*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, 18 Nov 2009 07:03:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/18/t1258553450zk8kgh63ve9dgo6.htm/, Retrieved Wed, 18 Nov 2009 15:11:02 +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/2009/Nov/18/t1258553450zk8kgh63ve9dgo6.htm/}, year = {2009}, } @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 = {2009}, 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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8.9 95.05 8.8 96.84 8.3 96.92 7.5 97.44 7.2 97.78 7.4 97.69 8.8 96.67 9.3 98.29 9.3 98.2 8.7 98.71 8.2 98.54 8.3 98.2 8.5 96.92 8.6 99.06 8.5 99.65 8.2 99.82 8.1 99.99 7.9 100.33 8.6 99.31 8.7 101.1 8.7 101.1 8.5 100.93 8.4 100.85 8.5 100.93 8.7 99.6 8.7 101.88 8.6 101.81 8.5 102.38 8.3 102.74 8 102.82 8.2 101.72 8.1 103.47 8.1 102.98 8 102.68 7.9 102.9 7.9 103.03 8 101.29 8 103.69 7.9 103.68 8 104.2 7.7 104.08 7.2 104.16 7.5 103.05 7.3 104.66 7 104.46 7 104.95 7 105.85 7.2 106.23 7.3 104.86 7.1 107.44 6.8 108.23 6.4 108.45 6.1 109.39 6.5 110.15 7.7 109.13 7.9 110.28 7.5 110.17 6.9 109.99 6.6 109.26 6.9 109.11

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkloosheidsgraad[t] = + 21.8542582437825 -0.135961536651284Consumptiepris[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) 21.8542582437825 1.64605 13.2768 0 0 Consumptiepris -0.135961536651284 0.016033 -8.4799 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.743998368902218 R-squared 0.553533572929161 Adjusted R-squared 0.545835875910698 F-TEST (value) 71.9089841548094 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 9.66049462647334e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.500923542678757 Sum Squared Residuals 14.5536149453705 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.9 8.93111418507803 -0.0311141850780302 2 8.8 8.68774303447218 0.112256965527816 3 8.3 8.67686611154008 -0.376866111540082 4 7.5 8.60616611248141 -1.10616611248142 5 7.2 8.55993919001998 -1.35993919001998 6 7.4 8.5721757283186 -1.17217572831859 7 8.8 8.7108564957029 0.0891435042970973 8 9.3 8.49059880632782 0.809401193672178 9 9.3 8.50283534462644 0.797164655373563 10 8.7 8.43349496093428 0.266505039065715 11 8.2 8.456608422165 -0.256608422165002 12 8.3 8.50283534462644 -0.202835344626438 13 8.5 8.67686611154008 -0.176866111540082 14 8.6 8.38590842310633 0.214091576893666 15 8.5 8.30569111648208 0.194308883517924 16 8.2 8.28257765525136 -0.08257765525136 17 8.1 8.25946419402064 -0.159464194020641 18 7.9 8.2132372715592 -0.313237271559203 19 8.6 8.35191803894351 0.248081961056487 20 8.7 8.10854688833771 0.591453111662284 21 8.7 8.10854688833771 0.591453111662284 22 8.5 8.13166034956843 0.368339650431568 23 8.4 8.14253727250054 0.257462727499464 24 8.5 8.13166034956843 0.368339650431568 25 8.7 8.31248919331464 0.387510806685358 26 8.7 8.00249688974971 0.697503110250286 27 8.6 8.0120141973153 0.587985802684697 28 8.5 7.93451612142407 0.565483878575929 29 8.3 7.8855699682296 0.414430031770392 30 8 7.8746930452975 0.125306954702493 31 8.2 8.02425073561392 0.175749264386081 32 8.1 7.78631804647417 0.313681953525829 33 8.1 7.8529391994333 0.2470608005667 34 8 7.89372766042868 0.106272339571316 35 7.9 7.8638161223654 0.0361838776345983 36 7.9 7.84614112260074 0.0538588773992646 37 8 8.08271419637397 -0.0827141963739696 38 8 7.75640650841089 0.243593491589111 39 7.9 7.7577661237774 0.1422338762226 40 8 7.68706612471873 0.312933875281267 41 7.7 7.70338150911689 -0.00338150911688754 42 7.2 7.69250458618479 -0.492504586184785 43 7.5 7.84342189186771 -0.343421891867711 44 7.3 7.62452381785914 -0.324523817859143 45 7 7.6517161251894 -0.6517161251894 46 7 7.58509497223027 -0.58509497223027 47 7 7.46272958924412 -0.462729589244115 48 7.2 7.41106420531663 -0.211064205316626 49 7.3 7.59733151052889 -0.297331510528886 50 7.1 7.24655074596857 -0.146550745968573 51 6.8 7.13914113201406 -0.339141132014058 52 6.4 7.10922959395077 -0.709229593950775 53 6.1 6.98142574949857 -0.881425749498568 54 6.5 6.87809498164359 -0.378094981643592 55 7.7 7.0167757490279 0.683224250972097 56 7.9 6.86041998187893 1.03958001812108 57 7.5 6.87537575091057 0.624624249089434 58 6.9 6.8998488275078 0.000151172492202026 59 6.6 6.99910074926323 -0.399100749263235 60 6.9 7.01949497976093 -0.119494979760928 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.712404484097454 0.575191031805092 0.287595515902546 6 0.676402630220011 0.647194739559978 0.323597369779989 7 0.719912016223904 0.560175967552192 0.280087983776096 8 0.99677361556438 0.00645276887124019 0.00322638443562010 9 0.99941912761184 0.00116174477631937 0.000580872388159686 10 0.998970339718087 0.00205932056382507 0.00102966028191254 11 0.99816077196389 0.00367845607222058 0.00183922803611029 12 0.996767403306458 0.00646519338708447 0.00323259669354224 13 0.994803830715779 0.0103923385684417 0.00519616928422084 14 0.991270314277962 0.0174593714440756 0.0087296857220378 15 0.98501392069513 0.0299721586097406 0.0149860793048703 16 0.977011080751185 0.0459778384976295 0.0229889192488147 17 0.968045538443341 0.0639089231133173 0.0319544615566586 18 0.96382156381916 0.0723568723616791 0.0361784361808395 19 0.949378570810054 0.101242858379891 0.0506214291899457 20 0.942977037481824 0.114045925036351 0.0570229625181755 21 0.932686497006605 0.13462700598679 0.067313502993395 22 0.906248054840286 0.187503890319427 0.0937519451597136 23 0.869670720753626 0.260658558492748 0.130329279246374 24 0.829245486612178 0.341509026775644 0.170754513387822 25 0.790200207681698 0.419599584636604 0.209799792318302 26 0.78644250034804 0.42711499930392 0.21355749965196 27 0.769600540732242 0.460798918535516 0.230399459267758 28 0.756895364404945 0.486209271190109 0.243104635595055 29 0.73283755051602 0.53432489896796 0.26716244948398 30 0.70075994623849 0.59848010752302 0.29924005376151 31 0.65072253348449 0.698554933031019 0.349277466515509 32 0.623072627664553 0.753854744670895 0.376927372335447 33 0.588357338777944 0.823285322444112 0.411642661222056 34 0.544798996830375 0.910402006339249 0.455201003169625 35 0.501353909335802 0.997292181328395 0.498646090664198 36 0.458001409024835 0.916002818049669 0.541998590975165 37 0.405426268916498 0.810852537832996 0.594573731083502 38 0.39427154047413 0.78854308094826 0.60572845952587 39 0.381270111472258 0.762540222944517 0.618729888527742 40 0.426617755895214 0.853235511790427 0.573382244104786 41 0.427073217380410 0.854146434760819 0.57292678261959 42 0.429344225582782 0.858688451165564 0.570655774417218 43 0.409224683242471 0.818449366484941 0.590775316757529 44 0.377442568340637 0.754885136681273 0.622557431659363 45 0.362954960576485 0.72590992115297 0.637045039423515 46 0.326238838045367 0.652477676090735 0.673761161954633 47 0.27111475937271 0.54222951874542 0.72888524062729 48 0.207990373650767 0.415980747301534 0.792009626349233 49 0.196371325319089 0.392742650638178 0.803628674680911 50 0.189260837017498 0.378521674034996 0.810739162982502 51 0.144325897825537 0.288651795651074 0.855674102174463 52 0.10384920659911 0.20769841319822 0.89615079340089 53 0.202032760609653 0.404065521219305 0.797967239390347 54 0.33064165760238 0.66128331520476 0.66935834239762 55 0.651680480657215 0.696639038685571 0.348319519342786 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0980392156862745 NOK 5% type I error level 9 0.176470588235294 NOK 10% type I error level 11 0.215686274509804 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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