Paper - Regressie analyse 1

*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 17:40:20 +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/29/t12910524234e94j1je0othrgr.htm/, Retrieved Mon, 29 Nov 2010 18:40:23 +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/t12910524234e94j1je0othrgr.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:

» Textbox « » Textfile « » CSV «

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] = + 356.324723219141 -47.2761696574225x[t] + 4.83489668297991M1[t] -0.247528276237083M2[t] -3.87569494290376M3[t] -7.28186160957042M4[t] -3.84333333333333M5[t] -3.52950000000001M6[t] + 12.9915M7[t] + 13.262M8[t] + 5.86350000000001M9[t] + 0.403999999999995M10[t] -5.74533333333334M11[t] + 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) 356.324723219141 12.495476 28.5163 0 0 x -47.2761696574225 7.834731 -6.0342 0 0 M1 4.83489668297991 16.656573 0.2903 0.772611 0.386305 M2 -0.247528276237083 17.330271 -0.0143 0.988652 0.494326 M3 -3.87569494290376 17.330271 -0.2236 0.823799 0.4119 M4 -7.28186160957042 17.330271 -0.4202 0.675854 0.337927 M5 -3.84333333333333 17.281007 -0.2224 0.824756 0.412378 M6 -3.52950000000001 17.281007 -0.2042 0.838856 0.419428 M7 12.9915 17.281007 0.7518 0.455123 0.227561 M8 13.262 17.281007 0.7674 0.445834 0.222917 M9 5.86350000000001 17.281007 0.3393 0.735566 0.367783 M10 0.403999999999995 17.281007 0.0234 0.981426 0.490713 M11 -5.74533333333334 17.281007 -0.3325 0.740697 0.370348 Multiple Linear Regression - Regression Statistics Multiple R 0.629441199774032 R-squared 0.396196223972973 Adjusted R-squared 0.275435468767568 F-TEST (value) 3.28083592470974 F-TEST (DF numerator) 12 F-TEST (DF denominator) 60 p-value 0.00110070269154061 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 29.9315815992984 Sum Squared Residuals 53753.9746221275 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 376.974 361.159619902121 15.8143800978794 2 377.632 356.077194942904 21.5548050570963 3 378.205 352.449028276237 25.7559717237629 4 370.861 349.042861609570 21.8181383904296 5 369.167 352.481389885808 16.6856101141925 6 371.551 352.795223219141 18.7557767808592 7 382.842 369.316223219141 13.5257767808591 8 381.903 369.586723219141 12.3162767808592 9 384.502 362.188223219141 22.3137767808592 10 392.058 356.728723219141 35.3292767808591 11 384.359 350.579389885807 33.7796101141925 12 388.884 356.324723219141 32.5592767808592 13 386.586 361.159619902121 25.4263800978793 14 387.495 356.077194942904 31.4178050570962 15 385.705 352.449028276237 33.2559717237629 16 378.67 349.042861609570 29.6271383904296 17 377.367 352.481389885808 24.8856101141925 18 376.911 352.795223219141 24.1157767808592 19 389.827 369.316223219141 20.5107767808592 20 387.82 369.586723219141 18.2332767808591 21 387.267 362.188223219141 25.0787767808592 22 380.575 356.728723219141 23.8462767808592 23 372.402 350.579389885807 21.8226101141925 24 376.74 356.324723219141 20.4152767808592 25 377.795 361.159619902121 16.6353800978793 26 376.126 356.077194942904 20.0488050570962 27 370.804 352.449028276237 18.3549717237629 28 367.98 349.042861609570 18.9371383904296 29 367.866 352.481389885808 15.3846101141925 30 366.121 352.795223219141 13.3257767808592 31 379.421 369.316223219141 10.1047767808592 32 378.519 369.586723219141 8.93227678085917 33 372.423 362.188223219141 10.2347767808592 34 355.072 356.728723219141 -1.65672321914083 35 344.693 350.579389885807 -5.88638988580751 36 342.892 356.324723219141 -13.4327232191408 37 344.178 361.159619902121 -16.9816199021207 38 337.606 356.077194942904 -18.4711949429038 39 327.103 352.449028276237 -25.3460282762371 40 323.953 349.042861609570 -25.0898616095704 41 316.532 352.481389885808 -35.9493898858075 42 306.307 352.795223219141 -46.4882232191408 43 327.225 369.316223219141 -42.0912232191408 44 329.573 369.586723219141 -40.0137232191409 45 313.761 362.188223219141 -48.4272232191408 46 307.836 356.728723219141 -48.8927232191408 47 300.074 350.579389885808 -50.5053898858075 48 304.198 356.324723219141 -52.1267232191409 49 306.122 361.159619902121 -55.0376199021207 50 300.414 356.077194942904 -55.6631949429038 51 292.133 352.449028276237 -60.3160282762371 52 290.616 349.042861609570 -58.4268616095704 53 280.244 305.205220228385 -24.9612202283850 54 285.179 305.519053561718 -20.3400535617183 55 305.486 322.040053561718 -16.5540535617183 56 305.957 322.310553561718 -16.3535535617183 57 293.886 314.912053561718 -21.0260535617183 58 289.441 309.452553561718 -20.0115535617184 59 288.776 303.303220228385 -14.5272202283850 60 299.149 309.048553561718 -9.89955356171833 61 306.532 313.883450244698 -7.35145024469825 62 309.914 308.801025285481 1.11297471451875 63 313.468 305.172858618815 8.29514138118545 64 314.901 301.766691952148 13.1343080478521 65 309.16 305.205220228385 3.95477977161503 66 316.15 305.519053561718 10.6309464382817 67 336.544 322.040053561718 14.5039464382817 68 339.196 322.310553561718 16.8854464382817 69 326.738 314.912053561718 11.8259464382817 70 320.838 309.452553561718 11.3854464382817 71 318.62 303.303220228385 15.3167797716150 72 331.533 309.048553561718 22.4844464382817 73 335.378 313.883450244698 21.4945497553017 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0187919702669659 0.0375839405339319 0.981208029733034 17 0.00566522655720795 0.0113304531144159 0.994334773442792 18 0.00143012353782181 0.00286024707564362 0.998569876462178 19 0.000402412940816499 0.000804825881632998 0.999597587059184 20 0.000103692575188188 0.000207385150376377 0.999896307424812 21 2.37953119736558e-05 4.75906239473116e-05 0.999976204688026 22 1.46476607274314e-05 2.92953214548629e-05 0.999985352339273 23 9.53215314877334e-06 1.90643062975467e-05 0.999990467846851 24 6.3584810796821e-06 1.27169621593642e-05 0.99999364151892 25 2.08350156700545e-06 4.16700313401091e-06 0.999997916498433 26 1.02378795540929e-06 2.04757591081858e-06 0.999998976212045 27 1.07671655477731e-06 2.15343310955463e-06 0.999998923283445 28 6.73851186899095e-07 1.34770237379819e-06 0.999999326148813 29 4.45385063188968e-07 8.90770126377936e-07 0.999999554614937 30 4.5333326737845e-07 9.066665347569e-07 0.999999546666733 31 3.91443143818547e-07 7.82886287637094e-07 0.999999608556856 32 3.58852209148264e-07 7.17704418296528e-07 0.99999964114779 33 1.81888303491693e-06 3.63776606983385e-06 0.999998181116965 34 0.000203043717351516 0.000406087434703032 0.999796956282649 35 0.00411132111031301 0.00822264222062601 0.995888678889687 36 0.0346566258467076 0.0693132516934153 0.965343374153292 37 0.106392263738071 0.212784527476141 0.89360773626193 38 0.292429281994899 0.584858563989798 0.707570718005101 39 0.544511180672736 0.910977638654528 0.455488819327264 40 0.699952833616599 0.600094332766801 0.300047166383401 41 0.838103223072391 0.323793553855218 0.161896776927609 42 0.909379329473689 0.181241341052622 0.090620670526311 43 0.930639502339951 0.138720995320098 0.0693604976600488 44 0.940027237730817 0.119945524538365 0.0599727622691827 45 0.955056861848616 0.089886276302768 0.044943138151384 46 0.963006425764777 0.0739871484704465 0.0369935742352233 47 0.963382480684975 0.0732350386300496 0.0366175193150248 48 0.95742213917194 0.0851557216561188 0.0425778608280594 49 0.94786215991361 0.104275680172779 0.0521378400863893 50 0.937479495393227 0.125041009213546 0.0625205046067731 51 0.91997512653909 0.160049746921820 0.0800248734609099 52 0.890220172053447 0.219559655893106 0.109779827946553 53 0.85390249730763 0.292195005384739 0.146097502692370 54 0.813450288228002 0.373099423543996 0.186549711771998 55 0.762939040879797 0.474121918240406 0.237060959120203 56 0.709429211122149 0.581141577755703 0.290570788877851 57 0.638429260615657 0.723141478768685 0.361570739384343 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.428571428571429 NOK 5% type I error level 20 0.476190476190476 NOK 10% type I error level 25 0.595238095238095 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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