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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 24 Jan 2017 19:43:26 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/24/t1485283499k23t75ngz846836.htm/, Retrieved Tue, 14 May 2024 20:27:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=305243, Retrieved Tue, 14 May 2024 20:27:33 +0000

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

-       [Multiple Regression] [x] [2017-01-24 18:43:26] [0fd2044a1b35b563c533995bdc13f5a1] [Current]

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0.7923 0 1
-2.468 1 0
-2.996 1 0
3.119 1 0
0.04315 1 0
0.731 0 1
2.45 1 0
2.119 1 0
-1.429 0 1
-1.644 1 0
-3.065 0 0
-1.461 1 0
1.141 0 0
1.329 0 1
0.3396 1 0
0.8429 0 0
2.225 0 0
-1.924 0 1
0.4999 1 1
-0.6433 0 0

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	Big Analytics Cloud Computing Center

\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 time7 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305243&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]

7 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=305243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305243&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	Big Analytics Cloud Computing Center

Multiple Linear Regression - Estimated Regression Equation
Resid[t] = + 0.000124559 + 6.73529e-05X2[t] -0.000269118X1[t] + e[t]
Warning: you did not specify the column number of the endogenous series! The first column was selected by default.

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Resid[t] =  +  0.000124559 +  6.73529e-05X2[t] -0.000269118X1[t]  + e[t] \tabularnewline
Warning: you did not specify the column number of the endogenous series! The first column was selected by default. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305243&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Resid[t] =  +  0.000124559 +  6.73529e-05X2[t] -0.000269118X1[t]  + e[t][/C][/ROW]
[ROW][C]Warning: you did not specify the column number of the endogenous series! The first column was selected by default.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305243&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
Resid[t] = + 0.000124559 + 6.73529e-05X2[t] -0.000269118X1[t] + e[t]
Warning: you did not specify the column number of the endogenous series! The first column was selected by default.

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	+0.0001246	0.8204	+1.5180e-04	0.9999	0.4999
X2	+6.735e-05	0.9789	+6.8810e-05	0.9999	0.5
X1	-0.0002691	1.068	-2.5200e-04	0.9998	0.4999

\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) & +0.0001246 &  0.8204 & +1.5180e-04 &  0.9999 &  0.4999 \tabularnewline
X2 & +6.735e-05 &  0.9789 & +6.8810e-05 &  0.9999 &  0.5 \tabularnewline
X1 & -0.0002691 &  1.068 & -2.5200e-04 &  0.9998 &  0.4999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305243&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]+0.0001246[/C][C] 0.8204[/C][C]+1.5180e-04[/C][C] 0.9999[/C][C] 0.4999[/C][/ROW]
[ROW][C]X2[/C][C]+6.735e-05[/C][C] 0.9789[/C][C]+6.8810e-05[/C][C] 0.9999[/C][C] 0.5[/C][/ROW]
[ROW][C]X1[/C][C]-0.0002691[/C][C] 1.068[/C][C]-2.5200e-04[/C][C] 0.9998[/C][C] 0.4999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305243&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305243&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)	+0.0001246	0.8204	+1.5180e-04	0.9999	0.4999
X2	+6.735e-05	0.9789	+6.8810e-05	0.9999	0.5
X1	-0.0002691	1.068	-2.5200e-04	0.9998	0.4999

Multiple Linear Regression - Regression Statistics
Multiple R	7.783e-05
R-squared	6.057e-09
Adjusted R-squared	-0.1176
F-TEST (value)	5.148e-08
F-TEST (DF numerator)	2
F-TEST (DF denominator)	17
p-value	1
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.969
Sum Squared Residuals	65.94

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  7.783e-05 \tabularnewline
R-squared &  6.057e-09 \tabularnewline
Adjusted R-squared & -0.1176 \tabularnewline
F-TEST (value) &  5.148e-08 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 17 \tabularnewline
p-value &  1 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  1.969 \tabularnewline
Sum Squared Residuals &  65.94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305243&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 7.783e-05[/C][/ROW]
[ROW][C]R-squared[/C][C] 6.057e-09[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.1176[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 5.148e-08[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]17[/C][/ROW]
[ROW][C]p-value[/C][C] 1[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 1.969[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 65.94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305243&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305243&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	7.783e-05
R-squared	6.057e-09
Adjusted R-squared	-0.1176
F-TEST (value)	5.148e-08
F-TEST (DF numerator)	2
F-TEST (DF denominator)	17
p-value	1
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.969
Sum Squared Residuals	65.94

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	0.7923	-0.0001446	0.7924
2	-2.468	0.0001919	-2.468
3	-2.996	0.0001919	-2.996
4	3.119	0.0001919	3.119
5	0.04315	0.0001919	0.04296
6	0.731	-0.0001446	0.7311
7	2.45	0.0001919	2.45
8	2.119	0.0001919	2.119
9	-1.429	-0.0001446	-1.429
10	-1.644	0.0001919	-1.644
11	-3.065	0.0001246	-3.065
12	-1.461	0.0001919	-1.461
13	1.141	0.0001246	1.141
14	1.329	-0.0001446	1.329
15	0.3396	0.0001919	0.3394
16	0.8429	0.0001246	0.8428
17	2.225	0.0001246	2.225
18	-1.924	-0.0001446	-1.924
19	0.4999	-7.721e-05	0.5
20	-0.6433	0.0001246	-0.6434

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  0.7923 & -0.0001446 &  0.7924 \tabularnewline
2 & -2.468 &  0.0001919 & -2.468 \tabularnewline
3 & -2.996 &  0.0001919 & -2.996 \tabularnewline
4 &  3.119 &  0.0001919 &  3.119 \tabularnewline
5 &  0.04315 &  0.0001919 &  0.04296 \tabularnewline
6 &  0.731 & -0.0001446 &  0.7311 \tabularnewline
7 &  2.45 &  0.0001919 &  2.45 \tabularnewline
8 &  2.119 &  0.0001919 &  2.119 \tabularnewline
9 & -1.429 & -0.0001446 & -1.429 \tabularnewline
10 & -1.644 &  0.0001919 & -1.644 \tabularnewline
11 & -3.065 &  0.0001246 & -3.065 \tabularnewline
12 & -1.461 &  0.0001919 & -1.461 \tabularnewline
13 &  1.141 &  0.0001246 &  1.141 \tabularnewline
14 &  1.329 & -0.0001446 &  1.329 \tabularnewline
15 &  0.3396 &  0.0001919 &  0.3394 \tabularnewline
16 &  0.8429 &  0.0001246 &  0.8428 \tabularnewline
17 &  2.225 &  0.0001246 &  2.225 \tabularnewline
18 & -1.924 & -0.0001446 & -1.924 \tabularnewline
19 &  0.4999 & -7.721e-05 &  0.5 \tabularnewline
20 & -0.6433 &  0.0001246 & -0.6434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305243&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] 0.7923[/C][C]-0.0001446[/C][C] 0.7924[/C][/ROW]
[ROW][C]2[/C][C]-2.468[/C][C] 0.0001919[/C][C]-2.468[/C][/ROW]
[ROW][C]3[/C][C]-2.996[/C][C] 0.0001919[/C][C]-2.996[/C][/ROW]
[ROW][C]4[/C][C] 3.119[/C][C] 0.0001919[/C][C] 3.119[/C][/ROW]
[ROW][C]5[/C][C] 0.04315[/C][C] 0.0001919[/C][C] 0.04296[/C][/ROW]
[ROW][C]6[/C][C] 0.731[/C][C]-0.0001446[/C][C] 0.7311[/C][/ROW]
[ROW][C]7[/C][C] 2.45[/C][C] 0.0001919[/C][C] 2.45[/C][/ROW]
[ROW][C]8[/C][C] 2.119[/C][C] 0.0001919[/C][C] 2.119[/C][/ROW]
[ROW][C]9[/C][C]-1.429[/C][C]-0.0001446[/C][C]-1.429[/C][/ROW]
[ROW][C]10[/C][C]-1.644[/C][C] 0.0001919[/C][C]-1.644[/C][/ROW]
[ROW][C]11[/C][C]-3.065[/C][C] 0.0001246[/C][C]-3.065[/C][/ROW]
[ROW][C]12[/C][C]-1.461[/C][C] 0.0001919[/C][C]-1.461[/C][/ROW]
[ROW][C]13[/C][C] 1.141[/C][C] 0.0001246[/C][C] 1.141[/C][/ROW]
[ROW][C]14[/C][C] 1.329[/C][C]-0.0001446[/C][C] 1.329[/C][/ROW]
[ROW][C]15[/C][C] 0.3396[/C][C] 0.0001919[/C][C] 0.3394[/C][/ROW]
[ROW][C]16[/C][C] 0.8429[/C][C] 0.0001246[/C][C] 0.8428[/C][/ROW]
[ROW][C]17[/C][C] 2.225[/C][C] 0.0001246[/C][C] 2.225[/C][/ROW]
[ROW][C]18[/C][C]-1.924[/C][C]-0.0001446[/C][C]-1.924[/C][/ROW]
[ROW][C]19[/C][C] 0.4999[/C][C]-7.721e-05[/C][C] 0.5[/C][/ROW]
[ROW][C]20[/C][C]-0.6433[/C][C] 0.0001246[/C][C]-0.6434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305243&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305243&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	0.7923	-0.0001446	0.7924
2	-2.468	0.0001919	-2.468
3	-2.996	0.0001919	-2.996
4	3.119	0.0001919	3.119
5	0.04315	0.0001919	0.04296
6	0.731	-0.0001446	0.7311
7	2.45	0.0001919	2.45
8	2.119	0.0001919	2.119
9	-1.429	-0.0001446	-1.429
10	-1.644	0.0001919	-1.644
11	-3.065	0.0001246	-3.065
12	-1.461	0.0001919	-1.461
13	1.141	0.0001246	1.141
14	1.329	-0.0001446	1.329
15	0.3396	0.0001919	0.3394
16	0.8429	0.0001246	0.8428
17	2.225	0.0001246	2.225
18	-1.924	-0.0001446	-1.924
19	0.4999	-7.721e-05	0.5
20	-0.6433	0.0001246	-0.6434

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 0.043215, df1 = 2, df2 = 15, p-value = 0.9578
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 0, df1 = 4, df2 = 13, p-value = 1
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 0.043215, df1 = 2, df2 = 15, p-value = 0.9578

\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 = 0.043215, df1 = 2, df2 = 15, p-value = 0.9578
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0, df1 = 4, df2 = 13, 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 = 0.043215, df1 = 2, df2 = 15, p-value = 0.9578
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305243&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 = 0.043215, df1 = 2, df2 = 15, p-value = 0.9578
[/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 = 4, df2 = 13, 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 = 0.043215, df1 = 2, df2 = 15, p-value = 0.9578
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305243&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305243&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 = 0.043215, df1 = 2, df2 = 15, p-value = 0.9578
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 0, df1 = 4, df2 = 13, p-value = 1
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 0.043215, df1 = 2, df2 = 15, p-value = 0.9578

Variance Inflation Factors (Multicollinearity)
> vif X2 X1 1.235294 1.235294

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
      X2       X1 
1.235294 1.235294 
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305243&T=6

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]> vif
      X2       X1 
1.235294 1.235294 
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=305243&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305243&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 X2 X1 1.235294 1.235294

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Parameters (Session):

par1 = additive ; par2 = 12 ;

Parameters (R input):

par1 = additive ; par2 = 12 ; par3 = No Linear Trend ; par4 = ; par5 = ;

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 <- ''
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 (par5=='') par5 <- 0
par5 <- as.numeric(par5)
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=12)'){
(n <- n - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s=12)'){
(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 - 12)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+12,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*12,par5), dimnames=list(1:(n-par5*12), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*12)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*12-j*12,par1]
}
}
x <- cbind(x[(par5*12+1):n,], x2)
n <- n - par5*12
}
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$resid)
myr
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code