*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 09:54:21 -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/t1260637752tviifbh4nsf3pau.htm/, Retrieved Sat, 12 Dec 2009 18:09:24 +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/t1260637752tviifbh4nsf3pau.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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99.9 98.8 98.6 100.5 107.2 110.4 95.7 96.4 93.7 101.9 106.7 106.2 86.7 81 95.3 94.7 99.3 101 101.8 109.4 96 102.3 91.7 90.7 95.3 96.2 96.6 96.1 107.2 106 108 103.1 98.4 102 103.1 104.7 81.1 86 96.6 92.1 103.7 106.9 106.6 112.6 97.6 101.7 87.6 92 99.4 97.4 98.5 97 105.2 105.4 104.6 102.7 97.5 98.1 108.9 104.5 86.8 87.4 88.9 89.9 110.3 109.8 114.8 111.7 94.6 98.6 92 96.9 93.8 95.1 93.8 97 107.6 112.7 101 102.9 95.4 97.4 96.5 111.4 89.2 87.4 87.1 96.8 110.5 114.1 110.8 110.3 104.2 103.9 88.9 101.6 89.8 94.6 90 95.9 93.9 104.7 91.3 102.8 87.8 98.1 99.7 113.9 73.5 80.9 79.2 95.7 96.9 113.2 95.2 105.9 95.6 108.8 89.7 102.3

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 Multiple Linear Regression - Estimated Regression Equation IndProd[t] = + 84.4853364381417 + 0.135748650387401ProdMetal[t] -1.04833736119274M1[t] -0.149332550138457M2[t] + 9.20693921848341M3[t] + 3.50350868507176M4[t] + 2.17827118122570M5[t] + 9.67526754496379M6[t] -11.2749187994741M7[t] -2.78398075578305M8[t] + 10.3777991105144M9[t] + 11.1270264048558M10[t] + 5.325595284048M11[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) 84.4853364381417 8.357482 10.1089 0 0 ProdMetal 0.135748650387401 0.091283 1.4871 0.143663 0.071831 M1 -1.04833736119274 2.24351 -0.4673 0.642462 0.321231 M2 -0.149332550138457 2.240602 -0.0666 0.947144 0.473572 M3 9.20693921848341 2.540879 3.6235 0.000712 0.000356 M4 3.50350868507176 2.371319 1.4775 0.146225 0.073112 M5 2.17827118122570 2.222878 0.9799 0.332137 0.166068 M6 9.67526754496379 2.484877 3.8937 0.000311 0.000155 M7 -11.2749187994741 2.262879 -4.9826 9e-06 4e-06 M8 -2.78398075578305 2.183806 -1.2748 0.208636 0.104318 M9 10.3777991105144 2.537151 4.0903 0.000167 8.4e-05 M10 11.1270264048558 2.619615 4.2476 0.000101 5.1e-05 M11 5.325595284048 2.291337 2.3242 0.024486 0.012243 Multiple Linear Regression - Regression Statistics Multiple R 0.921265756082445 R-squared 0.848730593330158 Adjusted R-squared 0.810108617159135 F-TEST (value) 21.975327973169 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 2.66453525910038e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.45195491173586 Sum Squared Residuals 560.051657494894 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.8 96.9982892506505 1.80171074934948 2 100.5 97.720820816201 2.77917918379904 3 110.4 108.244530978154 2.15546902184554 4 96.4 100.979990965288 -4.57999096528768 5 101.9 99.3832561606668 2.51674383933317 6 106.2 108.644984979441 -2.44498497944114 7 81 84.9798256272552 -3.97982562725518 8 94.7 94.638202064278 0.061797935722086 9 101 108.342976532125 -7.34297653212498 10 109.4 109.431575452435 -0.0315754524348984 11 102.3 102.842802159380 -0.54280215938016 12 90.7 96.9334876786663 -6.23348767866633 13 96.2 96.3738454588682 -0.173845458868235 14 96.1 97.4493235154261 -1.34932351542614 15 106 108.244530978154 -2.24453097815446 16 103.1 102.649699365053 0.45030063494727 17 102 100.021274817488 1.97872518251238 18 104.7 108.156289838046 -3.45628983804649 19 86 84.2196331850857 1.78036681491426 20 92.1 94.8146753097815 -2.71467530978155 21 106.9 108.940270593830 -2.04027059382954 22 112.6 110.083168974294 2.51683102570557 23 101.7 103.06 -1.36000000000000 24 92 96.376918212078 -4.37691821207798 25 97.4 96.9304149254566 0.469585074543429 26 97 97.7072459511622 -0.707245951162202 27 105.4 107.973033677380 -2.57303367737965 28 102.7 102.188153953736 0.511846046264444 29 98.1 99.899101032139 -1.79910103213897 30 104.5 108.943632010293 -4.44363201029342 31 87.4 84.993400492294 2.40659950770608 32 89.9 93.7694107017985 -3.86941070179855 33 109.8 109.836211686386 -0.036211686386394 34 111.7 111.196307907471 0.503692092528893 35 98.6 102.652754048838 -4.0527540488378 36 96.9 96.9742122737826 -0.0742122737825428 37 95.1 96.1702224832871 -1.07022248328714 38 97 97.0692272943414 -0.069227294341417 39 112.7 108.298830438309 4.40116956169059 40 102.9 101.699458812341 1.20054118765909 41 97.4 99.6140288663254 -2.21402886632541 42 111.4 107.260348745490 4.13965125451037 43 87.4 85.3191972532237 2.08080274677632 44 96.8 93.5250631311012 3.27493686889877 45 114.1 109.863361416464 4.23663858353612 46 110.3 110.653313305922 -0.353313305921513 47 103.9 103.955941092557 -0.0559410925568403 48 101.6 96.5533914575816 5.04660854241839 49 94.6 95.6272278817375 -1.02722788173753 50 95.9 96.5533824228693 -0.653382422869288 51 104.7 106.439073928002 -1.73907392800202 52 102.8 100.382696903583 2.41730309641687 53 98.1 98.5823391233812 -0.482339123381171 54 113.9 107.694744426729 6.20525557327068 55 80.9 83.1879434421415 -2.28794344214148 56 95.7 92.4526487930408 3.24735120695924 57 113.2 108.017179771195 5.18282022880479 58 105.9 108.535634359878 -2.63563435987805 59 108.8 102.788502699225 6.0114973007748 60 102.3 96.6619903778915 5.63800962210847 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.271117229841029 0.542234459682058 0.728882770158971 17 0.188117640137312 0.376235280274624 0.811882359862688 18 0.106486262239244 0.212972524478487 0.893513737760756 19 0.312380405695799 0.624760811391599 0.6876195943042 20 0.256789506441944 0.513579012883889 0.743210493558056 21 0.272516660049601 0.545033320099202 0.7274833399504 22 0.200231287119842 0.400462574239685 0.799768712880158 23 0.136707912068986 0.273415824137972 0.863292087931014 24 0.171297754798385 0.342595509596769 0.828702245201616 25 0.115868517149005 0.231737034298010 0.884131482850995 26 0.0781760045614825 0.156352009122965 0.921823995438517 27 0.0627387304761923 0.125477460952385 0.937261269523808 28 0.0423205024137596 0.0846410048275191 0.95767949758624 29 0.0474768954470265 0.094953790894053 0.952523104552974 30 0.117903615917635 0.235807231835270 0.882096384082365 31 0.101573456770861 0.203146913541722 0.898426543229139 32 0.169076558809241 0.338153117618481 0.83092344119076 33 0.219147479358587 0.438294958717174 0.780852520641413 34 0.194585820472787 0.389171640945574 0.805414179527213 35 0.359831634179349 0.719663268358698 0.640168365820651 36 0.614796607555171 0.770406784889658 0.385203392444829 37 0.510636928361818 0.978726143276364 0.489363071638182 38 0.403106324593866 0.806212649187732 0.596893675406134 39 0.614934655557761 0.770130688884479 0.385065344442239 40 0.540794028074474 0.918411943851052 0.459205971925526 41 0.475958562185786 0.951917124371571 0.524041437814214 42 0.565741811780439 0.868516376439123 0.434258188219561 43 0.597459674886877 0.805080650226247 0.402540325113123 44 0.472610741455947 0.945221482911894 0.527389258544053 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 2 0.0689655172413793 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly 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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