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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 05 Jun 2009 14:19:40 -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/2009/Jun/05/t124423328496ue81pejg2loi7.htm/, Retrieved Thu, 09 May 2024 23:11:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41913, Retrieved Thu, 09 May 2024 23:11:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDuncan Huysmans Opgave 10 Opdracht 2
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Opgave 9 ] [2009-06-02 02:28:18] [3ccda03dddd60e52bd63ea4afd424344]
- RMPD    [Exponential Smoothing] [Duncan Huysmans O...] [2009-06-05 20:19:40] [7ecc19fd9fa5f5e7f58eda40682a000b] [Current]
-    D      [Exponential Smoothing] [] [2009-06-06 15:28:21] [74be16979710d4c4e7c6647856088456]
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Post a new message
Dataseries X:
1664.81
2397.53
2840.71
3547.29
3752.96
3714.74
4349.61
3566.34
5021.82
6423.48
7600.60
19756.21
2499.81
5198.24
7225.14
4806.03
5900.88
4951.34
6179.12
4752.15
5496.43
5835.10
12600.08
28541.72
4717.02
5702.63
9957.58
5304.78
6492.43
6630.80
7349.62
8176.62
8573.17
9690.50
15151.84
34061.01
5921.10
5814.58
12421.25
6369.77
7609.12
7224.75
8121.22
7979.25
8093.06
8476.70
17914.66
30114.41
4826.64
6470.23
9638.77
8821.17
8722.37
10209.48
11276.55
12552.22
11637.39
13606.89
21822.11
45060.69
7615.03
9849.69
14558.40
11587.33
9332.56
13082.09
16732.78
19888.61
23933.38
25391.35
36024.80
80721.71
10243.24
11266.88
21826.84
17357.33
15997.79
18601.53
26155.15
28586.52
30505.41
30821.33
46634.38
104660.67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41913&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41913&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.488903716392153
beta0.0465372441384407
gamma0.947454970073025

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.488903716392153 \tabularnewline
beta & 0.0465372441384407 \tabularnewline
gamma & 0.947454970073025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41913&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]0.488903716392153[/C][/ROW]
[ROW][C]beta[/C][C]0.0465372441384407[/C][/ROW]
[ROW][C]gamma[/C][C]0.947454970073025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41913&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
alpha0.488903716392153
beta0.0465372441384407
gamma0.947454970073025







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132499.812094.39367811309405.416321886914
145198.244816.56402005839381.675979941614
157225.147085.97950572379139.160494276210
164806.034899.7479008483-93.7179008483026
175900.885962.72230169536-61.8423016953557
184951.344719.27181523893232.068184761075
196179.126003.72918904137175.390810958627
204752.154985.4572851177-233.307285117704
215496.436674.10111646775-1177.67111646775
225835.17669.30214520937-1834.20214520937
2312600.087978.97906365394621.10093634609
2428541.7226666.79327594031874.92672405971
254717.023807.00257376309910.017426236914
265702.638505.38475298753-2802.75475298753
279957.589763.6994469637193.880553036308
285304.786579.83538265766-1275.05538265767
296492.437281.90853964856-789.47853964856
306630.85584.41745840671046.38254159331
317349.627446.24219872818-96.6221987281779
328176.625789.925777760882386.69422223912
338573.178824.0750751731-250.905075173094
349690.510482.5750151408-792.075015140841
3515151.8416708.8825988694-1557.04259886937
3634061.0135009.7735615791-948.76356157905
375921.15061.18076645123859.919233548773
385814.587994.35792622826-2179.77792622826
3912421.2511745.5899383707675.660061629298
406369.777117.20428899281-747.434288992808
417609.128660.91093174328-1051.79093174328
427224.757530.0624350017-305.312435001703
438121.228207.73478065402-86.5147806540235
447979.257442.77961440537536.470385594627
458093.068175.56306823937-82.5030682393735
468476.79464.45362099461-987.753620994614
4717914.6614563.62134250343351.03865749662
4830114.4136632.6098584899-6518.19985848985
494826.645299.83716395774-473.197163957743
506470.235755.2482338799714.981766120101
519638.7712474.7316323203-2835.96163232033
528821.175959.141193593852862.02880640615
538722.379342.26261108106-619.892611081061
5410209.488734.549331445481474.93066855452
5511276.5510711.2978516089565.252148391053
5612552.2210451.088378692101.13162130999
5711637.3911791.9475416962-154.557541696195
5813606.8913041.1690625705565.720937429522
5921822.1125293.0891801767-3470.97918017666
6045060.6944001.51367772431059.1763222757
617615.037477.63237666557137.397623334435
629849.699550.00943106132299.680568938678
6314558.416515.8104435388-1957.41044353881
6411587.3311430.1019549011157.228045098867
659332.5611887.3401339983-2554.78013399832
6613082.0911406.19509485531675.89490514472
6716732.7813161.68378472153571.0962152785
6819888.6115070.44738283054818.16261716948
6923933.3816370.95329913157562.4267008685
7025391.3523103.39345664282287.95654335720
7136024.842162.4754632356-6137.67546323562
7280721.7180109.8347724822611.875227517798
7310243.2413559.8674871677-3316.6274871677
7411266.8815246.5065443697-3979.62654436974
7521826.8420922.411621172904.428378828004
7617357.3316836.9839506788520.346049321186
7715997.7915516.1542990580481.635700942026
7818601.5320488.2313864995-1886.70138649949
7926155.1522071.31484114034083.83515885965
8028586.5224719.02149760633867.49850239369
8130505.4126017.35729559894488.05270440106
8230821.3328590.10397495262231.2260250474
8346634.3845451.69398663841182.68601336162
84104660.67102035.0519320412625.61806795884

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2499.81 & 2094.39367811309 & 405.416321886914 \tabularnewline
14 & 5198.24 & 4816.56402005839 & 381.675979941614 \tabularnewline
15 & 7225.14 & 7085.97950572379 & 139.160494276210 \tabularnewline
16 & 4806.03 & 4899.7479008483 & -93.7179008483026 \tabularnewline
17 & 5900.88 & 5962.72230169536 & -61.8423016953557 \tabularnewline
18 & 4951.34 & 4719.27181523893 & 232.068184761075 \tabularnewline
19 & 6179.12 & 6003.72918904137 & 175.390810958627 \tabularnewline
20 & 4752.15 & 4985.4572851177 & -233.307285117704 \tabularnewline
21 & 5496.43 & 6674.10111646775 & -1177.67111646775 \tabularnewline
22 & 5835.1 & 7669.30214520937 & -1834.20214520937 \tabularnewline
23 & 12600.08 & 7978.9790636539 & 4621.10093634609 \tabularnewline
24 & 28541.72 & 26666.7932759403 & 1874.92672405971 \tabularnewline
25 & 4717.02 & 3807.00257376309 & 910.017426236914 \tabularnewline
26 & 5702.63 & 8505.38475298753 & -2802.75475298753 \tabularnewline
27 & 9957.58 & 9763.6994469637 & 193.880553036308 \tabularnewline
28 & 5304.78 & 6579.83538265766 & -1275.05538265767 \tabularnewline
29 & 6492.43 & 7281.90853964856 & -789.47853964856 \tabularnewline
30 & 6630.8 & 5584.4174584067 & 1046.38254159331 \tabularnewline
31 & 7349.62 & 7446.24219872818 & -96.6221987281779 \tabularnewline
32 & 8176.62 & 5789.92577776088 & 2386.69422223912 \tabularnewline
33 & 8573.17 & 8824.0750751731 & -250.905075173094 \tabularnewline
34 & 9690.5 & 10482.5750151408 & -792.075015140841 \tabularnewline
35 & 15151.84 & 16708.8825988694 & -1557.04259886937 \tabularnewline
36 & 34061.01 & 35009.7735615791 & -948.76356157905 \tabularnewline
37 & 5921.1 & 5061.18076645123 & 859.919233548773 \tabularnewline
38 & 5814.58 & 7994.35792622826 & -2179.77792622826 \tabularnewline
39 & 12421.25 & 11745.5899383707 & 675.660061629298 \tabularnewline
40 & 6369.77 & 7117.20428899281 & -747.434288992808 \tabularnewline
41 & 7609.12 & 8660.91093174328 & -1051.79093174328 \tabularnewline
42 & 7224.75 & 7530.0624350017 & -305.312435001703 \tabularnewline
43 & 8121.22 & 8207.73478065402 & -86.5147806540235 \tabularnewline
44 & 7979.25 & 7442.77961440537 & 536.470385594627 \tabularnewline
45 & 8093.06 & 8175.56306823937 & -82.5030682393735 \tabularnewline
46 & 8476.7 & 9464.45362099461 & -987.753620994614 \tabularnewline
47 & 17914.66 & 14563.6213425034 & 3351.03865749662 \tabularnewline
48 & 30114.41 & 36632.6098584899 & -6518.19985848985 \tabularnewline
49 & 4826.64 & 5299.83716395774 & -473.197163957743 \tabularnewline
50 & 6470.23 & 5755.2482338799 & 714.981766120101 \tabularnewline
51 & 9638.77 & 12474.7316323203 & -2835.96163232033 \tabularnewline
52 & 8821.17 & 5959.14119359385 & 2862.02880640615 \tabularnewline
53 & 8722.37 & 9342.26261108106 & -619.892611081061 \tabularnewline
54 & 10209.48 & 8734.54933144548 & 1474.93066855452 \tabularnewline
55 & 11276.55 & 10711.2978516089 & 565.252148391053 \tabularnewline
56 & 12552.22 & 10451.08837869 & 2101.13162130999 \tabularnewline
57 & 11637.39 & 11791.9475416962 & -154.557541696195 \tabularnewline
58 & 13606.89 & 13041.1690625705 & 565.720937429522 \tabularnewline
59 & 21822.11 & 25293.0891801767 & -3470.97918017666 \tabularnewline
60 & 45060.69 & 44001.5136777243 & 1059.1763222757 \tabularnewline
61 & 7615.03 & 7477.63237666557 & 137.397623334435 \tabularnewline
62 & 9849.69 & 9550.00943106132 & 299.680568938678 \tabularnewline
63 & 14558.4 & 16515.8104435388 & -1957.41044353881 \tabularnewline
64 & 11587.33 & 11430.1019549011 & 157.228045098867 \tabularnewline
65 & 9332.56 & 11887.3401339983 & -2554.78013399832 \tabularnewline
66 & 13082.09 & 11406.1950948553 & 1675.89490514472 \tabularnewline
67 & 16732.78 & 13161.6837847215 & 3571.0962152785 \tabularnewline
68 & 19888.61 & 15070.4473828305 & 4818.16261716948 \tabularnewline
69 & 23933.38 & 16370.9532991315 & 7562.4267008685 \tabularnewline
70 & 25391.35 & 23103.3934566428 & 2287.95654335720 \tabularnewline
71 & 36024.8 & 42162.4754632356 & -6137.67546323562 \tabularnewline
72 & 80721.71 & 80109.8347724822 & 611.875227517798 \tabularnewline
73 & 10243.24 & 13559.8674871677 & -3316.6274871677 \tabularnewline
74 & 11266.88 & 15246.5065443697 & -3979.62654436974 \tabularnewline
75 & 21826.84 & 20922.411621172 & 904.428378828004 \tabularnewline
76 & 17357.33 & 16836.9839506788 & 520.346049321186 \tabularnewline
77 & 15997.79 & 15516.1542990580 & 481.635700942026 \tabularnewline
78 & 18601.53 & 20488.2313864995 & -1886.70138649949 \tabularnewline
79 & 26155.15 & 22071.3148411403 & 4083.83515885965 \tabularnewline
80 & 28586.52 & 24719.0214976063 & 3867.49850239369 \tabularnewline
81 & 30505.41 & 26017.3572955989 & 4488.05270440106 \tabularnewline
82 & 30821.33 & 28590.1039749526 & 2231.2260250474 \tabularnewline
83 & 46634.38 & 45451.6939866384 & 1182.68601336162 \tabularnewline
84 & 104660.67 & 102035.051932041 & 2625.61806795884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41913&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]2499.81[/C][C]2094.39367811309[/C][C]405.416321886914[/C][/ROW]
[ROW][C]14[/C][C]5198.24[/C][C]4816.56402005839[/C][C]381.675979941614[/C][/ROW]
[ROW][C]15[/C][C]7225.14[/C][C]7085.97950572379[/C][C]139.160494276210[/C][/ROW]
[ROW][C]16[/C][C]4806.03[/C][C]4899.7479008483[/C][C]-93.7179008483026[/C][/ROW]
[ROW][C]17[/C][C]5900.88[/C][C]5962.72230169536[/C][C]-61.8423016953557[/C][/ROW]
[ROW][C]18[/C][C]4951.34[/C][C]4719.27181523893[/C][C]232.068184761075[/C][/ROW]
[ROW][C]19[/C][C]6179.12[/C][C]6003.72918904137[/C][C]175.390810958627[/C][/ROW]
[ROW][C]20[/C][C]4752.15[/C][C]4985.4572851177[/C][C]-233.307285117704[/C][/ROW]
[ROW][C]21[/C][C]5496.43[/C][C]6674.10111646775[/C][C]-1177.67111646775[/C][/ROW]
[ROW][C]22[/C][C]5835.1[/C][C]7669.30214520937[/C][C]-1834.20214520937[/C][/ROW]
[ROW][C]23[/C][C]12600.08[/C][C]7978.9790636539[/C][C]4621.10093634609[/C][/ROW]
[ROW][C]24[/C][C]28541.72[/C][C]26666.7932759403[/C][C]1874.92672405971[/C][/ROW]
[ROW][C]25[/C][C]4717.02[/C][C]3807.00257376309[/C][C]910.017426236914[/C][/ROW]
[ROW][C]26[/C][C]5702.63[/C][C]8505.38475298753[/C][C]-2802.75475298753[/C][/ROW]
[ROW][C]27[/C][C]9957.58[/C][C]9763.6994469637[/C][C]193.880553036308[/C][/ROW]
[ROW][C]28[/C][C]5304.78[/C][C]6579.83538265766[/C][C]-1275.05538265767[/C][/ROW]
[ROW][C]29[/C][C]6492.43[/C][C]7281.90853964856[/C][C]-789.47853964856[/C][/ROW]
[ROW][C]30[/C][C]6630.8[/C][C]5584.4174584067[/C][C]1046.38254159331[/C][/ROW]
[ROW][C]31[/C][C]7349.62[/C][C]7446.24219872818[/C][C]-96.6221987281779[/C][/ROW]
[ROW][C]32[/C][C]8176.62[/C][C]5789.92577776088[/C][C]2386.69422223912[/C][/ROW]
[ROW][C]33[/C][C]8573.17[/C][C]8824.0750751731[/C][C]-250.905075173094[/C][/ROW]
[ROW][C]34[/C][C]9690.5[/C][C]10482.5750151408[/C][C]-792.075015140841[/C][/ROW]
[ROW][C]35[/C][C]15151.84[/C][C]16708.8825988694[/C][C]-1557.04259886937[/C][/ROW]
[ROW][C]36[/C][C]34061.01[/C][C]35009.7735615791[/C][C]-948.76356157905[/C][/ROW]
[ROW][C]37[/C][C]5921.1[/C][C]5061.18076645123[/C][C]859.919233548773[/C][/ROW]
[ROW][C]38[/C][C]5814.58[/C][C]7994.35792622826[/C][C]-2179.77792622826[/C][/ROW]
[ROW][C]39[/C][C]12421.25[/C][C]11745.5899383707[/C][C]675.660061629298[/C][/ROW]
[ROW][C]40[/C][C]6369.77[/C][C]7117.20428899281[/C][C]-747.434288992808[/C][/ROW]
[ROW][C]41[/C][C]7609.12[/C][C]8660.91093174328[/C][C]-1051.79093174328[/C][/ROW]
[ROW][C]42[/C][C]7224.75[/C][C]7530.0624350017[/C][C]-305.312435001703[/C][/ROW]
[ROW][C]43[/C][C]8121.22[/C][C]8207.73478065402[/C][C]-86.5147806540235[/C][/ROW]
[ROW][C]44[/C][C]7979.25[/C][C]7442.77961440537[/C][C]536.470385594627[/C][/ROW]
[ROW][C]45[/C][C]8093.06[/C][C]8175.56306823937[/C][C]-82.5030682393735[/C][/ROW]
[ROW][C]46[/C][C]8476.7[/C][C]9464.45362099461[/C][C]-987.753620994614[/C][/ROW]
[ROW][C]47[/C][C]17914.66[/C][C]14563.6213425034[/C][C]3351.03865749662[/C][/ROW]
[ROW][C]48[/C][C]30114.41[/C][C]36632.6098584899[/C][C]-6518.19985848985[/C][/ROW]
[ROW][C]49[/C][C]4826.64[/C][C]5299.83716395774[/C][C]-473.197163957743[/C][/ROW]
[ROW][C]50[/C][C]6470.23[/C][C]5755.2482338799[/C][C]714.981766120101[/C][/ROW]
[ROW][C]51[/C][C]9638.77[/C][C]12474.7316323203[/C][C]-2835.96163232033[/C][/ROW]
[ROW][C]52[/C][C]8821.17[/C][C]5959.14119359385[/C][C]2862.02880640615[/C][/ROW]
[ROW][C]53[/C][C]8722.37[/C][C]9342.26261108106[/C][C]-619.892611081061[/C][/ROW]
[ROW][C]54[/C][C]10209.48[/C][C]8734.54933144548[/C][C]1474.93066855452[/C][/ROW]
[ROW][C]55[/C][C]11276.55[/C][C]10711.2978516089[/C][C]565.252148391053[/C][/ROW]
[ROW][C]56[/C][C]12552.22[/C][C]10451.08837869[/C][C]2101.13162130999[/C][/ROW]
[ROW][C]57[/C][C]11637.39[/C][C]11791.9475416962[/C][C]-154.557541696195[/C][/ROW]
[ROW][C]58[/C][C]13606.89[/C][C]13041.1690625705[/C][C]565.720937429522[/C][/ROW]
[ROW][C]59[/C][C]21822.11[/C][C]25293.0891801767[/C][C]-3470.97918017666[/C][/ROW]
[ROW][C]60[/C][C]45060.69[/C][C]44001.5136777243[/C][C]1059.1763222757[/C][/ROW]
[ROW][C]61[/C][C]7615.03[/C][C]7477.63237666557[/C][C]137.397623334435[/C][/ROW]
[ROW][C]62[/C][C]9849.69[/C][C]9550.00943106132[/C][C]299.680568938678[/C][/ROW]
[ROW][C]63[/C][C]14558.4[/C][C]16515.8104435388[/C][C]-1957.41044353881[/C][/ROW]
[ROW][C]64[/C][C]11587.33[/C][C]11430.1019549011[/C][C]157.228045098867[/C][/ROW]
[ROW][C]65[/C][C]9332.56[/C][C]11887.3401339983[/C][C]-2554.78013399832[/C][/ROW]
[ROW][C]66[/C][C]13082.09[/C][C]11406.1950948553[/C][C]1675.89490514472[/C][/ROW]
[ROW][C]67[/C][C]16732.78[/C][C]13161.6837847215[/C][C]3571.0962152785[/C][/ROW]
[ROW][C]68[/C][C]19888.61[/C][C]15070.4473828305[/C][C]4818.16261716948[/C][/ROW]
[ROW][C]69[/C][C]23933.38[/C][C]16370.9532991315[/C][C]7562.4267008685[/C][/ROW]
[ROW][C]70[/C][C]25391.35[/C][C]23103.3934566428[/C][C]2287.95654335720[/C][/ROW]
[ROW][C]71[/C][C]36024.8[/C][C]42162.4754632356[/C][C]-6137.67546323562[/C][/ROW]
[ROW][C]72[/C][C]80721.71[/C][C]80109.8347724822[/C][C]611.875227517798[/C][/ROW]
[ROW][C]73[/C][C]10243.24[/C][C]13559.8674871677[/C][C]-3316.6274871677[/C][/ROW]
[ROW][C]74[/C][C]11266.88[/C][C]15246.5065443697[/C][C]-3979.62654436974[/C][/ROW]
[ROW][C]75[/C][C]21826.84[/C][C]20922.411621172[/C][C]904.428378828004[/C][/ROW]
[ROW][C]76[/C][C]17357.33[/C][C]16836.9839506788[/C][C]520.346049321186[/C][/ROW]
[ROW][C]77[/C][C]15997.79[/C][C]15516.1542990580[/C][C]481.635700942026[/C][/ROW]
[ROW][C]78[/C][C]18601.53[/C][C]20488.2313864995[/C][C]-1886.70138649949[/C][/ROW]
[ROW][C]79[/C][C]26155.15[/C][C]22071.3148411403[/C][C]4083.83515885965[/C][/ROW]
[ROW][C]80[/C][C]28586.52[/C][C]24719.0214976063[/C][C]3867.49850239369[/C][/ROW]
[ROW][C]81[/C][C]30505.41[/C][C]26017.3572955989[/C][C]4488.05270440106[/C][/ROW]
[ROW][C]82[/C][C]30821.33[/C][C]28590.1039749526[/C][C]2231.2260250474[/C][/ROW]
[ROW][C]83[/C][C]46634.38[/C][C]45451.6939866384[/C][C]1182.68601336162[/C][/ROW]
[ROW][C]84[/C][C]104660.67[/C][C]102035.051932041[/C][C]2625.61806795884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41913&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41913&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
132499.812094.39367811309405.416321886914
145198.244816.56402005839381.675979941614
157225.147085.97950572379139.160494276210
164806.034899.7479008483-93.7179008483026
175900.885962.72230169536-61.8423016953557
184951.344719.27181523893232.068184761075
196179.126003.72918904137175.390810958627
204752.154985.4572851177-233.307285117704
215496.436674.10111646775-1177.67111646775
225835.17669.30214520937-1834.20214520937
2312600.087978.97906365394621.10093634609
2428541.7226666.79327594031874.92672405971
254717.023807.00257376309910.017426236914
265702.638505.38475298753-2802.75475298753
279957.589763.6994469637193.880553036308
285304.786579.83538265766-1275.05538265767
296492.437281.90853964856-789.47853964856
306630.85584.41745840671046.38254159331
317349.627446.24219872818-96.6221987281779
328176.625789.925777760882386.69422223912
338573.178824.0750751731-250.905075173094
349690.510482.5750151408-792.075015140841
3515151.8416708.8825988694-1557.04259886937
3634061.0135009.7735615791-948.76356157905
375921.15061.18076645123859.919233548773
385814.587994.35792622826-2179.77792622826
3912421.2511745.5899383707675.660061629298
406369.777117.20428899281-747.434288992808
417609.128660.91093174328-1051.79093174328
427224.757530.0624350017-305.312435001703
438121.228207.73478065402-86.5147806540235
447979.257442.77961440537536.470385594627
458093.068175.56306823937-82.5030682393735
468476.79464.45362099461-987.753620994614
4717914.6614563.62134250343351.03865749662
4830114.4136632.6098584899-6518.19985848985
494826.645299.83716395774-473.197163957743
506470.235755.2482338799714.981766120101
519638.7712474.7316323203-2835.96163232033
528821.175959.141193593852862.02880640615
538722.379342.26261108106-619.892611081061
5410209.488734.549331445481474.93066855452
5511276.5510711.2978516089565.252148391053
5612552.2210451.088378692101.13162130999
5711637.3911791.9475416962-154.557541696195
5813606.8913041.1690625705565.720937429522
5921822.1125293.0891801767-3470.97918017666
6045060.6944001.51367772431059.1763222757
617615.037477.63237666557137.397623334435
629849.699550.00943106132299.680568938678
6314558.416515.8104435388-1957.41044353881
6411587.3311430.1019549011157.228045098867
659332.5611887.3401339983-2554.78013399832
6613082.0911406.19509485531675.89490514472
6716732.7813161.68378472153571.0962152785
6819888.6115070.44738283054818.16261716948
6923933.3816370.95329913157562.4267008685
7025391.3523103.39345664282287.95654335720
7136024.842162.4754632356-6137.67546323562
7280721.7180109.8347724822611.875227517798
7310243.2413559.8674871677-3316.6274871677
7411266.8815246.5065443697-3979.62654436974
7521826.8420922.411621172904.428378828004
7617357.3316836.9839506788520.346049321186
7715997.7915516.1542990580481.635700942026
7818601.5320488.2313864995-1886.70138649949
7926155.1522071.31484114034083.83515885965
8028586.5224719.02149760633867.49850239369
8130505.4126017.35729559894488.05270440106
8230821.3328590.10397495262231.2260250474
8346634.3845451.69398663841182.68601336162
84104660.67102035.0519320412625.61806795884







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8514994.740538504610497.819535634319491.6615413749
8618948.092093010313580.857437864824315.3267481558
8735767.050890771327310.675380443044223.4264010997
8828159.426476604920617.143244715435701.7097084944
8925669.264058371318148.210131572133190.3179851706
9031472.701700214122232.108175695340713.295224733
9140496.448156936728592.117867700652400.7784461729
9241217.958490546628690.662244796753745.2547362965
9340537.849845041027771.046133964953304.6535561172
9439431.640459647326561.542362445852301.7385568489
9558785.199779729739615.015599752877955.3839597066
96129819.01236330887614.241560001172023.783166615

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 14994.7405385046 & 10497.8195356343 & 19491.6615413749 \tabularnewline
86 & 18948.0920930103 & 13580.8574378648 & 24315.3267481558 \tabularnewline
87 & 35767.0508907713 & 27310.6753804430 & 44223.4264010997 \tabularnewline
88 & 28159.4264766049 & 20617.1432447154 & 35701.7097084944 \tabularnewline
89 & 25669.2640583713 & 18148.2101315721 & 33190.3179851706 \tabularnewline
90 & 31472.7017002141 & 22232.1081756953 & 40713.295224733 \tabularnewline
91 & 40496.4481569367 & 28592.1178677006 & 52400.7784461729 \tabularnewline
92 & 41217.9584905466 & 28690.6622447967 & 53745.2547362965 \tabularnewline
93 & 40537.8498450410 & 27771.0461339649 & 53304.6535561172 \tabularnewline
94 & 39431.6404596473 & 26561.5423624458 & 52301.7385568489 \tabularnewline
95 & 58785.1997797297 & 39615.0155997528 & 77955.3839597066 \tabularnewline
96 & 129819.012363308 & 87614.241560001 & 172023.783166615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41913&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]85[/C][C]14994.7405385046[/C][C]10497.8195356343[/C][C]19491.6615413749[/C][/ROW]
[ROW][C]86[/C][C]18948.0920930103[/C][C]13580.8574378648[/C][C]24315.3267481558[/C][/ROW]
[ROW][C]87[/C][C]35767.0508907713[/C][C]27310.6753804430[/C][C]44223.4264010997[/C][/ROW]
[ROW][C]88[/C][C]28159.4264766049[/C][C]20617.1432447154[/C][C]35701.7097084944[/C][/ROW]
[ROW][C]89[/C][C]25669.2640583713[/C][C]18148.2101315721[/C][C]33190.3179851706[/C][/ROW]
[ROW][C]90[/C][C]31472.7017002141[/C][C]22232.1081756953[/C][C]40713.295224733[/C][/ROW]
[ROW][C]91[/C][C]40496.4481569367[/C][C]28592.1178677006[/C][C]52400.7784461729[/C][/ROW]
[ROW][C]92[/C][C]41217.9584905466[/C][C]28690.6622447967[/C][C]53745.2547362965[/C][/ROW]
[ROW][C]93[/C][C]40537.8498450410[/C][C]27771.0461339649[/C][C]53304.6535561172[/C][/ROW]
[ROW][C]94[/C][C]39431.6404596473[/C][C]26561.5423624458[/C][C]52301.7385568489[/C][/ROW]
[ROW][C]95[/C][C]58785.1997797297[/C][C]39615.0155997528[/C][C]77955.3839597066[/C][/ROW]
[ROW][C]96[/C][C]129819.012363308[/C][C]87614.241560001[/C][C]172023.783166615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41913&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41913&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
8514994.740538504610497.819535634319491.6615413749
8618948.092093010313580.857437864824315.3267481558
8735767.050890771327310.675380443044223.4264010997
8828159.426476604920617.143244715435701.7097084944
8925669.264058371318148.210131572133190.3179851706
9031472.701700214122232.108175695340713.295224733
9140496.448156936728592.117867700652400.7784461729
9241217.958490546628690.662244796753745.2547362965
9340537.849845041027771.046133964953304.6535561172
9439431.640459647326561.542362445852301.7385568489
9558785.199779729739615.015599752877955.3839597066
96129819.01236330887614.241560001172023.783166615



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')