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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: Mon, 06 Dec 2010 14:59:55 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/06/t1291647515k7ztmu28z48jmug.htm/, Retrieved Mon, 06 Dec 2010 15:58:45 +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/2010/Dec/06/t1291647515k7ztmu28z48jmug.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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1635.25 8169.75 7977.64 10171 -14.9 -18 1.8 2.05 1833.42 7905.84 8334.59 9721 -16.2 -11 1.5 2.05 1910.43 8145.82 8623.36 9897 -14.4 -9 1 1.81 1959.67 8895.71 9098.03 9828 -17.3 -10 1.6 1.58 1969.6 9676.31 9154.34 9924 -15.7 -13 1.5 1.57 2061.41 9884.59 9284.73 10371 -12.6 -11 1.8 1.76 2093.48 10637.44 9492.49 10846 -9.4 -5 1.8 1.76 2120.88 10717.13 9682.35 10413 -8.1 -15 1.6 1.89 2174.56 10205.29 9762.12 10709 -5.4 -6 1.9 1.9 2196.72 10295.98 10124.63 10662 -4.6 -6 1.7 1.9 2350.44 10892.76 10540.05 10570 -4.9 -3 1.6 1.92 2440.25 10631.92 10601.61 10297 -4 -1 1.3 1.76 2408.64 11441.08 10323.73 10635 -3.1 -3 1.1 1.64 2472.81 11950.95 10418.4 10872 -1.3 -4 1.9 1.57 2407.6 11037.54 10092.96 10296 0 -6 2.6 1.69 2454.62 11527.72 10364.91 10383 -0.4 0 2.3 1.76 2448.05 11383.89 10152.09 10431 3 -4 2.4 1.89 2497.84 10989.34 10032.8 10574 0.4 -2 2.2 1.78 2645.64 11079.42 10204.59 10653 1.2 -2 2 1.88 2756.76 11028.93 10001.6 10805 0.6 -6 2.9 1.86 2849.27 10973 10411.75 10872 -1.3 -7 2.6 1.88 2921.44 etc...

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 BEL_20[t] = + 392.801288384327 + 0.0390117340790035Nikkei[t] + 0.103211876652727DJ_Indust[t] -0.00376644874838964Goudprijs[t] -14.5419039745120Conjunct_Seizoenzuiver[t] + 2.61444593841881Cons_vertrouw[t] -9.80081512339516Alg_consumptie_index_BE[t] + 17.3973640331083Gem_rente_kasbon_1j[t] -57.0314960208367M1[t] -24.2910866948577M2[t] -68.8468361794204M3[t] -177.959481264132M4[t] -157.806908916677M5[t] -123.370114378759M6[t] -104.388896451179M7[t] -67.7757332668275M8[t] -73.258344759955M9[t] -80.9274531305978M10[t] -30.5574705031455M11[t] + 46.2909033428714t + 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) 392.801288384327 451.46816 0.8701 0.390959 0.195479 Nikkei 0.0390117340790035 0.025683 1.519 0.138907 0.069454 DJ_Indust 0.103211876652727 0.040347 2.5581 0.015631 0.007816 Goudprijs -0.00376644874838964 0.029935 -0.1258 0.900686 0.450343 Conjunct_Seizoenzuiver -14.5419039745120 3.735235 -3.8932 0.000491 0.000246 Cons_vertrouw 2.61444593841881 4.160018 0.6285 0.5343 0.26715 Alg_consumptie_index_BE -9.80081512339516 30.457203 -0.3218 0.749772 0.374886 Gem_rente_kasbon_1j 17.3973640331083 56.096561 0.3101 0.758536 0.379268 M1 -57.0314960208367 51.127239 -1.1155 0.273217 0.136608 M2 -24.2910866948577 49.266601 -0.4931 0.625449 0.312725 M3 -68.8468361794204 50.988367 -1.3502 0.186713 0.093357 M4 -177.959481264132 52.400296 -3.3962 0.00189 0.000945 M5 -157.806908916677 54.558946 -2.8924 0.006933 0.003466 M6 -123.370114378759 53.068577 -2.3247 0.026808 0.013404 M7 -104.388896451179 53.577203 -1.9484 0.060471 0.030236 M8 -67.7757332668275 56.453558 -1.2006 0.239017 0.119508 M9 -73.258344759955 53.008284 -1.382 0.176845 0.088422 M10 -80.9274531305978 53.817464 -1.5037 0.142769 0.071384 M11 -30.5574705031455 50.772152 -0.6019 0.551647 0.275824 t 46.2909033428714 3.413504 13.5611 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.99781758983681 R-squared 0.99563994258774 Adjusted R-squared 0.992967649335064 F-TEST (value) 372.57884836959 F-TEST (DF numerator) 19 F-TEST (DF denominator) 31 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 70.3151203550974 Sum Squared Residuals 153270.700667107 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1635.25 1673.49292701275 -38.2429270127463 2 1833.42 1820.91087552158 12.5091244784202 3 1910.43 1840.92816888193 69.5018311180717 4 1959.67 1886.28759564899 73.3824043510058 5 1969.6 1958.32963635339 11.2703636466069 6 2061.41 2019.4711363995 41.9388636005008 7 2093.48 2102.92006092129 -9.44006092128817 8 2120.88 2169.33253754454 -48.4525375445359 9 2174.56 2178.79200781225 -4.23200781224703 10 2196.72 2248.87077728972 -52.1507772897242 11 2350.44 2425.56981480826 -75.129814808255 12 2440.25 2491.92217616365 -51.6721761636549 13 2408.64 2464.35061615865 -55.7106161586485 14 2472.81 2534.30292101813 -61.4929210181315 15 2407.6 2440.07831424644 -32.47831424644 16 2454.62 2449.7816303697 4.83836963030146 17 2448.05 2429.84902576323 18.2009742367661 18 2497.84 2525.41819221783 -27.5781922178349 19 2645.64 2603.70408558155 41.9359144184471 20 2756.76 2652.21364834295 104.546351657051 21 2849.27 2761.22337647946 88.0466235205374 22 2921.44 2864.49720729208 56.9427927079155 23 2981.85 2940.37821053709 41.4717894629134 24 3080.58 3073.52065743784 7.05934256215633 25 3106.22 3075.02316385870 31.1968361413031 26 3119.31 3130.59273385449 -11.2827338544854 27 3061.26 3132.15080376903 -70.8908037690295 28 3097.31 3078.26377163835 19.0462283616461 29 3161.69 3170.05199828856 -8.36199828855813 30 3257.16 3263.88514642856 -6.72514642856179 31 3277.01 3287.84604739132 -10.8360473913194 32 3295.32 3357.13947360702 -61.8194736070175 33 3363.99 3458.07551070388 -94.0855107038814 34 3494.17 3555.73819354145 -61.5681935414468 35 3667.03 3680.32954003481 -13.2995400348056 36 3813.06 3745.12903704301 67.930962956988 37 3917.96 3745.11625910004 172.843740899956 38 3895.51 3840.5301065119 54.9798934880987 39 3801.06 3810.70877594373 -9.64877594372815 40 3570.12 3667.38700234295 -97.2670023429533 41 3701.61 3722.71933959481 -21.1093395948148 42 3862.27 3869.90552495410 -7.63552495410401 43 3970.1 3991.75980610584 -21.6598061058396 44 4138.52 4132.7943405055 5.72565949450227 45 4199.75 4189.47910500441 10.2708949955911 46 4290.89 4234.11382187674 56.7761781232554 47 4443.91 4396.95243461985 46.9575653801472 48 4502.64 4525.95812935549 -23.3181293554894 49 4356.98 4467.06703386986 -110.087033869865 50 4591.27 4585.9833630939 5.28663690609805 51 4696.96 4653.44393715887 43.516062841126 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 23 0.781207784446503 0.437584431106994 0.218792215553497 24 0.84607582312392 0.307848353752161 0.153924176876080 25 0.921450782707052 0.157098434585895 0.0785492172929477 26 0.969913392056217 0.0601732158875662 0.0300866079437831 27 0.985566722698223 0.0288665546035542 0.0144332773017771 28 0.95638680809909 0.08722638380182 0.04361319190091 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 1 0.166666666666667 NOK 10% type I error level 3 0.5 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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