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Workshop 8, Multiple Regression

*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Mon, 29 Nov 2010 20:25:47 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j.htm/, Retrieved Mon, 29 Nov 2010 21:24:30 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
9 911 8 915 9 452 9 112 8 472 8 230 8 384 8 625 8 221 8 649 8 625 10 443 10 357 8 586 8 892 8 329 8 101 7 922 8 120 7 838 7 735 8 406 8 209 9 451
 
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 computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time15 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 10.7769305310332 -0.00142148930178946V2[t] -0.126224441924607M1[t] -1.42498067086984M2[t] -1.00092731366402M3[t] -1.60708946602567M4[t] -1.97763090471127M5[t] -2.03046948444693M6[t] -1.95539175083042M7[t] -1.73814736322608M8[t] -2.06285463383341M9[t] -1.45685064599854M10[t] -1.57828494644998M11[t] -0.0356402673962946t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)10.77693053103320.24709243.615100
V2-0.001421489301789460.000243-5.85040.0001628.1e-05
M1-0.1262244419246070.255499-0.4940.6319550.315978
M2-1.424980670869840.259282-5.49590.0002630.000132
M3-1.000927313664020.252254-3.96790.0026520.001326
M4-1.607089466025670.25074-6.40947.7e-053.9e-05
M5-1.977630904711270.245652-8.05051.1e-056e-06
M6-2.030469484446930.242539-8.37178e-064e-06
M7-1.955391750830420.243953-8.01551.2e-056e-06
M8-1.738147363226080.247601-7.023.6e-051.8e-05
M9-2.062854633833410.237094-8.70066e-063e-06
M10-1.456850645998540.237092-6.14470.0001095.5e-05
M11-1.578284946449980.236018-6.68715.5e-052.7e-05
t-0.03564026739629460.008022-4.44260.0012490.000625


Multiple Linear Regression - Regression Statistics
Multiple R0.979886770587539
R-squared0.960178083172476
Adjusted R-squared0.908409591296696
F-TEST (value)18.5475382492586
F-TEST (DF numerator)13
F-TEST (DF denominator)10
p-value2.8662040530536e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.235764201915993
Sum Squared Residuals0.555847589050849


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
199.32008906778208-0.320089067782082
287.98000661423340.0199933857665987
399.02656925077145-0.0265692507714503
498.868073193621920.131926806378075
587.950155338895820.0498446611041782
688.20567690279692-0.205676902796923
788.02620501654156-0.0262050165415588
887.865230215018350.134769784981654
988.07916435493766-0.0791643549376605
1088.04113065421035-0.0411306542103476
1187.918171829605560.0818281703944409
12109.719527561584930.280472438415074
13109.679910932217920.320089067782082
1488.0199933857666-0.0199933857665987
1587.973430749228550.0265692507714503
1688.13192680637808-0.131926806378075
1788.04984466110418-0.0498446611041783
1876.794323097203080.205676902796923
1987.973794983458440.0262050165415587
2077.13476978498165-0.134769784981654
2176.920835645062340.0791643549376605
2287.958869345789650.0411306542103477
2388.08182817039444-0.081828170394441
2499.28047243841507-0.280472438415074
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/1oc3x1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/1oc3x1291062331.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/2oc3x1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/2oc3x1291062331.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/3oc3x1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/3oc3x1291062331.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/4oc3x1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/4oc3x1291062331.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/5oc3x1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/5oc3x1291062331.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/6g32i1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/6g32i1291062331.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/79c2l1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/79c2l1291062331.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/89c2l1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/89c2l1291062331.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/99c2l1291062331.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291062261tk0noa4hvzwt32j/99c2l1291062331.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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