Paper - Regressie analyse 2

*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: Sun, 28 Nov 2010 20:12:54 +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/28/t1290975092g9gcgzv68v1rqju.htm/, Retrieved Sun, 28 Nov 2010 21:11:41 +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/28/t1290975092g9gcgzv68v1rqju.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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376.974 377.632 378.205 370.861 369.167 371.551 382.842 381.903 384.502 392.058 384.359 388.884 386.586 387.495 385.705 378.67 377.367 376.911 389.827 387.82 387.267 380.575 372.402 376.74 377.795 376.126 370.804 367.98 367.866 366.121 379.421 378.519 372.423 355.072 344.693 342.892 344.178 337.606 327.103 323.953 316.532 306.307 327.225 329.573 313.761 307.836 300.074 304.198 306.122 300.414 292.133 290.616 280.244 285.179 305.486 305.957 293.886 289.441 288.776 299.149 306.532 309.914 313.468 314.901 309.16 316.15 336.544 339.196 326.738 320.838 318.62 331.533 335.378

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Maandelijksewerkloosheid[t] = + 399.088944444444 + 0.119125661375424M1[t] -6.30220105820107M2[t] -8.53696428571428M3[t] -10.5497275132276M4[t] -13.5971574074074M5[t] -11.8899206349206M6[t] + 6.02448280423279M7[t] + 7.68838624338623M8[t] + 1.68328968253969M9[t] -2.38280687830688M10[t] -7.13873677248678M11[t] -1.39340343915344t + 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) 399.088944444444 9.569634 41.7037 0 0 M1 0.119125661375424 11.308377 0.0105 0.99163 0.495815 M2 -6.30220105820107 11.775598 -0.5352 0.594495 0.297248 M3 -8.53696428571428 11.765123 -0.7256 0.470895 0.235447 M4 -10.5497275132276 11.755742 -0.8974 0.373087 0.186543 M5 -13.5971574074074 11.747459 -1.1575 0.251673 0.125837 M6 -11.8899206349206 11.740275 -1.0127 0.315248 0.157624 M7 6.02448280423279 11.734194 0.5134 0.609548 0.304774 M8 7.68838624338623 11.729215 0.6555 0.514658 0.257329 M9 1.68328968253969 11.725342 0.1436 0.886329 0.443165 M10 -2.38280687830688 11.722574 -0.2033 0.839615 0.419807 M11 -7.13873677248678 11.720913 -0.6091 0.544784 0.272392 t -1.39340343915344 0.113924 -12.231 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.849858359743331 R-squared 0.722259231625625 Adjusted R-squared 0.66671107795075 F-TEST (value) 13.0023985289058 F-TEST (DF numerator) 12 F-TEST (DF denominator) 60 p-value 1.38489220091742e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20.300258574558 Sum Squared Residuals 24726.029891635 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 376.974 397.814666666668 -20.8406666666681 2 377.632 389.999936507936 -12.3679365079365 3 378.205 386.37176984127 -8.16676984126978 4 370.861 382.965603174603 -12.1046031746032 5 369.167 378.52476984127 -9.35776984126975 6 371.551 378.838603174603 -7.28760317460311 7 382.842 395.359603174603 -12.5176031746031 8 381.903 395.630103174603 -13.7271031746031 9 384.502 388.231603174603 -3.72960317460311 10 392.058 382.772103174603 9.28589682539687 11 384.359 376.62276984127 7.7362301587302 12 388.884 382.368103174603 6.5158968253969 13 386.586 381.093825396825 5.49217460317498 14 387.495 373.279095238095 14.2159047619048 15 385.705 369.650928571429 16.0540714285714 16 378.67 366.244761904762 12.4252380952382 17 377.367 361.803928571429 15.5630714285715 18 376.911 362.117761904762 14.7932380952381 19 389.827 378.638761904762 11.1882380952381 20 387.82 378.909261904762 8.91073809523811 21 387.267 371.510761904762 15.7562380952381 22 380.575 366.051261904762 14.5237380952381 23 372.402 359.901928571429 12.5000714285714 24 376.74 365.647261904762 11.0927380952381 25 377.795 364.372984126984 13.4220158730161 26 376.126 356.558253968254 19.5677460317460 27 370.804 352.930087301587 17.8739126984127 28 367.98 349.523920634921 18.4560793650794 29 367.866 345.083087301587 22.7829126984127 30 366.121 345.396920634921 20.7240793650794 31 379.421 361.917920634921 17.5030793650794 32 378.519 362.188420634921 16.3305793650794 33 372.423 354.789920634921 17.6330793650794 34 355.072 349.330420634921 5.74157936507937 35 344.693 343.181087301587 1.51191269841268 36 342.892 348.926420634921 -6.03442063492065 37 344.178 347.652142857143 -3.47414285714263 38 337.606 339.837412698413 -2.23141269841271 39 327.103 336.209246031746 -9.10624603174603 40 323.953 332.803079365079 -8.8500793650794 41 316.532 328.362246031746 -11.8302460317461 42 306.307 328.676079365079 -22.3690793650794 43 327.225 345.197079365079 -17.9720793650794 44 329.573 345.467579365079 -15.8945793650794 45 313.761 338.069079365079 -24.3080793650794 46 307.836 332.609579365079 -24.7735793650794 47 300.074 326.460246031746 -26.386246031746 48 304.198 332.205579365079 -28.0075793650794 49 306.122 330.931301587301 -24.8093015873014 50 300.414 323.116571428571 -22.7025714285715 51 292.133 319.488404761905 -27.3554047619048 52 290.616 316.082238095238 -25.4662380952381 53 280.244 311.641404761905 -31.3974047619048 54 285.179 311.955238095238 -26.7762380952381 55 305.486 328.476238095238 -22.9902380952381 56 305.957 328.746738095238 -22.7897380952381 57 293.886 321.348238095238 -27.4622380952381 58 289.441 315.888738095238 -26.4477380952381 59 288.776 309.739404761905 -20.9634047619048 60 299.149 315.484738095238 -16.3357380952381 61 306.532 314.21046031746 -7.67846031746016 62 309.914 306.39573015873 3.51826984126978 63 313.468 302.767563492064 10.7004365079365 64 314.901 299.361396825397 15.5396031746031 65 309.16 294.920563492064 14.2394365079365 66 316.15 295.234396825397 20.9156031746031 67 336.544 311.755396825397 24.7886031746031 68 339.196 312.025896825397 27.1701031746031 69 326.738 304.627396825397 22.1106031746031 70 320.838 299.167896825397 21.6701031746031 71 318.62 293.018563492064 25.6014365079365 72 331.533 298.763896825397 32.7691031746031 73 335.378 297.489619047619 37.8883809523811 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 7.82716348216002e-05 0.000156543269643200 0.999921728365178 17 2.64739844036383e-06 5.29479688072766e-06 0.99999735260156 18 1.07224366610251e-06 2.14448733220503e-06 0.999998927756334 19 5.8294858276586e-08 1.16589716553172e-07 0.999999941705142 20 5.17741895871307e-09 1.03548379174261e-08 0.999999994822581 21 5.37506316177653e-09 1.07501263235531e-08 0.999999994624937 22 5.83555960711212e-06 1.16711192142242e-05 0.999994164440393 23 1.61781803239488e-05 3.23563606478976e-05 0.999983821819676 24 1.88342885362498e-05 3.76685770724996e-05 0.999981165711464 25 7.03128401072435e-06 1.40625680214487e-05 0.99999296871599 26 3.45055823378163e-06 6.90111646756326e-06 0.999996549441766 27 2.82393443080600e-06 5.64786886161200e-06 0.99999717606557 28 1.20425709091510e-06 2.40851418183021e-06 0.99999879574291 29 5.96895638894492e-07 1.19379127778898e-06 0.99999940310436 30 3.91125133886769e-07 7.82250267773539e-07 0.999999608874866 31 2.17072092921056e-07 4.34144185842111e-07 0.999999782927907 32 1.26816881117096e-07 2.53633762234192e-07 0.99999987318312 33 3.08561776688866e-07 6.17123553377732e-07 0.999999691438223 34 2.11861642261216e-05 4.23723284522431e-05 0.999978813835774 35 0.000358487666940773 0.000716975333881547 0.99964151233306 36 0.0035690813587 0.0071381627174 0.9964309186413 37 0.00976272737630628 0.0195254547526126 0.990237272623694 38 0.0368339022096982 0.0736678044193964 0.963166097790302 39 0.115873259643585 0.231746519287171 0.884126740356415 40 0.218934004818834 0.437868009637668 0.781065995181166 41 0.434438489495991 0.868876978991981 0.565561510504009 42 0.60434931925493 0.79130136149014 0.39565068074507 43 0.693889056419862 0.612221887160275 0.306110943580138 44 0.78420340544365 0.431593189112698 0.215796594556349 45 0.891926735924997 0.216146528150006 0.108073264075003 46 0.965461857297017 0.0690762854059666 0.0345381427029833 47 0.991414807632188 0.017170384735623 0.0085851923678115 48 0.99815173751065 0.00369652497870032 0.00184826248935016 49 0.999949916397746 0.000100167204508931 5.00836022544653e-05 50 0.999999674582958 6.50834084964026e-07 3.25417042482013e-07 51 0.99999994249132 1.15017359525667e-07 5.75086797628333e-08 52 0.999999993470988 1.30580241381422e-08 6.52901206907111e-09 53 0.999999967570653 6.48586940590337e-08 3.24293470295168e-08 54 0.999999497707042 1.00458591651325e-06 5.02292958256626e-07 55 0.999992465022608 1.50699547848338e-05 7.5349773924169e-06 56 0.999941229558563 0.000117540882874145 5.87704414370725e-05 57 0.999553295900513 0.000893408198973731 0.000446704099486866 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 31 0.738095238095238 NOK 5% type I error level 33 0.785714285714286 NOK 10% type I error level 35 0.833333333333333 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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