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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 03 Nov 2012 06:04:03 -0400
Cite this page as followsStatistical 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 Sun, 03 Jul 2022 15:18:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=185703, Retrieved Sun, 03 Jul 2022 15:18:02 +0000
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Original text written by user:
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User-defined keywords
Estimated Impact101
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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Dataseries X:
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.003797648883194560.032571-0.11660.9145490.457274
`2001`0.7446210599861050.3017622.46760.0902580.045129
`2002`1.469475639706470.460863.18850.0497660.024883
`2003`-1.10699759664090.56029-1.97580.1426450.071322
`2004`0.4454194100285520.6399270.6960.5364770.268239
`2005`0.7053836263144070.4775641.4770.2361660.118083
`2006`-1.593075580421190.705436-2.25830.1090990.054549
`2007`-0.850058938679990.348086-2.44210.0923270.046164
`2008`-0.29029246710590.300657-0.96550.4055030.202752
`2009`1.657276391799570.5511873.00670.057360.02868
`2010`0.05958011549452230.3530180.16880.8767120.438356

\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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.003797648883194560.032571-0.11660.9145490.457274
`2001`0.7446210599861050.3017622.46760.0902580.045129
`2002`1.469475639706470.460863.18850.0497660.024883
`2003`-1.10699759664090.56029-1.97580.1426450.071322
`2004`0.4454194100285520.6399270.6960.5364770.268239
`2005`0.7053836263144070.4775641.4770.2361660.118083
`2006`-1.593075580421190.705436-2.25830.1090990.054549
`2007`-0.850058938679990.348086-2.44210.0923270.046164
`2008`-0.29029246710590.300657-0.96550.4055030.202752
`2009`1.657276391799570.5511873.00670.057360.02868
`2010`0.05958011549452230.3530180.16880.8767120.438356







Multiple Linear Regression - Regression Statistics
Multiple R0.999999875739288
R-squared0.999999751478592
Adjusted R-squared0.9999989230739
F-TEST (value)1207139.16917269
F-TEST (DF numerator)10
F-TEST (DF denominator)3
p-value1.11793729828946e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0758428501486384
Sum Squared Residuals0.0172564137560065

\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 R0.999999875739288
R-squared0.999999751478592
Adjusted R-squared0.9999989230739
F-TEST (value)1207139.16917269
F-TEST (DF numerator)10
F-TEST (DF denominator)3
p-value1.11793729828946e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0758428501486384
Sum Squared Residuals0.0172564137560065







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
15.0295.04416323126643-0.0151632312664322
224.99424.99045590940710.00354409059291746
36.6396.65206296548628-0.0130629654862816
43.4513.426298634212470.0247013657875283
55.8445.89845048944829-0.0544504894482891
63.9543.909031138898130.0449688611018674
75.1065.089422085829260.0165779141707391
815.115.111290059657-0.0112900596570223
9279278.9997260216710.000273978329242531
101.5671.521375152891440.0456248471085576
115.6165.576847975013110.0391520249868846
124.564.57395169653826-0.0139516965382585
131.2621.34442709170879-0.0824270917087895
142.0952.079497547972660.0155024520273359

\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 IndexActualsInterpolationForecastResidualsPrediction Error
15.0295.04416323126643-0.0151632312664322
224.99424.99045590940710.00354409059291746
36.6396.65206296548628-0.0130629654862816
43.4513.426298634212470.0247013657875283
55.8445.89845048944829-0.0544504894482891
63.9543.909031138898130.0449688611018674
75.1065.089422085829260.0165779141707391
815.115.111290059657-0.0112900596570223
9279278.9997260216710.000273978329242531
101.5671.521375152891440.0456248471085576
115.6165.576847975013110.0391520249868846
124.564.57395169653826-0.0139516965382585
131.2621.34442709170879-0.0824270917087895
142.0952.079497547972660.0155024520273359



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')
}