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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSun, 20 Dec 2009 13:40:51 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/20/t1261341719e23936tx2ow3702.htm/, Retrieved Sat, 27 Apr 2024 10:12:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70019, Retrieved Sat, 27 Apr 2024 10:12:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [] [2009-12-20 20:40:51] [71596e6a53ccce532e52aaf6113616ef] [Current]
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Dataset

Dataseries X:
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Boxplots 
87.4	0	104.5	98.1	102.7	105.4	97	97.4
89.9	0	87.4	104.5	98.1	102.7	105.4	97
109.8	0	89.9	87.4	104.5	98.1	102.7	105.4
111.7	0	109.8	89.9	87.4	104.5	98.1	102.7
98.6	0	111.7	109.8	89.9	87.4	104.5	98.1
96.9	0	98.6	111.7	109.8	89.9	87.4	104.5
95.1	0	96.9	98.6	111.7	109.8	89.9	87.4
97	0	95.1	96.9	98.6	111.7	109.8	89.9
112.7	0	97	95.1	96.9	98.6	111.7	109.8
102.9	0	112.7	97	95.1	96.9	98.6	111.7
97.4	0	102.9	112.7	97	95.1	96.9	98.6
111.4	0	97.4	102.9	112.7	97	95.1	96.9
87.4	0	111.4	97.4	102.9	112.7	97	95.1
96.8	0	87.4	111.4	97.4	102.9	112.7	97
114.1	0	96.8	87.4	111.4	97.4	102.9	112.7
110.3	0	114.1	96.8	87.4	111.4	97.4	102.9
103.9	0	110.3	114.1	96.8	87.4	111.4	97.4
101.6	0	103.9	110.3	114.1	96.8	87.4	111.4
94.6	0	101.6	103.9	110.3	114.1	96.8	87.4
95.9	0	94.6	101.6	103.9	110.3	114.1	96.8
104.7	0	95.9	94.6	101.6	103.9	110.3	114.1
102.8	0	104.7	95.9	94.6	101.6	103.9	110.3
98.1	0	102.8	104.7	95.9	94.6	101.6	103.9
113.9	0	98.1	102.8	104.7	95.9	94.6	101.6
80.9	0	113.9	98.1	102.8	104.7	95.9	94.6
95.7	0	80.9	113.9	98.1	102.8	104.7	95.9
113.2	0	95.7	80.9	113.9	98.1	102.8	104.7
105.9	0	113.2	95.7	80.9	113.9	98.1	102.8
108.8	0	105.9	113.2	95.7	80.9	113.9	98.1
102.3	0	108.8	105.9	113.2	95.7	80.9	113.9
99	0	102.3	108.8	105.9	113.2	95.7	80.9
100.7	0	99	102.3	108.8	105.9	113.2	95.7
115.5	0	100.7	99	102.3	108.8	105.9	113.2
100.7	0	115.5	100.7	99	102.3	108.8	105.9
109.9	0	100.7	115.5	100.7	99	102.3	108.8
114.6	0	109.9	100.7	115.5	100.7	99	102.3
85.4	0	114.6	109.9	100.7	115.5	100.7	99
100.5	0	85.4	114.6	109.9	100.7	115.5	100.7
114.8	0	100.5	85.4	114.6	109.9	100.7	115.5
116.5	0	114.8	100.5	85.4	114.6	109.9	100.7
112.9	0	116.5	114.8	100.5	85.4	114.6	109.9
102	0	112.9	116.5	114.8	100.5	85.4	114.6
106	0	102	112.9	116.5	114.8	100.5	85.4
105.3	0	106	102	112.9	116.5	114.8	100.5
118.8	0	105.3	106	102	112.9	116.5	114.8
106.1	0	118.8	105.3	106	102	112.9	116.5
109.3	0	106.1	118.8	105.3	106	102	112.9
117.2	0	109.3	106.1	118.8	105.3	106	102
92.5	0	117.2	109.3	106.1	118.8	105.3	106
104.2	0	92.5	117.2	109.3	106.1	118.8	105.3
112.5	0	104.2	92.5	117.2	109.3	106.1	118.8
122.4	0	112.5	104.2	92.5	117.2	109.3	106.1
113.3	0	122.4	112.5	104.2	92.5	117.2	109.3
100	0	113.3	122.4	112.5	104.2	92.5	117.2
110.7	0	100	113.3	122.4	112.5	104.2	92.5
112.8	0	110.7	100	113.3	122.4	112.5	104.2
109.8	0	112.8	110.7	100	113.3	122.4	112.5
117.3	0	109.8	112.8	110.7	100	113.3	122.4
109.1	0	117.3	109.8	112.8	110.7	100	113.3
115.9	0	109.1	117.3	109.8	112.8	110.7	100
96	0	115.9	109.1	117.3	109.8	112.8	110.7
99.8	0	96	115.9	109.1	117.3	109.8	112.8
116.8	0	99.8	96	115.9	109.1	117.3	109.8
115.7	1	116.8	99.8	96	115.9	109.1	117.3
99.4	1	115.7	116.8	99.8	96	115.9	109.1
94.3	1	99.4	115.7	116.8	99.8	96	115.9
91	1	94.3	99.4	115.7	116.8	99.8	96
93.2	1	91	94.3	99.4	115.7	116.8	99.8
103.1	1	93.2	91	94.3	99.4	115.7	116.8
94.1	1	103.1	93.2	91	94.3	99.4	115.7
91.8	1	94.1	103.1	93.2	91	94.3	99.4
102.7	1	91.8	94.1	103.1	93.2	91	94.3
82.6	1	102.7	91.8	94.1	103.1	93.2	91
89.1	1	82.6	102.7	91.8	94.1	103.1	93.2
104.5	1	89.1	82.6	102.7	91.8	94.1	103.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70019&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70019&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Productie[t] = + 70.843171659092 -12.1409361201919Dummy[t] -0.170535875011005`Yt-1`[t] + 0.127341252226174`Yt-2`[t] + 0.406670131624456`Yt-3`[t] -0.115932126741984`Yt-4`[t] -0.0322030815182641`Yt-5`[t] + 0.125704389082812`Yt-6`[t] -19.0624672402896M1[t] -15.1805417856902M2[t] -0.526451480378921M3[t] + 14.7571552687538M4[t] -1.15645418805891M5[t] -16.4847096765184M6[t] -11.7529419581613M7[t] -7.21825953770693M8[t] + 2.70776198327648M9[t] -3.68093564071264M10[t] -7.4642631479732M11[t] + 0.128245177155806t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Productie[t] =  +  70.843171659092 -12.1409361201919Dummy[t] -0.170535875011005`Yt-1`[t] +  0.127341252226174`Yt-2`[t] +  0.406670131624456`Yt-3`[t] -0.115932126741984`Yt-4`[t] -0.0322030815182641`Yt-5`[t] +  0.125704389082812`Yt-6`[t] -19.0624672402896M1[t] -15.1805417856902M2[t] -0.526451480378921M3[t] +  14.7571552687538M4[t] -1.15645418805891M5[t] -16.4847096765184M6[t] -11.7529419581613M7[t] -7.21825953770693M8[t] +  2.70776198327648M9[t] -3.68093564071264M10[t] -7.4642631479732M11[t] +  0.128245177155806t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70019&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Productie[t] =  +  70.843171659092 -12.1409361201919Dummy[t] -0.170535875011005`Yt-1`[t] +  0.127341252226174`Yt-2`[t] +  0.406670131624456`Yt-3`[t] -0.115932126741984`Yt-4`[t] -0.0322030815182641`Yt-5`[t] +  0.125704389082812`Yt-6`[t] -19.0624672402896M1[t] -15.1805417856902M2[t] -0.526451480378921M3[t] +  14.7571552687538M4[t] -1.15645418805891M5[t] -16.4847096765184M6[t] -11.7529419581613M7[t] -7.21825953770693M8[t] +  2.70776198327648M9[t] -3.68093564071264M10[t] -7.4642631479732M11[t] +  0.128245177155806t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70019&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
Productie[t] = + 70.843171659092 -12.1409361201919Dummy[t] -0.170535875011005`Yt-1`[t] + 0.127341252226174`Yt-2`[t] + 0.406670131624456`Yt-3`[t] -0.115932126741984`Yt-4`[t] -0.0322030815182641`Yt-5`[t] + 0.125704389082812`Yt-6`[t] -19.0624672402896M1[t] -15.1805417856902M2[t] -0.526451480378921M3[t] + 14.7571552687538M4[t] -1.15645418805891M5[t] -16.4847096765184M6[t] -11.7529419581613M7[t] -7.21825953770693M8[t] + 2.70776198327648M9[t] -3.68093564071264M10[t] -7.4642631479732M11[t] + 0.128245177155806t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)70.84317165909215.4569064.58332.7e-051.3e-05
Dummy-12.14093612019192.59814-4.67292e-051e-05
`Yt-1`-0.1705358750110050.127664-1.33580.187110.093555
`Yt-2`0.1273412522261740.1278420.99610.3235730.161786
`Yt-3`0.4066701316244560.1315093.09230.0031170.001558
`Yt-4`-0.1159321267419840.121414-0.95480.3438330.171916
`Yt-5`-0.03220308151826410.120282-0.26770.7899090.394955
`Yt-6`0.1257043890828120.1281680.98080.3309950.165498
M1-19.06246724028962.382462-8.001200
M2-15.18054178569023.051581-4.97467e-063e-06
M3-0.5264514803789213.479885-0.15130.8803050.440153
M414.75715526875384.4554223.31220.001640.00082
M5-1.156454188058914.751963-0.24340.8086290.404315
M6-16.48470967651843.512189-4.69361.8e-059e-06
M7-11.75294195816133.371446-3.4860.0009710.000486
M8-7.218259537706933.443448-2.09620.0406760.020338
M92.707761983276484.2817350.63240.5297470.264873
M10-3.680935640712644.096295-0.89860.3727820.186391
M11-7.46426314797322.88189-2.59010.0122590.006129
t0.1282451771558060.0386193.32080.0015990.000799

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 70.843171659092 & 15.456906 & 4.5833 & 2.7e-05 & 1.3e-05 \tabularnewline
Dummy & -12.1409361201919 & 2.59814 & -4.6729 & 2e-05 & 1e-05 \tabularnewline
`Yt-1` & -0.170535875011005 & 0.127664 & -1.3358 & 0.18711 & 0.093555 \tabularnewline
`Yt-2` & 0.127341252226174 & 0.127842 & 0.9961 & 0.323573 & 0.161786 \tabularnewline
`Yt-3` & 0.406670131624456 & 0.131509 & 3.0923 & 0.003117 & 0.001558 \tabularnewline
`Yt-4` & -0.115932126741984 & 0.121414 & -0.9548 & 0.343833 & 0.171916 \tabularnewline
`Yt-5` & -0.0322030815182641 & 0.120282 & -0.2677 & 0.789909 & 0.394955 \tabularnewline
`Yt-6` & 0.125704389082812 & 0.128168 & 0.9808 & 0.330995 & 0.165498 \tabularnewline
M1 & -19.0624672402896 & 2.382462 & -8.0012 & 0 & 0 \tabularnewline
M2 & -15.1805417856902 & 3.051581 & -4.9746 & 7e-06 & 3e-06 \tabularnewline
M3 & -0.526451480378921 & 3.479885 & -0.1513 & 0.880305 & 0.440153 \tabularnewline
M4 & 14.7571552687538 & 4.455422 & 3.3122 & 0.00164 & 0.00082 \tabularnewline
M5 & -1.15645418805891 & 4.751963 & -0.2434 & 0.808629 & 0.404315 \tabularnewline
M6 & -16.4847096765184 & 3.512189 & -4.6936 & 1.8e-05 & 9e-06 \tabularnewline
M7 & -11.7529419581613 & 3.371446 & -3.486 & 0.000971 & 0.000486 \tabularnewline
M8 & -7.21825953770693 & 3.443448 & -2.0962 & 0.040676 & 0.020338 \tabularnewline
M9 & 2.70776198327648 & 4.281735 & 0.6324 & 0.529747 & 0.264873 \tabularnewline
M10 & -3.68093564071264 & 4.096295 & -0.8986 & 0.372782 & 0.186391 \tabularnewline
M11 & -7.4642631479732 & 2.88189 & -2.5901 & 0.012259 & 0.006129 \tabularnewline
t & 0.128245177155806 & 0.038619 & 3.3208 & 0.001599 & 0.000799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70019&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]70.843171659092[/C][C]15.456906[/C][C]4.5833[/C][C]2.7e-05[/C][C]1.3e-05[/C][/ROW]
[ROW][C]Dummy[/C][C]-12.1409361201919[/C][C]2.59814[/C][C]-4.6729[/C][C]2e-05[/C][C]1e-05[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]-0.170535875011005[/C][C]0.127664[/C][C]-1.3358[/C][C]0.18711[/C][C]0.093555[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]0.127341252226174[/C][C]0.127842[/C][C]0.9961[/C][C]0.323573[/C][C]0.161786[/C][/ROW]
[ROW][C]`Yt-3`[/C][C]0.406670131624456[/C][C]0.131509[/C][C]3.0923[/C][C]0.003117[/C][C]0.001558[/C][/ROW]
[ROW][C]`Yt-4`[/C][C]-0.115932126741984[/C][C]0.121414[/C][C]-0.9548[/C][C]0.343833[/C][C]0.171916[/C][/ROW]
[ROW][C]`Yt-5`[/C][C]-0.0322030815182641[/C][C]0.120282[/C][C]-0.2677[/C][C]0.789909[/C][C]0.394955[/C][/ROW]
[ROW][C]`Yt-6`[/C][C]0.125704389082812[/C][C]0.128168[/C][C]0.9808[/C][C]0.330995[/C][C]0.165498[/C][/ROW]
[ROW][C]M1[/C][C]-19.0624672402896[/C][C]2.382462[/C][C]-8.0012[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M2[/C][C]-15.1805417856902[/C][C]3.051581[/C][C]-4.9746[/C][C]7e-06[/C][C]3e-06[/C][/ROW]
[ROW][C]M3[/C][C]-0.526451480378921[/C][C]3.479885[/C][C]-0.1513[/C][C]0.880305[/C][C]0.440153[/C][/ROW]
[ROW][C]M4[/C][C]14.7571552687538[/C][C]4.455422[/C][C]3.3122[/C][C]0.00164[/C][C]0.00082[/C][/ROW]
[ROW][C]M5[/C][C]-1.15645418805891[/C][C]4.751963[/C][C]-0.2434[/C][C]0.808629[/C][C]0.404315[/C][/ROW]
[ROW][C]M6[/C][C]-16.4847096765184[/C][C]3.512189[/C][C]-4.6936[/C][C]1.8e-05[/C][C]9e-06[/C][/ROW]
[ROW][C]M7[/C][C]-11.7529419581613[/C][C]3.371446[/C][C]-3.486[/C][C]0.000971[/C][C]0.000486[/C][/ROW]
[ROW][C]M8[/C][C]-7.21825953770693[/C][C]3.443448[/C][C]-2.0962[/C][C]0.040676[/C][C]0.020338[/C][/ROW]
[ROW][C]M9[/C][C]2.70776198327648[/C][C]4.281735[/C][C]0.6324[/C][C]0.529747[/C][C]0.264873[/C][/ROW]
[ROW][C]M10[/C][C]-3.68093564071264[/C][C]4.096295[/C][C]-0.8986[/C][C]0.372782[/C][C]0.186391[/C][/ROW]
[ROW][C]M11[/C][C]-7.4642631479732[/C][C]2.88189[/C][C]-2.5901[/C][C]0.012259[/C][C]0.006129[/C][/ROW]
[ROW][C]t[/C][C]0.128245177155806[/C][C]0.038619[/C][C]3.3208[/C][C]0.001599[/C][C]0.000799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70019&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70019&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)70.84317165909215.4569064.58332.7e-051.3e-05
Dummy-12.14093612019192.59814-4.67292e-051e-05
`Yt-1`-0.1705358750110050.127664-1.33580.187110.093555
`Yt-2`0.1273412522261740.1278420.99610.3235730.161786
`Yt-3`0.4066701316244560.1315093.09230.0031170.001558
`Yt-4`-0.1159321267419840.121414-0.95480.3438330.171916
`Yt-5`-0.03220308151826410.120282-0.26770.7899090.394955
`Yt-6`0.1257043890828120.1281680.98080.3309950.165498
M1-19.06246724028962.382462-8.001200
M2-15.18054178569023.051581-4.97467e-063e-06
M3-0.5264514803789213.479885-0.15130.8803050.440153
M414.75715526875384.4554223.31220.001640.00082
M5-1.156454188058914.751963-0.24340.8086290.404315
M6-16.48470967651843.512189-4.69361.8e-059e-06
M7-11.75294195816133.371446-3.4860.0009710.000486
M8-7.218259537706933.443448-2.09620.0406760.020338
M92.707761983276484.2817350.63240.5297470.264873
M10-3.680935640712644.096295-0.89860.3727820.186391
M11-7.46426314797322.88189-2.59010.0122590.006129
t0.1282451771558060.0386193.32080.0015990.000799






Multiple Linear Regression - Regression Statistics
Multiple R0.956037433079494
R-squared0.914007573449228
Adjusted R-squared0.884301098822598
F-TEST (value)30.7679583301975
F-TEST (DF numerator)19
F-TEST (DF denominator)55
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.24878213411558
Sum Squared Residuals580.502194522171

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.956037433079494 \tabularnewline
R-squared & 0.914007573449228 \tabularnewline
Adjusted R-squared & 0.884301098822598 \tabularnewline
F-TEST (value) & 30.7679583301975 \tabularnewline
F-TEST (DF numerator) & 19 \tabularnewline
F-TEST (DF denominator) & 55 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.24878213411558 \tabularnewline
Sum Squared Residuals & 580.502194522171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70019&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.956037433079494[/C][/ROW]
[ROW][C]R-squared[/C][C]0.914007573449228[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.884301098822598[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]30.7679583301975[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]19[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]55[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.24878213411558[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]580.502194522171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70019&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70019&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R0.956037433079494
R-squared0.914007573449228
Adjusted R-squared0.884301098822598
F-TEST (value)30.7679583301975
F-TEST (DF numerator)19
F-TEST (DF denominator)55
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.24878213411558
Sum Squared Residuals580.502194522171






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
187.485.24581244931662.15418755068342
289.991.1086770543519-1.20867705435185
3109.8107.5659792500282.23402074997159
4111.7112.015227856697-0.315227856696888
598.6100.654711118671-2.05471111867122
696.997.0887552358055-0.188755235805451
795.196.8060798854834-1.70607988548339
89795.68526181473231.31473818526770
9112.7108.4539992207654.24600077923484
10102.999.88385900117283.01614099882724
1197.499.288654725945-1.88865472594506
12111.4112.579884202804-1.17988420280436
1387.484.464827567272.93517243273008
1496.892.98333580801333.81666419198670
15114.1111.7266016592512.37339834074884
16110.3112.947271720740-2.64727172073952
17103.9105.475800427504-1.57580042750357
18101.699.3616896471372.23831035286297
1994.696.9283644438593-2.32836444385928
2095.9100.954519472762-5.05451947276176
21104.7111.999382717118-7.29938271711795
22102.8101.5521342114191.24786578858060
2398.199.9514281190936-1.85142811909361
24113.9111.4677935468132.43220645318740
2580.986.5259300780725-5.62593007807252
2695.796.3647263809863-0.664726380986282
27113.2112.5585231439940.641476856006124
28105.9111.531321988285-5.6313219882853
29108.8107.9642003240160.835799675983572
30102.399.78980769918752.51019230081246
319996.50523878868152.49476121131850
32100.7104.225735573141-3.52573557314125
33115.5113.0252154323372.47478456766280
34100.7102.857828576880-2.15782857688021
35109.9105.2591057301054.64089426989528
36114.6114.5088584447380.0911415552623357
3785.487.7405741431553-2.34057414315528
38100.5102.523148752392-2.02314875239176
39114.8114.1938325746930.60616742530706
40116.5114.5135322494241.98646775057574
41112.9110.7902998739042.10970012609582
42102102.016647218873-0.0166472188729180
43106103.1537477631992.84625223680116
44105.3105.523047331630-0.223047331629558
45118.8113.9335328980494.86646710195109
46106.1108.501676524901-2.40167652490070
47109.3107.8815869012351.41841309876503
48117.2117.383355621630-0.183355621630165
4992.591.30495748377981.19504251622018
50104.2102.7843078788611.41569212113938
51112.5117.373744315871-4.87374431587117
52122.4120.1999294760192.20007052398130
53113.3111.5526061988341.74739380116604
54100102.972587744027-2.97258774402668
55110.7108.5240455689422.17595443105776
56112.8106.0236301724666.77636982753436
57109.8113.453128457005-3.65312845700514
58117.3115.4024894526661.89751054733407
59109.1108.9842888671120.115711132888437
60115.9115.4503415509490.449658449051261
619698.9875101288926-2.98751012889258
6299.8103.413667620248-3.61366762024811
63116.8118.111239914068-1.31123991406762
64115.7111.2927167088354.40728329116467
6599.4100.462382057071-1.06238205707065
6694.395.8705124549704-1.57051245497038
679194.4825235498348-3.48252354983475
6893.292.48780563526950.712194364730514
69103.1103.734741274726-0.634741274725637
7094.195.702012232961-1.60201223296099
7191.894.23493565651-2.43493565651008
72102.7104.309766633066-1.60976663306648
7382.677.93038814951334.66961185048669
7489.186.82213650514812.27786349485193
75104.5104.1700791420950.329920857905177

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 87.4 & 85.2458124493166 & 2.15418755068342 \tabularnewline
2 & 89.9 & 91.1086770543519 & -1.20867705435185 \tabularnewline
3 & 109.8 & 107.565979250028 & 2.23402074997159 \tabularnewline
4 & 111.7 & 112.015227856697 & -0.315227856696888 \tabularnewline
5 & 98.6 & 100.654711118671 & -2.05471111867122 \tabularnewline
6 & 96.9 & 97.0887552358055 & -0.188755235805451 \tabularnewline
7 & 95.1 & 96.8060798854834 & -1.70607988548339 \tabularnewline
8 & 97 & 95.6852618147323 & 1.31473818526770 \tabularnewline
9 & 112.7 & 108.453999220765 & 4.24600077923484 \tabularnewline
10 & 102.9 & 99.8838590011728 & 3.01614099882724 \tabularnewline
11 & 97.4 & 99.288654725945 & -1.88865472594506 \tabularnewline
12 & 111.4 & 112.579884202804 & -1.17988420280436 \tabularnewline
13 & 87.4 & 84.46482756727 & 2.93517243273008 \tabularnewline
14 & 96.8 & 92.9833358080133 & 3.81666419198670 \tabularnewline
15 & 114.1 & 111.726601659251 & 2.37339834074884 \tabularnewline
16 & 110.3 & 112.947271720740 & -2.64727172073952 \tabularnewline
17 & 103.9 & 105.475800427504 & -1.57580042750357 \tabularnewline
18 & 101.6 & 99.361689647137 & 2.23831035286297 \tabularnewline
19 & 94.6 & 96.9283644438593 & -2.32836444385928 \tabularnewline
20 & 95.9 & 100.954519472762 & -5.05451947276176 \tabularnewline
21 & 104.7 & 111.999382717118 & -7.29938271711795 \tabularnewline
22 & 102.8 & 101.552134211419 & 1.24786578858060 \tabularnewline
23 & 98.1 & 99.9514281190936 & -1.85142811909361 \tabularnewline
24 & 113.9 & 111.467793546813 & 2.43220645318740 \tabularnewline
25 & 80.9 & 86.5259300780725 & -5.62593007807252 \tabularnewline
26 & 95.7 & 96.3647263809863 & -0.664726380986282 \tabularnewline
27 & 113.2 & 112.558523143994 & 0.641476856006124 \tabularnewline
28 & 105.9 & 111.531321988285 & -5.6313219882853 \tabularnewline
29 & 108.8 & 107.964200324016 & 0.835799675983572 \tabularnewline
30 & 102.3 & 99.7898076991875 & 2.51019230081246 \tabularnewline
31 & 99 & 96.5052387886815 & 2.49476121131850 \tabularnewline
32 & 100.7 & 104.225735573141 & -3.52573557314125 \tabularnewline
33 & 115.5 & 113.025215432337 & 2.47478456766280 \tabularnewline
34 & 100.7 & 102.857828576880 & -2.15782857688021 \tabularnewline
35 & 109.9 & 105.259105730105 & 4.64089426989528 \tabularnewline
36 & 114.6 & 114.508858444738 & 0.0911415552623357 \tabularnewline
37 & 85.4 & 87.7405741431553 & -2.34057414315528 \tabularnewline
38 & 100.5 & 102.523148752392 & -2.02314875239176 \tabularnewline
39 & 114.8 & 114.193832574693 & 0.60616742530706 \tabularnewline
40 & 116.5 & 114.513532249424 & 1.98646775057574 \tabularnewline
41 & 112.9 & 110.790299873904 & 2.10970012609582 \tabularnewline
42 & 102 & 102.016647218873 & -0.0166472188729180 \tabularnewline
43 & 106 & 103.153747763199 & 2.84625223680116 \tabularnewline
44 & 105.3 & 105.523047331630 & -0.223047331629558 \tabularnewline
45 & 118.8 & 113.933532898049 & 4.86646710195109 \tabularnewline
46 & 106.1 & 108.501676524901 & -2.40167652490070 \tabularnewline
47 & 109.3 & 107.881586901235 & 1.41841309876503 \tabularnewline
48 & 117.2 & 117.383355621630 & -0.183355621630165 \tabularnewline
49 & 92.5 & 91.3049574837798 & 1.19504251622018 \tabularnewline
50 & 104.2 & 102.784307878861 & 1.41569212113938 \tabularnewline
51 & 112.5 & 117.373744315871 & -4.87374431587117 \tabularnewline
52 & 122.4 & 120.199929476019 & 2.20007052398130 \tabularnewline
53 & 113.3 & 111.552606198834 & 1.74739380116604 \tabularnewline
54 & 100 & 102.972587744027 & -2.97258774402668 \tabularnewline
55 & 110.7 & 108.524045568942 & 2.17595443105776 \tabularnewline
56 & 112.8 & 106.023630172466 & 6.77636982753436 \tabularnewline
57 & 109.8 & 113.453128457005 & -3.65312845700514 \tabularnewline
58 & 117.3 & 115.402489452666 & 1.89751054733407 \tabularnewline
59 & 109.1 & 108.984288867112 & 0.115711132888437 \tabularnewline
60 & 115.9 & 115.450341550949 & 0.449658449051261 \tabularnewline
61 & 96 & 98.9875101288926 & -2.98751012889258 \tabularnewline
62 & 99.8 & 103.413667620248 & -3.61366762024811 \tabularnewline
63 & 116.8 & 118.111239914068 & -1.31123991406762 \tabularnewline
64 & 115.7 & 111.292716708835 & 4.40728329116467 \tabularnewline
65 & 99.4 & 100.462382057071 & -1.06238205707065 \tabularnewline
66 & 94.3 & 95.8705124549704 & -1.57051245497038 \tabularnewline
67 & 91 & 94.4825235498348 & -3.48252354983475 \tabularnewline
68 & 93.2 & 92.4878056352695 & 0.712194364730514 \tabularnewline
69 & 103.1 & 103.734741274726 & -0.634741274725637 \tabularnewline
70 & 94.1 & 95.702012232961 & -1.60201223296099 \tabularnewline
71 & 91.8 & 94.23493565651 & -2.43493565651008 \tabularnewline
72 & 102.7 & 104.309766633066 & -1.60976663306648 \tabularnewline
73 & 82.6 & 77.9303881495133 & 4.66961185048669 \tabularnewline
74 & 89.1 & 86.8221365051481 & 2.27786349485193 \tabularnewline
75 & 104.5 & 104.170079142095 & 0.329920857905177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70019&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]87.4[/C][C]85.2458124493166[/C][C]2.15418755068342[/C][/ROW]
[ROW][C]2[/C][C]89.9[/C][C]91.1086770543519[/C][C]-1.20867705435185[/C][/ROW]
[ROW][C]3[/C][C]109.8[/C][C]107.565979250028[/C][C]2.23402074997159[/C][/ROW]
[ROW][C]4[/C][C]111.7[/C][C]112.015227856697[/C][C]-0.315227856696888[/C][/ROW]
[ROW][C]5[/C][C]98.6[/C][C]100.654711118671[/C][C]-2.05471111867122[/C][/ROW]
[ROW][C]6[/C][C]96.9[/C][C]97.0887552358055[/C][C]-0.188755235805451[/C][/ROW]
[ROW][C]7[/C][C]95.1[/C][C]96.8060798854834[/C][C]-1.70607988548339[/C][/ROW]
[ROW][C]8[/C][C]97[/C][C]95.6852618147323[/C][C]1.31473818526770[/C][/ROW]
[ROW][C]9[/C][C]112.7[/C][C]108.453999220765[/C][C]4.24600077923484[/C][/ROW]
[ROW][C]10[/C][C]102.9[/C][C]99.8838590011728[/C][C]3.01614099882724[/C][/ROW]
[ROW][C]11[/C][C]97.4[/C][C]99.288654725945[/C][C]-1.88865472594506[/C][/ROW]
[ROW][C]12[/C][C]111.4[/C][C]112.579884202804[/C][C]-1.17988420280436[/C][/ROW]
[ROW][C]13[/C][C]87.4[/C][C]84.46482756727[/C][C]2.93517243273008[/C][/ROW]
[ROW][C]14[/C][C]96.8[/C][C]92.9833358080133[/C][C]3.81666419198670[/C][/ROW]
[ROW][C]15[/C][C]114.1[/C][C]111.726601659251[/C][C]2.37339834074884[/C][/ROW]
[ROW][C]16[/C][C]110.3[/C][C]112.947271720740[/C][C]-2.64727172073952[/C][/ROW]
[ROW][C]17[/C][C]103.9[/C][C]105.475800427504[/C][C]-1.57580042750357[/C][/ROW]
[ROW][C]18[/C][C]101.6[/C][C]99.361689647137[/C][C]2.23831035286297[/C][/ROW]
[ROW][C]19[/C][C]94.6[/C][C]96.9283644438593[/C][C]-2.32836444385928[/C][/ROW]
[ROW][C]20[/C][C]95.9[/C][C]100.954519472762[/C][C]-5.05451947276176[/C][/ROW]
[ROW][C]21[/C][C]104.7[/C][C]111.999382717118[/C][C]-7.29938271711795[/C][/ROW]
[ROW][C]22[/C][C]102.8[/C][C]101.552134211419[/C][C]1.24786578858060[/C][/ROW]
[ROW][C]23[/C][C]98.1[/C][C]99.9514281190936[/C][C]-1.85142811909361[/C][/ROW]
[ROW][C]24[/C][C]113.9[/C][C]111.467793546813[/C][C]2.43220645318740[/C][/ROW]
[ROW][C]25[/C][C]80.9[/C][C]86.5259300780725[/C][C]-5.62593007807252[/C][/ROW]
[ROW][C]26[/C][C]95.7[/C][C]96.3647263809863[/C][C]-0.664726380986282[/C][/ROW]
[ROW][C]27[/C][C]113.2[/C][C]112.558523143994[/C][C]0.641476856006124[/C][/ROW]
[ROW][C]28[/C][C]105.9[/C][C]111.531321988285[/C][C]-5.6313219882853[/C][/ROW]
[ROW][C]29[/C][C]108.8[/C][C]107.964200324016[/C][C]0.835799675983572[/C][/ROW]
[ROW][C]30[/C][C]102.3[/C][C]99.7898076991875[/C][C]2.51019230081246[/C][/ROW]
[ROW][C]31[/C][C]99[/C][C]96.5052387886815[/C][C]2.49476121131850[/C][/ROW]
[ROW][C]32[/C][C]100.7[/C][C]104.225735573141[/C][C]-3.52573557314125[/C][/ROW]
[ROW][C]33[/C][C]115.5[/C][C]113.025215432337[/C][C]2.47478456766280[/C][/ROW]
[ROW][C]34[/C][C]100.7[/C][C]102.857828576880[/C][C]-2.15782857688021[/C][/ROW]
[ROW][C]35[/C][C]109.9[/C][C]105.259105730105[/C][C]4.64089426989528[/C][/ROW]
[ROW][C]36[/C][C]114.6[/C][C]114.508858444738[/C][C]0.0911415552623357[/C][/ROW]
[ROW][C]37[/C][C]85.4[/C][C]87.7405741431553[/C][C]-2.34057414315528[/C][/ROW]
[ROW][C]38[/C][C]100.5[/C][C]102.523148752392[/C][C]-2.02314875239176[/C][/ROW]
[ROW][C]39[/C][C]114.8[/C][C]114.193832574693[/C][C]0.60616742530706[/C][/ROW]
[ROW][C]40[/C][C]116.5[/C][C]114.513532249424[/C][C]1.98646775057574[/C][/ROW]
[ROW][C]41[/C][C]112.9[/C][C]110.790299873904[/C][C]2.10970012609582[/C][/ROW]
[ROW][C]42[/C][C]102[/C][C]102.016647218873[/C][C]-0.0166472188729180[/C][/ROW]
[ROW][C]43[/C][C]106[/C][C]103.153747763199[/C][C]2.84625223680116[/C][/ROW]
[ROW][C]44[/C][C]105.3[/C][C]105.523047331630[/C][C]-0.223047331629558[/C][/ROW]
[ROW][C]45[/C][C]118.8[/C][C]113.933532898049[/C][C]4.86646710195109[/C][/ROW]
[ROW][C]46[/C][C]106.1[/C][C]108.501676524901[/C][C]-2.40167652490070[/C][/ROW]
[ROW][C]47[/C][C]109.3[/C][C]107.881586901235[/C][C]1.41841309876503[/C][/ROW]
[ROW][C]48[/C][C]117.2[/C][C]117.383355621630[/C][C]-0.183355621630165[/C][/ROW]
[ROW][C]49[/C][C]92.5[/C][C]91.3049574837798[/C][C]1.19504251622018[/C][/ROW]
[ROW][C]50[/C][C]104.2[/C][C]102.784307878861[/C][C]1.41569212113938[/C][/ROW]
[ROW][C]51[/C][C]112.5[/C][C]117.373744315871[/C][C]-4.87374431587117[/C][/ROW]
[ROW][C]52[/C][C]122.4[/C][C]120.199929476019[/C][C]2.20007052398130[/C][/ROW]
[ROW][C]53[/C][C]113.3[/C][C]111.552606198834[/C][C]1.74739380116604[/C][/ROW]
[ROW][C]54[/C][C]100[/C][C]102.972587744027[/C][C]-2.97258774402668[/C][/ROW]
[ROW][C]55[/C][C]110.7[/C][C]108.524045568942[/C][C]2.17595443105776[/C][/ROW]
[ROW][C]56[/C][C]112.8[/C][C]106.023630172466[/C][C]6.77636982753436[/C][/ROW]
[ROW][C]57[/C][C]109.8[/C][C]113.453128457005[/C][C]-3.65312845700514[/C][/ROW]
[ROW][C]58[/C][C]117.3[/C][C]115.402489452666[/C][C]1.89751054733407[/C][/ROW]
[ROW][C]59[/C][C]109.1[/C][C]108.984288867112[/C][C]0.115711132888437[/C][/ROW]
[ROW][C]60[/C][C]115.9[/C][C]115.450341550949[/C][C]0.449658449051261[/C][/ROW]
[ROW][C]61[/C][C]96[/C][C]98.9875101288926[/C][C]-2.98751012889258[/C][/ROW]
[ROW][C]62[/C][C]99.8[/C][C]103.413667620248[/C][C]-3.61366762024811[/C][/ROW]
[ROW][C]63[/C][C]116.8[/C][C]118.111239914068[/C][C]-1.31123991406762[/C][/ROW]
[ROW][C]64[/C][C]115.7[/C][C]111.292716708835[/C][C]4.40728329116467[/C][/ROW]
[ROW][C]65[/C][C]99.4[/C][C]100.462382057071[/C][C]-1.06238205707065[/C][/ROW]
[ROW][C]66[/C][C]94.3[/C][C]95.8705124549704[/C][C]-1.57051245497038[/C][/ROW]
[ROW][C]67[/C][C]91[/C][C]94.4825235498348[/C][C]-3.48252354983475[/C][/ROW]
[ROW][C]68[/C][C]93.2[/C][C]92.4878056352695[/C][C]0.712194364730514[/C][/ROW]
[ROW][C]69[/C][C]103.1[/C][C]103.734741274726[/C][C]-0.634741274725637[/C][/ROW]
[ROW][C]70[/C][C]94.1[/C][C]95.702012232961[/C][C]-1.60201223296099[/C][/ROW]
[ROW][C]71[/C][C]91.8[/C][C]94.23493565651[/C][C]-2.43493565651008[/C][/ROW]
[ROW][C]72[/C][C]102.7[/C][C]104.309766633066[/C][C]-1.60976663306648[/C][/ROW]
[ROW][C]73[/C][C]82.6[/C][C]77.9303881495133[/C][C]4.66961185048669[/C][/ROW]
[ROW][C]74[/C][C]89.1[/C][C]86.8221365051481[/C][C]2.27786349485193[/C][/ROW]
[ROW][C]75[/C][C]104.5[/C][C]104.170079142095[/C][C]0.329920857905177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70019&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70019&T=4

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


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
187.485.24581244931662.15418755068342
289.991.1086770543519-1.20867705435185
3109.8107.5659792500282.23402074997159
4111.7112.015227856697-0.315227856696888
598.6100.654711118671-2.05471111867122
696.997.0887552358055-0.188755235805451
795.196.8060798854834-1.70607988548339
89795.68526181473231.31473818526770
9112.7108.4539992207654.24600077923484
10102.999.88385900117283.01614099882724
1197.499.288654725945-1.88865472594506
12111.4112.579884202804-1.17988420280436
1387.484.464827567272.93517243273008
1496.892.98333580801333.81666419198670
15114.1111.7266016592512.37339834074884
16110.3112.947271720740-2.64727172073952
17103.9105.475800427504-1.57580042750357
18101.699.3616896471372.23831035286297
1994.696.9283644438593-2.32836444385928
2095.9100.954519472762-5.05451947276176
21104.7111.999382717118-7.29938271711795
22102.8101.5521342114191.24786578858060
2398.199.9514281190936-1.85142811909361
24113.9111.4677935468132.43220645318740
2580.986.5259300780725-5.62593007807252
2695.796.3647263809863-0.664726380986282
27113.2112.5585231439940.641476856006124
28105.9111.531321988285-5.6313219882853
29108.8107.9642003240160.835799675983572
30102.399.78980769918752.51019230081246
319996.50523878868152.49476121131850
32100.7104.225735573141-3.52573557314125
33115.5113.0252154323372.47478456766280
34100.7102.857828576880-2.15782857688021
35109.9105.2591057301054.64089426989528
36114.6114.5088584447380.0911415552623357
3785.487.7405741431553-2.34057414315528
38100.5102.523148752392-2.02314875239176
39114.8114.1938325746930.60616742530706
40116.5114.5135322494241.98646775057574
41112.9110.7902998739042.10970012609582
42102102.016647218873-0.0166472188729180
43106103.1537477631992.84625223680116
44105.3105.523047331630-0.223047331629558
45118.8113.9335328980494.86646710195109
46106.1108.501676524901-2.40167652490070
47109.3107.8815869012351.41841309876503
48117.2117.383355621630-0.183355621630165
4992.591.30495748377981.19504251622018
50104.2102.7843078788611.41569212113938
51112.5117.373744315871-4.87374431587117
52122.4120.1999294760192.20007052398130
53113.3111.5526061988341.74739380116604
54100102.972587744027-2.97258774402668
55110.7108.5240455689422.17595443105776
56112.8106.0236301724666.77636982753436
57109.8113.453128457005-3.65312845700514
58117.3115.4024894526661.89751054733407
59109.1108.9842888671120.115711132888437
60115.9115.4503415509490.449658449051261
619698.9875101288926-2.98751012889258
6299.8103.413667620248-3.61366762024811
63116.8118.111239914068-1.31123991406762
64115.7111.2927167088354.40728329116467
6599.4100.462382057071-1.06238205707065
6694.395.8705124549704-1.57051245497038
679194.4825235498348-3.48252354983475
6893.292.48780563526950.712194364730514
69103.1103.734741274726-0.634741274725637
7094.195.702012232961-1.60201223296099
7191.894.23493565651-2.43493565651008
72102.7104.309766633066-1.60976663306648
7382.677.93038814951334.66961185048669
7489.186.82213650514812.27786349485193
75104.5104.1700791420950.329920857905177






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
230.7589497830207080.4821004339585840.241050216979292
240.6948077907708590.6103844184582810.305192209229141
250.7159134175749330.5681731648501340.284086582425067
260.7961560719737520.4076878560524960.203843928026248
270.7584851521130290.4830296957739420.241514847886971
280.8332945736280020.3334108527439970.166705426371998
290.7948731081699190.4102537836601620.205126891830081
300.8047284241779960.3905431516440090.195271575822004
310.7835918328431860.4328163343136280.216408167156814
320.8118522178659040.3762955642681930.188147782134096
330.8406491307424430.3187017385151150.159350869257557
340.8099502582326440.3800994835347110.190049741767356
350.8719528304449720.2560943391100560.128047169555028
360.815452710933650.3690945781326990.184547289066350
370.81436893136260.3712621372748010.185631068637401
380.7877504979608390.4244990040783230.212249502039161
390.7221803527843430.5556392944313140.277819647215657
400.6924187121056480.6151625757887040.307581287894352
410.6185666992441850.762866601511630.381433300755815
420.5248262860068060.9503474279863890.475173713993194
430.4581740907626540.9163481815253080.541825909237346
440.5578657001802630.8842685996394750.442134299819737
450.5601575474682410.8796849050635180.439842452531759
460.578081036698670.843837926602660.42191896330133
470.5774706664164660.8450586671670690.422529333583534
480.4938023450920070.9876046901840140.506197654907993
490.436883149728950.87376629945790.56311685027105
500.3271959850539990.6543919701079980.672804014946001
510.2603820910852080.5207641821704150.739617908914792
520.2224405069848590.4448810139697180.777559493015141

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
23 & 0.758949783020708 & 0.482100433958584 & 0.241050216979292 \tabularnewline
24 & 0.694807790770859 & 0.610384418458281 & 0.305192209229141 \tabularnewline
25 & 0.715913417574933 & 0.568173164850134 & 0.284086582425067 \tabularnewline
26 & 0.796156071973752 & 0.407687856052496 & 0.203843928026248 \tabularnewline
27 & 0.758485152113029 & 0.483029695773942 & 0.241514847886971 \tabularnewline
28 & 0.833294573628002 & 0.333410852743997 & 0.166705426371998 \tabularnewline
29 & 0.794873108169919 & 0.410253783660162 & 0.205126891830081 \tabularnewline
30 & 0.804728424177996 & 0.390543151644009 & 0.195271575822004 \tabularnewline
31 & 0.783591832843186 & 0.432816334313628 & 0.216408167156814 \tabularnewline
32 & 0.811852217865904 & 0.376295564268193 & 0.188147782134096 \tabularnewline
33 & 0.840649130742443 & 0.318701738515115 & 0.159350869257557 \tabularnewline
34 & 0.809950258232644 & 0.380099483534711 & 0.190049741767356 \tabularnewline
35 & 0.871952830444972 & 0.256094339110056 & 0.128047169555028 \tabularnewline
36 & 0.81545271093365 & 0.369094578132699 & 0.184547289066350 \tabularnewline
37 & 0.8143689313626 & 0.371262137274801 & 0.185631068637401 \tabularnewline
38 & 0.787750497960839 & 0.424499004078323 & 0.212249502039161 \tabularnewline
39 & 0.722180352784343 & 0.555639294431314 & 0.277819647215657 \tabularnewline
40 & 0.692418712105648 & 0.615162575788704 & 0.307581287894352 \tabularnewline
41 & 0.618566699244185 & 0.76286660151163 & 0.381433300755815 \tabularnewline
42 & 0.524826286006806 & 0.950347427986389 & 0.475173713993194 \tabularnewline
43 & 0.458174090762654 & 0.916348181525308 & 0.541825909237346 \tabularnewline
44 & 0.557865700180263 & 0.884268599639475 & 0.442134299819737 \tabularnewline
45 & 0.560157547468241 & 0.879684905063518 & 0.439842452531759 \tabularnewline
46 & 0.57808103669867 & 0.84383792660266 & 0.42191896330133 \tabularnewline
47 & 0.577470666416466 & 0.845058667167069 & 0.422529333583534 \tabularnewline
48 & 0.493802345092007 & 0.987604690184014 & 0.506197654907993 \tabularnewline
49 & 0.43688314972895 & 0.8737662994579 & 0.56311685027105 \tabularnewline
50 & 0.327195985053999 & 0.654391970107998 & 0.672804014946001 \tabularnewline
51 & 0.260382091085208 & 0.520764182170415 & 0.739617908914792 \tabularnewline
52 & 0.222440506984859 & 0.444881013969718 & 0.777559493015141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70019&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]23[/C][C]0.758949783020708[/C][C]0.482100433958584[/C][C]0.241050216979292[/C][/ROW]
[ROW][C]24[/C][C]0.694807790770859[/C][C]0.610384418458281[/C][C]0.305192209229141[/C][/ROW]
[ROW][C]25[/C][C]0.715913417574933[/C][C]0.568173164850134[/C][C]0.284086582425067[/C][/ROW]
[ROW][C]26[/C][C]0.796156071973752[/C][C]0.407687856052496[/C][C]0.203843928026248[/C][/ROW]
[ROW][C]27[/C][C]0.758485152113029[/C][C]0.483029695773942[/C][C]0.241514847886971[/C][/ROW]
[ROW][C]28[/C][C]0.833294573628002[/C][C]0.333410852743997[/C][C]0.166705426371998[/C][/ROW]
[ROW][C]29[/C][C]0.794873108169919[/C][C]0.410253783660162[/C][C]0.205126891830081[/C][/ROW]
[ROW][C]30[/C][C]0.804728424177996[/C][C]0.390543151644009[/C][C]0.195271575822004[/C][/ROW]
[ROW][C]31[/C][C]0.783591832843186[/C][C]0.432816334313628[/C][C]0.216408167156814[/C][/ROW]
[ROW][C]32[/C][C]0.811852217865904[/C][C]0.376295564268193[/C][C]0.188147782134096[/C][/ROW]
[ROW][C]33[/C][C]0.840649130742443[/C][C]0.318701738515115[/C][C]0.159350869257557[/C][/ROW]
[ROW][C]34[/C][C]0.809950258232644[/C][C]0.380099483534711[/C][C]0.190049741767356[/C][/ROW]
[ROW][C]35[/C][C]0.871952830444972[/C][C]0.256094339110056[/C][C]0.128047169555028[/C][/ROW]
[ROW][C]36[/C][C]0.81545271093365[/C][C]0.369094578132699[/C][C]0.184547289066350[/C][/ROW]
[ROW][C]37[/C][C]0.8143689313626[/C][C]0.371262137274801[/C][C]0.185631068637401[/C][/ROW]
[ROW][C]38[/C][C]0.787750497960839[/C][C]0.424499004078323[/C][C]0.212249502039161[/C][/ROW]
[ROW][C]39[/C][C]0.722180352784343[/C][C]0.555639294431314[/C][C]0.277819647215657[/C][/ROW]
[ROW][C]40[/C][C]0.692418712105648[/C][C]0.615162575788704[/C][C]0.307581287894352[/C][/ROW]
[ROW][C]41[/C][C]0.618566699244185[/C][C]0.76286660151163[/C][C]0.381433300755815[/C][/ROW]
[ROW][C]42[/C][C]0.524826286006806[/C][C]0.950347427986389[/C][C]0.475173713993194[/C][/ROW]
[ROW][C]43[/C][C]0.458174090762654[/C][C]0.916348181525308[/C][C]0.541825909237346[/C][/ROW]
[ROW][C]44[/C][C]0.557865700180263[/C][C]0.884268599639475[/C][C]0.442134299819737[/C][/ROW]
[ROW][C]45[/C][C]0.560157547468241[/C][C]0.879684905063518[/C][C]0.439842452531759[/C][/ROW]
[ROW][C]46[/C][C]0.57808103669867[/C][C]0.84383792660266[/C][C]0.42191896330133[/C][/ROW]
[ROW][C]47[/C][C]0.577470666416466[/C][C]0.845058667167069[/C][C]0.422529333583534[/C][/ROW]
[ROW][C]48[/C][C]0.493802345092007[/C][C]0.987604690184014[/C][C]0.506197654907993[/C][/ROW]
[ROW][C]49[/C][C]0.43688314972895[/C][C]0.8737662994579[/C][C]0.56311685027105[/C][/ROW]
[ROW][C]50[/C][C]0.327195985053999[/C][C]0.654391970107998[/C][C]0.672804014946001[/C][/ROW]
[ROW][C]51[/C][C]0.260382091085208[/C][C]0.520764182170415[/C][C]0.739617908914792[/C][/ROW]
[ROW][C]52[/C][C]0.222440506984859[/C][C]0.444881013969718[/C][C]0.777559493015141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70019&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70019&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
230.7589497830207080.4821004339585840.241050216979292
240.6948077907708590.6103844184582810.305192209229141
250.7159134175749330.5681731648501340.284086582425067
260.7961560719737520.4076878560524960.203843928026248
270.7584851521130290.4830296957739420.241514847886971
280.8332945736280020.3334108527439970.166705426371998
290.7948731081699190.4102537836601620.205126891830081
300.8047284241779960.3905431516440090.195271575822004
310.7835918328431860.4328163343136280.216408167156814
320.8118522178659040.3762955642681930.188147782134096
330.8406491307424430.3187017385151150.159350869257557
340.8099502582326440.3800994835347110.190049741767356
350.8719528304449720.2560943391100560.128047169555028
360.815452710933650.3690945781326990.184547289066350
370.81436893136260.3712621372748010.185631068637401
380.7877504979608390.4244990040783230.212249502039161
390.7221803527843430.5556392944313140.277819647215657
400.6924187121056480.6151625757887040.307581287894352
410.6185666992441850.762866601511630.381433300755815
420.5248262860068060.9503474279863890.475173713993194
430.4581740907626540.9163481815253080.541825909237346
440.5578657001802630.8842685996394750.442134299819737
450.5601575474682410.8796849050635180.439842452531759
460.578081036698670.843837926602660.42191896330133
470.5774706664164660.8450586671670690.422529333583534
480.4938023450920070.9876046901840140.506197654907993
490.436883149728950.87376629945790.56311685027105
500.3271959850539990.6543919701079980.672804014946001
510.2603820910852080.5207641821704150.739617908914792
520.2224405069848590.4448810139697180.777559493015141






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70019&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70019&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70019&T=6

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


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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}