Bonus: MR totaalmodel correct

*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: Mon, 13 Dec 2010 19:52:07 +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/13/t1292269844xlhq0cvl7tx67kh.htm/, Retrieved Mon, 13 Dec 2010 20:50:54 +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/13/t1292269844xlhq0cvl7tx67kh.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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6,30000000 0,30103000 0,65321251 0,00000000 0,81954394 1,62324929 3 1 3 2,10000000 0,25527251 1,83884909 3,40602894 3,66304097 2,79518459 3 5 4 9,10000000 -0,15490196 1,43136376 1,02325246 2,25406445 2,25527251 4 4 4 15,80000000 0,59106461 1,27875360 -1,63827216 -0,52287875 1,54406804 1 1 1 5,20000000 0,00000000 1,48287358 2,20411998 2,22788670 2,59328607 4 5 4 10,90000000 0,55630250 1,44715803 0,51851394 1,40823997 1,79934055 1 2 1 8,30000000 0,14612804 1,69897000 1,71733758 2,64345268 2,36172784 1 1 1 11,00000000 0,17609126 0,84509804 -0,37161107 0,80617997 2,04921802 5 4 4 3,20000000 -0,15490196 1,47712125 2,66745295 2,62634037 2,44870632 5 5 5 6,30000000 0,32221929 0,54406804 -1,12493874 0,07918125 1,62324929 1 1 1 6,60000000 0,61278386 0,77815125 -0,10513034 0,54406804 1,62324929 2 2 2 9,50000000 0,07918125 1,01703334 -0,69897000 0,69897000 2,07918125 2 2 2 3,30000000 -0,30103000 1,30103000 1,44185218 2,06069784 2,17026172 5 5 5 11,00000000 0,53147892 0,59106461 -0,92081875 0,00000000 1,2041 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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation SWS[t] = + 7.1951928995231 + 3.36679479806534logPS[t] + 3.43730613389774LogL[t] -1.65097896957639LogWb[t] -0.880440616713212LogWbr[t] -0.315657161277412LogTg[t] + 1.33733450509432P[t] + 0.31497942209904S[t] -1.88373963984934D[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) 7.1951928995231 4.516729 1.593 0.121641 0.060821 logPS 3.36679479806534 2.745137 1.2265 0.229566 0.114783 LogL 3.43730613389774 1.782017 1.9289 0.063254 0.031627 LogWb -1.65097896957639 1.157343 -1.4265 0.164042 0.082021 LogWbr -0.880440616713212 1.620254 -0.5434 0.590872 0.295436 LogTg -0.315657161277412 1.911325 -0.1652 0.869933 0.434967 P 1.33733450509432 0.993734 1.3458 0.188461 0.09423 S 0.31497942209904 0.626066 0.5031 0.618562 0.309281 D -1.88373963984934 1.344971 -1.4006 0.171599 0.085799 Multiple Linear Regression - Regression Statistics Multiple R 0.827535230476664 R-squared 0.684814557680065 Adjusted R-squared 0.600765106394749 F-TEST (value) 8.14775762610727 F-TEST (DF numerator) 8 F-TEST (DF denominator) 30 p-value 8.60521084933286e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.50737645171981 Sum Squared Residuals 188.608100119170 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 7.8958044878963 -1.5958044878963 2 2.1 2.69658014772338 -0.596580147723377 3 9.1 6.28217126293777 2.81782873706223 4 15.8 16.0269484715526 -0.226948471552595 5 5.2 5.26249293057238 -0.0624929305723761 6 10.9 11.4621261371318 -0.56212613713175 7 8.3 7.38744267234001 0.912557327659991 8 11 10.3614264972147 0.638573502785344 9 3.2 3.10466201262141 0.0953379873785867 10 6.3 11.1938873777178 -4.89388737771781 11 6.6 10.6523611679286 -4.05236116792863 12 9.5 10.3770581741205 -0.877058174120512 13 3.3 4.61674814027528 -1.31674814027528 14 11 12.7159103261441 -1.71591032614409 15 4.7 7.54681065354392 -2.84681065354392 16 10.4 14.2719906375552 -3.87199063755515 17 7.4 8.73478334003063 -1.33478334003063 18 2.1 3.66476365493473 -1.56476365493473 19 17.9 16.0172259470066 1.88277405299342 20 6.1 8.30425894808346 -2.20425894808346 21 11.9 11.9797381243703 -0.0797381243703365 22 13.8 11.7977816305844 2.00221836941558 23 14.3 10.2852261566821 4.01477384331789 24 15.2 10.1020749114234 5.09792508857664 25 10 6.43296801944043 3.56703198055957 26 11.9 9.44092967419295 2.45907032580705 27 6.5 5.72224178948455 0.777758210515445 28 7.5 8.11768635117774 -0.617686351177743 29 10.6 9.8282296170369 0.771770382963105 30 7.4 8.5755283622153 -1.17552836221530 31 8.4 8.28352819665816 0.116471803341846 32 5.7 7.98733731949211 -2.28733731949211 33 4.9 5.02211161370968 -0.122111613709682 34 3.2 4.22072100883204 -1.02072100883204 35 11 9.02941591510143 1.97058408489857 36 4.9 5.68237659159673 -0.782376591596732 37 13.2 11.4578087377807 1.74219126221931 38 9.7 6.63891893308388 3.06108106691612 39 12.8 10.9199240598061 1.88007594019387 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.0297158310186875 0.059431662037375 0.970284168981313 13 0.0605689380476924 0.121137876095385 0.939431061952308 14 0.0247739793110753 0.0495479586221505 0.975226020688925 15 0.0151794943195481 0.0303589886390962 0.984820505680452 16 0.45037671954694 0.90075343909388 0.54962328045306 17 0.342066135194997 0.684132270389995 0.657933864805003 18 0.329419613870677 0.658839227741353 0.670580386129323 19 0.229275168606590 0.458550337213179 0.77072483139341 20 0.4636319285755 0.927263857151 0.5363680714245 21 0.489587482592915 0.97917496518583 0.510412517407085 22 0.622229270510906 0.755541458978187 0.377770729489094 23 0.727030464689739 0.545939070620521 0.272969535310261 24 0.844470162644519 0.311059674710962 0.155529837355481 25 0.916201265648876 0.167597468702248 0.083798734351124 26 0.884110697720785 0.231778604558431 0.115889302279215 27 0.80626565432164 0.387468691356719 0.193734345678359 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 2 0.125 NOK 10% type I error level 3 0.1875 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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