M5

*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 09:32:12 -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/t12586485190w3e62h4jkqt1rg.htm/, Retrieved Thu, 19 Nov 2009 17:35:31 +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/t12586485190w3e62h4jkqt1rg.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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19 2407,6 21 25 2454,62 19 21 2448,05 25 23 2497,84 21 23 2645,64 23 19 2756,76 23 18 2849,27 19 19 2921,44 18 19 2981,85 19 22 3080,58 19 23 3106,22 22 20 3119,31 23 14 3061,26 20 14 3097,31 14 14 3161,69 14 15 3257,16 14 11 3277,01 15 17 3295,32 11 16 3363,99 17 20 3494,17 16 24 3667,03 20 23 3813,06 24 20 3917,96 23 21 3895,51 20 19 3801,06 21 23 3570,12 19 23 3701,61 23 23 3862,27 23 23 3970,1 23 27 4138,52 23 26 4199,75 27 17 4290,89 26 24 4443,91 17 26 4502,64 24 24 4356,98 26 27 4591,27 24 27 4696,96 27 26 4621,4 27 24 4562,84 26 23 4202,52 24 23 4296,49 23 24 4435,23 23 17 4105,18 24 21 4116,68 17 19 3844,49 21 22 3720,98 19 22 3674,4 22 18 3857,62 22 16 3801,06 18 14 3504,37 16 12 3032,6 14 14 3047,03 12 16 2962,34 14 8 2197,82 16 3 2014,45 8 0 1862,83 3 5 1905,41 0 1 1810,99 5 1 1670,07 1 3 1864,44 1

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 Consvertr[t] = + 0.705596169285437 + 0.00366456642861570Aand[t] + 0.459254170458587Y1[t] -0.110442093795957t + 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) 0.705596169285437 1.739958 0.4055 0.686637 0.343319 Aand 0.00366456642861570 0.000795 4.6092 2.4e-05 1.2e-05 Y1 0.459254170458587 0.108016 4.2517 8.1e-05 4.1e-05 t -0.110442093795957 0.027628 -3.9975 0.000189 9.5e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.915561174940805 R-squared 0.838252265058987 Adjusted R-squared 0.829587207830004 F-TEST (value) 96.7393801226384 F-TEST (DF numerator) 3 F-TEST (DF denominator) 56 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.84872942692069 Sum Squared Residuals 454.454523477017 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 19 19.062301788655 -0.0623017886549878 2 25 18.2056592674154 6.79434073258464 3 21 20.8266659949349 0.173334005065065 4 23 19.0616659817854 3.93833401821460 5 23 20.411355147056 2.58864485294399 6 19 20.7081196748078 -1.70811967480784 7 18 19.0996699394888 -1.09966993948877 8 19 18.7944454343874 0.205554565612584 9 19 19.3646339690027 -0.364633969002720 10 22 19.615994518704 2.38400548129601 11 23 20.9772744195135 2.02272558048650 12 20 21.3740556707267 -1.37405567072671 13 14 19.6731229843739 -5.67312298437385 14 14 16.9392634875780 -2.93926348757796 15 14 17.0647461804563 -3.06474618045629 16 15 17.3041602436003 -2.30416024360027 17 11 17.7257139638709 -6.72571396387092 18 17 15.8453533995486 1.15464660045143 19 16 18.7420821051572 -2.74208210515717 20 20 18.6494390985798 1.35056090142018 21 24 21.0094706394687 2.99052936053127 22 23 23.2711818630779 -0.271181863077868 23 20 23.0858986171851 -3.08589861718511 24 21 21.5154244956910 -0.515424495690969 25 19 21.5181182731708 -2.51811827317085 26 23 19.6428728674332 3.3571271325668 27 23 21.8513012951703 1.14869870482973 28 23 22.3296084437957 0.670391556204286 29 23 22.6143165479974 0.385683452002612 30 27 23.1210607321089 3.87893926789111 31 26 25.0720167225714 0.927983277428581 32 17 24.8363090426209 -7.83630904262091 33 24 21.1533313696044 2.84666863039556 34 26 24.4728884553712 1.52711154462880 35 24 24.7471739565002 -0.747173956500248 36 27 24.5767947903475 2.42320520965251 37 27 26.2314232337677 0.768576766232311 38 26 25.8440865006255 0.155913499374474 39 24 25.0597932263112 -1.05979322631125 40 23 22.7104262160393 0.289573783960693 41 23 22.4850892590818 0.514910740918223 42 24 22.8830691115920 1.11693088840804 43 17 22.02239103849 -5.02239103848998 44 21 18.739312265413 2.26068773458701 45 19 19.4684285172465 -0.468428517246474 46 22 17.9868674829350 4.01313251706498 47 22 19.0834923962699 2.9165076037301 48 18 19.6444721635249 -1.64447216352491 49 16 17.4897455106921 -1.48974551069210 50 14 15.3735548622730 -1.37355486227298 51 12 12.6157719235318 -0.615771923531813 52 14 11.6397011823836 2.36029881761639 53 16 12.1374152986654 3.86258470133464 54 8 10.1438472197813 -2.1438472197813 55 3 5.68740021630138 -2.68740021630138 56 0 2.72506570830577 -2.72506570830577 57 5 1.39289834166451 3.60710165833549 58 1 3.23271873797160 -2.23271873797160 59 1 0.768849261220764 0.231150738779236 60 3 1.37068894415484 1.62931105584516 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.612506659060428 0.774986681879145 0.387493340939572 8 0.450964525890642 0.901929051781283 0.549035474109358 9 0.306553662200775 0.61310732440155 0.693446337799225 10 0.427599916406898 0.855199832813795 0.572400083593102 11 0.491352827322583 0.982705654645165 0.508647172677418 12 0.438273010374284 0.876546020748567 0.561726989625716 13 0.682109336561436 0.635781326877129 0.317890663438564 14 0.590613439514566 0.818773120970868 0.409386560485434 15 0.503405905170304 0.993188189659392 0.496594094829696 16 0.426500472019748 0.853000944039496 0.573499527980252 17 0.538207903562695 0.92358419287461 0.461792096437305 18 0.695906885695507 0.608186228608986 0.304093114304493 19 0.698026213828288 0.603947572343425 0.301973786171712 20 0.796828211730261 0.406343576539478 0.203171788269739 21 0.879494042558763 0.241011914882474 0.120505957441237 22 0.834445852367038 0.331108295265923 0.165554147632962 23 0.828309692146075 0.343380615707849 0.171690307853925 24 0.789819843988213 0.420360312023575 0.210180156011787 25 0.781146555205996 0.437706889588008 0.218853444794004 26 0.857522288580872 0.284955422838256 0.142477711419128 27 0.819752359691907 0.360495280616187 0.180247640308093 28 0.769248328173383 0.461503343653235 0.230751671826617 29 0.708423283377555 0.583153433244891 0.291576716622445 30 0.803349028943521 0.393301942112958 0.196650971056479 31 0.821760879590498 0.356478240819004 0.178239120409502 32 0.97589427239832 0.0482114552033581 0.0241057276016790 33 0.97623566528571 0.0475286694285801 0.0237643347142900 34 0.966164017317105 0.0676719653657901 0.0338359826828951 35 0.947719757904089 0.104560484191823 0.0522802420959114 36 0.937225224323716 0.125549551352568 0.0627747756762838 37 0.90976757717954 0.180464845640921 0.0902324228204607 38 0.870906969100387 0.258186061799226 0.129093030899613 39 0.826780884371045 0.346438231257909 0.173219115628955 40 0.770500989092046 0.458998021815909 0.229499010907954 41 0.700664867752641 0.598670264494718 0.299335132247359 42 0.623253926793331 0.753492146413338 0.376746073206669 43 0.779640743431866 0.440718513136269 0.220359256568134 44 0.727264405710641 0.545471188578719 0.272735594289359 45 0.662441969317413 0.675116061365174 0.337558030682587 46 0.696624088439654 0.606751823120692 0.303375911560346 47 0.80559378091816 0.388812438163678 0.194406219081839 48 0.739889642992553 0.520220714014894 0.260110357007447 49 0.745210991752318 0.509578016495363 0.254789008247682 50 0.84669628440806 0.30660743118388 0.15330371559194 51 0.832450767001289 0.335098465997422 0.167549232998711 52 0.791115099713658 0.417769800572684 0.208884900286342 53 0.695165814512106 0.609668370975787 0.304834185487894 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 2 0.0425531914893617 OK 10% type I error level 3 0.0638297872340425 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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