*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: Mon, 27 Dec 2010 13:33:24 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456692ryg92vm22m8gq73.htm/, Retrieved Mon, 27 Dec 2010 14:31:42 +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/2010/Dec/27/t1293456692ryg92vm22m8gq73.htm/}, year = {2010}, } @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 = {2010}, 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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493 797 514 840 522 988 490 819 484 831 506 904 501 814 462 798 465 828 454 789 464 930 427 744 460 832 473 826 465 907 422 776 415 835 413 715 420 729 363 733 376 736 380 712 384 711 346 667 389 799 407 661 393 692 346 649 348 729 353 622 364 671 305 635 307 648 312 745 312 624 286 477 324 710 336 515 327 461 302 590 299 415 311 554 315 585 264 513 278 591 278 561 287 684 279 668 324 795 354 776 354 1 043 360 964 363 762 385 1 030 412 939 370 779 389 918 395 839 417 874 404 840

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation WLH[t] = + 262.466316248146 + 0.191310161094259Faill[t] + 14.7054212842817M1[t] + 46.744213843187M2[t] + 65.1015625856806M3[t] -30.860179676086M4[t] + 152.529575410477M5[t] + 120.447993594912M6[t] -13.7357806863045M7[t] -1.7382716970117M8[t] -1.17458612716618M9[t] -2.05980432449510M10[t] + 2.51594005568410M11[t] -1.18625240996687t + 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) 262.466316248146 116.020904 2.2622 0.028451 0.014226 Faill 0.191310161094259 0.107028 1.7875 0.080449 0.040224 M1 14.7054212842817 79.64767 0.1846 0.85433 0.427165 M2 46.744213843187 79.462956 0.5883 0.559241 0.27962 M3 65.1015625856806 80.509278 0.8086 0.422895 0.211448 M4 -30.860179676086 79.861019 -0.3864 0.700965 0.350482 M5 152.529575410477 79.754875 1.9125 0.062053 0.031027 M6 120.447993594912 79.589602 1.5134 0.137028 0.068514 M7 -13.7357806863045 80.605994 -0.1704 0.865438 0.432719 M8 -1.7382716970117 78.970099 -0.022 0.982534 0.491267 M9 -1.17458612716618 78.927473 -0.0149 0.988191 0.494095 M10 -2.05980432449510 79.049506 -0.0261 0.979324 0.489662 M11 2.51594005568410 79.183308 0.0318 0.97479 0.487395 t -1.18625240996687 1.134708 -1.0454 0.301289 0.150645 Multiple Linear Regression - Regression Statistics Multiple R 0.550948091396239 R-squared 0.303543799413159 Adjusted R-squared 0.106719220986443 F-TEST (value) 1.54220474820515 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.138692520770443 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 124.694906515412 Sum Squared Residuals 715245.70670082 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 493 428.459683514586 64.5403164854142 2 514 467.538560590577 46.4614394094232 3 522 513.023560765054 8.97643923494628 4 490 383.544148868390 106.455851131610 5 484 568.043373478117 -84.0433734781174 6 506 548.741181012466 -42.7411810124664 7 501 396.1532398228 104.8467601772 8 462 403.903533824618 58.0964661753822 9 465 409.020271817324 55.9797281826757 10 454 399.487704927352 54.5122950726477 11 464 429.851929611855 34.1480703881448 12 427 390.566047182672 36.433952817328 13 460 420.920510233282 39.0794897667183 14 473 450.625189415655 22.3748105843454 15 465 483.292408796816 -18.2924087968163 16 422 361.082783021735 60.9172169782652 17 415 554.573585202892 -139.573585202892 18 413 498.348531646049 -85.3485316460489 19 420 365.656847210186 54.3431527898145 20 363 377.233344433889 -14.2333444338885 21 376 377.18470807705 -1.18470807704993 22 380 370.521793603492 9.47820639650807 23 384 373.71997541261 10.2800245873900 24 346 361.600135858812 -15.6001358588116 25 389 400.372245997569 -11.3722459975687 26 407 404.823983915499 2.17601608450066 27 393 427.925695241948 -34.9256952419481 28 346 322.551363643161 23.4486363568386 29 348 520.059679207298 -172.059679207298 30 353 466.32165774468 -113.321657744680 31 364 340.325828947116 23.6741710528840 32 305 344.249919727049 -39.2499197270487 33 307 346.114384981153 -39.1143849811527 34 312 362.6 -50.6 35 312 342.840962477807 -30.840962477807 36 286 311.0161763313 -25.0161763312999 37 324 369.110612740577 -45.1106127405771 38 336 362.657671476135 -26.657671476135 39 327 369.498019109572 -42.4980191095718 40 302 297.029035218998 4.97096478100234 41 299 445.753259704098 -146.753259704098 42 311 439.077537870668 -128.077537870668 43 315 309.638126173407 5.36187382659272 44 264 306.675051153947 -42.6750511539466 45 278 320.974676879177 -42.9746768791774 46 278 313.163901439054 -35.1639014390538 47 287 340.08454322386 -53.0845432238601 48 279 333.321388180701 -54.3213881807009 49 324 371.136947513987 -47.1369475139867 50 354 398.354594602134 -44.3545946021342 51 354 267.26031608661 86.7396839133899 52 43 238.792669247716 -195.792669247716 53 964 421.570102407594 542.429897592406 54 762 392.511091726136 369.488908273864 55 1 189.225957846491 -188.225957846491 56 412 373.938150860498 38.0618491395015 57 370 342.705958245296 27.2940417547043 58 389 367.226600030102 21.7733999698981 59 395 355.502589273868 39.4974107261322 60 417 358.496252446516 58.5037475534841 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.000774011169901189 0.00154802233980238 0.999225988830099 18 5.37504827591877e-05 0.000107500965518375 0.99994624951724 19 4.99015348053716e-06 9.98030696107432e-06 0.99999500984652 20 2.34595013465747e-06 4.69190026931495e-06 0.999997654049865 21 2.29570716833964e-07 4.59141433667927e-07 0.999999770429283 22 1.74996333750944e-08 3.49992667501888e-08 0.999999982500367 23 3.39744512648134e-09 6.79489025296268e-09 0.999999996602555 24 2.93231058954377e-10 5.86462117908755e-10 0.999999999706769 25 2.19052700414342e-11 4.38105400828683e-11 0.999999999978095 26 1.09096837585834e-11 2.18193675171668e-11 0.99999999998909 27 1.55287224724834e-12 3.10574449449669e-12 0.999999999998447 28 1.88282540625561e-13 3.76565081251123e-13 0.999999999999812 29 3.0823787396115e-14 6.164757479223e-14 0.99999999999997 30 3.05367865397579e-15 6.10735730795158e-15 0.999999999999997 31 3.13767720464087e-16 6.27535440928173e-16 1 32 2.25990900112583e-17 4.51981800225166e-17 1 33 1.99934898712973e-18 3.99869797425947e-18 1 34 2.12096106913126e-19 4.24192213826252e-19 1 35 1.43687957342699e-20 2.87375914685398e-20 1 36 1.59393378646127e-21 3.18786757292254e-21 1 37 1.25564754472000e-22 2.51129508943999e-22 1 38 1.96969601882128e-23 3.93939203764256e-23 1 39 2.09573700830015e-24 4.1914740166003e-24 1 40 2.26530245821877e-24 4.53060491643755e-24 1 41 3.01694487465744e-20 6.03388974931488e-20 1 42 3.77574034486959e-05 7.55148068973918e-05 0.999962242596551 43 0.162677430931272 0.325354861862544 0.837322569068728 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 26 0.962962962962963 NOK 5% type I error level 26 0.962962962962963 NOK 10% type I error level 26 0.962962962962963 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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