*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 07:53:18 -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/t1258728935gm62bo0e7jacl44.htm/, Retrieved Fri, 20 Nov 2009 15:55:48 +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/t1258728935gm62bo0e7jacl44.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:

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User-defined keywords:

Dataseries X:

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100.6 33.5 107.1 107 111.9 115.6 99.2 31.5 100.6 107.1 107 111.9 108.4 31.2 99.2 100.6 107.1 107 103 27 108.4 99.2 100.6 107.1 99.8 26.7 103 108.4 99.2 100.6 115 26.5 99.8 103 108.4 99.2 90.8 26 115 99.8 103 108.4 95.9 27.2 90.8 115 99.8 103 114.4 30.5 95.9 90.8 115 99.8 108.2 33.7 114.4 95.9 90.8 115 112.6 34.2 108.2 114.4 95.9 90.8 109.1 36.7 112.6 108.2 114.4 95.9 105 36.2 109.1 112.6 108.2 114.4 105 38.5 105 109.1 112.6 108.2 118.5 40 105 105 109.1 112.6 103.7 42.5 118.5 105 105 109.1 112.5 43.5 103.7 118.5 105 105 116.6 43.3 112.5 103.7 118.5 105 96.6 45.5 116.6 112.5 103.7 118.5 101.9 44.3 96.6 116.6 112.5 103.7 116.5 43 101.9 96.6 116.6 112.5 119.3 43.5 116.5 101.9 96.6 116.6 115.4 41.5 119.3 116.5 101.9 96.6 108.5 42.5 115.4 119.3 116.5 101.9 111.5 41.3 108.5 115.4 119.3 116.5 108.8 39.5 111.5 108.5 115.4 119.3 121.8 38.5 108.8 111.5 108.5 115.4 109.6 41 121.8 108.8 111.5 108.5 112.2 44.5 109.6 121.8 108.8 111.5 119.6 46 112.2 109.6 121.8 108.8 104.1 44 119.6 112.2 109.6 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Ipzb[t] = + 37.9750577712368 + 0.35752597917971Cvn[t] -0.0972246665009244Y1[t] + 0.210673223544915Y2[t] + 0.471709841600752Y3[t] -0.130871652430054Y4[t] + 1.65159776730035M1[t] + 4.63924252137943M2[t] + 14.9692992911281M3[t] + 8.32260636552639M4[t] + 5.13879831352945M5[t] + 10.5730267079814M6[t] -0.424942244137813M7[t] -3.60594526919893M8[t] + 11.3518116431457M9[t] + 23.6135067770042M10[t] + 12.5920852084701M11[t] + 0.0661072462522717t + 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) 37.9750577712368 13.723465 2.7672 0.008687 0.004343 Cvn 0.35752597917971 0.08781 4.0716 0.000228 0.000114 Y1 -0.0972246665009244 0.164693 -0.5903 0.558458 0.279229 Y2 0.210673223544915 0.128717 1.6367 0.109947 0.054973 Y3 0.471709841600752 0.118607 3.9771 0.000302 0.000151 Y4 -0.130871652430054 0.148908 -0.8789 0.384992 0.192496 M1 1.65159776730035 3.926173 0.4207 0.67637 0.338185 M2 4.63924252137943 4.309825 1.0764 0.28852 0.14426 M3 14.9692992911281 3.838041 3.9002 0.000379 0.00019 M4 8.32260636552639 3.121846 2.6659 0.011212 0.005606 M5 5.13879831352945 2.935581 1.7505 0.088099 0.04405 M6 10.5730267079814 3.226022 3.2774 0.002244 0.001122 M7 -0.424942244137813 3.682638 -0.1154 0.908743 0.454372 M8 -3.60594526919893 3.749797 -0.9616 0.342311 0.171156 M9 11.3518116431457 4.799498 2.3652 0.023227 0.011614 M10 23.6135067770042 4.66452 5.0624 1.1e-05 5e-06 M11 12.5920852084701 3.195118 3.941 0.000336 0.000168 t 0.0661072462522717 0.038151 1.7328 0.091241 0.045621 Multiple Linear Regression - Regression Statistics Multiple R 0.951169221640086 R-squared 0.904722888195407 Adjusted R-squared 0.862098917124931 F-TEST (value) 21.2256827666176 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 2.39808173319034e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.32446883465033 Sum Squared Residuals 419.97953523733 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.6 101.454724478577 -0.85472447857655 2 99.2 102.619299065306 -3.41929906530648 3 108.4 112.363385948680 -3.96338594868014 4 103 100.012580576357 2.98741942364329 5 99.8 99.4411007951306 0.358899204869372 6 115 108.566365621788 6.43363437821166 7 90.8 91.5525193331732 -0.752519333173178 8 95.9 93.618960086585 2.28103991341506 9 114.4 111.817301047641 2.58269895235922 10 108.2 111.160336387264 -2.96033638726361 11 112.6 110.456846803429 2.14315319657057 12 109.1 105.149907912799 3.950092087201 13 105 102.610371865232 2.38962813476804 14 105 109.034626016033 -4.03462601603286 15 118.5 116.876499067974 1.62350093202566 16 103.7 108.401235771754 -4.70123577175384 17 112.5 110.460648302222 2.03935169777787 18 116.6 118.284020835028 -1.68402083502772 19 96.6 100.845946554401 -4.24594655440072 20 101.9 106.198220209180 -4.29822020918026 21 116.5 116.810885200669 -0.310885200668901 22 119.3 119.043767917266 0.256232082734123 23 115.4 115.294496843263 0.105503156737186 24 108.5 110.288450014996 -1.78845001499580 25 111.5 110.836409911567 0.663590088432707 26 108.8 109.295186898365 -0.495186898365405 27 121.8 117.483952742806 4.31604725719414 28 109.6 112.282587569892 -2.68258756989208 29 112.2 112.674888999059 -0.474888999059369 30 119.6 122.374097550754 -2.77409755075375 31 104.1 103.099280186517 1.00071981348258 32 105.3 104.979613392565 0.320386607435388 33 115 119.700254322106 -4.70025432210564 34 124.1 121.877996801324 2.2220031986757 35 116.8 114.676030704856 2.12396929514356 36 107.5 108.551911860442 -1.05191186044187 37 115.6 113.552811218520 2.0471887814802 38 116.2 109.225368560427 6.97463143957302 39 116.3 118.016875412683 -1.71687541268341 40 119 115.339586358247 3.66041364175254 41 111.9 111.489432578926 0.410567421074432 42 118.6 118.289034243896 0.310965756104348 43 106.9 105.755464834023 1.14453516597682 44 103.2 101.594372707854 1.60562729214648 45 118.6 116.171559429585 2.42844057041532 46 118.7 118.217898894146 0.482101105853787 47 102.8 107.172625648451 -4.37262564845132 48 100.6 101.709730211763 -1.10973021176333 49 94.9 99.1456825261044 -4.2456825261044 50 94.5 93.5255194598683 0.97448054013173 51 102.9 103.159286827856 -0.259286827856248 52 95.3 94.56400972375 0.735990276250078 53 92.5 94.8339293246623 -2.3339293246623 54 102.7 104.986481748535 -2.28648174853454 55 91.5 88.6467890918855 2.8532109081145 56 89.5 89.4088336038167 0.091166396183328 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.463790510710981 0.927581021421962 0.536209489289019 22 0.35868072858568 0.71736145717136 0.64131927141432 23 0.336295101830377 0.672590203660754 0.663704898169623 24 0.587601420382614 0.824797159234773 0.412398579617386 25 0.626052298832712 0.747895402334576 0.373947701167288 26 0.50808641570078 0.98382716859844 0.49191358429922 27 0.661235961156948 0.677528077686104 0.338764038843052 28 0.550928264830868 0.898143470338263 0.449071735169132 29 0.42475294985115 0.8495058997023 0.57524705014885 30 0.396714702921907 0.793429405843814 0.603285297078093 31 0.307851548743161 0.615703097486322 0.692148451256839 32 0.276697272001006 0.553394544002012 0.723302727998994 33 0.632153597544912 0.735692804910177 0.367846402455088 34 0.569635609149918 0.860728781700164 0.430364390850082 35 0.401314004018447 0.802628008036894 0.598685995981553 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 = 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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