verbetering evelyn ongena 3e stap

*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, 28 Nov 2008 02:16:12 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/28/t1227864094ys9u1fvepfxr8v8.htm/, Retrieved Fri, 28 Nov 2008 09:21:35 +0000

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/2008/Nov/28/t1227864094ys9u1fvepfxr8v8.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

46 0 48 0 48 0 48 0 45 0 44 0 45 0 45 0 45 0 42 0 43 0 50 0 46 0 46 0 45 0 49 0 46 0 45 0 49 0 47 0 45 0 48 0 51 0 48 0 49 0 51 0 54 0 52 0 52 0 53 0 51 0 55 0 53 0 51 0 52 0 54 0 58 0 57 0 52 0 50 0 53 0 50 0 50 0 51 0 53 0 49 0 54 0 57 0 58 0 56 0 60 0 55 0 54 0 52 0 55 0 56 0 54 0 53 0 59 1 62 1 63 1 64 1 75 1 77 1 79 1 77 1 82 1 83 1 81 1 78 1 79 1 79 1 73 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 11 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 43.739298110297 + 15.6259159274971d[t] -0.329075839102828M1[t] + 0.172270888044125M2[t] + 1.94880906469800M3[t] + 1.22534724135187M4[t] + 0.668552084672409M5[t] -0.88824307200705M6[t] + 0.721628437980155M7[t] + 1.33149994796736M8[t] + 0.108038124621234M9[t] -1.78209036539156M10[t] -1.77653817665387M11[t] + 0.223461823346127t + 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) 43.739298110297 2.013167 21.7266 0 0 d 15.6259159274971 1.726531 9.0505 0 0 M1 -0.329075839102828 2.332384 -0.1411 0.88828 0.44414 M2 0.172270888044125 2.429146 0.0709 0.943703 0.471851 M3 1.94880906469800 2.427632 0.8028 0.425335 0.212667 M4 1.22534724135187 2.426566 0.505 0.61546 0.30773 M5 0.668552084672409 2.425948 0.2756 0.783831 0.391915 M6 -0.88824307200705 2.425779 -0.3662 0.715549 0.357775 M7 0.721628437980155 2.426059 0.2974 0.767169 0.383584 M8 1.33149994796736 2.426787 0.5487 0.585304 0.292652 M9 0.108038124621234 2.427963 0.0445 0.964658 0.482329 M10 -1.78209036539156 2.429587 -0.7335 0.466161 0.233081 M11 -1.77653817665387 2.417331 -0.7349 0.465301 0.232651 t 0.223461823346127 0.032994 6.7729 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.937608765469224 R-squared 0.879110197084723 Adjusted R-squared 0.852473460849154 F-TEST (value) 33.0036754244238 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.18654953257768 Sum Squared Residuals 1034.10462233486 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 46 43.6336840945402 2.36631590545979 2 48 44.3584926450333 3.64150735496667 3 48 46.3584926450333 1.64150735496667 4 48 45.8584926450333 2.14150735496667 5 45 45.5251593117 -0.5251593117 6 44 44.1918259783667 -0.191825978366664 7 45 46.0251593117 -1.0251593117 8 45 46.8584926450333 -1.85849264503333 9 45 45.8584926450333 -0.858492645033332 10 42 44.1918259783667 -2.19182597836667 11 43 44.4208399904505 -1.42083999045048 12 50 46.4208399904505 3.57916000954952 13 46 46.3152259746938 -0.315225974693781 14 46 47.0400345251869 -1.04003452518687 15 45 49.0400345251869 -4.04003452518686 16 49 48.5400345251869 0.45996547481314 17 46 48.2067011918535 -2.20670119185353 18 45 46.8733678585202 -1.87336785852019 19 49 48.7067011918535 0.293298808146473 20 47 49.5400345251869 -2.54003452518686 21 45 48.5400345251869 -3.54003452518686 22 48 46.8733678585202 1.12663214147981 23 51 47.102381870604 3.89761812939599 24 48 49.102381870604 -1.10238187060401 25 49 48.9967678548473 0.00323214515269319 26 51 49.7215764053404 1.27842359465961 27 54 51.7215764053404 2.27842359465962 28 52 51.2215764053404 0.778423594659613 29 52 50.888243072007 1.11175692799295 30 53 49.5549097386737 3.44509026132628 31 51 51.388243072007 -0.388243072007053 32 55 52.2215764053404 2.77842359465961 33 53 51.2215764053404 1.77842359465961 34 51 49.5549097386737 1.44509026132628 35 52 49.7839237507575 2.21607624924247 36 54 51.7839237507575 2.21607624924247 37 58 51.6783097350008 6.32169026499917 38 57 52.4031182854939 4.59688171450609 39 52 54.4031182854939 -2.40311828549391 40 50 53.9031182854939 -3.90311828549391 41 53 53.5697849521606 -0.569784952160578 42 50 52.2364516188272 -2.23645161882724 43 50 54.0697849521606 -4.06978495216058 44 51 54.9031182854939 -3.90311828549391 45 53 53.9031182854939 -0.90311828549391 46 49 52.2364516188272 -3.23645161882724 47 54 52.4654656309111 1.53453436908894 48 57 54.4654656309111 2.53453436908894 49 58 54.3598516151544 3.64014838484564 50 56 55.0846601656474 0.915339834352563 51 60 57.0846601656474 2.91533983435256 52 55 56.5846601656474 -1.58466016564744 53 54 56.2513268323141 -2.25132683231410 54 52 54.9179934989808 -2.91799349898077 55 55 56.7513268323141 -1.75132683231410 56 56 57.5846601656474 -1.58466016564744 57 54 56.5846601656474 -2.58466016564744 58 53 54.9179934989808 -1.91799349898077 59 59 70.7729234385617 -11.7729234385617 60 62 72.7729234385617 -10.7729234385617 61 63 72.667309422805 -9.667309422805 62 64 73.392117973298 -9.39211797329807 63 75 75.392117973298 -0.392117973298072 64 77 74.892117973298 2.10788202670193 65 79 74.5587846399647 4.44121536003526 66 77 73.2254513066314 3.77454869336859 67 82 75.0587846399647 6.94121536003526 68 83 75.892117973298 7.10788202670193 69 81 74.892117973298 6.10788202670193 70 78 73.2254513066314 4.77454869336859 71 79 73.4544653187152 5.54553468128478 72 79 75.4544653187152 3.54553468128478 73 73 75.3488513029585 -2.34885130295852 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0390302848683057 0.0780605697366115 0.960969715131694 18 0.0129086984794576 0.0258173969589152 0.987091301520542 19 0.0162409141781781 0.0324818283563563 0.983759085821822 20 0.00644075738796314 0.0128815147759263 0.993559242612037 21 0.00212143271390563 0.00424286542781125 0.997878567286094 22 0.00494020853083222 0.00988041706166445 0.995059791469168 23 0.0136725100044509 0.0273450200089017 0.98632748999555 24 0.00904143715337014 0.0180828743067403 0.99095856284663 25 0.00404214974776842 0.00808429949553684 0.995957850252232 26 0.00194474640111277 0.00388949280222553 0.998055253598887 27 0.00227961616200582 0.00455923232401165 0.997720383837994 28 0.000968051053870408 0.00193610210774082 0.99903194894613 29 0.000615402648378194 0.00123080529675639 0.999384597351622 30 0.000721073735693396 0.00144214747138679 0.999278926264307 31 0.000296136960315883 0.000592273920631766 0.999703863039684 32 0.000324614016942985 0.00064922803388597 0.999675385983057 33 0.000214486959203180 0.000428973918406359 0.999785513040797 34 9.68672556483563e-05 0.000193734511296713 0.999903132744352 35 4.60689017953312e-05 9.21378035906625e-05 0.999953931098205 36 2.30714653782003e-05 4.61429307564006e-05 0.999976928534622 37 8.65709707487256e-05 0.000173141941497451 0.999913429029251 38 0.000174347207771754 0.000348694415543509 0.999825652792228 39 0.000149766845445165 0.00029953369089033 0.999850233154555 40 0.000282705915676223 0.000565411831352446 0.999717294084324 41 0.000142477900598374 0.000284955801196749 0.999857522099402 42 9.9313188453348e-05 0.000198626376906696 0.999900686811547 43 7.6037030907398e-05 0.000152074061814796 0.999923962969093 44 4.8381496039591e-05 9.6762992079182e-05 0.99995161850396 45 2.10483841499874e-05 4.20967682999748e-05 0.99997895161585 46 1.20446919377020e-05 2.40893838754040e-05 0.999987955308062 47 1.06060580489942e-05 2.12121160979885e-05 0.99998939394195 48 2.73047031717499e-05 5.46094063434998e-05 0.999972695296828 49 0.00513051168184392 0.0102610233636878 0.994869488318156 50 0.175266128973853 0.350532257947706 0.824733871026147 51 0.663226073162221 0.673547853675558 0.336773926837779 52 0.680056779790949 0.639886440418102 0.319943220209051 53 0.575410208048221 0.849179583903558 0.424589791951779 54 0.470114768990634 0.940229537981269 0.529885231009366 55 0.330530207387136 0.661060414774272 0.669469792612864 56 0.203052877388112 0.406105754776224 0.796947122611888 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 26 0.65 NOK 5% type I error level 32 0.8 NOK 10% type I error level 33 0.825 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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