*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: Sat, 12 Dec 2009 11:28:01 -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/Dec/12/t1260642714rcamnjjgizh1v9b.htm/, Retrieved Sat, 12 Dec 2009 19:32:06 +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/Dec/12/t1260642714rcamnjjgizh1v9b.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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19 80.2 18 74.8 19 77.8 19 73 22 72 23 75.8 20 72.6 14 71.9 14 74.8 14 72.9 15 72.9 11 79.9 17 74 16 76 20 69.6 24 77.3 23 75.2 20 75.8 21 77.6 19 76.7 23 77 23 77.9 23 76.7 23 71.9 27 73.4 26 72.5 17 73.7 24 69.5 26 74.7 24 72.5 27 72.1 27 70.7 26 71.4 24 69.5 23 73.5 23 72.4 24 74.5 17 72.2 21 73 19 73.3 22 71.3 22 73.6 18 71.3 16 71.2 14 81.4 12 76.1 14 71.1 16 75.7 8 70 3 68.5 0 56.7 5 57.9 1 58.8 1 59.3 3 61.3 6 62.9 7 61.4 8 64.5 14 63.8 14 61.6 13 64.7

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 '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 dzcg [t] = + 72.4908045413209 + 0.319429327394719indcvtr[t] -0.490112435046392M1[t] -0.64970861886656M2[t] -2.93836005470781M3[t] -3.63307120369111M4[t] -3.46503783240602M5[t] -2.04980340276834M6[t] -2.24622656956748M7[t] -1.93933454349295M8[t] + 0.612584693271081M9[t] -0.05606674257017M10[t] -0.987462698679808M11[t] -0.159690967721917t + 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) 72.4908045413209 2.874739 25.2165 0 0 indcvtr 0.319429327394719 0.082181 3.8869 0.000317 0.000159 M1 -0.490112435046392 2.333742 -0.21 0.834567 0.417283 M2 -0.64970861886656 2.466425 -0.2634 0.793377 0.396689 M3 -2.93836005470781 2.467267 -1.1909 0.239658 0.119829 M4 -3.63307120369111 2.444398 -1.4863 0.143882 0.071941 M5 -3.46503783240602 2.44078 -1.4196 0.162311 0.081155 M6 -2.04980340276834 2.439272 -0.8403 0.404976 0.202488 M7 -2.24622656956748 2.437427 -0.9216 0.361466 0.180733 M8 -1.93933454349295 2.440092 -0.7948 0.430737 0.215369 M9 0.612584693271081 2.436297 0.2514 0.802569 0.401285 M10 -0.05606674257017 2.437005 -0.023 0.981743 0.490871 M11 -0.987462698679808 2.432878 -0.4059 0.686671 0.343335 t -0.159690967721917 0.03341 -4.7798 1.8e-05 9e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.801118894752069 R-squared 0.641791483528776 Adjusted R-squared 0.542712532164395 F-TEST (value) 6.47757646493925 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 8.05769475142881e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.84637997846751 Sum Squared Residuals 695.348030121518 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 80.2 77.9101583590521 2.28984164094791 2 74.8 77.2714418801154 -2.47144188011544 3 77.8 75.142528803947 2.65747119605301 4 73 74.2881266872418 -1.28812668724177 5 72 75.2547570729891 -3.2547570729891 6 75.8 76.8297298622996 -1.02972986229960 7 72.6 75.5153277455944 -2.91532774559439 8 71.9 73.7459528395787 -1.84595283957867 9 74.8 76.1381811086208 -1.33818110862079 10 72.9 75.3098387050576 -2.40983870505761 11 72.9 74.5381811086208 -1.63818110862078 12 79.9 74.0882355299998 5.81176447000021 13 74 75.3550080915998 -1.35500809159981 14 76 74.716291612663 1.28370838733700 15 69.6 73.5456665186787 -3.94566651867871 16 77.3 73.9689817115524 3.33101828844763 17 75.2 73.6578947877208 1.54210521227918 18 75.8 73.9551502674524 1.84484973254756 19 77.6 73.9184654603261 3.6815345396739 20 76.7 73.4268078638893 3.27319213611073 21 77 77.0967534425103 -0.0967534425102625 22 77.9 76.2684110389471 1.63158896105291 23 76.7 75.1773241151155 1.52267588488446 24 71.9 76.0050958460734 -4.10509584607343 25 73.4 76.633009752884 -3.23300975288400 26 72.5 75.9942932739472 -3.49429327394720 27 73.7 70.6710869238316 3.02891307616845 28 69.5 72.0526900988894 -2.55269009888937 29 74.7 72.699891157242 2.00010884275802 30 72.5 73.3165759643683 -0.816575964368314 31 72.1 73.9187498120314 -1.81874981203142 32 70.7 74.065950870384 -3.36595087038402 33 71.4 76.1387498120314 -4.73874981203141 34 69.5 74.6715487536788 -5.17154875367881 35 73.5 73.2610325024525 0.238967497547458 36 72.4 74.0888042334104 -1.68880423341042 37 74.5 73.7584301580368 0.741569841963157 38 72.2 71.2031377147317 0.99686228526828 39 73 70.0325126207474 2.96748737925257 40 73.3 68.5392518492528 4.76074815074722 41 71.3 69.5058822350001 1.79411776499989 42 73.6 70.7614256969159 2.83857430308412 43 71.3 69.1275942528159 2.17240574718406 44 71.2 68.6359366563791 2.56406334362089 45 81.4 70.3893062706318 11.0106937293682 46 76.1 68.9221052122792 7.17789478772081 47 71.1 68.469876943237 2.63012305676293 48 75.7 69.9365073289844 5.76349267101561 49 70 66.7312693070583 3.26873069294167 50 68.5 64.8148355185427 3.68516448145735 51 56.7 61.4082051327953 -4.70820513279532 52 57.9 62.1509496530637 -4.25094965306371 53 58.8 60.881574747048 -2.081574747048 54 59.3 62.1371182089638 -2.83711820896377 55 61.3 62.4198627292322 -1.11986272923215 56 62.9 63.5253517697689 -0.625351769768922 57 61.4 66.2370093662058 -4.83700936620575 58 64.5 65.7280962900373 -1.22809629003730 59 63.8 66.553585330574 -2.75358533057407 60 61.6 67.381357061532 -5.78135706153195 61 64.7 66.412124331369 -1.71212433136893 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.565172458583366 0.86965508283327 0.434827541416634 18 0.440612804957991 0.881225609915981 0.559387195042009 19 0.385903343503185 0.77180668700637 0.614096656496815 20 0.266193696165814 0.532387392331627 0.733806303834186 21 0.194952719215423 0.389905438430847 0.805047280784577 22 0.118308234919717 0.236616469839434 0.881691765080283 23 0.0675350607085855 0.135070121417171 0.932464939291414 24 0.230193993748517 0.460387987497034 0.769806006251483 25 0.209430687633638 0.418861375267275 0.790569312366362 26 0.177900521285213 0.355801042570425 0.822099478714787 27 0.120120223332389 0.240240446664779 0.879879776667611 28 0.110358818998858 0.220717637997716 0.889641181001142 29 0.0734089008318157 0.146817801663631 0.926591099168184 30 0.048322623331416 0.096645246662832 0.951677376668584 31 0.031786586157926 0.063573172315852 0.968213413842074 32 0.0250687136069235 0.0501374272138469 0.974931286393077 33 0.0392325323619809 0.0784650647239618 0.96076746763802 34 0.120036639226036 0.240073278452072 0.879963360773964 35 0.103752415899016 0.207504831798032 0.896247584100984 36 0.169741387157036 0.339482774314072 0.830258612842964 37 0.311232397567229 0.622464795134459 0.68876760243277 38 0.51683084711368 0.96633830577264 0.48316915288632 39 0.421793397632605 0.843586795265211 0.578206602367395 40 0.346999406328356 0.693998812656713 0.653000593671644 41 0.250630349508465 0.50126069901693 0.749369650491535 42 0.158491201985265 0.316982403970530 0.841508798014735 43 0.148847327127035 0.297694654254069 0.851152672872965 44 0.640243385763786 0.719513228472428 0.359756614236214 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 4 0.142857142857143 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly 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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