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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 computationTue, 11 Jan 2011 17:11:15 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jan/11/t1294765746bdi7bpi4e8yaomu.htm/, Retrieved Thu, 16 May 2024 07:58:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117302, Retrieved Thu, 16 May 2024 07:58:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact257

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [MultipleRegression2] [2010-12-28 10:10:04] [9c3137400ced3280b419f1e434c29e1d]
-    D    [Multiple Regression] [] [2011-01-11 17:11:15] [9d4f9c24554023ef0148ede5dd3a4d11] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-6	-18	5
-3	-14	0
-3	-12	-2
-7	-17	6
-9	-23	11
-11	-28	9
-13	-31	17
-11	-21	21
-9	-19	21
-17	-22	41
-22	-22	57
-25	-25	65
-20	-16	68
-24	-22	73
-24	-21	71
-22	-10	71
-19	-7	70
-18	-5	69
-17	-4	65
-11	7	57
-11	6	57
-12	3	57
-10	10	55
-15	0	65
-15	-2	65
-15	-1	64
-13	2	60
-8	8	43
-13	-6	47
-9	-4	40
-7	4	31
-4	7	27
-4	3	24
-2	3	23
0	8	17
-2	3	16

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117302&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117302&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






Multiple Linear Regression - Estimated Regression Equation
IndVertr[t] = + 1.23684610450222 + 0.336358713273435EcoSit[t] -0.255267744122394`werkl `[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
IndVertr[t] =  +  1.23684610450222 +  0.336358713273435EcoSit[t] -0.255267744122394`werkl
`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117302&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]IndVertr[t] =  +  1.23684610450222 +  0.336358713273435EcoSit[t] -0.255267744122394`werkl
`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117302&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
IndVertr[t] = + 1.23684610450222 + 0.336358713273435EcoSit[t] -0.255267744122394`werkl `[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.236846104502220.3202653.86190.0004970.000248
EcoSit0.3363587132734350.01226327.429600
`werkl `-0.2552677441223940.006086-41.940600

\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) & 1.23684610450222 & 0.320265 & 3.8619 & 0.000497 & 0.000248 \tabularnewline
EcoSit & 0.336358713273435 & 0.012263 & 27.4296 & 0 & 0 \tabularnewline
`werkl
` & -0.255267744122394 & 0.006086 & -41.9406 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117302&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]1.23684610450222[/C][C]0.320265[/C][C]3.8619[/C][C]0.000497[/C][C]0.000248[/C][/ROW]
[ROW][C]EcoSit[/C][C]0.336358713273435[/C][C]0.012263[/C][C]27.4296[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`werkl
`[/C][C]-0.255267744122394[/C][C]0.006086[/C][C]-41.9406[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117302&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)1.236846104502220.3202653.86190.0004970.000248
EcoSit0.3363587132734350.01226327.429600
`werkl `-0.2552677441223940.006086-41.940600






Multiple Linear Regression - Regression Statistics
Multiple R0.992453659055503
R-squared0.984964265372656
Adjusted R-squared0.984053008728575
F-TEST (value)1080.8856887573
F-TEST (DF numerator)2
F-TEST (DF denominator)33
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.868886340829
Sum Squared Residuals24.9137946182139

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.992453659055503 \tabularnewline
R-squared & 0.984964265372656 \tabularnewline
Adjusted R-squared & 0.984053008728575 \tabularnewline
F-TEST (value) & 1080.8856887573 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 33 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.868886340829 \tabularnewline
Sum Squared Residuals & 24.9137946182139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117302&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.992453659055503[/C][/ROW]
[ROW][C]R-squared[/C][C]0.984964265372656[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.984053008728575[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1080.8856887573[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]33[/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]0.868886340829[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]24.9137946182139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117302&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117302&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 R0.992453659055503
R-squared0.984964265372656
Adjusted R-squared0.984053008728575
F-TEST (value)1080.8856887573
F-TEST (DF numerator)2
F-TEST (DF denominator)33
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.868886340829
Sum Squared Residuals24.9137946182139






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1-6-6.093949455031560.09394945503156
2-3-3.472175881325870.472175881325874
3-3-2.2889229665342-0.711077033465802
4-7-6.01285848588054-0.987141514119458
5-9-9.307349486133130.307349486133126
6-11-10.4786075642555-0.521392435744486
7-13-13.5298256570550.529825657054974
8-11-11.18730950081020.187309500810196
9-9-10.51459207426331.51459207426332
10-17-16.6290230965315-0.370976903468487
11-22-20.7133070024898-1.28669299751018
12-25-23.7645250952893-1.23547490471072
13-20-21.50309990819551.50309990819554
14-24-24.79759090844810.797590908448125
15-24-23.9506967069299-0.0493032930701001
16-22-20.2507508609221-1.74924913907789
17-19-18.9864069769794-0.0135930230205905
18-18-18.05842180631010.0584218063101438
19-17-16.7009921165471-0.299007883452868
20-11-10.9589043175602-0.0410956824398116
21-11-11.29526303083360.295263030833624
22-12-12.30433917065390.304339170653931
23-10-9.43929268949509-0.560707310504907
24-15-15.35555726345340.35555726345339
25-15-16.02827469000031.02827469000026
26-15-15.43664823260440.43664823260443
27-13-13.40650111629450.406501116294548
28-8-7.04879718657323-0.951202813426765
29-13-12.7788901488909-0.221109851109091
30-9-10.31929851348731.31929851348728
31-7-5.33101911019825-1.66898088980175
32-4-3.30087199388837-0.699128006111634
33-4-3.88050361461493-0.119496385385074
34-2-3.625235870492531.62523587049253
350-0.4118358393909890.411835839390989
36-2-1.83836166163577-0.161638338364227

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & -6 & -6.09394945503156 & 0.09394945503156 \tabularnewline
2 & -3 & -3.47217588132587 & 0.472175881325874 \tabularnewline
3 & -3 & -2.2889229665342 & -0.711077033465802 \tabularnewline
4 & -7 & -6.01285848588054 & -0.987141514119458 \tabularnewline
5 & -9 & -9.30734948613313 & 0.307349486133126 \tabularnewline
6 & -11 & -10.4786075642555 & -0.521392435744486 \tabularnewline
7 & -13 & -13.529825657055 & 0.529825657054974 \tabularnewline
8 & -11 & -11.1873095008102 & 0.187309500810196 \tabularnewline
9 & -9 & -10.5145920742633 & 1.51459207426332 \tabularnewline
10 & -17 & -16.6290230965315 & -0.370976903468487 \tabularnewline
11 & -22 & -20.7133070024898 & -1.28669299751018 \tabularnewline
12 & -25 & -23.7645250952893 & -1.23547490471072 \tabularnewline
13 & -20 & -21.5030999081955 & 1.50309990819554 \tabularnewline
14 & -24 & -24.7975909084481 & 0.797590908448125 \tabularnewline
15 & -24 & -23.9506967069299 & -0.0493032930701001 \tabularnewline
16 & -22 & -20.2507508609221 & -1.74924913907789 \tabularnewline
17 & -19 & -18.9864069769794 & -0.0135930230205905 \tabularnewline
18 & -18 & -18.0584218063101 & 0.0584218063101438 \tabularnewline
19 & -17 & -16.7009921165471 & -0.299007883452868 \tabularnewline
20 & -11 & -10.9589043175602 & -0.0410956824398116 \tabularnewline
21 & -11 & -11.2952630308336 & 0.295263030833624 \tabularnewline
22 & -12 & -12.3043391706539 & 0.304339170653931 \tabularnewline
23 & -10 & -9.43929268949509 & -0.560707310504907 \tabularnewline
24 & -15 & -15.3555572634534 & 0.35555726345339 \tabularnewline
25 & -15 & -16.0282746900003 & 1.02827469000026 \tabularnewline
26 & -15 & -15.4366482326044 & 0.43664823260443 \tabularnewline
27 & -13 & -13.4065011162945 & 0.406501116294548 \tabularnewline
28 & -8 & -7.04879718657323 & -0.951202813426765 \tabularnewline
29 & -13 & -12.7788901488909 & -0.221109851109091 \tabularnewline
30 & -9 & -10.3192985134873 & 1.31929851348728 \tabularnewline
31 & -7 & -5.33101911019825 & -1.66898088980175 \tabularnewline
32 & -4 & -3.30087199388837 & -0.699128006111634 \tabularnewline
33 & -4 & -3.88050361461493 & -0.119496385385074 \tabularnewline
34 & -2 & -3.62523587049253 & 1.62523587049253 \tabularnewline
35 & 0 & -0.411835839390989 & 0.411835839390989 \tabularnewline
36 & -2 & -1.83836166163577 & -0.161638338364227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117302&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]-6[/C][C]-6.09394945503156[/C][C]0.09394945503156[/C][/ROW]
[ROW][C]2[/C][C]-3[/C][C]-3.47217588132587[/C][C]0.472175881325874[/C][/ROW]
[ROW][C]3[/C][C]-3[/C][C]-2.2889229665342[/C][C]-0.711077033465802[/C][/ROW]
[ROW][C]4[/C][C]-7[/C][C]-6.01285848588054[/C][C]-0.987141514119458[/C][/ROW]
[ROW][C]5[/C][C]-9[/C][C]-9.30734948613313[/C][C]0.307349486133126[/C][/ROW]
[ROW][C]6[/C][C]-11[/C][C]-10.4786075642555[/C][C]-0.521392435744486[/C][/ROW]
[ROW][C]7[/C][C]-13[/C][C]-13.529825657055[/C][C]0.529825657054974[/C][/ROW]
[ROW][C]8[/C][C]-11[/C][C]-11.1873095008102[/C][C]0.187309500810196[/C][/ROW]
[ROW][C]9[/C][C]-9[/C][C]-10.5145920742633[/C][C]1.51459207426332[/C][/ROW]
[ROW][C]10[/C][C]-17[/C][C]-16.6290230965315[/C][C]-0.370976903468487[/C][/ROW]
[ROW][C]11[/C][C]-22[/C][C]-20.7133070024898[/C][C]-1.28669299751018[/C][/ROW]
[ROW][C]12[/C][C]-25[/C][C]-23.7645250952893[/C][C]-1.23547490471072[/C][/ROW]
[ROW][C]13[/C][C]-20[/C][C]-21.5030999081955[/C][C]1.50309990819554[/C][/ROW]
[ROW][C]14[/C][C]-24[/C][C]-24.7975909084481[/C][C]0.797590908448125[/C][/ROW]
[ROW][C]15[/C][C]-24[/C][C]-23.9506967069299[/C][C]-0.0493032930701001[/C][/ROW]
[ROW][C]16[/C][C]-22[/C][C]-20.2507508609221[/C][C]-1.74924913907789[/C][/ROW]
[ROW][C]17[/C][C]-19[/C][C]-18.9864069769794[/C][C]-0.0135930230205905[/C][/ROW]
[ROW][C]18[/C][C]-18[/C][C]-18.0584218063101[/C][C]0.0584218063101438[/C][/ROW]
[ROW][C]19[/C][C]-17[/C][C]-16.7009921165471[/C][C]-0.299007883452868[/C][/ROW]
[ROW][C]20[/C][C]-11[/C][C]-10.9589043175602[/C][C]-0.0410956824398116[/C][/ROW]
[ROW][C]21[/C][C]-11[/C][C]-11.2952630308336[/C][C]0.295263030833624[/C][/ROW]
[ROW][C]22[/C][C]-12[/C][C]-12.3043391706539[/C][C]0.304339170653931[/C][/ROW]
[ROW][C]23[/C][C]-10[/C][C]-9.43929268949509[/C][C]-0.560707310504907[/C][/ROW]
[ROW][C]24[/C][C]-15[/C][C]-15.3555572634534[/C][C]0.35555726345339[/C][/ROW]
[ROW][C]25[/C][C]-15[/C][C]-16.0282746900003[/C][C]1.02827469000026[/C][/ROW]
[ROW][C]26[/C][C]-15[/C][C]-15.4366482326044[/C][C]0.43664823260443[/C][/ROW]
[ROW][C]27[/C][C]-13[/C][C]-13.4065011162945[/C][C]0.406501116294548[/C][/ROW]
[ROW][C]28[/C][C]-8[/C][C]-7.04879718657323[/C][C]-0.951202813426765[/C][/ROW]
[ROW][C]29[/C][C]-13[/C][C]-12.7788901488909[/C][C]-0.221109851109091[/C][/ROW]
[ROW][C]30[/C][C]-9[/C][C]-10.3192985134873[/C][C]1.31929851348728[/C][/ROW]
[ROW][C]31[/C][C]-7[/C][C]-5.33101911019825[/C][C]-1.66898088980175[/C][/ROW]
[ROW][C]32[/C][C]-4[/C][C]-3.30087199388837[/C][C]-0.699128006111634[/C][/ROW]
[ROW][C]33[/C][C]-4[/C][C]-3.88050361461493[/C][C]-0.119496385385074[/C][/ROW]
[ROW][C]34[/C][C]-2[/C][C]-3.62523587049253[/C][C]1.62523587049253[/C][/ROW]
[ROW][C]35[/C][C]0[/C][C]-0.411835839390989[/C][C]0.411835839390989[/C][/ROW]
[ROW][C]36[/C][C]-2[/C][C]-1.83836166163577[/C][C]-0.161638338364227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117302&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117302&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
1-6-6.093949455031560.09394945503156
2-3-3.472175881325870.472175881325874
3-3-2.2889229665342-0.711077033465802
4-7-6.01285848588054-0.987141514119458
5-9-9.307349486133130.307349486133126
6-11-10.4786075642555-0.521392435744486
7-13-13.5298256570550.529825657054974
8-11-11.18730950081020.187309500810196
9-9-10.51459207426331.51459207426332
10-17-16.6290230965315-0.370976903468487
11-22-20.7133070024898-1.28669299751018
12-25-23.7645250952893-1.23547490471072
13-20-21.50309990819551.50309990819554
14-24-24.79759090844810.797590908448125
15-24-23.9506967069299-0.0493032930701001
16-22-20.2507508609221-1.74924913907789
17-19-18.9864069769794-0.0135930230205905
18-18-18.05842180631010.0584218063101438
19-17-16.7009921165471-0.299007883452868
20-11-10.9589043175602-0.0410956824398116
21-11-11.29526303083360.295263030833624
22-12-12.30433917065390.304339170653931
23-10-9.43929268949509-0.560707310504907
24-15-15.35555726345340.35555726345339
25-15-16.02827469000031.02827469000026
26-15-15.43664823260440.43664823260443
27-13-13.40650111629450.406501116294548
28-8-7.04879718657323-0.951202813426765
29-13-12.7788901488909-0.221109851109091
30-9-10.31929851348731.31929851348728
31-7-5.33101911019825-1.66898088980175
32-4-3.30087199388837-0.699128006111634
33-4-3.88050361461493-0.119496385385074
34-2-3.625235870492531.62523587049253
350-0.4118358393909890.411835839390989
36-2-1.83836166163577-0.161638338364227






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.4436279849217380.8872559698434760.556372015078262
70.3078783349947990.6157566699895970.692121665005201
80.1832465455748550.366493091149710.816753454425145
90.2334427221748490.4668854443496980.766557277825151
100.368479708413530.736959416827060.63152029158647
110.4415845057527290.8831690115054570.558415494247271
120.4478646926397830.8957293852795650.552135307360217
130.7510428541358660.4979142917282680.248957145864134
140.712590522872180.5748189542556410.287409477127821
150.6168560432274770.7662879135450470.383143956772523
160.8698128605858870.2603742788282260.130187139414113
170.8252340277145060.3495319445709880.174765972285494
180.7664633889597330.4670732220805330.233536611040267
190.7348598055195290.5302803889609420.265140194480471
200.6445230071648550.710953985670290.355476992835145
210.5683448837895950.863310232420810.431655116210405
220.4721044547194730.9442089094389460.527895545280527
230.3773026100807420.7546052201614830.622697389919258
240.2853321316481030.5706642632962050.714667868351897
250.2710749212041910.5421498424083820.728925078795809
260.1981430661758880.3962861323517760.801856933824112
270.202786521480940.405573042961880.79721347851906
280.1754562551934410.3509125103868830.824543744806558
290.1239029082716210.2478058165432420.876097091728379
300.1475480343742360.2950960687484730.852451965625764

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
6 & 0.443627984921738 & 0.887255969843476 & 0.556372015078262 \tabularnewline
7 & 0.307878334994799 & 0.615756669989597 & 0.692121665005201 \tabularnewline
8 & 0.183246545574855 & 0.36649309114971 & 0.816753454425145 \tabularnewline
9 & 0.233442722174849 & 0.466885444349698 & 0.766557277825151 \tabularnewline
10 & 0.36847970841353 & 0.73695941682706 & 0.63152029158647 \tabularnewline
11 & 0.441584505752729 & 0.883169011505457 & 0.558415494247271 \tabularnewline
12 & 0.447864692639783 & 0.895729385279565 & 0.552135307360217 \tabularnewline
13 & 0.751042854135866 & 0.497914291728268 & 0.248957145864134 \tabularnewline
14 & 0.71259052287218 & 0.574818954255641 & 0.287409477127821 \tabularnewline
15 & 0.616856043227477 & 0.766287913545047 & 0.383143956772523 \tabularnewline
16 & 0.869812860585887 & 0.260374278828226 & 0.130187139414113 \tabularnewline
17 & 0.825234027714506 & 0.349531944570988 & 0.174765972285494 \tabularnewline
18 & 0.766463388959733 & 0.467073222080533 & 0.233536611040267 \tabularnewline
19 & 0.734859805519529 & 0.530280388960942 & 0.265140194480471 \tabularnewline
20 & 0.644523007164855 & 0.71095398567029 & 0.355476992835145 \tabularnewline
21 & 0.568344883789595 & 0.86331023242081 & 0.431655116210405 \tabularnewline
22 & 0.472104454719473 & 0.944208909438946 & 0.527895545280527 \tabularnewline
23 & 0.377302610080742 & 0.754605220161483 & 0.622697389919258 \tabularnewline
24 & 0.285332131648103 & 0.570664263296205 & 0.714667868351897 \tabularnewline
25 & 0.271074921204191 & 0.542149842408382 & 0.728925078795809 \tabularnewline
26 & 0.198143066175888 & 0.396286132351776 & 0.801856933824112 \tabularnewline
27 & 0.20278652148094 & 0.40557304296188 & 0.79721347851906 \tabularnewline
28 & 0.175456255193441 & 0.350912510386883 & 0.824543744806558 \tabularnewline
29 & 0.123902908271621 & 0.247805816543242 & 0.876097091728379 \tabularnewline
30 & 0.147548034374236 & 0.295096068748473 & 0.852451965625764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117302&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]6[/C][C]0.443627984921738[/C][C]0.887255969843476[/C][C]0.556372015078262[/C][/ROW]
[ROW][C]7[/C][C]0.307878334994799[/C][C]0.615756669989597[/C][C]0.692121665005201[/C][/ROW]
[ROW][C]8[/C][C]0.183246545574855[/C][C]0.36649309114971[/C][C]0.816753454425145[/C][/ROW]
[ROW][C]9[/C][C]0.233442722174849[/C][C]0.466885444349698[/C][C]0.766557277825151[/C][/ROW]
[ROW][C]10[/C][C]0.36847970841353[/C][C]0.73695941682706[/C][C]0.63152029158647[/C][/ROW]
[ROW][C]11[/C][C]0.441584505752729[/C][C]0.883169011505457[/C][C]0.558415494247271[/C][/ROW]
[ROW][C]12[/C][C]0.447864692639783[/C][C]0.895729385279565[/C][C]0.552135307360217[/C][/ROW]
[ROW][C]13[/C][C]0.751042854135866[/C][C]0.497914291728268[/C][C]0.248957145864134[/C][/ROW]
[ROW][C]14[/C][C]0.71259052287218[/C][C]0.574818954255641[/C][C]0.287409477127821[/C][/ROW]
[ROW][C]15[/C][C]0.616856043227477[/C][C]0.766287913545047[/C][C]0.383143956772523[/C][/ROW]
[ROW][C]16[/C][C]0.869812860585887[/C][C]0.260374278828226[/C][C]0.130187139414113[/C][/ROW]
[ROW][C]17[/C][C]0.825234027714506[/C][C]0.349531944570988[/C][C]0.174765972285494[/C][/ROW]
[ROW][C]18[/C][C]0.766463388959733[/C][C]0.467073222080533[/C][C]0.233536611040267[/C][/ROW]
[ROW][C]19[/C][C]0.734859805519529[/C][C]0.530280388960942[/C][C]0.265140194480471[/C][/ROW]
[ROW][C]20[/C][C]0.644523007164855[/C][C]0.71095398567029[/C][C]0.355476992835145[/C][/ROW]
[ROW][C]21[/C][C]0.568344883789595[/C][C]0.86331023242081[/C][C]0.431655116210405[/C][/ROW]
[ROW][C]22[/C][C]0.472104454719473[/C][C]0.944208909438946[/C][C]0.527895545280527[/C][/ROW]
[ROW][C]23[/C][C]0.377302610080742[/C][C]0.754605220161483[/C][C]0.622697389919258[/C][/ROW]
[ROW][C]24[/C][C]0.285332131648103[/C][C]0.570664263296205[/C][C]0.714667868351897[/C][/ROW]
[ROW][C]25[/C][C]0.271074921204191[/C][C]0.542149842408382[/C][C]0.728925078795809[/C][/ROW]
[ROW][C]26[/C][C]0.198143066175888[/C][C]0.396286132351776[/C][C]0.801856933824112[/C][/ROW]
[ROW][C]27[/C][C]0.20278652148094[/C][C]0.40557304296188[/C][C]0.79721347851906[/C][/ROW]
[ROW][C]28[/C][C]0.175456255193441[/C][C]0.350912510386883[/C][C]0.824543744806558[/C][/ROW]
[ROW][C]29[/C][C]0.123902908271621[/C][C]0.247805816543242[/C][C]0.876097091728379[/C][/ROW]
[ROW][C]30[/C][C]0.147548034374236[/C][C]0.295096068748473[/C][C]0.852451965625764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117302&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117302&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
60.4436279849217380.8872559698434760.556372015078262
70.3078783349947990.6157566699895970.692121665005201
80.1832465455748550.366493091149710.816753454425145
90.2334427221748490.4668854443496980.766557277825151
100.368479708413530.736959416827060.63152029158647
110.4415845057527290.8831690115054570.558415494247271
120.4478646926397830.8957293852795650.552135307360217
130.7510428541358660.4979142917282680.248957145864134
140.712590522872180.5748189542556410.287409477127821
150.6168560432274770.7662879135450470.383143956772523
160.8698128605858870.2603742788282260.130187139414113
170.8252340277145060.3495319445709880.174765972285494
180.7664633889597330.4670732220805330.233536611040267
190.7348598055195290.5302803889609420.265140194480471
200.6445230071648550.710953985670290.355476992835145
210.5683448837895950.863310232420810.431655116210405
220.4721044547194730.9442089094389460.527895545280527
230.3773026100807420.7546052201614830.622697389919258
240.2853321316481030.5706642632962050.714667868351897
250.2710749212041910.5421498424083820.728925078795809
260.1981430661758880.3962861323517760.801856933824112
270.202786521480940.405573042961880.79721347851906
280.1754562551934410.3509125103868830.824543744806558
290.1239029082716210.2478058165432420.876097091728379
300.1475480343742360.2950960687484730.852451965625764






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=117302&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=117302&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117302&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 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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')
}