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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 11:36:15 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t14811069975c7jd4rn6jsepbt.htm/, Retrieved Tue, 07 May 2024 08:19:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297982, Retrieved Tue, 07 May 2024 08:19:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-07 10:36:15] [94ac3c9a028ddd47e8862e80eac9f626] [Current]
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Dataseries X:
3500
3600
3750
3800
4100
3900
3650
3800
4050
4250
4450
4200
4050
4050
4200
4450
4400
4450
4200
4050
4500
4650
4850
4700
4350
4500
4700
4800
4700
4600
4400
4300
4750
4800
5000
4900
4400
4650
4650
4900
4900
5000
4550
4500
5100
5000
5350
5150
4500
4600
4900
5050
5000
5350
4650
4650
5200
5300
5700
5250
4900
5200
5250
5450
5750
5450
5100
4950
5550
5800
6050
5650
5500
5600
5550
5900
5900
5850
5350
5150
5850
6000
6250
5800
5550
5700
5850
6150
6050
6050
5550
5100
5900
6050
6150
5700
5200
5400
5550
5750
5700
5650
5400
4950
5900
6050
6350
6350
5500
5800
6100
6350
6400
6850




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297982&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297982&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297982&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297982&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297982&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297982&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
236003500100
337503599.99338930386150.006610696135
438003749.9900835187850.0099164812159
541003799.99669399638300.003306003616
639004099.98016769304-199.980167693045
736503900.01322008122-250.013220081217
838003650.01652761428149.983472385723
940503799.99008504839250.009914951612
1042504049.98347260421200.016527395785
1144504249.98677751515200.013222484846
1242004449.98677773363-249.986777733631
1340504200.01652586625-150.016525866255
1440504050.00991713668-0.00991713667781369
1542004050.00000065559149.999999344408
1644504199.99008395584250.00991604416
1744004449.98347260414-49.9834726041427
1844504400.0033042554949.9966957445085
1942004449.99669487037-249.996694870367
2040504200.01652652185-150.016526521846
2145004050.00991713672449.990082863279
2246504499.97025252298150.029747477017
2348504649.99008198928200.009918010718
2447004849.98677795208-149.98677795208
2543504700.00991517013-350.009915170133
2645004350.02313809193149.976861908065
2747004499.99008548539200.009914514614
2848004699.98677795231100.013222047689
2947004799.9933884298-99.9933884297952
3046004700.00661025906-100.006610259064
3144004600.00661113312-200.00661113312
3243004400.01322182931-100.013221829312
3347504300.00661157019449.99338842981
3448004749.9702523044650.0297476955375
3550004799.9966926854200.003307314597
3649004999.98677838909-99.9867783890932
3744004900.0066098221-500.006609822095
3846504400.03305391763249.966946082369
3946504649.983475444760.0165245552443594
4049004649.99999890761250.000001092389
4149004899.983473259590.0165267404099723
4250004899.99999890747100.000001092532
4345504999.99338930379-449.993389303792
4445004550.0297476956-50.0297476955957
4551004500.0033073146599.996692685402
4650005099.96033604183-99.960336041825
4753505000.00660807407349.993391925928
4851505349.97686300037-199.976863000366
4945005150.01321986275-650.013219862753
5046004500.042970398899.9570296011962
5149004599.99339214451300.006607855492
5250504899.98016747477150.01983252523
5350005049.99008264473-49.9900826447292
5453505000.00330469246349.996695307539
5546505349.97686278199-699.97686278199
5646504650.04627334342-0.0462733434151232
5752004650.00000305899549.99999694101
5853005199.96364117146100.036358828541
5957005299.99338690029400.006613099707
6052505699.97355677829-449.973556778287
6149005250.02974638453-350.029746384527
6252004900.02313940292299.976860597083
6352505199.9801694412750.0198305587292
6454505249.99669334099200.003306659006
6557505449.98677838914300.013221610863
6654505749.98016703755-299.980167037555
6751005450.01983077731-350.019830777309
6849505100.02313874743-150.023138747426
6955504950.00991757384599.990082426165
7058005549.96033647881250.039663521191
7160505799.98347063763250.016529362372
7256506049.98347216696-399.983472166957
7355005650.02644169194-150.026441691936
7456005500.0099177921899.9900822078171
7555505599.9933899595-49.9933899594998
7659005550.0033049111349.996695088902
7759005899.9768627820.023137217996009
7858505899.99999847047-49.9999984704682
7953505850.00330534797-500.003305347966
8051505350.03305369918-200.033053699182
8158505150.01322357735699.98677642265
8260005849.95372600122150.046273998776
8362505999.99008089676250.009919103236
8458006249.98347260394-449.98347260394
8555505800.02974704003-250.029747040033
8657005550.01652870682149.983471293176
8758505699.99008504846150.00991495154
8861505849.99008330035300.009916699651
8960506149.98016725603-99.9801672560316
9060506050.00660938505-0.00660938505279773
9155506050.00000043693-500.000000436927
9251005550.0330534807-450.033053480704
9359005100.02975031767799.970249682327
9460505899.94711639762150.052883602379
9561506049.99008045982100.009919540177
9657006149.99338864811-449.993388648114
9752005700.02974769555-500.029747695552
9854005200.03305544721199.966944552794
9955505399.98678079292150.013219207075
10057505549.99008308192200.009916918085
10157005749.98677795215-49.9867779521528
10256505700.003304474-50.0033044739985
10354005650.00330556652-250.003305566516
10449505400.01652695886-450.016526958859
10559004950.02974922515949.970250774845
10660505899.93720035335150.062799646654
10763506049.9900798043300.009920195696
10863506349.98016725580.0198327441994479
10955006349.99999868892-849.999998688918
11058005500.05619091706299.943809082937
11161005799.98017162621300.019828373795
11263506099.9801666008250.019833399198
11364006349.9834719485450.0165280514639
11468506399.99669355931450.003306440686

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3600 & 3500 & 100 \tabularnewline
3 & 3750 & 3599.99338930386 & 150.006610696135 \tabularnewline
4 & 3800 & 3749.99008351878 & 50.0099164812159 \tabularnewline
5 & 4100 & 3799.99669399638 & 300.003306003616 \tabularnewline
6 & 3900 & 4099.98016769304 & -199.980167693045 \tabularnewline
7 & 3650 & 3900.01322008122 & -250.013220081217 \tabularnewline
8 & 3800 & 3650.01652761428 & 149.983472385723 \tabularnewline
9 & 4050 & 3799.99008504839 & 250.009914951612 \tabularnewline
10 & 4250 & 4049.98347260421 & 200.016527395785 \tabularnewline
11 & 4450 & 4249.98677751515 & 200.013222484846 \tabularnewline
12 & 4200 & 4449.98677773363 & -249.986777733631 \tabularnewline
13 & 4050 & 4200.01652586625 & -150.016525866255 \tabularnewline
14 & 4050 & 4050.00991713668 & -0.00991713667781369 \tabularnewline
15 & 4200 & 4050.00000065559 & 149.999999344408 \tabularnewline
16 & 4450 & 4199.99008395584 & 250.00991604416 \tabularnewline
17 & 4400 & 4449.98347260414 & -49.9834726041427 \tabularnewline
18 & 4450 & 4400.00330425549 & 49.9966957445085 \tabularnewline
19 & 4200 & 4449.99669487037 & -249.996694870367 \tabularnewline
20 & 4050 & 4200.01652652185 & -150.016526521846 \tabularnewline
21 & 4500 & 4050.00991713672 & 449.990082863279 \tabularnewline
22 & 4650 & 4499.97025252298 & 150.029747477017 \tabularnewline
23 & 4850 & 4649.99008198928 & 200.009918010718 \tabularnewline
24 & 4700 & 4849.98677795208 & -149.98677795208 \tabularnewline
25 & 4350 & 4700.00991517013 & -350.009915170133 \tabularnewline
26 & 4500 & 4350.02313809193 & 149.976861908065 \tabularnewline
27 & 4700 & 4499.99008548539 & 200.009914514614 \tabularnewline
28 & 4800 & 4699.98677795231 & 100.013222047689 \tabularnewline
29 & 4700 & 4799.9933884298 & -99.9933884297952 \tabularnewline
30 & 4600 & 4700.00661025906 & -100.006610259064 \tabularnewline
31 & 4400 & 4600.00661113312 & -200.00661113312 \tabularnewline
32 & 4300 & 4400.01322182931 & -100.013221829312 \tabularnewline
33 & 4750 & 4300.00661157019 & 449.99338842981 \tabularnewline
34 & 4800 & 4749.97025230446 & 50.0297476955375 \tabularnewline
35 & 5000 & 4799.9966926854 & 200.003307314597 \tabularnewline
36 & 4900 & 4999.98677838909 & -99.9867783890932 \tabularnewline
37 & 4400 & 4900.0066098221 & -500.006609822095 \tabularnewline
38 & 4650 & 4400.03305391763 & 249.966946082369 \tabularnewline
39 & 4650 & 4649.98347544476 & 0.0165245552443594 \tabularnewline
40 & 4900 & 4649.99999890761 & 250.000001092389 \tabularnewline
41 & 4900 & 4899.98347325959 & 0.0165267404099723 \tabularnewline
42 & 5000 & 4899.99999890747 & 100.000001092532 \tabularnewline
43 & 4550 & 4999.99338930379 & -449.993389303792 \tabularnewline
44 & 4500 & 4550.0297476956 & -50.0297476955957 \tabularnewline
45 & 5100 & 4500.0033073146 & 599.996692685402 \tabularnewline
46 & 5000 & 5099.96033604183 & -99.960336041825 \tabularnewline
47 & 5350 & 5000.00660807407 & 349.993391925928 \tabularnewline
48 & 5150 & 5349.97686300037 & -199.976863000366 \tabularnewline
49 & 4500 & 5150.01321986275 & -650.013219862753 \tabularnewline
50 & 4600 & 4500.0429703988 & 99.9570296011962 \tabularnewline
51 & 4900 & 4599.99339214451 & 300.006607855492 \tabularnewline
52 & 5050 & 4899.98016747477 & 150.01983252523 \tabularnewline
53 & 5000 & 5049.99008264473 & -49.9900826447292 \tabularnewline
54 & 5350 & 5000.00330469246 & 349.996695307539 \tabularnewline
55 & 4650 & 5349.97686278199 & -699.97686278199 \tabularnewline
56 & 4650 & 4650.04627334342 & -0.0462733434151232 \tabularnewline
57 & 5200 & 4650.00000305899 & 549.99999694101 \tabularnewline
58 & 5300 & 5199.96364117146 & 100.036358828541 \tabularnewline
59 & 5700 & 5299.99338690029 & 400.006613099707 \tabularnewline
60 & 5250 & 5699.97355677829 & -449.973556778287 \tabularnewline
61 & 4900 & 5250.02974638453 & -350.029746384527 \tabularnewline
62 & 5200 & 4900.02313940292 & 299.976860597083 \tabularnewline
63 & 5250 & 5199.98016944127 & 50.0198305587292 \tabularnewline
64 & 5450 & 5249.99669334099 & 200.003306659006 \tabularnewline
65 & 5750 & 5449.98677838914 & 300.013221610863 \tabularnewline
66 & 5450 & 5749.98016703755 & -299.980167037555 \tabularnewline
67 & 5100 & 5450.01983077731 & -350.019830777309 \tabularnewline
68 & 4950 & 5100.02313874743 & -150.023138747426 \tabularnewline
69 & 5550 & 4950.00991757384 & 599.990082426165 \tabularnewline
70 & 5800 & 5549.96033647881 & 250.039663521191 \tabularnewline
71 & 6050 & 5799.98347063763 & 250.016529362372 \tabularnewline
72 & 5650 & 6049.98347216696 & -399.983472166957 \tabularnewline
73 & 5500 & 5650.02644169194 & -150.026441691936 \tabularnewline
74 & 5600 & 5500.00991779218 & 99.9900822078171 \tabularnewline
75 & 5550 & 5599.9933899595 & -49.9933899594998 \tabularnewline
76 & 5900 & 5550.0033049111 & 349.996695088902 \tabularnewline
77 & 5900 & 5899.976862782 & 0.023137217996009 \tabularnewline
78 & 5850 & 5899.99999847047 & -49.9999984704682 \tabularnewline
79 & 5350 & 5850.00330534797 & -500.003305347966 \tabularnewline
80 & 5150 & 5350.03305369918 & -200.033053699182 \tabularnewline
81 & 5850 & 5150.01322357735 & 699.98677642265 \tabularnewline
82 & 6000 & 5849.95372600122 & 150.046273998776 \tabularnewline
83 & 6250 & 5999.99008089676 & 250.009919103236 \tabularnewline
84 & 5800 & 6249.98347260394 & -449.98347260394 \tabularnewline
85 & 5550 & 5800.02974704003 & -250.029747040033 \tabularnewline
86 & 5700 & 5550.01652870682 & 149.983471293176 \tabularnewline
87 & 5850 & 5699.99008504846 & 150.00991495154 \tabularnewline
88 & 6150 & 5849.99008330035 & 300.009916699651 \tabularnewline
89 & 6050 & 6149.98016725603 & -99.9801672560316 \tabularnewline
90 & 6050 & 6050.00660938505 & -0.00660938505279773 \tabularnewline
91 & 5550 & 6050.00000043693 & -500.000000436927 \tabularnewline
92 & 5100 & 5550.0330534807 & -450.033053480704 \tabularnewline
93 & 5900 & 5100.02975031767 & 799.970249682327 \tabularnewline
94 & 6050 & 5899.94711639762 & 150.052883602379 \tabularnewline
95 & 6150 & 6049.99008045982 & 100.009919540177 \tabularnewline
96 & 5700 & 6149.99338864811 & -449.993388648114 \tabularnewline
97 & 5200 & 5700.02974769555 & -500.029747695552 \tabularnewline
98 & 5400 & 5200.03305544721 & 199.966944552794 \tabularnewline
99 & 5550 & 5399.98678079292 & 150.013219207075 \tabularnewline
100 & 5750 & 5549.99008308192 & 200.009916918085 \tabularnewline
101 & 5700 & 5749.98677795215 & -49.9867779521528 \tabularnewline
102 & 5650 & 5700.003304474 & -50.0033044739985 \tabularnewline
103 & 5400 & 5650.00330556652 & -250.003305566516 \tabularnewline
104 & 4950 & 5400.01652695886 & -450.016526958859 \tabularnewline
105 & 5900 & 4950.02974922515 & 949.970250774845 \tabularnewline
106 & 6050 & 5899.93720035335 & 150.062799646654 \tabularnewline
107 & 6350 & 6049.9900798043 & 300.009920195696 \tabularnewline
108 & 6350 & 6349.9801672558 & 0.0198327441994479 \tabularnewline
109 & 5500 & 6349.99999868892 & -849.999998688918 \tabularnewline
110 & 5800 & 5500.05619091706 & 299.943809082937 \tabularnewline
111 & 6100 & 5799.98017162621 & 300.019828373795 \tabularnewline
112 & 6350 & 6099.9801666008 & 250.019833399198 \tabularnewline
113 & 6400 & 6349.98347194854 & 50.0165280514639 \tabularnewline
114 & 6850 & 6399.99669355931 & 450.003306440686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297982&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]2[/C][C]3600[/C][C]3500[/C][C]100[/C][/ROW]
[ROW][C]3[/C][C]3750[/C][C]3599.99338930386[/C][C]150.006610696135[/C][/ROW]
[ROW][C]4[/C][C]3800[/C][C]3749.99008351878[/C][C]50.0099164812159[/C][/ROW]
[ROW][C]5[/C][C]4100[/C][C]3799.99669399638[/C][C]300.003306003616[/C][/ROW]
[ROW][C]6[/C][C]3900[/C][C]4099.98016769304[/C][C]-199.980167693045[/C][/ROW]
[ROW][C]7[/C][C]3650[/C][C]3900.01322008122[/C][C]-250.013220081217[/C][/ROW]
[ROW][C]8[/C][C]3800[/C][C]3650.01652761428[/C][C]149.983472385723[/C][/ROW]
[ROW][C]9[/C][C]4050[/C][C]3799.99008504839[/C][C]250.009914951612[/C][/ROW]
[ROW][C]10[/C][C]4250[/C][C]4049.98347260421[/C][C]200.016527395785[/C][/ROW]
[ROW][C]11[/C][C]4450[/C][C]4249.98677751515[/C][C]200.013222484846[/C][/ROW]
[ROW][C]12[/C][C]4200[/C][C]4449.98677773363[/C][C]-249.986777733631[/C][/ROW]
[ROW][C]13[/C][C]4050[/C][C]4200.01652586625[/C][C]-150.016525866255[/C][/ROW]
[ROW][C]14[/C][C]4050[/C][C]4050.00991713668[/C][C]-0.00991713667781369[/C][/ROW]
[ROW][C]15[/C][C]4200[/C][C]4050.00000065559[/C][C]149.999999344408[/C][/ROW]
[ROW][C]16[/C][C]4450[/C][C]4199.99008395584[/C][C]250.00991604416[/C][/ROW]
[ROW][C]17[/C][C]4400[/C][C]4449.98347260414[/C][C]-49.9834726041427[/C][/ROW]
[ROW][C]18[/C][C]4450[/C][C]4400.00330425549[/C][C]49.9966957445085[/C][/ROW]
[ROW][C]19[/C][C]4200[/C][C]4449.99669487037[/C][C]-249.996694870367[/C][/ROW]
[ROW][C]20[/C][C]4050[/C][C]4200.01652652185[/C][C]-150.016526521846[/C][/ROW]
[ROW][C]21[/C][C]4500[/C][C]4050.00991713672[/C][C]449.990082863279[/C][/ROW]
[ROW][C]22[/C][C]4650[/C][C]4499.97025252298[/C][C]150.029747477017[/C][/ROW]
[ROW][C]23[/C][C]4850[/C][C]4649.99008198928[/C][C]200.009918010718[/C][/ROW]
[ROW][C]24[/C][C]4700[/C][C]4849.98677795208[/C][C]-149.98677795208[/C][/ROW]
[ROW][C]25[/C][C]4350[/C][C]4700.00991517013[/C][C]-350.009915170133[/C][/ROW]
[ROW][C]26[/C][C]4500[/C][C]4350.02313809193[/C][C]149.976861908065[/C][/ROW]
[ROW][C]27[/C][C]4700[/C][C]4499.99008548539[/C][C]200.009914514614[/C][/ROW]
[ROW][C]28[/C][C]4800[/C][C]4699.98677795231[/C][C]100.013222047689[/C][/ROW]
[ROW][C]29[/C][C]4700[/C][C]4799.9933884298[/C][C]-99.9933884297952[/C][/ROW]
[ROW][C]30[/C][C]4600[/C][C]4700.00661025906[/C][C]-100.006610259064[/C][/ROW]
[ROW][C]31[/C][C]4400[/C][C]4600.00661113312[/C][C]-200.00661113312[/C][/ROW]
[ROW][C]32[/C][C]4300[/C][C]4400.01322182931[/C][C]-100.013221829312[/C][/ROW]
[ROW][C]33[/C][C]4750[/C][C]4300.00661157019[/C][C]449.99338842981[/C][/ROW]
[ROW][C]34[/C][C]4800[/C][C]4749.97025230446[/C][C]50.0297476955375[/C][/ROW]
[ROW][C]35[/C][C]5000[/C][C]4799.9966926854[/C][C]200.003307314597[/C][/ROW]
[ROW][C]36[/C][C]4900[/C][C]4999.98677838909[/C][C]-99.9867783890932[/C][/ROW]
[ROW][C]37[/C][C]4400[/C][C]4900.0066098221[/C][C]-500.006609822095[/C][/ROW]
[ROW][C]38[/C][C]4650[/C][C]4400.03305391763[/C][C]249.966946082369[/C][/ROW]
[ROW][C]39[/C][C]4650[/C][C]4649.98347544476[/C][C]0.0165245552443594[/C][/ROW]
[ROW][C]40[/C][C]4900[/C][C]4649.99999890761[/C][C]250.000001092389[/C][/ROW]
[ROW][C]41[/C][C]4900[/C][C]4899.98347325959[/C][C]0.0165267404099723[/C][/ROW]
[ROW][C]42[/C][C]5000[/C][C]4899.99999890747[/C][C]100.000001092532[/C][/ROW]
[ROW][C]43[/C][C]4550[/C][C]4999.99338930379[/C][C]-449.993389303792[/C][/ROW]
[ROW][C]44[/C][C]4500[/C][C]4550.0297476956[/C][C]-50.0297476955957[/C][/ROW]
[ROW][C]45[/C][C]5100[/C][C]4500.0033073146[/C][C]599.996692685402[/C][/ROW]
[ROW][C]46[/C][C]5000[/C][C]5099.96033604183[/C][C]-99.960336041825[/C][/ROW]
[ROW][C]47[/C][C]5350[/C][C]5000.00660807407[/C][C]349.993391925928[/C][/ROW]
[ROW][C]48[/C][C]5150[/C][C]5349.97686300037[/C][C]-199.976863000366[/C][/ROW]
[ROW][C]49[/C][C]4500[/C][C]5150.01321986275[/C][C]-650.013219862753[/C][/ROW]
[ROW][C]50[/C][C]4600[/C][C]4500.0429703988[/C][C]99.9570296011962[/C][/ROW]
[ROW][C]51[/C][C]4900[/C][C]4599.99339214451[/C][C]300.006607855492[/C][/ROW]
[ROW][C]52[/C][C]5050[/C][C]4899.98016747477[/C][C]150.01983252523[/C][/ROW]
[ROW][C]53[/C][C]5000[/C][C]5049.99008264473[/C][C]-49.9900826447292[/C][/ROW]
[ROW][C]54[/C][C]5350[/C][C]5000.00330469246[/C][C]349.996695307539[/C][/ROW]
[ROW][C]55[/C][C]4650[/C][C]5349.97686278199[/C][C]-699.97686278199[/C][/ROW]
[ROW][C]56[/C][C]4650[/C][C]4650.04627334342[/C][C]-0.0462733434151232[/C][/ROW]
[ROW][C]57[/C][C]5200[/C][C]4650.00000305899[/C][C]549.99999694101[/C][/ROW]
[ROW][C]58[/C][C]5300[/C][C]5199.96364117146[/C][C]100.036358828541[/C][/ROW]
[ROW][C]59[/C][C]5700[/C][C]5299.99338690029[/C][C]400.006613099707[/C][/ROW]
[ROW][C]60[/C][C]5250[/C][C]5699.97355677829[/C][C]-449.973556778287[/C][/ROW]
[ROW][C]61[/C][C]4900[/C][C]5250.02974638453[/C][C]-350.029746384527[/C][/ROW]
[ROW][C]62[/C][C]5200[/C][C]4900.02313940292[/C][C]299.976860597083[/C][/ROW]
[ROW][C]63[/C][C]5250[/C][C]5199.98016944127[/C][C]50.0198305587292[/C][/ROW]
[ROW][C]64[/C][C]5450[/C][C]5249.99669334099[/C][C]200.003306659006[/C][/ROW]
[ROW][C]65[/C][C]5750[/C][C]5449.98677838914[/C][C]300.013221610863[/C][/ROW]
[ROW][C]66[/C][C]5450[/C][C]5749.98016703755[/C][C]-299.980167037555[/C][/ROW]
[ROW][C]67[/C][C]5100[/C][C]5450.01983077731[/C][C]-350.019830777309[/C][/ROW]
[ROW][C]68[/C][C]4950[/C][C]5100.02313874743[/C][C]-150.023138747426[/C][/ROW]
[ROW][C]69[/C][C]5550[/C][C]4950.00991757384[/C][C]599.990082426165[/C][/ROW]
[ROW][C]70[/C][C]5800[/C][C]5549.96033647881[/C][C]250.039663521191[/C][/ROW]
[ROW][C]71[/C][C]6050[/C][C]5799.98347063763[/C][C]250.016529362372[/C][/ROW]
[ROW][C]72[/C][C]5650[/C][C]6049.98347216696[/C][C]-399.983472166957[/C][/ROW]
[ROW][C]73[/C][C]5500[/C][C]5650.02644169194[/C][C]-150.026441691936[/C][/ROW]
[ROW][C]74[/C][C]5600[/C][C]5500.00991779218[/C][C]99.9900822078171[/C][/ROW]
[ROW][C]75[/C][C]5550[/C][C]5599.9933899595[/C][C]-49.9933899594998[/C][/ROW]
[ROW][C]76[/C][C]5900[/C][C]5550.0033049111[/C][C]349.996695088902[/C][/ROW]
[ROW][C]77[/C][C]5900[/C][C]5899.976862782[/C][C]0.023137217996009[/C][/ROW]
[ROW][C]78[/C][C]5850[/C][C]5899.99999847047[/C][C]-49.9999984704682[/C][/ROW]
[ROW][C]79[/C][C]5350[/C][C]5850.00330534797[/C][C]-500.003305347966[/C][/ROW]
[ROW][C]80[/C][C]5150[/C][C]5350.03305369918[/C][C]-200.033053699182[/C][/ROW]
[ROW][C]81[/C][C]5850[/C][C]5150.01322357735[/C][C]699.98677642265[/C][/ROW]
[ROW][C]82[/C][C]6000[/C][C]5849.95372600122[/C][C]150.046273998776[/C][/ROW]
[ROW][C]83[/C][C]6250[/C][C]5999.99008089676[/C][C]250.009919103236[/C][/ROW]
[ROW][C]84[/C][C]5800[/C][C]6249.98347260394[/C][C]-449.98347260394[/C][/ROW]
[ROW][C]85[/C][C]5550[/C][C]5800.02974704003[/C][C]-250.029747040033[/C][/ROW]
[ROW][C]86[/C][C]5700[/C][C]5550.01652870682[/C][C]149.983471293176[/C][/ROW]
[ROW][C]87[/C][C]5850[/C][C]5699.99008504846[/C][C]150.00991495154[/C][/ROW]
[ROW][C]88[/C][C]6150[/C][C]5849.99008330035[/C][C]300.009916699651[/C][/ROW]
[ROW][C]89[/C][C]6050[/C][C]6149.98016725603[/C][C]-99.9801672560316[/C][/ROW]
[ROW][C]90[/C][C]6050[/C][C]6050.00660938505[/C][C]-0.00660938505279773[/C][/ROW]
[ROW][C]91[/C][C]5550[/C][C]6050.00000043693[/C][C]-500.000000436927[/C][/ROW]
[ROW][C]92[/C][C]5100[/C][C]5550.0330534807[/C][C]-450.033053480704[/C][/ROW]
[ROW][C]93[/C][C]5900[/C][C]5100.02975031767[/C][C]799.970249682327[/C][/ROW]
[ROW][C]94[/C][C]6050[/C][C]5899.94711639762[/C][C]150.052883602379[/C][/ROW]
[ROW][C]95[/C][C]6150[/C][C]6049.99008045982[/C][C]100.009919540177[/C][/ROW]
[ROW][C]96[/C][C]5700[/C][C]6149.99338864811[/C][C]-449.993388648114[/C][/ROW]
[ROW][C]97[/C][C]5200[/C][C]5700.02974769555[/C][C]-500.029747695552[/C][/ROW]
[ROW][C]98[/C][C]5400[/C][C]5200.03305544721[/C][C]199.966944552794[/C][/ROW]
[ROW][C]99[/C][C]5550[/C][C]5399.98678079292[/C][C]150.013219207075[/C][/ROW]
[ROW][C]100[/C][C]5750[/C][C]5549.99008308192[/C][C]200.009916918085[/C][/ROW]
[ROW][C]101[/C][C]5700[/C][C]5749.98677795215[/C][C]-49.9867779521528[/C][/ROW]
[ROW][C]102[/C][C]5650[/C][C]5700.003304474[/C][C]-50.0033044739985[/C][/ROW]
[ROW][C]103[/C][C]5400[/C][C]5650.00330556652[/C][C]-250.003305566516[/C][/ROW]
[ROW][C]104[/C][C]4950[/C][C]5400.01652695886[/C][C]-450.016526958859[/C][/ROW]
[ROW][C]105[/C][C]5900[/C][C]4950.02974922515[/C][C]949.970250774845[/C][/ROW]
[ROW][C]106[/C][C]6050[/C][C]5899.93720035335[/C][C]150.062799646654[/C][/ROW]
[ROW][C]107[/C][C]6350[/C][C]6049.9900798043[/C][C]300.009920195696[/C][/ROW]
[ROW][C]108[/C][C]6350[/C][C]6349.9801672558[/C][C]0.0198327441994479[/C][/ROW]
[ROW][C]109[/C][C]5500[/C][C]6349.99999868892[/C][C]-849.999998688918[/C][/ROW]
[ROW][C]110[/C][C]5800[/C][C]5500.05619091706[/C][C]299.943809082937[/C][/ROW]
[ROW][C]111[/C][C]6100[/C][C]5799.98017162621[/C][C]300.019828373795[/C][/ROW]
[ROW][C]112[/C][C]6350[/C][C]6099.9801666008[/C][C]250.019833399198[/C][/ROW]
[ROW][C]113[/C][C]6400[/C][C]6349.98347194854[/C][C]50.0165280514639[/C][/ROW]
[ROW][C]114[/C][C]6850[/C][C]6399.99669355931[/C][C]450.003306440686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297982&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297982&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
236003500100
337503599.99338930386150.006610696135
438003749.9900835187850.0099164812159
541003799.99669399638300.003306003616
639004099.98016769304-199.980167693045
736503900.01322008122-250.013220081217
838003650.01652761428149.983472385723
940503799.99008504839250.009914951612
1042504049.98347260421200.016527395785
1144504249.98677751515200.013222484846
1242004449.98677773363-249.986777733631
1340504200.01652586625-150.016525866255
1440504050.00991713668-0.00991713667781369
1542004050.00000065559149.999999344408
1644504199.99008395584250.00991604416
1744004449.98347260414-49.9834726041427
1844504400.0033042554949.9966957445085
1942004449.99669487037-249.996694870367
2040504200.01652652185-150.016526521846
2145004050.00991713672449.990082863279
2246504499.97025252298150.029747477017
2348504649.99008198928200.009918010718
2447004849.98677795208-149.98677795208
2543504700.00991517013-350.009915170133
2645004350.02313809193149.976861908065
2747004499.99008548539200.009914514614
2848004699.98677795231100.013222047689
2947004799.9933884298-99.9933884297952
3046004700.00661025906-100.006610259064
3144004600.00661113312-200.00661113312
3243004400.01322182931-100.013221829312
3347504300.00661157019449.99338842981
3448004749.9702523044650.0297476955375
3550004799.9966926854200.003307314597
3649004999.98677838909-99.9867783890932
3744004900.0066098221-500.006609822095
3846504400.03305391763249.966946082369
3946504649.983475444760.0165245552443594
4049004649.99999890761250.000001092389
4149004899.983473259590.0165267404099723
4250004899.99999890747100.000001092532
4345504999.99338930379-449.993389303792
4445004550.0297476956-50.0297476955957
4551004500.0033073146599.996692685402
4650005099.96033604183-99.960336041825
4753505000.00660807407349.993391925928
4851505349.97686300037-199.976863000366
4945005150.01321986275-650.013219862753
5046004500.042970398899.9570296011962
5149004599.99339214451300.006607855492
5250504899.98016747477150.01983252523
5350005049.99008264473-49.9900826447292
5453505000.00330469246349.996695307539
5546505349.97686278199-699.97686278199
5646504650.04627334342-0.0462733434151232
5752004650.00000305899549.99999694101
5853005199.96364117146100.036358828541
5957005299.99338690029400.006613099707
6052505699.97355677829-449.973556778287
6149005250.02974638453-350.029746384527
6252004900.02313940292299.976860597083
6352505199.9801694412750.0198305587292
6454505249.99669334099200.003306659006
6557505449.98677838914300.013221610863
6654505749.98016703755-299.980167037555
6751005450.01983077731-350.019830777309
6849505100.02313874743-150.023138747426
6955504950.00991757384599.990082426165
7058005549.96033647881250.039663521191
7160505799.98347063763250.016529362372
7256506049.98347216696-399.983472166957
7355005650.02644169194-150.026441691936
7456005500.0099177921899.9900822078171
7555505599.9933899595-49.9933899594998
7659005550.0033049111349.996695088902
7759005899.9768627820.023137217996009
7858505899.99999847047-49.9999984704682
7953505850.00330534797-500.003305347966
8051505350.03305369918-200.033053699182
8158505150.01322357735699.98677642265
8260005849.95372600122150.046273998776
8362505999.99008089676250.009919103236
8458006249.98347260394-449.98347260394
8555505800.02974704003-250.029747040033
8657005550.01652870682149.983471293176
8758505699.99008504846150.00991495154
8861505849.99008330035300.009916699651
8960506149.98016725603-99.9801672560316
9060506050.00660938505-0.00660938505279773
9155506050.00000043693-500.000000436927
9251005550.0330534807-450.033053480704
9359005100.02975031767799.970249682327
9460505899.94711639762150.052883602379
9561506049.99008045982100.009919540177
9657006149.99338864811-449.993388648114
9752005700.02974769555-500.029747695552
9854005200.03305544721199.966944552794
9955505399.98678079292150.013219207075
10057505549.99008308192200.009916918085
10157005749.98677795215-49.9867779521528
10256505700.003304474-50.0033044739985
10354005650.00330556652-250.003305566516
10449505400.01652695886-450.016526958859
10559004950.02974922515949.970250774845
10660505899.93720035335150.062799646654
10763506049.9900798043300.009920195696
10863506349.98016725580.0198327441994479
10955006349.99999868892-849.999998688918
11058005500.05619091706299.943809082937
11161005799.98017162621300.019828373795
11263506099.9801666008250.019833399198
11364006349.9834719485450.0165280514639
11468506399.99669355931450.003306440686







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1156849.970251648816232.582148876967467.35835442067
1166849.970251648815976.88048259387723.06002070383
1176849.970251648815780.669816685447919.27068661218
1186849.970251648815615.255266076378084.68523722126
1196849.970251648815469.521494547898230.41900874973
1206849.970251648815337.767736650988362.17276664665
1216849.970251648815216.6074255298483.33307776862
1226849.970251648815103.834003489928596.10649980771
1236849.970251648814997.914779337388702.02572396025
1246849.970251648814897.733803904078802.20669939356
1256849.970251648814802.448622144668897.49188115297
1266849.970251648814711.404728062588988.53577523505
1276849.970251648814624.081625940889075.85887735675
1286849.970251648814540.05729886469159.88320443303
1296849.970251648814458.983943694589240.95655960304
1306849.970251648814380.570891438149319.36961185949
1316849.970251648814304.572271844249395.36823145339
1326849.970251648814230.777904573579469.16259872406

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 6849.97025164881 & 6232.58214887696 & 7467.35835442067 \tabularnewline
116 & 6849.97025164881 & 5976.8804825938 & 7723.06002070383 \tabularnewline
117 & 6849.97025164881 & 5780.66981668544 & 7919.27068661218 \tabularnewline
118 & 6849.97025164881 & 5615.25526607637 & 8084.68523722126 \tabularnewline
119 & 6849.97025164881 & 5469.52149454789 & 8230.41900874973 \tabularnewline
120 & 6849.97025164881 & 5337.76773665098 & 8362.17276664665 \tabularnewline
121 & 6849.97025164881 & 5216.607425529 & 8483.33307776862 \tabularnewline
122 & 6849.97025164881 & 5103.83400348992 & 8596.10649980771 \tabularnewline
123 & 6849.97025164881 & 4997.91477933738 & 8702.02572396025 \tabularnewline
124 & 6849.97025164881 & 4897.73380390407 & 8802.20669939356 \tabularnewline
125 & 6849.97025164881 & 4802.44862214466 & 8897.49188115297 \tabularnewline
126 & 6849.97025164881 & 4711.40472806258 & 8988.53577523505 \tabularnewline
127 & 6849.97025164881 & 4624.08162594088 & 9075.85887735675 \tabularnewline
128 & 6849.97025164881 & 4540.0572988646 & 9159.88320443303 \tabularnewline
129 & 6849.97025164881 & 4458.98394369458 & 9240.95655960304 \tabularnewline
130 & 6849.97025164881 & 4380.57089143814 & 9319.36961185949 \tabularnewline
131 & 6849.97025164881 & 4304.57227184424 & 9395.36823145339 \tabularnewline
132 & 6849.97025164881 & 4230.77790457357 & 9469.16259872406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297982&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]115[/C][C]6849.97025164881[/C][C]6232.58214887696[/C][C]7467.35835442067[/C][/ROW]
[ROW][C]116[/C][C]6849.97025164881[/C][C]5976.8804825938[/C][C]7723.06002070383[/C][/ROW]
[ROW][C]117[/C][C]6849.97025164881[/C][C]5780.66981668544[/C][C]7919.27068661218[/C][/ROW]
[ROW][C]118[/C][C]6849.97025164881[/C][C]5615.25526607637[/C][C]8084.68523722126[/C][/ROW]
[ROW][C]119[/C][C]6849.97025164881[/C][C]5469.52149454789[/C][C]8230.41900874973[/C][/ROW]
[ROW][C]120[/C][C]6849.97025164881[/C][C]5337.76773665098[/C][C]8362.17276664665[/C][/ROW]
[ROW][C]121[/C][C]6849.97025164881[/C][C]5216.607425529[/C][C]8483.33307776862[/C][/ROW]
[ROW][C]122[/C][C]6849.97025164881[/C][C]5103.83400348992[/C][C]8596.10649980771[/C][/ROW]
[ROW][C]123[/C][C]6849.97025164881[/C][C]4997.91477933738[/C][C]8702.02572396025[/C][/ROW]
[ROW][C]124[/C][C]6849.97025164881[/C][C]4897.73380390407[/C][C]8802.20669939356[/C][/ROW]
[ROW][C]125[/C][C]6849.97025164881[/C][C]4802.44862214466[/C][C]8897.49188115297[/C][/ROW]
[ROW][C]126[/C][C]6849.97025164881[/C][C]4711.40472806258[/C][C]8988.53577523505[/C][/ROW]
[ROW][C]127[/C][C]6849.97025164881[/C][C]4624.08162594088[/C][C]9075.85887735675[/C][/ROW]
[ROW][C]128[/C][C]6849.97025164881[/C][C]4540.0572988646[/C][C]9159.88320443303[/C][/ROW]
[ROW][C]129[/C][C]6849.97025164881[/C][C]4458.98394369458[/C][C]9240.95655960304[/C][/ROW]
[ROW][C]130[/C][C]6849.97025164881[/C][C]4380.57089143814[/C][C]9319.36961185949[/C][/ROW]
[ROW][C]131[/C][C]6849.97025164881[/C][C]4304.57227184424[/C][C]9395.36823145339[/C][/ROW]
[ROW][C]132[/C][C]6849.97025164881[/C][C]4230.77790457357[/C][C]9469.16259872406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297982&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297982&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
1156849.970251648816232.582148876967467.35835442067
1166849.970251648815976.88048259387723.06002070383
1176849.970251648815780.669816685447919.27068661218
1186849.970251648815615.255266076378084.68523722126
1196849.970251648815469.521494547898230.41900874973
1206849.970251648815337.767736650988362.17276664665
1216849.970251648815216.6074255298483.33307776862
1226849.970251648815103.834003489928596.10649980771
1236849.970251648814997.914779337388702.02572396025
1246849.970251648814897.733803904078802.20669939356
1256849.970251648814802.448622144668897.49188115297
1266849.970251648814711.404728062588988.53577523505
1276849.970251648814624.081625940889075.85887735675
1286849.970251648814540.05729886469159.88320443303
1296849.970251648814458.983943694589240.95655960304
1306849.970251648814380.570891438149319.36961185949
1316849.970251648814304.572271844249395.36823145339
1326849.970251648814230.777904573579469.16259872406



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')