*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, 18 Dec 2009 04:12:08 -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/Dec/18/t1261134767v3zbha3k9kt0llm.htm/, Retrieved Fri, 18 Dec 2009 12:12:59 +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/Dec/18/t1261134767v3zbha3k9kt0llm.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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8.1 92.9 7.7 107.7 7.5 103.5 7.6 91.1 7.8 79.8 7.8 71.9 7.8 82.9 7.5 90.1 7.5 100.7 7.1 90.7 7.5 108.8 7.5 44.1 7.6 93.6 7.7 107.4 7.7 96.5 7.9 93.6 8.1 76.5 8.2 76.7 8.2 84 8.2 103.3 7.9 88.5 7.3 99 6.9 105.9 6.6 44.7 6.7 94 6.9 107.1 7 104.8 7.1 102.5 7.2 77.7 7.1 85.2 6.9 91.3 7 106.5 6.8 92.4 6.4 97.5 6.7 107 6.6 51.1 6.4 98.6 6.3 102.2 6.2 114.3 6.5 99.4 6.8 72.5 6.8 92.3 6.4 99.4 6.1 85.9 5.8 109.4 6.1 97.6 7.2 104.7 7.3 56.9 6.9 86.7 6.1 108.5 5.8 103.4 6.2 86.2 7.1 71 7.7 75.9 7.9 87.1 7.7 102 7.4 88.5 7.5 87.8 8 100.8 8.1 50.6 8 85.9

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 Werkloosheidsgraad[t] = + 8.54364253391526 -0.0101361098022254Bruto_index[t] -0.0141856472841194t + 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) 8.54364253391526 0.469041 18.2151 0 0 Bruto_index -0.0101361098022254 0.004804 -2.1101 0.039172 0.019586 t -0.0141856472841194 0.004404 -3.2213 0.002094 0.001047 Multiple Linear Regression - Regression Statistics Multiple R 0.442544168297874 R-squared 0.195845340894457 Adjusted R-squared 0.168115869890817 F-TEST (value) 7.06271464279836 F-TEST (DF numerator) 2 F-TEST (DF denominator) 58 p-value 0.00179824098813464 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.604653831924191 Sum Squared Residuals 21.2051628747152 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.1 7.5878122860044 0.512187713995596 2 7.7 7.42361221364735 0.276387786352654 3 7.5 7.45199822753258 0.0480017724674245 4 7.6 7.56350034179605 0.0364996582039497 5 7.8 7.66385273527708 0.136147264722922 6 7.8 7.72974235543054 0.0702576445694606 7 7.8 7.60405950032194 0.195940499678060 8 7.5 7.5168938624618 -0.0168938624617976 9 7.5 7.39526545127409 0.104734548725912 10 7.1 7.48244090201222 -0.382440902012224 11 7.5 7.28479166730782 0.215208332692176 12 7.5 7.92641232422769 -0.426412324227690 13 7.6 7.41048924173341 0.189510758266588 14 7.7 7.25642527917858 0.443574720821419 15 7.7 7.35272322873872 0.347276771261281 16 7.9 7.36793229988105 0.532067700118947 17 8.1 7.52707413021499 0.572925869785011 18 8.2 7.51086126097042 0.689138739029575 19 8.2 7.42268201213006 0.777317987869941 20 8.2 7.21286944566299 0.98713055433701 21 7.9 7.3486982234518 0.551301776548195 22 7.3 7.22808342324432 0.0719165767556809 23 6.9 7.14395861832484 -0.243958618324844 24 6.6 7.75010289093692 -1.15010289093692 25 6.7 7.23620703040309 -0.536207030403087 26 6.9 7.08923834470982 -0.189238344709815 27 7 7.09836574997081 -0.0983657499708142 28 7.1 7.10749315523181 -0.00749315523181361 29 7.2 7.34468303104288 -0.144683031042884 30 7.1 7.25447656024207 -0.154476560242075 31 6.9 7.17846064316438 -0.278460643164379 32 7 7.01020612688643 -0.0102061268864337 33 6.8 7.1389396278137 -0.338939627813693 34 6.4 7.07305982053822 -0.673059820538223 35 6.7 6.96258113013296 -0.262581130132963 36 6.6 7.51500402079324 -0.915004020793245 37 6.4 7.01935315790342 -0.619353157903417 38 6.3 6.96867751533129 -0.668677515331287 39 6.2 6.83184493944024 -0.631844939440239 40 6.5 6.96868732820928 -0.468687328209279 41 6.8 7.22716303460502 -0.427163034605024 42 6.8 7.01228241323684 -0.212282413236841 43 6.4 6.92613038635692 -0.52613038635692 44 6.1 7.04878222140284 -0.948782221402845 45 5.8 6.79639799376643 -0.996397993766427 46 6.1 6.90181844214857 -0.801818442148568 47 7.2 6.81566641526865 0.384333584731352 48 7.3 7.2859868165309 0.0140131834690957 49 6.9 6.96974509714047 -0.0697450971404664 50 6.1 6.73459225616783 -0.634592256167833 51 5.8 6.77210076887506 -0.972100768875063 52 6.2 6.93225621018922 -0.73225621018922 53 7.1 7.07213943189893 0.0278605681010714 54 7.7 7.0082868465839 0.691713153416096 55 7.9 6.88057676951486 1.01942323048514 56 7.7 6.71536308617758 0.984636913822419 57 7.4 6.8380149212235 0.561985078776495 58 7.5 6.83092455080094 0.669075449199056 59 8 6.68496947608789 1.31503052391211 60 8.1 7.17961654087549 0.920383459124509 61 8 6.80762621757281 1.19237378242719 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.00216695892577810 0.00433391785155621 0.997833041074222 7 0.00692269567386608 0.0138453913477322 0.993077304326134 8 0.00154682033512742 0.00309364067025484 0.998453179664873 9 0.000604379160425753 0.00120875832085151 0.999395620839574 10 0.000580919113650867 0.00116183822730173 0.99941908088635 11 0.000666417062419629 0.00133283412483926 0.99933358293758 12 0.000202347598327799 0.000404695196655598 0.999797652401672 13 0.00015609141438329 0.00031218282876658 0.999843908585617 14 0.000166140753918378 0.000332281507836756 0.999833859246082 15 9.57662776240625e-05 0.000191532555248125 0.999904233722376 16 0.000117862555367309 0.000235725110734617 0.999882137444633 17 0.000223209246317802 0.000446418492635605 0.999776790753682 18 0.000377318768571976 0.000754637537143951 0.999622681231428 19 0.000530284837311999 0.00106056967462400 0.999469715162688 20 0.00103921015247825 0.00207842030495649 0.998960789847522 21 0.00104757750406639 0.00209515500813278 0.998952422495934 22 0.00315559085489962 0.00631118170979924 0.9968444091451 23 0.0144565657174011 0.0289131314348022 0.985543434282599 24 0.0730840848984758 0.146168169796952 0.926915915101524 25 0.102331129878426 0.204662259756851 0.897668870121574 26 0.101879083991794 0.203758167983588 0.898120916008206 27 0.094745689060154 0.189491378120308 0.905254310939846 28 0.093219868838307 0.186439737676614 0.906780131161693 29 0.0808180620915144 0.161636124183029 0.919181937908486 30 0.075152165184072 0.150304330368144 0.924847834815928 31 0.0704782854726402 0.140956570945280 0.92952171452736 32 0.0944883312118635 0.188976662423727 0.905511668788136 33 0.0989024646628162 0.197804929325632 0.901097535337184 34 0.103942004978206 0.207884009956412 0.896057995021794 35 0.129944905625151 0.259889811250302 0.870055094374849 36 0.0988909050057785 0.197781810011557 0.901109094994222 37 0.0897597706280734 0.179519541256147 0.910240229371927 38 0.0791233835874551 0.158246767174910 0.920876616412545 39 0.0730372072000101 0.146074414400020 0.92696279279999 40 0.065354059693066 0.130708119386132 0.934645940306934 41 0.0567343374520642 0.113468674904128 0.943265662547936 42 0.0798611957334425 0.159722391466885 0.920138804266557 43 0.0716691173786688 0.143338234757338 0.928330882621331 44 0.0524494062421316 0.104898812484263 0.947550593757868 45 0.0444432466766481 0.0888864933532963 0.955556753323352 46 0.0298691577610828 0.0597383155221656 0.970130842238917 47 0.160117565517789 0.320235131035577 0.839882434482211 48 0.235734839991908 0.471469679983817 0.764265160008092 49 0.316163679732988 0.632327359465975 0.683836320267012 50 0.231220510060614 0.462441020121227 0.768779489939386 51 0.380309925575024 0.760619851150049 0.619690074424976 52 0.81200017037042 0.37599965925916 0.18799982962958 53 0.865576381974384 0.268847236051232 0.134423618025616 54 0.813074862823922 0.373850274352156 0.186925137176078 55 0.855954383840418 0.288091232319163 0.144045616159582 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.32 NOK 5% type I error level 18 0.36 NOK 10% type I error level 20 0.4 NOK

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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