Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 12 Aug 2012 05:08:33 -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/2012/Aug/12/t1344762606wckfqhqg62dw91f.htm/, Retrieved Sun, 28 Apr 2024 07:17:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169227, Retrieved Sun, 28 Apr 2024 07:17:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVerbraken Frederik
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS A - STA...] [2012-08-12 09:08:33] [31886bd2f92a612f059dd2285dd41f3c] [Current]
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Dataseries X:
161949
161634
161287
160652
167176
166856
161949
158687
159007
159007
159323
159990
159990
157043
155745
157043
161634
160967
154763
149510
148527
146563
147892
149510
148874
147545
144950
147545
149856
149190
141656
138394
135132
132505
132190
134150
131523
130541
129559
135132
135768
132505
123670
119745
113541
110910
112208
114172
114172
112559
112208
117465
121710
119745
113190
109932
103061
98817
102079
105341
105341
101097
100781
106319
109932
108630
102079
97835
88652
85075
86372
91946
92261
84092
87039
94226
97488
95523
86692
80484
73297
67724
70004
74910
73613
66426
68706
75893
79821
77541
68706
64782
58893
52684
53666
58573
59208
53319
54302
62502
64462
61173
49075
42871
34671
26502
29129
32706
32075
25835
29444
38280
42204
40244
32391
26186
19631
12093
13427
15707




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169227&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169227&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169227&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0155382058176803
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0155382058176803 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169227&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0155382058176803[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169227&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169227&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
alpha1
beta0.0155382058176803
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3161287161319-32
4160652160971.502777414-319.502777413843
5167176160331.5382774996844.46172250094
6166856166961.888932455-105.888932454516
7161949166640.243608428-4691.24360842822
8158687161660.3500997-2973.35009969957
9159007158352.149573882654.85042611757
10159007158682.324774583324.675225416751
11159323158687.36964506635.630354940338
12159990159013.246200339976.753799661295
13159990159695.423201911294.576798088965
14157043159700.000396829-2657.00039682887
15155745156711.715377805-966.71537780526
16157043155398.6943552981644.3056447022
17161634156722.2439148324911.75608516764
18160967161389.56379181-422.563791809953
19154763160715.997908642-5952.9979086417
20149510154419.499001905-4909.499001905
21148527149090.214195952-563.214195951703
22146563148098.462857856-1535.46285785557
23147892146110.6045199451781.39548005519
24149510147467.2842095572042.71579044341
25148874149117.024347936-243.024347935541
26147545148477.248185599-932.248185598612
27144950147133.762721418-2183.76272141762
28147545144504.8309667953040.16903320476
29149856147147.0697389542708.93026104628
30149190149500.161654896-310.161654895608
31141656148829.342299265-7173.34229926509
32138394141183.881430218-2789.88143021843
33135132137878.531678349-2746.53167834878
34132505134573.855503846-2068.85550384581
35132190131914.70920122275.290798779984
36134150131603.9867263112546.01327368882
37131523133603.547204572-2080.5472045723
38130541130944.219233894-403.219233894255
39129559129955.953930448-396.953930448348
40135132128967.7859785776164.21402142309
41135768134636.5668047461131.43319525398
42132505135290.147246603-2785.14724660284
43123670131983.871055453-8313.87105545256
44119745123019.688415851-3274.68841585128
45113541119043.805633257-5502.80563325701
46110910112754.301906753-1844.30190675278
47112208110094.6447641362113.35523586429
48114172111425.4825127562746.51748724356
49114172113432.158466755739.841533244908
50112559113443.654276771-884.654276771122
51112208111816.908336541391.091663458836
52117465111471.9851993025993.01480069844
53121710116822.1058967434887.89410325678
54119745121143.055001335-1398.05500133465
55113190119156.331734979-5966.33173497947
56109932112508.625644505-2576.62564450481
57103061109210.589504925-6149.58950492537
5898817102244.035917504-3427.0359175036
5910207997946.78592807284132.21407192716
60105341101272.9931208054068.00687919484
61105341104598.202648962742.797351038171
62101097104609.744387083-3512.74438708309
63100781100311.162641812469.837358188306
64106319100002.4630713846316.53692861594
65109932105638.6107222364293.38927776413
66108630109318.322288489-688.322288489187
67102079108005.626995102-5926.62699510175
6897835101362.537845047-3527.53784504723
698865297063.7262359812-8411.72623598124
708507587750.0231024446-2675.02310244458
718637284131.45804291172240.54195708825
729194685463.27204498416482.72795501587
739226191138.00200620921122.99799379081
748409291470.4513801696-7378.45138016956
758703983186.80348400873852.19651599127
769422686193.65970632448032.34029367563
779748893505.46786300513982.53213699487
789552396829.3492670253-1306.34926702529
798669294844.0509432445-8152.05094324448
808048485886.3826978521-5402.38269785212
817329779594.439363587-6297.43936358704
826772472309.5884546313-4585.58845463126
837000466665.3366374283338.66336257198
847491068997.21347591165912.7865240884
857361373995.0875698789-382.087569878902
866642672692.1506145777-6266.15061457774
876870665407.78587664393298.21412335615
887589367739.03420652338153.96579347666
897982175052.73220525274768.2677947473
907754179054.8225316413-1513.8225316413
916870676751.3004455732-8045.30044557322
926478267791.2909113848-3009.29091138483
935889363820.5319298385-4927.53192983846
945268457854.9669245394-5170.96692453943
955366651565.61937618952100.38062381048
965857352580.25552261785992.74447738224
975920857580.37201972011627.62798027991
985331958240.6624382723-4921.66243827229
995430252275.18863434132026.81136565873
1006250253289.68164649459212.3183535055
1016446261632.82454512932829.17545487075
1026117363636.7848556414-2463.78485564137
1034907560309.5020594639-11234.5020594639
1044287148036.9380542048-5165.93805420482
1053467141752.6686454772-7081.6686454772
1062650233442.6322205312-6940.63222053116
1072912925165.78724858373963.21275141627
1083270627854.36846401454851.63153598551
1093207531506.7541133722568.245886627821
1102583530884.5836349137-5049.58363491365
1112944424566.12216510084877.87783489923
1123828028250.915634852910029.0843651471
1134220437242.74961188154961.25038811853
1144024441243.8385415251-999.838541525103
1153239139268.3028444824-6877.30284448244
1162618631308.4418974144-5122.44189741435
1171963125023.8483409232-5392.84834092322
1181209318385.0531534584-6292.05315345842
1191342710749.28593654422677.7140634558
1201570712124.89280878313582.10719121693

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 161287 & 161319 & -32 \tabularnewline
4 & 160652 & 160971.502777414 & -319.502777413843 \tabularnewline
5 & 167176 & 160331.538277499 & 6844.46172250094 \tabularnewline
6 & 166856 & 166961.888932455 & -105.888932454516 \tabularnewline
7 & 161949 & 166640.243608428 & -4691.24360842822 \tabularnewline
8 & 158687 & 161660.3500997 & -2973.35009969957 \tabularnewline
9 & 159007 & 158352.149573882 & 654.85042611757 \tabularnewline
10 & 159007 & 158682.324774583 & 324.675225416751 \tabularnewline
11 & 159323 & 158687.36964506 & 635.630354940338 \tabularnewline
12 & 159990 & 159013.246200339 & 976.753799661295 \tabularnewline
13 & 159990 & 159695.423201911 & 294.576798088965 \tabularnewline
14 & 157043 & 159700.000396829 & -2657.00039682887 \tabularnewline
15 & 155745 & 156711.715377805 & -966.71537780526 \tabularnewline
16 & 157043 & 155398.694355298 & 1644.3056447022 \tabularnewline
17 & 161634 & 156722.243914832 & 4911.75608516764 \tabularnewline
18 & 160967 & 161389.56379181 & -422.563791809953 \tabularnewline
19 & 154763 & 160715.997908642 & -5952.9979086417 \tabularnewline
20 & 149510 & 154419.499001905 & -4909.499001905 \tabularnewline
21 & 148527 & 149090.214195952 & -563.214195951703 \tabularnewline
22 & 146563 & 148098.462857856 & -1535.46285785557 \tabularnewline
23 & 147892 & 146110.604519945 & 1781.39548005519 \tabularnewline
24 & 149510 & 147467.284209557 & 2042.71579044341 \tabularnewline
25 & 148874 & 149117.024347936 & -243.024347935541 \tabularnewline
26 & 147545 & 148477.248185599 & -932.248185598612 \tabularnewline
27 & 144950 & 147133.762721418 & -2183.76272141762 \tabularnewline
28 & 147545 & 144504.830966795 & 3040.16903320476 \tabularnewline
29 & 149856 & 147147.069738954 & 2708.93026104628 \tabularnewline
30 & 149190 & 149500.161654896 & -310.161654895608 \tabularnewline
31 & 141656 & 148829.342299265 & -7173.34229926509 \tabularnewline
32 & 138394 & 141183.881430218 & -2789.88143021843 \tabularnewline
33 & 135132 & 137878.531678349 & -2746.53167834878 \tabularnewline
34 & 132505 & 134573.855503846 & -2068.85550384581 \tabularnewline
35 & 132190 & 131914.70920122 & 275.290798779984 \tabularnewline
36 & 134150 & 131603.986726311 & 2546.01327368882 \tabularnewline
37 & 131523 & 133603.547204572 & -2080.5472045723 \tabularnewline
38 & 130541 & 130944.219233894 & -403.219233894255 \tabularnewline
39 & 129559 & 129955.953930448 & -396.953930448348 \tabularnewline
40 & 135132 & 128967.785978577 & 6164.21402142309 \tabularnewline
41 & 135768 & 134636.566804746 & 1131.43319525398 \tabularnewline
42 & 132505 & 135290.147246603 & -2785.14724660284 \tabularnewline
43 & 123670 & 131983.871055453 & -8313.87105545256 \tabularnewline
44 & 119745 & 123019.688415851 & -3274.68841585128 \tabularnewline
45 & 113541 & 119043.805633257 & -5502.80563325701 \tabularnewline
46 & 110910 & 112754.301906753 & -1844.30190675278 \tabularnewline
47 & 112208 & 110094.644764136 & 2113.35523586429 \tabularnewline
48 & 114172 & 111425.482512756 & 2746.51748724356 \tabularnewline
49 & 114172 & 113432.158466755 & 739.841533244908 \tabularnewline
50 & 112559 & 113443.654276771 & -884.654276771122 \tabularnewline
51 & 112208 & 111816.908336541 & 391.091663458836 \tabularnewline
52 & 117465 & 111471.985199302 & 5993.01480069844 \tabularnewline
53 & 121710 & 116822.105896743 & 4887.89410325678 \tabularnewline
54 & 119745 & 121143.055001335 & -1398.05500133465 \tabularnewline
55 & 113190 & 119156.331734979 & -5966.33173497947 \tabularnewline
56 & 109932 & 112508.625644505 & -2576.62564450481 \tabularnewline
57 & 103061 & 109210.589504925 & -6149.58950492537 \tabularnewline
58 & 98817 & 102244.035917504 & -3427.0359175036 \tabularnewline
59 & 102079 & 97946.7859280728 & 4132.21407192716 \tabularnewline
60 & 105341 & 101272.993120805 & 4068.00687919484 \tabularnewline
61 & 105341 & 104598.202648962 & 742.797351038171 \tabularnewline
62 & 101097 & 104609.744387083 & -3512.74438708309 \tabularnewline
63 & 100781 & 100311.162641812 & 469.837358188306 \tabularnewline
64 & 106319 & 100002.463071384 & 6316.53692861594 \tabularnewline
65 & 109932 & 105638.610722236 & 4293.38927776413 \tabularnewline
66 & 108630 & 109318.322288489 & -688.322288489187 \tabularnewline
67 & 102079 & 108005.626995102 & -5926.62699510175 \tabularnewline
68 & 97835 & 101362.537845047 & -3527.53784504723 \tabularnewline
69 & 88652 & 97063.7262359812 & -8411.72623598124 \tabularnewline
70 & 85075 & 87750.0231024446 & -2675.02310244458 \tabularnewline
71 & 86372 & 84131.4580429117 & 2240.54195708825 \tabularnewline
72 & 91946 & 85463.2720449841 & 6482.72795501587 \tabularnewline
73 & 92261 & 91138.0020062092 & 1122.99799379081 \tabularnewline
74 & 84092 & 91470.4513801696 & -7378.45138016956 \tabularnewline
75 & 87039 & 83186.8034840087 & 3852.19651599127 \tabularnewline
76 & 94226 & 86193.6597063244 & 8032.34029367563 \tabularnewline
77 & 97488 & 93505.4678630051 & 3982.53213699487 \tabularnewline
78 & 95523 & 96829.3492670253 & -1306.34926702529 \tabularnewline
79 & 86692 & 94844.0509432445 & -8152.05094324448 \tabularnewline
80 & 80484 & 85886.3826978521 & -5402.38269785212 \tabularnewline
81 & 73297 & 79594.439363587 & -6297.43936358704 \tabularnewline
82 & 67724 & 72309.5884546313 & -4585.58845463126 \tabularnewline
83 & 70004 & 66665.336637428 & 3338.66336257198 \tabularnewline
84 & 74910 & 68997.2134759116 & 5912.7865240884 \tabularnewline
85 & 73613 & 73995.0875698789 & -382.087569878902 \tabularnewline
86 & 66426 & 72692.1506145777 & -6266.15061457774 \tabularnewline
87 & 68706 & 65407.7858766439 & 3298.21412335615 \tabularnewline
88 & 75893 & 67739.0342065233 & 8153.96579347666 \tabularnewline
89 & 79821 & 75052.7322052527 & 4768.2677947473 \tabularnewline
90 & 77541 & 79054.8225316413 & -1513.8225316413 \tabularnewline
91 & 68706 & 76751.3004455732 & -8045.30044557322 \tabularnewline
92 & 64782 & 67791.2909113848 & -3009.29091138483 \tabularnewline
93 & 58893 & 63820.5319298385 & -4927.53192983846 \tabularnewline
94 & 52684 & 57854.9669245394 & -5170.96692453943 \tabularnewline
95 & 53666 & 51565.6193761895 & 2100.38062381048 \tabularnewline
96 & 58573 & 52580.2555226178 & 5992.74447738224 \tabularnewline
97 & 59208 & 57580.3720197201 & 1627.62798027991 \tabularnewline
98 & 53319 & 58240.6624382723 & -4921.66243827229 \tabularnewline
99 & 54302 & 52275.1886343413 & 2026.81136565873 \tabularnewline
100 & 62502 & 53289.6816464945 & 9212.3183535055 \tabularnewline
101 & 64462 & 61632.8245451293 & 2829.17545487075 \tabularnewline
102 & 61173 & 63636.7848556414 & -2463.78485564137 \tabularnewline
103 & 49075 & 60309.5020594639 & -11234.5020594639 \tabularnewline
104 & 42871 & 48036.9380542048 & -5165.93805420482 \tabularnewline
105 & 34671 & 41752.6686454772 & -7081.6686454772 \tabularnewline
106 & 26502 & 33442.6322205312 & -6940.63222053116 \tabularnewline
107 & 29129 & 25165.7872485837 & 3963.21275141627 \tabularnewline
108 & 32706 & 27854.3684640145 & 4851.63153598551 \tabularnewline
109 & 32075 & 31506.7541133722 & 568.245886627821 \tabularnewline
110 & 25835 & 30884.5836349137 & -5049.58363491365 \tabularnewline
111 & 29444 & 24566.1221651008 & 4877.87783489923 \tabularnewline
112 & 38280 & 28250.9156348529 & 10029.0843651471 \tabularnewline
113 & 42204 & 37242.7496118815 & 4961.25038811853 \tabularnewline
114 & 40244 & 41243.8385415251 & -999.838541525103 \tabularnewline
115 & 32391 & 39268.3028444824 & -6877.30284448244 \tabularnewline
116 & 26186 & 31308.4418974144 & -5122.44189741435 \tabularnewline
117 & 19631 & 25023.8483409232 & -5392.84834092322 \tabularnewline
118 & 12093 & 18385.0531534584 & -6292.05315345842 \tabularnewline
119 & 13427 & 10749.2859365442 & 2677.7140634558 \tabularnewline
120 & 15707 & 12124.8928087831 & 3582.10719121693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169227&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]161287[/C][C]161319[/C][C]-32[/C][/ROW]
[ROW][C]4[/C][C]160652[/C][C]160971.502777414[/C][C]-319.502777413843[/C][/ROW]
[ROW][C]5[/C][C]167176[/C][C]160331.538277499[/C][C]6844.46172250094[/C][/ROW]
[ROW][C]6[/C][C]166856[/C][C]166961.888932455[/C][C]-105.888932454516[/C][/ROW]
[ROW][C]7[/C][C]161949[/C][C]166640.243608428[/C][C]-4691.24360842822[/C][/ROW]
[ROW][C]8[/C][C]158687[/C][C]161660.3500997[/C][C]-2973.35009969957[/C][/ROW]
[ROW][C]9[/C][C]159007[/C][C]158352.149573882[/C][C]654.85042611757[/C][/ROW]
[ROW][C]10[/C][C]159007[/C][C]158682.324774583[/C][C]324.675225416751[/C][/ROW]
[ROW][C]11[/C][C]159323[/C][C]158687.36964506[/C][C]635.630354940338[/C][/ROW]
[ROW][C]12[/C][C]159990[/C][C]159013.246200339[/C][C]976.753799661295[/C][/ROW]
[ROW][C]13[/C][C]159990[/C][C]159695.423201911[/C][C]294.576798088965[/C][/ROW]
[ROW][C]14[/C][C]157043[/C][C]159700.000396829[/C][C]-2657.00039682887[/C][/ROW]
[ROW][C]15[/C][C]155745[/C][C]156711.715377805[/C][C]-966.71537780526[/C][/ROW]
[ROW][C]16[/C][C]157043[/C][C]155398.694355298[/C][C]1644.3056447022[/C][/ROW]
[ROW][C]17[/C][C]161634[/C][C]156722.243914832[/C][C]4911.75608516764[/C][/ROW]
[ROW][C]18[/C][C]160967[/C][C]161389.56379181[/C][C]-422.563791809953[/C][/ROW]
[ROW][C]19[/C][C]154763[/C][C]160715.997908642[/C][C]-5952.9979086417[/C][/ROW]
[ROW][C]20[/C][C]149510[/C][C]154419.499001905[/C][C]-4909.499001905[/C][/ROW]
[ROW][C]21[/C][C]148527[/C][C]149090.214195952[/C][C]-563.214195951703[/C][/ROW]
[ROW][C]22[/C][C]146563[/C][C]148098.462857856[/C][C]-1535.46285785557[/C][/ROW]
[ROW][C]23[/C][C]147892[/C][C]146110.604519945[/C][C]1781.39548005519[/C][/ROW]
[ROW][C]24[/C][C]149510[/C][C]147467.284209557[/C][C]2042.71579044341[/C][/ROW]
[ROW][C]25[/C][C]148874[/C][C]149117.024347936[/C][C]-243.024347935541[/C][/ROW]
[ROW][C]26[/C][C]147545[/C][C]148477.248185599[/C][C]-932.248185598612[/C][/ROW]
[ROW][C]27[/C][C]144950[/C][C]147133.762721418[/C][C]-2183.76272141762[/C][/ROW]
[ROW][C]28[/C][C]147545[/C][C]144504.830966795[/C][C]3040.16903320476[/C][/ROW]
[ROW][C]29[/C][C]149856[/C][C]147147.069738954[/C][C]2708.93026104628[/C][/ROW]
[ROW][C]30[/C][C]149190[/C][C]149500.161654896[/C][C]-310.161654895608[/C][/ROW]
[ROW][C]31[/C][C]141656[/C][C]148829.342299265[/C][C]-7173.34229926509[/C][/ROW]
[ROW][C]32[/C][C]138394[/C][C]141183.881430218[/C][C]-2789.88143021843[/C][/ROW]
[ROW][C]33[/C][C]135132[/C][C]137878.531678349[/C][C]-2746.53167834878[/C][/ROW]
[ROW][C]34[/C][C]132505[/C][C]134573.855503846[/C][C]-2068.85550384581[/C][/ROW]
[ROW][C]35[/C][C]132190[/C][C]131914.70920122[/C][C]275.290798779984[/C][/ROW]
[ROW][C]36[/C][C]134150[/C][C]131603.986726311[/C][C]2546.01327368882[/C][/ROW]
[ROW][C]37[/C][C]131523[/C][C]133603.547204572[/C][C]-2080.5472045723[/C][/ROW]
[ROW][C]38[/C][C]130541[/C][C]130944.219233894[/C][C]-403.219233894255[/C][/ROW]
[ROW][C]39[/C][C]129559[/C][C]129955.953930448[/C][C]-396.953930448348[/C][/ROW]
[ROW][C]40[/C][C]135132[/C][C]128967.785978577[/C][C]6164.21402142309[/C][/ROW]
[ROW][C]41[/C][C]135768[/C][C]134636.566804746[/C][C]1131.43319525398[/C][/ROW]
[ROW][C]42[/C][C]132505[/C][C]135290.147246603[/C][C]-2785.14724660284[/C][/ROW]
[ROW][C]43[/C][C]123670[/C][C]131983.871055453[/C][C]-8313.87105545256[/C][/ROW]
[ROW][C]44[/C][C]119745[/C][C]123019.688415851[/C][C]-3274.68841585128[/C][/ROW]
[ROW][C]45[/C][C]113541[/C][C]119043.805633257[/C][C]-5502.80563325701[/C][/ROW]
[ROW][C]46[/C][C]110910[/C][C]112754.301906753[/C][C]-1844.30190675278[/C][/ROW]
[ROW][C]47[/C][C]112208[/C][C]110094.644764136[/C][C]2113.35523586429[/C][/ROW]
[ROW][C]48[/C][C]114172[/C][C]111425.482512756[/C][C]2746.51748724356[/C][/ROW]
[ROW][C]49[/C][C]114172[/C][C]113432.158466755[/C][C]739.841533244908[/C][/ROW]
[ROW][C]50[/C][C]112559[/C][C]113443.654276771[/C][C]-884.654276771122[/C][/ROW]
[ROW][C]51[/C][C]112208[/C][C]111816.908336541[/C][C]391.091663458836[/C][/ROW]
[ROW][C]52[/C][C]117465[/C][C]111471.985199302[/C][C]5993.01480069844[/C][/ROW]
[ROW][C]53[/C][C]121710[/C][C]116822.105896743[/C][C]4887.89410325678[/C][/ROW]
[ROW][C]54[/C][C]119745[/C][C]121143.055001335[/C][C]-1398.05500133465[/C][/ROW]
[ROW][C]55[/C][C]113190[/C][C]119156.331734979[/C][C]-5966.33173497947[/C][/ROW]
[ROW][C]56[/C][C]109932[/C][C]112508.625644505[/C][C]-2576.62564450481[/C][/ROW]
[ROW][C]57[/C][C]103061[/C][C]109210.589504925[/C][C]-6149.58950492537[/C][/ROW]
[ROW][C]58[/C][C]98817[/C][C]102244.035917504[/C][C]-3427.0359175036[/C][/ROW]
[ROW][C]59[/C][C]102079[/C][C]97946.7859280728[/C][C]4132.21407192716[/C][/ROW]
[ROW][C]60[/C][C]105341[/C][C]101272.993120805[/C][C]4068.00687919484[/C][/ROW]
[ROW][C]61[/C][C]105341[/C][C]104598.202648962[/C][C]742.797351038171[/C][/ROW]
[ROW][C]62[/C][C]101097[/C][C]104609.744387083[/C][C]-3512.74438708309[/C][/ROW]
[ROW][C]63[/C][C]100781[/C][C]100311.162641812[/C][C]469.837358188306[/C][/ROW]
[ROW][C]64[/C][C]106319[/C][C]100002.463071384[/C][C]6316.53692861594[/C][/ROW]
[ROW][C]65[/C][C]109932[/C][C]105638.610722236[/C][C]4293.38927776413[/C][/ROW]
[ROW][C]66[/C][C]108630[/C][C]109318.322288489[/C][C]-688.322288489187[/C][/ROW]
[ROW][C]67[/C][C]102079[/C][C]108005.626995102[/C][C]-5926.62699510175[/C][/ROW]
[ROW][C]68[/C][C]97835[/C][C]101362.537845047[/C][C]-3527.53784504723[/C][/ROW]
[ROW][C]69[/C][C]88652[/C][C]97063.7262359812[/C][C]-8411.72623598124[/C][/ROW]
[ROW][C]70[/C][C]85075[/C][C]87750.0231024446[/C][C]-2675.02310244458[/C][/ROW]
[ROW][C]71[/C][C]86372[/C][C]84131.4580429117[/C][C]2240.54195708825[/C][/ROW]
[ROW][C]72[/C][C]91946[/C][C]85463.2720449841[/C][C]6482.72795501587[/C][/ROW]
[ROW][C]73[/C][C]92261[/C][C]91138.0020062092[/C][C]1122.99799379081[/C][/ROW]
[ROW][C]74[/C][C]84092[/C][C]91470.4513801696[/C][C]-7378.45138016956[/C][/ROW]
[ROW][C]75[/C][C]87039[/C][C]83186.8034840087[/C][C]3852.19651599127[/C][/ROW]
[ROW][C]76[/C][C]94226[/C][C]86193.6597063244[/C][C]8032.34029367563[/C][/ROW]
[ROW][C]77[/C][C]97488[/C][C]93505.4678630051[/C][C]3982.53213699487[/C][/ROW]
[ROW][C]78[/C][C]95523[/C][C]96829.3492670253[/C][C]-1306.34926702529[/C][/ROW]
[ROW][C]79[/C][C]86692[/C][C]94844.0509432445[/C][C]-8152.05094324448[/C][/ROW]
[ROW][C]80[/C][C]80484[/C][C]85886.3826978521[/C][C]-5402.38269785212[/C][/ROW]
[ROW][C]81[/C][C]73297[/C][C]79594.439363587[/C][C]-6297.43936358704[/C][/ROW]
[ROW][C]82[/C][C]67724[/C][C]72309.5884546313[/C][C]-4585.58845463126[/C][/ROW]
[ROW][C]83[/C][C]70004[/C][C]66665.336637428[/C][C]3338.66336257198[/C][/ROW]
[ROW][C]84[/C][C]74910[/C][C]68997.2134759116[/C][C]5912.7865240884[/C][/ROW]
[ROW][C]85[/C][C]73613[/C][C]73995.0875698789[/C][C]-382.087569878902[/C][/ROW]
[ROW][C]86[/C][C]66426[/C][C]72692.1506145777[/C][C]-6266.15061457774[/C][/ROW]
[ROW][C]87[/C][C]68706[/C][C]65407.7858766439[/C][C]3298.21412335615[/C][/ROW]
[ROW][C]88[/C][C]75893[/C][C]67739.0342065233[/C][C]8153.96579347666[/C][/ROW]
[ROW][C]89[/C][C]79821[/C][C]75052.7322052527[/C][C]4768.2677947473[/C][/ROW]
[ROW][C]90[/C][C]77541[/C][C]79054.8225316413[/C][C]-1513.8225316413[/C][/ROW]
[ROW][C]91[/C][C]68706[/C][C]76751.3004455732[/C][C]-8045.30044557322[/C][/ROW]
[ROW][C]92[/C][C]64782[/C][C]67791.2909113848[/C][C]-3009.29091138483[/C][/ROW]
[ROW][C]93[/C][C]58893[/C][C]63820.5319298385[/C][C]-4927.53192983846[/C][/ROW]
[ROW][C]94[/C][C]52684[/C][C]57854.9669245394[/C][C]-5170.96692453943[/C][/ROW]
[ROW][C]95[/C][C]53666[/C][C]51565.6193761895[/C][C]2100.38062381048[/C][/ROW]
[ROW][C]96[/C][C]58573[/C][C]52580.2555226178[/C][C]5992.74447738224[/C][/ROW]
[ROW][C]97[/C][C]59208[/C][C]57580.3720197201[/C][C]1627.62798027991[/C][/ROW]
[ROW][C]98[/C][C]53319[/C][C]58240.6624382723[/C][C]-4921.66243827229[/C][/ROW]
[ROW][C]99[/C][C]54302[/C][C]52275.1886343413[/C][C]2026.81136565873[/C][/ROW]
[ROW][C]100[/C][C]62502[/C][C]53289.6816464945[/C][C]9212.3183535055[/C][/ROW]
[ROW][C]101[/C][C]64462[/C][C]61632.8245451293[/C][C]2829.17545487075[/C][/ROW]
[ROW][C]102[/C][C]61173[/C][C]63636.7848556414[/C][C]-2463.78485564137[/C][/ROW]
[ROW][C]103[/C][C]49075[/C][C]60309.5020594639[/C][C]-11234.5020594639[/C][/ROW]
[ROW][C]104[/C][C]42871[/C][C]48036.9380542048[/C][C]-5165.93805420482[/C][/ROW]
[ROW][C]105[/C][C]34671[/C][C]41752.6686454772[/C][C]-7081.6686454772[/C][/ROW]
[ROW][C]106[/C][C]26502[/C][C]33442.6322205312[/C][C]-6940.63222053116[/C][/ROW]
[ROW][C]107[/C][C]29129[/C][C]25165.7872485837[/C][C]3963.21275141627[/C][/ROW]
[ROW][C]108[/C][C]32706[/C][C]27854.3684640145[/C][C]4851.63153598551[/C][/ROW]
[ROW][C]109[/C][C]32075[/C][C]31506.7541133722[/C][C]568.245886627821[/C][/ROW]
[ROW][C]110[/C][C]25835[/C][C]30884.5836349137[/C][C]-5049.58363491365[/C][/ROW]
[ROW][C]111[/C][C]29444[/C][C]24566.1221651008[/C][C]4877.87783489923[/C][/ROW]
[ROW][C]112[/C][C]38280[/C][C]28250.9156348529[/C][C]10029.0843651471[/C][/ROW]
[ROW][C]113[/C][C]42204[/C][C]37242.7496118815[/C][C]4961.25038811853[/C][/ROW]
[ROW][C]114[/C][C]40244[/C][C]41243.8385415251[/C][C]-999.838541525103[/C][/ROW]
[ROW][C]115[/C][C]32391[/C][C]39268.3028444824[/C][C]-6877.30284448244[/C][/ROW]
[ROW][C]116[/C][C]26186[/C][C]31308.4418974144[/C][C]-5122.44189741435[/C][/ROW]
[ROW][C]117[/C][C]19631[/C][C]25023.8483409232[/C][C]-5392.84834092322[/C][/ROW]
[ROW][C]118[/C][C]12093[/C][C]18385.0531534584[/C][C]-6292.05315345842[/C][/ROW]
[ROW][C]119[/C][C]13427[/C][C]10749.2859365442[/C][C]2677.7140634558[/C][/ROW]
[ROW][C]120[/C][C]15707[/C][C]12124.8928087831[/C][C]3582.10719121693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169227&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169227&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
3161287161319-32
4160652160971.502777414-319.502777413843
5167176160331.5382774996844.46172250094
6166856166961.888932455-105.888932454516
7161949166640.243608428-4691.24360842822
8158687161660.3500997-2973.35009969957
9159007158352.149573882654.85042611757
10159007158682.324774583324.675225416751
11159323158687.36964506635.630354940338
12159990159013.246200339976.753799661295
13159990159695.423201911294.576798088965
14157043159700.000396829-2657.00039682887
15155745156711.715377805-966.71537780526
16157043155398.6943552981644.3056447022
17161634156722.2439148324911.75608516764
18160967161389.56379181-422.563791809953
19154763160715.997908642-5952.9979086417
20149510154419.499001905-4909.499001905
21148527149090.214195952-563.214195951703
22146563148098.462857856-1535.46285785557
23147892146110.6045199451781.39548005519
24149510147467.2842095572042.71579044341
25148874149117.024347936-243.024347935541
26147545148477.248185599-932.248185598612
27144950147133.762721418-2183.76272141762
28147545144504.8309667953040.16903320476
29149856147147.0697389542708.93026104628
30149190149500.161654896-310.161654895608
31141656148829.342299265-7173.34229926509
32138394141183.881430218-2789.88143021843
33135132137878.531678349-2746.53167834878
34132505134573.855503846-2068.85550384581
35132190131914.70920122275.290798779984
36134150131603.9867263112546.01327368882
37131523133603.547204572-2080.5472045723
38130541130944.219233894-403.219233894255
39129559129955.953930448-396.953930448348
40135132128967.7859785776164.21402142309
41135768134636.5668047461131.43319525398
42132505135290.147246603-2785.14724660284
43123670131983.871055453-8313.87105545256
44119745123019.688415851-3274.68841585128
45113541119043.805633257-5502.80563325701
46110910112754.301906753-1844.30190675278
47112208110094.6447641362113.35523586429
48114172111425.4825127562746.51748724356
49114172113432.158466755739.841533244908
50112559113443.654276771-884.654276771122
51112208111816.908336541391.091663458836
52117465111471.9851993025993.01480069844
53121710116822.1058967434887.89410325678
54119745121143.055001335-1398.05500133465
55113190119156.331734979-5966.33173497947
56109932112508.625644505-2576.62564450481
57103061109210.589504925-6149.58950492537
5898817102244.035917504-3427.0359175036
5910207997946.78592807284132.21407192716
60105341101272.9931208054068.00687919484
61105341104598.202648962742.797351038171
62101097104609.744387083-3512.74438708309
63100781100311.162641812469.837358188306
64106319100002.4630713846316.53692861594
65109932105638.6107222364293.38927776413
66108630109318.322288489-688.322288489187
67102079108005.626995102-5926.62699510175
6897835101362.537845047-3527.53784504723
698865297063.7262359812-8411.72623598124
708507587750.0231024446-2675.02310244458
718637284131.45804291172240.54195708825
729194685463.27204498416482.72795501587
739226191138.00200620921122.99799379081
748409291470.4513801696-7378.45138016956
758703983186.80348400873852.19651599127
769422686193.65970632448032.34029367563
779748893505.46786300513982.53213699487
789552396829.3492670253-1306.34926702529
798669294844.0509432445-8152.05094324448
808048485886.3826978521-5402.38269785212
817329779594.439363587-6297.43936358704
826772472309.5884546313-4585.58845463126
837000466665.3366374283338.66336257198
847491068997.21347591165912.7865240884
857361373995.0875698789-382.087569878902
866642672692.1506145777-6266.15061457774
876870665407.78587664393298.21412335615
887589367739.03420652338153.96579347666
897982175052.73220525274768.2677947473
907754179054.8225316413-1513.8225316413
916870676751.3004455732-8045.30044557322
926478267791.2909113848-3009.29091138483
935889363820.5319298385-4927.53192983846
945268457854.9669245394-5170.96692453943
955366651565.61937618952100.38062381048
965857352580.25552261785992.74447738224
975920857580.37201972011627.62798027991
985331958240.6624382723-4921.66243827229
995430252275.18863434132026.81136565873
1006250253289.68164649459212.3183535055
1016446261632.82454512932829.17545487075
1026117363636.7848556414-2463.78485564137
1034907560309.5020594639-11234.5020594639
1044287148036.9380542048-5165.93805420482
1053467141752.6686454772-7081.6686454772
1062650233442.6322205312-6940.63222053116
1072912925165.78724858373963.21275141627
1083270627854.36846401454851.63153598551
1093207531506.7541133722568.245886627821
1102583530884.5836349137-5049.58363491365
1112944424566.12216510084877.87783489923
1123828028250.915634852910029.0843651471
1134220437242.74961188154961.25038811853
1144024441243.8385415251-999.838541525103
1153239139268.3028444824-6877.30284448244
1162618631308.4418974144-5122.44189741435
1171963125023.8483409232-5392.84834092322
1181209318385.0531534584-6292.05315345842
1191342710749.28593654422677.7140634558
1201570712124.89280878313582.10719121693







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12114460.55232758125799.6466556633223121.4579994991
12213214.1046551624870.20874816732625558.0005621574
12311967.6569827436-3267.7510571093827203.0650225965
12410721.2093103248-7006.8809370291328449.2995576787
1259474.76163790595-10497.983892477729447.5071682896
1268228.31396548714-13817.774566867730274.402497842
1276981.86629306834-17011.461348370630975.1939345072
1285735.41862064953-20108.266102057631579.1033433567
1294488.97094823072-23128.325201363432106.2670978249
1303242.52327581191-26086.183000441432571.2295520653
1311996.0756033931-28992.731352441132984.8825592273
132749.62793097429-31856.363873634933355.6197355834

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 14460.5523275812 & 5799.64665566332 & 23121.4579994991 \tabularnewline
122 & 13214.1046551624 & 870.208748167326 & 25558.0005621574 \tabularnewline
123 & 11967.6569827436 & -3267.75105710938 & 27203.0650225965 \tabularnewline
124 & 10721.2093103248 & -7006.88093702913 & 28449.2995576787 \tabularnewline
125 & 9474.76163790595 & -10497.9838924777 & 29447.5071682896 \tabularnewline
126 & 8228.31396548714 & -13817.7745668677 & 30274.402497842 \tabularnewline
127 & 6981.86629306834 & -17011.4613483706 & 30975.1939345072 \tabularnewline
128 & 5735.41862064953 & -20108.2661020576 & 31579.1033433567 \tabularnewline
129 & 4488.97094823072 & -23128.3252013634 & 32106.2670978249 \tabularnewline
130 & 3242.52327581191 & -26086.1830004414 & 32571.2295520653 \tabularnewline
131 & 1996.0756033931 & -28992.7313524411 & 32984.8825592273 \tabularnewline
132 & 749.62793097429 & -31856.3638736349 & 33355.6197355834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169227&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]14460.5523275812[/C][C]5799.64665566332[/C][C]23121.4579994991[/C][/ROW]
[ROW][C]122[/C][C]13214.1046551624[/C][C]870.208748167326[/C][C]25558.0005621574[/C][/ROW]
[ROW][C]123[/C][C]11967.6569827436[/C][C]-3267.75105710938[/C][C]27203.0650225965[/C][/ROW]
[ROW][C]124[/C][C]10721.2093103248[/C][C]-7006.88093702913[/C][C]28449.2995576787[/C][/ROW]
[ROW][C]125[/C][C]9474.76163790595[/C][C]-10497.9838924777[/C][C]29447.5071682896[/C][/ROW]
[ROW][C]126[/C][C]8228.31396548714[/C][C]-13817.7745668677[/C][C]30274.402497842[/C][/ROW]
[ROW][C]127[/C][C]6981.86629306834[/C][C]-17011.4613483706[/C][C]30975.1939345072[/C][/ROW]
[ROW][C]128[/C][C]5735.41862064953[/C][C]-20108.2661020576[/C][C]31579.1033433567[/C][/ROW]
[ROW][C]129[/C][C]4488.97094823072[/C][C]-23128.3252013634[/C][C]32106.2670978249[/C][/ROW]
[ROW][C]130[/C][C]3242.52327581191[/C][C]-26086.1830004414[/C][C]32571.2295520653[/C][/ROW]
[ROW][C]131[/C][C]1996.0756033931[/C][C]-28992.7313524411[/C][C]32984.8825592273[/C][/ROW]
[ROW][C]132[/C][C]749.62793097429[/C][C]-31856.3638736349[/C][C]33355.6197355834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169227&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169227&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
12114460.55232758125799.6466556633223121.4579994991
12213214.1046551624870.20874816732625558.0005621574
12311967.6569827436-3267.7510571093827203.0650225965
12410721.2093103248-7006.8809370291328449.2995576787
1259474.76163790595-10497.983892477729447.5071682896
1268228.31396548714-13817.774566867730274.402497842
1276981.86629306834-17011.461348370630975.1939345072
1285735.41862064953-20108.266102057631579.1033433567
1294488.97094823072-23128.325201363432106.2670978249
1303242.52327581191-26086.183000441432571.2295520653
1311996.0756033931-28992.731352441132984.8825592273
132749.62793097429-31856.363873634933355.6197355834



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')