Paper: Multiple Regression (12 maanden)

*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: Sun, 19 Dec 2010 19:24:42 +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/19/t1292786608a20ptkg9sx6d2fk.htm/, Retrieved Sun, 19 Dec 2010 20:23:39 +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/19/t1292786608a20ptkg9sx6d2fk.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:

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Dataseries X:

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627 0 724 590 722 803 608 696 0 627 724 590 722 651 825 0 696 627 724 590 691 677 0 825 696 627 724 627 656 0 677 825 696 627 634 785 0 656 677 825 696 731 412 0 785 656 677 825 475 352 0 412 785 656 677 337 839 0 352 412 785 656 803 729 0 839 352 412 785 722 696 0 729 839 352 412 590 641 0 696 729 839 352 724 695 0 641 696 729 839 627 638 0 695 641 696 729 696 762 0 638 695 641 696 825 635 0 762 638 695 641 677 721 0 635 762 638 695 656 854 0 721 635 762 638 785 418 0 854 721 635 762 412 367 0 418 854 721 635 352 824 0 367 418 854 721 839 687 0 824 367 418 854 729 601 0 687 824 367 418 696 676 0 601 687 824 367 641 740 0 676 601 687 824 695 691 0 740 676 601 687 638 683 0 691 740 676 601 762 594 0 683 691 740 676 635 729 0 594 683 691 740 721 731 0 729 594 683 691 854 386 0 731 729 594 683 418 331 0 386 731 729 594 367 706 0 331 386 731 729 824 715 0 706 331 386 731 687 657 0 715 706 331 386 601 653 0 657 715 706 331 676 642 0 653 657 715 706 740 643 0 642 653 657 715 691 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 20 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation faillissement[t] = + 5.94989160883175 + 65.7319584895735crisis[t] + 0.0228416024126094`t-1`[t] + 0.0167861261156532`t-2`[t] + 0.0145983909933509`t-3`[t] -0.0246343658381229`t-4`[t] + 0.957064898875237`t-12`[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) 5.94989160883175 104.833963 0.0568 0.954914 0.477457 crisis 65.7319584895735 19.220521 3.4199 0.001087 0.000543 `t-1` 0.0228416024126094 0.067705 0.3374 0.736925 0.368462 `t-2` 0.0167861261156532 0.076456 0.2196 0.826907 0.413453 `t-3` 0.0145983909933509 0.068008 0.2147 0.830706 0.415353 `t-4` -0.0246343658381229 0.070634 -0.3488 0.728396 0.364198 `t-12` 0.957064898875237 0.07609 12.5781 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.887312132193456 R-squared 0.787322819937696 Adjusted R-squared 0.767691080239638 F-TEST (value) 40.1045873695823 F-TEST (DF numerator) 6 F-TEST (DF denominator) 65 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 75.4432942131509 Sum Squared Residuals 369959.891712583 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 627 605.045127209127 21.9548727908730 2 696 646.301019348002 49.6989806519978 3 825 689.739352320005 135.260647679995 4 677 627.874959256533 49.1250407434673 5 656 636.756089125352 19.2439108746483 6 785 726.81078519578 58.1892148042202 7 412 479.057834086383 -67.057834086383 8 352 343.967690543798 8.03230945620166 9 839 784.728726354506 54.2712736454936 10 729 708.700129319976 20.299870680024 11 696 596.3425448194 99.6574551806004 12 641 730.576472880393 -89.5764728803927 13 695 622.32818822255 72.6718117774498 14 638 690.903909178274 -52.9039091782744 15 762 813.97978317393 -51.9797831739303 16 635 676.352930885704 -41.3529308857043 17 721 653.272800099384 67.7271999006157 18 854 779.781071181035 74.2189288189652 19 418 422.368746847312 -4.36874684731188 20 367 361.602495123152 5.39750487684838 21 824 819.032458705961 4.96754129403881 22 687 713.696570570778 -26.6965705707779 23 601 696.651454576982 -95.6514545769819 24 676 647.676625395221 28.3233746047794 25 740 686.369758515372 53.6302414846283 26 691 636.657327786959 54.3426722130412 27 683 758.501883587252 -75.501883587252 28 594 635.036108016844 -41.0361080168443 29 729 712.884577124153 16.1154228758469 30 731 842.85415657409 -111.85415657409 31 386 426.783489023222 -40.7834890232219 32 331 374.289639944161 -43.2896399441611 33 706 801.32435448139 -95.3243544813906 34 715 672.763113679468 42.2368863205315 35 657 604.6518488008 52.3481511992003 36 653 682.087265155155 -29.0872651551553 37 642 733.167955288456 -91.1679552884562 38 643 684.884957142411 -41.8849571424108 39 718 678.437031821187 39.5629681788129 40 654 594.926117290778 59.073882709222 41 632 724.212551958415 -92.2125519584147 42 731 725.620099390349 5.3799006096509 43 392 460.274817170836 -68.2748171708362 44 344 402.810205812059 -58.8102058120594 45 792 756.909845978042 35.090154021958 46 852 767.563077130497 84.4369228695033 47 649 728.594320891745 -79.594320891745 48 629 728.858912298675 -99.8589122986746 49 685 704.306490325439 -19.3064903254392 50 617 701.76542711517 -84.7654271151699 51 715 777.640897074504 -62.6408970745037 52 715 718.79596121945 -3.79596121944998 53 629 697.013358729046 -68.013358729046 54 916 792.90418510455 123.095814895449 55 531 471.156949580182 59.8430504198177 56 357 419.985974075080 -62.9859740750805 57 917 844.622245074036 72.3777549259636 58 828 899.226206885507 -71.2262068855068 59 708 719.253471238712 -11.2534712387115 60 858 708.33869435951 149.661305640490 61 775 748.25173225678 26.7482677432203 62 785 684.234036690756 100.765963309244 63 1006 782.007446886633 223.992553113367 64 789 782.31648095281 6.68351904719002 65 734 700.95264207206 33.0473579279396 66 906 973.711291300612 -67.7112913006124 67 532 599.634778216472 -67.6347782164718 68 387 431.992686083995 -44.9926860839954 69 991 962.224799308998 28.7752006910016 70 841 878.711453723878 -37.7114537238784 71 892 777.672731800235 114.327268199765 72 782 932.268880643728 -150.268880643728 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.23549010318057 0.47098020636114 0.76450989681943 11 0.149765082380814 0.299530164761629 0.850234917619186 12 0.511168322632609 0.977663354734781 0.488831677367391 13 0.394928064626330 0.789856129252661 0.60507193537367 14 0.462464651796748 0.924929303593497 0.537535348203252 15 0.594903979871883 0.810192040256235 0.405096020128117 16 0.519051627016996 0.961896745966008 0.480948372983004 17 0.448608459217692 0.897216918435385 0.551391540782308 18 0.430635816236971 0.861271632473942 0.569364183763029 19 0.339010263294710 0.678020526589421 0.66098973670529 20 0.260769431105565 0.521538862211129 0.739230568894435 21 0.198222454989068 0.396444909978135 0.801777545010932 22 0.167292834876366 0.334585669752733 0.832707165123634 23 0.264959076823014 0.529918153646028 0.735040923176986 24 0.211406436650023 0.422812873300045 0.788593563349977 25 0.174887004261531 0.349774008523063 0.825112995738469 26 0.149379176367240 0.298758352734481 0.85062082363276 27 0.158841209652245 0.31768241930449 0.841158790347755 28 0.130632962579048 0.261265925158096 0.869367037420952 29 0.0963929902642912 0.192785980528582 0.90360700973571 30 0.135021934106525 0.270043868213049 0.864978065893475 31 0.109737449192589 0.219474898385179 0.89026255080741 32 0.092440905860779 0.184881811721558 0.907559094139221 33 0.109262125634911 0.218524251269822 0.89073787436509 34 0.0889583966466269 0.177916793293254 0.911041603353373 35 0.0760701624256922 0.152140324851384 0.923929837574308 36 0.0536473213927574 0.107294642785515 0.946352678607243 37 0.0583527674765869 0.116705534953174 0.941647232523413 38 0.0439209793182264 0.0878419586364528 0.956079020681774 39 0.0326485940470217 0.0652971880940434 0.967351405952978 40 0.0301575626972680 0.0603151253945360 0.969842437302732 41 0.0304563281278879 0.0609126562557757 0.969543671872112 42 0.0196743746459659 0.0393487492919317 0.980325625354034 43 0.0133953053900037 0.0267906107800073 0.986604694609996 44 0.00943264393837405 0.0188652878767481 0.990567356061626 45 0.00824779148576617 0.0164955829715323 0.991752208514234 46 0.0101694011272699 0.0203388022545399 0.98983059887273 47 0.00835784377367202 0.0167156875473440 0.991642156226328 48 0.0111461157304207 0.0222922314608414 0.98885388426958 49 0.00681209408816854 0.0136241881763371 0.993187905911831 50 0.00560609565112167 0.0112121913022433 0.994393904348878 51 0.0044270083971649 0.0088540167943298 0.995572991602835 52 0.00261675244633382 0.00523350489266764 0.997383247553666 53 0.00226830366641599 0.00453660733283198 0.997731696333584 54 0.00565794166036662 0.0113158833207332 0.994342058339633 55 0.00412986963224366 0.00825973926448732 0.995870130367756 56 0.00473696198288555 0.0094739239657711 0.995263038017114 57 0.00321109478905641 0.00642218957811282 0.996788905210944 58 0.00203067832799988 0.00406135665599977 0.997969321672 59 0.00183727757101266 0.00367455514202532 0.998162722428987 60 0.00720538103258091 0.0144107620651618 0.99279461896742 61 0.00341806659333626 0.00683613318667252 0.996581933406664 62 0.00236476766455643 0.00472953532911286 0.997635232335444 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.188679245283019 NOK 5% type I error level 21 0.39622641509434 NOK 10% type I error level 25 0.471698113207547 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') }

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