Minitutorial Multiple Regression invoeren 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, 30 Nov 2010 14:04:11 +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/Nov/30/t1291125868cqdl37tgi8b6yqd.htm/, Retrieved Tue, 30 Nov 2010 15:04:42 +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/Nov/30/t1291125868cqdl37tgi8b6yqd.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:

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No (this computation is public)

User-defined keywords:

Workshop 4

Dataseries X:

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30/11/2010 0 8 17 2 6 31/10/2010 -2 3 23 3 7 30/09/2010 -4 3 24 1 4 31/08/2010 -4 7 27 1 3 31/07/2010 -7 4 31 0 0 30/06/2010 -9 -4 40 1 6 31/05/2010 -13 -6 47 -1 3 30/04/2010 -8 8 43 2 1 31/03/2010 -13 2 60 2 6 28/02/2010 -15 -1 64 0 5 31/01/2010 -15 -2 65 1 7 31/12/2009 -15 0 65 1 4 30/11/2009 -10 10 55 3 3 31/10/2009 -12 3 57 3 6 30/09/2009 -11 6 57 1 6 31/08/2009 -11 7 57 1 5 31/07/2009 -17 -4 65 -2 2 30/06/2009 -18 -5 69 1 3 31/05/2009 -19 -7 70 1 -2 30/04/2009 -22 -10 71 -1 -4 31/03/2009 -24 -21 71 -4 0 28/02/2009 -24 -22 73 -2 1 31/01/2009 -20 -16 68 -1 4 31/12/2008 -25 -25 65 -5 -3 30/11/2008 -22 -22 57 -4 -3 31/10/2008 -17 -22 41 -5 0 30/09/2008 -9 -19 21 0 6 31/08/2008 -11 -21 21 -2 -1 31/07/2008 -13 -31 17 -4 0 30/06/2008 -11 -28 9 -6 -1 31/05/2008 -9 -23 11 -2 1 30/04/2008 -7 -17 6 -2 -4 31/03/2008 -3 -12 -2 -2 -1 29/02/2008 -3 -14 0 1 -1 31/01/2008 -6 -18 5 -2 0 31/12/2007 -4 -16 3 0 3 30/11/2007 -8 -22 7 -1 0 31/10/2007 -1 -9 4 2 8 30/09/2007 -2 -10 8 3 8 31 etc...

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation CVI[t] = + 0.112887779893211 + 26.0887388895069Maand[t] + 0.250165293372729Econ.Sit.[t] -0.253625189537363Werkloos[t] + 0.283963060245982Fin.Sit.[t] + 0.221586511866371`Spaarverm. `[t] -0.00248839513129872t + 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) 0.112887779893211 0.130251 0.8667 0.389943 0.194971 Maand 26.0887388895069 10.273489 2.5394 0.014016 0.007008 Econ.Sit. 0.250165293372729 0.009522 26.2726 0 0 Werkloos -0.253625189537363 0.001967 -128.9521 0 0 Fin.Sit. 0.283963060245982 0.039338 7.2185 0 0 `Spaarverm. ` 0.221586511866371 0.014498 15.2841 0 0 t -0.00248839513129872 0.004826 -0.5156 0.608216 0.304108 Multiple Linear Regression - Regression Statistics Multiple R 0.999268451452004 R-squared 0.998537438067286 Adjusted R-squared 0.998374931185873 F-TEST (value) 6144.58556700532 F-TEST (DF numerator) 6 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.298237209437717 Sum Squared Residuals 4.80305338703263 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 -0.267062738471258 0.267062738471258 2 -2 -2.53174136234659 0.531741362346592 3 -4 -4.01751205961998 0.0175120596199833 4 -4 -3.99477081435981 -0.00522918564018951 5 -7 -6.70379337870002 -0.29620662129998 6 -9 -9.36933185401417 0.369331854014165 7 -13 -12.8646374522423 -0.135362547757653 8 -8 -7.92472151129115 -0.0752784887088516 9 -13 -12.5951221585565 -0.404877841443459 10 -15 -15.1045284266713 0.104528426671263 11 -15 -14.6630201953003 -0.336979804699709 12 -15 -15.1987541809688 0.198754180968771 13 -10 -9.81512895108416 -0.184871048915843 14 -12 -11.4064250320034 -0.593574967996582 15 -11 -11.2233136165341 0.223313616534104 16 -11 -11.1901891832542 0.190189183254206 17 -17 -17.4829573967792 0.482957396779183 18 -18 -17.6692156178298 -0.330784382170161 19 -19 -19.5180092292789 0.518009229278944 20 -22 -21.5188361257189 -0.481163874281108 21 -24 -24.2018924051051 0.201892405105070 22 -24 -24.1246687535851 0.124668753585052 23 -20 -20.1885559882424 0.188555988242437 24 -25 -24.7376144947333 -0.262385505266719 25 -22 -21.6747723150419 -0.325227684958059 26 -17 -17.2336185804617 0.233618580461749 27 -9 -8.66074137233554 -0.339258627664461 28 -11 -11.2755545078526 0.275554507852613 29 -13 -13.1043424658444 0.104342465844365 30 -11 -11.1094218684338 0.109421868433836 31 -9 -8.7737180312451 -0.226281968754900 32 -7 -7.09813115798608 0.0981311579860777 33 -3 -3.11922023479383 0.119220234793828 34 -3 -3.22326541565164 0.223265415651644 35 -6 -5.91046900338362 -0.089530996616384 36 -4 -4.04187474889146 0.0418747488914551 37 -8 -7.50670720829633 -0.493292791703674 38 -1 -0.866744910674749 -0.133255089325251 39 -2 -1.84690322662507 -0.153096773374927 40 -2 -2.37993881512127 0.379938815121274 41 -1 -0.85774135905496 -0.142258640945040 42 1 1.35366702850198 -0.353667028501977 43 2 1.84374807204215 0.156251927957854 44 2 1.85392265181642 0.146077348183579 45 -1 -0.62475164913857 -0.37524835086143 46 1 0.930093133253654 0.069906866746346 47 -1 -0.972088642562461 -0.0279113574375386 48 -8 -8.04219359755118 0.0421935975511818 49 1 0.738137820891522 0.261862179108478 50 2 2.35221991790006 -0.352219917900064 51 -2 -1.7434524848397 -0.256547515160301 52 -2 -1.63926210213684 -0.360737897863158 53 -2 -2.00159180858946 0.00159180858946454 54 -2 -2.27193275192973 0.27193275192973 55 -6 -5.72824882259733 -0.271751177402674 56 -4 -3.72026903362548 -0.279730966374522 57 -5 -5.42924657659096 0.429246576590963 58 -2 -2.35262689698665 0.352626896986646 59 -1 -0.997512943741537 -0.00248705625846306 60 -5 -5.12981204412866 0.129812044128662 61 -9 -9.4238311216023 0.423831121602302 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.172391022280015 0.34478204456003 0.827608977719985 11 0.478033753366605 0.95606750673321 0.521966246633395 12 0.348732765077211 0.697465530154422 0.651267234922789 13 0.367347213468127 0.734694426936254 0.632652786531873 14 0.601320559748423 0.797358880503153 0.398679440251577 15 0.621659972983107 0.756680054033786 0.378340027016893 16 0.556044862698056 0.887910274603888 0.443955137301944 17 0.663398378883833 0.673203242232334 0.336601621116167 18 0.589909785524931 0.820180428950137 0.410090214475069 19 0.899976993614495 0.200046012771011 0.100023006385506 20 0.94704747482644 0.105905050347120 0.0529525251735599 21 0.924876240831386 0.150247518337229 0.0751237591686143 22 0.890712495242581 0.218575009514838 0.109287504757419 23 0.868429693130618 0.263140613738765 0.131570306869382 24 0.906330540613905 0.187338918772190 0.0936694593860952 25 0.944550971813936 0.110898056372129 0.0554490281860645 26 0.917443064140408 0.165113871719184 0.0825569358595918 27 0.926259820515012 0.147480358969976 0.0737401794849882 28 0.920161183242529 0.159677633514943 0.0798388167574714 29 0.888113919536646 0.223772160926708 0.111886080463354 30 0.869285131097911 0.261429737804178 0.130714868902089 31 0.834807369943865 0.330385260112271 0.165192630056136 32 0.79031783706558 0.419364325868838 0.209682162934419 33 0.772271210146567 0.455457579706866 0.227728789853433 34 0.747738514563861 0.504522970872278 0.252261485436139 35 0.697963669946869 0.604072660106261 0.302036330053131 36 0.674167503946457 0.651664992107086 0.325832496053543 37 0.724107370497969 0.551785259004062 0.275892629502031 38 0.645926565847062 0.708146868305876 0.354073434152938 39 0.592622663763586 0.814754672472829 0.407377336236414 40 0.848285424124717 0.303429151750565 0.151714575875283 41 0.798502926416181 0.402994147167638 0.201497073583819 42 0.762017169310401 0.475965661379198 0.237982830689599 43 0.802337056806706 0.395325886386588 0.197662943193294 44 0.75749825516923 0.485003489661542 0.242501744830771 45 0.683179884181721 0.633640231636559 0.316820115818279 46 0.766198284006976 0.467603431986048 0.233801715993024 47 0.672220975385235 0.65555804922953 0.327779024614765 48 0.597794302916177 0.804411394167647 0.402205697083823 49 0.539424648677848 0.921150702644305 0.460575351322152 50 0.466266428664613 0.932532857329227 0.533733571335387 51 0.489269816332315 0.97853963266463 0.510730183667685 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):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = 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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