Model 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: Thu, 19 Nov 2009 13:10:02 -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/19/t12586614488z4icofjcxxmgfq.htm/, Retrieved Thu, 19 Nov 2009 21:11:00 +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/19/t12586614488z4icofjcxxmgfq.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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7.2 102.9 7.4 97.4 8.8 111.4 9.3 87.4 9.3 96.8 8.7 114.1 8.2 110.3 8.3 103.9 8.5 101.6 8.6 94.6 8.5 95.9 8.2 104.7 8.1 102.8 7.9 98.1 8.6 113.9 8.7 80.9 8.7 95.7 8.5 113.2 8.4 105.9 8.5 108.8 8.7 102.3 8.7 99 8.6 100.7 8.5 115.5 8.3 100.7 8 109.9 8.2 114.6 8.1 85.4 8.1 100.5 8 114.8 7.9 116.5 7.9 112.9 8 102 8 106 7.9 105.3 8 118.8 7.7 106.1 7.2 109.3 7.5 117.2 7.3 92.5 7 104.2 7 112.5 7 122.4 7.2 113.3 7.3 100 7.1 110.7 6.8 112.8 6.4 109.8 6.1 117.3 6.5 109.1 7.7 115.9 7.9 96 7.5 99.8 6.9 116.8 6.6 115.7 6.9 99.4 7.7 94.3 8 91 8 93.2 7.7 103.1 7.3 94.1 7.4 91.8 8.1 102.7 8.3 82.6 8.2 89.1

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkl.graad[t] = + 13.0943338250401 -0.0408074251652485Industr.prod.[t] -0.686310695654252M1[t] -0.769705127263402M2[t] + 0.412105088011278M3[t] -0.474479148358612M4[t] -0.167840781384215M5[t] + 0.0808139189278146M6[t] -0.101027132222573M7[t] -0.203219555927245M8[t] -0.211116295816997M9[t] -0.139082822411200M10[t] -0.182161181323630M11[t] -0.0230558398694423t + 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) 13.0943338250401 1.134904 11.5378 0 0 Industr.prod. -0.0408074251652485 0.010068 -4.0531 0.000173 8.6e-05 M1 -0.686310695654252 0.285862 -2.4008 0.020043 0.010021 M2 -0.769705127263402 0.289174 -2.6617 0.010371 0.005186 M3 0.412105088011278 0.279178 1.4761 0.146055 0.073028 M4 -0.474479148358612 0.361374 -1.313 0.195064 0.097532 M5 -0.167840781384215 0.306095 -0.5483 0.585858 0.292929 M6 0.0808139189278146 0.293706 0.2752 0.784311 0.392155 M7 -0.101027132222573 0.29337 -0.3444 0.731986 0.365993 M8 -0.203219555927245 0.292018 -0.6959 0.489641 0.244821 M9 -0.211116295816997 0.308692 -0.6839 0.49713 0.248565 M10 -0.139082822411200 0.307882 -0.4517 0.653371 0.326686 M11 -0.182161181323630 0.303703 -0.5998 0.551295 0.275647 t -0.0230558398694423 0.00305 -7.5598 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.810885941911432 R-squared 0.65753601078959 Adjusted R-squared 0.570241268441839 F-TEST (value) 7.53236670508973 F-TEST (DF numerator) 13 F-TEST (DF denominator) 51 p-value 5.48792649102126e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.459290198692366 Sum Squared Residuals 10.7583218173585 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.2 8.18588324001229 -0.98588324001229 2 7.4 8.30387380694256 -0.903873806942562 3 8.8 8.89132423003432 -0.091324230034321 4 9.3 8.96106235776095 0.338937642239047 5 9.3 8.86105508831257 0.438944911687429 6 8.7 8.38068549339636 0.319314506603638 7 8.2 8.33085681800448 -0.130856818004476 8 8.3 8.46677607548795 -0.166776075487950 9 8.5 8.52968057360883 -0.0296805736088283 10 8.6 8.86431018330192 -0.264310183301923 11 8.5 8.74512633180523 -0.245126331805227 12 8.2 8.54512633180523 -0.345126331805228 13 8.1 7.9132939040955 0.186706095904494 14 7.9 7.99863853089358 -0.0986385308935782 15 8.6 8.51263558868789 0.087364411312107 16 8.7 8.94964054290176 -0.249640542901761 17 8.7 8.62927317756104 0.0707268224389616 18 8.5 8.14074209761178 0.359257902388224 19 8.4 8.23373941029826 0.16626058970174 20 8.5 7.99014961374492 0.509850386255075 21 8.7 8.22444529755985 0.475554702440153 22 8.7 8.40808743414152 0.291912565858479 23 8.6 8.27258061257873 0.327419387421273 24 8.5 7.82773606158724 0.672263938412764 25 8.3 7.72231941850922 0.577680581490781 26 8 7.24044083551034 0.75955916448966 27 8.2 8.20740031263891 -0.00740031263891179 28 8.1 8.48933705122483 -0.389337051224835 29 8.1 8.15672745833454 -0.0567274583345375 30 8 7.79878013891407 0.201219861085929 31 7.9 7.52451062511332 0.375489374886682 32 7.9 7.5461690921341 0.353830907865902 33 8 7.96001744667611 0.0399825533238874 34 8 7.84576537955147 0.154234620448527 35 7.9 7.80819637838528 0.0918036216147247 36 8 7.4164014801086 0.583598519891392 37 7.7 7.22528924418357 0.47471075581643 38 7.2 6.98825521217618 0.211744787823819 39 7.5 7.82463092877596 -0.324630928775957 40 7.3 7.92293425411826 -0.622934254118262 41 7 7.72906990678981 -0.72906990678981 42 7 7.61596713836083 -0.615967138360834 43 7 7.00707673820504 -0.007076738205044 44 7.2 7.25317604363469 -0.0531760436346909 45 7.3 7.7649622185733 -0.464962218573302 46 7.1 7.3773004028415 -0.277300402841498 47 6.8 7.2254706112126 -0.425470611212604 48 6.4 7.50699822816254 -1.10699822816254 49 6.1 6.49157600389948 -0.391576003899479 50 6.5 6.71974661877592 -0.219746618775923 51 7.7 7.60101050305747 0.0989894969425285 52 7.9 7.50343818760658 0.396561812393416 53 7.5 7.6319524990836 -0.131952499083595 54 6.9 7.16382513171696 -0.263825131716957 55 6.6 7.0038164083789 -0.403816408378902 56 6.9 7.54372917499834 -0.643729174998336 57 7.7 7.72089446358191 -0.0208944635819103 58 8 7.90453660016358 0.095463399836415 59 8 7.74862606601817 0.251373933981834 60 7.7 7.5037378983364 0.196262101663606 61 7.3 7.16163818929994 0.138361810700064 62 7.4 7.14904499570141 0.250955004298586 63 8.1 7.86299843680544 0.237001563194555 64 8.3 7.7735876063876 0.526412393612394 65 8.2 7.79192186991845 0.408078130081553 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.699321069338507 0.601357861322987 0.300678930661493 18 0.554480531446347 0.891038937107307 0.445519468553653 19 0.484748579389321 0.969497158778642 0.515251420610679 20 0.361642882058973 0.723285764117945 0.638357117941027 21 0.259167645743001 0.518335291486002 0.740832354256999 22 0.174023835513508 0.348047671027016 0.825976164486492 23 0.110160899469669 0.220321798939338 0.889839100530331 24 0.0779379571172396 0.155875914234479 0.92206204288276 25 0.0944937376146868 0.188987475229374 0.905506262385313 26 0.0698312732737105 0.139662546547421 0.93016872672629 27 0.094457235402011 0.188914470804022 0.905542764597989 28 0.231047372501227 0.462094745002454 0.768952627498773 29 0.306031216572079 0.612062433144159 0.69396878342792 30 0.279093409222885 0.55818681844577 0.720906590777115 31 0.236996611321063 0.473993222642126 0.763003388678937 32 0.241073865334726 0.482147730669451 0.758926134665274 33 0.20078307242327 0.40156614484654 0.79921692757673 34 0.178952974463081 0.357905948926163 0.821047025536919 35 0.147558303669742 0.295116607339484 0.852441696330258 36 0.323507975631900 0.647015951263801 0.6764920243681 37 0.484982288147108 0.969964576294216 0.515017711852892 38 0.595062453364856 0.809875093270288 0.404937546635144 39 0.576299275398337 0.847401449203326 0.423700724601663 40 0.648099548338894 0.703800903322212 0.351900451661106 41 0.719865526363002 0.560268947273997 0.280134473636998 42 0.669117140859071 0.661765718281858 0.330882859140929 43 0.743489388251478 0.513021223497045 0.256510611748522 44 0.934292638838479 0.131414722323042 0.0657073611615212 45 0.89694450933773 0.206110981324538 0.103055490662269 46 0.8253829119756 0.3492341760488 0.1746170880244 47 0.760467211092807 0.479065577814387 0.239532788907193 48 0.95075465204544 0.0984906959091225 0.0492453479545612 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 1 0.03125 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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