Loonkostindex

*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: Fri, 24 Dec 2010 11:40:47 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t1293190743pk3cj0blszccltl.htm/, Retrieved Fri, 24 Dec 2010 12:39:06 +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/2010/Dec/24/t1293190743pk3cj0blszccltl.htm/}, year = {2010}, } @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 = {2010}, 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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81,71 84,86 87,703 85,03 90,09 85,61 100,639 85,52 83,042 86,51 89,956 86,66 89,561 87,27 105,38 87,62 86,554 88,17 93,131 87,99 92,812 88,83 102,195 88,75 88,925 88,81 94,184 89,43 94,196 89,5 108,932 89,34 91,134 89,75 97,149 90,26 96,415 90,32 112,432 90,76 92,47 91,53 98,61410515 92,35 97,80117197 93,04 111,8560178 93,35 95,63981455 93,54 104,1120262 95,07 104,0148224 95,39 118,1743476 95,43 102,033431 96,09 109,3138852 96,35 108,1523649 96,6 121,30381 96,62 103,8725146 97,6 112,7185207 97,67 109,0381253 98,23 122,4434864 98,29 106,6325686 98,89 113,8153852 99,88 111,1071252 100,42 130,039536 100,81 109,6121057 101,5 116,8592117 102,59 113,8982545 103,58 128,9375926 103,47 111,8120023 103,77 119,9689463 104,65 117,018539 105,12 132,4743387 104,97 116,3369106 105,58 124,6405636 106,17 121,025249 106,52 137,2054829 107,87 120,0187687 109,63 127,0443429 111,54 124,349043 112,47 143,6114438 111,63

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 5 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation LKI[t] = -47.7762553333726 + 1.6142611431639CPI[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) -47.7762553333726 12.116984 -3.9429 0.000234 0.000117 CPI 1.6142611431639 0.125506 12.862 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.868279845574862 R-squared 0.753909890231506 Adjusted R-squared 0.749352665976534 F-TEST (value) 165.431817275386 F-TEST (DF numerator) 1 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.25340453011476 Sum Squared Residuals 2841.04137298442 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 81.71 89.2099452755156 -7.49994527551565 2 87.703 89.4843696698534 -1.78136966985342 3 90.09 90.4206411328885 -0.330641132888482 4 100.639 90.2753576300037 10.3636423699963 5 83.042 91.873476161736 -8.831476161736 6 89.956 92.1156153332106 -2.15961533321057 7 89.561 93.1003146305406 -3.53931463054054 8 105.38 93.665306030648 11.7146939693521 9 86.554 94.553149659388 -7.99914965938806 10 93.131 94.2625826536186 -1.13158265361855 11 92.812 95.6185620138762 -2.80656201387623 12 102.195 95.4894211224231 6.70557887757687 13 88.925 95.586276791013 -6.66127679101296 14 94.184 96.5871186997746 -2.40311869977458 15 94.196 96.700116979796 -2.50411697979604 16 108.932 96.4418351968898 12.4901648031102 17 91.134 97.103682265587 -5.96968226558702 18 97.149 97.9269554486006 -0.777955448600611 19 96.415 98.0238111171904 -1.60881111719042 20 112.432 98.7340860201826 13.6979139798174 21 92.47 99.9770671004188 -7.50706710041875 22 98.61410515 101.300761237813 -2.68665608781314 23 97.80117197 102.414601426596 -4.61342945659625 24 111.8560178 102.915022380977 8.94099541902297 25 95.63981455 103.221731998178 -7.5819174481782 26 104.1120262 105.691551547219 -1.57952534721893 27 104.0148224 106.208115113031 -2.19329271303139 28 118.1743476 106.272685558758 11.901662041242 29 102.033431 107.338097913246 -5.30466691324613 30 109.3138852 107.757805810469 1.55607938953128 31 108.1523649 108.16137109626 -0.00900619625969844 32 121.30381 108.193656319123 13.110153680877 33 103.8725146 109.775632239424 -5.90311763942359 34 112.7185207 109.888630519445 2.82989018055493 35 109.0381253 110.792616759617 -1.75449145961685 36 122.4434864 110.889472428207 11.5540139717933 37 106.6325686 111.858029114105 -5.22546051410503 38 113.8153852 113.456147645837 0.359237554162722 39 111.1071252 114.327848663146 -3.22072346314579 40 130.039536 114.95741050898 15.0821254910203 41 109.6121057 116.071250697763 -6.45914499776279 42 116.8592117 117.830795343811 -0.97158364381144 43 113.8982545 119.428913875544 -5.5306593755437 44 128.9375926 119.251345149796 9.68624745020432 45 111.8120023 119.735623492745 -7.92362119274482 46 119.9689463 121.156173298729 -1.18722699872907 47 117.018539 121.914876036016 -4.89633703601609 48 132.4743387 121.672736864542 10.8016018354585 49 116.3369106 122.657436161871 -6.32052556187149 50 124.6405636 123.609850236338 1.03071336366181 51 121.025249 124.174841636446 -3.14959263644554 52 137.2054829 126.354094179717 10.8513887202832 53 120.0187687 129.195193791685 -9.17642509168526 54 127.0443429 132.278432575128 -5.23408967512832 55 124.349043 133.779695438271 -9.43065243827073 56 143.6114438 132.423716078013 11.1877277219869 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.753466226164995 0.493067547670009 0.246533773835005 6 0.611667619349238 0.776664761301524 0.388332380650762 7 0.467554213735781 0.935108427471563 0.532445786264219 8 0.65934024140233 0.68131951719534 0.34065975859767 9 0.691579757638288 0.616840484723424 0.308420242361712 10 0.586060967305494 0.827878065389012 0.413939032694506 11 0.484733267465191 0.969466534930382 0.515266732534809 12 0.474684324922186 0.949368649844371 0.525315675077815 13 0.453309820044304 0.906619640088609 0.546690179955696 14 0.364926450397829 0.729852900795659 0.63507354960217 15 0.285659393052765 0.571318786105529 0.714340606947235 16 0.457843204079954 0.915686408159908 0.542156795920046 17 0.435886760961314 0.871773521922628 0.564113239038686 18 0.353453930929204 0.706907861858408 0.646546069070796 19 0.281906802114932 0.563813604229863 0.718093197885068 20 0.44540689856288 0.89081379712576 0.55459310143712 21 0.477694130936846 0.955388261873692 0.522305869063154 22 0.41401348703048 0.82802697406096 0.58598651296952 23 0.373647883287073 0.747295766574147 0.626352116712927 24 0.393093550455493 0.786187100910987 0.606906449544507 25 0.419705384611607 0.839410769223214 0.580294615388393 26 0.352950245262099 0.705900490524198 0.647049754737901 27 0.295937127460256 0.591874254920511 0.704062872539744 28 0.380142969143599 0.760285938287198 0.619857030856401 29 0.366773100365042 0.733546200730083 0.633226899634958 30 0.296131185534756 0.592262371069513 0.703868814465244 31 0.234953846508761 0.469907693017523 0.765046153491239 32 0.329107651076494 0.658215302152988 0.670892348923506 33 0.329592882501272 0.659185765002545 0.670407117498728 34 0.261645534698039 0.523291069396078 0.738354465301961 35 0.212055795516086 0.424111591032171 0.787944204483914 36 0.261907856142785 0.52381571228557 0.738092143857215 37 0.245569731609281 0.491139463218561 0.754430268390719 38 0.185376116352387 0.370752232704774 0.814623883647613 39 0.15294500619706 0.305890012394121 0.84705499380294 40 0.308696591857702 0.617393183715404 0.691303408142298 41 0.29673819656623 0.59347639313246 0.70326180343377 42 0.226310454616637 0.452620909233274 0.773689545383363 43 0.203439686013746 0.406879372027492 0.796560313986254 44 0.230672453352898 0.461344906705796 0.769327546647102 45 0.240253795729694 0.480507591459387 0.759746204270306 46 0.171052538316603 0.342105076633206 0.828947461683397 47 0.146533147330338 0.293066294660676 0.853466852669662 48 0.174910175293795 0.349820350587589 0.825089824706206 49 0.15167031133807 0.303340622676139 0.84832968866193 50 0.0860347266067153 0.172069453213431 0.913965273393285 51 0.0684863175825185 0.136972635165037 0.931513682417482 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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