DSHW-WS7-MultRegr.1.1

*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 08:10:50 -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/t1258729916o5kc3yoyshho06s.htm/, Retrieved Fri, 20 Nov 2009 16:12:07 +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/t1258729916o5kc3yoyshho06s.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:

SDHW, DSHW

Dataseries X:

» Textbox « » Textfile « » CSV «

1.4 0.0 1.6 0.0 1.7 0.0 2.0 0.0 2.0 0.0 2.1 0.0 2.5 0.0 2.5 0.0 2.6 0.0 2.7 0.0 3.7 0.0 4.0 0.0 5.0 0.0 5.1 0.0 5.1 0.0 5.0 0.0 5.1 0.0 4.7 0.0 4.5 0.0 4.5 0.0 4.6 0.0 4.6 0.0 4.6 0.0 4.6 0.0 5.3 0.0 5.4 0.0 5.3 0.0 5.2 0.0 5.0 0.0 4.2 0.0 4.3 0.0 4.3 0.0 4.3 0.0 4.0 0.0 4.0 0.0 4.1 0.0 4.4 0.0 3.6 0.0 3.7 0.0 3.8 0.0 3.3 0.0 3.3 0.0 3.3 0.0 3.5 0.0 3.3 0.0 3.3 0.0 3.4 0.0 3.4 0.0 5.2 0.0 5.3 0.0 4.8 1.0 5.0 1.0 4.6 1.0 4.6 1.0 3.5 1.0 3.5 1.0

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation IndGez[t] = + 3.888 + 0.445333333333333InvlMex[t] + 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) 3.888 0.152006 25.5779 0 0 InvlMex 0.445333333333333 0.464388 0.959 0.341848 0.170924 Multiple Linear Regression - Regression Statistics Multiple R 0.129401971531008 R-squared 0.0167448702361117 Adjusted R-squared -0.00146355809284926 F-TEST (value) 0.919621942849324 F-TEST (DF numerator) 1 F-TEST (DF denominator) 54 p-value 0.341848401095354 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.07484825228127 Sum Squared Residuals 62.3861333333334 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.4 3.88800000000001 -2.48800000000001 2 1.6 3.888 -2.288 3 1.7 3.888 -2.188 4 2 3.888 -1.888 5 2 3.888 -1.888 6 2.1 3.888 -1.788 7 2.5 3.888 -1.388 8 2.5 3.888 -1.388 9 2.6 3.888 -1.288 10 2.7 3.888 -1.188 11 3.7 3.888 -0.188000000000000 12 4 3.888 0.112000000000000 13 5 3.888 1.112 14 5.1 3.888 1.212 15 5.1 3.888 1.212 16 5 3.888 1.112 17 5.1 3.888 1.212 18 4.7 3.888 0.812 19 4.5 3.888 0.612 20 4.5 3.888 0.612 21 4.6 3.888 0.712 22 4.6 3.888 0.712 23 4.6 3.888 0.712 24 4.6 3.888 0.712 25 5.3 3.888 1.412 26 5.4 3.888 1.512 27 5.3 3.888 1.412 28 5.2 3.888 1.312 29 5 3.888 1.112 30 4.2 3.888 0.312000000000000 31 4.3 3.888 0.412 32 4.3 3.888 0.412 33 4.3 3.888 0.412 34 4 3.888 0.112000000000000 35 4 3.888 0.112000000000000 36 4.1 3.888 0.212000000000000 37 4.4 3.888 0.512 38 3.6 3.888 -0.288 39 3.7 3.888 -0.188000000000000 40 3.8 3.888 -0.088 41 3.3 3.888 -0.588 42 3.3 3.888 -0.588 43 3.3 3.888 -0.588 44 3.5 3.888 -0.388 45 3.3 3.888 -0.588 46 3.3 3.888 -0.588 47 3.4 3.888 -0.488 48 3.4 3.888 -0.488 49 5.2 3.888 1.312 50 5.3 3.888 1.412 51 4.8 4.33333333333333 0.466666666666667 52 5 4.33333333333333 0.666666666666667 53 4.6 4.33333333333333 0.266666666666666 54 4.6 4.33333333333333 0.266666666666666 55 3.5 4.33333333333333 -0.833333333333333 56 3.5 4.33333333333333 -0.833333333333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0531614825683917 0.106322965136783 0.946838517431608 6 0.0340179229386192 0.0680358458772383 0.96598207706138 7 0.065145749164675 0.13029149832935 0.934854250835325 8 0.0787321990381323 0.157464398076265 0.921267800961868 9 0.101464159399684 0.202928318799369 0.898535840600316 10 0.138929554728951 0.277859109457902 0.861070445271049 11 0.515614509030399 0.968770981939202 0.484385490969601 12 0.796116551304522 0.407766897390956 0.203883448695478 13 0.981304427295635 0.0373911454087293 0.0186955727043646 14 0.997523649318341 0.00495270136331689 0.00247635068165845 15 0.999433913792708 0.00113217241458469 0.000566086207292343 16 0.999763728716736 0.000472542566527683 0.000236271283263841 17 0.999896028322868 0.000207943354264450 0.000103971677132225 18 0.99989051997234 0.000218960055320541 0.000109480027660271 19 0.999843420066473 0.000313159867053388 0.000156579933526694 20 0.999767504842402 0.000464990315196521 0.000232495157598261 21 0.999675799540066 0.000648400919868067 0.000324200459934034 22 0.999536224041603 0.000927551916793296 0.000463775958396648 23 0.999325710314888 0.00134857937022339 0.000674289685111693 24 0.999010943473412 0.00197811305317674 0.000989056526588368 25 0.999425966194234 0.00114806761153131 0.000574033805765657 26 0.999748231633685 0.000503536732629599 0.000251768366314800 27 0.999880992088473 0.000238015823054826 0.000119007911527413 28 0.999940593219228 0.00011881356154399 5.9406780771995e-05 29 0.999959991543742 8.00169125161963e-05 4.00084562580981e-05 30 0.99991401917257 0.000171961654860196 8.59808274300981e-05 31 0.999834862923994 0.000330274152012833 0.000165137076006416 32 0.999693869276004 0.00061226144799282 0.00030613072399641 33 0.999453044865891 0.00109391026821726 0.000546955134108631 34 0.99886639640023 0.00226720719953896 0.00113360359976948 35 0.997736950485337 0.00452609902932693 0.00226304951466347 36 0.995823587544636 0.00835282491072746 0.00417641245536373 37 0.99408914287491 0.0118217142501795 0.00591085712508976 38 0.989036179787007 0.0219276404259859 0.0109638202129930 39 0.98010838019563 0.0397832396087414 0.0198916198043707 40 0.96527542880099 0.0694491423980222 0.0347245711990111 41 0.948471931685561 0.103056136628877 0.0515280683144387 42 0.926524849347066 0.146950301305868 0.0734751506529342 43 0.899902494308544 0.200195011382913 0.100097505691456 44 0.856651700314054 0.286696599371891 0.143348299685946 45 0.825607787721135 0.348784424557730 0.174392212278865 46 0.81012690481337 0.37974619037326 0.18987309518663 47 0.819851019309718 0.360297961380564 0.180148980690282 48 0.93410214279811 0.131795714403781 0.0658978572018906 49 0.876772837529341 0.246454324941318 0.123227162470659 50 0.78102313247377 0.437953735052459 0.218976867526230 51 0.667658528021919 0.664682943956163 0.332341471978081 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 23 0.489361702127660 NOK 5% type I error level 27 0.574468085106383 NOK 10% type I error level 29 0.617021276595745 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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