*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 06:35:13 -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/t1258724199e7wrt13al51a1z5.htm/, Retrieved Fri, 20 Nov 2009 14:36:51 +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/t1258724199e7wrt13al51a1z5.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:

ws72lags

Dataseries X:

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7,70 110,30 8,10 8,00 7,50 103,90 7,70 8,10 7,60 101,60 7,50 7,70 7,80 94,60 7,60 7,50 7,80 95,90 7,80 7,60 7,80 104,70 7,80 7,80 7,50 102,80 7,80 7,80 7,50 98,10 7,50 7,80 7,10 113,90 7,50 7,50 7,50 80,90 7,10 7,50 7,50 95,70 7,50 7,10 7,60 113,20 7,50 7,50 7,70 105,90 7,60 7,50 7,70 108,80 7,70 7,60 7,90 102,30 7,70 7,70 8,10 99,00 7,90 7,70 8,20 100,70 8,10 7,90 8,20 115,50 8,20 8,10 8,20 100,70 8,20 8,20 7,90 109,90 8,20 8,20 7,30 114,60 7,90 8,20 6,90 85,40 7,30 7,90 6,60 100,50 6,90 7,30 6,70 114,80 6,60 6,90 6,90 116,50 6,70 6,60 7,00 112,90 6,90 6,70 7,10 102,00 7,00 6,90 7,20 106,00 7,10 7,00 7,10 105,30 7,20 7,10 6,90 118,80 7,10 7,20 7,00 106,10 6,90 7,10 6,80 109,30 7,00 6,90 6,40 117,20 6,80 7,00 6,70 92,50 6,40 6,80 6,60 104,20 6,70 6,40 6,40 112,50 6,60 6,70 6,30 122,40 6,40 6,60 6,20 113,30 6,30 6,40 6,50 100,00 6,20 6,30 6,80 110,70 6,50 6,20 6,80 112,80 6,80 6,50 6,40 109,80 6,80 6,80 6,10 117,30 6,40 6,80 5,80 109,10 6,10 6,40 6,10 115,90 5,80 6,1 etc...

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 Y[t] = + 4.07580781441513 -0.0165836837962970X[t] + 1.37883885721972Y1[t] -0.67582544891961Y2[t] -0.0963430856947516M1[t] -0.0639092820674027M2[t] + 0.0374513471373744M3[t] + 0.0151821678867695M4[t] -0.1580414784M5[t] -0.0227755674317749M6[t] -0.0688470670504502M7[t] -0.154153022084673M8[t] + 0.0124870320512885M9[t] + 0.10368881377741M10[t] -0.481693411399994M11[t] -0.00500950379451003t + 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) 4.07580781441513 1.004399 4.058 0.000211 0.000105 X -0.0165836837962970 0.005499 -3.0157 0.004338 0.002169 Y1 1.37883885721972 0.112875 12.2156 0 0 Y2 -0.67582544891961 0.120155 -5.6246 1e-06 1e-06 M1 -0.0963430856947516 0.145639 -0.6615 0.511891 0.255946 M2 -0.0639092820674027 0.151328 -0.4223 0.674943 0.337471 M3 0.0374513471373744 0.16916 0.2214 0.825857 0.412929 M4 0.0151821678867695 0.170499 0.089 0.929469 0.464735 M5 -0.1580414784 0.16587 -0.9528 0.346141 0.173071 M6 -0.0227755674317749 0.149099 -0.1528 0.879323 0.439661 M7 -0.0688470670504502 0.153843 -0.4475 0.656804 0.328402 M8 -0.154153022084673 0.154904 -0.9952 0.325361 0.162681 M9 0.0124870320512885 0.147277 0.0848 0.932834 0.466417 M10 0.10368881377741 0.207027 0.5008 0.619094 0.309547 M11 -0.481693411399994 0.1816 -2.6525 0.011227 0.005614 t -0.00500950379451003 0.002393 -2.0934 0.042392 0.021196 Multiple Linear Regression - Regression Statistics Multiple R 0.957899251774148 R-squared 0.917570976549472 Adjusted R-squared 0.888132039602854 F-TEST (value) 31.168617882274 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.216671744732013 Sum Squared Residuals 1.97175908853902 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.7 7.9072660543172 -0.2072660543172 2 7.5 7.42170784266648 0.0782921573335173 3 7.6 7.55076384893213 0.0492361510678705 4 7.8 7.91261992796699 -0.112619927966989 5 7.8 7.92101321550251 -0.121013215502508 6 7.8 7.77016811548489 0.0298318845151131 7 7.5 7.75059611128467 -0.250596111284665 8 7.5 7.32457230913261 0.175427690867388 9 7.1 7.42692829016845 -0.326928290168453 10 7.5 7.50884659048998 -0.00884659048997798 11 7.5 7.4948820637886 0.00511793621139902 12 7.6 7.41102132539104 0.188978674608957 13 7.7 7.56861351333672 0.131386486663279 14 7.7 7.61824647099031 0.0817535290096892 15 7.9 7.75480899618455 0.145191003815453 16 8.1 8.05802424111116 0.041975758888842 17 8.2 7.9922015102362 0.207798489763805 18 8.2 7.87973819316276 0.320261806837236 19 8.2 8.00651316504281 0.193486834957186 20 7.9 7.76362781528815 0.136372184711853 21 7.3 7.43366339462109 -0.133663394621088 22 6.9 7.37954355974862 -0.479543559748621 23 6.6 6.3926979319165 0.2073020680835 24 6.7 6.48891368363686 0.211086316363139 25 6.9 6.70000035209175 0.199999647908249 26 7 6.99531114014324 0.00468885985675709 27 7.1 7.2751432148712 -0.175143214871198 28 7.2 7.25183113747091 -0.0518311374709055 29 7.1 7.15550790687705 -0.0555079068770469 30 6.9 6.85641815218682 0.0435818478131835 31 7 6.80776470643462 0.192235293565378 32 6.8 6.93743043496363 -0.137430434963631 33 6.4 6.62469956697843 -0.224699566978430 34 6.7 6.70413838157461 -0.00413838157461365 35 6.6 6.60369938891978 -0.00369938891978386 36 6.4 6.60210720061815 -0.202107200618146 37 6.3 6.12839091499356 0.171609085006438 38 6.2 6.30400794143465 -0.104007941434652 39 6.5 6.55062072050566 -0.05062072050566 40 6.8 6.82713082289804 -0.0271308228980438 41 6.8 6.82497595933457 -0.0249759593345744 42 6.4 6.8022357832213 -0.402235783221297 43 6.1 6.075241608448 0.0247583915520039 44 5.8 5.97759087915082 -0.177590879150825 45 6.1 5.81554835718742 0.284451642812577 46 7.2 6.84815523450715 0.351844765492855 47 7.3 7.50872061537512 -0.208720615375115 48 6.9 7.09795779035395 -0.197957790353950 49 6.1 6.39572916526077 -0.295729165260766 50 5.8 5.86072660476531 -0.0607266047653117 51 6.2 6.16866321950647 0.0313367804935349 52 7.1 6.9503938705529 0.149606129447097 53 7.7 7.70630140804968 -0.00630140804967544 54 7.9 7.89143975594424 0.0085602440557647 55 7.7 7.8598844087899 -0.159884408789902 56 7.4 7.39677856146479 0.00322143853521490 57 7.5 7.0991603910446 0.400839608955395 58 8 7.85931623367964 0.140683766320358 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.0424755472764217 0.0849510945528435 0.957524452723578 20 0.0219340250221237 0.0438680500442474 0.978065974977876 21 0.0455672978408001 0.0911345956816001 0.9544327021592 22 0.577244839484812 0.845510321030375 0.422755160515188 23 0.533683814102491 0.932632371795019 0.466316185897509 24 0.495500108273779 0.991000216547559 0.50449989172622 25 0.430509381573113 0.861018763146225 0.569490618426887 26 0.398872056180462 0.797744112360923 0.601127943819538 27 0.483755945161994 0.967511890323987 0.516244054838006 28 0.376110260487611 0.752220520975222 0.623889739512389 29 0.29315326143582 0.58630652287164 0.70684673856418 30 0.296210666717372 0.592421333434745 0.703789333282628 31 0.355043625524472 0.710087251048945 0.644956374475528 32 0.321178918837646 0.642357837675292 0.678821081162354 33 0.405420146281623 0.810840292563247 0.594579853718377 34 0.394869308148510 0.789738616297019 0.605130691851490 35 0.384746075411139 0.769492150822277 0.615253924588861 36 0.375468091705598 0.750936183411197 0.624531908294402 37 0.737898998386726 0.524202003226547 0.262101001613274 38 0.61562251239832 0.76875497520336 0.38437748760168 39 0.546782161056871 0.906435677886259 0.453217838943129 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 1 0.0476190476190476 OK 10% type I error level 3 0.142857142857143 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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