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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 17 Dec 2010 12:34:10 +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/2010/Dec/17/t1292589221whfhpo8xpm6l38l.htm/, Retrieved Mon, 16 Jun 2025 00:49:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111431, Retrieved Mon, 16 Jun 2025 00:49:53 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

257

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

-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD  [Multiple Regression] [] [2010-11-26 11:40:42] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D    [Multiple Regression] [] [2010-12-15 20:39:35] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D      [Multiple Regression] [] [2010-12-17 12:00:00] [d39e5c40c631ed6c22677d2e41dbfc7d]
-    D          [Multiple Regression] [] [2010-12-17 12:34:10] [1d094c42a82a95b45a19e32ad4bfff5f] [Current]

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Dataseries X:

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2
2,3
2,8
2,4
2,3
2,7
2,7
2,9
3
2,2
2,3
2,8
2,8
2,8
2,2
2,6
2,8
2,5
2,4
2,3
1,9
1,7
2
2,1
1,7
1,8
1,8
1,8
1,3
1,3
1,3
1,2
1,4
2,2
2,9
3,1
3,5
3,6
4,4
4,1
5,1
5,8
5,9
5,4
5,5
4,8
3,2
2,7
2,1
1,9
0,6
0,7
-0,2
-1
-1,7
-0,7
-1
-0,9
0
0,3
0,8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	19 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 19 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]19 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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	19 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
HPC[t] = + 3.11176470588236 -0.176633986928106M1[t] + 0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
HPC[t] =  +  3.11176470588236 -0.176633986928106M1[t] +  0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]HPC[t] =  +  3.11176470588236 -0.176633986928106M1[t] +  0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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
HPC[t] = + 3.11176470588236 -0.176633986928106M1[t] + 0.0267320261437896M2[t] -0.0679411764705897M3[t] -0.082614379084969M4[t] -0.117287581699348M5[t] -0.0919607843137269M6[t] -0.206633986928106M7[t] -0.0813071895424855M8[t] -0.115980392156864M9[t] -0.250653594771243M10[t] -0.145326797385622M11[t] -0.0253267973856209t + 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)	3.11176470588236	0.915522	3.3989	0.00137	0.000685
M1	-0.176633986928106	1.067714	-0.1654	0.869299	0.434649
M2	0.0267320261437896	1.120679	0.0239	0.981068	0.490534
M3	-0.0679411764705897	1.119248	-0.0607	0.951848	0.475924
M4	-0.082614379084969	1.117966	-0.0739	0.941399	0.4707
M5	-0.117287581699348	1.116834	-0.105	0.916799	0.4584
M6	-0.0919607843137269	1.115851	-0.0824	0.934661	0.46733
M7	-0.206633986928106	1.115019	-0.1853	0.85376	0.42688
M8	-0.0813071895424855	1.114338	-0.073	0.942138	0.471069
M9	-0.115980392156864	1.113808	-0.1041	0.9175	0.45875
M10	-0.250653594771243	1.113429	-0.2251	0.822843	0.411421
M11	-0.145326797385622	1.113202	-0.1305	0.896678	0.448339
t	-0.0253267973856209	0.012989	-1.9499	0.057048	0.028524

\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) & 3.11176470588236 & 0.915522 & 3.3989 & 0.00137 & 0.000685 \tabularnewline
M1 & -0.176633986928106 & 1.067714 & -0.1654 & 0.869299 & 0.434649 \tabularnewline
M2 & 0.0267320261437896 & 1.120679 & 0.0239 & 0.981068 & 0.490534 \tabularnewline
M3 & -0.0679411764705897 & 1.119248 & -0.0607 & 0.951848 & 0.475924 \tabularnewline
M4 & -0.082614379084969 & 1.117966 & -0.0739 & 0.941399 & 0.4707 \tabularnewline
M5 & -0.117287581699348 & 1.116834 & -0.105 & 0.916799 & 0.4584 \tabularnewline
M6 & -0.0919607843137269 & 1.115851 & -0.0824 & 0.934661 & 0.46733 \tabularnewline
M7 & -0.206633986928106 & 1.115019 & -0.1853 & 0.85376 & 0.42688 \tabularnewline
M8 & -0.0813071895424855 & 1.114338 & -0.073 & 0.942138 & 0.471069 \tabularnewline
M9 & -0.115980392156864 & 1.113808 & -0.1041 & 0.9175 & 0.45875 \tabularnewline
M10 & -0.250653594771243 & 1.113429 & -0.2251 & 0.822843 & 0.411421 \tabularnewline
M11 & -0.145326797385622 & 1.113202 & -0.1305 & 0.896678 & 0.448339 \tabularnewline
t & -0.0253267973856209 & 0.012989 & -1.9499 & 0.057048 & 0.028524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]3.11176470588236[/C][C]0.915522[/C][C]3.3989[/C][C]0.00137[/C][C]0.000685[/C][/ROW]
[ROW][C]M1[/C][C]-0.176633986928106[/C][C]1.067714[/C][C]-0.1654[/C][C]0.869299[/C][C]0.434649[/C][/ROW]
[ROW][C]M2[/C][C]0.0267320261437896[/C][C]1.120679[/C][C]0.0239[/C][C]0.981068[/C][C]0.490534[/C][/ROW]
[ROW][C]M3[/C][C]-0.0679411764705897[/C][C]1.119248[/C][C]-0.0607[/C][C]0.951848[/C][C]0.475924[/C][/ROW]
[ROW][C]M4[/C][C]-0.082614379084969[/C][C]1.117966[/C][C]-0.0739[/C][C]0.941399[/C][C]0.4707[/C][/ROW]
[ROW][C]M5[/C][C]-0.117287581699348[/C][C]1.116834[/C][C]-0.105[/C][C]0.916799[/C][C]0.4584[/C][/ROW]
[ROW][C]M6[/C][C]-0.0919607843137269[/C][C]1.115851[/C][C]-0.0824[/C][C]0.934661[/C][C]0.46733[/C][/ROW]
[ROW][C]M7[/C][C]-0.206633986928106[/C][C]1.115019[/C][C]-0.1853[/C][C]0.85376[/C][C]0.42688[/C][/ROW]
[ROW][C]M8[/C][C]-0.0813071895424855[/C][C]1.114338[/C][C]-0.073[/C][C]0.942138[/C][C]0.471069[/C][/ROW]
[ROW][C]M9[/C][C]-0.115980392156864[/C][C]1.113808[/C][C]-0.1041[/C][C]0.9175[/C][C]0.45875[/C][/ROW]
[ROW][C]M10[/C][C]-0.250653594771243[/C][C]1.113429[/C][C]-0.2251[/C][C]0.822843[/C][C]0.411421[/C][/ROW]
[ROW][C]M11[/C][C]-0.145326797385622[/C][C]1.113202[/C][C]-0.1305[/C][C]0.896678[/C][C]0.448339[/C][/ROW]
[ROW][C]t[/C][C]-0.0253267973856209[/C][C]0.012989[/C][C]-1.9499[/C][C]0.057048[/C][C]0.028524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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)	3.11176470588236	0.915522	3.3989	0.00137	0.000685
M1	-0.176633986928106	1.067714	-0.1654	0.869299	0.434649
M2	0.0267320261437896	1.120679	0.0239	0.981068	0.490534
M3	-0.0679411764705897	1.119248	-0.0607	0.951848	0.475924
M4	-0.082614379084969	1.117966	-0.0739	0.941399	0.4707
M5	-0.117287581699348	1.116834	-0.105	0.916799	0.4584
M6	-0.0919607843137269	1.115851	-0.0824	0.934661	0.46733
M7	-0.206633986928106	1.115019	-0.1853	0.85376	0.42688
M8	-0.0813071895424855	1.114338	-0.073	0.942138	0.471069
M9	-0.115980392156864	1.113808	-0.1041	0.9175	0.45875
M10	-0.250653594771243	1.113429	-0.2251	0.822843	0.411421
M11	-0.145326797385622	1.113202	-0.1305	0.896678	0.448339
t	-0.0253267973856209	0.012989	-1.9499	0.057048	0.028524

Multiple Linear Regression - Regression Statistics
Multiple R	0.280701934462105
R-squared	0.0787935760107679
Adjusted R-squared	-0.15150802998654
F-TEST (value)	0.34213211701046
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.976538597787572
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.76000733435786
Sum Squared Residuals	148.686039215686

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.280701934462105 \tabularnewline
R-squared & 0.0787935760107679 \tabularnewline
Adjusted R-squared & -0.15150802998654 \tabularnewline
F-TEST (value) & 0.34213211701046 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.976538597787572 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.76000733435786 \tabularnewline
Sum Squared Residuals & 148.686039215686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.280701934462105[/C][/ROW]
[ROW][C]R-squared[/C][C]0.0787935760107679[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.15150802998654[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.34213211701046[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.976538597787572[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1.76000733435786[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]148.686039215686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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	0.280701934462105
R-squared	0.0787935760107679
Adjusted R-squared	-0.15150802998654
F-TEST (value)	0.34213211701046
F-TEST (DF numerator)	12
F-TEST (DF denominator)	48
p-value	0.976538597787572
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.76000733435786
Sum Squared Residuals	148.686039215686

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	2	2.90980392156862	-0.909803921568623
2	2.3	3.0878431372549	-0.787843137254901
3	2.8	2.9678431372549	-0.167843137254902
4	2.4	2.9278431372549	-0.527843137254901
5	2.3	2.8678431372549	-0.567843137254902
6	2.7	2.8678431372549	-0.167843137254902
7	2.7	2.72784313725490	-0.0278431372549023
8	2.9	2.8278431372549	0.0721568627450983
9	3	2.7678431372549	0.232156862745098
10	2.2	2.60784313725490	-0.407843137254902
11	2.3	2.6878431372549	-0.387843137254902
12	2.8	2.80784313725490	-0.00784313725490308
13	2.8	2.60588235294118	0.194117647058822
14	2.8	2.78392156862745	0.0160784313725485
15	2.2	2.66392156862745	-0.463921568627451
16	2.6	2.62392156862745	-0.0239215686274506
17	2.8	2.56392156862745	0.236078431372549
18	2.5	2.56392156862745	-0.0639215686274504
19	2.4	2.42392156862745	-0.0239215686274508
20	2.3	2.52392156862745	-0.223921568627451
21	1.9	2.46392156862745	-0.563921568627451
22	1.7	2.30392156862745	-0.603921568627451
23	2	2.38392156862745	-0.383921568627451
24	2.1	2.50392156862745	-0.403921568627452
25	1.7	2.30196078431373	-0.601960784313726
26	1.8	2.48	-0.68
27	1.8	2.36	-0.56
28	1.8	2.32	-0.52
29	1.3	2.26	-0.96
30	1.3	2.26	-0.96
31	1.3	2.12	-0.82
32	1.2	2.22	-1.02
33	1.4	2.16	-0.76
34	2.2	2	0.200000000000001
35	2.9	2.08	0.82
36	3.1	2.2	0.899999999999999
37	3.5	1.99803921568627	1.50196078431373
38	3.6	2.17607843137255	1.42392156862745
39	4.4	2.05607843137255	2.34392156862745
40	4.1	2.01607843137255	2.08392156862745
41	5.1	1.95607843137255	3.14392156862745
42	5.8	1.95607843137255	3.84392156862745
43	5.9	1.81607843137255	4.08392156862745
44	5.4	1.91607843137255	3.48392156862745
45	5.5	1.85607843137255	3.64392156862745
46	4.8	1.69607843137255	3.10392156862745
47	3.2	1.77607843137255	1.42392156862745
48	2.7	1.89607843137255	0.80392156862745
49	2.1	1.69411764705882	0.405882352941176
50	1.9	1.8721568627451	0.0278431372549018
51	0.6	1.75215686274510	-1.15215686274510
52	0.7	1.71215686274510	-1.01215686274510
53	-0.2	1.6521568627451	-1.8521568627451
54	-1	1.65215686274510	-2.6521568627451
55	-1.7	1.51215686274510	-3.2121568627451
56	-0.7	1.6121568627451	-2.3121568627451
57	-1	1.5521568627451	-2.5521568627451
58	-0.9	1.3921568627451	-2.2921568627451
59	0	1.4721568627451	-1.4721568627451
60	0.3	1.5921568627451	-1.2921568627451
61	0.8	1.39019607843137	-0.590196078431373

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2 & 2.90980392156862 & -0.909803921568623 \tabularnewline
2 & 2.3 & 3.0878431372549 & -0.787843137254901 \tabularnewline
3 & 2.8 & 2.9678431372549 & -0.167843137254902 \tabularnewline
4 & 2.4 & 2.9278431372549 & -0.527843137254901 \tabularnewline
5 & 2.3 & 2.8678431372549 & -0.567843137254902 \tabularnewline
6 & 2.7 & 2.8678431372549 & -0.167843137254902 \tabularnewline
7 & 2.7 & 2.72784313725490 & -0.0278431372549023 \tabularnewline
8 & 2.9 & 2.8278431372549 & 0.0721568627450983 \tabularnewline
9 & 3 & 2.7678431372549 & 0.232156862745098 \tabularnewline
10 & 2.2 & 2.60784313725490 & -0.407843137254902 \tabularnewline
11 & 2.3 & 2.6878431372549 & -0.387843137254902 \tabularnewline
12 & 2.8 & 2.80784313725490 & -0.00784313725490308 \tabularnewline
13 & 2.8 & 2.60588235294118 & 0.194117647058822 \tabularnewline
14 & 2.8 & 2.78392156862745 & 0.0160784313725485 \tabularnewline
15 & 2.2 & 2.66392156862745 & -0.463921568627451 \tabularnewline
16 & 2.6 & 2.62392156862745 & -0.0239215686274506 \tabularnewline
17 & 2.8 & 2.56392156862745 & 0.236078431372549 \tabularnewline
18 & 2.5 & 2.56392156862745 & -0.0639215686274504 \tabularnewline
19 & 2.4 & 2.42392156862745 & -0.0239215686274508 \tabularnewline
20 & 2.3 & 2.52392156862745 & -0.223921568627451 \tabularnewline
21 & 1.9 & 2.46392156862745 & -0.563921568627451 \tabularnewline
22 & 1.7 & 2.30392156862745 & -0.603921568627451 \tabularnewline
23 & 2 & 2.38392156862745 & -0.383921568627451 \tabularnewline
24 & 2.1 & 2.50392156862745 & -0.403921568627452 \tabularnewline
25 & 1.7 & 2.30196078431373 & -0.601960784313726 \tabularnewline
26 & 1.8 & 2.48 & -0.68 \tabularnewline
27 & 1.8 & 2.36 & -0.56 \tabularnewline
28 & 1.8 & 2.32 & -0.52 \tabularnewline
29 & 1.3 & 2.26 & -0.96 \tabularnewline
30 & 1.3 & 2.26 & -0.96 \tabularnewline
31 & 1.3 & 2.12 & -0.82 \tabularnewline
32 & 1.2 & 2.22 & -1.02 \tabularnewline
33 & 1.4 & 2.16 & -0.76 \tabularnewline
34 & 2.2 & 2 & 0.200000000000001 \tabularnewline
35 & 2.9 & 2.08 & 0.82 \tabularnewline
36 & 3.1 & 2.2 & 0.899999999999999 \tabularnewline
37 & 3.5 & 1.99803921568627 & 1.50196078431373 \tabularnewline
38 & 3.6 & 2.17607843137255 & 1.42392156862745 \tabularnewline
39 & 4.4 & 2.05607843137255 & 2.34392156862745 \tabularnewline
40 & 4.1 & 2.01607843137255 & 2.08392156862745 \tabularnewline
41 & 5.1 & 1.95607843137255 & 3.14392156862745 \tabularnewline
42 & 5.8 & 1.95607843137255 & 3.84392156862745 \tabularnewline
43 & 5.9 & 1.81607843137255 & 4.08392156862745 \tabularnewline
44 & 5.4 & 1.91607843137255 & 3.48392156862745 \tabularnewline
45 & 5.5 & 1.85607843137255 & 3.64392156862745 \tabularnewline
46 & 4.8 & 1.69607843137255 & 3.10392156862745 \tabularnewline
47 & 3.2 & 1.77607843137255 & 1.42392156862745 \tabularnewline
48 & 2.7 & 1.89607843137255 & 0.80392156862745 \tabularnewline
49 & 2.1 & 1.69411764705882 & 0.405882352941176 \tabularnewline
50 & 1.9 & 1.8721568627451 & 0.0278431372549018 \tabularnewline
51 & 0.6 & 1.75215686274510 & -1.15215686274510 \tabularnewline
52 & 0.7 & 1.71215686274510 & -1.01215686274510 \tabularnewline
53 & -0.2 & 1.6521568627451 & -1.8521568627451 \tabularnewline
54 & -1 & 1.65215686274510 & -2.6521568627451 \tabularnewline
55 & -1.7 & 1.51215686274510 & -3.2121568627451 \tabularnewline
56 & -0.7 & 1.6121568627451 & -2.3121568627451 \tabularnewline
57 & -1 & 1.5521568627451 & -2.5521568627451 \tabularnewline
58 & -0.9 & 1.3921568627451 & -2.2921568627451 \tabularnewline
59 & 0 & 1.4721568627451 & -1.4721568627451 \tabularnewline
60 & 0.3 & 1.5921568627451 & -1.2921568627451 \tabularnewline
61 & 0.8 & 1.39019607843137 & -0.590196078431373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]2.90980392156862[/C][C]-0.909803921568623[/C][/ROW]
[ROW][C]2[/C][C]2.3[/C][C]3.0878431372549[/C][C]-0.787843137254901[/C][/ROW]
[ROW][C]3[/C][C]2.8[/C][C]2.9678431372549[/C][C]-0.167843137254902[/C][/ROW]
[ROW][C]4[/C][C]2.4[/C][C]2.9278431372549[/C][C]-0.527843137254901[/C][/ROW]
[ROW][C]5[/C][C]2.3[/C][C]2.8678431372549[/C][C]-0.567843137254902[/C][/ROW]
[ROW][C]6[/C][C]2.7[/C][C]2.8678431372549[/C][C]-0.167843137254902[/C][/ROW]
[ROW][C]7[/C][C]2.7[/C][C]2.72784313725490[/C][C]-0.0278431372549023[/C][/ROW]
[ROW][C]8[/C][C]2.9[/C][C]2.8278431372549[/C][C]0.0721568627450983[/C][/ROW]
[ROW][C]9[/C][C]3[/C][C]2.7678431372549[/C][C]0.232156862745098[/C][/ROW]
[ROW][C]10[/C][C]2.2[/C][C]2.60784313725490[/C][C]-0.407843137254902[/C][/ROW]
[ROW][C]11[/C][C]2.3[/C][C]2.6878431372549[/C][C]-0.387843137254902[/C][/ROW]
[ROW][C]12[/C][C]2.8[/C][C]2.80784313725490[/C][C]-0.00784313725490308[/C][/ROW]
[ROW][C]13[/C][C]2.8[/C][C]2.60588235294118[/C][C]0.194117647058822[/C][/ROW]
[ROW][C]14[/C][C]2.8[/C][C]2.78392156862745[/C][C]0.0160784313725485[/C][/ROW]
[ROW][C]15[/C][C]2.2[/C][C]2.66392156862745[/C][C]-0.463921568627451[/C][/ROW]
[ROW][C]16[/C][C]2.6[/C][C]2.62392156862745[/C][C]-0.0239215686274506[/C][/ROW]
[ROW][C]17[/C][C]2.8[/C][C]2.56392156862745[/C][C]0.236078431372549[/C][/ROW]
[ROW][C]18[/C][C]2.5[/C][C]2.56392156862745[/C][C]-0.0639215686274504[/C][/ROW]
[ROW][C]19[/C][C]2.4[/C][C]2.42392156862745[/C][C]-0.0239215686274508[/C][/ROW]
[ROW][C]20[/C][C]2.3[/C][C]2.52392156862745[/C][C]-0.223921568627451[/C][/ROW]
[ROW][C]21[/C][C]1.9[/C][C]2.46392156862745[/C][C]-0.563921568627451[/C][/ROW]
[ROW][C]22[/C][C]1.7[/C][C]2.30392156862745[/C][C]-0.603921568627451[/C][/ROW]
[ROW][C]23[/C][C]2[/C][C]2.38392156862745[/C][C]-0.383921568627451[/C][/ROW]
[ROW][C]24[/C][C]2.1[/C][C]2.50392156862745[/C][C]-0.403921568627452[/C][/ROW]
[ROW][C]25[/C][C]1.7[/C][C]2.30196078431373[/C][C]-0.601960784313726[/C][/ROW]
[ROW][C]26[/C][C]1.8[/C][C]2.48[/C][C]-0.68[/C][/ROW]
[ROW][C]27[/C][C]1.8[/C][C]2.36[/C][C]-0.56[/C][/ROW]
[ROW][C]28[/C][C]1.8[/C][C]2.32[/C][C]-0.52[/C][/ROW]
[ROW][C]29[/C][C]1.3[/C][C]2.26[/C][C]-0.96[/C][/ROW]
[ROW][C]30[/C][C]1.3[/C][C]2.26[/C][C]-0.96[/C][/ROW]
[ROW][C]31[/C][C]1.3[/C][C]2.12[/C][C]-0.82[/C][/ROW]
[ROW][C]32[/C][C]1.2[/C][C]2.22[/C][C]-1.02[/C][/ROW]
[ROW][C]33[/C][C]1.4[/C][C]2.16[/C][C]-0.76[/C][/ROW]
[ROW][C]34[/C][C]2.2[/C][C]2[/C][C]0.200000000000001[/C][/ROW]
[ROW][C]35[/C][C]2.9[/C][C]2.08[/C][C]0.82[/C][/ROW]
[ROW][C]36[/C][C]3.1[/C][C]2.2[/C][C]0.899999999999999[/C][/ROW]
[ROW][C]37[/C][C]3.5[/C][C]1.99803921568627[/C][C]1.50196078431373[/C][/ROW]
[ROW][C]38[/C][C]3.6[/C][C]2.17607843137255[/C][C]1.42392156862745[/C][/ROW]
[ROW][C]39[/C][C]4.4[/C][C]2.05607843137255[/C][C]2.34392156862745[/C][/ROW]
[ROW][C]40[/C][C]4.1[/C][C]2.01607843137255[/C][C]2.08392156862745[/C][/ROW]
[ROW][C]41[/C][C]5.1[/C][C]1.95607843137255[/C][C]3.14392156862745[/C][/ROW]
[ROW][C]42[/C][C]5.8[/C][C]1.95607843137255[/C][C]3.84392156862745[/C][/ROW]
[ROW][C]43[/C][C]5.9[/C][C]1.81607843137255[/C][C]4.08392156862745[/C][/ROW]
[ROW][C]44[/C][C]5.4[/C][C]1.91607843137255[/C][C]3.48392156862745[/C][/ROW]
[ROW][C]45[/C][C]5.5[/C][C]1.85607843137255[/C][C]3.64392156862745[/C][/ROW]
[ROW][C]46[/C][C]4.8[/C][C]1.69607843137255[/C][C]3.10392156862745[/C][/ROW]
[ROW][C]47[/C][C]3.2[/C][C]1.77607843137255[/C][C]1.42392156862745[/C][/ROW]
[ROW][C]48[/C][C]2.7[/C][C]1.89607843137255[/C][C]0.80392156862745[/C][/ROW]
[ROW][C]49[/C][C]2.1[/C][C]1.69411764705882[/C][C]0.405882352941176[/C][/ROW]
[ROW][C]50[/C][C]1.9[/C][C]1.8721568627451[/C][C]0.0278431372549018[/C][/ROW]
[ROW][C]51[/C][C]0.6[/C][C]1.75215686274510[/C][C]-1.15215686274510[/C][/ROW]
[ROW][C]52[/C][C]0.7[/C][C]1.71215686274510[/C][C]-1.01215686274510[/C][/ROW]
[ROW][C]53[/C][C]-0.2[/C][C]1.6521568627451[/C][C]-1.8521568627451[/C][/ROW]
[ROW][C]54[/C][C]-1[/C][C]1.65215686274510[/C][C]-2.6521568627451[/C][/ROW]
[ROW][C]55[/C][C]-1.7[/C][C]1.51215686274510[/C][C]-3.2121568627451[/C][/ROW]
[ROW][C]56[/C][C]-0.7[/C][C]1.6121568627451[/C][C]-2.3121568627451[/C][/ROW]
[ROW][C]57[/C][C]-1[/C][C]1.5521568627451[/C][C]-2.5521568627451[/C][/ROW]
[ROW][C]58[/C][C]-0.9[/C][C]1.3921568627451[/C][C]-2.2921568627451[/C][/ROW]
[ROW][C]59[/C][C]0[/C][C]1.4721568627451[/C][C]-1.4721568627451[/C][/ROW]
[ROW][C]60[/C][C]0.3[/C][C]1.5921568627451[/C][C]-1.2921568627451[/C][/ROW]
[ROW][C]61[/C][C]0.8[/C][C]1.39019607843137[/C][C]-0.590196078431373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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	2	2.90980392156862	-0.909803921568623
2	2.3	3.0878431372549	-0.787843137254901
3	2.8	2.9678431372549	-0.167843137254902
4	2.4	2.9278431372549	-0.527843137254901
5	2.3	2.8678431372549	-0.567843137254902
6	2.7	2.8678431372549	-0.167843137254902
7	2.7	2.72784313725490	-0.0278431372549023
8	2.9	2.8278431372549	0.0721568627450983
9	3	2.7678431372549	0.232156862745098
10	2.2	2.60784313725490	-0.407843137254902
11	2.3	2.6878431372549	-0.387843137254902
12	2.8	2.80784313725490	-0.00784313725490308
13	2.8	2.60588235294118	0.194117647058822
14	2.8	2.78392156862745	0.0160784313725485
15	2.2	2.66392156862745	-0.463921568627451
16	2.6	2.62392156862745	-0.0239215686274506
17	2.8	2.56392156862745	0.236078431372549
18	2.5	2.56392156862745	-0.0639215686274504
19	2.4	2.42392156862745	-0.0239215686274508
20	2.3	2.52392156862745	-0.223921568627451
21	1.9	2.46392156862745	-0.563921568627451
22	1.7	2.30392156862745	-0.603921568627451
23	2	2.38392156862745	-0.383921568627451
24	2.1	2.50392156862745	-0.403921568627452
25	1.7	2.30196078431373	-0.601960784313726
26	1.8	2.48	-0.68
27	1.8	2.36	-0.56
28	1.8	2.32	-0.52
29	1.3	2.26	-0.96
30	1.3	2.26	-0.96
31	1.3	2.12	-0.82
32	1.2	2.22	-1.02
33	1.4	2.16	-0.76
34	2.2	2	0.200000000000001
35	2.9	2.08	0.82
36	3.1	2.2	0.899999999999999
37	3.5	1.99803921568627	1.50196078431373
38	3.6	2.17607843137255	1.42392156862745
39	4.4	2.05607843137255	2.34392156862745
40	4.1	2.01607843137255	2.08392156862745
41	5.1	1.95607843137255	3.14392156862745
42	5.8	1.95607843137255	3.84392156862745
43	5.9	1.81607843137255	4.08392156862745
44	5.4	1.91607843137255	3.48392156862745
45	5.5	1.85607843137255	3.64392156862745
46	4.8	1.69607843137255	3.10392156862745
47	3.2	1.77607843137255	1.42392156862745
48	2.7	1.89607843137255	0.80392156862745
49	2.1	1.69411764705882	0.405882352941176
50	1.9	1.8721568627451	0.0278431372549018
51	0.6	1.75215686274510	-1.15215686274510
52	0.7	1.71215686274510	-1.01215686274510
53	-0.2	1.6521568627451	-1.8521568627451
54	-1	1.65215686274510	-2.6521568627451
55	-1.7	1.51215686274510	-3.2121568627451
56	-0.7	1.6121568627451	-2.3121568627451
57	-1	1.5521568627451	-2.5521568627451
58	-0.9	1.3921568627451	-2.2921568627451
59	0	1.4721568627451	-1.4721568627451
60	0.3	1.5921568627451	-1.2921568627451
61	0.8	1.39019607843137	-0.590196078431373

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.0111321750190376	0.0222643500380752	0.988867824980962
17	0.00197603005051437	0.00395206010102874	0.998023969949486
18	0.000423622507114023	0.000847245014228047	0.999576377492886
19	9.40906718038906e-05	0.000188181343607781	0.999905909328196
20	3.28433449934913e-05	6.56866899869825e-05	0.999967156655007
21	2.90369671519759e-05	5.80739343039517e-05	0.999970963032848
22	6.61332579055521e-06	1.32266515811104e-05	0.99999338667421
23	1.22411756558044e-06	2.44823513116087e-06	0.999998775882434
24	3.21460393808537e-07	6.42920787617074e-07	0.999999678539606
25	7.9648074379939e-08	1.59296148759878e-07	0.999999920351926
26	1.95519261053518e-08	3.91038522107036e-08	0.999999980448074
27	4.20133902652341e-09	8.40267805304683e-09	0.99999999579866
28	8.86851316440512e-10	1.77370263288102e-09	0.999999999113149
29	6.60105038255032e-10	1.32021007651006e-09	0.999999999339895
30	5.10036308418355e-10	1.02007261683671e-09	0.999999999489964
31	3.30649947531936e-10	6.61299895063872e-10	0.99999999966935
32	4.71654399629039e-10	9.43308799258079e-10	0.999999999528346
33	5.63848792077113e-10	1.12769758415423e-09	0.999999999436151
34	3.38770359436159e-09	6.77540718872317e-09	0.999999996612296
35	5.57372018510203e-08	1.11474403702041e-07	0.999999944262798
36	6.62492956223794e-07	1.32498591244759e-06	0.999999337507044
37	0.000132745521241138	0.000265491042482275	0.999867254478759
38	0.00098702668318747	0.00197405336637494	0.999012973316812
39	0.00373914924367656	0.00747829848735312	0.996260850756323
40	0.0060112605081933	0.0120225210163866	0.993988739491807
41	0.0131309617567897	0.0262619235135795	0.98686903824321
42	0.0388821827480898	0.0777643654961795	0.96111781725191
43	0.134193415413995	0.26838683082799	0.865806584586005
44	0.164748019909935	0.329496039819871	0.835251980090065
45	0.334078787897395	0.66815757579479	0.665921212102605

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0111321750190376 & 0.0222643500380752 & 0.988867824980962 \tabularnewline
17 & 0.00197603005051437 & 0.00395206010102874 & 0.998023969949486 \tabularnewline
18 & 0.000423622507114023 & 0.000847245014228047 & 0.999576377492886 \tabularnewline
19 & 9.40906718038906e-05 & 0.000188181343607781 & 0.999905909328196 \tabularnewline
20 & 3.28433449934913e-05 & 6.56866899869825e-05 & 0.999967156655007 \tabularnewline
21 & 2.90369671519759e-05 & 5.80739343039517e-05 & 0.999970963032848 \tabularnewline
22 & 6.61332579055521e-06 & 1.32266515811104e-05 & 0.99999338667421 \tabularnewline
23 & 1.22411756558044e-06 & 2.44823513116087e-06 & 0.999998775882434 \tabularnewline
24 & 3.21460393808537e-07 & 6.42920787617074e-07 & 0.999999678539606 \tabularnewline
25 & 7.9648074379939e-08 & 1.59296148759878e-07 & 0.999999920351926 \tabularnewline
26 & 1.95519261053518e-08 & 3.91038522107036e-08 & 0.999999980448074 \tabularnewline
27 & 4.20133902652341e-09 & 8.40267805304683e-09 & 0.99999999579866 \tabularnewline
28 & 8.86851316440512e-10 & 1.77370263288102e-09 & 0.999999999113149 \tabularnewline
29 & 6.60105038255032e-10 & 1.32021007651006e-09 & 0.999999999339895 \tabularnewline
30 & 5.10036308418355e-10 & 1.02007261683671e-09 & 0.999999999489964 \tabularnewline
31 & 3.30649947531936e-10 & 6.61299895063872e-10 & 0.99999999966935 \tabularnewline
32 & 4.71654399629039e-10 & 9.43308799258079e-10 & 0.999999999528346 \tabularnewline
33 & 5.63848792077113e-10 & 1.12769758415423e-09 & 0.999999999436151 \tabularnewline
34 & 3.38770359436159e-09 & 6.77540718872317e-09 & 0.999999996612296 \tabularnewline
35 & 5.57372018510203e-08 & 1.11474403702041e-07 & 0.999999944262798 \tabularnewline
36 & 6.62492956223794e-07 & 1.32498591244759e-06 & 0.999999337507044 \tabularnewline
37 & 0.000132745521241138 & 0.000265491042482275 & 0.999867254478759 \tabularnewline
38 & 0.00098702668318747 & 0.00197405336637494 & 0.999012973316812 \tabularnewline
39 & 0.00373914924367656 & 0.00747829848735312 & 0.996260850756323 \tabularnewline
40 & 0.0060112605081933 & 0.0120225210163866 & 0.993988739491807 \tabularnewline
41 & 0.0131309617567897 & 0.0262619235135795 & 0.98686903824321 \tabularnewline
42 & 0.0388821827480898 & 0.0777643654961795 & 0.96111781725191 \tabularnewline
43 & 0.134193415413995 & 0.26838683082799 & 0.865806584586005 \tabularnewline
44 & 0.164748019909935 & 0.329496039819871 & 0.835251980090065 \tabularnewline
45 & 0.334078787897395 & 0.66815757579479 & 0.665921212102605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]16[/C][C]0.0111321750190376[/C][C]0.0222643500380752[/C][C]0.988867824980962[/C][/ROW]
[ROW][C]17[/C][C]0.00197603005051437[/C][C]0.00395206010102874[/C][C]0.998023969949486[/C][/ROW]
[ROW][C]18[/C][C]0.000423622507114023[/C][C]0.000847245014228047[/C][C]0.999576377492886[/C][/ROW]
[ROW][C]19[/C][C]9.40906718038906e-05[/C][C]0.000188181343607781[/C][C]0.999905909328196[/C][/ROW]
[ROW][C]20[/C][C]3.28433449934913e-05[/C][C]6.56866899869825e-05[/C][C]0.999967156655007[/C][/ROW]
[ROW][C]21[/C][C]2.90369671519759e-05[/C][C]5.80739343039517e-05[/C][C]0.999970963032848[/C][/ROW]
[ROW][C]22[/C][C]6.61332579055521e-06[/C][C]1.32266515811104e-05[/C][C]0.99999338667421[/C][/ROW]
[ROW][C]23[/C][C]1.22411756558044e-06[/C][C]2.44823513116087e-06[/C][C]0.999998775882434[/C][/ROW]
[ROW][C]24[/C][C]3.21460393808537e-07[/C][C]6.42920787617074e-07[/C][C]0.999999678539606[/C][/ROW]
[ROW][C]25[/C][C]7.9648074379939e-08[/C][C]1.59296148759878e-07[/C][C]0.999999920351926[/C][/ROW]
[ROW][C]26[/C][C]1.95519261053518e-08[/C][C]3.91038522107036e-08[/C][C]0.999999980448074[/C][/ROW]
[ROW][C]27[/C][C]4.20133902652341e-09[/C][C]8.40267805304683e-09[/C][C]0.99999999579866[/C][/ROW]
[ROW][C]28[/C][C]8.86851316440512e-10[/C][C]1.77370263288102e-09[/C][C]0.999999999113149[/C][/ROW]
[ROW][C]29[/C][C]6.60105038255032e-10[/C][C]1.32021007651006e-09[/C][C]0.999999999339895[/C][/ROW]
[ROW][C]30[/C][C]5.10036308418355e-10[/C][C]1.02007261683671e-09[/C][C]0.999999999489964[/C][/ROW]
[ROW][C]31[/C][C]3.30649947531936e-10[/C][C]6.61299895063872e-10[/C][C]0.99999999966935[/C][/ROW]
[ROW][C]32[/C][C]4.71654399629039e-10[/C][C]9.43308799258079e-10[/C][C]0.999999999528346[/C][/ROW]
[ROW][C]33[/C][C]5.63848792077113e-10[/C][C]1.12769758415423e-09[/C][C]0.999999999436151[/C][/ROW]
[ROW][C]34[/C][C]3.38770359436159e-09[/C][C]6.77540718872317e-09[/C][C]0.999999996612296[/C][/ROW]
[ROW][C]35[/C][C]5.57372018510203e-08[/C][C]1.11474403702041e-07[/C][C]0.999999944262798[/C][/ROW]
[ROW][C]36[/C][C]6.62492956223794e-07[/C][C]1.32498591244759e-06[/C][C]0.999999337507044[/C][/ROW]
[ROW][C]37[/C][C]0.000132745521241138[/C][C]0.000265491042482275[/C][C]0.999867254478759[/C][/ROW]
[ROW][C]38[/C][C]0.00098702668318747[/C][C]0.00197405336637494[/C][C]0.999012973316812[/C][/ROW]
[ROW][C]39[/C][C]0.00373914924367656[/C][C]0.00747829848735312[/C][C]0.996260850756323[/C][/ROW]
[ROW][C]40[/C][C]0.0060112605081933[/C][C]0.0120225210163866[/C][C]0.993988739491807[/C][/ROW]
[ROW][C]41[/C][C]0.0131309617567897[/C][C]0.0262619235135795[/C][C]0.98686903824321[/C][/ROW]
[ROW][C]42[/C][C]0.0388821827480898[/C][C]0.0777643654961795[/C][C]0.96111781725191[/C][/ROW]
[ROW][C]43[/C][C]0.134193415413995[/C][C]0.26838683082799[/C][C]0.865806584586005[/C][/ROW]
[ROW][C]44[/C][C]0.164748019909935[/C][C]0.329496039819871[/C][C]0.835251980090065[/C][/ROW]
[ROW][C]45[/C][C]0.334078787897395[/C][C]0.66815757579479[/C][C]0.665921212102605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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
16	0.0111321750190376	0.0222643500380752	0.988867824980962
17	0.00197603005051437	0.00395206010102874	0.998023969949486
18	0.000423622507114023	0.000847245014228047	0.999576377492886
19	9.40906718038906e-05	0.000188181343607781	0.999905909328196
20	3.28433449934913e-05	6.56866899869825e-05	0.999967156655007
21	2.90369671519759e-05	5.80739343039517e-05	0.999970963032848
22	6.61332579055521e-06	1.32266515811104e-05	0.99999338667421
23	1.22411756558044e-06	2.44823513116087e-06	0.999998775882434
24	3.21460393808537e-07	6.42920787617074e-07	0.999999678539606
25	7.9648074379939e-08	1.59296148759878e-07	0.999999920351926
26	1.95519261053518e-08	3.91038522107036e-08	0.999999980448074
27	4.20133902652341e-09	8.40267805304683e-09	0.99999999579866
28	8.86851316440512e-10	1.77370263288102e-09	0.999999999113149
29	6.60105038255032e-10	1.32021007651006e-09	0.999999999339895
30	5.10036308418355e-10	1.02007261683671e-09	0.999999999489964
31	3.30649947531936e-10	6.61299895063872e-10	0.99999999966935
32	4.71654399629039e-10	9.43308799258079e-10	0.999999999528346
33	5.63848792077113e-10	1.12769758415423e-09	0.999999999436151
34	3.38770359436159e-09	6.77540718872317e-09	0.999999996612296
35	5.57372018510203e-08	1.11474403702041e-07	0.999999944262798
36	6.62492956223794e-07	1.32498591244759e-06	0.999999337507044
37	0.000132745521241138	0.000265491042482275	0.999867254478759
38	0.00098702668318747	0.00197405336637494	0.999012973316812
39	0.00373914924367656	0.00747829848735312	0.996260850756323
40	0.0060112605081933	0.0120225210163866	0.993988739491807
41	0.0131309617567897	0.0262619235135795	0.98686903824321
42	0.0388821827480898	0.0777643654961795	0.96111781725191
43	0.134193415413995	0.26838683082799	0.865806584586005
44	0.164748019909935	0.329496039819871	0.835251980090065
45	0.334078787897395	0.66815757579479	0.665921212102605

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	23	0.766666666666667	NOK
5% type I error level	26	0.866666666666667	NOK
10% type I error level	27	0.9	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 & 23 & 0.766666666666667 & NOK \tabularnewline
5% type I error level & 26 & 0.866666666666667 & NOK \tabularnewline
10% type I error level & 27 & 0.9 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111431&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]23[/C][C]0.766666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]26[/C][C]0.866666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]27[/C][C]0.9[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111431&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111431&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	23	0.766666666666667	NOK
5% type I error level	26	0.866666666666667	NOK
10% type I error level	27	0.9	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

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code