vraag 3

*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: Sun, 23 Nov 2008 13:23:12 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t12274718194i0nebkxt90ksk1.htm/, Retrieved Sun, 23 Nov 2008 20:23:48 +0000

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/2008/Nov/23/t12274718194i0nebkxt90ksk1.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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User-defined keywords:

Dataseries X:

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519 0 517 0 510 0 509 0 501 0 507 0 569 0 580 0 578 0 565 0 547 0 555 0 562 0 561 0 555 0 544 0 537 0 543 0 594 0 611 0 613 0 611 0 594 0 595 0 591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 1 549 1 532 1 526 1 511 1 499 1 555 1 565 1 542 1 527 1 510 1 514 1 517 1 508 1 493 1 490 1 469 1 478 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Aantal_werklozen[t] = + 537.846078431373 -90.8186274509804Dummyvariabele[t] + 11.7754901960784M1[t] + 5.72222222222224M2[t] -5.49771241830064M3[t] -13.0509803921569M4[t] -23.9375816993464M5[t] -23.3241830065359M6[t] + 34.2996732026144M7[t] + 43.4797385620915M8[t] + 36.2598039215686M9[t] + 19.4398692810458M10[t] + 0.0199346405228985M11[t] + 1.21993464052288t + 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) 537.846078431373 11.106666 48.4255 0 0 Dummyvariabele -90.8186274509804 9.17482 -9.8987 0 0 M1 11.7754901960784 12.542424 0.9389 0.352147 0.176073 M2 5.72222222222224 12.509841 0.4574 0.649276 0.324638 M3 -5.49771241830064 12.480808 -0.4405 0.661406 0.330703 M4 -13.0509803921569 12.455348 -1.0478 0.299567 0.149783 M5 -23.9375816993464 12.433483 -1.9253 0.059675 0.029838 M6 -23.3241830065359 12.415234 -1.8787 0.0659 0.03295 M7 34.2996732026144 12.94804 2.649 0.010665 0.005333 M8 43.4797385620915 12.93227 3.3621 0.001457 0.000728 M9 36.2598039215686 12.919992 2.8065 0.007033 0.003516 M10 19.4398692810458 12.911214 1.5057 0.138206 0.069103 M11 0.0199346405228985 12.905944 0.0015 0.998773 0.499387 t 1.21993464052288 0.212951 5.7287 1e-06 0 Multiple Linear Regression - Regression Statistics Multiple R 0.894377518331342 R-squared 0.79991114529653 Adjusted R-squared 0.749888931620663 F-TEST (value) 15.9911184754792 F-TEST (DF numerator) 13 F-TEST (DF denominator) 52 p-value 8.34887714518118e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20.4033115737979 Sum Squared Residuals 21647.3464052288 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 519 550.841503267974 -31.8415032679741 2 517 546.00816993464 -29.0081699346405 3 510 536.008169934640 -26.0081699346405 4 509 529.674836601307 -20.6748366013072 5 501 520.008169934640 -19.0081699346405 6 507 521.841503267974 -14.8415032679739 7 569 580.685294117647 -11.6852941176470 8 580 591.085294117647 -11.0852941176470 9 578 585.085294117647 -7.08529411764702 10 565 569.485294117647 -4.48529411764705 11 547 551.285294117647 -4.28529411764703 12 555 552.485294117647 2.51470588235297 13 562 565.480718954248 -3.48071895424830 14 561 560.647385620915 0.352614379084963 15 555 550.647385620915 4.35261437908497 16 544 544.314052287582 -0.314052287581688 17 537 534.647385620915 2.35261437908497 18 543 536.480718954248 6.51928104575164 19 594 595.324509803922 -1.32450980392157 20 611 605.724509803922 5.27549019607845 21 613 599.724509803922 13.2754901960784 22 611 584.124509803922 26.8754901960784 23 594 565.924509803922 28.0754901960784 24 595 567.124509803922 27.8754901960785 25 591 580.119934640523 10.8800653594772 26 589 575.28660130719 13.7133986928104 27 584 565.28660130719 18.7133986928105 28 573 558.953267973856 14.0467320261438 29 567 549.28660130719 17.7133986928104 30 569 551.119934640523 17.8800653594771 31 621 609.963725490196 11.0362745098039 32 629 620.363725490196 8.63627450980392 33 628 614.363725490196 13.6362745098039 34 612 598.763725490196 13.2362745098039 35 595 580.563725490196 14.4362745098039 36 597 581.763725490196 15.2362745098039 37 593 594.759150326797 -1.75915032679735 38 590 589.925816993464 0.0741830065359235 39 580 579.925816993464 0.0741830065359395 40 574 573.592483660131 0.40751633986927 41 573 563.925816993464 9.07418300653593 42 573 565.759150326797 7.2408496732026 43 620 624.602941176471 -4.60294117647060 44 626 635.00294117647 -9.0029411764706 45 620 629.00294117647 -9.00294117647061 46 588 613.402941176471 -25.4029411764706 47 566 595.202941176471 -29.2029411764706 48 557 596.402941176471 -39.4029411764706 49 561 518.579738562092 42.4202614379085 50 549 513.746405228758 35.2535947712418 51 532 503.746405228758 28.2535947712418 52 526 497.413071895425 28.5869281045752 53 511 487.746405228758 23.2535947712418 54 499 489.579738562092 9.4202614379085 55 555 548.423529411765 6.5764705882353 56 565 558.823529411765 6.1764705882353 57 542 552.823529411765 -10.8235294117647 58 527 537.223529411765 -10.2235294117647 59 510 519.023529411765 -9.02352941176471 60 514 520.223529411765 -6.22352941176471 61 517 533.218954248366 -16.2189542483660 62 508 528.385620915033 -20.3856209150327 63 493 518.385620915033 -25.3856209150327 64 490 512.052287581699 -22.0522875816993 65 469 502.385620915033 -33.3856209150327 66 478 504.218954248366 -26.218954248366 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0235219369933885 0.047043873986777 0.976478063006611 18 0.00847185855002765 0.0169437171000553 0.991528141449972 19 0.0293122634752981 0.0586245269505961 0.970687736524702 20 0.0221658188484346 0.0443316376968693 0.977834181151565 21 0.0116821305751881 0.0233642611503762 0.988317869424812 22 0.00895668351130625 0.0179133670226125 0.991043316488694 23 0.00677993246011938 0.0135598649202388 0.99322006753988 24 0.00276677907681676 0.00553355815363352 0.997233220923183 25 0.00303553676277588 0.00607107352555176 0.996964463237224 26 0.00290618674808884 0.00581237349617767 0.997093813251911 27 0.00179236249844191 0.00358472499688381 0.998207637501558 28 0.00294624942609406 0.00589249885218812 0.997053750573906 29 0.00324388370699651 0.00648776741399301 0.996756116293003 30 0.00595609381470089 0.0119121876294018 0.9940439061853 31 0.0218220072340152 0.0436440144680305 0.978177992765985 32 0.143107497508510 0.286214995017021 0.85689250249149 33 0.267242947082313 0.534485894164627 0.732757052917687 34 0.477262368703305 0.95452473740661 0.522737631296695 35 0.58062054566354 0.83875890867292 0.41937945433646 36 0.647252963591526 0.705494072816948 0.352747036408474 37 0.850037871351656 0.299924257296687 0.149962128648344 38 0.918814559800388 0.162370880399224 0.0811854401996122 39 0.943569706036755 0.112860587926489 0.0564302939632446 40 0.967466795555844 0.0650664088883127 0.0325332044441563 41 0.94846435943348 0.10307128113304 0.05153564056652 42 0.92965653343387 0.140686933132259 0.0703434665661293 43 0.914148092915082 0.171703814169836 0.085851907084918 44 0.894310281229086 0.211379437541828 0.105689718770914 45 0.973723385724356 0.0525532285512878 0.0262766142756439 46 0.98273508185996 0.0345298362800796 0.0172649181400398 47 0.983840108445313 0.0323197831093741 0.0161598915546870 48 0.970739666764706 0.0585206664705885 0.0292603332352943 49 0.929625808589027 0.140748382821947 0.0703741914109735 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.181818181818182 NOK 5% type I error level 16 0.484848484848485 NOK 10% type I error level 20 0.606060606060606 NOK

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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