Multiple Lineair Regression 1

*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, 12 Dec 2008 07:47:57 -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/12/t12290935513jyfq40kn4e9aku.htm/, Retrieved Fri, 12 Dec 2008 15:52:40 +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/2008/Dec/12/t12290935513jyfq40kn4e9aku.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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91.2 0 99.2 0 108.2 0 101.5 0 106.9 0 104.4 0 77.9 0 60 0 99.5 0 95 0 105.6 0 102.5 0 93.3 0 97.3 0 127 0 111.7 0 96.4 0 133 0 72.2 0 95.8 0 124.1 0 127.6 0 110.7 0 104.6 0 112.7 0 115.3 0 139.4 0 119 0 97.4 0 154 0 81.5 0 88.8 0 127.7 1 105.1 1 114.9 1 106.4 1 104.5 1 121.6 1 141.4 1 99 1 126.7 1 134.1 1 81.3 1 88.6 1 132.7 1 132.9 1 134.4 1 103.7 1 119.7 1 115 1 132.9 1 108.5 1 113.9 1 142 1 97.7 1 92.2 1 128.8 1 134.9 1 128.2 1 114.8 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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation transportmiddelen[t] = + 104.803125 + 12.4683035714286conjunctuur[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) 104.803125 3.206102 32.6886 0 0 conjunctuur 12.4683035714286 4.693252 2.6566 0.010177 0.005088 Multiple Linear Regression - Regression Statistics Multiple R 0.32936990584511 R-squared 0.108484534876417 Adjusted R-squared 0.0931135785811824 F-TEST (value) 7.05776093515095 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0101768945923602 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 18.1364496917106 Sum Squared Residuals 19077.9868303571 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 91.2 104.803125000000 -13.6031249999999 2 99.2 104.803125 -5.60312499999998 3 108.2 104.803125 3.396875 4 101.5 104.803125 -3.30312500000001 5 106.9 104.803125 2.096875 6 104.4 104.803125 -0.403125 7 77.9 104.803125 -26.903125 8 60 104.803125 -44.803125 9 99.5 104.803125 -5.30312500000001 10 95 104.803125 -9.803125 11 105.6 104.803125 0.796874999999988 12 102.5 104.803125 -2.30312500000001 13 93.3 104.803125 -11.503125 14 97.3 104.803125 -7.50312500000001 15 127 104.803125 22.196875 16 111.7 104.803125 6.896875 17 96.4 104.803125 -8.403125 18 133 104.803125 28.196875 19 72.2 104.803125 -32.603125 20 95.8 104.803125 -9.0031250 21 124.1 104.803125 19.296875 22 127.6 104.803125 22.796875 23 110.7 104.803125 5.896875 24 104.6 104.803125 -0.203125000000011 25 112.7 104.803125 7.896875 26 115.3 104.803125 10.496875 27 139.4 104.803125 34.596875 28 119 104.803125 14.196875 29 97.4 104.803125 -7.403125 30 154 104.803125 49.196875 31 81.5 104.803125 -23.303125 32 88.8 104.803125 -16.003125 33 127.7 117.271428571429 10.4285714285714 34 105.1 117.271428571429 -12.1714285714286 35 114.9 117.271428571429 -2.37142857142857 36 106.4 117.271428571429 -10.8714285714286 37 104.5 117.271428571429 -12.7714285714286 38 121.6 117.271428571429 4.32857142857142 39 141.4 117.271428571429 24.1285714285714 40 99 117.271428571429 -18.2714285714286 41 126.7 117.271428571429 9.42857142857143 42 134.1 117.271428571429 16.8285714285714 43 81.3 117.271428571429 -35.9714285714286 44 88.6 117.271428571429 -28.6714285714286 45 132.7 117.271428571429 15.4285714285714 46 132.9 117.271428571429 15.6285714285714 47 134.4 117.271428571429 17.1285714285714 48 103.7 117.271428571429 -13.5714285714286 49 119.7 117.271428571429 2.42857142857143 50 115 117.271428571429 -2.27142857142857 51 132.9 117.271428571429 15.6285714285714 52 108.5 117.271428571429 -8.77142857142857 53 113.9 117.271428571429 -3.37142857142857 54 142 117.271428571429 24.7285714285714 55 97.7 117.271428571429 -19.5714285714286 56 92.2 117.271428571429 -25.0714285714286 57 128.8 117.271428571429 11.5285714285714 58 134.9 117.271428571429 17.6285714285714 59 128.2 117.271428571429 10.9285714285714 60 114.8 117.271428571429 -2.47142857142858 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0864681851499541 0.172936370299908 0.913531814850046 6 0.0305315688352193 0.0610631376704386 0.96946843116478 7 0.145495917116075 0.29099183423215 0.854504082883925 8 0.593279009803058 0.813441980393885 0.406720990196942 9 0.484194169393849 0.968388338787698 0.515805830606151 10 0.377530879283842 0.755061758567685 0.622469120716158 11 0.310201211069927 0.620402422139855 0.689798788930073 12 0.235384159598903 0.470768319197805 0.764615840401097 13 0.173101699460701 0.346203398921401 0.8268983005393 14 0.120975545482612 0.241951090965225 0.879024454517388 15 0.243171738991683 0.486343477983367 0.756828261008317 16 0.207917816749665 0.41583563349933 0.792082183250335 17 0.157025900566992 0.314051801133985 0.842974099433008 18 0.306447196465831 0.612894392931662 0.693552803534169 19 0.473164295666108 0.946328591332215 0.526835704333892 20 0.417946560022385 0.83589312004477 0.582053439977615 21 0.451269993615424 0.902539987230848 0.548730006384576 22 0.50517444969984 0.98965110060032 0.49482555030016 23 0.438763540302504 0.877527080605009 0.561236459697496 24 0.369078883763133 0.738157767526265 0.630921116236868 25 0.312688988152641 0.625377976305283 0.687311011847359 26 0.266845844288737 0.533691688577473 0.733154155711263 27 0.426341686731123 0.852683373462245 0.573658313268877 28 0.391186992623366 0.782373985246732 0.608813007376634 29 0.333016188659558 0.666032377319116 0.666983811340442 30 0.828655686441014 0.342688627117972 0.171344313558986 31 0.81679603650052 0.366407926998961 0.183203963499481 32 0.77925817248307 0.441483655033861 0.220741827516930 33 0.730811728310268 0.538376543379463 0.269188271689732 34 0.70108676578975 0.5978264684205 0.29891323421025 35 0.631017402658805 0.737965194682391 0.368982597341195 36 0.578395708295505 0.84320858340899 0.421604291704495 37 0.532545276651478 0.934909446697043 0.467454723348522 38 0.461334874367819 0.922669748735638 0.538665125632181 39 0.518898250243879 0.962203499512241 0.481101749756121 40 0.515269687802493 0.969460624395014 0.484730312197507 41 0.453959463554674 0.907918927109349 0.546040536445326 42 0.437640153093296 0.875280306186593 0.562359846906704 43 0.675720160968142 0.648559678063715 0.324279839031858 44 0.810584414762741 0.378831170474518 0.189415585237259 45 0.785975101535987 0.428049796928026 0.214024898464013 46 0.76132974041394 0.47734051917212 0.23867025958606 47 0.750350198430034 0.499299603139932 0.249649801569966 48 0.723051049095489 0.553897901809022 0.276948950904511 49 0.627502998831565 0.74499400233687 0.372497001168435 50 0.523933030707078 0.952133938585844 0.476066969292922 51 0.478288653427017 0.956577306854034 0.521711346572983 52 0.389294707036798 0.778589414073595 0.610705292963202 53 0.279297949396222 0.558595898792444 0.720702050603778 54 0.335423214478039 0.670846428956077 0.664576785521962 55 0.336452200551578 0.672904401103155 0.663547799448422 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 0.0196078431372549 OK

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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