Multiple Regression met Brain Weight

*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 22:49:21 +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/t12922804772cbinzflwmiuz3q.htm/, Retrieved Mon, 13 Dec 2010 23:48:07 +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/t12922804772cbinzflwmiuz3q.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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6.3 3 4 2.1 4 7 9.1 4 5 15.8 1 -1 5.2 4 5 10.9 1 4 8.3 1 6 11.0 4 4 3.2 5 6 7.6 2 3 6.3 1 3 8.6 2 4 6.6 2 4 9.5 2 4 4.8 1 4 12.0 1 5 3.3 5 5 11.0 2 3 4.7 1 6 10.4 3 4 7.4 4 4 2.1 5 6 7.7 4 -1 17.9 1 -1 6.1 1 6 8.2 1 3 8.4 3 4 11.9 3 0 10.8 3 0 13.8 1 4 14.3 1 4 15.2 2 4 10.0 4 5 11.9 2 4 6.5 4 5 7.5 5 4 10.6 3 3 7.4 1 5 8.4 2 5 5.7 2 4 4.9 3 4 3.2 5 5 8.1 2 3 11.0 2 3 4.9 3 4 13.2 2 3 9.7 4 5 12.8 1 4

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation SWS[t] = + 15.0954977616851 -1.03456535198758D[t] -0.98387149057833Wb[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) 15.0954977616851 1.114348 13.5465 0 0 D -1.03456535198758 0.300534 -3.4424 0.001257 0.000628 Wb -0.98387149057833 0.227929 -4.3166 8.6e-05 4.3e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.677036296046545 R-squared 0.458378146164426 Adjusted R-squared 0.434306063771733 F-TEST (value) 19.0418983570603 F-TEST (DF numerator) 2 F-TEST (DF denominator) 45 p-value 1.01897618698388e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.75763464965191 Sum Squared Residuals 342.204698743237 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 8.05631574340903 -1.75631574340903 2 2.1 4.07013591968648 -1.97013591968648 3 9.1 6.03787890084313 3.06212109915687 4 15.8 15.0448039002759 0.755196099724141 5 5.2 6.03787890084314 -0.837878900843137 6 10.9 10.1254464473842 0.774553552615798 7 8.3 8.15770346622754 0.142296533772461 8 11 7.02175039142147 3.97824960857853 9 3.2 4.01944205827723 -0.819442058277227 10 7.6 10.0747525859750 -2.47475258597496 11 6.3 11.1093179379625 -4.80931793796253 12 8.6 9.09088109539663 -0.490881095396625 13 6.6 9.09088109539663 -2.49088109539662 14 9.5 9.09088109539663 0.409118904603376 15 4.8 10.1254464473842 -5.3254464473842 16 12 9.14157495680587 2.85842504319413 17 3.3 5.00331354885556 -1.70331354885556 18 11 10.0747525859750 0.925247414025044 19 4.7 8.15770346622754 -3.45770346622754 20 10.4 8.05631574340905 2.34368425659095 21 7.4 7.02175039142147 0.378249608578532 22 2.1 4.01944205827723 -1.91944205827723 23 7.7 11.9411078443131 -4.24110784431312 24 17.9 15.0448039002759 2.85519609972414 25 6.1 8.15770346622754 -2.05770346622754 26 8.2 11.1093179379625 -2.90931793796253 27 8.4 8.05631574340905 0.343684256590954 28 11.9 11.9918017057224 -0.091801705722372 29 10.8 11.9918017057224 -1.19180170572237 30 13.8 10.1254464473842 3.6745535526158 31 14.3 10.1254464473842 4.1745535526158 32 15.2 9.09088109539663 6.10911890460337 33 10 6.03787890084314 3.96212109915686 34 11.9 9.09088109539663 2.80911890460338 35 6.5 6.03787890084314 0.462121099156863 36 7.5 5.98718503943389 1.51281496056611 37 10.6 9.04018723398738 1.55981276601262 38 7.4 9.14157495680587 -1.74157495680587 39 8.4 8.1070096048183 0.292990395181707 40 5.7 9.09088109539663 -3.39088109539662 41 4.9 8.05631574340905 -3.15631574340905 42 3.2 5.00331354885556 -1.80331354885556 43 8.1 10.0747525859750 -1.97475258597496 44 11 10.0747525859750 0.925247414025044 45 4.9 8.05631574340905 -3.15631574340905 46 13.2 10.0747525859750 3.12524741402504 47 9.7 6.03787890084314 3.66212109915686 48 12.8 10.1254464473842 2.6745535526158 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.423861295191279 0.847722590382558 0.576138704808721 7 0.260228189970984 0.520456379941969 0.739771810029016 8 0.366297150183025 0.73259430036605 0.633702849816975 9 0.267984127224859 0.535968254449718 0.732015872775141 10 0.281153846450956 0.562307692901912 0.718846153549044 11 0.440126842677651 0.880253685355301 0.55987315732235 12 0.332447685998356 0.664895371996711 0.667552314001644 13 0.282416625614242 0.564833251228483 0.717583374385758 14 0.213026387610186 0.426052775220372 0.786973612389814 15 0.338387463506205 0.67677492701241 0.661612536493795 16 0.467577126351105 0.93515425270221 0.532422873648895 17 0.41809236024404 0.83618472048808 0.58190763975596 18 0.347705563759944 0.695411127519889 0.652294436240056 19 0.366568478452729 0.733136956905458 0.633431521547271 20 0.347174110120574 0.694348220241148 0.652825889879426 21 0.268154361923832 0.536308723847665 0.731845638076168 22 0.235096396893202 0.470192793786404 0.764903603106798 23 0.337157462959194 0.674314925918389 0.662842537040806 24 0.363194945884475 0.72638989176895 0.636805054115525 25 0.346426255897513 0.692852511795026 0.653573744102487 26 0.370380888881959 0.740761777763918 0.629619111118041 27 0.295363708050509 0.590727416101019 0.704636291949491 28 0.223841681000484 0.447683362000969 0.776158318999516 29 0.168889636641274 0.337779273282547 0.831110363358726 30 0.201946529481057 0.403893058962113 0.798053470518943 31 0.260394494696064 0.520788989392128 0.739605505303936 32 0.547106705652693 0.905786588694615 0.452893294347307 33 0.626362372952135 0.74727525409573 0.373637627047865 34 0.627273582248895 0.745452835502211 0.372726417751105 35 0.530875674886723 0.938248650226554 0.469124325113277 36 0.454220880854544 0.908441761709087 0.545779119145456 37 0.380276209400378 0.760552418800757 0.619723790599622 38 0.326312831447448 0.652625662894897 0.673687168552552 39 0.227480368437817 0.454960736875633 0.772519631562183 40 0.30860098053579 0.61720196107158 0.69139901946421 41 0.326799091966036 0.653598183932072 0.673200908033964 42 0.227165983525365 0.45433196705073 0.772834016474635 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

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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