review ws8

*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: Sat, 04 Dec 2010 08:52:11 +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/04/t12914526486pe2pbmkivhxuxj.htm/, Retrieved Sat, 04 Dec 2010 09:50:58 +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/04/t12914526486pe2pbmkivhxuxj.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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19554.2 19691.6 0 16554.2 16198.9 15903.8 15930.7 0 19554.2 16554.2 18003.8 17444.6 0 15903.8 19554.2 18329.6 17699.4 0 18003.8 15903.8 16260.7 15189.8 0 18329.6 18003.8 14851.9 15672.7 0 16260.7 18329.6 18174.1 17180.8 0 14851.9 16260.7 18406.6 17664.9 0 18174.1 14851.9 18466.5 17862.9 0 18406.6 18174.1 16016.5 16162.3 0 18466.5 18406.6 17428.5 17463.6 0 16016.5 18466.5 17167.2 16772.1 0 17428.5 16016.5 19630 19106.9 0 17167.2 17428.5 17183.6 16721.3 0 19630 17167.2 18344.7 18161.3 0 17183.6 19630 19301.4 18509.9 0 18344.7 17183.6 18147.5 17802.7 0 19301.4 18344.7 16192.9 16409.9 0 18147.5 19301.4 18374.4 17967.7 0 16192.9 18147.5 20515.2 20286.6 0 18374.4 16192.9 18957.2 19537.3 0 20515.2 18374.4 16471.5 18021.9 0 18957.2 20515.2 18746.8 20194.3 0 16471.5 18957.2 19009.5 19049.6 0 18746.8 16471.5 19211.2 20244.7 0 19009.5 18746.8 20547.7 21473.3 0 19211.2 19009.5 19325.8 19673.6 0 20547.7 19211.2 20605.5 21053.2 0 19325.8 20547.7 20056.9 20159.5 0 20605.5 19325.8 16141.4 18203.6 etc...

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation uitvoer[t] = + 5955.77107260798 + 0.900208484398036invoer[t] -867.895942836455crisis[t] -0.0883075849666572`y-1t`[t] -0.138612433670325`y-2t`[t] + 47.9932567530819M1[t] + 12.2726899811716M2[t] + 442.313077321896M3[t] + 699.792225468448M4[t] + 886.719663826503M5[t] -701.240818544068M6[t] + 326.178227477193M7[t] + 336.934312118696M8[t] + 477.992501240360M9[t] -333.713518950042M10[t] -664.563611004632M11[t] -16.2181101813024t + 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) 5955.77107260798 846.151316 7.0387 0 0 invoer 0.900208484398036 0.060331 14.9211 0 0 crisis -867.895942836455 195.974054 -4.4286 8.5e-05 4.2e-05 `y-1t` -0.0883075849666572 0.059826 -1.4761 0.148615 0.074308 `y-2t` -0.138612433670325 0.061502 -2.2538 0.030394 0.015197 M1 47.9932567530819 278.291626 0.1725 0.864044 0.432022 M2 12.2726899811716 275.367336 0.0446 0.964698 0.482349 M3 442.313077321896 290.448953 1.5229 0.136531 0.068265 M4 699.792225468448 264.841537 2.6423 0.012111 0.006055 M5 886.719663826503 288.613652 3.0723 0.004032 0.002016 M6 -701.240818544068 326.830462 -2.1456 0.038724 0.019362 M7 326.178227477193 314.451323 1.0373 0.306517 0.153258 M8 336.934312118696 342.157035 0.9847 0.331326 0.165663 M9 477.992501240360 316.019554 1.5125 0.139126 0.069563 M10 -333.713518950042 324.548101 -1.0282 0.310696 0.155348 M11 -664.563611004632 289.250609 -2.2975 0.027508 0.013754 t -16.2181101813024 4.361496 -3.7185 0.00068 0.00034 Multiple Linear Regression - Regression Statistics Multiple R 0.98801967954049 R-squared 0.976182887159291 Adjusted R-squared 0.965597503674532 F-TEST (value) 92.2198887328718 F-TEST (DF numerator) 16 F-TEST (DF denominator) 36 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 380.234952554574 Sum Squared Residuals 5204830.28919044 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 19554.2 20006.8612357149 -452.661235714887 2 15903.8 16255.1567172060 -351.356717206033 3 18003.8 17938.3253260470 65.4746739530497 4 18329.6 18729.504385277 -399.904385276993 5 16260.7 16321.1937791186 -60.4937791186145 6 14851.9 15289.2654953303 -437.365495330281 7 18174.1 18069.2538362125 104.846163787522 8 18406.6 18401.4844757483 5.1155242517048 9 18466.5 18223.5360939552 242.963906044835 10 16016.5 15827.2003998483 189.299600151695 11 17428.5 16859.6241967510 568.875803248966 12 17167.2 17100.3856831325 66.8143168675023 13 19630 19061.3216146861 568.678385313898 14 17183.6 16680.5810860151 503.018913984892 15 18344.7 18265.3645549269 79.3354450731468 16 19301.4 19057.0057913796 244.394208620444 17 18147.5 18345.6609161178 -198.160916117803 18 16192.9 15456.9595534970 735.940446503026 19 18374.4 18203.0561591202 171.343840879794 20 20515.2 20363.3764542983 151.823545701736 21 18957.2 19322.2584139307 -365.058413930744 22 16471.5 16971.0000656789 -499.50006567888 23 18746.8 19015.0091105593 -268.209110559266 24 19009.5 18776.5086375919 232.991362408146 25 19211.2 19545.5396709669 -334.339670966895 26 20547.7 20545.3720117321 2.32798826786109 27 19325.8 19193.1078643412 132.692135658825 28 20605.5 20598.9440478523 6.55595214767582 29 20056.9 20021.5003697425 35.3996302575103 30 16141.4 16527.6672123013 -386.267212301292 31 20359.8 20738.6326401936 -378.832640193638 32 19711.6 19263.8362266042 447.763773395803 33 15638.6 15933.8066215111 -295.206621511076 34 14384.5 14327.8835748885 56.6164251114918 35 13855.6 13985.475036422 -129.875036421998 36 14308.3 14358.6154596421 -50.3154596421506 37 15290.6 15456.8951562114 -166.295156211382 38 14423.8 14065.4764942971 358.323505702895 39 13779.7 14000.2776596302 -220.577659630219 40 15686.3 15845.3072975004 -159.007297500377 41 14733.8 14831.7436964113 -97.9436964112903 42 12522.5 12434.8077388715 87.6922611285465 43 16189.4 16086.7573644737 102.642635526322 44 16059.1 16663.8028433492 -604.702843349243 45 16007.1 15589.7988706030 417.301129396984 46 15806.8 15553.2159595843 253.584040415694 47 15160 15330.7916562677 -170.791656267702 48 15692.1 15941.5902196335 -249.490219633498 49 18908.9 18524.2823224207 384.617677579268 50 16969.9 17482.2136907496 -512.313690749615 51 16997.5 17054.4245950548 -56.924595054803 52 19858.9 19550.9384779908 307.961522009251 53 17681.2 17360.0012386098 321.198761390197 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.794176875529977 0.411646248940046 0.205823124470023 21 0.755399573385654 0.489200853228692 0.244600426614346 22 0.804104763825089 0.391790472349822 0.195895236174911 23 0.75066526745761 0.498669465084778 0.249334732542389 24 0.719601358831505 0.56079728233699 0.280398641168495 25 0.755940667016647 0.488118665966707 0.244059332983353 26 0.675324236071908 0.649351527856184 0.324675763928092 27 0.660683421727873 0.678633156544253 0.339316578272127 28 0.586501284779378 0.826997430441244 0.413498715220622 29 0.479844294973393 0.959688589946786 0.520155705026607 30 0.373334514281935 0.74666902856387 0.626665485718065 31 0.322947253826737 0.645894507653473 0.677052746173263 32 0.505678935217407 0.988642129565187 0.494321064782593 33 0.432018698394426 0.864037396788852 0.567981301605574 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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