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*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: Fri, 27 Nov 2009 11:06:27 -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/Nov/27/t1259345238e59hf5frzavmlny.htm/, Retrieved Fri, 27 Nov 2009 19:07:29 +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/Nov/27/t1259345238e59hf5frzavmlny.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 1.9 9 1.6 9 1.7 9 2 9 2.5 9 2.4 9 2.3 9 2.3 9 2.1 9 2.4 9 2.2 9.1 2.4 9 1.9 9 2.1 9.1 2.1 9 2.1 9 2 9 2.1 9 2.2 8.9 2.2 8.9 2.6 8.9 2.5 8.9 2.3 8.8 2.2 8.8 2.4 8.7 2.3 8.7 2.2 8.5 2.5 8.5 2.5 8.4 2.5 8.2 2.4 8.2 2.3 8.1 1.7 8.1 1.6 8 1.9 7.9 1.9 7.8 1.8 7.7 1.8 7.6 1.9 7.5 1.9 7.5 1.9 7.5 1.9 7.5 1.8 7.5 1.7 7.4 2.1 7.4 2.6 7.3 3.1 7.3 3.1 7.3 3.2 7.2 3.3 7.2 3.6 7.3 3.3 7.4 3.7 7.4 4 7.5 4 7.6 3.8 7.7 3.6 7.9 3.2 8 2.1 8.2 1.6
 
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
werkl[t] = + 9.50211597447777 + 0.0382783046099624infl[t] -0.305734809579039M1[t] -0.308084260797827M2[t] -0.274261542477623M3[t] -0.299673258065217M4[t] -0.248912804113808M5[t] -0.234324519701403M6[t] -0.215908404828002M7[t] -0.175961157770203M8[t] -0.157545042896801M9[t] -0.0821911923921968M10[t] -0.0599472470577996M11[t] -0.0368849826890027t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)9.502115974477770.21712443.763500
infl0.03827830460996240.0817530.46820.6418410.32092
M1-0.3057348095790390.213143-1.43440.1582180.079109
M2-0.3080842607978270.212605-1.44910.1540960.077048
M3-0.2742615424776230.212696-1.28950.2036860.101843
M4-0.2996732580652170.212761-1.40850.1657070.082854
M5-0.2489128041138080.214034-1.1630.2508450.125422
M6-0.2343245197014030.214397-1.09290.2801080.140054
M7-0.2159084048280020.213464-1.01150.317090.158545
M8-0.1759611577702030.212269-0.8290.4114110.205705
M9-0.1575450428968010.211676-0.74430.4604950.230248
M10-0.08219119239219680.211768-0.38810.6997180.349859
M11-0.05994724705779960.210832-0.28430.7774290.388714
t-0.03688498268900270.002947-12.516600


Multiple Linear Regression - Regression Statistics
Multiple R0.903710861624867
R-squared0.81669332141876
Adjusted R-squared0.764889260080584
F-TEST (value)15.7650442903963
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value8.58646487245096e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.333088119752957
Sum Squared Residuals5.10359399394578


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.99.23222496096872-0.332224960968718
299.18150703567789-0.181507035677888
399.18227260177009-0.182272601770087
499.13145939487648-0.131459394876479
599.16447401844387-0.164474018443865
699.13834948970627-0.138349489706272
799.11605279142967-0.116052791429674
899.11911505579847-0.119115055798471
999.09299052706088-0.092990527060877
1099.14294288625947-0.142942886259467
1199.12064618798287-0.120646187982870
129.19.15136411327366-0.0513641132736598
1398.789605168700640.210394831299365
1498.758026395714840.241973604285163
159.18.754964131346040.34503586865396
1698.692667433069440.307332566930558
1798.702715073870850.297284926129148
1898.684246206055250.315753793944749
1998.669605168700650.330394831299355
208.98.672667433069440.227332566930558
218.98.669509887097830.230490112902174
228.98.704150924452430.195849075547569
238.98.681854226175830.218145773824167
248.88.701088660083630.0989113399163669
258.88.366124528737580.433875471262416
268.78.32306226436880.376937735631202
278.78.3161721695390.383827830460996
288.58.26535896264540.234641037354605
298.58.27923443390780.220765566092199
308.48.25693773563120.143062264368797
318.28.2346410373546-0.0346410373546059
328.28.2338754712624-0.0338754712624065
338.18.19243962068083-0.092439620680827
348.18.22708065803543-0.127080658035433
3588.22392311206382-0.223923112063816
367.98.24698537643261-0.346985376432612
377.87.90053775370357-0.100537753703574
387.77.86130331979578-0.161303319795783
397.67.86206888588798-0.262068885887982
407.57.79977218761139-0.299772187611385
417.57.81364765887379-0.313647658873791
427.57.79135096059719-0.291350960597193
437.57.7690542623206-0.269054262320595
447.57.7682886962284-0.268288696228396
457.47.76513115025678-0.365131150256779
467.47.82273917037736-0.422739170377362
477.37.82723728532774-0.527237285327739
487.37.85029954969654-0.550299549696535
497.37.51150758788949-0.211507587889489
507.27.4761009844427-0.276100984442694
517.27.48452221145689-0.284522211456886
527.37.4107420217973-0.110742021797300
537.47.43992881490369-0.0399288149036907
547.47.42911560801008-0.0291156080100815
557.57.410646740194480.08935325980552
567.67.406053343641280.193946656358715
577.77.379928814903690.320071185096309
587.97.40308636087530.496913639124693
5987.346339188449740.653660811550257
608.27.350262300513560.84973769948644


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.002092317042467030.004184634084934060.997907682957533
180.0002127924988043790.0004255849976087580.999787207501196
192.109948659405e-054.21989731881e-050.999978900513406
201.40731864865647e-052.81463729731295e-050.999985926813513
216.94130624600258e-061.38826124920052e-050.999993058693754
221.85863720755150e-063.71727441510301e-060.999998141362793
234.40402031589288e-078.80804063178576e-070.999999559597968
242.69810284734183e-065.39620569468367e-060.999997301897153
251.09282810463414e-062.18565620926828e-060.999998907171895
262.13525277768341e-064.27050555536683e-060.999997864747222
275.83896801659248e-061.16779360331850e-050.999994161031983
284.28452850313248e-058.56905700626496e-050.999957154714969
290.0001974409824728530.0003948819649457050.999802559017527
300.001444462520000750.002888925040001490.99855553748
310.01489446597559330.02978893195118660.985105534024407
320.05473762504020270.1094752500804050.945262374959797
330.09939762030801340.1987952406160270.900602379691987
340.1077028538921660.2154057077843310.892297146107834
350.2124768148464210.4249536296928410.78752318515358
360.4106508453146990.8213016906293970.589349154685301
370.5701193536585620.8597612926828760.429880646341438
380.8125998278918280.3748003442163430.187400172108172
390.9470947256297950.1058105487404110.0529052743702053
400.9889410580915690.02211788381686230.0110589419084311
410.9919359316637110.01612813667257800.00806406833628901
420.9948298479625080.01034030407498350.00517015203749175
430.990260339230480.01947932153903870.00973966076951937


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level140.518518518518518NOK
5% type I error level190.703703703703704NOK
10% type I error level190.703703703703704NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/10con21259345182.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/10con21259345182.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/115ur1259345182.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/29gxm1259345182.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/6vcn01259345182.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/7r8nx1259345182.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/8ksjp1259345182.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/8ksjp1259345182.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/92oyv1259345182.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/27/t1259345238e59hf5frzavmlny/92oyv1259345182.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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Software written by Ed van Stee & Patrick Wessa


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