Model 5

*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 08:42:18 -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/t12587318021x3xrihq1kza4g8.htm/, Retrieved Fri, 20 Nov 2009 16:43:33 +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/2009/Nov/20/t12587318021x3xrihq1kza4g8.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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3.37 100.7 101.1 101.2 3.51 100.1 100.7 101.1 3.75 99.9 100.1 100.7 4.11 99.7 99.9 100.1 4.25 99.5 99.7 99.9 4.25 99.2 99.5 99.7 4.5 99 99.2 99.5 4.7 99 99 99.2 4.75 99.3 99 99 4.75 99.5 99.3 99 4.75 99.7 99.5 99.3 4.75 100 99.7 99.5 4.75 100.4 100 99.7 4.75 100.6 100.4 100 4.58 100.7 100.6 100.4 4.5 100.7 100.7 100.6 4.5 100.6 100.7 100.7 4.49 100.5 100.6 100.7 4.03 100.6 100.5 100.6 3.75 100.5 100.6 100.5 3.39 100.4 100.5 100.6 3.25 100.3 100.4 100.5 3.25 100.4 100.3 100.4 3.25 100.4 100.4 100.3 3.25 100.4 100.4 100.4 3.25 100.4 100.4 100.4 3.25 100.4 100.4 100.4 3.25 100.5 100.4 100.4 3.25 100.6 100.5 100.4 3.25 100.6 100.6 100.5 3.25 100.5 100.6 100.6 3.25 100.5 100.5 100.6 3.25 100.7 100.5 100.5 2.85 101.1 100.7 100.5 2.75 101.5 101.1 100.7 2.75 101.9 101.5 101.1 2.55 102.1 101.9 101.5 2.5 102.1 102.1 101.9 2.5 102.1 102.1 102.1 2.1 102.4 102.1 102.1 2 102.8 102.4 102.1 2 103.1 102.8 102.4 2 103.1 103.1 102.8 2 102.9 103.1 103.1 2 102.4 102.9 103.1 2 101.9 102 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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation tprod[t] = + 12.9908192957064 + 0.00822602769769642rente[t] + 1.71770940750858y1[t] -0.849061836576314y2[t] + 0.00908552672304065t + 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) 12.9908192957064 3.641248 3.5677 0.000774 0.000387 rente 0.00822602769769642 0.059448 0.1384 0.890471 0.445235 y1 1.71770940750858 0.080118 21.4397 0 0 y2 -0.849061836576314 0.085439 -9.9377 0 0 t 0.00908552672304065 0.003184 2.8535 0.006156 0.003078 Multiple Linear Regression - Regression Statistics Multiple R 0.992463563783446 R-squared 0.984983925437739 Adjusted R-squared 0.98385063679153 F-TEST (value) 869.137733562538 F-TEST (DF numerator) 4 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.153589057440373 Sum Squared Residuals 1.25024872396738 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.7 100.762989773365 -0.062989773365053 2 100.1 100.17104936462 -0.071049364619917 3 99.9 99.4911082281157 0.408891771884256 4 99.7 99.669050345254 0.0309496547459434 5 99.5 99.5055580016683 -0.00555800166831006 6 99.2 99.3409140142049 -0.140914014204893 7 99 99.006555592915 -0.00655559291505667 8 99 98.9284629946488 0.0715370053511918 9 99.3 99.107772190072 0.192227809927998 10 99.5 99.6321705390476 -0.132170539047608 11 99.7 99.7300793962995 -0.0300793962994748 12 100 99.912894437209 0.0871055627910264 13 100.4 100.267480418869 0.132519581130688 14 100.6 100.708931157623 -0.108931157622913 15 100.7 100.720535406509 -0.0205354065085027 16 100.7 100.730921424451 -0.0309214244513468 17 100.6 100.655100767517 -0.0551007675167573 18 100.5 100.492333093212 0.00766690678805705 19 100.6 100.410769890101 0.189230109899161 20 100.5 100.674229253477 -0.174229253476994 21 100.4 100.423676285820 -0.0236762858203833 22 100.3 100.344745411573 -0.0447454115725334 23 100.4 100.266966181202 0.133033818797680 24 100.4 100.532728832334 -0.132728832333871 25 100.4 100.456908175399 -0.0569081753992734 26 100.4 100.465993702122 -0.065993702122314 27 100.4 100.475079228845 -0.0750792288453547 28 100.5 100.484164755568 0.0158352444315989 29 100.6 100.665021223042 -0.0650212230422954 30 100.6 100.760971506859 -0.160971506858558 31 100.5 100.685150849924 -0.185150849923966 32 100.5 100.522465435896 -0.0224654358961586 33 100.7 100.616457146277 0.083542853723177 34 101.1 100.965794143423 0.134205856577486 35 101.5 101.491328463064 0.00867153693606944 36 101.9 101.847873018160 0.0521269818401117 37 102.1 102.202772367716 -0.102772367716312 38 102.1 102.215363739926 -0.115363739925633 39 102.1 102.054636899333 0.0453631006665791 40 102.4 102.060432014977 0.339567985022629 41 102.8 102.584007761183 0.215992238816756 42 103.1 103.025458499937 0.0745415000631995 43 103.1 103.210232114282 -0.110232114281891 44 102.9 102.964599090032 -0.064599090032029 45 102.4 102.630142735253 -0.230142735253373 46 101.9 101.950185925537 -0.0501859255373783 47 101.3 101.524947666794 -0.224947666794295 48 100.7 100.927938467300 -0.227938467300325 49 100.6 100.415835451464 0.184164548535967 50 101 100.762587139382 0.237412860618021 51 101.5 101.543662612766 -0.043662612766099 52 101.9 102.071978108613 -0.171978108612893 53 102.1 102.343616480051 -0.243616480051229 54 102.3 102.356619153645 -0.0566191536454327 55 102.5 102.539434194555 -0.039434194554938 56 102.9 102.722249235464 0.177750764535572 57 103.6 103.248606157876 0.351393842124344 58 104.3 104.120463535224 0.179536464775851 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.559511774984523 0.880976450030955 0.440488225015477 9 0.836521855502964 0.326956288994072 0.163478144497036 10 0.745483415163598 0.509033169672804 0.254516584836402 11 0.635149374753572 0.729701250492857 0.364850625246428 12 0.523746082529187 0.952507834941626 0.476253917470813 13 0.426493273265642 0.852986546531284 0.573506726734358 14 0.445741022594597 0.891482045189195 0.554258977405403 15 0.404646620098383 0.809293240196765 0.595353379901617 16 0.342242782490781 0.684485564981562 0.657757217509219 17 0.282301246858076 0.564602493716151 0.717698753141924 18 0.206113240920712 0.412226481841423 0.793886759079288 19 0.237583420066054 0.475166840132108 0.762416579933946 20 0.240033386596318 0.480066773192636 0.759966613403682 21 0.176882594588919 0.353765189177839 0.823117405411081 22 0.124544526983814 0.249089053967628 0.875455473016186 23 0.134918283884376 0.269836567768752 0.865081716115624 24 0.102022074909373 0.204044149818746 0.897977925090627 25 0.0688416707011073 0.137683341402215 0.931158329298893 26 0.0451449215336397 0.0902898430672794 0.95485507846636 27 0.0289087478070724 0.0578174956141449 0.971091252192928 28 0.0188992705785260 0.0377985411570519 0.981100729421474 29 0.0110820878850113 0.0221641757700226 0.988917912114989 30 0.0085756642230614 0.0171513284461228 0.991424335776939 31 0.0095382150288086 0.0190764300576172 0.990461784971191 32 0.00546666794050588 0.0109333358810118 0.994533332059494 33 0.00416697604882772 0.00833395209765544 0.995833023951172 34 0.00855758550309936 0.0171151710061987 0.9914424144969 35 0.00697827941798127 0.0139565588359625 0.993021720582019 36 0.00602549283527164 0.0120509856705433 0.993974507164728 37 0.00361472228435484 0.00722944456870968 0.996385277715645 38 0.00271531047543415 0.00543062095086831 0.997284689524566 39 0.00666681626034248 0.0133336325206850 0.993333183739658 40 0.0149187595399062 0.0298375190798124 0.985081240460094 41 0.0397830753337333 0.0795661506674665 0.960216924666267 42 0.0537816919434082 0.107563383886816 0.946218308056592 43 0.0490762789923609 0.0981525579847217 0.95092372100764 44 0.070105598972849 0.140211197945698 0.929894401027151 45 0.0748503970522165 0.149700794104433 0.925149602947783 46 0.135811889852485 0.271623779704971 0.864188110147515 47 0.165804602285627 0.331609204571253 0.834195397714373 48 0.110897507652459 0.221795015304918 0.88910249234754 49 0.116296644335282 0.232593288670563 0.883703355664718 50 0.808370413123654 0.383259173752691 0.191629586876346 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0697674418604651 NOK 5% type I error level 13 0.302325581395349 NOK 10% type I error level 17 0.395348837209302 NOK

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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