ws 8

*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: Tue, 30 Nov 2010 13:11:23 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s.htm/, Retrieved Tue, 30 Nov 2010 14:09:34 +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/2010/Nov/30/t12911225740oeucqvloxsu15s.htm/}, year = {2010}, } @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 = {2010}, 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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101.76 102.37 102.38 102.86 102.87 102.92 102.95 103.02 104.08 104.16 104.24 104.33 104.73 104.86 105.03 105.62 105.63 105.63 105.94 106.61 107.69 107.78 107.93 108.48 108.14 108.48 108.48 108.89 108.93 109.21 109.47 109.80 111.73 111.85 112.12 112.15 112.17 112.67 112.80 113.44 113.53 114.53 114.51 115.05 116.67 117.07 116.92 117.00 117.02 117.35 117.36 117.82 117.88 118.24 118.50 118.80 119.76 120.09

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 vrijetijdsbesteding[t] = + 100.676931818182 -0.0904886363636757M1[t] -0.0355909090909093M2[t] -0.298693181818184M3[t] -0.109795454545457M4[t] -0.394897727272728M5[t] -0.384000000000005M6[t] -0.543102272727275M7[t] -0.488204545454551M8[t] + 0.514693181818181M9[t] + 0.391590909090904M10[t] + 0.139602272727273M11[t] + 0.327102272727273t + 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) 100.676931818182 0.337006 298.7392 0 0 M1 -0.0904886363636757 0.40885 -0.2213 0.825841 0.41292 M2 -0.0355909090909093 0.408592 -0.0871 0.930974 0.465487 M3 -0.298693181818184 0.408392 -0.7314 0.468334 0.234167 M4 -0.109795454545457 0.408249 -0.2689 0.789203 0.394602 M5 -0.394897727272728 0.408163 -0.9675 0.338466 0.169233 M6 -0.384000000000005 0.408135 -0.9409 0.351797 0.175899 M7 -0.543102272727275 0.408163 -1.3306 0.190024 0.095012 M8 -0.488204545454551 0.408249 -1.1958 0.238019 0.119009 M9 0.514693181818181 0.408392 1.2603 0.214061 0.10703 M10 0.391590909090904 0.408592 0.9584 0.342987 0.171494 M11 0.139602272727273 0.430239 0.3245 0.747081 0.373541 t 0.327102272727273 0.004834 67.665 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.995287469888219 R-squared 0.990597147716492 Adjusted R-squared 0.98808972044089 F-TEST (value) 395.065155968917 F-TEST (DF numerator) 12 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.608411215437963 Sum Squared Residuals 16.6573893181815 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.76 100.913545454546 0.8464545454544 2 102.37 101.295545454545 1.07445454545456 3 102.38 101.359545454545 1.02045454545455 4 102.86 101.875545454545 0.984454545454554 5 102.87 101.917545454545 0.952454545454556 6 102.92 102.255545454545 0.664454545454556 7 102.95 102.423545454545 0.526454545454552 8 103.02 102.805545454545 0.214454545454550 9 104.08 104.135545454545 -0.0555454545454519 10 104.16 104.339545454545 -0.179545454545448 11 104.24 104.414659090909 -0.174659090909094 12 104.33 104.602159090909 -0.272159090909090 13 104.73 104.838772727273 -0.108772727272686 14 104.86 105.220772727273 -0.360772727272726 15 105.03 105.284772727273 -0.254772727272721 16 105.62 105.800772727273 -0.180772727272719 17 105.63 105.842772727273 -0.212772727272730 18 105.63 106.180772727273 -0.550772727272726 19 105.94 106.348772727273 -0.408772727272727 20 106.61 106.730772727273 -0.120772727272722 21 107.69 108.060772727273 -0.370772727272728 22 107.78 108.264772727273 -0.484772727272721 23 107.93 108.339886363636 -0.409886363636357 24 108.48 108.527386363636 -0.0473863636363603 25 108.14 108.764 -0.623999999999961 26 108.48 109.146 -0.665999999999997 27 108.48 109.21 -0.729999999999996 28 108.89 109.726 -0.836 29 108.93 109.768 -0.837999999999994 30 109.21 110.106 -0.896000000000003 31 109.47 110.274 -0.804000000000001 32 109.8 110.656 -0.856 33 111.73 111.986 -0.255999999999998 34 111.85 112.19 -0.340000000000003 35 112.12 112.265113636364 -0.145113636363636 36 112.15 112.452613636364 -0.302613636363634 37 112.17 112.689227272727 -0.519227272727236 38 112.67 113.071227272727 -0.401227272727275 39 112.8 113.135227272727 -0.335227272727279 40 113.44 113.651227272727 -0.211227272727276 41 113.53 113.693227272727 -0.163227272727276 42 114.53 114.031227272727 0.498772727272728 43 114.51 114.199227272727 0.31077272727273 44 115.05 114.581227272727 0.468772727272723 45 116.67 115.911227272727 0.758772727272726 46 117.07 116.115227272727 0.954772727272719 47 116.92 116.190340909091 0.729659090909087 48 117 116.377840909091 0.622159090909084 49 117.02 116.614454545455 0.405545454545484 50 117.35 116.996454545455 0.353545454545441 51 117.36 117.060454545455 0.299545454545449 52 117.82 117.576454545455 0.243545454545441 53 117.88 117.618454545455 0.261545454545443 54 118.24 117.956454545455 0.283545454545445 55 118.5 118.124454545455 0.375545454545446 56 118.8 118.506454545455 0.293545454545448 57 119.76 119.836454545455 -0.0764545454545479 58 120.09 120.040454545455 0.0495454545454534 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0577063209451337 0.115412641890267 0.942293679054866 17 0.019739302720929 0.039478605441858 0.98026069727907 18 0.00535063146476295 0.0107012629295259 0.994649368535237 19 0.00426899606102586 0.00853799212205172 0.995731003938974 20 0.101377248225139 0.202754496450278 0.898622751774861 21 0.193496468950704 0.386992937901409 0.806503531049296 22 0.23564473531261 0.47128947062522 0.76435526468739 23 0.260027382888729 0.520054765777459 0.73997261711127 24 0.459618447572013 0.919236895144027 0.540381552427987 25 0.364204097994080 0.728408195988161 0.63579590200592 26 0.272759828499019 0.545519656998037 0.727240171500981 27 0.192915890128645 0.38583178025729 0.807084109871355 28 0.133282101613712 0.266564203227424 0.866717898386288 29 0.087544386586833 0.175088773173666 0.912455613413167 30 0.0735845586927203 0.147169117385441 0.92641544130728 31 0.0612717359939966 0.122543471987993 0.938728264006003 32 0.0618462774547846 0.123692554909569 0.938153722545215 33 0.124886854057839 0.249773708115677 0.875113145942161 34 0.191697033206658 0.383394066413315 0.808302966793342 35 0.293236428130620 0.586472856261239 0.70676357186938 36 0.347076714499657 0.694153428999314 0.652923285500343 37 0.415023206029050 0.830046412058099 0.58497679397095 38 0.481716329291994 0.963432658583987 0.518283670708006 39 0.554444443730949 0.891111112538102 0.445555556269051 40 0.612593154997251 0.774813690005497 0.387406845002749 41 0.743354509673895 0.51329098065221 0.256645490326105 42 0.698178696460079 0.603642607079842 0.301821303539921 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.037037037037037 NOK 5% type I error level 3 0.111111111111111 NOK 10% type I error level 3 0.111111111111111 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/104cxt1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/104cxt1291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/1xtih1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/1xtih1291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/2xtih1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/2xtih1291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/38l0k1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/38l0k1291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/48l0k1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/48l0k1291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/58l0k1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/58l0k1291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/61uh51291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/61uh51291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/7tlgp1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/7tlgp1291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/8tlgp1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/8tlgp1291122665.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/9tlgp1291122665.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911225740oeucqvloxsu15s/9tlgp1291122665.ps (open in new window)

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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