*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 02:25:35 -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/t1258623405b46qtjrukj489de.htm/, Retrieved Thu, 19 Nov 2009 10:36:57 +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/t1258623405b46qtjrukj489de.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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96,8 610763 114,1 612613 110,3 611324 103,9 594167 101,6 595454 94,6 590865 95,9 589379 104,7 584428 102,8 573100 98,1 567456 113,9 569028 80,9 620735 95,7 628884 113,2 628232 105,9 612117 108,8 595404 102,3 597141 99 593408 100,7 590072 115,5 579799 100,7 574205 109,9 572775 114,6 572942 85,4 619567 100,5 625809 114,8 619916 116,5 587625 112,9 565742 102 557274 106 560576 105,3 548854 118,8 531673 106,1 525919 109,3 511038 117,2 498662 92,5 555362 104,2 564591 112,5 541657 122,4 527070 113,3 509846 100 514258 110,7 516922 112,8 507561 109,8 492622 117,3 490243 109,1 469357 115,9 477580 96 528379 99,8 533590 116,8 517945 115,7 506174 99,4 501866 94,3 516141 91 528222 93,2 532638 103,1 536322 94,1 536535 91,8 523597 102,7 536214 82,6 586570 89,1 596594

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Tot_nietwerkende_werkzoekenden[t] = + 694667.103500438 -1304.78132670624Tot_ind_productie[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) 694667.103500438 57785.998873 12.0214 0 0 Tot_ind_productie -1304.78132670624 551.185712 -2.3672 0.021221 0.010611 Multiple Linear Regression - Regression Statistics Multiple R 0.294517348709906 R-squared 0.0867404686911123 Adjusted R-squared 0.071261493584182 F-TEST (value) 5.60376046165205 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.0212210767954628 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 40970.7777175414 Sum Squared Residuals 99037672980.0309 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 610763 568364.271075274 42398.7289247257 2 612613 545791.554123256 66821.4458767443 3 611324 550749.72316474 60574.2768352606 4 594167 559100.323655659 35066.6763443406 5 595454 562101.320707084 33352.6792929163 6 590865 571234.789994027 19630.2100059726 7 589379 569538.574269309 19840.4257306907 8 584428 558056.498594294 26371.5014057056 9 573100 560535.583115036 12564.4168849638 10 567456 566668.055350556 787.944649444424 11 569028 546052.510388597 22975.4896114030 12 620735 589110.294169903 31624.7058300971 13 628884 569799.530534651 59084.4694653495 14 628232 546965.857317291 81266.1426827087 15 612117 556490.761002247 55626.2389977531 16 595404 552706.895154799 42697.1048452012 17 597141 561187.97377839 35953.0262216106 18 593408 565493.75215652 27914.2478434800 19 590072 563275.623901119 26796.3760988807 20 579799 543964.860265867 35834.139734133 21 574205 563275.623901119 10929.3760988807 22 572775 551271.635695422 21503.3643045781 23 572942 545139.163459903 27802.8365400974 24 619567 583238.778199725 36328.2218002752 25 625809 563536.58016646 62272.4198335394 26 619916 544878.207194561 75037.7928054386 27 587625 542660.078939161 44964.9210608393 28 565742 547357.291715303 18384.7082846968 29 557274 561579.408176401 -4305.40817640123 30 560576 556360.282869576 4215.71713042373 31 548854 557273.629798271 -8419.62979827064 32 531673 539659.081887736 -7986.08188773639 33 525919 556229.804736906 -30310.8047369056 34 511038 552054.504491446 -41016.5044914457 35 498662 541746.732010466 -43084.7320104664 36 555362 573974.83078011 -18612.8307801105 37 564591 558708.889257647 5882.1107423525 38 541657 547879.204245986 -6222.2042459857 39 527070 534961.869111594 -7891.86911159391 40 509846 546835.379184621 -36989.3791846207 41 514258 564188.970829814 -49930.9708298137 42 516922 550227.810634057 -33305.8106340569 43 507561 547487.769847974 -39926.7698479738 44 492622 551402.113828093 -58780.1138280926 45 490243 541616.253877796 -51373.2538777958 46 469357 552315.460756787 -82958.460756787 47 477580 543442.947735184 -65862.9477351845 48 528379 569408.096136639 -41029.0961366387 49 533590 564449.927095155 -30859.9270951550 50 517945 542268.644541149 -24323.6445411489 51 506174 543703.904000526 -37529.9040005257 52 501866 564971.839625837 -63105.8396258374 53 516141 571626.224392039 -55485.2243920393 54 528222 575932.00277017 -47710.0027701699 55 532638 573061.483851416 -40423.4838514161 56 536322 560144.148717024 -23822.1487170244 57 536535 571887.180657380 -35352.1806573805 58 523597 574888.177708805 -51291.1777088049 59 536214 560666.061247707 -24452.0612477069 60 586570 586892.165914502 -322.165914502305 61 596594 578411.087290912 18182.9127090883 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0195804206942934 0.0391608413885868 0.980419579305707 6 0.00495274847015945 0.0099054969403189 0.99504725152984 7 0.00122828268542173 0.00245656537084346 0.998771717314578 8 0.00124696066482485 0.00249392132964971 0.998753039335175 9 0.00227966636146128 0.00455933272292256 0.997720333638539 10 0.00230525641095028 0.00461051282190056 0.99769474358905 11 0.00400191701009776 0.00800383402019553 0.995998082989902 12 0.00393035231648447 0.00786070463296894 0.996069647683516 13 0.00630563694120721 0.0126112738824144 0.993694363058793 14 0.0155012255138299 0.0310024510276599 0.98449877448617 15 0.0125693972637179 0.0251387945274359 0.987430602736282 16 0.00812743821824705 0.0162548764364941 0.991872561781753 17 0.00507065478853671 0.0101413095770734 0.994929345211463 18 0.00309762827157153 0.00619525654314305 0.996902371728428 19 0.0019701055935854 0.0039402111871708 0.998029894406415 20 0.00159335234317818 0.00318670468635636 0.998406647656822 21 0.00147680921724561 0.00295361843449123 0.998523190782754 22 0.001337169936542 0.002674339873084 0.998662830063458 23 0.00118376337934293 0.00236752675868586 0.998816236620657 24 0.00125603245477119 0.00251206490954239 0.998743967545229 25 0.00523478219400947 0.0104695643880189 0.99476521780599 26 0.0415874828925621 0.0831749657851241 0.958412517107438 27 0.0928354671093457 0.185670934218691 0.907164532890654 28 0.159706431887909 0.319412863775818 0.840293568112091 29 0.241231977443139 0.482463954886279 0.75876802255686 30 0.331277360011943 0.662554720023886 0.668722639988057 31 0.442069856590356 0.884139713180711 0.557930143409644 32 0.592243678466655 0.81551264306669 0.407756321533345 33 0.722676227916057 0.554647544167886 0.277323772083943 34 0.834834864966896 0.330330270066209 0.165165135033104 35 0.89023289997352 0.219534200052961 0.109767100026481 36 0.888492123150279 0.223015753699442 0.111507876849721 37 0.918570411589826 0.162859176820348 0.0814295884101741 38 0.936222306360681 0.127555387278638 0.0637776936393188 39 0.96601567188766 0.0679686562246804 0.0339843281123402 40 0.967887838051665 0.0642243238966695 0.0321121619483347 41 0.974525862502486 0.0509482749950291 0.0254741374975146 42 0.971604819754348 0.0567903604913037 0.0283951802456518 43 0.967102485474748 0.0657950290505035 0.0328975145252517 44 0.967822753842978 0.0643544923140446 0.0321772461570223 45 0.958696441737228 0.0826071165255444 0.0413035582627722 46 0.983749006197761 0.0325019876044778 0.0162509938022389 47 0.983714836862464 0.0325703262750718 0.0162851631375359 48 0.97577383649827 0.04845232700346 0.02422616350173 49 0.95876911163602 0.0824617767279589 0.0412308883639794 50 0.941852658677682 0.116294682644637 0.0581473413223184 51 0.916962600386062 0.166074799227875 0.0830373996139375 52 0.910704991696426 0.178590016607147 0.0892950083035735 53 0.90382494947107 0.192350101057861 0.0961750505289303 54 0.888108377773425 0.223783244453150 0.111891622226575 55 0.834804033967068 0.330391932065864 0.165195966032932 56 0.706418602283325 0.587162795433351 0.293581397716675 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 14 0.269230769230769 NOK 5% type I error level 24 0.461538461538462 NOK 10% type I error level 33 0.634615384615385 NOK

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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