Model 2 Seizonaliteit modereren

*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: Sat, 05 Dec 2009 07:50:04 -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/Dec/05/t1260024661e09xswb54811ho4.htm/, Retrieved Sat, 05 Dec 2009 15:51:13 +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/2009/Dec/05/t1260024661e09xswb54811ho4.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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No (this computation is public)

User-defined keywords:

Dataseries X:

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6.3 2.7 6.1 2.5 6.1 2.2 6.3 2.9 6.3 3.1 6 3 6.2 2.8 6.4 2.5 6.8 1.9 7.5 1.9 7.5 1.8 7.6 2 7.6 2.6 7.4 2.5 7.3 2.5 7.1 1.6 6.9 1.4 6.8 0.8 7.5 1.1 7.6 1.3 7.8 1.2 8 1.3 8.1 1.1 8.2 1.3 8.3 1.2 8.2 1.6 8 1.7 7.9 1.5 7.6 0.9 7.6 1.5 8.3 1.4 8.4 1.6 8.4 1.7 8.4 1.4 8.4 1.8 8.6 1.7 8.9 1.4 8.8 1.2 8.3 1 7.5 1.7 7.2 2.4 7.4 2 8.8 2.1 9.3 2 9.3 1.8 8.7 2.7 8.2 2.3 8.3 1.9 8.5 2 8.6 2.3 8.5 2.8 8.2 2.4 8.1 2.3 7.9 2.7 8.6 2.7 8.7 2.9 8.7 3 8.5 2.2 8.4 2.3 8.5 2.8 8.7 2.8

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkl[t] = + 8.7074311913167 -0.240943913049847Inflatie[t] -0.147433242027858M1[t] -0.400724486956013M2[t] -0.575905608695016M3[t] -0.820724486956013M4[t] -1.00072448695601M5[t] -1.08554336521701M6[t] -0.340724486956012M7[t] -0.131086730434018M8[t] -0.0448188782609970M9[t] -0.0296377565219940M10[t] -0.139275513043988M11[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) 8.7074311913167 0.505421 17.2281 0 0 Inflatie -0.240943913049847 0.175277 -1.3746 0.175626 0.087813 M1 -0.147433242027858 0.507251 -0.2907 0.77257 0.386285 M2 -0.400724486956013 0.529005 -0.7575 0.452449 0.226225 M3 -0.575905608695016 0.529109 -1.0884 0.281834 0.140917 M4 -0.820724486956013 0.529005 -1.5515 0.127363 0.063681 M5 -1.00072448695601 0.529005 -1.8917 0.064571 0.032285 M6 -1.08554336521701 0.528923 -2.0524 0.045609 0.022804 M7 -0.340724486956012 0.529005 -0.6441 0.522586 0.261293 M8 -0.131086730434018 0.529237 -0.2477 0.805431 0.402715 M9 -0.0448188782609970 0.52883 -0.0848 0.932812 0.466406 M10 -0.0296377565219940 0.528865 -0.056 0.955542 0.477771 M11 -0.139275513043988 0.529005 -0.2633 0.793463 0.396731 Multiple Linear Regression - Regression Statistics Multiple R 0.478874385794768 R-squared 0.229320677370316 Adjusted R-squared 0.0366508467128952 F-TEST (value) 1.19022618428550 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.317049346785684 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.836135761065297 Sum Squared Residuals 33.5579045247477 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 7.90944938405425 -1.60944938405425 2 6.1 7.70434692173608 -1.60434692173608 3 6.1 7.60144897391203 -1.50144897391203 4 6.3 7.18796935651613 -0.887969356516134 5 6.3 6.95978057390616 -0.659780573906164 6 6 6.89905608695015 -0.899056086950153 7 6.2 7.69206374782112 -1.49206374782112 8 6.4 7.97398467825807 -1.57398467825807 9 6.8 8.204818878261 -1.40481887826100 10 7.5 8.22 -0.72 11 7.5 8.13445663478299 -0.634456634782991 12 7.6 8.22554336521701 -0.62554336521701 13 7.6 7.93354377535924 -0.333543775359243 14 7.4 7.70434692173607 -0.304346921736073 15 7.3 7.52916579999707 -0.229165799997070 16 7.1 7.50119644348094 -0.401196443480936 17 6.9 7.3693852260909 -0.469385226090905 18 6.8 7.42913269565982 -0.629132695659816 19 7.5 8.10166840000586 -0.60166840000586 20 7.6 8.26311737391788 -0.663117373917884 21 7.8 8.37347961739589 -0.57347961739589 22 8 8.3645663478299 -0.364566347829908 23 8.1 8.30311737391788 -0.203117373917884 24 8.2 8.3942041043519 -0.194204104351903 25 8.3 8.27086525362903 0.0291347463709725 26 8.2 7.92119644348094 0.278803556519064 27 8 7.72192093043695 0.278079069563052 28 7.9 7.52529083478592 0.37470916521408 29 7.6 7.48985718261583 0.110142817384171 30 7.6 7.26047195652492 0.339528043475076 31 8.3 8.0293852260909 0.270614773909095 32 8.4 8.19083420000293 0.209165799997070 33 8.4 8.25300766087097 0.146992339129034 34 8.4 8.34047195652492 0.0595280434750769 35 8.4 8.13445663478299 0.265543365217009 36 8.6 8.29782653913196 0.302173460868037 37 8.9 8.22267647101906 0.677323528980941 38 8.8 8.01757400870087 0.782425991299127 39 8.3 7.89058166957184 0.40941833042816 40 7.5 7.47710205217595 0.0228979478240489 41 7.2 7.12844131304106 0.0715586869589422 42 7.4 7.14 0.260000000000000 43 8.8 7.86072448695601 0.939275513043988 44 9.3 8.09445663478299 1.20554336521701 45 9.3 8.22891326956598 1.07108673043402 46 8.7 8.02724486956012 0.672755130439878 47 8.2 8.01398467825807 0.186015321741932 48 8.3 8.24963775652199 0.0503622434780068 49 8.5 8.07811012318915 0.421889876810849 50 8.6 7.75253570434604 0.847464295653957 51 8.5 7.45688262608212 1.04311737391788 52 8.2 7.30844131304106 0.891558686958941 53 8.1 7.15253570434604 0.947464295653956 54 7.9 6.9713392608651 0.928660739134893 55 8.6 7.7161581391261 0.883841860873896 56 8.7 7.87760711303813 0.82239288696187 57 8.7 7.93978057390617 0.760219426093834 58 8.5 8.14771682608505 0.352283173914954 59 8.4 8.01398467825807 0.386015321741933 60 8.5 8.03278823477713 0.467211765222868 61 8.7 7.88535499274927 0.814645007250726 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.99726216622278 0.00547566755444006 0.00273783377722003 17 0.994334803432443 0.0113303931351133 0.00566519656755664 18 0.988621490869797 0.0227570182604056 0.0113785091302028 19 0.990104142110398 0.0197917157792038 0.0098958578896019 20 0.995664147992209 0.00867170401558286 0.00433585200779143 21 0.997994419231452 0.0040111615370963 0.00200558076854815 22 0.996936342295463 0.00612731540907337 0.00306365770453668 23 0.993871314984384 0.0122573700312326 0.00612868501561631 24 0.988815327475064 0.0223693450498724 0.0111846725249362 25 0.985981394175572 0.0280372116488571 0.0140186058244285 26 0.991412686873553 0.0171746262528940 0.00858731312644702 27 0.9933082651005 0.0133834697989981 0.00669173489949904 28 0.99081796435801 0.0183640712839786 0.00918203564198932 29 0.98273429994343 0.0345314001131397 0.0172657000565699 30 0.981475888036376 0.0370482239272485 0.0185241119636242 31 0.984448452719084 0.031103094561831 0.0155515472809155 32 0.991909984630696 0.0161800307386077 0.00809001536930386 33 0.996352266992391 0.00729546601521725 0.00364773300760862 34 0.993818976617273 0.0123620467654531 0.00618102338272657 35 0.990418461993898 0.0191630760122044 0.00958153800610218 36 0.984534211578813 0.0309315768423742 0.0154657884211871 37 0.979101071675194 0.0417978566496115 0.0208989283248058 38 0.966218019233858 0.0675639615322841 0.0337819807661421 39 0.939768180842576 0.120463638314848 0.060231819157424 40 0.947379537213923 0.105240925572155 0.0526204627860774 41 0.978495006302386 0.043009987395229 0.0215049936976145 42 0.98465850589066 0.0306829882186801 0.0153414941093400 43 0.973516492027997 0.0529670159440063 0.0264835079720031 44 0.974091368299484 0.0518172634010322 0.0259086317005161 45 0.997828471630278 0.00434305673944364 0.00217152836972182 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.2 NOK 5% type I error level 25 0.833333333333333 NOK 10% type I error level 28 0.933333333333333 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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