multiple regression toevoeging variabele uit het verleden

*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 12:14:20 -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/t1258744810zca9ti5ifyno8wr.htm/, Retrieved Fri, 20 Nov 2009 20:20:21 +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/t1258744810zca9ti5ifyno8wr.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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463 1802 461 461 455 462 462 1863 463 461 461 455 456 1989 462 463 461 461 455 2197 456 462 463 461 456 2409 455 456 462 463 472 2502 456 455 456 462 472 2593 472 456 455 456 471 2598 472 472 456 455 465 2053 471 472 472 456 459 2213 465 471 472 472 465 2238 459 465 471 472 468 2359 465 459 465 471 467 2151 468 465 459 465 463 2474 467 468 465 459 460 3079 463 467 468 465 462 2312 460 463 467 468 461 2565 462 460 463 467 476 1972 461 462 460 463 476 2484 476 461 462 460 471 2202 476 476 461 462 453 2151 471 476 476 461 443 1976 453 471 476 476 442 2012 443 453 471 476 444 2114 442 443 453 471 438 1772 444 442 443 453 427 1957 438 444 442 443 424 2070 427 438 444 442 416 1990 424 427 438 444 406 2182 416 424 427 438 431 2008 406 416 424 427 434 1916 431 406 416 424 418 2397 434 431 406 416 412 2114 418 434 431 406 404 1778 412 418 434 431 409 1641 404 412 418 434 412 2186 409 404 412 418 406 1773 412 409 404 412 398 1785 406 412 409 404 397 2217 398 406 412 409 385 2153 3 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] = + 38.5210955524794 -0.00152089568579747bvg[t] + 1.09898403346457Y1[t] -0.082394676964828Y2[t] + 0.409148238270283Y3[t] -0.483746709978272Y4[t] -7.65892149435435M1[t] -15.0130071036027M2[t] -11.2938298789452M3[t] -12.1334166166230M4[t] -4.62991986405527M5[t] + 13.4100542052650M6[t] -6.78455588173178M7[t] -18.0900002095661M8[t] -23.8068515987059M9[t] -12.9528577185224M10[t] + 2.41394734964293M11[t] -0.0688079449944023t + 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) 38.5210955524794 22.308104 1.7268 0.092122 0.046061 bvg -0.00152089568579747 0.002951 -0.5154 0.60919 0.304595 Y1 1.09898403346457 0.143791 7.643 0 0 Y2 -0.082394676964828 0.22076 -0.3732 0.710998 0.355499 Y3 0.409148238270283 0.226494 1.8064 0.07857 0.039285 Y4 -0.483746709978272 0.157295 -3.0754 0.00383 0.001915 M1 -7.65892149435435 3.784777 -2.0236 0.049901 0.02495 M2 -15.0130071036027 4.295187 -3.4953 0.001196 0.000598 M3 -11.2938298789452 4.014019 -2.8136 0.007636 0.003818 M4 -12.1334166166230 3.601294 -3.3692 0.001709 0.000854 M5 -4.62991986405527 3.654506 -1.2669 0.212702 0.106351 M6 13.4100542052650 3.392235 3.9532 0.000315 0.000157 M7 -6.78455588173178 3.848867 -1.7627 0.08578 0.04289 M8 -18.0900002095661 5.252776 -3.4439 0.001384 0.000692 M9 -23.8068515987059 5.934347 -4.0117 0.000264 0.000132 M10 -12.9528577185224 4.268398 -3.0346 0.004274 0.002137 M11 2.41394734964293 3.746094 0.6444 0.523095 0.261547 t -0.0688079449944023 0.075876 -0.9068 0.370056 0.185028 Multiple Linear Regression - Regression Statistics Multiple R 0.988899182665083 R-squared 0.97792159347567 Adjusted R-squared 0.968297672683013 F-TEST (value) 101.613636951569 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.71069167719526 Sum Squared Residuals 865.434027026272 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 463 459.371873836721 3.62812616327886 2 462 459.895290112043 2.10470988795653 3 456 459.187772888032 -3.18777288803227 4 455 452.269818855432 2.7301811445679 5 456 457.400820147714 -1.40082014771398 6 472 474.440778964047 -2.44077896404659 7 472 474.033641304716 -2.03364130471551 8 471 462.226364670269 8.7736353297309 9 465 462.233234553776 2.76676544622374 10 459 458.523620295763 0.476379704237281 11 465 467.27491064952 -2.27491064952004 12 468 469.725256519834 -1.72525651983418 13 467 465.564048251984 1.43595174801603 14 463 461.661107016361 1.33889298363914 15 460 458.402757404164 1.59724259583569 16 462 453.833127951759 8.16687204824076 17 461 462.175336005547 -1.1753360055466 18 476 480.492162009258 -4.49216200925834 19 476 478.286737171548 -2.28673717154764 20 471 464.728815669415 6.27118433058544 21 453 460.146772131966 -7.14677213196571 22 443 444.572174944957 -1.57217494495710 23 442 448.262942482809 -6.26294248280918 24 444 440.40408382543 3.59591617456951 25 438 440.092821851425 -2.09282185142451 26 427 430.058187902105 -3.05818790210455 27 424 423.24428284947 0.755717150529872 28 416 416.644566318303 -0.644566318302859 29 406 413.644404556278 -7.64440455627754 30 431 425.643292705955 5.35670729404479 31 434 431.996398907092 2.00360109290750 32 418 420.906172282792 -2.90617228279153 33 412 412.78617091795 -0.786170917950232 34 404 407.940565399571 -3.94056539957111 35 409 407.151809083509 1.8481909164906 36 412 415.279301153185 -3.27930115318458 37 406 410.693974701347 -4.69397470134713 38 398 402.32745703837 -4.32745703837046 39 397 395.832006340761 1.16799365923901 40 385 390.674992804677 -5.67499280467734 41 390 385.025953328284 4.9740466717162 42 413 412.059481687304 0.940518312696215 43 413 413.271941748622 -0.271941748622342 44 401 407.070052338508 -6.07005233850753 45 397 395.479130724374 1.52086927562637 46 397 391.963639359709 5.03636064029093 47 409 402.310337784161 6.68966221583862 48 419 417.591358501551 1.40864149844925 49 424 422.277281358523 1.72271864147675 50 428 424.057957931121 3.94204206887936 51 430 430.333180517572 -0.333180517572299 52 424 428.577494069828 -4.57749406982845 53 433 427.753485962178 5.24651403782191 54 456 455.364284633436 0.635715366563918 55 459 456.411280868022 2.588719131978 56 446 452.068595039017 -6.06859503901729 57 441 437.354691671934 3.64530832806583 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.50727684712697 0.98544630574606 0.49272315287303 22 0.413092348982315 0.82618469796463 0.586907651017685 23 0.359773217904678 0.719546435809355 0.640226782095322 24 0.401480106737047 0.802960213474095 0.598519893262953 25 0.325812235902037 0.651624471804075 0.674187764097963 26 0.215854766906257 0.431709533812513 0.784145233093743 27 0.253765663876886 0.507531327753773 0.746234336123114 28 0.313846253597398 0.627692507194797 0.686153746402602 29 0.484639349196203 0.969278698392407 0.515360650803797 30 0.89555664116932 0.208886717661359 0.104443358830679 31 0.989837169542928 0.0203256609141437 0.0101628304570718 32 0.980980072592555 0.0380398548148891 0.0190199274074445 33 0.954443894920125 0.0911122101597489 0.0455561050798744 34 0.92238308259875 0.155233834802499 0.0776169174012495 35 0.956259521417266 0.0874809571654685 0.0437404785827342 36 0.950274280638667 0.099451438722667 0.0497257193613335 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 2 0.125 NOK 10% type I error level 5 0.3125 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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