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The Seatbelt Law - Q3

*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 13:54:10 -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/t1227473778eeeojmcib3wq9uq.htm/, Retrieved Sun, 23 Nov 2008 20:56:28 +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/t1227473778eeeojmcib3wq9uq.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:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
2173 2363 2126 1905 2121 1983 1734 2074 2049 2406 2558 2251 2059 2397 1747 1707 2319 1631 1627 1791 2034 1997 2169 2028 2253 2218 1855 2187 1852 1570 1851 1954 1828 2251 2277 2085 2282 2266 1878 2267 2069 1746 2299 2360 2214 2825 2355 2333 3016 2155 2172 2150 2533 2058 2160 2259 2498 2695 2799 2945 2930 2318 2540 2570 2669 2450 2842 3439 2677 2979 2257 2842 2546 2455 2293 2379 2478 2054 2272 2351 2271 2542 2304 2194 2722 2395 2146 1894 2548 2087 2063 2481 2476 2212 2834 2148 2598
 
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
Bouwvergunningen[t] = + 2353.25 + 155.527777777778M1[t] -32.375M2[t] -258.625000000001M3[t] -220.875M4[t] -29.6250000000004M5[t] -405.874999999999M6[t] -247.25M7[t] -14.6250000000002M8[t] -97.3750000000001M9[t] + 135.125M10[t] + 90.8749999999999M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2353.25112.58576420.901800
M1155.527777777778154.7343331.00510.3176880.158844
M2-32.375159.220315-0.20330.8393590.41968
M3-258.625000000001159.220315-1.62430.108010.054005
M4-220.875159.220315-1.38720.1689990.084499
M5-29.6250000000004159.220315-0.18610.8528390.426419
M6-405.874999999999159.220315-2.54910.0125940.006297
M7-247.25159.220315-1.55290.1241670.062084
M8-14.6250000000002159.220315-0.09190.927030.463515
M9-97.3750000000001159.220315-0.61160.5424520.271226
M10135.125159.2203150.84870.398450.199225
M1190.8749999999999159.2203150.57080.5696750.284837


Multiple Linear Regression - Regression Statistics
Multiple R0.48935329547902
R-squared0.239466647796177
Adjusted R-squared0.1410446845698
F-TEST (value)2.43306107647322
F-TEST (DF numerator)11
F-TEST (DF denominator)85
p-value0.0109407357077824
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation318.440629438400
Sum Squared Residuals8619376.93055555


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
121732508.77777777778-335.777777777776
223632320.87542.1250000000004
321262094.62531.3749999999995
419052132.375-227.374999999999
521212323.625-202.625
619831947.37535.6250000000005
717342106-372.000000000001
820742338.625-264.625
920492255.875-206.875000000000
1024062488.375-82.375
1125582444.125113.875000000000
1222512353.25-102.250000000000
1320592508.77777777778-449.777777777778
1423972320.87576.125
1517472094.625-347.625
1617072132.375-425.375
1723192323.625-4.62499999999991
1816311947.375-316.375000000000
1916272106-479
2017912338.625-547.625
2120342255.875-221.875
2219972488.375-491.375
2321692444.125-275.125
2420282353.25-325.25
2522532508.77777777778-255.777777777778
2622182320.875-102.875
2718552094.625-239.625
2821872132.37554.6249999999998
2918522323.625-471.625
3015701947.375-377.375
3118512106-255
3219542338.625-384.625
3318282255.875-427.875
3422512488.375-237.375
3522772444.125-167.125
3620852353.25-268.25
3722822508.77777777778-226.777777777778
3822662320.875-54.875
3918782094.625-216.625
4022672132.375134.625000000000
4120692323.625-254.625
4217461947.375-201.375000000000
4322992106193
4423602338.62521.3750000000000
4522142255.875-41.875
4628252488.375336.625
4723552444.125-89.125
4823332353.25-20.2500000000002
4930162508.77777777778507.222222222222
5021552320.875-165.875
5121722094.62577.375
5221502132.37517.6249999999998
5325332323.625209.375
5420581947.375110.625000000000
552160210654.0000000000002
5622592338.625-79.625
5724982255.875242.125
5826952488.375206.625
5927992444.125354.875
6029452353.25591.75
6129302508.77777777778421.222222222222
6223182320.875-2.87499999999999
6325402094.625445.375
6425702132.375437.625
6526692323.625345.375
6624501947.375502.625
6728422106736
6834392338.6251100.375
6926772255.875421.125
7029792488.375490.625
7122572444.125-187.125
7228422353.25488.75
7325462508.7777777777837.2222222222221
7424552320.875134.125
7522932094.625198.375
7623792132.375246.625
7724782323.625154.375
7820541947.375106.625000000000
7922722106166.000000000000
8023512338.62512.3750000000000
8122712255.87515.125
8225422488.37553.625
8323042444.125-140.125
8421942353.25-159.250000000000
8527222508.77777777778213.222222222222
8623952320.87574.125
8721462094.62551.375
8818942132.375-238.375
8925482323.625224.375
9020871947.375139.625000000000
9120632106-42.9999999999998
9224812338.625142.375
9324762255.875220.125
9422122488.375-276.375
9528342444.125389.875
9621482353.25-205.25
9725982508.7777777777889.222222222222


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
150.132547600872320.265095201744640.86745239912768
160.07923019698630260.1584603939726050.920769803013697
170.04600785747993250.0920157149598650.953992142520067
180.05374658024429030.1074931604885810.94625341975571
190.03021970053368680.06043940106737370.969780299466313
200.0297355674667910.0594711349335820.97026443253321
210.01450025098558620.02900050197117240.985499749014414
220.02568959173657250.05137918347314510.974310408263428
230.03202439473129740.06404878946259470.967975605268703
240.02441024335716350.0488204867143270.975589756642836
250.01685044356592590.03370088713185180.983149556434074
260.01090407459984590.02180814919969170.989095925400154
270.006537142078024790.01307428415604960.993462857921975
280.009802852016631460.01960570403326290.990197147983369
290.01658815559367440.03317631118734880.983411844406326
300.01633024681777570.03266049363555130.983669753182224
310.01379164297461120.02758328594922250.986208357025389
320.01197313234483850.02394626468967690.988026867655162
330.01359756467337820.02719512934675640.986402435326622
340.009933154097127290.01986630819425460.990066845902873
350.006524045677508480.01304809135501700.993475954322492
360.004824665897934780.009649331795869570.995175334102065
370.004350323745940410.008700647491880820.99564967625406
380.002551220409974090.005102440819948180.997448779590026
390.001891215089869760.003782430179739510.99810878491013
400.002486616128783320.004973232257566650.997513383871217
410.002168905559178730.004337811118357470.997831094440821
420.001713060104247840.003426120208495680.998286939895752
430.007578461664226070.01515692332845210.992421538335774
440.01288298911202840.02576597822405680.987117010887972
450.01216876223652740.02433752447305480.987831237763473
460.03468339313852020.06936678627704030.96531660686148
470.02508263318156570.05016526636313140.974917366818434
480.02089506183170900.04179012366341790.97910493816829
490.1067864242458080.2135728484916170.893213575754191
500.08946325211778680.1789265042355740.910536747882213
510.0788620780291540.1577241560583080.921137921970846
520.06078405139726310.1215681027945260.939215948602737
530.06575788666312490.1315157733262500.934242113336875
540.05993149091735320.1198629818347060.940068509082647
550.05420522897130130.1084104579426030.945794771028699
560.06227362265582370.1245472453116470.937726377344176
570.06608005951987290.1321601190397460.933919940480127
580.05789904501070150.1157980900214030.942100954989298
590.06979230881315210.1395846176263040.930207691186848
600.1713061993094220.3426123986188440.828693800690578
610.2076219936317260.4152439872634530.792378006368274
620.1632642488618320.3265284977236640.836735751138168
630.1939150247371830.3878300494743660.806084975262817
640.2334542553303850.466908510660770.766545744669615
650.2232475811282340.4464951622564670.776752418871766
660.2703307991874530.5406615983749060.729669200812547
670.488837905994590.977675811989180.51116209400541
680.9411951249188550.1176097501622910.0588048750811454
690.9402198405379740.1195603189240520.0597801594620261
700.9755853019955150.04882939600896910.0244146980044845
710.9723555041414030.05528899171719470.0276444958585973
720.9967631250281160.006473749943767880.00323687497188394
730.993741717036920.01251656592615810.00625828296307905
740.987404552893170.02519089421365810.0125954471068291
750.9778860728694490.04422785426110220.0221139271305511
760.988367193478880.02326561304223940.0116328065211197
770.9756687839439350.04866243211213080.0243312160560654
780.9499735246747120.1000529506505760.0500264753252879
790.9204211487937780.1591577024124440.0795788512062218
800.8580964812047130.2838070375905750.141903518795287
810.7782727667642110.4434544664715770.221727233235789
820.7269438673998760.5461122652002480.273056132600124


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level80.117647058823529NOK
5% type I error level310.455882352941176NOK
10% type I error level390.573529411764706NOK
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227473778eeeojmcib3wq9uq/10x8j61227473645.png (open in new window)
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227473778eeeojmcib3wq9uq/9dklc1227473645.png (open in new window)
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Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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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