Multiple Lineair Regression 3

*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, 12 Dec 2008 08:01:15 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/12/t1229094143puyq4t76e5x3pv4.htm/, Retrieved Fri, 12 Dec 2008 16:02:33 +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/2008/Dec/12/t1229094143puyq4t76e5x3pv4.htm/}, year = {2008}, } @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 = {2008}, 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:

» Textbox « » Textfile « » CSV «

91,2 0 99,2 0 108,2 0 101,5 0 106,9 0 104,4 0 77,9 0 60 0 99,5 0 95 0 105,6 0 102,5 0 93,3 0 97,3 0 127 0 111,7 0 96,4 0 133 0 72,2 0 95,8 0 124,1 0 127,6 0 110,7 0 104,6 0 112,7 0 115,3 0 139,4 0 119 0 97,4 0 154 0 81,5 0 88,8 0 127,7 1 105,1 1 114,9 1 106,4 1 104,5 1 121,6 1 141,4 1 99 1 126,7 1 134,1 1 81,3 1 88,6 1 132,7 1 132,9 1 134,4 1 103,7 1 119,7 1 115 1 132,9 1 108,5 1 113,9 1 142 1 97,7 1 92,2 1 128,8 1 134,9 1 128,2 1 114,8 1

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Transportmiddelen[t] = + 96.4804960208562 -2.66374911792379Conjunctuur[t] + 0.504401756311745t + 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) 96.4804960208562 5.349188 18.0365 0 0 Conjunctuur -2.66374911792379 9.119563 -0.2921 0.771277 0.385638 t 0.504401756311745 0.26271 1.92 0.059868 0.029934 Multiple Linear Regression - Regression Statistics Multiple R 0.40328581964221 R-squared 0.162639452324489 Adjusted R-squared 0.133258380476226 F-TEST (value) 5.53551800847939 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 0.00635339875354957 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 17.7304864693868 Sum Squared Residuals 17919.0985751431 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 91.2 96.9848977771678 -5.78489777716781 2 99.2 97.4892995334797 1.71070046652032 3 108.2 97.9937012897915 10.2062987102085 4 101.5 98.4981030461032 3.00189695389681 5 106.9 99.002504802415 7.89749519758507 6 104.4 99.5069065587267 4.89309344127332 7 77.9 100.011308315038 -22.1113083150384 8 60 100.515710071350 -40.5157100713502 9 99.5 101.020111827662 -1.52011182766192 10 95 101.524513583974 -6.52451358397366 11 105.6 102.028915340285 3.57108465971459 12 102.5 102.533317096597 -0.0333170965971528 13 93.3 103.037718852909 -9.7377188529089 14 97.3 103.542120609221 -6.24212060922065 15 127 104.046522365532 22.9534776344676 16 111.7 104.550924121844 7.14907587815587 17 96.4 105.055325878156 -8.65532587815587 18 133 105.559727634468 27.4402723655324 19 72.2 106.064129390779 -33.8641293907794 20 95.8 106.568531147091 -10.7685311470911 21 124.1 107.072932903403 17.0270670965971 22 127.6 107.577334659715 20.0226653402854 23 110.7 108.081736416026 2.61826358397366 24 104.6 108.586138172338 -3.9861381723381 25 112.7 109.090539928650 3.60946007135017 26 115.3 109.594941684962 5.70505831503842 27 139.4 110.099343441273 29.3006565587267 28 119 110.603745197585 8.39625480241493 29 97.4 111.108146953897 -13.7081469538968 30 154 111.612548710209 42.3874512897914 31 81.5 112.116950466520 -30.6169504665203 32 88.8 112.621352222832 -23.8213522228321 33 127.7 110.46200486122 17.23799513878 34 105.1 110.966406617532 -5.86640661753177 35 114.9 111.470808373844 3.4291916261565 36 106.4 111.975210130155 -5.57521013015525 37 104.5 112.479611886467 -7.979611886467 38 121.6 112.984013642779 8.61598635722126 39 141.4 113.488415399090 27.9115846009095 40 99 113.992817155402 -14.9928171554022 41 126.7 114.497218911714 12.2027810882860 42 134.1 115.001620668026 19.0983793319743 43 81.3 115.506022424337 -34.2060224243375 44 88.6 116.010424180649 -27.4104241806492 45 132.7 116.514825936961 16.1851740630390 46 132.9 117.019227693273 15.8807723067273 47 134.4 117.523629449584 16.8763705504156 48 103.7 118.028031205896 -14.3280312058962 49 119.7 118.532432962208 1.16756703779207 50 115 119.036834718520 -4.03683471851968 51 132.9 119.541236474831 13.3587635251686 52 108.5 120.045638231143 -11.5456382311432 53 113.9 120.550039987455 -6.65003998745491 54 142 121.054441743767 20.9455582562333 55 97.7 121.558843500078 -23.8588435000784 56 92.2 122.063245256390 -29.8632452563901 57 128.8 122.567647012702 6.23235298729812 58 134.9 123.072048769014 11.8279512309864 59 128.2 123.576450525325 4.62354947467460 60 114.8 124.080852281637 -9.28085228163713 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0361168623278712 0.0722337246557424 0.963883137672129 7 0.245809570480188 0.491619140960375 0.754190429519812 8 0.475867069542606 0.951734139085211 0.524132930457394 9 0.477063644183093 0.954127288366185 0.522936355816907 10 0.394378591341517 0.788757182683033 0.605621408658483 11 0.375605629925297 0.751211259850595 0.624394370074703 12 0.301864307030029 0.603728614060058 0.698135692969971 13 0.222214295352703 0.444428590705406 0.777785704647297 14 0.158496009118256 0.316992018236511 0.841503990881744 15 0.27361027782424 0.54722055564848 0.72638972217576 16 0.211406442953728 0.422812885907456 0.788593557046272 17 0.166288650824639 0.332577301649278 0.83371134917536 18 0.239939993082266 0.479879986164532 0.760060006917734 19 0.484226300823645 0.96845260164729 0.515773699176355 20 0.432884399678604 0.865768799357209 0.567115600321396 21 0.424256299522673 0.848512599045347 0.575743700477326 22 0.418980700864636 0.837961401729271 0.581019299135364 23 0.341212211036791 0.682424422073582 0.658787788963209 24 0.281618232619988 0.563236465239975 0.718381767380012 25 0.217719459415038 0.435438918830077 0.782280540584962 26 0.164117676969185 0.328235353938371 0.835882323030815 27 0.222042717428781 0.444085434857563 0.777957282571219 28 0.177200813960459 0.354401627920918 0.822799186039541 29 0.174462017168065 0.348924034336131 0.825537982831935 30 0.574017667196200 0.851964665607601 0.425982332803800 31 0.675562498517075 0.64887500296585 0.324437501482925 32 0.680363150235737 0.639273699528527 0.319636849764263 33 0.634975425634738 0.730049148730524 0.365024574365262 34 0.593179831346759 0.813640337306482 0.406820168653241 35 0.515319028221204 0.969361943557593 0.484680971778796 36 0.453983119541585 0.907966239083169 0.546016880458415 37 0.404311274622593 0.808622549245186 0.595688725377407 38 0.334800019800259 0.669600039600518 0.665199980199741 39 0.406163362710234 0.812326725420468 0.593836637289766 40 0.392556676526815 0.78511335305363 0.607443323473185 41 0.340502196426332 0.681004392852663 0.659497803573668 42 0.355824638856462 0.711649277712924 0.644175361143538 43 0.565304145688244 0.869391708623512 0.434695854311756 44 0.745449218212654 0.509101563574693 0.254550781787347 45 0.694557573071346 0.610884853857309 0.305442426928654 46 0.652369158275095 0.69526168344981 0.347630841724905 47 0.653298796195749 0.693402407608502 0.346701203804251 48 0.604556814118102 0.790886371763796 0.395443185881898 49 0.496777702422594 0.993555404845189 0.503222297577406 50 0.387105181907172 0.774210363814345 0.612894818092828 51 0.365307340685464 0.730614681370928 0.634692659314536 52 0.263645281205042 0.527290562410084 0.736354718794958 53 0.165554796998075 0.331109593996150 0.834445203001925 54 0.372686376214101 0.745372752428202 0.627313623785899 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 1 0.0204081632653061 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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