Free Statistics

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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 16 Dec 2017 18:08:59 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/16/t151344425628ael8wyzyj8hh4.htm/, Retrieved Wed, 15 May 2024 12:12:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309925, Retrieved Wed, 15 May 2024 12:12:07 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
12.74311265023880	0	0	0	0	0	0
14.22097699940490	0	0	1	0	0	0
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10.90599267722570	0	0	0	0	0	0
13.80985157608760	0	1	0	0	0	0
11.77609709573750	0	1	0	0	0	0
9.23620303150191	0	0	0	0	0	0
9.34320904505061	0	0	0	0	0	0
8.73230457103318	0	0	0	0	0	0
8.87724243599392	0	0	0	0	0	0
8.80207133653528	0	1	0	0	0	0
9.08273424737104	0	1	0	0	0	0
12.70016504655450	0	0	0	0	0	0
15.06938747721460	0	0	0	0	0	1
11.53106985540620	0	0	0	0	0	0
9.94241976253791	0	0	0	0	0	0
11.75667132375120	0	0	0	0	0	0
9.72865786150047	0	0	0	0	0	0
11.01043170132380	0	0	0	0	0	0
10.04111678752420	0	0	0	0	1	0
9.35824300189968	0	0	0	0	1	0
9.25855894424666	0	0	0	0	0	0
12.27840260939210	0	0	0	0	0	0
10.24842386756950	0	0	0	0	0	0
9.20903952624314	0	1	0	0	0	0
7.99159228206809	0	1	0	0	0	0
11.30915552737040	0	0	0	0	0	0
9.83563688562795	0	1	0	0	0	0
11.60825382642740	0	0	0	0	0	0
9.38605682971800	0	1	0	0	0	0
9.61593880452958	0	0	0	0	0	0
8.08332860878638	0	0	0	0	0	0
11.28980691334350	0	0	0	0	0	0
11.08217331763520	0	0	0	0	0	0
12.01794627334780	0	0	0	0	0	0
11.13380039219390	0	1	0	0	0	0
10.85853735256040	0	1	0	0	0	0
9.96707249416124	0	0	0	1	0	0
9.75492953789498	0	0	0	0	0	0
8.19450550976564	0	0	0	0	0	0
10.22208672762260	0	0	0	0	0	0
10.04333644765250	0	0	0	0	0	0
11.39198871156970	1	0	0	0	0	0
10.22019430402850	0	0	0	0	0	0
5.60211882087970	0	0	0	0	0	0
10.84063917507760	0	1	0	0	0	0
9.21213875391756	0	0	0	0	0	0
13.35680130643100	0	0	0	0	0	0
11.68815526795040	1	0	0	0	0	0




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time35 seconds
R ServerBig Analytics Cloud Computing Center
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 Outputview raw output of R engine  \tabularnewline
Computing time35 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \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=309925&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]35 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [ROW]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=309925&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309925&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 Outputview raw output of R engine
Computing time35 seconds
R ServerBig Analytics Cloud Computing Center
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
LNTOTMDG[t] = + 9.98258 -0.165063TX[t] -0.323735IL[t] -0.467669CA[t] -0.174816OH[t] -0.672277PA[t] + 0.82587`NE\r`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
LNTOTMDG[t] =  +  9.98258 -0.165063TX[t] -0.323735IL[t] -0.467669CA[t] -0.174816OH[t] -0.672277PA[t] +  0.82587`NE\r`[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309925&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]LNTOTMDG[t] =  +  9.98258 -0.165063TX[t] -0.323735IL[t] -0.467669CA[t] -0.174816OH[t] -0.672277PA[t] +  0.82587`NE\r`[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309925&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309925&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
LNTOTMDG[t] = + 9.98258 -0.165063TX[t] -0.323735IL[t] -0.467669CA[t] -0.174816OH[t] -0.672277PA[t] + 0.82587`NE\r`[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)+9.983 0.05617+1.7770e+02 0 0
TX-0.1651 0.1381-1.1950e+00 0.2322 0.1161
IL-0.3237 0.156-2.0760e+00 0.038 0.019
CA-0.4677 0.2045-2.2870e+00 0.02229 0.01114
OH-0.1748 0.2283-7.6560e-01 0.444 0.222
PA-0.6723 0.2406-2.7950e+00 0.005234 0.002617
`NE\r`+0.8259 0.2418+3.4160e+00 0.0006456 0.0003228

\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) & +9.983 &  0.05617 & +1.7770e+02 &  0 &  0 \tabularnewline
TX & -0.1651 &  0.1381 & -1.1950e+00 &  0.2322 &  0.1161 \tabularnewline
IL & -0.3237 &  0.156 & -2.0760e+00 &  0.038 &  0.019 \tabularnewline
CA & -0.4677 &  0.2045 & -2.2870e+00 &  0.02229 &  0.01114 \tabularnewline
OH & -0.1748 &  0.2283 & -7.6560e-01 &  0.444 &  0.222 \tabularnewline
PA & -0.6723 &  0.2406 & -2.7950e+00 &  0.005234 &  0.002617 \tabularnewline
`NE\r` & +0.8259 &  0.2418 & +3.4160e+00 &  0.0006456 &  0.0003228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309925&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]+9.983[/C][C] 0.05617[/C][C]+1.7770e+02[/C][C] 0[/C][C] 0[/C][/ROW]
[ROW][C]TX[/C][C]-0.1651[/C][C] 0.1381[/C][C]-1.1950e+00[/C][C] 0.2322[/C][C] 0.1161[/C][/ROW]
[ROW][C]IL[/C][C]-0.3237[/C][C] 0.156[/C][C]-2.0760e+00[/C][C] 0.038[/C][C] 0.019[/C][/ROW]
[ROW][C]CA[/C][C]-0.4677[/C][C] 0.2045[/C][C]-2.2870e+00[/C][C] 0.02229[/C][C] 0.01114[/C][/ROW]
[ROW][C]OH[/C][C]-0.1748[/C][C] 0.2283[/C][C]-7.6560e-01[/C][C] 0.444[/C][C] 0.222[/C][/ROW]
[ROW][C]PA[/C][C]-0.6723[/C][C] 0.2406[/C][C]-2.7950e+00[/C][C] 0.005234[/C][C] 0.002617[/C][/ROW]
[ROW][C]`NE\r`[/C][C]+0.8259[/C][C] 0.2418[/C][C]+3.4160e+00[/C][C] 0.0006456[/C][C] 0.0003228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309925&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309925&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)+9.983 0.05617+1.7770e+02 0 0
TX-0.1651 0.1381-1.1950e+00 0.2322 0.1161
IL-0.3237 0.156-2.0760e+00 0.038 0.019
CA-0.4677 0.2045-2.2870e+00 0.02229 0.01114
OH-0.1748 0.2283-7.6560e-01 0.444 0.222
PA-0.6723 0.2406-2.7950e+00 0.005234 0.002617
`NE\r`+0.8259 0.2418+3.4160e+00 0.0006456 0.0003228







Multiple Linear Regression - Regression Statistics
Multiple R 0.1076
R-squared 0.01157
Adjusted R-squared 0.009302
F-TEST (value) 5.1
F-TEST (DF numerator)6
F-TEST (DF denominator)2614
p-value 3.232e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 2.268
Sum Squared Residuals 1.344e+04

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.1076 \tabularnewline
R-squared &  0.01157 \tabularnewline
Adjusted R-squared &  0.009302 \tabularnewline
F-TEST (value) &  5.1 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 2614 \tabularnewline
p-value &  3.232e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  2.268 \tabularnewline
Sum Squared Residuals &  1.344e+04 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309925&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.1076[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.01157[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.009302[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 5.1[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]2614[/C][/ROW]
[ROW][C]p-value[/C][C] 3.232e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 2.268[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 1.344e+04[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309925&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309925&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 0.1076
R-squared 0.01157
Adjusted R-squared 0.009302
F-TEST (value) 5.1
F-TEST (DF numerator)6
F-TEST (DF denominator)2614
p-value 3.232e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 2.268
Sum Squared Residuals 1.344e+04







Menu of Residual Diagnostics
DescriptionLink
HistogramCompute
Central TendencyCompute
QQ PlotCompute
Kernel Density PlotCompute
Skewness/Kurtosis TestCompute
Skewness-Kurtosis PlotCompute
Harrell-Davis PlotCompute
Bootstrap Plot -- Central TendencyCompute
Blocked Bootstrap Plot -- Central TendencyCompute
(Partial) Autocorrelation PlotCompute
Spectral AnalysisCompute
Tukey lambda PPCC PlotCompute
Box-Cox Normality PlotCompute
Summary StatisticsCompute

\begin{tabular}{lllllllll}
\hline
Menu of Residual Diagnostics \tabularnewline
Description & Link \tabularnewline
Histogram & Compute \tabularnewline
Central Tendency & Compute \tabularnewline
QQ Plot & Compute \tabularnewline
Kernel Density Plot & Compute \tabularnewline
Skewness/Kurtosis Test & Compute \tabularnewline
Skewness-Kurtosis Plot & Compute \tabularnewline
Harrell-Davis Plot & Compute \tabularnewline
Bootstrap Plot -- Central Tendency & Compute \tabularnewline
Blocked Bootstrap Plot -- Central Tendency & Compute \tabularnewline
(Partial) Autocorrelation Plot & Compute \tabularnewline
Spectral Analysis & Compute \tabularnewline
Tukey lambda PPCC Plot & Compute \tabularnewline
Box-Cox Normality Plot & Compute \tabularnewline
Summary Statistics & Compute \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309925&T=4

[TABLE]
[ROW][C]Menu of Residual Diagnostics[/C][/ROW]
[ROW][C]Description[/C][C]Link[/C][/ROW]
[ROW][C]Histogram[/C][C]Compute[/C][/ROW]
[ROW][C]Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]QQ Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Kernel Density Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness/Kurtosis Test[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness-Kurtosis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Harrell-Davis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]Blocked Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C](Partial) Autocorrelation Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Spectral Analysis[/C][C]Compute[/C][/ROW]
[ROW][C]Tukey lambda PPCC Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Box-Cox Normality Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Summary Statistics[/C][C]Compute[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309925&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309925&T=4

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Menu of Residual Diagnostics
DescriptionLink
HistogramCompute
Central TendencyCompute
QQ PlotCompute
Kernel Density PlotCompute
Skewness/Kurtosis TestCompute
Skewness-Kurtosis PlotCompute
Harrell-Davis PlotCompute
Bootstrap Plot -- Central TendencyCompute
Blocked Bootstrap Plot -- Central TendencyCompute
(Partial) Autocorrelation PlotCompute
Spectral AnalysisCompute
Tukey lambda PPCC PlotCompute
Box-Cox Normality PlotCompute
Summary StatisticsCompute







Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0, df1 = 2, df2 = 2612, p-value = 1
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0, df1 = 12, df2 = 2602, p-value = 1
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.13678, df1 = 2, df2 = 2612, p-value = 0.8722

\begin{tabular}{lllllllll}
\hline
Ramsey RESET F-Test for powers (2 and 3) of fitted values \tabularnewline
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0, df1 = 2, df2 = 2612, p-value = 1
\tabularnewline Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0, df1 = 12, df2 = 2602, p-value = 1
\tabularnewline Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.13678, df1 = 2, df2 = 2612, p-value = 0.8722
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=309925&T=5

[TABLE]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of fitted values[/C][/ROW]
[ROW][C]
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0, df1 = 2, df2 = 2612, p-value = 1
[/C][/ROW] [ROW][C]Ramsey RESET F-Test for powers (2 and 3) of regressors[/C][/ROW] [ROW][C]
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0, df1 = 12, df2 = 2602, p-value = 1
[/C][/ROW] [ROW][C]Ramsey RESET F-Test for powers (2 and 3) of principal components[/C][/ROW] [ROW][C]
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.13678, df1 = 2, df2 = 2612, p-value = 0.8722
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309925&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309925&T=5

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0, df1 = 2, df2 = 2612, p-value = 1
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0, df1 = 12, df2 = 2602, p-value = 1
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.13678, df1 = 2, df2 = 2612, p-value = 0.8722







Variance Inflation Factors (Multicollinearity)
> vif
      TX       IL       CA       OH       PA  `NE\\r` 
1.050504 1.042545 1.026711 1.021776 1.019736 1.019548 

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
      TX       IL       CA       OH       PA  `NE\\r` 
1.050504 1.042545 1.026711 1.021776 1.019736 1.019548 
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=309925&T=6

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]
> vif
      TX       IL       CA       OH       PA  `NE\\r` 
1.050504 1.042545 1.026711 1.021776 1.019736 1.019548 
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309925&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309925&T=6

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Variance Inflation Factors (Multicollinearity)
> vif
      TX       IL       CA       OH       PA  `NE\\r` 
1.050504 1.042545 1.026711 1.021776 1.019736 1.019548 



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
library(car)
library(MASS)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par6 <- as.numeric(par6)
if(is.na(par6)) {
par6 <- 12
mywarning = 'Warning: you did not specify the seasonality. The seasonal period was set to s = 12.'
}
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
if (par4=='') par4 <- 0
par4 <- as.numeric(par4)
if (!is.numeric(par4)) par4 <- 0
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
if (!is.numeric(par5)) par5 <- 0
x <- na.omit(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'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'Seasonal Differences (s)'){
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s)'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if(par4 > 0) {
x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep='')))
for (i in 1:(n-par4)) {
for (j in 1:par4) {
x2[i,j] <- x[i+par4-j,par1]
}
}
x <- cbind(x[(par4+1):n,], x2)
n <- n - par4
}
if(par5 > 0) {
x2 <- array(0, dim=c(n-par5*par6,par5), dimnames=list(1:(n-par5*par6), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*par6)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*par6-j*par6,par1]
}
}
x <- cbind(x[(par5*par6+1):n,], x2)
n <- n - par5*par6
}
if (par2 == 'Include Seasonal Dummies'){
x2 <- array(0, dim=c(n,par6-1), dimnames=list(1:n, paste('M', seq(1:(par6-1)), sep ='')))
for (i in 1:(par6-1)){
x2[seq(i,n,par6),i] <- 1
}
x <- cbind(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[n,]))
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
print(x)
(k <- length(x[n,]))
head(x)
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$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
sresid <- studres(mylm)
hist(sresid, freq=FALSE, main='Distribution of Studentized Residuals')
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqPlot(mylm, main='QQ Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
print(z)
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, mywarning)
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,'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$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
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,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
myr <- as.numeric(mysum$resid)
myr
a <-table.start()
a <- table.row.start(a)
a <- table.element(a,'Menu of Residual Diagnostics',2,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Description',1,TRUE)
a <- table.element(a,'Link',1,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Histogram',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_histogram.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_centraltendency.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'QQ Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_fitdistrnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Kernel Density Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_density.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness/Kurtosis Test',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness-Kurtosis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis_plot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Harrell-Davis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_harrell_davis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Blocked Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'(Partial) Autocorrelation Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_autocorrelation.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Spectral Analysis',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_spectrum.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Tukey lambda PPCC Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_tukeylambda.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Box-Cox Normality Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_boxcoxnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Summary Statistics',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_summary1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable7.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of fitted values',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_fitted <- resettest(mylm,power=2:3,type='fitted')
a<-table.element(a,paste('
',RC.texteval('reset_test_fitted'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of regressors',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_regressors <- resettest(mylm,power=2:3,type='regressor')
a<-table.element(a,paste('
',RC.texteval('reset_test_regressors'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of principal components',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_principal_components <- resettest(mylm,power=2:3,type='princomp')
a<-table.element(a,paste('
',RC.texteval('reset_test_principal_components'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable8.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Inflation Factors (Multicollinearity)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
vif <- vif(mylm)
a<-table.element(a,paste('
',RC.texteval('vif'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable9.tab')