*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, 20 Nov 2009 05:46:36 -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/20/t1258721321wodwep9749n7vdc.htm/, Retrieved Fri, 20 Nov 2009 13:48:54 +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/20/t1258721321wodwep9749n7vdc.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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2.155 22.782 2.172 19.169 2.15 13.807 2.533 29.743 2.058 25.591 2.16 29.096 2.26 26.482 2.498 22.405 2.695 27.044 2.799 17.97 2.947 18.73 2.93 19.684 2.318 19.785 2.54 18.479 2.57 10.698 2.669 31.956 2.45 29.506 2.842 34.506 3.44 27.165 2.678 26.736 2.981 23.691 2.26 18.157 2.844 17.328 2.546 18.205 2.456 20.995 2.295 17.382 2.379 9.367 2.479 31.124 2.057 26.551 2.28 30.651 2.351 25.859 2.276 25.1 2.548 25.778 2.311 20.418 2.201 18.688 2.725 20.424 2.408 24.776 2.139 19.814 1.898 12.738 2.537 31.566 2.069 30.111 2.063 30.019 2.524 31.934 2.437 25.826 2.189 26.835 2.793 20.205 2.074 17.789 2.622 20.52 2.278 22.518 2.144 15.572 2.427 11.509 2.139 25.447 1.828 24.09 2.072 27.786 1.8 26.195 1.758 20.516 2.246 22.759 1.987 19.028 1.868 16.971 2.514 20.036 2.121 22.485

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation geb[t] = + 2.25568655873471 + 0.00518056008851177auto[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) 2.25568655873471 0.174453 12.93 0 0 auto 0.00518056008851177 0.007439 0.6964 0.48893 0.244465 Multiple Linear Regression - Regression Statistics Multiple R 0.090289779416755 R-squared 0.00815224426712628 Adjusted R-squared -0.00865873464360045 F-TEST (value) 0.484935726254735 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.488929557573516 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.329111628192011 Sum Squared Residuals 6.39055336486061 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.155 2.37371007867118 -0.218710078671178 2 2.172 2.35499271507139 -0.182992715071388 3 2.15 2.32721455187679 -0.177214551876788 4 2.533 2.40977195744731 0.123228042552688 5 2.058 2.38826227195981 -0.330262271959811 6 2.16 2.40642013507004 -0.246420135070045 7 2.26 2.39287815099867 -0.132878150998675 8 2.498 2.37175700751781 0.126242992482188 9 2.695 2.39578962576842 0.299210374231581 10 2.799 2.34878122352526 0.450218776474737 11 2.947 2.35271844919253 0.594281550807468 12 2.93 2.35766070351697 0.572339296483028 13 2.318 2.35818394008591 -0.0401839400859115 14 2.54 2.35141812861032 0.188581871389685 15 2.57 2.31110819056161 0.258891809438395 16 2.669 2.42123653692319 0.247763463076812 17 2.45 2.40854416470633 0.0414558352936657 18 2.842 2.43444696514889 0.407553034851107 19 3.44 2.39641647353913 1.04358352646087 20 2.678 2.39419401326116 0.283805986738843 21 2.981 2.37841920779164 0.602580792208361 22 2.26 2.34974998826181 -0.0897499882618146 23 2.844 2.34545530394844 0.498544696051562 24 2.546 2.34999865514606 0.196001344853937 25 2.456 2.36445241779301 0.0915475822069892 26 2.295 2.34573505419322 -0.0507350541932179 27 2.379 2.30421286508380 0.074787134916204 28 2.479 2.41692631092955 0.0620736890704536 29 2.057 2.39323560964478 -0.336235609644782 30 2.28 2.41447590600768 -0.134475906007681 31 2.351 2.38965066206353 -0.0386506620635321 32 2.276 2.38571861695635 -0.109718616956352 33 2.548 2.38923103669636 0.158768963303637 34 2.311 2.36146323462194 -0.0504632346219396 35 2.201 2.35250086566881 -0.151500865668814 36 2.725 2.36149431798247 0.363505682017530 37 2.408 2.38404011548767 0.0239598845123261 38 2.139 2.35833417632848 -0.219334176328479 39 1.898 2.32167653314217 -0.423676533142169 40 2.537 2.41921611848867 0.117783881511331 41 2.069 2.41167840355988 -0.342678403559884 42 2.063 2.41120179203174 -0.348201792031741 43 2.524 2.42112256460124 0.102877435398759 44 2.437 2.38947970358061 0.0475202964193887 45 2.189 2.39470688870992 -0.205706888709919 46 2.793 2.36035977532309 0.432640224676914 47 2.074 2.34784354214924 -0.273843542149242 48 2.622 2.36199165175097 0.260008348249032 49 2.278 2.37234241080781 -0.0943424108078142 50 2.144 2.33635824043301 -0.192358240433011 51 2.427 2.31530962479339 0.111690375206612 52 2.139 2.38751627130707 -0.248516271307065 53 1.828 2.38048625126695 -0.552486251266955 54 2.072 2.39963360135409 -0.327633601354094 55 1.8 2.39139133025327 -0.591391330253272 56 1.758 2.36197092951061 -0.603970929510614 57 2.246 2.37359092578915 -0.127590925789146 58 1.987 2.35426225609891 -0.367262256098908 59 1.868 2.34360584399684 -0.475605843996839 60 2.514 2.35948426066813 0.154515739331872 61 2.121 2.37217145232489 -0.251171452324893 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.155272057440774 0.310544114881548 0.844727942559226 6 0.0882425640186288 0.176485128037258 0.911757435981371 7 0.0361526923853145 0.072305384770629 0.963847307614686 8 0.0514079343248494 0.102815868649699 0.94859206567515 9 0.103313030245672 0.206626060491344 0.896686969754328 10 0.269609857466106 0.539219714932213 0.730390142533894 11 0.479385324141844 0.958770648283689 0.520614675858156 12 0.596248125623177 0.807503748753645 0.403751874376823 13 0.515804755694768 0.968390488610463 0.484195244305232 14 0.430167851484381 0.860335702968762 0.569832148515619 15 0.359133086496969 0.718266172993938 0.640866913503031 16 0.339847538645462 0.679695077290923 0.660152461354538 17 0.262470725399036 0.524941450798073 0.737529274600964 18 0.298652280942175 0.597304561884349 0.701347719057825 19 0.869377958160475 0.261244083679049 0.130622041839525 20 0.851893053494913 0.296213893010174 0.148106946505087 21 0.927982312806564 0.144035374386873 0.0720176871934364 22 0.908639659958935 0.182720680082130 0.0913603400410648 23 0.944239401512995 0.111521196974011 0.0557605984870054 24 0.933074024593712 0.133851950812576 0.0669259754062878 25 0.91417011985187 0.171659760296259 0.0858298801481295 26 0.89041294864393 0.219174102712138 0.109587051356069 27 0.862672533278229 0.274654933443542 0.137327466721771 28 0.832517407688786 0.334965184622429 0.167482592311214 29 0.854789965335394 0.290420069329212 0.145210034664606 30 0.825216861304845 0.349566277390311 0.174783138695155 31 0.782870246059426 0.434259507881148 0.217129753940574 32 0.738920390299766 0.522159219400468 0.261079609700234 33 0.713546352701121 0.572907294597758 0.286453647298879 34 0.659736149542526 0.680527700914949 0.340263850457474 35 0.610562100139168 0.778875799721665 0.389437899860832 36 0.693269289816343 0.613461420367314 0.306730710183657 37 0.646042122097132 0.707915755805736 0.353957877902868 38 0.604407731024801 0.791184537950398 0.395592268975199 39 0.637390586662685 0.725218826674631 0.362609413337315 40 0.631392945251274 0.737214109497451 0.368607054748726 41 0.609161907496162 0.781676185007677 0.390838092503838 42 0.581210800271958 0.837578399456085 0.418789199728042 43 0.592137786117669 0.815724427764661 0.407862213882331 44 0.577298507078165 0.84540298584367 0.422701492921835 45 0.516712025041128 0.966575949917744 0.483287974958872 46 0.757418700150713 0.485162599698574 0.242581299849287 47 0.707647443068747 0.584705113862506 0.292352556931253 48 0.836404515097618 0.327190969804764 0.163595484902382 49 0.81008784232423 0.379824315351539 0.189912157675770 50 0.737687842590025 0.524624314819951 0.262312157409975 51 0.709836071608148 0.580327856783704 0.290163928391852 52 0.632009155522194 0.735981688955611 0.367990844477806 53 0.606073591614996 0.787852816770007 0.393926408385004 54 0.489025237064886 0.978050474129772 0.510974762935114 55 0.5483606679293 0.9032786641414 0.4516393320707 56 0.640130774576604 0.719738450846792 0.359869225423396 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 0.0192307692307692 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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