tinneke_debock.workshop3.Q3.2

*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: Thu, 27 Nov 2008 01:57:07 -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/Nov/27/t1227776421v3dn6intbgrjh7w.htm/, Retrieved Thu, 27 Nov 2008 09:00:21 +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/Nov/27/t1227776421v3dn6intbgrjh7w.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}, }

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Dataseries X:

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71.7 0 77.5 0 89.8 0 80.3 0 78.7 0 93.8 0 57.6 0 60.6 0 91 0 85.3 0 77.4 0 77.3 0 68.3 0 69.9 0 81.7 0 75.1 0 69.9 0 84 0 54.3 0 60 0 89.9 0 77 0 85.3 0 77.6 0 69.2 0 75.5 0 85.7 0 72.2 0 79.9 0 85.3 0 52.2 0 61.2 0 82.4 0 85.4 0 78.2 0 70.2 1 70.2 1 69.3 1 77.5 1 66.1 1 69 1 79.2 1 56.2 1 63.3 1 77.8 1 92 1 78.1 1 65.1 1 71.1 1 70.9 1 72 1 81.9 1 70.6 1 72.5 1 65.1 1 61.1 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 75.7532769556025 -0.730373502466528x[t] -2.99605238430819M1[t] -0.381449377495886M2[t] + 8.43315362931643M3[t] + 2.30775663612873M4[t] + 0.902359642941043M5[t] + 10.3369626497534M6[t] -15.4484343434343M7[t] -11.1938313366220M8[t] + 12.2585976039464M9[t] + 12.0032006107588M10[t] + 6.92280361757106M11[t] -0.0946030068123091t + 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) 75.7532769556025 2.911389 26.0196 0 0 x -0.730373502466528 2.682994 -0.2722 0.786784 0.393392 M1 -2.99605238430819 3.397212 -0.8819 0.382842 0.191421 M2 -0.381449377495886 3.394088 -0.1124 0.911052 0.455526 M3 8.43315362931643 3.392854 2.4856 0.017 0.0085 M4 2.30775663612873 3.393513 0.68 0.500205 0.250102 M5 0.902359642941043 3.396064 0.2657 0.791764 0.395882 M6 10.3369626497534 3.400503 3.0398 0.004064 0.002032 M7 -15.4484343434343 3.406822 -4.5346 4.8e-05 2.4e-05 M8 -11.1938313366220 3.415011 -3.2778 0.002105 0.001052 M9 12.2585976039464 3.605765 3.3997 0.001489 0.000745 M10 12.0032006107588 3.613987 3.3213 0.001862 0.000931 M11 6.92280361757106 3.623963 1.9103 0.06294 0.03147 t -0.0946030068123091 0.080148 -1.1804 0.244499 0.122249 Multiple Linear Regression - Regression Statistics Multiple R 0.894983517526208 R-squared 0.800995496643584 Adjusted R-squared 0.739398864652312 F-TEST (value) 13.0038846402688 F-TEST (DF numerator) 13 F-TEST (DF denominator) 42 p-value 8.41903213810724e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.05336804766105 Sum Squared Residuals 1072.53420225511 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 71.7 72.662621564482 -0.962621564482007 2 77.5 75.182621564482 2.31737843551797 3 89.8 83.902621564482 5.89737843551797 4 80.3 77.682621564482 2.61737843551797 5 78.7 76.182621564482 2.51737843551797 6 93.8 85.522621564482 8.27737843551797 7 57.6 59.642621564482 -2.04262156448203 8 60.6 63.802621564482 -3.20262156448203 9 91 87.1604474982382 3.8395525017618 10 85.3 86.8104474982382 -1.51044749823820 11 77.4 81.6354474982382 -4.23544749823819 12 77.3 74.6180408738548 2.68195912614517 13 68.3 71.5273854827343 -3.22738548273433 14 69.9 74.0473854827343 -4.14738548273432 15 81.7 82.7673854827343 -1.06738548273432 16 75.1 76.5473854827343 -1.44738548273433 17 69.9 75.0473854827343 -5.14738548273432 18 84 84.3873854827343 -0.387385482734323 19 54.3 58.5073854827343 -4.20738548273432 20 60 62.6673854827343 -2.66738548273432 21 89.9 86.0252114164905 3.87478858350952 22 77 85.6752114164905 -8.67521141649049 23 85.3 80.5002114164905 4.79978858350951 24 77.6 73.4828047921071 4.11719520789288 25 69.2 70.3921494009866 -1.19214940098661 26 75.5 72.9121494009866 2.58785059901339 27 85.7 81.6321494009866 4.06785059901339 28 72.2 75.4121494009866 -3.21214940098661 29 79.9 73.9121494009866 5.98785059901339 30 85.3 83.2521494009866 2.04785059901338 31 52.2 57.3721494009866 -5.17214940098661 32 61.2 61.5321494009866 -0.332149400986608 33 82.4 84.8899753347428 -2.48997533474277 34 85.4 84.5399753347428 0.860024665257231 35 78.2 79.3649753347428 -1.16497533474278 36 70.2 71.6171952078929 -1.41719520789287 37 70.2 68.5265398167724 1.67346018322762 38 69.3 71.0465398167724 -1.74653981677238 39 77.5 79.7665398167724 -2.26653981677237 40 66.1 73.5465398167724 -7.44653981677238 41 69 72.0465398167724 -3.04653981677237 42 79.2 81.3865398167724 -2.18653981677237 43 56.2 55.5065398167724 0.693460183227629 44 63.3 59.6665398167724 3.63346018322762 45 77.8 83.0243657505285 -5.22436575052854 46 92 82.6743657505286 9.32563424947145 47 78.1 77.4993657505285 0.600634249471452 48 65.1 70.4819591261452 -5.38195912614518 49 71.1 67.3913037350247 3.70869626497533 50 70.9 69.9113037350247 0.98869626497534 51 72 78.6313037350247 -6.63130373502467 52 81.9 72.4113037350247 9.48869626497534 53 70.6 70.9113037350247 -0.311303735024671 54 72.5 80.2513037350247 -7.75130373502466 55 65.1 54.3713037350247 10.7286962649753 56 61.1 58.5313037350247 2.56869626497534 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0475836760179097 0.0951673520358193 0.95241632398209 18 0.0243849350988834 0.0487698701977668 0.975615064901117 19 0.0162362978337845 0.0324725956675690 0.983763702166216 20 0.0221843981228946 0.0443687962457892 0.977815601877105 21 0.0204244132296193 0.0408488264592385 0.97957558677038 22 0.0182766841764268 0.0365533683528536 0.981723315823573 23 0.161500444401927 0.323000888803853 0.838499555598073 24 0.144278429396362 0.288556858792724 0.855721570603638 25 0.121122122420703 0.242244244841406 0.878877877579297 26 0.118325398769585 0.236650797539171 0.881674601230415 27 0.122830900059573 0.245661800119146 0.877169099940427 28 0.081990162157897 0.163980324315794 0.918009837842103 29 0.166730796488720 0.333461592977439 0.83326920351128 30 0.223339553171987 0.446679106343975 0.776660446828013 31 0.199836446525087 0.399672893050175 0.800163553474913 32 0.143881216276784 0.287762432553568 0.856118783723216 33 0.144981043856615 0.28996208771323 0.855018956143385 34 0.143412458842267 0.286824917684534 0.856587541157733 35 0.0863598802684038 0.172719760536808 0.913640119731596 36 0.0673625427646534 0.134725085529307 0.932637457235347 37 0.0463047715723972 0.0926095431447943 0.953695228427603 38 0.0216374066011634 0.0432748132023268 0.978362593398837 39 0.0202840060210348 0.0405680120420697 0.979715993978965 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 7 0.304347826086957 NOK 10% type I error level 9 0.391304347826087 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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