Multiple lineair regression: zonder monthly dummy en zonder Lineaire 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: Fri, 19 Dec 2008 13:37:22 -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/19/t1229720857z9ntw17n0zr6cbf.htm/, Retrieved Fri, 19 Dec 2008 22:07:47 +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/19/t1229720857z9ntw17n0zr6cbf.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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2174.56 0 2196.72 0 2350.44 0 2440.25 0 2408.64 0 2472.81 0 2407.6 0 2454.62 0 2448.05 0 2497.84 0 2645.64 0 2756.76 0 2849.27 0 2921.44 0 2981.85 0 3080.58 0 3106.22 0 3119.31 0 3061.26 0 3097.31 0 3161.69 0 3257.16 0 3277.01 0 3295.32 0 3363.99 0 3494.17 0 3667.03 0 3813.06 0 3917.96 0 3895.51 0 3801.06 0 3570.12 0 3701.61 0 3862.27 0 3970.1 0 4138.52 0 4199.75 0 4290.89 0 4443.91 0 4502.64 0 4356.98 0 4591.27 0 4696.96 0 4621.4 0 4562.84 0 4202.52 0 4296.49 0 4435.23 0 4105.18 0 4116.68 0 3844.49 0 3720.98 0 3674.4 0 3857.62 0 3801.06 0 3504.37 1 3032.6 1 3047.03 1 2962.34 1 2197.82 1 2014.45 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Bel_20[t] = + 3490.528 -697.426333333333dummy[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) 3490.528 97.509357 35.7969 0 0 dummy -697.426333333333 310.910641 -2.2432 0.028654 0.014327 Multiple Linear Regression - Regression Statistics Multiple R 0.280326926902796 R-squared 0.0785831859467657 Adjusted R-squared 0.0629659518102702 F-TEST (value) 5.031824794323 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.0286544189394422 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 723.148747651468 Sum Squared Residuals 30853702.5625633 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2174.56 3490.52799999999 -1315.96800000000 2 2196.72 3490.528 -1293.808 3 2350.44 3490.528 -1140.088 4 2440.25 3490.528 -1050.278 5 2408.64 3490.528 -1081.888 6 2472.81 3490.528 -1017.718 7 2407.6 3490.528 -1082.928 8 2454.62 3490.528 -1035.908 9 2448.05 3490.528 -1042.478 10 2497.84 3490.528 -992.688 11 2645.64 3490.528 -844.888 12 2756.76 3490.528 -733.768 13 2849.27 3490.528 -641.258 14 2921.44 3490.528 -569.088 15 2981.85 3490.528 -508.678 16 3080.58 3490.528 -409.948 17 3106.22 3490.528 -384.308 18 3119.31 3490.528 -371.218 19 3061.26 3490.528 -429.268 20 3097.31 3490.528 -393.218 21 3161.69 3490.528 -328.838 22 3257.16 3490.528 -233.368 23 3277.01 3490.528 -213.518 24 3295.32 3490.528 -195.208 25 3363.99 3490.528 -126.538000000000 26 3494.17 3490.528 3.64200000000000 27 3667.03 3490.528 176.502 28 3813.06 3490.528 322.532 29 3917.96 3490.528 427.432 30 3895.51 3490.528 404.982 31 3801.06 3490.528 310.532 32 3570.12 3490.528 79.5919999999998 33 3701.61 3490.528 211.082 34 3862.27 3490.528 371.742 35 3970.1 3490.528 479.572 36 4138.52 3490.528 647.992 37 4199.75 3490.528 709.222 38 4290.89 3490.528 800.362 39 4443.91 3490.528 953.382 40 4502.64 3490.528 1012.112 41 4356.98 3490.528 866.452 42 4591.27 3490.528 1100.742 43 4696.96 3490.528 1206.432 44 4621.4 3490.528 1130.872 45 4562.84 3490.528 1072.312 46 4202.52 3490.528 711.992 47 4296.49 3490.528 805.962 48 4435.23 3490.528 944.702 49 4105.18 3490.528 614.652 50 4116.68 3490.528 626.152 51 3844.49 3490.528 353.962 52 3720.98 3490.528 230.452 53 3674.4 3490.528 183.872 54 3857.62 3490.528 367.092 55 3801.06 3490.528 310.532 56 3504.37 2793.10166666667 711.268333333333 57 3032.6 2793.10166666667 239.498333333333 58 3047.03 2793.10166666667 253.928333333334 59 2962.34 2793.10166666667 169.238333333334 60 2197.82 2793.10166666667 -595.281666666666 61 2014.45 2793.10166666667 -778.651666666666 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0132923574561359 0.0265847149122718 0.986707642543864 6 0.00459593741373135 0.0091918748274627 0.995404062586269 7 0.00113030277296722 0.00226060554593443 0.998869697227033 8 0.000342752823620339 0.000685505647240678 0.99965724717638 9 0.000103353983141420 0.000206707966282841 0.999896646016859 10 4.40662603938418e-05 8.81325207876836e-05 0.999955933739606 11 7.46402386683225e-05 0.000149280477336645 0.999925359761332 12 0.000231012113265665 0.00046202422653133 0.999768987886734 13 0.00076535704445796 0.00153071408891592 0.999234642955542 14 0.00219840101397261 0.00439680202794522 0.997801598986027 15 0.00542254217201906 0.0108450843440381 0.99457745782798 16 0.0137838955673560 0.0275677911347120 0.986216104432644 17 0.0271858986226457 0.0543717972452914 0.972814101377354 18 0.0455144706196353 0.0910289412392707 0.954485529380365 19 0.0640235909884882 0.128047181976976 0.935976409011512 20 0.0921182438380329 0.184236487676066 0.907881756161967 21 0.136764657546682 0.273529315093365 0.863235342453318 22 0.207012865909423 0.414025731818846 0.792987134090577 23 0.294557090352204 0.589114180704408 0.705442909647796 24 0.398976098636546 0.797952197273093 0.601023901363454 25 0.519407498224375 0.96118500355125 0.480592501775625 26 0.645494184458852 0.709011631082296 0.354505815541148 27 0.762203930008549 0.475592139982903 0.237796069991451 28 0.850932832967588 0.298134334064825 0.149067167032412 29 0.907287524829812 0.185424950340377 0.0927124751701883 30 0.934293515038812 0.131412969922376 0.0657064849611878 31 0.947049569572132 0.105900860855735 0.0529504304278676 32 0.959669801179562 0.0806603976408751 0.0403301988204376 33 0.96757439531105 0.0648512093779014 0.0324256046889507 34 0.972175630440333 0.0556487391193341 0.0278243695596671 35 0.974997632129917 0.0500047357401666 0.0250023678700833 36 0.977560233866196 0.0448795322676079 0.0224397661338039 37 0.978860785103083 0.0422784297938342 0.0211392148969171 38 0.979971545548131 0.0400569089037369 0.0200284544518684 39 0.982993757714626 0.0340124845707473 0.0170062422853737 40 0.985607870644937 0.0287842587101258 0.0143921293550629 41 0.98362432460191 0.0327513507961785 0.0163756753980892 42 0.98661799034246 0.0267640193150779 0.0133820096575389 43 0.9914400278777 0.0171199442445985 0.00855997212229925 44 0.993612540656892 0.0127749186862154 0.00638745934310771 45 0.994805204516841 0.0103895909663170 0.00519479548315852 46 0.99149146384607 0.0170170723078611 0.00850853615393053 47 0.988121299078322 0.0237574018433559 0.0118787009216780 48 0.988573223785129 0.0228535524297430 0.0114267762148715 49 0.980695262707068 0.0386094745858648 0.0193047372929324 50 0.969716809680826 0.0605663806383481 0.0302831903191740 51 0.94270395972841 0.114592080543178 0.057296040271589 52 0.89584061773215 0.2083187645357 0.10415938226785 53 0.82411283141041 0.351774337179178 0.175887168589589 54 0.717203877638674 0.565592244722653 0.282796122361327 55 0.573633053853515 0.85273389229297 0.426366946146485 56 0.603965383777711 0.792069232444578 0.396034616222289 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 9 0.173076923076923 NOK 5% type I error level 26 0.5 NOK 10% type I error level 33 0.634615384615385 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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