cs.shw.ws7.v3

*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, 26 Nov 2009 09:20:28 -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/26/t1259252642jazkfz9jzntunrn.htm/, Retrieved Thu, 26 Nov 2009 17:24:14 +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/26/t1259252642jazkfz9jzntunrn.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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8.9 1.9 9 1.6 9 1.7 9 2 9 2.5 9 2.4 9 2.3 9 2.3 9 2.1 9 2.4 9 2.2 9.1 2.4 9 1.9 9 2.1 9.1 2.1 9 2.1 9 2 9 2.1 9 2.2 8.9 2.2 8.9 2.6 8.9 2.5 8.9 2.3 8.8 2.2 8.8 2.4 8.7 2.3 8.7 2.2 8.5 2.5 8.5 2.5 8.4 2.5 8.2 2.4 8.2 2.3 8.1 1.7 8.1 1.6 8 1.9 7.9 1.9 7.8 1.8 7.7 1.8 7.6 1.9 7.5 1.9 7.5 1.9 7.5 1.9 7.5 1.8 7.5 1.7 7.4 2.1 7.4 2.6 7.3 3.1 7.3 3.1 7.3 3.2 7.2 3.3 7.2 3.6 7.3 3.3 7.4 3.7 7.4 4 7.5 4 7.6 3.8 7.7 3.6 7.9 3.2 8 2.1 8.2 1.6

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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation werkl[t] = + 9.30898187654872 + 0.018081433726898`infl `[t] -0.0354262196972614t + 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) 9.30898187654872 0.16128 57.7194 0 0 `infl ` 0.018081433726898 0.075323 0.2401 0.811151 0.405576 t -0.0354262196972614 0.002712 -13.0645 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.89249899629478 R-squared 0.796554458387191 Adjusted R-squared 0.7894160183306 F-TEST (value) 111.586628461194 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.315235831018274 Sum Squared Residuals 5.66429686199357 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.9 9.30791038093262 -0.407910380932623 2 9 9.26705973111724 -0.267059731117243 3 9 9.23344165479267 -0.233441654792672 4 9 9.20343986521348 -0.203439865213480 5 9 9.17705436237967 -0.177054362379668 6 9 9.13981999930972 -0.139819999309717 7 9 9.10258563623977 -0.102585636239765 8 9 9.0671594165425 -0.067159416542504 9 9 9.02811691009986 -0.0281169100998631 10 9 8.99811512052067 0.00188487947932885 11 9 8.95907261407803 0.0409273859219698 12 9.1 8.92726268112615 0.172737318873851 13 9 8.88279574456544 0.117204255434562 14 9 8.85098581161356 0.149014188386444 15 9.1 8.8155595919163 0.284440408083705 16 9 8.78013337221903 0.219866627780966 17 9 8.74289900914908 0.257100990850918 18 9 8.70928093282451 0.290719067175489 19 9 8.67566285649994 0.324337143500061 20 8.9 8.64023663680268 0.259763363197323 21 8.9 8.61204299059618 0.287957009403825 22 8.9 8.57480862752622 0.325191372473776 23 8.9 8.53576612108358 0.364233878916417 24 8.8 8.49853175801363 0.301468241986368 25 8.8 8.46672182506175 0.33327817493825 26 8.7 8.4294874619918 0.2705125380082 27 8.7 8.39225309892185 0.307746901078151 28 8.5 8.36225130934266 0.137748690657344 29 8.5 8.3268250896454 0.173174910354605 30 8.4 8.29139886994813 0.108601130051867 31 8.2 8.25416450687818 -0.054164506878183 32 8.2 8.21693014380823 -0.0169301438082319 33 8.1 8.17065506387483 -0.0706550638748311 34 8.1 8.13342070080488 -0.0334207008048802 35 8 8.10341891122569 -0.103418911225688 36 7.9 8.06799269152843 -0.167992691528426 37 7.8 8.03075832845848 -0.230758328458476 38 7.7 7.99533210876121 -0.295332108761214 39 7.6 7.96171403243664 -0.361714032436643 40 7.5 7.92628781273938 -0.426287812739381 41 7.5 7.89086159304212 -0.390861593042119 42 7.5 7.85543537334486 -0.355435373344858 43 7.5 7.8182010102749 -0.318201010274907 44 7.5 7.78096664720496 -0.280966647204956 45 7.4 7.75277300099845 -0.352773000998453 46 7.4 7.72638749816464 -0.326387498164641 47 7.3 7.70000199533083 -0.400001995330829 48 7.3 7.66457577563357 -0.364575775633568 49 7.3 7.630957699309 -0.330957699308996 50 7.2 7.59733962298442 -0.397339622984424 51 7.2 7.56733783340523 -0.367337833405232 52 7.3 7.5264871835899 -0.226487183589902 53 7.4 7.4982935373834 -0.0982935373833993 54 7.4 7.46829174780421 -0.0682917478042073 55 7.5 7.43286552810695 0.0671344718930538 56 7.6 7.3938230216643 0.206176978335694 57 7.7 7.35478051522166 0.345219484778336 58 7.9 7.31212172203364 0.587878277966357 59 8 7.25680592523679 0.743194074763206 60 8.2 7.21233898867608 0.987661011323915 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.000510078478959477 0.00102015695791895 0.99948992152104 7 0.000150511101582926 0.000301022203165853 0.999849488898417 8 2.66622389606095e-05 5.3324477921219e-05 0.99997333776104 9 4.36128812915743e-06 8.72257625831486e-06 0.999995638711871 10 4.71056185983211e-07 9.42112371966423e-07 0.999999528943814 11 5.13396596182943e-08 1.02679319236589e-07 0.99999994866034 12 4.16627613406895e-08 8.3325522681379e-08 0.999999958337239 13 8.50687574708849e-09 1.70137514941770e-08 0.999999991493124 14 1.26366856588611e-09 2.52733713177223e-09 0.999999998736331 15 4.63497506359284e-10 9.26995012718568e-10 0.999999999536503 16 1.08181197321542e-10 2.16362394643084e-10 0.999999999891819 17 1.92097831773501e-11 3.84195663547003e-11 0.99999999998079 18 3.23484864250228e-12 6.46969728500455e-12 0.999999999996765 19 5.48681577793259e-13 1.09736315558652e-12 0.999999999999451 20 3.11520516714971e-12 6.23041033429941e-12 0.999999999996885 21 4.15847588525734e-12 8.31695177051467e-12 0.999999999995842 22 2.28161362734472e-12 4.56322725468944e-12 0.999999999997718 23 1.04408123949083e-12 2.08816247898167e-12 0.999999999998956 24 4.84255620391903e-12 9.68511240783807e-12 0.999999999995157 25 8.71916537782425e-12 1.74383307556485e-11 0.99999999999128 26 9.80546162489402e-11 1.96109232497880e-10 0.999999999901945 27 3.75509250817738e-10 7.51018501635476e-10 0.99999999962449 28 5.17237861502007e-08 1.03447572300401e-07 0.999999948276214 29 8.57566790497002e-07 1.71513358099400e-06 0.99999914243321 30 2.45149225498837e-05 4.90298450997673e-05 0.99997548507745 31 0.00127793541646139 0.00255587083292278 0.998722064583539 32 0.0167983236092652 0.0335966472185303 0.983201676390735 33 0.0547237487971186 0.109447497594237 0.945276251202881 34 0.118358137000718 0.236716274001435 0.881641862999282 35 0.343887245432838 0.687774490865677 0.656112754567162 36 0.691307682675051 0.617384634649898 0.308692317324949 37 0.900470979606976 0.199058040786048 0.099529020393024 38 0.975288805991337 0.0494223880173254 0.0247111940086627 39 0.995073160017353 0.0098536799652946 0.0049268399826473 40 0.99781731010353 0.00436537979294001 0.00218268989647001 41 0.998750958653226 0.00249808269354845 0.00124904134677423 42 0.99915644077056 0.00168711845888127 0.000843559229440634 43 0.99906066448525 0.00187867102950260 0.000939335514751298 44 0.998463436870279 0.00307312625944255 0.00153656312972127 45 0.997591183769014 0.00481763246197203 0.00240881623098601 46 0.998957546530833 0.00208490693833476 0.00104245346916738 47 0.999674832394855 0.000650335210290767 0.000325167605145383 48 0.999886874353813 0.000226251292373737 0.000113125646186868 49 0.99999722462309 5.55075381929596e-06 2.77537690964798e-06 50 0.999992210473382 1.55790532359767e-05 7.78952661798837e-06 51 0.999944977572154 0.000110044855692506 5.5022427846253e-05 52 0.999659306879606 0.0006813862407875 0.00034069312039375 53 0.999058315023556 0.00188336995288718 0.000941684976443589 54 0.99391667254334 0.0121666549133199 0.00608332745665995 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 41 0.836734693877551 NOK 5% type I error level 44 0.897959183673469 NOK 10% type I error level 44 0.897959183673469 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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