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paper multiple regression 1

*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: Wed, 30 Dec 2009 09:08:31 -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/30/t1262189405cl3n6vsqnwm6tub.htm/, Retrieved Wed, 30 Dec 2009 17:10:17 +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/30/t1262189405cl3n6vsqnwm6tub.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 «
4223,4 401 4627,3 394 5175,3 372 4550,7 334 4639,3 320 5498,7 334 5031,0 400 4033,3 427 4643,5 423 4873,2 395 4608,7 373 4733,5 377 3955,6 391 4590,9 398 5127,5 393 5257,3 375 5416,9 371 5813,3 364 5261,9 400 4669,2 406 5855,8 407 5274,6 397 5516,7 389 5819,5 394 5156,0 399 5377,3 401 6386,8 396 5144,0 392 6138,5 384 5567,8 370 5822,6 380 5145,5 376 5706,6 378 6078,5 376 6074,5 373 5577,6 374 5727,5 379 6067,0 376 7069,9 371 5490,0 375 5948,3 360 6177,5 338 6890,1 352 5756,2 344 6528,8 330 6792,0 334 6657,4 333 5753,7 343 5750,9 350 5968,4 341 5871,7 320 7004,9 302 6363,4 287 6694,7 304 7101,6 370 5364,0 385 6958,6 365 6503,3 333 5316,0 313 5312,7 330 4478,0 367
 
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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Werkloosheid[t] = + 476.464276058344 -0.0194424865219139Export[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)476.46427605834425.36879118.781500
Export-0.01944248652191390.004496-4.32446e-053e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.490586298742127
R-squared0.2406749165135
Adjusted R-squared0.227804999844237
F-TEST (value)18.7005807961682
F-TEST (DF numerator)1
F-TEST (DF denominator)59
p-value5.97589999016268e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation27.2726845465216
Sum Squared Residuals43884.1600200707


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1401394.3508784816936.64912151830708
2394386.4980581754927.50194182450838
3372375.843575561483-3.84357556148283
4334387.98735264307-53.9873526430703
5320386.264748337229-66.2647483372287
6334369.555875420296-35.5558754202959
7400378.64912636659521.350873633405
8427398.04689516950928.9531048304915
9423386.18308989383736.8169101061633
10395381.71715073975313.2828492602470
11373386.859688424799-13.8596884247993
12377384.433266106864-7.43326610686441
13391399.557576372261-8.55757637226126
14398387.20576468488910.7942353151107
15393376.77292641723016.2270735827697
16375374.2492916666860.750708333314111
17371371.146270817788-0.146270817788435
18364363.4392691605020.56073083949826
19400374.15985622868525.8401437713149
20406385.68341799022320.3165820097765
21407362.61296348332044.3870365166796
22397373.91293664985723.0870633501432
23389369.20591066290119.7940893370986
24394363.31872574406630.6812742559341
25399376.21881555135622.7811844486442
26401371.91619328405629.0838067159438
27396352.28900314018443.7109968598159
28392376.45212538961915.5478746103813
29384357.11657254357526.8834274564247
30370368.2123996016321.78760039836839
31380363.25845403584816.7415459641521
32376376.422961659836-0.42296165983587
33378365.5137824723912.4862175276100
34376358.2831217348917.7168782651098
35373358.36089168097814.6391083190222
36374368.0218632337175.97813676628315
37379365.10743450408213.8925654959180
38376358.50671032989217.4932896701078
39371339.00784059706531.9921594029353
40375369.7250250530375.27497494696348
41360360.814533480043-0.814533480043359
42338356.358315569221-18.3583155692207
43352342.5035996737059.49640032629519
44344364.549435140903-20.5494351409030
45330349.528170054072-19.5281700540723
46334344.410907601505-10.4109076015046
47333347.027866287354-14.0278662873542
48343364.598041357208-21.5980413572078
49350364.652480319469-14.6524803194692
50341360.423739500953-19.4237395009529
51320362.303827947622-42.303827947622
52302340.271602220989-38.2716022209891
53287352.743957324797-65.7439573247969
54304346.302661540087-42.3026615400868
55370338.3915137743231.60848622568
56385372.17477835479812.8252216452023
57365341.17178934695423.8282106530463
58333350.023953460381-17.0239534603811
59313373.108017707850-60.1080177078495
60330373.172177913372-43.1721779133719
61367389.400821413213-22.4008214132134


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.9318613226325180.1362773547349640.0681386773674818
60.8855099914727170.2289800170545670.114490008527283
70.9220893658701570.1558212682596850.0779106341298425
80.9286732496838180.1426535006323640.0713267503161822
90.954422309059770.0911553818804590.0455776909402295
100.937190042404250.1256199151915000.0628099575957499
110.9066682147620780.1866635704758440.0933317852379222
120.8606993550321180.2786012899357640.139300644967882
130.8162878290974340.3674243418051320.183712170902566
140.7635359440162420.4729281119675160.236464055983758
150.7354380195773420.5291239608453160.264561980422658
160.6630609388432280.6738781223135440.336939061156772
170.5841935926478280.8316128147043430.415806407352172
180.5038477106361260.9923045787277490.496152289363874
190.4994357742847060.9988715485694120.500564225715294
200.460512312734120.921024625468240.53948768726588
210.5607606086398750.878478782720250.439239391360125
220.5246076682964770.9507846634070460.475392331703523
230.4727099630173140.9454199260346280.527290036982686
240.4574149022599720.9148298045199430.542585097740028
250.4297509280520560.8595018561041120.570249071947944
260.430798355165710.861596710331420.56920164483429
270.4725676284546290.9451352569092580.527432371545371
280.4357632868347660.8715265736695320.564236713165234
290.4184063639990170.8368127279980330.581593636000983
300.3670861269767140.7341722539534270.632913873023286
310.3347959716962120.6695919433924230.665204028303788
320.2866957922086160.5733915844172320.713304207791384
330.2575275752851990.5150551505703990.7424724247148
340.2379092469082260.4758184938164530.762090753091774
350.2168172542311280.4336345084622570.783182745768872
360.1934442281109930.3868884562219860.806555771889007
370.1906251257634980.3812502515269970.809374874236502
380.1943173759640970.3886347519281940.805682624035903
390.2212762863365680.4425525726731360.778723713663432
400.2245107156534080.4490214313068160.775489284346592
410.2103192280529480.4206384561058950.789680771947052
420.2085088067657680.4170176135315350.791491193234232
430.1896573714602190.3793147429204370.810342628539781
440.1713544655408340.3427089310816670.828645534459166
450.1575413989723270.3150827979446550.842458601027673
460.1267863782061410.2535727564122820.87321362179386
470.0990817221332180.1981634442664360.900918277866782
480.07722430337483880.1544486067496780.922775696625161
490.05703457959699580.1140691591939920.942965420403004
500.04024808546844360.08049617093688730.959751914531556
510.04124691986881110.08249383973762220.95875308013119
520.04757542158445130.09515084316890270.952424578415549
530.1811498597472360.3622997194944720.818850140252764
540.3193525696353260.6387051392706510.680647430364674
550.2564748493330990.5129496986661980.743525150666901
560.3637387754331330.7274775508662660.636261224566867


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 level40.0769230769230769OK
 
Charts produced by software:
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http://www.freestatistics.org/blog/date/2009/Dec/30/t1262189405cl3n6vsqnwm6tub/10tfru1262189305.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/30/t1262189405cl3n6vsqnwm6tub/1wgfk1262189305.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/30/t1262189405cl3n6vsqnwm6tub/2s8tc1262189305.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/30/t1262189405cl3n6vsqnwm6tub/9liri1262189305.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/30/t1262189405cl3n6vsqnwm6tub/9liri1262189305.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 2 ; 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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$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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