Paper Multiple regression dummy

*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, 18 Dec 2010 15:41:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/18/t1292687576sa90jvhqyqyj4sn.htm/, Retrieved Sat, 18 Dec 2010 16:53:07 +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/2010/Dec/18/t1292687576sa90jvhqyqyj4sn.htm/}, year = {2010}, } @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 = {2010}, 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:

» Textbox « » Textfile « » CSV «

1 41 25 25 15 15 9 9 3 3 1 38 25 25 15 15 9 9 4 4 1 37 19 19 14 14 9 9 4 4 1 42 18 18 10 10 8 8 4 4 1 40 23 23 18 18 15 15 3 3 1 43 25 25 14 14 9 9 4 4 1 40 23 23 11 11 11 11 4 4 1 45 30 30 17 17 6 6 5 5 1 45 32 32 21 21 10 10 4 4 1 44 25 25 7 7 11 11 4 4 1 42 26 26 18 18 16 16 4 4 1 32 25 25 13 13 11 11 5 5 1 32 25 25 13 13 11 11 5 5 1 41 35 35 18 18 7 7 4 4 1 38 20 20 12 12 10 10 4 4 1 38 21 21 9 9 9 9 4 4 1 24 23 23 11 11 15 15 3 3 1 46 17 17 11 11 6 6 5 5 1 42 27 27 16 16 12 12 4 4 1 46 25 25 12 12 10 10 4 4 1 43 18 18 14 14 14 14 5 5 1 38 22 22 13 13 9 9 4 4 1 39 23 23 17 17 14 14 4 4 1 40 25 25 13 13 14 14 3 3 1 37 19 19 13 13 9 9 2 2 1 41 20 20 12 12 8 8 4 4 1 46 26 26 12 12 10 10 4 4 1 26 16 16 12 12 9 9 3 3 1 37 22 22 9 9 9 9 3 3 1 39 25 25 17 17 9 9 4 4 1 44 29 29 18 18 11 11 5 5 1 38 22 22 12 12 10 10 2 2 1 38 32 32 12 12 8 8 0 0 1 38 23 23 9 9 14 14 4 4 1 33 18 18 13 13 10 10 3 3 1 43 26 26 11 11 14 14 4 4 1 41 14 14 13 13 15 15 2 2 1 49 20 20 6 6 8 8 4 4 1 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 Career[t] = + 35.6197069170407 -1.39109054250955G[t] + 0.20798572444025PersonalStandards[t] -0.0619444415950565PeG[t] + 0.304770109016755ParentalExpectations[t] -0.222891855918395PaG[t] -0.0280035539064598Doubts[t] -0.143741846502613DoG[t] -0.286076268589505LeadershipPreference[t] + 1.16963899061508LeaderG[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) 35.6197069170407 5.253618 6.78 0 0 G -1.39109054250955 6.622594 -0.2101 0.833944 0.416972 PersonalStandards 0.20798572444025 0.308607 0.6739 0.501496 0.250748 PeG -0.0619444415950565 0.209717 -0.2954 0.768164 0.384082 ParentalExpectations 0.304770109016755 0.405079 0.7524 0.453137 0.226569 PaG -0.222891855918395 0.268232 -0.831 0.40746 0.20373 Doubts -0.0280035539064598 0.475306 -0.0589 0.953105 0.476553 DoG -0.143741846502613 0.311976 -0.4607 0.645722 0.322861 LeadershipPreference -0.286076268589505 1.418512 -0.2017 0.840476 0.420238 LeaderG 1.16963899061508 1.01608 1.1511 0.251714 0.125857 Multiple Linear Regression - Regression Statistics Multiple R 0.360462109240757 R-squared 0.129932932198296 Adjusted R-squared 0.0719284610115152 F-TEST (value) 2.24005028474268 F-TEST (DF numerator) 9 F-TEST (DF denominator) 135 p-value 0.0230062379670575 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.80099053007766 Sum Squared Residuals 3111.68385943587 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 40.2128018045313 0.787198195468745 2 38 41.096364526557 -3.09636452655697 3 37 40.1382385763875 -3.13823857638747 4 42 39.8364296815579 2.16357031844209 5 40 39.1358815956817 0.864118404318318 6 43 41.0144862734586 1.98551372654136 7 40 40.133278147655 -0.133278147655021 8 45 43.3891263702325 1.61087362976753 9 45 42.4381776246544 2.56182237534557 10 44 40.097847700952 3.90215229904804 11 42 40.2858227658338 1.71417723416624 12 32 41.4726799415677 -9.4726799415677 13 32 41.4726799415677 -9.4726799415677 14 41 43.1459029151222 -2.14590291512216 15 38 39.9487779526269 -1.94877795262687 16 38 40.0209298765861 -2.02092987658606 17 24 38.5627338239932 -14.5627338239932 18 46 40.9993201746548 5.00067982534521 19 42 40.9550891441185 1.04491085588148 20 46 40.6789843668528 5.32101563314716 21 43 40.0170330135225 2.98296698647752 22 38 40.4944841718247 -2.49448417182469 23 39 40.109311465018 -1.10931146501796 24 40 39.1903182962893 0.80968170371066 25 37 38.289234879238 -1.28923487923797 26 41 40.292268753445 0.707731246554982 27 46 40.825025649698 5.17497435030197 28 26 38.6527954996296 -12.6527954996296 29 37 39.2834084374057 -2.28340843740568 30 39 41.2601210327537 -2.26012103275372 31 44 42.4662363384403 1.53376366155973 32 38 38.4737350742661 -0.473735074266121 33 38 38.5105132594851 -0.510513259485067 34 38 39.4542854402311 -1.45428544023108 35 33 38.8550109180093 -5.85501091800928 36 43 40.0561657949634 2.94383420503662 37 41 36.5285560625576 4.47144393744243 38 49 39.8009992348549 9.19900076514515 39 45 41.4806688357801 3.51933116421995 40 31 39.1872898308094 -8.18728983080944 41 30 39.1872898308094 -9.18728983080944 42 38 40.6325365604575 -2.63253656045754 43 39 40.2793194305002 -1.27931943050021 44 40 40.2585757416688 -0.258575741668787 45 36 36.7130562575857 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41.2583835978269 2.74161640217311 71 38 37.5717832596311 0.42821674036892 72 39 39.414283621447 -0.414283621447033 73 41 42.2720098142729 -1.27200981427295 74 39 39.2721965493877 -0.272196549387701 75 40 39.786758881357 0.213241118643025 76 44 40.3276992001481 3.67230079985193 77 42 39.4801840861207 2.51981591387931 78 46 42.0488561787361 3.95114382126388 79 44 40.0177068827804 3.98229311721957 80 37 40.4430759366969 -3.44307593669693 81 39 38.2940007796447 0.705999220355303 82 40 38.8420615950645 1.15793840493553 83 42 39.5178313086828 2.48216869131722 84 37 39.3011236607572 -2.30112366075721 85 33 38.7530628453374 -5.75306284533743 86 35 39.7545514284595 -4.75455142845955 87 42 36.8929850805329 5.10701491946713 88 36 35.4128959998605 0.587104000139514 89 44 40.0807972342125 3.9192027657875 90 45 39.8828668698226 5.11713313017744 91 47 40.8376688054637 6.16233119453627 92 40 40.7552350902808 -0.755235090280824 93 49 38.8711481726115 10.1288518273885 94 48 42.5003962747737 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3.88898073042661 119 28 38.9849816957513 -10.9849816957513 120 35 37.1016091553493 -2.10160915534929 121 38 38.5765610437887 -0.576561043788678 122 42 40.3273041652662 1.67269583473378 123 36 38.1242522860047 -2.12425228600474 124 37 41.6075966687924 -4.60759666879241 125 38 39.476578076493 -1.47657807649300 126 43 39.0974253738542 3.90257462614578 127 35 33.8860965652806 1.11390343471943 128 36 40.4929412455571 -4.49294124555707 129 33 35.6333896084065 -2.63338960840651 130 39 38.5222008844282 0.477799115571802 131 32 40.7933119670766 -8.79331196707659 132 45 39.3292845120816 5.67071548791841 133 35 40.7243316512186 -5.72433165121862 134 38 38.4694762148061 -0.469476214806086 135 36 37.8322217593913 -1.83222175939134 136 42 38.3619226532577 3.63807734674233 137 41 39.8113299517552 1.18867004824482 138 47 37.6777547572464 9.32224524275364 139 35 37.7346715188163 -2.73467151881626 140 43 37.4932777921814 5.50672220781863 141 40 39.9544037878899 0.0455962121100531 142 46 41.3762062631309 4.62379373686914 143 44 42.7984334819481 1.20156651805187 144 35 38.7045899798496 -3.70458997984960 145 29 39.1506187760422 -10.1506187760422 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.839064146569973 0.321871706860054 0.160935853430027 14 0.819316656074214 0.361366687851572 0.180683343925786 15 0.718067014927231 0.563865970145538 0.281932985072769 16 0.61303135927393 0.773937281452139 0.386968640726069 17 0.958907348804297 0.082185302391407 0.0410926511957035 18 0.951108017572725 0.0977839648545498 0.0488919824272749 19 0.933089920112493 0.133820159775014 0.0669100798875071 20 0.945430356658354 0.109139286683292 0.0545696433416459 21 0.94153942446569 0.116921151068620 0.0584605755343101 22 0.920650535249232 0.158698929501535 0.0793494647507677 23 0.886943524926092 0.226112950147816 0.113056475073908 24 0.862599100321135 0.274801799357731 0.137400899678865 25 0.824005102261382 0.351989795477236 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0.98572777977901 130 0.00808673661285469 0.0161734732257094 0.991913263387145 131 0.0222373387352303 0.0444746774704606 0.97776266126477 132 0.0101899821557542 0.0203799643115083 0.989810017844246 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 6 0.05 NOK 10% type I error level 10 0.0833333333333333 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal 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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Software written by Ed van Stee & Patrick Wessa

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