model 4

*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: Thu, 19 Nov 2009 01:47:36 -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/19/t1258620525uiydyy9ld26l6kb.htm/, Retrieved Thu, 19 Nov 2009 09:48:58 +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/19/t1258620525uiydyy9ld26l6kb.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:

» Textbox « » Textfile « » CSV «

127 0 130 135 139 149 122 0 127 130 135 139 117 0 122 127 130 135 112 0 117 122 127 130 113 0 112 117 122 127 149 0 113 112 117 122 157 0 149 113 112 117 157 0 157 149 113 112 147 0 157 157 149 113 137 0 147 157 157 149 132 0 137 147 157 157 125 0 132 137 147 157 123 0 125 132 137 147 117 0 123 125 132 137 114 0 117 123 125 132 111 0 114 117 123 125 112 0 111 114 117 123 144 0 112 111 114 117 150 0 144 112 111 114 149 0 150 144 112 111 134 0 149 150 144 112 123 0 134 149 150 144 116 0 123 134 149 150 117 0 116 123 134 149 111 0 117 116 123 134 105 0 111 117 116 123 102 0 105 111 117 116 95 0 102 105 111 117 93 0 95 102 105 111 124 0 93 95 102 105 130 0 124 93 95 102 124 0 130 124 93 95 115 0 124 130 124 93 106 0 115 124 130 124 105 0 106 115 124 130 105 0 105 106 115 124 101 0 105 105 106 115 95 0 101 105 105 106 93 0 95 101 105 105 84 0 93 95 101 105 87 0 84 93 95 101 116 0 87 84 93 95 120 0 116 87 84 93 117 1 120 116 87 84 109 1 117 120 116 87 105 1 109 117 120 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 WLH[t] = + 28.0537721653424 + 4.5783344490655X[t] + 0.89389373351237`Y(t-1)`[t] + 0.269258267201097`Y(t-2)`[t] -0.239285433868153`Y(t-3)`[t] -0.102477680079240`Y(t-4)`[t] -4.41387550198146M1[t] -7.48459972952515M2[t] -5.74169225100387M3[t] -9.06607666309207M4[t] -2.46464716599568M5[t] + 28.2278520152218M6[t] + 4.32563125183533M7[t] -12.8925239435589M8[t] -15.4919697862306M9[t] -9.03535197334436M10[t] -1.16080135981364M11[t] -0.182589577259004t + 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) 28.0537721653424 8.902464 3.1512 0.003166 0.001583 X 4.5783344490655 1.277807 3.583 0.000952 0.000476 `Y(t-1)` 0.89389373351237 0.149715 5.9706 1e-06 0 `Y(t-2)` 0.269258267201097 0.202592 1.3291 0.191751 0.095876 `Y(t-3)` -0.239285433868153 0.206193 -1.1605 0.253087 0.126543 `Y(t-4)` -0.102477680079240 0.15661 -0.6544 0.516827 0.258413 M1 -4.41387550198146 1.710078 -2.5811 0.013833 0.006917 M2 -7.48459972952515 2.199846 -3.4023 0.001586 0.000793 M3 -5.74169225100387 2.412995 -2.3795 0.022461 0.011231 M4 -9.06607666309207 2.203365 -4.1147 0.000201 1e-04 M5 -2.46464716599568 2.424432 -1.0166 0.315779 0.157889 M6 28.2278520152218 2.263018 12.4735 0 0 M7 4.32563125183533 4.875251 0.8873 0.380519 0.190259 M8 -12.8925239435589 5.422589 -2.3776 0.022564 0.011282 M9 -15.4919697862306 6.683822 -2.3178 0.02594 0.01297 M10 -9.03535197334436 3.373712 -2.6782 0.010875 0.005437 M11 -1.16080135981364 2.258899 -0.5139 0.610312 0.305156 t -0.182589577259004 0.053886 -3.3884 0.001649 0.000825 Multiple Linear Regression - Regression Statistics Multiple R 0.99431080101004 R-squared 0.988653969005226 Adjusted R-squared 0.98357811303388 F-TEST (value) 194.775812116472 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.23576648500679 Sum Squared Residuals 189.948767468226 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 127 127.483508875378 -0.483508875378087 2 122 122.184141070298 -0.184141070297849 3 117 120.073553392053 -3.07355339205266 4 112 111.981064101139 0.0189358988611628 5 113 114.088004226987 -1.08800422698736 6 149 145.854331798190 3.14566820181027 7 157 155.927769700928 1.07223029907242 8 157 155.644575382141 1.35542461785918 9 147 146.299852800486 0.70014719951383 10 137 138.031463747192 -1.03146374719181 11 132 133.272083335695 -1.27208333569496 12 125 129.481098117358 -4.4810981173583 13 123 120.698716707000 2.30128329300029 14 117 115.994011534898 1.00598846510224 15 114 113.839836938157 0.160163061843093 16 111 107.231546773357 3.768453226643 17 112 111.801598654421 0.198401345578616 18 144 143.730349572369 0.269650427631110 19 150 149.544686313162 0.455313686837538 20 149 146.191716098388 2.80828390161191 21 134 136.371724984291 -2.37172498429149 22 123 124.253090584287 -1.25309058428748 23 116 117.697765897299 -1.69776589729938 24 117 113.148639794157 3.85136020584309 25 111 111.730565551759 -0.730565551759419 26 105 106.185400131032 -1.18540013103232 27 102 101.244864354700 0.755135645299677 28 95 94.7738944847391 0.226105515260888 29 93 96.178282152071 -3.17828215207097 30 124 124.348318800677 -0.348318800676983 31 130 129.418128741828 0.581871258172482 32 124 126.923667281773 -2.92366728177347 33 115 113.180925974221 1.81907402577911 34 106 105.181840319365 0.818159680635145 35 105 103.226279871949 1.77372012805115 36 105 103.65570850147 1.34429149852994 37 101 101.865853180555 -0.865853180555036 38 95 96.1985489962842 -1.19854899628418 39 93 91.420949107747 1.57905089225291 40 84 85.4677797836412 -1.46777978364118 41 87 85.148682890991 1.85131710900907 42 116 117.010386238888 -1.01038623888843 43 120 122.014793236677 -2.01479323667678 44 117 120.780890415079 -3.780890415079 45 109 109.147496241001 -0.147496241001446 46 105 103.533605349156 1.46639465084415 47 107 105.803870895057 1.19612910494319 48 109 109.714553587015 -0.714553587014742 49 109 109.221355685308 -0.221355685307748 50 108 106.437898267488 1.5621017325121 51 107 106.420796207343 0.579203792656976 52 99 101.545714857124 -2.54571485712387 53 103 100.783432075529 2.21656792447064 54 131 133.056613589876 -2.05661358987597 55 137 137.094622007406 -0.0946220074056544 56 135 132.459150822619 2.54084917738138 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.858978567074072 0.282042865851856 0.141021432925928 22 0.748910600734388 0.502178798531224 0.251089399265612 23 0.795026493359863 0.409947013280273 0.204973506640137 24 0.905465966812411 0.189068066375178 0.094534033187589 25 0.90324433443906 0.193511331121879 0.0967556655609394 26 0.872399980906038 0.255200038187924 0.127600019093962 27 0.834075310273311 0.331849379453378 0.165924689726689 28 0.855784004972193 0.288431990055613 0.144215995027807 29 0.910307441243277 0.179385117513447 0.0896925587567233 30 0.946557047745036 0.106885904509928 0.0534429522549638 31 0.954534962440294 0.0909300751194115 0.0454650375597057 32 0.94161311948581 0.116773761028379 0.0583868805141893 33 0.948020736681656 0.103958526636688 0.0519792633183439 34 0.896484029189595 0.20703194162081 0.103515970810405 35 0.854737349677325 0.290525300645350 0.145262650322675 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 0.0666666666666667 OK

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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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