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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 10 Dec 2012 16:28:04 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/10/t1355174903hoktvba32ufyv9l.htm/, Retrieved Thu, 18 Apr 2024 17:29:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198344, Retrieved Thu, 18 Apr 2024 17:29:55 +0000

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No (this computation is public)

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Estimated Impact

115

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

-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
-   PD  [Multiple Regression] [] [2012-11-20 19:56:15] [147786ccb76fa00e429d4b9f5f28b291]
-   PD    [Multiple Regression] [] [2012-12-10 20:26:46] [147786ccb76fa00e429d4b9f5f28b291]
- R PD        [Multiple Regression] [] [2012-12-10 21:28:04] [26ce3afa84a4087bb435ca409d5552c3] [Current]

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Dataseries X:

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6.80	225.00	0.44	0.67	9.20
6.30	180.00	0.44	0.80	11.70
6.40	190.00	0.46	0.76	15.80
6.20	180.00	0.42	0.65	8.60
6.90	205.00	0.45	0.90	23.20
6.40	225.00	0.43	0.78	27.40
6.30	185.00	0.49	0.77	9.30
6.80	235.00	0.47	0.75	16.00
6.90	235.00	0.44	0.82	4.70
6.70	210.00	0.48	0.83	12.50
6.90	245.00	0.52	0.63	20.10
6.90	245.00	0.49	0.76	9.10
6.30	185.00	0.37	0.71	8.10
6.10	185.00	0.42	0.78	8.60
6.20	180.00	0.44	0.78	20.30
6.80	220.00	0.50	0.88	25.00
6.50	194.00	0.50	0.83	19.20
7.60	225.00	0.43	0.57	3.30
6.30	210.00	0.37	0.82	11.20
7.10	240.00	0.50	0.71	10.50
6.80	225.00	0.40	0.77	10.10
7.30	263.00	0.48	0.66	7.20
6.40	210.00	0.48	0.24	13.60
6.80	235.00	0.43	0.73	9.00
7.20	230.00	0.56	0.72	24.60
6.40	190.00	0.44	0.76	12.60
6.60	220.00	0.49	0.75	5.60
6.80	210.00	0.40	0.74	8.70
6.10	180.00	0.42	0.71	7.70
6.50	235.00	0.49	0.74	24.10
6.40	185.00	0.48	0.86	11.70
6.00	175.00	0.39	0.72	7.70
6.00	192.00	0.44	0.79	9.60
7.30	263.00	0.48	0.66	7.20
6.10	180.00	0.34	0.82	12.30
6.70	240.00	0.52	0.73	8.90
6.40	210.00	0.48	0.85	13.60
5.80	160.00	0.41	0.81	11.20
6.90	230.00	0.41	0.60	2.80
7.00	245.00	0.41	0.57	3.20
7.30	228.00	0.45	0.73	9.40
5.90	155.00	0.29	0.71	11.90
6.20	200.00	0.45	0.80	15.40
6.80	235.00	0.55	0.78	7.40
7.00	235.00	0.48	0.74	18.90
5.90	105.00	0.36	0.84	7.90
6.10	180.00	0.53	0.79	12.20
5.70	185.00	0.35	0.70	11.00
7.10	245.00	0.41	0.78	2.80
5.80	180.00	0.43	0.87	11.80
7.40	240.00	0.60	0.71	17.10
6.80	225.00	0.48	0.70	11.60
6.80	215.00	0.46	0.73	5.80
7.00	230.00	0.44	0.76	8.30

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 7 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198344&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198344&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198344&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	7 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation
X1[t] = + 3.78840611306684 + 0.0115218273554624X2[t] + 1.12253997026526X3[t] -0.0380422350614909X4[t] -0.00819222035276419`X5\r`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X1[t] =  +  3.78840611306684 +  0.0115218273554624X2[t] +  1.12253997026526X3[t] -0.0380422350614909X4[t] -0.00819222035276419`X5\r`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198344&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X1[t] =  +  3.78840611306684 +  0.0115218273554624X2[t] +  1.12253997026526X3[t] -0.0380422350614909X4[t] -0.00819222035276419`X5\r`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198344&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198344&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
X1[t] = + 3.78840611306684 + 0.0115218273554624X2[t] + 1.12253997026526X3[t] -0.0380422350614909X4[t] -0.00819222035276419`X5\r`[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)	3.78840611306684	0.448754	8.4421	0	0
X2	0.0115218273554624	0.001441	7.9983	0	0
X3	1.12253997026526	0.783126	1.4334	0.158091	0.079046
X4	-0.0380422350614909	0.377025	-0.1009	0.920041	0.46002
`X5\r`	-0.00819222035276419	0.006628	-1.236	0.222337	0.111168

\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) & 3.78840611306684 & 0.448754 & 8.4421 & 0 & 0 \tabularnewline
X2 & 0.0115218273554624 & 0.001441 & 7.9983 & 0 & 0 \tabularnewline
X3 & 1.12253997026526 & 0.783126 & 1.4334 & 0.158091 & 0.079046 \tabularnewline
X4 & -0.0380422350614909 & 0.377025 & -0.1009 & 0.920041 & 0.46002 \tabularnewline
`X5\r` & -0.00819222035276419 & 0.006628 & -1.236 & 0.222337 & 0.111168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198344&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]3.78840611306684[/C][C]0.448754[/C][C]8.4421[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X2[/C][C]0.0115218273554624[/C][C]0.001441[/C][C]7.9983[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X3[/C][C]1.12253997026526[/C][C]0.783126[/C][C]1.4334[/C][C]0.158091[/C][C]0.079046[/C][/ROW]
[ROW][C]X4[/C][C]-0.0380422350614909[/C][C]0.377025[/C][C]-0.1009[/C][C]0.920041[/C][C]0.46002[/C][/ROW]
[ROW][C]`X5\r`[/C][C]-0.00819222035276419[/C][C]0.006628[/C][C]-1.236[/C][C]0.222337[/C][C]0.111168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198344&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198344&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)	3.78840611306684	0.448754	8.4421	0	0
X2	0.0115218273554624	0.001441	7.9983	0	0
X3	1.12253997026526	0.783126	1.4334	0.158091	0.079046
X4	-0.0380422350614909	0.377025	-0.1009	0.920041	0.46002
`X5\r`	-0.00819222035276419	0.006628	-1.236	0.222337	0.111168

Multiple Linear Regression - Regression Statistics
Multiple R	0.84372399458813
R-squared	0.71187017904375
Adjusted R-squared	0.688349377333036
F-TEST (value)	30.265557602974
F-TEST (DF numerator)	4
F-TEST (DF denominator)	49
p-value	1.0609291223318e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.256180564061598
Sum Squared Residuals	3.215795588743

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.84372399458813 \tabularnewline
R-squared & 0.71187017904375 \tabularnewline
Adjusted R-squared & 0.688349377333036 \tabularnewline
F-TEST (value) & 30.265557602974 \tabularnewline
F-TEST (DF numerator) & 4 \tabularnewline
F-TEST (DF denominator) & 49 \tabularnewline
p-value & 1.0609291223318e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.256180564061598 \tabularnewline
Sum Squared Residuals & 3.215795588743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198344&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.84372399458813[/C][/ROW]
[ROW][C]R-squared[/C][C]0.71187017904375[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.688349377333036[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]30.265557602974[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]4[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]49[/C][/ROW]
[ROW][C]p-value[/C][C]1.0609291223318e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.256180564061598[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]3.215795588743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198344&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198344&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	0.84372399458813
R-squared	0.71187017904375
Adjusted R-squared	0.688349377333036
F-TEST (value)	30.265557602974
F-TEST (DF numerator)	4
F-TEST (DF denominator)	49
p-value	1.0609291223318e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.256180564061598
Sum Squared Residuals	3.215795588743

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	6.8	6.77387813022596	0.0261218697740364
2	6.3	6.22996985779025	0.0700301422097456
3	6.4	6.33557251670631	0.0644274832936906
4	6.2	6.23862127673774	-0.0386212767377413
5	6.9	6.43122618381653	0.468773816183471
6	6.4	6.60936967424624	-0.209369674246241
7	6.3	6.36450858897931	-0.0645085889793082
8	6.8	6.86402212568483	-0.0640221256848324
9	6.9	6.92025506010881	-0.0202550601088051
10	6.7	6.61283123393068	0.0871687660693198
11	6.9	7.00634436251377	-0.106344362513765
12	6.9	7.05783709672822	-0.157837096728219
13	6.3	6.24191699107448	0.0580830089255168
14	6.1	6.29128492295706	-0.19128492295706
15	6.2	6.16027760745771	0.0397223925422883
16	6.8	6.64619544072798	0.153804559272017
17	6.5	6.39604491928507	0.103955080714933
18	7.6	6.81479105411077	0.785208945889228
19	6.3	6.50038214601071	-0.20038214601071
20	7.1	7.00188636291276	0.0981136370872348
21	6.8	6.71779930959172	0.082200690408281
22	7.3	7.27337403160029	0.0266259683997088
23	6.4	6.62626471022892	-0.226264710228919
24	6.8	6.8772269140448	-0.0772269140448011
25	7.2	6.83812975824947	0.361870241750534
26	6.4	6.33933682242985	0.0606631775701504
27	6.6	6.79884460642695	-0.19884460642695
28	6.8	6.5575822748055	0.242417725194502
29	6.1	6.24371174095154	-0.14371174095154
30	6.5	6.82049636258336	-0.320496362583363
31	6.4	6.33019805927449	0.0698019407255132
32	6	6.15204598271565	-0.152045982715655
33	6	6.38581587114722	-0.385815871147223
34	7.3	7.27337403160029	0.0266259683997088
35	6.1	6.11203968385084	-0.0120396838508399
36	6.7	7.03668387018126	-0.336683870181263
37	6.4	6.60305894684141	-0.20305894684141
38	5.8	5.96957279939882	-0.169572799398816
39	6.9	6.85290423460732	0.0470957653926849
40	7	7.02359602384999	-0.0235960238499904
41	7.3	6.81574803382076	0.484251966179236
42	5.9	5.77532853544889	0.124671464551114
43	6.2	6.44132058929693	-0.241320589296927
44	6.8	7.02313715128798	-0.223137151287981
45	7	6.85187050871508	0.148129491284916
46	5.9	5.3056383564474	0.594361643552602
47	6.1	6.32728276728836	-0.227282767288361
48	5.7	6.19608917499678	-0.496089174996776
49	7.1	7.01888404262818	0.0811159573718166
50	5.8	6.21526227959802	-0.415262279598021
51	7.4	7.06007170561105	0.339928294388953
52	6.8	6.7979771331381	0.0020228668619019
53	6.8	6.70668167117236	0.0933183288276435
54	7	6.83543646416523	0.164563535834768

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 6.8 & 6.77387813022596 & 0.0261218697740364 \tabularnewline
2 & 6.3 & 6.22996985779025 & 0.0700301422097456 \tabularnewline
3 & 6.4 & 6.33557251670631 & 0.0644274832936906 \tabularnewline
4 & 6.2 & 6.23862127673774 & -0.0386212767377413 \tabularnewline
5 & 6.9 & 6.43122618381653 & 0.468773816183471 \tabularnewline
6 & 6.4 & 6.60936967424624 & -0.209369674246241 \tabularnewline
7 & 6.3 & 6.36450858897931 & -0.0645085889793082 \tabularnewline
8 & 6.8 & 6.86402212568483 & -0.0640221256848324 \tabularnewline
9 & 6.9 & 6.92025506010881 & -0.0202550601088051 \tabularnewline
10 & 6.7 & 6.61283123393068 & 0.0871687660693198 \tabularnewline
11 & 6.9 & 7.00634436251377 & -0.106344362513765 \tabularnewline
12 & 6.9 & 7.05783709672822 & -0.157837096728219 \tabularnewline
13 & 6.3 & 6.24191699107448 & 0.0580830089255168 \tabularnewline
14 & 6.1 & 6.29128492295706 & -0.19128492295706 \tabularnewline
15 & 6.2 & 6.16027760745771 & 0.0397223925422883 \tabularnewline
16 & 6.8 & 6.64619544072798 & 0.153804559272017 \tabularnewline
17 & 6.5 & 6.39604491928507 & 0.103955080714933 \tabularnewline
18 & 7.6 & 6.81479105411077 & 0.785208945889228 \tabularnewline
19 & 6.3 & 6.50038214601071 & -0.20038214601071 \tabularnewline
20 & 7.1 & 7.00188636291276 & 0.0981136370872348 \tabularnewline
21 & 6.8 & 6.71779930959172 & 0.082200690408281 \tabularnewline
22 & 7.3 & 7.27337403160029 & 0.0266259683997088 \tabularnewline
23 & 6.4 & 6.62626471022892 & -0.226264710228919 \tabularnewline
24 & 6.8 & 6.8772269140448 & -0.0772269140448011 \tabularnewline
25 & 7.2 & 6.83812975824947 & 0.361870241750534 \tabularnewline
26 & 6.4 & 6.33933682242985 & 0.0606631775701504 \tabularnewline
27 & 6.6 & 6.79884460642695 & -0.19884460642695 \tabularnewline
28 & 6.8 & 6.5575822748055 & 0.242417725194502 \tabularnewline
29 & 6.1 & 6.24371174095154 & -0.14371174095154 \tabularnewline
30 & 6.5 & 6.82049636258336 & -0.320496362583363 \tabularnewline
31 & 6.4 & 6.33019805927449 & 0.0698019407255132 \tabularnewline
32 & 6 & 6.15204598271565 & -0.152045982715655 \tabularnewline
33 & 6 & 6.38581587114722 & -0.385815871147223 \tabularnewline
34 & 7.3 & 7.27337403160029 & 0.0266259683997088 \tabularnewline
35 & 6.1 & 6.11203968385084 & -0.0120396838508399 \tabularnewline
36 & 6.7 & 7.03668387018126 & -0.336683870181263 \tabularnewline
37 & 6.4 & 6.60305894684141 & -0.20305894684141 \tabularnewline
38 & 5.8 & 5.96957279939882 & -0.169572799398816 \tabularnewline
39 & 6.9 & 6.85290423460732 & 0.0470957653926849 \tabularnewline
40 & 7 & 7.02359602384999 & -0.0235960238499904 \tabularnewline
41 & 7.3 & 6.81574803382076 & 0.484251966179236 \tabularnewline
42 & 5.9 & 5.77532853544889 & 0.124671464551114 \tabularnewline
43 & 6.2 & 6.44132058929693 & -0.241320589296927 \tabularnewline
44 & 6.8 & 7.02313715128798 & -0.223137151287981 \tabularnewline
45 & 7 & 6.85187050871508 & 0.148129491284916 \tabularnewline
46 & 5.9 & 5.3056383564474 & 0.594361643552602 \tabularnewline
47 & 6.1 & 6.32728276728836 & -0.227282767288361 \tabularnewline
48 & 5.7 & 6.19608917499678 & -0.496089174996776 \tabularnewline
49 & 7.1 & 7.01888404262818 & 0.0811159573718166 \tabularnewline
50 & 5.8 & 6.21526227959802 & -0.415262279598021 \tabularnewline
51 & 7.4 & 7.06007170561105 & 0.339928294388953 \tabularnewline
52 & 6.8 & 6.7979771331381 & 0.0020228668619019 \tabularnewline
53 & 6.8 & 6.70668167117236 & 0.0933183288276435 \tabularnewline
54 & 7 & 6.83543646416523 & 0.164563535834768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198344&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]6.8[/C][C]6.77387813022596[/C][C]0.0261218697740364[/C][/ROW]
[ROW][C]2[/C][C]6.3[/C][C]6.22996985779025[/C][C]0.0700301422097456[/C][/ROW]
[ROW][C]3[/C][C]6.4[/C][C]6.33557251670631[/C][C]0.0644274832936906[/C][/ROW]
[ROW][C]4[/C][C]6.2[/C][C]6.23862127673774[/C][C]-0.0386212767377413[/C][/ROW]
[ROW][C]5[/C][C]6.9[/C][C]6.43122618381653[/C][C]0.468773816183471[/C][/ROW]
[ROW][C]6[/C][C]6.4[/C][C]6.60936967424624[/C][C]-0.209369674246241[/C][/ROW]
[ROW][C]7[/C][C]6.3[/C][C]6.36450858897931[/C][C]-0.0645085889793082[/C][/ROW]
[ROW][C]8[/C][C]6.8[/C][C]6.86402212568483[/C][C]-0.0640221256848324[/C][/ROW]
[ROW][C]9[/C][C]6.9[/C][C]6.92025506010881[/C][C]-0.0202550601088051[/C][/ROW]
[ROW][C]10[/C][C]6.7[/C][C]6.61283123393068[/C][C]0.0871687660693198[/C][/ROW]
[ROW][C]11[/C][C]6.9[/C][C]7.00634436251377[/C][C]-0.106344362513765[/C][/ROW]
[ROW][C]12[/C][C]6.9[/C][C]7.05783709672822[/C][C]-0.157837096728219[/C][/ROW]
[ROW][C]13[/C][C]6.3[/C][C]6.24191699107448[/C][C]0.0580830089255168[/C][/ROW]
[ROW][C]14[/C][C]6.1[/C][C]6.29128492295706[/C][C]-0.19128492295706[/C][/ROW]
[ROW][C]15[/C][C]6.2[/C][C]6.16027760745771[/C][C]0.0397223925422883[/C][/ROW]
[ROW][C]16[/C][C]6.8[/C][C]6.64619544072798[/C][C]0.153804559272017[/C][/ROW]
[ROW][C]17[/C][C]6.5[/C][C]6.39604491928507[/C][C]0.103955080714933[/C][/ROW]
[ROW][C]18[/C][C]7.6[/C][C]6.81479105411077[/C][C]0.785208945889228[/C][/ROW]
[ROW][C]19[/C][C]6.3[/C][C]6.50038214601071[/C][C]-0.20038214601071[/C][/ROW]
[ROW][C]20[/C][C]7.1[/C][C]7.00188636291276[/C][C]0.0981136370872348[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]6.71779930959172[/C][C]0.082200690408281[/C][/ROW]
[ROW][C]22[/C][C]7.3[/C][C]7.27337403160029[/C][C]0.0266259683997088[/C][/ROW]
[ROW][C]23[/C][C]6.4[/C][C]6.62626471022892[/C][C]-0.226264710228919[/C][/ROW]
[ROW][C]24[/C][C]6.8[/C][C]6.8772269140448[/C][C]-0.0772269140448011[/C][/ROW]
[ROW][C]25[/C][C]7.2[/C][C]6.83812975824947[/C][C]0.361870241750534[/C][/ROW]
[ROW][C]26[/C][C]6.4[/C][C]6.33933682242985[/C][C]0.0606631775701504[/C][/ROW]
[ROW][C]27[/C][C]6.6[/C][C]6.79884460642695[/C][C]-0.19884460642695[/C][/ROW]
[ROW][C]28[/C][C]6.8[/C][C]6.5575822748055[/C][C]0.242417725194502[/C][/ROW]
[ROW][C]29[/C][C]6.1[/C][C]6.24371174095154[/C][C]-0.14371174095154[/C][/ROW]
[ROW][C]30[/C][C]6.5[/C][C]6.82049636258336[/C][C]-0.320496362583363[/C][/ROW]
[ROW][C]31[/C][C]6.4[/C][C]6.33019805927449[/C][C]0.0698019407255132[/C][/ROW]
[ROW][C]32[/C][C]6[/C][C]6.15204598271565[/C][C]-0.152045982715655[/C][/ROW]
[ROW][C]33[/C][C]6[/C][C]6.38581587114722[/C][C]-0.385815871147223[/C][/ROW]
[ROW][C]34[/C][C]7.3[/C][C]7.27337403160029[/C][C]0.0266259683997088[/C][/ROW]
[ROW][C]35[/C][C]6.1[/C][C]6.11203968385084[/C][C]-0.0120396838508399[/C][/ROW]
[ROW][C]36[/C][C]6.7[/C][C]7.03668387018126[/C][C]-0.336683870181263[/C][/ROW]
[ROW][C]37[/C][C]6.4[/C][C]6.60305894684141[/C][C]-0.20305894684141[/C][/ROW]
[ROW][C]38[/C][C]5.8[/C][C]5.96957279939882[/C][C]-0.169572799398816[/C][/ROW]
[ROW][C]39[/C][C]6.9[/C][C]6.85290423460732[/C][C]0.0470957653926849[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]7.02359602384999[/C][C]-0.0235960238499904[/C][/ROW]
[ROW][C]41[/C][C]7.3[/C][C]6.81574803382076[/C][C]0.484251966179236[/C][/ROW]
[ROW][C]42[/C][C]5.9[/C][C]5.77532853544889[/C][C]0.124671464551114[/C][/ROW]
[ROW][C]43[/C][C]6.2[/C][C]6.44132058929693[/C][C]-0.241320589296927[/C][/ROW]
[ROW][C]44[/C][C]6.8[/C][C]7.02313715128798[/C][C]-0.223137151287981[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]6.85187050871508[/C][C]0.148129491284916[/C][/ROW]
[ROW][C]46[/C][C]5.9[/C][C]5.3056383564474[/C][C]0.594361643552602[/C][/ROW]
[ROW][C]47[/C][C]6.1[/C][C]6.32728276728836[/C][C]-0.227282767288361[/C][/ROW]
[ROW][C]48[/C][C]5.7[/C][C]6.19608917499678[/C][C]-0.496089174996776[/C][/ROW]
[ROW][C]49[/C][C]7.1[/C][C]7.01888404262818[/C][C]0.0811159573718166[/C][/ROW]
[ROW][C]50[/C][C]5.8[/C][C]6.21526227959802[/C][C]-0.415262279598021[/C][/ROW]
[ROW][C]51[/C][C]7.4[/C][C]7.06007170561105[/C][C]0.339928294388953[/C][/ROW]
[ROW][C]52[/C][C]6.8[/C][C]6.7979771331381[/C][C]0.0020228668619019[/C][/ROW]
[ROW][C]53[/C][C]6.8[/C][C]6.70668167117236[/C][C]0.0933183288276435[/C][/ROW]
[ROW][C]54[/C][C]7[/C][C]6.83543646416523[/C][C]0.164563535834768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198344&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198344&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	6.8	6.77387813022596	0.0261218697740364
2	6.3	6.22996985779025	0.0700301422097456
3	6.4	6.33557251670631	0.0644274832936906
4	6.2	6.23862127673774	-0.0386212767377413
5	6.9	6.43122618381653	0.468773816183471
6	6.4	6.60936967424624	-0.209369674246241
7	6.3	6.36450858897931	-0.0645085889793082
8	6.8	6.86402212568483	-0.0640221256848324
9	6.9	6.92025506010881	-0.0202550601088051
10	6.7	6.61283123393068	0.0871687660693198
11	6.9	7.00634436251377	-0.106344362513765
12	6.9	7.05783709672822	-0.157837096728219
13	6.3	6.24191699107448	0.0580830089255168
14	6.1	6.29128492295706	-0.19128492295706
15	6.2	6.16027760745771	0.0397223925422883
16	6.8	6.64619544072798	0.153804559272017
17	6.5	6.39604491928507	0.103955080714933
18	7.6	6.81479105411077	0.785208945889228
19	6.3	6.50038214601071	-0.20038214601071
20	7.1	7.00188636291276	0.0981136370872348
21	6.8	6.71779930959172	0.082200690408281
22	7.3	7.27337403160029	0.0266259683997088
23	6.4	6.62626471022892	-0.226264710228919
24	6.8	6.8772269140448	-0.0772269140448011
25	7.2	6.83812975824947	0.361870241750534
26	6.4	6.33933682242985	0.0606631775701504
27	6.6	6.79884460642695	-0.19884460642695
28	6.8	6.5575822748055	0.242417725194502
29	6.1	6.24371174095154	-0.14371174095154
30	6.5	6.82049636258336	-0.320496362583363
31	6.4	6.33019805927449	0.0698019407255132
32	6	6.15204598271565	-0.152045982715655
33	6	6.38581587114722	-0.385815871147223
34	7.3	7.27337403160029	0.0266259683997088
35	6.1	6.11203968385084	-0.0120396838508399
36	6.7	7.03668387018126	-0.336683870181263
37	6.4	6.60305894684141	-0.20305894684141
38	5.8	5.96957279939882	-0.169572799398816
39	6.9	6.85290423460732	0.0470957653926849
40	7	7.02359602384999	-0.0235960238499904
41	7.3	6.81574803382076	0.484251966179236
42	5.9	5.77532853544889	0.124671464551114
43	6.2	6.44132058929693	-0.241320589296927
44	6.8	7.02313715128798	-0.223137151287981
45	7	6.85187050871508	0.148129491284916
46	5.9	5.3056383564474	0.594361643552602
47	6.1	6.32728276728836	-0.227282767288361
48	5.7	6.19608917499678	-0.496089174996776
49	7.1	7.01888404262818	0.0811159573718166
50	5.8	6.21526227959802	-0.415262279598021
51	7.4	7.06007170561105	0.339928294388953
52	6.8	6.7979771331381	0.0020228668619019
53	6.8	6.70668167117236	0.0933183288276435
54	7	6.83543646416523	0.164563535834768

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.298835572381041	0.597671144762082	0.701164427618959
9	0.310980189661388	0.621960379322776	0.689019810338612
10	0.184277409392748	0.368554818785496	0.815722590607252
11	0.12152781639281	0.24305563278562	0.87847218360719
12	0.0757649892166197	0.151529978433239	0.92423501078338
13	0.0400891255804423	0.0801782511608846	0.959910874419558
14	0.0503932783614803	0.100786556722961	0.94960672163852
15	0.0271021677597761	0.0542043355195523	0.972897832240224
16	0.0143975786319957	0.0287951572639915	0.985602421368004
17	0.00712695340333373	0.0142539068066675	0.992873046596666
18	0.554378620123371	0.891242759753259	0.445621379876629
19	0.519853133219558	0.960293733560884	0.480146866780442
20	0.434075521002937	0.868151042005873	0.565924478997063
21	0.353339666523789	0.706679333047577	0.646660333476211
22	0.27637423738274	0.552748474765481	0.72362576261726
23	0.284443984991086	0.568887969982173	0.715556015008914
24	0.222953399390374	0.445906798780748	0.777046600609626
25	0.269881591298047	0.539763182596094	0.730118408701953
26	0.206577780622736	0.413155561245472	0.793422219377264
27	0.197699479304393	0.395398958608786	0.802300520695607
28	0.191362525418138	0.382725050836277	0.808637474581862
29	0.157571048757461	0.315142097514921	0.842428951242539
30	0.168225289065994	0.336450578131987	0.831774710934006
31	0.126026820485123	0.252053640970245	0.873973179514877
32	0.100467840406922	0.200935680813844	0.899532159593078
33	0.142233541654074	0.284467083308148	0.857766458345926
34	0.098294412855655	0.19658882571131	0.901705587144345
35	0.0654547498720778	0.130909499744156	0.934545250127922
36	0.0820581087618944	0.164116217523789	0.917941891238106
37	0.0610713039559149	0.12214260791183	0.938928696044085
38	0.0450965734923729	0.0901931469847458	0.954903426507627
39	0.0271673557490538	0.0543347114981077	0.972832644250946
40	0.018686534079436	0.037373068158872	0.981313465920564
41	0.0461763568055887	0.0923527136111775	0.953823643194411
42	0.0276911801271985	0.055382360254397	0.972308819872801
43	0.0181125344383768	0.0362250688767536	0.981887465561623
44	0.0161113585101868	0.0322227170203736	0.983888641489813
45	0.0250544000310359	0.0501088000620717	0.974945599968964
46	0.917170041142346	0.165659917715309	0.0828299588576545

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
8 & 0.298835572381041 & 0.597671144762082 & 0.701164427618959 \tabularnewline
9 & 0.310980189661388 & 0.621960379322776 & 0.689019810338612 \tabularnewline
10 & 0.184277409392748 & 0.368554818785496 & 0.815722590607252 \tabularnewline
11 & 0.12152781639281 & 0.24305563278562 & 0.87847218360719 \tabularnewline
12 & 0.0757649892166197 & 0.151529978433239 & 0.92423501078338 \tabularnewline
13 & 0.0400891255804423 & 0.0801782511608846 & 0.959910874419558 \tabularnewline
14 & 0.0503932783614803 & 0.100786556722961 & 0.94960672163852 \tabularnewline
15 & 0.0271021677597761 & 0.0542043355195523 & 0.972897832240224 \tabularnewline
16 & 0.0143975786319957 & 0.0287951572639915 & 0.985602421368004 \tabularnewline
17 & 0.00712695340333373 & 0.0142539068066675 & 0.992873046596666 \tabularnewline
18 & 0.554378620123371 & 0.891242759753259 & 0.445621379876629 \tabularnewline
19 & 0.519853133219558 & 0.960293733560884 & 0.480146866780442 \tabularnewline
20 & 0.434075521002937 & 0.868151042005873 & 0.565924478997063 \tabularnewline
21 & 0.353339666523789 & 0.706679333047577 & 0.646660333476211 \tabularnewline
22 & 0.27637423738274 & 0.552748474765481 & 0.72362576261726 \tabularnewline
23 & 0.284443984991086 & 0.568887969982173 & 0.715556015008914 \tabularnewline
24 & 0.222953399390374 & 0.445906798780748 & 0.777046600609626 \tabularnewline
25 & 0.269881591298047 & 0.539763182596094 & 0.730118408701953 \tabularnewline
26 & 0.206577780622736 & 0.413155561245472 & 0.793422219377264 \tabularnewline
27 & 0.197699479304393 & 0.395398958608786 & 0.802300520695607 \tabularnewline
28 & 0.191362525418138 & 0.382725050836277 & 0.808637474581862 \tabularnewline
29 & 0.157571048757461 & 0.315142097514921 & 0.842428951242539 \tabularnewline
30 & 0.168225289065994 & 0.336450578131987 & 0.831774710934006 \tabularnewline
31 & 0.126026820485123 & 0.252053640970245 & 0.873973179514877 \tabularnewline
32 & 0.100467840406922 & 0.200935680813844 & 0.899532159593078 \tabularnewline
33 & 0.142233541654074 & 0.284467083308148 & 0.857766458345926 \tabularnewline
34 & 0.098294412855655 & 0.19658882571131 & 0.901705587144345 \tabularnewline
35 & 0.0654547498720778 & 0.130909499744156 & 0.934545250127922 \tabularnewline
36 & 0.0820581087618944 & 0.164116217523789 & 0.917941891238106 \tabularnewline
37 & 0.0610713039559149 & 0.12214260791183 & 0.938928696044085 \tabularnewline
38 & 0.0450965734923729 & 0.0901931469847458 & 0.954903426507627 \tabularnewline
39 & 0.0271673557490538 & 0.0543347114981077 & 0.972832644250946 \tabularnewline
40 & 0.018686534079436 & 0.037373068158872 & 0.981313465920564 \tabularnewline
41 & 0.0461763568055887 & 0.0923527136111775 & 0.953823643194411 \tabularnewline
42 & 0.0276911801271985 & 0.055382360254397 & 0.972308819872801 \tabularnewline
43 & 0.0181125344383768 & 0.0362250688767536 & 0.981887465561623 \tabularnewline
44 & 0.0161113585101868 & 0.0322227170203736 & 0.983888641489813 \tabularnewline
45 & 0.0250544000310359 & 0.0501088000620717 & 0.974945599968964 \tabularnewline
46 & 0.917170041142346 & 0.165659917715309 & 0.0828299588576545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198344&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]8[/C][C]0.298835572381041[/C][C]0.597671144762082[/C][C]0.701164427618959[/C][/ROW]
[ROW][C]9[/C][C]0.310980189661388[/C][C]0.621960379322776[/C][C]0.689019810338612[/C][/ROW]
[ROW][C]10[/C][C]0.184277409392748[/C][C]0.368554818785496[/C][C]0.815722590607252[/C][/ROW]
[ROW][C]11[/C][C]0.12152781639281[/C][C]0.24305563278562[/C][C]0.87847218360719[/C][/ROW]
[ROW][C]12[/C][C]0.0757649892166197[/C][C]0.151529978433239[/C][C]0.92423501078338[/C][/ROW]
[ROW][C]13[/C][C]0.0400891255804423[/C][C]0.0801782511608846[/C][C]0.959910874419558[/C][/ROW]
[ROW][C]14[/C][C]0.0503932783614803[/C][C]0.100786556722961[/C][C]0.94960672163852[/C][/ROW]
[ROW][C]15[/C][C]0.0271021677597761[/C][C]0.0542043355195523[/C][C]0.972897832240224[/C][/ROW]
[ROW][C]16[/C][C]0.0143975786319957[/C][C]0.0287951572639915[/C][C]0.985602421368004[/C][/ROW]
[ROW][C]17[/C][C]0.00712695340333373[/C][C]0.0142539068066675[/C][C]0.992873046596666[/C][/ROW]
[ROW][C]18[/C][C]0.554378620123371[/C][C]0.891242759753259[/C][C]0.445621379876629[/C][/ROW]
[ROW][C]19[/C][C]0.519853133219558[/C][C]0.960293733560884[/C][C]0.480146866780442[/C][/ROW]
[ROW][C]20[/C][C]0.434075521002937[/C][C]0.868151042005873[/C][C]0.565924478997063[/C][/ROW]
[ROW][C]21[/C][C]0.353339666523789[/C][C]0.706679333047577[/C][C]0.646660333476211[/C][/ROW]
[ROW][C]22[/C][C]0.27637423738274[/C][C]0.552748474765481[/C][C]0.72362576261726[/C][/ROW]
[ROW][C]23[/C][C]0.284443984991086[/C][C]0.568887969982173[/C][C]0.715556015008914[/C][/ROW]
[ROW][C]24[/C][C]0.222953399390374[/C][C]0.445906798780748[/C][C]0.777046600609626[/C][/ROW]
[ROW][C]25[/C][C]0.269881591298047[/C][C]0.539763182596094[/C][C]0.730118408701953[/C][/ROW]
[ROW][C]26[/C][C]0.206577780622736[/C][C]0.413155561245472[/C][C]0.793422219377264[/C][/ROW]
[ROW][C]27[/C][C]0.197699479304393[/C][C]0.395398958608786[/C][C]0.802300520695607[/C][/ROW]
[ROW][C]28[/C][C]0.191362525418138[/C][C]0.382725050836277[/C][C]0.808637474581862[/C][/ROW]
[ROW][C]29[/C][C]0.157571048757461[/C][C]0.315142097514921[/C][C]0.842428951242539[/C][/ROW]
[ROW][C]30[/C][C]0.168225289065994[/C][C]0.336450578131987[/C][C]0.831774710934006[/C][/ROW]
[ROW][C]31[/C][C]0.126026820485123[/C][C]0.252053640970245[/C][C]0.873973179514877[/C][/ROW]
[ROW][C]32[/C][C]0.100467840406922[/C][C]0.200935680813844[/C][C]0.899532159593078[/C][/ROW]
[ROW][C]33[/C][C]0.142233541654074[/C][C]0.284467083308148[/C][C]0.857766458345926[/C][/ROW]
[ROW][C]34[/C][C]0.098294412855655[/C][C]0.19658882571131[/C][C]0.901705587144345[/C][/ROW]
[ROW][C]35[/C][C]0.0654547498720778[/C][C]0.130909499744156[/C][C]0.934545250127922[/C][/ROW]
[ROW][C]36[/C][C]0.0820581087618944[/C][C]0.164116217523789[/C][C]0.917941891238106[/C][/ROW]
[ROW][C]37[/C][C]0.0610713039559149[/C][C]0.12214260791183[/C][C]0.938928696044085[/C][/ROW]
[ROW][C]38[/C][C]0.0450965734923729[/C][C]0.0901931469847458[/C][C]0.954903426507627[/C][/ROW]
[ROW][C]39[/C][C]0.0271673557490538[/C][C]0.0543347114981077[/C][C]0.972832644250946[/C][/ROW]
[ROW][C]40[/C][C]0.018686534079436[/C][C]0.037373068158872[/C][C]0.981313465920564[/C][/ROW]
[ROW][C]41[/C][C]0.0461763568055887[/C][C]0.0923527136111775[/C][C]0.953823643194411[/C][/ROW]
[ROW][C]42[/C][C]0.0276911801271985[/C][C]0.055382360254397[/C][C]0.972308819872801[/C][/ROW]
[ROW][C]43[/C][C]0.0181125344383768[/C][C]0.0362250688767536[/C][C]0.981887465561623[/C][/ROW]
[ROW][C]44[/C][C]0.0161113585101868[/C][C]0.0322227170203736[/C][C]0.983888641489813[/C][/ROW]
[ROW][C]45[/C][C]0.0250544000310359[/C][C]0.0501088000620717[/C][C]0.974945599968964[/C][/ROW]
[ROW][C]46[/C][C]0.917170041142346[/C][C]0.165659917715309[/C][C]0.0828299588576545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198344&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198344&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
8	0.298835572381041	0.597671144762082	0.701164427618959
9	0.310980189661388	0.621960379322776	0.689019810338612
10	0.184277409392748	0.368554818785496	0.815722590607252
11	0.12152781639281	0.24305563278562	0.87847218360719
12	0.0757649892166197	0.151529978433239	0.92423501078338
13	0.0400891255804423	0.0801782511608846	0.959910874419558
14	0.0503932783614803	0.100786556722961	0.94960672163852
15	0.0271021677597761	0.0542043355195523	0.972897832240224
16	0.0143975786319957	0.0287951572639915	0.985602421368004
17	0.00712695340333373	0.0142539068066675	0.992873046596666
18	0.554378620123371	0.891242759753259	0.445621379876629
19	0.519853133219558	0.960293733560884	0.480146866780442
20	0.434075521002937	0.868151042005873	0.565924478997063
21	0.353339666523789	0.706679333047577	0.646660333476211
22	0.27637423738274	0.552748474765481	0.72362576261726
23	0.284443984991086	0.568887969982173	0.715556015008914
24	0.222953399390374	0.445906798780748	0.777046600609626
25	0.269881591298047	0.539763182596094	0.730118408701953
26	0.206577780622736	0.413155561245472	0.793422219377264
27	0.197699479304393	0.395398958608786	0.802300520695607
28	0.191362525418138	0.382725050836277	0.808637474581862
29	0.157571048757461	0.315142097514921	0.842428951242539
30	0.168225289065994	0.336450578131987	0.831774710934006
31	0.126026820485123	0.252053640970245	0.873973179514877
32	0.100467840406922	0.200935680813844	0.899532159593078
33	0.142233541654074	0.284467083308148	0.857766458345926
34	0.098294412855655	0.19658882571131	0.901705587144345
35	0.0654547498720778	0.130909499744156	0.934545250127922
36	0.0820581087618944	0.164116217523789	0.917941891238106
37	0.0610713039559149	0.12214260791183	0.938928696044085
38	0.0450965734923729	0.0901931469847458	0.954903426507627
39	0.0271673557490538	0.0543347114981077	0.972832644250946
40	0.018686534079436	0.037373068158872	0.981313465920564
41	0.0461763568055887	0.0923527136111775	0.953823643194411
42	0.0276911801271985	0.055382360254397	0.972308819872801
43	0.0181125344383768	0.0362250688767536	0.981887465561623
44	0.0161113585101868	0.0322227170203736	0.983888641489813
45	0.0250544000310359	0.0501088000620717	0.974945599968964
46	0.917170041142346	0.165659917715309	0.0828299588576545

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	5	0.128205128205128	NOK
10% type I error level	12	0.307692307692308	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 & 5 & 0.128205128205128 & NOK \tabularnewline
10% type I error level & 12 & 0.307692307692308 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198344&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]5[/C][C]0.128205128205128[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]12[/C][C]0.307692307692308[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198344&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198344&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	5	0.128205128205128	NOK
10% type I error level	12	0.307692307692308	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):

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code