multiple regression met 2 maanden minder, totale industrie zonder bouwnijverheid, prijsindex van de industriele grondstoffen

*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: Thu, 19 Nov 2009 08:49:29 -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/t1258645938mpf0gppb9hwysbo.htm/, Retrieved Thu, 19 Nov 2009 16:52:31 +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/Nov/19/t1258645938mpf0gppb9hwysbo.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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105.6 86.2 96.9 97.6 102.8 86.1 105.6 96.9 101.7 86.2 102.8 105.6 104.2 88.8 101.7 102.8 92.7 89.6 104.2 101.7 91.9 87.8 92.7 104.2 106.5 88.3 91.9 92.7 112.3 88.6 106.5 91.9 102.8 91 112.3 106.5 96.5 91.5 102.8 112.3 101 95.4 96.5 102.8 98.9 98.7 101 96.5 105.1 99.9 98.9 101 103 98.6 105.1 98.9 99 100.3 103 105.1 104.3 100.2 99 103 94.6 100.4 104.3 99 90.4 101.4 94.6 104.3 108.9 103 90.4 94.6 111.4 109.1 108.9 90.4 100.8 111.4 111.4 108.9 102.5 114.1 100.8 111.4 98.2 121.8 102.5 100.8 98.7 127.6 98.2 102.5 113.3 129.9 98.7 98.2 104.6 128 113.3 98.7 99.3 123.5 104.6 113.3 111.8 124 99.3 104.6 97.3 127.4 111.8 99.3 97.7 127.6 97.3 111.8 115.6 128.4 97.7 97.3 111.9 131.4 115.6 97.7 107 135.1 111.9 115.6 107.1 134 107 111.9 100.6 144.5 107.1 107 99.2 147.3 100.6 107.1 108.4 150.9 99.2 100.6 103 148.7 108.4 99.2 99.8 141.4 103 108.4 115 138.9 99.8 103 90.8 139.8 115 99.8 95.9 145.6 90.8 115 114.4 147.9 95.9 90.8 108.2 148.5 114.4 95.9 112.6 151.1 108.2 114.4 109.1 157. etc...

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 tot_indus[t] = + 134.94014688261 + 0.128373522157055prijsindex[t] -0.0277011889880574`y(t-1)`[t] -0.425165410701896`y(t-2)`[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) 134.94014688261 14.894294 9.0599 0 0 prijsindex 0.128373522157055 0.020226 6.3469 0 0 `y(t-1)` -0.0277011889880574 0.110892 -0.2498 0.803504 0.401752 `y(t-2)` -0.425165410701896 0.111934 -3.7984 0.000316 0.000158 Multiple Linear Regression - Regression Statistics Multiple R 0.657695865815495 R-squared 0.432563851910793 Adjusted R-squared 0.407156263190381 F-TEST (value) 17.0249863798872 F-TEST (DF numerator) 3 F-TEST (DF denominator) 67 p-value 2.52390219834808e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.01689199427035 Sum Squared Residuals 2425.60028113788 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.6 101.825555195101 3.77444480489936 2 102.8 101.869333286180 0.930666713820146 3 101.7 98.2607948944556 3.43920510554437 4 104.2 99.8155005099161 4.38449949008386 5 92.7 100.316628306944 -7.61662830694372 6 91.9 99.341206113669 -7.44120611366894 7 106.5 104.316956049010 2.18304395099027 8 112.3 104.291163074993 8.00883692500728 9 102.8 98.2311776357912 4.56882236420876 10 96.5 96.0925663101853 0.407433689814681 11 101 100.806811938891 0.193188061109394 12 98.9 103.784331298985 -4.88433129898457 13 105.1 102.083307674289 3.01669232571057 14 103 102.637522086233 0.362477913766722 15 99 100.277904024423 -1.27790402442344 16 104.3 101.268718790634 3.03128120936605 17 94.6 102.848238836236 -8.24823883623624 18 90.4 100.991937214857 -10.5919372148574 19 108.9 105.437784327867 3.46221567213308 20 111.4 107.494085541694 3.90591445830615 21 100.8 99.8545315721999 0.945468427800138 22 102.5 99.4318591585426 3.06814084145743 23 98.2 104.879996611312 -6.6799966113123 24 98.7 105.020896954279 -6.32089695427864 25 113.3 107.130516726764 6.169483273236 26 104.6 106.269586970089 -1.66958697008901 27 99.3 99.7254914683307 -0.425491468330677 28 111.8 103.635433604152 8.1645663958476 29 97.3 105.979015393856 -8.67901539385572 30 97.7 101.091789704840 -3.39178970484026 31 115.6 107.348306502148 8.25169349785182 32 111.9 107.067509621452 4.83249037854765 33 107 100.034525201125 6.96547479887467 34 107.1 101.602162172391 5.49783782760893 35 100.6 105.030624548581 -4.43062454858063 36 99.2 105.527611597973 -6.32761159797257 37 108.4 108.792113111884 -0.392113111883563 38 103 108.850071999431 -5.85007199943057 39 99.8 104.151009929762 -4.35100992976214 40 115 106.214613146922 8.78538685307848 41 90.8 107.269620558490 -16.4696205584905 42 95.9 102.222041517844 -6.32204151784355 43 114.4 112.665027493952 1.73497250604843 44 108.2 110.061236016387 -1.86123601638707 45 112.6 102.701194447736 9.8988055522637 46 109.1 106.036925304346 3.06307469565425 47 105 105.546886880286 -0.546886880286158 48 105 107.764733598948 -2.76473359894769 49 118.5 109.661960009414 8.83803999058607 50 103.7 111.085223268274 -7.38522326827392 51 112.5 108.066191219649 4.43380878035144 52 116.6 112.779784204508 3.82021579549165 53 96.6 110.131464823757 -13.5314648237570 54 101.9 108.942310419640 -7.04231041964032 55 116.5 116.939356470002 -0.43935647000178 56 119.3 114.961922101488 4.33807789851151 57 115.4 108.625594367211 6.77440563278858 58 108.5 108.056659942928 0.443340057072246 59 111.5 109.970130009761 1.52986999023873 60 108.8 113.321324513053 -4.5213245130527 61 121.8 113.263145838413 8.53685416158744 62 109.6 115.886718357309 -6.28671835730882 63 112.2 110.787383989348 1.4126160106516 64 119.6 114.708505152482 4.89149484751802 65 104.1 113.731857443754 -9.63185744375376 66 105.3 109.718429260088 -4.41842926008837 67 115 116.211064938104 -1.21106493810356 68 124.1 116.163893988372 7.93610601162766 69 116.8 110.978955495183 5.82104450481682 70 107.5 106.362204873447 1.13779512655346 71 115.6 113.549064389440 2.05093561056045 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.604709665213233 0.790580669573534 0.395290334786767 8 0.513615581581438 0.972768836837124 0.486384418418562 9 0.466447919296947 0.932895838593893 0.533552080703053 10 0.381645798411021 0.763291596822042 0.618354201588979 11 0.272297811039761 0.544595622079523 0.727702188960239 12 0.24425681994379 0.48851363988758 0.75574318005621 13 0.232004708020128 0.464009416040256 0.767995291979872 14 0.159118298593071 0.318236597186141 0.84088170140693 15 0.103504579283692 0.207009158567385 0.896495420716308 16 0.0869875459867457 0.173975091973491 0.913012454013254 17 0.148616070986027 0.297232141972054 0.851383929013973 18 0.179507251887657 0.359014503775314 0.820492748112343 19 0.200931151612792 0.401862303225583 0.799068848387208 20 0.157803696758137 0.315607393516274 0.842196303241863 21 0.121624288517198 0.243248577034396 0.878375711482802 22 0.125158864984555 0.250317729969109 0.874841135015445 23 0.121085691168029 0.242171382336059 0.87891430883197 24 0.0971267500960517 0.194253500192103 0.902873249903948 25 0.139869329471796 0.279738658943591 0.860130670528204 26 0.106677360406060 0.213354720812120 0.89332263959394 27 0.0787899613702235 0.157579922740447 0.921210038629777 28 0.127725959518898 0.255451919037796 0.872274040481102 29 0.176427684257517 0.352855368515034 0.823572315742483 30 0.138938750635644 0.277877501271287 0.861061249364356 31 0.184832737108953 0.369665474217906 0.815167262891047 32 0.166944226885047 0.333888453770094 0.833055773114953 33 0.192138634326907 0.384277268653815 0.807861365673093 34 0.188696016627616 0.377392033255233 0.811303983372384 35 0.168356348030113 0.336712696060225 0.831643651969887 36 0.162421925654995 0.32484385130999 0.837578074345005 37 0.122008033375421 0.244016066750842 0.877991966624579 38 0.113413312602252 0.226826625204504 0.886586687397748 39 0.0916248259698815 0.183249651939763 0.908375174030118 40 0.141210155011787 0.282420310023573 0.858789844988213 41 0.46909999422072 0.93819998844144 0.53090000577928 42 0.482867035999918 0.965734071999836 0.517132964000082 43 0.416550444794156 0.833100889588313 0.583449555205844 44 0.362423441234250 0.724846882468499 0.63757655876575 45 0.458562730419559 0.917125460839118 0.541437269580441 46 0.403849637393957 0.807699274787914 0.596150362606043 47 0.331852305311396 0.663704610622792 0.668147694688604 48 0.278898294959515 0.55779658991903 0.721101705040485 49 0.356054614435577 0.712109228871154 0.643945385564423 50 0.369381490717368 0.738762981434737 0.630618509282632 51 0.346267902771499 0.692535805542997 0.653732097228501 52 0.301578933931952 0.603157867863904 0.698421066068048 53 0.631579401824409 0.736841196351182 0.368420598175591 54 0.651545485184074 0.696909029631852 0.348454514815926 55 0.586480766028127 0.827038467943746 0.413519233971873 56 0.511594050500018 0.976811898999964 0.488405949499982 57 0.494412937986824 0.988825875973648 0.505587062013176 58 0.394404131319849 0.788808262639698 0.605595868680151 59 0.298553583889329 0.597107167778658 0.701446416110671 60 0.297915036689472 0.595830073378944 0.702084963310528 61 0.31784850169245 0.6356970033849 0.68215149830755 62 0.334598870892672 0.669197741785345 0.665401129107328 63 0.231610329905622 0.463220659811244 0.768389670094378 64 0.158859615593022 0.317719231186045 0.841140384406978 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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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