Model 4

*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 08:08:36 -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/t1258643434cj2qidsjntkjf7k.htm/, Retrieved Thu, 19 Nov 2009 16:10:46 +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/t1258643434cj2qidsjntkjf7k.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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83.7 0 137.5 114.6 111.3 115.6 106.0 0 83.7 137.5 114.6 111.3 123.4 0 106.0 83.7 137.5 114.6 126.5 0 123.4 106.0 83.7 137.5 120.0 0 126.5 123.4 106.0 83.7 141.6 0 120.0 126.5 123.4 106.0 90.5 0 141.6 120.0 126.5 123.4 96.5 0 90.5 141.6 120.0 126.5 113.5 0 96.5 90.5 141.6 120.0 120.1 0 113.5 96.5 90.5 141.6 123.9 0 120.1 113.5 96.5 90.5 144.4 0 123.9 120.1 113.5 96.5 90.8 0 144.4 123.9 120.1 113.5 114.2 0 90.8 144.4 123.9 120.1 138.1 0 114.2 90.8 144.4 123.9 135.0 0 138.1 114.2 90.8 144.4 131.3 0 135.0 138.1 114.2 90.8 144.6 0 131.3 135.0 138.1 114.2 101.7 0 144.6 131.3 135.0 138.1 108.7 0 101.7 144.6 131.3 135.0 135.3 0 108.7 101.7 144.6 131.3 124.3 0 135.3 108.7 101.7 144.6 138.3 0 124.3 135.3 108.7 101.7 158.2 0 138.3 124.3 135.3 108.7 93.5 0 158.2 138.3 124.3 135.3 124.8 0 93.5 158.2 138.3 124.3 154.4 0 124.8 93.5 158.2 138.3 152.8 0 154.4 124.8 93.5 158.2 148.9 0 152.8 154.4 124.8 93.5 170.3 0 148.9 152.8 154.4 124.8 124.8 0 170.3 148.9 152.8 154.4 134.4 0 124.8 170.3 148.9 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 47.6452791080674 -2.61492695465629X[t] + 0.168332065218935Y1[t] + 0.178485936109504Y2[t] + 0.407679280677300Y3[t] + 0.053273699457221Y4[t] -64.4595287059618M1[t] -37.304278203556M2[t] -12.7597221628184M3[t] + 1.64489339837566M4[t] -15.9606489351920M5[t] -13.1969103636244M6[t] -61.9077462099704M7[t] -42.7379786905838M8[t] -25.0967505219815M9[t] -12.9261758561011M10[t] -9.07613292450198M11[t] + 0.205736207577392t + 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) 47.6452791080674 24.115344 1.9757 0.055292 0.027646 X -2.61492695465629 3.341649 -0.7825 0.438631 0.219316 Y1 0.168332065218935 0.164445 1.0236 0.312314 0.156157 Y2 0.178485936109504 0.159587 1.1184 0.270227 0.135114 Y3 0.407679280677300 0.173984 2.3432 0.024313 0.012156 Y4 0.053273699457221 0.181553 0.2934 0.770747 0.385373 M1 -64.4595287059618 5.429632 -11.8718 0 0 M2 -37.304278203556 10.939564 -3.41 0.001523 0.000762 M3 -12.7597221628184 10.602045 -1.2035 0.236032 0.118016 M4 1.64489339837566 10.57292 0.1556 0.87717 0.438585 M5 -15.9606489351920 7.051891 -2.2633 0.029259 0.014629 M6 -13.1969103636244 5.498351 -2.4002 0.02126 0.01063 M7 -61.9077462099704 6.504014 -9.5184 0 0 M8 -42.7379786905838 10.687725 -3.9988 0.000275 0.000137 M9 -25.0967505219815 9.772276 -2.5682 0.014169 0.007084 M10 -12.9261758561011 9.377625 -1.3784 0.175934 0.087967 M11 -9.07613292450198 5.466635 -1.6603 0.104879 0.05244 t 0.205736207577392 0.27365 0.7518 0.456671 0.228335 Multiple Linear Regression - Regression Statistics Multiple R 0.976124683817898 R-squared 0.95281939835859 Adjusted R-squared 0.932253495079002 F-TEST (value) 46.3300534581549 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.76798289851965 Sum Squared Residuals 1786.41810807153 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 83.7 78.524777452074 5.17522254792598 2 106 102.033091708755 3.96690829124484 3 123.4 130.44630438448 -7.04630438448 4 126.5 131.252692880435 -4.75269288043451 5 120 123.705494373234 -3.70549437323354 6 141.6 134.415740112076 7.184259887924 7 90.5 90.57722263798 -0.077222637979992 8 96.5 102.721487196137 -6.2214871961366 9 113.5 120.917406044592 -7.41740604459194 10 120.1 117.544578309095 2.55542169090537 11 123.9 125.469399634377 -1.56939963437743 12 144.4 143.819127760869 0.580872239131105 13 90.8 87.2907252999318 3.50927470006823 14 114.2 111.188862687416 3.01113731258373 15 138.1 138.871144398207 -0.771144398206966 16 135 140.921704825243 -5.92170482524313 17 131.3 133.950108047033 -2.65010804703304 18 144.6 146.733587158415 -2.13358715841498 19 101.7 99.816341670381 1.883658329619 20 108.7 112.670700942886 -3.97070094288573 21 135.3 129.263964861517 6.03603513848342 22 124.3 130.586409284289 -6.28640928428948 23 138.3 138.106574864597 0.193425135403223 24 158.2 158.998932374753 -0.798932374753439 25 93.5 97.5263593978706 -4.02635939787064 26 124.8 122.669630852221 2.13036914777932 27 154.4 149.999326153483 4.40067384651726 28 152.8 149.862214012340 2.93778598766044 29 148.9 146.789813421158 2.11018657884242 30 170.3 162.551989149233 7.74801085076738 31 124.8 117.877715210172 6.92228478982777 32 134.4 131.738521888645 2.66147811135491 33 154 151.596933176555 2.40306682344484 34 147.9 151.576667412523 -3.67666741252271 35 168.1 159.593713070808 8.50628692919152 36 175.7 179.689067126107 -3.98906712610677 37 116.7 118.877335130028 -2.17733513002824 38 140.8 145.573375009519 -4.77337500951892 39 164.2 168.024291061333 -3.82429106133284 40 173.8 167.226926772381 6.5730732276194 41 167.8 162.301601773801 5.49839822619864 42 166.6 176.798140473052 -10.1981404730519 43 135.1 129.565525446508 5.53447455349176 44 158.1 141.48973782647 16.6102621735300 45 151.8 156.777175381680 -4.97717538167963 46 166.7 159.292344994093 7.40765500590683 47 165.3 172.430312430217 -7.13031243021731 48 187 182.792872738271 4.20712726172911 49 125.2 127.680802720095 -2.48080272009532 50 144.4 148.735039742089 -4.33503974208898 51 181.7 174.458934002497 7.24106599750255 52 175.9 174.736461509602 1.16353849039780 53 166.3 167.552982384775 -1.25298238477449 54 181.5 184.100543107225 -2.60054310722453 55 121.8 136.063195034959 -14.2631950349585 56 134.8 143.879552145863 -9.07955214586262 57 162.9 158.944520535657 3.95547946434331 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.0830376652643334 0.166075330528667 0.916962334735667 22 0.0281955021571149 0.0563910043142298 0.971804497842885 23 0.0256652877513923 0.0513305755027847 0.974334712248608 24 0.05320779521483 0.10641559042966 0.94679220478517 25 0.166316999647596 0.332633999295193 0.833683000352404 26 0.0941801390643515 0.188360278128703 0.905819860935648 27 0.0651917857959028 0.130383571591806 0.934808214204097 28 0.0613962689480755 0.122792537896151 0.938603731051925 29 0.189826371762835 0.379652743525669 0.810173628237165 30 0.343100602378543 0.686201204757085 0.656899397621457 31 0.242760433070904 0.485520866141809 0.757239566929096 32 0.199550484303713 0.399100968607426 0.800449515696287 33 0.123361700531559 0.246723401063117 0.876638299468441 34 0.360078664405100 0.720157328810199 0.6399213355949 35 0.338622327168357 0.677244654336714 0.661377672831643 36 0.338848769057837 0.677697538115675 0.661151230942163 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 2 0.125 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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