Multiple Regression Bouwaanvragen

*Unverified author*

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 13:13:56 -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/t1229458492hm23d7lqyq2qdqc.htm/, Retrieved Tue, 16 Dec 2008 21:15:01 +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/t1229458492hm23d7lqyq2qdqc.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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28.24 1969.6 111.5 3796 29.58 2061.41 112 3711 26.95 2093.48 111.9 3949 29.08 2120.88 111.8 3740 28.76 2174.56 112.2 3243 29.59 2196.72 112.5 4407 30.7 2350.44 114.3 4814 30.52 2440.25 116.9 3908 32.67 2408.64 124.5 5250 33.19 2472.81 130.3 3937 37.13 2407.6 133.4 4004 35.54 2454.62 134.4 5560 37.75 2448.05 134.5 3922 41.84 2497.84 136.3 3759 42.94 2645.64 138 4138 49.14 2756.76 138.8 4634 44.61 2849.27 138.3 3996 40.22 2921.44 138.3 4308 44.23 2981.85 141.2 4142 45.85 3080.58 142.4 4429 53.38 3106.22 141.5 5219 53.26 3119.31 140.9 4929 51.8 3061.26 140.5 5754 55.3 3097.31 140 5592 57.81 3161.69 139.3 4163 63.96 3257.16 138.7 4962 63.77 3277.01 139.1 5208 59.15 3295.32 138.4 4755 56.12 3363.99 138.4 4491 57.42 3494.17 138.5 5732 63.52 3667.03 140.4 5730 61.71 3813.06 140.7 5024 63.01 3917.96 142.2 6056 68.18 3895.51 144.2 4901 72.03 3801.06 145.6 5353 69.75 3570.12 147.5 5578 74.41 3701.61 149.7 4618 74.33 3862.27 151.5 4724 64.24 3970.1 153.8 5011 60.03 4138.52 153.9 5298 59.44 4199.75 154.3 4143 62.5 4290.89 154.9 4617 55.04 4443.91 156.3 4736 58.34 4502.64 156.2 4214 61.92 4356.98 157.7 5112 67.65 4591.27 158.6 4197 67.68 4696.96 159.8 4119 70.3 4621.4 160.2 5104 75.26 4562.84 159.9 4194 71.44 4202.52 160.1 4583 76.36 4296.49 159.2 3790 81.71 4435.23 160.7 5557 92.6 4105.18 158.7 4304 90.6 4116.68 158.6 3838 92.23 3844.49 159 4277 94.09 3720.98 159.7 4951 102.79 3674.4 164.1 4479 109.65 3857.62 165.9 4677 124.05 3801.06 170.4 4274 132.69 3504.37 174.5 4782

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 olie[t] = + 47.950868525666 -0.0223120146777083Bel20[t] + 0.0211610369424831Metaal[t] + 0.00437910398233475bouwaanvragen[t] + 4.14482496021094M1[t] + 2.82658129900088M2[t] + 0.823853361633086M3[t] + 0.114628069556997M4[t] + 1.60986689727842M5[t] -1.65009307396808M6[t] -2.19996647120571M7[t] -1.12002279828299M8[t] -2.17769483427941M9[t] + 4.47415130022531M10[t] + 4.98715599900658M11[t] + 2.08941443458687t + 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) 47.950868525666 22.295389 2.1507 0.037032 0.018516 Bel20 -0.0223120146777083 0.002459 -9.0754 0 0 Metaal 0.0211610369424831 0.173327 0.1221 0.903386 0.451693 bouwaanvragen 0.00437910398233475 0.001639 2.671 0.01056 0.00528 M1 4.14482496021094 4.411505 0.9395 0.352578 0.176289 M2 2.82658129900088 4.249083 0.6652 0.509381 0.25469 M3 0.823853361633086 4.230304 0.1948 0.846485 0.423242 M4 0.114628069556997 4.082093 0.0281 0.977725 0.488862 M5 1.60986689727842 4.565653 0.3526 0.726069 0.363034 M6 -1.65009307396808 4.24273 -0.3889 0.699209 0.349605 M7 -2.19996647120571 4.135717 -0.5319 0.597441 0.298721 M8 -1.12002279828299 4.264154 -0.2627 0.794039 0.397019 M9 -2.17769483427941 3.903831 -0.5578 0.579784 0.289892 M10 4.47415130022531 4.157883 1.0761 0.287763 0.143882 M11 4.98715599900658 4.014784 1.2422 0.220744 0.110372 t 2.08941443458687 0.169723 12.3107 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.975007393121551 R-squared 0.950639416641684 Adjusted R-squared 0.933811945042258 F-TEST (value) 56.493300911238 F-TEST (DF numerator) 15 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.06149239613482 Sum Squared Residuals 1616.63436300961 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 28.24 29.2218981472794 -0.981898147279352 2 29.58 27.5829595330682 1.99704046693175 3 26.95 27.9942103636747 -1.04421036367473 4 29.08 27.8457014680141 1.23429853198591 5 28.76 28.0646955179796 0.69530448202037 6 29.59 31.5033410825824 -1.91334108258238 7 30.7 31.433464410981 -0.733464410981009 8 30.52 28.6865309683408 1.83346903165922 9 32.67 36.4611375759497 -3.7911375759497 10 33.19 38.1436066486336 -4.9536066486336 11 37.13 42.5599914404732 -5.42999144047323 12 35.54 45.448185779363 -9.90818577936302 13 37.75 44.6581588912233 -6.9081588912233 14 41.84 43.6427103711729 -1.80271037117291 15 42.94 42.1273352711338 0.812664728866192 16 49.14 43.2171777474496 5.92282225255036 17 44.61 41.9332976727223 2.67670232727766 18 40.22 40.5187744792609 -0.298774479260949 19 44.23 40.0448824559954 4.18511754400454 20 45.85 42.2935714416359 3.55642855836405 21 53.38 46.1936809966862 7.18631900331381 22 53.26 53.360240516604 -0.100240516603996 23 51.8 60.8621684726623 -9.06216847266227 24 55.3 56.4400834155017 -1.14008341550171 25 57.81 54.9653229887326 2.84467701126744 26 63.96 57.0925731805485 6.86742681945147 27 63.77 57.8220901808464 5.94790981915357 28 59.15 56.795199504751 2.35480049524899 29 56.12 57.6916032678047 -1.57160326780471 30 57.42 59.0530638061727 -1.63306380617267 31 63.52 56.7671977485593 6.75280225144071 32 61.71 53.5930332522376 8.11696674776244 33 63.01 56.8352221763196 6.1747778236804 34 68.18 61.061844449214 7.11815555078595 35 72.03 67.7806138206265 4.24938617937348 36 69.75 71.0611132920928 -1.31111329209281 37 74.41 70.2041603351508 4.20583966484915 38 74.33 67.892957719031 6.437042280969 39 64.24 66.8792129014506 -2.63921290145057 40 60.03 65.760531478566 -5.73053147856603 41 59.44 62.9296193973386 -3.48961939733861 42 62.5 61.8139487527448 0.686051247255202 43 55.04 60.4900441297284 -5.45004412972844 44 58.34 60.0610092327432 -1.72100923274321 45 61.92 68.306896620839 -6.386896620839 46 67.65 67.8328400605022 -0.18284006050222 47 67.68 67.7609254962922 -0.080925496292241 48 70.3 70.8709615982969 -0.570961598296917 49 75.26 74.420459637614 0.839540362386068 50 71.44 84.9387991961793 -13.4987991961793 51 76.36 79.4371512828945 -3.07715128289446 52 81.71 85.4913898012192 -3.78138980121923 53 92.6 90.9107841441547 1.68921585584528 54 90.6 87.4408718792392 3.1591281207608 55 92.23 96.9844112547358 -4.75441125473581 56 94.09 105.875855105043 -11.7858551050425 57 102.79 105.973062630206 -3.18306263020552 58 109.65 111.531468325046 -1.88146832504615 59 124.05 113.726300769946 10.3236992300543 60 132.69 119.759655914746 12.9303440852545 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.000315936783726073 0.000631873567452147 0.999684063216274 20 6.16936279098246e-05 0.000123387255819649 0.99993830637209 21 0.0178747308626385 0.0357494617252769 0.982125269137362 22 0.00677940006455064 0.0135588001291013 0.99322059993545 23 0.0152926719389966 0.0305853438779931 0.984707328061003 24 0.00992771464303833 0.0198554292860767 0.990072285356962 25 0.00482373917361315 0.0096474783472263 0.995176260826387 26 0.00197891353064059 0.00395782706128119 0.99802108646936 27 0.000914368960480653 0.00182873792096131 0.99908563103952 28 0.000898823554855657 0.00179764710971131 0.999101176445144 29 0.000927039335344729 0.00185407867068946 0.999072960664655 30 0.00071660552070714 0.00143321104141428 0.999283394479293 31 0.000370749967719804 0.000741499935439608 0.99962925003228 32 0.000526692692774887 0.00105338538554977 0.999473307307225 33 0.00493556940956785 0.0098711388191357 0.995064430590432 34 0.0050542730594027 0.0101085461188054 0.994945726940597 35 0.00420497031338899 0.00840994062677797 0.995795029686611 36 0.00246418854858100 0.00492837709716201 0.99753581145142 37 0.00114863532778098 0.00229727065556195 0.99885136467222 38 0.196593487794717 0.393186975589435 0.803406512205283 39 0.651441538882692 0.697116922234616 0.348558461117308 40 0.858412313955236 0.283175372089529 0.141587686044764 41 0.845132446198487 0.309735107603026 0.154867553801513 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 14 0.608695652173913 NOK 5% type I error level 19 0.826086956521739 NOK 10% type I error level 19 0.826086956521739 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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