seatbeltlaw q4: werkloos

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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: Mon, 24 Nov 2008 10:41:08 -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/t1227548729sve550yjf98w7s9.htm/, Retrieved Mon, 24 Nov 2008 17:45:42 +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/t1227548729sve550yjf98w7s9.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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0 7,3 0 7,1 0 6,9 0 6,8 0 7,5 0 7,6 0 7,8 0 8 0 8,1 0 8,2 0 8,3 0 8,2 0 8 0 7,9 0 7,6 0 7,6 0 8,2 0 8,3 0 8,4 0 8,4 0 8,4 0 8,6 0 8,9 0 8,8 0 8,3 0 7,5 0 7,2 0 7,5 0 8,8 0 9,3 0 9,3 0 8,7 0 8,2 0 8,3 0 8,5 0 8,6 0 8,6 0 8,2 0 8,1 0 8 0 8,6 0 8,7 0 8,8 0 8,5 0 8,4 0 8,5 0 8,7 0 8,7 0 8,6 0 8,5 0 8,3 0 8,1 0 8,2 0 8,1 0 8,1 0 7,9 0 7,9 0 7,9 0 8 0 8 0 7,9 0 8 1 7,7 1 7,2 1 7,5 1 7,3 1 7 1 7 1 7 1 7,2 1 7,3 1 7,1 1 6,8 1 6,6 1 6,2 1 6,2 1 6,8 1 6,9 1 6,8

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 y[t] = + 3.53116842365287 -0.419139688749723x[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) 3.53116842365287 0.379862 9.2959 0 0 x -0.419139688749723 0.047831 -8.7628 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.706618073433047 R-squared 0.499309101702231 Adjusted R-squared 0.492806622503559 F-TEST (value) 76.7874969602641 F-TEST (DF numerator) 1 F-TEST (DF denominator) 77 p-value 3.43725048423948e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.294541331380075 Sum Squared Residuals 6.68010388361833 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 0.471448695779921 -0.471448695779921 2 0 0.555276633529838 -0.555276633529838 3 0 0.639104571279783 -0.639104571279783 4 0 0.681018540154755 -0.681018540154755 5 0 0.387620758029949 -0.387620758029949 6 0 0.345706789154977 -0.345706789154977 7 0 0.261878851405032 -0.261878851405032 8 0 0.178050913655087 -0.178050913655087 9 0 0.136136944780115 -0.136136944780115 10 0 0.094222975905143 -0.094222975905143 11 0 0.0523090070301702 -0.0523090070301702 12 0 0.094222975905143 -0.094222975905143 13 0 0.178050913655087 -0.178050913655087 14 0 0.219964882530060 -0.219964882530060 15 0 0.345706789154977 -0.345706789154977 16 0 0.345706789154977 -0.345706789154977 17 0 0.094222975905143 -0.094222975905143 18 0 0.0523090070301702 -0.0523090070301702 19 0 0.010395038155198 -0.010395038155198 20 0 0.010395038155198 -0.010395038155198 21 0 0.010395038155198 -0.010395038155198 22 0 -0.0734328995947464 0.0734328995947464 23 0 -0.199174806219664 0.199174806219664 24 0 -0.157260837344691 0.157260837344691 25 0 0.0523090070301702 -0.0523090070301702 26 0 0.387620758029949 -0.387620758029949 27 0 0.513362664654866 -0.513362664654866 28 0 0.387620758029949 -0.387620758029949 29 0 -0.157260837344691 0.157260837344691 30 0 -0.366830681719553 0.366830681719553 31 0 -0.366830681719553 0.366830681719553 32 0 -0.115346868469719 0.115346868469719 33 0 0.094222975905143 -0.094222975905143 34 0 0.0523090070301702 -0.0523090070301702 35 0 -0.0315189307197742 0.0315189307197742 36 0 -0.0734328995947464 0.0734328995947464 37 0 -0.0734328995947464 0.0734328995947464 38 0 0.094222975905143 -0.094222975905143 39 0 0.136136944780115 -0.136136944780115 40 0 0.178050913655087 -0.178050913655087 41 0 -0.0734328995947464 0.0734328995947464 42 0 -0.115346868469719 0.115346868469719 43 0 -0.157260837344691 0.157260837344691 44 0 -0.0315189307197742 0.0315189307197742 45 0 0.010395038155198 -0.010395038155198 46 0 -0.0315189307197742 0.0315189307197742 47 0 -0.115346868469719 0.115346868469719 48 0 -0.115346868469719 0.115346868469719 49 0 -0.0734328995947464 0.0734328995947464 50 0 -0.0315189307197742 0.0315189307197742 51 0 0.0523090070301702 -0.0523090070301702 52 0 0.136136944780115 -0.136136944780115 53 0 0.094222975905143 -0.094222975905143 54 0 0.136136944780115 -0.136136944780115 55 0 0.136136944780115 -0.136136944780115 56 0 0.219964882530060 -0.219964882530060 57 0 0.219964882530060 -0.219964882530060 58 0 0.219964882530060 -0.219964882530060 59 0 0.178050913655087 -0.178050913655087 60 0 0.178050913655087 -0.178050913655087 61 0 0.219964882530060 -0.219964882530060 62 0 0.178050913655087 -0.178050913655087 63 1 0.303792820280004 0.696207179719996 64 1 0.513362664654866 0.486637335345134 65 1 0.387620758029949 0.612379241970051 66 1 0.471448695779894 0.528551304220106 67 1 0.59719060240481 0.402809397595189 68 1 0.59719060240481 0.402809397595189 69 1 0.59719060240481 0.402809397595189 70 1 0.513362664654866 0.486637335345134 71 1 0.471448695779894 0.528551304220106 72 1 0.555276633529838 0.444723366470161 73 1 0.681018540154755 0.318981459845245 74 1 0.7648464779047 0.2351535220953 75 1 0.932502353404589 0.0674976465954109 76 1 0.932502353404589 0.0674976465954109 77 1 0.681018540154755 0.318981459845245 78 1 0.639104571279783 0.360895428720217 79 1 0.681018540154755 0.318981459845245 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0 0 1 6 0 0 1 7 0 0 1 8 0 0 1 9 0 0 1 10 0 0 1 11 0 0 1 12 0 0 1 13 0 0 1 14 0 0 1 15 0 0 1 16 0 0 1 17 0 0 1 18 0 0 1 19 0 0 1 20 0 0 1 21 0 0 1 22 0 0 1 23 0 0 1 24 0 0 1 25 0 0 1 26 0 0 1 27 0 0 1 28 0 0 1 29 0 0 1 30 0 0 1 31 0 0 1 32 0 0 1 33 0 0 1 34 0 0 1 35 0 0 1 36 0 0 1 37 0 0 1 38 0 0 1 39 0 0 1 40 0 0 1 41 0 0 1 42 0 0 1 43 0 0 1 44 0 0 1 45 0 0 1 46 0 0 1 47 0 0 1 48 0 0 1 49 0 0 1 50 0 0 1 51 0 0 1 52 0 0 1 53 0 0 1 54 0 0 1 55 0 0 1 56 0 0 1 57 0 0 1 58 0 0 1 59 0 0 1 60 0 0 1 61 0 0 1 62 0 0 1 63 1 0 0 64 1 4.11379165299424e-192 2.05689582649712e-192 65 1 0 0 66 1 0 0 67 1 3.86270695114505e-146 1.93135347557252e-146 68 1 1.56506863580105e-134 7.82534317900524e-135 69 1 0 0 70 1 0 0 71 1 1.27946105249142e-90 6.3973052624571e-91 72 1 0 0 73 1 2.08817011094297e-60 1.04408505547148e-60 74 1 9.2077471278377e-46 4.60387356391885e-46 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 70 1 NOK 5% type I error level 70 1 NOK 10% type I error level 70 1 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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