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: Sun, 28 Nov 2010 20:30:20 +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/t1290976115kkewdx53c21lnnk.htm/, Retrieved Sun, 28 Nov 2010 21:28:45 +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/t1290976115kkewdx53c21lnnk.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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User-defined keywords:

Dataseries X:

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370.861 378.205 377.632 369.167 370.861 378.205 371.551 369.167 370.861 382.842 371.551 369.167 381.903 382.842 371.551 384.502 381.903 382.842 392.058 384.502 381.903 384.359 392.058 384.502 388.884 384.359 392.058 386.586 388.884 384.359 387.495 386.586 388.884 385.705 387.495 386.586 378.67 385.705 387.495 377.367 378.67 385.705 376.911 377.367 378.67 389.827 376.911 377.367 387.82 389.827 376.911 387.267 387.82 389.827 380.575 387.267 387.82 372.402 380.575 387.267 376.74 372.402 380.575 377.795 376.74 372.402 376.126 377.795 376.74 370.804 376.126 377.795 367.98 370.804 376.126 367.866 367.98 370.804 366.121 367.866 367.98 379.421 366.121 367.866 378.519 379.421 366.121 372.423 378.519 379.421 355.072 372.423 378.519 344.693 355.072 372.423 342.892 344.693 355.072 344.178 342.892 344.693 337.606 344.178 342.892 327.103 337.606 344.178 323.953 327.103 337.606 316.532 323.953 327.103 306.307 316.532 323.953 327.225 306.307 316.532 329.573 327.225 306.307 313.761 329 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Maandelijksewerkloosheid[t] = -0.183652070354275 + 1.20254216823031`y-1`[t] -0.214870097411409`y-2`[t] + 1.50326958825658M1[t] + 0.369180753062720M2[t] + 5.28169004288971M3[t] + 20.4613599093827M4[t] + 0.922364121497752M5[t] -3.26128468113092M6[t] + 0.224615886414515M7[t] -0.958884920620017M8[t] + 10.9984677302770M9[t] + 4.95759091526634M10[t] + 1.75349249114326M11[t] + 0.0097300254562701t + 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) -0.183652070354275 13.970307 -0.0131 0.989559 0.494779 `y-1` 1.20254216823031 0.130462 9.2176 0 0 `y-2` -0.214870097411409 0.134291 -1.6 0.115321 0.057661 M1 1.50326958825658 3.048158 0.4932 0.623854 0.311927 M2 0.369180753062720 3.049144 0.1211 0.904071 0.452036 M3 5.28169004288971 3.064567 1.7235 0.090422 0.045211 M4 20.4613599093827 3.071182 6.6624 0 0 M5 0.922364121497752 3.884017 0.2375 0.813169 0.406585 M6 -3.26128468113092 3.065967 -1.0637 0.29211 0.146055 M7 0.224615886414515 3.140223 0.0715 0.943236 0.471618 M8 -0.958884920620017 3.075958 -0.3117 0.75642 0.37821 M9 10.9984677302770 3.087704 3.562 0.000769 0.000384 M10 4.95759091526634 3.195328 1.5515 0.126515 0.063257 M11 1.75349249114326 3.210875 0.5461 0.587198 0.293599 t 0.0097300254562701 0.06012 0.1618 0.872023 0.436011 Multiple Linear Regression - Regression Statistics Multiple R 0.991883600157207 R-squared 0.983833076260821 Adjusted R-squared 0.97971785930903 F-TEST (value) 239.071982786391 F-TEST (DF numerator) 14 F-TEST (DF denominator) 55 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.01201653518303 Sum Squared Residuals 1381.61703619215 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 370.861 374.994983653238 -4.13398365323801 2 369.167 364.9160345942 4.25096540580037 3 371.551 369.37917347189 2.1718265281099 4 382.842 387.799423837915 -4.95742383791536 5 381.903 381.335811384746 0.56718861525373 6 384.502 373.606607241733 10.8953927582666 7 392.058 380.429407951435 11.6285920485650 8 384.359 387.783598409833 -3.42459840983272 9 388.884 388.86875047694 0.0152495230597461 10 386.586 389.933391878598 -3.34739187859845 11 387.495 383.003294386552 4.49170561344823 12 385.705 382.846414235638 2.85858576436245 13 378.67 382.011546449671 -3.34154644967112 14 377.367 372.8119209608 4.55507903920022 15 376.911 377.678858966168 -0.767858966168222 16 389.827 392.599875366332 -2.77287536633149 17 387.82 388.700625013185 -0.880625013185109 18 387.267 379.337941926209 7.9290580737913 19 380.575 382.599810985684 -2.02481098568376 20 372.402 373.497451178177 -1.09545117817678 21 376.74 377.074067405461 -0.334067405460917 22 377.795 378.015681847833 -0.220681847833032 23 376.126 375.157888954079 0.968111045921455 24 370.804 371.180395656846 -0.376395656846087 25 367.98 366.652084043817 1.32791595618317 26 367.866 363.275284809420 4.59071519057954 27 366.121 368.667227472615 -2.54622747261524 28 379.421 381.782686472107 -2.36168647210748 29 378.519 378.622179867125 -0.103179867124845 30 372.423 370.505795758637 1.91720424136302 31 355.072 366.864542121972 -11.7925421219718 32 344.693 346.135310293249 -1.44231029324942 33 342.892 349.349418865726 -6.4574188657257 34 344.178 343.382630372222 0.79536962777849 35 337.606 342.121712247337 -4.51571224733682 36 327.103 332.198519706769 -5.09551970676916 37 323.953 322.493345207747 1.45965479225310 38 316.532 319.837759201196 -3.30575920119582 39 306.307 316.512773892888 -10.2057738928879 40 327.225 321.000731107572 6.22426889242769 41 329.573 328.823289166217 0.749710833783046 42 313.761 322.978286702397 -9.21728670239736 43 307.836 306.954805542620 0.881194457380497 44 300.074 302.053498394546 -1.97949839454584 45 304.198 305.959554088258 -1.76155408825816 46 306.122 306.555512896593 -0.433512896592794 47 300.414 304.788711347877 -4.37471134787652 48 292.133 295.767428118511 -3.63442811851135 49 290.616 288.548654553133 2.06734544686668 50 280.244 287.379378550854 -7.1353785508542 51 285.179 280.154808435026 5.0241915649741 52 305.486 303.507386577543 1.97861342245723 53 305.957 307.337760694642 -1.38076069464172 54 293.886 299.366872210572 -5.48087221057227 55 289.441 288.245412474985 1.19558752501477 56 288.776 284.320038701476 4.45596129852374 57 299.149 296.44252841895 2.70647158104979 58 306.532 303.028240155227 3.50375984477264 59 309.914 306.483393064156 3.43060693584366 60 313.468 307.220242282236 6.24775771776418 61 314.901 312.280386092394 2.62061390760617 62 309.16 312.11562188353 -2.95562188353011 63 316.15 309.826157761413 6.32384223858733 64 336.544 334.654896638531 1.88910336146939 65 339.196 338.148333874085 1.0476661259149 66 326.738 332.781496160451 -6.04349616045127 67 320.838 320.726020923305 0.111979076695329 68 318.62 315.134103022719 3.48589697728102 69 331.533 325.701680744665 5.83131925533524 70 335.378 335.675542849527 -0.297542849526853 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0613927983134604 0.122785596626921 0.93860720168654 19 0.237595046330777 0.475190092661554 0.762404953669223 20 0.502768429770029 0.994463140459942 0.497231570229971 21 0.431734984074524 0.863469968149048 0.568265015925476 22 0.340696652678709 0.681393305357418 0.659303347321291 23 0.273940825325893 0.547881650651786 0.726059174674107 24 0.208602716216194 0.417205432432388 0.791397283783806 25 0.218960499643957 0.437920999287914 0.781039500356043 26 0.269725615581302 0.539451231162605 0.730274384418698 27 0.218730610098741 0.437461220197483 0.781269389901259 28 0.158392070491130 0.316784140982260 0.84160792950887 29 0.113497563873309 0.226995127746618 0.88650243612669 30 0.469017451989853 0.938034903979706 0.530982548010147 31 0.881987614315669 0.236024771368662 0.118012385684331 32 0.844248604821949 0.311502790356102 0.155751395178051 33 0.823473541072964 0.353052917854072 0.176526458927036 34 0.81112088507921 0.377758229841579 0.188879114920789 35 0.774501512566393 0.450996974867214 0.225498487433607 36 0.722254775241118 0.555490449517763 0.277745224758882 37 0.723830929054035 0.552338141891931 0.276169070945965 38 0.765902708580048 0.468194582839903 0.234097291419952 39 0.930427298703822 0.139145402592356 0.069572701296178 40 0.99385427993023 0.0122914401395389 0.00614572006976943 41 0.994567832972944 0.0108643340541110 0.00543216702705549 42 0.995056823462872 0.0098863530742565 0.00494317653712825 43 0.998036679355187 0.00392664128962641 0.00196332064481320 44 0.995712319377329 0.00857536124534284 0.00428768062267142 45 0.991250976025947 0.0174980479481063 0.00874902397405313 46 0.999142580882296 0.00171483823540861 0.000857419117704304 47 0.999887878864775 0.000224242270450462 0.000112121135225231 48 0.999534775219657 0.00093044956068597 0.000465224780342985 49 0.99879830172989 0.00240339654022173 0.00120169827011087 50 0.99638761196404 0.00722477607191922 0.00361238803595961 51 0.987315831898554 0.0253683362028922 0.0126841681014461 52 0.955975005935158 0.088049988129684 0.044024994064842 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.228571428571429 NOK 5% type I error level 12 0.342857142857143 NOK 10% type I error level 13 0.371428571428571 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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