multiple regression, opnemen van 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, 19 Nov 2009 11:21:09 -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/Nov/19/t12586549439e20588ba3ovee3.htm/, Retrieved Thu, 19 Nov 2009 19:22:36 +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/Nov/19/t12586549439e20588ba3ovee3.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

y = aantal bouwvergunningen x= rente

Dataseries X:

» Textbox « » Textfile « » CSV «

2360 2 2267 1746 2069 2299 2214 2 2360 2267 1746 2069 2825 2 2214 2360 2267 1746 2355 2 2825 2214 2360 2267 2333 2 2355 2825 2214 2360 3016 2 2333 2355 2825 2214 2155 2 3016 2333 2355 2825 2172 2 2155 3016 2333 2355 2150 2 2172 2155 3016 2333 2533 2 2150 2172 2155 3016 2058 2 2533 2150 2172 2155 2160 2 2058 2533 2150 2172 2260 2 2160 2058 2533 2150 2498 2 2260 2160 2058 2533 2695 2 2498 2260 2160 2058 2799 2 2695 2498 2260 2160 2947 2 2799 2695 2498 2260 2930 2 2947 2799 2695 2498 2318 2 2930 2947 2799 2695 2540 2 2318 2930 2947 2799 2570 2 2540 2318 2930 2947 2669 2 2570 2540 2318 2930 2450 2 2669 2570 2540 2318 2842 2 2450 2669 2570 2540 3440 2 2842 2450 2669 2570 2678 2 3440 2842 2450 2669 2981 2 2678 3440 2842 2450 2260 2,21 2981 2678 3440 2842 2844 2,25 2260 2981 2678 3440 2546 2,25 2844 2260 2981 2678 2456 2,45 2546 2844 2260 2981 2295 2,5 2456 2546 2844 2260 2379 2,5 2295 2456 2546 2844 2479 2,64 2379 2295 2456 2546 2057 2,75 2479 2379 2295 2456 2280 2,93 2057 2479 23 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2543.65104195461 -332.852461340271X[t] -0.00897260626492228Y1[t] + 0.189452813460899Y2[t] + 0.0589636885733872Y3[t] -0.103950946153406Y4[t] + 254.931163373105M1[t] + 180.446464753134M2[t] + 295.839564571899M3[t] + 207.577948072379M4[t] + 175.647916374566M5[t] + 448.898639026695M6[t] + 55.4442951055209M7[t] -82.8238967667418M8[t] -2.92881928519086M9[t] + 260.561703653976M10[t] -149.418332236016M11[t] + 11.1347397110506t + 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) 2543.65104195461 1051.899372 2.4182 0.019909 0.009954 X -332.852461340271 191.479044 -1.7383 0.089311 0.044655 Y1 -0.00897260626492228 0.165852 -0.0541 0.957106 0.478553 Y2 0.189452813460899 0.167123 1.1336 0.263238 0.131619 Y3 0.0589636885733872 0.166855 0.3534 0.725528 0.362764 Y4 -0.103950946153406 0.164072 -0.6336 0.529718 0.264859 M1 254.931163373105 171.545617 1.4861 0.144553 0.072276 M2 180.446464753134 188.337934 0.9581 0.343369 0.171684 M3 295.839564571899 172.475163 1.7153 0.093497 0.046748 M4 207.577948072379 190.803704 1.0879 0.282694 0.141347 M5 175.647916374566 187.713706 0.9357 0.354642 0.177321 M6 448.898639026695 182.079982 2.4654 0.017754 0.008877 M7 55.4442951055209 208.18079 0.2663 0.79126 0.39563 M8 -82.8238967667418 179.470854 -0.4615 0.646774 0.323387 M9 -2.92881928519086 183.373895 -0.016 0.987331 0.493665 M10 260.561703653976 185.982212 1.401 0.168389 0.084195 M11 -149.418332236016 173.915755 -0.8591 0.395027 0.197513 t 11.1347397110506 8.573994 1.2987 0.200981 0.10049 Multiple Linear Regression - Regression Statistics Multiple R 0.741783509030645 R-squared 0.550242774269817 Adjusted R-squared 0.372431778050907 F-TEST (value) 3.09453737941152 F-TEST (DF numerator) 17 F-TEST (DF denominator) 43 p-value 0.00139595311085983 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 252.423589587147 Sum Squared Residuals 2739859.74894261 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2360 2337.46838271003 22.5316172899689 2 2214 2376.85233343769 -162.852333437686 3 2825 2586.60552248833 238.394477511670 4 2355 2427.6614525981 -72.661452598102 5 2333 2508.56281805648 -175.562818056482 6 3016 2755.30650728760 260.693492712397 7 2155 2271.46368937317 -116.463689373175 8 2172 2329.01166634334 -157.011666343342 9 2150 2299.32919695060 -149.329196950604 10 2533 2455.60632268302 77.3936773169778 11 2058 2139.66070375231 -81.6607037523058 12 2160 2373.97182399751 -213.971823997512 13 2260 2574.0024483877 -314.002448387701 14 2498 2461.25845137619 36.7415486238139 15 2695 2659.98708761839 35.0129123816067 16 2799 2621.47574934912 177.52425065088 17 2947 2640.70777382773 306.292226172271 18 2930 2930.34390452808 -0.343904528079557 19 2318 2561.86973823608 -243.869738236084 20 2540 2434.92255078908 105.077449210923 21 2570 2391.62820481634 178.371795183657 22 2669 2673.72420254463 -4.72420254462778 23 2450 2356.38212065846 93.6178793415375 24 2842 2516.34782252132 325.652177478679 25 3440 2740.12517458585 699.874825414146 26 2678 2722.47090854042 -44.4709085404226 27 2981 3015.00767962209 -34.0076796220907 28 2260 2715.41155727144 -455.411557271438 29 2844 2638.08262193407 205.917378065931 30 2546 2877.70922233986 -331.709222339856 31 2456 2468.12344944390 -12.1234494438971 32 2295 2378.08139667163 -83.0813966716299 33 2379 2375.22651851294 3.77348148705526 34 2479 2597.66748466418 -118.667484664176 35 2057 2177.08762473552 -120.087624735520 36 2280 2322.14802700209 -42.1480270020869 37 2351 2480.1287686953 -129.128768695299 38 2276 2366.52704252219 -90.5270425221932 39 2548 2537.56698219898 10.4330178010174 40 2311 2378.19661180575 -67.1966118057504 41 2201 2362.64242819781 -161.642428197814 42 2725 2626.94900471337 98.0509952866323 43 2408 2126.91102459307 281.088975406933 44 2139 2086.76028523260 52.2397147673964 45 1898 2162.47876853269 -264.478768532693 46 2537 2265.21396820859 271.786031791413 47 2069 1798.78302015264 270.216979847355 48 2063 2098.34817520229 -35.348175202289 49 2524 2338.5339722457 185.466027754302 50 2437 2175.89126412351 261.108735876489 51 2189 2438.83272807220 -249.832728072203 52 2793 2375.25462897559 417.745371024411 53 2074 2249.00435798391 -175.004357983906 54 2622 2648.69136113109 -26.6913611310936 55 2278 2186.63209835378 91.3679016462235 56 2144 2061.22410096335 82.7758990366518 57 2427 2195.33731118741 231.662688812585 58 2139 2364.78802189959 -225.788021899587 59 1828 1990.08653070107 -162.086530701067 60 2072 2106.18415127679 -34.1841512767911 61 1800 2264.74125337542 -464.741253375417 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.608757415731514 0.782485168536971 0.391242584268486 22 0.432382726713473 0.864765453426947 0.567617273286527 23 0.324743188724523 0.649486377449046 0.675256811275477 24 0.312903034628554 0.625806069257107 0.687096965371446 25 0.760206269838633 0.479587460322735 0.239793730161367 26 0.806833021858897 0.386333956282207 0.193166978141103 27 0.811105919085628 0.377788161828745 0.188894080914372 28 0.79697111329699 0.406057773406022 0.203028886703011 29 0.82686922478783 0.346261550424341 0.173130775212170 30 0.776232269593693 0.447535460812613 0.223767730406307 31 0.814978286170295 0.370043427659411 0.185021713829705 32 0.758341593175053 0.483316813649893 0.241658406824947 33 0.702234442790076 0.595531114419847 0.297765557209924 34 0.599846067733304 0.800307864533393 0.400153932266696 35 0.481474571703589 0.962949143407179 0.518525428296411 36 0.386779402140268 0.773558804280536 0.613220597859732 37 0.410912875273493 0.821825750546986 0.589087124726507 38 0.299626517385597 0.599253034771194 0.700373482614403 39 0.292959089074945 0.585918178149891 0.707040910925055 40 0.177005057880631 0.354010115761261 0.82299494211937 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 0 0 OK 10% type I error level 0 0 OK

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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