Q3 Eigen data

*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, 27 Nov 2008 05:38:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227789588xhbmfd3v8ndwoco.htm/, Retrieved Thu, 27 Nov 2008 12:40:02 +0000

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/2008/Nov/27/t1227789588xhbmfd3v8ndwoco.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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IsPrivate?

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User-defined keywords:

Dataseries X:

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97.3 0 97.4 0 97.5 0 95.5 0 95.3 0 95.4 0 95.4 0 95.4 0 95.5 0 94.6 0 95.2 0 95.2 0 94.7 0 94.7 0 94.7 0 95.3 0 94.7 0 94.8 0 94.9 0 95.4 0 96 0 95.9 0 95.8 0 95.8 0 95.1 0 95.2 0 95.2 0 95.3 0 95.4 0 95.3 0 95.3 0 95 0 94.9 0 95.7 0 95.7 0 96.3 0 91.7 1 92.2 1 92.2 1 92.6 1 93 1 93 1 93 1 93.7 1 93.1 1 93.1 1 93.2 1 93.2 1 93 1 93.7 1 94 1 93.1 1 94.2 1 94.2 1 93.5 1 95 1 93.7 1 93.9 1 94.6 1 93.8 1 91.2 1 91.4 1 91.3 1 91.5 1 91.5 1 91.5 1 91.3 1 92.8 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation X[t] = + 95.8311835273956 -1.88424378748928Y[t] -0.0197036140934528t + 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) 95.8311835273956 0.247658 386.9495 0 0 Y -1.88424378748928 0.424655 -4.4371 3.6e-05 1.8e-05 t -0.0197036140934528 0.010799 -1.8246 0.07266 0.03633 Multiple Linear Regression - Regression Statistics Multiple R 0.832390685477736 R-squared 0.692874253270094 Adjusted R-squared 0.68342423029379 F-TEST (value) 73.3198485344876 F-TEST (DF numerator) 2 F-TEST (DF denominator) 65 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.878176599408147 Sum Squared Residuals 50.1276190836237 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 95.811479913302 1.48852008669809 2 97.4 95.7917762992086 1.60822370079136 3 97.5 95.7720726851152 1.72792731488481 4 95.5 95.7523690710217 -0.252369071021739 5 95.3 95.7326654569283 -0.432665456928289 6 95.4 95.7129618428348 -0.312961842834828 7 95.4 95.6932582287414 -0.293258228741375 8 95.4 95.673554614648 -0.273554614647922 9 95.5 95.6538510005545 -0.153851000554475 10 94.6 95.634147386461 -1.03414738646103 11 95.2 95.6144437723676 -0.414443772367566 12 95.2 95.5947401582741 -0.394740158274113 13 94.7 95.5750365441807 -0.87503654418066 14 94.7 95.5553329300872 -0.855332930087208 15 94.7 95.5356293159938 -0.835629315993755 16 95.3 95.5159257019003 -0.215925701900308 17 94.7 95.4962220878069 -0.79622208780685 18 94.8 95.4765184737134 -0.676518473713402 19 94.9 95.45681485962 -0.55681485961994 20 95.4 95.4371112455265 -0.0371112455264878 21 96 95.417407631433 0.582592368566959 22 95.9 95.3977040173396 0.502295982660418 23 95.8 95.3780004032461 0.421999596753862 24 95.8 95.3582967891527 0.441703210847315 25 95.1 95.3385931750592 -0.238593175059235 26 95.2 95.3188895609658 -0.118889560965774 27 95.2 95.2991859468723 -0.0991859468723209 28 95.3 95.2794823327789 0.0205176672211264 29 95.4 95.2597787186854 0.140221281314588 30 95.3 95.240075104592 0.0599248954080321 31 95.3 95.2203714904985 0.079628509501485 32 95 95.200667876405 -0.200667876405059 33 94.9 95.1809642623116 -0.280964262311601 34 95.7 95.1612606482182 0.538739351781849 35 95.7 95.1415570341247 0.558442965875302 36 96.3 95.1218534200312 1.17814657996875 37 91.7 93.2179060184485 -1.51790601844852 38 92.2 93.198202404355 -0.998202404355063 39 92.2 93.1784987902616 -0.97849879026161 40 92.6 93.1587951761682 -0.558795176168166 41 93 93.1390915620747 -0.139091562074708 42 93 93.1193879479813 -0.119387947981255 43 93 93.0996843338878 -0.0996843338878021 44 93.7 93.0799807197943 0.620019280205653 45 93.1 93.0602771057009 0.0397228942990979 46 93.1 93.0405734916074 0.0594265083925507 47 93.2 93.020869877514 0.179130122486012 48 93.2 93.0011662634205 0.198833736579465 49 93 92.9814626493271 0.0185373506729149 50 93.7 92.9617590352336 0.73824096476637 51 94 92.9420554211402 1.05794457885982 52 93.1 92.9223518070467 0.177648192953268 53 94.2 92.9026481929533 1.29735180704673 54 94.2 92.8829445788598 1.31705542114018 55 93.5 92.8632409647664 0.636759035233632 56 95 92.843537350673 2.15646264932708 57 93.7 92.8238337365795 0.87616626342054 58 93.9 92.804130122486 1.09586987751400 59 94.6 92.7844265083926 1.81557349160744 60 93.8 92.7647228942991 1.03527710570089 61 91.2 92.7450192802057 -1.54501928020565 62 91.4 92.7253156661122 -1.32531566611219 63 91.3 92.7056120520188 -1.40561205201875 64 91.5 92.6859084379253 -1.18590843792529 65 91.5 92.6662048238318 -1.16620482383184 66 91.5 92.6465012097384 -1.14650120973839 67 91.3 92.626797595645 -1.32679759564494 68 92.8 92.6070939815515 0.192906018448516 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.466844142257911 0.933688284515822 0.533155857742089 7 0.379092755185602 0.758185510371204 0.620907244814398 8 0.328274410904980 0.656548821809959 0.67172558909502 9 0.311585158284963 0.623170316569925 0.688414841715037 10 0.212150454810284 0.424300909620569 0.787849545189716 11 0.200618915943903 0.401237831887805 0.799381084056097 12 0.186142891468107 0.372285782936214 0.813857108531893 13 0.132648955494793 0.265297910989586 0.867351044505207 14 0.0984336128890737 0.196867225778147 0.901566387110926 15 0.0769203476931403 0.153840695386281 0.92307965230686 16 0.107233376639586 0.214466753279172 0.892766623360414 17 0.0842630395361718 0.168526079072344 0.915736960463828 18 0.0716144164448251 0.143228832889650 0.928385583555175 19 0.0656517495915544 0.131303499183109 0.934348250408445 20 0.089565900471191 0.179131800942382 0.910434099528809 21 0.179739804997328 0.359479609994657 0.820260195002672 22 0.224397236698003 0.448794473396006 0.775602763301997 23 0.229943357917729 0.459886715835458 0.770056642082271 24 0.220866579888203 0.441733159776405 0.779133420111797 25 0.171429380069043 0.342858760138086 0.828570619930957 26 0.13120637316142 0.26241274632284 0.86879362683858 27 0.0984208985612749 0.196841797122550 0.901579101438725 28 0.0733802543598168 0.146760508719634 0.926619745640183 29 0.0547262811548506 0.109452562309701 0.94527371884515 30 0.0388689686193677 0.0777379372387354 0.961131031380632 31 0.0269958254619486 0.0539916509238972 0.973004174538051 32 0.0186040443022528 0.0372080886045055 0.981395955697747 33 0.0136856716313304 0.0273713432626609 0.98631432836867 34 0.0112510739187755 0.0225021478375510 0.988748926081225 35 0.00900978128963941 0.0180195625792788 0.99099021871036 36 0.0106531824162533 0.0213063648325067 0.989346817583747 37 0.0121717132393504 0.0243434264787008 0.98782828676065 38 0.0121681450937946 0.0243362901875892 0.987831854906205 39 0.0134391536852940 0.0268783073705879 0.986560846314706 40 0.0139526922156530 0.0279053844313059 0.986047307784347 41 0.0139968885396785 0.0279937770793571 0.986003111460321 42 0.0135829125238601 0.0271658250477201 0.98641708747614 43 0.0133808425284663 0.0267616850569326 0.986619157471534 44 0.0142176378430031 0.0284352756860062 0.985782362156997 45 0.0131217337995923 0.0262434675991845 0.986878266200408 46 0.0128106885724892 0.0256213771449785 0.98718931142751 47 0.0127984888457799 0.0255969776915598 0.98720151115422 48 0.0138114137444325 0.0276228274888651 0.986188586255567 49 0.0205159824734536 0.0410319649469072 0.979484017526546 50 0.0219182426225509 0.0438364852451017 0.97808175737745 51 0.0216436359127816 0.0432872718255633 0.978356364087218 52 0.0343411139321147 0.0686822278642294 0.965658886067885 53 0.032577290969469 0.065154581938938 0.967422709030531 54 0.0271963480927148 0.0543926961854297 0.972803651907285 55 0.0227851305925228 0.0455702611850456 0.977214869407477 56 0.0397325129532112 0.0794650259064223 0.960267487046789 57 0.0237064763660094 0.0474129527320188 0.97629352363399 58 0.016710240226713 0.033420480453426 0.983289759773287 59 0.108166269409139 0.216332538818278 0.89183373059086 60 0.850379653359477 0.299240693281047 0.149620346640523 61 0.787980866523729 0.424038266952543 0.212019133476271 62 0.698590231897838 0.602819536204324 0.301409768102162 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 23 0.403508771929825 NOK 10% type I error level 29 0.508771929824561 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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