Multiple Lineair Regression 3 Bouwproductie

*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, 11 Dec 2008 15:37:16 -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/12/t1229037660sa84l9jk4xs9koe.htm/, Retrieved Thu, 11 Dec 2008 23:21:11 +0000

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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/2008/Dec/12/t1229037660sa84l9jk4xs9koe.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}, }

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Dataseries X:

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82.7 0 88.9 0 105.9 0 100.8 0 94 0 105 0 58.5 0 87.6 0 113.1 0 112.5 0 89.6 0 74.5 0 82.7 0 90.1 0 109.4 0 96 0 89.2 0 109.1 0 49.1 0 92.9 0 107.7 0 103.5 0 91.1 0 79.8 0 71.9 0 82.9 0 90.1 0 100.7 0 90.7 0 108.8 0 44.1 0 93.6 0 107.4 0 96.5 0 93.6 0 76.5 0 76.7 1 84 1 103.3 1 88.5 1 99 1 105.9 1 44.7 1 94 1 107.1 1 104.8 1 102.5 1 77.7 1 85.2 1 91.3 1 106.5 1 92.4 1 97.5 1 107 1 51.1 1 98.6 1 102.2 1 114.3 1 99.4 1 72.5 1 92.3 1 99.4 1 85.9 1 109.4 1 97.6 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Bouwproductie[t] = + 76.3577450980393 + 2.97696078431372d[t] + 5.23167483660141M1[t] + 12.7858006535948M2[t] + 23.5732598039216M3[t] + 21.3940522875817M4[t] + 18.1315114379085M5[t] + 30.7352450980393M6[t] -26.887295751634M7[t] + 16.9901633986928M8[t] + 31.1876225490196M9[t] + 30.0450816993464M10[t] + 19.0025408496732M11[t] -0.0374591503267978t + 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) 76.3577450980393 3.299238 23.1441 0 0 d 2.97696078431372 3.033524 0.9814 0.331051 0.165525 M1 5.23167483660141 3.684582 1.4199 0.161726 0.080863 M2 12.7858006535948 3.67093 3.483 0.001027 0.000513 M3 23.5732598039216 3.65899 6.4426 0 0 M4 21.3940522875817 3.648779 5.8633 0 0 M5 18.1315114379085 3.640313 4.9808 8e-06 4e-06 M6 30.7352450980393 3.812506 8.0617 0 0 M7 -26.887295751634 3.803188 -7.0697 0 0 M8 16.9901633986928 3.795547 4.4763 4.3e-05 2.1e-05 M9 31.1876225490196 3.789593 8.2298 0 0 M10 30.0450816993464 3.785335 7.9372 0 0 M11 19.0025408496732 3.782778 5.0234 7e-06 3e-06 t -0.0374591503267978 0.08032 -0.4664 0.642935 0.321467 Multiple Linear Regression - Regression Statistics Multiple R 0.944502770685145 R-squared 0.892085483831915 Adjusted R-squared 0.86457786206358 F-TEST (value) 32.4304838617061 F-TEST (DF numerator) 13 F-TEST (DF denominator) 51 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.9797483742205 Sum Squared Residuals 1823.62692156863 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 82.7 81.5519607843134 1.14803921568658 2 88.9 89.0686274509804 -0.168627450980381 3 105.9 99.8186274509804 6.08137254901956 4 100.8 97.6019607843138 3.19803921568617 5 94 94.3019607843138 -0.301960784313789 6 105 106.868235294118 -1.86823529411759 7 58.5 49.2082352941177 9.29176470588231 8 87.6 93.0482352941177 -5.44823529411769 9 113.1 107.208235294118 5.89176470588242 10 112.5 106.028235294118 6.47176470588232 11 89.6 94.9482352941176 -5.34823529411765 12 74.5 75.9082352941177 -1.40823529411767 13 82.7 81.1024509803922 1.59754901960777 14 90.1 88.6191176470588 1.48088235294116 15 109.4 99.3691176470588 10.0308823529412 16 96 97.1524509803921 -1.15245098039215 17 89.2 93.8524509803922 -4.65245098039215 18 109.1 106.418725490196 2.6812745098039 19 49.1 48.7587254901961 0.341274509803928 20 92.9 92.598725490196 0.301274509803939 21 107.7 106.758725490196 0.941274509803898 22 103.5 105.578725490196 -2.07872549019607 23 91.1 94.498725490196 -3.39872549019608 24 79.8 75.458725490196 4.34127450980394 25 71.9 80.6529411764706 -8.75294117647065 26 82.9 88.1696078431373 -5.26960784313725 27 90.1 98.9196078431372 -8.81960784313725 28 100.7 96.7029411764706 3.99705882352943 29 90.7 93.4029411764706 -2.70294117647058 30 108.8 105.969215686275 2.83078431372548 31 44.1 48.3092156862745 -4.2092156862745 32 93.6 92.1492156862745 1.45078431372550 33 107.4 106.309215686275 1.09078431372548 34 96.5 105.129215686274 -8.6292156862745 35 93.6 94.0492156862745 -0.449215686274509 36 76.5 75.0092156862745 1.49078431372552 37 76.7 83.1803921568628 -6.4803921568628 38 84 90.6970588235294 -6.69705882352942 39 103.3 101.447058823529 1.85294117647059 40 88.5 99.2303921568627 -10.7303921568627 41 99 95.9303921568627 3.06960784313726 42 105.9 108.496666666667 -2.59666666666668 43 44.7 50.8366666666667 -6.13666666666666 44 94 94.6766666666667 -0.676666666666657 45 107.1 108.836666666667 -1.73666666666669 46 104.8 107.656666666667 -2.85666666666666 47 102.5 96.5766666666667 5.92333333333333 48 77.7 77.5366666666667 0.163333333333346 49 85.2 82.7308823529412 2.46911764705877 50 91.3 90.2475490196078 1.05245098039215 51 106.5 100.997549019608 5.50245098039217 52 92.4 98.7808823529412 -6.38088235294115 53 97.5 95.4808823529412 2.01911764705884 54 107 108.047156862745 -1.04715686274511 55 51.1 50.3871568627451 0.712843137254909 56 98.6 94.2271568627451 4.37284313725491 57 102.2 108.387156862745 -6.18715686274511 58 114.3 107.207156862745 7.0928431372549 59 99.4 96.1271568627451 3.27284313725491 60 72.5 77.087156862745 -4.58715686274508 61 92.3 82.2813725490197 10.0186274509803 62 99.4 89.7980392156863 9.60196078431374 63 85.9 100.548039215686 -14.6480392156863 64 109.4 98.3313725490196 11.0686274509804 65 97.6 95.0313725490196 2.56862745098041 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.149906699694105 0.299813399388210 0.850093300305895 18 0.107365624702375 0.214731249404751 0.892634375297625 19 0.175185575888596 0.350371151777192 0.824814424111404 20 0.153515105634586 0.307030211269173 0.846484894365414 21 0.115706815967983 0.231413631935967 0.884293184032017 22 0.118609309978142 0.237218619956283 0.881390690021858 23 0.0767023805013685 0.153404761002737 0.923297619498632 24 0.0818551898937539 0.163710379787508 0.918144810106246 25 0.119463753498987 0.238927506997975 0.880536246501013 26 0.0842105018660957 0.168421003732191 0.915789498133904 27 0.194828948420027 0.389657896840055 0.805171051579973 28 0.217174449487669 0.434348898975337 0.782825550512331 29 0.16698522492741 0.33397044985482 0.83301477507259 30 0.149217468718310 0.298434937436619 0.85078253128169 31 0.119899712126812 0.239799424253625 0.880100287873188 32 0.107420546751904 0.214841093503808 0.892579453248096 33 0.0844681201758073 0.168936240351615 0.915531879824193 34 0.0929459634471926 0.185891926894385 0.907054036552807 35 0.0893970625864506 0.178794125172901 0.91060293741355 36 0.0594033115157745 0.118806623031549 0.940596688484225 37 0.0483115846041904 0.0966231692083808 0.95168841539581 38 0.0409411767806307 0.0818823535612614 0.95905882321937 39 0.0423280957837121 0.0846561915674243 0.957671904216288 40 0.0607486482841821 0.121497296568364 0.939251351715818 41 0.0656546322687352 0.131309264537470 0.934345367731265 42 0.0385313502723885 0.077062700544777 0.961468649727611 43 0.0256899019030017 0.0513798038060034 0.974310098096998 44 0.0156066739855302 0.0312133479710604 0.98439332601447 45 0.00912860041764336 0.0182572008352867 0.990871399582357 46 0.00625397466285416 0.0125079493257083 0.993746025337146 47 0.00587436719794457 0.0117487343958891 0.994125632802055 48 0.00285913663446607 0.00571827326893215 0.997140863365534 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.03125 NOK 5% type I error level 5 0.15625 NOK 10% type I error level 10 0.3125 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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