Multiple Regression Monthly Dummies werkhloosheid ecogr

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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: Thu, 17 Dec 2009 06:53:54 -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/17/t12610581154i4mqkwlmk3dmtr.htm/, Retrieved Thu, 17 Dec 2009 14:55:27 +0100

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@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/17/t12610581154i4mqkwlmk3dmtr.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}, }

Original text written by user:

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Dataseries X:

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9.3 96.8 9.3 114.1 8.7 110.3 8.2 103.9 8.3 101.6 8.5 94.6 8.6 95.9 8.5 104.7 8.2 102.8 8.1 98.1 7.9 113.9 8.6 80.9 8.7 95.7 8.7 113.2 8.5 105.9 8.4 108.8 8.5 102.3 8.7 99 8.7 100.7 8.6 115.5 8.5 100.7 8.3 109.9 8 114.6 8.2 85.4 8.1 100.5 8.1 114.8 8 116.5 7.9 112.9 7.9 102 8 106 8 105.3 7.9 118.8 8 106.1 7.7 109.3 7.2 117.2 7.5 92.5 7.3 104.2 7 112.5 7 122.4 7 113.3 7.2 100 7.3 110.7 7.1 112.8 6.8 109.8 6.4 117.3 6.1 109.1 6.5 115.9 7.7 96 7.9 99.8 7.5 116.8 6.9 115.7 6.6 99.4 6.9 94.3 7.7 91 8 93.2 8 103.1 7.7 94.1 7.3 91.8 7.4 102.7 8.1 82.6

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 werklh[t] = + 11.1601866545664 -0.0358960522927116ecogr[t] + 0.667880943329111M1[t] + 1.06201420144467M2[t] + 0.757706675169545M3[t] + 0.32438233526692M4[t] + 0.190854416796458M5[t] + 0.478751548300854M6[t] + 0.566134337327233M7[t] + 0.762019597503095M8[t] + 0.340181994334138M9[t] + 0.0600802050502195M10[t] + 0.291041807189020M11[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) 11.1601866545664 1.425609 7.8284 0 0 ecogr -0.0358960522927116 0.015895 -2.2583 0.028608 0.014304 M1 0.667880943329111 0.483396 1.3816 0.173614 0.086807 M2 1.06201420144467 0.615822 1.7245 0.091181 0.045591 M3 0.757706675169545 0.614505 1.233 0.223694 0.111847 M4 0.32438233526692 0.548326 0.5916 0.556962 0.278481 M5 0.190854416796458 0.487473 0.3915 0.697184 0.348592 M6 0.478751548300854 0.488916 0.9792 0.332489 0.166245 M7 0.566134337327233 0.497999 1.1368 0.261377 0.130689 M8 0.762019597503095 0.574688 1.326 0.191257 0.095629 M9 0.340181994334138 0.518077 0.6566 0.514625 0.257312 M10 0.0600802050502195 0.513568 0.117 0.90737 0.453685 M11 0.291041807189020 0.600431 0.4847 0.630125 0.315063 Multiple Linear Regression - Regression Statistics Multiple R 0.463074144446394 R-squared 0.21443766325476 Adjusted R-squared 0.0138685560006561 F-TEST (value) 1.06914602248833 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.406474500246614 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.703159648930356 Sum Squared Residuals 23.2383741185415 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.3 8.3533297359611 0.946670264038907 2 9.3 8.12646128941269 1.17353871058731 3 8.7 7.95855876184987 0.741441238150132 4 8.2 7.7549691566206 0.445030843379403 5 8.3 7.70400215842337 0.59599784157663 6 8.5 8.24317165597675 0.256828344023252 7 8.6 8.2838895770226 0.316110422977398 8 8.5 8.1638895770226 0.336110422977398 9 8.2 7.8102544732098 0.389745526790203 10 8.1 7.69886412970162 0.401135870298378 11 7.9 7.36266810561558 0.53733189438442 12 8.6 8.25619602408604 0.343803975913958 13 8.7 8.39281539348302 0.307184606516977 14 8.7 8.15876773647613 0.541232263523871 15 8.5 8.1165013919378 0.383498608062202 16 8.4 7.57907850038631 0.820921499613692 17 8.5 7.67887492181847 0.821125078181528 18 8.7 8.08522902588882 0.614770974111183 19 8.7 8.11158852601759 0.588411473982413 20 8.6 7.77621221226132 0.823787787738683 21 8.5 7.88563618302449 0.61436381697551 22 8.3 7.27529071264763 1.02470928735238 23 8 7.33754086901068 0.662459130989318 24 8.2 8.09466378876884 0.105336211231159 25 8.1 8.22051434247801 -0.120514342478007 26 8.1 8.10133405280779 -0.00133405280779036 27 8 7.73600323763505 0.263996762364945 28 7.9 7.43190468598619 0.468095314013809 29 7.9 7.68964373750629 0.210356262493715 30 8 7.83395665983983 0.166043340160165 31 8 7.94646668547111 0.0535333145288874 32 7.9 7.65775523969537 0.242244760304632 33 8 7.69179750064385 0.308202499356152 34 7.7 7.29682834402325 0.403171655976748 35 7.2 7.24421113304963 -0.0442111330496315 36 7.5 7.83980181749059 -0.339801817490588 37 7.3 8.08769894899497 -0.787698948994973 38 7 8.18389497308103 -1.18389497308103 39 7 7.52421652910806 -0.524216529108056 40 7 7.4175462650691 -0.417546265069107 41 7.2 7.76143584209171 -0.561435842091708 42 7.3 7.66524521406409 -0.365245214064091 43 7.1 7.67724629327578 -0.577246293275776 44 6.8 7.98081971032977 -1.18081971032977 45 6.4 7.28976171496548 -0.889761714965477 46 6.1 7.3040075544818 -1.20400755448180 47 6.5 7.29087600103016 -0.790876001030157 48 7.7 7.7141656344661 -0.0141656344660969 49 7.9 8.2456415790829 -0.345641579082904 50 7.5 8.02954194822237 -0.529541948222367 51 6.9 7.76472007946922 -0.864720079469223 52 6.6 7.9165013919378 -1.31650139193780 53 6.9 7.96604334016016 -1.06604334016016 54 7.7 8.37239744423051 -0.672397444230509 55 8 8.38080891821292 -0.380808918212923 56 8 8.22132326069094 -0.221323260690941 57 7.7 8.12255012815639 -0.422550128156387 58 7.3 7.9250092591457 -0.625009259145706 59 7.4 7.76470389129395 -0.36470389129395 60 8.1 8.19517273518843 -0.0951727351884332 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.115094199162433 0.230188398324865 0.884905800837567 17 0.0512277867285024 0.102455573457005 0.948772213271498 18 0.0203797628783442 0.0407595257566883 0.979620237121656 19 0.0086104899816373 0.0172209799632746 0.991389510018363 20 0.00514965172994423 0.0102993034598885 0.994850348270056 21 0.00372060436294124 0.00744120872588248 0.99627939563706 22 0.00228060980378700 0.00456121960757401 0.997719390196213 23 0.00118932998137589 0.00237865996275179 0.998810670018624 24 0.00121902953897520 0.00243805907795040 0.998780970461025 25 0.0127284012551027 0.0254568025102054 0.987271598744897 26 0.0402010366076997 0.0804020732153994 0.9597989633923 27 0.0493313087649599 0.0986626175299198 0.95066869123504 28 0.0621916891983942 0.124383378396788 0.937808310801606 29 0.0812092781080408 0.162418556216082 0.918790721891959 30 0.0735844477333746 0.147168895466749 0.926415552266625 31 0.0654123053320155 0.130824610664031 0.934587694667985 32 0.0733338780810351 0.146667756162070 0.926666121918965 33 0.0925854152649433 0.185170830529887 0.907414584735057 34 0.265924611188881 0.531849222377762 0.734075388811119 35 0.322283840711904 0.644567681423808 0.677716159288096 36 0.283154201448110 0.566308402896221 0.71684579855189 37 0.395456062310683 0.790912124621367 0.604543937689317 38 0.72900139841382 0.541997203172359 0.270998601586180 39 0.68651360331455 0.626972793370899 0.313486396685450 40 0.845330423845355 0.30933915230929 0.154669576154645 41 0.87368313308349 0.252633733833019 0.126316866916509 42 0.890492957766166 0.219014084467667 0.109507042233834 43 0.816207597537539 0.367584804924923 0.183792402462461 44 0.960362050153879 0.0792758996922427 0.0396379498461213 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.137931034482759 NOK 5% type I error level 8 0.275862068965517 NOK 10% type I error level 11 0.379310344827586 NOK

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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