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Author

*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 22 Nov 2010 21:35:34 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/22/t1290461641hay6rm9z7if4cuv.htm/, Retrieved Fri, 03 May 2024 18:28:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98748, Retrieved Fri, 03 May 2024 18:28:32 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

172

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

-     [Multiple Regression] [Decreasing Compet...] [2010-11-17 09:04:39] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [WS 7 Maandinvloed?] [2010-11-22 21:35:34] [89d441ae0711e9b79b5d358f420c1317] [Current]
-    D      [Multiple Regression] [WS 7 Deterministi...] [2010-11-22 21:45:11] [18fa53e8b37a5effc0c5f8a5122cdd2d] 

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Dataseries X:

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Histogram

Boxplots

9	24	14	11	12	24	26
9	25	11	7	8	25	23
9	17	6	17	8	30	25
9	18	12	10	8	19	23
9	18	8	12	9	22	19
9	16	10	12	7	22	29
9	20	10	11	4	25	25
9	16	11	11	11	23	21
9	18	16	12	7	17	22
9	17	11	13	7	21	25
9	23	13	14	12	19	24
9	30	12	16	10	19	18
9	23	8	11	10	15	22
9	18	12	10	8	16	15
9	15	11	11	8	23	22
9	12	4	15	4	27	28
9	21	9	9	9	22	20
9	15	8	11	8	14	12
9	20	8	17	7	22	24
9	31	14	17	11	23	20
9	27	15	11	9	23	21
9	34	16	18	11	21	20
9	21	9	14	13	19	21
9	31	14	10	8	18	23
9	19	11	11	8	20	28
9	16	8	15	9	23	24
9	20	9	15	6	25	24
9	21	9	13	9	19	24
9	22	9	16	9	24	23
9	17	9	13	6	22	23
9	24	10	9	6	25	29
9	25	16	18	16	26	24
9	26	11	18	5	29	18
9	25	8	12	7	32	25
9	17	9	17	9	25	21
9	32	16	9	6	29	26
9	33	11	9	6	28	22
9	13	16	12	5	17	22
9	32	12	18	12	28	22
9	25	12	12	7	29	23
9	29	14	18	10	26	30
9	22	9	14	9	25	23
9	18	10	15	8	14	17
9	17	9	16	5	25	23
9	20	10	10	8	26	23
9	15	12	11	8	20	25
9	20	14	14	10	18	24
9	33	14	9	6	32	24
9	29	10	12	8	25	23
9	23	14	17	7	25	21
9	26	16	5	4	23	24
9	18	9	12	8	21	24
9	20	10	12	8	20	28
9	11	6	6	4	15	16
9	28	8	24	20	30	20
9	26	13	12	8	24	29
9	22	10	12	8	26	27
9	17	8	14	6	24	22
9	12	7	7	4	22	28
9	14	15	13	8	14	16
9	17	9	12	9	24	25
9	21	10	13	6	24	24
9	19	12	14	7	24	28
9	18	13	8	9	24	24
9	10	10	11	5	19	23
9	29	11	9	5	31	30
9	31	8	11	8	22	24
9	19	9	13	8	27	21
9	9	13	10	6	19	25
9	20	11	11	8	25	25
9	28	8	12	7	20	22
9	19	9	9	7	21	23
9	30	9	15	9	27	26
9	29	15	18	11	23	23
9	26	9	15	6	25	25
9	23	10	12	8	20	21
9	13	14	13	6	21	25
9	21	12	14	9	22	24
9	19	12	10	8	23	29
9	28	11	13	6	25	22
9	23	14	13	10	25	27
9	18	6	11	8	17	26
9	21	12	13	8	19	22
9	20	8	16	10	25	24
9	23	14	8	5	19	27
9	21	11	16	7	20	24
9	21	10	11	5	26	24
9	15	14	9	8	23	29
9	28	12	16	14	27	22
9	19	10	12	7	17	21
9	26	14	14	8	17	24
9	10	5	8	6	19	24
9	16	11	9	5	17	23
9	22	10	15	6	22	20
9	19	9	11	10	21	27
9	31	10	21	12	32	26
9	31	16	14	9	21	25
9	29	13	18	12	21	21
9	19	9	12	7	18	21
9	22	10	13	8	18	19
9	23	10	15	10	23	21
9	15	7	12	6	19	21
9	20	9	19	10	20	16
9	18	8	15	10	21	22
9	23	14	11	10	20	29
9	25	14	11	5	17	15
9	21	8	10	7	18	17
9	24	9	13	10	19	15
9	25	14	15	11	22	21
9	17	14	12	6	15	21
9	13	8	12	7	14	19
9	28	8	16	12	18	24
9	21	8	9	11	24	20
9	25	7	18	11	35	17
9	9	6	8	11	29	23
9	16	8	13	5	21	24
9	19	6	17	8	25	14
9	17	11	9	6	20	19
9	25	14	15	9	22	24
9	20	11	8	4	13	13
9	29	11	7	4	26	22
9	14	11	12	7	17	16
9	22	14	14	11	25	19
9	15	8	6	6	20	25
9	19	20	8	7	19	25
9	20	11	17	8	21	23
9	15	8	10	4	22	24
9	20	11	11	8	24	26
9	18	10	14	9	21	26
9	33	14	11	8	26	25
9	22	11	13	11	24	18
9	16	9	12	8	16	21
9	17	9	11	5	23	26
9	16	8	9	4	18	23
9	21	10	12	8	16	23
9	26	13	20	10	26	22
9	18	13	12	6	19	20
9	18	12	13	9	21	13
9	17	8	12	9	21	24
9	22	13	12	13	22	15
9	30	14	9	9	23	14
9	30	12	15	10	29	22
9	24	14	24	20	21	10
9	21	15	7	5	21	24
9	21	13	17	11	23	22
9	29	16	11	6	27	24
9	31	9	17	9	25	19
9	20	9	11	7	21	20
9	16	9	12	9	10	13
9	22	8	14	10	20	20
9	20	7	11	9	26	22
9	28	16	16	8	24	24
9	38	11	21	7	29	29
9	22	9	14	6	19	12
9	20	11	20	13	24	20
9	17	9	13	6	19	21
9	28	14	11	8	24	24
9	22	13	15	10	22	22
9	31	16	19	16	17	20

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98748&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98748&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98748&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	'George Udny Yule' @ 72.249.76.132

Figure 1

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Figure 3

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Figure 6

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Figure 7

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Figure 9

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Figure 10

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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