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: Fri, 21 Nov 2008 05:04:38 -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/21/t1227269136u5ci9aq5e8rwx2e.htm/, Retrieved Fri, 21 Nov 2008 12:05:47 +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/21/t1227269136u5ci9aq5e8rwx2e.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}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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99.29 0 98.69 0 107.92 0 101.03 0 97.55 0 103.02 0 94.08 0 94.12 0 115.08 0 116.48 0 103.42 0 112.51 0 95.55 0 97.53 0 119.26 0 100.94 0 97.73 0 115.25 0 92.8 0 99.2 0 118.69 0 110.12 0 110.26 0 112.9 0 102.17 1 99.38 1 116.1 1 103.77 1 101.81 1 113.74 1 89.67 1 99.5 1 122.89 1 108.61 1 114.37 1 110.5 1 104.08 1 103.64 1 121.61 1 101.14 1 115.97 1 120.12 1 95.97 1 105.01 1 124.68 1 123.89 1 123.61 1 114.76 1 108.75 1 106.09 1 123.17 1 106.16 1 115.18 1 120.6 1 109.48 1 114.44 1 121.44 1 129.48 1 124.32 1 112.59 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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation omzet[t] = + 104.725833333333 + 7.18222222222222dummievariabele[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 104.725833333333 1.886817 55.504 0 0 dummievariabele 7.18222222222222 2.43587 2.9485 0.004596 0.002298 Multiple Linear Regression - Regression Statistics Multiple R 0.36104555223933 R-squared 0.130353890791803 Adjusted R-squared 0.115359992357179 F-TEST (value) 8.69379577033735 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.00459560607013443 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.2434770544182 Sum Squared Residuals 4955.62834722222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.29 104.725833333334 -5.43583333333359 2 98.69 104.725833333333 -6.0358333333333 3 107.92 104.725833333333 3.19416666666668 4 101.03 104.725833333333 -3.69583333333332 5 97.55 104.725833333333 -7.17583333333333 6 103.02 104.725833333333 -1.70583333333333 7 94.08 104.725833333333 -10.6458333333333 8 94.12 104.725833333333 -10.6058333333333 9 115.08 104.725833333333 10.3541666666667 10 116.48 104.725833333333 11.7541666666667 11 103.42 104.725833333333 -1.30583333333332 12 112.51 104.725833333333 7.78416666666668 13 95.55 104.725833333333 -9.17583333333333 14 97.53 104.725833333333 -7.19583333333332 15 119.26 104.725833333333 14.5341666666667 16 100.94 104.725833333333 -3.78583333333333 17 97.73 104.725833333333 -6.99583333333332 18 115.25 104.725833333333 10.5241666666667 19 92.8 104.725833333333 -11.9258333333333 20 99.2 104.725833333333 -5.52583333333332 21 118.69 104.725833333333 13.9641666666667 22 110.12 104.725833333333 5.39416666666668 23 110.26 104.725833333333 5.53416666666668 24 112.9 104.725833333333 8.17416666666668 25 102.17 111.908055555556 -9.73805555555555 26 99.38 111.908055555556 -12.5280555555556 27 116.1 111.908055555556 4.19194444444444 28 103.77 111.908055555556 -8.13805555555556 29 101.81 111.908055555556 -10.0980555555556 30 113.74 111.908055555556 1.83194444444444 31 89.67 111.908055555556 -22.2380555555556 32 99.5 111.908055555556 -12.4080555555556 33 122.89 111.908055555556 10.9819444444444 34 108.61 111.908055555556 -3.29805555555556 35 114.37 111.908055555556 2.46194444444445 36 110.5 111.908055555556 -1.40805555555556 37 104.08 111.908055555556 -7.82805555555556 38 103.64 111.908055555556 -8.26805555555556 39 121.61 111.908055555556 9.70194444444444 40 101.14 111.908055555556 -10.7680555555556 41 115.97 111.908055555556 4.06194444444444 42 120.12 111.908055555556 8.21194444444445 43 95.97 111.908055555556 -15.9380555555556 44 105.01 111.908055555556 -6.89805555555555 45 124.68 111.908055555556 12.7719444444445 46 123.89 111.908055555556 11.9819444444444 47 123.61 111.908055555556 11.7019444444444 48 114.76 111.908055555556 2.85194444444445 49 108.75 111.908055555556 -3.15805555555556 50 106.09 111.908055555556 -5.81805555555555 51 123.17 111.908055555556 11.2619444444444 52 106.16 111.908055555556 -5.74805555555556 53 115.18 111.908055555556 3.27194444444445 54 120.6 111.908055555556 8.69194444444444 55 109.48 111.908055555556 -2.42805555555555 56 114.44 111.908055555556 2.53194444444444 57 121.44 111.908055555556 9.53194444444444 58 129.48 111.908055555556 17.5719444444444 59 124.32 111.908055555556 12.4119444444444 60 112.59 111.908055555556 0.681944444444448 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.139391693670224 0.278783387340448 0.860608306329776 6 0.0599983273632408 0.119996654726482 0.94000167263676 7 0.0644499048817331 0.128899809763466 0.935550095118267 8 0.0545683618897502 0.109136723779500 0.94543163811025 9 0.230954170809286 0.461908341618572 0.769045829190714 10 0.395144543513644 0.790289087027288 0.604855456486356 11 0.293460943683254 0.586921887366509 0.706539056316746 12 0.294000341043571 0.588000682087142 0.70599965895643 13 0.279787782214098 0.559575564428195 0.720212217785902 14 0.237657733952239 0.475315467904479 0.76234226604776 15 0.397006618789495 0.79401323757899 0.602993381210505 16 0.323875513953876 0.647751027907752 0.676124486046124 17 0.288865405818878 0.577730811637755 0.711134594181122 18 0.320410337456051 0.640820674912101 0.67958966254395 19 0.382160824755882 0.764321649511764 0.617839175244118 20 0.354167735127762 0.708335470255524 0.645832264872238 21 0.438891918749313 0.877783837498625 0.561108081250687 22 0.38366535040245 0.7673307008049 0.61633464959755 23 0.330692002068461 0.661384004136922 0.669307997931539 24 0.297407557283313 0.594815114566625 0.702592442716687 25 0.256906552002086 0.513813104004172 0.743093447997914 26 0.240700984741012 0.481401969482024 0.759299015258988 27 0.25404884850264 0.50809769700528 0.74595115149736 28 0.216873376133119 0.433746752266239 0.78312662386688 29 0.197689824076904 0.395379648153808 0.802310175923096 30 0.171598743022068 0.343197486044136 0.828401256977932 31 0.402136827398426 0.804273654796851 0.597863172601574 32 0.438581432323834 0.877162864647667 0.561418567676166 33 0.55273495416826 0.894530091663479 0.447265045831740 34 0.496097353865913 0.992194707731826 0.503902646134087 35 0.445806638340582 0.891613276681163 0.554193361659418 36 0.383147124541979 0.766294249083959 0.616852875458021 37 0.370858523622316 0.741717047244632 0.629141476377684 38 0.373612027392071 0.747224054784142 0.626387972607929 39 0.396558460762005 0.79311692152401 0.603441539237995 40 0.462356291312511 0.924712582625022 0.537643708687489 41 0.405548797105215 0.81109759421043 0.594451202894785 42 0.383599054464375 0.76719810892875 0.616400945535625 43 0.657390978314482 0.685218043371037 0.342609021685518 44 0.706059162129614 0.587881675740773 0.293940837870387 45 0.737275271908854 0.525449456182291 0.262724728091146 46 0.747403321711823 0.505193356576353 0.252596678288177 47 0.751045130127579 0.497909739744842 0.248954869872421 48 0.6684337396943 0.6631325206114 0.3315662603057 49 0.631686514579406 0.736626970841188 0.368313485420594 50 0.676683837951909 0.646632324096182 0.323316162048091 51 0.636023412276664 0.727953175446671 0.363976587723336 52 0.71581793682135 0.568364126357299 0.284182063178650 53 0.610652977495997 0.778694045008007 0.389347022504003 54 0.478349916640591 0.956699833281183 0.521650083359409 55 0.501531230155355 0.99693753968929 0.498468769844645 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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