MR: PS (te verklaren) = D + Tg (verklarende)

*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, 14 Dec 2010 17:03:27 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t.htm/, Retrieved Tue, 14 Dec 2010 18:02:39 +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/2010/Dec/14/t12923461561qj0v1oudkkgb5t.htm/}, year = {2010}, } @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 = {2010}, 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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0,301029996 3 1,62324929 0,255272505 4 2,79518459 -0,15490196 4 2,255272505 0,591064607 1 1,544068044 0 4 2,593286067 0,556302501 1 1,799340549 0,146128036 1 2,361727836 0,176091259 4 2,049218023 -0,15490196 5 2,44870632 0,322219295 1 1,62324929 0 2 1,447158031 0,612783857 2 1,62324929 0,079181246 2 2,079181246 -0,301029996 5 2,170261715 0,531478917 2 1,204119983 0,176091259 1 2,491361694 0,531478917 3 1,447158031 -0,096910013 4 1,832508913 -0,096910013 5 2,526339277 0,146128036 4 1,33243846 0,301029996 1 1,698970004 0,278753601 1 2,426511261 0,113943352 3 1,278753601 0,301029996 3 1,477121255 0,748188027 1 1,079181246 0,491361694 1 2,079181246 0,255272505 2 2,146128036 -0,045757491 4 2,230448921 0,255272505 2 1,230448921 0,278753601 4 2,06069784 -0,045757491 5 1,491361694 0,414973348 3 1,322219295 0,380211242 1 1,716003344 0,079181246 2 2,214843848 -0,045757491 2 2,352182518 -0,301029996 3 2,352182518 -0,22184875 5 2,178976947 0,361727836 2 1,77815125 -0,301029996 3 2,30 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation PS[t] = + 1.01286297246682 -0.111002079465273D[t] -0.276532324735665Tg[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) 1.01286297246682 0.125069 8.0984 0 0 D -0.111002079465273 0.022068 -5.03 1.1e-05 6e-06 Tg -0.276532324735665 0.066448 -4.1617 0.000168 8.4e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.78228935349227 R-squared 0.611976632587354 Adjusted R-squared 0.592077998361065 F-TEST (value) 30.7547053545427 F-TEST (DF numerator) 2 F-TEST (DF denominator) 39 p-value 9.61011681344104e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.186453483961759 Sum Squared Residuals 1.35583116557764 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.301029996 0.230975834281787 0.0700541617182133 2 0.255272505 -0.204104238132274 0.459376743132274 3 -0.15490196 -0.0548010941143446 -0.100100865885655 4 0.591064607 0.474876167244179 0.116188439755821 5 0 -0.148272770206387 0.148272770206387 6 0.556302501 0.404285067995433 0.152017433004567 7 0.146128036 0.248766804119539 -0.102638768119539 8 0.176091259 0.0021796308153188 0.173911628184681 9 -0.15490196 -0.219293876124056 0.0643919161240558 10 0.322219295 0.452979993212333 -0.130760698212333 11 0 0.39067283896396 -0.39067283896396 12 0.612783857 0.34197791374706 0.27080594325294 13 0.079181246 0.215897990033101 -0.136716744033101 14 -0.301029996 -0.142294942193302 -0.158735053806698 15 0.531478917 0.457880715376618 0.0735982016233817 16 0.176091259 0.212918852002346 -0.036827593002346 17 0.531478917 0.279670759498687 0.251808157501313 18 -0.096910013 0.0621067047950157 -0.159016717795016 19 -0.096910013 -0.24076189819937 0.14385188519937 20 0.146128036 0.200392349694723 -0.0542643136947228 21 0.301029996 0.432040768139269 -0.131010772139268 22 0.278753601 0.230852092999951 0.0479015080000494 23 0.113943352 0.326240028022372 -0.212296676022372 24 0.301029996 0.271384959509392 0.0296450364906081 25 0.748188027 0.603432394234039 0.144755632765961 26 0.491361694 0.326900069498374 0.164461624501626 27 0.255272505 0.197385038560811 0.0578874664391892 28 -0.045757491 -0.0479365707225534 0.0021790797225534 29 0.255272505 0.450599912943657 -0.195327407943657 30 0.278753601 -0.000994909667231259 0.279748510667231 31 -0.045757491 0.0454428588769199 -0.0912003498769199 32 0.414973348 0.314220358614303 0.100752989385697 33 0.380211242 0.427330499031055 -0.0471192570310555 34 0.079181246 0.178382895322352 -0.0992016493223519 35 -0.045757491 0.140404313631148 -0.186161804631148 36 -0.301029996 0.0294022341658747 -0.330432230165875 37 -0.22184875 -0.144704985558873 -0.0771437644411274 38 0.361727836 0.299142514642149 0.0625853213578509 39 -0.301029996 0.043547559990627 -0.344577555990627 40 0.414973348 0.331052524780883 0.0839208232191166 41 -0.22184875 -0.0733140455866349 -0.148534704413365 42 0.819543936 0.584919442761749 0.234624493238251 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.56055032911684 0.87889934176632 0.43944967088316 7 0.773019163324786 0.453961673350428 0.226980836675214 8 0.678180453588924 0.643639092822152 0.321819546411076 9 0.598619417506705 0.802761164986591 0.401380582493295 10 0.55161708690293 0.896765826194139 0.448382913097069 11 0.811376018300675 0.37724796339865 0.188623981699325 12 0.897465293041335 0.205069413917329 0.102534706958665 13 0.884260351661738 0.231479296676525 0.115739648338262 14 0.880438874214097 0.239122251571805 0.119561125785903 15 0.849750081687015 0.300499836625969 0.150249918312985 16 0.798104857086246 0.403790285827508 0.201895142913754 17 0.841906486946654 0.316187026106693 0.158093513053346 18 0.828366391540143 0.343267216919714 0.171633608459857 19 0.834714493726769 0.330571012546462 0.165285506273231 20 0.772035302077229 0.455929395845542 0.227964697922771 21 0.741370529228301 0.517258941543397 0.258629470771699 22 0.670610926146319 0.658778147707363 0.329389073853681 23 0.71925330478267 0.561493390434659 0.280746695217329 24 0.635085668312883 0.729828663374233 0.364914331687117 25 0.588974992423562 0.822050015152876 0.411025007576438 26 0.600071840929075 0.79985631814185 0.399928159070925 27 0.552541283054197 0.894917433891605 0.447458716945803 28 0.483989600645406 0.967979201290811 0.516010399354594 29 0.653128248176499 0.693743503647002 0.346871751823501 30 0.96936650447633 0.0612669910473412 0.0306334955236706 31 0.976552203528233 0.0468955929435339 0.023447796471767 32 0.969403119374236 0.0611937612515285 0.0305968806257642 33 0.9441648237251 0.111670352549802 0.055835176274901 34 0.925693654972276 0.148612690055448 0.074306345027724 35 0.943421133188992 0.113157733622015 0.0565788668110077 36 0.887599495934966 0.224801008130068 0.112400504065034 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 0.032258064516129 OK 10% type I error level 3 0.0967741935483871 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/106kjv1292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/106kjv1292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/1h14j1292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/1h14j1292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/2h14j1292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/2h14j1292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/3ss341292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/3ss341292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/4ss341292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/4ss341292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/5ss341292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/5ss341292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/62j3p1292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/62j3p1292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/7daka1292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/7daka1292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/8daka1292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/8daka1292346198.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/9daka1292346198.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t12923461561qj0v1oudkkgb5t/9daka1292346198.ps (open in new window)

Parameters (Session):

par1 = 2 ; 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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