Paper H4 Mannen Multiple Regression (No seasonal, trend)

*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: Tue, 16 Dec 2008 13:59:44 -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/16/t1229461262qmtpfoiqpkrrycy.htm/, Retrieved Tue, 16 Dec 2008 22:01:02 +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/2008/Dec/16/t1229461262qmtpfoiqpkrrycy.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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269645 0 267037 0 258113 0 262813 0 267413 0 267366 0 264777 0 258863 0 254844 0 254868 0 277267 0 285351 0 286602 0 283042 0 276687 0 277915 0 277128 0 277103 0 275037 0 270150 0 267140 0 264993 0 287259 0 291186 0 292300 0 288186 0 281477 0 282656 1 280190 1 280408 1 276836 1 275216 1 274352 1 271311 1 289802 1 290726 1 292300 1 278506 1 269826 1 265861 1 269034 1 264176 1 255198 1 253353 1 246057 1 235372 1 258556 1 260993 1 254663 1 250643 1 243422 1 247105 1 248541 1 245039 1 237080 1 237085 1 225554 1 226839 1 247934 1 248333 1 246969 1 245098 1 246263 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 Mannen[t] = + 284198.776651176 + 9489.70116884944Dummy[t] -764.034311062827t + 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) 284198.776651176 3736.979957 76.0504 0 0 Dummy 9489.70116884944 6861.072594 1.3831 0.171753 0.085876 t -764.034311062827 186.719377 -4.0919 0.00013 6.5e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.60011510884437 R-squared 0.36013814386329 Adjusted R-squared 0.3388094153254 F-TEST (value) 16.8851201431678 F-TEST (DF numerator) 2 F-TEST (DF denominator) 60 p-value 1.52260287267225e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13876.4031962403 Sum Squared Residuals 11553273939.8777 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 269645 283434.742340114 -13789.7423401135 2 267037 282670.70802905 -15633.7080290502 3 258113 281906.673717987 -23793.6737179874 4 262813 281142.639406925 -18329.6394069245 5 267413 280378.605095862 -12965.6050958617 6 267366 279614.570784799 -12248.5707847989 7 264777 278850.536473736 -14073.5364737361 8 258863 278086.502162673 -19223.5021626732 9 254844 277322.467851610 -22478.4678516104 10 254868 276558.433540548 -21690.4335405476 11 277267 275794.399229485 1472.60077051524 12 285351 275030.364918422 10320.6350815781 13 286602 274266.330607359 12335.6693926409 14 283042 273502.296296296 9539.70370370372 15 276687 272738.261985233 3948.73801476655 16 277915 271974.227674171 5940.77232582938 17 277128 271210.193363108 5917.8066368922 18 277103 270446.159052045 6656.84094795503 19 275037 269682.124740982 5354.87525901786 20 270150 268918.090429919 1231.90957008068 21 267140 268154.056118856 -1014.05611885649 22 264993 267390.021807794 -2397.02180779366 23 287259 266625.987496731 20633.0125032692 24 291186 265861.953185668 25324.046814332 25 292300 265097.918874605 27202.0811253948 26 288186 264333.884563542 23852.1154364576 27 281477 263569.850252480 17907.1497475205 28 282656 272295.517110266 10360.4828897339 29 280190 271531.482799203 8658.51720079669 30 280408 270767.448488140 9640.55151185952 31 276836 270003.414177078 6832.58582292234 32 275216 269239.379866015 5976.62013398517 33 274352 268475.345554952 5876.654445048 34 271311 267711.311243889 3599.68875611082 35 289802 266947.276932826 22854.7230671736 36 290726 266183.242621764 24542.7573782365 37 292300 265419.208310701 26880.7916892993 38 278506 264655.173999638 13850.8260003621 39 269826 263891.139688575 5934.86031142496 40 265861 263127.105377512 2733.89462248778 41 269034 262363.071066449 6670.92893355061 42 264176 261599.036755387 2576.96324461344 43 255198 260835.002444324 -5637.00244432374 44 253353 260070.968133261 -6717.96813326091 45 246057 259306.933822198 -13249.9338221981 46 235372 258542.899511135 -23170.8995111353 47 258556 257778.865200072 777.134799927573 48 260993 257014.830889010 3978.1691109904 49 254663 256250.796577947 -1587.79657794677 50 250643 255486.762266884 -4843.76226688394 51 243422 254722.727955821 -11300.7279558211 52 247105 253958.693644758 -6853.69364475829 53 248541 253194.659333695 -4653.65933369546 54 245039 252430.625022633 -7391.62502263264 55 237080 251666.59071157 -14586.5907115698 56 237085 250902.556400507 -13817.5564005070 57 225554 250138.522089444 -24584.5220894442 58 226839 249374.487778381 -22535.4877783813 59 247934 248610.453467318 -676.453467318503 60 248333 247846.419156256 486.580843744325 61 246969 247082.384845193 -113.384845192848 62 245098 246318.35053413 -1220.35053413002 63 246263 245554.316223067 708.683776932805 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0867256362419845 0.173451272483969 0.913274363758016 7 0.0316016525882620 0.0632033051765239 0.968398347411738 8 0.0191274704242043 0.0382549408484086 0.980872529575796 9 0.0176763236282471 0.0353526472564942 0.982323676371753 10 0.0138255062727802 0.0276510125455604 0.98617449372722 11 0.187081443798907 0.374162887597814 0.812918556201093 12 0.445673361231083 0.891346722462167 0.554326638768917 13 0.512806451820066 0.974387096359868 0.487193548179934 14 0.449222217841953 0.898444435683907 0.550777782158047 15 0.375952198664182 0.751904397328363 0.624047801335818 16 0.303944579447875 0.607889158895751 0.696055420552125 17 0.245844273342035 0.491688546684069 0.754155726657965 18 0.196841201820712 0.393682403641424 0.803158798179288 19 0.169555213726711 0.339110427453422 0.830444786273289 20 0.196531258504358 0.393062517008716 0.803468741495642 21 0.279197000918432 0.558394001836863 0.720802999081568 22 0.454649571882003 0.909299143764005 0.545350428117997 23 0.437623517189992 0.875247034379985 0.562376482810008 24 0.430994386651128 0.861988773302256 0.569005613348872 25 0.410909713127115 0.82181942625423 0.589090286872885 26 0.347410507069115 0.69482101413823 0.652589492930885 27 0.286258115394469 0.572516230788939 0.71374188460553 28 0.225264033410780 0.450528066821559 0.77473596658922 29 0.176054503965658 0.352109007931315 0.823945496034342 30 0.132551733636644 0.265103467273287 0.867448266363356 31 0.105141237131144 0.210282474262289 0.894858762868856 32 0.0854426368304803 0.170885273660961 0.91455736316952 33 0.069501743896725 0.13900348779345 0.930498256103275 34 0.0648827201111173 0.129765440222235 0.935117279888883 35 0.0718151497209508 0.143630299441902 0.92818485027905 36 0.100756291693314 0.201512583386627 0.899243708306686 37 0.228602150972958 0.457204301945915 0.771397849027042 38 0.277785392854400 0.555570785708801 0.7222146071456 39 0.340568957701901 0.681137915403802 0.659431042298099 40 0.418164568517433 0.836329137034866 0.581835431482567 41 0.509549409256922 0.980901181486155 0.490450590743077 42 0.605769151737969 0.788461696524062 0.394230848262031 43 0.694261419805778 0.611477160388443 0.305738580194221 44 0.744116817036732 0.511766365926535 0.255883182963268 45 0.805263520458175 0.389472959083650 0.194736479541825 46 0.93743207466747 0.125135850665059 0.0625679253325293 47 0.922704225970412 0.154591548059176 0.077295774029588 48 0.932258954402863 0.135482091194274 0.067741045597137 49 0.929539643764973 0.140920712470054 0.070460356235027 50 0.921135697254224 0.157728605491551 0.0788643027457757 51 0.893371106927227 0.213257786145547 0.106628893072773 52 0.870638495535062 0.258723008929876 0.129361504464938 53 0.884683405822516 0.230633188354968 0.115316594177484 54 0.907694327377694 0.184611345244613 0.0923056726223063 55 0.87450228447505 0.250995431049899 0.125497715524950 56 0.833252553696892 0.333494892606215 0.166747446303108 57 0.765422307780687 0.469155384438626 0.234577692219313 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 3 0.0576923076923077 NOK 10% type I error level 4 0.076923076923077 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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