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*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, 21 Nov 2008 09:47:19 -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/Nov/21/t1227286445v4pe354k6oulab7.htm/, Retrieved Fri, 21 Nov 2008 16:54:15 +0000

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/Nov/21/t1227286445v4pe354k6oulab7.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}, }

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User-defined keywords:

Dataseries X:

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82.7 0 88.9 0 105.9 0 100.8 0 94 0 105 0 58.5 0 87.6 0 113.1 0 112.5 0 89.6 0 74.5 0 82.7 0 90.1 0 109.4 0 96 0 89.2 0 109.1 0 49.1 0 92.9 0 107.7 0 103.5 0 91.1 0 79.8 0 71.9 0 82.9 0 90.1 0 100.7 0 90.7 0 108.8 0 44.1 0 93.6 0 107.4 0 96.5 0 93.6 0 76.5 0 76.7 1 84 1 103.3 1 88.5 1 99 1 105.9 1 44.7 1 94 1 107.1 1 104.8 1 102.5 1 77.7 1 85.2 1 91.3 1 106.5 1 92.4 1 97.5 1 107 1 51.1 1 98.6 1 102.2 1 114.3 1 99.4 1 72.5 1 92.3 1 99.4 1 85.9 1 109.4 1 97.6 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 90.9899990607684 + 2.18980885015370d[t] -0.0077176669484373t + 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) 90.9899990607684 4.822658 18.8672 0 0 d 2.18980885015370 8.087372 0.2708 0.787468 0.393734 t -0.0077176669484373 0.214276 -0.036 0.971384 0.485692 Multiple Linear Regression - Regression Statistics Multiple R 0.059951922032331 R-squared 0.0035942329553707 Adjusted R-squared -0.0285478885621979 F-TEST (value) 0.111823140031566 F-TEST (DF numerator) 2 F-TEST (DF denominator) 62 p-value 0.894382324107778 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16.4797392192238 Sum Squared Residuals 16838.0718934846 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 82.7 90.9822813938195 -8.28228139381952 2 88.9 90.9745637268715 -2.07456372687144 3 105.9 90.966846059923 14.9331539400770 4 100.8 90.9591283929746 9.84087160702542 5 94 90.9514107260261 3.04858927397386 6 105 90.9436930590777 14.0563069409223 7 58.5 90.9359753921293 -32.4359753921293 8 87.6 90.9282577251808 -3.32825772518083 9 113.1 90.9205400582324 22.1794599417676 10 112.5 90.912822391284 21.5871776087160 11 89.6 90.9051047243355 -1.30510472433552 12 74.5 90.8973870573871 -16.3973870573871 13 82.7 90.8896693904386 -8.18966939043863 14 90.1 90.8819517234902 -0.781951723490206 15 109.4 90.8742340565418 18.5257659434582 16 96 90.8665163895933 5.13348361040667 17 89.2 90.8587987226449 -1.65879872264489 18 109.1 90.8510810556965 18.2489189443035 19 49.1 90.843363388748 -41.743363388748 20 92.9 90.8356457217996 2.06435427820043 21 107.7 90.8279280548511 16.8720719451489 22 103.5 90.8202103879027 12.6797896120973 23 91.1 90.8124927209543 0.287507279045730 24 79.8 90.8047750540058 -11.0047750540058 25 71.9 90.7970573870574 -18.8970573870574 26 82.9 90.789339720109 -7.88933972010895 27 90.1 90.7816220531605 -0.68162205316052 28 100.7 90.7739043862121 9.92609561378793 29 90.7 90.7661867192636 -0.0661867192636364 30 108.8 90.7584690523152 18.0415309476848 31 44.1 90.7507513853668 -46.6507513853668 32 93.6 90.7430337184183 2.85696628158167 33 107.4 90.7353160514699 16.6646839485301 34 96.5 90.7275983845215 5.77240161547855 35 93.6 90.719880717573 2.88011928242698 36 76.5 90.7121630506246 -14.2121630506246 37 76.7 92.8942542338299 -16.1942542338298 38 84 92.8865365668814 -8.88653656688141 39 103.3 92.878818899933 10.4211811000670 40 88.5 92.8711012329845 -4.37110123298454 41 99 92.863383566036 6.1366164339639 42 105.9 92.8556658990877 13.0443341009123 43 44.7 92.8479482321392 -48.1479482321392 44 94 92.8402305651908 1.15976943480921 45 107.1 92.8325128982424 14.2674871017576 46 104.8 92.824795231294 11.9752047687061 47 102.5 92.8170775643455 9.68292243565453 48 77.7 92.809359897397 -15.1093598973970 49 85.2 92.8016422304486 -7.6016422304486 50 91.3 92.7939245635002 -1.49392456350016 51 106.5 92.7862068965517 13.7137931034483 52 92.4 92.7784892296033 -0.378489229603281 53 97.5 92.7707715626548 4.72922843734515 54 107 92.7630538957064 14.2369461042936 55 51.1 92.755336228758 -41.655336228758 56 98.6 92.7476185618095 5.85238143819046 57 102.2 92.7399008948611 9.4600991051389 58 114.3 92.7321832279127 21.5678167720873 59 99.4 92.7244655609642 6.67553443903578 60 72.5 92.7167478940158 -20.2167478940158 61 92.3 92.7090302270673 -0.409030227067353 62 99.4 92.7013125601189 6.69868743988109 63 85.9 92.6935948931705 -6.79359489317047 64 109.4 92.685877226222 16.7141227737780 65 97.6 92.6781595592736 4.92184044072639 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.143311476708232 0.286622953416465 0.856688523291768 7 0.756429964928072 0.487140070143856 0.243570035071928 8 0.636039868184002 0.727920263631997 0.363960131815998 9 0.713143501739327 0.573712996521347 0.286856498260673 10 0.689481522004451 0.621036955991098 0.310518477995549 11 0.619052598291741 0.761894803416518 0.380947401708259 12 0.647136089482892 0.705727821034216 0.352863910517108 13 0.567075710749563 0.865848578500875 0.432924289250437 14 0.468773468045727 0.937546936091454 0.531226531954273 15 0.488537224442044 0.977074448884088 0.511462775557956 16 0.402606865533267 0.805213731066534 0.597393134466733 17 0.323093502201637 0.646187004403275 0.676906497798363 18 0.322473985628523 0.644947971257046 0.677526014371477 19 0.731167605975445 0.53766478804911 0.268832394024555 20 0.665210591083511 0.669578817832977 0.334789408916489 21 0.677955052050889 0.644089895898222 0.322044947949111 22 0.650823932607462 0.698352134785076 0.349176067392538 23 0.579061212844988 0.841877574310024 0.420938787155012 24 0.53088124811073 0.93823750377854 0.46911875188927 25 0.52858350482985 0.9428329903403 0.47141649517015 26 0.458346890285494 0.916693780570988 0.541653109714506 27 0.385280199656145 0.770560399312291 0.614719800343855 28 0.353885408603120 0.707770817206241 0.64611459139688 29 0.287620044140989 0.575240088281978 0.712379955859011 30 0.320190620580571 0.640381241161141 0.679809379419429 31 0.737399128479292 0.525201743041416 0.262600871520708 32 0.680283763009471 0.639432473981059 0.319716236990529 33 0.692445486825828 0.615109026348345 0.307554513174172 34 0.643638620942187 0.712722758115627 0.356361379057813 35 0.595806027065576 0.808387945868847 0.404193972934424 36 0.538453616535616 0.923092766928768 0.461546383464384 37 0.488239551003127 0.976479102006253 0.511760448996873 38 0.424193840348842 0.848387680697683 0.575806159651158 39 0.411197219422921 0.822394438845843 0.588802780577079 40 0.339232488088491 0.678464976176982 0.660767511911509 41 0.291332024796721 0.582664049593442 0.708667975203279 42 0.286669974748074 0.573339949496149 0.713330025251926 43 0.763169241668882 0.473661516662237 0.236830758331118 44 0.700330217262597 0.599339565474805 0.299669782737403 45 0.685584187492718 0.628831625014563 0.314415812507282 46 0.659636166144128 0.680727667711744 0.340363833855872 47 0.625603646102031 0.748792707795937 0.374396353897969 48 0.587691460746728 0.824617078506544 0.412308539253272 49 0.51353953539301 0.97292092921398 0.48646046460699 50 0.424165978530379 0.848331957060759 0.575834021469621 51 0.395423256004548 0.790846512009095 0.604576743995452 52 0.305912869979526 0.611825739959052 0.694087130020474 53 0.236160387679390 0.472320775358779 0.76383961232061 54 0.25200877455939 0.50401754911878 0.74799122544061 55 0.756481087289957 0.487037825420087 0.243518912710043 56 0.64774775332795 0.7045044933441 0.35225224667205 57 0.525739804773061 0.948520390453878 0.474260195226939 58 0.661640549812736 0.676718900374528 0.338359450187264 59 0.690409829269035 0.61918034146193 0.309590170730965 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 = 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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