Case Seatbelt Q3 A

*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 05:14:47 -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/t1227788183pf4azlvi6u109ut.htm/, Retrieved Thu, 27 Nov 2008 12:16:33 +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/t1227788183pf4azlvi6u109ut.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)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

no seasonal dummies no trendline

Dataseries X:

» Textbox « » Textfile « » CSV «

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

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation alg_indexcijfer_grondstoffen[t] = -46.0196124318759 + 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) -46.0196124318759 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 58648.082273873 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 239.4 221.748050306465 17.651949693535 2 321.9 276.417281448876 45.4827185511244 3 362.7 303.751897020081 58.948102979919 4 413.6 328.297266104429 85.3027338955712 5 407.1 326.205331239285 80.8946687607145 6 383.2 328.436728428772 54.7632715712283 7 347.7 328.018341455743 19.6816585442570 8 333.8 323.973934049799 9.82606595020062 9 312.3 307.935766750368 4.36423324963245 10 295.4 293.431685018707 1.96831498129252 11 283.3 251.871912364528 31.4280876354724 12 287.6 262.192124365901 25.4078756340989 13 265.7 270.978250799503 -5.27825079950291 14 250.2 263.028898311958 -12.8288983119584 15 234.7 263.726209933673 -29.0262099336728 16 244 277.811904692304 -33.8119046923043 17 231.2 274.185884259389 -42.9858842593893 18 223.8 287.155880423278 -63.3558804232776 19 223.5 286.179644152877 -62.6796441528774 20 210.5 266.236531771845 -55.7365317718448 21 201.6 253.824384905328 -52.224384905328 22 190.7 248.385354255955 -57.6853542559554 23 207.5 247.688042634241 -40.188042634241 24 198.8 242.109549660526 -43.3095496605256 25 196.6 242.667398957897 -46.0673989578971 26 204.2 235.275895767724 -31.0758957677242 27 227.4 239.180840849325 -11.780840849325 28 229.7 239.180840849325 -9.480840849325 29 217.9 226.071382361094 -8.17138236109375 30 221.4 240.575464092754 -19.1754640927538 31 216.3 215.472245711034 0.827754288965548 32 197 195.947520303031 1.05247969696950 33 193.8 194.273972410916 -0.473972410915874 34 196.8 187.579780842457 9.22021915754265 35 180.5 173.633548408169 6.86645159183118 36 174.8 164.707959650224 10.0920403497759 37 181.6 161.081939217309 20.5180607826909 38 190 160.245165271252 29.7548347287482 39 190.6 157.037531811365 33.5624681886346 40 179 148.948716999478 30.0512830005219 41 174.1 147.693556080392 26.4064439196079 42 161.1 151.180114188964 9.91988581103574 43 168.6 161.360863865995 7.23913613400512 44 169.4 164.429035001538 4.97096499846163 45 152.2 159.408391325195 -7.20839132519452 46 148.3 155.503446243594 -7.2034462435937 47 137.7 140.859902187591 -3.15990218759073 48 145 142.393987755362 2.60601224463754 49 153.4 137.233881754676 16.1661182453243 50 141.7 133.050012024389 8.64998797561084 51 142.7 131.934313429646 10.7656865703539 52 135.9 131.655388780960 4.24461121903972 53 131.8 126.913669753302 4.88633024669783 54 134.6 126.216358131588 8.38364186841225 55 127.5 132.492162727018 -4.9921627270176 56 126.5 135.141946889532 -8.64194688953242 57 118.7 131.934313429646 -13.2343134296460 58 117.1 123.845498617759 -6.74549861775869 59 110.7 113.106899643356 -2.4068996433565 60 107.1 109.341416886099 -2.24141688609862 61 105.4 106.133783426212 -0.733783426212228 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0129198767813636 0.0258397535627271 0.987080123218636 6 0.108199618798981 0.216399237597963 0.891800381201019 7 0.67424943359047 0.651501132819059 0.325750566409529 8 0.893953460587468 0.212093078825064 0.106046539412532 9 0.953464774842486 0.0930704503150287 0.0465352251575143 10 0.972432937105238 0.0551341257895229 0.0275670628947615 11 0.982090872945851 0.0358182541082977 0.0179091270541488 12 0.991339936010638 0.0173201279787236 0.00866006398936182 13 0.996041210404069 0.00791757919186263 0.00395878959593131 14 0.997761988009412 0.00447602398117505 0.00223801199058752 15 0.999073493895845 0.00185301220830997 0.000926506104154985 16 0.999717799007614 0.00056440198477131 0.000282200992385655 17 0.999906798999027 0.000186402001945347 9.32010009726733e-05 18 0.999994162253221 1.16754935576711e-05 5.83774677883556e-06 19 0.999999187566106 1.62486778891266e-06 8.12433894456331e-07 20 0.999999589352272 8.21295455417018e-07 4.10647727708509e-07 21 0.999999698002058 6.03995884540951e-07 3.01997942270475e-07 22 0.999999909399929 1.81200142808071e-07 9.06000714040357e-08 23 0.99999988324882 2.33502360483392e-07 1.16751180241696e-07 24 0.99999992276041 1.54479181919758e-07 7.7239590959879e-08 25 0.999999983568973 3.28620543906194e-08 1.64310271953097e-08 26 0.9999999904732 1.90535996007255e-08 9.52679980036274e-09 27 0.999999980640096 3.87198085563219e-08 1.93599042781610e-08 28 0.999999960247284 7.95054320352092e-08 3.97527160176046e-08 29 0.999999934787637 1.30424725685775e-07 6.52123628428877e-08 30 0.999999970460185 5.90796309143401e-08 2.95398154571701e-08 31 0.999999965121162 6.97576761169482e-08 3.48788380584741e-08 32 0.999999963493949 7.30121025950621e-08 3.65060512975311e-08 33 0.999999967927496 6.41450076204281e-08 3.20725038102141e-08 34 0.999999951916974 9.6166050981359e-08 4.80830254906795e-08 35 0.999999919840158 1.60319683303637e-07 8.01598416518187e-08 36 0.999999827158689 3.45682623043297e-07 1.72841311521649e-07 37 0.999999675153482 6.49693035417102e-07 3.24846517708551e-07 38 0.999999729033815 5.41932369698445e-07 2.70966184849223e-07 39 0.999999922331166 1.55337668964367e-07 7.76688344821837e-08 40 0.999999985577012 2.88459768668763e-08 1.44229884334382e-08 41 0.999999998155952 3.68809647131264e-09 1.84404823565632e-09 42 0.999999994677597 1.06448061286088e-08 5.32240306430439e-09 43 0.999999981160817 3.7678366375751e-08 1.88391831878755e-08 44 0.99999993057061 1.38858780989518e-07 6.94293904947592e-08 45 0.999999755704373 4.8859125421659e-07 2.44295627108295e-07 46 0.99999938671394 1.22657212158557e-06 6.13286060792784e-07 47 0.999997836951773 4.32609645433198e-06 2.16304822716599e-06 48 0.9999905588443 1.88823114019959e-05 9.44115570099796e-06 49 0.99998950829397 2.09834120581331e-05 1.04917060290665e-05 50 0.999973554020281 5.28919594371539e-05 2.64459797185769e-05 51 0.99996871626255 6.25674749007064e-05 3.12837374503532e-05 52 0.999912171548918 0.000175656902164232 8.7828451082116e-05 53 0.999806063053782 0.000387873892436699 0.000193936946218349 54 0.99998853834772 2.29233045593849e-05 1.14616522796924e-05 55 0.999966592261187 6.68154776252294e-05 3.34077388126147e-05 56 0.999902063335099 0.000195873329802997 9.79366649014987e-05 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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