paper: multiple regression: jobtonic

*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: Tue, 16 Dec 2008 13:36:46 -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/Dec/16/t12294599562n9pkvm86gnc3f7.htm/, Retrieved Tue, 16 Dec 2008 21:39:16 +0100

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/Dec/16/t12294599562n9pkvm86gnc3f7.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}, }

Original text written by user:

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paper: multiple regression: jobtonic

Dataseries X:

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25 0 23.6 0 22.3 0 21.8 0 20.8 0 19.7 0 18.3 0 17.4 0 17 0 18.1 0 23.9 0 25.6 0 25.3 0 23.6 0 21.9 0 21.4 0 20.6 0 20.5 0 20.2 0 20.6 0 19.7 0 19.3 0 22.8 0 23.5 0 23.8 0 22.6 0 22 0 21.7 0 20.7 0 20.2 0 19.1 0 19.5 0 18.7 0 18.6 0 22.2 0 23.2 0 23.5 0 21.3 0 20 0 18.7 0 18.9 0 18.3 0 18.4 0 19.9 0 19.2 0 18.5 0 20.9 1 20.5 1 19.4 1 18.1 1 17 1 17 1 17.3 1 16.7 1 15.5 1 15.3 1 13.7 1 14.1 1 17.3 1 18.1 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 Werklozen[t] = + 24.6129370629371 -3.19825174825175Jobtonic[t] + 0.227849650349645M1[t] -1.30010489510489M2[t] -2.46805944055944M3[t] -2.95601398601399M4[t] -3.38396853146853M5[t] -3.93192307692308M6[t] -4.67987762237762M7[t] -4.40783216783217M8[t] -5.25578671328671M9[t] -5.16374125874126M10[t] -0.792045454545456M11[t] -0.0320454545454545t + 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) 24.6129370629371 0.529961 46.4429 0 0 Jobtonic -3.19825174825175 0.452226 -7.0722 0 0 M1 0.227849650349645 0.629886 0.3617 0.719209 0.359604 M2 -1.30010489510489 0.629006 -2.0669 0.044396 0.022198 M3 -2.46805944055944 0.628321 -3.928 0.000285 0.000143 M4 -2.95601398601399 0.627831 -4.7083 2.3e-05 1.2e-05 M5 -3.38396853146853 0.627536 -5.3925 2e-06 1e-06 M6 -3.93192307692308 0.627438 -6.2666 0 0 M7 -4.67987762237762 0.627536 -7.4575 0 0 M8 -4.40783216783217 0.627831 -7.0207 0 0 M9 -5.25578671328671 0.628321 -8.3648 0 0 M10 -5.16374125874126 0.629006 -8.2094 0 0 M11 -0.792045454545456 0.624542 -1.2682 0.211107 0.105553 t -0.0320454545454545 0.011094 -2.8885 0.005884 0.002942 Multiple Linear Regression - Regression Statistics Multiple R 0.946005853644991 R-squared 0.894927075130589 Adjusted R-squared 0.865232552884885 F-TEST (value) 30.1377832492350 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.987331736879781 Sum Squared Residuals 44.8419020979021 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 24.8087412587413 0.191258741258724 2 23.6 23.2487412587413 0.351258741258743 3 22.3 22.0487412587413 0.251258741258743 4 21.8 21.5287412587413 0.271258741258744 5 20.8 21.0687412587413 -0.268741258741257 6 19.7 20.4887412587413 -0.78874125874126 7 18.3 19.7087412587413 -1.40874125874126 8 17.4 19.9487412587413 -2.54874125874126 9 17 19.0687412587413 -2.06874125874126 10 18.1 19.1287412587413 -1.02874125874126 11 23.9 23.4683916083916 0.431608391608392 12 25.6 24.2283916083916 1.37160839160840 13 25.3 24.4241958041958 0.875804195804202 14 23.6 22.8641958041958 0.735804195804197 15 21.9 21.6641958041958 0.235804195804194 16 21.4 21.1441958041958 0.255804195804194 17 20.6 20.6841958041958 -0.0841958041958031 18 20.5 20.1041958041958 0.395804195804196 19 20.2 19.3241958041958 0.875804195804195 20 20.6 19.5641958041958 1.03580419580420 21 19.7 18.6841958041958 1.01580419580420 22 19.3 18.7441958041958 0.555804195804196 23 22.8 23.0838461538462 -0.283846153846153 24 23.5 23.8438461538462 -0.343846153846155 25 23.8 24.0396503496503 -0.239650349650345 26 22.6 22.4796503496504 0.120349650349649 27 22 21.2796503496503 0.72034965034965 28 21.7 20.7596503496504 0.94034965034965 29 20.7 20.2996503496503 0.400349650349649 30 20.2 19.7196503496504 0.48034965034965 31 19.1 18.9396503496503 0.160349650349651 32 19.5 19.1796503496503 0.32034965034965 33 18.7 18.2996503496503 0.400349650349651 34 18.6 18.3596503496504 0.240349650349651 35 22.2 22.6993006993007 -0.499300699300699 36 23.2 23.4593006993007 -0.259300699300701 37 23.5 23.6551048951049 -0.155104895104891 38 21.3 22.0951048951049 -0.795104895104896 39 20 20.8951048951049 -0.895104895104895 40 18.7 20.3751048951049 -1.67510489510490 41 18.9 19.9151048951049 -1.01510489510490 42 18.3 19.3351048951049 -1.03510489510489 43 18.4 18.5551048951049 -0.155104895104897 44 19.9 18.7951048951049 1.10489510489510 45 19.2 17.9151048951049 1.28489510489510 46 18.5 17.9751048951049 0.524895104895104 47 20.9 19.1165034965035 1.7834965034965 48 20.5 19.8765034965035 0.623496503496502 49 19.4 20.0723076923077 -0.67230769230769 50 18.1 18.5123076923077 -0.412307692307693 51 17 17.3123076923077 -0.312307692307692 52 17 16.7923076923077 0.207692307692308 53 17.3 16.3323076923077 0.967692307692308 54 16.7 15.7523076923077 0.947692307692307 55 15.5 14.9723076923077 0.527692307692308 56 15.3 15.2123076923077 0.0876923076923092 57 13.7 14.3323076923077 -0.632307692307692 58 14.1 14.3923076923077 -0.292307692307694 59 17.3 18.7319580419580 -1.43195804195804 60 18.1 19.4919580419580 -1.39195804195804 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0418640808706616 0.0837281617413231 0.958135919129338 18 0.0819133419307704 0.163826683861541 0.91808665806923 19 0.35722539840752 0.71445079681504 0.64277460159248 20 0.794099925845611 0.411800148308777 0.205900074154389 21 0.840612859936617 0.318774280126766 0.159387140063383 22 0.772036911543537 0.455926176912925 0.227963088456463 23 0.825491137058008 0.349017725883985 0.174508862941992 24 0.912194428856883 0.175611142286233 0.0878055711431166 25 0.923737679277816 0.152524641444367 0.0762623207221835 26 0.900974068688298 0.198051862623405 0.0990259313117024 27 0.856270311247347 0.287459377505305 0.143729688752653 28 0.818521765721964 0.362956468556072 0.181478234278036 29 0.743817500969674 0.512364998060651 0.256182499030326 30 0.65498301266737 0.690033974665259 0.345016987332629 31 0.575323613425095 0.84935277314981 0.424676386574905 32 0.528441439182331 0.943117121635337 0.471558560817669 33 0.471847599766229 0.943695199532458 0.528152400233771 34 0.457658025666357 0.915316051332714 0.542341974333643 35 0.481863792729868 0.963727585459736 0.518136207270132 36 0.450184208343046 0.900368416686092 0.549815791656954 37 0.401722503330545 0.80344500666109 0.598277496669455 38 0.35800420303172 0.71600840606344 0.64199579696828 39 0.302099366522436 0.604198733044873 0.697900633477564 40 0.37541930808523 0.75083861617046 0.62458069191477 41 0.448382519036136 0.896765038072272 0.551617480963864 42 0.730108916083473 0.539782167833054 0.269891083916527 43 0.871641015482161 0.256717969035678 0.128358984517839 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 0 0 OK 10% type I error level 1 0.037037037037037 OK

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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