Regressie Analyse

*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: Sat, 25 Dec 2010 19:33:12 +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/25/t1293305537hxb7qdvruxmcfzs.htm/, Retrieved Sat, 25 Dec 2010 20:32:27 +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/25/t1293305537hxb7qdvruxmcfzs.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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493 797 514 840 522 988 490 819 484 831 506 904 501 814 462 798 465 828 454 789 464 930 427 744 460 832 473 826 465 907 422 776 415 835 413 715 420 729 363 733 376 736 380 712 384 711 346 667 389 799 407 661 393 692 346 649 348 729 353 622 364 671 305 635 307 648 312 745 312 624 286 477 324 710 336 515 327 461 302 590 299 415 311 554 315 585 264 513 278 591 278 561 287 684 279 668 324 795 354 776 354 1 043 360 964 363 762 385 1 030 412 939 370 779 389 918 395 839 417 874 404 840

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation WLH[t] = + 238.252733996356 + 0.216708479297129Faill[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) 238.252733996356 60.643639 3.9287 0.00023 0.000115 Faill 0.216708479297129 0.085236 2.5425 0.013699 0.00685 Multiple Linear Regression - Regression Statistics Multiple R 0.316661441317002 R-squared 0.100274468416961 Adjusted R-squared 0.0847619592517364 F-TEST (value) 6.46410373389184 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0136994828546096 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 126.218132664543 Sum Squared Residuals 923998.986772809 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 493 410.969391996168 82.0306080038316 2 514 420.287856605944 93.7121433940557 3 522 452.360711541919 69.6392884580807 4 490 415.736978540705 74.2630214592955 5 484 418.33748029227 65.6625197077299 6 506 434.157199280960 71.8428007190395 7 501 414.653436144219 86.3465638557811 8 462 411.186100475465 50.8138995245352 9 465 417.687354854379 47.3126451456213 10 454 409.235724161791 44.7642758382094 11 464 439.791619742686 24.2083802573142 12 427 399.48384259342 27.5161574065802 13 460 418.554188771567 41.4458112284328 14 473 417.253937895784 55.7460621042156 15 465 434.807324718852 30.1926752811481 16 422 406.418513930928 15.5814860690720 17 415 419.204314209459 -4.20431420945858 18 413 393.199296693803 19.8007033061969 19 420 396.233215403963 23.7667845960371 20 363 397.100049321151 -34.1000493211514 21 376 397.750174759043 -21.7501747590428 22 380 392.549171255912 -12.5491712559117 23 384 392.332462776615 -8.33246277661458 24 346 382.797289687541 -36.7972896875409 25 389 411.402808954762 -22.4028089547619 26 407 381.497038811758 25.5029611882419 27 393 388.215001669969 4.78499833003087 28 346 378.896537060193 -32.8965370601926 29 348 396.233215403963 -48.2332154039629 30 353 373.04540811917 -20.0454081191701 31 364 383.664123604729 -19.6641236047294 32 305 375.862618350033 -70.8626183500328 33 307 378.679828580895 -71.6798285808955 34 312 399.700551072717 -87.700551072717 35 312 373.478825077764 -61.4788250777644 36 286 341.622678621086 -55.6226786210864 37 324 392.115754297317 -68.1157542973175 38 336 349.857600834377 -13.8576008343773 39 327 338.155342952332 -11.1553429523323 40 302 366.110736781662 -64.110736781662 41 299 328.186752904664 -29.1867529046644 42 311 358.309231526965 -47.3092315269653 43 315 365.027194385176 -50.0271943851763 44 264 349.424183875783 -85.424183875783 45 278 366.327445260959 -88.3274452609591 46 278 359.826190882045 -81.8261908820452 47 287 386.481333835592 -99.4813338355921 48 279 383.013998166838 -104.013998166838 49 324 410.535975037573 -86.5359750375734 50 354 406.418513930928 -52.418513930928 51 354 238.469442475653 115.530557524347 52 43 316.267786543322 -273.267786543322 53 964 316.917911981214 647.082088018786 54 762 321.685498525751 440.314501474249 55 1 244.753988375270 -243.753988375270 56 412 441.74199605636 -29.74199605636 57 370 407.068639368819 -37.0686393688193 58 389 437.19111799112 -48.1911179911203 59 395 420.071148126647 -25.0711481266471 60 417 427.655944902047 -10.6559449020466 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0011277187527187 0.0022554375054374 0.998872281247281 6 8.81814211320073e-05 0.000176362842264015 0.999911818578868 7 7.81653814919834e-06 1.56330762983967e-05 0.99999218346185 8 8.14725325849e-06 1.629450651698e-05 0.999991852746742 9 3.46965149368275e-06 6.9393029873655e-06 0.999996530348506 10 1.11093389761539e-06 2.22186779523078e-06 0.999998889066102 11 1.42874121514483e-06 2.85748243028966e-06 0.999998571258785 12 8.10401047048716e-07 1.62080209409743e-06 0.999999189598953 13 1.86262954734251e-07 3.72525909468502e-07 0.999999813737045 14 3.10543974762305e-08 6.21087949524611e-08 0.999999968945603 15 1.14127892855033e-08 2.28255785710066e-08 0.99999998858721 16 7.3077962604366e-09 1.46155925208732e-08 0.999999992692204 17 1.31805677265179e-08 2.63611354530358e-08 0.999999986819432 18 3.47676554661281e-09 6.95353109322562e-09 0.999999996523234 19 7.63215965606024e-10 1.52643193121205e-09 0.999999999236784 20 1.95816192594289e-09 3.91632385188578e-09 0.999999998041838 21 1.20706745816785e-09 2.41413491633570e-09 0.999999998792933 22 3.61139313402538e-10 7.22278626805076e-10 0.99999999963886 23 8.8828207892772e-11 1.77656415785544e-10 0.999999999911172 24 2.92388479345311e-11 5.84776958690621e-11 0.999999999970761 25 2.1894089654191e-11 4.3788179308382e-11 0.999999999978106 26 7.42032769866762e-12 1.48406553973352e-11 0.99999999999258 27 1.47534690156053e-12 2.95069380312107e-12 0.999999999998525 28 3.52445018511716e-13 7.04890037023432e-13 0.999999999999648 29 2.93423532089552e-13 5.86847064179105e-13 0.999999999999707 30 5.52353921970559e-14 1.10470784394112e-13 0.999999999999945 31 1.04884204868252e-14 2.09768409736505e-14 0.99999999999999 32 5.22185070394647e-15 1.04437014078929e-14 0.999999999999995 33 2.54186069252230e-15 5.08372138504461e-15 0.999999999999997 34 1.43645484572826e-14 2.87290969145651e-14 0.999999999999986 35 3.28640866936711e-15 6.57281733873422e-15 0.999999999999997 36 9.85039092685998e-16 1.97007818537200e-15 0.999999999999999 37 6.51629956158993e-16 1.30325991231799e-15 1 38 3.49314705933293e-16 6.98629411866586e-16 1 39 2.42532771602973e-16 4.85065543205947e-16 1 40 5.8135822242872e-17 1.16271644485744e-16 1 41 2.38280133980836e-17 4.76560267961672e-17 1 42 4.26737446507367e-18 8.53474893014733e-18 1 43 7.8763835726494e-19 1.57527671452988e-18 1 44 2.07143090489578e-19 4.14286180979155e-19 1 45 9.17795290887289e-20 1.83559058177458e-19 1 46 2.54265175016614e-20 5.08530350033227e-20 1 47 4.36690132325945e-20 8.7338026465189e-20 1 48 6.29670328253349e-20 1.25934065650670e-19 1 49 1.44194349826495e-19 2.8838869965299e-19 1 50 5.37556069305754e-20 1.07511213861151e-19 1 51 2.65973607893268e-16 5.31947215786536e-16 1 52 5.32400859033375e-13 1.06480171806675e-12 0.999999999999468 53 0.00413011958480449 0.00826023916960897 0.995869880415196 54 0.998213854110998 0.00357229177800346 0.00178614588900173 55 0.997485974289856 0.00502805142028888 0.00251402571014444 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 51 1 NOK 5% type I error level 51 1 NOK 10% type I error level 51 1 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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