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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 16:36:29 +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/t1293037260j2dppatwtxlj26l.htm/, Retrieved Sun, 05 May 2024 21:21:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114409, Retrieved Sun, 05 May 2024 21:21:22 +0000

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No (this computation is public)

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Estimated Impact

165

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

-       [Multiple Regression] [bonus - MR log P] [2010-12-22 16:36:29] [e569a00cc6e8044e6afea1f18dd335a0] [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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132
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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \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=114409&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/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=114409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114409&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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132
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 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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