*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, 20 Dec 2009 07:08:50 -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/Dec/20/t1261318377hf19wsodvd4mn3b.htm/, Retrieved Sun, 20 Dec 2009 15:13:09 +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/Dec/20/t1261318377hf19wsodvd4mn3b.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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120,9 611 0 0 119,6 594 0 0 125,9 595 0 0 116,1 591 0 0 107,5 589 0 0 116,7 584 0 0 112,5 573 0 0 113 567 0 0 126,4 569 0 0 114,1 621 0 0 112,5 629 0 0 112,4 628 0 0 113,1 612 0 0 116,3 595 0 0 111,7 597 0 0 118,8 593 0 0 116,5 590 0 0 125,1 580 0 0 113,1 574 0 0 119,6 573 0 0 114,4 573 0 0 114 620 0 0 117,8 626 0 0 117 620 0 0 120,9 588 0 0 115 566 0 0 117,3 557 0 0 119,4 561 0 0 114,9 549 0 0 125,8 532 0 0 117,6 526 0 0 117,6 511 0 0 114,9 499 0 0 121,9 555 0 0 117 565 0 1 106,4 542 0 1 110,5 527 0 1 113,6 510 0 1 114,2 514 0 1 125,4 517 0 1 124,6 508 0 1 120,2 493 0 1 120,8 490 0 1 111,4 469 0 1 124,1 478 0 1 120,2 528 0 1 125,5 534 0 1 116 518 1 0 117 506 1 0 105,7 502 1 0 102 516 1 0 106,4 528 1 0 96,9 533 1 0 107,6 536 1 0 98,8 537 1 0 101,1 524 1 0 105,7 536 1 0 104,6 587 1 0 103,2 597 1 0 101,6 581 1 0

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 ChemischeIndustrie[t] = + 176.025891938060 -0.0971364760405873Werkloosheid[t] -13.0379049225199Dummy[t] -4.05345478350426Dummy2[t] + 1.34206810010027M1[t] -2.50509520992201M2[t] -2.00322924642182M3[t] + 1.29920942187024M4[t] -4.16002535649746M5[t] + 2.07391207534814M6[t] -4.84303188385203M7[t] -5.86222199450384M8[t] -0.999783326211778M9[t] + 1.92234266806906M10[t] + 3.83886385409737M11[t] -0.0887384210027683t + 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) 176.025891938060 24.398066 7.2147 0 0 Werkloosheid -0.0971364760405873 0.037984 -2.5573 0.014073 0.007037 Dummy -13.0379049225199 3.654226 -3.5679 0.000883 0.000442 Dummy2 -4.05345478350426 2.961919 -1.3685 0.178096 0.089048 M1 1.34206810010027 3.329481 0.4031 0.688837 0.344418 M2 -2.50509520992201 3.503696 -0.715 0.478394 0.239197 M3 -2.00322924642182 3.438544 -0.5826 0.563149 0.281575 M4 1.29920942187024 3.383912 0.3839 0.702874 0.351437 M5 -4.16002535649746 3.418004 -1.2171 0.230057 0.115029 M6 2.07391207534814 3.528434 0.5878 0.559691 0.279845 M7 -4.84303188385203 3.589542 -1.3492 0.184173 0.092087 M8 -5.86222199450384 3.776293 -1.5524 0.127737 0.063868 M9 -0.999783326211778 3.709066 -0.2696 0.788766 0.394383 M10 1.92234266806906 3.21984 0.597 0.553547 0.276773 M11 3.83886385409737 3.285144 1.1686 0.248876 0.124438 t -0.0887384210027683 0.107547 -0.8251 0.41376 0.20688 Multiple Linear Regression - Regression Statistics Multiple R 0.800909028923958 R-squared 0.641455272611917 Adjusted R-squared 0.519224115547798 F-TEST (value) 5.24788677469057 F-TEST (DF numerator) 15 F-TEST (DF denominator) 44 p-value 8.11206960560362e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.00485304078557 Sum Squared Residuals 1102.13637423387 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 120.9 117.928834756359 2.97116524364149 2 119.6 115.644253118023 3.95574688197655 3 125.9 115.960244184480 9.93975581551975 4 116.1 119.562490335932 -3.4624903359319 5 107.5 114.208790088643 -6.70879008864261 6 116.7 120.839671479688 -4.13967147968837 7 112.5 114.902490335932 -2.40249033593189 8 113 114.377380660521 -1.37738066052084 9 126.4 118.956807955729 7.44319204427103 10 114.1 116.739098774896 -2.63909877489649 11 112.5 117.789789731597 -5.28978973159734 12 112.4 113.959323932538 -1.55932393253778 13 113.1 116.766837228285 -3.66683722828469 14 116.3 114.482255589950 1.81774441005038 15 111.7 114.701110180366 -3.00111018036586 16 118.8 118.303356331817 0.496643668182495 17 116.5 113.046792560569 3.45320743943121 18 125.1 120.163356331817 4.9366436681825 19 113.1 113.740492807858 -0.640492807858089 20 119.6 112.729700752244 6.8702992477559 21 114.4 117.503400999533 -3.10340099953339 22 114 115.771374198904 -1.77137419890386 23 117.8 117.016338107686 0.783661892314115 24 117 113.671554688829 3.32844531117074 25 120.9 118.033251601226 2.86674839877445 26 115 116.234352343093 -1.23435234309343 27 117.3 117.521708169956 -0.221708169956131 28 119.4 120.346862513083 -0.946862513083068 29 114.9 115.964527026200 -1.06452702619964 30 125.8 123.761046129732 2.03895387026753 31 117.6 117.338182605773 0.261817394226945 32 117.6 117.687301214727 -0.0873012147272914 33 114.9 123.626639174504 -8.72663917450362 34 121.9 121.020384089509 0.879615910491202 35 117 117.823347310624 -0.823347310624221 36 106.4 116.129883984458 -9.72988398445757 37 110.5 118.840260804164 -8.34026080416389 38 113.6 116.555679165829 -2.95567916582884 39 114.2 116.580260804164 -2.38026080416390 40 125.4 119.502551623331 5.89744837666858 41 124.6 114.828806708326 9.77119329167375 42 120.2 122.431052859778 -2.23105285977788 43 120.8 115.716779907697 5.08322009230329 44 111.4 116.648717372894 -5.24871737289446 45 124.1 120.548189335818 3.55181066418152 46 120.2 118.524753107067 1.67524689293283 47 125.5 119.769717015849 5.7302829841508 48 116 108.411848218383 7.58815178161719 49 117 110.830815609967 6.16918439003264 50 105.7 107.283459783105 -1.58345978310466 51 102 106.336676661034 -4.33667666103386 52 106.4 108.384739195836 -1.9847391958361 53 96.9 102.351083616263 -5.45108361626269 54 107.6 108.204873198984 -0.604873198983777 55 98.8 101.102054342740 -2.30205434274025 56 101.1 101.256899999613 -0.156899999613309 57 105.7 104.864962534416 0.83503746558445 58 104.6 102.744389829624 1.85561017037632 59 103.2 103.600807834243 -0.400807834243344 60 101.6 101.227389175793 0.372610824207394 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.844909026701814 0.310181946596373 0.155090973298186 20 0.914174580542675 0.17165083891465 0.085825419457325 21 0.905057874753116 0.189884250493768 0.0949421252468842 22 0.836912612073963 0.326174775852073 0.163087387926037 23 0.751771517585683 0.496456964828633 0.248228482414317 24 0.686007238815383 0.627985522369234 0.313992761184617 25 0.667046504373955 0.665906991252091 0.332953495626045 26 0.650875055303291 0.698249889393417 0.349124944696709 27 0.600453018443376 0.799093963113249 0.399546981556624 28 0.494808241241212 0.989616482482423 0.505191758758788 29 0.388759290319535 0.77751858063907 0.611240709680465 30 0.335907825327388 0.671815650654777 0.664092174672612 31 0.251958801453341 0.503917602906682 0.748041198546659 32 0.245146679419943 0.490293358839887 0.754853320580057 33 0.284254890868330 0.568509781736661 0.71574510913167 34 0.227346837207815 0.454693674415629 0.772653162792185 35 0.160662875760086 0.321325751520172 0.839337124239914 36 0.238470784097287 0.476941568194574 0.761529215902713 37 0.471315022069339 0.942630044138679 0.528684977930661 38 0.463613696333829 0.927227392667658 0.536386303666171 39 0.471615495698494 0.943230991396988 0.528384504301506 40 0.46551750865253 0.93103501730506 0.53448249134747 41 0.577625026230328 0.844749947539343 0.422374973769672 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 = 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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