ws7

*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: Wed, 24 Nov 2010 12:45:58 +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/Nov/24/t12906027057srdwll8yvmzo1b.htm/, Retrieved Wed, 24 Nov 2010 13:45:09 +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/Nov/24/t12906027057srdwll8yvmzo1b.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:

» Textbox « » Textfile « » CSV «

1 102,89 167,16 100,70 106,88 97,69 1 106,14 196,07 100,12 109,96 100,90 1 108,26 369,59 99,10 113,15 106,83 1 112,79 239,36 99,84 118,27 110,67 1 117,31 201,19 97,90 121,81 102,75 2 102,64 179,84 99,62 107,45 101,69 2 105,85 199,98 100,40 110,49 103,91 2 108,93 425,00 99,48 113,28 112,51 2 113,87 224,69 99,68 118,88 113,28 2 117,77 194,37 97,88 122,21 107,21 3 103,33 174,44 99,83 107,65 102,72 3 106,27 199,10 100,51 111,37 103,81 3 109,43 439,72 99,74 113,83 113,61 3 114,28 230,98 99,74 119,11 112,08 3 118,37 191,08 97,56 122,82 107,24 4 103,56 180,35 100,74 107,72 101,85 4 106,51 198,31 100,70 111,56 104,59 4 109,61 362,23 100,42 114,49 114,96 4 115,51 233,47 99,71 119,29 111,41 4 117,91 192,87 96,86 123,02 106,01 5 103,60 193,17 100,84 108,10 114,94 5 106,82 195,72 100,62 111,90 104,94 5 109,74 328,76 100,80 114,76 118,66 5 116,76 256,70 99,35 119,36 113,81 5 118,12 181,61 96,86 123,14 121,36 6 104,24 195,16 100,85 108,38 106,20 6 106,53 223,04 99,70 111,96 111,64 6 110,12 348,55 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 suiker[t] = + 114.597307770066 + 0.00106518222376726month[t] + 0.166950547178408Bier[t] + 0.00186452253761169Tarwe[t] -0.338281167276215minerwater[t] + 0.0455394914285356fruit[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) 114.597307770066 2.694921 42.5234 0 0 month 0.00106518222376726 0.030571 0.0348 0.972338 0.486169 Bier 0.166950547178408 0.128996 1.2942 0.201304 0.100652 Tarwe 0.00186452253761169 0.001782 1.046 0.300388 0.150194 minerwater -0.338281167276215 0.126346 -2.6774 0.009904 0.004952 fruit 0.0455394914285356 0.023818 1.912 0.061397 0.030698 Multiple Linear Regression - Regression Statistics Multiple R 0.78793835686911 R-squared 0.620846854225593 Adjusted R-squared 0.584389820978054 F-TEST (value) 17.0295495524859 F-TEST (DF numerator) 5 F-TEST (DF denominator) 52 p-value 6.06275363246311e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.773754810920322 Sum Squared Residuals 31.1322183859618 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.7 100.380850098035 0.319149901965114 2 100.12 100.081618495202 0.0383815047983082 3 99.1 99.9500178665064 -0.850017866506393 4 99.84 98.9063591457828 0.933640854217241 5 97.9 98.0316186894967 -0.131618689496714 6 99.62 100.353157489607 -0.733157489607435 7 100.4 99.9993431524093 0.400656847590722 8 99.48 100.380940868717 -0.900940868716924 9 99.68 98.9728849339224 0.707115066077574 10 97.88 98.1645587445768 -0.284558744576831 11 99.83 100.438599570397 -0.608599570397354 12 100.51 99.766645408269 0.743354591731047 13 99.74 100.356965894853 -0.61696589485302 14 99.74 98.9216756290631 0.818324370936845 15 97.56 98.0546746486633 -0.494674648663261 16 100.74 100.425783667417 0.314216332582715 17 100.7 99.7775531305426 0.922446869457393 18 100.42 100.081813067156 0.338186932844415 19 99.71 99.0413305760682 0.668669423931821 20 96.86 97.858610266615 -0.998610266614945 21 100.84 100.924995149695 -0.084995149694932 22 100.62 99.7264670941453 0.893532905854665 23 100.8 100.1193364543 0.680663545700315 24 99.35 99.3800118985328 -0.0300118985328279 25 96.86 98.5321779933276 -1.67217799332755 26 100.85 100.54388520004 0.306114799960005 27 99.7 100.01487309595 -0.314873095949539 28 100.66 100.070203637615 0.589796362384588 29 99.21 99.1476330084688 0.0623669915312252 30 96.75 98.4367807425143 -1.68678074251432 31 99.71 100.681457181647 -0.971457181646782 32 99.48 100.031484673017 -0.551484673016562 33 101.03 100.085836780075 0.94416321992501 34 99.21 98.6270955846882 0.582904415311775 35 97.12 97.8635961344115 -0.743596134411503 36 100.8 100.638555248394 0.161444751605555 37 99.36 99.8640290122612 -0.504029012261163 38 101.22 99.818666177038 1.40133382296201 39 99.16 98.4815436065466 0.678456393453394 40 97.22 98.0406608705551 -0.820660870555144 41 100.06 100.617857146736 -0.557857146735523 42 99.39 99.9759365988755 -0.58593659887552 43 101.23 99.7050366009956 1.52496339900443 44 99.2 98.4028074206525 0.79719257934755 45 97.52 97.480983474113 0.0390165258869077 46 100.57 100.55638828787 0.0136117121296998 47 99.45 100.202620522544 -0.752620522543992 48 100.1 99.4733943762418 0.626605623758204 49 99.08 98.3674826704247 0.712517329575329 50 97.57 97.562944480744 0.00705551925601923 51 99.79 100.422324974208 -0.632324974207634 52 99.28 100.12219865646 -0.84219865646044 53 99.98 99.0437461505427 0.936253849457267 54 98.16 98.5341249919447 -0.374124991944726 55 99.9 100.338779309043 -0.438779309042806 56 99.4 100.038406283549 -0.638406283548776 57 99.91 98.9855187161627 0.924481283837321 58 98 98.2651584523718 -0.265158452371856 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.217491514081586 0.434983028163172 0.782508485918414 10 0.112980212900156 0.225960425800311 0.887019787099844 11 0.0518187612263096 0.103637522452619 0.94818123877369 12 0.241710515661302 0.483421031322604 0.758289484338698 13 0.209427070728857 0.418854141457714 0.790572929271143 14 0.168998591592344 0.337997183184687 0.831001408407656 15 0.127961300208441 0.255922600416882 0.87203869979156 16 0.113090322250809 0.226180644501619 0.88690967774919 17 0.117391285518436 0.234782571036871 0.882608714481564 18 0.0784448391371442 0.156889678274288 0.921555160862856 19 0.0681014820938346 0.136202964187669 0.931898517906165 20 0.0945466341298567 0.189093268259713 0.905453365870143 21 0.171629712814677 0.343259425629355 0.828370287185323 22 0.205150397948714 0.410300795897429 0.794849602051286 23 0.16256961557763 0.32513923115526 0.83743038442237 24 0.119949604656611 0.239899209313223 0.880050395343389 25 0.52280685732696 0.95438628534608 0.47719314267304 26 0.492793773375854 0.985587546751707 0.507206226624146 27 0.446963337895411 0.893926675790822 0.553036662104589 28 0.397744961796961 0.795489923593921 0.602255038203039 29 0.352112398994944 0.704224797989887 0.647887601005056 30 0.819372882938005 0.36125423412399 0.180627117061995 31 0.851809464631993 0.296381070736015 0.148190535368007 32 0.81339375318673 0.373212493626539 0.18660624681327 33 0.804099238788498 0.391801522423004 0.195900761211502 34 0.758136434133106 0.483727131733787 0.241863565866894 35 0.78895818839555 0.4220836232089 0.21104181160445 36 0.71876447443205 0.562471051135898 0.281235525567949 37 0.651517205553297 0.696965588893407 0.348482794446703 38 0.72652639266393 0.546947214672141 0.27347360733607 39 0.692803285464031 0.614393429071938 0.307196714535969 40 0.824213506001612 0.351572987996777 0.175786493998388 41 0.832416983075452 0.335166033849096 0.167583016924548 42 0.772679197532607 0.454641604934785 0.227320802467393 43 0.868726290322214 0.262547419355573 0.131273709677786 44 0.856338840514395 0.28732231897121 0.143661159485605 45 0.773253386530192 0.453493226939615 0.226746613469808 46 0.681127909572446 0.637744180855108 0.318872090427554 47 0.566753787873911 0.866492424252178 0.433246212126089 48 0.438447303637501 0.876894607275002 0.561552696362499 49 0.795705428215611 0.408589143568778 0.204294571784389 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):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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