Totale productieindex

*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 13:20:00 -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/t1258575762ee5g8dbb0sk1uht.htm/, Retrieved Wed, 18 Nov 2009 21:22:54 +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/t1258575762ee5g8dbb0sk1uht.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 «

97 95,1 112,7 97 102,9 112,7 97,4 102,9 111,4 97,4 87,4 111,4 96,8 87,4 114,1 96,8 110,3 114,1 103,9 110,3 101,6 103,9 94,6 101,6 95,9 94,6 104,7 95,9 102,8 104,7 98,1 102,8 113,9 98,1 80,9 113,9 95,7 80,9 113,2 95,7 105,9 113,2 108,8 105,9 102,3 108,8 99 102,3 100,7 99 115,5 100,7 100,7 115,5 109,9 100,7 114,6 109,9 85,4 114,6 100,5 85,4 114,8 100,5 116,5 114,8 112,9 116,5 102 112,9 106 102 105,3 106 118,8 105,3 106,1 118,8 109,3 106,1 117,2 109,3 92,5 117,2 104,2 92,5 112,5 104,2 122,4 112,5 113,3 122,4 100 113,3 110,7 100 112,8 110,7 109,8 112,8 117,3 109,8 109,1 117,3 115,9 109,1 96 115,9 99,8 96 116,8 99,8 115,7 116,8 99,4 115,7 94,3 99,4 91 94,3

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 Y1[t] = + 97.8054993871467 + 0.0491656425600409Y2[t] + 4.03172874511132Q1[t] -3.82809578374928Q2[t] -4.56928736546918Q3[t] + 0.113211610424201t + 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) 97.8054993871467 14.05185 6.9603 0 0 Y2 0.0491656425600409 0.142307 0.3455 0.731069 0.365534 Q1 4.03172874511132 3.212576 1.255 0.214889 0.107445 Q2 -3.82809578374928 3.363404 -1.1382 0.260078 0.130039 Q3 -4.56928736546918 3.118295 -1.4653 0.148633 0.074317 t 0.113211610424201 0.067963 1.6658 0.10155 0.050775 Multiple Linear Regression - Regression Statistics Multiple R 0.442267014501563 R-squared 0.195600112116126 Adjusted R-squared 0.121118641015767 F-TEST (value) 2.62615801254204 F-TEST (DF numerator) 5 F-TEST (DF denominator) 54 p-value 0.0338316094165916 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.52590672585904 Sum Squared Residuals 3925.31861689461 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97 106.626092350142 -9.62609235014232 2 112.7 98.9728941525699 13.7271058474302 3 102.9 99.1168147694668 3.78318523053323 4 97.4 103.317490448272 -5.91749044827176 5 111.4 107.192019769727 4.20798023027294 6 87.4 100.133725847131 -12.7337258471312 7 96.8 98.3257704543946 -1.52577045439456 8 114.1 103.470426470352 10.6295735296477 9 110.3 108.465932442177 1.83406755782345 10 103.9 100.532490082012 3.36750991798802 11 101.6 99.589849998332 2.01015000166796 12 94.6 104.159267996337 -9.55926799633732 13 95.9 107.960048853953 -12.0600488539525 14 104.7 100.277351270844 4.4226487291558 15 102.8 100.082028954077 2.71797104592313 16 98.1 104.671113209106 -6.57111320910617 17 113.9 108.584975044609 5.31502495539051 18 80.9 101.615179278622 -20.7151792786217 19 95.7 99.3647331028447 -3.6647331028447 20 113.2 104.774883588627 8.42511641137332 21 105.9 109.780222688963 -3.88022268896291 22 108.8 101.674700579838 7.12529942016179 23 102.3 101.189300971967 1.11069902803336 24 99 105.552223271220 -6.55222327121975 25 100.7 109.534917006307 -8.83491700630714 26 115.5 101.871885680223 13.6281143197772 27 100.7 101.971557218816 -1.27155721881571 28 109.9 105.926404684820 3.97359531517952 29 114.6 110.523668951908 4.07633104809161 30 85.4 103.008134553504 -17.6081345535042 31 100.5 100.944517819455 -0.44451781945529 32 114.8 106.369417998005 8.43058200199472 33 116.5 111.217427042149 5.28257295785061 34 112.9 103.554395716065 9.34560428393495 35 102 102.749419431553 -0.749419431553215 36 106 106.896012903542 -0.896012903542142 37 105.3 111.237615829318 -5.93761582931784 38 118.8 103.456586961089 15.3434130389106 39 106.1 103.492343164354 2.60765683564573 40 109.3 107.550438479735 1.74956152026488 41 117.2 111.852708891463 5.34729110853723 42 92.5 104.494504549251 -11.9945045492507 43 104.2 102.652133206722 1.54786679327802 44 112.5 107.909870200568 4.59012979943216 45 122.4 112.462885389352 9.9371146106483 46 113.3 105.203012332260 8.0969876677403 47 100 104.127625013668 -4.12762501366764 48 110.7 108.156220943512 2.54377905648754 49 112.8 112.827233674440 -0.0272336744404358 50 109.8 105.183868605380 4.61613139461988 51 117.3 104.408391706404 12.8916082935957 52 109.1 109.459633001498 -0.359633001497983 53 115.9 113.201415088041 2.69858491195884 54 96 105.789128539013 -9.78912853901304 55 99.8 104.182752280773 -4.38275228077254 56 116.8 109.052080698394 7.74791930160593 57 115.7 114.032836977450 1.66716302254972 58 99.4 106.232141852198 -6.83214185219783 59 94.3 104.802761907173 -10.5027619071735 60 91 109.234516106011 -18.2345161060106 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.941051504237183 0.117896991525634 0.0589484957628168 10 0.884072232892064 0.231855534215871 0.115927767107936 11 0.803920107933187 0.392159784133627 0.196079892066813 12 0.808293258677418 0.383413482645164 0.191706741322582 13 0.798875142040497 0.402249715919006 0.201124857959503 14 0.732436468404674 0.535127063190651 0.267563531595326 15 0.647215496983055 0.70556900603389 0.352784503016945 16 0.568406556476597 0.863186887046806 0.431593443523403 17 0.55462819719598 0.89074360560804 0.44537180280402 18 0.814759690924949 0.370480618150102 0.185240309075051 19 0.76801783450962 0.46396433098076 0.23198216549038 20 0.791411146264309 0.417177707471382 0.208588853735691 21 0.746359515320784 0.507280969358432 0.253640484679216 22 0.738732959830807 0.522534080338386 0.261267040169193 23 0.66833452148799 0.66333095702402 0.33166547851201 24 0.637778627305903 0.724442745388195 0.362221372694097 25 0.652534388914355 0.69493122217129 0.347465611085645 26 0.73165142456126 0.536697150877481 0.268348575438740 27 0.671925056339152 0.656149887321695 0.328074943660848 28 0.607557000255724 0.784885999488552 0.392442999744276 29 0.556788545963637 0.886422908072726 0.443211454036363 30 0.838080819876808 0.323838360246384 0.161919180123192 31 0.790806129959747 0.418387740080507 0.209193870040253 32 0.760987865559793 0.478024268880415 0.239012134440207 33 0.722125871541213 0.555748256917573 0.277874128458787 34 0.695277504995027 0.609444990009945 0.304722495004973 35 0.639710312990836 0.720579374018329 0.360289687009164 36 0.581038060226788 0.837923879546423 0.418961939773212 37 0.659450709215525 0.68109858156895 0.340549290784475 38 0.75721217132348 0.485575657353041 0.242787828676520 39 0.705308739402783 0.589382521194435 0.294691260597217 40 0.634297108002892 0.731405783994216 0.365702891997108 41 0.55610644261167 0.88778711477666 0.44389355738833 42 0.780886075255423 0.438227849489153 0.219113924744577 43 0.707070618075861 0.585858763848278 0.292929381924139 44 0.621756658666389 0.756486682667221 0.378243341333611 45 0.540091737419002 0.919816525161996 0.459908262580998 46 0.450294139250525 0.900588278501051 0.549705860749474 47 0.565113958720405 0.86977208255919 0.434886041279595 48 0.449409761324765 0.89881952264953 0.550590238675235 49 0.458653446098489 0.917306892196979 0.541346553901511 50 0.32414699662025 0.6482939932405 0.67585300337975 51 0.286837692536864 0.573675385073729 0.713162307463136 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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