Multiple Regression werkloosh ecogr 2 vertragingen

*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: Thu, 17 Dec 2009 12:37:52 -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/t1261078856k5nmt9kutld2nc6.htm/, Retrieved Thu, 17 Dec 2009 20:41:07 +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/17/t1261078856k5nmt9kutld2nc6.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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8.7 110.3 9.3 9.3 8.2 103.9 8.7 9.3 8.3 101.6 8.2 8.7 8.5 94.6 8.3 8.2 8.6 95.9 8.5 8.3 8.5 104.7 8.6 8.5 8.2 102.8 8.5 8.6 8.1 98.1 8.2 8.5 7.9 113.9 8.1 8.2 8.6 80.9 7.9 8.1 8.7 95.7 8.6 7.9 8.7 113.2 8.7 8.6 8.5 105.9 8.7 8.7 8.4 108.8 8.5 8.7 8.5 102.3 8.4 8.5 8.7 99 8.5 8.4 8.7 100.7 8.7 8.5 8.6 115.5 8.7 8.7 8.5 100.7 8.6 8.7 8.3 109.9 8.5 8.6 8 114.6 8.3 8.5 8.2 85.4 8 8.3 8.1 100.5 8.2 8 8.1 114.8 8.1 8.2 8 116.5 8.1 8.1 7.9 112.9 8 8.1 7.9 102 7.9 8 8 106 7.9 7.9 8 105.3 8 7.9 7.9 118.8 8 8 8 106.1 7.9 8 7.7 109.3 8 7.9 7.2 117.2 7.7 8 7.5 92.5 7.2 7.7 7.3 104.2 7.5 7.2 7 112.5 7.3 7.5 7 122.4 7 7.3 7 113.3 7 7 7.2 100 7 7 7.3 110.7 7.2 7 7.1 112.8 7.3 7.2 6.8 109.8 7.1 7.3 6.4 117.3 6.8 7.1 6.1 109.1 6.4 6.8 6.5 115.9 6.1 6.4 7.7 96 6.5 6.1 7.9 99.8 7.7 6.5 7.5 116.8 7.9 7.7 6.9 115.7 7.5 7.9 6.6 99.4 6.9 7.5 6.9 94.3 6.6 6.9 7.7 91 6.9 6.6 8 93.2 7.7 6.9 8 103.1 8 7.7 7.7 94.1 8 8 7.3 91.8 7.7 8 7.4 102.7 7.3 7.7 8.1 82.6 7.4 7.3

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 Y[t] = + 5.05136942371016 -0.0187338824930496X[t] + 1.05792207436861Y1[t] -0.418657763778208Y2[t] -0.0092399573649387t + 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) 5.05136942371016 0.695912 7.2586 0 0 X -0.0187338824930496 0.003139 -5.9687 0 0 Y1 1.05792207436861 0.099071 10.6784 0 0 Y2 -0.418657763778208 0.098669 -4.2431 8.9e-05 4.4e-05 t -0.0092399573649387 0.002802 -3.2979 0.001744 0.000872 Multiple Linear Regression - Regression Statistics Multiple R 0.947184344706652 R-squared 0.89715818285737 Adjusted R-squared 0.889396536280568 F-TEST (value) 115.588641402298 F-TEST (DF numerator) 4 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.221574875791143 Sum Squared Residuals 2.60205755583859 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 8.92094031585258 -0.220940315852585 2 8.2 8.39684396182199 -0.196843961821989 3 8.3 8.15292555527368 0.147074444726316 4 8.5 8.58994386468606 -0.0899438646860576 5 8.6 8.72606849857605 -0.126068498576054 6 8.5 8.5740310299535 -0.0740310299534974 7 8.2 8.45272746551067 -0.252727465510673 8 8.1 8.2560259099303 -0.156025909930305 9 7.9 7.97059573087178 -0.0705957308717822 10 8.6 8.40985525728158 0.190144742718417 11 8.7 8.94763084383318 -0.247630843833176 12 8.7 8.42327971563198 0.276720284368016 13 8.5 8.50893132408849 -0.00893132408848618 14 8.4 8.23377869261998 0.166221307380018 15 8.5 8.32424831677865 0.175751683221353 16 8.7 8.52448815545545 0.175511844544545 17 8.7 8.65311923634823 0.0468807636517683 18 8.6 8.28288626533052 0.317113734669484 19 8.5 8.44511556142585 0.0548844385741481 20 8.3 8.19959745406582 0.100402545934184 21 8 7.93258961048764 0.067410389512356 22 8.2 8.23673395236481 -0.0367339523648140 23 8.1 8.28179411336201 -0.181794113362009 24 8.1 7.81513587615396 0.284864123846042 25 8 7.81591409492866 0.184085905071345 26 7.9 7.76832390710184 0.131676092898166 27 7.9 7.8993568378521 0.00064316214790279 28 8 7.85704712689278 0.142952873107219 29 8 7.96671309470984 0.0332869052901626 30 7.9 7.66269994731091 0.237300052689093 31 8 7.78558809017084 0.214411909829161 32 7.7 7.86405769264282 -0.164057692642823 33 7.2 7.34757766489439 -0.147577664894388 34 7.5 7.39770089705693 0.102299102943066 35 7.3 7.695980018723 -0.395980018723001 36 7 7.19406709265857 -0.194067092658566 37 7 6.7657166290575 0.234283370942506 38 7 7.05255233151277 -0.0525523315127703 39 7.2 7.29247301130539 -0.092473011305392 40 7.3 7.29436492613854 0.00563507386145595 41 7.1 7.26784447021942 -0.167844470219420 42 6.8 7.06135596908209 -0.261355969082088 43 6.4 6.67796682346434 -0.277966823464335 44 6.1 6.52477320192842 -0.424773201928424 45 6.5 6.23822932681145 0.261770673188553 46 7.7 7.1505597899391 0.549440210060898 47 7.9 8.17217446283162 -0.272174462831622 48 7.5 7.55365360142471 -0.0536536014247121 49 6.9 7.05812053229904 -0.158120532299042 50 6.6 6.88695272046093 -0.286952720460932 51 6.9 6.90707359976689 -0.00707359976688766 52 7.7 7.40262940607306 0.297370593926941 53 8 8.07291523758484 -0.072915237584835 54 8 7.86066025482672 0.139339745173279 55 7.7 7.89442791076577 -0.194427910765767 56 7.3 7.61089926082426 -0.310899260824260 57 7.4 7.0998884836711 0.300111516328902 58 8.1 7.7404548773646 0.359545122635397 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0359755850833632 0.0719511701667265 0.964024414916637 9 0.0413270171542474 0.0826540343084948 0.958672982845753 10 0.106252714052201 0.212505428104402 0.893747285947799 11 0.0587287618538226 0.117457523707645 0.941271238146177 12 0.309462314920359 0.618924629840718 0.690537685079641 13 0.220460736940989 0.440921473881978 0.779539263059011 14 0.146908895731286 0.293817791462572 0.853091104268714 15 0.0928965208354048 0.185793041670810 0.907103479164595 16 0.0570079068545938 0.114015813709188 0.942992093145406 17 0.034860604700073 0.069721209400146 0.965139395299927 18 0.0276666931837042 0.0553333863674083 0.972333306816296 19 0.0233409947484227 0.0466819894968453 0.976659005251577 20 0.0175714714675325 0.0351429429350650 0.982428528532467 21 0.0167225340157463 0.0334450680314926 0.983277465984254 22 0.0187271213245380 0.0374542426490761 0.981272878675462 23 0.0343601608992298 0.0687203217984595 0.96563983910077 24 0.0267879313871812 0.0535758627743624 0.973212068612819 25 0.0183825112953664 0.0367650225907329 0.981617488704634 26 0.0127269753966484 0.0254539507932968 0.987273024603352 27 0.00967715832015302 0.0193543166403060 0.990322841679847 28 0.00602741465280708 0.0120548293056142 0.993972585347193 29 0.0038593490837472 0.0077186981674944 0.996140650916253 30 0.00422618650491524 0.00845237300983047 0.995773813495085 31 0.0052743032853768 0.0105486065707536 0.994725696714623 32 0.009822588015903 0.019645176031806 0.990177411984097 33 0.0190841973438305 0.038168394687661 0.98091580265617 34 0.0254988483396822 0.0509976966793644 0.974501151660318 35 0.0458535090233887 0.0917070180467775 0.954146490976611 36 0.0410679967547569 0.0821359935095138 0.958932003245243 37 0.0930832311451965 0.186166462290393 0.906916768854804 38 0.0745825797021078 0.149165159404216 0.925417420297892 39 0.0689181307624017 0.137836261524803 0.931081869237598 40 0.0910304452813795 0.182060890562759 0.90896955471862 41 0.109148256005978 0.218296512011957 0.890851743994022 42 0.190288939024930 0.380577878049861 0.80971106097507 43 0.160804444908831 0.321608889817662 0.839195555091169 44 0.241426492442936 0.482852984885872 0.758573507557064 45 0.294824928612561 0.589649857225122 0.705175071387439 46 0.825666411447065 0.34866717710587 0.174333588552935 47 0.800972926268687 0.398054147462626 0.199027073731313 48 0.739952489672282 0.520095020655437 0.260047510327719 49 0.655390745227448 0.689218509545104 0.344609254772552 50 0.498680872511527 0.997361745023055 0.501319127488473 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0465116279069767 NOK 5% type I error level 13 0.302325581395349 NOK 10% type I error level 22 0.511627906976744 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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