*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: Fri, 20 Nov 2009 07:35:18 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727856qcde1o40rr5s9w6.htm/, Retrieved Fri, 20 Nov 2009 15:37:49 +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/2009/Nov/20/t1258727856qcde1o40rr5s9w6.htm/}, year = {2009}, } @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 = {2009}, 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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115.6 37.2 111.9 37.2 107 34.7 107.1 32.5 100.6 33.5 99.2 31.5 108.4 31.2 103 27 99.8 26.7 115 26.5 90.8 26 95.9 27.2 114.4 30.5 108.2 33.7 112.6 34.2 109.1 36.7 105 36.2 105 38.5 118.5 40 103.7 42.5 112.5 43.5 116.6 43.3 96.6 45.5 101.9 44.3 116.5 43 119.3 43.5 115.4 41.5 108.5 42.5 111.5 41.3 108.8 39.5 121.8 38.5 109.6 41 112.2 44.5 119.6 46 104.1 44 105.3 41.5 115 41.3 124.1 38 116.8 38 107.5 36.2 115.6 38.7 116.2 38.7 116.3 39.2 119 35.7 111.9 36.5 118.6 36.7 106.9 34.7 103.2 35 118.6 28.2 118.7 23.7 102.8 15 100.6 8.7 94.9 11 94.5 7.5 102.9 5.7 95.3 9.3 92.5 10.2 102.7 15.7 91.5 18.1 89.5 20.8

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 Ipzb[t] = + 92.7883118554799 + 0.466768869596956Cvn[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) 92.7883118554799 2.965563 31.2886 0 0 Cvn 0.466768869596956 0.085851 5.437 1e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.581036051386542 R-squared 0.337602893010864 Adjusted R-squared 0.326182253235189 F-TEST (value) 29.5607688922942 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 1.13073368412930e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.15468539341114 Sum Squared Residuals 2968.99233856406 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 115.6 110.152113804487 5.44788619551324 2 111.9 110.152113804487 1.74788619551332 3 107 108.985191630494 -1.98519163049429 4 107.1 107.958300117381 -0.858300117380993 5 100.6 108.425068986978 -7.82506898697795 6 99.2 107.491531247784 -8.29153124778403 7 108.4 107.351500586905 1.04849941309506 8 103 105.391071334598 -2.39107133459773 9 99.8 105.251040673719 -5.45104067371865 10 115 105.157686899799 9.84231310020075 11 90.8 104.924302465001 -14.1243024650008 12 95.9 105.484425108517 -9.58442510851711 13 114.4 107.024762378187 7.37523762181293 14 108.2 108.518422760897 -0.318422760897333 15 112.6 108.751807195696 3.84819280430418 16 109.1 109.918729369688 -0.81872936968821 17 105 109.685344934890 -4.68534493488973 18 105 110.758913334963 -5.75891333496272 19 118.5 111.459066639358 7.04093336064184 20 103.7 112.625988813351 -8.92598881335054 21 112.5 113.092757682948 -0.592757682947502 22 116.6 112.999403909028 3.60059609097188 23 96.6 114.026295422141 -17.4262954221414 24 101.9 113.466172778625 -11.5661727786251 25 116.5 112.859373248149 3.64062675185097 26 119.3 113.092757682948 6.20724231705249 27 115.4 112.159219943754 3.24078005624642 28 108.5 112.625988813351 -4.12598881335055 29 111.5 112.065866169834 -0.565866169834198 30 108.8 111.225682204560 -2.42568220455968 31 121.8 110.758913334963 11.0410866650373 32 109.6 111.925835508955 -2.32583550895512 33 112.2 113.559526552544 -1.35952655254446 34 119.6 114.259679856940 5.3403201430601 35 104.1 113.326142117746 -9.22614211774598 36 105.3 112.159219943754 -6.8592199437536 37 115 112.065866169834 2.9341338301658 38 124.1 110.525528900164 13.5744710998357 39 116.8 110.525528900164 6.27447109983575 40 107.5 109.685344934890 -2.18534493488973 41 115.6 110.852267108882 4.74773289111788 42 116.2 110.852267108882 5.34773289111789 43 116.3 111.085651543681 5.2143484563194 44 119 109.451960500091 9.54803949990875 45 111.9 109.825375595769 2.07462440423119 46 118.6 109.918729369688 8.68127063031179 47 106.9 108.985191630494 -2.08519163049429 48 103.2 109.125222291373 -5.92522229137337 49 118.6 105.951193978114 12.6488060218859 50 118.7 103.850734064928 14.8492659350722 51 102.8 99.7898448994343 3.01015510056574 52 100.6 96.8492010209734 3.75079897902656 53 94.9 97.9227694210464 -3.02276942104643 54 94.5 96.289078377457 -1.78907837745709 55 102.9 95.4488944121826 7.45110558781744 56 95.3 97.1292623427316 -1.82926234273161 57 92.5 97.5493543253689 -5.04935432536887 58 102.7 100.116583108152 2.58341689184788 59 91.5 101.236828395185 -9.73682839518482 60 89.5 102.497104343097 -12.9971043430966 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.161402860693162 0.322805721386324 0.838597139306838 6 0.0738066644931193 0.147613328986239 0.92619333550688 7 0.129010399575073 0.258020799150146 0.870989600424927 8 0.102022810276731 0.204045620553461 0.89797718972327 9 0.0539031008596462 0.107806201719292 0.946096899140354 10 0.27541138055563 0.55082276111126 0.72458861944437 11 0.459047434503921 0.918094869007842 0.540952565496079 12 0.436488555853893 0.872977111707786 0.563511444146107 13 0.510375635666066 0.979248728667867 0.489624364333934 14 0.414715909889877 0.829431819779754 0.585284090110123 15 0.349620700864776 0.699241401729552 0.650379299135224 16 0.275627828369667 0.551255656739334 0.724372171630333 17 0.244992127340294 0.489984254680588 0.755007872659706 18 0.234017020094633 0.468034040189265 0.765982979905367 19 0.218616703373837 0.437233406747674 0.781383296626163 20 0.290199206493377 0.580398412986754 0.709800793506623 21 0.224361821607450 0.448723643214901 0.77563817839255 22 0.178769285580115 0.357538571160231 0.821230714419885 23 0.528453165219947 0.943093669560105 0.471546834780053 24 0.628076254641014 0.743847490717972 0.371923745358986 25 0.595707460149301 0.808585079701397 0.404292539850699 26 0.593601676697045 0.81279664660591 0.406398323302955 27 0.539550655288127 0.920898689423746 0.460449344711873 28 0.494753426740882 0.989506853481765 0.505246573259118 29 0.425714032631519 0.851428065263038 0.574285967368481 30 0.36842334590105 0.7368466918021 0.63157665409895 31 0.468082937538729 0.936165875077457 0.531917062461271 32 0.409714636696674 0.819429273393348 0.590285363303326 33 0.35025451507765 0.7005090301553 0.64974548492235 34 0.308773389549936 0.617546779099873 0.691226610450064 35 0.406370317160314 0.812740634320629 0.593629682839686 36 0.467371090622479 0.934742181244958 0.532628909377521 37 0.407140328892311 0.814280657784623 0.592859671107689 38 0.544078615066625 0.91184276986675 0.455921384933375 39 0.49863201422767 0.99726402845534 0.50136798577233 40 0.453800020028339 0.907600040056677 0.546199979971661 41 0.388912393105709 0.777824786211418 0.611087606894291 42 0.329193333843537 0.658386667687073 0.670806666156463 43 0.270689417326139 0.541378834652278 0.729310582673861 44 0.277884709103342 0.555769418206684 0.722115290896658 45 0.21085361222753 0.42170722445506 0.78914638777247 46 0.213301578830093 0.426603157660186 0.786698421169907 47 0.157705944632871 0.315411889265743 0.842294055367129 48 0.172045543526914 0.344091087053828 0.827954456473086 49 0.237399123241764 0.474798246483527 0.762600876758236 50 0.866083236051614 0.267833527896771 0.133916763948386 51 0.901556757240594 0.196886485518812 0.098443242759406 52 0.853181428724144 0.293637142551713 0.146818571275856 53 0.762654669584415 0.47469066083117 0.237345330415585 54 0.677547891042183 0.644904217915634 0.322452108957817 55 0.579359632129682 0.841280735740636 0.420640367870318 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 0 0 OK

Charts produced by software:

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Parameters (Session):

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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