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: Fri, 20 Nov 2009 12:37:54 -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/Nov/20/t1258745941k6e4mbreexgnz7h.htm/, Retrieved Fri, 20 Nov 2009 20:39:13 +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/Nov/20/t1258745941k6e4mbreexgnz7h.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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461 1870 455 462 461 2263 461 455 463 1802 461 461 462 1863 463 461 456 1989 462 463 455 2197 456 462 456 2409 455 456 472 2502 456 455 472 2593 472 456 471 2598 472 472 465 2053 471 472 459 2213 465 471 465 2238 459 465 468 2359 465 459 467 2151 468 465 463 2474 467 468 460 3079 463 467 462 2312 460 463 461 2565 462 460 476 1972 461 462 476 2484 476 461 471 2202 476 476 453 2151 471 476 443 1976 453 471 442 2012 443 453 444 2114 442 443 438 1772 444 442 427 1957 438 444 424 2070 427 438 416 1990 424 427 406 2182 416 424 431 2008 406 416 434 1916 431 406 418 2397 434 431 412 2114 418 434 404 1778 412 418 409 1641 404 412 412 2186 409 404 406 1773 412 409 398 1785 406 412 397 2217 398 406 385 2153 397 398 390 1895 385 397 413 2475 390 385 413 1793 413 390 401 2308 413 413 397 2051 401 413 397 1898 397 401 409 2142 397 397 419 1874 409 397 424 1560 419 409 428 1808 424 419 430 1575 428 424 424 1525 430 428 433 1997 424 430 456 1753 433 424 459 1623 456 433 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] = -4.01215883998919 -0.000280109648396460bvg[t] + 1.15480150856078Y1[t] -0.157907674857242Y2[t] + 11.448070491494M1[t] + 7.6106411436112M2[t] + 2.9987316791792M3[t] + 0.957862399611235M4[t] + 3.20446919765004M5[t] + 0.0296764049751569M6[t] + 6.26354126481267M7[t] + 24.8896853724151M8[t] + 2.59965723779642M9[t] -4.93086736514187M10[t] -1.81164970260289M11[t] + 0.0415408990311207t + 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) -4.01215883998919 20.454621 -0.1961 0.845417 0.422709 bvg -0.000280109648396460 0.003006 -0.0932 0.926199 0.463099 Y1 1.15480150856078 0.150984 7.6485 0 0 Y2 -0.157907674857242 0.156917 -1.0063 0.319896 0.159948 M1 11.448070491494 3.431728 3.3359 0.00176 0.00088 M2 7.6106411436112 4.099468 1.8565 0.070243 0.035121 M3 2.9987316791792 3.898325 0.7692 0.445958 0.222979 M4 0.957862399611235 3.567971 0.2685 0.789628 0.394814 M5 3.20446919765004 3.520117 0.9103 0.367723 0.183862 M6 0.0296764049751569 3.53216 0.0084 0.993335 0.496668 M7 6.26354126481267 3.522985 1.7779 0.082491 0.041246 M8 24.8896853724151 3.739534 6.6558 0 0 M9 2.59965723779642 5.55097 0.4683 0.641918 0.320959 M10 -4.93086736514187 3.949867 -1.2484 0.218653 0.109326 M11 -1.81164970260289 3.481531 -0.5204 0.605482 0.302741 t 0.0415408990311207 0.067318 0.6171 0.540433 0.270216 Multiple Linear Regression - Regression Statistics Multiple R 0.986330732011576 R-squared 0.972848312910491 Adjusted R-squared 0.963376794158337 F-TEST (value) 102.713021888831 F-TEST (DF numerator) 15 F-TEST (DF denominator) 43 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.04826909520104 Sum Squared Residuals 1095.85589687516 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 461 459.434988119143 1.56501188085739 2 461 463.563179353837 -2.56317935383657 3 463 458.174495287203 4.82550471279691 4 462 458.467683235236 3.53231676476441 5 456 459.249920258332 -3.24992025833231 6 455 449.287504181315 5.71249581868537 7 456 455.296171235306 0.703828764694123 8 472 475.250515228057 -3.25051522805659 9 472 471.29545447658 0.704545523419844 10 471 461.278547426715 9.72145257328487 11 465 463.437164238101 1.56283576189946 12 459 458.474635919484 0.525364080516317 13 465 463.975881566578 1.02411843342234 14 468 468.022354950778 -0.0223549507781517 15 467 466.027207668783 0.972792331217376 16 463 462.308879338681 0.691120661318806 17 460 459.966262339085 0.0337376609146295 18 462 454.215080719508 7.78491928049164 19 461 463.202944779026 -2.20294477902595 20 476 480.566117948883 -4.56611794888338 21 476 475.654144876586 0.345855123414272 22 471 465.875536970668 5.12446302933226 23 453 463.276573581502 -10.2765735815022 24 443 445.181894591798 -2.18189459179776 25 442 447.955745096803 -5.95574509680317 26 444 444.555560703827 -0.555560703826707 27 438 442.548500330156 -4.54850033015622 28 427 433.252727263587 -6.25272726358687 29 424 423.753852025363 0.246147974637118 30 416 418.915588801338 -2.91558880133817 31 406 416.3725244638 -10.3725244638002 32 431 424.804194862505 6.19580513749513 33 434 433.030592177162 0.969407822838323 34 418 424.923588386627 -6.92358838662707 35 412 409.213070817149 2.78692918285082 36 404 406.758092006996 -2.75809200699563 37 409 409.995112400008 -0.995112400008286 38 412 413.083833134442 -1.08383313444235 39 406 411.304016005225 -5.30401600522536 40 398 401.898794232971 -3.89879423297135 41 397 395.774968542591 1.22503145740878 42 385 392.768103556742 -7.76810355674199 43 390 385.416067177025 4.5839328229752 44 413 411.590188228679 1.40981177132079 45 413 415.30363209591 -2.30363209590975 46 401 404.038515401362 -3.03851540136181 47 397 393.41364403984 3.58635596015953 48 397 392.585377481723 4.41462251827706 49 409 404.638272817468 4.36172718253173 50 419 414.775071857116 4.22492814288378 51 424 419.945780708633 4.05421929136729 52 428 422.071915929525 5.928084070475 53 430 428.254996834628 1.74500316537178 54 424 426.813722741097 -2.81372274109687 55 433 425.712292344843 7.2877076551568 56 456 455.788983731876 0.211016268124042 57 459 458.716176373763 0.283823626237321 58 446 450.883811814628 -4.88381181462826 59 441 438.659547323408 2.34045267659235 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.0117706822355485 0.0235413644710969 0.988229317764452 20 0.00226135138533448 0.00452270277066896 0.997738648614666 21 0.000517123244952553 0.00103424648990511 0.999482876755047 22 0.0190381692260883 0.0380763384521767 0.980961830773912 23 0.310082330915587 0.620164661831174 0.689917669084413 24 0.229476887439123 0.458953774878245 0.770523112560877 25 0.17508936642015 0.3501787328403 0.82491063357985 26 0.192054371172327 0.384108742344654 0.807945628827673 27 0.154229045065239 0.308458090130478 0.845770954934761 28 0.112840068647842 0.225680137295684 0.887159931352158 29 0.152415879541353 0.304831759082706 0.847584120458647 30 0.173681865769602 0.347363731539204 0.826318134230398 31 0.35616476221701 0.71232952443402 0.64383523778299 32 0.956407737092184 0.0871845258156331 0.0435922629078166 33 0.956247098943606 0.0875058021127881 0.0437529010563940 34 0.958390964811724 0.0832180703765518 0.0416090351882759 35 0.983807158870345 0.0323856822593108 0.0161928411296554 36 0.965001054822588 0.0699978903548239 0.0349989451774120 37 0.970461333219701 0.0590773335605973 0.0295386667802987 38 0.98624742175923 0.0275051564815399 0.0137525782407699 39 0.992765328746094 0.0144693425078121 0.00723467125390604 40 0.969693894140539 0.060612211718922 0.030306105859461 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.090909090909091 NOK 5% type I error level 7 0.318181818181818 NOK 10% type I error level 13 0.590909090909091 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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