Seatbelt Q3 Aok

*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 05:29:10 -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/27/t1227789028k7vt3xsqndk1c3j.htm/, Retrieved Thu, 27 Nov 2008 12:30:38 +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/t1227789028k7vt3xsqndk1c3j.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?

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User-defined keywords:

Dataseries X:

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105,4 109,1 107,1 111,4 110,7 114,1 117,1 121,8 118,7 127,6 126,5 129,9 127,5 128 134,6 123,5 131,8 124 135,9 127,4 142,7 127,6 141,7 128,4 153,4 131,4 145 135,1 137,7 134 148,3 144,5 152,2 147,3 169,4 150,9 168,6 148,7 161,1 141,4 174,1 138,9 179 139,8 190,6 145,6 190 147,9 181,6 148,5 174,8 151,1 180,5 157,5 196,8 167,5 193,8 172,3 197 173,5 216,3 187,5 221,4 205,5 217,9 195,1 229,7 204,5 227,4 204,5 204,2 201,7 196,6 207 198,8 206,6 207,5 210,6 190,7 211,1 201,6 215 210,5 223,9 223,5 238,2 223,8 238,9 231,2 229,6 244 232,2 234,7 222,1 250,2 221,6 265,7 227,3 287,6 221 283,3 213,6 295,4 243,4 312,3 253,8 333,8 265,3 347,7 268,2 383,2 268,5 407,1 266,9 413,6 268,4 362,7 250,8 321,9 231,2 239,4 192

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation alg_indexcijfer_grondstoffen[t] = -46.0196124318757 + 1.39462324342885indexcijfer_industr_grondstoffen[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) -46.0196124318757 15.708824 -2.9295 0.00482 0.00241 indexcijfer_industr_grondstoffen 1.39462324342885 0.082871 16.8288 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.90972043899777 R-squared 0.827591277130294 Adjusted R-squared 0.82466909538674 F-TEST (value) 283.210063493064 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 31.5283252453648 Sum Squared Residuals 58648.0822738731 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.4 106.133783426212 -0.73378342621179 2 107.1 109.341416886099 -2.24141688609858 3 110.7 113.106899643357 -2.40689964335655 4 117.1 123.845498617759 -6.74549861775874 5 118.7 131.934313429646 -13.2343134296461 6 126.5 135.141946889532 -8.64194688953247 7 127.5 132.492162727018 -4.99216272701765 8 134.6 126.216358131588 8.3836418684122 9 131.8 126.913669753302 4.88633024669779 10 135.9 131.655388780960 4.24461121903968 11 142.7 131.934313429646 10.7656865703539 12 141.7 133.050012024389 8.6499879756108 13 153.4 137.233881754676 16.1661182453243 14 145 142.393987755363 2.60601224463750 15 137.7 140.859902187591 -3.15990218759078 16 148.3 155.503446243594 -7.20344624359373 17 152.2 159.408391325195 -7.20839132519456 18 169.4 164.429035001538 4.97096499846159 19 168.6 161.360863865995 7.23913613400508 20 161.1 151.180114188964 9.9198858110357 21 174.1 147.693556080392 26.4064439196078 22 179 148.948716999478 30.0512830005219 23 190.6 157.037531811365 33.5624681886345 24 190 160.245165271252 29.7548347287482 25 181.6 161.081939217309 20.5180607826908 26 174.8 164.707959650224 10.0920403497758 27 180.5 173.633548408169 6.86645159183115 28 196.8 187.579780842457 9.22021915754262 29 193.8 194.273972410916 -0.473972410915902 30 197 195.947520303031 1.05247969696948 31 216.3 215.472245711034 0.827754288965523 32 221.4 240.575464092754 -19.1754640927539 33 217.9 226.071382361094 -8.17138236109377 34 229.7 239.180840849325 -9.48084084932503 35 227.4 239.180840849325 -11.780840849325 36 204.2 235.275895767724 -31.0758957677242 37 196.6 242.667398957897 -46.0673989578971 38 198.8 242.109549660526 -43.3095496605256 39 207.5 247.688042634241 -40.188042634241 40 190.7 248.385354255955 -57.6853542559555 41 201.6 253.824384905328 -52.224384905328 42 210.5 266.236531771845 -55.7365317718448 43 223.5 286.179644152877 -62.6796441528774 44 223.8 287.155880423278 -63.3558804232776 45 231.2 274.185884259389 -42.9858842593893 46 244 277.811904692304 -33.8119046923043 47 234.7 263.726209933673 -29.0262099336729 48 250.2 263.028898311958 -12.8288983119584 49 265.7 270.978250799503 -5.27825079950293 50 287.6 262.192124365901 25.4078756340989 51 283.3 251.871912364528 31.4280876354724 52 295.4 293.431685018707 1.96831498129251 53 312.3 307.935766750368 4.36423324963245 54 333.8 323.973934049799 9.82606595020063 55 347.7 328.018341455743 19.6816585442570 56 383.2 328.436728428772 54.7632715712283 57 407.1 326.205331239285 80.8946687607145 58 413.6 328.297266104429 85.3027338955713 59 362.7 303.751897020081 58.948102979919 60 321.9 276.417281448875 45.4827185511246 61 239.4 221.748050306464 17.6519496935357 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 9.79366649014987e-05 0.000195873329802997 0.999902063335099 6 3.34077388126155e-05 6.6815477625231e-05 0.999966592261187 7 1.14616522796924e-05 2.29233045593849e-05 0.99998853834772 8 0.00019393694621835 0.0003878738924367 0.999806063053782 9 8.78284510821172e-05 0.000175656902164234 0.999912171548918 10 3.12837374503535e-05 6.2567474900707e-05 0.99996871626255 11 2.64459797185769e-05 5.28919594371539e-05 0.999973554020281 12 1.04917060290666e-05 2.09834120581331e-05 0.99998950829397 13 9.4411557009979e-06 1.88823114019958e-05 0.9999905588443 14 2.16304822716597e-06 4.32609645433194e-06 0.999997836951773 15 6.13286060792786e-07 1.22657212158557e-06 0.99999938671394 16 2.44295627108289e-07 4.88591254216578e-07 0.999999755704373 17 6.94293904947602e-08 1.38858780989520e-07 0.99999993057061 18 1.88391831878756e-08 3.76783663757512e-08 0.999999981160817 19 5.32240306430435e-09 1.06448061286087e-08 0.999999994677597 20 1.84404823565633e-09 3.68809647131266e-09 0.999999998155952 21 1.44229884334388e-08 2.88459768668777e-08 0.999999985577012 22 7.76688344821844e-08 1.55337668964369e-07 0.999999922331166 23 2.7096618484922e-07 5.4193236969844e-07 0.999999729033815 24 3.24846517708548e-07 6.49693035417095e-07 0.999999675153482 25 1.72841311521649e-07 3.45682623043297e-07 0.999999827158689 26 8.01598416518198e-08 1.60319683303640e-07 0.999999919840158 27 4.80830254906791e-08 9.61660509813583e-08 0.999999951916974 28 3.20725038102145e-08 6.41450076204289e-08 0.999999967927496 29 3.65060512975315e-08 7.3012102595063e-08 0.999999963493949 30 3.48788380584725e-08 6.9757676116945e-08 0.999999965121162 31 2.95398154571691e-08 5.90796309143381e-08 0.999999970460185 32 6.52123628428886e-08 1.30424725685777e-07 0.999999934787637 33 3.97527160176032e-08 7.95054320352063e-08 0.999999960247284 34 1.93599042781608e-08 3.87198085563217e-08 0.999999980640096 35 9.52679980036306e-09 1.90535996007261e-08 0.9999999904732 36 1.64310271953090e-08 3.28620543906179e-08 0.999999983568973 37 7.72395909598805e-08 1.54479181919761e-07 0.99999992276041 38 1.16751180241692e-07 2.33502360483384e-07 0.99999988324882 39 9.06000714040414e-08 1.81200142808083e-07 0.999999909399929 40 3.01997942270462e-07 6.03995884540925e-07 0.999999698002058 41 4.10647727708522e-07 8.21295455417044e-07 0.999999589352272 42 8.12433894456334e-07 1.62486778891267e-06 0.999999187566106 43 5.83774677883556e-06 1.16754935576711e-05 0.999994162253221 44 9.3201000972674e-05 0.000186402001945348 0.999906798999027 45 0.000282200992385644 0.000564401984771289 0.999717799007614 46 0.000926506104154986 0.00185301220830997 0.999073493895845 47 0.00223801199058760 0.00447602398117519 0.997761988009412 48 0.00395878959593126 0.00791757919186251 0.996041210404069 49 0.0086600639893618 0.0173201279787236 0.991339936010638 50 0.0179091270541489 0.0358182541082977 0.982090872945851 51 0.0275670628947618 0.0551341257895236 0.972432937105238 52 0.0465352251575137 0.0930704503150275 0.953464774842486 53 0.106046539412530 0.212093078825059 0.89395346058747 54 0.325750566409531 0.651501132819063 0.674249433590469 55 0.891800381201018 0.216399237597964 0.108199618798982 56 0.987080123218637 0.0258397535627269 0.0129198767813634 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 44 0.846153846153846 NOK 5% type I error level 47 0.903846153846154 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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