multiple lineair regression aantal werklozen en nationale consumptieprijsindex met lineaire trend en seinzonalteit

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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: Thu, 19 Nov 2009 03:31:14 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t12586268359tltg901o59th5o.htm/, Retrieved Thu, 19 Nov 2009 11:34:08 +0100

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@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/2009/Nov/19/t12586268359tltg901o59th5o.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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User-defined keywords:

Dataseries X:

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8.4 1.8 8.4 1.6 8.4 1.9 8.6 1.7 8.9 1.6 8.8 1.3 8.3 1.1 7.5 1.9 7.2 2.6 7.4 2.3 8.8 2.4 9.3 2.2 9.3 2 8.7 2.9 8.2 2.6 8.3 2.3 8.5 2.3 8.6 2.6 8.5 3.1 8.2 2.8 8.1 2.5 7.9 2.9 8.6 3.1 8.7 3.1 8.7 3.2 8.5 2.5 8.4 2.6 8.5 2.9 8.7 2.6 8.7 2.4 8.6 1.7 8.5 2 8.3 2.2 8 1.9 8.2 1.6 8.1 1.6 8.1 1.2 8 1.2 7.9 1.5 7.9 1.6 8 1.7 8 1.8 7.9 1.8 8 1.8 7.7 1.3 7.2 1.3 7.5 1.4 7.3 1.1 7 1.5 7 2.2 7 2.9 7.2 3.1 7.3 3.5 7.1 3.6 6.8 4.4 6.4 4.2 6.1 5.2 6.5 5.8 7.7 5.9 7.9 5.4 7.5 5.5

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 Twk[t] = + 9.32102219883499 -0.0434462039257918Ncp[t] -0.230897994952704M1[t] -0.428452825775995M2[t] -0.532656150570269M3[t] -0.385548716149701M4[t] -0.178441281729133M5[t] -0.192202771387081M6[t] -0.382488564730965M7[t] -0.651036509917819M8[t] -0.855239834712093M9[t] -0.905525628055978M10[t] -0.117549269556894M11[t] -0.0262385103420519t + 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) 9.32102219883499 0.264782 35.2026 0 0 Ncp -0.0434462039257918 0.059251 -0.7333 0.467043 0.233521 M1 -0.230897994952704 0.287762 -0.8024 0.426365 0.213183 M2 -0.428452825775995 0.30258 -1.416 0.16337 0.081685 M3 -0.532656150570269 0.301729 -1.7653 0.084002 0.042001 M4 -0.385548716149701 0.301396 -1.2792 0.207103 0.103552 M5 -0.178441281729133 0.301105 -0.5926 0.556276 0.278138 M6 -0.192202771387081 0.300892 -0.6388 0.526069 0.263034 M7 -0.382488564730965 0.300586 -1.2725 0.209463 0.104732 M8 -0.651036509917819 0.300331 -2.1677 0.035277 0.017639 M9 -0.855239834712093 0.300351 -2.8475 0.006515 0.003258 M10 -0.905525628055978 0.300363 -3.0148 0.004137 0.002069 M11 -0.117549269556894 0.30033 -0.3914 0.69727 0.348635 t -0.0262385103420519 0.00391 -6.7098 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.801550717980588 R-squared 0.642483553495197 Adjusted R-squared 0.543596025738549 F-TEST (value) 6.49711412622514 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 7.74234612421765e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.474343937759637 Sum Squared Residuals 10.5751020505980 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.4 8.98568252647378 -0.58568252647378 2 8.4 8.77057842609363 -0.370578426093626 3 8.4 8.62710272977956 -0.227102729779563 4 8.6 8.75666089464324 -0.156660894643237 5 8.9 8.94187443911433 -0.0418744391143314 6 8.8 8.91490830029207 -0.114908300292068 7 8.3 8.7070732373913 -0.407073237391291 8 7.5 8.37752981872175 -0.877529818721754 9 7.2 8.11667564083737 -0.916675640837373 10 7.4 8.05318519832917 -0.653185198329174 11 8.8 8.81057842609363 -0.0105784260936254 12 9.3 8.91057842609363 0.389421573906375 13 9.3 8.66213116158403 0.637868838415972 14 8.7 8.39923623688547 0.300763763114525 15 8.2 8.28182826292689 -0.0818282629268865 16 8.3 8.41573104818314 -0.115731048183139 17 8.5 8.59659997226166 -0.096599972261655 18 8.6 8.54356611108392 0.0564338889160823 19 8.5 8.30531870543509 0.194681294564915 20 8.2 8.02356611108392 0.176433888916082 21 8.1 7.80615813712533 0.293841862874671 22 7.9 7.71225535186908 0.187744648130924 23 8.6 8.46530395924095 0.134696040759050 24 8.7 8.5566147184558 0.143385281544209 25 8.7 8.29513359276845 0.404866407231544 26 8.5 8.10175259435117 0.398247405648832 27 8.4 7.96696613882226 0.433033861177738 28 8.5 8.07480120172304 0.425198798276959 29 8.7 8.2687039869793 0.431296013020705 30 8.7 8.23739322776445 0.462606772235547 31 8.6 8.05128126682657 0.54871873317343 32 8.5 7.74346095011993 0.756539049880073 33 8.3 7.50432987419844 0.795670125801557 34 8 7.44083943169024 0.559160568309756 35 8.2 8.21561114102501 -0.0156111410250142 36 8.1 8.30692190023986 -0.206921900239855 37 8.1 8.06716387651542 0.0328361234845840 38 8 7.84337053535007 0.156629464649926 39 7.9 7.69989483903601 0.20010516096399 40 7.9 7.81641914272195 0.083580857278053 41 8 7.99294344640788 0.00705655359211643 42 8 7.9485988260153 0.0514011739846958 43 7.9 7.73207452232937 0.167925477670632 44 8 7.43728806680046 0.562711933199538 45 7.7 7.22856933362703 0.471430666372967 46 7.2 7.1520450299411 0.0479549700589036 47 7.5 7.90943825770555 -0.409438257705548 48 7.3 8.01378287809813 -0.713782878098128 49 7 7.73926789123306 -0.739267891233055 50 7 7.48506220731966 -0.485062207319659 51 7 7.32420802943528 -0.324208029435278 52 7.2 7.43638771272864 -0.236387712728636 53 7.3 7.59987815523684 -0.299878155236835 54 7.1 7.55553353484426 -0.455533534844256 55 6.8 7.30425226801769 -0.504252268017686 56 6.4 7.01815505327394 -0.618155053273939 57 6.1 6.74426701421182 -0.644267014211822 58 6.5 6.64167498817041 -0.141674988170410 59 7.7 7.39906821593486 0.300931784065137 60 7.9 7.5121020771126 0.3878979228874 61 7.5 7.25062095142526 0.249379048574735 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.664956018083472 0.670087963833056 0.335043981916528 18 0.510224224439032 0.979551551121936 0.489775775560968 19 0.439357003310565 0.87871400662113 0.560642996689435 20 0.480090980996885 0.96018196199377 0.519909019003115 21 0.468541768255543 0.937083536511085 0.531458231744457 22 0.403493317970034 0.806986635940069 0.596506682029966 23 0.394187358196784 0.788374716393568 0.605812641803216 24 0.479367971847125 0.95873594369425 0.520632028152875 25 0.421380806050195 0.84276161210039 0.578619193949805 26 0.378287514507964 0.756575029015929 0.621712485492036 27 0.298400813506859 0.596801627013719 0.701599186493141 28 0.231543980788470 0.463087961576941 0.76845601921153 29 0.171707929791365 0.343415859582731 0.828292070208635 30 0.120274111426856 0.240548222853712 0.879725888573144 31 0.0774232902550289 0.154846580510058 0.922576709744971 32 0.0588709183042959 0.117741836608592 0.941129081695704 33 0.0420266481859371 0.0840532963718742 0.957973351814063 34 0.0246297331657295 0.049259466331459 0.97537026683427 35 0.0557114183358508 0.111422836671702 0.94428858166415 36 0.159465922834610 0.318931845669221 0.84053407716539 37 0.184348535547362 0.368697071094723 0.815651464452638 38 0.135275781991563 0.270551563983126 0.864724218008437 39 0.0906463595088442 0.181292719017688 0.909353640491156 40 0.0715251764301083 0.143050352860217 0.928474823569892 41 0.0641806852260076 0.128361370452015 0.935819314773992 42 0.0649612001712713 0.129922400342543 0.935038799828729 43 0.0380669489810984 0.0761338979621969 0.961933051018902 44 0.0171030843324180 0.0342061686648360 0.982896915667582 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 2 0.0714285714285714 NOK 10% type I error level 4 0.142857142857143 NOK

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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