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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 06:29:11 -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/t1230125408lhwukil2kbj9q4o.htm/, Retrieved Wed, 24 Dec 2008 14:30:17 +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/t1230125408lhwukil2kbj9q4o.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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Totale_werkloosheid[t] = + 592.016666666667 -64.3611111111111Dummyvariabele[t] -2.67222222222214M1[t] -1.47222222222219M2[t] -6.87222222222217M3[t] -17.4722222222222M4[t] -24.8722222222221M5[t] -34.8722222222222M6[t] -33.8722222222222M7[t] + 17.3277777777778M8[t] + 26.7277777777778M9[t] + 17.9277777777778M10[t] + 15.4M11[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) 592.016666666667 9.826351 60.2479 0 0 Dummyvariabele -64.3611111111111 5.459084 -11.7897 0 0 M1 -2.67222222222214 13.147215 -0.2033 0.839814 0.419907 M2 -1.47222222222219 13.147215 -0.112 0.911316 0.455658 M3 -6.87222222222217 13.147215 -0.5227 0.603629 0.301815 M4 -17.4722222222222 13.147215 -1.329 0.190275 0.095137 M5 -24.8722222222221 13.147215 -1.8918 0.064685 0.032342 M6 -34.8722222222222 13.147215 -2.6524 0.010863 0.005431 M7 -33.8722222222222 13.147215 -2.5764 0.013186 0.006593 M8 17.3277777777778 13.147215 1.318 0.193898 0.096949 M9 26.7277777777778 13.147215 2.033 0.047726 0.023863 M10 17.9277777777778 13.147215 1.3636 0.179184 0.089592 M11 15.4 13.101802 1.1754 0.245751 0.122875 Multiple Linear Regression - Regression Statistics Multiple R 0.89569960655592 R-squared 0.80227778518443 Adjusted R-squared 0.751795517571944 F-TEST (value) 15.8922691695014 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.08402176124400e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20.7157675697698 Sum Squared Residuals 20169.7222222222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 555 589.344444444444 -34.3444444444442 2 562 590.544444444444 -28.5444444444445 3 561 585.144444444444 -24.1444444444444 4 555 574.544444444444 -19.5444444444445 5 544 567.144444444445 -23.1444444444445 6 537 557.144444444444 -20.1444444444444 7 543 558.144444444445 -15.1444444444445 8 594 609.344444444444 -15.3444444444444 9 611 618.744444444444 -7.74444444444445 10 613 609.944444444444 3.05555555555555 11 611 607.416666666667 3.58333333333333 12 594 592.016666666667 1.98333333333337 13 595 589.344444444445 5.65555555555548 14 591 590.544444444444 0.455555555555553 15 589 585.144444444445 3.85555555555554 16 584 574.544444444444 9.45555555555556 17 573 567.144444444445 5.85555555555555 18 567 557.144444444445 9.85555555555555 19 569 558.144444444444 10.8555555555556 20 621 609.344444444444 11.6555555555556 21 629 618.744444444444 10.2555555555556 22 628 609.944444444444 18.0555555555556 23 612 607.416666666667 4.58333333333333 24 595 592.016666666667 2.98333333333336 25 597 589.344444444445 7.6555555555555 26 593 590.544444444444 2.45555555555555 27 590 585.144444444445 4.85555555555554 28 580 574.544444444444 5.45555555555556 29 574 567.144444444444 6.85555555555555 30 573 557.144444444444 15.8555555555556 31 573 558.144444444444 14.8555555555556 32 620 609.344444444444 10.6555555555556 33 626 618.744444444444 7.25555555555556 34 620 609.944444444444 10.0555555555556 35 588 543.055555555556 44.9444444444444 36 566 527.655555555556 38.3444444444445 37 557 524.983333333333 32.0166666666666 38 561 526.183333333333 34.8166666666667 39 549 520.783333333333 28.2166666666667 40 532 510.183333333333 21.8166666666667 41 526 502.783333333333 23.2166666666667 42 511 492.783333333333 18.2166666666667 43 499 493.783333333333 5.21666666666669 44 555 544.983333333333 10.0166666666667 45 565 554.383333333333 10.6166666666667 46 542 545.583333333333 -3.58333333333333 47 527 543.055555555556 -16.0555555555556 48 510 527.655555555556 -17.6555555555555 49 514 524.983333333333 -10.9833333333334 50 517 526.183333333333 -9.18333333333334 51 508 520.783333333333 -12.7833333333333 52 493 510.183333333333 -17.1833333333333 53 490 502.783333333333 -12.7833333333333 54 469 492.783333333333 -23.7833333333333 55 478 493.783333333333 -15.7833333333333 56 528 544.983333333333 -16.9833333333333 57 534 554.383333333333 -20.3833333333333 58 518 545.583333333333 -27.5833333333333 59 506 543.055555555556 -37.0555555555556 60 502 527.655555555556 -25.6555555555555 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.776075129636242 0.447849740727517 0.223924870363758 17 0.725807340647654 0.548385318704693 0.274192659352346 18 0.682370758146992 0.635258483706016 0.317629241853008 19 0.619221748106134 0.761556503787731 0.380778251893866 20 0.562006283480217 0.875987433039566 0.437993716519783 21 0.470554101426591 0.941108202853181 0.529445898573409 22 0.389335599464401 0.778671198928802 0.610664400535599 23 0.285588526345371 0.571177052690742 0.71441147365463 24 0.199361059531174 0.398722119062348 0.800638940468826 25 0.168215434058265 0.336430868116529 0.831784565941735 26 0.133447076124072 0.266894152248145 0.866552923875928 27 0.0991264256970006 0.198252851394001 0.900873574303 28 0.0665355280688348 0.133071056137670 0.933464471931165 29 0.0474583053829723 0.0949166107659445 0.952541694617028 30 0.0352758288641135 0.070551657728227 0.964724171135886 31 0.0234548510923576 0.0469097021847151 0.976545148907642 32 0.0139634096148639 0.0279268192297278 0.986036590385136 33 0.00752988503258068 0.0150597700651614 0.99247011496742 34 0.0036565002944022 0.0073130005888044 0.996343499705598 35 0.0108303315335195 0.021660663067039 0.98916966846648 36 0.0271031029537285 0.054206205907457 0.972896897046271 37 0.0299148809888896 0.0598297619777792 0.97008511901111 38 0.0381900104780481 0.0763800209560962 0.961809989521952 39 0.049028426173713 0.098056852347426 0.950971573826287 40 0.0696984125696849 0.139396825139370 0.930301587430315 41 0.0900500536802928 0.180100107360586 0.909949946319707 42 0.193008356387487 0.386016712774974 0.806991643612513 43 0.197866652336922 0.395733304673844 0.802133347663078 44 0.218573166972228 0.437146333944456 0.781426833027772 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0344827586206897 NOK 5% type I error level 5 0.172413793103448 NOK 10% type I error level 11 0.379310344827586 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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