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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Aug 2013 06:16:03 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/21/t13770801819szvc0smqjftfqo.htm/, Retrieved Sat, 27 Apr 2024 06:16:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211326, Retrieved Sat, 27 Apr 2024 06:16:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-08-21 10:16:03] [bdb7c0ed7ba273e65f9ee772c5dda4f0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1165010
1160665
1156265
1147162,5
1237238,75
1232481,25
1165010
1120157,5
1124488,75
1124488,75
1129328,75
1138005
1151507,5
1151507,5
1142831,25
1120157,5
1237238,75
1255086,25
1228136,25
1165010
1192015
1151507,5
1169781,25
1178512,5
1187615
1165010
1169781,25
1138005
1237238,75
1268588,75
1241638,75
1192015
1245983,75
1187615
1241638,75
1237238,75
1250755
1201131,25
1255086,25
1250755
1331715
1313441,25
1241638,75
1205462,5
1255086,25
1187615
1237238,75
1245983,75
1264257,5
1223805
1245983,75
1259486,25
1309110
1268588,75
1214633,75
1156265
1210288,75
1061788,75
1133660
1174112,5
1214633,75
1156265
1156265
1156265
1187615
1142831,25
1084036,25
1034838,75
1070533,75
931205
1016578,75
1066188,75
1075305
1025681,25
1030012,5
1016578,75
1061788,75
1030012,5
967381,25
922102,5
998662,5
832383,75
940362,5
989560
989560
931205
877236,25
872905
922102,5
877236,25
791931,25
733136,25
796276,25
647831,25
782760
854562,5
877236,25
827626,25
764926,25
809778,75
827626,25
814110
679126,25
616481,25
661278,75
526350
665678,75
715302,5
755755
688283,75
625157,5
661278,75
679126,25
643431,25
508502,5
449707,5
503676,25
355231,25
517178,75
616481,25

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211326&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211326&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211326&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.379247820246123
beta0.0506958573991331
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.379247820246123 \tabularnewline
beta & 0.0506958573991331 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211326&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]0.379247820246123[/C][/ROW]
[ROW][C]beta[/C][C]0.0506958573991331[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211326&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211326&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.379247820246123
beta0.0506958573991331
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131151507.51151594.1448823-86.6448823018
141151507.51149045.504268622461.99573137914
151142831.251138701.185567734130.06443226524
161120157.51115882.843266474274.65673353476
171237238.751233644.199838643594.55016136332
181255086.251251621.328029423464.92197058303
191228136.251184541.1313751943595.1186248071
2011650101158812.673897946197.32610206376
2111920151169772.6094528422242.3905471619
221151507.51183531.41065833-32023.9106583335
231169781.251180579.79237187-10798.5423718716
241178512.51187370.54872265-8858.04872264527
2511876151196974.60188464-9359.60188464285
2611650101192921.77851697-27911.7785169745
271169781.251171716.15363577-1934.90363576985
2811380051145875.71017138-7870.71017137682
291237238.751260474.56522635-23235.8152263493
301268588.751267398.058915511190.69108448504
311241638.751222556.4481135519082.30188645
3211920151162840.4665461729174.5334538266
331245983.751191545.1995266554438.5504733513
3411876151182754.809722064860.19027793757
351241638.751207881.1056961933757.6443038108
361237238.751234408.458710522830.29128948483
3712507551250081.77149143673.228508573025
381201131.251239044.39318589-37913.1431858863
391255086.251231812.0268556123274.2231443923
4012507551211870.8400425138884.1599574855
4113317151345874.28793947-14159.2879394703
421313441.251377158.40601952-63717.1560195154
431241638.751318354.77931904-76716.0293190449
441205462.51226140.67343124-20678.1734312396
451255086.251250866.898330754219.35166924726
4611876151190169.56502526-2554.56502526184
471237238.751228298.944123668939.80587634281
481245983.751223867.7963793422115.9536206599
491264257.51243411.9098214920845.5901785134
5012238051214151.701664969653.29833503859
511245983.751262664.91831582-16681.168315822
521259486.251235450.9623805424035.2876194585
5313091101328544.4887657-19434.4887657035
541268588.751324336.10000809-55747.3500080924
551214633.751257946.30785052-43312.5578505159
5611562651211892.18613604-55627.186136042
571210288.751236286.42579398-25997.6757939786
581061788.751159068.84457197-97280.0945719676
5911336601161541.34475644-27881.3447564435
601174112.51146238.0276138827874.4723861194
611214633.751161492.4228894353141.3271105681
6211562651136317.4389029619947.5610970433
6311562651166523.77706928-10258.7770692797
6411562651162769.15974949-6504.15974949091
6511876151208174.51851488-20559.5185148802
661142831.251177556.99910333-34725.7491033303
671084036.251125497.94085571-41461.6908557054
681034838.751071128.55455774-36289.8045577446
691070533.751111676.05826235-41142.3082623512
70931205989265.969346551-58060.9693465512
711016578.751038496.29195199-21917.5419519891
721066188.751053429.4397235312759.3102764727
7310753051072005.336817043299.66318295687
741025681.251010158.9816082115522.2683917896
751030012.51014606.4321422715406.0678577299
761016578.751018238.43372816-1659.68372816022
771061788.751047529.9186565414258.8313434628
781030012.51020962.08791359050.41208650172
79967381.25982617.89357988-15236.6435798795
80922102.5942295.939308562-20193.4393085619
81998662.5978414.38955938120248.1104406188
82832383.75876345.18142936-43961.4314293602
83940362.5945197.356315097-4834.85631509696
84989560984308.5726843555251.42731564539
85989560992847.470329039-3287.47032903903
86931205939531.612917444-8326.61291744444
87877236.25933615.030012265-56378.780012265
88872905898065.516599032-25160.5165990321
89922102.5919769.8694414522332.6305585478
90877236.25886473.494498662-9237.2444986623
91791931.25830367.492782142-38436.2427821424
92733136.25779739.647921219-46603.3979212185
93796276.25813602.533189375-17326.2831893754
94647831.25680514.157334414-32682.9073344142
95782760750341.06797838732418.9320216129
96854562.5795454.98001167159107.5199883291
97877236.25814566.50357799762669.7464220033
98827626.25788771.34995732438854.9000426763
99764926.25772936.600490295-8010.35049029498
100809778.75773427.56141790236351.1885820976
101827626.25831230.733126777-3604.48312677676
102814110792928.28357822321181.7164217768
103679126.25736912.956175916-57786.7061759157
104616481.25677623.435782713-61142.1857827127
105661278.75716435.872618498-55157.1226184982
106526350575413.530907292-49063.5309072918
107665678.75660138.6295596345540.12044036551
108715302.5700606.86842999214695.6315700084
109755755700837.51819385954917.481806141
110688283.75665044.94414938223238.8058506183
111625157.5621915.1332589893242.36674101092
112661278.75644811.58470459116467.1652954092
113679126.25662714.57825089216411.6717491081
114643431.25648088.700220319-4657.45022031909
115508502.5552344.082881729-43841.5828817288
116449707.5500318.660285809-50611.1602858093
117503676.25527825.505304519-24149.255304519
118355231.25423776.35943946-68545.1094394599
119517178.75496685.52993073420493.220069266
120616481.25532948.37608860383532.8739113974

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1151507.5 & 1151594.1448823 & -86.6448823018 \tabularnewline
14 & 1151507.5 & 1149045.50426862 & 2461.99573137914 \tabularnewline
15 & 1142831.25 & 1138701.18556773 & 4130.06443226524 \tabularnewline
16 & 1120157.5 & 1115882.84326647 & 4274.65673353476 \tabularnewline
17 & 1237238.75 & 1233644.19983864 & 3594.55016136332 \tabularnewline
18 & 1255086.25 & 1251621.32802942 & 3464.92197058303 \tabularnewline
19 & 1228136.25 & 1184541.13137519 & 43595.1186248071 \tabularnewline
20 & 1165010 & 1158812.67389794 & 6197.32610206376 \tabularnewline
21 & 1192015 & 1169772.60945284 & 22242.3905471619 \tabularnewline
22 & 1151507.5 & 1183531.41065833 & -32023.9106583335 \tabularnewline
23 & 1169781.25 & 1180579.79237187 & -10798.5423718716 \tabularnewline
24 & 1178512.5 & 1187370.54872265 & -8858.04872264527 \tabularnewline
25 & 1187615 & 1196974.60188464 & -9359.60188464285 \tabularnewline
26 & 1165010 & 1192921.77851697 & -27911.7785169745 \tabularnewline
27 & 1169781.25 & 1171716.15363577 & -1934.90363576985 \tabularnewline
28 & 1138005 & 1145875.71017138 & -7870.71017137682 \tabularnewline
29 & 1237238.75 & 1260474.56522635 & -23235.8152263493 \tabularnewline
30 & 1268588.75 & 1267398.05891551 & 1190.69108448504 \tabularnewline
31 & 1241638.75 & 1222556.44811355 & 19082.30188645 \tabularnewline
32 & 1192015 & 1162840.46654617 & 29174.5334538266 \tabularnewline
33 & 1245983.75 & 1191545.19952665 & 54438.5504733513 \tabularnewline
34 & 1187615 & 1182754.80972206 & 4860.19027793757 \tabularnewline
35 & 1241638.75 & 1207881.10569619 & 33757.6443038108 \tabularnewline
36 & 1237238.75 & 1234408.45871052 & 2830.29128948483 \tabularnewline
37 & 1250755 & 1250081.77149143 & 673.228508573025 \tabularnewline
38 & 1201131.25 & 1239044.39318589 & -37913.1431858863 \tabularnewline
39 & 1255086.25 & 1231812.02685561 & 23274.2231443923 \tabularnewline
40 & 1250755 & 1211870.84004251 & 38884.1599574855 \tabularnewline
41 & 1331715 & 1345874.28793947 & -14159.2879394703 \tabularnewline
42 & 1313441.25 & 1377158.40601952 & -63717.1560195154 \tabularnewline
43 & 1241638.75 & 1318354.77931904 & -76716.0293190449 \tabularnewline
44 & 1205462.5 & 1226140.67343124 & -20678.1734312396 \tabularnewline
45 & 1255086.25 & 1250866.89833075 & 4219.35166924726 \tabularnewline
46 & 1187615 & 1190169.56502526 & -2554.56502526184 \tabularnewline
47 & 1237238.75 & 1228298.94412366 & 8939.80587634281 \tabularnewline
48 & 1245983.75 & 1223867.79637934 & 22115.9536206599 \tabularnewline
49 & 1264257.5 & 1243411.90982149 & 20845.5901785134 \tabularnewline
50 & 1223805 & 1214151.70166496 & 9653.29833503859 \tabularnewline
51 & 1245983.75 & 1262664.91831582 & -16681.168315822 \tabularnewline
52 & 1259486.25 & 1235450.96238054 & 24035.2876194585 \tabularnewline
53 & 1309110 & 1328544.4887657 & -19434.4887657035 \tabularnewline
54 & 1268588.75 & 1324336.10000809 & -55747.3500080924 \tabularnewline
55 & 1214633.75 & 1257946.30785052 & -43312.5578505159 \tabularnewline
56 & 1156265 & 1211892.18613604 & -55627.186136042 \tabularnewline
57 & 1210288.75 & 1236286.42579398 & -25997.6757939786 \tabularnewline
58 & 1061788.75 & 1159068.84457197 & -97280.0945719676 \tabularnewline
59 & 1133660 & 1161541.34475644 & -27881.3447564435 \tabularnewline
60 & 1174112.5 & 1146238.02761388 & 27874.4723861194 \tabularnewline
61 & 1214633.75 & 1161492.42288943 & 53141.3271105681 \tabularnewline
62 & 1156265 & 1136317.43890296 & 19947.5610970433 \tabularnewline
63 & 1156265 & 1166523.77706928 & -10258.7770692797 \tabularnewline
64 & 1156265 & 1162769.15974949 & -6504.15974949091 \tabularnewline
65 & 1187615 & 1208174.51851488 & -20559.5185148802 \tabularnewline
66 & 1142831.25 & 1177556.99910333 & -34725.7491033303 \tabularnewline
67 & 1084036.25 & 1125497.94085571 & -41461.6908557054 \tabularnewline
68 & 1034838.75 & 1071128.55455774 & -36289.8045577446 \tabularnewline
69 & 1070533.75 & 1111676.05826235 & -41142.3082623512 \tabularnewline
70 & 931205 & 989265.969346551 & -58060.9693465512 \tabularnewline
71 & 1016578.75 & 1038496.29195199 & -21917.5419519891 \tabularnewline
72 & 1066188.75 & 1053429.43972353 & 12759.3102764727 \tabularnewline
73 & 1075305 & 1072005.33681704 & 3299.66318295687 \tabularnewline
74 & 1025681.25 & 1010158.98160821 & 15522.2683917896 \tabularnewline
75 & 1030012.5 & 1014606.43214227 & 15406.0678577299 \tabularnewline
76 & 1016578.75 & 1018238.43372816 & -1659.68372816022 \tabularnewline
77 & 1061788.75 & 1047529.91865654 & 14258.8313434628 \tabularnewline
78 & 1030012.5 & 1020962.0879135 & 9050.41208650172 \tabularnewline
79 & 967381.25 & 982617.89357988 & -15236.6435798795 \tabularnewline
80 & 922102.5 & 942295.939308562 & -20193.4393085619 \tabularnewline
81 & 998662.5 & 978414.389559381 & 20248.1104406188 \tabularnewline
82 & 832383.75 & 876345.18142936 & -43961.4314293602 \tabularnewline
83 & 940362.5 & 945197.356315097 & -4834.85631509696 \tabularnewline
84 & 989560 & 984308.572684355 & 5251.42731564539 \tabularnewline
85 & 989560 & 992847.470329039 & -3287.47032903903 \tabularnewline
86 & 931205 & 939531.612917444 & -8326.61291744444 \tabularnewline
87 & 877236.25 & 933615.030012265 & -56378.780012265 \tabularnewline
88 & 872905 & 898065.516599032 & -25160.5165990321 \tabularnewline
89 & 922102.5 & 919769.869441452 & 2332.6305585478 \tabularnewline
90 & 877236.25 & 886473.494498662 & -9237.2444986623 \tabularnewline
91 & 791931.25 & 830367.492782142 & -38436.2427821424 \tabularnewline
92 & 733136.25 & 779739.647921219 & -46603.3979212185 \tabularnewline
93 & 796276.25 & 813602.533189375 & -17326.2831893754 \tabularnewline
94 & 647831.25 & 680514.157334414 & -32682.9073344142 \tabularnewline
95 & 782760 & 750341.067978387 & 32418.9320216129 \tabularnewline
96 & 854562.5 & 795454.980011671 & 59107.5199883291 \tabularnewline
97 & 877236.25 & 814566.503577997 & 62669.7464220033 \tabularnewline
98 & 827626.25 & 788771.349957324 & 38854.9000426763 \tabularnewline
99 & 764926.25 & 772936.600490295 & -8010.35049029498 \tabularnewline
100 & 809778.75 & 773427.561417902 & 36351.1885820976 \tabularnewline
101 & 827626.25 & 831230.733126777 & -3604.48312677676 \tabularnewline
102 & 814110 & 792928.283578223 & 21181.7164217768 \tabularnewline
103 & 679126.25 & 736912.956175916 & -57786.7061759157 \tabularnewline
104 & 616481.25 & 677623.435782713 & -61142.1857827127 \tabularnewline
105 & 661278.75 & 716435.872618498 & -55157.1226184982 \tabularnewline
106 & 526350 & 575413.530907292 & -49063.5309072918 \tabularnewline
107 & 665678.75 & 660138.629559634 & 5540.12044036551 \tabularnewline
108 & 715302.5 & 700606.868429992 & 14695.6315700084 \tabularnewline
109 & 755755 & 700837.518193859 & 54917.481806141 \tabularnewline
110 & 688283.75 & 665044.944149382 & 23238.8058506183 \tabularnewline
111 & 625157.5 & 621915.133258989 & 3242.36674101092 \tabularnewline
112 & 661278.75 & 644811.584704591 & 16467.1652954092 \tabularnewline
113 & 679126.25 & 662714.578250892 & 16411.6717491081 \tabularnewline
114 & 643431.25 & 648088.700220319 & -4657.45022031909 \tabularnewline
115 & 508502.5 & 552344.082881729 & -43841.5828817288 \tabularnewline
116 & 449707.5 & 500318.660285809 & -50611.1602858093 \tabularnewline
117 & 503676.25 & 527825.505304519 & -24149.255304519 \tabularnewline
118 & 355231.25 & 423776.35943946 & -68545.1094394599 \tabularnewline
119 & 517178.75 & 496685.529930734 & 20493.220069266 \tabularnewline
120 & 616481.25 & 532948.376088603 & 83532.8739113974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211326&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]1151507.5[/C][C]1151594.1448823[/C][C]-86.6448823018[/C][/ROW]
[ROW][C]14[/C][C]1151507.5[/C][C]1149045.50426862[/C][C]2461.99573137914[/C][/ROW]
[ROW][C]15[/C][C]1142831.25[/C][C]1138701.18556773[/C][C]4130.06443226524[/C][/ROW]
[ROW][C]16[/C][C]1120157.5[/C][C]1115882.84326647[/C][C]4274.65673353476[/C][/ROW]
[ROW][C]17[/C][C]1237238.75[/C][C]1233644.19983864[/C][C]3594.55016136332[/C][/ROW]
[ROW][C]18[/C][C]1255086.25[/C][C]1251621.32802942[/C][C]3464.92197058303[/C][/ROW]
[ROW][C]19[/C][C]1228136.25[/C][C]1184541.13137519[/C][C]43595.1186248071[/C][/ROW]
[ROW][C]20[/C][C]1165010[/C][C]1158812.67389794[/C][C]6197.32610206376[/C][/ROW]
[ROW][C]21[/C][C]1192015[/C][C]1169772.60945284[/C][C]22242.3905471619[/C][/ROW]
[ROW][C]22[/C][C]1151507.5[/C][C]1183531.41065833[/C][C]-32023.9106583335[/C][/ROW]
[ROW][C]23[/C][C]1169781.25[/C][C]1180579.79237187[/C][C]-10798.5423718716[/C][/ROW]
[ROW][C]24[/C][C]1178512.5[/C][C]1187370.54872265[/C][C]-8858.04872264527[/C][/ROW]
[ROW][C]25[/C][C]1187615[/C][C]1196974.60188464[/C][C]-9359.60188464285[/C][/ROW]
[ROW][C]26[/C][C]1165010[/C][C]1192921.77851697[/C][C]-27911.7785169745[/C][/ROW]
[ROW][C]27[/C][C]1169781.25[/C][C]1171716.15363577[/C][C]-1934.90363576985[/C][/ROW]
[ROW][C]28[/C][C]1138005[/C][C]1145875.71017138[/C][C]-7870.71017137682[/C][/ROW]
[ROW][C]29[/C][C]1237238.75[/C][C]1260474.56522635[/C][C]-23235.8152263493[/C][/ROW]
[ROW][C]30[/C][C]1268588.75[/C][C]1267398.05891551[/C][C]1190.69108448504[/C][/ROW]
[ROW][C]31[/C][C]1241638.75[/C][C]1222556.44811355[/C][C]19082.30188645[/C][/ROW]
[ROW][C]32[/C][C]1192015[/C][C]1162840.46654617[/C][C]29174.5334538266[/C][/ROW]
[ROW][C]33[/C][C]1245983.75[/C][C]1191545.19952665[/C][C]54438.5504733513[/C][/ROW]
[ROW][C]34[/C][C]1187615[/C][C]1182754.80972206[/C][C]4860.19027793757[/C][/ROW]
[ROW][C]35[/C][C]1241638.75[/C][C]1207881.10569619[/C][C]33757.6443038108[/C][/ROW]
[ROW][C]36[/C][C]1237238.75[/C][C]1234408.45871052[/C][C]2830.29128948483[/C][/ROW]
[ROW][C]37[/C][C]1250755[/C][C]1250081.77149143[/C][C]673.228508573025[/C][/ROW]
[ROW][C]38[/C][C]1201131.25[/C][C]1239044.39318589[/C][C]-37913.1431858863[/C][/ROW]
[ROW][C]39[/C][C]1255086.25[/C][C]1231812.02685561[/C][C]23274.2231443923[/C][/ROW]
[ROW][C]40[/C][C]1250755[/C][C]1211870.84004251[/C][C]38884.1599574855[/C][/ROW]
[ROW][C]41[/C][C]1331715[/C][C]1345874.28793947[/C][C]-14159.2879394703[/C][/ROW]
[ROW][C]42[/C][C]1313441.25[/C][C]1377158.40601952[/C][C]-63717.1560195154[/C][/ROW]
[ROW][C]43[/C][C]1241638.75[/C][C]1318354.77931904[/C][C]-76716.0293190449[/C][/ROW]
[ROW][C]44[/C][C]1205462.5[/C][C]1226140.67343124[/C][C]-20678.1734312396[/C][/ROW]
[ROW][C]45[/C][C]1255086.25[/C][C]1250866.89833075[/C][C]4219.35166924726[/C][/ROW]
[ROW][C]46[/C][C]1187615[/C][C]1190169.56502526[/C][C]-2554.56502526184[/C][/ROW]
[ROW][C]47[/C][C]1237238.75[/C][C]1228298.94412366[/C][C]8939.80587634281[/C][/ROW]
[ROW][C]48[/C][C]1245983.75[/C][C]1223867.79637934[/C][C]22115.9536206599[/C][/ROW]
[ROW][C]49[/C][C]1264257.5[/C][C]1243411.90982149[/C][C]20845.5901785134[/C][/ROW]
[ROW][C]50[/C][C]1223805[/C][C]1214151.70166496[/C][C]9653.29833503859[/C][/ROW]
[ROW][C]51[/C][C]1245983.75[/C][C]1262664.91831582[/C][C]-16681.168315822[/C][/ROW]
[ROW][C]52[/C][C]1259486.25[/C][C]1235450.96238054[/C][C]24035.2876194585[/C][/ROW]
[ROW][C]53[/C][C]1309110[/C][C]1328544.4887657[/C][C]-19434.4887657035[/C][/ROW]
[ROW][C]54[/C][C]1268588.75[/C][C]1324336.10000809[/C][C]-55747.3500080924[/C][/ROW]
[ROW][C]55[/C][C]1214633.75[/C][C]1257946.30785052[/C][C]-43312.5578505159[/C][/ROW]
[ROW][C]56[/C][C]1156265[/C][C]1211892.18613604[/C][C]-55627.186136042[/C][/ROW]
[ROW][C]57[/C][C]1210288.75[/C][C]1236286.42579398[/C][C]-25997.6757939786[/C][/ROW]
[ROW][C]58[/C][C]1061788.75[/C][C]1159068.84457197[/C][C]-97280.0945719676[/C][/ROW]
[ROW][C]59[/C][C]1133660[/C][C]1161541.34475644[/C][C]-27881.3447564435[/C][/ROW]
[ROW][C]60[/C][C]1174112.5[/C][C]1146238.02761388[/C][C]27874.4723861194[/C][/ROW]
[ROW][C]61[/C][C]1214633.75[/C][C]1161492.42288943[/C][C]53141.3271105681[/C][/ROW]
[ROW][C]62[/C][C]1156265[/C][C]1136317.43890296[/C][C]19947.5610970433[/C][/ROW]
[ROW][C]63[/C][C]1156265[/C][C]1166523.77706928[/C][C]-10258.7770692797[/C][/ROW]
[ROW][C]64[/C][C]1156265[/C][C]1162769.15974949[/C][C]-6504.15974949091[/C][/ROW]
[ROW][C]65[/C][C]1187615[/C][C]1208174.51851488[/C][C]-20559.5185148802[/C][/ROW]
[ROW][C]66[/C][C]1142831.25[/C][C]1177556.99910333[/C][C]-34725.7491033303[/C][/ROW]
[ROW][C]67[/C][C]1084036.25[/C][C]1125497.94085571[/C][C]-41461.6908557054[/C][/ROW]
[ROW][C]68[/C][C]1034838.75[/C][C]1071128.55455774[/C][C]-36289.8045577446[/C][/ROW]
[ROW][C]69[/C][C]1070533.75[/C][C]1111676.05826235[/C][C]-41142.3082623512[/C][/ROW]
[ROW][C]70[/C][C]931205[/C][C]989265.969346551[/C][C]-58060.9693465512[/C][/ROW]
[ROW][C]71[/C][C]1016578.75[/C][C]1038496.29195199[/C][C]-21917.5419519891[/C][/ROW]
[ROW][C]72[/C][C]1066188.75[/C][C]1053429.43972353[/C][C]12759.3102764727[/C][/ROW]
[ROW][C]73[/C][C]1075305[/C][C]1072005.33681704[/C][C]3299.66318295687[/C][/ROW]
[ROW][C]74[/C][C]1025681.25[/C][C]1010158.98160821[/C][C]15522.2683917896[/C][/ROW]
[ROW][C]75[/C][C]1030012.5[/C][C]1014606.43214227[/C][C]15406.0678577299[/C][/ROW]
[ROW][C]76[/C][C]1016578.75[/C][C]1018238.43372816[/C][C]-1659.68372816022[/C][/ROW]
[ROW][C]77[/C][C]1061788.75[/C][C]1047529.91865654[/C][C]14258.8313434628[/C][/ROW]
[ROW][C]78[/C][C]1030012.5[/C][C]1020962.0879135[/C][C]9050.41208650172[/C][/ROW]
[ROW][C]79[/C][C]967381.25[/C][C]982617.89357988[/C][C]-15236.6435798795[/C][/ROW]
[ROW][C]80[/C][C]922102.5[/C][C]942295.939308562[/C][C]-20193.4393085619[/C][/ROW]
[ROW][C]81[/C][C]998662.5[/C][C]978414.389559381[/C][C]20248.1104406188[/C][/ROW]
[ROW][C]82[/C][C]832383.75[/C][C]876345.18142936[/C][C]-43961.4314293602[/C][/ROW]
[ROW][C]83[/C][C]940362.5[/C][C]945197.356315097[/C][C]-4834.85631509696[/C][/ROW]
[ROW][C]84[/C][C]989560[/C][C]984308.572684355[/C][C]5251.42731564539[/C][/ROW]
[ROW][C]85[/C][C]989560[/C][C]992847.470329039[/C][C]-3287.47032903903[/C][/ROW]
[ROW][C]86[/C][C]931205[/C][C]939531.612917444[/C][C]-8326.61291744444[/C][/ROW]
[ROW][C]87[/C][C]877236.25[/C][C]933615.030012265[/C][C]-56378.780012265[/C][/ROW]
[ROW][C]88[/C][C]872905[/C][C]898065.516599032[/C][C]-25160.5165990321[/C][/ROW]
[ROW][C]89[/C][C]922102.5[/C][C]919769.869441452[/C][C]2332.6305585478[/C][/ROW]
[ROW][C]90[/C][C]877236.25[/C][C]886473.494498662[/C][C]-9237.2444986623[/C][/ROW]
[ROW][C]91[/C][C]791931.25[/C][C]830367.492782142[/C][C]-38436.2427821424[/C][/ROW]
[ROW][C]92[/C][C]733136.25[/C][C]779739.647921219[/C][C]-46603.3979212185[/C][/ROW]
[ROW][C]93[/C][C]796276.25[/C][C]813602.533189375[/C][C]-17326.2831893754[/C][/ROW]
[ROW][C]94[/C][C]647831.25[/C][C]680514.157334414[/C][C]-32682.9073344142[/C][/ROW]
[ROW][C]95[/C][C]782760[/C][C]750341.067978387[/C][C]32418.9320216129[/C][/ROW]
[ROW][C]96[/C][C]854562.5[/C][C]795454.980011671[/C][C]59107.5199883291[/C][/ROW]
[ROW][C]97[/C][C]877236.25[/C][C]814566.503577997[/C][C]62669.7464220033[/C][/ROW]
[ROW][C]98[/C][C]827626.25[/C][C]788771.349957324[/C][C]38854.9000426763[/C][/ROW]
[ROW][C]99[/C][C]764926.25[/C][C]772936.600490295[/C][C]-8010.35049029498[/C][/ROW]
[ROW][C]100[/C][C]809778.75[/C][C]773427.561417902[/C][C]36351.1885820976[/C][/ROW]
[ROW][C]101[/C][C]827626.25[/C][C]831230.733126777[/C][C]-3604.48312677676[/C][/ROW]
[ROW][C]102[/C][C]814110[/C][C]792928.283578223[/C][C]21181.7164217768[/C][/ROW]
[ROW][C]103[/C][C]679126.25[/C][C]736912.956175916[/C][C]-57786.7061759157[/C][/ROW]
[ROW][C]104[/C][C]616481.25[/C][C]677623.435782713[/C][C]-61142.1857827127[/C][/ROW]
[ROW][C]105[/C][C]661278.75[/C][C]716435.872618498[/C][C]-55157.1226184982[/C][/ROW]
[ROW][C]106[/C][C]526350[/C][C]575413.530907292[/C][C]-49063.5309072918[/C][/ROW]
[ROW][C]107[/C][C]665678.75[/C][C]660138.629559634[/C][C]5540.12044036551[/C][/ROW]
[ROW][C]108[/C][C]715302.5[/C][C]700606.868429992[/C][C]14695.6315700084[/C][/ROW]
[ROW][C]109[/C][C]755755[/C][C]700837.518193859[/C][C]54917.481806141[/C][/ROW]
[ROW][C]110[/C][C]688283.75[/C][C]665044.944149382[/C][C]23238.8058506183[/C][/ROW]
[ROW][C]111[/C][C]625157.5[/C][C]621915.133258989[/C][C]3242.36674101092[/C][/ROW]
[ROW][C]112[/C][C]661278.75[/C][C]644811.584704591[/C][C]16467.1652954092[/C][/ROW]
[ROW][C]113[/C][C]679126.25[/C][C]662714.578250892[/C][C]16411.6717491081[/C][/ROW]
[ROW][C]114[/C][C]643431.25[/C][C]648088.700220319[/C][C]-4657.45022031909[/C][/ROW]
[ROW][C]115[/C][C]508502.5[/C][C]552344.082881729[/C][C]-43841.5828817288[/C][/ROW]
[ROW][C]116[/C][C]449707.5[/C][C]500318.660285809[/C][C]-50611.1602858093[/C][/ROW]
[ROW][C]117[/C][C]503676.25[/C][C]527825.505304519[/C][C]-24149.255304519[/C][/ROW]
[ROW][C]118[/C][C]355231.25[/C][C]423776.35943946[/C][C]-68545.1094394599[/C][/ROW]
[ROW][C]119[/C][C]517178.75[/C][C]496685.529930734[/C][C]20493.220069266[/C][/ROW]
[ROW][C]120[/C][C]616481.25[/C][C]532948.376088603[/C][C]83532.8739113974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211326&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211326&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131151507.51151594.1448823-86.6448823018
141151507.51149045.504268622461.99573137914
151142831.251138701.185567734130.06443226524
161120157.51115882.843266474274.65673353476
171237238.751233644.199838643594.55016136332
181255086.251251621.328029423464.92197058303
191228136.251184541.1313751943595.1186248071
2011650101158812.673897946197.32610206376
2111920151169772.6094528422242.3905471619
221151507.51183531.41065833-32023.9106583335
231169781.251180579.79237187-10798.5423718716
241178512.51187370.54872265-8858.04872264527
2511876151196974.60188464-9359.60188464285
2611650101192921.77851697-27911.7785169745
271169781.251171716.15363577-1934.90363576985
2811380051145875.71017138-7870.71017137682
291237238.751260474.56522635-23235.8152263493
301268588.751267398.058915511190.69108448504
311241638.751222556.4481135519082.30188645
3211920151162840.4665461729174.5334538266
331245983.751191545.1995266554438.5504733513
3411876151182754.809722064860.19027793757
351241638.751207881.1056961933757.6443038108
361237238.751234408.458710522830.29128948483
3712507551250081.77149143673.228508573025
381201131.251239044.39318589-37913.1431858863
391255086.251231812.0268556123274.2231443923
4012507551211870.8400425138884.1599574855
4113317151345874.28793947-14159.2879394703
421313441.251377158.40601952-63717.1560195154
431241638.751318354.77931904-76716.0293190449
441205462.51226140.67343124-20678.1734312396
451255086.251250866.898330754219.35166924726
4611876151190169.56502526-2554.56502526184
471237238.751228298.944123668939.80587634281
481245983.751223867.7963793422115.9536206599
491264257.51243411.9098214920845.5901785134
5012238051214151.701664969653.29833503859
511245983.751262664.91831582-16681.168315822
521259486.251235450.9623805424035.2876194585
5313091101328544.4887657-19434.4887657035
541268588.751324336.10000809-55747.3500080924
551214633.751257946.30785052-43312.5578505159
5611562651211892.18613604-55627.186136042
571210288.751236286.42579398-25997.6757939786
581061788.751159068.84457197-97280.0945719676
5911336601161541.34475644-27881.3447564435
601174112.51146238.0276138827874.4723861194
611214633.751161492.4228894353141.3271105681
6211562651136317.4389029619947.5610970433
6311562651166523.77706928-10258.7770692797
6411562651162769.15974949-6504.15974949091
6511876151208174.51851488-20559.5185148802
661142831.251177556.99910333-34725.7491033303
671084036.251125497.94085571-41461.6908557054
681034838.751071128.55455774-36289.8045577446
691070533.751111676.05826235-41142.3082623512
70931205989265.969346551-58060.9693465512
711016578.751038496.29195199-21917.5419519891
721066188.751053429.4397235312759.3102764727
7310753051072005.336817043299.66318295687
741025681.251010158.9816082115522.2683917896
751030012.51014606.4321422715406.0678577299
761016578.751018238.43372816-1659.68372816022
771061788.751047529.9186565414258.8313434628
781030012.51020962.08791359050.41208650172
79967381.25982617.89357988-15236.6435798795
80922102.5942295.939308562-20193.4393085619
81998662.5978414.38955938120248.1104406188
82832383.75876345.18142936-43961.4314293602
83940362.5945197.356315097-4834.85631509696
84989560984308.5726843555251.42731564539
85989560992847.470329039-3287.47032903903
86931205939531.612917444-8326.61291744444
87877236.25933615.030012265-56378.780012265
88872905898065.516599032-25160.5165990321
89922102.5919769.8694414522332.6305585478
90877236.25886473.494498662-9237.2444986623
91791931.25830367.492782142-38436.2427821424
92733136.25779739.647921219-46603.3979212185
93796276.25813602.533189375-17326.2831893754
94647831.25680514.157334414-32682.9073344142
95782760750341.06797838732418.9320216129
96854562.5795454.98001167159107.5199883291
97877236.25814566.50357799762669.7464220033
98827626.25788771.34995732438854.9000426763
99764926.25772936.600490295-8010.35049029498
100809778.75773427.56141790236351.1885820976
101827626.25831230.733126777-3604.48312677676
102814110792928.28357822321181.7164217768
103679126.25736912.956175916-57786.7061759157
104616481.25677623.435782713-61142.1857827127
105661278.75716435.872618498-55157.1226184982
106526350575413.530907292-49063.5309072918
107665678.75660138.6295596345540.12044036551
108715302.5700606.86842999214695.6315700084
109755755700837.51819385954917.481806141
110688283.75665044.94414938223238.8058506183
111625157.5621915.1332589893242.36674101092
112661278.75644811.58470459116467.1652954092
113679126.25662714.57825089216411.6717491081
114643431.25648088.700220319-4657.45022031909
115508502.5552344.082881729-43841.5828817288
116449707.5500318.660285809-50611.1602858093
117503676.25527825.505304519-24149.255304519
118355231.25423776.35943946-68545.1094394599
119517178.75496685.52993073420493.220069266
120616481.25532948.37608860383532.8739113974






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121576149.860549576511735.656642673640564.064456478
122513848.030448258445303.102374241582392.958522275
123461646.153965348389408.950561342533883.357369354
124479087.332383984400215.174103373557959.490664594
125482358.259491963397098.516204545567618.002779382
126453000.578937885363969.818522683542031.339353086
127364776.049217985278666.185186141450885.913249829
128332042.541208002243529.995656178420555.086759827
129375449.66514579273200.502889404477698.827402177
130280105.771443693187516.70016287372694.842724515
131400478.79959121274092.129000908526865.470181511
132448794.553607006314756.941294218582832.165919795

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 576149.860549576 & 511735.656642673 & 640564.064456478 \tabularnewline
122 & 513848.030448258 & 445303.102374241 & 582392.958522275 \tabularnewline
123 & 461646.153965348 & 389408.950561342 & 533883.357369354 \tabularnewline
124 & 479087.332383984 & 400215.174103373 & 557959.490664594 \tabularnewline
125 & 482358.259491963 & 397098.516204545 & 567618.002779382 \tabularnewline
126 & 453000.578937885 & 363969.818522683 & 542031.339353086 \tabularnewline
127 & 364776.049217985 & 278666.185186141 & 450885.913249829 \tabularnewline
128 & 332042.541208002 & 243529.995656178 & 420555.086759827 \tabularnewline
129 & 375449.66514579 & 273200.502889404 & 477698.827402177 \tabularnewline
130 & 280105.771443693 & 187516.70016287 & 372694.842724515 \tabularnewline
131 & 400478.79959121 & 274092.129000908 & 526865.470181511 \tabularnewline
132 & 448794.553607006 & 314756.941294218 & 582832.165919795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211326&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]121[/C][C]576149.860549576[/C][C]511735.656642673[/C][C]640564.064456478[/C][/ROW]
[ROW][C]122[/C][C]513848.030448258[/C][C]445303.102374241[/C][C]582392.958522275[/C][/ROW]
[ROW][C]123[/C][C]461646.153965348[/C][C]389408.950561342[/C][C]533883.357369354[/C][/ROW]
[ROW][C]124[/C][C]479087.332383984[/C][C]400215.174103373[/C][C]557959.490664594[/C][/ROW]
[ROW][C]125[/C][C]482358.259491963[/C][C]397098.516204545[/C][C]567618.002779382[/C][/ROW]
[ROW][C]126[/C][C]453000.578937885[/C][C]363969.818522683[/C][C]542031.339353086[/C][/ROW]
[ROW][C]127[/C][C]364776.049217985[/C][C]278666.185186141[/C][C]450885.913249829[/C][/ROW]
[ROW][C]128[/C][C]332042.541208002[/C][C]243529.995656178[/C][C]420555.086759827[/C][/ROW]
[ROW][C]129[/C][C]375449.66514579[/C][C]273200.502889404[/C][C]477698.827402177[/C][/ROW]
[ROW][C]130[/C][C]280105.771443693[/C][C]187516.70016287[/C][C]372694.842724515[/C][/ROW]
[ROW][C]131[/C][C]400478.79959121[/C][C]274092.129000908[/C][C]526865.470181511[/C][/ROW]
[ROW][C]132[/C][C]448794.553607006[/C][C]314756.941294218[/C][C]582832.165919795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211326&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211326&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121576149.860549576511735.656642673640564.064456478
122513848.030448258445303.102374241582392.958522275
123461646.153965348389408.950561342533883.357369354
124479087.332383984400215.174103373557959.490664594
125482358.259491963397098.516204545567618.002779382
126453000.578937885363969.818522683542031.339353086
127364776.049217985278666.185186141450885.913249829
128332042.541208002243529.995656178420555.086759827
129375449.66514579273200.502889404477698.827402177
130280105.771443693187516.70016287372694.842724515
131400478.79959121274092.129000908526865.470181511
132448794.553607006314756.941294218582832.165919795


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
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')