Paper H4 Mannen Multiple Regression (seasonal, trend)

*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 14:01:39 -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/t122946146068sjvq4cpn9k1py.htm/, Retrieved Tue, 16 Dec 2008 22:04:29 +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/t122946146068sjvq4cpn9k1py.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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No (this computation is public)

User-defined keywords:

Dataseries X:

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269645 0 267037 0 258113 0 262813 0 267413 0 267366 0 264777 0 258863 0 254844 0 254868 0 277267 0 285351 0 286602 0 283042 0 276687 0 277915 0 277128 0 277103 0 275037 0 270150 0 267140 0 264993 0 287259 0 291186 0 292300 0 288186 0 281477 0 282656 1 280190 1 280408 1 276836 1 275216 1 274352 1 271311 1 289802 1 290726 1 292300 1 278506 1 269826 1 265861 1 269034 1 264176 1 255198 1 253353 1 246057 1 235372 1 258556 1 260993 1 254663 1 250643 1 243422 1 247105 1 248541 1 245039 1 237080 1 237085 1 225554 1 226839 1 247934 1 248333 1 246969 1 245098 1 246263 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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Mannen[t] = + 298214.333333333 + 12494.8194444444Dummy[t] -4543.12708333343M1[t] -8693.36527777776M2[t] -13969.7701388889M3[t] -14801.8944444444M4[t] -12766.4326388888M5[t] -13564.9708333333M6[t] -17753.5090277777M7[t] -19761.4472222222M8[t] -24261.1854166666M9[t] -26329.7236111111M10[t] -3998.46180555552M11[t] -844.261805555553t + 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) 298214.333333333 6725.537343 44.3406 0 0 Dummy 12494.8194444444 6529.178246 1.9137 0.061511 0.030755 M1 -4543.12708333343 7710.044 -0.5892 0.558402 0.279201 M2 -8693.36527777776 7704.585647 -1.1283 0.264672 0.132336 M3 -13969.7701388889 7703.250795 -1.8135 0.075883 0.037941 M4 -14801.8944444444 8164.106964 -1.813 0.075953 0.037976 M5 -12766.4326388888 8134.8545 -1.5693 0.123002 0.061501 M6 -13564.9708333333 8109.417011 -1.6727 0.100752 0.050376 M7 -17753.5090277777 8087.830493 -2.1951 0.032925 0.016462 M8 -19761.4472222222 8070.125849 -2.4487 0.017962 0.008981 M9 -24261.1854166666 8056.328671 -3.0114 0.004104 0.002052 M10 -26329.7236111111 8046.459059 -3.2722 0.001959 0.00098 M11 -3998.46180555552 8040.531477 -0.4973 0.62121 0.310605 t -844.261805555553 178.285311 -4.7355 1.9e-05 1e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.749397988144867 R-squared 0.561597344635575 Adjusted R-squared 0.445286436069503 F-TEST (value) 4.8284150778218 F-TEST (DF numerator) 13 F-TEST (DF denominator) 49 p-value 2.50802456935872e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 12710.0708874232 Sum Squared Residuals 7915749196.20282 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 269645 292826.944444445 -23181.9444444451 2 267037 287832.444444444 -20795.4444444445 3 258113 281711.777777778 -23598.7777777777 4 262813 280035.391666667 -17222.3916666666 5 267413 281226.591666667 -13813.5916666666 6 267366 279583.791666667 -12217.7916666666 7 264777 274550.991666667 -9773.99166666666 8 258863 271698.791666667 -12835.7916666667 9 254844 266354.791666667 -11510.7916666666 10 254868 263441.991666667 -8573.99166666663 11 277267 284928.991666667 -7661.99166666662 12 285351 288083.191666667 -2732.19166666659 13 286602 282695.802777778 3906.19722222237 14 283042 277701.302777778 5340.69722222223 15 276687 271580.636111111 5106.36388888891 16 277915 269904.25 8010.75 17 277128 271095.45 6032.54999999999 18 277103 269452.65 7650.34999999999 19 275037 264419.85 10617.15 20 270150 261567.65 8582.35 21 267140 256223.65 10916.35 22 264993 253310.85 11682.15 23 287259 274797.85 12461.1500000000 24 291186 277952.05 13233.95 25 292300 272564.661111111 19735.338888889 26 288186 267570.161111111 20615.8388888889 27 281477 261449.494444444 20027.5055555555 28 282656 272267.927777778 10388.0722222223 29 280190 273459.127777778 6730.87222222225 30 280408 271816.327777778 8591.67222222225 31 276836 266783.527777778 10052.4722222223 32 275216 263931.327777778 11284.6722222223 33 274352 258587.327777778 15764.6722222223 34 271311 255674.527777778 15636.4722222223 35 289802 277161.527777778 12640.4722222223 36 290726 280315.727777778 10410.2722222223 37 292300 274928.338888889 17371.6611111113 38 278506 269933.838888889 8572.16111111113 39 269826 263813.172222222 6012.82777777779 40 265861 262136.786111111 3724.21388888888 41 269034 263327.986111111 5706.01388888887 42 264176 261685.186111111 2490.81388888888 43 255198 256652.386111111 -1454.38611111111 44 253353 253800.186111111 -447.186111111114 45 246057 248456.186111111 -2399.18611111111 46 235372 245543.386111111 -10171.3861111111 47 258556 267030.386111111 -8474.38611111112 48 260993 270184.586111111 -9191.58611111109 49 254663 264797.197222222 -10134.1972222221 50 250643 259802.697222222 -9159.69722222223 51 243422 253682.030555556 -10260.0305555556 52 247105 252005.644444444 -4900.64444444449 53 248541 253196.844444444 -4655.8444444445 54 245039 251554.044444445 -6515.0444444445 55 237080 246521.244444444 -9441.24444444449 56 237085 243669.044444445 -6584.04444444449 57 225554 238325.044444445 -12771.0444444445 58 226839 235412.244444444 -8573.2444444445 59 247934 256899.244444444 -8965.2444444445 60 248333 260053.444444444 -11720.4444444445 61 246969 254666.055555555 -7697.05555555549 62 245098 249671.555555556 -4573.5555555556 63 246263 243550.888888889 2712.11111111105 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.113181367309528 0.226362734619055 0.886818632690472 18 0.0948680652179009 0.189736130435802 0.9051319347821 19 0.0581720677119515 0.116344135423903 0.941827932288049 20 0.0318096074505767 0.0636192149011533 0.968190392549423 21 0.0143707126518669 0.0287414253037337 0.985629287348133 22 0.0080392078963723 0.0160784157927446 0.991960792103628 23 0.00433830821255005 0.0086766164251001 0.99566169178745 24 0.00646200012319221 0.0129240002463844 0.993537999876808 25 0.00420020734911314 0.00840041469822628 0.995799792650887 26 0.0028694764964475 0.005738952992895 0.997130523503553 27 0.00140701813137136 0.00281403626274272 0.998592981868629 28 0.000556265369321416 0.00111253073864283 0.999443734630679 29 0.000383548368549137 0.000767096737098273 0.99961645163145 30 0.000164787289486917 0.000329574578973835 0.999835212710513 31 7.02665180447784e-05 0.000140533036089557 0.999929733481955 32 2.65088410980220e-05 5.30176821960439e-05 0.999973491158902 33 2.65083203751321e-05 5.30166407502642e-05 0.999973491679625 34 2.52337979192162e-05 5.04675958384324e-05 0.999974766202081 35 2.18773658567291e-05 4.37547317134581e-05 0.999978122634143 36 0.000108760427281868 0.000217520854563737 0.999891239572718 37 0.00219580172453533 0.00439160344907067 0.997804198275465 38 0.0630239805622959 0.126047961124592 0.936976019437704 39 0.171206361530693 0.342412723061385 0.828793638469307 40 0.479835071548635 0.95967014309727 0.520164928451365 41 0.621506804827469 0.756986390345062 0.378493195172531 42 0.737492433308824 0.525015133382352 0.262507566691176 43 0.824267314599867 0.351465370800266 0.175732685400133 44 0.825804855708163 0.348390288583673 0.174195144291837 45 0.923849276721383 0.152301446557234 0.076150723278617 46 0.872632704798393 0.254734590403215 0.127367295201607 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 14 0.466666666666667 NOK 5% type I error level 17 0.566666666666667 NOK 10% type I error level 18 0.6 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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