Paper - Regressie analyse 3

*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: Mon, 29 Nov 2010 18:29:27 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/29/t129105534740d6ggp64a17h7j.htm/, Retrieved Mon, 29 Nov 2010 19:29:07 +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/2010/Nov/29/t129105534740d6ggp64a17h7j.htm/}, year = {2010}, } @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 = {2010}, 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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378.205 0 377.632 376.974 370.861 0 378.205 377.632 369.167 0 370.861 378.205 371.551 0 369.167 370.861 382.842 0 371.551 369.167 381.903 0 382.842 371.551 384.502 0 381.903 382.842 392.058 0 384.502 381.903 384.359 0 392.058 384.502 388.884 0 384.359 392.058 386.586 0 388.884 384.359 387.495 0 386.586 388.884 385.705 0 387.495 386.586 378.67 0 385.705 387.495 377.367 0 378.67 385.705 376.911 0 377.367 378.67 389.827 0 376.911 377.367 387.82 0 389.827 376.911 387.267 0 387.82 389.827 380.575 0 387.267 387.82 372.402 0 380.575 387.267 376.74 0 372.402 380.575 377.795 0 376.74 372.402 376.126 0 377.795 376.74 370.804 0 376.126 377.795 367.98 0 370.804 376.126 367.866 0 367.98 370.804 366.121 0 367.866 367.98 379.421 0 366.121 367.866 378.519 0 379.421 366.121 372.423 0 378.519 379.421 355.072 0 372.423 378.519 344.693 0 355.072 372.423 342.892 0 344.693 355.072 344.178 0 342.892 344.693 337.606 0 344.178 342.892 327.103 0 337.606 344.178 323.953 0 327.103 337.606 316.532 0 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Maandelijksewerkloosheid[t] = + 6.06645265428026 + 6.51400634022988x[t] + 1.04111636612974`y-1`[t] -0.0567105374733346`y-2`[t] -1.78757398818603M1[t] -1.38927597259309M2[t] -3.46312965581879M3[t] + 1.39314919046846M4[t] + 17.4477569184918M5[t] + 0.647957883429362M6[t] -5.98306251125522M7[t] -3.6123360833013M8[t] -4.38508073448924M9[t] + 7.56499978638544M10[t] + 3.54606068516857M11[t] -0.112186792756548t + 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) 6.06645265428026 12.975936 0.4675 0.641978 0.320989 x 6.51400634022988 2.269125 2.8707 0.005803 0.002902 `y-1` 1.04111636612974 0.135979 7.6565 0 0 `y-2` -0.0567105374733346 0.139013 -0.408 0.684893 0.342446 M1 -1.78757398818603 2.901074 -0.6162 0.54032 0.27016 M2 -1.38927597259309 2.958344 -0.4696 0.640488 0.320244 M3 -3.46312965581879 3.01557 -1.1484 0.255767 0.127884 M4 1.39314919046846 3.052924 0.4563 0.649948 0.324974 M5 17.4477569184918 2.900739 6.0149 0 0 M6 0.647957883429362 3.417894 0.1896 0.850338 0.425169 M7 -5.98306251125522 2.910269 -2.0558 0.044556 0.022278 M8 -3.6123360833013 3.198459 -1.1294 0.263631 0.131816 M9 -4.38508073448924 3.067963 -1.4293 0.15857 0.079285 M10 7.56499978638544 3.088139 2.4497 0.01751 0.008755 M11 3.54606068516857 2.895201 1.2248 0.225868 0.112934 t -0.112186792756548 0.067224 -1.6689 0.10083 0.050415 Multiple Linear Regression - Regression Statistics Multiple R 0.992938292177012 R-squared 0.985926452071402 Adjusted R-squared 0.982088211727238 F-TEST (value) 256.869389008090 F-TEST (DF numerator) 15 F-TEST (DF denominator) 55 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.71073709484016 Sum Squared Residuals 1220.50741871867 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 378.205 375.94714929417 2.25785070583032 2 370.861 376.792504661141 -5.93150466114085 3 369.167 366.928010454330 2.23898954567037 4 371.551 370.324933570841 1.22606642915933 5 382.842 388.845443573441 -6.00344357344062 6 381.903 383.553504714256 -1.65050471425601 7 384.502 375.192370580408 9.30962941959232 8 392.058 380.210022845864 11.8479771541363 9 384.359 387.044375977502 -2.6853759775023 10 388.884 390.438209981639 -1.55420998163903 11 386.586 391.45475007241 -4.86875007240991 12 387.495 385.147402003052 2.34759799694818 13 385.705 384.324336814035 1.38066318596509 14 378.67 382.695299862936 -4.02529986293576 15 377.367 373.286517613308 4.08048238669189 16 376.911 377.072993672897 -0.161993672896697 17 389.827 392.614559375536 -2.78755937553608 18 387.82 389.175492537737 -1.35549253773660 19 387.267 379.610291501467 7.65670849853251 20 380.575 381.406911834904 -0.831911834904114 21 372.402 373.586190596042 -1.18419059604217 22 376.74 377.294547180554 -0.554547180553501 23 377.795 378.143279305620 -0.348279305620464 24 376.126 375.337399282403 0.788600717597068 25 370.804 371.640185669355 -0.836185669355417 26 367.98 366.480125478692 1.4998745213077 27 367.866 361.655785865193 6.21021413480716 28 366.121 366.441341210809 -0.320341210809422 29 379.421 380.573479088452 -1.15247908845178 30 378.519 377.607300818049 0.911699181950759 31 372.423 369.170756519964 3.25224348003624 32 355.072 365.133803692035 -10.0618036920352 33 344.693 346.530169615811 -1.83716961581112 34 342.892 348.546301115568 -5.6543011155685 35 344.178 343.128723314631 1.04927668536882 36 337.606 340.911487161538 -3.30548716153839 37 327.103 332.096579871200 -4.99357987120045 38 323.953 321.820547552851 2.13245244714898 39 316.532 316.950621298642 -0.418621298642485 40 306.307 314.147226992165 -7.8402269921654 41 327.225 319.865081982345 7.35991801765472 42 329.573 325.311033546893 4.26196645310698 43 313.761 319.826096564257 -6.0650965642572 44 307.836 305.489347876224 2.34665212377615 45 300.074 299.332508981489 0.741491018510982 46 304.198 303.425267410238 0.772732589762322 47 306.122 304.027892602051 2.09410739794875 48 300.414 302.13887875602 -1.72487875601977 49 292.133 294.18731468311 -2.05431468310993 50 290.616 286.175645025924 4.44035497407624 51 280.244 289.393857323569 -9.1498573235692 52 285.179 283.425520312949 1.75347968705057 53 305.486 305.09405220974 0.391947790260164 54 305.957 309.044149926487 -3.08714992648651 55 293.886 301.639687663022 -7.75368766302145 56 289.441 291.304200979517 -1.86320097951692 57 288.776 286.476060185966 2.29993981403372 58 299.149 297.873689869677 1.27531013032284 59 306.532 304.579776548987 1.95222345101272 60 309.914 308.019832796987 1.89416720301292 61 313.468 309.222433668130 4.24556633187039 62 314.901 313.016877418456 1.88412258154369 63 309.16 312.121207444958 -2.96120744495772 64 316.15 310.806984240338 5.34301575966162 65 336.544 334.352383770486 2.19161622951359 66 339.196 338.276518456579 0.919481543421384 67 326.738 333.137797170882 -6.39979717088243 68 320.838 322.275712771456 -1.43771277145621 69 318.62 315.954694643189 2.66530535681088 70 331.533 325.817984442324 5.71501555767586 71 335.378 335.2565781563 0.121421843700092 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.074220852144216 0.148441704288432 0.925779147855784 20 0.464578127209132 0.929156254418264 0.535421872790868 21 0.565203142099856 0.869593715800287 0.434796857900144 22 0.486524746415984 0.973049492831967 0.513475253584016 23 0.392204405870877 0.784408811741755 0.607795594129123 24 0.312526464953824 0.625052929907647 0.687473535046176 25 0.239670740316477 0.479341480632954 0.760329259683523 26 0.252696539562258 0.505393079124516 0.747303460437742 27 0.309145137621708 0.618290275243416 0.690854862378292 28 0.253675229982960 0.507350459965921 0.74632477001704 29 0.190087880912163 0.380175761824326 0.809912119087837 30 0.135260817610666 0.270521635221332 0.864739182389334 31 0.488045921370259 0.976091842740519 0.511954078629741 32 0.887902643416638 0.224194713166724 0.112097356583362 33 0.848332645666047 0.303334708667907 0.151667354333953 34 0.849142742425357 0.301714515149285 0.150857257574643 35 0.8167229195321 0.366554160935799 0.183277080467900 36 0.778419072512152 0.443161854975697 0.221580927487848 37 0.774186741795286 0.451626516409428 0.225813258204714 38 0.777703045058638 0.444593909882723 0.222296954941362 39 0.7772816479985 0.445436704003 0.2227183520015 40 0.977263652141724 0.0454726957165512 0.0227363478582756 41 0.990829605402045 0.0183407891959106 0.00917039459795532 42 0.992242547639804 0.0155149047203924 0.00775745236019619 43 0.99267122193836 0.0146575561232811 0.00732877806164057 44 0.996175937123683 0.00764812575263317 0.00382406287631659 45 0.99197536721962 0.0160492655607603 0.00802463278038013 46 0.983378086352252 0.0332438272954956 0.0166219136477478 47 0.997989294399354 0.00402141120129116 0.00201070560064558 48 0.999722493768495 0.00055501246301022 0.00027750623150511 49 0.998793678553814 0.00241264289237245 0.00120632144618623 50 0.995367767418999 0.00926446516200247 0.00463223258100123 51 0.985409283929187 0.0291814321416255 0.0145907160708128 52 0.95386534637526 0.0922693072494796 0.0461346536247398 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.147058823529412 NOK 5% type I error level 12 0.352941176470588 NOK 10% type I error level 13 0.382352941176471 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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