*Unverified author*

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 06:54:15 -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/t12587252874811aocplxgnj9g.htm/, Retrieved Fri, 20 Nov 2009 14:54:59 +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/t12587252874811aocplxgnj9g.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 «

89.1 0 82.6 0 102.7 0 91.8 0 94.1 0 103.1 0 93.2 0 91 0 94.3 0 99.4 0 115.7 0 116.8 0 99.8 0 96 0 115.9 0 109.1 0 117.3 0 109.8 0 112.8 0 110.7 0 100 0 113.3 0 122.4 0 112.5 0 104.2 0 92.5 0 117.2 0 109.3 0 106.1 0 118.8 0 105.3 0 106 0 102 0 112.9 0 116.5 0 114.8 0 100.5 0 85.4 0 114.6 0 109.9 0 100.7 0 115.5 0 100.7 1 99 1 102.3 1 108.8 1 105.9 1 113.2 1 95.7 1 80.9 1 113.9 1 98.1 1 102.8 1 104.7 1 95.9 1 94.6 1 101.6 1 103.9 1 110.3 1 114.1 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation TotaleIndustrieleProductie[t] = + 109.712666666667 -11.4566666666667X[t] -15.9155000000001M1[t] -26.5496666666667M2[t] -1.42383333333331M3[t] -10.898M4[t] -10.5921666666666M5[t] -4.66633333333331M6[t] -11.4291666666667M7[t] -13.0033333333333M8[t] -13.4775000000000M9[t] -6.11166666666665M10[t] + 0.134166666666678M11[t] + 0.254166666666668t + 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) 109.712666666667 3.086156 35.5499 0 0 X -11.4566666666667 2.646357 -4.3292 8e-05 4e-05 M1 -15.9155000000001 3.582234 -4.4429 5.5e-05 2.8e-05 M2 -26.5496666666667 3.57612 -7.4242 0 0 M3 -1.42383333333331 3.571357 -0.3987 0.691973 0.345986 M4 -10.898 3.56795 -3.0544 0.003744 0.001872 M5 -10.5921666666666 3.565905 -2.9704 0.004715 0.002357 M6 -4.66633333333331 3.565223 -1.3088 0.197087 0.098544 M7 -11.4291666666667 3.567542 -3.2037 0.002465 0.001233 M8 -13.0033333333333 3.561402 -3.6512 0.000666 0.000333 M9 -13.4775000000000 3.556619 -3.7894 0.000437 0.000219 M10 -6.11166666666665 3.553199 -1.72 0.092146 0.046073 M11 0.134166666666678 3.551145 0.0378 0.970026 0.485013 t 0.254166666666668 0.069738 3.6446 0.000679 0.000339 Multiple Linear Regression - Regression Statistics Multiple R 0.857208457316521 R-squared 0.73480633929497 Adjusted R-squared 0.659860304747895 F-TEST (value) 9.80447256129922 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 2.42340281175757e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.6137708528587 Sum Squared Residuals 1449.66346666667 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 89.1 94.0513333333336 -4.95133333333362 2 82.6 83.6713333333333 -1.07133333333334 3 102.7 109.051333333333 -6.35133333333332 4 91.8 99.8313333333333 -8.0313333333333 5 94.1 100.391333333333 -6.29133333333332 6 103.1 106.571333333333 -3.4713333333333 7 93.2 100.062666666667 -6.86266666666668 8 91 98.7426666666667 -7.74266666666666 9 94.3 98.5226666666666 -4.22266666666664 10 99.4 106.142666666667 -6.74266666666664 11 115.7 112.642666666667 3.05733333333334 12 116.8 112.762666666667 4.03733333333336 13 99.8 97.1013333333333 2.69866666666675 14 96 86.7213333333333 9.27866666666669 15 115.9 112.101333333333 3.79866666666668 16 109.1 102.881333333333 6.21866666666667 17 117.3 103.441333333333 13.8586666666667 18 109.8 109.621333333333 0.178666666666672 19 112.8 103.112666666667 9.68733333333334 20 110.7 101.792666666667 8.90733333333335 21 100 101.572666666667 -1.57266666666666 22 113.3 109.192666666667 4.10733333333333 23 122.4 115.692666666667 6.70733333333334 24 112.5 115.812666666667 -3.31266666666665 25 104.2 100.151333333333 4.04866666666674 26 92.5 89.7713333333333 2.72866666666666 27 117.2 115.151333333333 2.04866666666666 28 109.3 105.931333333333 3.36866666666666 29 106.1 106.491333333333 -0.391333333333342 30 118.8 112.671333333333 6.12866666666666 31 105.3 106.162666666667 -0.862666666666674 32 106 104.842666666667 1.15733333333333 33 102 104.622666666667 -2.62266666666668 34 112.9 112.242666666667 0.657333333333323 35 116.5 118.742666666667 -2.24266666666668 36 114.8 118.862666666667 -4.06266666666667 37 100.5 103.201333333333 -2.70133333333328 38 85.4 92.8213333333334 -7.42133333333335 39 114.6 118.201333333333 -3.60133333333336 40 109.9 108.981333333333 0.918666666666654 41 100.7 109.541333333333 -8.84133333333335 42 115.5 115.721333333333 -0.221333333333357 43 100.7 97.756 2.94400000000001 44 99 96.436 2.56400000000001 45 102.3 96.216 6.084 46 108.8 103.836 4.96399999999999 47 105.9 110.336 -4.43599999999999 48 113.2 110.456 2.74400000000001 49 95.7 94.7946666666666 0.905333333333403 50 80.9 84.4146666666667 -3.51466666666666 51 113.9 109.794666666667 4.10533333333333 52 98.1 100.574666666667 -2.47466666666668 53 102.8 101.134666666667 1.66533333333333 54 104.7 107.314666666667 -2.61466666666667 55 95.9 100.806 -4.906 56 94.6 99.486 -4.88600000000002 57 101.6 99.266 2.33399999999998 58 103.9 106.886 -2.98600000000001 59 110.3 113.386 -3.08600000000001 60 114.1 113.506 0.593999999999992 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.654037143263733 0.691925713472535 0.345962856736267 18 0.797349290720702 0.405301418558595 0.202650709279297 19 0.79385254113572 0.412294917728559 0.206147458864279 20 0.776461723399421 0.447076553201157 0.223538276600579 21 0.906285040792449 0.187429918415102 0.093714959207551 22 0.850298051724517 0.299403896550965 0.149701948275483 23 0.893830019364036 0.212339961271927 0.106169980635964 24 0.994909372752204 0.0101812544955916 0.00509062724779578 25 0.994374679264144 0.0112506414717111 0.00562532073585553 26 0.9980879075216 0.00382418495680065 0.00191209247840032 27 0.996970850608534 0.00605829878293114 0.00302914939146557 28 0.994367058493369 0.0112658830132623 0.00563294150663116 29 0.99516645582047 0.00966708835906185 0.00483354417953092 30 0.993227845940574 0.0135443081188529 0.00677215405942646 31 0.99110282937804 0.0177943412439202 0.0088971706219601 32 0.98848855595336 0.0230228880932785 0.0115114440466393 33 0.988181466545673 0.0236370669086538 0.0118185334543269 34 0.977543587726243 0.0449128245475137 0.0224564122737569 35 0.977577219928843 0.0448455601423148 0.0224227800711574 36 0.974317220473345 0.0513655590533091 0.0256827795266546 37 0.956948688184412 0.0861026236311758 0.0430513118155879 38 0.947911687939157 0.104176624121687 0.0520883120608433 39 0.9326018127078 0.134796374584401 0.0673981872922007 40 0.91877926090023 0.162441478199540 0.0812207390997702 41 0.972245074980095 0.0555098500398108 0.0277549250199054 42 0.92665934132174 0.146681317356520 0.0733406586782598 43 0.861958948889852 0.276082102220296 0.138041051110148 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.111111111111111 NOK 5% type I error level 12 0.444444444444444 NOK 10% type I error level 15 0.555555555555556 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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Software written by Ed van Stee & Patrick Wessa

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