Multiplelineairregression1

*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: Wed, 18 Nov 2009 08:35:27 -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/18/t12585588668zyd4dnt4zhxgjz.htm/, Retrieved Wed, 18 Nov 2009 16:41:19 +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/18/t12585588668zyd4dnt4zhxgjz.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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17823.2 0 17872 0 17420.4 0 16704.4 0 15991.2 0 16583.6 0 19123.5 0 17838.7 0 17209.4 0 18586.5 0 16258.1 0 15141.6 0 19202.1 0 17746.5 0 19090.1 0 18040.3 0 17515.5 0 17751.8 0 21072.4 0 17170 0 19439.5 0 19795.4 0 17574.9 0 16165.4 0 19464.6 0 19932.1 0 19961.2 0 17343.4 0 18924.2 0 18574.1 0 21350.6 0 18594.6 0 19823.1 0 20844.4 0 19640.2 0 17735.4 0 19813.6 0 22160 0 20664.3 0 17877.4 0 20906.5 0 21164.1 0 21374.4 0 22952.3 0 21343.5 0 23899.3 0 22392.9 0 18274.1 0 22786.7 0 22321.5 0 17842.2 1 16373.5 1 15993.8 1 16446.1 1 17729 1 16643 1 16196.7 1 18252.1 1 17570.4 1 15836.8 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation uitvoer[t] = + 19144.7 -2256.34dummy[t] + 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) 19144.7 269.722849 70.9792 0 0 dummy -2256.34 660.683352 -3.4152 0.00117 0.000585 Multiple Linear Regression - Regression Statistics Multiple R 0.409174990530932 R-squared 0.167424172875988 Adjusted R-squared 0.153069417235919 F-TEST (value) 11.6633244810276 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.00116971635339957 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1907.22855547718 Sum Squared Residuals 210976204.244000 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 17823.2 19144.6999999999 -1321.49999999994 2 17872 19144.7 -1272.70000000000 3 17420.4 19144.7 -1724.3 4 16704.4 19144.7 -2440.3 5 15991.2 19144.7 -3153.5 6 16583.6 19144.7 -2561.1 7 19123.5 19144.7 -21.2000000000010 8 17838.7 19144.7 -1306 9 17209.4 19144.7 -1935.3 10 18586.5 19144.7 -558.200000000001 11 16258.1 19144.7 -2886.6 12 15141.6 19144.7 -4003.1 13 19202.1 19144.7 57.3999999999975 14 17746.5 19144.7 -1398.2 15 19090.1 19144.7 -54.6000000000025 16 18040.3 19144.7 -1104.40000000000 17 17515.5 19144.7 -1629.2 18 17751.8 19144.7 -1392.90000000000 19 21072.4 19144.7 1927.7 20 17170 19144.7 -1974.7 21 19439.5 19144.7 294.799999999999 22 19795.4 19144.7 650.7 23 17574.9 19144.7 -1569.8 24 16165.4 19144.7 -2979.3 25 19464.6 19144.7 319.899999999997 26 19932.1 19144.7 787.399999999997 27 19961.2 19144.7 816.5 28 17343.4 19144.7 -1801.3 29 18924.2 19144.7 -220.500000000000 30 18574.1 19144.7 -570.600000000003 31 21350.6 19144.7 2205.9 32 18594.6 19144.7 -550.100000000003 33 19823.1 19144.7 678.399999999997 34 20844.4 19144.7 1699.7 35 19640.2 19144.7 495.5 36 17735.4 19144.7 -1409.3 37 19813.6 19144.7 668.899999999997 38 22160 19144.7 3015.3 39 20664.3 19144.7 1519.60000000000 40 17877.4 19144.7 -1267.3 41 20906.5 19144.7 1761.8 42 21164.1 19144.7 2019.40000000000 43 21374.4 19144.7 2229.7 44 22952.3 19144.7 3807.6 45 21343.5 19144.7 2198.8 46 23899.3 19144.7 4754.6 47 22392.9 19144.7 3248.2 48 18274.1 19144.7 -870.600000000003 49 22786.7 19144.7 3642 50 22321.5 19144.7 3176.8 51 17842.2 16888.36 953.840000000001 52 16373.5 16888.36 -514.86 53 15993.8 16888.36 -894.56 54 16446.1 16888.36 -442.260000000001 55 17729 16888.36 840.64 56 16643 16888.36 -245.360000000000 57 16196.7 16888.36 -691.659999999999 58 18252.1 16888.36 1363.74 59 17570.4 16888.36 682.040000000002 60 15836.8 16888.36 -1051.56 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.135552612531627 0.271105225063254 0.864447387468373 6 0.0675097875949313 0.135019575189863 0.932490212405069 7 0.133916235901251 0.267832471802501 0.86608376409875 8 0.0749998987498878 0.149999797499776 0.925000101250112 9 0.0397039349161856 0.0794078698323711 0.960296065083814 10 0.0315886433455039 0.0631772866910078 0.968411356654496 11 0.0324943852142294 0.0649887704284588 0.96750561478577 12 0.100007586618615 0.200015173237229 0.899992413381385 13 0.126514890227056 0.253029780454112 0.873485109772944 14 0.0918499675944954 0.183699935188991 0.908150032405505 15 0.0959720392018785 0.191944078403757 0.904027960798122 16 0.0707239584852093 0.141447916970419 0.92927604151479 17 0.0533509919469233 0.106701983893847 0.946649008053077 18 0.0397459259110619 0.0794918518221237 0.960254074088938 19 0.160140069343606 0.320280138687212 0.839859930656394 20 0.153956631812664 0.307913263625329 0.846043368187336 21 0.152170688514168 0.304341377028337 0.847829311485832 22 0.161012160048687 0.322024320097374 0.838987839951313 23 0.150901811675263 0.301803623350527 0.849098188324737 24 0.270904325576894 0.541808651153789 0.729095674423106 25 0.265100924203554 0.530201848407108 0.734899075796446 26 0.276184713749737 0.552369427499473 0.723815286250263 27 0.279376759065228 0.558753518130456 0.720623240934772 28 0.338082037393549 0.676164074787097 0.661917962606451 29 0.322255433000430 0.644510866000859 0.67774456699957 30 0.323551472094952 0.647102944189904 0.676448527905048 31 0.430922485433585 0.86184497086717 0.569077514566415 32 0.4406323765707 0.8812647531414 0.5593676234293 33 0.426727361845483 0.853454723690965 0.573272638154517 34 0.447143598710469 0.894287197420938 0.552856401289531 35 0.427109380666656 0.854218761333313 0.572890619333344 36 0.588748090748114 0.822503818503772 0.411251909251886 37 0.590959968938301 0.818080062123399 0.409040031061699 38 0.682090897444745 0.63581820511051 0.317909102555255 39 0.662456746478298 0.675086507043404 0.337543253521702 40 0.874164554838158 0.251670890323685 0.125835445161842 41 0.868722970388352 0.262554059223296 0.131277029611648 42 0.8596193025031 0.280761394993801 0.140380697496901 43 0.846534237394567 0.306931525210866 0.153465762605433 44 0.878918605287323 0.242162789425354 0.121081394712677 45 0.852718088886522 0.294563822226955 0.147281911113478 46 0.93489142596583 0.130217148068341 0.0651085740341706 47 0.930462595198347 0.139074809603306 0.0695374048016532 48 0.997089620347097 0.00582075930580514 0.00291037965290257 49 0.994827359720657 0.0103452805586854 0.00517264027934268 50 0.989287153773006 0.0214256924539876 0.0107128462269938 51 0.983974622464761 0.0320507550704772 0.0160253775352386 52 0.965186437655594 0.0696271246888126 0.0348135623444063 53 0.943036455839095 0.113927088321810 0.0569635441609052 54 0.885450739088869 0.229098521822261 0.114549260911131 55 0.79740597104089 0.40518805791822 0.20259402895911 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0196078431372549 NOK 5% type I error level 4 0.0784313725490196 NOK 10% type I error level 9 0.176470588235294 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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