Multiple Regression Workshop 4

*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, 29 Nov 2010 14:00:19 +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/29/t129103914268e84ksboijfk60.htm/, Retrieved Mon, 29 Nov 2010 14:59:20 +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/29/t129103914268e84ksboijfk60.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:

Workshop 4

Dataseries X:

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30/11/2010 0 8 17 2 6 31/10/2010 -2 3 23 3 7 30/09/2010 -4 3 24 1 4 31/08/2010 -4 7 27 1 3 31/07/2010 -7 4 31 0 0 30/06/2010 -9 -4 40 1 6 31/05/2010 -13 -6 47 -1 3 30/04/2010 -8 8 43 2 1 31/03/2010 -13 2 60 2 6 28/02/2010 -15 -1 64 0 5 31/01/2010 -15 -2 65 1 7 31/12/2009 -15 0 65 1 4 30/11/2009 -10 10 55 3 3 31/10/2009 -12 3 57 3 6 30/09/2009 -11 6 57 1 6 31/08/2009 -11 7 57 1 5 31/07/2009 -17 -4 65 -2 2 30/06/2009 -18 -5 69 1 3 31/05/2009 -19 -7 70 1 -2 30/04/2009 -22 -10 71 -1 -4 31/03/2009 -24 -21 71 -4 0 28/02/2009 -24 -22 73 -2 1 31/01/2009 -20 -16 68 -1 4 31/12/2008 -25 -25 65 -5 -3 30/11/2008 -22 -22 57 -4 -3 31/10/2008 -17 -22 41 -5 0 30/09/2008 -9 -19 21 0 6 31/08/2008 -11 -21 21 -2 -1 31/07/2008 -13 -31 17 -4 0 30/06/2008 -11 -28 9 -6 -1 31/05/2008 -9 -23 11 -2 1 30/04/2008 -7 -17 6 -2 -4 31/03/2008 -3 -12 -2 -2 -1 29/02/2008 -3 -14 0 1 -1 31/01/2008 -6 -18 5 -2 0 31/12/2007 -4 -16 3 0 3 30/11/2007 -8 -22 7 -1 0 31/10/2007 -1 -9 4 2 8 30/09/2007 -2 -10 8 3 8 31 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 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation CVI[t] = + 0.0799791163793411 + 26.4477403759069Maand[t] + 0.253996016630743Econ.Sit.[t] -0.253388443883417Werkloos[t] + 0.27108634384964Fin.Sit.[t] + 0.219859137240139`Spaarverm. `[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) 0.0799791163793411 0.112782 0.7091 0.48123 0.240615 Maand 26.4477403759069 10.181234 2.5977 0.012019 0.00601 Econ.Sit. 0.253996016630743 0.005916 42.933 0 0 Werkloos -0.253388443883417 0.0019 -133.3855 0 0 Fin.Sit. 0.27108634384964 0.030192 8.9789 0 0 `Spaarverm. ` 0.219859137240139 0.014011 15.6918 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.999264848251209 R-squared 0.99853023695051 Adjusted R-squared 0.99839662212783 F-TEST (value) 7473.19958157405 F-TEST (DF numerator) 5 F-TEST (DF denominator) 55 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.296240131543268 Sum Squared Residuals 4.8267018545225 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 -0.298443113300859 0.298443113300859 2 -2 -2.59290400347121 0.59290400347121 3 -4 -4.04497232815689 0.0449723281568858 4 -4 -4.00188543730525 0.00188543730525317 5 -7 -6.70080708127515 -0.299192918724847 6 -9 -9.4155111392448 0.415511139244800 7 -13 -12.8831826833631 -0.116817316636904 8 -8 -7.92303841420467 -0.0769615857953326 9 -13 -12.6180411477377 -0.381958852262333 10 -15 -15.1073685055433 0.107368505543285 11 -15 -14.6802609913144 -0.319739008685614 12 -15 -15.2057382173966 0.205738217396625 13 -10 -9.80768515302496 -0.192314846975036 14 -12 -11.4279499290903 -0.57205007090969 15 -11 -11.2050628200477 0.205062820047663 16 -11 -11.1637950997560 0.16379509975597 17 -17 -17.4504077143517 0.450407714351686 18 -18 -17.6773166923808 -0.322683307619162 19 -19 -19.5221953004994 0.522195300499415 20 -22 -21.502348738292 -0.497651261707988 21 -24 -24.1928276206436 0.192827620643640 22 -24 -24.1432983924637 0.143298392463668 23 -20 -20.1979176186426 0.197917618642585 24 -25 -24.7211537203774 -0.278846279622633 25 -22 -21.6590759231176 -0.340924076882425 26 -17 -17.2114604930822 0.211460493082190 27 -9 -8.70404374622848 -0.295956253771521 28 -11 -11.2860880357535 0.286088035753545 29 -13 -13.1275167850430 0.127516785043033 30 -11 -11.0929266173394 0.0929266173393619 31 -9 -8.78985434953824 -0.210145650461761 32 -7 -7.08110917545737 0.0811091754573694 33 -3 -3.08712577075176 0.0871257707517571 34 -3 -3.23375572087212 0.233755720872118 35 -6 -5.89275734125917 -0.107242658740825 36 -4 -4.05050255379564 0.0505025537956398 37 -8 -7.51679938761318 -0.483200612386816 38 -1 -0.877642004194529 -0.122357995805471 39 -2 -1.87103064462637 -0.128969355373631 40 -2 -2.38836748548833 0.388367485488334 41 -1 -0.836968369924042 -0.163031630075958 42 1 1.3699904650592 -0.3699904650592 43 2 1.84261236444202 0.157387635557976 44 2 1.87580459169011 0.124195408309894 45 -1 -0.624010506096923 -0.375989493903077 46 1 0.930629878357439 0.0693701216425612 47 -1 -0.974636845616245 -0.0253631543837553 48 -8 -8.04328694025541 0.0432869402554104 49 1 0.748799075644756 0.251200924355244 50 2 2.36039337696585 -0.360393376965846 51 -2 -1.71395521421972 -0.286044785780283 52 -2 -1.63910374796901 -0.360896252030986 53 -2 -1.98274378671843 -0.0172562132815725 54 -2 -2.26395035992353 0.263950359923532 55 -6 -5.69927625795652 -0.300723742043484 56 -4 -3.72022121447945 -0.27977878552055 57 -5 -5.4230554495174 0.423055449517398 58 -2 -2.34806031481857 0.348060314818572 59 -1 -0.990494356211112 -0.00950564378888785 60 -5 -5.11842038023906 0.118420380239059 61 -9 -9.39587811216905 0.395878112169048 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.129279904168142 0.258559808336284 0.870720095831858 10 0.242912986557658 0.485825973115317 0.757087013442342 11 0.429780493866755 0.85956098773351 0.570219506133245 12 0.354259385805492 0.708518771610983 0.645740614194508 13 0.26709868375136 0.53419736750272 0.73290131624864 14 0.690949024552089 0.618101950895822 0.309050975447911 15 0.605665538639405 0.78866892272119 0.394334461360595 16 0.516505765589159 0.966988468821682 0.483494234410841 17 0.603531009401829 0.792937981196342 0.396468990598171 18 0.539186375635423 0.921627248729154 0.460813624364577 19 0.891173975542306 0.217652048915387 0.108826024457694 20 0.93870613366178 0.122587732676442 0.0612938663382212 21 0.913212673323481 0.173574653353038 0.0867873266765188 22 0.875133521488487 0.249732957023025 0.124866478511512 23 0.858700752440159 0.282598495119682 0.141299247559841 24 0.892751835368344 0.214496329263311 0.107248164631656 25 0.941409473820812 0.117181052358377 0.0585905261791884 26 0.913448876995767 0.173102246008465 0.0865511230042327 27 0.935941436786937 0.128117126426126 0.064058563213063 28 0.92439513721129 0.151209725577420 0.0756048627887099 29 0.89397996029746 0.212040079405079 0.106020039702540 30 0.878883721341814 0.242232557316371 0.121116278658186 31 0.853208464917081 0.293583070165838 0.146791535082919 32 0.806690164412242 0.386619671175516 0.193309835587758 33 0.784688884330966 0.430622231338068 0.215311115669034 34 0.761221615273634 0.477556769452732 0.238778384726366 35 0.71219282962857 0.57561434074286 0.28780717037143 36 0.689162074397924 0.621675851204152 0.310837925602076 37 0.75347424843546 0.49305150312908 0.24652575156454 38 0.687267732669992 0.625464534660016 0.312732267330008 39 0.628609961328287 0.742780077343425 0.371390038671713 40 0.87351211682093 0.252975766358141 0.126487883179070 41 0.834296534488333 0.331406931023334 0.165703465511667 42 0.818355201407705 0.36328959718459 0.181644798592295 43 0.828212105341082 0.343575789317836 0.171787894658918 44 0.790587050193042 0.418825899613917 0.209412949806958 45 0.730081487365116 0.539837025269768 0.269918512634884 46 0.738301422877662 0.523397154244676 0.261698577122338 47 0.694462131676103 0.611075736647794 0.305537868323897 48 0.691154141263193 0.617691717473613 0.308845858736807 49 0.651262941629279 0.697474116741443 0.348737058370721 50 0.60103250733996 0.797934985320079 0.398967492660039 51 0.614725532730804 0.770548934538392 0.385274467269196 52 0.477122658539395 0.95424531707879 0.522877341460605 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 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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