paper: regression: jobtonic

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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: Tue, 16 Dec 2008 08:25:05 -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/t1229441192glcojbplve3ike2.htm/, Retrieved Tue, 16 Dec 2008 16:26:42 +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/t1229441192glcojbplve3ike2.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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User-defined keywords:

paper: 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 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werklozen[t] = + 24.6962295081967 -3.23729508196721Jobtonic[t] -0.0487795992714024M1[t] -1.32671220400729M2[t] -2.4927868852459M3[t] -2.97886156648452M4[t] -3.40493624772313M5[t] -3.95101092896175M6[t] -4.69708561020036M7[t] -4.42316029143898M8[t] -5.26923497267759M9[t] -5.17530965391621M10[t] -0.793925318761386M11[t] -0.0339253187613844t + 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) 24.6962295081967 0.532401 46.3865 0 0 Jobtonic -3.23729508196721 0.456267 -7.0952 0 0 M1 -0.0487795992714024 0.605544 -0.0806 0.936138 0.468069 M2 -1.32671220400729 0.635518 -2.0876 0.04228 0.02114 M3 -2.4927868852459 0.634864 -3.9265 0.000281 0.00014 M4 -2.97886156648452 0.634404 -4.6955 2.3e-05 1.2e-05 M5 -3.40493624772313 0.63414 -5.3694 2e-06 1e-06 M6 -3.95101092896175 0.63407 -6.2312 0 0 M7 -4.69708561020036 0.634197 -7.4064 0 0 M8 -4.42316029143898 0.634519 -6.9709 0 0 M9 -5.26923497267759 0.635035 -8.2975 0 0 M10 -5.17530965391621 0.635747 -8.1405 0 0 M11 -0.793925318761386 0.631287 -1.2576 0.214738 0.107369 t -0.0339253187613844 0.011134 -3.0469 0.003785 0.001893 Multiple Linear Regression - Regression Statistics Multiple R 0.944066116465137 R-squared 0.891260832257565 Adjusted R-squared 0.86118404117987 F-TEST (value) 29.6328431432478 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.997996452379922 Sum Squared Residuals 46.8118551912568 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 24.6135245901639 0.38647540983607 2 23.6 23.3016666666667 0.298333333333331 3 22.3 22.1016666666667 0.198333333333337 4 21.8 21.5816666666667 0.218333333333337 5 20.8 21.1216666666667 -0.321666666666669 6 19.7 20.5416666666667 -0.841666666666666 7 18.3 19.7616666666667 -1.46166666666667 8 17.4 20.0016666666667 -2.60166666666667 9 17 19.1216666666667 -2.12166666666667 10 18.1 19.1816666666667 -1.08166666666667 11 23.9 23.5291256830601 0.370874316939885 12 25.6 24.2891256830601 1.31087431693989 13 25.3 24.2064207650273 1.09357923497268 14 23.6 22.8945628415301 0.705437158469946 15 21.9 21.6945628415301 0.205437158469943 16 21.4 21.1745628415301 0.225437158469943 17 20.6 20.7145628415301 -0.114562841530053 18 20.5 20.1345628415301 0.365437158469945 19 20.2 19.3545628415301 0.845437158469945 20 20.6 19.5945628415301 1.00543715846995 21 19.7 18.7145628415301 0.985437158469944 22 19.3 18.7745628415301 0.525437158469944 23 22.8 23.1220218579235 -0.322021857923495 24 23.5 23.8820218579235 -0.382021857923497 25 23.8 23.7993169398907 0.000683060109289271 26 22.6 22.4874590163934 0.112540983606558 27 22 21.2874590163934 0.712540983606557 28 21.7 20.7674590163934 0.932540983606557 29 20.7 20.3074590163934 0.392540983606557 30 20.2 19.7274590163934 0.472540983606557 31 19.1 18.9474590163934 0.152540983606559 32 19.5 19.1874590163934 0.312540983606557 33 18.7 18.3074590163934 0.392540983606557 34 18.6 18.3674590163934 0.232540983606558 35 22.2 22.7149180327869 -0.514918032786883 36 23.2 23.4749180327869 -0.274918032786885 37 23.5 23.3922131147541 0.107786885245901 38 21.3 22.0803551912568 -0.78035519125683 39 20 20.8803551912568 -0.88035519125683 40 18.7 20.3603551912568 -1.66035519125683 41 18.9 19.9003551912568 -1.00035519125683 42 18.3 19.3203551912568 -1.02035519125683 43 18.4 18.5403551912568 -0.140355191256831 44 19.9 18.7803551912568 1.11964480874317 45 19.2 17.9003551912568 1.29964480874317 46 18.5 17.9603551912568 0.539644808743169 47 20.9 19.0705191256831 1.82948087431694 48 20.5 19.8305191256831 0.66948087431694 49 19.4 19.7478142076503 -0.347814207650276 50 18.1 18.435956284153 -0.335956284153005 51 17 17.235956284153 -0.235956284153007 52 17 16.715956284153 0.284043715846994 53 17.3 16.255956284153 1.04404371584699 54 16.7 15.675956284153 1.02404371584699 55 15.5 14.895956284153 0.604043715846995 56 15.3 15.135956284153 0.164043715846996 57 13.7 14.255956284153 -0.555956284153005 58 14.1 14.315956284153 -0.215956284153006 59 17.3 18.6634153005464 -1.36341530054645 60 18.1 19.4234153005464 -1.32341530054645 61 18.1 19.3407103825137 -1.24071038251366 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0423500214789181 0.0847000429578361 0.957649978521082 18 0.0835289811821318 0.167057962364264 0.916471018817868 19 0.364474848033266 0.728949696066531 0.635525151966734 20 0.804088090706064 0.391823818587871 0.195911909293936 21 0.851503437432511 0.296993125134977 0.148496562567489 22 0.788836353129312 0.422327293741376 0.211163646870688 23 0.844008300523828 0.311983398952344 0.155991699476172 24 0.926343176865881 0.147313646268237 0.0736568231341187 25 0.93648976596431 0.127020468071381 0.0635102340356905 26 0.917382841095384 0.165234317809233 0.0826171589046164 27 0.877635935342318 0.244728129315365 0.122364064657682 28 0.841805889119005 0.31638822176199 0.158194110880995 29 0.774475296569182 0.451049406861636 0.225524703430818 30 0.69249551557291 0.615008968854179 0.307504484427089 31 0.621761182301006 0.756477635397987 0.378238817698994 32 0.584128899273287 0.831742201453427 0.415871100726713 33 0.532292616836026 0.935414766327948 0.467707383163974 34 0.508360428280592 0.983279143438817 0.491639571719408 35 0.51657541436035 0.9668491712793 0.48342458563965 36 0.47206632004190 0.94413264008380 0.5279336799581 37 0.401596937275674 0.803193874551348 0.598403062724326 38 0.365004098056953 0.730008196113907 0.634995901943046 39 0.315865623965913 0.631731247931825 0.684134376034087 40 0.395488982093776 0.790977964187552 0.604511017906224 41 0.464585079166668 0.929170158333337 0.535414920833332 42 0.705692704003009 0.588614591993981 0.294307295996991 43 0.795250818481266 0.409498363037468 0.204749181518734 44 0.667282536997715 0.665434926004571 0.332717463002285 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 0.0357142857142857 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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