Multiplelineairregression3

*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: Wed, 18 Nov 2009 09:10:40 -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/18/t1258560709pr2y7x1g1cjk061.htm/, Retrieved Wed, 18 Nov 2009 17:12:01 +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/18/t1258560709pr2y7x1g1cjk061.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:

Dataseries X:

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17823.2 0 17872 0 17420.4 0 16704.4 0 15991.2 0 16583.6 0 19123.5 0 17838.7 0 17209.4 0 18586.5 0 16258.1 0 15141.6 0 19202.1 0 17746.5 0 19090.1 0 18040.3 0 17515.5 0 17751.8 0 21072.4 0 17170 0 19439.5 0 19795.4 0 17574.9 0 16165.4 0 19464.6 0 19932.1 0 19961.2 0 17343.4 0 18924.2 0 18574.1 0 21350.6 0 18594.6 0 19823.1 0 20844.4 0 19640.2 0 17735.4 0 19813.6 0 22160 0 20664.3 0 17877.4 0 20906.5 0 21164.1 0 21374.4 0 22952.3 0 21343.5 0 23899.3 0 22392.9 0 18274.1 0 22786.7 0 22321.5 0 17842.2 1 16373.5 1 15993.8 1 16446.1 1 17729 1 16643 1 16196.7 1 18252.1 1 17570.4 1 15836.8 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation uitvoer[t] = + 13885.4782857143 -5222.53071428571dummy[t] + 3300.83403571430M1[t] + 3383.94492857143M2[t] + 3312.40196428572M3[t] + 1479.29285714285M4[t] + 1972.46375000000M5[t] + 2104.89464285714M6[t] + 4025.66553571428M7[t] + 2430.13642857143M8[t] + 2487.58732142857M9[t] + 3855.41821428571M10[t] + 2161.90910714286M11[t] + 105.269107142857t + 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) 13885.4782857143 459.748416 30.2023 0 0 dummy -5222.53071428571 392.312604 -13.3122 0 0 M1 3300.83403571430 540.98956 6.1015 0 0 M2 3383.94492857143 540.396536 6.262 0 0 M3 3312.40196428572 541.358225 6.1187 0 0 M4 1479.29285714285 540.238286 2.7382 0.008756 0.004378 M5 1972.46375000000 539.248173 3.6578 0.000652 0.000326 M6 2104.89464285714 538.388602 3.9096 0.000302 0.000151 M7 4025.66553571428 537.6602 7.4874 0 0 M8 2430.13642857143 537.063499 4.5249 4.2e-05 2.1e-05 M9 2487.58732142857 536.59894 4.6358 3e-05 1.5e-05 M10 3855.41821428571 536.266865 7.1894 0 0 M11 2161.90910714286 536.067522 4.0329 0.000206 0.000103 t 105.269107142857 8.441223 12.4708 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.932532816632137 R-squared 0.869617454095868 Adjusted R-squared 0.832770212862091 F-TEST (value) 23.6006122840676 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 4.44089209850063e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 847.492085553841 Sum Squared Residuals 33039170.4135144 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 17823.2 17291.5814285714 531.618571428623 2 17872 17479.9614285714 392.038571428562 3 17420.4 17513.6875714286 -93.287571428569 4 16704.4 15785.8475714286 918.552428571425 5 15991.2 16384.2875714286 -393.087571428578 6 16583.6 16621.9875714286 -38.3875714285738 7 19123.5 18648.0275714286 475.472428571427 8 17838.7 17157.7675714286 680.932428571427 9 17209.4 17320.4875714286 -111.087571428570 10 18586.5 18793.5875714286 -207.087571428575 11 16258.1 17205.3475714286 -947.247571428577 12 15141.6 15148.7075714286 -7.10757142857226 13 19202.1 18554.8107142857 647.289285714269 14 17746.5 18743.1907142857 -996.690714285716 15 19090.1 18776.9168571429 313.183142857139 16 18040.3 17049.0768571429 991.22314285714 17 17515.5 17647.5168571429 -132.016857142857 18 17751.8 17885.2168571429 -133.416857142858 19 21072.4 19911.2568571429 1161.14314285714 20 17170 18420.9968571429 -1250.99685714286 21 19439.5 18583.7168571429 855.783142857141 22 19795.4 20056.8168571429 -261.416857142857 23 17574.9 18468.5768571429 -893.676857142858 24 16165.4 16411.9368571429 -246.536857142859 25 19464.6 19818.04 -353.440000000014 26 19932.1 20006.42 -74.3199999999989 27 19961.2 20040.1461428571 -78.9461428571426 28 17343.4 18312.3061428571 -968.906142857141 29 18924.2 18910.7461428571 13.4538571428598 30 18574.1 19148.4461428571 -574.346142857143 31 21350.6 21174.4861428571 176.113857142855 32 18594.6 19684.2261428571 -1089.62614285714 33 19823.1 19846.9461428571 -23.8461428571441 34 20844.4 21320.0461428571 -475.646142857141 35 19640.2 19731.8061428571 -91.606142857142 36 17735.4 17675.1661428571 60.233857142859 37 19813.6 21081.2692857143 -1267.66928571430 38 22160 21269.6492857143 890.350714285718 39 20664.3 21303.3754285714 -639.075428571428 40 17877.4 19575.5354285714 -1698.13542857142 41 20906.5 20173.9754285714 732.524571428576 42 21164.1 20411.6754285714 752.424571428574 43 21374.4 22437.7154285714 -1063.31542857142 44 22952.3 20947.4554285714 2004.84457142857 45 21343.5 21110.1754285714 233.324571428574 46 23899.3 22583.2754285714 1316.02457142857 47 22392.9 20995.0354285714 1397.86457142857 48 18274.1 18938.3954285714 -664.295428571428 49 22786.7 22344.4985714286 442.201428571421 50 22321.5 22532.8785714286 -211.378571428566 51 17842.2 17344.074 498.126 52 16373.5 15616.234 757.266 53 15993.8 16214.674 -220.873999999998 54 16446.1 16452.374 -6.27399999999999 55 17729 18478.414 -749.414 56 16643 16988.154 -345.154 57 16196.7 17150.874 -954.174 58 18252.1 18623.974 -371.874000000001 59 17570.4 17035.734 534.666000000001 60 15836.8 14979.094 857.706 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.263978226984574 0.527956453969148 0.736021773015426 18 0.130170854301685 0.260341708603369 0.869829145698315 19 0.120962216140878 0.241924432281755 0.879037783859122 20 0.307166303240842 0.614332606481684 0.692833696759158 21 0.343955574412707 0.687911148825414 0.656044425587293 22 0.236692948738663 0.473385897477326 0.763307051261337 23 0.167070463452561 0.334140926905121 0.832929536547439 24 0.104590270935149 0.209180541870299 0.89540972906485 25 0.0855582692634885 0.171116538526977 0.914441730736511 26 0.0571023601980193 0.114204720396039 0.94289763980198 27 0.0324893425166943 0.0649786850333886 0.967510657483306 28 0.066664048310132 0.133328096620264 0.933335951689868 29 0.0470669607733143 0.0941339215466286 0.952933039226686 30 0.0279640412501427 0.0559280825002854 0.972035958749857 31 0.0249083341640035 0.0498166683280071 0.975091665835996 32 0.0224489060758926 0.0448978121517853 0.977551093924107 33 0.0136674374803500 0.0273348749606999 0.98633256251965 34 0.00740607119974195 0.0148121423994839 0.992593928800258 35 0.00903411893295755 0.0180682378659151 0.990965881067043 36 0.00490164241674041 0.00980328483348083 0.99509835758326 37 0.0107791622217323 0.0215583244434646 0.989220837778268 38 0.0141818039287866 0.0283636078575731 0.985818196071213 39 0.0118860294186950 0.0237720588373901 0.988113970581305 40 0.138737756053352 0.277475512106704 0.861262243946648 41 0.111307123704572 0.222614247409144 0.888692876295428 42 0.079021168107202 0.158042336214404 0.920978831892798 43 0.070990839699788 0.141981679399576 0.929009160300212 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0370370370370370 NOK 5% type I error level 9 0.333333333333333 NOK 10% type I error level 12 0.444444444444444 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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