multiple regression, opnemen van slechts 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, 19 Nov 2009 11:25:54 -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/t12586552336fm2ihgvszv47il.htm/, Retrieved Thu, 19 Nov 2009 19:27:25 +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/t12586552336fm2ihgvszv47il.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 2214 2 2360 2267 2825 2 2214 2360 2355 2 2825 2214 2333 2 2355 2825 3016 2 2333 2355 2155 2 3016 2333 2172 2 2155 3016 2150 2 2172 2155 2533 2 2150 2172 2058 2 2533 2150 2160 2 2058 2533 2260 2 2160 2058 2498 2 2260 2160 2695 2 2498 2260 2799 2 2695 2498 2947 2 2799 2695 2930 2 2947 2799 2318 2 2930 2947 2540 2 2318 2930 2570 2 2540 2318 2669 2 2570 2540 2450 2 2669 2570 2842 2 2450 2669 3440 2 2842 2450 2678 2 3440 2842 2981 2 2678 3440 2260 2,21 2981 2678 2844 2,25 2260 2981 2546 2,25 2844 2260 2456 2,45 2546 2844 2295 2,5 2456 2546 2379 2,5 2295 2456 2479 2,64 2379 2295 2057 2,75 2479 2379 2280 2,93 2057 2479 2351 3 2280 2057 2276 3,17 2351 2280 2548 3,25 2276 2351 2311 3,39 2548 2276 2201 3,5 2311 2548 2725 3,5 2201 2311 2408 3,65 2725 2201 2139 3,75 2408 2725 1898 3,75 2139 2408 2537 3,9 1898 2139 2069 4 2537 1898 2063 4 2069 2537 2524 4 2063 2069 2437 4 2524 2063 2189 4 2437 2524 2793 4 2189 2437 2074 4 2793 2189 2622 4 2074 2793 227 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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2433.44637791450 -315.074157998355X[t] -0.00125846806695553Y1[t] + 0.177146531235082Y2[t] + 250.885789760826M1[t] + 140.710806349446M2[t] + 315.354276985791M3[t] + 212.856988453909M4[t] + 147.800396561370M5[t] + 450.964210878744M6[t] + 22.4825935448227M7[t] -94.9584839475962M8[t] + 0.239158080932078M9[t] + 206.346376078827M10[t] -162.905871133591M11[t] + 10.3153346404841t + 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) 2433.44637791450 751.624049 3.2376 0.002266 0.001133 X -315.074157998355 148.716908 -2.1186 0.039677 0.019839 Y1 -0.00125846806695553 0.162594 -0.0077 0.993859 0.496929 Y2 0.177146531235082 0.163519 1.0833 0.284428 0.142214 M1 250.885789760826 167.364603 1.499 0.140847 0.070424 M2 140.710806349446 177.56239 0.7925 0.432252 0.216126 M3 315.354276985791 167.428143 1.8835 0.066102 0.033051 M4 212.856988453909 181.417717 1.1733 0.24685 0.123425 M5 147.800396561370 174.40691 0.8474 0.401232 0.200616 M6 450.964210878744 168.335187 2.679 0.010277 0.005138 M7 22.4825935448227 191.025309 0.1177 0.906834 0.453417 M8 -94.9584839475962 168.855391 -0.5624 0.576658 0.288329 M9 0.239158080932078 161.031948 0.0015 0.998822 0.499411 M10 206.346376078827 163.50571 1.262 0.213446 0.106723 M11 -162.905871133591 170.220741 -0.957 0.343667 0.171834 t 10.3153346404841 6.705311 1.5384 0.130958 0.065479 Multiple Linear Regression - Regression Statistics Multiple R 0.737666102933429 R-squared 0.544151279416992 Adjusted R-squared 0.392201705889323 F-TEST (value) 3.58113067897427 F-TEST (DF numerator) 15 F-TEST (DF denominator) 45 p-value 0.000455865512472009 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 248.415794172444 Sum Squared Residuals 2776968.30574466 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2360 2370.94408274775 -10.9440827477537 2 2214 2363.26073922011 -149.260739220114 3 2825 2564.87790823958 260.122091760418 4 2355 2446.06363679895 -91.0636367989512 5 2333 2500.150390123 -167.150390123001 6 3016 2730.39835569784 285.601644302156 7 2155 2307.47531562750 -152.475315627505 8 2172 2322.42419461478 -150.424194614779 9 2150 2275.39261393325 -125.392613933248 10 2533 2494.8543439001 38.1456560999033 11 2058 2131.53821437135 -73.5382143713462 12 2160 2373.20431394026 -213.204313940262 13 2260 2550.13247226208 -290.132472262079 14 2498 2468.21592287047 29.7840771295347 15 2695 2670.58986587087 24.4101341291327 16 2799 2620.32086820423 178.679131795772 17 2947 2600.34659692652 346.653403073479 18 2930 2932.06273185892 -2.06273185891864 19 2318 2540.13552974541 -222.135529745412 20 2540 2430.76847831946 109.231521680542 21 2570 2427.58839796174 142.411602038264 22 2669 2683.29972649229 -14.2997264922944 23 2450 2329.55262151878 120.447378481216 24 2842 2520.58693839180 321.413061608205 25 3440 2742.49965297038 697.500347029623 26 2678 2711.32888053959 -33.3288805395925 27 2981 3003.18026416202 -22.1802641620213 28 2260 2709.46576446555 -449.465764465548 29 2844 2696.70429533406 147.295704665936 30 2546 2881.72584992033 -335.725849920326 31 2456 2504.37333335246 -48.3733333524587 32 2295 2328.81747841858 -33.8174784185778 33 2379 2418.58988063521 -39.5898806352127 34 2479 2562.27574830735 -83.2757483073498 35 2057 2183.43514017265 -126.435140172648 36 2280 2318.18872415478 -38.1887241547824 37 2351 2482.29818293607 -131.298182936073 38 2276 2368.29025253813 -92.290252538125 39 2548 2540.7149139978 7.28508600220146 40 2311 2390.79428482979 -79.7942848297873 41 2201 2349.87698362572 -148.876983625724 42 2725 2621.51083616823 103.489163831767 43 2408 2135.9378740721 272.062125927901 44 2139 2090.52843216474 48.471567835263 45 1898 2140.22448634224 -242.224486342240 46 2537 2262.03678918277 274.963210817235 47 2069 1828.09598568856 240.904014311445 48 2063 2115.10278797718 -52.1027879771833 49 2524 2293.40688656888 230.593113431123 50 2437 2191.90420483170 245.095795168296 51 2189 2458.63704772973 -269.637047729731 52 2793 2351.35544570149 441.644554298514 53 2074 2251.92173399069 -177.921733990689 54 2622 2673.30222635468 -51.3022263546779 55 2278 2127.07794720253 150.922052797475 56 2144 2117.46141648245 26.5385835175518 57 2427 2162.20462112756 264.795378872436 58 2139 2354.53339211749 -215.533392117494 59 1828 1989.37803824867 -161.378038248667 60 2072 2089.91723553598 -17.9172355359773 61 1800 2295.71872251484 -495.718722514840 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.623056513133948 0.753886973732104 0.376943486866052 20 0.458930282725312 0.917860565450623 0.541069717274688 21 0.363106115145856 0.726212230291712 0.636893884854144 22 0.236816897522628 0.473633795045256 0.763183102477372 23 0.179178263923844 0.358356527847687 0.820821736076156 24 0.220765873412846 0.441531746825693 0.779234126587154 25 0.745158705811795 0.50968258837641 0.254841294188205 26 0.756577684268115 0.48684463146377 0.243422315731885 27 0.790014784024543 0.419970431950915 0.209985215975457 28 0.718255912800268 0.563488174399464 0.281744087199732 29 0.822619667130648 0.354760665738704 0.177380332869352 30 0.798668078201681 0.402663843596638 0.201331921798319 31 0.848519545741891 0.302960908516217 0.151480454258109 32 0.785574892876411 0.428850214247177 0.214425107123588 33 0.711496912560833 0.577006174878333 0.288503087439167 34 0.618358890631537 0.763282218736926 0.381641109368463 35 0.511721393043547 0.976557213912906 0.488278606956453 36 0.428726070812379 0.857452141624757 0.571273929187621 37 0.392199772951912 0.784399545903825 0.607800227048088 38 0.299410227208471 0.598820454416941 0.70058977279153 39 0.278790207778067 0.557580415556134 0.721209792221933 40 0.230257676855056 0.460515353710112 0.769742323144944 41 0.136603671674612 0.273207343349224 0.863396328325388 42 0.0774747899692988 0.154949579938598 0.922525210030701 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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