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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 31 Aug 2016 09:45:59 +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/2016/Aug/31/t1472633354h6kcimunlkbqov4.htm/, Retrieved Sun, 05 May 2024 16:22:39 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 16:22:39 +0200

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6 1 1 0 0 0 3.2 3.2 10.24
7 0 0 1 0 1 3.3 0 10.89
2 1 0 1 1 1 3 3 9
11 0 0 1 0 1 3.5 0 12.25
13 1 0 1 0 0 3.7 3.7 13.69
3 0 1 0 0 0 2.7 0 7.29
17 1 0 1 1 1 3.6 3.6 12.96
10 0 0 1 0 1 3.5 0 12.25
4 1 1 0 0 0 3.8 3.8 14.44
12 0 0 1 0 0 3.4 0 11.56
7 1 0 0 0 1 3.7 3.7 13.69
11 0 0 1 0 0 3.5 0 12.25
3 1 0 0 1 0 2.8 2.8 7.84
5 0 1 0 1 0 3.8 0 14.44
1 1 0 1 0 0 4.3 4.3 18.49
12 0 0 0 0 1 3.3 0 10.89
18 1 0 0 0 0 3.6 3.6 12.96
8 0 1 0 1 0 3.6 0 12.96
6 1 1 1 0 0 3.3 3.3 10.89
1 0 0 0 0 0 2.8 0 7.84

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	4 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Multiple Linear Regression - Estimated Regression Equation
Numeracy[t] = -258.613 -45.4581Geslacht[t] -5.1149Drugs[t] -0.476887Fruit[t] + 3.38782Sport[t] -3.28597Alcohol[t] + 164.222Gebgewicht[t] + 13.378Inter[t] -24.7568Gebgew2[t] -0.0605754t + 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
Numeracy[t] =  -258.613 -45.4581Geslacht[t] -5.1149Drugs[t] -0.476887Fruit[t] +  3.38782Sport[t] -3.28597Alcohol[t] +  164.222Gebgewicht[t] +  13.378Inter[t] -24.7568Gebgew2[t] -0.0605754t  + 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=&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Numeracy[t] =  -258.613 -45.4581Geslacht[t] -5.1149Drugs[t] -0.476887Fruit[t] +  3.38782Sport[t] -3.28597Alcohol[t] +  164.222Gebgewicht[t] +  13.378Inter[t] -24.7568Gebgew2[t] -0.0605754t  + 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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Numeracy[t] = -258.613 -45.4581Geslacht[t] -5.1149Drugs[t] -0.476887Fruit[t] + 3.38782Sport[t] -3.28597Alcohol[t] + 164.222Gebgewicht[t] + 13.378Inter[t] -24.7568Gebgew2[t] -0.0605754t + 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)	-258.6	60.27	-4.2910e+00	0.001583	0.0007916
Geslacht	-45.46	26.18	-1.7370e+00	0.1131	0.05655
Drugs	-5.115	2.362	-2.1650e+00	0.0556	0.0278
Fruit	-0.4769	2.071	-2.3020e-01	0.8226	0.4113
Sport	+3.388	2.757	+1.2290e+00	0.2472	0.1236
Alcohol	-3.286	2.449	-1.3420e+00	0.2094	0.1047
Gebgewicht	+164.2	38.39	+4.2780e+00	0.001617	0.0008085
Inter	+13.38	7.676	+1.7430e+00	0.112	0.05598
Gebgew2	-24.76	6.065	-4.0820e+00	0.002207	0.001104
t	-0.06057	0.1767	-3.4280e-01	0.7388	0.3694

\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) & -258.6 &  60.27 & -4.2910e+00 &  0.001583 &  0.0007916 \tabularnewline
Geslacht & -45.46 &  26.18 & -1.7370e+00 &  0.1131 &  0.05655 \tabularnewline
Drugs & -5.115 &  2.362 & -2.1650e+00 &  0.0556 &  0.0278 \tabularnewline
Fruit & -0.4769 &  2.071 & -2.3020e-01 &  0.8226 &  0.4113 \tabularnewline
Sport & +3.388 &  2.757 & +1.2290e+00 &  0.2472 &  0.1236 \tabularnewline
Alcohol & -3.286 &  2.449 & -1.3420e+00 &  0.2094 &  0.1047 \tabularnewline
Gebgewicht & +164.2 &  38.39 & +4.2780e+00 &  0.001617 &  0.0008085 \tabularnewline
Inter & +13.38 &  7.676 & +1.7430e+00 &  0.112 &  0.05598 \tabularnewline
Gebgew2 & -24.76 &  6.065 & -4.0820e+00 &  0.002207 &  0.001104 \tabularnewline
t & -0.06057 &  0.1767 & -3.4280e-01 &  0.7388 &  0.3694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-258.6[/C][C] 60.27[/C][C]-4.2910e+00[/C][C] 0.001583[/C][C] 0.0007916[/C][/ROW]
[ROW][C]Geslacht[/C][C]-45.46[/C][C] 26.18[/C][C]-1.7370e+00[/C][C] 0.1131[/C][C] 0.05655[/C][/ROW]
[ROW][C]Drugs[/C][C]-5.115[/C][C] 2.362[/C][C]-2.1650e+00[/C][C] 0.0556[/C][C] 0.0278[/C][/ROW]
[ROW][C]Fruit[/C][C]-0.4769[/C][C] 2.071[/C][C]-2.3020e-01[/C][C] 0.8226[/C][C] 0.4113[/C][/ROW]
[ROW][C]Sport[/C][C]+3.388[/C][C] 2.757[/C][C]+1.2290e+00[/C][C] 0.2472[/C][C] 0.1236[/C][/ROW]
[ROW][C]Alcohol[/C][C]-3.286[/C][C] 2.449[/C][C]-1.3420e+00[/C][C] 0.2094[/C][C] 0.1047[/C][/ROW]
[ROW][C]Gebgewicht[/C][C]+164.2[/C][C] 38.39[/C][C]+4.2780e+00[/C][C] 0.001617[/C][C] 0.0008085[/C][/ROW]
[ROW][C]Inter[/C][C]+13.38[/C][C] 7.676[/C][C]+1.7430e+00[/C][C] 0.112[/C][C] 0.05598[/C][/ROW]
[ROW][C]Gebgew2[/C][C]-24.76[/C][C] 6.065[/C][C]-4.0820e+00[/C][C] 0.002207[/C][C] 0.001104[/C][/ROW]
[ROW][C]t[/C][C]-0.06057[/C][C] 0.1767[/C][C]-3.4280e-01[/C][C] 0.7388[/C][C] 0.3694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)	-258.6	60.27	-4.2910e+00	0.001583	0.0007916
Geslacht	-45.46	26.18	-1.7370e+00	0.1131	0.05655
Drugs	-5.115	2.362	-2.1650e+00	0.0556	0.0278
Fruit	-0.4769	2.071	-2.3020e-01	0.8226	0.4113
Sport	+3.388	2.757	+1.2290e+00	0.2472	0.1236
Alcohol	-3.286	2.449	-1.3420e+00	0.2094	0.1047
Gebgewicht	+164.2	38.39	+4.2780e+00	0.001617	0.0008085
Inter	+13.38	7.676	+1.7430e+00	0.112	0.05598
Gebgew2	-24.76	6.065	-4.0820e+00	0.002207	0.001104
t	-0.06057	0.1767	-3.4280e-01	0.7388	0.3694

Multiple Linear Regression - Regression Statistics
Multiple R	0.8493
R-squared	0.7214
Adjusted R-squared	0.4706
F-TEST (value)	2.876
F-TEST (DF numerator)	9
F-TEST (DF denominator)	10
p-value	0.05761
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.652
Sum Squared Residuals	133.3

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.8493 \tabularnewline
R-squared &  0.7214 \tabularnewline
Adjusted R-squared &  0.4706 \tabularnewline
F-TEST (value) &  2.876 \tabularnewline
F-TEST (DF numerator) & 9 \tabularnewline
F-TEST (DF denominator) & 10 \tabularnewline
p-value &  0.05761 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  3.652 \tabularnewline
Sum Squared Residuals &  133.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.8493[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.7214[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.4706[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 2.876[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]9[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]10[/C][/ROW]
[ROW][C]p-value[/C][C] 0.05761[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 3.652[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 133.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.8493
R-squared	0.7214
Adjusted R-squared	0.4706
F-TEST (value)	2.876
F-TEST (DF numerator)	9
F-TEST (DF denominator)	10
p-value	0.05761
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.652
Sum Squared Residuals	133.3

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	6	5.563	0.4374
2	7	9.833	-2.833
3	2	5.36	-3.36
4	11	8.887	2.113
5	13	13.35	-0.3471
6	3	-1.17	4.17
7	17	13.64	3.36
8	10	8.644	1.356
9	4	7.659	-3.659
10	12	12.47	-0.4692
11	7	10.17	-3.175
12	11	11.69	-0.688
13	3	1.715	1.285
14	5	5.366	-0.3657
15	1	0.4684	0.5316
16	12	9.462	2.538
17	18	13.41	4.59
18	8	8.919	-0.9192
19	6	5.663	0.3366
20	1	5.903	-4.903

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  6 &  5.563 &  0.4374 \tabularnewline
2 &  7 &  9.833 & -2.833 \tabularnewline
3 &  2 &  5.36 & -3.36 \tabularnewline
4 &  11 &  8.887 &  2.113 \tabularnewline
5 &  13 &  13.35 & -0.3471 \tabularnewline
6 &  3 & -1.17 &  4.17 \tabularnewline
7 &  17 &  13.64 &  3.36 \tabularnewline
8 &  10 &  8.644 &  1.356 \tabularnewline
9 &  4 &  7.659 & -3.659 \tabularnewline
10 &  12 &  12.47 & -0.4692 \tabularnewline
11 &  7 &  10.17 & -3.175 \tabularnewline
12 &  11 &  11.69 & -0.688 \tabularnewline
13 &  3 &  1.715 &  1.285 \tabularnewline
14 &  5 &  5.366 & -0.3657 \tabularnewline
15 &  1 &  0.4684 &  0.5316 \tabularnewline
16 &  12 &  9.462 &  2.538 \tabularnewline
17 &  18 &  13.41 &  4.59 \tabularnewline
18 &  8 &  8.919 & -0.9192 \tabularnewline
19 &  6 &  5.663 &  0.3366 \tabularnewline
20 &  1 &  5.903 & -4.903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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] 6[/C][C] 5.563[/C][C] 0.4374[/C][/ROW]
[ROW][C]2[/C][C] 7[/C][C] 9.833[/C][C]-2.833[/C][/ROW]
[ROW][C]3[/C][C] 2[/C][C] 5.36[/C][C]-3.36[/C][/ROW]
[ROW][C]4[/C][C] 11[/C][C] 8.887[/C][C] 2.113[/C][/ROW]
[ROW][C]5[/C][C] 13[/C][C] 13.35[/C][C]-0.3471[/C][/ROW]
[ROW][C]6[/C][C] 3[/C][C]-1.17[/C][C] 4.17[/C][/ROW]
[ROW][C]7[/C][C] 17[/C][C] 13.64[/C][C] 3.36[/C][/ROW]
[ROW][C]8[/C][C] 10[/C][C] 8.644[/C][C] 1.356[/C][/ROW]
[ROW][C]9[/C][C] 4[/C][C] 7.659[/C][C]-3.659[/C][/ROW]
[ROW][C]10[/C][C] 12[/C][C] 12.47[/C][C]-0.4692[/C][/ROW]
[ROW][C]11[/C][C] 7[/C][C] 10.17[/C][C]-3.175[/C][/ROW]
[ROW][C]12[/C][C] 11[/C][C] 11.69[/C][C]-0.688[/C][/ROW]
[ROW][C]13[/C][C] 3[/C][C] 1.715[/C][C] 1.285[/C][/ROW]
[ROW][C]14[/C][C] 5[/C][C] 5.366[/C][C]-0.3657[/C][/ROW]
[ROW][C]15[/C][C] 1[/C][C] 0.4684[/C][C] 0.5316[/C][/ROW]
[ROW][C]16[/C][C] 12[/C][C] 9.462[/C][C] 2.538[/C][/ROW]
[ROW][C]17[/C][C] 18[/C][C] 13.41[/C][C] 4.59[/C][/ROW]
[ROW][C]18[/C][C] 8[/C][C] 8.919[/C][C]-0.9192[/C][/ROW]
[ROW][C]19[/C][C] 6[/C][C] 5.663[/C][C] 0.3366[/C][/ROW]
[ROW][C]20[/C][C] 1[/C][C] 5.903[/C][C]-4.903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	6	5.563	0.4374
2	7	9.833	-2.833
3	2	5.36	-3.36
4	11	8.887	2.113
5	13	13.35	-0.3471
6	3	-1.17	4.17
7	17	13.64	3.36
8	10	8.644	1.356
9	4	7.659	-3.659
10	12	12.47	-0.4692
11	7	10.17	-3.175
12	11	11.69	-0.688
13	3	1.715	1.285
14	5	5.366	-0.3657
15	1	0.4684	0.5316
16	12	9.462	2.538
17	18	13.41	4.59
18	8	8.919	-0.9192
19	6	5.663	0.3366
20	1	5.903	-4.903

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Parameters (Session):

par1 = pearson ;

Parameters (R input):

par1 = ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; par4 = ; par5 = ;

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

library(lattice)
library(lmtest)
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'
}
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$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, mywarning)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,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$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$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')
}
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code