multiple regression van prijsindexcijfer grondstoffen, incl. energie & indexcijfer van de industriële productie

*Unverified author*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 18 Nov 2009 13:21:11 -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/18/t1258575742xp0wtw1ehi80sj6.htm/, Retrieved Wed, 18 Nov 2009 21:22:34 +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/Nov/18/t1258575742xp0wtw1ehi80sj6.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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117.1 95.1 118.7 97 126.5 112.7 127.5 102.9 134.6 97.4 131.8 111.4 135.9 87.4 142.7 96.8 141.7 114.1 153.4 110.3 145 103.9 137.7 101.6 148.3 94.6 152.2 95.9 169.4 104.7 168.6 102.8 161.1 98.1 174.1 113.9 179 80.9 190.6 95.7 190 113.2 181.6 105.9 174.8 108.8 180.5 102.3 196.8 99 193.8 100.7 197 115.5 216.3 100.7 221.4 109.9 217.9 114.6 229.7 85.4 227.4 100.5 204.2 114.8 196.6 116.5 198.8 112.9 207.5 102 190.7 106 201.6 105.3 210.5 118.8 223.5 106.1 223.8 109.3 231.2 117.2 244 92.5 234.7 104.2 250.2 112.5 265.7 122.4 287.6 113.3 283.3 100 295.4 110.7 312.3 112.8 333.8 109.8 347.7 117.3 383.2 109.1 407.1 115.9 413.6 96 362.7 99.8 321.9 116.8 239.4 115.7 191 99.4 159.7 94.3 163.4 91

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 prijsindgrondst[t] = -40.0102897317963 + 2.40158782962229indexindustrprod[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) -40.0102897317963 103.886828 -0.3851 0.701524 0.350762 indexindustrprod 2.40158782962229 0.98406 2.4405 0.017689 0.008845 Multiple Linear Regression - Regression Statistics Multiple R 0.302807907985026 R-squared 0.0916926291382681 Adjusted R-squared 0.0762975889541710 F-TEST (value) 5.95598504724822 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.0176891166963649 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 69.4662191260859 Sum Squared Residuals 284707.780380730 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 117.1 188.380712865283 -71.280712865283 2 118.7 192.943729741566 -74.2437297415658 3 126.5 230.648658666636 -104.148658666636 4 127.5 207.113097936337 -79.6130979363374 5 134.6 193.904364873415 -59.3043648734147 6 131.8 227.526594488127 -95.7265944881268 7 135.9 169.888486577192 -33.9884865771918 8 142.7 192.463412175641 -49.7634121756414 9 141.7 234.010881628107 -92.310881628107 10 153.4 224.884847875542 -71.4848478755423 11 145 209.514685765960 -64.5146857659596 12 137.7 203.991033757828 -66.2910337578284 13 148.3 187.179918950472 -38.8799189504723 14 152.2 190.301983128981 -38.1019831289813 15 169.4 211.435956029657 -42.0359560296575 16 168.6 206.872939153375 -38.2729391533751 17 161.1 195.585476354150 -34.4854763541503 18 174.1 233.530564062183 -59.4305640621826 19 179 154.278165684647 24.7218343153530 20 190.6 189.821665563057 0.77833443694315 21 190 231.849452581447 -41.8494525814469 22 181.6 214.317861425204 -32.7178614252042 23 174.8 221.282466131109 -46.4824661311088 24 180.5 205.672145238564 -25.1721452385639 25 196.8 197.746905400810 -0.946905400810386 26 193.8 201.829604711168 -8.02960471116829 27 197 237.373104589578 -40.3731045895782 28 216.3 201.829604711168 14.4703952888317 29 221.4 223.924212743693 -2.52421274369338 30 217.9 235.211675542918 -17.3116755429181 31 229.7 165.085310917947 64.6146890820527 32 227.4 201.349287145244 26.0507128547562 33 204.2 235.691993108843 -31.4919931088426 34 196.6 239.774692419201 -43.1746924192005 35 198.8 231.128976232560 -32.3289762325602 36 207.5 204.951668889677 2.54833111032273 37 190.7 214.558020208166 -23.8580202081664 38 201.6 212.876908727431 -11.2769087274308 39 210.5 245.298344427332 -34.7983444273318 40 223.5 214.798178991129 8.70182100887135 41 223.8 222.48326004592 1.31673995408002 42 231.2 241.455803899936 -10.2558038999361 43 244 182.136584508266 61.8634154917345 44 234.7 210.235162114846 24.4648378851537 45 250.2 230.168341100711 20.0316588992887 46 265.7 253.944060613972 11.7559393860280 47 287.6 232.089611364409 55.5103886355909 48 283.3 200.148493230433 83.1515067695673 49 295.4 225.845483007391 69.5545169926088 50 312.3 230.888817449598 81.411182550402 51 333.8 223.684053960731 110.115946039269 52 347.7 241.695962682898 106.004037317102 53 383.2 222.002942479996 161.197057520004 54 407.1 238.333739721427 168.766260278573 55 413.6 190.542141911944 223.057858088056 56 362.7 199.668175664508 163.031824335492 57 321.9 240.495168768087 81.4048312319128 58 239.4 237.853422155503 1.54657784449734 59 191 198.707540532659 -7.70754053265933 60 159.7 186.459442601586 -26.7594426015856 61 163.4 178.534202763832 -15.1342027638321 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00212800725174869 0.00425601450349738 0.997871992748251 6 0.000234934875661048 0.000469869751322096 0.99976506512434 7 7.53622846936056e-05 0.000150724569387211 0.999924637715306 8 3.30718468346579e-05 6.61436936693158e-05 0.999966928153165 9 1.00420533444249e-05 2.00841066888499e-05 0.999989957946656 10 8.78507831664667e-06 1.75701566332933e-05 0.999991214921683 11 2.4998205185364e-06 4.9996410370728e-06 0.999997500179481 12 4.88437919065135e-07 9.7687583813027e-07 0.99999951156208 13 2.24871699145993e-07 4.49743398291985e-07 0.9999997751283 14 1.19411927743264e-07 2.38823855486528e-07 0.999999880588072 15 3.78416339237948e-07 7.56832678475897e-07 0.99999962158366 16 5.10026675462674e-07 1.02005335092535e-06 0.999999489973325 17 2.95783097882315e-07 5.91566195764629e-07 0.999999704216902 18 3.13564951340734e-07 6.27129902681469e-07 0.999999686435049 19 6.13608081510266e-07 1.22721616302053e-06 0.999999386391919 20 1.44168793024032e-06 2.88337586048063e-06 0.99999855831207 21 2.83699316188593e-06 5.67398632377186e-06 0.999997163006838 22 2.41301801228236e-06 4.82603602456473e-06 0.999997586981988 23 1.56735830655739e-06 3.13471661311478e-06 0.999998432641694 24 1.16827633649235e-06 2.3365526729847e-06 0.999998831723663 25 1.69471734117948e-06 3.38943468235897e-06 0.99999830528266 26 1.80211665090772e-06 3.60423330181543e-06 0.999998197883349 27 1.93806027991559e-06 3.87612055983117e-06 0.99999806193972 28 4.72880417183402e-06 9.45760834366805e-06 0.999995271195828 29 9.08364268273567e-06 1.81672853654713e-05 0.999990916357317 30 1.06253133114512e-05 2.12506266229024e-05 0.999989374686689 31 3.14747614098436e-05 6.29495228196872e-05 0.99996852523859 32 4.3587120163884e-05 8.7174240327768e-05 0.999956412879836 33 3.57768025684938e-05 7.15536051369876e-05 0.999964223197432 34 3.02935343730347e-05 6.05870687460693e-05 0.999969706465627 35 2.58578111268122e-05 5.17156222536244e-05 0.999974142188873 36 2.06492701798448e-05 4.12985403596896e-05 0.99997935072982 37 1.69209243580322e-05 3.38418487160643e-05 0.999983079075642 38 1.44039037736971e-05 2.88078075473942e-05 0.999985596096226 39 1.82672041632283e-05 3.65344083264566e-05 0.999981732795837 40 2.01188035488831e-05 4.02376070977662e-05 0.99997988119645 41 2.31250282355324e-05 4.62500564710647e-05 0.999976874971764 42 3.5610827115818e-05 7.1221654231636e-05 0.999964389172884 43 5.66657065439823e-05 0.000113331413087965 0.999943334293456 44 6.09873683608313e-05 0.000121974736721663 0.99993901263164 45 8.64310036451164e-05 0.000172862007290233 0.999913568996355 46 0.000196632291070630 0.000393264582141261 0.99980336770893 47 0.000374497538657624 0.000748995077315248 0.999625502461342 48 0.000627369800283813 0.00125473960056763 0.999372630199716 49 0.000837635472757288 0.00167527094551458 0.999162364527243 50 0.00112825422889140 0.00225650845778280 0.998871745771109 51 0.00182726707044893 0.00365453414089786 0.99817273292955 52 0.00212820566839659 0.00425641133679318 0.997871794331603 53 0.0062855595671137 0.0125711191342274 0.993714440432886 54 0.0157670066025537 0.0315340132051074 0.984232993397446 55 0.257822567970304 0.515645135940608 0.742177432029696 56 0.890971406431063 0.218057187137873 0.109028593568937 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 48 0.923076923076923 NOK 5% type I error level 50 0.961538461538462 NOK 10% type I error level 50 0.961538461538462 NOK

Charts produced by software:

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Parameters (Session):

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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