multiple regression dummies

*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, 06 Dec 2009 05:47:31 -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/06/t12601046403u8h0qqvmkmqzjk.htm/, Retrieved Sun, 06 Dec 2009 14:04:13 +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/06/t12601046403u8h0qqvmkmqzjk.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}, }

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Dataseries X:

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3,4 4,9 3,2 3,3 3,6 3,9 3,4 4,5 3,4 3,2 3,3 3,6 3,5 4,6 3,4 3,4 3,2 3,3 3,2 4,7 3,5 3,4 3,4 3,2 3,3 4,7 3,2 3,5 3,4 3,4 3,3 4,3 3,3 3,2 3,5 3,4 3,4 4,2 3,3 3,3 3,2 3,5 3,7 4,4 3,4 3,3 3,3 3,2 3,9 4 3,7 3,4 3,3 3,3 4 3,8 3,9 3,7 3,4 3,3 3,7 3,6 4 3,9 3,7 3,4 3,9 3,6 3,7 4 3,9 3,7 4,2 3,3 3,9 3,7 4 3,9 4,4 3,4 4,2 3,9 3,7 4 4,3 3,4 4,4 4,2 3,9 3,7 4,2 3,3 4,3 4,4 4,2 3,9 4,3 3,3 4,2 4,3 4,4 4,2 4,3 3,2 4,3 4,2 4,3 4,4 4,3 3,1 4,3 4,3 4,2 4,3 4,5 3,1 4,3 4,3 4,3 4,2 5 2,4 4,5 4,3 4,3 4,3 5,2 2,4 5 4,5 4,3 4,3 5,2 2,4 5,2 5 4,5 4,3 5,4 2,1 5,2 5,2 5 4,5 5,5 2 5,4 5,2 5,2 5 5,4 2 5,5 5,4 5,2 5,2 5,5 2,1 5,4 5,5 5,4 5,2 5,4 2,1 5,5 5,4 5,5 5,4 5,7 2 5,4 5,5 5,4 5,5 5,7 2 5,7 5,4 5,5 5,4 6,1 2 5,7 5,7 5,4 5,5 6,5 1,7 6,1 5,7 5,7 5,4 6,9 1,3 6,5 6,1 5,7 5,7 6,8 1,2 6,9 6,5 6,1 5,7 6,7 1,1 6,8 6,9 6,5 6,1 6,6 1,4 6,7 6,8 6,9 6,5 6,5 1,5 6,6 6,7 6,8 6,9 6,4 1,4 6,5 6,6 6,7 6,8 6,1 1,1 6,4 6,5 6,6 6,7 6,2 1,1 6,1 6,4 6,5 6,6 6,3 1 6,2 6,1 6,4 6,5 6,4 1,4 6,3 6,2 6,1 6,4 6,5 1,3 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkl[t] = + 1.42982007691866 -0.161193787467765Infl[t] + 0.929871660400964`M1(t)`[t] + 0.274012559640936`M2(t)`[t] -0.624835761341823`M3(t)`[t] + 0.251487269084980`M4(t)`[t] + 0.0239056796988475M1[t] -0.225226304943252M2[t] -0.22089214657853M3[t] -0.230237762317641M4[t] -0.000204885143931201M5[t] -0.149127441415511M6[t] -0.104503412749335M7[t] + 0.113480030247102M8[t] + 0.120527017026366M9[t] -0.150903024914468M10[t] -0.313224104489284M11[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) 1.42982007691866 0.377707 3.7855 0.000517 0.000259 Infl -0.161193787467765 0.050531 -3.19 0.002807 0.001403 `M1(t)` 0.929871660400964 0.155055 5.9971 1e-06 0 `M2(t)` 0.274012559640936 0.198656 1.3793 0.175651 0.087825 `M3(t)` -0.624835761341823 0.199402 -3.1336 0.003273 0.001637 `M4(t)` 0.251487269084980 0.132088 1.9039 0.064316 0.032158 M1 0.0239056796988475 0.101803 0.2348 0.815574 0.407787 M2 -0.225226304943252 0.117582 -1.9155 0.062784 0.031392 M3 -0.22089214657853 0.093864 -2.3533 0.023743 0.011872 M4 -0.230237762317641 0.087698 -2.6254 0.0123 0.00615 M5 -0.000204885143931201 0.094075 -0.0022 0.998273 0.499137 M6 -0.149127441415511 0.111541 -1.337 0.188979 0.09449 M7 -0.104503412749335 0.108288 -0.965 0.340467 0.170234 M8 0.113480030247102 0.096637 1.1743 0.247398 0.123699 M9 0.120527017026366 0.118167 1.02 0.314029 0.157015 M10 -0.150903024914468 0.120953 -1.2476 0.219612 0.109806 M11 -0.313224104489284 0.097684 -3.2065 0.002683 0.001341 Multiple Linear Regression - Regression Statistics Multiple R 0.996807176456464 R-squared 0.993624547035107 Adjusted R-squared 0.991008976587972 F-TEST (value) 379.888275662138 F-TEST (DF numerator) 16 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.116875093448220 Sum Squared Residuals 0.532731711272674 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.4 3.27509856672449 0.124901433275512 2 3.4 3.36102172086265 0.0389782791373494 3 3.5 3.39107640781747 0.108923592182528 4 3.2 3.30848270019482 -0.108482700194818 5 3.3 3.33725278902933 -0.0372527890293275 6 3.3 3.20110756975849 0.0988924302415132 7 3.4 3.50185168844658 -0.101851688446578 8 3.7 3.64265378312988 0.0573462168701186 9 3.9 4.04568976588913 -0.145689765889134 10 4 4.01219300528014 -0.0121930052801432 11 3.7 3.86759835967312 -0.167598359673116 12 3.9 3.87974125046333 0.0202587495366665 13 4.2 4.04358950827324 0.156410491726764 14 4.4 4.32470161024388 0.0752983897561186 15 4.3 4.39680053558722 -0.0968005355872196 16 4.2 4.22823636989742 -0.0282363698974241 17 4.3 4.28835985352407 0.0116401464759263 18 4.3 4.33392361602645 -0.0339236160264512 19 4.3 4.45940312862918 -0.159403128629182 20 4.5 4.58975426858294 -0.089754268582938 21 5 4.92075996557833 0.0792400344216706 22 5.2 5.16906826576616 0.0309317342338359 23 5.2 5.20476064582365 -0.00476064582364498 24 5.4 5.35902497162753 0.0409750283724701 25 5.5 5.58580084442747 -0.085800844427473 26 5.4 5.53475599157065 -0.134755991570653 27 5.5 5.33241770884423 0.167582291155769 28 5.4 5.37647188086394 0.0235281191360633 29 5.7 5.6446705297511 0.0553294702488997 30 5.7 5.65967591259304 0.0403240874069642 31 6.1 5.87413601219417 0.225863987805826 32 6.5 6.29982680028028 0.20017319971972 33 6.9 6.9283511707889 -0.0283511707889048 34 6.8 6.90465989107488 -0.104659891074879 35 6.7 6.62573665116038 0.07426334883962 36 6.6 6.6208748005024 -0.0208748005024079 37 6.5 6.67135116321846 -0.171351163218463 38 6.4 6.35528498454463 0.0447150154553664 39 6.1 6.32492370637118 -0.224923706371181 40 6.2 6.04655018577337 0.153449814226630 41 6.3 6.34082068906736 -0.0408206890673564 42 6.4 6.41011104130691 -0.0101110413069089 43 6.5 6.45331311386438 0.0466868861356242 44 6.7 6.7704695083861 -0.0704695083860944 45 7 6.90519909774363 0.0948009022563681 46 7 6.91407883787881 0.0859211621211865 47 6.8 6.70190434334286 0.0980956566571407 48 6.7 6.74035897740673 -0.0403589774067283 49 6.7 6.72415991735634 -0.0241599173563395 50 6.5 6.52423569277818 -0.0242356927781820 51 6.4 6.3547816413799 0.0452183586201034 52 6.1 6.14025886327045 -0.040258863270452 53 6.2 6.18889613862814 0.0111038613718579 54 6 6.09518186031512 -0.0951818603151173 55 6.1 6.11129605686569 -0.0112960568656909 56 6.1 6.1972956396208 -0.0972956396208063 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.444609482169224 0.889218964338448 0.555390517830776 21 0.331363661541434 0.662727323082869 0.668636338458566 22 0.219802344045940 0.439604688091879 0.78019765595406 23 0.396147561896778 0.792295123793556 0.603852438103222 24 0.337892565477966 0.675785130955932 0.662107434522034 25 0.286841858082224 0.573683716164447 0.713158141917776 26 0.278514984570846 0.557029969141691 0.721485015429155 27 0.303692115391616 0.607384230783233 0.696307884608384 28 0.232324628376928 0.464649256753855 0.767675371623072 29 0.157637251458795 0.315274502917589 0.842362748541205 30 0.113104715705583 0.226209431411165 0.886895284294417 31 0.34828830891974 0.69657661783948 0.65171169108026 32 0.708270493012058 0.583459013975884 0.291729506987942 33 0.594740216237934 0.810519567524133 0.405259783762066 34 0.54782766782052 0.90434466435896 0.45217233217948 35 0.498366910491389 0.996733820982778 0.501633089508611 36 0.369362786686858 0.738725573373716 0.630637213313142 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):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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