H1: multiple linear regression export poland

*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, 03 Dec 2008 15:54:46 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/03/t122834494392dime3uf95yhw9.htm/, Retrieved Wed, 03 Dec 2008 22:55:53 +0000

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/2008/Dec/03/t122834494392dime3uf95yhw9.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

156.3 0 151.5 0 159.1 0 166.9 0 160.5 0 162.8 0 178.9 0 148.5 0 184.1 0 197 0 186.8 0 139.2 0 162.7 0 187.5 0 235.8 0 219.4 0 212.4 1 220.2 1 197.5 1 185.6 1 232.4 1 223.8 1 219.4 1 191.4 1 210.4 1 212.6 1 274.4 1 256 1 227.6 1 261.7 1 237 1 234.9 1 310.6 1 274.2 1 288.1 1 242.5 1 271.7 1 282.2 1 317.4 1 280.3 1 322.6 1 328.2 1 280.7 1 288.8 1 347.9 1 360.1 1 348 1 275.7 1 332.6 1 340.8 1 390.5 1 351.2 1 377.4 1 413.5 1 366.9 1 364.8 1 388 1 429.8 1 423.6 1 326.4 1

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Poland[t] = + 174.8125 + 118.864772727273Dummy[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) 174.8125 14.908791 11.7255 0 0 Dummy 118.864772727273 17.409717 6.8275 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.667521250439188 R-squared 0.445584619787897 Adjusted R-squared 0.436025733922171 F-TEST (value) 46.6147023876049 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 5.70843161629142e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 59.6351630206148 Sum Squared Residuals 206268.454772727 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 156.3 174.812500000000 -18.5125000000004 2 151.5 174.8125 -23.3125000000001 3 159.1 174.8125 -15.7125000000000 4 166.9 174.8125 -7.91249999999994 5 160.5 174.8125 -14.3124999999999 6 162.8 174.8125 -12.0124999999999 7 178.9 174.8125 4.08750000000006 8 148.5 174.8125 -26.3124999999999 9 184.1 174.8125 9.28750000000005 10 197 174.8125 22.1875000000001 11 186.8 174.8125 11.9875000000001 12 139.2 174.8125 -35.6125000000000 13 162.7 174.8125 -12.1125000000000 14 187.5 174.8125 12.6875000000001 15 235.8 174.8125 60.9875000000001 16 219.4 174.8125 44.5875000000001 17 212.4 293.677272727273 -81.2772727272727 18 220.2 293.677272727273 -73.4772727272727 19 197.5 293.677272727273 -96.1772727272727 20 185.6 293.677272727273 -108.077272727273 21 232.4 293.677272727273 -61.2772727272727 22 223.8 293.677272727273 -69.8772727272727 23 219.4 293.677272727273 -74.2772727272727 24 191.4 293.677272727273 -102.277272727273 25 210.4 293.677272727273 -83.2772727272727 26 212.6 293.677272727273 -81.0772727272727 27 274.4 293.677272727273 -19.2772727272727 28 256 293.677272727273 -37.6772727272727 29 227.6 293.677272727273 -66.0772727272727 30 261.7 293.677272727273 -31.9772727272727 31 237 293.677272727273 -56.6772727272727 32 234.9 293.677272727273 -58.7772727272727 33 310.6 293.677272727273 16.9227272727273 34 274.2 293.677272727273 -19.4772727272727 35 288.1 293.677272727273 -5.5772727272727 36 242.5 293.677272727273 -51.1772727272727 37 271.7 293.677272727273 -21.9772727272727 38 282.2 293.677272727273 -11.4772727272727 39 317.4 293.677272727273 23.7227272727273 40 280.3 293.677272727273 -13.3772727272727 41 322.6 293.677272727273 28.9227272727273 42 328.2 293.677272727273 34.5227272727273 43 280.7 293.677272727273 -12.9772727272727 44 288.8 293.677272727273 -4.87727272727271 45 347.9 293.677272727273 54.2227272727273 46 360.1 293.677272727273 66.4227272727273 47 348 293.677272727273 54.3227272727273 48 275.7 293.677272727273 -17.9772727272727 49 332.6 293.677272727273 38.9227272727273 50 340.8 293.677272727273 47.1227272727273 51 390.5 293.677272727273 96.8227272727273 52 351.2 293.677272727273 57.5227272727273 53 377.4 293.677272727273 83.7227272727273 54 413.5 293.677272727273 119.822727272727 55 366.9 293.677272727273 73.2227272727273 56 364.8 293.677272727273 71.1227272727273 57 388 293.677272727273 94.3227272727273 58 429.8 293.677272727273 136.122727272727 59 423.6 293.677272727273 129.922727272727 60 326.4 293.677272727273 32.7227272727273 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00161714008027505 0.0032342801605501 0.998382859919725 6 0.000165838557731464 0.000331677115462928 0.999834161442269 7 0.000249515507090338 0.000499031014180675 0.99975048449291 8 8.24195296359191e-05 0.000164839059271838 0.999917580470364 9 8.35896580041033e-05 0.000167179316008207 0.999916410341996 10 0.000177284926037305 0.000354569852074609 0.999822715073963 11 7.91191391961849e-05 0.000158238278392370 0.999920880860804 12 6.92778199440554e-05 0.000138555639888111 0.999930722180056 13 1.86400134457655e-05 3.72800268915311e-05 0.999981359986554 14 9.27199685518291e-06 1.85439937103658e-05 0.999990728003145 15 0.000205731503176449 0.000411463006352897 0.999794268496824 16 0.000276470703285254 0.000552941406570508 0.999723529296715 17 0.000125890934597509 0.000251781869195018 0.999874109065402 18 5.64305042716156e-05 0.000112861008543231 0.999943569495728 19 3.47125302796719e-05 6.94250605593439e-05 0.99996528746972 20 3.00677896348129e-05 6.01355792696258e-05 0.999969932210365 21 2.15063398392615e-05 4.3012679678523e-05 0.99997849366016 22 1.23888155216186e-05 2.47776310432371e-05 0.999987611184478 23 7.2218294242005e-06 1.4443658848401e-05 0.999992778170576 24 8.85877606338048e-06 1.77175521267610e-05 0.999991141223937 25 7.21077205415314e-06 1.44215441083063e-05 0.999992789227946 26 6.69174692914068e-06 1.33834938582814e-05 0.99999330825307 27 3.59543704523615e-05 7.1908740904723e-05 0.999964045629548 28 4.86885829250711e-05 9.73771658501422e-05 0.999951311417075 29 5.30009010148538e-05 0.000106001802029708 0.999946999098985 30 8.1378147219624e-05 0.000162756294439248 0.99991862185278 31 0.000104173795072864 0.000208347590145728 0.999895826204927 32 0.000168400107745713 0.000336800215491425 0.999831599892254 33 0.00131833722138291 0.00263667444276582 0.998681662778617 34 0.00195119171610915 0.00390238343221831 0.99804880828389 35 0.00320297784996423 0.00640595569992847 0.996797022150036 36 0.00659329310423774 0.0131865862084755 0.993406706895762 37 0.0108157530155644 0.0216315060311289 0.989184246984436 38 0.0179595380798310 0.0359190761596619 0.98204046192017 39 0.0340513720424962 0.0681027440849923 0.965948627957504 40 0.0545536815401675 0.109107363080335 0.945446318459833 41 0.0815741969518864 0.163148393903773 0.918425803048114 42 0.108854455028349 0.217708910056698 0.891145544971651 43 0.175572325330536 0.351144650661071 0.824427674669464 44 0.278937538551384 0.557875077102768 0.721062461448616 45 0.328889959667323 0.657779919334646 0.671110040332677 46 0.369052154995683 0.738104309991365 0.630947845004317 47 0.370662096800333 0.741324193600667 0.629337903199667 48 0.681475474922616 0.637049050154768 0.318524525077384 49 0.725146792120657 0.549706415758687 0.274853207879343 50 0.751815027791771 0.496369944416457 0.248184972208229 51 0.731596320558435 0.536807358883129 0.268403679441564 52 0.709787288299782 0.580425423400437 0.290212711700218 53 0.631844018744781 0.736311962510437 0.368155981255219 54 0.597656655850352 0.804686688299296 0.402343344149648 55 0.466446843894067 0.932893687788134 0.533553156105933 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 31 0.607843137254902 NOK 5% type I error level 34 0.666666666666667 NOK 10% type I error level 35 0.686274509803922 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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