MRLM 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: Wed, 22 Dec 2010 14:43:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/22/t12930289015cfoayyf5eost1o.htm/, Retrieved Wed, 22 Dec 2010 15:41:44 +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/2010/Dec/22/t12930289015cfoayyf5eost1o.htm/}, year = {2010}, } @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 = {2010}, 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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216.234 627 1.59 213.586 696 1.26 209.465 825 1.13 204.045 677 1.92 200.237 656 2.61 203.666 785 2.26 241.476 412 2.41 260.307 352 2.26 243.324 839 2.03 244.460 729 2.86 233.575 696 2.55 237.217 641 2.27 235.243 695 2.26 230.354 638 2.57 227.184 762 3.07 221.678 635 2.76 217.142 721 2.51 219.452 854 2.87 256.446 418 3.14 265.845 367 3.11 248.624 824 3.16 241.114 687 2.47 229.245 601 2.57 231.805 676 2.89 219.277 740 2.63 219.313 691 2.38 212.610 683 1.69 214.771 594 1.96 211.142 729 2.19 211.457 731 1.87 240.048 386 1.6 240.636 331 1.63 230.580 707 1.22 208.795 715 1.21 197.922 657 1.49 194.596 653 1.64 194.581 642 1.66 185.686 643 1.77 178.106 718 1.82 172.608 654 1.78 167.302 632 1.28 168.053 731 1.29 202.300 392 1.37 202.388 344 1.12 182.516 792 1.51 173.476 852 2.24 166.444 649 2.94 171.297 629 3.09 169.701 685 3.46 164.182 617 3.64 161.914 715 4.39 159.612 715 4.15 151.001 629 5.21 158.114 916 5.8 186.530 531 5.91 187.069 357 5.39 174.330 917 5.46 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation werklozen[t] = + 276.783271150381 -0.0411872037745392faillissementen[t] -6.86282765284943inflatie[t] -0.793778070678376t + 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) 276.783271150381 11.625465 23.8084 0 0 faillissementen -0.0411872037745392 0.015564 -2.6463 0.010101 0.005051 inflatie -6.86282765284943 1.545746 -4.4398 3.4e-05 1.7e-05 t -0.793778070678376 0.11781 -6.7378 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.71884657803498 R-squared 0.516740402752601 Adjusted R-squared 0.495420126403451 F-TEST (value) 24.2370405659964 F-TEST (DF numerator) 3 F-TEST (DF denominator) 68 p-value 8.85936879413407e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19.9208584476987 Sum Squared Residuals 26985.160887941 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 216.234 239.253220345035 -23.0192203450348 2 213.586 237.882258339354 -24.2962583393541 3 209.465 232.667498576631 -23.2024985766306 4 204.045 232.547792818833 -28.502792818833 5 200.237 227.883594946954 -27.6465949469539 6 203.666 224.178657267857 -20.5126572678572 7 241.476 237.718282057155 3.75771794284543 8 260.307 240.425160360876 19.8818396391241 9 243.324 221.151664412152 22.1723355878477 10 244.46 219.192331804808 25.2676681951917 11 233.575 221.885208031073 11.689791968927 12 237.217 225.278317910792 11.9386820892079 13 235.243 222.329059112817 12.9139408871829 14 230.354 221.755475084904 8.59852491509585 15 227.184 212.423069919758 14.7609300802418 16 221.678 218.98754330083 2.69045669917036 17 217.142 216.367372618753 0.774627381246751 18 219.452 207.625078491035 11.8269215089646 19 256.446 222.935957799787 33.5100422002133 20 265.845 224.448611951195 41.3963880488047 21 248.624 204.48914037291 44.1348596270899 22 241.114 214.07336029981 27.0406397001903 23 229.245 216.135398988457 13.1096010115433 24 231.805 210.056475785776 21.7485242142239 25 219.277 208.411051863268 10.8659481367319 26 219.313 211.351153690754 7.96184630924553 27 212.61 215.622224330739 -3.01222433073849 28 214.771 216.641143929725 -1.87014392972479 29 211.142 208.708642989328 2.43335701067176 30 211.457 210.028595360013 1.4284046399874 31 240.048 225.29736605782 14.7506339421804 32 240.636 226.562999365155 14.0730006348446 33 230.58 213.096592012919 17.4834079870815 34 208.795 212.041944588572 -3.24694458857236 35 197.922 211.715432594019 -13.7934325940194 36 194.596 210.056979190512 -15.4609791905118 37 194.581 209.579003808296 -14.9980038082964 38 185.686 207.98912749203 -22.30312749203 39 178.106 203.763167755619 -25.6571677556187 40 172.608 205.879883832625 -33.2718838326248 41 167.302 209.423638071411 -42.121638071411 42 168.053 204.483698550525 -36.4306985505248 43 202.3 217.103356347187 -14.8033563471872 44 202.388 220.002270970899 -17.6142709708991 45 182.516 198.080122824616 -15.5641228246159 46 173.476 189.805248340885 -16.329248340885 47 166.444 192.568493279444 -26.1244932794435 48 171.297 191.569035136329 -20.2720351363285 49 169.701 185.929527422722 -16.2285274227217 50 164.182 186.701170231199 -22.5191702311991 51 161.914 176.723925450979 -14.8099254509788 52 159.612 177.577226016984 -17.9652260169842 53 151.001 173.050950158896 -22.0499501588958 54 158.114 156.387376289744 1.72662371025646 55 186.53 170.695760630449 15.8342393695507 56 187.069 180.637226396022 6.43177360397751 57 174.33 156.298216275903 18.0317837240973 58 169.362 164.248591804267 5.11340819573312 59 166.827 179.240545878035 -12.4135458780353 60 178.037 175.768729344129 2.26827065587074 61 186.413 180.520965759121 5.89203424087904 62 189.226 181.991818435308 7.23418156469152 63 191.563 181.08597255569 10.4770274443103 64 188.906 189.367074257143 -0.461074257143318 65 186.005 197.495535217329 -11.4905352173286 66 195.309 194.62742228401 0.681577715990475 67 223.532 213.218098463661 10.3139015363385 68 226.899 212.219920052727 14.6790799472732 69 214.126 189.362830239895 24.763169760105 70 206.903 193.237310651771 13.6656893482293 71 204.442 184.509581683669 19.9324183163313 72 220.375 185.638521520107 34.7364784798931 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.0331131010842578 0.0662262021685155 0.966886898915742 8 0.0103584181175638 0.0207168362351277 0.989641581882436 9 0.0468644854677811 0.0937289709355622 0.953135514532219 10 0.0518141774321725 0.103628354864345 0.948185822567827 11 0.0606423650257791 0.121284730051558 0.93935763497422 12 0.0967198358408713 0.193439671681743 0.903280164159129 13 0.0907768646173153 0.181553729234631 0.909223135382685 14 0.10151058092457 0.203021161849139 0.89848941907543 15 0.0698474564527438 0.139694912905488 0.930152543547256 16 0.105928715593876 0.211857431187752 0.894071284406124 17 0.11702687343912 0.234053746878241 0.88297312656088 18 0.0803843470484665 0.160768694096933 0.919615652951533 19 0.064916862282057 0.129833724564114 0.935083137717943 20 0.070236451109094 0.140472902218188 0.929763548890906 21 0.111810498111364 0.223620996222729 0.888189501888636 22 0.110609054071755 0.22121810814351 0.889390945928245 23 0.144883132954704 0.289766265909408 0.855116867045296 24 0.166483739516504 0.332967479033008 0.833516260483496 25 0.191224974489975 0.382449948979951 0.808775025510025 26 0.205224303931587 0.410448607863173 0.794775696068413 27 0.180284021587245 0.360568043174489 0.819715978412755 28 0.169096947829252 0.338193895658503 0.830903052170748 29 0.161564716599608 0.323129433199216 0.838435283400392 30 0.148185876903391 0.296371753806781 0.85181412309661 31 0.206914667425311 0.413829334850622 0.793085332574689 32 0.334035134479999 0.668070268959998 0.665964865520001 33 0.721743024910062 0.556513950179876 0.278256975089938 34 0.818102847805956 0.363794304388088 0.181897152194044 35 0.885171873431044 0.229656253137913 0.114828126568957 36 0.937290499425068 0.125419001149864 0.062709500574932 37 0.970484715361512 0.0590305692769762 0.0295152846384881 38 0.985455746095959 0.0290885078080826 0.0145442539040413 39 0.991018823349142 0.017962353301715 0.00898117665085749 40 0.994148527165817 0.0117029456683654 0.0058514728341827 41 0.995654662827273 0.0086906743454545 0.00434533717272725 42 0.994578730585479 0.010842538829043 0.00542126941452152 43 0.994724552418879 0.0105508951622424 0.0052754475811212 44 0.995389908692077 0.00922018261584523 0.00461009130792261 45 0.996706439258753 0.0065871214824944 0.0032935607412472 46 0.998157699976172 0.00368460004765695 0.00184230002382848 47 0.998958732960022 0.0020825340799563 0.00104126703997815 48 0.999268296124829 0.0014634077503429 0.00073170387517145 49 0.999539362176383 0.000921275647233242 0.000460637823616621 50 0.999460772440024 0.00107845511995208 0.000539227559976038 51 0.999236060567794 0.00152787886441103 0.000763939432205517 52 0.998568297365074 0.00286340526985281 0.00143170263492641 53 0.999198261940252 0.00160347611949533 0.000801738059747666 54 0.998166689018047 0.00366662196390547 0.00183331098195274 55 0.997861294721543 0.00427741055691409 0.00213870527845705 56 0.995872439776185 0.00825512044762909 0.00412756022381454 57 0.996562048561299 0.00687590287740252 0.00343795143870126 58 0.992939316023863 0.0141213679522745 0.00706068397613726 59 0.991544626505805 0.0169107469883908 0.00845537349419541 60 0.982693297759446 0.0346134044811074 0.0173067022405537 61 0.967416586128045 0.0651668277439108 0.0325834138719554 62 0.945148057344529 0.109703885310943 0.0548519426554714 63 0.96798146157803 0.064037076843942 0.032018538421971 64 0.96436958273749 0.0712608345250221 0.0356304172625111 65 0.91103239501335 0.177935209973299 0.0889676049866496 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.254237288135593 NOK 5% type I error level 24 0.406779661016949 NOK 10% type I error level 30 0.508474576271186 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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