*Unverified author*

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 06:33:01 -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/t12277928152xlln9gs9n9p69g.htm/, Retrieved Thu, 27 Nov 2008 13:33:45 +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/t12277928152xlln9gs9n9p69g.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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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

kleuter

Dataseries X:

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104,3 0 119,8 0 116,8 0 118,2 0 107,4 0 110,8 0 94,8 0 96,5 0 113,4 0 109,8 0 118,7 0 117,2 0 110,3 0 111,6 0 128,1 0 121,3 0 107,3 0 120,5 0 98,5 0 97,7 0 113,2 0 114,6 0 118,3 0 123,9 0 113,6 0 117,5 0 130,1 0 124,7 0 114,2 0 127,3 0 105,9 0 101,5 0 120,2 0 117,1 0 131,1 0 130 0 120,6 0 123,1 0 135,3 0 134,1 0 123,7 0 134,6 0 108,3 1 110,4 1 127,8 1 126,6 1 131,4 1 141,1 1 127 1 127,3 1 143,6 1 149,4 1 126,6 1 136,5 1 116 1 118 1 131,4 1 140,7 1 144,9 1 143,9 1 127,1 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation x[t] = + 114.799616724739 + 2.59224738675958y[t] -11.7605884630275M1[t] -6.56836043360433M2[t] + 3.92432055749128M3[t] + 2.25700154858691M4[t] -11.8703174603174M5[t] -2.19763646922184M6[t] -24.3834049554781M7[t] -24.6907239643825M8[t] -8.73804297328687M9[t] -8.60536198219127M10[t] -1.91268099109563M11[t] + 0.427319008904374t + 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) 114.799616724739 1.883033 60.9653 0 0 y 2.59224738675958 1.625029 1.5952 0.117371 0.058685 M1 -11.7605884630275 2.092623 -5.62 1e-06 1e-06 M2 -6.56836043360433 2.195527 -2.9917 0.004408 0.002204 M3 3.92432055749128 2.192757 1.7897 0.07995 0.039975 M4 2.25700154858691 2.190805 1.0302 0.308181 0.154091 M5 -11.8703174603174 2.189676 -5.421 2e-06 1e-06 M6 -2.19763646922184 2.189369 -1.0038 0.320627 0.160313 M7 -24.3834049554781 2.190989 -11.1289 0 0 M8 -24.6907239643825 2.187284 -11.2883 0 0 M9 -8.73804297328687 2.184397 -4.0002 0.000223 0.000111 M10 -8.60536198219127 2.182333 -3.9432 0.000266 0.000133 M11 -1.91268099109563 2.181094 -0.8769 0.384982 0.192491 t 0.427319008904374 0.042458 10.0645 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.970185957751532 R-squared 0.941260792618257 Adjusted R-squared 0.92501377781054 F-TEST (value) 57.934383870397 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.44795854182024 Sum Squared Residuals 558.755650987225 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 104.3 103.466347270615 0.833652729384565 2 119.8 109.085894308943 10.7141056910569 3 116.8 120.005894308943 -3.20589430894311 4 118.2 118.765894308943 -0.565894308943107 5 107.4 105.065894308943 2.33410569105691 6 110.8 115.165894308943 -4.3658943089431 7 94.8 93.4074448315912 1.3925551684088 8 96.5 93.5274448315912 2.97255516840881 9 113.4 109.907444831591 3.49255516840883 10 109.8 110.467444831591 -0.6674448315912 11 118.7 117.587444831591 1.11255516840882 12 117.2 119.927444831591 -2.72744483159118 13 110.3 108.594175377468 1.7058246225319 14 111.6 114.213722415796 -2.61372241579561 15 128.1 125.133722415796 2.96627758420440 16 121.3 123.893722415796 -2.59372241579559 17 107.3 110.193722415796 -2.8937224157956 18 120.5 120.293722415796 0.206277584204412 19 98.5 98.5352729384437 -0.0352729384436661 20 97.7 98.6552729384437 -0.955272938443672 21 113.2 115.035272938444 -1.83527293844367 22 114.6 115.595272938444 -0.995272938443663 23 118.3 122.715272938444 -4.41527293844368 24 123.9 125.055272938444 -1.15527293844367 25 113.6 113.722003484321 -0.122003484320589 26 117.5 119.341550522648 -1.84155052264808 27 130.1 130.261550522648 -0.161550522648086 28 124.7 129.021550522648 -4.32155052264808 29 114.2 115.321550522648 -1.12155052264808 30 127.3 125.421550522648 1.87844947735192 31 105.9 103.663101045296 2.23689895470385 32 101.5 103.783101045296 -2.28310104529616 33 120.2 120.163101045296 0.0368989547038367 34 117.1 120.723101045296 -3.62310104529615 35 131.1 127.843101045296 3.25689895470383 36 130 130.183101045296 -0.183101045296158 37 120.6 118.849831591173 1.75016840882692 38 123.1 124.469378629501 -1.36937862950058 39 135.3 135.389378629501 -0.089378629500551 40 134.1 134.149378629501 -0.0493786295005712 41 123.7 120.449378629501 3.25062137049943 42 134.6 130.549378629501 4.05062137049943 43 108.3 111.383176538908 -3.08317653890825 44 110.4 111.503176538908 -1.10317653890824 45 127.8 127.883176538908 -0.0831765389082544 46 126.6 128.443176538908 -1.84317653890824 47 131.4 135.563176538908 -4.16317653890824 48 141.1 137.903176538908 3.19682346109174 49 127 126.569907084785 0.430092915214842 50 127.3 132.189454123113 -4.88945412311267 51 143.6 143.109454123113 0.490545876887339 52 149.4 141.869454123113 7.53054587688735 53 126.6 128.169454123113 -1.56945412311267 54 136.5 138.269454123113 -1.76945412311265 55 116 116.511004645761 -0.511004645760733 56 118 116.631004645761 1.36899535423927 57 131.4 133.011004645761 -1.61100464576074 58 140.7 133.571004645761 7.12899535423926 59 144.9 140.691004645761 4.20899535423927 60 143.9 143.031004645761 0.868995354239274 61 127.1 131.697735191638 -4.59773519163766 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.98265272004147 0.0346945599170585 0.0173472799585293 18 0.980678326740391 0.0386433465192176 0.0193216732596088 19 0.96042595393575 0.0791480921285006 0.0395740460642503 20 0.931671758525832 0.136656482948336 0.0683282414741679 21 0.89696314492517 0.206073710149660 0.103036855074830 22 0.840334609499383 0.319330781001234 0.159665390500617 23 0.804978975336592 0.390042049326816 0.195021024663408 24 0.751261996492935 0.497476007014131 0.248738003507065 25 0.678360691674782 0.643278616650436 0.321639308325218 26 0.624278471216273 0.751443057567454 0.375721528783727 27 0.555018144495557 0.889963711008886 0.444981855504443 28 0.552091629703333 0.895816740593333 0.447908370296667 29 0.462857633937679 0.925715267875358 0.537142366062321 30 0.485408917555307 0.970817835110614 0.514591082444693 31 0.457972761647405 0.91594552329481 0.542027238352595 32 0.380665734289095 0.76133146857819 0.619334265710905 33 0.292427029138627 0.584854058277255 0.707572970861372 34 0.322375318477102 0.644750636954204 0.677624681522898 35 0.339029931945942 0.678059863891885 0.660970068054058 36 0.289329123441000 0.578658246881999 0.710670876559 37 0.239825256128015 0.47965051225603 0.760174743871985 38 0.181680531531310 0.363361063062619 0.81831946846869 39 0.121884514916035 0.243769029832071 0.878115485083965 40 0.309363089725026 0.618726179450052 0.690636910274974 41 0.240324862678129 0.480649725356257 0.759675137321871 42 0.179154484401181 0.358308968802363 0.820845515598819 43 0.102193074118312 0.204386148236623 0.897806925881688 44 0.0516146736417748 0.103229347283550 0.948385326358225 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 2 0.0714285714285714 NOK 10% type I error level 3 0.107142857142857 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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