MLRM 2

*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, 17 Dec 2010 18:56:54 +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/17/t1292612103i4e08rpd4cqv2ns.htm/, Retrieved Fri, 17 Dec 2010 19:55:14 +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/2010/Dec/17/t1292612103i4e08rpd4cqv2ns.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:

» Textbox « » Textfile « » CSV «

1 216234,00 627 2 213586,00 696 3 209465,00 825 4 204045,00 677 5 200237,00 656 6 203666,00 785 7 241476,00 412 8 260307,00 352 9 243324,00 839 10 244460,00 729 11 233575,00 696 12 237217,00 641 1 235243,00 695 2 230354,00 638 3 227184,00 762 4 221678,00 635 5 217142,00 721 6 219452,00 854 7 256446,00 418 8 265845,00 367 9 248624,00 824 10 241114,00 687 11 229245,00 601 12 231805,00 676 1 219277,00 740 2 219313,00 691 3 212610,00 683 4 214771,00 594 5 211142,00 729 6 211457,00 731 7 240048,00 386 8 240636,00 331 9 230580,00 707 10 208795,00 715 11 197922,00 657 12 194596,00 653 1 194581,00 642 2 185686,00 643 3 178106,00 718 4 172608,00 654 5 167302,00 632 6 168053,00 731 7 202300,00 392 8 202388,00 344 9 182516,00 792 10 173476,00 852 11 166444,00 649 12 171297,00 629 1 169701,00 685 2 164182,00 617 3 161914,00 715 4 159612,00 715 5 151001,00 629 6 158114,00 916 7 186530,00 531 8 187069,00 357 9 174330,00 917 10 169362,00 828 11 166827,00 708 12 1780 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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation werklozen[t] = + 237704.099217795 + 1197.29428041116month[t] -59.5262196333698faillissementen[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) 237704.099217795 15295.646298 15.5406 0 0 month 1197.29428041116 903.784949 1.3248 0.189623 0.094811 faillissementen -59.5262196333698 20.071758 -2.9657 0.004145 0.002073 Multiple Linear Regression - Regression Statistics Multiple R 0.366487177533564 R-squared 0.134312851296518 Adjusted R-squared 0.109220470174678 F-TEST (value) 5.35273438755537 F-TEST (DF numerator) 2 F-TEST (DF denominator) 69 p-value 0.00690165868774717 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 26468.4312427775 Sum Squared Residuals 48339871819.3012 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 216234 201578.453788083 14655.5462119170 2 213586 198668.438913792 14917.5610862082 3 209465 192186.850861498 17278.1491385018 4 204045 202194.025647648 1850.97435235183 5 200237 204641.37054036 -4404.37054036009 6 203666 198159.782488067 5506.21751193346 7 241476 221560.356691725 19915.6433082754 8 260307 226329.224150138 33977.775849862 9 243324 198537.249469098 44786.7505309020 10 244460 206282.42790918 38177.5720908201 11 233575 209444.087437492 24130.9125625078 12 237217 213915.323797739 23301.6762022613 13 235243 197530.670853014 37712.3291469860 14 230354 202120.959652527 28233.0403474727 15 227184 195937.002698401 31246.9973015994 16 221678 204694.126872250 16983.8731277503 17 217142 200772.166264191 16369.8337358089 18 219452 194052.473333364 25399.526666636 19 256446 221203.199373924 35242.8006260756 20 265845 225436.330855637 40408.6691443626 21 248624 199430.142763599 49193.8572364014 22 241114 208782.529133781 32331.4708662186 23 229245 215099.078302662 14145.9216973376 24 231805 211831.906110571 19973.0938894292 25 219277 194851.990969512 24425.0090304876 26 219313 198966.070011959 20346.9299880413 27 212610 200639.574049437 11970.4259505632 28 214771 207134.701877218 7636.29812278214 29 211142 200295.956507124 10846.0434928759 30 211457 201374.198348269 10082.8016517315 31 240048 223108.038402192 16939.9615978077 32 240636 227579.274762439 13056.7252375613 33 230580 206394.710460703 24185.2895392971 34 208795 207115.794984047 1679.20501595295 35 197922 211765.610003194 -13843.6100031937 36 194596 213201.009162138 -18605.0091621383 37 194581 200685.560493583 -6104.56049358264 38 185686 201823.328554360 -16137.3285543604 39 178106 198556.156362269 -20450.1563622688 40 172608 203563.128699216 -30955.1286992157 41 167302 206069.999811561 -38767.999811561 42 168053 201374.198348269 -33321.1983482685 43 202300 222750.881084392 -20450.8810843920 44 202388 226805.433907205 -24417.4339072049 45 182516 201334.981791866 -18818.9817918664 46 173476 198960.702894275 -25484.7028942754 47 166444 212241.819760261 -45797.8197602606 48 171297 214629.638433339 -43332.6384333392 49 169701 198125.933049348 -28424.9330493477 50 164182 203371.010264828 -39189.010264828 51 161914 198734.735021169 -36820.7350211690 52 159612 199932.02930158 -40320.0293015801 53 151001 206248.578470461 -55247.5784704611 54 158114 190361.847716095 -32247.8477160951 55 186530 214476.736555354 -27946.7365553536 56 187069 226031.593051971 -38962.5930519711 57 174330 193894.204337695 -19564.2043376952 58 169362 200389.332165476 -31027.3321654763 59 166827 208729.772801892 -41902.7728018918 60 178037 200998.134137297 -22961.1341372975 61 186413 192768.573282344 -6355.57328234446 62 189226 193370.605366422 -4144.60536642192 63 191563 181412.605107858 10150.3948921417 64 188906 195527.089048711 -6621.08904871075 65 186005 199998.325408957 -13993.3254089572 66 195309 190957.109912429 4351.89008757120 67 223532 214417.210335720 9114.78966427974 68 226899 224245.80646297 2653.19353702996 69 214126 189489.264084826 24636.7359151742 70 206903 199615.491310242 7287.50868975755 71 204442 197776.948389352 6665.05161064825 72 220375 205522.126829434 14852.8731705664 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.00121844896356674 0.00243689792713349 0.998781551036433 7 0.0305317147269220 0.0610634294538439 0.969468285273078 8 0.0249289341898581 0.0498578683797162 0.975071065810142 9 0.0663672232126066 0.132734446425213 0.933632776787393 10 0.0363234224383769 0.0726468448767538 0.963676577561623 11 0.0232449585814649 0.0464899171629297 0.976755041418535 12 0.0147537603300565 0.0295075206601129 0.985246239669944 13 0.0327336852098661 0.0654673704197323 0.967266314790134 14 0.0241281380401124 0.0482562760802248 0.975871861959888 15 0.0186242149551600 0.0372484299103199 0.98137578504484 16 0.010549757734328 0.021099515468656 0.989450242265672 17 0.00597943286027305 0.0119588657205461 0.994020567139727 18 0.00347447740877852 0.00694895481755704 0.996525522591222 19 0.003117213000459 0.006234426000918 0.99688278699954 20 0.00360416862158796 0.00720833724317592 0.996395831378412 21 0.00884328522872347 0.0176865704574469 0.991156714771277 22 0.00745677093541117 0.0149135418708223 0.992543229064589 23 0.00839582727741918 0.0167916545548384 0.99160417272258 24 0.00782002597075991 0.0156400519415198 0.99217997402924 25 0.0065686476784567 0.0131372953569134 0.993431352321543 26 0.00530758911298822 0.0106151782259764 0.994692410887012 27 0.00439899650496177 0.00879799300992354 0.995601003495038 28 0.00431000375040448 0.00862000750080896 0.995689996249596 29 0.00391740878282377 0.00783481756564754 0.996082591217176 30 0.00377634236064765 0.0075526847212953 0.996223657639352 31 0.00471648666874131 0.00943297333748263 0.99528351333126 32 0.00771809403743091 0.0154361880748618 0.99228190596257 33 0.0117586440800862 0.0235172881601724 0.988241355919914 34 0.0201468745822802 0.0402937491645603 0.97985312541772 35 0.0592142208336376 0.118428441667275 0.940785779166362 36 0.12307996165293 0.24615992330586 0.87692003834707 37 0.145899528561962 0.291799057123924 0.854100471438038 38 0.189522542069073 0.379045084138146 0.810477457930927 39 0.240497440596860 0.480994881193721 0.75950255940314 40 0.352019569020166 0.704039138040332 0.647980430979834 41 0.517428650092237 0.965142699815526 0.482571349907763 42 0.611015978693705 0.77796804261259 0.388984021306295 43 0.619866224838183 0.760267550323633 0.380133775161817 44 0.626144180928253 0.747711638143494 0.373855819071747 45 0.616833551545562 0.766332896908876 0.383166448454438 46 0.637093372736436 0.725813254527129 0.362906627263564 47 0.746679775017674 0.506640449964652 0.253320224982326 48 0.812069224409852 0.375861551180297 0.187930775590149 49 0.794431478668953 0.411137042662094 0.205568521331047 50 0.802912986631687 0.394174026736625 0.197087013368313 51 0.812437830545348 0.375124338909305 0.187562169454652 52 0.843013188365664 0.313973623268671 0.156986811634336 53 0.936701284565022 0.126597430869956 0.0632987154349778 54 0.955473557141397 0.0890528857172066 0.0445264428586033 55 0.943105599918377 0.113788800163247 0.0568944000816233 56 0.948333448909877 0.103333102180245 0.0516665510901225 57 0.935630118346023 0.128739763307953 0.0643698816539767 58 0.952555769990722 0.094888460018556 0.047444230009278 59 0.994104501058554 0.0117909978828926 0.0058954989414463 60 0.99976553552968 0.000468928940637981 0.000234464470318991 61 0.999166900396008 0.00166619920798376 0.000833099603991881 62 0.997211860144836 0.00557627971032774 0.00278813985516387 63 0.995385863033583 0.00922827393283347 0.00461413696641674 64 0.985318298815703 0.0293634023685943 0.0146817011842971 65 0.987848427943993 0.0243031441120147 0.0121515720560073 66 0.977457703275439 0.045084593449123 0.0225422967245615 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.213114754098361 NOK 5% type I error level 33 0.540983606557377 NOK 10% type I error level 38 0.622950819672131 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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') }

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