muliple regression_basic. indexcijfer van de totale industriële productie & indexcijfer van grondstoffen, incl.energie

*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 08:13:51 -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/t1258643952mpqnlalfe9cp583.htm/, Retrieved Thu, 19 Nov 2009 16:19:25 +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/t1258643952mpqnlalfe9cp583.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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95.1 117.1 97 118.7 112.7 126.5 102.9 127.5 97.4 134.6 111.4 131.8 87.4 135.9 96.8 142.7 114.1 141.7 110.3 153.4 103.9 145 101.6 137.7 94.6 148.3 95.9 152.2 104.7 169.4 102.8 168.6 98.1 161.1 113.9 174.1 80.9 179 95.7 190.6 113.2 190 105.9 181.6 108.8 174.8 102.3 180.5 99 196.8 100.7 193.8 115.5 197 100.7 216.3 109.9 221.4 114.6 217.9 85.4 229.7 100.5 227.4 114.8 204.2 116.5 196.6 112.9 198.8 102 207.5 106 190.7 105.3 201.6 118.8 210.5 106.1 223.5 109.3 223.8 117.2 231.2 92.5 244 104.2 234.7 112.5 250.2 122.4 265.7 113.3 287.6 100 283.3 110.7 295.4 112.8 312.3 109.8 333.8 117.3 347.7 109.1 383.2 115.9 407.1 96 413.6 99.8 362.7 116.8 321.9 115.7 239.4 99.4 191 94.3 159.7 91 163.4

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation tot.ind.prod.index[t] = + 97.0651490600515 + 0.0381800024164384prijsindex.grondst.incl.energie[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) 97.0651490600515 3.509877 27.6549 0 0 prijsindex.grondst.incl.energie 0.0381800024164384 0.015644 2.4405 0.017689 0.008845 Multiple Linear Regression - Regression Statistics Multiple R 0.302807907985026 R-squared 0.091692629138268 Adjusted R-squared 0.0762975889541708 F-TEST (value) 5.95598504724821 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.0176891166963650 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.75875544910125 Sum Squared Residuals 4526.23202401249 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 101.536027343016 -6.43602734301649 2 97 101.597115346883 -4.59711534688277 3 112.7 101.894919365731 10.805080634269 4 102.9 101.933099368147 0.966900631852572 5 97.4 102.204177385304 -4.80417738530414 6 111.4 102.097273378538 9.30272662146189 7 87.4 102.253811388446 -14.8538113884455 8 96.8 102.513435404877 -5.7134354048773 9 114.1 102.475255402461 11.6247445975391 10 110.3 102.921961430733 7.37803856926681 11 103.9 102.601249410435 1.2987505895649 12 101.6 102.322535392795 -0.72253539279511 13 94.6 102.727243418409 -8.12724341840936 14 95.9 102.876145427833 -6.97614542783346 15 104.7 103.532841469396 1.16715853060380 16 102.8 103.502297467463 -0.702297467463053 17 98.1 103.215947449340 -5.11594744933977 18 113.9 103.712287480753 10.1877125192465 19 80.9 103.899369492594 -22.999369492594 20 95.7 104.342257520625 -8.6422575206247 21 113.2 104.319349519175 8.88065048082517 22 105.9 103.998637498877 1.90136250112326 23 108.8 103.739013482445 5.06098651755503 24 102.3 103.956639496219 -1.65663949621867 25 99 104.578973535607 -5.57897353560661 26 100.7 104.464433528357 -3.76443352835729 27 115.5 104.58660953609 10.9133904639101 28 100.7 105.323483582727 -4.62348358272716 29 109.9 105.518201595051 4.38179840494901 30 114.6 105.384571586593 9.21542841340653 31 85.4 105.835095615107 -20.4350956151074 32 100.5 105.747281609550 -5.24728160954963 33 114.8 104.861505553488 9.93849444651174 34 116.5 104.571337535123 11.9286624648767 35 112.9 104.655333540439 8.24466645956052 36 102 104.987499561462 -2.9874995614625 37 106 104.346075520866 1.65392447913366 38 105.3 104.762237547206 0.537762452794481 39 118.8 105.102039568712 13.6979604312882 40 106.1 105.598379600126 0.501620399874478 41 109.3 105.609833600850 3.69016639914955 42 117.2 105.892365618732 11.3076343812679 43 92.5 106.381069649663 -13.8810696496625 44 104.2 106.025995627190 -1.82599562718962 45 112.5 106.617785664644 5.88221433535558 46 122.4 107.209575702099 15.1904242979008 47 113.3 108.045717755019 5.25428224498078 48 100 107.881543744629 -7.88154374462853 49 110.7 108.343521773867 2.35647822613257 50 112.8 108.988763814705 3.81123618529475 51 109.8 109.809633866659 -0.00963386665867005 52 117.3 110.340335900247 6.95966409975284 53 109.1 111.695725986031 -2.59572598603073 54 115.9 112.608228043784 3.29177195621641 55 96 112.856398059490 -16.8563980594904 56 99.8 110.913035936494 -11.1130359364937 57 116.8 109.355291837903 7.44470816209695 58 115.7 106.205441638547 9.49455836145312 59 99.4 104.357529521591 -4.95752952159126 60 94.3 103.162495445957 -8.86249544595675 61 91 103.303761454898 -12.3037614548976 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.48852038055793 0.97704076111586 0.51147961944207 6 0.428458910274713 0.856917820549426 0.571541089725287 7 0.71557030272188 0.56885939455624 0.28442969727812 8 0.609286736705344 0.781426526589311 0.390713263294656 9 0.70266326295086 0.59467347409828 0.29733673704914 10 0.625207867714216 0.749584264571568 0.374792132285784 11 0.521607312123254 0.956785375753493 0.478392687876746 12 0.421190775049421 0.842381550098842 0.578809224950579 13 0.440110285932732 0.880220571865464 0.559889714067268 14 0.408454249576488 0.816908499152976 0.591545750423512 15 0.321280151393456 0.642560302786911 0.678719848606544 16 0.244119043610301 0.488238087220602 0.755880956389699 17 0.198337163713323 0.396674327426646 0.801662836286677 18 0.216273555822111 0.432547111644221 0.78372644417789 19 0.646423846269238 0.707152307461524 0.353576153730762 20 0.609420193752477 0.781159612495047 0.390579806247523 21 0.65424185088829 0.69151629822342 0.34575814911171 22 0.587654158742085 0.82469168251583 0.412345841257915 23 0.539067037226234 0.921865925547532 0.460932962773766 24 0.464522837943202 0.929045675886404 0.535477162056798 25 0.415326426731082 0.830652853462164 0.584673573268918 26 0.354391153321591 0.708782306643182 0.64560884667841 27 0.397008316296813 0.794016632593626 0.602991683703187 28 0.345435367254843 0.690870734509686 0.654564632745157 29 0.293850043565377 0.587700087130755 0.706149956434623 30 0.288189512860958 0.576379025721917 0.711810487139042 31 0.612133271886826 0.775733456226348 0.387866728113174 32 0.567073623823013 0.865852752353973 0.432926376176987 33 0.58076415191958 0.83847169616084 0.41923584808042 34 0.626739926317229 0.746520147365542 0.373260073682771 35 0.608536122972555 0.78292775405489 0.391463877027445 36 0.544258707418428 0.911482585163144 0.455741292581572 37 0.468184108557091 0.936368217114181 0.531815891442909 38 0.391673603726995 0.783347207453991 0.608326396273005 39 0.482937244043709 0.965874488087417 0.517062755956291 40 0.404306075572635 0.80861215114527 0.595693924427365 41 0.340321362029421 0.680642724058842 0.659678637970579 42 0.387717356944843 0.775434713889685 0.612282643055157 43 0.49536785703022 0.99073571406044 0.50463214296978 44 0.413600009961027 0.827200019922053 0.586399990038973 45 0.367850711102947 0.735701422205894 0.632149288897053 46 0.554732145437648 0.890535709124704 0.445267854562352 47 0.514210114887598 0.971579770224804 0.485789885112402 48 0.477761851449873 0.955523702899746 0.522238148550127 49 0.399128694765867 0.798257389531733 0.600871305234133 50 0.3382228611141 0.6764457222282 0.6617771388859 51 0.254036744574418 0.508073489148835 0.745963255425582 52 0.252887259762176 0.505774519524352 0.747112740237824 53 0.174935562141397 0.349871124282795 0.825064437858603 54 0.150318755398436 0.300637510796873 0.849681244601564 55 0.249077853181075 0.498155706362151 0.750922146818925 56 0.722328815731794 0.555342368536411 0.277671184268206 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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