Paper - Multiple Regression SPAREN 1

*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, 05 Dec 2008 09:55:46 -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/05/t12284963045w1qsz5b6clr4gp.htm/, Retrieved Fri, 05 Dec 2008 16:58:38 +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/Dec/05/t12284963045w1qsz5b6clr4gp.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0 0 9 0 1 0 4 0 6 0 21 0 24 0 23 0 22 0 21 0 20 0 16 0 18 0 18 0 24 0 16 0 15 0 24 0 18 0 15 0 4 0 3 0 6 0 5 0 12 0 12 0 12 0 14 0 12 0 17 0 12 0 20 0 21 0 15 0 22 0 19 0 19 0 26 0 25 0 19 0 20 0 30 0 31 0 35 0 33 0 26 0 25 0 17 0 14 0 8 0 12 0 7 0 4 0 10 0 8 0 16 1 14 1 20 1 9 1 10 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 Spa[t] = + 16.1818181818182 -2.38181818181818Val[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) 16.1818181818182 1.090423 14.8399 0 0 Val -2.38181818181818 3.777336 -0.6306 0.530808 0.265404 Multiple Linear Regression - Regression Statistics Multiple R 0.0825135830762714 R-squared 0.00680849139208475 Adjusted R-squared -0.0103155001356379 F-TEST (value) 0.397599553881011 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.530808328082919 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.08679406467817 Sum Squared Residuals 3792.98181818182 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 16.1818181818182 -16.1818181818182 2 9 16.1818181818182 -7.18181818181818 3 1 16.1818181818182 -15.1818181818182 4 4 16.1818181818182 -12.1818181818182 5 6 16.1818181818182 -10.1818181818182 6 21 16.1818181818182 4.81818181818182 7 24 16.1818181818182 7.81818181818182 8 23 16.1818181818182 6.81818181818182 9 22 16.1818181818182 5.81818181818182 10 21 16.1818181818182 4.81818181818182 11 20 16.1818181818182 3.81818181818182 12 16 16.1818181818182 -0.181818181818181 13 18 16.1818181818182 1.81818181818182 14 18 16.1818181818182 1.81818181818182 15 24 16.1818181818182 7.81818181818182 16 16 16.1818181818182 -0.181818181818181 17 15 16.1818181818182 -1.18181818181818 18 24 16.1818181818182 7.81818181818182 19 18 16.1818181818182 1.81818181818182 20 15 16.1818181818182 -1.18181818181818 21 4 16.1818181818182 -12.1818181818182 22 3 16.1818181818182 -13.1818181818182 23 6 16.1818181818182 -10.1818181818182 24 5 16.1818181818182 -11.1818181818182 25 12 16.1818181818182 -4.18181818181818 26 12 16.1818181818182 -4.18181818181818 27 12 16.1818181818182 -4.18181818181818 28 14 16.1818181818182 -2.18181818181818 29 12 16.1818181818182 -4.18181818181818 30 17 16.1818181818182 0.818181818181818 31 12 16.1818181818182 -4.18181818181818 32 20 16.1818181818182 3.81818181818182 33 21 16.1818181818182 4.81818181818182 34 15 16.1818181818182 -1.18181818181818 35 22 16.1818181818182 5.81818181818182 36 19 16.1818181818182 2.81818181818182 37 19 16.1818181818182 2.81818181818182 38 26 16.1818181818182 9.81818181818182 39 25 16.1818181818182 8.81818181818182 40 19 16.1818181818182 2.81818181818182 41 20 16.1818181818182 3.81818181818182 42 30 16.1818181818182 13.8181818181818 43 31 16.1818181818182 14.8181818181818 44 35 16.1818181818182 18.8181818181818 45 33 16.1818181818182 16.8181818181818 46 26 16.1818181818182 9.81818181818182 47 25 16.1818181818182 8.81818181818182 48 17 16.1818181818182 0.818181818181818 49 14 16.1818181818182 -2.18181818181818 50 8 16.1818181818182 -8.18181818181818 51 12 16.1818181818182 -4.18181818181818 52 7 16.1818181818182 -9.18181818181818 53 4 16.1818181818182 -12.1818181818182 54 10 16.1818181818182 -6.18181818181818 55 8 16.1818181818182 -8.18181818181818 56 16 13.8 2.2 57 14 13.8 0.200000000000001 58 20 13.8 6.2 59 9 13.8 -4.8 60 10 13.8 -3.8 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.193746818429295 0.387493636858591 0.806253181570705 6 0.724190560942023 0.551618878115955 0.275809439057977 7 0.897745998006867 0.204508003986266 0.102254001993133 8 0.929923770580151 0.140152458839698 0.0700762294198491 9 0.932136342305738 0.135727315388525 0.0678636576942623 10 0.920329564058086 0.159340871883827 0.0796704359419137 11 0.896541020777662 0.206917958444677 0.103458979222338 12 0.84791946392622 0.30416107214756 0.15208053607378 13 0.795389782432376 0.409220435135249 0.204610217567624 14 0.733615182656482 0.532769634687036 0.266384817343518 15 0.736040770920725 0.527918458158551 0.263959229079275 16 0.65939528992448 0.68120942015104 0.34060471007552 17 0.577132112448044 0.845735775103911 0.422867887551956 18 0.57486760715514 0.85026478568972 0.42513239284486 19 0.496389069930454 0.992778139860909 0.503610930069546 20 0.415076594395225 0.83015318879045 0.584923405604775 21 0.500276044469706 0.999447911060588 0.499723955530294 22 0.606896999771159 0.786206000457683 0.393103000228841 23 0.635624186565976 0.728751626868048 0.364375813434024 24 0.688265239378958 0.623469521242083 0.311734760621042 25 0.636668019689568 0.726663960620863 0.363331980310432 26 0.58439416332386 0.83121167335228 0.41560583667614 27 0.5327494480245 0.934501103951 0.4672505519755 28 0.468232411011379 0.936464822022758 0.531767588988621 29 0.420818357660988 0.841636715321975 0.579181642339012 30 0.356736143324384 0.713472286648767 0.643263856675616 31 0.316682114474407 0.633364228948815 0.683317885525593 32 0.272575932301962 0.545151864603925 0.727424067698037 33 0.237368224714204 0.474736449428407 0.762631775285797 34 0.190276955260531 0.380553910521063 0.809723044739469 35 0.166651357541848 0.333302715083697 0.833348642458152 36 0.129348454042087 0.258696908084174 0.870651545957913 37 0.0977583204536848 0.195516640907370 0.902241679546315 38 0.107131192924745 0.214262385849491 0.892868807075255 39 0.105719012850106 0.211438025700213 0.894280987149894 40 0.0762906771138791 0.152581354227758 0.923709322886121 41 0.0546959746461893 0.109391949292379 0.94530402535381 42 0.0916059215744523 0.183211843148905 0.908394078425548 43 0.167833310313644 0.335666620627287 0.832166689686356 44 0.464420233824857 0.928840467649714 0.535579766175143 45 0.816043530081747 0.367912939836506 0.183956469918253 46 0.923948674479914 0.152102651040172 0.076051325520086 47 0.99066404952096 0.0186719009580785 0.00933595047903926 48 0.994396030871132 0.0112079382577366 0.0056039691288683 49 0.994287624020408 0.0114247519591844 0.00571237597959221 50 0.98725439607645 0.0254912078470978 0.0127456039235489 51 0.982060585455268 0.0358788290894642 0.0179394145447321 52 0.960862953679823 0.0782740926403547 0.0391370463201773 53 0.945608814596336 0.108782370807327 0.0543911854036637 54 0.884297412610042 0.231405174779916 0.115702587389958 55 0.764563474866143 0.470873050267714 0.235436525133857 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 5 0.0980392156862745 NOK 10% type I error level 6 0.117647058823529 NOK

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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