paper: multiple regression (gewoon)

*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, 16 Dec 2010 07:12:46 +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/16/t129248348043yl5f45bfbrad8.htm/, Retrieved Thu, 16 Dec 2010 08:11:20 +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/16/t129248348043yl5f45bfbrad8.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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591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 1 565 1 542 1 527 1 510 1 514 1 517 1 508 1 493 1 490 1 469 1 478 1 528 1 534 1 518 1 506 1 502 1 516 1 528 1 533 1 536 1 537 1 524 1 536 1 587 1 597 1 581 1 564 1 558 1 575 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Werk[t] = + 579.766666666667 -48.8333333333333Crisis[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) 579.766666666667 5.956028 97.3412 0 0 Crisis -48.8333333333333 8.423096 -5.7976 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.605716466197904 R-squared 0.366892437423277 Adjusted R-squared 0.355976789792644 F-TEST (value) 33.6116050864126 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 2.93230160042235e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 32.622510034017 Sum Squared Residuals 61725.2333333333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 591 579.766666666667 11.2333333333331 2 589 579.766666666667 9.23333333333332 3 584 579.766666666667 4.23333333333334 4 573 579.766666666667 -6.76666666666666 5 567 579.766666666667 -12.7666666666667 6 569 579.766666666667 -10.7666666666667 7 621 579.766666666667 41.2333333333333 8 629 579.766666666667 49.2333333333333 9 628 579.766666666667 48.2333333333333 10 612 579.766666666667 32.2333333333333 11 595 579.766666666667 15.2333333333333 12 597 579.766666666667 17.2333333333333 13 593 579.766666666667 13.2333333333333 14 590 579.766666666667 10.2333333333333 15 580 579.766666666667 0.233333333333341 16 574 579.766666666667 -5.76666666666666 17 573 579.766666666667 -6.76666666666666 18 573 579.766666666667 -6.76666666666666 19 620 579.766666666667 40.2333333333333 20 626 579.766666666667 46.2333333333333 21 620 579.766666666667 40.2333333333333 22 588 579.766666666667 8.23333333333334 23 566 579.766666666667 -13.7666666666667 24 557 579.766666666667 -22.7666666666667 25 561 579.766666666667 -18.7666666666667 26 549 579.766666666667 -30.7666666666667 27 532 579.766666666667 -47.7666666666667 28 526 579.766666666667 -53.7666666666667 29 511 579.766666666667 -68.7666666666667 30 499 579.766666666667 -80.7666666666667 31 555 530.933333333333 24.0666666666667 32 565 530.933333333333 34.0666666666667 33 542 530.933333333333 11.0666666666667 34 527 530.933333333333 -3.93333333333333 35 510 530.933333333333 -20.9333333333333 36 514 530.933333333333 -16.9333333333333 37 517 530.933333333333 -13.9333333333333 38 508 530.933333333333 -22.9333333333333 39 493 530.933333333333 -37.9333333333333 40 490 530.933333333333 -40.9333333333333 41 469 530.933333333333 -61.9333333333333 42 478 530.933333333333 -52.9333333333333 43 528 530.933333333333 -2.93333333333333 44 534 530.933333333333 3.06666666666667 45 518 530.933333333333 -12.9333333333333 46 506 530.933333333333 -24.9333333333333 47 502 530.933333333333 -28.9333333333333 48 516 530.933333333333 -14.9333333333333 49 528 530.933333333333 -2.93333333333333 50 533 530.933333333333 2.06666666666667 51 536 530.933333333333 5.06666666666667 52 537 530.933333333333 6.06666666666667 53 524 530.933333333333 -6.93333333333333 54 536 530.933333333333 5.06666666666667 55 587 530.933333333333 56.0666666666667 56 597 530.933333333333 66.0666666666667 57 581 530.933333333333 50.0666666666667 58 564 530.933333333333 33.0666666666667 59 558 530.933333333333 27.0666666666667 60 575 530.933333333333 44.0666666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0549383971667756 0.109876794333551 0.945061602833224 6 0.0239541817510202 0.0479083635020405 0.97604581824898 7 0.123884613227811 0.247769226455622 0.87611538677219 8 0.23628454384061 0.47256908768122 0.76371545615939 9 0.291018679893621 0.582037359787243 0.708981320106379 10 0.23426492535306 0.46852985070612 0.76573507464694 11 0.159351422712555 0.31870284542511 0.840648577287445 12 0.105181500172157 0.210363000344314 0.894818499827843 13 0.066876686444593 0.133753372889186 0.933123313555407 14 0.041591814554777 0.083183629109554 0.958408185445223 15 0.0282958248948287 0.0565916497896573 0.971704175105171 16 0.0213878820384937 0.0427757640769874 0.978612117961506 17 0.0159190700033861 0.0318381400067722 0.984080929996614 18 0.0113875554407250 0.0227751108814501 0.988612444559275 19 0.0164871779332076 0.0329743558664152 0.983512822066792 20 0.0340215490195383 0.0680430980390767 0.965978450980462 21 0.0579255926602987 0.115851185320597 0.942074407339701 22 0.0526785976649833 0.105357195329967 0.947321402335017 23 0.0587218235677628 0.117443647135526 0.941278176432237 24 0.0761016451121058 0.152203290224212 0.923898354887894 25 0.0891306377832721 0.178261275566544 0.910869362216728 26 0.124080108604964 0.248160217209928 0.875919891395036 27 0.210115646730339 0.420231293460677 0.789884353269661 28 0.315797186833254 0.631594373666508 0.684202813166746 29 0.471078442138938 0.942156884277876 0.528921557861062 30 0.632431627799593 0.735136744400813 0.367568372200407 31 0.57974545161066 0.840509096778679 0.420254548389340 32 0.552617025358935 0.89476594928213 0.447382974641065 33 0.48963248779514 0.97926497559028 0.51036751220486 34 0.429978354864592 0.859956709729184 0.570021645135408 35 0.400571217843664 0.801142435687328 0.599428782156336 36 0.351032188431821 0.702064376863643 0.648967811568179 37 0.294379572482890 0.588759144965781 0.70562042751711 38 0.258612744688129 0.517225489376257 0.741387255311872 39 0.272488979620201 0.544977959240402 0.727511020379799 40 0.302482731609461 0.604965463218922 0.697517268390539 41 0.505061218812085 0.98987756237583 0.494938781187915 42 0.682487655647984 0.635024688704033 0.317512344352016 43 0.618643553484916 0.762712893030169 0.381356446515084 44 0.544450171252314 0.911099657495372 0.455549828747686 45 0.502171930236297 0.995656139527406 0.497828069763703 46 0.533263156287701 0.933473687424598 0.466736843712299 47 0.631560541996327 0.736878916007346 0.368439458003673 48 0.663375397526319 0.673249204947362 0.336624602473681 49 0.645184978064905 0.709630043870191 0.354815021935095 50 0.613704374940838 0.772591250118324 0.386295625059162 51 0.577763644884807 0.844472710230386 0.422236355115193 52 0.551165153848087 0.897669692303825 0.448834846151913 53 0.721588221110976 0.556823557778048 0.278411778889024 54 0.873351632571878 0.253296734856244 0.126648367428122 55 0.800553965696675 0.39889206860665 0.199446034303325 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 5 0.0980392156862745 NOK 10% type I error level 8 0.156862745098039 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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