*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: Sun, 13 Dec 2009 12:40:15 -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/13/t12607334051lf8whxqyhwj9i4.htm/, Retrieved Sun, 13 Dec 2009 20:43:37 +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/13/t12607334051lf8whxqyhwj9i4.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 75.8 18 72.6 19 71.9 19 74.8 22 72.9 23 72.9 20 79.9 14 74 14 76 14 69.6 15 77.3 11 75.2 17 75.8 16 77.6 20 76.7 24 77 23 77.9 20 76.7 21 71.9 19 73.4 23 72.5 23 73.7 23 69.5 23 74.7 27 72.5 26 72.1 17 70.7 24 71.4 26 69.5 24 73.5 27 72.4 27 74.5 26 72.2 24 73 23 73.3 23 71.3 24 73.6 17 71.3 21 71.2 19 81.4 22 76.1 22 71.1 18 75.7 16 70 14 68.5 12 56.7 14 57.9 16 58.8 8 59.3 3 61.3 0 62.9 5 61.4 1 64.5 1 63.8 3 61.6 6 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 3 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] = + 69.7953336755647 + 0.306108829568788indcvtr[t] + 0.273448408624239M1[t] + 0.95116889117043M2[t] + 1.01422818275155M3[t] + 2.85651745379877M4[t] + 1.83224614989734M5[t] + 1.6765272073922M6[t] + 2.6171429671458M7[t] + 2.24508932238194M8[t] + 1.45570918891171M9[t] -2.10878798767967M10[t] -0.83244840862423M11[t] -0.179393993839836t + 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) 69.7953336755647 3.065008 22.7717 0 0 indcvtr 0.306108829568788 0.08601 3.559 0.00094 0.00047 M1 0.273448408624239 2.676107 0.1022 0.919099 0.459549 M2 0.95116889117043 2.687255 0.354 0.725143 0.362571 M3 1.01422818275155 2.689356 0.3771 0.707978 0.353989 M4 2.85651745379877 2.671968 1.0691 0.291145 0.145572 M5 1.83224614989734 2.67121 0.6859 0.49653 0.248265 M6 1.6765272073922 2.670928 0.6277 0.533602 0.266801 M7 2.6171429671458 2.671129 0.9798 0.332801 0.1664 M8 2.24508932238194 2.674509 0.8394 0.405975 0.202988 M9 1.45570918891171 2.817258 0.5167 0.608068 0.304034 M10 -2.10878798767967 2.816324 -0.7488 0.458167 0.229084 M11 -0.83244840862423 2.815622 -0.2957 0.768952 0.384476 t -0.179393993839836 0.037708 -4.7574 2.3e-05 1.2e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.794895346236096 R-squared 0.631858611467803 Adjusted R-squared 0.517910086445933 F-TEST (value) 5.54512321547408 F-TEST (DF numerator) 13 F-TEST (DF denominator) 42 p-value 1.01696678999064e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.98145592962503 Sum Squared Residuals 665.783635420945 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 75.8 75.705455852156 0.0945441478439736 2 72.6 75.8976735112936 -3.29767351129364 3 71.9 76.0874476386037 -4.18744763860369 4 74.8 77.7503429158111 -2.9503429158111 5 72.9 77.4650041067762 -4.56500410677618 6 72.9 77.436 -4.5360 7 79.9 77.2788952772074 2.62110472279261 8 74 74.890794661191 -0.890794661190969 9 76 73.9220205338809 2.07797946611909 10 69.6 70.1781293634497 -0.578129363449698 11 77.3 71.5811837782341 5.71881622176591 12 75.2 71.0098028747433 4.19019712525667 13 75.8 72.9405102669405 2.85948973305954 14 77.6 73.132727926078 4.46727207392197 15 76.7 74.2408285420945 2.45917145790554 16 77 77.128159137577 -0.128159137577004 17 77.9 75.618385010267 2.28161498973306 18 76.7 74.3649455852156 2.33505441478440 19 71.9 75.4322761806982 -3.53227618069815 20 73.4 74.2686108829569 -0.868610882956876 21 72.5 74.524272073922 -2.02427207392197 22 73.7 70.7803809034908 2.91961909650924 23 69.5 71.8773264887064 -2.37732648870636 24 74.7 72.5303809034908 2.16961909650925 25 72.5 73.8488706365503 -1.34887063655031 26 72.1 74.0410882956879 -1.94108829568789 27 70.7 71.16977412731 -0.469774127310062 28 71.4 74.975431211499 -3.57543121149897 29 69.5 74.3839835728953 -4.88398357289528 30 73.5 73.4366529774127 0.0633470225872678 31 72.4 75.1162012320329 -2.71620123203285 32 74.5 74.5647535934292 -0.0647535934291621 33 72.2 73.2898706365503 -1.08987063655031 34 73 68.9337618069815 4.06623819301848 35 73.3 69.7245985626283 3.57540143737166 36 71.3 70.3776529774127 0.92234702258727 37 73.6 70.7778162217659 2.82218377823407 38 71.3 69.1333809034908 2.16661909650924 39 71.2 70.2414815195072 0.958518480492813 40 81.4 71.292159137577 10.107840862423 41 76.1 71.0068203285421 5.0931796714579 42 71.1 70.6717073921971 0.428292607802869 43 75.7 70.2084938398357 5.49150616016427 44 70 69.0448285420945 0.955171457905543 45 68.5 67.4638367556468 1.03616324435318 46 56.7 63.107727926078 -6.40772792607802 47 57.9 64.8168911704312 -6.91689117043121 48 58.8 66.0821632443532 -7.28216324435318 49 59.3 63.7273470225873 -4.42734702258728 50 61.3 62.6951293634497 -1.39512936344969 51 62.9 61.6604681724846 1.2395318275154 52 61.4 64.853907597536 -3.45390759753593 53 64.5 62.4258069815195 2.07419301848049 54 63.8 62.0906940451745 1.70930595482546 55 61.6 63.4641334702259 -1.86413347022587 56 64.7 63.8310123203285 0.868987679671462 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0987663768146036 0.197532753629207 0.901233623185396 18 0.0345285413246412 0.0690570826492823 0.965471458675359 19 0.375095551441394 0.750191102882787 0.624904448558606 20 0.24833998472399 0.49667996944798 0.75166001527601 21 0.159016368192979 0.318032736385959 0.84098363180702 22 0.152597315034320 0.305194630068640 0.84740268496568 23 0.173191390757733 0.346382781515466 0.826808609242267 24 0.144936743138430 0.289873486276861 0.85506325686157 25 0.0972737155468126 0.194547431093625 0.902726284453187 26 0.0617102525245052 0.123420505049010 0.938289747475495 27 0.057558882642169 0.115117765284338 0.94244111735783 28 0.055531012408959 0.111062024817918 0.94446898759104 29 0.101182528339676 0.202365056679353 0.898817471660324 30 0.0742513501735438 0.148502700347088 0.925748649826456 31 0.126685721581526 0.253371443163053 0.873314278418474 32 0.262716484195710 0.525432968391421 0.73728351580429 33 0.388972378687372 0.777944757374745 0.611027621312628 34 0.352094842682924 0.704189685365848 0.647905157317076 35 0.274551636381035 0.54910327276207 0.725448363618965 36 0.185589111931391 0.371178223862782 0.81441088806861 37 0.130191638226567 0.260383276453134 0.869808361773433 38 0.0743907717111535 0.148781543422307 0.925609228288847 39 0.0396939237952997 0.0793878475905994 0.9603060762047 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 0.0869565217391304 OK

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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