Paper Dummy Variable Model 2

*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: Tue, 16 Dec 2008 13:25:55 -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/16/t1229459251drlt27acpp8qlth.htm/, Retrieved Tue, 16 Dec 2008 21:27:31 +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/16/t1229459251drlt27acpp8qlth.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:

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Dataseries X:

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117.3 0 118.8 0 131.3 0 125.9 0 133.1 0 147 0 145.8 0 164.4 0 149.8 0 137.7 0 151.7 0 156.8 0 180 0 180.4 0 170.4 0 191.6 0 199.5 0 218.2 1 217.5 1 205 1 194 0 199.3 0 219.3 1 211.1 1 215.2 1 240.2 1 242.2 1 240.7 1 255.4 1 253 1 218.2 1 203.7 1 205.6 1 215.6 1 188.5 1 202.9 1 214 1 230.3 1 230 1 241 1 259.6 1 247.8 1 270.3 1 289.7 1 322.7 1 315 1 320.2 1 329.5 1 360.6 1 382.2 1 435.4 1 464 1 468.8 1 403 1 351.6 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 82.647598105548 -34.8087280108254x[t] + 15.2126821154714M1[t] + 22.5548838520523M2[t] + 28.4170855886333M3[t] + 33.5792873252143M4[t] + 38.6014890617952M5[t] + 30.4654364005413M6[t] + 11.7276381371222M7[t] + 13.0961930536761M8[t] + 1.10121278755075M9[t] -5.64158547586829M10[t] + 0.467798263419038M11[t] + 5.61779826341904t + 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) 82.647598105548 22.733991 3.6354 0.000767 0.000383 x -34.8087280108254 20.507326 -1.6974 0.097204 0.048602 M1 15.2126821154714 27.192395 0.5594 0.578901 0.28945 M2 22.5548838520523 27.188071 0.8296 0.411576 0.205788 M3 28.4170855886333 27.197143 1.0449 0.302211 0.151106 M4 33.5792873252143 27.219599 1.2336 0.224361 0.112181 M5 38.6014890617952 27.255406 1.4163 0.164244 0.082122 M6 30.4654364005413 27.150052 1.1221 0.268343 0.134171 M7 11.7276381371222 27.138075 0.4321 0.667899 0.333949 M8 13.0961930536761 28.699976 0.4563 0.650573 0.325286 M9 1.10121278755075 28.847975 0.0382 0.969735 0.484868 M10 -5.64158547586829 28.904267 -0.1952 0.846215 0.423107 M11 0.467798263419038 28.604619 0.0164 0.987031 0.493516 t 5.61779826341904 0.603567 9.3077 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.912024212966634 R-squared 0.831788165037409 Adjusted R-squared 0.778452705171222 F-TEST (value) 15.5954062667552 F-TEST (DF numerator) 13 F-TEST (DF denominator) 41 p-value 6.52644605025898e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 40.4440337782315 Sum Squared Residuals 67064.5145984439 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 117.3 103.478078484438 13.8219215155616 2 118.8 116.438078484438 2.36192151556155 3 131.3 127.918078484438 3.38192151556156 4 125.9 138.698078484438 -12.7980784844384 5 133.1 149.338078484438 -16.2380784844384 6 147 146.819824086604 0.180175913396473 7 145.8 133.699824086604 12.1001759133965 8 164.4 140.686177266576 23.7138227334236 9 149.8 134.30899526387 15.4910047361299 10 137.7 133.18399526387 4.51600473612988 11 151.7 144.911177266576 6.78882273342354 12 156.8 150.061177266576 6.73882273342357 13 180 170.891657645467 9.10834235453313 14 180.4 183.851657645467 -3.45165764546684 15 170.4 195.331657645467 -24.9316576454669 16 191.6 206.111657645467 -14.5116576454668 17 199.5 216.751657645467 -17.2516576454669 18 218.2 179.424675236807 38.7753247631935 19 217.5 166.304675236807 51.1953247631935 20 205 173.291028416779 31.7089715832206 21 194 201.722574424899 -7.72257442489851 22 199.3 200.597574424899 -1.29757442489849 23 219.3 177.516028416779 41.7839715832206 24 211.1 182.666028416779 28.4339715832206 25 215.2 203.49650879567 11.7034912043302 26 240.2 216.45650879567 23.7434912043302 27 242.2 227.93650879567 14.2634912043302 28 240.7 238.71650879567 1.98349120433017 29 255.4 249.35650879567 6.04349120433017 30 253 246.838254397835 6.16174560216509 31 218.2 233.718254397835 -15.5182543978349 32 203.7 240.704607577808 -37.0046075778079 33 205.6 234.327425575101 -28.7274255751015 34 215.6 233.202425575101 -17.6024255751015 35 188.5 244.929607577808 -56.4296075778079 36 202.9 250.079607577808 -47.1796075778079 37 214 270.910087956698 -56.9100879566983 38 230.3 283.870087956698 -53.5700879566982 39 230 295.350087956698 -65.3500879566983 40 241 306.130087956698 -65.1300879566982 41 259.6 316.770087956698 -57.1700879566982 42 247.8 314.251833558863 -66.4518335588633 43 270.3 301.131833558863 -30.8318335588633 44 289.7 308.118186738836 -18.4181867388363 45 322.7 301.74100473613 20.9589952638701 46 315 300.61600473613 14.3839952638701 47 320.2 312.343186738836 7.85681326116372 48 329.5 317.493186738836 12.0068132611637 49 360.6 338.323667117727 22.2763328822734 50 382.2 351.283667117727 30.9163328822733 51 435.4 362.763667117727 72.6363328822734 52 464 373.543667117727 90.4563328822733 53 468.8 384.183667117727 84.6163328822733 54 403 381.665412719892 21.3345872801083 55 351.6 368.545412719892 -16.9454127198917 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00820557292267091 0.0164111458453418 0.99179442707733 18 0.00125806524510739 0.00251613049021478 0.998741934754893 19 0.000203951889602817 0.000407903779205635 0.999796048110397 20 0.000319151401241633 0.000638302802483265 0.999680848598758 21 8.98073635863037e-05 0.000179614727172607 0.999910192636414 22 1.60132749334858e-05 3.20265498669716e-05 0.999983986725066 23 4.43136218305577e-06 8.86272436611155e-06 0.999995568637817 24 1.26634497153885e-06 2.53268994307771e-06 0.999998733655028 25 1.50711559121674e-06 3.01423118243349e-06 0.999998492884409 26 5.53320340787194e-07 1.10664068157439e-06 0.99999944667966 27 1.69610449071008e-07 3.39220898142015e-07 0.99999983038955 28 4.15426055304693e-08 8.30852110609385e-08 0.999999958457394 29 1.18401398353989e-08 2.36802796707978e-08 0.99999998815986 30 4.81639141793363e-08 9.63278283586727e-08 0.999999951836086 31 7.11959888556145e-05 0.000142391977711229 0.999928804011144 32 0.00260593999818117 0.00521187999636235 0.997394060001819 33 0.00513647114855901 0.0102729422971180 0.994863528851441 34 0.00775408178946081 0.0155081635789216 0.99224591821054 35 0.0212238270006265 0.0424476540012529 0.978776172999374 36 0.0239127080930571 0.0478254161861141 0.976087291906943 37 0.0162517728772952 0.0325035457545904 0.983748227122705 38 0.00798313815581533 0.0159662763116307 0.992016861844185 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.681818181818182 NOK 5% type I error level 22 1 NOK 10% type I error level 22 1 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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