*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, 17 Nov 2009 12:35:42 -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/17/t1258486714vqwg3ml850bvok7.htm/, Retrieved Tue, 17 Nov 2009 20:38:47 +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/17/t1258486714vqwg3ml850bvok7.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:

» Textbox « » Textfile « » CSV «

103.8 122.5 80.2 19 103.5 122.4 74.8 18 104.1 121.9 77.8 19 101.9 122.2 73 19 102 123.7 72 22 100.7 122.6 75.8 23 99 115.7 72.6 20 96.5 116.1 71.9 14 101.8 120.5 74.8 14 100.5 122.6 72.9 14 103.3 119.9 72.9 15 102.3 120.7 79.9 11 100.4 120.2 74 17 103 122.1 76 16 99 119.3 69.6 20 104.8 121.7 77.3 24 104.5 113.5 75.2 23 104.8 123.7 75.8 20 103.8 123.4 77.6 21 106.3 126.4 76.7 19 105.2 124.1 77 23 108.2 125.6 77.9 23 106.2 124.8 76.7 23 103.9 123 71.9 23 104.9 126.9 73.4 27 106.2 127.3 72.5 26 107.9 129 73.7 17 106.9 126.2 69.5 24 110.3 125.4 74.7 26 109.8 126.3 72.5 24 108.3 126.3 72.1 27 110.9 128.4 70.7 27 109.8 127.2 71.4 26 109.3 128.5 69.5 24 109 129 73.5 23 107.9 128.9 72.4 23 108.4 128.3 74.5 24 107.2 124.6 72.2 17 109.5 126.2 73 21 109.9 129.1 73.3 19 108 127.3 71.3 22 114.7 129.2 73.6 22 115.6 130.4 71.3 18 107.6 125.9 71.2 16 1 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation dzcg[t] = + 77.4426660376957 + 0.756479459281622totid[t] -0.720234730937658ndzcg[t] + 0.27624207061515`indc `[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) 77.4426660376957 16.198668 4.7808 1.3e-05 6e-06 totid 0.756479459281622 0.161372 4.6878 1.8e-05 9e-06 ndzcg -0.720234730937658 0.196732 -3.661 0.000551 0.000276 `indc ` 0.27624207061515 0.085093 3.2463 0.00196 0.00098 Multiple Linear Regression - Regression Statistics Multiple R 0.76256897325449 R-squared 0.581511438970407 Adjusted R-squared 0.559485725232007 F-TEST (value) 26.4014799192000 F-TEST (DF numerator) 3 F-TEST (DF denominator) 57 p-value 7.78024311642866e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.77517882779633 Sum Squared Residuals 812.362585364977 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 80.2 72.9850787129528 7.21492128704717 2 74.8 72.553916277647 2.24608372235302 3 77.8 73.6441633892999 4.15583661070009 4 73 71.763838159599 1.23616184040094 5 72 71.5878602209662 0.412139779033817 6 75.8 71.6729371985467 4.12706280145334 7 72.6 74.5278155493923 -1.92781554939228 8 71.9 70.6910705851223 1.20892941487774 9 74.8 71.5313789031892 3.26862109681083 10 72.9 69.035462671154 3.86453732884602 11 72.9 73.3744810012893 -0.47448100128933 12 79.9 70.936845474797 8.96315452520301 13 74 71.5171042913216 2.48289570867836 14 76 71.8392628260572 4.16073717394284 15 69.6 71.9349705180167 -2.33497051801672 16 77.3 75.6989563100603 1.60104368993966 17 75.2 81.1016951953495 -5.90169519534949 18 75.8 73.1535185657244 2.64648143427558 19 77.6 72.8893515963392 4.71064840366075 20 76.7 72.0673619105 4.63263808949998 21 77 73.9967426689075 3.00325733109253 22 77.9 75.1858289503459 2.71417104965416 23 76.7 74.2490578165327 2.45094218346728 24 71.9 73.8055775758728 -1.90557757587277 25 73.4 72.8581098669581 0.541890133041872 26 72.5 73.277197201034 -0.777197201034032 27 73.7 70.8526346036824 2.84736539631758 28 69.5 74.0465068853323 -4.54650688533229 29 74.7 77.7472089728702 -3.04720897287022 30 72.5 76.1682738441552 -3.66827384415522 31 72.1 75.8622808670782 -3.76228086707825 32 70.7 76.3166345262414 -5.61663452624137 33 71.4 76.0725467275416 -4.67254672754162 34 69.5 74.2055177064516 -4.70551770645156 35 73.5 73.3422144325831 0.157785567416899 36 72.4 72.5821105004671 -0.182110500467078 37 74.5 73.6687331392856 0.831266860714366 38 72.2 73.492131798311 -1.29213179831098 39 73 75.184627267619 -2.18462726761905 40 73.3 72.8460541903822 0.453945809617794 41 71.3 73.5338919452803 -2.23389194528035 42 73.6 77.2338583336857 -3.63385833368568 43 71.3 75.9454398874533 -4.64543988745333 44 71.2 72.5821763611895 -1.38217636118951 45 81.4 71.1781478957139 10.2218521042861 46 76.1 74.2943044422429 1.80569555775710 47 71.1 71.2523978908595 -0.152397890859551 48 75.7 71.991956668696 3.70804333130403 49 70 70.8909019992623 -0.890901999262271 50 68.5 66.1816480089415 2.31835199105846 51 56.7 64.3223803531828 -7.62238035318283 52 57.9 64.7160769527639 -6.81607695276391 53 58.8 60.7405771814617 -1.94057718146172 54 59.3 62.4582671172089 -3.1582671172089 55 61.3 63.3201260042265 -2.02012600422649 56 62.9 63.8503508887878 -0.950350888787848 57 61.4 62.4908679480644 -1.09086794806443 58 64.5 63.3038945858455 1.19610541415449 59 63.8 65.5733135390363 -1.77331353903634 60 61.6 65.7142019959836 -4.11420199598363 61 64.7 64.4581611011368 0.241838898863238 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.330883140661123 0.661766281322245 0.669116859338877 8 0.306615251444900 0.613230502889801 0.6933847485551 9 0.190755980142293 0.381511960284586 0.809244019857707 10 0.112761385157002 0.225522770314003 0.887238614842998 11 0.119116497095482 0.238232994190964 0.880883502904518 12 0.260316456612487 0.520632913224975 0.739683543387513 13 0.191743532548235 0.38348706509647 0.808256467451765 14 0.152217388801154 0.304434777602309 0.847782611198846 15 0.130683180156204 0.261366360312409 0.869316819843796 16 0.094730088579176 0.189460177158352 0.905269911420824 17 0.0639868605975354 0.127973721195071 0.936013139402465 18 0.0500027331045407 0.100005466209081 0.94999726689546 19 0.055725222922247 0.111450445844494 0.944274777077753 20 0.057814424751571 0.115628849503142 0.94218557524843 21 0.0538605429090855 0.107721085818171 0.946139457090915 22 0.052298675062481 0.104597350124962 0.94770132493752 23 0.0536657673802234 0.107331534760447 0.946334232619777 24 0.0706802789068912 0.141360557813782 0.929319721093109 25 0.0538055097356303 0.107611019471261 0.94619449026437 26 0.0549360083310147 0.109872016662029 0.945063991668985 27 0.096829505424212 0.193659010848424 0.903170494575788 28 0.208467267827513 0.416934535655027 0.791532732172487 29 0.177205502030119 0.354411004060239 0.82279449796988 30 0.181063536626334 0.362127073252667 0.818936463373666 31 0.151957522829256 0.303915045658512 0.848042477170744 32 0.206769486197014 0.413538972394029 0.793230513802986 33 0.209759229475018 0.419518458950036 0.790240770524982 34 0.313684411808084 0.627368823616169 0.686315588191916 35 0.250888063543353 0.501776127086707 0.749111936456647 36 0.205549994485081 0.411099988970162 0.794450005514919 37 0.156034305655474 0.312068611310948 0.843965694344526 38 0.146530762240531 0.293061524481063 0.853469237759469 39 0.110320243250338 0.220640486500675 0.889679756749662 40 0.0789187386511197 0.157837477302239 0.92108126134888 41 0.0692874155226142 0.138574831045228 0.930712584477386 42 0.0807506559452565 0.161501311890513 0.919249344054744 43 0.284410319087084 0.568820638174168 0.715589680912916 44 0.278657642113115 0.55731528422623 0.721342357886885 45 0.425523603305933 0.851047206611865 0.574476396694067 46 0.359391623515959 0.718783247031919 0.64060837648404 47 0.354259117267709 0.708518234535418 0.645740882732291 48 0.281716115878698 0.563432231757395 0.718283884121302 49 0.282976424644732 0.565952849289464 0.717023575355268 50 0.952423803322037 0.0951523933559261 0.0475761966779631 51 0.96556566096102 0.0688686780779618 0.0344343390389809 52 0.960550815089572 0.0788983698208551 0.0394491849104276 53 0.929823459512642 0.140353080974717 0.0701765404873585 54 0.88613171060993 0.22773657878014 0.11386828939007 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 3 0.0625 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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