Workshop7/module4

*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, 24 Nov 2009 11:29:59 -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/24/t12590874782x5cd6u1nixzcil.htm/, Retrieved Tue, 24 Nov 2009 19:31:30 +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/24/t12590874782x5cd6u1nixzcil.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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114.08 136.49 112.95 142.62 135.31 141.71 134.31 149.51 133.03 147.39 140.11 131.96 124.69 136.38 131.68 127.34 150.95 133.85 137.26 125.14 130.51 141.25 143.15 149.32 118.01 120.92 122.56 134.85 147.97 131.93 135.74 134.22 151.62 143.07 154.82 145.37 145.59 134.32 147.12 126.31 175.86 162.21 140.66 124.09 152.69 153.91 154.38 154.34 132.45 138.70 136.44 150.98 153.24 146.39 154.11 178.30 155.93 168.23 142.53 162.52 148.73 158.86 147.73 152.17 166.79 171.01 144.30 171.49 156.07 189.62 161.70 177.46 152.10 179.98 140.45 156.96 155.56 167.89 174.53 194.78 167.16 192.78 159.48 165.06 173.22 196.60 176.13 151.64 180.31 187.02 185.84 210.99 169.43 219.08 195.25 235.68 174.99 241.44 156.42 187.46 182.08 229.57 182.00 208.44 153.28 215.09 136.72 217.00 130.19 171.08 132.04 178.41 143.89 196.34 133.38 172.11 127.98 154.93 150.45 182.26 133.55 181.74

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 InvoerEU[t] = + 75.9046167757232 + 0.469785279416574InvoerAM[t] -0.14179725109994t + 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) 75.9046167757232 12.229983 6.2064 0 0 InvoerAM 0.469785279416574 0.093544 5.0221 5e-06 3e-06 t -0.14179725109994 0.159358 -0.8898 0.377249 0.188624 Multiple Linear Regression - Regression Statistics Multiple R 0.6678574402613 R-squared 0.446033560512376 Adjusted R-squared 0.426931269495561 F-TEST (value) 23.3497416681464 F-TEST (DF numerator) 2 F-TEST (DF denominator) 58 p-value 3.63931959013186e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 14.0324313472979 Sum Squared Residuals 11420.7295119645 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 114.08 139.883812312192 -25.8038123121919 2 112.95 142.621798823915 -29.6717988239151 3 135.31 142.052496968546 -6.74249696854607 4 134.31 145.575024896895 -11.2650248968954 5 133.03 144.437282853432 -11.4072828534323 6 140.11 137.046698740935 3.06330125906536 7 124.69 138.981352424856 -14.2913524248560 8 131.68 134.592696247830 -2.9126962478302 9 150.95 137.509201165732 13.4407988342678 10 137.26 133.275574130914 3.98442586908613 11 130.51 140.702017731215 -10.1920177312149 12 143.15 144.351387685007 -1.20138768500673 13 118.01 130.867688498476 -12.8576884984761 14 122.56 137.270000189649 -14.7100001896490 15 147.97 135.756429922653 12.2135700773473 16 135.74 136.690440961417 -0.9504409614167 17 151.62 140.706243433153 10.9137565668466 18 154.82 141.644952324712 13.1750476752884 19 145.59 136.312027736059 9.27797226394146 20 147.12 132.407250396832 14.7127496031682 21 175.86 149.130744676787 26.7292553232131 22 140.66 131.080732574327 9.57926742567281 23 152.69 144.947932355429 7.74206764457053 24 154.38 145.008142774479 9.37185722552134 25 132.45 137.518903753304 -5.06890375330351 26 136.44 143.146069733439 -6.70606973343908 27 153.24 140.847958049817 12.3920419501829 28 154.11 155.6970090649 -1.58700906490000 29 155.93 150.824474050075 5.10552594992484 30 142.53 148.000202853507 -5.47020285350659 31 148.73 146.138991479742 2.59100852025799 32 147.73 142.854330709345 4.87566929065482 33 166.79 151.563288122453 15.2267118775465 34 144.3 151.646987805474 -7.34698780547349 35 156.07 160.022397670196 -3.95239767019605 36 161.7 154.168011421391 7.53198857860942 37 152.1 155.210073074420 -3.11007307442039 38 140.45 144.253818691151 -3.80381869115093 39 155.56 149.246774544074 6.31322545592588 40 174.53 161.737503456486 12.7924965435141 41 167.16 160.656135646553 6.50386435344722 42 159.48 147.491890450025 11.9881095499746 43 173.22 162.167120911724 11.0528790882758 44 176.13 140.903777498055 35.2262225019449 45 180.31 157.382983432714 22.9270165672865 46 185.84 168.501939329229 17.3380606707711 47 169.43 172.160704988609 -2.73070498860903 48 195.25 179.817343375824 15.4326566241758 49 174.99 182.381509334164 -7.39150933416373 50 156.42 156.880702700157 -0.460702700157158 51 182.08 176.521563565289 5.55843643471088 52 182 166.453203360117 15.5467966398830 53 153.28 169.435478217137 -16.1554782171373 54 136.72 170.190970849723 -33.470970849723 55 130.19 148.476633567814 -18.2866335678140 56 132.04 151.778362414838 -19.7383624148375 57 143.89 160.059815223677 -16.1698152236768 58 133.38 148.535120652313 -15.1551206523132 59 127.98 140.322412300837 -12.3424123008365 60 150.45 153.019846736192 -2.56984673619157 61 133.55 152.633761139795 -19.083761139795 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.200409520698652 0.400819041397305 0.799590479301348 7 0.361369166489672 0.722738332979344 0.638630833510328 8 0.236878552060553 0.473757104121106 0.763121447939447 9 0.198799583505457 0.397599167010913 0.801200416494543 10 0.130759053211962 0.261518106423923 0.869240946788038 11 0.224672158598207 0.449344317196414 0.775327841401793 12 0.155157528370919 0.310315056741839 0.84484247162908 13 0.325665027233271 0.651330054466543 0.674334972766729 14 0.436324713732386 0.872649427464772 0.563675286267614 15 0.406382460652449 0.812764921304898 0.593617539347551 16 0.347885897876889 0.695771795753779 0.65211410212311 17 0.289704788162917 0.579409576325833 0.710295211837083 18 0.230485765114461 0.460971530228922 0.769514234885539 19 0.169081429790242 0.338162859580483 0.830918570209758 20 0.123164616028218 0.246329232056436 0.876835383971782 21 0.123043022303712 0.246086044607425 0.876956977696288 22 0.0908949161294361 0.181789832258872 0.909105083870564 23 0.0848620471279466 0.169724094255893 0.915137952872053 24 0.0685090191586774 0.137018038317355 0.931490980841323 25 0.126807805210444 0.253615610420889 0.873192194789556 26 0.207552777550295 0.41510555510059 0.792447222449705 27 0.156646880058718 0.313293760117436 0.843353119941282 28 0.158321275218987 0.316642550437974 0.841678724781013 29 0.122696585741972 0.245393171483943 0.877303414258028 30 0.152985531175528 0.305971062351055 0.847014468824473 31 0.129541493258589 0.259082986517178 0.870458506741411 32 0.103672393565907 0.207344787131814 0.896327606434093 33 0.0782540633842072 0.156508126768414 0.921745936615793 34 0.115107882345866 0.230215764691731 0.884892117654134 35 0.126740718355195 0.253481436710390 0.873259281644805 36 0.0981275421568135 0.196255084313627 0.901872457843186 37 0.122038504534604 0.244077009069209 0.877961495465395 38 0.221243433870777 0.442486867741555 0.778756566129223 39 0.235052193055871 0.470104386111743 0.764947806944129 40 0.210575782932960 0.421151565865921 0.78942421706704 41 0.214943020057361 0.429886040114722 0.785056979942639 42 0.220407691147149 0.440815382294299 0.779592308852851 43 0.206798053481686 0.413596106963372 0.793201946518314 44 0.211589692262726 0.423179384525453 0.788410307737274 45 0.188857629391007 0.377715258782015 0.811142370608993 46 0.175938557430807 0.351877114861614 0.824061442569193 47 0.142815500941397 0.285631001882793 0.857184499058603 48 0.168956094992029 0.337912189984058 0.831043905007971 49 0.129181773477079 0.258363546954158 0.870818226522921 50 0.10136490550192 0.20272981100384 0.89863509449808 51 0.100032380172889 0.200064760345778 0.89996761982711 52 0.785977133083017 0.428045733833967 0.214022866916983 53 0.87401563680653 0.25196872638694 0.12598436319347 54 0.892151230689806 0.215697538620388 0.107848769310194 55 0.80708895897255 0.3858220820549 0.19291104102745 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):

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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