Multiple regression werkloosheid

*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: Mon, 24 Nov 2008 07:26:32 -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/t12275370213igt1jkb6p788zs.htm/, Retrieved Mon, 24 Nov 2008 14:30:31 +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/t12275370213igt1jkb6p788zs.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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User-defined keywords:

Multiple regression

Dataseries X:

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9,5 0 9,1 0 9 0 9,3 0 9,9 0 9,8 0 9,4 0 8,3 0 8 0 8,5 0 10,4 0 11,1 0 10,9 0 9,9 0 9,2 0 9,2 0 9,5 1 9,6 1 9,5 1 9,1 1 8,9 1 9 1 10,1 1 10,3 1 10,2 1 9,6 1 9,2 1 9,3 1 9,4 1 9,4 1 9,2 1 9 1 9 1 9 1 9,8 1 10 1 9,9 1 9,3 1 9 1 9 1 9,1 1 9,1 1 9,1 1 9,2 1 8,8 1 8,3 1 8,4 1 8,1 1 7,8 1 7,9 1 7,9 1 8 1 7,9 1 7,5 1 7,2 1 6,9 1 6,6 1 6,7 1 7,3 1 7,5 1 7,2 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 10.6824503311258 + 1.14917218543046x[t] -0.302580941869024M1[t] -0.621773362766744M2[t] -0.860612582781459M3[t] -0.699451802796175M4[t] -0.668125459896984M5[t] -0.6869646799117M6[t] -0.825803899926419M7[t] -1.14464311994113M8[t] -1.32348233995585M9[t] -1.22232155997057M10[t] -0.261160779985284M11[t] -0.0611607799852832t + 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) 10.6824503311258 0.317696 33.6248 0 0 x 1.14917218543046 0.279101 4.1174 0.000154 7.7e-05 M1 -0.302580941869024 0.368681 -0.8207 0.415953 0.207977 M2 -0.621773362766744 0.386816 -1.6074 0.114661 0.057331 M3 -0.860612582781459 0.386398 -2.2273 0.030756 0.015378 M4 -0.699451802796175 0.386104 -1.8116 0.076446 0.038223 M5 -0.668125459896984 0.387252 -1.7253 0.091044 0.045522 M6 -0.6869646799117 0.386444 -1.7777 0.081931 0.040965 M7 -0.825803899926419 0.385759 -2.1407 0.037514 0.018757 M8 -1.14464311994113 0.385198 -2.9716 0.004658 0.002329 M9 -1.32348233995585 0.38476 -3.4398 0.001231 0.000615 M10 -1.22232155997057 0.384448 -3.1794 0.002612 0.001306 M11 -0.261160779985284 0.38426 -0.6796 0.500063 0.250031 t -0.0611607799852832 0.006934 -8.82 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.843134768534354 R-squared 0.710876237911478 Adjusted R-squared 0.630905835631674 F-TEST (value) 8.88924174001568 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 8.87170503727219e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.607469784246304 Sum Squared Residuals 17.3439183222958 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.5 10.3187086092715 -0.818708609271526 2 9.1 9.93835540838852 -0.838355408388524 3 9 9.63835540838852 -0.63835540838852 4 9.3 9.73835540838852 -0.438355408388518 5 9.9 9.70852097130243 0.191479028697571 6 9.8 9.62852097130243 0.171479028697572 7 9.4 9.42852097130243 -0.0285209713024277 8 8.3 9.04852097130243 -0.748520971302428 9 8 8.80852097130243 -0.808520971302427 10 8.5 8.84852097130243 -0.348520971302430 11 10.4 9.74852097130243 0.651479028697572 12 11.1 9.94852097130243 1.15147902869757 13 10.9 9.58477924944812 1.31522075055188 14 9.9 9.20442604856512 0.69557395143488 15 9.2 8.90442604856512 0.295573951434877 16 9.2 9.00442604856512 0.195573951434877 17 9.5 10.1237637969095 -0.623763796909491 18 9.6 10.0437637969095 -0.443763796909492 19 9.5 9.84376379690949 -0.343763796909491 20 9.1 9.46376379690949 -0.363763796909492 21 8.9 9.2237637969095 -0.323763796909492 22 9 9.26376379690949 -0.263763796909491 23 10.1 10.1637637969095 -0.0637637969094924 24 10.3 10.3637637969095 -0.0637637969094917 25 10.2 10.0000220750552 0.199977924944813 26 9.6 9.61966887417218 -0.0196688741721843 27 9.2 9.31966887417218 -0.119668874172185 28 9.3 9.41966887417219 -0.119668874172184 29 9.4 9.3898344370861 0.0101655629139079 30 9.4 9.3098344370861 0.0901655629139079 31 9.2 9.10983443708609 0.0901655629139074 32 9 8.7298344370861 0.270165562913908 33 9 8.4898344370861 0.510165562913907 34 9 8.5298344370861 0.470165562913908 35 9.8 9.4298344370861 0.370165562913908 36 10 9.6298344370861 0.370165562913907 37 9.9 9.26609271523179 0.633907284768214 38 9.3 8.88573951434878 0.414260485651216 39 9 8.58573951434879 0.414260485651215 40 9 8.68573951434879 0.314260485651214 41 9.1 8.6559050772627 0.444094922737306 42 9.1 8.57590507726269 0.524094922737306 43 9.1 8.3759050772627 0.724094922737307 44 9.2 7.9959050772627 1.20409492273731 45 8.8 7.7559050772627 1.04409492273731 46 8.3 7.7959050772627 0.504094922737307 47 8.4 8.6959050772627 -0.295905077262693 48 8.1 8.8959050772627 -0.795905077262695 49 7.8 8.53216335540839 -0.732163355408388 50 7.9 8.15181015452539 -0.251810154525386 51 7.9 7.85181015452539 0.048189845474614 52 8 7.95181015452539 0.0481898454746131 53 7.9 7.9219757174393 -0.0219757174392934 54 7.5 7.8419757174393 -0.341975717439294 55 7.2 7.6419757174393 -0.441975717439294 56 6.9 7.2619757174393 -0.361975717439294 57 6.6 7.0219757174393 -0.421975717439295 58 6.7 7.0619757174393 -0.361975717439294 59 7.3 7.9619757174393 -0.661975717439295 60 7.5 8.1619757174393 -0.661975717439296 61 7.2 7.79823399558499 -0.598233995584989 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.498069256162071 0.996138512324142 0.501930743837929 18 0.347421345445323 0.694842690890645 0.652578654554677 19 0.2556090795576 0.5112181591152 0.7443909204424 20 0.359697283161392 0.719394566322784 0.640302716838608 21 0.438479242457744 0.876958484915488 0.561520757542256 22 0.398714722241636 0.797429444483273 0.601285277758364 23 0.361614435233314 0.723228870466628 0.638385564766686 24 0.427297900345729 0.854595800691457 0.572702099654271 25 0.34744406500983 0.69488813001966 0.65255593499017 26 0.282100262219580 0.564200524439159 0.71789973778042 27 0.257806590717468 0.515613181434936 0.742193409282532 28 0.246235158948868 0.492470317897736 0.753764841051132 29 0.323164725884838 0.646329451769677 0.676835274115162 30 0.349767049604433 0.699534099208865 0.650232950395567 31 0.383048383505603 0.766096767011206 0.616951616494397 32 0.469397426451138 0.938794852902276 0.530602573548862 33 0.511974585867898 0.976050828264204 0.488025414132102 34 0.502026425072197 0.995947149855606 0.497973574927803 35 0.476854010990796 0.953708021981593 0.523145989009204 36 0.473148580247288 0.946297160494577 0.526851419752712 37 0.411512461460494 0.823024922920987 0.588487538539506 38 0.31720224116315 0.6344044823263 0.68279775883685 39 0.239710286391192 0.479420572782385 0.760289713608808 40 0.190002153236101 0.380004306472203 0.809997846763899 41 0.139998671140920 0.279997342281841 0.86000132885908 42 0.0881934094134802 0.176386818826960 0.91180659058652 43 0.0575648625144175 0.115129725028835 0.942435137485582 44 0.104445437214147 0.208890874428294 0.895554562785853 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 0 0 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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