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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, 12 Dec 2010 18:20:28 +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/2010/Dec/12/t1292177942142ssssezg8wrjn.htm/, Retrieved Tue, 07 May 2024 20:50:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108598, Retrieved Tue, 07 May 2024 20:50:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Workshop 10 part ...] [2010-12-12 18:20:28] [c9b1b69acb8f4b2b921fdfd5091a94b7] [Current]
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Dataseries X:
2.0	1000	42.0	3	3
1.8	2547000	624.0	3	4
.7	10550	180.0	4	4
3.9	0,023	35.0	1	1
1.0	160000	392.0	4	4
3.6	3300	63.0	1	1
1.4	52160	230.0	1	1
1.5	0,425	112.0	5	4
.7	465000	281.0	5	5
2.1	0,075	42.0	1	1
4.1	0,785	42.0	2	2
1.2	0,2	120.0	2	2
.5	27660	148.0	5	5
3.4	0,12	16.0	3	2
1.5	85000	310.0	1	1
3.4	0,101	28.0	5	3
.8	1040	68.0	5	4
.8	521000	336.0	5	5
2.0	0,01	50.0	1	1
1.9	62000	267.0	1	1
1.3	0,023	19.0	4	3
5.6	1700	12.0	2	1
3.1	3500	120.0	2	1
1.8	0,48	140.0	2	2
.9	10000	170.0	4	4
1.8	1620	17.0	2	2
1.9	192000	115.0	4	4
.9	2500	31.0	5	5
2.6	0,28	21.0	3	3
2.4	4235	52.0	1	1
1.2	6800	164.0	2	2
.9	0,75	225.0	2	2
.5	3600	225.0	3	3
.6	55500	151.0	5	5
2.3	0,9	60.0	2	2
.5	2000	200.0	3	3
2.6	0,104	46.0	3	2
.6	4190	210.0	4	4
6.6	3500	14.0	2	1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
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 & 5 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \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=108598&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/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=108598&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108598&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
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
PS[t] = + 3.7791885546538 + 1.90547089316906e-06Wb[t] -0.00579207803438209Tg[t] + 0.798598377850773P[t] -1.32821473057373`D `[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
PS[t] =  +  3.7791885546538 +  1.90547089316906e-06Wb[t] -0.00579207803438209Tg[t] +  0.798598377850773P[t] -1.32821473057373`D
`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108598&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]PS[t] =  +  3.7791885546538 +  1.90547089316906e-06Wb[t] -0.00579207803438209Tg[t] +  0.798598377850773P[t] -1.32821473057373`D
`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108598&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108598&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
PS[t] = + 3.7791885546538 + 1.90547089316906e-06Wb[t] -0.00579207803438209Tg[t] + 0.798598377850773P[t] -1.32821473057373`D `[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.77918855465380.36085610.472800
Wb1.90547089316906e-0603.87920.0004570.000229
Tg-0.005792078034382090.001741-3.32650.0021190.00106
P0.7985983778507730.3134572.54770.0155340.007767
`D `-1.328214730573730.33622-3.95040.0003730.000187

\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) & 3.7791885546538 & 0.360856 & 10.4728 & 0 & 0 \tabularnewline
Wb & 1.90547089316906e-06 & 0 & 3.8792 & 0.000457 & 0.000229 \tabularnewline
Tg & -0.00579207803438209 & 0.001741 & -3.3265 & 0.002119 & 0.00106 \tabularnewline
P & 0.798598377850773 & 0.313457 & 2.5477 & 0.015534 & 0.007767 \tabularnewline
`D
` & -1.32821473057373 & 0.33622 & -3.9504 & 0.000373 & 0.000187 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108598&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]3.7791885546538[/C][C]0.360856[/C][C]10.4728[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Wb[/C][C]1.90547089316906e-06[/C][C]0[/C][C]3.8792[/C][C]0.000457[/C][C]0.000229[/C][/ROW]
[ROW][C]Tg[/C][C]-0.00579207803438209[/C][C]0.001741[/C][C]-3.3265[/C][C]0.002119[/C][C]0.00106[/C][/ROW]
[ROW][C]P[/C][C]0.798598377850773[/C][C]0.313457[/C][C]2.5477[/C][C]0.015534[/C][C]0.007767[/C][/ROW]
[ROW][C]`D
`[/C][C]-1.32821473057373[/C][C]0.33622[/C][C]-3.9504[/C][C]0.000373[/C][C]0.000187[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108598&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108598&T=2

As an alternative you can also use a 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)3.77918855465380.36085610.472800
Wb1.90547089316906e-0603.87920.0004570.000229
Tg-0.005792078034382090.001741-3.32650.0021190.00106
P0.7985983778507730.3134572.54770.0155340.007767
`D `-1.328214730573730.33622-3.95040.0003730.000187







Multiple Linear Regression - Regression Statistics
Multiple R0.808413774271965
R-squared0.653532830432643
Adjusted R-squared0.61277198695413
F-TEST (value)16.0333490345252
F-TEST (DF numerator)4
F-TEST (DF denominator)34
p-value1.80884655032187e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.874656246105222
Sum Squared Residuals26.0108006609299

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.808413774271965 \tabularnewline
R-squared & 0.653532830432643 \tabularnewline
Adjusted R-squared & 0.61277198695413 \tabularnewline
F-TEST (value) & 16.0333490345252 \tabularnewline
F-TEST (DF numerator) & 4 \tabularnewline
F-TEST (DF denominator) & 34 \tabularnewline
p-value & 1.80884655032187e-07 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.874656246105222 \tabularnewline
Sum Squared Residuals & 26.0108006609299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108598&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.808413774271965[/C][/ROW]
[ROW][C]R-squared[/C][C]0.653532830432643[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.61277198695413[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]16.0333490345252[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]4[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]34[/C][/ROW]
[ROW][C]p-value[/C][C]1.80884655032187e-07[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.874656246105222[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]26.0108006609299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108598&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108598&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.808413774271965
R-squared0.653532830432643
Adjusted R-squared0.61277198695413
F-TEST (value)16.0333490345252
F-TEST (DF numerator)4
F-TEST (DF denominator)34
p-value1.80884655032187e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.874656246105222
Sum Squared Residuals26.0108006609299







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
121.948977689934040.0510223100659579
21.82.10110243735835-0.301102437358345
30.70.6382518154961130.0617481845038873
43.93.04684951455330.853150485446703
51-0.3048961028087741.30489610280877
63.62.890959339712230.709040660287774
71.42.01678361581066-0.616783615810657
81.51.81060959158707-0.310609591587066
90.70.389576828701240.31042317129876
102.13.00630506739711-0.906305067397108
114.12.476690067558481.62330993244152
121.22.02490686617621-0.824906866176207
130.50.3265845668555030.173415433144497
143.43.42588120716505-0.0258812071650459
151.51.61599303719176-0.115993037191761
163.43.62535825967633-0.225358259676327
170.82.06744190500364-1.26744190500364
180.80.1777189068276920.622281093172308
1922.95996831926644-0.959968319266444
201.91.82122656212730.0787734378726974
211.32.87888843550826-1.57888843550826
225.63.981904943887421.61809505611258
233.13.35979036378185-0.259790363781854
241.81.90906583902041-0.109065839020415
250.90.6951245868486920.204875413151308
261.82.62457738547032-0.824577385470317
271.91.360484581296480.539515418703524
280.90.956316049206074-0.0563160492060738
292.62.068706391294740.531293608705256
302.42.95645381337554-0.556453813375542
311.21.78301225364277-0.583012253642766
320.91.41673972057508-0.516739720575078
330.50.893981633964356-0.393981633964356
340.60.3622566424181830.237743357581817
352.32.37243288206876-0.0724328820687575
360.51.03573483139484-0.535734831394838
372.63.25211883564605-0.652118835646049
380.60.4523706795840960.147629320415904
396.63.973750635426362.62624936457364

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2 & 1.94897768993404 & 0.0510223100659579 \tabularnewline
2 & 1.8 & 2.10110243735835 & -0.301102437358345 \tabularnewline
3 & 0.7 & 0.638251815496113 & 0.0617481845038873 \tabularnewline
4 & 3.9 & 3.0468495145533 & 0.853150485446703 \tabularnewline
5 & 1 & -0.304896102808774 & 1.30489610280877 \tabularnewline
6 & 3.6 & 2.89095933971223 & 0.709040660287774 \tabularnewline
7 & 1.4 & 2.01678361581066 & -0.616783615810657 \tabularnewline
8 & 1.5 & 1.81060959158707 & -0.310609591587066 \tabularnewline
9 & 0.7 & 0.38957682870124 & 0.31042317129876 \tabularnewline
10 & 2.1 & 3.00630506739711 & -0.906305067397108 \tabularnewline
11 & 4.1 & 2.47669006755848 & 1.62330993244152 \tabularnewline
12 & 1.2 & 2.02490686617621 & -0.824906866176207 \tabularnewline
13 & 0.5 & 0.326584566855503 & 0.173415433144497 \tabularnewline
14 & 3.4 & 3.42588120716505 & -0.0258812071650459 \tabularnewline
15 & 1.5 & 1.61599303719176 & -0.115993037191761 \tabularnewline
16 & 3.4 & 3.62535825967633 & -0.225358259676327 \tabularnewline
17 & 0.8 & 2.06744190500364 & -1.26744190500364 \tabularnewline
18 & 0.8 & 0.177718906827692 & 0.622281093172308 \tabularnewline
19 & 2 & 2.95996831926644 & -0.959968319266444 \tabularnewline
20 & 1.9 & 1.8212265621273 & 0.0787734378726974 \tabularnewline
21 & 1.3 & 2.87888843550826 & -1.57888843550826 \tabularnewline
22 & 5.6 & 3.98190494388742 & 1.61809505611258 \tabularnewline
23 & 3.1 & 3.35979036378185 & -0.259790363781854 \tabularnewline
24 & 1.8 & 1.90906583902041 & -0.109065839020415 \tabularnewline
25 & 0.9 & 0.695124586848692 & 0.204875413151308 \tabularnewline
26 & 1.8 & 2.62457738547032 & -0.824577385470317 \tabularnewline
27 & 1.9 & 1.36048458129648 & 0.539515418703524 \tabularnewline
28 & 0.9 & 0.956316049206074 & -0.0563160492060738 \tabularnewline
29 & 2.6 & 2.06870639129474 & 0.531293608705256 \tabularnewline
30 & 2.4 & 2.95645381337554 & -0.556453813375542 \tabularnewline
31 & 1.2 & 1.78301225364277 & -0.583012253642766 \tabularnewline
32 & 0.9 & 1.41673972057508 & -0.516739720575078 \tabularnewline
33 & 0.5 & 0.893981633964356 & -0.393981633964356 \tabularnewline
34 & 0.6 & 0.362256642418183 & 0.237743357581817 \tabularnewline
35 & 2.3 & 2.37243288206876 & -0.0724328820687575 \tabularnewline
36 & 0.5 & 1.03573483139484 & -0.535734831394838 \tabularnewline
37 & 2.6 & 3.25211883564605 & -0.652118835646049 \tabularnewline
38 & 0.6 & 0.452370679584096 & 0.147629320415904 \tabularnewline
39 & 6.6 & 3.97375063542636 & 2.62624936457364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108598&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]2[/C][C]1.94897768993404[/C][C]0.0510223100659579[/C][/ROW]
[ROW][C]2[/C][C]1.8[/C][C]2.10110243735835[/C][C]-0.301102437358345[/C][/ROW]
[ROW][C]3[/C][C]0.7[/C][C]0.638251815496113[/C][C]0.0617481845038873[/C][/ROW]
[ROW][C]4[/C][C]3.9[/C][C]3.0468495145533[/C][C]0.853150485446703[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]-0.304896102808774[/C][C]1.30489610280877[/C][/ROW]
[ROW][C]6[/C][C]3.6[/C][C]2.89095933971223[/C][C]0.709040660287774[/C][/ROW]
[ROW][C]7[/C][C]1.4[/C][C]2.01678361581066[/C][C]-0.616783615810657[/C][/ROW]
[ROW][C]8[/C][C]1.5[/C][C]1.81060959158707[/C][C]-0.310609591587066[/C][/ROW]
[ROW][C]9[/C][C]0.7[/C][C]0.38957682870124[/C][C]0.31042317129876[/C][/ROW]
[ROW][C]10[/C][C]2.1[/C][C]3.00630506739711[/C][C]-0.906305067397108[/C][/ROW]
[ROW][C]11[/C][C]4.1[/C][C]2.47669006755848[/C][C]1.62330993244152[/C][/ROW]
[ROW][C]12[/C][C]1.2[/C][C]2.02490686617621[/C][C]-0.824906866176207[/C][/ROW]
[ROW][C]13[/C][C]0.5[/C][C]0.326584566855503[/C][C]0.173415433144497[/C][/ROW]
[ROW][C]14[/C][C]3.4[/C][C]3.42588120716505[/C][C]-0.0258812071650459[/C][/ROW]
[ROW][C]15[/C][C]1.5[/C][C]1.61599303719176[/C][C]-0.115993037191761[/C][/ROW]
[ROW][C]16[/C][C]3.4[/C][C]3.62535825967633[/C][C]-0.225358259676327[/C][/ROW]
[ROW][C]17[/C][C]0.8[/C][C]2.06744190500364[/C][C]-1.26744190500364[/C][/ROW]
[ROW][C]18[/C][C]0.8[/C][C]0.177718906827692[/C][C]0.622281093172308[/C][/ROW]
[ROW][C]19[/C][C]2[/C][C]2.95996831926644[/C][C]-0.959968319266444[/C][/ROW]
[ROW][C]20[/C][C]1.9[/C][C]1.8212265621273[/C][C]0.0787734378726974[/C][/ROW]
[ROW][C]21[/C][C]1.3[/C][C]2.87888843550826[/C][C]-1.57888843550826[/C][/ROW]
[ROW][C]22[/C][C]5.6[/C][C]3.98190494388742[/C][C]1.61809505611258[/C][/ROW]
[ROW][C]23[/C][C]3.1[/C][C]3.35979036378185[/C][C]-0.259790363781854[/C][/ROW]
[ROW][C]24[/C][C]1.8[/C][C]1.90906583902041[/C][C]-0.109065839020415[/C][/ROW]
[ROW][C]25[/C][C]0.9[/C][C]0.695124586848692[/C][C]0.204875413151308[/C][/ROW]
[ROW][C]26[/C][C]1.8[/C][C]2.62457738547032[/C][C]-0.824577385470317[/C][/ROW]
[ROW][C]27[/C][C]1.9[/C][C]1.36048458129648[/C][C]0.539515418703524[/C][/ROW]
[ROW][C]28[/C][C]0.9[/C][C]0.956316049206074[/C][C]-0.0563160492060738[/C][/ROW]
[ROW][C]29[/C][C]2.6[/C][C]2.06870639129474[/C][C]0.531293608705256[/C][/ROW]
[ROW][C]30[/C][C]2.4[/C][C]2.95645381337554[/C][C]-0.556453813375542[/C][/ROW]
[ROW][C]31[/C][C]1.2[/C][C]1.78301225364277[/C][C]-0.583012253642766[/C][/ROW]
[ROW][C]32[/C][C]0.9[/C][C]1.41673972057508[/C][C]-0.516739720575078[/C][/ROW]
[ROW][C]33[/C][C]0.5[/C][C]0.893981633964356[/C][C]-0.393981633964356[/C][/ROW]
[ROW][C]34[/C][C]0.6[/C][C]0.362256642418183[/C][C]0.237743357581817[/C][/ROW]
[ROW][C]35[/C][C]2.3[/C][C]2.37243288206876[/C][C]-0.0724328820687575[/C][/ROW]
[ROW][C]36[/C][C]0.5[/C][C]1.03573483139484[/C][C]-0.535734831394838[/C][/ROW]
[ROW][C]37[/C][C]2.6[/C][C]3.25211883564605[/C][C]-0.652118835646049[/C][/ROW]
[ROW][C]38[/C][C]0.6[/C][C]0.452370679584096[/C][C]0.147629320415904[/C][/ROW]
[ROW][C]39[/C][C]6.6[/C][C]3.97375063542636[/C][C]2.62624936457364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108598&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108598&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
121.948977689934040.0510223100659579
21.82.10110243735835-0.301102437358345
30.70.6382518154961130.0617481845038873
43.93.04684951455330.853150485446703
51-0.3048961028087741.30489610280877
63.62.890959339712230.709040660287774
71.42.01678361581066-0.616783615810657
81.51.81060959158707-0.310609591587066
90.70.389576828701240.31042317129876
102.13.00630506739711-0.906305067397108
114.12.476690067558481.62330993244152
121.22.02490686617621-0.824906866176207
130.50.3265845668555030.173415433144497
143.43.42588120716505-0.0258812071650459
151.51.61599303719176-0.115993037191761
163.43.62535825967633-0.225358259676327
170.82.06744190500364-1.26744190500364
180.80.1777189068276920.622281093172308
1922.95996831926644-0.959968319266444
201.91.82122656212730.0787734378726974
211.32.87888843550826-1.57888843550826
225.63.981904943887421.61809505611258
233.13.35979036378185-0.259790363781854
241.81.90906583902041-0.109065839020415
250.90.6951245868486920.204875413151308
261.82.62457738547032-0.824577385470317
271.91.360484581296480.539515418703524
280.90.956316049206074-0.0563160492060738
292.62.068706391294740.531293608705256
302.42.95645381337554-0.556453813375542
311.21.78301225364277-0.583012253642766
320.91.41673972057508-0.516739720575078
330.50.893981633964356-0.393981633964356
340.60.3622566424181830.237743357581817
352.32.37243288206876-0.0724328820687575
360.51.03573483139484-0.535734831394838
372.63.25211883564605-0.652118835646049
380.60.4523706795840960.147629320415904
396.63.973750635426362.62624936457364







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
80.5868407159099170.8263185681801650.413159284090083
90.4122938342114760.8245876684229520.587706165788524
100.454256944025630.908513888051260.54574305597437
110.6578670051296150.684265989740770.342132994870385
120.6802914832408050.6394170335183890.319708516759195
130.5958742866012880.8082514267974240.404125713398712
140.4881329565151640.9762659130303270.511867043484836
150.3768554421484380.7537108842968750.623144557851562
160.2804041679187750.560808335837550.719595832081225
170.3749086485076730.7498172970153460.625091351492327
180.3044745331310210.6089490662620410.69552546686898
190.3109215180139340.6218430360278680.689078481986066
200.2225771303153560.4451542606307110.777422869684644
210.5412262776461410.9175474447077180.458773722353859
220.7228169368173870.5543661263652250.277183063182613
230.6872994269989040.6254011460021920.312700573001096
240.5881674124352650.823665175129470.411832587564735
250.4884581439551430.9769162879102850.511541856044857
260.4572295511449330.9144591022898660.542770448855067
270.35957452552840.71914905105680.6404254744716
280.2530626706331130.5061253412662250.746937329366887
290.1855431349048490.3710862698096980.81445686509515
300.1311195866339570.2622391732679140.868880413366043
310.08702610080379460.1740522016075890.912973899196205

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
8 & 0.586840715909917 & 0.826318568180165 & 0.413159284090083 \tabularnewline
9 & 0.412293834211476 & 0.824587668422952 & 0.587706165788524 \tabularnewline
10 & 0.45425694402563 & 0.90851388805126 & 0.54574305597437 \tabularnewline
11 & 0.657867005129615 & 0.68426598974077 & 0.342132994870385 \tabularnewline
12 & 0.680291483240805 & 0.639417033518389 & 0.319708516759195 \tabularnewline
13 & 0.595874286601288 & 0.808251426797424 & 0.404125713398712 \tabularnewline
14 & 0.488132956515164 & 0.976265913030327 & 0.511867043484836 \tabularnewline
15 & 0.376855442148438 & 0.753710884296875 & 0.623144557851562 \tabularnewline
16 & 0.280404167918775 & 0.56080833583755 & 0.719595832081225 \tabularnewline
17 & 0.374908648507673 & 0.749817297015346 & 0.625091351492327 \tabularnewline
18 & 0.304474533131021 & 0.608949066262041 & 0.69552546686898 \tabularnewline
19 & 0.310921518013934 & 0.621843036027868 & 0.689078481986066 \tabularnewline
20 & 0.222577130315356 & 0.445154260630711 & 0.777422869684644 \tabularnewline
21 & 0.541226277646141 & 0.917547444707718 & 0.458773722353859 \tabularnewline
22 & 0.722816936817387 & 0.554366126365225 & 0.277183063182613 \tabularnewline
23 & 0.687299426998904 & 0.625401146002192 & 0.312700573001096 \tabularnewline
24 & 0.588167412435265 & 0.82366517512947 & 0.411832587564735 \tabularnewline
25 & 0.488458143955143 & 0.976916287910285 & 0.511541856044857 \tabularnewline
26 & 0.457229551144933 & 0.914459102289866 & 0.542770448855067 \tabularnewline
27 & 0.3595745255284 & 0.7191490510568 & 0.6404254744716 \tabularnewline
28 & 0.253062670633113 & 0.506125341266225 & 0.746937329366887 \tabularnewline
29 & 0.185543134904849 & 0.371086269809698 & 0.81445686509515 \tabularnewline
30 & 0.131119586633957 & 0.262239173267914 & 0.868880413366043 \tabularnewline
31 & 0.0870261008037946 & 0.174052201607589 & 0.912973899196205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108598&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]8[/C][C]0.586840715909917[/C][C]0.826318568180165[/C][C]0.413159284090083[/C][/ROW]
[ROW][C]9[/C][C]0.412293834211476[/C][C]0.824587668422952[/C][C]0.587706165788524[/C][/ROW]
[ROW][C]10[/C][C]0.45425694402563[/C][C]0.90851388805126[/C][C]0.54574305597437[/C][/ROW]
[ROW][C]11[/C][C]0.657867005129615[/C][C]0.68426598974077[/C][C]0.342132994870385[/C][/ROW]
[ROW][C]12[/C][C]0.680291483240805[/C][C]0.639417033518389[/C][C]0.319708516759195[/C][/ROW]
[ROW][C]13[/C][C]0.595874286601288[/C][C]0.808251426797424[/C][C]0.404125713398712[/C][/ROW]
[ROW][C]14[/C][C]0.488132956515164[/C][C]0.976265913030327[/C][C]0.511867043484836[/C][/ROW]
[ROW][C]15[/C][C]0.376855442148438[/C][C]0.753710884296875[/C][C]0.623144557851562[/C][/ROW]
[ROW][C]16[/C][C]0.280404167918775[/C][C]0.56080833583755[/C][C]0.719595832081225[/C][/ROW]
[ROW][C]17[/C][C]0.374908648507673[/C][C]0.749817297015346[/C][C]0.625091351492327[/C][/ROW]
[ROW][C]18[/C][C]0.304474533131021[/C][C]0.608949066262041[/C][C]0.69552546686898[/C][/ROW]
[ROW][C]19[/C][C]0.310921518013934[/C][C]0.621843036027868[/C][C]0.689078481986066[/C][/ROW]
[ROW][C]20[/C][C]0.222577130315356[/C][C]0.445154260630711[/C][C]0.777422869684644[/C][/ROW]
[ROW][C]21[/C][C]0.541226277646141[/C][C]0.917547444707718[/C][C]0.458773722353859[/C][/ROW]
[ROW][C]22[/C][C]0.722816936817387[/C][C]0.554366126365225[/C][C]0.277183063182613[/C][/ROW]
[ROW][C]23[/C][C]0.687299426998904[/C][C]0.625401146002192[/C][C]0.312700573001096[/C][/ROW]
[ROW][C]24[/C][C]0.588167412435265[/C][C]0.82366517512947[/C][C]0.411832587564735[/C][/ROW]
[ROW][C]25[/C][C]0.488458143955143[/C][C]0.976916287910285[/C][C]0.511541856044857[/C][/ROW]
[ROW][C]26[/C][C]0.457229551144933[/C][C]0.914459102289866[/C][C]0.542770448855067[/C][/ROW]
[ROW][C]27[/C][C]0.3595745255284[/C][C]0.7191490510568[/C][C]0.6404254744716[/C][/ROW]
[ROW][C]28[/C][C]0.253062670633113[/C][C]0.506125341266225[/C][C]0.746937329366887[/C][/ROW]
[ROW][C]29[/C][C]0.185543134904849[/C][C]0.371086269809698[/C][C]0.81445686509515[/C][/ROW]
[ROW][C]30[/C][C]0.131119586633957[/C][C]0.262239173267914[/C][C]0.868880413366043[/C][/ROW]
[ROW][C]31[/C][C]0.0870261008037946[/C][C]0.174052201607589[/C][C]0.912973899196205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108598&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108598&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
80.5868407159099170.8263185681801650.413159284090083
90.4122938342114760.8245876684229520.587706165788524
100.454256944025630.908513888051260.54574305597437
110.6578670051296150.684265989740770.342132994870385
120.6802914832408050.6394170335183890.319708516759195
130.5958742866012880.8082514267974240.404125713398712
140.4881329565151640.9762659130303270.511867043484836
150.3768554421484380.7537108842968750.623144557851562
160.2804041679187750.560808335837550.719595832081225
170.3749086485076730.7498172970153460.625091351492327
180.3044745331310210.6089490662620410.69552546686898
190.3109215180139340.6218430360278680.689078481986066
200.2225771303153560.4451542606307110.777422869684644
210.5412262776461410.9175474447077180.458773722353859
220.7228169368173870.5543661263652250.277183063182613
230.6872994269989040.6254011460021920.312700573001096
240.5881674124352650.823665175129470.411832587564735
250.4884581439551430.9769162879102850.511541856044857
260.4572295511449330.9144591022898660.542770448855067
270.35957452552840.71914905105680.6404254744716
280.2530626706331130.5061253412662250.746937329366887
290.1855431349048490.3710862698096980.81445686509515
300.1311195866339570.2622391732679140.868880413366043
310.08702610080379460.1740522016075890.912973899196205







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=108598&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=108598&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108598&T=6

As an alternative you can also use a 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



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')
}