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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 25 Nov 2015 14:21:14 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/25/t1448465157sai2mant8zci7vn.htm/, Retrieved Wed, 15 May 2024 20:39:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284137, Retrieved Wed, 15 May 2024 20:39:08 +0000

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User-defined keywords

Estimated Impact

614

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Multiple Regression] [] [2015-11-25 14:21:14] [63a9f0ea7bb98050796b649e85481845] [Current]
- RMPD    [Kendall tau Correlation Matrix] [CM X3] [2015-11-29 22:17:11] [f59657f1a0fa4fc4e0fb7285a3a88ff5] 
- RMPD    [Kendall tau Correlation Matrix] [CM X4] [2015-11-29 22:19:35] [f59657f1a0fa4fc4e0fb7285a3a88ff5] 
- RMPD    [Kendall tau Correlation Matrix] [CM X5] [2015-11-29 22:20:36] [f59657f1a0fa4fc4e0fb7285a3a88ff5] 
- R PD    [Multiple Regression] [MLR X5] [2015-11-29 22:21:27] [f59657f1a0fa4fc4e0fb7285a3a88ff5] 
- R PD    [Multiple Regression] [MLR X4] [2015-11-29 22:22:42] [f59657f1a0fa4fc4e0fb7285a3a88ff5] 
- RMPD      [Partial Correlation Matrix] [Partial Correlati...] [2015-12-01 13:02:39] [f59657f1a0fa4fc4e0fb7285a3a88ff5] 
- RMPD      [Partial Correlation Matrix] [Partial Correlati...] [2015-12-01 13:03:37] [f59657f1a0fa4fc4e0fb7285a3a88ff5] 
- R PD    [Multiple Regression] [Multiple regression] [2015-12-07 18:44:29] [ff209a53ac5670f5187bbc09ce80d491] 
- RMPD    [Multiple Regression] [Hurricanes ] [2015-12-13 13:34:37] [74be16979710d4c4e7c6647856088456] 
- RMPD    [Multiple Regression] [Orkanen] [2015-12-13 13:34:37] [74be16979710d4c4e7c6647856088456] 
- RMPD    [Multiple Regression] [Computatie orkanen] [2015-12-13 14:12:23] [74be16979710d4c4e7c6647856088456] 
- R P       [Multiple Regression] [Orkanen] [2015-12-13 18:27:55] [74be16979710d4c4e7c6647856088456] 
- R P       [Multiple Regression] [Orkanen] [2015-12-13 19:32:21] [74be16979710d4c4e7c6647856088456] 
- R P     [Multiple Regression] [] [2015-12-25 11:32:45] [efdcb1bd2b42e1de885d17c8d6bec4aa] 
- RMPD    [Kendall tau Correlation Matrix] [Pearson correlati...] [2016-12-16 09:06:34] [061bcad4f8cbfaa4a6cadfe6faec1e5a] 
- RMPD    [Kendall tau Correlation Matrix] [Kendall correlati...] [2016-12-16 09:12:28] [061bcad4f8cbfaa4a6cadfe6faec1e5a] 
- R PD    [Multiple Regression] [examen vraag 8] [2017-01-07 08:23:01] [86d4234e3968eed16c07bb6bc1d88c85] 
- RMPD    [Simple Linear Regression] [] [2017-01-24 10:01:56] [8364c55eb31cfb87b60a70b7b20749c9] 
- RMPD    [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2017-01-24 10:02:56] [8364c55eb31cfb87b60a70b7b20749c9] 
- RMPD    [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2017-01-24 10:04:44] [8364c55eb31cfb87b60a70b7b20749c9] 
- R PD    [Multiple Regression] [] [2017-01-24 10:10:24] [8364c55eb31cfb87b60a70b7b20749c9] 
- RMPD    [Two-Way ANOVA] [] [2017-01-24 10:14:05] [8364c55eb31cfb87b60a70b7b20749c9] 
- R  D    [Multiple Regression] [multiple regression] [2017-01-24 15:06:32] [86d4234e3968eed16c07bb6bc1d88c85] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284137&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284137&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Multiple Linear Regression - Estimated Regression Equation
R[t] = + 3.05 -1.6AorB[t] -2.13875MorF[t] + 1.24875Interaction[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
R[t] =  +  3.05 -1.6AorB[t] -2.13875MorF[t] +  1.24875Interaction[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284137&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]R[t] =  +  3.05 -1.6AorB[t] -2.13875MorF[t] +  1.24875Interaction[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284137&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
R[t] = + 3.05 -1.6AorB[t] -2.13875MorF[t] + 1.24875Interaction[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	+3.05	0.1	+3.0490e+01	5.063e-23	2.532e-23
AorB	-1.6	0.1415	-1.1310e+01	5.951e-12	2.975e-12
MorF	-2.139	0.1415	-1.5120e+01	5.369e-15	2.684e-15
Interaction	+1.249	0.2001	+6.2410e+00	9.582e-07	4.791e-07

\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) & +3.05 &  0.1 & +3.0490e+01 &  5.063e-23 &  2.532e-23 \tabularnewline
AorB & -1.6 &  0.1415 & -1.1310e+01 &  5.951e-12 &  2.975e-12 \tabularnewline
MorF & -2.139 &  0.1415 & -1.5120e+01 &  5.369e-15 &  2.684e-15 \tabularnewline
Interaction & +1.249 &  0.2001 & +6.2410e+00 &  9.582e-07 &  4.791e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284137&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]+3.05[/C][C] 0.1[/C][C]+3.0490e+01[/C][C] 5.063e-23[/C][C] 2.532e-23[/C][/ROW]
[ROW][C]AorB[/C][C]-1.6[/C][C] 0.1415[/C][C]-1.1310e+01[/C][C] 5.951e-12[/C][C] 2.975e-12[/C][/ROW]
[ROW][C]MorF[/C][C]-2.139[/C][C] 0.1415[/C][C]-1.5120e+01[/C][C] 5.369e-15[/C][C] 2.684e-15[/C][/ROW]
[ROW][C]Interaction[/C][C]+1.249[/C][C] 0.2001[/C][C]+6.2410e+00[/C][C] 9.582e-07[/C][C] 4.791e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284137&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284137&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
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	+3.05	0.1	+3.0490e+01	5.063e-23	2.532e-23
AorB	-1.6	0.1415	-1.1310e+01	5.951e-12	2.975e-12
MorF	-2.139	0.1415	-1.5120e+01	5.369e-15	2.684e-15
Interaction	+1.249	0.2001	+6.2410e+00	9.582e-07	4.791e-07

Multiple Linear Regression - Regression Statistics
Multiple R	0.9636
R-squared	0.9284
Adjusted R-squared	0.9208
F-TEST (value)	121.1
F-TEST (DF numerator)	3
F-TEST (DF denominator)	28
p-value	4.441e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.2829
Sum Squared Residuals	2.242

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.9636 \tabularnewline
R-squared &  0.9284 \tabularnewline
Adjusted R-squared &  0.9208 \tabularnewline
F-TEST (value) &  121.1 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 28 \tabularnewline
p-value &  4.441e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  0.2829 \tabularnewline
Sum Squared Residuals &  2.242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284137&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.9636[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.9284[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.9208[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 121.1[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]28[/C][/ROW]
[ROW][C]p-value[/C][C] 4.441e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 0.2829[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 2.242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284137&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284137&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 R	0.9636
R-squared	0.9284
Adjusted R-squared	0.9208
F-TEST (value)	121.1
F-TEST (DF numerator)	3
F-TEST (DF denominator)	28
p-value	4.441e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.2829
Sum Squared Residuals	2.242

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	0.28	0.56	-0.28
2	0.95	0.56	0.39
3	0.96	0.56	0.4
4	0.97	0.56	0.41
5	0.4	0.56	-0.16
6	0.18	0.56	-0.38
7	0.12	0.56	-0.44
8	0.62	0.56	0.06
9	1.81	1.45	0.36
10	1.51	1.45	0.06
11	1.41	1.45	-0.04
12	1.39	1.45	-0.06
13	1.2	1.45	-0.25
14	1.55	1.45	0.1
15	1.48	1.45	0.03
16	1.25	1.45	-0.2
17	0.95	0.9113	0.03875
18	1.33	0.9113	0.4188
19	0.92	0.9113	0.00875
20	0.85	0.9113	-0.06125
21	1.06	0.9113	0.1487
22	0.69	0.9113	-0.2213
23	0.7	0.9113	-0.2112
24	0.79	0.9113	-0.1212
25	2.93	3.05	-0.12
26	3.24	3.05	0.19
27	3.42	3.05	0.37
28	2.79	3.05	-0.26
29	2.54	3.05	-0.51
30	3.28	3.05	0.23
31	2.8	3.05	-0.25
32	3.4	3.05	0.35

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  0.28 &  0.56 & -0.28 \tabularnewline
2 &  0.95 &  0.56 &  0.39 \tabularnewline
3 &  0.96 &  0.56 &  0.4 \tabularnewline
4 &  0.97 &  0.56 &  0.41 \tabularnewline
5 &  0.4 &  0.56 & -0.16 \tabularnewline
6 &  0.18 &  0.56 & -0.38 \tabularnewline
7 &  0.12 &  0.56 & -0.44 \tabularnewline
8 &  0.62 &  0.56 &  0.06 \tabularnewline
9 &  1.81 &  1.45 &  0.36 \tabularnewline
10 &  1.51 &  1.45 &  0.06 \tabularnewline
11 &  1.41 &  1.45 & -0.04 \tabularnewline
12 &  1.39 &  1.45 & -0.06 \tabularnewline
13 &  1.2 &  1.45 & -0.25 \tabularnewline
14 &  1.55 &  1.45 &  0.1 \tabularnewline
15 &  1.48 &  1.45 &  0.03 \tabularnewline
16 &  1.25 &  1.45 & -0.2 \tabularnewline
17 &  0.95 &  0.9113 &  0.03875 \tabularnewline
18 &  1.33 &  0.9113 &  0.4188 \tabularnewline
19 &  0.92 &  0.9113 &  0.00875 \tabularnewline
20 &  0.85 &  0.9113 & -0.06125 \tabularnewline
21 &  1.06 &  0.9113 &  0.1487 \tabularnewline
22 &  0.69 &  0.9113 & -0.2213 \tabularnewline
23 &  0.7 &  0.9113 & -0.2112 \tabularnewline
24 &  0.79 &  0.9113 & -0.1212 \tabularnewline
25 &  2.93 &  3.05 & -0.12 \tabularnewline
26 &  3.24 &  3.05 &  0.19 \tabularnewline
27 &  3.42 &  3.05 &  0.37 \tabularnewline
28 &  2.79 &  3.05 & -0.26 \tabularnewline
29 &  2.54 &  3.05 & -0.51 \tabularnewline
30 &  3.28 &  3.05 &  0.23 \tabularnewline
31 &  2.8 &  3.05 & -0.25 \tabularnewline
32 &  3.4 &  3.05 &  0.35 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284137&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] 0.28[/C][C] 0.56[/C][C]-0.28[/C][/ROW]
[ROW][C]2[/C][C] 0.95[/C][C] 0.56[/C][C] 0.39[/C][/ROW]
[ROW][C]3[/C][C] 0.96[/C][C] 0.56[/C][C] 0.4[/C][/ROW]
[ROW][C]4[/C][C] 0.97[/C][C] 0.56[/C][C] 0.41[/C][/ROW]
[ROW][C]5[/C][C] 0.4[/C][C] 0.56[/C][C]-0.16[/C][/ROW]
[ROW][C]6[/C][C] 0.18[/C][C] 0.56[/C][C]-0.38[/C][/ROW]
[ROW][C]7[/C][C] 0.12[/C][C] 0.56[/C][C]-0.44[/C][/ROW]
[ROW][C]8[/C][C] 0.62[/C][C] 0.56[/C][C] 0.06[/C][/ROW]
[ROW][C]9[/C][C] 1.81[/C][C] 1.45[/C][C] 0.36[/C][/ROW]
[ROW][C]10[/C][C] 1.51[/C][C] 1.45[/C][C] 0.06[/C][/ROW]
[ROW][C]11[/C][C] 1.41[/C][C] 1.45[/C][C]-0.04[/C][/ROW]
[ROW][C]12[/C][C] 1.39[/C][C] 1.45[/C][C]-0.06[/C][/ROW]
[ROW][C]13[/C][C] 1.2[/C][C] 1.45[/C][C]-0.25[/C][/ROW]
[ROW][C]14[/C][C] 1.55[/C][C] 1.45[/C][C] 0.1[/C][/ROW]
[ROW][C]15[/C][C] 1.48[/C][C] 1.45[/C][C] 0.03[/C][/ROW]
[ROW][C]16[/C][C] 1.25[/C][C] 1.45[/C][C]-0.2[/C][/ROW]
[ROW][C]17[/C][C] 0.95[/C][C] 0.9113[/C][C] 0.03875[/C][/ROW]
[ROW][C]18[/C][C] 1.33[/C][C] 0.9113[/C][C] 0.4188[/C][/ROW]
[ROW][C]19[/C][C] 0.92[/C][C] 0.9113[/C][C] 0.00875[/C][/ROW]
[ROW][C]20[/C][C] 0.85[/C][C] 0.9113[/C][C]-0.06125[/C][/ROW]
[ROW][C]21[/C][C] 1.06[/C][C] 0.9113[/C][C] 0.1487[/C][/ROW]
[ROW][C]22[/C][C] 0.69[/C][C] 0.9113[/C][C]-0.2213[/C][/ROW]
[ROW][C]23[/C][C] 0.7[/C][C] 0.9113[/C][C]-0.2112[/C][/ROW]
[ROW][C]24[/C][C] 0.79[/C][C] 0.9113[/C][C]-0.1212[/C][/ROW]
[ROW][C]25[/C][C] 2.93[/C][C] 3.05[/C][C]-0.12[/C][/ROW]
[ROW][C]26[/C][C] 3.24[/C][C] 3.05[/C][C] 0.19[/C][/ROW]
[ROW][C]27[/C][C] 3.42[/C][C] 3.05[/C][C] 0.37[/C][/ROW]
[ROW][C]28[/C][C] 2.79[/C][C] 3.05[/C][C]-0.26[/C][/ROW]
[ROW][C]29[/C][C] 2.54[/C][C] 3.05[/C][C]-0.51[/C][/ROW]
[ROW][C]30[/C][C] 3.28[/C][C] 3.05[/C][C] 0.23[/C][/ROW]
[ROW][C]31[/C][C] 2.8[/C][C] 3.05[/C][C]-0.25[/C][/ROW]
[ROW][C]32[/C][C] 3.4[/C][C] 3.05[/C][C] 0.35[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284137&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284137&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 Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	0.28	0.56	-0.28
2	0.95	0.56	0.39
3	0.96	0.56	0.4
4	0.97	0.56	0.41
5	0.4	0.56	-0.16
6	0.18	0.56	-0.38
7	0.12	0.56	-0.44
8	0.62	0.56	0.06
9	1.81	1.45	0.36
10	1.51	1.45	0.06
11	1.41	1.45	-0.04
12	1.39	1.45	-0.06
13	1.2	1.45	-0.25
14	1.55	1.45	0.1
15	1.48	1.45	0.03
16	1.25	1.45	-0.2
17	0.95	0.9113	0.03875
18	1.33	0.9113	0.4188
19	0.92	0.9113	0.00875
20	0.85	0.9113	-0.06125
21	1.06	0.9113	0.1487
22	0.69	0.9113	-0.2213
23	0.7	0.9113	-0.2112
24	0.79	0.9113	-0.1212
25	2.93	3.05	-0.12
26	3.24	3.05	0.19
27	3.42	3.05	0.37
28	2.79	3.05	-0.26
29	2.54	3.05	-0.51
30	3.28	3.05	0.23
31	2.8	3.05	-0.25
32	3.4	3.05	0.35

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.9902	0.01952	0.009761
8	0.9751	0.04984	0.02492
9	0.9638	0.07237	0.03618
10	0.9405	0.119	0.05952
11	0.9044	0.1913	0.09563
12	0.8499	0.3003	0.1501
13	0.8215	0.357	0.1785
14	0.7462	0.5077	0.2538
15	0.6568	0.6863	0.3432
16	0.5682	0.8635	0.4318
17	0.4504	0.9008	0.5496
18	0.5177	0.9646	0.4823
19	0.4198	0.8396	0.5802
20	0.3203	0.6405	0.6797
21	0.2691	0.5382	0.7309
22	0.2017	0.4034	0.7983
23	0.134	0.2681	0.866
24	0.07272	0.1454	0.9273
25	0.03461	0.06922	0.9654

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
7 &  0.9902 &  0.01952 &  0.009761 \tabularnewline
8 &  0.9751 &  0.04984 &  0.02492 \tabularnewline
9 &  0.9638 &  0.07237 &  0.03618 \tabularnewline
10 &  0.9405 &  0.119 &  0.05952 \tabularnewline
11 &  0.9044 &  0.1913 &  0.09563 \tabularnewline
12 &  0.8499 &  0.3003 &  0.1501 \tabularnewline
13 &  0.8215 &  0.357 &  0.1785 \tabularnewline
14 &  0.7462 &  0.5077 &  0.2538 \tabularnewline
15 &  0.6568 &  0.6863 &  0.3432 \tabularnewline
16 &  0.5682 &  0.8635 &  0.4318 \tabularnewline
17 &  0.4504 &  0.9008 &  0.5496 \tabularnewline
18 &  0.5177 &  0.9646 &  0.4823 \tabularnewline
19 &  0.4198 &  0.8396 &  0.5802 \tabularnewline
20 &  0.3203 &  0.6405 &  0.6797 \tabularnewline
21 &  0.2691 &  0.5382 &  0.7309 \tabularnewline
22 &  0.2017 &  0.4034 &  0.7983 \tabularnewline
23 &  0.134 &  0.2681 &  0.866 \tabularnewline
24 &  0.07272 &  0.1454 &  0.9273 \tabularnewline
25 &  0.03461 &  0.06922 &  0.9654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284137&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]7[/C][C] 0.9902[/C][C] 0.01952[/C][C] 0.009761[/C][/ROW]
[ROW][C]8[/C][C] 0.9751[/C][C] 0.04984[/C][C] 0.02492[/C][/ROW]
[ROW][C]9[/C][C] 0.9638[/C][C] 0.07237[/C][C] 0.03618[/C][/ROW]
[ROW][C]10[/C][C] 0.9405[/C][C] 0.119[/C][C] 0.05952[/C][/ROW]
[ROW][C]11[/C][C] 0.9044[/C][C] 0.1913[/C][C] 0.09563[/C][/ROW]
[ROW][C]12[/C][C] 0.8499[/C][C] 0.3003[/C][C] 0.1501[/C][/ROW]
[ROW][C]13[/C][C] 0.8215[/C][C] 0.357[/C][C] 0.1785[/C][/ROW]
[ROW][C]14[/C][C] 0.7462[/C][C] 0.5077[/C][C] 0.2538[/C][/ROW]
[ROW][C]15[/C][C] 0.6568[/C][C] 0.6863[/C][C] 0.3432[/C][/ROW]
[ROW][C]16[/C][C] 0.5682[/C][C] 0.8635[/C][C] 0.4318[/C][/ROW]
[ROW][C]17[/C][C] 0.4504[/C][C] 0.9008[/C][C] 0.5496[/C][/ROW]
[ROW][C]18[/C][C] 0.5177[/C][C] 0.9646[/C][C] 0.4823[/C][/ROW]
[ROW][C]19[/C][C] 0.4198[/C][C] 0.8396[/C][C] 0.5802[/C][/ROW]
[ROW][C]20[/C][C] 0.3203[/C][C] 0.6405[/C][C] 0.6797[/C][/ROW]
[ROW][C]21[/C][C] 0.2691[/C][C] 0.5382[/C][C] 0.7309[/C][/ROW]
[ROW][C]22[/C][C] 0.2017[/C][C] 0.4034[/C][C] 0.7983[/C][/ROW]
[ROW][C]23[/C][C] 0.134[/C][C] 0.2681[/C][C] 0.866[/C][/ROW]
[ROW][C]24[/C][C] 0.07272[/C][C] 0.1454[/C][C] 0.9273[/C][/ROW]
[ROW][C]25[/C][C] 0.03461[/C][C] 0.06922[/C][C] 0.9654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284137&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284137&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-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.9902	0.01952	0.009761
8	0.9751	0.04984	0.02492
9	0.9638	0.07237	0.03618
10	0.9405	0.119	0.05952
11	0.9044	0.1913	0.09563
12	0.8499	0.3003	0.1501
13	0.8215	0.357	0.1785
14	0.7462	0.5077	0.2538
15	0.6568	0.6863	0.3432
16	0.5682	0.8635	0.4318
17	0.4504	0.9008	0.5496
18	0.5177	0.9646	0.4823
19	0.4198	0.8396	0.5802
20	0.3203	0.6405	0.6797
21	0.2691	0.5382	0.7309
22	0.2017	0.4034	0.7983
23	0.134	0.2681	0.866
24	0.07272	0.1454	0.9273
25	0.03461	0.06922	0.9654

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	2	0.105263	NOK
10% type I error level	4	0.210526	NOK

\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 & 2 & 0.105263 & NOK \tabularnewline
10% type I error level & 4 & 0.210526 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284137&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]2[/C][C]0.105263[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.210526[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284137&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284137&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 tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	2	0.105263	NOK
10% type I error level	4	0.210526	NOK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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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

PNG link

Postscript link

PDF link

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):

par3 <- 'No Linear Trend'
par2 <- 'Do not include Seasonal Dummies'
par1 <- '1'
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
x <- na.omit(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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, mywarning)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
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,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
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,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code