Paper1GeoffreyMoos

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 19 Dec 2008 03:16:07 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/19/t12296819027407tvfl6z2t2n7.htm/, Retrieved Fri, 19 Dec 2008 11:18:47 +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/2008/Dec/19/t12296819027407tvfl6z2t2n7.htm/}, year = {2008}, } @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 = {2008}, 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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0,89 0 0,89 0 0,89 0 0,89 0 0,89 0 0,89 0 0,89 0 0,9 0 0,91 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 0,92 0 1,01 1 1,01 1 1,01 1 1,01 1 1,01 1 1,04 1 1,05 1 1,05 1 1,06 1 1,06 1 1,06 1 1,06 1 1,08 1 1,08 1 1,08 1 1,08 1 1,08 1 1,08 1 1,09 1 1,09 1 1,1 1 1,1 1 1,1 1

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 0.893237154150196 + 0.105662055335968x[t] -0.00188669301712875M1[t] -0.00739591567852424M2[t] -0.00787549407114603M3[t] -0.00922266139657425M4[t] -0.0105698287220025M5[t] -0.0119169960474307M6[t] -0.0132641633728589M7[t] -0.00661133069828712M8[t] -0.00195849802371534M9[t] -0.00130566534914356M10[t] + 0.00134716732542821M11[t] + 0.00134716732542822t + 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) 0.893237154150196 0.00987 90.5006 0 0 x 0.105662055335968 0.008745 12.0821 0 0 M1 -0.00188669301712875 0.010579 -0.1784 0.859213 0.429607 M2 -0.00739591567852424 0.011098 -0.6664 0.50839 0.254195 M3 -0.00787549407114603 0.011233 -0.7011 0.486693 0.243347 M4 -0.00922266139657425 0.011188 -0.8243 0.413926 0.206963 M5 -0.0105698287220025 0.011149 -0.9481 0.347943 0.173971 M6 -0.0119169960474307 0.011114 -1.0722 0.289099 0.14455 M7 -0.0132641633728589 0.011085 -1.1966 0.237478 0.118739 M8 -0.00661133069828712 0.011061 -0.5977 0.55291 0.276455 M9 -0.00195849802371534 0.011043 -0.1774 0.85999 0.429995 M10 -0.00130566534914356 0.011029 -0.1184 0.90627 0.453135 M11 0.00134716732542821 0.011021 0.1222 0.903236 0.451618 t 0.00134716732542822 0.000243 5.5521 1e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.978537207620351 R-squared 0.957535066697435 Adjusted R-squared 0.94578944684779 F-TEST (value) 81.5227360458389 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0174219911547682 Sum Squared Residuals 0.0142657114624507 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.89 0.892697628458503 -0.00269762845850255 2 0.89 0.88853557312253 0.00146442687747086 3 0.89 0.889403162055336 0.000596837944664412 4 0.89 0.889403162055336 0.000596837944664324 5 0.89 0.889403162055336 0.000596837944664384 6 0.89 0.889403162055336 0.000596837944664333 7 0.89 0.889403162055336 0.000596837944664376 8 0.9 0.897403162055336 0.00259683794466436 9 0.91 0.903403162055336 0.00659683794466438 10 0.92 0.905403162055336 0.0145968379446644 11 0.92 0.909403162055336 0.0105968379446644 12 0.92 0.909403162055336 0.0105968379446644 13 0.92 0.908863636363635 0.0111363636363649 14 0.92 0.904701581027668 0.0152984189723321 15 0.92 0.905569169960474 0.0144308300395257 16 0.92 0.905569169960474 0.0144308300395258 17 0.92 0.905569169960474 0.0144308300395258 18 0.92 0.905569169960474 0.0144308300395258 19 0.92 0.905569169960474 0.0144308300395258 20 0.92 0.913569169960474 0.00643083003952575 21 0.92 0.919569169960474 0.000430830039525739 22 0.92 0.921569169960474 -0.00156916996047426 23 0.92 0.925569169960474 -0.00556916996047426 24 0.92 0.925569169960474 -0.00556916996047426 25 0.92 0.925029644268774 -0.00502964426877375 26 0.92 0.920867588932807 -0.000867588932806436 27 0.92 0.921735177865613 -0.00173517786561289 28 0.92 0.921735177865613 -0.00173517786561287 29 0.92 0.921735177865613 -0.00173517786561288 30 0.92 0.921735177865613 -0.00173517786561286 31 0.92 0.921735177865613 -0.00173517786561288 32 0.92 0.929735177865613 -0.00973517786561288 33 0.92 0.935735177865613 -0.0157351778656129 34 0.92 0.937735177865613 -0.0177351778656129 35 0.92 0.941735177865613 -0.0217351778656129 36 0.92 0.941735177865613 -0.0217351778656129 37 0.92 0.941195652173912 -0.0211956521739124 38 0.92 0.937033596837945 -0.0170335968379451 39 1.01 1.04356324110672 -0.0335632411067193 40 1.01 1.04356324110672 -0.0335632411067193 41 1.01 1.04356324110672 -0.0335632411067194 42 1.01 1.04356324110672 -0.0335632411067193 43 1.01 1.04356324110672 -0.0335632411067194 44 1.04 1.05156324110672 -0.0115632411067193 45 1.05 1.05756324110672 -0.00756324110671932 46 1.05 1.05956324110672 -0.00956324110671931 47 1.06 1.06356324110672 -0.00356324110671931 48 1.06 1.06356324110672 -0.00356324110671930 49 1.06 1.06302371541502 -0.0030237154150188 50 1.06 1.05886166007905 0.00113833992094852 51 1.08 1.05972924901186 0.0202707509881421 52 1.08 1.05972924901186 0.0202707509881421 53 1.08 1.05972924901186 0.0202707509881421 54 1.08 1.05972924901186 0.0202707509881421 55 1.08 1.05972924901186 0.0202707509881421 56 1.08 1.06772924901186 0.0122707509881421 57 1.09 1.07372924901186 0.0162707509881421 58 1.09 1.07572924901186 0.0142707509881421 59 1.1 1.07972924901186 0.0202707509881421 60 1.1 1.07972924901186 0.0202707509881421 61 1.1 1.07918972332016 0.0208102766798426 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 1.32661052953698e-42 2.65322105907396e-42 1 18 2.62975256265686e-55 5.25950512531372e-55 1 19 2.26340034435676e-72 4.52680068871352e-72 1 20 9.93647598646616e-05 0.000198729519729323 0.999900635240135 21 0.00278147062124583 0.00556294124249166 0.997218529378754 22 0.027701048863691 0.055402097727382 0.972298951136309 23 0.0598041405223617 0.119608281044723 0.940195859477638 24 0.0975215336620576 0.195043067324115 0.902478466337942 25 0.137751755995303 0.275503511990606 0.862248244004697 26 0.223181299776170 0.446362599552339 0.77681870022383 27 0.207533843060371 0.415067686120741 0.79246615693963 28 0.199206857440226 0.398413714880452 0.800793142559774 29 0.206485136317861 0.412970272635722 0.793514863682139 30 0.246425353981852 0.492850707963704 0.753574646018148 31 0.371328845939342 0.742657691878683 0.628671154060658 32 0.401770891691380 0.803541783382761 0.598229108308620 33 0.395630328084145 0.791260656168289 0.604369671915856 34 0.432948368804974 0.865896737609948 0.567051631195026 35 0.406509282829102 0.813018565658205 0.593490717170898 36 0.364987744346943 0.729975488693887 0.635012255653057 37 0.296054542699971 0.592109085399941 0.70394545730003 38 0.221844829950187 0.443689659900374 0.778155170049813 39 0.207985974335174 0.415971948670348 0.792014025664826 40 0.216696179415554 0.433392358831107 0.783303820584446 41 0.270907797429717 0.541815594859434 0.729092202570283 42 0.459623313379127 0.919246626758255 0.540376686620873 43 1 6.76959227119712e-54 3.38479613559856e-54 44 1 3.57754690268425e-40 1.78877345134212e-40 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.25 NOK 5% type I error level 7 0.25 NOK 10% type I error level 8 0.285714285714286 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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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