Paper H4 Vrouwen Multiple Regression (No seasonal, No trend)

*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: Tue, 16 Dec 2008 14:15:33 -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/16/t1229462183ts5g0298vruh8f7.htm/, Retrieved Tue, 16 Dec 2008 22:16:33 +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/16/t1229462183ts5g0298vruh8f7.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:

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308347 0 298427 0 289231 0 291975 0 294912 0 293488 0 290555 0 284736 0 281818 0 287854 0 316263 0 325412 0 326011 0 328282 0 317480 0 317539 0 313737 0 312276 0 309391 0 302950 0 300316 0 304035 0 333476 0 337698 0 335932 0 323931 0 313927 0 314485 1 313218 1 309664 1 302963 1 298989 1 298423 1 301631 1 329765 1 335083 1 327616 1 309119 1 295916 1 291413 1 291542 1 284678 1 276475 1 272566 1 264981 1 263290 1 296806 1 303598 1 286994 1 276427 1 266424 1 267153 1 268381 1 262522 1 255542 1 253158 1 243803 1 250741 1 280445 1 285257 1 270976 1 261076 1 255603 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Vrouwen[t] = + 308888.851851852 -23702.1018518519Dummy[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) 308888.851851852 4042.479058 76.4107 0 0 Dummy -23702.1018518519 5347.697134 -4.4322 4e-05 2e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.493551851599653 R-squared 0.243593430217446 Adjusted R-squared 0.231193322516093 F-TEST (value) 19.6444608453570 F-TEST (DF numerator) 1 F-TEST (DF denominator) 61 p-value 3.95266524808591e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21005.3373530171 Sum Squared Residuals 26914676036.1574 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 308347 308888.851851852 -541.851851852005 2 298427 308888.851851852 -10461.8518518518 3 289231 308888.851851852 -19657.8518518519 4 291975 308888.851851852 -16913.8518518519 5 294912 308888.851851852 -13976.8518518519 6 293488 308888.851851852 -15400.8518518519 7 290555 308888.851851852 -18333.8518518519 8 284736 308888.851851852 -24152.8518518519 9 281818 308888.851851852 -27070.8518518519 10 287854 308888.851851852 -21034.8518518519 11 316263 308888.851851852 7374.14814814815 12 325412 308888.851851852 16523.1481481481 13 326011 308888.851851852 17122.1481481481 14 328282 308888.851851852 19393.1481481481 15 317480 308888.851851852 8591.14814814815 16 317539 308888.851851852 8650.14814814815 17 313737 308888.851851852 4848.14814814815 18 312276 308888.851851852 3387.14814814815 19 309391 308888.851851852 502.148148148146 20 302950 308888.851851852 -5938.85185185185 21 300316 308888.851851852 -8572.85185185185 22 304035 308888.851851852 -4853.85185185185 23 333476 308888.851851852 24587.1481481481 24 337698 308888.851851852 28809.1481481481 25 335932 308888.851851852 27043.1481481481 26 323931 308888.851851852 15042.1481481481 27 313927 308888.851851852 5038.14814814815 28 314485 285186.75 29298.25 29 313218 285186.75 28031.25 30 309664 285186.75 24477.25 31 302963 285186.75 17776.25 32 298989 285186.75 13802.25 33 298423 285186.75 13236.25 34 301631 285186.75 16444.25 35 329765 285186.75 44578.25 36 335083 285186.75 49896.25 37 327616 285186.75 42429.25 38 309119 285186.75 23932.25 39 295916 285186.75 10729.25 40 291413 285186.75 6226.25 41 291542 285186.75 6355.25 42 284678 285186.75 -508.750000000001 43 276475 285186.75 -8711.75 44 272566 285186.75 -12620.75 45 264981 285186.75 -20205.75 46 263290 285186.75 -21896.75 47 296806 285186.75 11619.25 48 303598 285186.75 18411.25 49 286994 285186.75 1807.25 50 276427 285186.75 -8759.75 51 266424 285186.75 -18762.75 52 267153 285186.75 -18033.75 53 268381 285186.75 -16805.75 54 262522 285186.75 -22664.75 55 255542 285186.75 -29644.75 56 253158 285186.75 -32028.75 57 243803 285186.75 -41383.75 58 250741 285186.75 -34445.75 59 280445 285186.75 -4741.75 60 285257 285186.75 70.2499999999991 61 270976 285186.75 -14210.75 62 261076 285186.75 -24110.75 63 255603 285186.75 -29583.75 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0767533489513503 0.153506697902701 0.92324665104865 6 0.0264623328982949 0.0529246657965899 0.973537667101705 7 0.0103451595765502 0.0206903191531004 0.98965484042345 8 0.00785407474211892 0.0157081494842378 0.992145925257881 9 0.00768957251091282 0.0153791450218256 0.992310427489087 10 0.0035670318883359 0.0071340637766718 0.996432968111664 11 0.0179107765244847 0.0358215530489694 0.982089223475515 12 0.0746326808995893 0.149265361799179 0.92536731910041 13 0.13342185167894 0.26684370335788 0.86657814832106 14 0.192875680624417 0.385751361248835 0.807124319375583 15 0.16514494374217 0.33028988748434 0.83485505625783 16 0.137095160986726 0.274190321973453 0.862904839013274 17 0.102296416041039 0.204592832082079 0.89770358395896 18 0.0725875687092488 0.145175137418498 0.927412431290751 19 0.0486899155609904 0.0973798311219807 0.95131008443901 20 0.0325511992016963 0.0651023984033926 0.967448800798304 21 0.0229251706555469 0.0458503413110939 0.977074829344453 22 0.0156869784024708 0.0313739568049415 0.98431302159753 23 0.0254827212900318 0.0509654425800637 0.974517278709968 24 0.0433593384453717 0.0867186768907434 0.956640661554628 25 0.0569964734643575 0.113992946928715 0.943003526535642 26 0.0460459122969619 0.0920918245939239 0.953954087703038 27 0.0307246894982358 0.0614493789964716 0.969275310501764 28 0.0255715464607692 0.0511430929215383 0.974428453539231 29 0.0214018176862068 0.0428036353724136 0.978598182313793 30 0.0173609655596178 0.0347219311192355 0.982639034440382 31 0.0134015721898193 0.0268031443796385 0.98659842781018 32 0.0100820699654820 0.0201641399309640 0.989917930034518 33 0.00735334203483606 0.0147066840696721 0.992646657965164 34 0.00538038275408806 0.0107607655081761 0.994619617245912 35 0.0176604300945876 0.0353208601891752 0.982339569905412 36 0.0921921822751352 0.184384364550270 0.907807817724865 37 0.274221861962773 0.548443723925546 0.725778138037227 38 0.385363406552857 0.770726813105714 0.614636593447143 39 0.436275387984521 0.872550775969043 0.563724612015479 40 0.475429746224406 0.950859492448812 0.524570253775594 41 0.518953075173725 0.96209384965255 0.481046924826275 42 0.539933099806194 0.920133800387611 0.460066900193806 43 0.550985706302149 0.898028587395703 0.449014293697851 44 0.554742913448649 0.890514173102702 0.445257086551351 45 0.577121186793523 0.845757626412953 0.422878813206477 46 0.587891999816314 0.824216000367372 0.412108000183686 47 0.668445983220611 0.663108033558778 0.331554016779389 48 0.878709638038235 0.24258072392353 0.121290361961765 49 0.9186555616289 0.162688876742201 0.0813444383711004 50 0.913829783554896 0.172340432890207 0.0861702164451036 51 0.887053188577327 0.225893622845347 0.112946811422673 52 0.84957207893492 0.300855842130161 0.150427921065081 53 0.801127066846571 0.397745866306858 0.198872933153429 54 0.73300869811494 0.53398260377012 0.26699130188506 55 0.671349239304539 0.657301521390921 0.328650760695461 56 0.612934875204541 0.774130249590917 0.387065124795459 57 0.694837240187852 0.610325519624297 0.305162759812148 58 0.706244797147246 0.587510405705507 0.293755202852754 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0185185185185185 NOK 5% type I error level 14 0.259259259259259 NOK 10% type I error level 22 0.407407407407407 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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