*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 24 Dec 2008 06:18:29 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/24/t1230124751z7z4snbabk9jk8j.htm/, Retrieved Wed, 24 Dec 2008 14:19:12 +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/2008/Dec/24/t1230124751z7z4snbabk9jk8j.htm/}, year = {2008}, } @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 = {2008}, 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 «

555 0 562 0 561 0 555 0 544 0 537 0 543 0 594 0 611 0 613 0 611 0 594 0 595 0 591 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 1 566 1 557 1 561 1 549 1 532 1 526 1 511 1 499 1 555 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

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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Totale_werkloosheid[t] = + 587.617647058823 -62.8099547511312Dummyvariabele[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) 587.617647058823 4.717478 124.5618 0 0 Dummyvariabele -62.8099547511312 7.166363 -8.7646 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.754843226993062 R-squared 0.5697882973373 Adjusted R-squared 0.562370854187943 F-TEST (value) 76.8173460671148 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 3.25062199380000e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 27.5073870559012 Sum Squared Residuals 43886.0678733032 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 555 587.617647058824 -32.6176470588242 2 562 587.617647058824 -25.6176470588236 3 561 587.617647058824 -26.6176470588235 4 555 587.617647058824 -32.6176470588235 5 544 587.617647058824 -43.6176470588235 6 537 587.617647058824 -50.6176470588235 7 543 587.617647058824 -44.6176470588235 8 594 587.617647058824 6.38235294117649 9 611 587.617647058824 23.3823529411765 10 613 587.617647058824 25.3823529411765 11 611 587.617647058824 23.3823529411765 12 594 587.617647058824 6.38235294117649 13 595 587.617647058824 7.38235294117649 14 591 587.617647058824 3.38235294117650 15 589 587.617647058824 1.38235294117650 16 584 587.617647058824 -3.6176470588235 17 573 587.617647058824 -14.6176470588235 18 567 587.617647058824 -20.6176470588235 19 569 587.617647058824 -18.6176470588235 20 621 587.617647058824 33.3823529411765 21 629 587.617647058824 41.3823529411765 22 628 587.617647058824 40.3823529411765 23 612 587.617647058824 24.3823529411765 24 595 587.617647058824 7.38235294117649 25 597 587.617647058824 9.3823529411765 26 593 587.617647058824 5.38235294117649 27 590 587.617647058824 2.38235294117650 28 580 587.617647058824 -7.6176470588235 29 574 587.617647058824 -13.6176470588235 30 573 587.617647058824 -14.6176470588235 31 573 587.617647058824 -14.6176470588235 32 620 587.617647058824 32.3823529411765 33 626 587.617647058824 38.3823529411765 34 620 587.617647058824 32.3823529411765 35 588 524.807692307692 63.1923076923077 36 566 524.807692307692 41.1923076923077 37 557 524.807692307692 32.1923076923077 38 561 524.807692307692 36.1923076923077 39 549 524.807692307692 24.1923076923077 40 532 524.807692307692 7.19230769230769 41 526 524.807692307692 1.19230769230769 42 511 524.807692307692 -13.8076923076923 43 499 524.807692307692 -25.8076923076923 44 555 524.807692307692 30.1923076923077 45 565 524.807692307692 40.1923076923077 46 542 524.807692307692 17.1923076923077 47 527 524.807692307692 2.19230769230769 48 510 524.807692307692 -14.8076923076923 49 514 524.807692307692 -10.8076923076923 50 517 524.807692307692 -7.80769230769231 51 508 524.807692307692 -16.8076923076923 52 493 524.807692307692 -31.8076923076923 53 490 524.807692307692 -34.8076923076923 54 469 524.807692307692 -55.8076923076923 55 478 524.807692307692 -46.8076923076923 56 528 524.807692307692 3.19230769230769 57 534 524.807692307692 9.1923076923077 58 518 524.807692307692 -6.80769230769231 59 506 524.807692307692 -18.8076923076923 60 502 524.807692307692 -22.8076923076923 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0383225844609982 0.0766451689219965 0.961677415539002 6 0.0545865900135515 0.109173180027103 0.945413409986449 7 0.0318338039978040 0.0636676079956081 0.968166196002196 8 0.253049926310102 0.506099852620204 0.746950073689898 9 0.610050029785007 0.779899940429987 0.389949970214993 10 0.770476826973353 0.459046346053295 0.229523173026647 11 0.824756352734028 0.350487294531943 0.175243647265972 12 0.78611855520254 0.427762889594921 0.213881444797460 13 0.74211150455504 0.515776990889921 0.257888495444960 14 0.680586342781923 0.638827314436154 0.319413657218077 15 0.609215454629469 0.781569090741062 0.390784545370531 16 0.529339554092905 0.94132089181419 0.470660445907095 17 0.460767279531377 0.921534559062755 0.539232720468623 18 0.415631303429921 0.831262606859842 0.584368696570079 19 0.370867408258984 0.741734816517968 0.629132591741016 20 0.459649784659331 0.919299569318662 0.540350215340669 21 0.586653165802903 0.826693668394194 0.413346834197097 22 0.673375094993228 0.653249810013545 0.326624905006772 23 0.654738356480973 0.690523287038053 0.345261643519027 24 0.586115902852387 0.827768194295226 0.413884097147613 25 0.517411853789413 0.965176292421174 0.482588146210587 26 0.44341973922996 0.88683947845992 0.55658026077004 27 0.370331084845229 0.740662169690458 0.629668915154771 28 0.311266465882612 0.622532931765225 0.688733534117388 29 0.275522727230752 0.551045454461504 0.724477272769248 30 0.257684238743656 0.515368477487311 0.742315761256344 31 0.269529617588413 0.539059235176826 0.730470382411587 32 0.262684738776393 0.525369477552786 0.737315261223607 33 0.267649662102651 0.535299324205301 0.73235033789735 34 0.247432332207166 0.494864664414332 0.752567667792834 35 0.374865690130322 0.749731380260644 0.625134309869678 36 0.43133263798017 0.86266527596034 0.56866736201983 37 0.460916136000841 0.921832272001681 0.539083863999159 38 0.526780512442625 0.94643897511475 0.473219487557375 39 0.549909395448216 0.900181209103568 0.450090604551784 40 0.529606849478551 0.940786301042898 0.470393150521449 41 0.495306396892832 0.990612793785663 0.504693603107168 42 0.472046907852564 0.944093815705129 0.527953092147436 43 0.481940845448708 0.963881690897416 0.518059154551292 44 0.558199755013554 0.883600489972892 0.441800244986446 45 0.793000657565146 0.413998684869709 0.206999342434854 46 0.845406336689878 0.309187326620244 0.154593663310122 47 0.834852925060345 0.330294149879310 0.165147074939655 48 0.784787068063595 0.430425863872811 0.215212931936406 49 0.725100544236279 0.549798911527442 0.274899455763721 50 0.66379767194833 0.67240465610334 0.33620232805167 51 0.573341775735737 0.853316448528527 0.426658224264263 52 0.498220649590934 0.996441299181868 0.501779350409066 53 0.428856479983994 0.857712959967987 0.571143520016006 54 0.619459238564571 0.761081522870859 0.380540761435429 55 0.816856701233882 0.366286597532236 0.183143298766118 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 0 0 OK 10% type I error level 2 0.0392156862745098 OK

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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