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SHW paper

*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: Sun, 06 Dec 2009 05:38:48 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d.htm/, Retrieved Sun, 06 Dec 2009 13:42:55 +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/2009/Dec/06/t1260103363h7k29j70wet1j1d.htm/},
    year = {2009},
}
@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 = {2009},
    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 «
8,9 0 8,8 0 8,3 0 7,5 0 7,2 0 7,4 0 8,8 0 9,3 0 9,3 0 8,7 0 8,2 0 8,3 0 8,5 0 8,6 0 8,5 0 8,2 0 8,1 0 7,9 0 8,6 0 8,7 0 8,7 0 8,5 0 8,4 0 8,5 0 8,7 0 8,7 0 8,6 0 8,5 0 8,3 0 8 0 8,2 0 8,1 0 8,1 0 8 0 7,9 0 7,9 0 8 0 8 0 7,9 0 8 0 7,7 0 7,2 0 7,5 0 7,3 0 7 0 7 0 7 0 7,2 0 7,3 1 7,1 1 6,8 1 6,4 1 6,1 1 6,5 1 7,7 1 7,9 1 7,5 1 6,9 1 6,6 1 6,9 1
 
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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 8.72 -0.437500000000001X[t] + 0.253402777777773M1[t] + 0.237638888888889M2[t] + 0.0418750000000011M3[t] -0.233888888888888M4[t] -0.449652777777777M5[t] -0.505416666666666M6[t] + 0.278819444444445M7[t] + 0.403055555555556M8[t] + 0.287291666666667M9[t] + 0.0115277777777778M10[t] -0.164236111111111M11[t] -0.0242361111111111t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)8.720.24682435.328800
X-0.4375000000000010.202888-2.15640.0363180.018159
M10.2534027777777730.2860090.8860.3802280.190114
M20.2376388888888890.2851680.83330.4089660.204483
M30.04187500000000110.2844050.14720.8835880.441794
M4-0.2338888888888880.283721-0.82440.4139880.206994
M5-0.4496527777777770.283116-1.58820.1190850.059543
M6-0.5054166666666660.28259-1.78850.080280.04014
M70.2788194444444450.2821450.98820.3282180.164109
M80.4030555555555560.281781.43040.1593630.079681
M90.2872916666666670.2814961.02060.3127870.156393
M100.01152777777777780.2812930.0410.9674880.483744
M11-0.1642361111111110.281171-0.58410.5619960.280998
t-0.02423611111111110.004782-5.06817e-063e-06


Multiple Linear Regression - Regression Statistics
Multiple R0.849220859124403
R-squared0.72117606757199
Adjusted R-squared0.6423779997119
F-TEST (value)9.15220496081801
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value6.96668389643662e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.444505506071113
Sum Squared Residuals9.08891666666667


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.98.94916666666669-0.0491666666666857
28.88.90916666666667-0.109166666666665
38.38.68916666666667-0.389166666666665
47.58.38916666666666-0.889166666666665
57.28.14916666666667-0.949166666666666
67.48.06916666666667-0.669166666666665
78.88.82916666666667-0.0291666666666649
89.38.929166666666670.370833333333336
99.38.789166666666660.510833333333335
108.78.489166666666670.210833333333334
118.28.28916666666666-0.089166666666666
128.38.42916666666667-0.129166666666665
138.58.65833333333333-0.158333333333328
148.68.61833333333333-0.0183333333333327
158.58.398333333333330.101666666666667
168.28.098333333333330.101666666666666
178.17.858333333333330.241666666666666
187.97.778333333333330.121666666666667
198.68.538333333333330.0616666666666667
208.78.638333333333330.0616666666666663
218.78.498333333333330.201666666666666
228.58.198333333333330.301666666666667
238.47.998333333333330.401666666666668
248.58.138333333333330.361666666666667
258.78.36750.332500000000004
268.78.32750.372499999999999
278.68.10750.492499999999999
288.57.80750.6925
298.37.56750.7325
3087.48750.5125
318.28.2475-0.0475000000000008
328.18.3475-0.247500000000001
338.18.2075-0.107500000000000
3487.90750.0924999999999999
357.97.70750.1925
367.97.84750.0525000000000001
3788.07666666666666-0.0766666666666623
3888.03666666666667-0.0366666666666675
397.97.816666666666670.0833333333333324
4087.516666666666670.483333333333333
417.77.276666666666670.423333333333332
427.27.196666666666670.00333333333333241
437.57.95666666666667-0.456666666666667
447.38.05666666666667-0.756666666666667
4577.91666666666667-0.916666666666667
4677.61666666666667-0.616666666666667
4777.41666666666667-0.416666666666668
487.27.55666666666667-0.356666666666667
497.37.34833333333333-0.0483333333333286
507.17.30833333333333-0.208333333333334
516.87.08833333333333-0.288333333333334
526.46.78833333333333-0.388333333333334
536.16.54833333333333-0.448333333333335
546.56.468333333333330.0316666666666661
557.77.228333333333330.471666666666666
567.97.328333333333330.571666666666667
577.57.188333333333330.311666666666666
586.96.888333333333330.0116666666666668
596.66.68833333333333-0.0883333333333339
606.96.828333333333330.0716666666666668


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.7632729868833180.4734540262333640.236727013116682
180.6636586609156570.6726826781686870.336341339084343
190.617200795249510.765598409500980.38279920475049
200.6882781321132710.6234437357734570.311721867886729
210.6926142500397030.6147714999205940.307385749960297
220.59493687308760.8101262538247990.405063126912400
230.4902932055435600.9805864110871190.509706794456440
240.394140577615920.788281155231840.60585942238408
250.2930655311209510.5861310622419020.706934468879049
260.2089677534319830.4179355068639650.791032246568017
270.1499033914641010.2998067829282030.850096608535899
280.1582571627112840.3165143254225680.841742837288716
290.1618870143148640.3237740286297280.838112985685136
300.116402555936370.232805111872740.88359744406363
310.1340050070894290.2680100141788590.86599499291057
320.2324361531849850.4648723063699690.767563846815015
330.2719905068279290.5439810136558580.728009493172071
340.2287886179503170.4575772359006330.771211382049683
350.1704239288845680.3408478577691360.829576071115432
360.1228448053270840.2456896106541680.877155194672916
370.09432853015746360.1886570603149270.905671469842536
380.0729385910286060.1458771820572120.927061408971394
390.06025563388484060.1205112677696810.93974436611516
400.124389106176670.248778212353340.87561089382333
410.4876997759773450.975399551954690.512300224022655
420.5823730671996390.8352538656007220.417626932800361
430.4546104154662570.9092208309325140.545389584533743


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/10l23r1260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/10l23r1260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/1fu661260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/1fu661260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/2njsz1260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/2njsz1260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/3wpez1260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/3wpez1260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/4354i1260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/4354i1260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/5nz1s1260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/5nz1s1260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/60pp71260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/60pp71260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/7wmub1260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/7wmub1260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/8y0ig1260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/8y0ig1260103124.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/948ep1260103124.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/06/t1260103363h7k29j70wet1j1d/948ep1260103124.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)
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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$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')
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')
}
 





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