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loiqueverhasselt

*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, 23 Nov 2008 13:07:02 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227470940j9gr1hk1x1g9ye9.htm/, Retrieved Sun, 23 Nov 2008 20:09:01 +0000
 
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/2008/Nov/23/t1227470940j9gr1hk1x1g9ye9.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
Seatbelt Q3
 
Dataseries X:
» Textbox « » Textfile « » CSV «
99.4 0 97.5 0 94.6 0 92.6 0 92.5 0 89.8 0 88.8 0 87.4 0 85.2 0 83.1 0 84.7 0 84.8 0 85.8 0 86.3 0 89 0 89 0 89.3 0 91.9 0 94.9 0 94.4 0 96.8 0 96.9 0 98 0 97.9 0 100.9 0 103.9 0 103.1 0 102.5 0 104.3 0 102.6 0 101.7 0 102.8 0 105.4 0 110.9 1 113.5 1 116.3 1 124 1 128.8 1 133.5 1 132.6 1 128.4 1 127.3 1 126.7 1 123.3 1 123.2 1 124.4 1 128.2 1 128.7 1 135.7 1 139 1 145.4 1 142.4 1 137.7 1 137 1 137.1 1 139.3 1 139.6 1 140.4 1 142.3 1 148.3 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 time9 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
Grondstofprijzen[t] = + 83.0241658485503 + 16.9368028739519Wet[t] + 0.673801295896329t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)83.02416584855031.7038348.72800
Wet16.93680287395192.8625755.916600
t0.6738012958963290.0822338.193800


Multiple Linear Regression - Regression Statistics
Multiple R0.962708348317625
R-squared0.92680736392045
Adjusted R-squared0.924239201250991
F-TEST (value)360.883434270959
F-TEST (DF numerator)2
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.59544543012153
Sum Squared Residuals1784.61354500367


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
199.483.697967144446715.7020328555533
297.584.37176844034313.1282315596571
394.685.04556973623939.55443026376071
492.685.71937103213566.88062896786439
592.586.3931723280326.10682767196807
689.887.06697362392832.73302637607174
788.887.74077491982461.05922508017541
887.488.414576215721-1.01457621572091
985.289.0883775116173-3.88837751161725
1083.189.7621788075136-6.66217880751358
1184.790.4359801034099-5.7359801034099
1284.891.1097813993062-6.30978139930624
1385.891.7835826952026-5.98358269520257
1486.392.4573839910989-6.1573839910989
158993.1311852869952-4.13118528699522
168993.8049865828915-4.80498658289155
1789.394.4787878787879-5.17878787878788
1891.995.1525891746842-3.2525891746842
1994.995.8263904705805-0.926390470580529
2094.496.5001917664769-2.10019176647686
2196.897.1739930623732-0.373993062373196
2296.997.8477943582695-0.947794358269515
239898.5215956541658-0.52159565416585
2497.999.1953969500622-1.29539695006217
25100.999.86919824595851.0308017540415
26103.9100.5429995418553.35700045814517
27103.1101.2168008377511.88319916224883
28102.5101.8906021336470.609397866352507
29104.3102.5644034295441.73559657045618
30102.6103.238204725440-0.638204725440157
31101.7103.912006021336-2.21200602133648
32102.8104.585807317233-1.78580731723281
33105.4105.2596086131290.140391386870868
34110.9122.870212782977-11.9702127829774
35113.5123.544014078874-10.0440140788737
36116.3124.21781537477-7.91781537477001
37124124.891616670666-0.891616670666342
38128.8125.5654179665633.23458203343734
39133.5126.2392192624597.260780737541
40132.6126.9130205583555.68697944164467
41128.4127.5868218542520.813178145748348
42127.3128.260623150148-0.960623150147989
43126.7128.934424446044-2.23442444604431
44123.3129.608225741941-6.30822574194065
45123.2130.282027037837-7.08202703783697
46124.4130.955828333733-6.5558283337333
47128.2131.629629629630-3.42962962962964
48128.7132.303430925526-3.60343092552597
49135.7132.9772322214222.7227677785777
50139133.6510335173195.34896648268138
51145.4134.32483481321511.0751651867851
52142.4134.9986361091117.40136389088873
53137.7135.6724374050082.02756259499239
54137136.3462387009040.65376129909607
55137.1137.0200399968000.0799600031997352
56139.3137.6938412926971.60615870730342
57139.6138.3676425885931.23235741140708
58140.4139.0414438844891.35855611551076
59142.3139.7152451803862.58475481961444
60148.3140.3890464762827.9109535237181


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.01433765998128310.02867531996256630.985662340018717
70.003997808600029940.007995617200059880.99600219139997
80.001094843438450980.002189686876901950.998905156561549
90.0001984465454817160.0003968930909634310.999801553454518
103.68051753433521e-057.36103506867043e-050.999963194824657
110.0003490263925429750.0006980527850859490.999650973607457
120.001586840674622350.003173681349244710.998413159325378
130.008805632381292780.01761126476258560.991194367618707
140.02524685501559170.05049371003118340.974753144984408
150.1125038325063820.2250076650127630.887496167493618
160.1880952573258650.376190514651730.811904742674135
170.2439476060378280.4878952120756550.756052393962172
180.3691224116045860.7382448232091710.630877588395414
190.5607882048707450.878423590258510.439211795129255
200.6198773730459990.7602452539080020.380122626954001
210.7004123645791280.5991752708417430.299587635420872
220.722791640471690.5544167190566210.277208359528311
230.7348005129628830.5303989740742350.265199487037117
240.7170341033207460.5659317933585080.282965896679254
250.7351251492790020.5297497014419970.264874850720998
260.7926243706166330.4147512587667330.207375629383367
270.7926748893168960.4146502213662070.207325110683104
280.762916406276170.4741671874476610.237083593723830
290.7468508686952070.5062982626095860.253149131304793
300.6914895295772660.6170209408454680.308510470422734
310.6220660380510680.7558679238978630.377933961948932
320.5511991365520790.8976017268958410.448800863447921
330.4883967135693350.976793427138670.511603286430665
340.5121314134470910.9757371731058190.487868586552909
350.5354604031133580.9290791937732850.464539596886642
360.5519346537693130.8961306924613750.448065346230687
370.5498089833157330.9003820333685340.450191016684267
380.6059103071805570.7881793856388850.394089692819442
390.7933030257612790.4133939484774420.206696974238721
400.890259575413710.2194808491725800.109740424586290
410.880851501983550.2382969960329000.119148498016450
420.8490245708892340.3019508582215320.150975429110766
430.7968669200086540.4062661599826920.203133079991346
440.749970839598670.5000583208026590.250029160401330
450.7437506783615780.5124986432768440.256249321638422
460.7811207831181230.4377584337637540.218879216881877
470.7833906296487230.4332187407025550.216609370351277
480.8747991211887620.2504017576224760.125200878811238
490.8424703580700060.3150592838599880.157529641929994
500.783004804231530.4339903915369410.216995195768470
510.917957131881060.1640857362378790.0820428681189397
520.981615710559470.03676857888106170.0183842894405309
530.9737148882164820.05257022356703540.0262851117835177
540.9387771295177670.1224457409644660.0612228704822329


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level60.122448979591837NOK
5% type I error level90.183673469387755NOK
10% type I error level110.224489795918367NOK
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227470940j9gr1hk1x1g9ye9/5h4rx1227470806.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227470940j9gr1hk1x1g9ye9/81vut1227470806.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227470940j9gr1hk1x1g9ye9/9g2p71227470806.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227470940j9gr1hk1x1g9ye9/9g2p71227470806.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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Software written by Ed van Stee & Patrick Wessa


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