Grondstofprijsindex

*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, 18 Nov 2009 13:13:05 -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/t1258575352cag7ipy5rtudn7c.htm/, Retrieved Wed, 18 Nov 2009 21:16:04 +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/t1258575352cag7ipy5rtudn7c.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:

Tijdsperiode Jan 2004 - Jan 2009 Basisjaar 2000=100 Quarterly dummies Linear trend Y1 = y(t-1) Y2= y(t-2) ...

Dataseries X:

» Textbox « » Textfile « » CSV «

102,9 112,7 97 95,1 97,4 102,9 112,7 97 111,4 97,4 102,9 112,7 87,4 111,4 97,4 102,9 96,8 87,4 111,4 97,4 114,1 96,8 87,4 111,4 110,3 114,1 96,8 87,4 103,9 110,3 114,1 96,8 101,6 103,9 110,3 114,1 94,6 101,6 103,9 110,3 95,9 94,6 101,6 103,9 104,7 95,9 94,6 101,6 102,8 104,7 95,9 94,6 98,1 102,8 104,7 95,9 113,9 98,1 102,8 104,7 80,9 113,9 98,1 102,8 95,7 80,9 113,9 98,1 113,2 95,7 80,9 113,9 105,9 113,2 95,7 80,9 108,8 105,9 113,2 95,7 102,3 108,8 105,9 113,2 99 102,3 108,8 105,9 100,7 99 102,3 108,8 115,5 100,7 99 102,3 100,7 115,5 100,7 99 109,9 100,7 115,5 100,7 114,6 109,9 100,7 115,5 85,4 114,6 109,9 100,7 100,5 85,4 114,6 109,9 114,8 100,5 85,4 114,6 116,5 114,8 100,5 85,4 112,9 116,5 114,8 100,5 102 112,9 116,5 114,8 106 102 112,9 116,5 105,3 106 102 112,9 118,8 105,3 106 102 106,1 118,8 105,3 106 109,3 106,1 118,8 105,3 117,2 109,3 106,1 118,8 92,5 117,2 109,3 106,1 104,2 92,5 117,2 109,3 112,5 104,2 92,5 117,2 122,4 112,5 104,2 92,5 113,3 122,4 112,5 104,2 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y1[t] = + 116.939613337068 + 0.0430137979567748Y2[t] -0.160013323006682Y3[t] -0.071958961534734Y4[t] + 1.00573465873926Q1[t] + 4.57015060910835Q2[t] + 8.77475886672209Q3[t] + 0.164533502720915t + 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) 116.939613337068 29.223151 4.0016 0.000208 0.000104 Y2 0.0430137979567748 0.147533 0.2916 0.771834 0.385917 Y3 -0.160013323006682 0.144964 -1.1038 0.274956 0.137478 Y4 -0.071958961534734 0.14995 -0.4799 0.633401 0.316701 Q1 1.00573465873926 3.391478 0.2965 0.76804 0.38402 Q2 4.57015060910835 3.579587 1.2767 0.207597 0.103798 Q3 8.77475886672209 3.303078 2.6565 0.010568 0.005284 t 0.164533502720915 0.082545 1.9933 0.051703 0.025852 Multiple Linear Regression - Regression Statistics Multiple R 0.508795301197775 R-squared 0.258872658520935 Adjusted R-squared 0.155114830713866 F-TEST (value) 2.49496991207537 F-TEST (DF numerator) 7 F-TEST (DF denominator) 50 p-value 0.0280160670640583 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.39623371672563 Sum Squared Residuals 3524.83703129402 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.9 100.592946954656 2.30705304534434 2 97.4 101.251429989648 -3.85142998964828 3 111.4 105.822370730591 5.57762926940915 4 87.4 99.3996096375617 -11.9996096375616 5 96.8 97.6931344144067 -0.893134414406719 6 114.1 104.659307858965 9.44069214103548 7 110.3 109.995478164522 0.304521835477825 8 103.9 97.7771556418432 6.12284435815686 9 101.6 98.0352960892545 3.56470391074554 10 94.6 102.962843128119 -8.36284312811865 11 95.9 107.859456299494 -11.9594562994935 12 104.7 100.590747745413 4.10925225458716 13 102.8 102.435232739727 0.364767260272917 14 98.1 104.580792084245 -6.48079208424526 15 113.9 108.418555446390 5.4814445536099 16 80.9 101.376732735153 -20.4767327351534 17 95.7 98.9375421797476 -3.23754217974764 18 113.2 107.446583909570 5.75341609043036 19 105.9 112.574915684295 -6.67491568429517 20 108.8 99.7854638118785 9.01453618812146 21 102.3 100.989287418504 1.3107125814957 22 99 104.499908967359 -5.49990896735945 23 100.7 109.558510805529 -8.85851080552945 24 115.5 102.017186113953 13.4828138860474 25 100.7 103.789500409126 -3.08950040912632 26 109.9 104.391318237348 5.5086817626519 27 114.6 110.45939148867 4.14060851133006 28 85.4 101.644201034118 -16.2442010341182 29 100.5 100.144381230990 0.355618769010429 30 114.8 108.857020945809 5.94297905419124 31 116.5 113.526260516339 2.97373948366138 32 112.9 101.614387770694 11.2856122293061 33 102 101.328770460452 0.671229539548353 34 106 105.042587244028 0.957412755972183 35 105.3 111.586981678487 -6.28698167848746 36 118.8 103.090946044618 15.7090539553816 37 106.1 104.666073958461 1.43392604153921 38 109.3 105.738939589984 3.56106041001615 39 117.2 111.306448725246 5.89355127475386 40 92.5 103.437868542973 -10.9378685429732 41 104.2 102.051321966237 2.14867803376288 42 112.5 109.667386137562 2.83261386243794 43 122.4 114.298772891668 8.10122710833232 44 113.3 103.944353696527 9.35564630347327 45 100 102.541805018076 -2.54180501807580 46 110.7 106.442398478508 4.25760152149236 47 112.8 114.054791622935 -1.25479162293475 48 109.8 104.779806866883 5.02019313311674 49 117.3 104.715044767737 12.5849552322626 50 109.1 109.095523855300 0.00447614469964736 51 115.9 112.127729434444 3.77227056555648 52 96 104.582414933693 -8.58241493369272 53 99.8 104.398681403952 -4.59868140395245 54 116.8 110.986027478675 5.813972521325 55 115.7 116.910336511391 -1.21033651139063 56 99.4 105.259125424691 -5.8591254246914 57 94.3 104.680980988673 -10.3809809886730 58 91 110.877932094881 -19.8779320948806 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.877548519919547 0.244902960160907 0.122451480080453 12 0.81973254734533 0.360534905309339 0.180267452654669 13 0.711202683820628 0.577594632358745 0.288797316179372 14 0.604915842013872 0.790168315972257 0.395084157986128 15 0.554644069399737 0.890711861200527 0.445355930600263 16 0.781760852966076 0.436478294067848 0.218239147033924 17 0.704629478107317 0.590741043785365 0.295370521892682 18 0.645464851278552 0.709070297442897 0.354535148721448 19 0.589428896523827 0.821142206952347 0.410571103476173 20 0.725572253140659 0.548855493718681 0.274427746859341 21 0.642090283978489 0.715819432043023 0.357909716021512 22 0.592659286727232 0.814681426545536 0.407340713272768 23 0.603228550387419 0.793542899225161 0.396771449612581 24 0.693471964484283 0.613056071031434 0.306528035515717 25 0.637742549298866 0.724514901402269 0.362257450701135 26 0.591897249877757 0.816205500244487 0.408102750122243 27 0.523780756668128 0.952438486663743 0.476219243331872 28 0.797339802631258 0.405320394737483 0.202660197368742 29 0.739269426609011 0.521461146781978 0.260730573390989 30 0.669796294822427 0.660407410355146 0.330203705177573 31 0.660427958645135 0.67914408270973 0.339572041354865 32 0.669688845137591 0.660622309724818 0.330311154862409 33 0.594534173494466 0.810931653011067 0.405465826505533 34 0.518076653841722 0.963846692316556 0.481923346158278 35 0.578069735109601 0.843860529780797 0.421930264890399 36 0.656112766107032 0.687774467785936 0.343887233892968 37 0.610564001384789 0.778871997230421 0.389435998615211 38 0.539801204975346 0.920397590049307 0.460198795024654 39 0.451596704730048 0.903193409460096 0.548403295269952 40 0.697634353727699 0.604731292544603 0.302365646272302 41 0.615039382607166 0.769921234785669 0.384960617392834 42 0.535669263740292 0.928661472519416 0.464330736259708 43 0.482781972460387 0.965563944920774 0.517218027539613 44 0.376966363182743 0.753932726365486 0.623033636817257 45 0.484888477591635 0.96977695518327 0.515111522408365 46 0.339935111991353 0.679870223982705 0.660064888008647 47 0.323763860342543 0.647527720685086 0.676236139657457 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 = Include Quarterly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly Dummies ; par3 = 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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