643[/C][C]46.039711051447[/C][/ROW]
[ROW][C]98[/C][C]32.1152770418056[/C][C]12.9290395150948[/C][C]51.3015145685164[/C][/ROW]
[ROW][C]99[/C][C]32.1152770418056[/C][C]8.82722091052072[/C][C]55.4033331730905[/C][/ROW]
[ROW][C]100[/C][C]32.1152770418056[/C][C]5.34672447883752[/C][C]58.8838296047737[/C][/ROW]
[ROW][C]101[/C][C]32.1152770418056[/C][C]2.26938529337739[/C][C]61.9611687902339[/C][/ROW]
[ROW][C]102[/C][C]32.1152770418056[/C][C]-0.519046946924497[/C][C]64.7496010305358[/C][/ROW]
[ROW][C]103[/C][C]32.1152770418056[/C][C]-3.08729317890293[/C][C]67.3178472625142[/C][/ROW]
[ROW][C]104[/C][C]32.1152770418056[/C][C]-5.48050461101317[/C][C]69.7110586946244[/C][/ROW]
[ROW][C]105[/C][C]32.1152770418056[/C][C]-7.7302326930307[/C][C]71.960786776642[/C][/ROW]
[ROW][C]106[/C][C]32.1152770418056[/C][C]-9.85955463113199[/C][C]74.0901087147433[/C][/ROW]
[ROW][C]107[/C][C]32.1152770418056[/C][C]-11.8859540990836[/C][C]76.1165081826948[/C][/ROW]
[ROW][C]108[/C][C]32.1152770418056[/C][C]-13.8230532484484[/C][C]78.0536073320596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278644&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278644&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
9732.115277041805618.190843032164346.039711051447
9832.115277041805612.929039515094851.3015145685164
9932.11527704180568.8272209105207255.4033331730905
10032.11527704180565.3467244788375258.8838296047737
10132.11527704180562.2693852933773961.9611687902339
10232.1152770418056-0.51904694692449764.7496010305358
10332.1152770418056-3.0872931789029367.3178472625142
10432.1152770418056-5.4805046110131769.7110586946244
10532.1152770418056-7.730232693030771.960786776642
10632.1152770418056-9.8595546311319974.0901087147433
10732.1152770418056-11.885954099083676.1165081826948
10832.1152770418056-13.823053248448478.0536073320596



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