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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 20 Dec 2009 00:00:57 -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/20/t1261292727l81wk1o93orxlvk.htm/, Retrieved Sun, 20 Dec 2009 08:05:43 +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/20/t1261292727l81wk1o93orxlvk.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:

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User-defined keywords:

Dataseries X:

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101.68 0 102.11 102.71 101.09 101.7 0 101.68 102.11 102.71 101.53 0 101.7 101.68 102.11 101.76 0 101.53 101.7 101.68 101.15 0 101.76 101.53 101.7 100.92 0 101.15 101.76 101.53 100.73 0 100.92 101.15 101.76 100.55 0 100.73 100.92 101.15 102.15 0 100.55 100.73 100.92 100.79 0 102.15 100.55 100.73 99.93 0 100.79 102.15 100.55 100.03 0 99.93 100.79 102.15 100.25 0 100.03 99.93 100.79 99.6 0 100.25 100.03 99.93 100.16 0 99.6 100.25 100.03 100.49 0 100.16 99.6 100.25 99.72 0 100.49 100.16 99.6 100.14 0 99.72 100.49 100.16 98.48 0 100.14 99.72 100.49 100.38 0 98.48 100.14 99.72 101.45 0 100.38 98.48 100.14 98.42 0 101.45 100.38 98.48 98.6 0 98.42 101.45 100.38 100.06 0 98.6 98.42 101.45 98.62 0 100.06 98.6 98.42 100.84 0 98.62 100.06 98.6 100.02 0 100.84 98.62 100.06 97.95 0 100.02 100.84 98.62 98.32 0 97.95 100.02 100.84 98.27 0 98.32 97.95 100.02 97.22 0 98.27 98.32 97.95 99.28 0 97.22 98.27 98.32 100.38 0 99.28 97.22 98.27 99.02 0 100.38 99.28 97.22 100.32 0 99.02 100.38 99.28 9 etc...

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 9.57163647419904 -0.895777001450823X[t] + 0.510443451262783Y1[t] + 0.069926144750079Y2[t] + 0.32209278622004Y3[t] + 0.184045519935524M1[t] + 0.42493619565798M2[t] -0.266547955685569M3[t] -0.0195626395711653M4[t] -0.347632735869259M5[t] + 0.085924062365643M6[t] -0.976484902148307M7[t] + 0.589330506720091M8[t] + 0.698736392866317M9[t] -0.536921805692414M10[t] -0.228775212256733M11[t] + 0.00858164404031952t + 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) 9.57163647419904 11.290167 0.8478 0.40148 0.20074 X -0.895777001450823 0.439234 -2.0394 0.04789 0.023945 Y1 0.510443451262783 0.149766 3.4083 0.001478 0.000739 Y2 0.069926144750079 0.171956 0.4067 0.686379 0.343189 Y3 0.32209278622004 0.160887 2.002 0.051932 0.025966 M1 0.184045519935524 0.669672 0.2748 0.784827 0.392414 M2 0.42493619565798 0.659722 0.6441 0.523089 0.261544 M3 -0.266547955685569 0.647923 -0.4114 0.68293 0.341465 M4 -0.0195626395711653 0.653785 -0.0299 0.976274 0.488137 M5 -0.347632735869259 0.624573 -0.5566 0.580831 0.290416 M6 0.085924062365643 0.642128 0.1338 0.894206 0.447103 M7 -0.976484902148307 0.637742 -1.5312 0.13341 0.066705 M8 0.589330506720091 0.652546 0.9031 0.371736 0.185868 M9 0.698736392866317 0.642181 1.0881 0.28292 0.14146 M10 -0.536921805692414 0.752804 -0.7132 0.479744 0.239872 M11 -0.228775212256733 0.74094 -0.3088 0.759065 0.379532 t 0.00858164404031952 0.011222 0.7647 0.448802 0.224401 Multiple Linear Regression - Regression Statistics Multiple R 0.861077793082703 R-squared 0.741454965740179 Adjusted R-squared 0.640559342614395 F-TEST (value) 7.3487327078185 F-TEST (DF numerator) 16 F-TEST (DF denominator) 41 p-value 1.28898840601188e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.902740058097228 Sum Squared Residuals 33.4125241122289 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.68 101.628118532882 0.0518814671180148 2 101.7 102.137934795428 -0.437934795428357 3 101.53 101.241917243176 0.288082756824178 4 101.76 101.273607441436 0.486392558563743 5 101.15 101.066075394086 0.0839246059141901 6 100.92 101.158170570726 -0.23817057072585 7 100.73 100.018367648995 0.711632351005163 8 100.55 101.283220833277 -0.733220833276891 9 102.15 101.221961233903 0.928038766097003 10 100.79 100.737809865968 0.0521901340317782 11 99.93 100.414240139807 -0.484240139807354 12 100.03 100.632864529110 -0.602864529110379 13 100.25 100.378353364468 -0.128353364468177 14 99.6 100.470116061835 -0.870116061834543 15 100.16 99.5030183416775 0.656981658322482 16 100.49 100.069842053420 0.420157946579741 17 99.72 99.7485982700962 -0.0285982700962151 18 100.14 100.001142842950 0.138857157050156 19 98.48 99.2141492600016 -0.734149260001632 20 100.38 99.7225677192197 0.657432280780257 21 101.45 100.829599376733 0.62040062326715 22 98.42 99.7468829649655 -1.32688296496551 23 98.6 99.203764813816 -0.60376481381594 24 100.06 99.665764554003 0.394235445997012 25 98.62 99.6402847206308 -1.02028472063079 26 100.84 99.31478734343 1.52521265657012 27 100.02 100.134631117371 -0.114631117371182 28 97.95 99.6630568766787 -1.71305687667873 29 98.32 98.9446570270204 -0.624657027020433 30 98.27 99.1667963419298 -0.896796341929778 31 97.22 97.446587454975 -0.226587454975053 32 99.28 98.6006969077218 0.679303092278244 33 100.38 99.680670856211 0.699329143788943 34 99.02 98.8209325307358 0.199067469264175 35 100.32 99.1838875733328 1.13611242666718 36 99.81 100.344023424253 -0.53402342425341 37 100.6 99.929182227001 0.670817772998906 38 101.19 100.964963161525 0.225036838475027 39 100.47 100.474196623847 -0.00419662384713008 40 101.77 100.657954025609 1.11204597439097 41 102.32 101.141729979643 1.17827002035736 42 102.39 101.723609502209 0.66639049779094 43 101.16 101.162693225022 -0.00269322502242635 44 100.63 102.291290695431 -1.66129069543145 45 101.48 102.075280533442 -0.595280533441516 46 101.44 99.9530689272775 1.48693107272254 47 100.09 100.138107473044 -0.0481074730438910 48 100.7 99.9573474926332 0.742652507366776 49 100.78 100.354061155018 0.425938844982044 50 99.81 100.252198637782 -0.442198637782247 51 98.45 99.2762366739284 -0.82623667392835 52 98.49 98.7955396028557 -0.305539602855722 53 97.48 98.088939329155 -0.6089393291549 54 97.91 97.5802807421855 0.32971925781453 55 96.94 96.688202411006 0.251797588993949 56 98.53 97.4722238443502 1.05777615564984 57 96.82 98.4724879997116 -1.65248799971158 58 95.76 96.171305711053 -0.411305711052982 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.0497432174902092 0.0994864349804184 0.95025678250979 21 0.0769172776722236 0.153834555344447 0.923082722327776 22 0.0693973546435627 0.138794709287125 0.930602645356437 23 0.0459058333298366 0.0918116666596731 0.954094166670163 24 0.0401385862178826 0.0802771724357652 0.959861413782117 25 0.0231356869383544 0.0462713738767088 0.976864313061646 26 0.124936436979262 0.249872873958525 0.875063563020738 27 0.083613121285817 0.167226242571634 0.916386878714183 28 0.195009651661356 0.390019303322713 0.804990348338644 29 0.168209176478803 0.336418352957607 0.831790823521196 30 0.178003992086628 0.356007984173256 0.821996007913372 31 0.173738660072794 0.347477320145588 0.826261339927206 32 0.127453561183697 0.254907122367394 0.872546438816303 33 0.0778284502389225 0.155656900477845 0.922171549761078 34 0.158216087292043 0.316432174584085 0.841783912707957 35 0.226008742511805 0.452017485023609 0.773991257488195 36 0.24010492036141 0.48020984072282 0.75989507963859 37 0.372432775181059 0.744865550362118 0.627567224818941 38 0.228060311071386 0.456120622142773 0.771939688928614 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 1 0.0526315789473684 NOK 10% type I error level 4 0.210526315789474 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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