multiple regression dummies+trend

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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 06:06:41 -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/t1260104876bp2devaqukifjld.htm/, Retrieved Sun, 06 Dec 2009 14:08:13 +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/t1260104876bp2devaqukifjld.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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3,6 4,5 3,9 3,3 4,6 3,6 3,2 4,9 3,3 3,4 4,9 3,2 3,4 4,5 3,4 3,5 4,6 3,4 3,2 4,7 3,5 3,3 4,7 3,2 3,3 4,3 3,3 3,4 4,2 3,3 3,7 4,4 3,4 3,9 4 3,7 4 3,8 3,9 3,7 3,6 4 3,9 3,6 3,7 4,2 3,3 3,9 4,4 3,4 4,2 4,3 3,4 4,4 4,2 3,3 4,3 4,3 3,3 4,2 4,3 3,2 4,3 4,3 3,1 4,3 4,5 3,1 4,3 5 2,4 4,5 5,2 2,4 5 5,2 2,4 5,2 5,4 2,1 5,2 5,5 2 5,4 5,4 2 5,5 5,5 2,1 5,4 5,4 2,1 5,5 5,7 2 5,4 5,7 2 5,7 6,1 2 5,7 6,5 1,7 6,1 6,9 1,3 6,5 6,8 1,2 6,9 6,7 1,1 6,8 6,6 1,4 6,7 6,5 1,5 6,6 6,4 1,4 6,5 6,1 1,1 6,4 6,2 1,1 6,1 6,3 1 6,2 6,4 1,4 6,3 6,5 1,3 6,4 6,7 1,2 6,5 7 1,5 6,7 7 1,6 7 6,8 1,8 7 6,7 1,5 6,8 6,7 1,3 6,7 6,5 1,6 6,7 6,4 1,6 6,5 6,1 1,8 6,4 6,2 1,8 6,1 6 1,6 6,2 6,1 1,8 6 6,1 2 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkl[t] = + 1.81590223889269 -0.200998083864732Infl[t] + 0.82498581429753`M1(t)`[t] -0.302564367060396M1[t] -0.463821959024594M2[t] -0.293081820701185M3[t] -0.227438653623756M4[t] -0.351714504980950M5[t] -0.380492342336491M6[t] -0.460710578374196M7[t] -0.211009795977278M8[t] -0.356325003260963M9[t] -0.201602556902454M10[t] -0.0948578791542544M11[t] -0.00224269174985331t + 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) 1.81590223889269 0.416745 4.3573 7.8e-05 3.9e-05 Infl -0.200998083864732 0.052076 -3.8597 0.000368 0.000184 `M1(t)` 0.82498581429753 0.066791 12.3518 0 0 M1 -0.302564367060396 0.091674 -3.3004 0.00192 0.00096 M2 -0.463821959024594 0.090772 -5.1097 7e-06 3e-06 M3 -0.293081820701185 0.088408 -3.3151 0.001841 0.000921 M4 -0.227438653623756 0.08797 -2.5854 0.013117 0.006558 M5 -0.351714504980950 0.088296 -3.9834 0.000252 0.000126 M6 -0.380492342336491 0.088137 -4.317 8.8e-05 4.4e-05 M7 -0.460710578374196 0.088588 -5.2006 5e-06 2e-06 M8 -0.211009795977278 0.090105 -2.3418 0.023781 0.01189 M9 -0.356325003260963 0.089442 -3.9839 0.000251 0.000126 M10 -0.201602556902454 0.090357 -2.2312 0.030813 0.015406 M11 -0.0948578791542544 0.089853 -1.0557 0.296865 0.148433 t -0.00224269174985331 0.003246 -0.6909 0.493251 0.246625 Multiple Linear Regression - Regression Statistics Multiple R 0.996027266261953 R-squared 0.99207031513726 Adjusted R-squared 0.989547233590024 F-TEST (value) 393.197879879969 F-TEST (DF numerator) 14 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.130727785118641 Sum Squared Residuals 0.75194916728912 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.6 3.82404847845151 -0.224048478451508 2 3.3 3.39295264206174 -0.0929526420617366 3 3.2 3.25365491918661 -0.0536549191866102 4 3.4 3.23455681308444 0.165443186915564 5 3.4 3.35343466638279 0.0465653336172135 6 3.5 3.30231432889092 0.197685671109080 7 3.2 3.28225217414664 -0.0822521741466406 8 3.3 3.28221452050445 0.0177854794955533 9 3.3 3.29755443644655 0.00244556355344526 10 3.4 3.47013399944168 -0.070133999441683 11 3.7 3.61693495009684 0.0830650499031642 12 3.9 4.03744511533639 -0.137445115336390 13 4 3.93783483615859 0.0621651638414075 14 3.7 3.89703275064724 -0.19703275064724 15 3.9 3.81803445293154 0.0819655470684627 16 4.2 4.10673151627804 0.0932684837219614 17 4.4 4.20760890907378 0.192391090926223 18 4.3 4.34158554282789 -0.0415855428278899 19 4.2 4.19672584199705 0.00327415800294924 20 4.3 4.36168535121436 -0.061685351214363 21 4.3 4.31672584199705 -0.0167258419970509 22 4.3 4.48930540499218 -0.18930540499218 23 4.5 4.59380739099053 -0.0938073909905258 24 5 4.99211839995975 0.007881600040254 25 5.2 5.09980424829826 0.100195751701738 26 5.2 5.10130112744372 0.0986988725562839 27 5.4 5.33009799917669 0.0699020008233085 28 5.5 5.57859544575025 -0.0785954457502471 29 5.4 5.53457548407295 -0.134575484072952 30 5.5 5.40095656515133 0.0990434348486674 31 5.4 5.40099421879353 -0.00099421879352644 32 5.7 5.58605353639731 0.113946463602688 33 5.7 5.68599138165303 0.0140086183469673 34 6.1 5.83847113626169 0.261528863738311 35 6.5 6.33326687313847 0.166733126861534 36 6.9 6.83627561980777 0.0637243801922278 37 6.8 6.88156269510301 -0.0815626951030091 38 6.7 6.65566363834568 0.0443363616543233 39 6.6 6.68136307833006 -0.0813630783300608 40 6.5 6.64216516384141 -0.142165163841409 41 6.4 6.45324784769108 -0.0532478476910823 42 6.1 6.40002816231536 -0.300028162315356 43 6.2 6.07007149023854 0.129928509761463 44 6.3 6.42012797070183 -0.120127970701829 45 6.4 6.27466941955215 0.125330580447850 46 6.5 6.52974756397703 -0.0297475639770330 47 6.7 6.7368479397916 -0.0368479397916049 48 7 6.9341608648961 0.0658391351039074 49 7 6.85674974198863 0.143250258011371 50 6.8 6.65304984150163 0.146950158498369 51 6.7 6.7168495503751 -0.0168495503751000 52 6.7 6.73795106104587 -0.0379510610458694 53 6.5 6.5511330927794 -0.0511330927794023 54 6.4 6.3551154008145 0.044884599185498 55 6.1 6.14995627482424 -0.049956274824245 56 6.2 6.14991862118205 0.0500813788179506 57 6 6.12505892035121 -0.125058920351211 58 6.1 6.07234189532741 0.0276581046725850 59 6.1 6.21914284598257 -0.119142845982567 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.629185698876544 0.741628602246912 0.370814301123456 19 0.55151716355763 0.89696567288474 0.44848283644237 20 0.406737328972787 0.813474657945574 0.593262671027213 21 0.287666338860325 0.575332677720651 0.712333661139675 22 0.300771334330866 0.601542668661732 0.699228665669134 23 0.300606090894782 0.601212181789564 0.699393909105218 24 0.308835404731654 0.617670809463308 0.691164595268346 25 0.330354365707124 0.660708731414249 0.669645634292876 26 0.47845095754510 0.95690191509020 0.5215490424549 27 0.422638776914335 0.84527755382867 0.577361223085665 28 0.369626490201975 0.73925298040395 0.630373509798025 29 0.387887961846617 0.775775923693233 0.612112038153383 30 0.325310384510069 0.650620769020138 0.674689615489931 31 0.302950218145301 0.605900436290603 0.697049781854699 32 0.291818432742032 0.583636865484064 0.708181567257968 33 0.259296149987314 0.518592299974627 0.740703850012686 34 0.400367147473926 0.800734294947852 0.599632852526074 35 0.478909249911716 0.957818499823431 0.521090750088284 36 0.375821425891059 0.751642851782117 0.624178574108941 37 0.367246640495871 0.734493280991743 0.632753359504129 38 0.26153368943602 0.52306737887204 0.73846631056398 39 0.208499007144928 0.416998014289856 0.791500992855072 40 0.187607246300094 0.375214492600189 0.812392753699906 41 0.106231023408595 0.212462046817191 0.893768976591405 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 = 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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