Seatbelt Law Q3 met seasonal dummies

*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: Thu, 27 Nov 2008 07:12:02 -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/27/t122779519232ko1i1llor7jdv.htm/, Retrieved Thu, 27 Nov 2008 14:13:13 +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/27/t122779519232ko1i1llor7jdv.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Jonas Scheltjens

Dataseries X:

» Textbox « » Textfile « » CSV «

101,2 0 100,5 0 98 0 106,6 0 90,1 0 96,9 0 125,9 0 112 0 100 0 123,9 0 79,8 0 83,4 0 113,6 0 112,9 0 104 0 109,9 0 99 0 106,3 0 128,9 0 111,1 0 102,9 0 130 0 87 0 87,5 0 117,6 0 103,4 0 110,8 0 112,6 0 102,5 0 112,4 0 135,6 0 105,1 0 127,7 0 137 0 91 0 90,5 0 122,4 1 123,3 1 124,3 1 120 1 118,1 1 119 1 142,7 1 123,6 1 129,6 1 151,6 1 110,4 1 99,2 1 130,5 1 136,2 1 129,7 1 128 1 121,6 1 135,8 1 143,8 1 147,5 1 136,2 1 156,6 1 123,3 1 100,4 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 71.7922222222222 + 5.86944444444444x[t] + 30.3783333333333M1[t] + 28.0766666666667M2[t] + 25.675M3[t] + 27.2333333333333M4[t] + 17.5716666666667M5[t] + 24.89M6[t] + 45.6883333333333M7[t] + 29.6666666666667M8[t] + 28.585M9[t] + 48.6233333333333M10[t] + 6.60166666666666M11[t] + 0.501666666666667t + 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) 71.7922222222222 3.128677 22.9465 0 0 x 5.86944444444444 2.809635 2.089 0.042265 0.021132 M1 30.3783333333333 3.487609 8.7104 0 0 M2 28.0766666666667 3.467747 8.0965 0 0 M3 25.675 3.449678 7.4427 0 0 M4 27.2333333333333 3.433431 7.9318 0 0 M5 17.5716666666667 3.419031 5.1394 5e-06 3e-06 M6 24.89 3.406501 7.3066 0 0 M7 45.6883333333333 3.395864 13.4541 0 0 M8 29.6666666666667 3.387135 8.7586 0 0 M9 28.585 3.380331 8.4563 0 0 M10 48.6233333333333 3.375462 14.4049 0 0 M11 6.60166666666666 3.372538 1.9575 0.056375 0.028187 t 0.501666666666667 0.081107 6.1852 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.963946307315686 R-squared 0.929192483387547 Adjusted R-squared 0.909181663475332 F-TEST (value) 46.4345033069011 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.33090773646346 Sum Squared Residuals 1307.25455555556 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.2 102.672222222222 -1.47222222222230 2 100.5 100.872222222222 -0.372222222222224 3 98 98.9722222222222 -0.972222222222216 4 106.6 101.032222222222 5.56777777777778 5 90.1 91.8722222222222 -1.77222222222224 6 96.9 99.6922222222222 -2.79222222222221 7 125.9 120.992222222222 4.90777777777779 8 112 105.472222222222 6.5277777777778 9 100 104.892222222222 -4.89222222222221 10 123.9 125.432222222222 -1.53222222222221 11 79.8 83.9122222222222 -4.11222222222223 12 83.4 77.8122222222222 5.58777777777778 13 113.6 108.692222222222 4.90777777777779 14 112.9 106.892222222222 6.00777777777779 15 104 104.992222222222 -0.992222222222218 16 109.9 107.052222222222 2.84777777777778 17 99 97.8922222222222 1.10777777777778 18 106.3 105.712222222222 0.58777777777777 19 128.9 127.012222222222 1.88777777777779 20 111.1 111.492222222222 -0.392222222222227 21 102.9 110.912222222222 -8.01222222222222 22 130 131.452222222222 -1.45222222222221 23 87 89.9322222222222 -2.93222222222222 24 87.5 83.8322222222222 3.66777777777777 25 117.6 114.712222222222 2.88777777777779 26 103.4 112.912222222222 -9.51222222222222 27 110.8 111.012222222222 -0.212222222222229 28 112.6 113.072222222222 -0.472222222222233 29 102.5 103.912222222222 -1.41222222222222 30 112.4 111.732222222222 0.667777777777774 31 135.6 133.032222222222 2.56777777777777 32 105.1 117.512222222222 -12.4122222222222 33 127.7 116.932222222222 10.7677777777778 34 137 137.472222222222 -0.472222222222223 35 91 95.9522222222222 -4.95222222222222 36 90.5 89.8522222222222 0.647777777777775 37 122.4 126.601666666667 -4.20166666666664 38 123.3 124.801666666667 -1.50166666666666 39 124.3 122.901666666667 1.39833333333334 40 120 124.961666666667 -4.96166666666666 41 118.1 115.801666666667 2.29833333333334 42 119 123.621666666667 -4.62166666666667 43 142.7 144.921666666667 -2.22166666666668 44 123.6 129.401666666667 -5.80166666666667 45 129.6 128.821666666667 0.77833333333333 46 151.6 149.361666666667 2.23833333333332 47 110.4 107.841666666667 2.55833333333334 48 99.2 101.741666666667 -2.54166666666666 49 130.5 132.621666666667 -2.12166666666665 50 136.2 130.821666666667 5.37833333333332 51 129.7 128.921666666667 0.778333333333327 52 128 130.981666666667 -2.98166666666666 53 121.6 121.821666666667 -0.221666666666668 54 135.8 129.641666666667 6.15833333333334 55 143.8 150.941666666667 -7.14166666666666 56 147.5 135.421666666667 12.0783333333333 57 136.2 134.841666666667 1.35833333333332 58 156.6 155.381666666667 1.21833333333332 59 123.3 113.861666666667 9.43833333333333 60 100.4 107.761666666667 -7.36166666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.198302878458138 0.396605756916276 0.801697121541862 18 0.0890528385052401 0.178105677010480 0.91094716149476 19 0.0805258905654684 0.161051781130937 0.919474109434532 20 0.127085981732430 0.254171963464859 0.87291401826757 21 0.0982807448182065 0.196561489636413 0.901719255181794 22 0.0514997079964185 0.102999415992837 0.948500292003582 23 0.0262237069833475 0.0524474139666949 0.973776293016653 24 0.0183612712061619 0.0367225424123239 0.981638728793838 25 0.0104166186346044 0.0208332372692088 0.989583381365396 26 0.099258706195291 0.198517412390582 0.900741293804709 27 0.0633999763273431 0.126799952654686 0.936600023672657 28 0.0448041902174484 0.0896083804348969 0.955195809782552 29 0.0251480385785784 0.0502960771571568 0.974851961421422 30 0.0156038041512740 0.0312076083025479 0.984396195848726 31 0.0125096185975338 0.0250192371950677 0.987490381402466 32 0.153538580982368 0.307077161964737 0.846461419017632 33 0.573186573816551 0.853626852366899 0.426813426183449 34 0.471755705992637 0.943511411985274 0.528244294007363 35 0.595341018258678 0.809317963482643 0.404658981741322 36 0.494015564019838 0.988031128039677 0.505984435980162 37 0.383924641465449 0.767849282930897 0.616075358534551 38 0.316825229536833 0.633650459073666 0.683174770463167 39 0.243104417617130 0.486208835234261 0.75689558238287 40 0.171897746311778 0.343795492623557 0.828102253688222 41 0.135669749713352 0.271339499426704 0.864330250286648 42 0.111904218338591 0.223808436677182 0.888095781661409 43 0.093481326897028 0.186962653794056 0.906518673102972 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 4 0.148148148148148 NOK 10% type I error level 7 0.259259259259259 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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