*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, 01 Dec 2010 19:53:48 +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/01/t1291233118ken3r8lfteqfmzw.htm/, Retrieved Wed, 01 Dec 2010 20:52:08 +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/01/t1291233118ken3r8lfteqfmzw.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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0 1 0 14 3 0 3 0 2 0 2 0 0 2 0 18 5 0 4 0 1 0 2 0 0 3 0 11 3 0 2 0 2 0 4 0 1 4 4 12 3 3 2 2 2 2 3 3 0 5 0 16 4 0 4 0 1 0 3 0 0 6 0 18 5 0 4 0 1 0 2 0 0 7 0 14 4 0 4 0 2 0 4 0 0 8 0 14 4 0 4 0 3 0 3 0 0 9 0 15 4 0 3 0 2 0 2 0 0 10 0 15 4 0 3 0 2 0 2 0 1 11 11 17 4 4 5 5 2 2 2 2 0 12 0 19 5 0 4 0 1 0 1 0 1 13 13 10 2 2 2 2 4 4 2 2 0 14 0 16 4 0 3 0 2 0 1 0 0 15 0 18 5 0 5 0 2 0 2 0 1 16 16 14 4 4 4 4 3 3 3 3 1 17 17 14 4 4 3 3 3 3 2 2 0 18 0 17 4 0 4 0 1 0 2 0 1 19 19 14 4 4 2 2 1 1 3 3 0 20 0 16 5 0 3 0 2 0 2 0 1 21 21 18 4 4 4 4 1 1 1 1 0 22 0 11 3 0 2 0 3 0 3 0 0 23 0 14 3 0 5 0 2 0 4 0 0 24 0 12 3 0 3 0 3 0 3 0 1 25 25 17 5 5 4 4 2 2 2 2 0 26 0 9 2 0 3 0 4 0 4 0 1 27 27 16 4 4 4 4 2 2 2 2 0 28 0 14 4 0 4 0 2 0 4 0 0 29 0 15 4 0 4 0 2 0 3 0 1 30 30 11 3 3 2 2 2 2 4 4 0 31 0 16 4 0 4 0 2 0 2 0 1 32 32 13 3 3 4 4 3 3 3 3 0 33 0 17 4 0 4 0 2 0 1 0 0 34 0 15 4 0 3 0 2 0 2 0 1 35 35 14 4 4 4 4 3 3 3 3 1 36 36 16 4 4 4 4 2 2 2 2 1 37 37 9 2 2 3 3 4 4 4 4 1 38 38 15 4 4 3 3 2 2 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 9 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 PSS[t] = + 10.2762770653839 -0.115368910871645G[t] -0.0340374480008491T[t] + 0.0258113556187273`T-G`[t] + 1.21566788645044HPP[t] -0.233157283641215`HPP-G`[t] + 1.08065169306244TGYW[t] + 0.0279738297900182`TGYW-G`[t] -0.706210467475044POP[t] + 0.0201781082769354`POP-G`[t] -0.779717192161222IDT[t] + 0.112898678160323`IDT-G `[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) 10.2762770653839 0.569076 18.0578 0 0 G -0.115368910871645 0.014626 -7.8882 0 0 T -0.0340374480008491 0.012952 -2.6279 0.011161 0.00558 `T-G` 0.0258113556187273 0.023488 1.0989 0.276682 0.138341 HPP 1.21566788645044 0.196742 6.179 0 0 `HPP-G` -0.233157283641215 0.217404 -1.0725 0.288283 0.144141 TGYW 1.08065169306244 0.183667 5.8837 0 0 `TGYW-G` 0.0279738297900182 0.193194 0.1448 0.885411 0.442705 POP -0.706210467475044 0.198308 -3.5612 0.00078 0.00039 `POP-G` 0.0201781082769354 0.193512 0.1043 0.917339 0.458669 IDT -0.779717192161222 0.165482 -4.7118 1.8e-05 9e-06 `IDT-G ` 0.112898678160323 0.243858 0.463 0.645247 0.322623 Multiple Linear Regression - Regression Statistics Multiple R 0.986956099413074 R-squared 0.974082342168669 Adjusted R-squared 0.968802819277101 F-TEST (value) 184.501963941569 F-TEST (DF numerator) 11 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.976960556198783 Sum Squared Residuals 51.5404041318847 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 14.1593430366490 -0.159343036649043 2 18 18.3435035220867 -0.343503522086658 3 11 11.4511820632625 -0.451182063262546 4 12 11.9202663787174 0.07973362128259 5 16 16.2460060994724 -0.246006099472436 6 18 18.2073537300833 -0.207353730083254 7 14 14.6920035438345 -0.69200354383447 8 14 14.7314728205198 -0.731472820519804 9 15 15.1027113390928 -0.102711339092777 10 15 15.0686738910919 -0.0686738910919283 11 17 16.8378894174101 0.162110582589929 12 19 18.7828462342394 0.217153765760619 13 10 10.1584747400738 -0.158474740073772 14 16 15.7122412912498 0.287758708750245 15 18 18.275457923663 -0.275457923663011 16 14 14.335282559448 -0.33528255944799 17 14 13.8852494582143 0.114750541785694 18 17 16.5832364676226 0.416763532377376 19 14 13.4654179549929 0.534582045007084 20 16 15.9439672975339 0.0560327024661226 21 18 16.9998538439354 1.00014615606460 22 11 10.8779772759326 0.122022724067412 23 14 14.0123881824329 -0.0123881824328909 24 12 11.8905540729933 0.109445927006666 25 17 16.5966092040171 0.403390795982874 26 9 9.12088363090493 -0.120883630904928 27 16 15.5976464164437 0.402353583556342 28 14 13.9772171358166 0.0227828641833576 29 15 14.722896879977 0.277103120022984 30 11 11.0395694627813 -0.0395694627813415 31 16 15.4345391761365 0.56546082386346 32 13 13.2211544785248 -0.221154478524815 33 17 16.1461814722961 0.853818527703936 34 15 14.2517751390715 0.748224860928451 35 14 14.1789868041877 -0.178986804187675 36 16 15.5236115850046 0.476388414995438 37 9 9.73603701775351 -0.73603701775351 38 15 14.3985338773879 0.601466122612144 39 17 16.3779074785802 0.622092521419813 40 13 13.1361318942706 -0.136131894270632 41 15 14.7964487638958 0.203551236104156 42 16 15.0601272481272 0.93987275187280 43 16 15.7625071819408 0.237492818059175 44 12 12.4364090107412 -0.436409010741244 45 12 13.7035673272813 -1.70356732728132 46 3 4.71839414864835 -1.71839414864835 47 4 4.43275716005653 -0.432757160056534 48 4 4.52257170303609 -0.522571703036086 49 5 4.33077117640792 0.66922882359208 50 4 6.15203190796087 -2.15203190796087 51 3 4.05404389076897 -1.05404389076897 52 3 6.29533950531307 -3.29533950531307 53 4 4.12645907299968 -0.126459072999678 54 3 3.92177050869039 -0.921770508690395 55 4 4.95151233823011 -0.951512338230114 56 4 3.39443696221173 0.605563037788269 57 4 3.27690557716880 0.723094422831205 58 3 3.24862398883875 -0.248623988838746 59 3 3.64719788223852 -0.647197882238519 60 3 3.21396560043436 -0.213965600434360 61 3 0.313229205304116 2.68677079469588 62 4 4.44045804769021 -0.440458047690205 63 4 2.98248422595853 1.01751577404147 64 4 2.67103588174798 1.32896411825202 65 4 2.46121972101417 1.53878027898583 66 3 0.942697165588093 2.05730283441191 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 3.81580574671502e-44 7.63161149343004e-44 1 16 9.73436777170028e-61 1.94687355434006e-60 1 17 1.74621832128781e-75 3.49243664257563e-75 1 18 3.78698856062550e-87 7.57397712125101e-87 1 19 3.27486288708833e-101 6.54972577417665e-101 1 20 1.25475107269315e-120 2.50950214538631e-120 1 21 6.18543887774056e-128 1.23708777554811e-127 1 22 4.80928537814385e-145 9.6185707562877e-145 1 23 2.07391860526198e-158 4.14783721052397e-158 1 24 7.28223467152904e-173 1.45644693430581e-172 1 25 3.05294000980883e-191 6.10588001961766e-191 1 26 1.09440851092711e-203 2.18881702185421e-203 1 27 1.19607701610786e-221 2.39215403221571e-221 1 28 7.28791881962743e-227 1.45758376392549e-226 1 29 2.15995611956016e-247 4.31991223912032e-247 1 30 1.42878603150679e-253 2.85757206301359e-253 1 31 1.13781453135499e-274 2.27562906270999e-274 1 32 9.14324111245473e-294 1.82864822249095e-293 1 33 2.63688129818922e-304 5.27376259637844e-304 1 34 3.03244647710565e-318 6.0648929542113e-318 1 35 0 0 1 36 0 0 1 37 0 0 1 38 0 0 1 39 0 0 1 40 0 0 1 41 0 0 1 42 0 0 1 43 0 0 1 44 0 0 1 45 1 3.87760287613849e-125 1.93880143806924e-125 46 1 9.00013478176091e-118 4.50006739088046e-118 47 1 4.23144574578171e-96 2.11572287289085e-96 48 1 2.20110915578591e-87 1.10055457789295e-87 49 1 2.76733906589568e-71 1.38366953294784e-71 50 1 1.40597924373098e-58 7.02989621865492e-59 51 1 4.21748410459427e-45 2.10874205229713e-45 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 37 1 NOK 5% type I error level 37 1 NOK 10% type I error level 37 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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