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Paper TSA Multiple Regression Model 4

*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: Sat, 18 Dec 2010 17:15:14 +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/Dec/18/t12926928896ltif501wuq1w0b.htm/, Retrieved Sat, 18 Dec 2010 18:21:32 +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/Dec/18/t12926928896ltif501wuq1w0b.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 «
80900 0 35600 36700 174000 0 80900 35600 169422 0 174000 80900 153452 0 169422 174000 173570 0 153452 169422 193036 0 173570 153452 174652 0 193036 173570 105367 0 174652 193036 95963 0 105367 174652 82896 0 95963 105367 121747 0 82896 95963 120196 0 121747 82896 103983 0 120196 121747 81103 0 103983 120196 70944 0 81103 103983 57248 0 70944 81103 47830 0 57248 70944 60095 0 47830 57248 60931 0 60095 47830 82955 0 60931 60095 99559 0 82955 60931 77911 0 99559 82955 70753 0 77911 99559 69287 0 70753 77911 88426 0 69287 70753 91756 1 88426 69287 96933 1 91756 88426 174484 1 96933 91756 232595 1 174484 96933 266197 1 232595 174484 290435 1 266197 232595 304296 1 290435 266197 322310 1 304296 290435 415555 1 322310 304296 490042 1 415555 322310 545109 1 490042 415555 545720 1 545109 490042 505944 1 545720 545109 477930 1 505944 545720 466106 1 477930 505944 424476 1 466106 477930 383018 1 424476 466106 364696 1 383018 424476 391116 1 364696 383018 435721 1 391116 364696 etc...
 
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 time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Multiple Linear Regression - Estimated Regression Equation
Werklozen[t] = + 7083.61427550935 + 27769.2857221576Oliecrisis[t] + 1.4167263043587Y1[t] -0.534958190946436Y2[t] + 496.549472685872t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)7083.614275509358192.6137030.86460.3912110.195605
Oliecrisis27769.285722157615843.5596311.75270.0855450.042772
Y11.41672630435870.11703212.105400
Y2-0.5349581909464360.113884-4.69742e-051e-05
t496.549472685872543.7941210.91310.3653940.182697


Multiple Linear Regression - Regression Statistics
Multiple R0.98987994432335
R-squared0.979862304173597
Adjusted R-squared0.978313250648489
F-TEST (value)632.555485198821
F-TEST (DF numerator)4
F-TEST (DF denominator)52
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation27974.9745735618
Sum Squared Residuals40695158524.3543


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18090038382.654575630342517.3454243697
2174000103645.35964580670354.6403541936
3169422211805.522004414-42383.5220044136
4153452156011.690878632-2559.69087863203
5173570136332.15986886237237.8401311377
6193036173873.69144205119162.3085579491
7174652191185.946269923-16533.9462699228
8105367155223.903218315-49856.9032183151
99596367397.24207586828565.757924132
108289691635.4756420885-8739.47564208845
1112174778650.409323379543096.5906766205
12120196141178.491127802-20982.4911278022
13103983118694.037425968-14711.0374259677
148110397050.923480244-15947.923480244
157094473806.0522590175-2862.05225901745
165724872149.9226145778-14901.9226145778
174783058677.6288845918-10847.6288845918
186009553158.23740602986936.76259397016
196093176069.1712440086-15138.1712440086
208295571188.841695180411766.1583048196
2199559102440.146247431-2881.14624743093
2277911114678.100080284-36767.1000802843
237075375622.9127137385-4869.9127137385
246928777559.3102174333-8272.31021743326
258842679808.16965872398617.83034127613
2691756135972.978300616-44216.9783006159
2796933130948.661550292-34015.6615502924
28174484136998.19232479237485.8076752084
29232595244593.804872269-11998.8048722691
30266197285931.193951456-19734.1939514561
31290435302945.625269115-12510.6252691146
32304296319805.121774664-15509.1217746644
33322310326972.597919906-4662.59791990642
34415555345574.99955460169980.0004453987
35490042468537.45642550521504.5435744953
36545109524679.52161615620429.4783838436
37545720563343.507721936-17623.5077219355
38505944535247.134265737-29303.1342657372
39477930479065.118801583-1135.11880158323
40466106461151.994587054954.00541294999
41424476459883.490998172-35407.4909981721
42383018407727.070070156-24709.0700701561
43364696371759.289905839-7063.28990583926
44391116368476.87671032222639.1232896775
45435721416204.83911868619516.1608813144
46511435465760.86999248645674.1300075137
47553997549661.6247662214335.37523377918
48555252569953.054735703-14701.0547357031
49544897549458.705197297-4561.70519729692
50540562534613.6812587115948.31874128929
51505282534508.214269252-29226.214269252
52507626487341.70348191620284.2965180842
53474427510032.384388609-35605.3843886088
54469740462241.0952833127498.90471668822
55491480473857.52554869917622.4744513008
56538974507661.05391910931312.946080891
57576612563813.61141983112798.3885801686


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
80.9674347440526450.06513051189471080.0325652559473554
90.9447169542496920.1105660915006150.0552830457503077
100.9028357892013050.1943284215973890.0971642107986946
110.9403397676793820.1193204646412360.059660232320618
120.9017933012774470.1964133974451070.0982066987225533
130.8468330942535940.3063338114928130.153166905746406
140.7839743292123710.4320513415752580.216025670787629
150.707215879869080.585568240261840.29278412013092
160.6247413447270380.7505173105459230.375258655272962
170.5317026646242540.936594670751490.468297335375746
180.4693732205147580.9387464410295160.530626779485242
190.3808386424214680.7616772848429360.619161357578532
200.3964567330485550.792913466097110.603543266951445
210.3719971189346010.7439942378692030.628002881065398
220.3284902664219230.6569805328438460.671509733578077
230.2742931697888990.5485863395777990.7257068302111
240.2221811520985030.4443623041970070.777818847901497
250.2185148375732940.4370296751465880.781485162426706
260.2260751002622030.4521502005244060.773924899737797
270.2441199670420790.4882399340841580.755880032957921
280.5236511131701270.9526977736597450.476348886829873
290.5817474521331560.8365050957336890.418252547866844
300.6555758797007430.6888482405985140.344424120299257
310.7030257245754580.5939485508490830.296974275424542
320.772572764204260.4548544715914810.22742723579574
330.8319583228725230.3360833542549540.168041677127477
340.970925083235190.0581498335296210.0290749167648105
350.960733279063530.07853344187294170.0392667209364709
360.952324116537560.09535176692488030.0476758834624402
370.930904231243330.1381915375133380.069095768756669
380.9075374868159760.1849250263680480.092462513184024
390.9022474233664940.1955051532670130.0977525766335064
400.9169944777547440.1660110444905120.0830055222452562
410.8987175315506390.2025649368987220.101282468449361
420.869754845172150.26049030965570.13024515482785
430.839808049535270.3203839009294610.16019195046473
440.781444448599690.4371111028006210.21855555140031
450.7532855407322560.4934289185354880.246714459267744
460.7277297502527660.5445404994944680.272270249747234
470.617714129138570.764571741722860.38228587086143
480.4818852415408890.9637704830817780.518114758459111
490.3776500079259310.7553000158518620.622349992074069


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 level40.0952380952380952OK
 
Charts produced by software:
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http://www.freestatistics.org/blog/date/2010/Dec/18/t12926928896ltif501wuq1w0b/10evc11292692506.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t12926928896ltif501wuq1w0b/17ufq1292692506.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Dec/18/t12926928896ltif501wuq1w0b/73mcy1292692506.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Dec/18/t12926928896ltif501wuq1w0b/83mcy1292692506.png (open in new window)
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http://www.freestatistics.org/blog/date/2010/Dec/18/t12926928896ltif501wuq1w0b/93mcy1292692506.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t12926928896ltif501wuq1w0b/93mcy1292692506.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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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