*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, 21 Dec 2010 22:04:23 +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/21/t1292968997i9bp4u914pu8ccx.htm/, Retrieved Tue, 21 Dec 2010 23:03:28 +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/21/t1292968997i9bp4u914pu8ccx.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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9 2 3 2 14 9 2 4 1 18 9 4 2 2 11 9 3 2 2 12 9 3 4 1 16 9 2 4 1 18 9 4 4 2 14 9 3 4 3 14 9 2 3 2 15 9 2 3 2 15 9 2 5 2 17 9 1 4 1 19 9 2 2 4 10 9 1 3 2 16 9 2 5 2 18 9 3 4 3 14 9 2 3 3 14 9 2 4 1 17 9 3 2 1 14 9 2 3 2 16 9 1 4 1 18 9 3 2 3 11 9 4 5 2 14 9 3 3 3 12 9 2 4 2 17 9 4 3 4 9 9 2 4 2 16 9 4 4 2 14 9 3 4 2 15 9 4 2 2 11 9 2 4 2 16 9 3 4 3 13 9 1 4 2 17 9 2 3 2 15 9 3 4 3 14 9 2 4 2 16 9 4 3 4 9 9 2 3 2 15 9 2 4 2 17 9 2 4 4 13 9 2 4 3 15 9 2 4 2 16 9 2 4 3 16 9 3 4 4 12 9 2 2 12 9 4 3 3 11 9 2 4 3 15 9 2 3 2 15 9 3 4 1 17 9 4 3 2 13 9 2 4 1 16 9 2 3 2 14 9 4 2 3 11 9 2 3 4 12 9 3 4 5 12 9 2 4 3 15 9 2 4 2 16 9 2 4 2 15 9 3 3 3 12 9 4 3 2 12 9 5 2 4 8 9 3 3 3 13 9 5 2 2 11 9 3 3 2 14 9 3 4 2 15 10 4 2 3 10

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation PSS [t] = + 17.5056184987945 -0.171507752660072month[t] -1.15792639251861IDT[t] + 0.874466763783774TGYW[t] -0.284405176049270POP[t] -0.0459412607388270t + 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) 17.5056184987945 2.879982 6.0784 0 0 month -0.171507752660072 0.233938 -0.7331 0.466332 0.233166 IDT -1.15792639251861 0.246396 -4.6995 1.6e-05 8e-06 TGYW 0.874466763783774 0.254737 3.4328 0.001088 0.000544 POP -0.284405176049270 0.148417 -1.9163 0.060099 0.03005 t -0.0459412607388270 0.017736 -2.5903 0.012018 0.006009 Multiple Linear Regression - Regression Statistics Multiple R 0.895825388051245 R-squared 0.802503125877163 Adjusted R-squared 0.786045053033593 F-TEST (value) 48.7604553403532 F-TEST (DF numerator) 5 F-TEST (DF denominator) 60 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.53745837144318 Sum Squared Residuals 141.826694635242 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 15.6548446183307 -1.65484461833068 2 18 16.7677752974248 1.23222470257518 3 11 12.3726425480320 -1.37264254803196 4 12 13.4846276798118 -1.48462767981175 5 16 15.4720251226897 0.527974877310258 6 18 16.5840102544695 1.41598974553048 7 14 13.9378110326442 0.0621889673557953 8 14 14.7653909883747 -0.765390988374717 9 15 15.28731453242 -0.287314532419996 10 15 15.2413732716812 -0.241373271681169 11 17 16.9443655385099 0.0556344614901125 12 19 17.4662890825552 1.53371091744483 13 10 13.6602723735824 -3.66027237358237 14 16 16.2155346212445 -0.215534621244469 15 18 16.7606004955546 1.23939950444542 16 14 14.3978609024641 -0.397860902464101 17 14 14.6353792704601 -0.635379270460109 18 17 16.0327151256036 0.967284874396405 19 14 13.0799139447786 0.920086055221387 20 16 14.7819606642929 1.21803933570710 21 18 17.0528177359057 0.947182264094277 22 11 12.3732798104636 -1.37327981046359 23 14 14.0772176246067 -0.0772176246067448 24 12 13.1558640527697 -1.15586405276971 25 17 15.4267211243825 1.57327887561746 26 9 11.6216499627242 -2.62164996272418 27 16 15.3348386029049 0.665161397095118 28 14 12.9730445571288 1.02695544287116 29 15 14.0850296889086 0.914970311091381 30 11 11.1322285080836 -0.132228508083636 31 16 15.1510735599496 0.848926440050427 32 13 13.6628007306429 -0.662800730642868 33 17 16.2171174309905 0.782882569009472 34 15 14.1387830139493 0.86121698605068 35 14 13.5249769484264 0.475023051573613 36 16 14.9213672562554 1.07863274374456 37 9 11.1162960945971 -2.11629609459708 38 15 13.955017970994 1.04498202900599 39 17 14.7835434740390 2.21645652596104 40 13 14.1687918612016 -1.16879186120159 41 15 14.4072557765120 0.592744223487967 42 16 14.6457196918225 1.35428030817752 43 16 14.3153732550344 1.68462674496562 44 12 12.8271004257277 -0.827100425727673 45 9 9.91491062154575 -0.914910621545748 46 9 10.7274536714217 -1.72745367142172 47 9 8.72898081928735 0.271019180712648 48 9 8.96649918728336 0.0335008127166395 49 9 6.14784666548354 2.85215333451646 50 9 9.1004115125841 -0.100411512584100 51 9 6.51187707271523 2.48812292728477 52 9 9.06713932037732 -0.0671393203773225 53 9 11.5637912387685 -2.56379123876854 54 9 11.2930006785658 -2.29300067856575 55 9 10.7920920364320 -1.79209203643202 56 9 8.3155094726379 0.684490527362092 57 9 7.11069627206604 1.88930372793396 58 9 7.34916018737648 1.65083981262352 59 9 10.0173198584278 -1.01731985842777 60 9 8.9254040812451 0.0745959187549002 61 9 12.7524356921294 -3.75243569212943 62 9 9.59509090016202 -0.595090900162022 63 9 10.0584041149364 -1.05840411493642 64 9 8.34433643885133 0.655663561148675 65 10 6.85606360954462 3.14393639045538 66 9 11.2509600252131 -2.25096002521306 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.0508553784643285 0.101710756928657 0.949144621535672 10 0.0142230710018726 0.0284461420037452 0.985776928998127 11 0.0142793445502126 0.0285586891004252 0.985720655449787 12 0.00455648151819264 0.00911296303638529 0.995443518481807 13 0.00265737598490932 0.00531475196981863 0.99734262401509 14 0.000807127103066639 0.00161425420613328 0.999192872896933 15 0.000259693492902669 0.000519386985805337 0.999740306507097 16 7.6947538608062e-05 0.000153895077216124 0.999923052461392 17 3.46611313405889e-05 6.93222626811778e-05 0.99996533886866 18 8.06905416258585e-05 0.000161381083251717 0.999919309458374 19 2.66415559411347e-05 5.32831118822694e-05 0.99997335844406 20 3.36145325744142e-05 6.72290651488284e-05 0.999966385467426 21 5.01806712810299e-05 0.000100361342562060 0.999949819328719 22 2.76827459556973e-05 5.53654919113945e-05 0.999972317254044 23 7.16250412062143e-05 0.000143250082412429 0.999928374958794 24 3.91666940771069e-05 7.83333881542137e-05 0.999960833305923 25 3.30701734512486e-05 6.61403469024972e-05 0.999966929826549 26 7.13859699099065e-05 0.000142771939819813 0.99992861403009 27 2.95726178109381e-05 5.91452356218762e-05 0.99997042738219 28 1.30211043228389e-05 2.60422086456779e-05 0.999986978895677 29 4.94348378870591e-06 9.88696757741182e-06 0.999995056516211 30 5.72630980663814e-06 1.14526196132763e-05 0.999994273690193 31 2.3796695950299e-06 4.7593391900598e-06 0.999997620330405 32 1.43550374544619e-06 2.87100749089237e-06 0.999998564496255 33 8.93272368580986e-07 1.78654473716197e-06 0.999999106727631 34 3.28548655882999e-07 6.57097311765999e-07 0.999999671451344 35 1.70580524162967e-07 3.41161048325934e-07 0.999999829419476 36 8.23142123841147e-08 1.64628424768229e-07 0.999999917685788 37 0.000325960022649634 0.000651920045299269 0.99967403997735 38 0.000245720011723065 0.000491440023446131 0.999754279988277 39 0.000933467845772229 0.00186693569154446 0.999066532154228 40 0.000551327373360388 0.00110265474672078 0.99944867262664 41 0.000425037762487242 0.000850075524974483 0.999574962237513 42 0.00106276749590859 0.00212553499181719 0.998937232504091 43 0.975958349067143 0.0480833018657144 0.0240416509328572 44 0.999924047635591 0.000151904728817567 7.59523644087836e-05 45 0.999999838995521 3.22008957078702e-07 1.61004478539351e-07 46 0.999999410054888 1.17989022348582e-06 5.8994511174291e-07 47 0.999998766238296 2.46752340808809e-06 1.23376170404404e-06 48 0.999996232825573 7.53434885313891e-06 3.76717442656946e-06 49 0.99999847308227 3.05383545943858e-06 1.52691772971929e-06 50 0.999992473063763 1.50538724747329e-05 7.52693623736643e-06 51 0.999975494296955 4.90114060891385e-05 2.45057030445693e-05 52 0.999922033988623 0.000155932022754489 7.79660113772447e-05 53 0.999946477697151 0.000107044605697136 5.3522302848568e-05 54 0.999990929823395 1.81403532099344e-05 9.07017660496722e-06 55 0.99998587489681 2.82502063807626e-05 1.41251031903813e-05 56 0.999831510821697 0.000336978356605744 0.000168489178302872 57 0.998315452203347 0.00336909559330587 0.00168454779665293 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 45 0.918367346938776 NOK 5% type I error level 48 0.979591836734694 NOK 10% type I error level 48 0.979591836734694 NOK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal 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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