Paper - Multiple Regression VOORUITZICHTEN WERKLOOSHEID 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: Sun, 07 Dec 2008 10:11:28 -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/07/t12286699481nhuyel6nf0m3um.htm/, Retrieved Sun, 07 Dec 2008 17:12:28 +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/07/t12286699481nhuyel6nf0m3um.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

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No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

41 0 35 0 34 0 36 0 39 0 40 0 30 0 33 0 30 0 32 0 41 0 40 0 41 0 40 0 39 0 34 0 34 0 46 0 45 0 44 0 40 0 39 0 37 0 39 0 35 0 26 0 26 0 33 0 27 0 30 0 26 0 27 0 18 0 19 0 13 0 14 0 41 0 21 0 16 0 17 0 9 0 14 0 14 0 16 0 11 0 10 0 6 0 9 0 5 0 7 0 2 0 0 0 8 0 13 0 11 0 19 1 23 1 23 1 43 1 59 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Wer[t] = + 26.0545454545454 + 7.34545454545455Val[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) 26.0545454545454 1.825115 14.2756 0 0 Val 7.34545454545455 6.322385 1.1618 0.250069 0.125034 Multiple Linear Regression - Regression Statistics Multiple R 0.150809272993043 R-squared 0.0227434368206900 Adjusted R-squared 0.00589418573139167 F-TEST (value) 1.34981885545852 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.250068600176982 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.5354173748345 Sum Squared Residuals 10626.0363636364 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 26.0545454545455 14.9454545454545 2 35 26.0545454545455 8.94545454545454 3 34 26.0545454545455 7.94545454545455 4 36 26.0545454545455 9.94545454545455 5 39 26.0545454545455 12.9454545454545 6 40 26.0545454545455 13.9454545454545 7 30 26.0545454545455 3.94545454545455 8 33 26.0545454545455 6.94545454545455 9 30 26.0545454545455 3.94545454545455 10 32 26.0545454545455 5.94545454545455 11 41 26.0545454545455 14.9454545454545 12 40 26.0545454545455 13.9454545454545 13 41 26.0545454545455 14.9454545454545 14 40 26.0545454545455 13.9454545454545 15 39 26.0545454545455 12.9454545454545 16 34 26.0545454545455 7.94545454545455 17 34 26.0545454545455 7.94545454545455 18 46 26.0545454545455 19.9454545454545 19 45 26.0545454545455 18.9454545454545 20 44 26.0545454545455 17.9454545454545 21 40 26.0545454545455 13.9454545454545 22 39 26.0545454545455 12.9454545454545 23 37 26.0545454545455 10.9454545454545 24 39 26.0545454545455 12.9454545454545 25 35 26.0545454545455 8.94545454545455 26 26 26.0545454545455 -0.0545454545454533 27 26 26.0545454545455 -0.0545454545454533 28 33 26.0545454545455 6.94545454545455 29 27 26.0545454545455 0.945454545454547 30 30 26.0545454545455 3.94545454545455 31 26 26.0545454545455 -0.0545454545454533 32 27 26.0545454545455 0.945454545454547 33 18 26.0545454545455 -8.05454545454545 34 19 26.0545454545455 -7.05454545454545 35 13 26.0545454545455 -13.0545454545455 36 14 26.0545454545455 -12.0545454545455 37 41 26.0545454545455 14.9454545454545 38 21 26.0545454545455 -5.05454545454545 39 16 26.0545454545455 -10.0545454545455 40 17 26.0545454545455 -9.05454545454545 41 9 26.0545454545455 -17.0545454545455 42 14 26.0545454545455 -12.0545454545455 43 14 26.0545454545455 -12.0545454545455 44 16 26.0545454545455 -10.0545454545455 45 11 26.0545454545455 -15.0545454545455 46 10 26.0545454545455 -16.0545454545455 47 6 26.0545454545455 -20.0545454545455 48 9 26.0545454545455 -17.0545454545455 49 5 26.0545454545455 -21.0545454545455 50 7 26.0545454545455 -19.0545454545455 51 2 26.0545454545455 -24.0545454545455 52 0 26.0545454545455 -26.0545454545455 53 8 26.0545454545455 -18.0545454545455 54 13 26.0545454545455 -13.0545454545455 55 11 26.0545454545455 -15.0545454545455 56 19 33.4 -14.4 57 23 33.4 -10.4 58 23 33.4 -10.4 59 43 33.4 9.6 60 59 33.4 25.6 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0196827193805096 0.0393654387610191 0.98031728061949 6 0.00593207528699494 0.0118641505739899 0.994067924713005 7 0.0073204249127079 0.0146408498254158 0.992679575087292 8 0.00266312559710151 0.00532625119420302 0.997336874402899 9 0.00170399177884545 0.00340798355769091 0.998296008221154 10 0.000628105433227604 0.00125621086645521 0.999371894566772 11 0.000450748035905536 0.000901496071811073 0.999549251964094 12 0.000230163842944158 0.000460327685888316 0.999769836157056 13 0.000141047967901859 0.000282095935803717 0.999858952032098 14 6.80125259123386e-05 0.000136025051824677 0.999931987474088 15 2.78854919606179e-05 5.57709839212358e-05 0.99997211450804 16 1.08126320012769e-05 2.16252640025537e-05 0.999989187367999 17 4.11747379977539e-06 8.23494759955079e-06 0.9999958825262 18 1.70920221453815e-05 3.4184044290763e-05 0.999982907977855 19 3.50868269342349e-05 7.01736538684697e-05 0.999964913173066 20 5.19336975163917e-05 0.000103867395032783 0.999948066302484 21 3.76524878224546e-05 7.53049756449093e-05 0.999962347512177 22 2.7114411086047e-05 5.4228822172094e-05 0.999972885588914 23 1.91014787381564e-05 3.82029574763129e-05 0.999980898521262 24 1.82960026448414e-05 3.65920052896827e-05 0.999981703997355 25 1.70812015233777e-05 3.41624030467555e-05 0.999982918798477 26 8.20242235473254e-05 0.000164048447094651 0.999917975776453 27 0.000233858929541847 0.000467717859083694 0.999766141070458 28 0.000274478572574541 0.000548957145149083 0.999725521427425 29 0.000528946455045159 0.00105789291009032 0.999471053544955 30 0.000765791112982492 0.00153158222596498 0.999234208887018 31 0.00150441320733945 0.00300882641467891 0.99849558679266 32 0.00259309230136096 0.00518618460272192 0.99740690769864 33 0.0103177139019358 0.0206354278038716 0.989682286098064 34 0.0217148964162832 0.0434297928325665 0.978285103583717 35 0.0598305081388067 0.119661016277613 0.940169491861193 36 0.0984586196012912 0.196917239202582 0.901541380398709 37 0.37114822553066 0.74229645106132 0.62885177446934 38 0.42503606745005 0.8500721349001 0.57496393254995 39 0.474915870707857 0.949831741415714 0.525084129292143 40 0.511838041870906 0.976323916258189 0.488161958129094 41 0.578233770924791 0.843532458150418 0.421766229075209 42 0.586394179510736 0.827211640978528 0.413605820489264 43 0.58559196741248 0.82881606517504 0.41440803258752 44 0.585596889026603 0.828806221946794 0.414403110973397 45 0.574028090335614 0.851943819328773 0.425971909664386 46 0.553484464965653 0.893031070068695 0.446515535034347 47 0.539403311925541 0.921193376148918 0.460596688074459 48 0.495937196848973 0.991874393697946 0.504062803151027 49 0.460166286171109 0.920332572342218 0.539833713828891 50 0.400673629030679 0.801347258061359 0.59932637096932 51 0.367536284286819 0.735072568573637 0.632463715713181 52 0.355945970122891 0.711891940245783 0.644054029877109 53 0.269188936252596 0.538377872505192 0.730811063747404 54 0.175617788154156 0.351235576308312 0.824382211845844 55 0.100203216324037 0.200406432648074 0.899796783675963 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 25 0.490196078431373 NOK 5% type I error level 30 0.588235294117647 NOK 10% type I error level 30 0.588235294117647 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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