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: Mon, 29 Nov 2010 17:52:52 +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/t1291053064216b98mktc082lv.htm/, Retrieved Mon, 29 Nov 2010 18:51:04 +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/t1291053064216b98mktc082lv.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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376.974 0 377.632 0 378.205 0 370.861 0 369.167 0 371.551 0 382.842 0 381.903 0 384.502 0 392.058 0 384.359 0 388.884 0 386.586 0 387.495 0 385.705 0 378.67 0 377.367 0 376.911 0 389.827 0 387.82 0 387.267 0 380.575 0 372.402 0 376.74 0 377.795 0 376.126 0 370.804 0 367.98 0 367.866 0 366.121 0 379.421 0 378.519 0 372.423 0 355.072 0 344.693 0 342.892 0 344.178 0 337.606 0 327.103 0 323.953 0 316.532 0 306.307 0 327.225 0 329.573 0 313.761 0 307.836 0 300.074 0 304.198 0 306.122 0 300.414 0 292.133 0 290.616 0 280.244 1 285.179 1 305.486 1 305.957 1 293.886 1 289.441 1 288.776 1 299.149 1 306.532 1 309.914 1 313.468 1 314.901 1 309.16 1 316.15 1 336.544 1 339.196 1 326.738 1 320.838 1 318.62 1 331.533 1 335.378 1

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Maandelijksewerkloosheid[t] = + 402.681268612009 + 9.6304860662359x[t] -0.232099548522936M1[t] -6.31675961612434M2[t] -8.3895588867413M3[t] -10.2403581573583M4[t] -14.7309051056812M5[t] -12.8617043762982M6[t] + 5.2146630197515M7[t] + 7.04053041580121M8[t] + 1.19739781185091M9[t] -2.7067347920994M10[t] -7.30070072938304M11[t] -1.55536739604970t + 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) 402.681268612009 10.066576 40.0018 0 0 x 9.6304860662359 8.548172 1.1266 0.264467 0.132234 M1 -0.232099548522936 11.287394 -0.0206 0.983664 0.491832 M2 -6.31675961612434 11.749271 -0.5376 0.592855 0.296427 M3 -8.3895588867413 11.739541 -0.7146 0.477649 0.238825 M4 -10.2403581573583 11.732667 -0.8728 0.386306 0.193153 M5 -14.7309051056812 11.764309 -1.2522 0.215449 0.107725 M6 -12.8617043762982 11.745736 -1.095 0.277962 0.138981 M7 5.2146630197515 11.729997 0.4446 0.658266 0.329133 M8 7.04053041580121 11.717105 0.6009 0.550224 0.275112 M9 1.19739781185091 11.707067 0.1023 0.918881 0.459441 M10 -2.7067347920994 11.699893 -0.2313 0.817846 0.408923 M11 -7.30070072938304 11.695586 -0.6242 0.534885 0.267442 t -1.55536739604970 0.183271 -8.4867 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.853292678047315 R-squared 0.728108394409158 Adjusted R-squared 0.66820007453321 F-TEST (value) 12.153710802053 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 2.87281309852006e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20.2548612485385 Sum Squared Residuals 24205.3048476554 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 376.974 400.893801667436 -23.9198016674358 2 377.632 393.253774203785 -15.6217742037849 3 378.205 389.625607537118 -11.4206075371183 4 370.861 386.219440870452 -15.3584408704516 5 369.167 380.173526526079 -11.0065265260790 6 371.551 380.487359859412 -8.93635985941227 7 382.842 397.008359859412 -14.1663598594123 8 381.903 397.278859859412 -15.3758598594123 9 384.502 389.880359859412 -5.37835985941227 10 392.058 384.420859859412 7.63714014058772 11 384.359 378.271526526079 6.08747347392105 12 388.884 384.016859859412 4.86714014058774 13 386.586 382.22939291484 4.35660708516037 14 387.495 374.589365451189 12.9056345488115 15 385.705 370.961198784522 14.7438012154781 16 378.67 367.555032117855 11.1149678821448 17 377.367 361.509117773483 15.8578822265174 18 376.911 361.822951106816 15.0880488931841 19 389.827 378.343951106816 11.4830488931841 20 387.82 378.614451106816 9.20554889318407 21 387.267 371.215951106816 16.0510488931841 22 380.575 365.756451106816 14.8185488931841 23 372.402 359.607117773483 12.7948822265174 24 376.74 365.352451106816 11.3875488931841 25 377.795 363.564984162243 14.2300158377567 26 376.126 355.924956698592 20.2010433014078 27 370.804 352.296790031926 18.5072099680745 28 367.98 348.890623365259 19.0893766347412 29 367.866 342.844709020886 25.0212909791138 30 366.121 343.158542354220 22.9624576457804 31 379.421 359.679542354220 19.7414576457804 32 378.519 359.950042354220 18.5689576457805 33 372.423 352.551542354220 19.8714576457804 34 355.072 347.092042354220 7.97995764578045 35 344.693 340.942709020886 3.75029097911376 36 342.892 346.688042354220 -3.79604235421957 37 344.178 344.900575409647 -0.722575409646927 38 337.606 337.260547945996 0.345452054004159 39 327.103 333.632381279329 -6.52938127932917 40 323.953 330.226214612662 -6.27321461266254 41 316.532 324.18030026829 -7.64830026828988 42 306.307 324.494133601623 -18.1871336016232 43 327.225 341.015133601623 -13.7901336016232 44 329.573 341.285633601623 -11.7126336016232 45 313.761 333.887133601623 -20.1261336016232 46 307.836 328.427633601623 -20.5916336016232 47 300.074 322.27830026829 -22.2043002682898 48 304.198 328.023633601623 -23.8256336016232 49 306.122 326.236166657051 -20.1141666570505 50 300.414 318.596139193399 -18.1821391933995 51 292.133 314.967972526733 -22.8349725267328 52 290.616 311.561805860066 -20.9458058600662 53 280.244 315.146377581929 -34.9023775819294 54 285.179 315.460210915263 -30.2812109152627 55 305.486 331.981210915263 -26.4952109152627 56 305.957 332.251710915263 -26.2947109152627 57 293.886 324.853210915263 -30.9672109152627 58 289.441 319.393710915263 -29.9527109152627 59 288.776 313.244377581929 -24.4683775819294 60 299.149 318.989710915263 -19.8407109152627 61 306.532 317.20224397069 -10.6702439706901 62 309.914 309.562216507039 0.351783492960995 63 313.468 305.934049840372 7.5339501596277 64 314.901 302.527883173706 12.3731168262943 65 309.16 296.481968829333 12.678031170667 66 316.15 296.795802162666 19.3541978373336 67 336.544 313.316802162666 23.2271978373336 68 339.196 313.587302162666 25.6086978373337 69 326.738 306.188802162666 20.5491978373336 70 320.838 300.729302162666 20.1086978373337 71 318.62 294.579968829333 24.040031170667 72 331.533 300.325302162666 31.2076978373337 73 335.378 298.537835218094 36.8401647819063 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 9.00208910280787e-05 0.000180041782056157 0.999909979108972 18 2.4131030518827e-05 4.8262061037654e-05 0.999975868969481 19 1.40471110705488e-06 2.80942221410977e-06 0.999998595288893 20 1.22981276788471e-07 2.45962553576942e-07 0.999999877018723 21 9.12901214212345e-08 1.82580242842469e-07 0.999999908709879 22 3.42759698565856e-05 6.85519397131712e-05 0.999965724030143 23 7.32471563773426e-05 0.000146494312754685 0.999926752843623 24 7.38444110392607e-05 0.000147688822078521 0.99992615558896 25 2.67449358866237e-05 5.34898717732475e-05 0.999973255064113 26 1.19833611639213e-05 2.39667223278426e-05 0.999988016638836 27 8.58191700531684e-06 1.71638340106337e-05 0.999991418082995 28 3.39802193531959e-06 6.79604387063918e-06 0.999996601978065 29 1.6085746310344e-06 3.2171492620688e-06 0.999998391425369 30 9.95498387234975e-07 1.99099677446995e-06 0.999999004501613 31 5.33879055853094e-07 1.06775811170619e-06 0.999999466120944 32 3.06508845170268e-07 6.13017690340536e-07 0.999999693491155 33 7.2271282749216e-07 1.44542565498432e-06 0.999999277287173 34 4.34063808228959e-05 8.68127616457918e-05 0.999956593619177 35 0.000748739020663584 0.00149747804132717 0.999251260979336 36 0.00794968778675096 0.0158993755735019 0.99205031221325 37 0.0283518461682531 0.0567036923365063 0.971648153831747 38 0.132726047106551 0.265452094213102 0.86727395289345 39 0.4326116926676 0.8652233853352 0.5673883073324 40 0.809454481410959 0.381091037178082 0.190545518589041 41 0.942823282077513 0.114353435844973 0.0571767179224866 42 0.972516043263558 0.0549679134728838 0.0274839567364419 43 0.981897617965762 0.036204764068476 0.018102382034238 44 0.990030145198153 0.0199397096036933 0.00996985480184666 45 0.99633289605923 0.00733420788154066 0.00366710394077033 46 0.999306820975637 0.00138635804872543 0.000693179024362714 47 0.99987799482309 0.000244010353819942 0.000122005176909971 48 0.999970205269955 5.95894600895687e-05 2.97947300447843e-05 49 0.9999996326085 7.34783001564008e-07 3.67391500782004e-07 50 0.999999999049314 1.90137277147092e-09 9.50686385735459e-10 51 0.999999994195528 1.16089445035575e-08 5.80447225177874e-09 52 0.999999915911455 1.68177090924744e-07 8.4088545462372e-08 53 0.999999478306883 1.04338623465317e-06 5.21693117326586e-07 54 0.999992198446221 1.56031075576671e-05 7.80155377883353e-06 55 0.999892932244835 0.000214135510330832 0.000107067755165416 56 0.999132564568438 0.00173487086312335 0.000867435431561675 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 31 0.775 NOK 5% type I error level 34 0.85 NOK 10% type I error level 36 0.9 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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