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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 16 Dec 2016 10:15:29 +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/Dec/16/t1481879776mfdoa7o8dv2uz01.htm/, Retrieved Fri, 03 May 2024 00:39:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300159, Retrieved Fri, 03 May 2024 00:39:34 +0000

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Estimated Impact

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

-       [Multiple Regression] [] [2016-12-16 09:15:29] [8fee619fda962476c4dedef05f7f9476] [Current]

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Dataseries X:

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Histogram

Boxplots

99.2	96.7	101.0
99.0	98.1	100.1
100.0	100.0	100.0
111.6	104.9	90.6
122.2	104.9	86.5
117.6	109.5	89.7
121.1	110.8	90.6
136.0	112.3	82.8
154.2	109.3	70.1
153.6	105.3	65.4
158.5	101.7	61.3
140.6	95.4	62.5
136.2	96.4	63.6
168.0	97.6	52.6
154.3	102.4	59.7
149.0	101.6	59.5
165.5	103.8	61.3

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 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 time6 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300159&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]

6 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300159&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	6 seconds
R Server	Big Analytics Cloud Computing Center

Multiple Linear Regression - Estimated Regression Equation
c[t] = + 90.7546 -0.687712a[t] + 0.757979b[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
c[t] =  +  90.7546 -0.687712a[t] +  0.757979b[t]  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300159&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]c[t] =  +  90.7546 -0.687712a[t] +  0.757979b[t]  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300159&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
c[t] = + 90.7546 -0.687712a[t] + 0.757979b[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	+90.75	19.58	+4.6340e+00	0.0003866	0.0001933
a	-0.6877	0.04168	-1.6500e+01	1.433e-10	7.163e-11
b	+0.758	0.1854	+4.0890e+00	0.001106	0.0005529

\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) & +90.75 &  19.58 & +4.6340e+00 &  0.0003866 &  0.0001933 \tabularnewline
a & -0.6877 &  0.04168 & -1.6500e+01 &  1.433e-10 &  7.163e-11 \tabularnewline
b & +0.758 &  0.1854 & +4.0890e+00 &  0.001106 &  0.0005529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300159&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]+90.75[/C][C] 19.58[/C][C]+4.6340e+00[/C][C] 0.0003866[/C][C] 0.0001933[/C][/ROW]
[ROW][C]a[/C][C]-0.6877[/C][C] 0.04168[/C][C]-1.6500e+01[/C][C] 1.433e-10[/C][C] 7.163e-11[/C][/ROW]
[ROW][C]b[/C][C]+0.758[/C][C] 0.1854[/C][C]+4.0890e+00[/C][C] 0.001106[/C][C] 0.0005529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300159&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300159&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)	+90.75	19.58	+4.6340e+00	0.0003866	0.0001933
a	-0.6877	0.04168	-1.6500e+01	1.433e-10	7.163e-11
b	+0.758	0.1854	+4.0890e+00	0.001106	0.0005529

Multiple Linear Regression - Regression Statistics
Multiple R	0.976
R-squared	0.9527
Adjusted R-squared	0.9459
F-TEST (value)	140.9
F-TEST (DF numerator)	2
F-TEST (DF denominator)	14
p-value	5.329e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.923
Sum Squared Residuals	215.5

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.976 \tabularnewline
R-squared &  0.9527 \tabularnewline
Adjusted R-squared &  0.9459 \tabularnewline
F-TEST (value) &  140.9 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 14 \tabularnewline
p-value &  5.329e-10 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  3.923 \tabularnewline
Sum Squared Residuals &  215.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300159&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.976[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.9527[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.9459[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 140.9[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]14[/C][/ROW]
[ROW][C]p-value[/C][C] 5.329e-10[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 3.923[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 215.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300159&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300159&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	0.976
R-squared	0.9527
Adjusted R-squared	0.9459
F-TEST (value)	140.9
F-TEST (DF numerator)	2
F-TEST (DF denominator)	14
p-value	5.329e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.923
Sum Squared Residuals	215.5

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	101	95.83	5.17
2	100.1	97.03	3.071
3	100	97.78	2.219
4	90.6	93.52	-2.918
5	86.5	86.23	0.2718
6	89.7	92.88	-3.178
7	90.6	91.46	-0.8568
8	82.8	82.35	0.4532
9	70.1	67.56	2.543
10	65.4	64.94	0.4628
11	61.3	58.84	2.461
12	62.5	66.37	-3.874
13	63.6	70.16	-6.557
14	52.6	49.2	3.402
15	59.7	62.26	-2.558
16	59.5	65.3	-5.796
17	61.3	55.62	5.683

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  101 &  95.83 &  5.17 \tabularnewline
2 &  100.1 &  97.03 &  3.071 \tabularnewline
3 &  100 &  97.78 &  2.219 \tabularnewline
4 &  90.6 &  93.52 & -2.918 \tabularnewline
5 &  86.5 &  86.23 &  0.2718 \tabularnewline
6 &  89.7 &  92.88 & -3.178 \tabularnewline
7 &  90.6 &  91.46 & -0.8568 \tabularnewline
8 &  82.8 &  82.35 &  0.4532 \tabularnewline
9 &  70.1 &  67.56 &  2.543 \tabularnewline
10 &  65.4 &  64.94 &  0.4628 \tabularnewline
11 &  61.3 &  58.84 &  2.461 \tabularnewline
12 &  62.5 &  66.37 & -3.874 \tabularnewline
13 &  63.6 &  70.16 & -6.557 \tabularnewline
14 &  52.6 &  49.2 &  3.402 \tabularnewline
15 &  59.7 &  62.26 & -2.558 \tabularnewline
16 &  59.5 &  65.3 & -5.796 \tabularnewline
17 &  61.3 &  55.62 &  5.683 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300159&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] 101[/C][C] 95.83[/C][C] 5.17[/C][/ROW]
[ROW][C]2[/C][C] 100.1[/C][C] 97.03[/C][C] 3.071[/C][/ROW]
[ROW][C]3[/C][C] 100[/C][C] 97.78[/C][C] 2.219[/C][/ROW]
[ROW][C]4[/C][C] 90.6[/C][C] 93.52[/C][C]-2.918[/C][/ROW]
[ROW][C]5[/C][C] 86.5[/C][C] 86.23[/C][C] 0.2718[/C][/ROW]
[ROW][C]6[/C][C] 89.7[/C][C] 92.88[/C][C]-3.178[/C][/ROW]
[ROW][C]7[/C][C] 90.6[/C][C] 91.46[/C][C]-0.8568[/C][/ROW]
[ROW][C]8[/C][C] 82.8[/C][C] 82.35[/C][C] 0.4532[/C][/ROW]
[ROW][C]9[/C][C] 70.1[/C][C] 67.56[/C][C] 2.543[/C][/ROW]
[ROW][C]10[/C][C] 65.4[/C][C] 64.94[/C][C] 0.4628[/C][/ROW]
[ROW][C]11[/C][C] 61.3[/C][C] 58.84[/C][C] 2.461[/C][/ROW]
[ROW][C]12[/C][C] 62.5[/C][C] 66.37[/C][C]-3.874[/C][/ROW]
[ROW][C]13[/C][C] 63.6[/C][C] 70.16[/C][C]-6.557[/C][/ROW]
[ROW][C]14[/C][C] 52.6[/C][C] 49.2[/C][C] 3.402[/C][/ROW]
[ROW][C]15[/C][C] 59.7[/C][C] 62.26[/C][C]-2.558[/C][/ROW]
[ROW][C]16[/C][C] 59.5[/C][C] 65.3[/C][C]-5.796[/C][/ROW]
[ROW][C]17[/C][C] 61.3[/C][C] 55.62[/C][C] 5.683[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300159&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300159&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	101	95.83	5.17
2	100.1	97.03	3.071
3	100	97.78	2.219
4	90.6	93.52	-2.918
5	86.5	86.23	0.2718
6	89.7	92.88	-3.178
7	90.6	91.46	-0.8568
8	82.8	82.35	0.4532
9	70.1	67.56	2.543
10	65.4	64.94	0.4628
11	61.3	58.84	2.461
12	62.5	66.37	-3.874
13	63.6	70.16	-6.557
14	52.6	49.2	3.402
15	59.7	62.26	-2.558
16	59.5	65.3	-5.796
17	61.3	55.62	5.683

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 4.4505, df1 = 2, df2 = 12, p-value = 0.03582
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 8.3556, df1 = 4, df2 = 10, p-value = 0.003141
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 16.111, df1 = 2, df2 = 12, p-value = 0.0003992

\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 = 4.4505, df1 = 2, df2 = 12, p-value = 0.03582
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 8.3556, df1 = 4, df2 = 10, p-value = 0.003141
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 16.111, df1 = 2, df2 = 12, p-value = 0.0003992
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300159&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 = 4.4505, df1 = 2, df2 = 12, p-value = 0.03582
[/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 = 8.3556, df1 = 4, df2 = 10, p-value = 0.003141
[/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 = 16.111, df1 = 2, df2 = 12, p-value = 0.0003992
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300159&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300159&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 = 4.4505, df1 = 2, df2 = 12, p-value = 0.03582
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 8.3556, df1 = 4, df2 = 10, p-value = 0.003141
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 16.111, df1 = 2, df2 = 12, p-value = 0.0003992

Variance Inflation Factors (Multicollinearity)
> vif a b 1.00383 1.00383

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
      a       b 
1.00383 1.00383 
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300159&T=6

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]> vif
      a       b 
1.00383 1.00383 
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300159&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300159&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 a b 1.00383 1.00383

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ;

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