*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: Fri, 20 Nov 2009 06:55:17 -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/20/t1258726471y7zvnaruaeii9nc.htm/, Retrieved Fri, 20 Nov 2009 15:14:43 +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/20/t1258726471y7zvnaruaeii9nc.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 «

111.4 91,2 111.5 92,2 111.6 93,2 111.7 94,2 111.8 95,2 111.9 96,2 111.10 97,2 111.11 98,2 111.12 99,2 111.13 100,2 111.14 101,2 111.15 102,2 111.16 103,2 111.17 104,2 111.18 105,2 111.19 106,2 111.20 107,2 111.21 108,2 111.22 109,2 111.23 110,2 111.24 111,2 111.25 112,2 111.26 113,2 111.27 114,2 111.28 115,2 111.29 116,2 111.30 117,2 111.31 118,2 111.32 119,2 111.33 120,2 111.34 121,2 111.35 122,2 111.36 123,2 111.37 124,2 111.38 125,2 111.39 126,2 111.40 127,2 111.41 128,2 111.42 129,2 111.43 130,2 111.44 131,2 111.45 132,2 111.46 133,2 111.47 134,2 111.48 135,2 111.49 136,2 111.50 137,2 111.51 138,2 111.52 139,2 111.53 140,2 111.54 141,2 111.55 142,2 111.56 143,2 111.57 144,2 111.58 145,2 111.59 146,2 111.60 147,2 111.61 148,2 111.62 149,2 111.63 150,2 111.64 151,2

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation biti[t] = + 110.794104706504 + 0.00497884717080904`Bosnië`[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) 110.794104706504 0.14278 775.9753 0 0 `Bosnië` 0.00497884717080904 0.001166 4.2707 7.2e-05 3.6e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.485936988710422 R-squared 0.236134756996953 Adjusted R-squared 0.223187888471478 F-TEST (value) 18.2387545322110 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 7.18542786055654e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.160316037791106 Sum Squared Residuals 1.51637268640932 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 111.4 111.248175568482 0.151824431517746 2 111.5 111.253154415653 0.246845584346904 3 111.6 111.258133262824 0.341866737176090 4 111.7 111.263112109995 0.436887890005289 5 111.8 111.268090957166 0.531909042834474 6 111.9 111.273069804336 0.626930195663674 7 111.1 111.278048651507 -0.178048651507147 8 111.11 111.283027498678 -0.173027498677951 9 111.12 111.288006345849 -0.168006345848754 10 111.13 111.292985193020 -0.162985193019573 11 111.14 111.297964040190 -0.157964040190376 12 111.15 111.302942887361 -0.152942887361180 13 111.16 111.307921734532 -0.147921734531999 14 111.17 111.312900581703 -0.142900581702802 15 111.18 111.317879428874 -0.137879428873606 16 111.19 111.322858276044 -0.132858276044425 17 111.2 111.327837123215 -0.127837123215228 18 111.21 111.332815970386 -0.122815970386047 19 111.22 111.337794817557 -0.117794817556851 20 111.23 111.342773664728 -0.112773664727654 21 111.24 111.347752511898 -0.107752511898473 22 111.25 111.352731359069 -0.102731359069276 23 111.26 111.35771020624 -0.0977102062400804 24 111.27 111.362689053411 -0.0926890534108986 25 111.28 111.367667900582 -0.0876679005817025 26 111.29 111.372646747753 -0.0826467477525064 27 111.3 111.377625594923 -0.0776255949233245 28 111.31 111.382604442094 -0.0726044420941285 29 111.32 111.387583289265 -0.0675832892649466 30 111.33 111.392562136436 -0.0625621364357505 31 111.34 111.397540983607 -0.0575409836065544 32 111.35 111.402519830777 -0.0525198307773726 33 111.36 111.407498677948 -0.0474986779481765 34 111.37 111.412477525119 -0.0424775251189804 35 111.38 111.417456372290 -0.0374563722897986 36 111.39 111.422435219461 -0.0324352194606025 37 111.4 111.427414066631 -0.0274140666314064 38 111.41 111.432392913802 -0.0223929138022245 39 111.42 111.437371760973 -0.0173717609730284 40 111.43 111.442350608144 -0.0123506081438323 41 111.44 111.447329455315 -0.00732945531465045 42 111.45 111.452308302485 -0.00230830248545437 43 111.46 111.457287149656 0.00271285034372749 44 111.47 111.462265996827 0.00773400317292357 45 111.48 111.467244843998 0.0127551560021196 46 111.49 111.472223691169 0.0177763088313015 47 111.5 111.477202538339 0.0227974616604976 48 111.51 111.482181385510 0.0278186144896937 49 111.52 111.487160232681 0.0328397673188755 50 111.53 111.492139079852 0.0378609201480716 51 111.54 111.497117927023 0.0428820729772677 52 111.55 111.502096774194 0.0479032258064496 53 111.56 111.507075621364 0.0529243786356456 54 111.57 111.512054468535 0.0579455314648275 55 111.58 111.517033315706 0.0629666842940236 56 111.59 111.522012162877 0.0679878371232197 57 111.6 111.526991010048 0.0730089899524015 58 111.61 111.531969857218 0.0780301427815976 59 111.62 111.536948704389 0.0830512956107937 60 111.63 111.54192755156 0.0880724484399755 61 111.64 111.546906398731 0.0930936012691716 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 5.74174410334181e-41 1.14834882066836e-40 1 6 0.66891206270431 0.66217587459138 0.33108793729569 7 1 0 0 8 1 0 0 9 1 0 0 10 1 0 0 11 1 0 0 12 1 0 0 13 1 0 0 14 1 0 0 15 1 0 0 16 1 0 0 17 1 0 0 18 1 0 0 19 1 0 0 20 1 0 0 21 1 0 0 22 1 0 0 23 1 0 0 24 1 0 0 25 1 0 0 26 1 0 0 27 1 0 0 28 1 0 0 29 1 0 0 30 1 0 0 31 1 0 0 32 1 0 0 33 1 6.91691904177745e-322 3.45845952088873e-322 34 1 2.71821852281784e-315 1.35910926140892e-315 35 1 3.75371227743421e-313 1.87685613871710e-313 36 1 3.05674766522315e-309 1.52837383261157e-309 37 1 1.98484004503375e-276 9.92420022516877e-277 38 1 7.03931875902687e-275 3.51965937951344e-275 39 1 1.58155063731923e-252 7.90775318659615e-253 40 1 5.7884942588019e-244 2.89424712940095e-244 41 1 2.83615019628197e-225 1.41807509814098e-225 42 1 5.28442217127445e-215 2.64221108563722e-215 43 1 7.88947414431829e-205 3.94473707215914e-205 44 1 1.23957622093428e-200 6.19788110467141e-201 45 1 3.61618661672094e-180 1.80809330836047e-180 46 1 2.62996980084302e-173 1.31498490042151e-173 47 1 6.30056044728085e-153 3.15028022364042e-153 48 1 9.86266938694187e-146 4.93133469347094e-146 49 1 5.92107724989251e-126 2.96053862494625e-126 50 1 1.88498303179141e-117 9.42491515895704e-118 51 1 3.40285618524393e-103 1.70142809262197e-103 52 1 7.07212172074543e-90 3.53606086037271e-90 53 1 9.84622237139753e-79 4.92311118569876e-79 54 1 4.33427280348829e-65 2.16713640174415e-65 55 1 2.13440006054049e-51 1.06720003027024e-51 56 1 8.26119226757836e-41 4.13059613378918e-41 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 51 0.98076923076923 NOK 5% type I error level 51 0.98076923076923 NOK 10% type I error level 51 0.98076923076923 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Omvatten niet seizoensgebonden Dummies ; par3 = Geen lineaire trend ;

Parameters (R input):

par1 = 1 ; par2 = Omvatten niet seizoensgebonden Dummies ; par3 = Geen lineaire 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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Software written by Ed van Stee & Patrick Wessa

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