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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, 20 Nov 2012 07:10:00 -0500

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/2012/Nov/20/t1353413413mqv3hmlfuk3ejsj.htm/, Retrieved Mon, 29 Apr 2024 17:45:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=190991, Retrieved Mon, 29 Apr 2024 17:45:00 +0000

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No (this computation is public)

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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] [gg] [2012-11-20 12:10:00] [2715be8b6e97cdb2c6fe0b5c822d3851] [Current]

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Dataseries X:

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Histogram

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101.8	87.6	94.8	92.3
106.6	87.8	95.8	93.2
115.6	88.0	95.1	93.3
108.1	88.0	95.3	93.0
115.8	88.5	97.0	94.5
98.0	88.2	98.4	94.3
91.4	87.4	96.9	92.8
101.3	87.0	95.7	92.5
105.9	87.7	94.5	92.4
105.1	86.6	92.7	90.9
104.7	85.8	92.6	90.5
104.3	85.2	91.5	89.6
102.8	86.4	92.2	90.4
102.5	86.3	93.1	90.8
112.3	87.0	94.6	92.4
100.8	88.0	93.2	91.5
103.7	88.1	93.4	91.8
94.4	87.9	92.9	90.9
86.6	87.9	92.3	90.2
89.9	88.3	93.4	91.2
102.0	89.7	94.0	92.7
99.7	90.4	93.8	92.8
99.9	89.5	92.4	91.6
101.6	90.2	93.8	92.7
97.0	88.5	93.1	91.4
99.9	89.3	93.9	92.4
106.5	89.6	94.1	92.9
96.2	88.7	92.0	90.9
100.0	87.8	89.7	89.5
107.9	87.8	93.2	91.8
109.4	88.0	89.0	89.6
102.0	88.2	92.3	91.1
108.3	88.4	94.4	92.7
106.3	88.4	88.9	89.6
105.6	88.5	94.7	92.8
103.3	88.3	89.5	89.7
108.9	89.4	88.2	89.7
116.1	89.3	90.7	91.4
103.3	90.4	92.3	92.1
101.3	92.1	95.0	94.2
101.4	93.8	93.2	93.8
111.5	94.4	96.5	96.4
101.8	94.9	95.4	95.6
91.7	96.3	94.5	95.1
95.3	97.2	97.4	97.2
93.6	99.2	94.8	96.5
99.3	99.0	97.3	98.1
101.2	99.0	92.4	95.5
91.4	98.5	95.0	96.3
92.8	98.6	97.4	97.6
94.6	99.2	102.0	100.5
87.7	99.0	97.8	97.8
97.8	98.9	96.5	97.5
91.0	99.5	99.7	99.2
91.2	100.3	100.3	99.8
99.7	100.2	103.1	101.8
92.9	101.5	101.9	101.2
93.8	101.9	101.2	101.1
98.1	101.0	103.7	102.4
100.7	101.3	101.5	101.4
100.8	104.2	105.5	104.7
107.8	104.6	105.6	105.3
108.4	105.1	106.2	105.9
109.0	105.7	104.7	105.3
114.7	105.9	104.7	105.7
109.0	107.0	103.4	105.2
104.2	106.9	103.7	105.0
120.7	106.2	109.1	108.5
106.1	106.2	108.0	107.2
106.4	105.6	102.7	104.1
109.8	106.0	107.1	106.8
116.0	105.9	102.7	104.7
120.9	106.3	104.0	105.8
122.1	106.6	104.5	106.2
119.5	106.8	108.5	108.4
123.1	106.8	105.2	106.7
126.9	107.0	104.8	106.8
109.2	107.1	107.1	107.2
108.7	107.4	107.4	107.4
109.6	107.4	109.6	108.7
113.8	108.0	111.1	110.0
116.1	109.0	111.3	110.6
116.9	111.1	114.0	113.0
119.5	112.0	110.9	111.7
121.0	114.1	109.6	111.9
124.0	115.7	111.2	113.6
122.4	117.2	113.3	115.3
119.5	117.6	113.0	115.2
121.2	118.9	110.8	114.5
117.2	120.5	116.8	118.3
116.9	121.5	117.3	118.9
111.0	120.3	117.1	118.1
109.8	120.6	117.8	118.5
109.4	119.4	114.1	116.0
106.0	117.0	113.0	114.3
109.1	113.5	107.0	109.7
112.9	112.3	105.6	108.6
107.5	110.3	105.8	107.7
107.2	108.2	105.6	106.7
104.6	108.1	101.6	104.3
105.3	108.6	100.8	104.1
99.5	109.1	101.6	104.5
92.6	108.9	101.8	104.1
93.5	109.8	101.9	104.6
94.5	109.2	104.0	105.6
92.7	109.5	101.7	104.3
96.8	110.3	101.6	104.8
101.0	110.5	103.6	106.3
104.4	111.5	106.6	108.5
105.1	112.4	107.5	109.3
106.9	113.6	110.0	111.2
106.4	114.4	110.7	111.9
109.5	115.1	112.0	113.1
104.5	115.5	113.9	114.1
98.3	115.6	114.3	114.0
112.2	116.3	115.1	115.4
112.2	117.2	115.8	116.2
106.0	117.4	116.9	116.5
116.7	117.8	115.5	116.5
121.7	119.2	118.4	118.9
121.4	121.5	120.1	120.7
119.4	123.8	120.4	121.7
112.5	125.1	121.4	122.5
114.8	126.5	122.3	123.6
114.4	126.2	122.5	123.6
119.3	125.9	123.2	124.1
106.4	125.4	122.2	122.7
106.6	124.6	123.0	122.8
104.6	125.3	123.1	123.1
100.7	124.7	123.0	122.6
110.9	124.5	126.4	124.9
116.2	124.6	123.9	123.8
110.7	125.8	123.1	123.6
121.7	128.3	127.4	127.5
123.7	128.6	128.8	128.4
119.9	129.0	126.0	126.9
120.8	129.4	126.0	127.1
109.1	129.2	124.8	125.8
NA	128.7	125.5	NA
NA	128.7	NA	NA
NA	129.2	NA	NA

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	'Gwilym Jenkins' @ jenkins.wessa.net
R Engine error message	Error in array(list(101.8, 87.6, 94.8, 92.3, 106.6, 87.8, 95.8, 93.2, : length of 'dimnames' [1] not equal to array extent 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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Engine error message & Error in array(list(101.8, 87.6, 94.8, 92.3, 106.6, 87.8, 95.8, 93.2,  : 
  length of 'dimnames' [1] not equal to array extent
Execution halted
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190991&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Engine error message[/C][C]Error in array(list(101.8, 87.6, 94.8, 92.3, 106.6, 87.8, 95.8, 93.2,  : 
  length of 'dimnames' [1] not equal to array extent
Execution halted
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190991&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190991&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	'Gwilym Jenkins' @ jenkins.wessa.net
R Engine error message	Error in array(list(101.8, 87.6, 94.8, 92.3, 106.6, 87.8, 95.8, 93.2, : length of 'dimnames' [1] not equal to array extent Execution halted

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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