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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 21 Nov 2007 05:23:09 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/21/t1195647339k571gm9s1or6go7.htm/, Retrieved Wed, 21 Nov 2007 13:15:40 +0100
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.44 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.57 0 1.58 0 1.58 0 1.58 0 1.58 0 1.59 1 1.6 1 1.6 1 1.61 1 1.61 1 1.61 1 1.62 1 1.63 1 1.63 1 1.64 1 1.64 1 1.64 1 1.64 1 1.64 1 1.65 1 1.65 1 1.65 1 1.65 1
 
Text written by user:
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
x[t] = + 1.47166666666667 + 0.156111111111111y[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.471666666666670.005083289.530600
y0.1561111111111110.01016615.356400


Multiple Linear Regression - Regression Statistics
Multiple R0.878126429243398
R-squared0.771106025735761
Adjusted R-squared0.7678361118177
F-TEST (value)235.818448148359
F-TEST (DF numerator)1
F-TEST (DF denominator)70
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0373518236523831
Sum Squared Residuals0.097661111111111


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.431.47166666666666-0.0416666666666631
21.431.47166666666667-0.0416666666666669
31.431.47166666666667-0.0416666666666668
41.431.47166666666667-0.0416666666666668
51.431.47166666666667-0.0416666666666668
61.431.47166666666667-0.0416666666666668
71.431.47166666666667-0.0416666666666668
81.431.47166666666667-0.0416666666666668
91.431.47166666666667-0.0416666666666668
101.431.47166666666667-0.0416666666666668
111.431.47166666666667-0.0416666666666668
121.431.47166666666667-0.0416666666666668
131.431.47166666666667-0.0416666666666668
141.431.47166666666667-0.0416666666666668
151.431.47166666666667-0.0416666666666668
161.431.47166666666667-0.0416666666666668
171.431.47166666666667-0.0416666666666668
181.431.47166666666667-0.0416666666666668
191.441.47166666666667-0.0316666666666668
201.481.471666666666670.00833333333333328
211.481.471666666666670.00833333333333328
221.481.471666666666670.00833333333333328
231.481.471666666666670.00833333333333328
241.481.471666666666670.00833333333333328
251.481.471666666666670.00833333333333328
261.481.471666666666670.00833333333333328
271.481.471666666666670.00833333333333328
281.481.471666666666670.00833333333333328
291.481.471666666666670.00833333333333328
301.481.471666666666670.00833333333333328
311.481.471666666666670.00833333333333328
321.481.471666666666670.00833333333333328
331.481.471666666666670.00833333333333328
341.481.471666666666670.00833333333333328
351.481.471666666666670.00833333333333328
361.481.471666666666670.00833333333333328
371.481.471666666666670.00833333333333328
381.481.471666666666670.00833333333333328
391.481.471666666666670.00833333333333328
401.481.471666666666670.00833333333333328
411.481.471666666666670.00833333333333328
421.481.471666666666670.00833333333333328
431.481.471666666666670.00833333333333328
441.481.471666666666670.00833333333333328
451.481.471666666666670.00833333333333328
461.481.471666666666670.00833333333333328
471.481.471666666666670.00833333333333328
481.481.471666666666670.00833333333333328
491.481.471666666666670.00833333333333328
501.571.471666666666670.0983333333333333
511.581.471666666666670.108333333333333
521.581.471666666666670.108333333333333
531.581.471666666666670.108333333333333
541.581.471666666666670.108333333333333
551.591.62777777777778-0.0377777777777777
561.61.62777777777778-0.0277777777777777
571.61.62777777777778-0.0277777777777777
581.611.62777777777778-0.0177777777777777
591.611.62777777777778-0.0177777777777777
601.611.62777777777778-0.0177777777777777
611.621.62777777777778-0.00777777777777766
621.631.627777777777780.00222222222222215
631.631.627777777777780.00222222222222215
641.641.627777777777780.0122222222222222
651.641.627777777777780.0122222222222222
661.641.627777777777780.0122222222222222
671.641.627777777777780.0122222222222222
681.641.627777777777780.0122222222222222
691.651.627777777777780.0222222222222222
701.651.627777777777780.0222222222222222
711.651.627777777777780.0222222222222222
721.651.627777777777780.0222222222222222
 
Charts produced by software:
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Parameters:
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
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))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$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$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
 





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Software written by Ed van Stee & Patrick Wessa


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