multiple regression toevoeging variabele uit het verleden 2 periodes terug in de tijd

*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, 14 Dec 2009 12:59:10 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/14/t1260820774tef8n6nrg1rpd0k.htm/, Retrieved Mon, 14 Dec 2009 20:59:46 +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/2009/Dec/14/t1260820774tef8n6nrg1rpd0k.htm/}, year = {2009}, } @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 = {2009}, 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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452 1870 449 441 462 2263 452 449 455 1802 462 452 461 1863 455 462 461 1989 461 455 463 2197 461 461 462 2409 463 461 456 2502 462 463 455 2593 456 462 456 2598 455 456 472 2053 456 455 472 2213 472 456 471 2238 472 472 465 2359 471 472 459 2151 465 471 465 2474 459 465 468 3079 465 459 467 2312 468 465 463 2565 467 468 460 1972 463 467 462 2484 460 463 461 2202 462 460 476 2151 461 462 476 1976 476 461 471 2012 476 476 453 2114 471 476 443 1772 453 471 442 1957 443 453 444 2070 442 443 438 1990 444 442 427 2182 438 444 424 2008 427 438 416 1916 424 427 406 2397 416 424 431 2114 406 416 434 1778 431 406 418 1641 434 431 412 2186 418 434 404 1773 412 418 409 1785 404 412 412 2217 409 404 406 2153 412 409 398 1895 406 412 397 2475 398 406 385 1793 397 398 390 2308 385 397 413 2051 390 385 413 1898 413 390 401 2142 413 413 397 1874 401 413 397 1560 397 401 409 1808 397 397 419 1575 409 397 424 1525 419 409 428 1997 424 419 430 1753 428 424 424 1623 430 428 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation wkl[t] = + 14.1829759293675 + 0.00268635618666913bvg[t] + 1.29322834059705Y1[t] -0.348397687511171Y2[t] -0.976702766630424M1[t] + 2.55733833239759M2[t] + 1.36787980492116M3[t] + 12.8975224505603M4[t] + 6.56433786984919M5[t] + 3.09364182521555M6[t] + 1.46111795099527M7[t] + 4.22688545632968M8[t] + 0.869449387776794M9[t] + 6.67474551128959M10[t] + 25.1318031332856M11[t] -0.0293336897408048t + 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) 14.1829759293675 23.730103 0.5977 0.553189 0.276595 bvg 0.00268635618666913 0.003438 0.7814 0.438834 0.219417 Y1 1.29322834059705 0.147281 8.7807 0 0 Y2 -0.348397687511171 0.147768 -2.3577 0.023006 0.011503 M1 -0.976702766630424 4.5515 -0.2146 0.831102 0.415551 M2 2.55733833239759 5.248527 0.4872 0.628557 0.314278 M3 1.36787980492116 5.313725 0.2574 0.798079 0.39904 M4 12.8975224505603 5.322429 2.4232 0.019666 0.009833 M5 6.56433786984919 4.248698 1.545 0.129669 0.064835 M6 3.09364182521555 4.387333 0.7051 0.484531 0.242266 M7 1.46111795099527 4.76278 0.3068 0.760493 0.380246 M8 4.22688545632968 5.019576 0.8421 0.404402 0.202201 M9 0.869449387776794 4.860084 0.1789 0.85886 0.42943 M10 6.67474551128959 5.146016 1.2971 0.201524 0.100762 M11 25.1318031332856 4.604406 5.4582 2e-06 1e-06 t -0.0293336897408048 0.076274 -0.3846 0.702441 0.351221 Multiple Linear Regression - Regression Statistics Multiple R 0.983592476882252 R-squared 0.967454160579364 Adjusted R-squared 0.956100960781468 F-TEST (value) 85.214228393887 F-TEST (DF numerator) 15 F-TEST (DF denominator) 43 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.56592155017987 Sum Squared Residuals 1332.11775621854 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 452 445.216570277716 6.78342972228414 2 462 450.869519190066 11.1304808099344 3 455 460.299407114231 -5.2994071142308 4 461 459.427008538225 1.57299146177506 5 461 463.601125003454 -2.60112500345382 6 463 458.569471230840 4.43052876916047 7 462 460.063577859646 1.93642214035361 8 456 461.059819084981 -5.05981908498085 9 455 450.506535383603 4.49346461639707 10 456 457.093087382778 -1.09308738277824 11 472 475.698373221407 -3.69837322140704 12 472 471.310309150289 0.689690849710761 13 471 464.797068598406 6.202931401594 14 465 467.333596765683 -2.33359676568312 15 459 458.145070105568 0.8549298944324 16 465 464.844088191245 0.155911808755206 17 468 469.956571582377 -1.95657158237703 18 467 466.185405549551 0.81459445044852 19 463 462.864774697687 0.135225302312889 20 460 459.183683619709 0.816316380291088 21 462 454.686233957243 7.31376604275664 22 461 463.336293690102 -2.33629369010226 23 476 479.636989741218 -3.63698974121799 24 476 473.752563381991 2.24743661800868 25 471 467.617270435673 3.38272956432737 26 453 464.929844473015 -11.9298444730149 27 443 441.256196746766 1.74380325323422 28 442 446.592356566429 -4.59235656642849 29 444 442.724145079585 1.27585492041514 30 438 441.944061218982 -3.94406121898215 31 427 432.341818624257 -5.34181862425691 32 424 422.47570084187 1.52429915813040 33 416 418.794475855234 -2.79447585523408 34 406 416.561941952551 -10.5619419525511 35 431 424.084325178098 6.91567482190215 36 434 433.835258066388 0.164741933611551 37 418 427.630933646455 -9.63093364645542 38 412 410.862858665391 1.13714133460895 39 404 406.349594299676 -2.34959429967591 40 409 409.626698930105 -0.626698930104898 41 412 413.678009735369 -1.67800973536868 42 406 412.143749789283 -6.1437497892827 43 398 400.984249223045 -2.98424922304517 44 397 397.023329027198 -0.0233290271975336 45 385 393.298417509088 -8.2984175090878 46 390 385.287510979341 4.71248902065898 47 413 413.671755324742 -0.671755324741569 48 413 416.101869401331 -3.10186940133097 49 401 407.73815704175 -6.73815704175009 50 397 395.004180905845 1.99581909415459 51 397 391.94973173376 5.05026826624008 52 409 405.509847773997 3.49015222600313 53 419 414.040148599216 4.95985140078437 54 424 419.157312211344 4.84268778865585 55 428 421.745579595364 6.25442040463558 56 430 427.257467426243 2.74253257375690 57 424 424.714337294832 -0.714337294831822 58 433 423.721165995227 9.27883400477259 59 456 454.908556534536 1.09144346546445 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.24207247956577 0.48414495913154 0.75792752043423 20 0.234180244660917 0.468360489321835 0.765819755339083 21 0.289487140338802 0.578974280677603 0.710512859661198 22 0.200220846414650 0.400441692829301 0.79977915358535 23 0.115943065668301 0.231886131336602 0.884056934331699 24 0.0631455080387463 0.126291016077493 0.936854491961254 25 0.130604593187146 0.261209186374293 0.869395406812854 26 0.748127411261518 0.503745177476963 0.251872588738482 27 0.661312189240779 0.677375621518443 0.338687810759221 28 0.674963368380459 0.650073263239082 0.325036631619541 29 0.574148412912715 0.85170317417457 0.425851587087285 30 0.529158401461126 0.941683197077747 0.470841598538874 31 0.492851717631697 0.985703435263394 0.507148282368303 32 0.392723840568664 0.785447681137328 0.607276159431336 33 0.487565022004941 0.975130044009882 0.512434977995059 34 0.651374037028129 0.697251925943742 0.348625962971871 35 0.925784345714922 0.148431308570156 0.0742156542850778 36 0.940453920711118 0.119092158577765 0.0595460792888824 37 0.916756959707875 0.166486080584251 0.0832430402921253 38 0.93207140585536 0.135857188289281 0.0679285941446407 39 0.856889538557479 0.286220922885043 0.143110461442521 40 0.91397096831126 0.172058063377481 0.0860290316887407 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

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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