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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 14 Dec 2010 18:25:57 +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/14/t12923510584kwlxbfld42bgtg.htm/, Retrieved Fri, 03 May 2024 03:43:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109989, Retrieved Fri, 03 May 2024 03:43:20 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

131

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

-     [Recursive Partitioning (Regression Trees)] [] [2010-12-05 18:59:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [WS 10 - Multiple ...] [2010-12-11 15:55:17] [033eb2749a430605d9b2be7c4aac4a0c]
-   PD      [Multiple Regression] [SP] [2010-12-14 18:25:57] [cda497ce08bc921f0aec22acd67c882b] [Current]

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Dataseries X:

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Boxplots

1	1	6.3	2.1	3.5	0.075	1.2	42	1
2	2	6.6	4.1	6	0.785	3.5	42	2
2	2	9.5	1.2	10.4	0.2	5	120	2
5	5	3.3	0.5	20	27.66	115	148	5
1	2	11	3.4	3.9	0.12	1	16	3
3	1	4.7	1.5	41	85	325	310	1
1	3	10.4	3.4	9	0.101	4	28	5
3	4	7.4	0.8	7.6	1.04	5.5	68	5
5	5	2.1	0.8	46	521	655	336	5
1	1	17.9	2	24	0.01	0.25	50	1
1	1	6.1	1.9	100	62	1320	267	1
1	3	11.9	1.3	3.2	0.023	0.4	19	4
1	1	13.8	5.6	5	1.7	6.3	12	2
1	1	14.3	3.1	6.5	3.5	10.8	120	2
2	2	15.2	1.8	12	0.48	15.5	140	2
4	4	10	0.9	20.2	10	115	170	4
1	2	11.9	1.8	13	1.62	11.4	17	2
4	4	6.5	1.9	27	192	180	115	4
5	5	7.5	0.9	18	2.5	12.1	31	5
1	3	10.6	2.6	4.7	0.28	1.9	21	3
1	1	7.4	2.4	9.8	4.235	50.4	52	1
3	2	8.4	1.2	29	6.8	179	164	2
2	2	5.7	0.9	7	0.75	12.3	225	2
2	3	4.9	0.5	6	3.6	21	225	3
5	5	3.2	0.6	20	55.5	175	151	5
1	2	11	2.3	4.5	0.9	2.6	60	2
1	3	4.9	0.5	7.5	2	12.3	200	3
2	2	13.2	2.6	2.3	0.104	2.5	46	3
3	4	9.7	0.6	24	4.19	58	210	4
1	1	12.8	6.6	3	3.5	3.9	14	2

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109989&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109989&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109989&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation
D[t] = + 1.01094397494045 + 0.206933332354438S[t] -0.029218929310028SWS[t] -0.202025353648924PS[t] + 0.00450221431253059L[t] + 0.000800985796989966WB[t] -0.000394691214193767Wbr[t] -0.00142938933566244Tg[t] + 0.652380532727226p[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
D[t] =  +  1.01094397494045 +  0.206933332354438S[t] -0.029218929310028SWS[t] -0.202025353648924PS[t] +  0.00450221431253059L[t] +  0.000800985796989966WB[t] -0.000394691214193767Wbr[t] -0.00142938933566244Tg[t] +  0.652380532727226p[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109989&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]D[t] =  +  1.01094397494045 +  0.206933332354438S[t] -0.029218929310028SWS[t] -0.202025353648924PS[t] +  0.00450221431253059L[t] +  0.000800985796989966WB[t] -0.000394691214193767Wbr[t] -0.00142938933566244Tg[t] +  0.652380532727226p[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109989&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109989&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
D[t] = + 1.01094397494045 + 0.206933332354438S[t] -0.029218929310028SWS[t] -0.202025353648924PS[t] + 0.00450221431253059L[t] + 0.000800985796989966WB[t] -0.000394691214193767Wbr[t] -0.00142938933566244Tg[t] + 0.652380532727226p[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)	1.01094397494045	0.413091	2.4473	0.023276	0.011638
S	0.206933332354438	0.087331	2.3695	0.027469	0.013735
SWS	-0.029218929310028	0.025462	-1.1476	0.264052	0.132026
PS	-0.202025353648924	0.064205	-3.1466	0.00487	0.002435
L	0.00450221431253059	0.015052	0.2991	0.767789	0.383895
WB	0.000800985796989966	0.00093	0.8608	0.39905	0.199525
Wbr	-0.000394691214193767	0.001131	-0.349	0.730533	0.365267
Tg	-0.00142938933566244	0.001188	-1.2036	0.242145	0.121072
p	0.652380532727226	0.071072	9.1792	0	0

\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) & 1.01094397494045 & 0.413091 & 2.4473 & 0.023276 & 0.011638 \tabularnewline
S & 0.206933332354438 & 0.087331 & 2.3695 & 0.027469 & 0.013735 \tabularnewline
SWS & -0.029218929310028 & 0.025462 & -1.1476 & 0.264052 & 0.132026 \tabularnewline
PS & -0.202025353648924 & 0.064205 & -3.1466 & 0.00487 & 0.002435 \tabularnewline
L & 0.00450221431253059 & 0.015052 & 0.2991 & 0.767789 & 0.383895 \tabularnewline
WB & 0.000800985796989966 & 0.00093 & 0.8608 & 0.39905 & 0.199525 \tabularnewline
Wbr & -0.000394691214193767 & 0.001131 & -0.349 & 0.730533 & 0.365267 \tabularnewline
Tg & -0.00142938933566244 & 0.001188 & -1.2036 & 0.242145 & 0.121072 \tabularnewline
p & 0.652380532727226 & 0.071072 & 9.1792 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109989&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]1.01094397494045[/C][C]0.413091[/C][C]2.4473[/C][C]0.023276[/C][C]0.011638[/C][/ROW]
[ROW][C]S[/C][C]0.206933332354438[/C][C]0.087331[/C][C]2.3695[/C][C]0.027469[/C][C]0.013735[/C][/ROW]
[ROW][C]SWS[/C][C]-0.029218929310028[/C][C]0.025462[/C][C]-1.1476[/C][C]0.264052[/C][C]0.132026[/C][/ROW]
[ROW][C]PS[/C][C]-0.202025353648924[/C][C]0.064205[/C][C]-3.1466[/C][C]0.00487[/C][C]0.002435[/C][/ROW]
[ROW][C]L[/C][C]0.00450221431253059[/C][C]0.015052[/C][C]0.2991[/C][C]0.767789[/C][C]0.383895[/C][/ROW]
[ROW][C]WB[/C][C]0.000800985796989966[/C][C]0.00093[/C][C]0.8608[/C][C]0.39905[/C][C]0.199525[/C][/ROW]
[ROW][C]Wbr[/C][C]-0.000394691214193767[/C][C]0.001131[/C][C]-0.349[/C][C]0.730533[/C][C]0.365267[/C][/ROW]
[ROW][C]Tg[/C][C]-0.00142938933566244[/C][C]0.001188[/C][C]-1.2036[/C][C]0.242145[/C][C]0.121072[/C][/ROW]
[ROW][C]p[/C][C]0.652380532727226[/C][C]0.071072[/C][C]9.1792[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109989&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109989&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)	1.01094397494045	0.413091	2.4473	0.023276	0.011638
S	0.206933332354438	0.087331	2.3695	0.027469	0.013735
SWS	-0.029218929310028	0.025462	-1.1476	0.264052	0.132026
PS	-0.202025353648924	0.064205	-3.1466	0.00487	0.002435
L	0.00450221431253059	0.015052	0.2991	0.767789	0.383895
WB	0.000800985796989966	0.00093	0.8608	0.39905	0.199525
Wbr	-0.000394691214193767	0.001131	-0.349	0.730533	0.365267
Tg	-0.00142938933566244	0.001188	-1.2036	0.242145	0.121072
p	0.652380532727226	0.071072	9.1792	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.97859716996643
R-squared	0.957652421066308
Adjusted R-squared	0.94152001004395
F-TEST (value)	59.3620147502473
F-TEST (DF numerator)	8
F-TEST (DF denominator)	21
p-value	1.09678932602719e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.33414028184368
Sum Squared Residuals	2.34464428696206

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.97859716996643 \tabularnewline
R-squared & 0.957652421066308 \tabularnewline
Adjusted R-squared & 0.94152001004395 \tabularnewline
F-TEST (value) & 59.3620147502473 \tabularnewline
F-TEST (DF numerator) & 8 \tabularnewline
F-TEST (DF denominator) & 21 \tabularnewline
p-value & 1.09678932602719e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.33414028184368 \tabularnewline
Sum Squared Residuals & 2.34464428696206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109989&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.97859716996643[/C][/ROW]
[ROW][C]R-squared[/C][C]0.957652421066308[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.94152001004395[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]59.3620147502473[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]8[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]21[/C][/ROW]
[ROW][C]p-value[/C][C]1.09678932602719e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.33414028184368[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2.34464428696206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109989&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109989&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	0.97859716996643
R-squared	0.957652421066308
Adjusted R-squared	0.94152001004395
F-TEST (value)	59.3620147502473
F-TEST (DF numerator)	8
F-TEST (DF denominator)	21
p-value	1.09678932602719e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.33414028184368
Sum Squared Residuals	2.34464428696206

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1	1.21723518517997	-0.217235185179969
2	2	1.67464911007532	0.32535088992468
3	2	2.08304450193905	-0.0830445019390538
4	5	4.96533859888624	0.0346614011137578
5	2	2.16111431418963	-0.161114314189627
6	1	1.52504674739004	-0.525046747390038
7	3	3.48801606582333	-0.488016065823328
8	4	4.45148685332753	-0.451486853327534
9	5	4.97015116240725	0.0298488375927499
10	1	0.979681311846795	0.0203186881532055
11	1	0.905417394606775	0.0945826053932246
12	3	3.20417045428102	-0.204170454281018
13	1	0.99230868857714	0.00769131142286031
14	1	1.3348075452324	-0.334807545232398
15	2	1.76997716714346	0.230022832856538
16	4	3.78475623427091	0.21524376572909
17	2	1.84231476189789	0.157685238102109
18	4	3.91435309012331	0.0856469098766945
19	5	4.94050400126027	0.0594959987397291
20	3	2.33064992923923	0.669350070760766
21	1	1.12247010683372	-0.122470106833725
22	2	2.27957694696886	-0.279576946968863
23	2	2.08684992682941	-0.0868499268294069
24	3	2.83776252610963	0.16223747389037
25	5	4.94238776018194	0.05761223981806
26	2	1.67076313127353	0.329236868726469
27	3	2.67546948490385	0.32453051509615
28	2	2.41469620941718	-0.414696209417178
29	4	3.62497269949381	0.375027300506191
30	1	0.810028090290504	0.189971909709496

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1 & 1.21723518517997 & -0.217235185179969 \tabularnewline
2 & 2 & 1.67464911007532 & 0.32535088992468 \tabularnewline
3 & 2 & 2.08304450193905 & -0.0830445019390538 \tabularnewline
4 & 5 & 4.96533859888624 & 0.0346614011137578 \tabularnewline
5 & 2 & 2.16111431418963 & -0.161114314189627 \tabularnewline
6 & 1 & 1.52504674739004 & -0.525046747390038 \tabularnewline
7 & 3 & 3.48801606582333 & -0.488016065823328 \tabularnewline
8 & 4 & 4.45148685332753 & -0.451486853327534 \tabularnewline
9 & 5 & 4.97015116240725 & 0.0298488375927499 \tabularnewline
10 & 1 & 0.979681311846795 & 0.0203186881532055 \tabularnewline
11 & 1 & 0.905417394606775 & 0.0945826053932246 \tabularnewline
12 & 3 & 3.20417045428102 & -0.204170454281018 \tabularnewline
13 & 1 & 0.99230868857714 & 0.00769131142286031 \tabularnewline
14 & 1 & 1.3348075452324 & -0.334807545232398 \tabularnewline
15 & 2 & 1.76997716714346 & 0.230022832856538 \tabularnewline
16 & 4 & 3.78475623427091 & 0.21524376572909 \tabularnewline
17 & 2 & 1.84231476189789 & 0.157685238102109 \tabularnewline
18 & 4 & 3.91435309012331 & 0.0856469098766945 \tabularnewline
19 & 5 & 4.94050400126027 & 0.0594959987397291 \tabularnewline
20 & 3 & 2.33064992923923 & 0.669350070760766 \tabularnewline
21 & 1 & 1.12247010683372 & -0.122470106833725 \tabularnewline
22 & 2 & 2.27957694696886 & -0.279576946968863 \tabularnewline
23 & 2 & 2.08684992682941 & -0.0868499268294069 \tabularnewline
24 & 3 & 2.83776252610963 & 0.16223747389037 \tabularnewline
25 & 5 & 4.94238776018194 & 0.05761223981806 \tabularnewline
26 & 2 & 1.67076313127353 & 0.329236868726469 \tabularnewline
27 & 3 & 2.67546948490385 & 0.32453051509615 \tabularnewline
28 & 2 & 2.41469620941718 & -0.414696209417178 \tabularnewline
29 & 4 & 3.62497269949381 & 0.375027300506191 \tabularnewline
30 & 1 & 0.810028090290504 & 0.189971909709496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109989&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]1[/C][C]1.21723518517997[/C][C]-0.217235185179969[/C][/ROW]
[ROW][C]2[/C][C]2[/C][C]1.67464911007532[/C][C]0.32535088992468[/C][/ROW]
[ROW][C]3[/C][C]2[/C][C]2.08304450193905[/C][C]-0.0830445019390538[/C][/ROW]
[ROW][C]4[/C][C]5[/C][C]4.96533859888624[/C][C]0.0346614011137578[/C][/ROW]
[ROW][C]5[/C][C]2[/C][C]2.16111431418963[/C][C]-0.161114314189627[/C][/ROW]
[ROW][C]6[/C][C]1[/C][C]1.52504674739004[/C][C]-0.525046747390038[/C][/ROW]
[ROW][C]7[/C][C]3[/C][C]3.48801606582333[/C][C]-0.488016065823328[/C][/ROW]
[ROW][C]8[/C][C]4[/C][C]4.45148685332753[/C][C]-0.451486853327534[/C][/ROW]
[ROW][C]9[/C][C]5[/C][C]4.97015116240725[/C][C]0.0298488375927499[/C][/ROW]
[ROW][C]10[/C][C]1[/C][C]0.979681311846795[/C][C]0.0203186881532055[/C][/ROW]
[ROW][C]11[/C][C]1[/C][C]0.905417394606775[/C][C]0.0945826053932246[/C][/ROW]
[ROW][C]12[/C][C]3[/C][C]3.20417045428102[/C][C]-0.204170454281018[/C][/ROW]
[ROW][C]13[/C][C]1[/C][C]0.99230868857714[/C][C]0.00769131142286031[/C][/ROW]
[ROW][C]14[/C][C]1[/C][C]1.3348075452324[/C][C]-0.334807545232398[/C][/ROW]
[ROW][C]15[/C][C]2[/C][C]1.76997716714346[/C][C]0.230022832856538[/C][/ROW]
[ROW][C]16[/C][C]4[/C][C]3.78475623427091[/C][C]0.21524376572909[/C][/ROW]
[ROW][C]17[/C][C]2[/C][C]1.84231476189789[/C][C]0.157685238102109[/C][/ROW]
[ROW][C]18[/C][C]4[/C][C]3.91435309012331[/C][C]0.0856469098766945[/C][/ROW]
[ROW][C]19[/C][C]5[/C][C]4.94050400126027[/C][C]0.0594959987397291[/C][/ROW]
[ROW][C]20[/C][C]3[/C][C]2.33064992923923[/C][C]0.669350070760766[/C][/ROW]
[ROW][C]21[/C][C]1[/C][C]1.12247010683372[/C][C]-0.122470106833725[/C][/ROW]
[ROW][C]22[/C][C]2[/C][C]2.27957694696886[/C][C]-0.279576946968863[/C][/ROW]
[ROW][C]23[/C][C]2[/C][C]2.08684992682941[/C][C]-0.0868499268294069[/C][/ROW]
[ROW][C]24[/C][C]3[/C][C]2.83776252610963[/C][C]0.16223747389037[/C][/ROW]
[ROW][C]25[/C][C]5[/C][C]4.94238776018194[/C][C]0.05761223981806[/C][/ROW]
[ROW][C]26[/C][C]2[/C][C]1.67076313127353[/C][C]0.329236868726469[/C][/ROW]
[ROW][C]27[/C][C]3[/C][C]2.67546948490385[/C][C]0.32453051509615[/C][/ROW]
[ROW][C]28[/C][C]2[/C][C]2.41469620941718[/C][C]-0.414696209417178[/C][/ROW]
[ROW][C]29[/C][C]4[/C][C]3.62497269949381[/C][C]0.375027300506191[/C][/ROW]
[ROW][C]30[/C][C]1[/C][C]0.810028090290504[/C][C]0.189971909709496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109989&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109989&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	1	1.21723518517997	-0.217235185179969
2	2	1.67464911007532	0.32535088992468
3	2	2.08304450193905	-0.0830445019390538
4	5	4.96533859888624	0.0346614011137578
5	2	2.16111431418963	-0.161114314189627
6	1	1.52504674739004	-0.525046747390038
7	3	3.48801606582333	-0.488016065823328
8	4	4.45148685332753	-0.451486853327534
9	5	4.97015116240725	0.0298488375927499
10	1	0.979681311846795	0.0203186881532055
11	1	0.905417394606775	0.0945826053932246
12	3	3.20417045428102	-0.204170454281018
13	1	0.99230868857714	0.00769131142286031
14	1	1.3348075452324	-0.334807545232398
15	2	1.76997716714346	0.230022832856538
16	4	3.78475623427091	0.21524376572909
17	2	1.84231476189789	0.157685238102109
18	4	3.91435309012331	0.0856469098766945
19	5	4.94050400126027	0.0594959987397291
20	3	2.33064992923923	0.669350070760766
21	1	1.12247010683372	-0.122470106833725
22	2	2.27957694696886	-0.279576946968863
23	2	2.08684992682941	-0.0868499268294069
24	3	2.83776252610963	0.16223747389037
25	5	4.94238776018194	0.05761223981806
26	2	1.67076313127353	0.329236868726469
27	3	2.67546948490385	0.32453051509615
28	2	2.41469620941718	-0.414696209417178
29	4	3.62497269949381	0.375027300506191
30	1	0.810028090290504	0.189971909709496

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.279720438320635	0.55944087664127	0.720279561679365
13	0.275695124100859	0.551390248201718	0.724304875899141
14	0.244094274804881	0.488188549609762	0.755905725195119
15	0.335118846894124	0.670237693788248	0.664881153105876
16	0.322294411675245	0.64458882335049	0.677705588324755
17	0.231445017847192	0.462890035694384	0.768554982152808
18	0.154115780515103	0.308231561030207	0.845884219484896

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
12 & 0.279720438320635 & 0.55944087664127 & 0.720279561679365 \tabularnewline
13 & 0.275695124100859 & 0.551390248201718 & 0.724304875899141 \tabularnewline
14 & 0.244094274804881 & 0.488188549609762 & 0.755905725195119 \tabularnewline
15 & 0.335118846894124 & 0.670237693788248 & 0.664881153105876 \tabularnewline
16 & 0.322294411675245 & 0.64458882335049 & 0.677705588324755 \tabularnewline
17 & 0.231445017847192 & 0.462890035694384 & 0.768554982152808 \tabularnewline
18 & 0.154115780515103 & 0.308231561030207 & 0.845884219484896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109989&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]12[/C][C]0.279720438320635[/C][C]0.55944087664127[/C][C]0.720279561679365[/C][/ROW]
[ROW][C]13[/C][C]0.275695124100859[/C][C]0.551390248201718[/C][C]0.724304875899141[/C][/ROW]
[ROW][C]14[/C][C]0.244094274804881[/C][C]0.488188549609762[/C][C]0.755905725195119[/C][/ROW]
[ROW][C]15[/C][C]0.335118846894124[/C][C]0.670237693788248[/C][C]0.664881153105876[/C][/ROW]
[ROW][C]16[/C][C]0.322294411675245[/C][C]0.64458882335049[/C][C]0.677705588324755[/C][/ROW]
[ROW][C]17[/C][C]0.231445017847192[/C][C]0.462890035694384[/C][C]0.768554982152808[/C][/ROW]
[ROW][C]18[/C][C]0.154115780515103[/C][C]0.308231561030207[/C][C]0.845884219484896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109989&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109989&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
12	0.279720438320635	0.55944087664127	0.720279561679365
13	0.275695124100859	0.551390248201718	0.724304875899141
14	0.244094274804881	0.488188549609762	0.755905725195119
15	0.335118846894124	0.670237693788248	0.664881153105876
16	0.322294411675245	0.64458882335049	0.677705588324755
17	0.231445017847192	0.462890035694384	0.768554982152808
18	0.154115780515103	0.308231561030207	0.845884219484896

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=109989&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=109989&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109989&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 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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