BBWS-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: Mon, 23 Nov 2009 13:14:10 -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/23/t1259007294k4fz4t16lnyd1k7.htm/, Retrieved Mon, 23 Nov 2009 21:15:06 +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/23/t1259007294k4fz4t16lnyd1k7.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:

seizoenaliteit modeleren

Dataseries X:

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3922 8.1 3759 7.7 4138 7.5 4634 7.6 3996 7.8 4308 7.8 4143 7.8 4429 7.5 5219 7.5 4929 7.1 5755 7.5 5592 7.5 4163 7.6 4962 7.7 5208 7.7 4755 7.9 4491 8.1 5732 8.2 5731 8.2 5040 8.2 6102 7.9 4904 7.3 5369 6.9 5578 6.6 4619 6.7 4731 6.9 5011 7 5299 7.1 4146 7.2 4625 7.1 4736 6.9 4219 7 5116 6.8 4205 6.4 4121 6.7 5103 6.6 4300 6.4 4578 6.3 3809 6.2 5526 6.5 4247 6.8 3830 6.8 4394 6.4 4826 6.1 4409 5.8 4569 6.1 4106 7.2 4794 7.3 3914 6.9 3793 6.1 4405 5.8 4022 6.2 4100 7.1 4788 7.7 3163 7.9 3585 7.7 3903 7.4 4178 7.5 3863 8 4187 8.1

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Bouw[t] = + 4216.37859380438 + 115.570831883049Wman[t] -857.954333449357M1[t] -653.840167072746M2[t] -492.683083884441M3[t] -185.108666898712M4[t] -875.602749738948M5[t] -428.871249564914M6[t] -642.82558301427M7[t] -640.245666550643M8[t] -84.8200835363729M9[t] -454.505917159763M10[t] -412.622833275321M11[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) 4216.37859380438 988.032271 4.2675 9.5e-05 4.8e-05 Wman 115.570831883049 131.184677 0.881 0.382813 0.191406 M1 -857.954333449357 397.902828 -2.1562 0.036218 0.018109 M2 -653.840167072746 399.456804 -1.6368 0.108347 0.054173 M3 -492.683083884441 400.875991 -1.229 0.225184 0.112592 M4 -185.108666898712 398.317814 -0.4647 0.644273 0.322137 M5 -875.602749738948 398.464685 -2.1974 0.032953 0.016476 M6 -428.871249564914 399.706602 -1.073 0.288765 0.144383 M7 -642.82558301427 398.81005 -1.6119 0.113689 0.056844 M8 -640.245666550643 397.902828 -1.6091 0.114303 0.057151 M9 -84.8200835363729 398.188178 -0.213 0.832236 0.416118 M10 -454.505917159763 400.257328 -1.1355 0.261909 0.130955 M11 -412.622833275321 397.799014 -1.0373 0.30492 0.15246 Multiple Linear Regression - Regression Statistics Multiple R 0.441907959629601 R-squared 0.195282644783997 Adjusted R-squared -0.0101771054839188 F-TEST (value) 0.950466670622114 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.507315791219589 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 628.920742405079 Sum Squared Residuals 18590441.1106857 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3922 4294.54799860773 -372.547998607734 2 3759 4452.43383223112 -693.433832231117 3 4138 4590.47674904281 -452.476749042813 4 4634 4909.60824921685 -275.608249216847 5 3996 4242.22833275322 -246.228332753219 6 4308 4688.95983292725 -380.959832927254 7 4143 4475.0054994779 -332.005499477897 8 4429 4442.91416637661 -13.9141663766096 9 5219 4998.33974939088 220.660250609119 10 4929 4582.42558301427 346.574416985729 11 5755 4670.53699965193 1084.46300034807 12 5592 5083.15983292725 508.840167072747 13 4163 4236.7625826662 -73.7625826662007 14 4962 4452.43383223112 509.566167768883 15 5208 4613.59091541942 594.409084580578 16 4755 4944.27949878176 -189.279498781761 17 4491 4276.89958231813 214.100417681866 18 5732 4735.18816568047 996.811834319527 19 5731 4521.23383223112 1209.76616776888 20 5040 4523.81374869474 516.186251305256 21 6102 5044.5680821441 1057.4319178559 22 4904 4605.53974939088 298.460250609119 23 5369 4601.1945005221 767.805499477897 24 5578 4979.14608423251 598.853915767491 25 4619 4132.74883397146 486.251166028543 26 4731 4359.97716672468 371.022833275322 27 5011 4532.69133310129 478.308666898713 28 5299 4851.82283327532 447.177166724678 29 4146 4172.88583362339 -26.8858336233903 30 4625 4608.06025060912 16.9397493908805 31 4736 4370.99175078315 365.008249216846 32 4219 4385.12875043508 -166.128750435085 33 5116 4917.44016707275 198.559832927253 34 4205 4501.52600069614 -296.526000696136 35 4121 4578.08033414549 -457.080334145493 36 5103 4979.14608423251 123.853915767491 37 4300 4098.07758440654 201.922415593458 38 4578 4290.63466759485 287.365332405151 39 3809 4440.23466759485 -631.234667594848 40 5526 4782.48033414549 743.519665854508 41 4247 4126.65750087017 120.342499129829 42 3830 4573.38900104420 -743.389001044205 43 4394 4313.20633484163 80.7936651583706 44 4826 4281.11500174034 544.884998259659 45 4409 4801.8693351897 -392.869335189698 46 4569 4466.85475113122 102.145248868778 47 4106 4635.86575008702 -529.865750087017 48 4794 5060.04566655064 -266.045666550643 49 3914 4155.86300034807 -241.863000348066 50 3793 4267.52050121824 -474.520501218239 51 4405 4394.00633484163 10.9936651583711 52 4022 4747.80908458058 -725.809084580578 53 4100 4161.32875043509 -61.3287504350853 54 4788 4677.40274973895 110.597250261051 55 3163 4486.5625826662 -1323.56258266620 56 3585 4466.02833275322 -881.02833275322 57 3903 4986.78266620258 -1083.78266620258 58 4178 4628.65391576749 -450.65391576749 59 3863 4728.32241559346 -865.322415593456 60 4187 5152.50233205708 -965.502332057083 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.565706868449081 0.868586263101838 0.434293131550919 17 0.410928882732691 0.821857765465382 0.589071117267309 18 0.457274421776229 0.914548843552458 0.542725578223771 19 0.524720107956398 0.950559784087203 0.475279892043602 20 0.467581503592027 0.935163007184055 0.532418496407973 21 0.528912872198566 0.942174255602868 0.471087127801434 22 0.464466474268928 0.928932948537856 0.535533525731072 23 0.494348272399964 0.98869654479993 0.505651727600036 24 0.557791357083775 0.88441728583245 0.442208642916225 25 0.697770583923264 0.604458832153472 0.302229416076736 26 0.684932248337868 0.630135503324264 0.315067751662132 27 0.740901936861212 0.518196126277577 0.259098063138788 28 0.760702023300128 0.478595953399745 0.239297976699872 29 0.677813067423983 0.644373865152034 0.322186932576017 30 0.60178077145969 0.796438457080619 0.398219228540309 31 0.598155800432275 0.80368839913545 0.401844199567725 32 0.515267302102748 0.969465395794504 0.484732697897252 33 0.586943325417405 0.82611334916519 0.413056674582595 34 0.529962442119704 0.940075115760593 0.470037557880296 35 0.579474802443565 0.841050395112869 0.420525197556435 36 0.486796196949236 0.973592393898473 0.513203803050764 37 0.398289376004189 0.796578752008379 0.601710623995811 38 0.395775593460887 0.791551186921775 0.604224406539112 39 0.340411922840675 0.68082384568135 0.659588077159325 40 0.714298337086806 0.571403325826389 0.285701662913194 41 0.594877347431877 0.810245305136247 0.405122652568123 42 0.949347960649416 0.101304078701169 0.0506520393505844 43 0.93783819023559 0.124323619528820 0.0621618097644102 44 0.974563611740079 0.0508727765198416 0.0254363882599208 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 0 0 OK 10% type I error level 1 0.0344827586206897 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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