Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 11 Nov 2014 09:13:11 +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/2014/Nov/11/t1415697216cpzkriicdhy7g9n.htm/, Retrieved Sun, 19 May 2024 19:08:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=253520, Retrieved Sun, 19 May 2024 19:08:57 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

108

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

-       [Multiple Regression] [] [2014-11-11 09:13:11] [578aae52f3152e8435e37fe3b2f57a45] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

41 38 13 12 14
39 32 16 11 18
30 35 19 15 11
31 33 15 6 12
34 37 14 13 16
35 29 13 10 18
39 31 19 12 14
34 36 15 14 14
36 35 14 12 15
37 38 15 9 15
38 31 16 10 17
36 34 16 12 19
38 35 16 12 10
39 38 16 11 16
33 37 17 15 18
32 33 15 12 14
36 32 15 10 14
38 38 20 12 17
39 38 18 11 14
32 32 16 12 16
32 33 16 11 18
31 31 16 12 11
39 38 19 13 14
37 39 16 11 12
39 32 17 12 17
41 32 17 13 9
36 35 16 10 16
33 37 15 14 14
33 33 16 12 15
34 33 14 10 11
31 31 15 12 16
27 32 12 8 13
37 31 14 10 17
34 37 16 12 15
34 30 14 12 14
32 33 10 7 16
29 31 10 9 9
36 33 14 12 15
29 31 16 10 17
35 33 16 10 13
37 32 16 10 15
34 33 14 12 16
38 32 20 15 16
35 33 14 10 12
38 28 14 10 15
37 35 11 12 11
38 39 14 13 15
33 34 15 11 15
36 38 16 11 17
38 32 14 12 13
32 38 16 14 16
32 30 14 10 14
32 33 12 12 11
34 38 16 13 12
32 32 9 5 12
37 35 14 6 15
39 34 16 12 16
29 34 16 12 15
37 36 15 11 12
35 34 16 10 12
30 28 12 7 8
38 34 16 12 13
34 35 16 14 11
31 35 14 11 14
34 31 16 12 15
35 37 17 13 10
36 35 18 14 11
30 27 18 11 12
39 40 12 12 15
35 37 16 12 15
38 36 10 8 14
31 38 14 11 16
34 39 18 14 15
38 41 18 14 15
34 27 16 12 13
39 30 17 9 12
37 37 16 13 17
34 31 16 11 13
28 31 13 12 15
37 27 16 12 13
33 36 16 12 15
35 37 16 12 15
37 33 15 12 16
32 34 15 11 15
33 31 16 10 14
38 39 14 9 15
33 34 16 12 14
29 32 16 12 13
33 33 15 12 7
31 36 12 9 17
36 32 17 15 13
35 41 16 12 15
32 28 15 12 14
29 30 13 12 13
39 36 16 10 16
37 35 16 13 12
35 31 16 9 14
37 34 16 12 17
32 36 14 10 15
38 36 16 14 17
37 35 16 11 12
36 37 20 15 16
32 28 15 11 11
33 39 16 11 15
40 32 13 12 9
38 35 17 12 16
41 39 16 12 15
36 35 16 11 10
43 42 12 7 10
30 34 16 12 15
31 33 16 14 11
32 41 17 11 13
32 33 13 11 14
37 34 12 10 18
37 32 18 13 16
33 40 14 13 14
34 40 14 8 14
33 35 13 11 14
38 36 16 12 14
33 37 13 11 12
31 27 16 13 14
38 39 13 12 15
37 38 16 14 15
36 31 15 13 15
31 33 16 15 13
39 32 15 10 17
44 39 17 11 17
33 36 15 9 19
35 33 12 11 15
32 33 16 10 13
28 32 10 11 9
40 37 16 8 15
27 30 12 11 15
37 38 14 12 15
32 29 15 12 16
28 22 13 9 11
34 35 15 11 14
30 35 11 10 11
35 34 12 8 15
31 35 11 9 13
32 34 16 8 15
30 37 15 9 16
30 35 17 15 14
31 23 16 11 15
40 31 10 8 16
32 27 18 13 16
36 36 13 12 11
32 31 16 12 12
35 32 13 9 9
38 39 10 7 16
42 37 15 13 13
34 38 16 9 16
35 39 16 6 12
38 34 14 8 9
33 31 10 8 13
36 32 17 15 13
32 37 13 6 14
33 36 15 9 19
34 32 16 11 13
32 38 12 8 12
34 36 13 8 13
27 26 13 10 10
31 26 12 8 14
38 33 17 14 16
34 39 15 10 10
24 30 10 8 11
30 33 14 11 14
26 25 11 12 12
34 38 13 12 9
27 37 16 12 9
37 31 12 5 11
36 37 16 12 16
41 35 12 10 9
29 25 9 7 13
36 28 12 12 16
32 35 15 11 13
37 33 12 8 9
30 30 12 9 12
31 31 14 10 16
38 37 12 9 11
36 36 16 12 14
35 30 11 6 13
31 36 19 15 15
38 32 15 12 14
22 28 8 12 16
32 36 16 12 13
36 34 17 11 14
39 31 12 7 15
28 28 11 7 13
32 36 11 5 11
32 36 14 12 11
38 40 16 12 14
32 33 12 3 15
35 37 16 11 11
32 32 13 10 15
37 38 15 12 12
34 31 16 9 14
33 37 16 12 14
33 33 14 9 8
26 32 16 12 13
30 30 16 12 9
24 30 14 10 15
34 31 11 9 17
34 32 12 12 13
33 34 15 8 15
34 36 15 11 15
35 37 16 11 14
35 36 16 12 16
36 33 11 10 13
34 33 15 10 16
34 33 12 12 9
41 44 12 12 16
32 39 15 11 11
30 32 15 8 10
35 35 16 12 11
28 25 14 10 15
33 35 17 11 17
39 34 14 10 14
36 35 13 8 8
36 39 15 12 15
35 33 13 12 11
38 36 14 10 16
33 32 15 12 10
31 32 12 9 15
34 36 13 9 9
32 36 8 6 16
31 32 14 10 19
33 34 14 9 12
34 33 11 9 8
34 35 12 9 11
34 30 13 6 14
33 38 10 10 9
32 34 16 6 15
41 33 18 14 13
34 32 13 10 16
36 31 11 10 11
37 30 4 6 12
36 27 13 12 13
29 31 16 12 10
37 30 10 7 11
27 32 12 8 12
35 35 12 11 8
28 28 10 3 12
35 33 13 6 12
37 31 15 10 15
29 35 12 8 11
32 35 14 9 13
36 32 10 9 14
19 21 12 8 10
21 20 12 9 12
31 34 11 7 15
33 32 10 7 13
36 34 12 6 13
33 32 16 9 13
37 33 12 10 12
34 33 14 11 12
35 37 16 12 9
31 32 14 8 9
37 34 13 11 15
35 30 4 3 10
27 30 15 11 14
34 38 11 12 15
40 36 11 7 7
29 32 14 9 14

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	'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.
R Engine error message	Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 0 (non-NA) cases Calls: lm -> lm.fit In addition: Warning messages: 1: In model.matrix.default(mt, mf, contrasts) : the response appeared on the right-hand side and was dropped 2: In model.matrix.default(mt, mf, contrasts) : problem with term 1 in model.matrix: no columns are assigned 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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
R Engine error message & Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases
Calls: lm -> lm.fit
In addition: Warning messages:
1: In model.matrix.default(mt, mf, contrasts) :
  the response appeared on the right-hand side and was dropped
2: In model.matrix.default(mt, mf, contrasts) :
  problem with term 1 in model.matrix: no columns are assigned
Execution halted
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=253520&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[ROW][C]R Engine error message[/C][C]Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases
Calls: lm -> lm.fit
In addition: Warning messages:
1: In model.matrix.default(mt, mf, contrasts) :
  the response appeared on the right-hand side and was dropped
2: In model.matrix.default(mt, mf, contrasts) :
  problem with term 1 in model.matrix: no columns are assigned
Execution halted
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=253520&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=253520&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	'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.
R Engine error message	Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 0 (non-NA) cases Calls: lm -> lm.fit In addition: Warning messages: 1: In model.matrix.default(mt, mf, contrasts) : the response appeared on the right-hand side and was dropped 2: In model.matrix.default(mt, mf, contrasts) : problem with term 1 in model.matrix: no columns are assigned Execution halted

Parameters (Session):

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

Parameters (R input):

par1 = ; 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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,signif(mysum$coefficients[i,1],6))
a<-table.element(a, signif(mysum$coefficients[i,2],6))
a<-table.element(a, signif(mysum$coefficients[i,3],4))
a<-table.element(a, signif(mysum$coefficients[i,4],6))
a<-table.element(a, signif(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, signif(sqrt(mysum$r.squared),6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, signif(mysum$r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, signif(mysum$adj.r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[1],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$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$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6))
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, signif(mysum$sigma,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, signif(sum(myerror*myerror),6))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,signif(x[i],6))
a<-table.element(a,signif(x[i]-mysum$resid[i],6))
a<-table.element(a,signif(mysum$resid[i],6))
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,signif(gqarr[mypoint-kp3+1,1],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6))
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,signif(numsignificant1/numgqtests,6))
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