Seatbelt law - Q3(2)

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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 01:59:33 -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/t1227776410x0b5o3bzros9y44.htm/, Retrieved Thu, 27 Nov 2008 09:00:22 +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/t1227776410x0b5o3bzros9y44.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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Dataseries X:

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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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 71.7922222222222 + 5.86944444444442x[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 5.86944444444442 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 1307.25455555555 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.2 102.672222222222 -1.47222222222213 2 100.5 100.872222222222 -0.372222222222198 3 98 98.9722222222222 -0.972222222222179 4 106.6 101.032222222222 5.5677777777777 5 90.1 91.8722222222222 -1.77222222222224 6 96.9 99.6922222222223 -2.79222222222226 7 125.9 120.992222222222 4.90777777777775 8 112 105.472222222222 6.52777777777777 9 100 104.892222222222 -4.8922222222222 10 123.9 125.432222222222 -1.53222222222222 11 79.8 83.9122222222223 -4.11222222222225 12 83.4 77.8122222222222 5.5877777777778 13 113.6 108.692222222222 4.90777777777775 14 112.9 106.892222222222 6.00777777777777 15 104 104.992222222222 -0.99222222222223 16 109.9 107.052222222222 2.8477777777778 17 99 97.8922222222222 1.10777777777778 18 106.3 105.712222222222 0.587777777777778 19 128.9 127.012222222222 1.88777777777779 20 111.1 111.492222222222 -0.392222222222224 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 2.88777777777775 26 103.4 112.912222222222 -9.51222222222223 27 110.8 111.012222222222 -0.212222222222234 28 112.6 113.072222222222 -0.472222222222211 29 102.5 103.912222222222 -1.41222222222222 30 112.4 111.732222222222 0.66777777777779 31 135.6 133.032222222222 2.56777777777778 32 105.1 117.512222222222 -12.4122222222222 33 127.7 116.932222222222 10.7677777777778 34 137 137.472222222222 -0.472222222222213 35 91 95.9522222222222 -4.95222222222222 36 90.5 89.8522222222222 0.647777777777767 37 122.4 126.601666666667 -4.20166666666668 38 123.3 124.801666666667 -1.50166666666667 39 124.3 122.901666666667 1.39833333333333 40 120 124.961666666667 -4.96166666666664 41 118.1 115.801666666667 2.29833333333334 42 119 123.621666666667 -4.62166666666666 43 142.7 144.921666666667 -2.22166666666668 44 123.6 129.401666666667 -5.80166666666666 45 129.6 128.821666666667 0.778333333333324 46 151.6 149.361666666667 2.23833333333333 47 110.4 107.841666666667 2.55833333333335 48 99.2 101.741666666667 -2.54166666666667 49 130.5 132.621666666667 -2.12166666666668 50 136.2 130.821666666667 5.37833333333332 51 129.7 128.921666666667 0.778333333333318 52 128 130.981666666667 -2.98166666666665 53 121.6 121.821666666667 -0.221666666666660 54 135.8 129.641666666667 6.15833333333335 55 143.8 150.941666666667 -7.14166666666665 56 147.5 135.421666666667 12.0783333333333 57 136.2 134.841666666667 1.35833333333332 58 156.6 155.381666666667 1.21833333333333 59 123.3 113.861666666667 9.43833333333334 60 100.4 107.761666666667 -7.36166666666666 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.198302878458139 0.396605756916278 0.801697121541861 18 0.0890528385052413 0.178105677010483 0.910947161494759 19 0.0805258905654674 0.161051781130935 0.919474109434533 20 0.127085981732430 0.254171963464859 0.87291401826757 21 0.0982807448182086 0.196561489636417 0.901719255181791 22 0.0514997079964199 0.102999415992840 0.94850029200358 23 0.0262237069833472 0.0524474139666945 0.973776293016653 24 0.0183612712061619 0.0367225424123238 0.981638728793838 25 0.0104166186346040 0.0208332372692080 0.989583381365396 26 0.0992587061952927 0.198517412390585 0.900741293804707 27 0.0633999763273408 0.126799952654682 0.93660002367266 28 0.0448041902174464 0.0896083804348928 0.955195809782554 29 0.0251480385785781 0.0502960771571562 0.974851961421422 30 0.0156038041512741 0.0312076083025482 0.984396195848726 31 0.0125096185975334 0.0250192371950668 0.987490381402467 32 0.153538580982372 0.307077161964744 0.846461419017628 33 0.573186573816551 0.853626852366898 0.426813426183449 34 0.47175570599263 0.94351141198526 0.52824429400737 35 0.59534101825868 0.80931796348264 0.40465898174132 36 0.494015564019835 0.98803112803967 0.505984435980165 37 0.383924641465447 0.767849282930894 0.616075358534553 38 0.316825229536835 0.63365045907367 0.683174770463165 39 0.243104417617129 0.486208835234257 0.756895582382871 40 0.171897746311782 0.343795492623564 0.828102253688218 41 0.135669749713353 0.271339499426706 0.864330250286647 42 0.111904218338593 0.223808436677187 0.888095781661407 43 0.0934813268970274 0.186962653794055 0.906518673102973 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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