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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 10:25:23 -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/2011/Aug/18/t1313677718xpkzyqc49tnpccg.htm/, Retrieved Wed, 15 May 2024 17:37:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124088, Retrieved Wed, 15 May 2024 17:37:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHuynh Tuyet Trang
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1, Stap 32] [2011-08-18 14:25:23] [0291ee60c135beb64d296f3dc8feb2dc] [Current]
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Dataseries X:
181896
181580
181234
180598
187123
186807
181896
178638
178954
178954
179269
179936
181580
179616
181580
179936
185158
187469
177656
175025
177305
176989
175025
175345
179269
178638
179269
179269
183545
184176
172398
172398
176989
174709
170785
172398
176327
174363
174047
169803
176007
177305
164545
164229
170785
167176
160967
163598
166509
167176
165212
161287
169456
169456
155078
154101
158025
150838
143616
145932
150838
146910
144283
138710
146247
146563
132190
131839
134470
126301
117465
121043
125950
120728
120412
115154
123670
125319
109266
105688
107968
99132
89981
92928
98470
91946
92928
89004
97172
98150
78524
77221
80799
71333
62817
65764
72950
64462
63799
57244
64462
66742
46448
46448
49391
41542
32706
37297
45466
36631
40244
35333
43186
45813
24853
23240
26502
18649
12444
15040




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124088&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124088&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124088&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.410624444915098
beta0.056140346857493
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.410624444915098 \tabularnewline
beta & 0.056140346857493 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124088&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]0.410624444915098[/C][/ROW]
[ROW][C]beta[/C][C]0.056140346857493[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124088&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124088&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
alpha0.410624444915098
beta0.056140346857493
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3181234181264-30
4180598180934.98968869-336.989688689559
5187123180472.1534187856650.84658121518
6186807183032.0128360563774.98716394376
7181896184497.997340893-2601.99734089282
8178638183285.45332251-4647.45332250965
9178954181125.859200351-2171.85920035068
10178954179932.737541717-978.737541717041
11179269179206.9783580362.0216419701173
12179936178910.0100964621025.98990353831
13181580179032.52250082547.47749920035
14179616179838.520881205-222.520881205244
15181580179501.960529652078.03947035037
16179936180157.970705575-221.970705574524
17185158179864.4234780985293.5765219022
18187469181957.7254649025511.27453509835
19177656184267.468778079-6611.46877807853
20175025181446.905810441-6421.90581044095
21177305178556.140413207-1251.14041320683
22176989177759.775649053-770.775649052928
23175025177142.892017761-2117.89201776055
24175345175924.026560417-579.026560417027
25179269175323.7088103223945.29118967778
26178638176672.1357397891965.86426021089
27179269177253.0798651122015.92013488786
28179269177901.0503542021367.94964579761
29183545178314.4831152055230.51688479513
30184176180434.557411753741.44258824969
31172398182029.431376631-9631.43137663128
32172398177911.046869699-5513.04686969859
33176989175356.6816574081632.31834259161
34174709175774.00724894-1065.00724894021
35170785175059.193831902-4274.19383190159
36172398172928.078680152-530.078680151812
37176327172322.169043164004.83095684031
38174363173670.72591977692.274080229894
39174047173675.02468428371.975315719901
40169803173556.37594411-3753.37594411022
41176007171657.2320631364349.76793686362
42177305173185.7105953274119.28940467298
43164545174714.509334018-10169.5093340178
44164229170141.544403809-5912.54440380892
45170785167180.2938212653604.70617873524
46167176168210.156821502-1034.15682150229
47160967167311.349274963-6344.34927496317
48163598164085.793161564-487.793161564186
49166509163253.837251313255.1627486904
50167176164033.8704948083142.12950519242
51165212164839.92377619372.076223809709
52161287164517.102790418-3230.10279041776
53169456162640.6767828446815.3232171562
54169456165046.2591651494409.74083485079
55155078166565.706603149-11487.7066031495
56154101161292.452020293-7191.45202029345
57158025157617.56293277407.43706722997
58150838157072.355942015-6234.35594201542
59143616153656.148277505-10040.1482775046
60145932148445.737737982-2513.73773798201
61150838146267.9071609784570.09283902188
62146910147104.223099069-194.223099069
63144283145979.717102507-1696.71710250727
64138710144199.136601212-5489.13660121246
65146247140734.7570847395512.24291526122
66146563141914.8844497424648.11555025796
67132190142847.331137952-10657.3311379516
68131839137249.308097001-5410.30809700105
69134470133681.119317939788.880682061397
70126301132676.65474004-6375.6547400401
71117465128583.281370776-11118.2813707759
72121043122286.164294422-1243.16429442157
73125950120015.3535183385934.64648166229
74120728120828.736332047-100.736332046916
75120412119161.5211937831250.47880621716
76115154118077.974807814-2923.97480781408
77123670115212.8905057148457.10949428563
78125319117216.1159795868102.88402041436
79109266119260.680349041-9994.68034904133
80105688113643.539039096-7955.53903909617
81107968108680.323148218-712.323148217532
8299132106674.927862204-7542.92786220377
8389981101690.835217549-11709.835217549
849292894725.7664202103-1797.7664202103
859847091789.39218277956680.60781722047
869194692488.4510318976-542.451031897595
879292890209.04044451912718.95955548089
888900489331.5238529158-327.523852915794
899717287195.49642682919976.50357317092
909815089520.5388769268629.46112307395
917852491491.3842735093-12967.3842735093
927722184295.1051105055-7074.10511050549
938079979355.6739258011443.32607419901
947133377946.9806102949-6613.98061029491
956281773077.2907687046-10260.2907687046
966576466473.8104760186-709.810476018596
977295063775.6278760869174.37212391396
986446265347.6253891901-885.625389190071
996379962768.32604087481030.67395912522
1005724460999.6657619906-3755.66576199059
1016446257179.03953603897282.96046396111
1026674258059.0342421468682.96575785401
1034644859714.0702706482-13266.0702706482
1044644852050.4781683784-5602.47816837835
1054939147404.59263784961986.40736215041
1064154245920.6808677233-4378.68086772329
1073270641722.1683032028-9016.16830320282
1083729735411.54392439011885.45607560992
1094546633620.857667201611845.1423327984
1103663136192.9233644203438.076635579731
1114024434091.06784651716152.93215348289
1123533334477.7127795897855.28722041026
1134318632708.731795783710477.2682042163
1144581335132.29967250910680.700327491
1152485337885.6196511182-13032.6196511182
1162324030601.2350247338-7361.23502473376
1172650225475.96396501321026.03603498677
1181864923818.3642255766-5169.36422557661
1191244419497.6144137533-7053.61441375332
1201504014240.5412714006799.458728599409

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 181234 & 181264 & -30 \tabularnewline
4 & 180598 & 180934.98968869 & -336.989688689559 \tabularnewline
5 & 187123 & 180472.153418785 & 6650.84658121518 \tabularnewline
6 & 186807 & 183032.012836056 & 3774.98716394376 \tabularnewline
7 & 181896 & 184497.997340893 & -2601.99734089282 \tabularnewline
8 & 178638 & 183285.45332251 & -4647.45332250965 \tabularnewline
9 & 178954 & 181125.859200351 & -2171.85920035068 \tabularnewline
10 & 178954 & 179932.737541717 & -978.737541717041 \tabularnewline
11 & 179269 & 179206.97835803 & 62.0216419701173 \tabularnewline
12 & 179936 & 178910.010096462 & 1025.98990353831 \tabularnewline
13 & 181580 & 179032.5225008 & 2547.47749920035 \tabularnewline
14 & 179616 & 179838.520881205 & -222.520881205244 \tabularnewline
15 & 181580 & 179501.96052965 & 2078.03947035037 \tabularnewline
16 & 179936 & 180157.970705575 & -221.970705574524 \tabularnewline
17 & 185158 & 179864.423478098 & 5293.5765219022 \tabularnewline
18 & 187469 & 181957.725464902 & 5511.27453509835 \tabularnewline
19 & 177656 & 184267.468778079 & -6611.46877807853 \tabularnewline
20 & 175025 & 181446.905810441 & -6421.90581044095 \tabularnewline
21 & 177305 & 178556.140413207 & -1251.14041320683 \tabularnewline
22 & 176989 & 177759.775649053 & -770.775649052928 \tabularnewline
23 & 175025 & 177142.892017761 & -2117.89201776055 \tabularnewline
24 & 175345 & 175924.026560417 & -579.026560417027 \tabularnewline
25 & 179269 & 175323.708810322 & 3945.29118967778 \tabularnewline
26 & 178638 & 176672.135739789 & 1965.86426021089 \tabularnewline
27 & 179269 & 177253.079865112 & 2015.92013488786 \tabularnewline
28 & 179269 & 177901.050354202 & 1367.94964579761 \tabularnewline
29 & 183545 & 178314.483115205 & 5230.51688479513 \tabularnewline
30 & 184176 & 180434.55741175 & 3741.44258824969 \tabularnewline
31 & 172398 & 182029.431376631 & -9631.43137663128 \tabularnewline
32 & 172398 & 177911.046869699 & -5513.04686969859 \tabularnewline
33 & 176989 & 175356.681657408 & 1632.31834259161 \tabularnewline
34 & 174709 & 175774.00724894 & -1065.00724894021 \tabularnewline
35 & 170785 & 175059.193831902 & -4274.19383190159 \tabularnewline
36 & 172398 & 172928.078680152 & -530.078680151812 \tabularnewline
37 & 176327 & 172322.16904316 & 4004.83095684031 \tabularnewline
38 & 174363 & 173670.72591977 & 692.274080229894 \tabularnewline
39 & 174047 & 173675.02468428 & 371.975315719901 \tabularnewline
40 & 169803 & 173556.37594411 & -3753.37594411022 \tabularnewline
41 & 176007 & 171657.232063136 & 4349.76793686362 \tabularnewline
42 & 177305 & 173185.710595327 & 4119.28940467298 \tabularnewline
43 & 164545 & 174714.509334018 & -10169.5093340178 \tabularnewline
44 & 164229 & 170141.544403809 & -5912.54440380892 \tabularnewline
45 & 170785 & 167180.293821265 & 3604.70617873524 \tabularnewline
46 & 167176 & 168210.156821502 & -1034.15682150229 \tabularnewline
47 & 160967 & 167311.349274963 & -6344.34927496317 \tabularnewline
48 & 163598 & 164085.793161564 & -487.793161564186 \tabularnewline
49 & 166509 & 163253.83725131 & 3255.1627486904 \tabularnewline
50 & 167176 & 164033.870494808 & 3142.12950519242 \tabularnewline
51 & 165212 & 164839.92377619 & 372.076223809709 \tabularnewline
52 & 161287 & 164517.102790418 & -3230.10279041776 \tabularnewline
53 & 169456 & 162640.676782844 & 6815.3232171562 \tabularnewline
54 & 169456 & 165046.259165149 & 4409.74083485079 \tabularnewline
55 & 155078 & 166565.706603149 & -11487.7066031495 \tabularnewline
56 & 154101 & 161292.452020293 & -7191.45202029345 \tabularnewline
57 & 158025 & 157617.56293277 & 407.43706722997 \tabularnewline
58 & 150838 & 157072.355942015 & -6234.35594201542 \tabularnewline
59 & 143616 & 153656.148277505 & -10040.1482775046 \tabularnewline
60 & 145932 & 148445.737737982 & -2513.73773798201 \tabularnewline
61 & 150838 & 146267.907160978 & 4570.09283902188 \tabularnewline
62 & 146910 & 147104.223099069 & -194.223099069 \tabularnewline
63 & 144283 & 145979.717102507 & -1696.71710250727 \tabularnewline
64 & 138710 & 144199.136601212 & -5489.13660121246 \tabularnewline
65 & 146247 & 140734.757084739 & 5512.24291526122 \tabularnewline
66 & 146563 & 141914.884449742 & 4648.11555025796 \tabularnewline
67 & 132190 & 142847.331137952 & -10657.3311379516 \tabularnewline
68 & 131839 & 137249.308097001 & -5410.30809700105 \tabularnewline
69 & 134470 & 133681.119317939 & 788.880682061397 \tabularnewline
70 & 126301 & 132676.65474004 & -6375.6547400401 \tabularnewline
71 & 117465 & 128583.281370776 & -11118.2813707759 \tabularnewline
72 & 121043 & 122286.164294422 & -1243.16429442157 \tabularnewline
73 & 125950 & 120015.353518338 & 5934.64648166229 \tabularnewline
74 & 120728 & 120828.736332047 & -100.736332046916 \tabularnewline
75 & 120412 & 119161.521193783 & 1250.47880621716 \tabularnewline
76 & 115154 & 118077.974807814 & -2923.97480781408 \tabularnewline
77 & 123670 & 115212.890505714 & 8457.10949428563 \tabularnewline
78 & 125319 & 117216.115979586 & 8102.88402041436 \tabularnewline
79 & 109266 & 119260.680349041 & -9994.68034904133 \tabularnewline
80 & 105688 & 113643.539039096 & -7955.53903909617 \tabularnewline
81 & 107968 & 108680.323148218 & -712.323148217532 \tabularnewline
82 & 99132 & 106674.927862204 & -7542.92786220377 \tabularnewline
83 & 89981 & 101690.835217549 & -11709.835217549 \tabularnewline
84 & 92928 & 94725.7664202103 & -1797.7664202103 \tabularnewline
85 & 98470 & 91789.3921827795 & 6680.60781722047 \tabularnewline
86 & 91946 & 92488.4510318976 & -542.451031897595 \tabularnewline
87 & 92928 & 90209.0404445191 & 2718.95955548089 \tabularnewline
88 & 89004 & 89331.5238529158 & -327.523852915794 \tabularnewline
89 & 97172 & 87195.4964268291 & 9976.50357317092 \tabularnewline
90 & 98150 & 89520.538876926 & 8629.46112307395 \tabularnewline
91 & 78524 & 91491.3842735093 & -12967.3842735093 \tabularnewline
92 & 77221 & 84295.1051105055 & -7074.10511050549 \tabularnewline
93 & 80799 & 79355.673925801 & 1443.32607419901 \tabularnewline
94 & 71333 & 77946.9806102949 & -6613.98061029491 \tabularnewline
95 & 62817 & 73077.2907687046 & -10260.2907687046 \tabularnewline
96 & 65764 & 66473.8104760186 & -709.810476018596 \tabularnewline
97 & 72950 & 63775.627876086 & 9174.37212391396 \tabularnewline
98 & 64462 & 65347.6253891901 & -885.625389190071 \tabularnewline
99 & 63799 & 62768.3260408748 & 1030.67395912522 \tabularnewline
100 & 57244 & 60999.6657619906 & -3755.66576199059 \tabularnewline
101 & 64462 & 57179.0395360389 & 7282.96046396111 \tabularnewline
102 & 66742 & 58059.034242146 & 8682.96575785401 \tabularnewline
103 & 46448 & 59714.0702706482 & -13266.0702706482 \tabularnewline
104 & 46448 & 52050.4781683784 & -5602.47816837835 \tabularnewline
105 & 49391 & 47404.5926378496 & 1986.40736215041 \tabularnewline
106 & 41542 & 45920.6808677233 & -4378.68086772329 \tabularnewline
107 & 32706 & 41722.1683032028 & -9016.16830320282 \tabularnewline
108 & 37297 & 35411.5439243901 & 1885.45607560992 \tabularnewline
109 & 45466 & 33620.8576672016 & 11845.1423327984 \tabularnewline
110 & 36631 & 36192.9233644203 & 438.076635579731 \tabularnewline
111 & 40244 & 34091.0678465171 & 6152.93215348289 \tabularnewline
112 & 35333 & 34477.7127795897 & 855.28722041026 \tabularnewline
113 & 43186 & 32708.7317957837 & 10477.2682042163 \tabularnewline
114 & 45813 & 35132.299672509 & 10680.700327491 \tabularnewline
115 & 24853 & 37885.6196511182 & -13032.6196511182 \tabularnewline
116 & 23240 & 30601.2350247338 & -7361.23502473376 \tabularnewline
117 & 26502 & 25475.9639650132 & 1026.03603498677 \tabularnewline
118 & 18649 & 23818.3642255766 & -5169.36422557661 \tabularnewline
119 & 12444 & 19497.6144137533 & -7053.61441375332 \tabularnewline
120 & 15040 & 14240.5412714006 & 799.458728599409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124088&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]3[/C][C]181234[/C][C]181264[/C][C]-30[/C][/ROW]
[ROW][C]4[/C][C]180598[/C][C]180934.98968869[/C][C]-336.989688689559[/C][/ROW]
[ROW][C]5[/C][C]187123[/C][C]180472.153418785[/C][C]6650.84658121518[/C][/ROW]
[ROW][C]6[/C][C]186807[/C][C]183032.012836056[/C][C]3774.98716394376[/C][/ROW]
[ROW][C]7[/C][C]181896[/C][C]184497.997340893[/C][C]-2601.99734089282[/C][/ROW]
[ROW][C]8[/C][C]178638[/C][C]183285.45332251[/C][C]-4647.45332250965[/C][/ROW]
[ROW][C]9[/C][C]178954[/C][C]181125.859200351[/C][C]-2171.85920035068[/C][/ROW]
[ROW][C]10[/C][C]178954[/C][C]179932.737541717[/C][C]-978.737541717041[/C][/ROW]
[ROW][C]11[/C][C]179269[/C][C]179206.97835803[/C][C]62.0216419701173[/C][/ROW]
[ROW][C]12[/C][C]179936[/C][C]178910.010096462[/C][C]1025.98990353831[/C][/ROW]
[ROW][C]13[/C][C]181580[/C][C]179032.5225008[/C][C]2547.47749920035[/C][/ROW]
[ROW][C]14[/C][C]179616[/C][C]179838.520881205[/C][C]-222.520881205244[/C][/ROW]
[ROW][C]15[/C][C]181580[/C][C]179501.96052965[/C][C]2078.03947035037[/C][/ROW]
[ROW][C]16[/C][C]179936[/C][C]180157.970705575[/C][C]-221.970705574524[/C][/ROW]
[ROW][C]17[/C][C]185158[/C][C]179864.423478098[/C][C]5293.5765219022[/C][/ROW]
[ROW][C]18[/C][C]187469[/C][C]181957.725464902[/C][C]5511.27453509835[/C][/ROW]
[ROW][C]19[/C][C]177656[/C][C]184267.468778079[/C][C]-6611.46877807853[/C][/ROW]
[ROW][C]20[/C][C]175025[/C][C]181446.905810441[/C][C]-6421.90581044095[/C][/ROW]
[ROW][C]21[/C][C]177305[/C][C]178556.140413207[/C][C]-1251.14041320683[/C][/ROW]
[ROW][C]22[/C][C]176989[/C][C]177759.775649053[/C][C]-770.775649052928[/C][/ROW]
[ROW][C]23[/C][C]175025[/C][C]177142.892017761[/C][C]-2117.89201776055[/C][/ROW]
[ROW][C]24[/C][C]175345[/C][C]175924.026560417[/C][C]-579.026560417027[/C][/ROW]
[ROW][C]25[/C][C]179269[/C][C]175323.708810322[/C][C]3945.29118967778[/C][/ROW]
[ROW][C]26[/C][C]178638[/C][C]176672.135739789[/C][C]1965.86426021089[/C][/ROW]
[ROW][C]27[/C][C]179269[/C][C]177253.079865112[/C][C]2015.92013488786[/C][/ROW]
[ROW][C]28[/C][C]179269[/C][C]177901.050354202[/C][C]1367.94964579761[/C][/ROW]
[ROW][C]29[/C][C]183545[/C][C]178314.483115205[/C][C]5230.51688479513[/C][/ROW]
[ROW][C]30[/C][C]184176[/C][C]180434.55741175[/C][C]3741.44258824969[/C][/ROW]
[ROW][C]31[/C][C]172398[/C][C]182029.431376631[/C][C]-9631.43137663128[/C][/ROW]
[ROW][C]32[/C][C]172398[/C][C]177911.046869699[/C][C]-5513.04686969859[/C][/ROW]
[ROW][C]33[/C][C]176989[/C][C]175356.681657408[/C][C]1632.31834259161[/C][/ROW]
[ROW][C]34[/C][C]174709[/C][C]175774.00724894[/C][C]-1065.00724894021[/C][/ROW]
[ROW][C]35[/C][C]170785[/C][C]175059.193831902[/C][C]-4274.19383190159[/C][/ROW]
[ROW][C]36[/C][C]172398[/C][C]172928.078680152[/C][C]-530.078680151812[/C][/ROW]
[ROW][C]37[/C][C]176327[/C][C]172322.16904316[/C][C]4004.83095684031[/C][/ROW]
[ROW][C]38[/C][C]174363[/C][C]173670.72591977[/C][C]692.274080229894[/C][/ROW]
[ROW][C]39[/C][C]174047[/C][C]173675.02468428[/C][C]371.975315719901[/C][/ROW]
[ROW][C]40[/C][C]169803[/C][C]173556.37594411[/C][C]-3753.37594411022[/C][/ROW]
[ROW][C]41[/C][C]176007[/C][C]171657.232063136[/C][C]4349.76793686362[/C][/ROW]
[ROW][C]42[/C][C]177305[/C][C]173185.710595327[/C][C]4119.28940467298[/C][/ROW]
[ROW][C]43[/C][C]164545[/C][C]174714.509334018[/C][C]-10169.5093340178[/C][/ROW]
[ROW][C]44[/C][C]164229[/C][C]170141.544403809[/C][C]-5912.54440380892[/C][/ROW]
[ROW][C]45[/C][C]170785[/C][C]167180.293821265[/C][C]3604.70617873524[/C][/ROW]
[ROW][C]46[/C][C]167176[/C][C]168210.156821502[/C][C]-1034.15682150229[/C][/ROW]
[ROW][C]47[/C][C]160967[/C][C]167311.349274963[/C][C]-6344.34927496317[/C][/ROW]
[ROW][C]48[/C][C]163598[/C][C]164085.793161564[/C][C]-487.793161564186[/C][/ROW]
[ROW][C]49[/C][C]166509[/C][C]163253.83725131[/C][C]3255.1627486904[/C][/ROW]
[ROW][C]50[/C][C]167176[/C][C]164033.870494808[/C][C]3142.12950519242[/C][/ROW]
[ROW][C]51[/C][C]165212[/C][C]164839.92377619[/C][C]372.076223809709[/C][/ROW]
[ROW][C]52[/C][C]161287[/C][C]164517.102790418[/C][C]-3230.10279041776[/C][/ROW]
[ROW][C]53[/C][C]169456[/C][C]162640.676782844[/C][C]6815.3232171562[/C][/ROW]
[ROW][C]54[/C][C]169456[/C][C]165046.259165149[/C][C]4409.74083485079[/C][/ROW]
[ROW][C]55[/C][C]155078[/C][C]166565.706603149[/C][C]-11487.7066031495[/C][/ROW]
[ROW][C]56[/C][C]154101[/C][C]161292.452020293[/C][C]-7191.45202029345[/C][/ROW]
[ROW][C]57[/C][C]158025[/C][C]157617.56293277[/C][C]407.43706722997[/C][/ROW]
[ROW][C]58[/C][C]150838[/C][C]157072.355942015[/C][C]-6234.35594201542[/C][/ROW]
[ROW][C]59[/C][C]143616[/C][C]153656.148277505[/C][C]-10040.1482775046[/C][/ROW]
[ROW][C]60[/C][C]145932[/C][C]148445.737737982[/C][C]-2513.73773798201[/C][/ROW]
[ROW][C]61[/C][C]150838[/C][C]146267.907160978[/C][C]4570.09283902188[/C][/ROW]
[ROW][C]62[/C][C]146910[/C][C]147104.223099069[/C][C]-194.223099069[/C][/ROW]
[ROW][C]63[/C][C]144283[/C][C]145979.717102507[/C][C]-1696.71710250727[/C][/ROW]
[ROW][C]64[/C][C]138710[/C][C]144199.136601212[/C][C]-5489.13660121246[/C][/ROW]
[ROW][C]65[/C][C]146247[/C][C]140734.757084739[/C][C]5512.24291526122[/C][/ROW]
[ROW][C]66[/C][C]146563[/C][C]141914.884449742[/C][C]4648.11555025796[/C][/ROW]
[ROW][C]67[/C][C]132190[/C][C]142847.331137952[/C][C]-10657.3311379516[/C][/ROW]
[ROW][C]68[/C][C]131839[/C][C]137249.308097001[/C][C]-5410.30809700105[/C][/ROW]
[ROW][C]69[/C][C]134470[/C][C]133681.119317939[/C][C]788.880682061397[/C][/ROW]
[ROW][C]70[/C][C]126301[/C][C]132676.65474004[/C][C]-6375.6547400401[/C][/ROW]
[ROW][C]71[/C][C]117465[/C][C]128583.281370776[/C][C]-11118.2813707759[/C][/ROW]
[ROW][C]72[/C][C]121043[/C][C]122286.164294422[/C][C]-1243.16429442157[/C][/ROW]
[ROW][C]73[/C][C]125950[/C][C]120015.353518338[/C][C]5934.64648166229[/C][/ROW]
[ROW][C]74[/C][C]120728[/C][C]120828.736332047[/C][C]-100.736332046916[/C][/ROW]
[ROW][C]75[/C][C]120412[/C][C]119161.521193783[/C][C]1250.47880621716[/C][/ROW]
[ROW][C]76[/C][C]115154[/C][C]118077.974807814[/C][C]-2923.97480781408[/C][/ROW]
[ROW][C]77[/C][C]123670[/C][C]115212.890505714[/C][C]8457.10949428563[/C][/ROW]
[ROW][C]78[/C][C]125319[/C][C]117216.115979586[/C][C]8102.88402041436[/C][/ROW]
[ROW][C]79[/C][C]109266[/C][C]119260.680349041[/C][C]-9994.68034904133[/C][/ROW]
[ROW][C]80[/C][C]105688[/C][C]113643.539039096[/C][C]-7955.53903909617[/C][/ROW]
[ROW][C]81[/C][C]107968[/C][C]108680.323148218[/C][C]-712.323148217532[/C][/ROW]
[ROW][C]82[/C][C]99132[/C][C]106674.927862204[/C][C]-7542.92786220377[/C][/ROW]
[ROW][C]83[/C][C]89981[/C][C]101690.835217549[/C][C]-11709.835217549[/C][/ROW]
[ROW][C]84[/C][C]92928[/C][C]94725.7664202103[/C][C]-1797.7664202103[/C][/ROW]
[ROW][C]85[/C][C]98470[/C][C]91789.3921827795[/C][C]6680.60781722047[/C][/ROW]
[ROW][C]86[/C][C]91946[/C][C]92488.4510318976[/C][C]-542.451031897595[/C][/ROW]
[ROW][C]87[/C][C]92928[/C][C]90209.0404445191[/C][C]2718.95955548089[/C][/ROW]
[ROW][C]88[/C][C]89004[/C][C]89331.5238529158[/C][C]-327.523852915794[/C][/ROW]
[ROW][C]89[/C][C]97172[/C][C]87195.4964268291[/C][C]9976.50357317092[/C][/ROW]
[ROW][C]90[/C][C]98150[/C][C]89520.538876926[/C][C]8629.46112307395[/C][/ROW]
[ROW][C]91[/C][C]78524[/C][C]91491.3842735093[/C][C]-12967.3842735093[/C][/ROW]
[ROW][C]92[/C][C]77221[/C][C]84295.1051105055[/C][C]-7074.10511050549[/C][/ROW]
[ROW][C]93[/C][C]80799[/C][C]79355.673925801[/C][C]1443.32607419901[/C][/ROW]
[ROW][C]94[/C][C]71333[/C][C]77946.9806102949[/C][C]-6613.98061029491[/C][/ROW]
[ROW][C]95[/C][C]62817[/C][C]73077.2907687046[/C][C]-10260.2907687046[/C][/ROW]
[ROW][C]96[/C][C]65764[/C][C]66473.8104760186[/C][C]-709.810476018596[/C][/ROW]
[ROW][C]97[/C][C]72950[/C][C]63775.627876086[/C][C]9174.37212391396[/C][/ROW]
[ROW][C]98[/C][C]64462[/C][C]65347.6253891901[/C][C]-885.625389190071[/C][/ROW]
[ROW][C]99[/C][C]63799[/C][C]62768.3260408748[/C][C]1030.67395912522[/C][/ROW]
[ROW][C]100[/C][C]57244[/C][C]60999.6657619906[/C][C]-3755.66576199059[/C][/ROW]
[ROW][C]101[/C][C]64462[/C][C]57179.0395360389[/C][C]7282.96046396111[/C][/ROW]
[ROW][C]102[/C][C]66742[/C][C]58059.034242146[/C][C]8682.96575785401[/C][/ROW]
[ROW][C]103[/C][C]46448[/C][C]59714.0702706482[/C][C]-13266.0702706482[/C][/ROW]
[ROW][C]104[/C][C]46448[/C][C]52050.4781683784[/C][C]-5602.47816837835[/C][/ROW]
[ROW][C]105[/C][C]49391[/C][C]47404.5926378496[/C][C]1986.40736215041[/C][/ROW]
[ROW][C]106[/C][C]41542[/C][C]45920.6808677233[/C][C]-4378.68086772329[/C][/ROW]
[ROW][C]107[/C][C]32706[/C][C]41722.1683032028[/C][C]-9016.16830320282[/C][/ROW]
[ROW][C]108[/C][C]37297[/C][C]35411.5439243901[/C][C]1885.45607560992[/C][/ROW]
[ROW][C]109[/C][C]45466[/C][C]33620.8576672016[/C][C]11845.1423327984[/C][/ROW]
[ROW][C]110[/C][C]36631[/C][C]36192.9233644203[/C][C]438.076635579731[/C][/ROW]
[ROW][C]111[/C][C]40244[/C][C]34091.0678465171[/C][C]6152.93215348289[/C][/ROW]
[ROW][C]112[/C][C]35333[/C][C]34477.7127795897[/C][C]855.28722041026[/C][/ROW]
[ROW][C]113[/C][C]43186[/C][C]32708.7317957837[/C][C]10477.2682042163[/C][/ROW]
[ROW][C]114[/C][C]45813[/C][C]35132.299672509[/C][C]10680.700327491[/C][/ROW]
[ROW][C]115[/C][C]24853[/C][C]37885.6196511182[/C][C]-13032.6196511182[/C][/ROW]
[ROW][C]116[/C][C]23240[/C][C]30601.2350247338[/C][C]-7361.23502473376[/C][/ROW]
[ROW][C]117[/C][C]26502[/C][C]25475.9639650132[/C][C]1026.03603498677[/C][/ROW]
[ROW][C]118[/C][C]18649[/C][C]23818.3642255766[/C][C]-5169.36422557661[/C][/ROW]
[ROW][C]119[/C][C]12444[/C][C]19497.6144137533[/C][C]-7053.61441375332[/C][/ROW]
[ROW][C]120[/C][C]15040[/C][C]14240.5412714006[/C][C]799.458728599409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124088&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124088&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
3181234181264-30
4180598180934.98968869-336.989688689559
5187123180472.1534187856650.84658121518
6186807183032.0128360563774.98716394376
7181896184497.997340893-2601.99734089282
8178638183285.45332251-4647.45332250965
9178954181125.859200351-2171.85920035068
10178954179932.737541717-978.737541717041
11179269179206.9783580362.0216419701173
12179936178910.0100964621025.98990353831
13181580179032.52250082547.47749920035
14179616179838.520881205-222.520881205244
15181580179501.960529652078.03947035037
16179936180157.970705575-221.970705574524
17185158179864.4234780985293.5765219022
18187469181957.7254649025511.27453509835
19177656184267.468778079-6611.46877807853
20175025181446.905810441-6421.90581044095
21177305178556.140413207-1251.14041320683
22176989177759.775649053-770.775649052928
23175025177142.892017761-2117.89201776055
24175345175924.026560417-579.026560417027
25179269175323.7088103223945.29118967778
26178638176672.1357397891965.86426021089
27179269177253.0798651122015.92013488786
28179269177901.0503542021367.94964579761
29183545178314.4831152055230.51688479513
30184176180434.557411753741.44258824969
31172398182029.431376631-9631.43137663128
32172398177911.046869699-5513.04686969859
33176989175356.6816574081632.31834259161
34174709175774.00724894-1065.00724894021
35170785175059.193831902-4274.19383190159
36172398172928.078680152-530.078680151812
37176327172322.169043164004.83095684031
38174363173670.72591977692.274080229894
39174047173675.02468428371.975315719901
40169803173556.37594411-3753.37594411022
41176007171657.2320631364349.76793686362
42177305173185.7105953274119.28940467298
43164545174714.509334018-10169.5093340178
44164229170141.544403809-5912.54440380892
45170785167180.2938212653604.70617873524
46167176168210.156821502-1034.15682150229
47160967167311.349274963-6344.34927496317
48163598164085.793161564-487.793161564186
49166509163253.837251313255.1627486904
50167176164033.8704948083142.12950519242
51165212164839.92377619372.076223809709
52161287164517.102790418-3230.10279041776
53169456162640.6767828446815.3232171562
54169456165046.2591651494409.74083485079
55155078166565.706603149-11487.7066031495
56154101161292.452020293-7191.45202029345
57158025157617.56293277407.43706722997
58150838157072.355942015-6234.35594201542
59143616153656.148277505-10040.1482775046
60145932148445.737737982-2513.73773798201
61150838146267.9071609784570.09283902188
62146910147104.223099069-194.223099069
63144283145979.717102507-1696.71710250727
64138710144199.136601212-5489.13660121246
65146247140734.7570847395512.24291526122
66146563141914.8844497424648.11555025796
67132190142847.331137952-10657.3311379516
68131839137249.308097001-5410.30809700105
69134470133681.119317939788.880682061397
70126301132676.65474004-6375.6547400401
71117465128583.281370776-11118.2813707759
72121043122286.164294422-1243.16429442157
73125950120015.3535183385934.64648166229
74120728120828.736332047-100.736332046916
75120412119161.5211937831250.47880621716
76115154118077.974807814-2923.97480781408
77123670115212.8905057148457.10949428563
78125319117216.1159795868102.88402041436
79109266119260.680349041-9994.68034904133
80105688113643.539039096-7955.53903909617
81107968108680.323148218-712.323148217532
8299132106674.927862204-7542.92786220377
8389981101690.835217549-11709.835217549
849292894725.7664202103-1797.7664202103
859847091789.39218277956680.60781722047
869194692488.4510318976-542.451031897595
879292890209.04044451912718.95955548089
888900489331.5238529158-327.523852915794
899717287195.49642682919976.50357317092
909815089520.5388769268629.46112307395
917852491491.3842735093-12967.3842735093
927722184295.1051105055-7074.10511050549
938079979355.6739258011443.32607419901
947133377946.9806102949-6613.98061029491
956281773077.2907687046-10260.2907687046
966576466473.8104760186-709.810476018596
977295063775.6278760869174.37212391396
986446265347.6253891901-885.625389190071
996379962768.32604087481030.67395912522
1005724460999.6657619906-3755.66576199059
1016446257179.03953603897282.96046396111
1026674258059.0342421468682.96575785401
1034644859714.0702706482-13266.0702706482
1044644852050.4781683784-5602.47816837835
1054939147404.59263784961986.40736215041
1064154245920.6808677233-4378.68086772329
1073270641722.1683032028-9016.16830320282
1083729735411.54392439011885.45607560992
1094546633620.857667201611845.1423327984
1103663136192.9233644203438.076635579731
1114024434091.06784651716152.93215348289
1123533334477.7127795897855.28722041026
1134318632708.731795783710477.2682042163
1144581335132.29967250910680.700327491
1152485337885.6196511182-13032.6196511182
1162324030601.2350247338-7361.23502473376
1172650225475.96396501321026.03603498677
1181864923818.3642255766-5169.36422557661
1191244419497.6144137533-7053.61441375332
1201504014240.5412714006799.458728599409







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12112226.5615303043922.36989896380123530.7531616447
1229884.30449254425-2437.1387851183422205.7477702068
1237542.04745478425-5817.3729754073820901.4678849759
1245199.79041702425-9218.5663939414219618.1472279899
1252857.53337926424-12640.80448226518355.8712407935
126515.276341504243-16084.070621203317114.6233042118
127-1826.98069625576-19548.277426895815894.3160343843
128-4169.23773401576-23033.288372296114694.8129042646
129-6511.49477177576-26538.932973536313515.9434299848
130-8853.75180953577-30065.017600924812357.5139818532
131-11196.0088472958-33611.333258483711219.3155638922
132-13538.2658850558-37177.661228745210101.1294586337

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 12226.5615303043 & 922.369898963801 & 23530.7531616447 \tabularnewline
122 & 9884.30449254425 & -2437.13878511834 & 22205.7477702068 \tabularnewline
123 & 7542.04745478425 & -5817.37297540738 & 20901.4678849759 \tabularnewline
124 & 5199.79041702425 & -9218.56639394142 & 19618.1472279899 \tabularnewline
125 & 2857.53337926424 & -12640.804482265 & 18355.8712407935 \tabularnewline
126 & 515.276341504243 & -16084.0706212033 & 17114.6233042118 \tabularnewline
127 & -1826.98069625576 & -19548.2774268958 & 15894.3160343843 \tabularnewline
128 & -4169.23773401576 & -23033.2883722961 & 14694.8129042646 \tabularnewline
129 & -6511.49477177576 & -26538.9329735363 & 13515.9434299848 \tabularnewline
130 & -8853.75180953577 & -30065.0176009248 & 12357.5139818532 \tabularnewline
131 & -11196.0088472958 & -33611.3332584837 & 11219.3155638922 \tabularnewline
132 & -13538.2658850558 & -37177.6612287452 & 10101.1294586337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124088&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]12226.5615303043[/C][C]922.369898963801[/C][C]23530.7531616447[/C][/ROW]
[ROW][C]122[/C][C]9884.30449254425[/C][C]-2437.13878511834[/C][C]22205.7477702068[/C][/ROW]
[ROW][C]123[/C][C]7542.04745478425[/C][C]-5817.37297540738[/C][C]20901.4678849759[/C][/ROW]
[ROW][C]124[/C][C]5199.79041702425[/C][C]-9218.56639394142[/C][C]19618.1472279899[/C][/ROW]
[ROW][C]125[/C][C]2857.53337926424[/C][C]-12640.804482265[/C][C]18355.8712407935[/C][/ROW]
[ROW][C]126[/C][C]515.276341504243[/C][C]-16084.0706212033[/C][C]17114.6233042118[/C][/ROW]
[ROW][C]127[/C][C]-1826.98069625576[/C][C]-19548.2774268958[/C][C]15894.3160343843[/C][/ROW]
[ROW][C]128[/C][C]-4169.23773401576[/C][C]-23033.2883722961[/C][C]14694.8129042646[/C][/ROW]
[ROW][C]129[/C][C]-6511.49477177576[/C][C]-26538.9329735363[/C][C]13515.9434299848[/C][/ROW]
[ROW][C]130[/C][C]-8853.75180953577[/C][C]-30065.0176009248[/C][C]12357.5139818532[/C][/ROW]
[ROW][C]131[/C][C]-11196.0088472958[/C][C]-33611.3332584837[/C][C]11219.3155638922[/C][/ROW]
[ROW][C]132[/C][C]-13538.2658850558[/C][C]-37177.6612287452[/C][C]10101.1294586337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124088&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124088&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
12112226.5615303043922.36989896380123530.7531616447
1229884.30449254425-2437.1387851183422205.7477702068
1237542.04745478425-5817.3729754073820901.4678849759
1245199.79041702425-9218.5663939414219618.1472279899
1252857.53337926424-12640.80448226518355.8712407935
126515.276341504243-16084.070621203317114.6233042118
127-1826.98069625576-19548.277426895815894.3160343843
128-4169.23773401576-23033.288372296114694.8129042646
129-6511.49477177576-26538.932973536313515.9434299848
130-8853.75180953577-30065.017600924812357.5139818532
131-11196.0088472958-33611.333258483711219.3155638922
132-13538.2658850558-37177.661228745210101.1294586337



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