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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 03 Nov 2012 06:04:03 -0400

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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/Nov/03/t13519371060jyez3vpbb9x80m.htm/, Retrieved Sat, 20 Apr 2024 00:50:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=185703, Retrieved Sat, 20 Apr 2024 00:50:30 +0000

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Estimated Impact

138

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

-       [Multiple Regression] [Multiple regressi...] [2012-11-03 10:04:03] [a641906195a0eb35087b0121beaccdc9] [Current]

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5.029	4.768	4.812	5.302	5.562	5.307	5.350	5.372	5.199	5.070	4.552
24.994	23.191	22.269	23.291	24.151	24.046	25.278	25.919	26.277	25.048	24.926
6.639	6.100	6.054	6.321	6.702	6.671	7.101	7.353	7.320	7.117	6.999
3.451	3.099	2.936	3.116	3.286	3.398	3.435	3.657	3.699	3.526	3.493
5.844	5.409	5.263	5.391	5.609	5.429	5.835	5.995	6.234	5.812	5.874
3.954	3.603	3.587	3.765	3.842	3.834	4.039	3.977	4.065	3.907	3.881
5.106	4.980	4.429	4.698	4.712	4.714	4.868	4.937	4.959	4.686	4.679
15.100	14.151	13.353	13.184	13.583	13.788	14.185	14.270	14.137	13.185	12.681
279	274	277	266	279	256	283	328	335	282	287
1.567	1.451	1.439	1.441	1.562	1.532	1.616	1.497	1.578	1.430	1.411
5.616	5.082	4.801	4.676	4.826	4.851	4.990	5.149	4.934	4.728	4.524
4.560	4.425	4.182	4.170	4.321	4.318	4.429	4.518	4.441	4.063	3.946
1.262	1.277	1.158	1.121	1.102	1.209	1.212	1.253	1.229	1.133	1.141
2.095	1.916	1.773	1.776	1.772	1.878	1.938	1.853	1.955	1.831	1.659

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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185703&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185703&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185703&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

Multiple Linear Regression - Estimated Regression Equation
2000[t] = -0.00379764888319456 + 0.744621059986105`2001`[t] + 1.46947563970647`2002`[t] -1.1069975966409`2003`[t] + 0.445419410028552`2004`[t] + 0.705383626314407`2005`[t] -1.59307558042119`2006`[t] -0.85005893867999`2007`[t] -0.2902924671059`2008`[t] + 1.65727639179957`2009`[t] + 0.0595801154945223`2010`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
2000[t] =  -0.00379764888319456 +  0.744621059986105`2001`[t] +  1.46947563970647`2002`[t] -1.1069975966409`2003`[t] +  0.445419410028552`2004`[t] +  0.705383626314407`2005`[t] -1.59307558042119`2006`[t] -0.85005893867999`2007`[t] -0.2902924671059`2008`[t] +  1.65727639179957`2009`[t] +  0.0595801154945223`2010`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185703&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]2000[t] =  -0.00379764888319456 +  0.744621059986105`2001`[t] +  1.46947563970647`2002`[t] -1.1069975966409`2003`[t] +  0.445419410028552`2004`[t] +  0.705383626314407`2005`[t] -1.59307558042119`2006`[t] -0.85005893867999`2007`[t] -0.2902924671059`2008`[t] +  1.65727639179957`2009`[t] +  0.0595801154945223`2010`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185703&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185703&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
2000[t] = -0.00379764888319456 + 0.744621059986105`2001`[t] + 1.46947563970647`2002`[t] -1.1069975966409`2003`[t] + 0.445419410028552`2004`[t] + 0.705383626314407`2005`[t] -1.59307558042119`2006`[t] -0.85005893867999`2007`[t] -0.2902924671059`2008`[t] + 1.65727639179957`2009`[t] + 0.0595801154945223`2010`[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)	-0.00379764888319456	0.032571	-0.1166	0.914549	0.457274
`2001`	0.744621059986105	0.301762	2.4676	0.090258	0.045129
`2002`	1.46947563970647	0.46086	3.1885	0.049766	0.024883
`2003`	-1.1069975966409	0.56029	-1.9758	0.142645	0.071322
`2004`	0.445419410028552	0.639927	0.696	0.536477	0.268239
`2005`	0.705383626314407	0.477564	1.477	0.236166	0.118083
`2006`	-1.59307558042119	0.705436	-2.2583	0.109099	0.054549
`2007`	-0.85005893867999	0.348086	-2.4421	0.092327	0.046164
`2008`	-0.2902924671059	0.300657	-0.9655	0.405503	0.202752
`2009`	1.65727639179957	0.551187	3.0067	0.05736	0.02868
`2010`	0.0595801154945223	0.353018	0.1688	0.876712	0.438356

\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) & -0.00379764888319456 & 0.032571 & -0.1166 & 0.914549 & 0.457274 \tabularnewline
`2001` & 0.744621059986105 & 0.301762 & 2.4676 & 0.090258 & 0.045129 \tabularnewline
`2002` & 1.46947563970647 & 0.46086 & 3.1885 & 0.049766 & 0.024883 \tabularnewline
`2003` & -1.1069975966409 & 0.56029 & -1.9758 & 0.142645 & 0.071322 \tabularnewline
`2004` & 0.445419410028552 & 0.639927 & 0.696 & 0.536477 & 0.268239 \tabularnewline
`2005` & 0.705383626314407 & 0.477564 & 1.477 & 0.236166 & 0.118083 \tabularnewline
`2006` & -1.59307558042119 & 0.705436 & -2.2583 & 0.109099 & 0.054549 \tabularnewline
`2007` & -0.85005893867999 & 0.348086 & -2.4421 & 0.092327 & 0.046164 \tabularnewline
`2008` & -0.2902924671059 & 0.300657 & -0.9655 & 0.405503 & 0.202752 \tabularnewline
`2009` & 1.65727639179957 & 0.551187 & 3.0067 & 0.05736 & 0.02868 \tabularnewline
`2010` & 0.0595801154945223 & 0.353018 & 0.1688 & 0.876712 & 0.438356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185703&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]-0.00379764888319456[/C][C]0.032571[/C][C]-0.1166[/C][C]0.914549[/C][C]0.457274[/C][/ROW]
[ROW][C]`2001`[/C][C]0.744621059986105[/C][C]0.301762[/C][C]2.4676[/C][C]0.090258[/C][C]0.045129[/C][/ROW]
[ROW][C]`2002`[/C][C]1.46947563970647[/C][C]0.46086[/C][C]3.1885[/C][C]0.049766[/C][C]0.024883[/C][/ROW]
[ROW][C]`2003`[/C][C]-1.1069975966409[/C][C]0.56029[/C][C]-1.9758[/C][C]0.142645[/C][C]0.071322[/C][/ROW]
[ROW][C]`2004`[/C][C]0.445419410028552[/C][C]0.639927[/C][C]0.696[/C][C]0.536477[/C][C]0.268239[/C][/ROW]
[ROW][C]`2005`[/C][C]0.705383626314407[/C][C]0.477564[/C][C]1.477[/C][C]0.236166[/C][C]0.118083[/C][/ROW]
[ROW][C]`2006`[/C][C]-1.59307558042119[/C][C]0.705436[/C][C]-2.2583[/C][C]0.109099[/C][C]0.054549[/C][/ROW]
[ROW][C]`2007`[/C][C]-0.85005893867999[/C][C]0.348086[/C][C]-2.4421[/C][C]0.092327[/C][C]0.046164[/C][/ROW]
[ROW][C]`2008`[/C][C]-0.2902924671059[/C][C]0.300657[/C][C]-0.9655[/C][C]0.405503[/C][C]0.202752[/C][/ROW]
[ROW][C]`2009`[/C][C]1.65727639179957[/C][C]0.551187[/C][C]3.0067[/C][C]0.05736[/C][C]0.02868[/C][/ROW]
[ROW][C]`2010`[/C][C]0.0595801154945223[/C][C]0.353018[/C][C]0.1688[/C][C]0.876712[/C][C]0.438356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185703&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185703&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)	-0.00379764888319456	0.032571	-0.1166	0.914549	0.457274
`2001`	0.744621059986105	0.301762	2.4676	0.090258	0.045129
`2002`	1.46947563970647	0.46086	3.1885	0.049766	0.024883
`2003`	-1.1069975966409	0.56029	-1.9758	0.142645	0.071322
`2004`	0.445419410028552	0.639927	0.696	0.536477	0.268239
`2005`	0.705383626314407	0.477564	1.477	0.236166	0.118083
`2006`	-1.59307558042119	0.705436	-2.2583	0.109099	0.054549
`2007`	-0.85005893867999	0.348086	-2.4421	0.092327	0.046164
`2008`	-0.2902924671059	0.300657	-0.9655	0.405503	0.202752
`2009`	1.65727639179957	0.551187	3.0067	0.05736	0.02868
`2010`	0.0595801154945223	0.353018	0.1688	0.876712	0.438356

Multiple Linear Regression - Regression Statistics
Multiple R	0.999999875739288
R-squared	0.999999751478592
Adjusted R-squared	0.9999989230739
F-TEST (value)	1207139.16917269
F-TEST (DF numerator)	10
F-TEST (DF denominator)	3
p-value	1.11793729828946e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0758428501486384
Sum Squared Residuals	0.0172564137560065

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.999999875739288 \tabularnewline
R-squared & 0.999999751478592 \tabularnewline
Adjusted R-squared & 0.9999989230739 \tabularnewline
F-TEST (value) & 1207139.16917269 \tabularnewline
F-TEST (DF numerator) & 10 \tabularnewline
F-TEST (DF denominator) & 3 \tabularnewline
p-value & 1.11793729828946e-09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.0758428501486384 \tabularnewline
Sum Squared Residuals & 0.0172564137560065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185703&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.999999875739288[/C][/ROW]
[ROW][C]R-squared[/C][C]0.999999751478592[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.9999989230739[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1207139.16917269[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]10[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]3[/C][/ROW]
[ROW][C]p-value[/C][C]1.11793729828946e-09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.0758428501486384[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.0172564137560065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185703&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185703&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	0.999999875739288
R-squared	0.999999751478592
Adjusted R-squared	0.9999989230739
F-TEST (value)	1207139.16917269
F-TEST (DF numerator)	10
F-TEST (DF denominator)	3
p-value	1.11793729828946e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0758428501486384
Sum Squared Residuals	0.0172564137560065

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	5.029	5.04416323126643	-0.0151632312664322
2	24.994	24.9904559094071	0.00354409059291746
3	6.639	6.65206296548628	-0.0130629654862816
4	3.451	3.42629863421247	0.0247013657875283
5	5.844	5.89845048944829	-0.0544504894482891
6	3.954	3.90903113889813	0.0449688611018674
7	5.106	5.08942208582926	0.0165779141707391
8	15.1	15.111290059657	-0.0112900596570223
9	279	278.999726021671	0.000273978329242531
10	1.567	1.52137515289144	0.0456248471085576
11	5.616	5.57684797501311	0.0391520249868846
12	4.56	4.57395169653826	-0.0139516965382585
13	1.262	1.34442709170879	-0.0824270917087895
14	2.095	2.07949754797266	0.0155024520273359

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 5.029 & 5.04416323126643 & -0.0151632312664322 \tabularnewline
2 & 24.994 & 24.9904559094071 & 0.00354409059291746 \tabularnewline
3 & 6.639 & 6.65206296548628 & -0.0130629654862816 \tabularnewline
4 & 3.451 & 3.42629863421247 & 0.0247013657875283 \tabularnewline
5 & 5.844 & 5.89845048944829 & -0.0544504894482891 \tabularnewline
6 & 3.954 & 3.90903113889813 & 0.0449688611018674 \tabularnewline
7 & 5.106 & 5.08942208582926 & 0.0165779141707391 \tabularnewline
8 & 15.1 & 15.111290059657 & -0.0112900596570223 \tabularnewline
9 & 279 & 278.999726021671 & 0.000273978329242531 \tabularnewline
10 & 1.567 & 1.52137515289144 & 0.0456248471085576 \tabularnewline
11 & 5.616 & 5.57684797501311 & 0.0391520249868846 \tabularnewline
12 & 4.56 & 4.57395169653826 & -0.0139516965382585 \tabularnewline
13 & 1.262 & 1.34442709170879 & -0.0824270917087895 \tabularnewline
14 & 2.095 & 2.07949754797266 & 0.0155024520273359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185703&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]5.029[/C][C]5.04416323126643[/C][C]-0.0151632312664322[/C][/ROW]
[ROW][C]2[/C][C]24.994[/C][C]24.9904559094071[/C][C]0.00354409059291746[/C][/ROW]
[ROW][C]3[/C][C]6.639[/C][C]6.65206296548628[/C][C]-0.0130629654862816[/C][/ROW]
[ROW][C]4[/C][C]3.451[/C][C]3.42629863421247[/C][C]0.0247013657875283[/C][/ROW]
[ROW][C]5[/C][C]5.844[/C][C]5.89845048944829[/C][C]-0.0544504894482891[/C][/ROW]
[ROW][C]6[/C][C]3.954[/C][C]3.90903113889813[/C][C]0.0449688611018674[/C][/ROW]
[ROW][C]7[/C][C]5.106[/C][C]5.08942208582926[/C][C]0.0165779141707391[/C][/ROW]
[ROW][C]8[/C][C]15.1[/C][C]15.111290059657[/C][C]-0.0112900596570223[/C][/ROW]
[ROW][C]9[/C][C]279[/C][C]278.999726021671[/C][C]0.000273978329242531[/C][/ROW]
[ROW][C]10[/C][C]1.567[/C][C]1.52137515289144[/C][C]0.0456248471085576[/C][/ROW]
[ROW][C]11[/C][C]5.616[/C][C]5.57684797501311[/C][C]0.0391520249868846[/C][/ROW]
[ROW][C]12[/C][C]4.56[/C][C]4.57395169653826[/C][C]-0.0139516965382585[/C][/ROW]
[ROW][C]13[/C][C]1.262[/C][C]1.34442709170879[/C][C]-0.0824270917087895[/C][/ROW]
[ROW][C]14[/C][C]2.095[/C][C]2.07949754797266[/C][C]0.0155024520273359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185703&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185703&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	5.029	5.04416323126643	-0.0151632312664322
2	24.994	24.9904559094071	0.00354409059291746
3	6.639	6.65206296548628	-0.0130629654862816
4	3.451	3.42629863421247	0.0247013657875283
5	5.844	5.89845048944829	-0.0544504894482891
6	3.954	3.90903113889813	0.0449688611018674
7	5.106	5.08942208582926	0.0165779141707391
8	15.1	15.111290059657	-0.0112900596570223
9	279	278.999726021671	0.000273978329242531
10	1.567	1.52137515289144	0.0456248471085576
11	5.616	5.57684797501311	0.0391520249868846
12	4.56	4.57395169653826	-0.0139516965382585
13	1.262	1.34442709170879	-0.0824270917087895
14	2.095	2.07949754797266	0.0155024520273359

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Figure 10

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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