Model 2, rekening houdend met seizonaliteit

*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: Wed, 16 Dec 2009 06:53:56 -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/16/t1260973522v8hgvm32t5jtrzs.htm/, Retrieved Wed, 16 Dec 2009 15:25:34 +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/16/t1260973522v8hgvm32t5jtrzs.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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95.1 136 97 133 112.7 126 102.9 120 97.4 114 111.4 116 87.4 153 96.8 162 114.1 161 110.3 149 103.9 139 101.6 135 94.6 130 95.9 127 104.7 122 102.8 117 98.1 112 113.9 113 80.9 149 95.7 157 113.2 157 105.9 147 108.8 137 102.3 132 99 125 100.7 123 115.5 117 100.7 114 109.9 111 114.6 112 85.4 144 100.5 150 114.8 149 116.5 134 112.9 123 102 116 106 117 105.3 111 118.8 105 106.1 102 109.3 95 117.2 93 92.5 124 104.2 130 112.5 124 122.4 115 113.3 106 100 105 110.7 105 112.8 101 109.8 95 117.3 93 109.1 84 115.9 87 96 116 99.8 120 116.8 117 115.7 109 99.4 105 94.3 107 91 109

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 tip[t] = + 121.394817113588 -0.179452244652004wrk[t] -0.400730340464006M1[t] + 2.3M2[t] + 11.1832865320880M3[t] + 4.16136800241036M4[t] + 1.88465453449834M5[t] + 11.9041067791503M6[t] -8.33396914733354M7[t] + 3.81041566736967M8[t] + 18.2956207291353M9[t] + 16.2375364868936M10[t] + 8.15835673395602M11[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) 121.394817113588 5.920244 20.505 0 0 wrk -0.179452244652004 0.046266 -3.8787 0.000319 0.00016 M1 -0.400730340464006 2.94741 -0.136 0.892421 0.446211 M2 2.3 3.077795 0.7473 0.458535 0.229267 M3 11.1832865320880 3.090288 3.6188 0.00071 0.000355 M4 4.16136800241036 3.111013 1.3376 0.187322 0.093661 M5 1.88465453449834 3.163415 0.5958 0.554131 0.277065 M6 11.9041067791503 3.153045 3.7754 0.00044 0.00022 M7 -8.33396914733354 3.190904 -2.6118 0.011986 0.005993 M8 3.81041566736967 3.284717 1.16 0.251769 0.125884 M9 18.2956207291353 3.250561 5.6285 1e-06 0 M10 16.2375364868936 3.12584 5.1946 4e-06 2e-06 M11 8.15835673395602 3.080923 2.648 0.010923 0.005462 Multiple Linear Regression - Regression Statistics Multiple R 0.878569063356793 R-squared 0.771883599087633 Adjusted R-squared 0.714854498859542 F-TEST (value) 13.5349075472072 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 1.36221034452433e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.86642040031007 Sum Squared Residuals 1136.73828060259 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 96.588581500452 -1.48858150045198 2 97 99.827668574872 -2.82766857487196 3 112.7 109.967120819524 2.73287918047606 4 102.9 104.021915757758 -1.12191575775836 5 97.4 102.821915757758 -5.42191575775836 6 111.4 112.482463513106 -1.08246351310636 7 87.4 85.6046545344984 1.79534546550166 8 96.8 96.1339691473335 0.66603085266646 9 114.1 110.798626453751 3.30137354624887 10 110.3 110.893969147334 -0.59396914733352 11 103.9 104.609311840916 -0.709311840915936 12 101.6 97.168764085568 4.43123591443206 13 94.6 97.665294968364 -3.06529496836396 14 95.9 100.904382042784 -5.00438204278396 15 104.7 110.684929798132 -5.98492979813197 16 102.8 104.560272491714 -1.76027249171437 17 98.1 103.180820247062 -5.08082024706237 18 113.9 113.020820247062 0.879179752937634 19 80.9 86.3224635131064 -5.42246351310636 20 95.7 97.0312303705935 -1.33123037059355 21 113.2 111.516435432359 1.68356456764086 22 105.9 111.252873636638 -5.35287363663755 23 108.8 104.96821633022 3.83178366978005 24 102.3 97.707120819524 4.59287918047604 25 99 98.562556191624 0.437443808376024 26 100.7 101.622191021392 -0.92219102139198 27 115.5 111.582191021392 3.91780897860801 28 100.7 105.098629225670 -4.39862922567038 29 109.9 103.360272491714 6.53972750828563 30 114.6 113.200272491714 1.39972750828562 31 85.4 87.2197247363664 -1.81972473636638 32 100.5 98.2873960831576 2.21260391684242 33 114.8 112.952053389575 1.84794661042483 34 116.5 113.585752817114 2.91424718288641 35 112.9 107.480547755348 5.41945224465201 36 102 100.578356733956 1.42164326604399 37 106 99.99817414884 6.00182585115999 38 105.3 103.775617957216 1.52438204278397 39 118.8 113.735617957216 5.06438204278397 40 106.1 107.252056161494 -1.15205616149443 41 109.3 106.231508406146 3.06849159385357 42 117.2 116.609865140102 0.590134859897562 43 92.5 90.8087696294065 1.69123037059355 44 104.2 101.876440976198 2.32355902380235 45 112.5 117.438359505875 -4.93835950587527 46 122.4 116.995345465502 5.40465453449834 47 113.3 110.531235914432 2.76876408556794 48 100 102.552331425128 -2.55233142512805 49 110.7 102.151601084664 8.54839891533596 50 112.8 105.570140403736 7.22985959626394 51 109.8 115.530140403736 -5.73014040373607 52 117.3 108.867126363362 8.43287363663755 53 109.1 108.205483097318 0.894516902681529 54 115.9 117.686578608014 -1.78657860801446 55 96 92.2443875866225 3.75561241337752 56 99.8 103.670963422718 -3.87096342271769 57 116.8 118.694525218439 -1.89452521843929 58 115.7 118.072058933414 -2.37205893341368 59 99.4 110.710688159084 -11.3106881590841 60 94.3 102.193426935824 -7.89342693582405 61 91 101.433792106056 -10.4337921060560 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.155807742206136 0.311615484412272 0.844192257793864 17 0.076846625956661 0.153693251913322 0.92315337404334 18 0.0474884735704068 0.0949769471408135 0.952511526429593 19 0.0477199697815761 0.0954399395631522 0.952280030218424 20 0.0219261381343761 0.0438522762687523 0.978073861865624 21 0.00908073518397626 0.0181614703679525 0.990919264816024 22 0.00786877003815199 0.0157375400763040 0.992131229961848 23 0.00955812919828087 0.0191162583965617 0.99044187080172 24 0.00513985914235924 0.0102797182847185 0.99486014085764 25 0.00761270150024891 0.0152254030004978 0.99238729849975 26 0.0075653230722832 0.0151306461445664 0.992434676927717 27 0.00931214718811198 0.0186242943762240 0.990687852811888 28 0.00924918128439385 0.0184983625687877 0.990750818715606 29 0.0526308169487893 0.105261633897579 0.94736918305121 30 0.0315075174139895 0.063015034827979 0.96849248258601 31 0.0255704308216063 0.0511408616432125 0.974429569178394 32 0.0149995939161897 0.0299991878323794 0.98500040608381 33 0.00812724110279539 0.0162544822055908 0.991872758897205 34 0.00611448857758184 0.0122289771551637 0.993885511422418 35 0.00378625815004067 0.00757251630008134 0.99621374184996 36 0.00358091881440668 0.00716183762881336 0.996419081185593 37 0.00402778060465449 0.00805556120930899 0.995972219395346 38 0.00250945357175160 0.00501890714350321 0.997490546428248 39 0.00278917250609998 0.00557834501219996 0.9972108274939 40 0.00271486404368972 0.00542972808737944 0.99728513595631 41 0.00118937713576875 0.00237875427153749 0.998810622864231 42 0.000591390796176683 0.00118278159235337 0.999408609203823 43 0.000218101638430536 0.000436203276861072 0.99978189836157 44 0.000142087401796409 0.000284174803592818 0.999857912598204 45 0.00023004963601989 0.00046009927203978 0.99976995036398 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.366666666666667 NOK 5% type I error level 23 0.766666666666667 NOK 10% type I error level 27 0.9 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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