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*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 22 Dec 2010 16:34:21 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t1293035557qt5hwers4w6k7r7.htm/, Retrieved Mon, 06 May 2024 08:18:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114374, Retrieved Mon, 06 May 2024 08:18:02 +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] [bonus - SWS MR] [2010-12-22 16:34:21] [54d0a09f418287eaabab8ba43e4b06f8] [Current]

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NA	NA	0,52	6,82	6,76	2,81	3,00	5,00	3,00
6,30	0,30	0,92	3,00	3,82	1,62	3,00	1,00	3,00
NA	NA	1,10	3,53	4,65	1,78	1,00	1,00	1,00
NA	NA	1,22	-0,04	3,76	1,40	5,00	2,00	3,00
2,10	0,26	0,59	6,41	6,66	2,80	3,00	5,00	4,00
9,10	-0,15	0,99	4,02	5,25	2,26	4,00	4,00	4,00
15,80	0,59	1,29	-1,64	-0,52	1,54	1,00	1,00	1,00
5,20	0,00	0,79	5,20	5,23	2,59	4,00	5,00	4,00
10,90	0,56	1,16	3,52	4,41	1,80	1,00	2,00	1,00
8,30	0,15	0,99	4,72	5,64	2,36	1,00	1,00	1,00
11,00	0,18	1,10	-0,37	3,81	2,05	5,00	4,00	4,00
3,20	-0,15	0,59	5,67	5,63	2,45	5,00	5,00	5,00
7,60	0,43	1,01	-0,26	3,38	NA	2,00	1,00	2,00
NA	NA	0,49	5,27	5,62	2,56	5,00	5,00	5,00
6,30	0,32	0,92	-1,12	3,08	1,62	1,00	1,00	1,00
8,60	NA	0,93	3,48	4,40	1,45	2,00	2,00	2,00
6,60	0,61	1,03	-0,11	3,54	1,62	2,00	2,00	2,00
9,50	0,08	1,03	-0,70	3,70	2,08	2,00	2,00	2,00
4,80	0,11	0,79	3,15	4,24	NA	1,00	2,00	1,00
12,00	0,79	1,26	4,78	4,91	NA	1,00	1,00	1,00
NA	-0,52	NA	5,72	5,83	2,60	5,00	5,00	5,00
3,30	-0,30	0,58	4,44	5,06	2,17	5,00	5,00	5,00
11,00	0,53	1,16	-0,92	3,00	1,20	3,00	1,00	2,00
NA	NA	1,08	5,32	5,61	2,40	1,00	4,00	1,00
4,70	0,18	0,79	4,93	5,51	2,49	1,00	3,00	1,00
NA	NA	1,11	4,56	5,08	1,80	1,00	1,00	1,00
10,40	0,53	1,14	-1,00	3,60	1,45	5,00	1,00	3,00
7,40	-0,10	0,91	3,02	3,74	1,83	5,00	3,00	4,00
2,10	-0,10	0,46	5,72	5,82	2,53	5,00	5,00	5,00
NA	NA	1,03	5,00	5,20	2,00	1,00	1,00	1,00
NA	NA	NA	4,54	4,75	1,52	3,00	5,00	4,00
7,70	0,15	0,96	-2,30	-0,85	1,33	5,00	2,00	4,00
17,90	0,30	1,30	-2,00	-0,60	1,70	1,00	1,00	1,00
6,10	0,28	0,90	4,79	6,12	2,43	1,00	1,00	1,00
8,20	0,38	1,03	-0,91	3,48	1,48	2,00	1,00	1,00
8,40	0,45	1,05	3,13	3,91	1,65	3,00	1,00	3,00
11,90	0,11	1,12	-1,64	-0,40	1,28	4,00	1,00	3,00
10,80	0,30	1,11	-1,32	-0,48	1,48	4,00	1,00	3,00
13,80	0,75	1,29	3,23	3,80	1,08	2,00	1,00	1,00
14,30	0,49	1,24	3,54	4,03	2,08	2,00	1,00	1,00
NA	0,00	NA	5,40	5,69	2,64	5,00	5,00	5,00
15,20	0,26	1,23	-0,32	4,19	2,15	2,00	2,00	2,00
10,00	-0,05	1,04	4,00	5,06	2,23	4,00	4,00	4,00
11,90	0,26	1,14	3,21	4,06	1,23	2,00	1,00	2,00
6,50	0,28	0,92	5,28	5,26	2,06	4,00	4,00	4,00
7,50	-0,05	0,92	3,40	4,08	1,49	5,00	5,00	5,00
NA	NA	1,10	3,63	4,59	1,80	2,00	2,00	2,00
10,60	0,41	1,12	-0,55	3,28	1,32	3,00	1,00	3,00
7,40	0,38	0,99	3,63	4,70	1,72	1,00	1,00	1,00
8,40	0,08	0,98	3,83	5,25	2,21	2,00	3,00	2,00
5,70	-0,05	0,82	-0,12	4,09	2,35	2,00	2,00	2,00
4,90	-0,30	0,73	3,56	4,32	2,35	3,00	2,00	3,00
NA	NA	0,41	4,17	4,99	2,18	5,00	5,00	5,00
3,20	-0,22	0,58	4,74	5,24	2,18	5,00	5,00	5,00
NA	NA	1,04	3,15	4,10	1,95	2,00	2,00	2,00
8,10	0,34	1,01	-1,22	3,00	NA	3,00	1,00	2,00
11,00	0,36	1,12	-0,05	3,41	1,78	2,00	1,00	2,00
4,90	-0,30	0,73	3,30	4,09	2,30	3,00	1,00	3,00
13,20	0,41	1,20	-0,98	3,40	1,66	3,00	2,00	2,00
9,70	-0,22	1,01	3,62	4,76	2,32	4,00	3,00	4,00
12,80	0,82	1,29	3,54	3,59	1,15	2,00	1,00	1,00
NA	NA	NA	3,61	4,23	1,58	3,00	1,00	1,00

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk
R Engine error message	Error in if (gqarr[mypoint - kp3 + 1, 2] < 0.01) numsignificant1 <- numsignificant1 + : missing value where TRUE/FALSE needed Execution halted

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
R Engine error message & Error in if (gqarr[mypoint - kp3 + 1, 2] < 0.01) numsignificant1 <- numsignificant1 +  : 
  missing value where TRUE/FALSE needed
Execution halted
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114374&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[ROW][C]R Engine error message[/C][C]Error in if (gqarr[mypoint - kp3 + 1, 2] < 0.01) numsignificant1 <- numsignificant1 +  : 
  missing value where TRUE/FALSE needed
Execution halted
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114374&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk
R Engine error message	Error in if (gqarr[mypoint - kp3 + 1, 2] < 0.01) numsignificant1 <- numsignificant1 + : missing value where TRUE/FALSE needed Execution halted

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code