SHWWS7model1b

*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 09:18:59 -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/t1258647577stpo86r503zybfl.htm/, Retrieved Thu, 19 Nov 2009 17:19:48 +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/t1258647577stpo86r503zybfl.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 «

25,60 0 23,70 0 22,00 0 21,30 0 20,70 0 20,40 0 20,30 0 20,40 0 19,80 0 19,50 0 23,10 0 23,50 0 23,50 0 22,90 0 21,90 0 21,50 0 20,50 0 20,20 0 19,40 0 19,20 0 18,80 0 18,80 0 22,60 0 23,30 0 23,00 0 21,40 0 19,90 0 18,80 0 18,60 0 18,40 0 18,60 0 19,90 0 19,20 0 18,40 0 21,10 0 20,50 0 19,10 0 18,10 0 17,00 0 17,10 0 17,40 1 16,80 1 15,30 1 14,30 1 13,40 1 15,30 1 22,10 1 23,70 1 22,20 1 19,50 1 16,60 1 17,30 1 19,80 1 21,20 1 21,50 1 20,60 1 19,10 1 19,60 1 23,50 1 24,00 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 Y[t] = + 20.55 -1.39000000000000X[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) 20.55 0.390561 52.6166 0 0 X -1.39000000000000 0.676472 -2.0548 0.044414 0.022207 Multiple Linear Regression - Regression Statistics Multiple R 0.260491074856844 R-squared 0.0678556000800737 Adjusted R-squared 0.0517841449090405 F-TEST (value) 4.22211923923198 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0444142895959601 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.47012494448749 Sum Squared Residuals 353.888000000001 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25.6 20.5499999999999 5.05000000000007 2 23.7 20.55 3.15000000000000 3 22 20.55 1.45 4 21.3 20.55 0.75 5 20.7 20.55 0.149999999999998 6 20.4 20.55 -0.150000000000003 7 20.3 20.55 -0.250000000000001 8 20.4 20.55 -0.150000000000003 9 19.8 20.55 -0.750000000000001 10 19.5 20.55 -1.05000000000000 11 23.1 20.55 2.55 12 23.5 20.55 2.95 13 23.5 20.55 2.95 14 22.9 20.55 2.35000000000000 15 21.9 20.55 1.35000000000000 16 21.5 20.55 0.949999999999999 17 20.5 20.55 -0.0500000000000013 18 20.2 20.55 -0.350000000000002 19 19.4 20.55 -1.15000000000000 20 19.2 20.55 -1.35000000000000 21 18.8 20.55 -1.75 22 18.8 20.55 -1.75 23 22.6 20.55 2.05 24 23.3 20.55 2.75 25 23 20.55 2.45 26 21.4 20.55 0.849999999999997 27 19.9 20.55 -0.650000000000003 28 18.8 20.55 -1.75 29 18.6 20.55 -1.95 30 18.4 20.55 -2.15000000000000 31 18.6 20.55 -1.95 32 19.9 20.55 -0.650000000000003 33 19.2 20.55 -1.35000000000000 34 18.4 20.55 -2.15000000000000 35 21.1 20.55 0.55 36 20.5 20.55 -0.0500000000000013 37 19.1 20.55 -1.45 38 18.1 20.55 -2.45 39 17 20.55 -3.55 40 17.1 20.55 -3.45 41 17.4 19.16 -1.76 42 16.8 19.16 -2.36 43 15.3 19.16 -3.86 44 14.3 19.16 -4.86 45 13.4 19.16 -5.76 46 15.3 19.16 -3.86 47 22.1 19.16 2.94 48 23.7 19.16 4.54 49 22.2 19.16 3.04 50 19.5 19.16 0.34 51 16.6 19.16 -2.56 52 17.3 19.16 -1.86 53 19.8 19.16 0.640000000000001 54 21.2 19.16 2.04 55 21.5 19.16 2.34 56 20.6 19.16 1.44 57 19.1 19.16 -0.0599999999999986 58 19.6 19.16 0.440000000000001 59 23.5 19.16 4.34 60 24 19.16 4.84 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.550550632381411 0.898898735237178 0.449449367618589 6 0.491620940680111 0.983241881360223 0.508379059319889 7 0.421563703990961 0.843127407981922 0.578436296009039 8 0.338095116792878 0.676190233585756 0.661904883207122 9 0.292452149325845 0.584904298651691 0.707547850674155 10 0.258312812959611 0.516625625919222 0.741687187040389 11 0.223896359803290 0.447792719606579 0.77610364019671 12 0.212176531785646 0.424353063571293 0.787823468214354 13 0.198704602402846 0.397409204805692 0.801295397597154 14 0.161409928663144 0.322819857326288 0.838590071336856 15 0.114728768661619 0.229457537323239 0.88527123133838 16 0.0791835762820856 0.158367152564171 0.920816423717914 17 0.0595269909251739 0.119053981850348 0.940473009074826 18 0.0465307419901775 0.093061483980355 0.953469258009823 19 0.0452655481762238 0.0905310963524476 0.954734451823776 20 0.0445515897626246 0.0891031795252492 0.955448410237375 21 0.0479450681879375 0.095890136375875 0.952054931812063 22 0.0481020465801534 0.0962040931603068 0.951897953419847 23 0.0414400864009375 0.082880172801875 0.958559913599063 24 0.0471646418739981 0.0943292837479962 0.952835358126002 25 0.049961099366754 0.099922198733508 0.950038900633246 26 0.0374834853387862 0.0749669706775724 0.962516514661214 27 0.0288370432068362 0.0576740864136725 0.971162956793164 28 0.0281538593374076 0.0563077186748152 0.971846140662592 29 0.0278412607745475 0.055682521549095 0.972158739225452 30 0.0278946715343626 0.0557893430687253 0.972105328465637 31 0.0250316803488206 0.0500633606976412 0.97496831965118 32 0.0173594603777824 0.0347189207555648 0.982640539622218 33 0.0128255145434331 0.0256510290868662 0.987174485456567 34 0.0111658967202548 0.0223317934405095 0.988834103279745 35 0.00821084239954392 0.0164216847990878 0.991789157600456 36 0.00591375112570793 0.0118275022514159 0.994086248874292 37 0.00441207589121028 0.00882415178242056 0.99558792410879 38 0.0039460390483017 0.0078920780966034 0.996053960951698 39 0.00476291986913538 0.00952583973827076 0.995237080130865 40 0.00499077360163284 0.00998154720326568 0.995009226398367 41 0.00314931753327100 0.00629863506654200 0.996850682466729 42 0.00223319956213706 0.00446639912427413 0.997766800437863 43 0.00292795963116611 0.00585591926233222 0.997072040368834 44 0.00804358708321273 0.0160871741664255 0.991956412916787 45 0.0596046389833684 0.119209277966737 0.940395361016632 46 0.168980876766466 0.337961753532932 0.831019123233534 47 0.254201242860869 0.508402485721739 0.74579875713913 48 0.450509480745305 0.90101896149061 0.549490519254695 49 0.462015214637105 0.92403042927421 0.537984785362895 50 0.37198205049435 0.7439641009887 0.62801794950565 51 0.512891016395464 0.974217967209071 0.487108983604536 52 0.670607159440637 0.658785681118727 0.329392840559363 53 0.598276887041172 0.803446225917656 0.401723112958828 54 0.465940098504739 0.931880197009479 0.534059901495261 55 0.321629164976322 0.643258329952645 0.678370835023678 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.137254901960784 NOK 5% type I error level 13 0.254901960784314 NOK 10% type I error level 27 0.529411764705882 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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