Q3 Seatbelt Law

*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: Mon, 24 Nov 2008 10:31:09 -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/24/t1227548015wzh4u98lak22gdk.htm/, Retrieved Mon, 24 Nov 2008 17:33:35 +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/24/t1227548015wzh4u98lak22gdk.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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IsPrivate?

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User-defined keywords:

Dataseries X:

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94,7 0 101,8 0 102,5 0 105,3 0 110,3 0 109,8 0 117,3 0 118,8 0 131,3 0 125,9 0 133,1 0 147 0 145,8 0 164,4 0 149,8 0 137,7 0 151,7 0 156,8 0 180 0 180,4 0 170,4 0 191,6 0 199,5 0 218,2 1 217,5 1 205 1 194 1 199,3 1 219,3 1 211,1 1 215,2 1 240,2 1 242,2 1 240,7 1 255,4 1 253 1 218,2 1 203,7 1 205,6 1 215,6 1 188,5 1 202,9 1 214 1 230,3 1 230 1 241 1 259,6 1 247,8 1 270,3 1 289,7 1 322,7 1 315 1 320,2 1 329,5 1 360,6 1 382,2 1 435,4 1 464 1 468,8 1 403 1 351,6 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 140.256521739130 + 130.304004576659D[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) 140.256521739130 13.498125 10.3908 0 0 D 130.304004576659 17.101986 7.6192 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.704239679247679 R-squared 0.495953525826874 Adjusted R-squared 0.487410365247668 F-TEST (value) 58.0526985567905 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 2.41473618878274e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 64.7347321586154 Sum Squared Residuals 247244.547311213 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 94.7 140.256521739130 -45.5565217391304 2 101.8 140.256521739130 -38.4565217391303 3 102.5 140.256521739130 -37.7565217391304 4 105.3 140.256521739130 -34.9565217391304 5 110.3 140.256521739130 -29.9565217391304 6 109.8 140.256521739130 -30.4565217391304 7 117.3 140.256521739130 -22.9565217391305 8 118.8 140.256521739130 -21.4565217391305 9 131.3 140.256521739130 -8.95652173913044 10 125.9 140.256521739130 -14.3565217391304 11 133.1 140.256521739130 -7.15652173913045 12 147 140.256521739130 6.74347826086956 13 145.8 140.256521739130 5.54347826086957 14 164.4 140.256521739130 24.1434782608696 15 149.8 140.256521739130 9.54347826086957 16 137.7 140.256521739130 -2.55652173913046 17 151.7 140.256521739130 11.4434782608696 18 156.8 140.256521739130 16.5434782608696 19 180 140.256521739130 39.7434782608696 20 180.4 140.256521739130 40.1434782608696 21 170.4 140.256521739130 30.1434782608696 22 191.6 140.256521739130 51.3434782608696 23 199.5 140.256521739130 59.2434782608696 24 218.2 270.560526315790 -52.3605263157895 25 217.5 270.560526315790 -53.0605263157895 26 205 270.560526315790 -65.5605263157895 27 194 270.560526315790 -76.5605263157895 28 199.3 270.560526315790 -71.2605263157895 29 219.3 270.560526315790 -51.2605263157895 30 211.1 270.560526315790 -59.4605263157895 31 215.2 270.560526315790 -55.3605263157895 32 240.2 270.560526315789 -30.3605263157895 33 242.2 270.560526315789 -28.3605263157895 34 240.7 270.560526315789 -29.8605263157895 35 255.4 270.560526315789 -15.1605263157895 36 253 270.560526315789 -17.5605263157895 37 218.2 270.560526315790 -52.3605263157895 38 203.7 270.560526315790 -66.8605263157895 39 205.6 270.560526315790 -64.9605263157895 40 215.6 270.560526315790 -54.9605263157895 41 188.5 270.560526315790 -82.0605263157895 42 202.9 270.560526315790 -67.6605263157895 43 214 270.560526315790 -56.5605263157895 44 230.3 270.560526315789 -40.2605263157895 45 230 270.560526315789 -40.5605263157895 46 241 270.560526315789 -29.5605263157895 47 259.6 270.560526315789 -10.9605263157894 48 247.8 270.560526315789 -22.7605263157895 49 270.3 270.560526315789 -0.260526315789458 50 289.7 270.560526315790 19.1394736842105 51 322.7 270.560526315790 52.1394736842105 52 315 270.560526315790 44.4394736842105 53 320.2 270.560526315790 49.6394736842105 54 329.5 270.560526315790 58.9394736842105 55 360.6 270.560526315790 90.0394736842105 56 382.2 270.560526315790 111.639473684211 57 435.4 270.560526315790 164.839473684211 58 464 270.560526315790 193.439473684211 59 468.8 270.560526315790 198.239473684211 60 403 270.560526315790 132.439473684211 61 351.6 270.560526315790 81.0394736842105 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00133794824660410 0.00267589649320821 0.998662051753396 6 0.000182722650249481 0.000365445300498962 0.99981727734975 7 7.32384952876095e-05 0.000146476990575219 0.999926761504712 8 2.30965192716154e-05 4.61930385432308e-05 0.999976903480728 9 3.30675316361133e-05 6.61350632722266e-05 0.999966932468364 10 1.1582856244052e-05 2.3165712488104e-05 0.999988417143756 11 6.93014865030034e-06 1.38602973006007e-05 0.99999306985135 12 1.28474574036979e-05 2.56949148073958e-05 0.999987152542596 13 1.08349652426183e-05 2.16699304852365e-05 0.999989165034757 14 3.01300053793589e-05 6.02600107587179e-05 0.99996986999462 15 1.74769699093751e-05 3.49539398187501e-05 0.99998252303009 16 6.02341429267133e-06 1.20468285853427e-05 0.999993976585707 17 3.35484836018337e-06 6.70969672036674e-06 0.99999664515164 18 2.19858347203941e-06 4.39716694407883e-06 0.999997801416528 19 5.16358159804898e-06 1.03271631960980e-05 0.999994836418402 20 7.70994580467199e-06 1.54198916093440e-05 0.999992290054195 21 5.64754803924338e-06 1.12950960784868e-05 0.99999435245196 22 9.67712557038542e-06 1.93542511407708e-05 0.99999032287443 23 1.77515576009952e-05 3.55031152019904e-05 0.9999822484424 24 7.35341066421623e-06 1.47068213284325e-05 0.999992646589336 25 3.00915588159492e-06 6.01831176318985e-06 0.999996990844118 26 1.37541259979514e-06 2.75082519959028e-06 0.9999986245874 27 7.50192296295964e-07 1.50038459259193e-06 0.999999249807704 28 3.64300439232477e-07 7.28600878464954e-07 0.99999963569956 29 1.59726099742204e-07 3.19452199484408e-07 0.9999998402739 30 7.04877153395258e-08 1.40975430679052e-07 0.999999929512285 31 3.10323558933102e-08 6.20647117866204e-08 0.999999968967644 32 1.76723283488476e-08 3.53446566976952e-08 0.999999982327672 33 9.63205560932718e-09 1.92641112186544e-08 0.999999990367944 34 4.75883774504711e-09 9.51767549009421e-09 0.999999995241162 35 3.15460060152373e-09 6.30920120304746e-09 0.9999999968454 36 1.75345743842300e-09 3.50691487684601e-09 0.999999998246543 37 8.53257180497277e-10 1.70651436099455e-09 0.999999999146743 38 6.67164846357351e-10 1.33432969271470e-09 0.999999999332835 39 5.44423533635361e-10 1.08884706727072e-09 0.999999999455576 40 3.75933451196404e-10 7.51866902392808e-10 0.999999999624066 41 1.04083607402059e-09 2.08167214804118e-09 0.999999998959164 42 1.87235925436916e-09 3.74471850873832e-09 0.99999999812764 43 3.14771039106203e-09 6.29542078212406e-09 0.99999999685229 44 4.98381559144907e-09 9.96763118289814e-09 0.999999995016184 45 1.19824742737539e-08 2.39649485475079e-08 0.999999988017526 46 3.75833473355604e-08 7.51666946711207e-08 0.999999962416653 47 1.49478215397357e-07 2.98956430794714e-07 0.999999850521785 48 1.25049998959755e-06 2.50099997919509e-06 0.99999874950001 49 1.2452919120355e-05 2.490583824071e-05 0.99998754708088 50 0.000130581894874628 0.000261163789749256 0.999869418105125 51 0.000971745042934215 0.00194349008586843 0.999028254957066 52 0.00496319886011604 0.00992639772023208 0.995036801139884 53 0.0219933768834781 0.0439867537669563 0.978006623116522 54 0.081831875992727 0.163663751985454 0.918168124007273 55 0.152213351301301 0.304426702602603 0.847786648698698 56 0.183476981527964 0.366953963055928 0.816523018472036 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 48 0.923076923076923 NOK 5% type I error level 49 0.942307692307692 NOK 10% type I error level 49 0.942307692307692 NOK

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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