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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 04 Jun 2015 13:29:07 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jun/04/t14334211513n2oecq5us3d408.htm/, Retrieved Fri, 17 May 2024 22:46:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279514, Retrieved Fri, 17 May 2024 22:46:41 +0000

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No (this computation is public)

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Estimated Impact

170

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

-       [Multiple Regression] [regressioni linea...] [2015-06-04 12:29:07] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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0,9	0,96	1,01	0,77	0,91	0,65
1,02	0,83	0,87	0,68	0,79	0,74
0,93	0,93	0,99	0,86	0,93	0,9
0,94	0,67	0,73	0,54	0,65	0,9
1,01	0,99	1,08	0,98	1,02	0,9
0,91	1,02	0,88	0,96	0,95	0,93
0,97	1,01	0,99	0,85	0,95	0,99
0,98	0,97	0,85	0,84	0,88	0,8
0,83	0,86	0,91	0,84	0,87	0,83
0,94	0,93	0,85	0,94	0,91	0,91
0,97	0,98	1	0,91	0,96	1
0,97	0,75	0,74	0,65	0,71	0,67
0,93	1,01	0,96	1,05	1,01	0,89
0,83	0,76	0,66	0,7	0,71	0,73
0,88	0,35	0,49	0,65	0,5	0,81
0,9	1,01	0,95	0,6	0,85	0,95
1,01	0,95	0,8	0,66	0,81	0,85
1,02	0,75	1	1,01	0,92	0,8
0,91	0,67	0,95	0,82	0,81	0,84
0,91	0,49	0,89	0,9	0,76	0,63
1,06	1,05	1,11	1,13	1,1	0,96
0,93	1	0,82	0,92	0,91	0,91
0,93	0,86	0,89	0,89	0,88	0,74
0,84	0	0	0	0	0,12
0,97	0,86	0,99	0,95	0,93	0,79
0,9	0,41	0,5	0,69	0,53	0,44
0,85	0,79	0,87	0,81	0,82	0,75
0,93	0,87	0,92	0,98	0,92	0,72
0,96	1,04	0,88	0,91	0,94	0,95
0,9	0,63	0,8	0,65	0,69	0,67
0,98	0,51	0,77	0,79	0,69	0,99
1,04	1,43	0,51	0,83	0,92	0,85
0,88	0,95	1,13	0,85	0,98	0,75
0,99	1,12	0,85	0,75	0,9	0,86
0,87	0,78	0,77	0,69	0,75	0,94
0,94	0,59	0,62	0,69	0,64	0,82
0,98	1,02	0,83	0,76	0,87	0,87
0,97	1,03	0,7	0,81	0,84	0,98
0,87	0,82	0,49	0,46	0,59	0,8
0,9	0,73	0,66	0,65	0,68	0,86
1,05	0,99	0,91	0,97	0,96	0,9

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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279514&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279514&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 Ronald Aylmer Fisher' @ fisher.wessa.net

Multiple Linear Regression - Estimated Regression Equation
VR[t] = + 0.803528 -0.0662106AT1[t] -0.19806AT2[t] -0.039574AT3[t] + 0.442889ATM[t] + 0.0287931NAH[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
VR[t] =  +  0.803528 -0.0662106AT1[t] -0.19806AT2[t] -0.039574AT3[t] +  0.442889ATM[t] +  0.0287931NAH[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279514&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]VR[t] =  +  0.803528 -0.0662106AT1[t] -0.19806AT2[t] -0.039574AT3[t] +  0.442889ATM[t] +  0.0287931NAH[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279514&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
VR[t] = + 0.803528 -0.0662106AT1[t] -0.19806AT2[t] -0.039574AT3[t] + 0.442889ATM[t] + 0.0287931NAH[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)	0.803528	0.0458254	17.53	6.52193e-19	3.26097e-19
AT1	-0.0662106	0.834513	-0.07934	0.937214	0.468607
AT2	-0.19806	0.854353	-0.2318	0.818024	0.409012
AT3	-0.039574	0.854356	-0.04632	0.963318	0.481659
ATM	0.442889	2.55061	0.1736	0.863149	0.431574
NAH	0.0287931	0.0774454	0.3718	0.712294	0.356147

\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) & 0.803528 & 0.0458254 & 17.53 & 6.52193e-19 & 3.26097e-19 \tabularnewline
AT1 & -0.0662106 & 0.834513 & -0.07934 & 0.937214 & 0.468607 \tabularnewline
AT2 & -0.19806 & 0.854353 & -0.2318 & 0.818024 & 0.409012 \tabularnewline
AT3 & -0.039574 & 0.854356 & -0.04632 & 0.963318 & 0.481659 \tabularnewline
ATM & 0.442889 & 2.55061 & 0.1736 & 0.863149 & 0.431574 \tabularnewline
NAH & 0.0287931 & 0.0774454 & 0.3718 & 0.712294 & 0.356147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279514&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]0.803528[/C][C]0.0458254[/C][C]17.53[/C][C]6.52193e-19[/C][C]3.26097e-19[/C][/ROW]
[ROW][C]AT1[/C][C]-0.0662106[/C][C]0.834513[/C][C]-0.07934[/C][C]0.937214[/C][C]0.468607[/C][/ROW]
[ROW][C]AT2[/C][C]-0.19806[/C][C]0.854353[/C][C]-0.2318[/C][C]0.818024[/C][C]0.409012[/C][/ROW]
[ROW][C]AT3[/C][C]-0.039574[/C][C]0.854356[/C][C]-0.04632[/C][C]0.963318[/C][C]0.481659[/C][/ROW]
[ROW][C]ATM[/C][C]0.442889[/C][C]2.55061[/C][C]0.1736[/C][C]0.863149[/C][C]0.431574[/C][/ROW]
[ROW][C]NAH[/C][C]0.0287931[/C][C]0.0774454[/C][C]0.3718[/C][C]0.712294[/C][C]0.356147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279514&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279514&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)	0.803528	0.0458254	17.53	6.52193e-19	3.26097e-19
AT1	-0.0662106	0.834513	-0.07934	0.937214	0.468607
AT2	-0.19806	0.854353	-0.2318	0.818024	0.409012
AT3	-0.039574	0.854356	-0.04632	0.963318	0.481659
ATM	0.442889	2.55061	0.1736	0.863149	0.431574
NAH	0.0287931	0.0774454	0.3718	0.712294	0.356147

Multiple Linear Regression - Regression Statistics
Multiple R	0.543634
R-squared	0.295538
Adjusted R-squared	0.1949
F-TEST (value)	2.93666
F-TEST (DF numerator)	5
F-TEST (DF denominator)	35
p-value	0.0257041
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0534162
Sum Squared Residuals	0.0998653

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.543634 \tabularnewline
R-squared & 0.295538 \tabularnewline
Adjusted R-squared & 0.1949 \tabularnewline
F-TEST (value) & 2.93666 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 35 \tabularnewline
p-value & 0.0257041 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0534162 \tabularnewline
Sum Squared Residuals & 0.0998653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279514&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.543634[/C][/ROW]
[ROW][C]R-squared[/C][C]0.295538[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.1949[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.93666[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]35[/C][/ROW]
[ROW][C]p-value[/C][C]0.0257041[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0534162[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.0998653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279514&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279514&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	0.543634
R-squared	0.295538
Adjusted R-squared	0.1949
F-TEST (value)	2.93666
F-TEST (DF numerator)	5
F-TEST (DF denominator)	35
p-value	0.0257041
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0534162
Sum Squared Residuals	0.0998653

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	0.9	0.931197	-0.0311972
2	1.02	0.920539	0.0994606
3	0.93	0.949639	-0.0196391
4	0.94	0.907004	0.0329956
5	1.01	0.962952	0.0470479
6	0.91	0.971231	-0.0612309
7	0.97	0.956187	0.0138129
8	0.98	0.950487	0.0295132
9	0.83	0.942321	-0.112321
10	0.94	0.965632	-0.0256318
11	0.97	0.958535	0.0114648
12	0.97	0.915325	0.0546753
13	0.93	0.977908	-0.0479081
14	0.83	0.930256	-0.100256
15	0.88	0.902348	-0.0223484
16	0.9	0.928562	-0.0285624
17	1.01	0.939275	0.0707252
18	1.02	0.946332	0.0736679
19	0.91	0.921485	-0.011485
20	0.91	0.91393	-0.00392959
21	1.06	0.98426	0.0757398
22	0.93	0.96773	-0.0377303
23	0.93	0.946141	-0.0161413
24	0.84	0.806983	0.0330167
25	0.97	0.947545	0.0224551
26	0.9	0.897445	0.00255454
27	0.85	0.931618	-0.0816178
28	0.93	0.953115	-0.0231154
29	0.96	0.968032	-0.00803238
30	0.9	0.902529	-0.00252856
31	0.98	0.920089	0.0599109
32	1.04	1.00692	0.0330786
33	0.88	0.938808	-0.0588076
34	0.99	0.954702	0.0352977
35	0.87	0.931303	-0.0613033
36	0.94	0.921419	0.0185806
37	0.98	0.95189	0.0281099
38	0.97	0.964878	0.00512232
39	0.87	0.918321	-0.0483206
40	0.9	0.924678	-0.0246778
41	1.05	0.970445	0.0795552

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 0.9 & 0.931197 & -0.0311972 \tabularnewline
2 & 1.02 & 0.920539 & 0.0994606 \tabularnewline
3 & 0.93 & 0.949639 & -0.0196391 \tabularnewline
4 & 0.94 & 0.907004 & 0.0329956 \tabularnewline
5 & 1.01 & 0.962952 & 0.0470479 \tabularnewline
6 & 0.91 & 0.971231 & -0.0612309 \tabularnewline
7 & 0.97 & 0.956187 & 0.0138129 \tabularnewline
8 & 0.98 & 0.950487 & 0.0295132 \tabularnewline
9 & 0.83 & 0.942321 & -0.112321 \tabularnewline
10 & 0.94 & 0.965632 & -0.0256318 \tabularnewline
11 & 0.97 & 0.958535 & 0.0114648 \tabularnewline
12 & 0.97 & 0.915325 & 0.0546753 \tabularnewline
13 & 0.93 & 0.977908 & -0.0479081 \tabularnewline
14 & 0.83 & 0.930256 & -0.100256 \tabularnewline
15 & 0.88 & 0.902348 & -0.0223484 \tabularnewline
16 & 0.9 & 0.928562 & -0.0285624 \tabularnewline
17 & 1.01 & 0.939275 & 0.0707252 \tabularnewline
18 & 1.02 & 0.946332 & 0.0736679 \tabularnewline
19 & 0.91 & 0.921485 & -0.011485 \tabularnewline
20 & 0.91 & 0.91393 & -0.00392959 \tabularnewline
21 & 1.06 & 0.98426 & 0.0757398 \tabularnewline
22 & 0.93 & 0.96773 & -0.0377303 \tabularnewline
23 & 0.93 & 0.946141 & -0.0161413 \tabularnewline
24 & 0.84 & 0.806983 & 0.0330167 \tabularnewline
25 & 0.97 & 0.947545 & 0.0224551 \tabularnewline
26 & 0.9 & 0.897445 & 0.00255454 \tabularnewline
27 & 0.85 & 0.931618 & -0.0816178 \tabularnewline
28 & 0.93 & 0.953115 & -0.0231154 \tabularnewline
29 & 0.96 & 0.968032 & -0.00803238 \tabularnewline
30 & 0.9 & 0.902529 & -0.00252856 \tabularnewline
31 & 0.98 & 0.920089 & 0.0599109 \tabularnewline
32 & 1.04 & 1.00692 & 0.0330786 \tabularnewline
33 & 0.88 & 0.938808 & -0.0588076 \tabularnewline
34 & 0.99 & 0.954702 & 0.0352977 \tabularnewline
35 & 0.87 & 0.931303 & -0.0613033 \tabularnewline
36 & 0.94 & 0.921419 & 0.0185806 \tabularnewline
37 & 0.98 & 0.95189 & 0.0281099 \tabularnewline
38 & 0.97 & 0.964878 & 0.00512232 \tabularnewline
39 & 0.87 & 0.918321 & -0.0483206 \tabularnewline
40 & 0.9 & 0.924678 & -0.0246778 \tabularnewline
41 & 1.05 & 0.970445 & 0.0795552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279514&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]0.9[/C][C]0.931197[/C][C]-0.0311972[/C][/ROW]
[ROW][C]2[/C][C]1.02[/C][C]0.920539[/C][C]0.0994606[/C][/ROW]
[ROW][C]3[/C][C]0.93[/C][C]0.949639[/C][C]-0.0196391[/C][/ROW]
[ROW][C]4[/C][C]0.94[/C][C]0.907004[/C][C]0.0329956[/C][/ROW]
[ROW][C]5[/C][C]1.01[/C][C]0.962952[/C][C]0.0470479[/C][/ROW]
[ROW][C]6[/C][C]0.91[/C][C]0.971231[/C][C]-0.0612309[/C][/ROW]
[ROW][C]7[/C][C]0.97[/C][C]0.956187[/C][C]0.0138129[/C][/ROW]
[ROW][C]8[/C][C]0.98[/C][C]0.950487[/C][C]0.0295132[/C][/ROW]
[ROW][C]9[/C][C]0.83[/C][C]0.942321[/C][C]-0.112321[/C][/ROW]
[ROW][C]10[/C][C]0.94[/C][C]0.965632[/C][C]-0.0256318[/C][/ROW]
[ROW][C]11[/C][C]0.97[/C][C]0.958535[/C][C]0.0114648[/C][/ROW]
[ROW][C]12[/C][C]0.97[/C][C]0.915325[/C][C]0.0546753[/C][/ROW]
[ROW][C]13[/C][C]0.93[/C][C]0.977908[/C][C]-0.0479081[/C][/ROW]
[ROW][C]14[/C][C]0.83[/C][C]0.930256[/C][C]-0.100256[/C][/ROW]
[ROW][C]15[/C][C]0.88[/C][C]0.902348[/C][C]-0.0223484[/C][/ROW]
[ROW][C]16[/C][C]0.9[/C][C]0.928562[/C][C]-0.0285624[/C][/ROW]
[ROW][C]17[/C][C]1.01[/C][C]0.939275[/C][C]0.0707252[/C][/ROW]
[ROW][C]18[/C][C]1.02[/C][C]0.946332[/C][C]0.0736679[/C][/ROW]
[ROW][C]19[/C][C]0.91[/C][C]0.921485[/C][C]-0.011485[/C][/ROW]
[ROW][C]20[/C][C]0.91[/C][C]0.91393[/C][C]-0.00392959[/C][/ROW]
[ROW][C]21[/C][C]1.06[/C][C]0.98426[/C][C]0.0757398[/C][/ROW]
[ROW][C]22[/C][C]0.93[/C][C]0.96773[/C][C]-0.0377303[/C][/ROW]
[ROW][C]23[/C][C]0.93[/C][C]0.946141[/C][C]-0.0161413[/C][/ROW]
[ROW][C]24[/C][C]0.84[/C][C]0.806983[/C][C]0.0330167[/C][/ROW]
[ROW][C]25[/C][C]0.97[/C][C]0.947545[/C][C]0.0224551[/C][/ROW]
[ROW][C]26[/C][C]0.9[/C][C]0.897445[/C][C]0.00255454[/C][/ROW]
[ROW][C]27[/C][C]0.85[/C][C]0.931618[/C][C]-0.0816178[/C][/ROW]
[ROW][C]28[/C][C]0.93[/C][C]0.953115[/C][C]-0.0231154[/C][/ROW]
[ROW][C]29[/C][C]0.96[/C][C]0.968032[/C][C]-0.00803238[/C][/ROW]
[ROW][C]30[/C][C]0.9[/C][C]0.902529[/C][C]-0.00252856[/C][/ROW]
[ROW][C]31[/C][C]0.98[/C][C]0.920089[/C][C]0.0599109[/C][/ROW]
[ROW][C]32[/C][C]1.04[/C][C]1.00692[/C][C]0.0330786[/C][/ROW]
[ROW][C]33[/C][C]0.88[/C][C]0.938808[/C][C]-0.0588076[/C][/ROW]
[ROW][C]34[/C][C]0.99[/C][C]0.954702[/C][C]0.0352977[/C][/ROW]
[ROW][C]35[/C][C]0.87[/C][C]0.931303[/C][C]-0.0613033[/C][/ROW]
[ROW][C]36[/C][C]0.94[/C][C]0.921419[/C][C]0.0185806[/C][/ROW]
[ROW][C]37[/C][C]0.98[/C][C]0.95189[/C][C]0.0281099[/C][/ROW]
[ROW][C]38[/C][C]0.97[/C][C]0.964878[/C][C]0.00512232[/C][/ROW]
[ROW][C]39[/C][C]0.87[/C][C]0.918321[/C][C]-0.0483206[/C][/ROW]
[ROW][C]40[/C][C]0.9[/C][C]0.924678[/C][C]-0.0246778[/C][/ROW]
[ROW][C]41[/C][C]1.05[/C][C]0.970445[/C][C]0.0795552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279514&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279514&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	0.9	0.931197	-0.0311972
2	1.02	0.920539	0.0994606
3	0.93	0.949639	-0.0196391
4	0.94	0.907004	0.0329956
5	1.01	0.962952	0.0470479
6	0.91	0.971231	-0.0612309
7	0.97	0.956187	0.0138129
8	0.98	0.950487	0.0295132
9	0.83	0.942321	-0.112321
10	0.94	0.965632	-0.0256318
11	0.97	0.958535	0.0114648
12	0.97	0.915325	0.0546753
13	0.93	0.977908	-0.0479081
14	0.83	0.930256	-0.100256
15	0.88	0.902348	-0.0223484
16	0.9	0.928562	-0.0285624
17	1.01	0.939275	0.0707252
18	1.02	0.946332	0.0736679
19	0.91	0.921485	-0.011485
20	0.91	0.91393	-0.00392959
21	1.06	0.98426	0.0757398
22	0.93	0.96773	-0.0377303
23	0.93	0.946141	-0.0161413
24	0.84	0.806983	0.0330167
25	0.97	0.947545	0.0224551
26	0.9	0.897445	0.00255454
27	0.85	0.931618	-0.0816178
28	0.93	0.953115	-0.0231154
29	0.96	0.968032	-0.00803238
30	0.9	0.902529	-0.00252856
31	0.98	0.920089	0.0599109
32	1.04	1.00692	0.0330786
33	0.88	0.938808	-0.0588076
34	0.99	0.954702	0.0352977
35	0.87	0.931303	-0.0613033
36	0.94	0.921419	0.0185806
37	0.98	0.95189	0.0281099
38	0.97	0.964878	0.00512232
39	0.87	0.918321	-0.0483206
40	0.9	0.924678	-0.0246778
41	1.05	0.970445	0.0795552

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.945836	0.108328	0.0541642
10	0.925299	0.149402	0.0747011
11	0.862273	0.275454	0.137727
12	0.836787	0.326426	0.163213
13	0.787116	0.425768	0.212884
14	0.878686	0.242627	0.121314
15	0.834554	0.330893	0.165446
16	0.826864	0.346273	0.173136
17	0.908551	0.182898	0.0914489
18	0.923334	0.153332	0.0766661
19	0.892344	0.215312	0.107656
20	0.840808	0.318385	0.159192
21	0.879859	0.240283	0.120141
22	0.851531	0.296937	0.148469
23	0.783421	0.433159	0.216579
24	0.815252	0.369496	0.184748
25	0.741301	0.517398	0.258699
26	0.654271	0.691458	0.345729
27	0.749102	0.501795	0.250898
28	0.808235	0.38353	0.191765
29	0.796323	0.407353	0.203677
30	0.68405	0.6319	0.31595
31	0.572394	0.855212	0.427606
32	0.731192	0.537616	0.268808

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
9 & 0.945836 & 0.108328 & 0.0541642 \tabularnewline
10 & 0.925299 & 0.149402 & 0.0747011 \tabularnewline
11 & 0.862273 & 0.275454 & 0.137727 \tabularnewline
12 & 0.836787 & 0.326426 & 0.163213 \tabularnewline
13 & 0.787116 & 0.425768 & 0.212884 \tabularnewline
14 & 0.878686 & 0.242627 & 0.121314 \tabularnewline
15 & 0.834554 & 0.330893 & 0.165446 \tabularnewline
16 & 0.826864 & 0.346273 & 0.173136 \tabularnewline
17 & 0.908551 & 0.182898 & 0.0914489 \tabularnewline
18 & 0.923334 & 0.153332 & 0.0766661 \tabularnewline
19 & 0.892344 & 0.215312 & 0.107656 \tabularnewline
20 & 0.840808 & 0.318385 & 0.159192 \tabularnewline
21 & 0.879859 & 0.240283 & 0.120141 \tabularnewline
22 & 0.851531 & 0.296937 & 0.148469 \tabularnewline
23 & 0.783421 & 0.433159 & 0.216579 \tabularnewline
24 & 0.815252 & 0.369496 & 0.184748 \tabularnewline
25 & 0.741301 & 0.517398 & 0.258699 \tabularnewline
26 & 0.654271 & 0.691458 & 0.345729 \tabularnewline
27 & 0.749102 & 0.501795 & 0.250898 \tabularnewline
28 & 0.808235 & 0.38353 & 0.191765 \tabularnewline
29 & 0.796323 & 0.407353 & 0.203677 \tabularnewline
30 & 0.68405 & 0.6319 & 0.31595 \tabularnewline
31 & 0.572394 & 0.855212 & 0.427606 \tabularnewline
32 & 0.731192 & 0.537616 & 0.268808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279514&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]9[/C][C]0.945836[/C][C]0.108328[/C][C]0.0541642[/C][/ROW]
[ROW][C]10[/C][C]0.925299[/C][C]0.149402[/C][C]0.0747011[/C][/ROW]
[ROW][C]11[/C][C]0.862273[/C][C]0.275454[/C][C]0.137727[/C][/ROW]
[ROW][C]12[/C][C]0.836787[/C][C]0.326426[/C][C]0.163213[/C][/ROW]
[ROW][C]13[/C][C]0.787116[/C][C]0.425768[/C][C]0.212884[/C][/ROW]
[ROW][C]14[/C][C]0.878686[/C][C]0.242627[/C][C]0.121314[/C][/ROW]
[ROW][C]15[/C][C]0.834554[/C][C]0.330893[/C][C]0.165446[/C][/ROW]
[ROW][C]16[/C][C]0.826864[/C][C]0.346273[/C][C]0.173136[/C][/ROW]
[ROW][C]17[/C][C]0.908551[/C][C]0.182898[/C][C]0.0914489[/C][/ROW]
[ROW][C]18[/C][C]0.923334[/C][C]0.153332[/C][C]0.0766661[/C][/ROW]
[ROW][C]19[/C][C]0.892344[/C][C]0.215312[/C][C]0.107656[/C][/ROW]
[ROW][C]20[/C][C]0.840808[/C][C]0.318385[/C][C]0.159192[/C][/ROW]
[ROW][C]21[/C][C]0.879859[/C][C]0.240283[/C][C]0.120141[/C][/ROW]
[ROW][C]22[/C][C]0.851531[/C][C]0.296937[/C][C]0.148469[/C][/ROW]
[ROW][C]23[/C][C]0.783421[/C][C]0.433159[/C][C]0.216579[/C][/ROW]
[ROW][C]24[/C][C]0.815252[/C][C]0.369496[/C][C]0.184748[/C][/ROW]
[ROW][C]25[/C][C]0.741301[/C][C]0.517398[/C][C]0.258699[/C][/ROW]
[ROW][C]26[/C][C]0.654271[/C][C]0.691458[/C][C]0.345729[/C][/ROW]
[ROW][C]27[/C][C]0.749102[/C][C]0.501795[/C][C]0.250898[/C][/ROW]
[ROW][C]28[/C][C]0.808235[/C][C]0.38353[/C][C]0.191765[/C][/ROW]
[ROW][C]29[/C][C]0.796323[/C][C]0.407353[/C][C]0.203677[/C][/ROW]
[ROW][C]30[/C][C]0.68405[/C][C]0.6319[/C][C]0.31595[/C][/ROW]
[ROW][C]31[/C][C]0.572394[/C][C]0.855212[/C][C]0.427606[/C][/ROW]
[ROW][C]32[/C][C]0.731192[/C][C]0.537616[/C][C]0.268808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279514&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279514&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
9	0.945836	0.108328	0.0541642
10	0.925299	0.149402	0.0747011
11	0.862273	0.275454	0.137727
12	0.836787	0.326426	0.163213
13	0.787116	0.425768	0.212884
14	0.878686	0.242627	0.121314
15	0.834554	0.330893	0.165446
16	0.826864	0.346273	0.173136
17	0.908551	0.182898	0.0914489
18	0.923334	0.153332	0.0766661
19	0.892344	0.215312	0.107656
20	0.840808	0.318385	0.159192
21	0.879859	0.240283	0.120141
22	0.851531	0.296937	0.148469
23	0.783421	0.433159	0.216579
24	0.815252	0.369496	0.184748
25	0.741301	0.517398	0.258699
26	0.654271	0.691458	0.345729
27	0.749102	0.501795	0.250898
28	0.808235	0.38353	0.191765
29	0.796323	0.407353	0.203677
30	0.68405	0.6319	0.31595
31	0.572394	0.855212	0.427606
32	0.731192	0.537616	0.268808

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	0	0	OK
10% type I error level	0	0	OK

\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=279514&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=279514&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279514&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	0	0	OK
10% type I error level	0	0	OK

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 = 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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,signif(mysum$coefficients[i,1],6))
a<-table.element(a, signif(mysum$coefficients[i,2],6))
a<-table.element(a, signif(mysum$coefficients[i,3],4))
a<-table.element(a, signif(mysum$coefficients[i,4],6))
a<-table.element(a, signif(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, signif(sqrt(mysum$r.squared),6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, signif(mysum$r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, signif(mysum$adj.r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[1],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$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$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6))
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, signif(mysum$sigma,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, signif(sum(myerror*myerror),6))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,signif(x[i],6))
a<-table.element(a,signif(x[i]-mysum$resid[i],6))
a<-table.element(a,signif(mysum$resid[i],6))
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,signif(gqarr[mypoint-kp3+1,1],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6))
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,signif(numsignificant1/numgqtests,6))
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