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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 computationMon, 31 May 2010 17:30:18 +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/2010/May/31/t1275327126eeeug6elr9gkltz.htm/, Retrieved Mon, 29 Apr 2024 15:19:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76771, Retrieved Mon, 29 Apr 2024 15:19:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2010-05-26 09:51:23] [5edb365c4f087800016d5ba2104a2ab8]
- R PD    [Exponential Smoothing] [] [2010-05-31 17:30:18] [433c0f5c340be2129e00593f0b5065e3] [Current]
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Dataseries X:
66857.2
64722.8
68489.6
71342.9	
63542.5
69425.0
58927.9
61009.0
66837.0
66147.6
65982.3
65527.5
65914.6
59189.9
66211.4
66400.8
60167.7
64547.9
57706.2
58642.6
60082.1
63414.8
66044.0
57628.5
62838.8
55758.6
61004.5
66173.4
57489.0
59552.2
57061.8
55895.3
56314.7
61232.8
60014.1
57685.4
60403.1
52349.7
55693.3
65676.1
54898.8
55518.2
53779.1
52340.9
55704.4
60330.3
52837.4
55388.1
60383.4
52070.3
54077.0
62887.8
49212.8
57722.0
53936.8
46991.0
54984.2
56485.1
51277.8
53596.4
54252.5
49413.0
53213.2
58695.3
48723.5
54510.0
49454.1
46136.6
54622.5
50583.0
53224.3
53056.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76771&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76771&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76771&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0775686079515321
beta0.141640000501599
gamma0.670983617686526

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0775686079515321 \tabularnewline
beta & 0.141640000501599 \tabularnewline
gamma & 0.670983617686526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76771&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]0.0775686079515321[/C][/ROW]
[ROW][C]beta[/C][C]0.141640000501599[/C][/ROW]
[ROW][C]gamma[/C][C]0.670983617686526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76771&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76771&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
alpha0.0775686079515321
beta0.141640000501599
gamma0.670983617686526







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1365914.667882.8211538462-1968.22115384619
1459189.960840.47026691-1650.57026690995
1566211.467781.3746025152-1569.97460251523
1666400.867894.4482735782-1493.64827357818
1760167.761290.5070304832-1122.80703048316
1864547.965531.5536835978-983.65368359779
1957706.256242.49954445081463.70045554917
2058642.658333.6105024026308.989497597358
2160082.164141.0969500315-4058.99695003153
2263414.863023.1526432903391.647356709655
236604462824.53324467593219.46675532407
2457628.562588.4272212497-4959.92722124972
2562838.861197.3470552581641.45294474201
2655758.654534.75790673091223.8420932691
2761004.561683.2493009422-678.749300942232
2866173.461857.22625414244316.17374585757
295748955941.83443560911547.1655643909
3059552.260513.8112049269-961.611204926929
3157061.852779.16248482044282.63751517962
3255895.354443.15219585851452.14780414152
3356314.757717.2762321708-1402.5762321708
3461232.859670.7079360961562.092063904
3560014.161436.6335907519-1422.5335907519
3657685.455850.4440399211834.95596007899
3760403.159219.43605863511183.66394136492
3852349.752405.0010665963-55.3010665962938
3955693.358404.7731654094-2711.47316540936
4065676.161618.36587997074057.73412002931
4154898.854071.9998767351826.800123264853
4255518.257130.3236761668-1612.12367616685
4353779.152678.92263919371100.17736080632
4452340.952397.046114724-56.1461147239534
4555704.453823.59580472751880.80419527246
4660330.357939.04403723822391.25596276176
4752837.458003.4916354791-5166.09163547907
4855388.154183.46658004411204.63341995594
4960383.457133.90019226023249.49980773985
5052070.349769.00883370062301.29116629938
515407754389.6085942253-312.608594225334
5262887.862087.3738016488800.426198351226
5349212.852361.200446708-3148.40044670802
545772253630.56005987034091.43994012966
5553936.851391.90742593862544.89257406144
564699150613.866840064-3622.86684006401
5754984.253030.87504289261953.32495710743
5856485.157536.9576520233-1051.85765202333
5951277.852688.0535885619-1410.25358856188
6053596.453174.9447240306421.455275969405
6154252.557394.173539077-3141.67353907702
624941348940.3314044521472.668595547941
6353213.251774.84357290361438.35642709644
6458695.360290.1576265646-1594.85762656457
6548723.547900.6277648954822.872235104638
665451053969.1802079779540.819792022077
6749454.150469.0328443371-1014.93284433713
6846136.645529.4362067718607.163793228196
6954622.551704.36954999362918.13045000644
705058354414.3738982551-3831.37389825513
7153224.349086.60419968284137.69580031715
7253056.451157.06940267021899.33059732983

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 65914.6 & 67882.8211538462 & -1968.22115384619 \tabularnewline
14 & 59189.9 & 60840.47026691 & -1650.57026690995 \tabularnewline
15 & 66211.4 & 67781.3746025152 & -1569.97460251523 \tabularnewline
16 & 66400.8 & 67894.4482735782 & -1493.64827357818 \tabularnewline
17 & 60167.7 & 61290.5070304832 & -1122.80703048316 \tabularnewline
18 & 64547.9 & 65531.5536835978 & -983.65368359779 \tabularnewline
19 & 57706.2 & 56242.4995444508 & 1463.70045554917 \tabularnewline
20 & 58642.6 & 58333.6105024026 & 308.989497597358 \tabularnewline
21 & 60082.1 & 64141.0969500315 & -4058.99695003153 \tabularnewline
22 & 63414.8 & 63023.1526432903 & 391.647356709655 \tabularnewline
23 & 66044 & 62824.5332446759 & 3219.46675532407 \tabularnewline
24 & 57628.5 & 62588.4272212497 & -4959.92722124972 \tabularnewline
25 & 62838.8 & 61197.347055258 & 1641.45294474201 \tabularnewline
26 & 55758.6 & 54534.7579067309 & 1223.8420932691 \tabularnewline
27 & 61004.5 & 61683.2493009422 & -678.749300942232 \tabularnewline
28 & 66173.4 & 61857.2262541424 & 4316.17374585757 \tabularnewline
29 & 57489 & 55941.8344356091 & 1547.1655643909 \tabularnewline
30 & 59552.2 & 60513.8112049269 & -961.611204926929 \tabularnewline
31 & 57061.8 & 52779.1624848204 & 4282.63751517962 \tabularnewline
32 & 55895.3 & 54443.1521958585 & 1452.14780414152 \tabularnewline
33 & 56314.7 & 57717.2762321708 & -1402.5762321708 \tabularnewline
34 & 61232.8 & 59670.707936096 & 1562.092063904 \tabularnewline
35 & 60014.1 & 61436.6335907519 & -1422.5335907519 \tabularnewline
36 & 57685.4 & 55850.444039921 & 1834.95596007899 \tabularnewline
37 & 60403.1 & 59219.4360586351 & 1183.66394136492 \tabularnewline
38 & 52349.7 & 52405.0010665963 & -55.3010665962938 \tabularnewline
39 & 55693.3 & 58404.7731654094 & -2711.47316540936 \tabularnewline
40 & 65676.1 & 61618.3658799707 & 4057.73412002931 \tabularnewline
41 & 54898.8 & 54071.9998767351 & 826.800123264853 \tabularnewline
42 & 55518.2 & 57130.3236761668 & -1612.12367616685 \tabularnewline
43 & 53779.1 & 52678.9226391937 & 1100.17736080632 \tabularnewline
44 & 52340.9 & 52397.046114724 & -56.1461147239534 \tabularnewline
45 & 55704.4 & 53823.5958047275 & 1880.80419527246 \tabularnewline
46 & 60330.3 & 57939.0440372382 & 2391.25596276176 \tabularnewline
47 & 52837.4 & 58003.4916354791 & -5166.09163547907 \tabularnewline
48 & 55388.1 & 54183.4665800441 & 1204.63341995594 \tabularnewline
49 & 60383.4 & 57133.9001922602 & 3249.49980773985 \tabularnewline
50 & 52070.3 & 49769.0088337006 & 2301.29116629938 \tabularnewline
51 & 54077 & 54389.6085942253 & -312.608594225334 \tabularnewline
52 & 62887.8 & 62087.3738016488 & 800.426198351226 \tabularnewline
53 & 49212.8 & 52361.200446708 & -3148.40044670802 \tabularnewline
54 & 57722 & 53630.5600598703 & 4091.43994012966 \tabularnewline
55 & 53936.8 & 51391.9074259386 & 2544.89257406144 \tabularnewline
56 & 46991 & 50613.866840064 & -3622.86684006401 \tabularnewline
57 & 54984.2 & 53030.8750428926 & 1953.32495710743 \tabularnewline
58 & 56485.1 & 57536.9576520233 & -1051.85765202333 \tabularnewline
59 & 51277.8 & 52688.0535885619 & -1410.25358856188 \tabularnewline
60 & 53596.4 & 53174.9447240306 & 421.455275969405 \tabularnewline
61 & 54252.5 & 57394.173539077 & -3141.67353907702 \tabularnewline
62 & 49413 & 48940.3314044521 & 472.668595547941 \tabularnewline
63 & 53213.2 & 51774.8435729036 & 1438.35642709644 \tabularnewline
64 & 58695.3 & 60290.1576265646 & -1594.85762656457 \tabularnewline
65 & 48723.5 & 47900.6277648954 & 822.872235104638 \tabularnewline
66 & 54510 & 53969.1802079779 & 540.819792022077 \tabularnewline
67 & 49454.1 & 50469.0328443371 & -1014.93284433713 \tabularnewline
68 & 46136.6 & 45529.4362067718 & 607.163793228196 \tabularnewline
69 & 54622.5 & 51704.3695499936 & 2918.13045000644 \tabularnewline
70 & 50583 & 54414.3738982551 & -3831.37389825513 \tabularnewline
71 & 53224.3 & 49086.6041996828 & 4137.69580031715 \tabularnewline
72 & 53056.4 & 51157.0694026702 & 1899.33059732983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76771&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]65914.6[/C][C]67882.8211538462[/C][C]-1968.22115384619[/C][/ROW]
[ROW][C]14[/C][C]59189.9[/C][C]60840.47026691[/C][C]-1650.57026690995[/C][/ROW]
[ROW][C]15[/C][C]66211.4[/C][C]67781.3746025152[/C][C]-1569.97460251523[/C][/ROW]
[ROW][C]16[/C][C]66400.8[/C][C]67894.4482735782[/C][C]-1493.64827357818[/C][/ROW]
[ROW][C]17[/C][C]60167.7[/C][C]61290.5070304832[/C][C]-1122.80703048316[/C][/ROW]
[ROW][C]18[/C][C]64547.9[/C][C]65531.5536835978[/C][C]-983.65368359779[/C][/ROW]
[ROW][C]19[/C][C]57706.2[/C][C]56242.4995444508[/C][C]1463.70045554917[/C][/ROW]
[ROW][C]20[/C][C]58642.6[/C][C]58333.6105024026[/C][C]308.989497597358[/C][/ROW]
[ROW][C]21[/C][C]60082.1[/C][C]64141.0969500315[/C][C]-4058.99695003153[/C][/ROW]
[ROW][C]22[/C][C]63414.8[/C][C]63023.1526432903[/C][C]391.647356709655[/C][/ROW]
[ROW][C]23[/C][C]66044[/C][C]62824.5332446759[/C][C]3219.46675532407[/C][/ROW]
[ROW][C]24[/C][C]57628.5[/C][C]62588.4272212497[/C][C]-4959.92722124972[/C][/ROW]
[ROW][C]25[/C][C]62838.8[/C][C]61197.347055258[/C][C]1641.45294474201[/C][/ROW]
[ROW][C]26[/C][C]55758.6[/C][C]54534.7579067309[/C][C]1223.8420932691[/C][/ROW]
[ROW][C]27[/C][C]61004.5[/C][C]61683.2493009422[/C][C]-678.749300942232[/C][/ROW]
[ROW][C]28[/C][C]66173.4[/C][C]61857.2262541424[/C][C]4316.17374585757[/C][/ROW]
[ROW][C]29[/C][C]57489[/C][C]55941.8344356091[/C][C]1547.1655643909[/C][/ROW]
[ROW][C]30[/C][C]59552.2[/C][C]60513.8112049269[/C][C]-961.611204926929[/C][/ROW]
[ROW][C]31[/C][C]57061.8[/C][C]52779.1624848204[/C][C]4282.63751517962[/C][/ROW]
[ROW][C]32[/C][C]55895.3[/C][C]54443.1521958585[/C][C]1452.14780414152[/C][/ROW]
[ROW][C]33[/C][C]56314.7[/C][C]57717.2762321708[/C][C]-1402.5762321708[/C][/ROW]
[ROW][C]34[/C][C]61232.8[/C][C]59670.707936096[/C][C]1562.092063904[/C][/ROW]
[ROW][C]35[/C][C]60014.1[/C][C]61436.6335907519[/C][C]-1422.5335907519[/C][/ROW]
[ROW][C]36[/C][C]57685.4[/C][C]55850.444039921[/C][C]1834.95596007899[/C][/ROW]
[ROW][C]37[/C][C]60403.1[/C][C]59219.4360586351[/C][C]1183.66394136492[/C][/ROW]
[ROW][C]38[/C][C]52349.7[/C][C]52405.0010665963[/C][C]-55.3010665962938[/C][/ROW]
[ROW][C]39[/C][C]55693.3[/C][C]58404.7731654094[/C][C]-2711.47316540936[/C][/ROW]
[ROW][C]40[/C][C]65676.1[/C][C]61618.3658799707[/C][C]4057.73412002931[/C][/ROW]
[ROW][C]41[/C][C]54898.8[/C][C]54071.9998767351[/C][C]826.800123264853[/C][/ROW]
[ROW][C]42[/C][C]55518.2[/C][C]57130.3236761668[/C][C]-1612.12367616685[/C][/ROW]
[ROW][C]43[/C][C]53779.1[/C][C]52678.9226391937[/C][C]1100.17736080632[/C][/ROW]
[ROW][C]44[/C][C]52340.9[/C][C]52397.046114724[/C][C]-56.1461147239534[/C][/ROW]
[ROW][C]45[/C][C]55704.4[/C][C]53823.5958047275[/C][C]1880.80419527246[/C][/ROW]
[ROW][C]46[/C][C]60330.3[/C][C]57939.0440372382[/C][C]2391.25596276176[/C][/ROW]
[ROW][C]47[/C][C]52837.4[/C][C]58003.4916354791[/C][C]-5166.09163547907[/C][/ROW]
[ROW][C]48[/C][C]55388.1[/C][C]54183.4665800441[/C][C]1204.63341995594[/C][/ROW]
[ROW][C]49[/C][C]60383.4[/C][C]57133.9001922602[/C][C]3249.49980773985[/C][/ROW]
[ROW][C]50[/C][C]52070.3[/C][C]49769.0088337006[/C][C]2301.29116629938[/C][/ROW]
[ROW][C]51[/C][C]54077[/C][C]54389.6085942253[/C][C]-312.608594225334[/C][/ROW]
[ROW][C]52[/C][C]62887.8[/C][C]62087.3738016488[/C][C]800.426198351226[/C][/ROW]
[ROW][C]53[/C][C]49212.8[/C][C]52361.200446708[/C][C]-3148.40044670802[/C][/ROW]
[ROW][C]54[/C][C]57722[/C][C]53630.5600598703[/C][C]4091.43994012966[/C][/ROW]
[ROW][C]55[/C][C]53936.8[/C][C]51391.9074259386[/C][C]2544.89257406144[/C][/ROW]
[ROW][C]56[/C][C]46991[/C][C]50613.866840064[/C][C]-3622.86684006401[/C][/ROW]
[ROW][C]57[/C][C]54984.2[/C][C]53030.8750428926[/C][C]1953.32495710743[/C][/ROW]
[ROW][C]58[/C][C]56485.1[/C][C]57536.9576520233[/C][C]-1051.85765202333[/C][/ROW]
[ROW][C]59[/C][C]51277.8[/C][C]52688.0535885619[/C][C]-1410.25358856188[/C][/ROW]
[ROW][C]60[/C][C]53596.4[/C][C]53174.9447240306[/C][C]421.455275969405[/C][/ROW]
[ROW][C]61[/C][C]54252.5[/C][C]57394.173539077[/C][C]-3141.67353907702[/C][/ROW]
[ROW][C]62[/C][C]49413[/C][C]48940.3314044521[/C][C]472.668595547941[/C][/ROW]
[ROW][C]63[/C][C]53213.2[/C][C]51774.8435729036[/C][C]1438.35642709644[/C][/ROW]
[ROW][C]64[/C][C]58695.3[/C][C]60290.1576265646[/C][C]-1594.85762656457[/C][/ROW]
[ROW][C]65[/C][C]48723.5[/C][C]47900.6277648954[/C][C]822.872235104638[/C][/ROW]
[ROW][C]66[/C][C]54510[/C][C]53969.1802079779[/C][C]540.819792022077[/C][/ROW]
[ROW][C]67[/C][C]49454.1[/C][C]50469.0328443371[/C][C]-1014.93284433713[/C][/ROW]
[ROW][C]68[/C][C]46136.6[/C][C]45529.4362067718[/C][C]607.163793228196[/C][/ROW]
[ROW][C]69[/C][C]54622.5[/C][C]51704.3695499936[/C][C]2918.13045000644[/C][/ROW]
[ROW][C]70[/C][C]50583[/C][C]54414.3738982551[/C][C]-3831.37389825513[/C][/ROW]
[ROW][C]71[/C][C]53224.3[/C][C]49086.6041996828[/C][C]4137.69580031715[/C][/ROW]
[ROW][C]72[/C][C]53056.4[/C][C]51157.0694026702[/C][C]1899.33059732983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76771&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76771&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
1365914.667882.8211538462-1968.22115384619
1459189.960840.47026691-1650.57026690995
1566211.467781.3746025152-1569.97460251523
1666400.867894.4482735782-1493.64827357818
1760167.761290.5070304832-1122.80703048316
1864547.965531.5536835978-983.65368359779
1957706.256242.49954445081463.70045554917
2058642.658333.6105024026308.989497597358
2160082.164141.0969500315-4058.99695003153
2263414.863023.1526432903391.647356709655
236604462824.53324467593219.46675532407
2457628.562588.4272212497-4959.92722124972
2562838.861197.3470552581641.45294474201
2655758.654534.75790673091223.8420932691
2761004.561683.2493009422-678.749300942232
2866173.461857.22625414244316.17374585757
295748955941.83443560911547.1655643909
3059552.260513.8112049269-961.611204926929
3157061.852779.16248482044282.63751517962
3255895.354443.15219585851452.14780414152
3356314.757717.2762321708-1402.5762321708
3461232.859670.7079360961562.092063904
3560014.161436.6335907519-1422.5335907519
3657685.455850.4440399211834.95596007899
3760403.159219.43605863511183.66394136492
3852349.752405.0010665963-55.3010665962938
3955693.358404.7731654094-2711.47316540936
4065676.161618.36587997074057.73412002931
4154898.854071.9998767351826.800123264853
4255518.257130.3236761668-1612.12367616685
4353779.152678.92263919371100.17736080632
4452340.952397.046114724-56.1461147239534
4555704.453823.59580472751880.80419527246
4660330.357939.04403723822391.25596276176
4752837.458003.4916354791-5166.09163547907
4855388.154183.46658004411204.63341995594
4960383.457133.90019226023249.49980773985
5052070.349769.00883370062301.29116629938
515407754389.6085942253-312.608594225334
5262887.862087.3738016488800.426198351226
5349212.852361.200446708-3148.40044670802
545772253630.56005987034091.43994012966
5553936.851391.90742593862544.89257406144
564699150613.866840064-3622.86684006401
5754984.253030.87504289261953.32495710743
5856485.157536.9576520233-1051.85765202333
5951277.852688.0535885619-1410.25358856188
6053596.453174.9447240306421.455275969405
6154252.557394.173539077-3141.67353907702
624941348940.3314044521472.668595547941
6353213.251774.84357290361438.35642709644
6458695.360290.1576265646-1594.85762656457
6548723.547900.6277648954822.872235104638
665451053969.1802079779540.819792022077
6749454.150469.0328443371-1014.93284433713
6846136.645529.4362067718607.163793228196
6954622.551704.36954999362918.13045000644
705058354414.3738982551-3831.37389825513
7153224.349086.60419968284137.69580031715
7253056.451157.06940267021899.33059732983







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7353321.338296501148761.113148680357881.5634443219
7447418.509436466242840.438420049251996.5804528833
7550879.133834396246278.61307551355479.6545932794
7657454.784350064852826.734549458662082.8341506711
7746752.182896776142091.07617876551413.2896147872
7852640.089648995747939.980673056157340.1986249353
7948186.893769613843441.454791252452932.3327479752
8044392.96350314539595.522887043449190.4041192467
8152007.435338474347151.018863117156863.8518138315
8250337.803869235345415.178031123155260.4297073476
8350305.903150874345309.619588243855302.1867135048
8450690.875055160945613.31517230355768.4349380187

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 53321.3382965011 & 48761.1131486803 & 57881.5634443219 \tabularnewline
74 & 47418.5094364662 & 42840.4384200492 & 51996.5804528833 \tabularnewline
75 & 50879.1338343962 & 46278.613075513 & 55479.6545932794 \tabularnewline
76 & 57454.7843500648 & 52826.7345494586 & 62082.8341506711 \tabularnewline
77 & 46752.1828967761 & 42091.076178765 & 51413.2896147872 \tabularnewline
78 & 52640.0896489957 & 47939.9806730561 & 57340.1986249353 \tabularnewline
79 & 48186.8937696138 & 43441.4547912524 & 52932.3327479752 \tabularnewline
80 & 44392.963503145 & 39595.5228870434 & 49190.4041192467 \tabularnewline
81 & 52007.4353384743 & 47151.0188631171 & 56863.8518138315 \tabularnewline
82 & 50337.8038692353 & 45415.1780311231 & 55260.4297073476 \tabularnewline
83 & 50305.9031508743 & 45309.6195882438 & 55302.1867135048 \tabularnewline
84 & 50690.8750551609 & 45613.315172303 & 55768.4349380187 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76771&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]73[/C][C]53321.3382965011[/C][C]48761.1131486803[/C][C]57881.5634443219[/C][/ROW]
[ROW][C]74[/C][C]47418.5094364662[/C][C]42840.4384200492[/C][C]51996.5804528833[/C][/ROW]
[ROW][C]75[/C][C]50879.1338343962[/C][C]46278.613075513[/C][C]55479.6545932794[/C][/ROW]
[ROW][C]76[/C][C]57454.7843500648[/C][C]52826.7345494586[/C][C]62082.8341506711[/C][/ROW]
[ROW][C]77[/C][C]46752.1828967761[/C][C]42091.076178765[/C][C]51413.2896147872[/C][/ROW]
[ROW][C]78[/C][C]52640.0896489957[/C][C]47939.9806730561[/C][C]57340.1986249353[/C][/ROW]
[ROW][C]79[/C][C]48186.8937696138[/C][C]43441.4547912524[/C][C]52932.3327479752[/C][/ROW]
[ROW][C]80[/C][C]44392.963503145[/C][C]39595.5228870434[/C][C]49190.4041192467[/C][/ROW]
[ROW][C]81[/C][C]52007.4353384743[/C][C]47151.0188631171[/C][C]56863.8518138315[/C][/ROW]
[ROW][C]82[/C][C]50337.8038692353[/C][C]45415.1780311231[/C][C]55260.4297073476[/C][/ROW]
[ROW][C]83[/C][C]50305.9031508743[/C][C]45309.6195882438[/C][C]55302.1867135048[/C][/ROW]
[ROW][C]84[/C][C]50690.8750551609[/C][C]45613.315172303[/C][C]55768.4349380187[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76771&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76771&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
7353321.338296501148761.113148680357881.5634443219
7447418.509436466242840.438420049251996.5804528833
7550879.133834396246278.61307551355479.6545932794
7657454.784350064852826.734549458662082.8341506711
7746752.182896776142091.07617876551413.2896147872
7852640.089648995747939.980673056157340.1986249353
7948186.893769613843441.454791252452932.3327479752
8044392.96350314539595.522887043449190.4041192467
8152007.435338474347151.018863117156863.8518138315
8250337.803869235345415.178031123155260.4297073476
8350305.903150874345309.619588243855302.1867135048
8450690.875055160945613.31517230355768.4349380187



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')