*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, 29 Dec 2010 14:37:31 +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/29/t12936333147eh0uxu2z1z48x4.htm/, Retrieved Wed, 29 Dec 2010 15:35:14 +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/29/t12936333147eh0uxu2z1z48x4.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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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] -0.034037448000849T[t] + 0.0258113556187272`T-G`[t] + 1.21566788645044HPP[t] -0.233157283641214`HPP-G`[t] + 1.08065169306244TGYW[t] + 0.0279738297900176`TGYW-G`[t] -0.706210467475046POP[t] + 0.0201781082769364`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 -0.034037448000849 0.012952 -2.6279 0.011161 0.00558 `T-G` 0.0258113556187272 0.023488 1.0989 0.276682 0.138341 HPP 1.21566788645044 0.196742 6.179 0 0 `HPP-G` -0.233157283641214 0.217404 -1.0725 0.288283 0.144141 TGYW 1.08065169306244 0.183667 5.8837 0 0 `TGYW-G` 0.0279738297900176 0.193194 0.1448 0.885411 0.442705 POP -0.706210467475046 0.198308 -3.5612 0.00078 0.00039 `POP-G` 0.0201781082769364 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 14.1593430366491 -0.159343036649138 2 18 18.3435035220866 -0.343503522086643 3 11 11.4511820632625 -0.451182063262535 4 12 11.9202663787174 0.07973362128259 5 16 16.2460060994724 -0.246006099472436 6 18 18.2073537300832 -0.207353730083249 7 14 14.6920035438345 -0.69200354383447 8 14 14.7314728205198 -0.731472820519797 9 15 15.1027113390928 -0.102711339092772 10 15 15.0686738910919 -0.0686738910919228 11 17 16.8378894174101 0.162110582589931 12 19 18.7828462342394 0.217153765760621 13 10 10.1584747400738 -0.158474740073768 14 16 15.7122412912498 0.287758708750251 15 18 18.275457923663 -0.275457923663007 16 14 14.335282559448 -0.335282559447990 17 14 13.8852494582143 0.114750541785695 18 17 16.5832364676226 0.41676353237738 19 14 13.4654179549929 0.534582045007081 20 16 15.9439672975339 0.0560327024661264 21 18 16.9998538439354 1.00014615606460 22 11 10.8779772759326 0.122022724067418 23 14 14.0123881824329 -0.0123881824328886 24 12 11.8905540729933 0.109445927006671 25 17 16.5966092040171 0.40339079598287 26 9 9.12088363090492 -0.120883630904922 27 16 15.5976464164437 0.402353583556341 28 14 13.9772171358166 0.0227828641833592 29 15 14.722896879977 0.277103120022986 30 11 11.0395694627813 -0.0395694627813440 31 16 15.4345391761365 0.565460823863461 32 13 13.2211544785248 -0.221154478524814 33 17 16.1461814722961 0.853818527703937 34 15 14.2517751390715 0.748224860928453 35 14 14.1789868041877 -0.178986804187676 36 16 15.5236115850046 0.476388414995437 37 9 9.7360370177535 -0.736037017753507 38 15 14.3985338773879 0.601466122612143 39 17 16.3779074785802 0.622092521419813 40 13 13.1361318942706 -0.136131894270630 41 15 14.7964487638958 0.203551236104156 42 16 15.0601272481272 0.9398727518728 43 16 15.7625071819408 0.237492818059173 44 12 12.4364090107412 -0.436409010741242 45 12 13.7035673272813 -1.70356732728132 46 3 4.71839414864835 -1.71839414864835 47 4 4.43275716005653 -0.432757160056531 48 4 4.52257170303608 -0.522571703036082 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 -0.126459072999681 54 3 3.92177050869039 -0.921770508690391 55 4 4.95151233823011 -0.95151233823011 56 4 3.39443696221173 0.605563037788271 57 4 3.27690557716879 0.723094422831207 58 3 3.24862398883875 -0.248623988838746 59 3 3.64719788223852 -0.647197882238522 60 3 3.21396560043436 -0.213965600434361 61 3 0.313229205304118 2.68677079469588 62 4 4.44045804769021 -0.440458047690209 63 4 2.98248422595853 1.01751577404147 64 4 2.67103588174798 1.32896411825202 65 4 2.46121972101417 1.53878027898583 66 3 0.942697165588096 2.05730283441190 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 3.27546150420365e-46 6.55092300840731e-46 1 16 8.96407902070025e-63 1.79281580414005e-62 1 17 1.26195156110071e-74 2.52390312220143e-74 1 18 5.28098335318425e-89 1.05619667063685e-88 1 19 1.44388085084654e-102 2.88776170169308e-102 1 20 3.53228177085652e-121 7.06456354171305e-121 1 21 3.53852669562443e-138 7.07705339124886e-138 1 22 9.99809141128964e-148 1.99961828225793e-147 1 23 1.18439747930645e-163 2.36879495861291e-163 1 24 3.04689969793533e-180 6.09379939587067e-180 1 25 1.26134831717725e-199 2.5226966343545e-199 1 26 3.41948288701283e-206 6.83896577402565e-206 1 27 2.85018361786788e-224 5.70036723573576e-224 1 28 8.97161354570427e-238 1.79432270914085e-237 1 29 3.42299848787061e-253 6.84599697574122e-253 1 30 3.19620151350113e-261 6.39240302700226e-261 1 31 4.50685558632148e-290 9.01371117264295e-290 1 32 9.852684624043e-293 1.9705369248086e-292 1 33 1.08199317552590e-309 2.16398635105179e-309 1 34 1.48219693752374e-323 2.96439387504748e-323 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 4.79493237056467e-129 2.39746618528234e-129 46 1 6.50526225231077e-118 3.25263112615539e-118 47 1 4.95022766509705e-98 2.47511383254853e-98 48 1 2.48072570741738e-87 1.24036285370869e-87 49 1 1.2838600417397e-74 6.4193002086985e-75 50 1 2.67871065317829e-58 1.33935532658914e-58 51 1 4.92610463050927e-44 2.46305231525464e-44 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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