*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: Tue, 15 Dec 2009 09:17:38 -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/15/t12608939089vs6brq1hi4l63v.htm/, Retrieved Tue, 15 Dec 2009 17:18:40 +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/15/t12608939089vs6brq1hi4l63v.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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594 0 611 595 0 594 591 0 595 589 0 591 584 0 589 573 0 584 567 0 573 569 0 567 621 0 569 629 0 621 628 0 629 612 0 628 595 0 612 597 0 595 593 0 597 590 0 593 580 0 590 574 0 580 573 0 574 573 0 573 620 0 573 626 0 620 620 0 626 588 0 620 566 0 588 557 0 566 561 0 557 549 0 561 532 0 549 526 0 532 511 0 526 499 0 511 555 0 499 565 0 555 542 0 565 527 0 542 510 0 527 514 0 510 517 0 514 508 0 517 493 0 508 490 0 493 469 0 490 478 0 469 528 0 478 534 0 528 518 1 534 506 1 518 502 1 506 516 1 502 528 1 516 533 1 528 536 1 533 537 1 536 524 1 537 536 1 524 587 1 536 597 1 587 581 1 597 564 1 581 558 1 564

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 WklBe[t] = + 20.2333699019754 + 12.2075193097678X[t] + 0.938893442766383Y1[t] + 3.6415169074981M1[t] + 19.4702236275926M2[t] + 19.6449073887394M3[t] + 13.6073698384394M4[t] + 8.97875032184423M5[t] + 12.4690406419745M6[t] + 6.19153587959245M7[t] + 19.1351704623620M8[t] + 68.497632912062M9[t] + 28.6543166662093M10[t] + 6.52969328591078M11[t] -0.228028023786069t + 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) 20.2333699019754 24.365096 0.8304 0.410588 0.205294 X 12.2075193097678 3.246616 3.7601 0.000478 0.000239 Y1 0.938893442766383 0.037378 25.1188 0 0 M1 3.6415169074981 3.787682 0.9614 0.341373 0.170686 M2 19.4702236275926 4.175241 4.6633 2.7e-05 1.3e-05 M3 19.6449073887394 4.111743 4.7778 1.8e-05 9e-06 M4 13.6073698384394 4.058346 3.3529 0.001607 0.000804 M5 8.97875032184423 4.076171 2.2027 0.032662 0.016331 M6 12.4690406419745 4.152328 3.0029 0.004314 0.002157 M7 6.19153587959245 4.187855 1.4785 0.146103 0.073051 M8 19.1351704623620 4.321045 4.4284 5.8e-05 2.9e-05 M9 68.497632912062 4.253086 16.1054 0 0 M10 28.6543166662093 3.920295 7.3092 0 0 M11 6.52969328591078 3.898342 1.675 0.100722 0.050361 t -0.228028023786069 0.112217 -2.032 0.047948 0.023974 Multiple Linear Regression - Regression Statistics Multiple R 0.99131764863593 R-squared 0.982710680497068 Adjusted R-squared 0.977448713691828 F-TEST (value) 186.757293778141 F-TEST (DF numerator) 14 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.13434875972176 Sum Squared Residuals 1730.99079647139 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 594 597.310752315947 -3.31075231594699 2 595 596.950242485227 -1.95024248522725 3 591 597.835791665354 -6.83579166535411 4 589 587.814652320203 1.18534767979727 5 584 581.080217894289 2.91978210571125 6 573 579.648012976801 -6.64801297680103 7 567 562.814652320203 4.18534767979728 8 569 569.896898222588 -0.896898222587899 9 621 620.909119534035 0.090880465965351 10 629 629.660234288248 -0.660234288247722 11 628 614.818730426294 13.1812695737058 12 612 607.122115673831 4.8778843261691 13 595 595.513309473281 -0.51330947328087 14 597 595.152799642561 1.84720035743922 15 593 596.977242265454 -3.97724226545428 16 590 586.956102920303 3.04389707969735 17 580 579.282775051622 0.717224948377686 18 574 573.156102920303 0.843897079697348 19 573 561.017209477536 11.9827905224637 20 573 572.793922593753 0.206077406246619 21 620 621.928357019667 -1.92835701966734 22 626 625.985004560049 0.0149954399514611 23 620 609.265713812562 10.7342861874378 24 588 596.874631846267 -8.87463184626706 25 566 570.243530561455 -4.24353056145485 26 557 565.188553516903 -8.18855351690285 27 561 556.685168269366 4.31483173063386 28 549 554.175176466346 -5.17517646634559 29 532 538.051807612768 -6.0518076127678 30 526 525.352881382083 0.647118617916534 31 511 513.213987939317 -2.21398793931709 32 499 511.846192856805 -12.8461928568048 33 555 549.713905969522 5.28609403047781 34 565 562.220594494801 2.77940550519916 35 542 549.25687751838 -7.25687751838005 36 527 520.904607025056 6.0953929749436 37 510 510.234694267273 -0.234694267272696 38 514 509.874184436553 4.12581556344739 39 517 513.576413944979 3.42358605502113 40 508 510.127528699192 -2.12752869919194 41 493 496.820840173913 -3.82084017391330 42 490 485.999700828762 4.00029917123828 43 469 476.677487714295 -7.67748771429449 44 478 469.676331975184 8.32366802481606 45 528 527.260807385995 0.739192614004657 46 534 534.134135254676 -0.134135254675692 47 518 529.622363816957 -11.6223638169572 48 506 507.842347422998 -1.84234742299818 49 502 499.989114993514 2.01088500648638 50 516 511.834219918757 4.16578008124349 51 528 524.925383854847 3.0746161451534 52 533 529.926539593957 3.07346040604291 53 536 529.764359267408 6.23564073259218 54 537 535.843301892051 1.15669810794887 55 524 530.276662548649 -6.27666254864943 56 536 530.78665435167 5.21334564833005 57 587 591.18781009078 -4.18781009078047 58 597 599.000031402227 -2.00003140222721 59 581 586.036314425806 -5.03631442580641 60 564 564.256298031847 -0.256298031847452 61 558 551.708598388531 6.29140161146902 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0380137260471209 0.0760274520942418 0.96198627395288 19 0.0512038254832221 0.102407650966444 0.948796174516778 20 0.0195148631008568 0.0390297262017137 0.980485136899143 21 0.00940613096043565 0.0188122619208713 0.990593869039564 22 0.00536555308338682 0.0107311061667736 0.994634446916613 23 0.0448834995103829 0.0897669990207659 0.955116500489617 24 0.237795248467616 0.475590496935232 0.762204751532384 25 0.211425904749342 0.422851809498684 0.788574095250658 26 0.178418454394204 0.356836908788408 0.821581545605796 27 0.467685655697874 0.935371311395748 0.532314344302126 28 0.436746902133036 0.873493804266072 0.563253097866964 29 0.390688411543659 0.781376823087318 0.609311588456341 30 0.361564390777614 0.723128781555228 0.638435609222386 31 0.388793030245388 0.777586060490775 0.611206969754612 32 0.860815723653575 0.278368552692850 0.139184276346425 33 0.929773952092231 0.140452095815538 0.070226047907769 34 0.926751926895026 0.146496146209948 0.0732480731049739 35 0.947846406621162 0.104307186757676 0.0521535933788382 36 0.994089279971152 0.0118214400576969 0.00591072002884845 37 0.988316409654688 0.0233671806906243 0.0116835903453122 38 0.986990140864586 0.0260197182708283 0.0130098591354142 39 0.9951569324387 0.00968613512259855 0.00484306756129928 40 0.99535105706347 0.00929788587305844 0.00464894293652922 41 0.994127063214608 0.011745873570783 0.0058729367853915 42 0.98920670612142 0.0215865877571617 0.0107932938785808 43 0.972566608180448 0.0548667836391033 0.0274333918195516 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0769230769230769 NOK 5% type I error level 10 0.384615384615385 NOK 10% type I error level 13 0.5 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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