Paper statistiek: Verklaren broodprijs d.m.v. dummy

*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 10:39:20 -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/t1258738864541o6n2en7lojvw.htm/, Retrieved Fri, 20 Nov 2009 18:41:16 +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/t1258738864541o6n2en7lojvw.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:

ETSHWP(6)

Dataseries X:

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1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.44 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.57 0 1.58 0 1.58 0 1.58 0 1.58 0 1.59 1 1.6 1 1.6 1 1.61 1 1.61 1 1.61 1 1.62 1 1.63 1 1.63 1 1.64 1 1.64 1 1.64 1 1.64 1 1.64 1 1.65 1 1.65 1 1.65 1 1.65 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Broodprijzen[t] = + 1.48357142857143 + 0.144206349206349X[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) 1.48357142857143 0.005394 275.0422 0 0 X 0.144206349206349 0.009848 14.6432 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.887184293010393 R-squared 0.78709596976435 Adjusted R-squared 0.783425210622356 F-TEST (value) 214.423213105940 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0349569678381563 Sum Squared Residuals 0.0708753968253977 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.43 1.48357142857144 -0.0535714285714358 2 1.43 1.48357142857143 -0.0535714285714285 3 1.43 1.48357142857143 -0.0535714285714284 4 1.43 1.48357142857143 -0.0535714285714284 5 1.43 1.48357142857143 -0.0535714285714284 6 1.43 1.48357142857143 -0.0535714285714284 7 1.44 1.48357142857143 -0.0435714285714284 8 1.48 1.48357142857143 -0.00357142857142839 9 1.48 1.48357142857143 -0.00357142857142839 10 1.48 1.48357142857143 -0.00357142857142839 11 1.48 1.48357142857143 -0.00357142857142839 12 1.48 1.48357142857143 -0.00357142857142839 13 1.48 1.48357142857143 -0.00357142857142839 14 1.48 1.48357142857143 -0.00357142857142839 15 1.48 1.48357142857143 -0.00357142857142839 16 1.48 1.48357142857143 -0.00357142857142839 17 1.48 1.48357142857143 -0.00357142857142839 18 1.48 1.48357142857143 -0.00357142857142839 19 1.48 1.48357142857143 -0.00357142857142839 20 1.48 1.48357142857143 -0.00357142857142839 21 1.48 1.48357142857143 -0.00357142857142839 22 1.48 1.48357142857143 -0.00357142857142839 23 1.48 1.48357142857143 -0.00357142857142839 24 1.48 1.48357142857143 -0.00357142857142839 25 1.48 1.48357142857143 -0.00357142857142839 26 1.48 1.48357142857143 -0.00357142857142839 27 1.48 1.48357142857143 -0.00357142857142839 28 1.48 1.48357142857143 -0.00357142857142839 29 1.48 1.48357142857143 -0.00357142857142839 30 1.48 1.48357142857143 -0.00357142857142839 31 1.48 1.48357142857143 -0.00357142857142839 32 1.48 1.48357142857143 -0.00357142857142839 33 1.48 1.48357142857143 -0.00357142857142839 34 1.48 1.48357142857143 -0.00357142857142839 35 1.48 1.48357142857143 -0.00357142857142839 36 1.48 1.48357142857143 -0.00357142857142839 37 1.48 1.48357142857143 -0.00357142857142839 38 1.57 1.48357142857143 0.0864285714285717 39 1.58 1.48357142857143 0.0964285714285717 40 1.58 1.48357142857143 0.0964285714285717 41 1.58 1.48357142857143 0.0964285714285717 42 1.58 1.48357142857143 0.0964285714285717 43 1.59 1.62777777777778 -0.0377777777777777 44 1.6 1.62777777777778 -0.0277777777777777 45 1.6 1.62777777777778 -0.0277777777777777 46 1.61 1.62777777777778 -0.0177777777777777 47 1.61 1.62777777777778 -0.0177777777777777 48 1.61 1.62777777777778 -0.0177777777777777 49 1.62 1.62777777777778 -0.00777777777777766 50 1.63 1.62777777777778 0.00222222222222213 51 1.63 1.62777777777778 0.00222222222222213 52 1.64 1.62777777777778 0.0122222222222221 53 1.64 1.62777777777778 0.0122222222222221 54 1.64 1.62777777777778 0.0122222222222221 55 1.64 1.62777777777778 0.0122222222222221 56 1.64 1.62777777777778 0.0122222222222221 57 1.65 1.62777777777778 0.0222222222222221 58 1.65 1.62777777777778 0.0222222222222221 59 1.65 1.62777777777778 0.0222222222222221 60 1.65 1.62777777777778 0.0222222222222221 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 7.14630308801285e-43 1.42926061760257e-42 1 6 8.27023994676323e-57 1.65404798935265e-56 1 7 0.000138371836115829 0.000276743672231658 0.999861628163884 8 0.108680452970389 0.217360905940778 0.891319547029611 9 0.210152825582720 0.420305651165441 0.78984717441728 10 0.259157386504413 0.518314773008826 0.740842613495587 11 0.273529285793125 0.547058571586251 0.726470714206875 12 0.267016408752022 0.534032817504043 0.732983591247978 13 0.248175846465299 0.496351692930598 0.751824153534701 14 0.222512063649534 0.445024127299067 0.777487936350466 15 0.193753486975310 0.387506973950621 0.80624651302469 16 0.164492383318729 0.328984766637458 0.83550761668127 17 0.136508919669979 0.273017839339959 0.86349108033002 18 0.110955043076622 0.221910086153245 0.889044956923378 19 0.0884822584137946 0.176964516827589 0.911517741586205 20 0.0693493983377766 0.138698796675553 0.930650601662223 21 0.0535222611131611 0.107044522226322 0.94647773888684 22 0.0407656867445339 0.0815313734890678 0.959234313255466 23 0.0307245901612458 0.0614491803224916 0.969275409838754 24 0.0229903738534968 0.0459807477069935 0.977009626146503 25 0.0171508712479357 0.0343017424958713 0.982849128752064 26 0.0128241476327695 0.0256482952655389 0.98717585236723 27 0.0096783268133805 0.019356653626761 0.99032167318662 28 0.00744083928889499 0.0148816785777900 0.992559160711105 29 0.00590125851283211 0.0118025170256642 0.994098741487168 30 0.00491289423840015 0.0098257884768003 0.9950871057616 31 0.00440153200775632 0.00880306401551264 0.995598467992244 32 0.00440220136182641 0.00880440272365281 0.995597798638174 33 0.00519885995647063 0.0103977199129413 0.99480114004353 34 0.00792863763299 0.01585727526598 0.99207136236701 35 0.0181055435275036 0.0362110870550072 0.981894456472496 36 0.0782963631373643 0.156592726274729 0.921703636862636 37 0.65787132400277 0.684257351994461 0.342128675997231 38 0.93654406632843 0.126911867343139 0.0634559336715694 39 0.98577139593951 0.0284572081209819 0.0142286040604909 40 0.994347269993482 0.0113054600130361 0.00565273000651803 41 0.996600471885729 0.00679905622854223 0.00339952811427112 42 0.997247186285895 0.00550562742821065 0.00275281371410532 43 0.99860448375039 0.0027910324992196 0.0013955162496098 44 0.998965150267602 0.00206969946479526 0.00103484973239763 45 0.999480188305885 0.00103962338823054 0.000519811694115269 46 0.999552704487728 0.000894591024544798 0.000447295512272399 47 0.999743986939277 0.000512026121446937 0.000256013060723469 48 0.999949411824568 0.000101176350863831 5.05881754319154e-05 49 0.999982931680362 3.41366392754347e-05 1.70683196377174e-05 50 0.999976217574927 4.75648501460316e-05 2.37824250730158e-05 51 0.999984424078114 3.1151843771419e-05 1.55759218857095e-05 52 0.999924967424218 0.000150065151563575 7.50325757817875e-05 53 0.99966621027988 0.000667579440240536 0.000333789720120268 54 0.998681071054985 0.00263785789003034 0.00131892894501517 55 0.995879523201662 0.00824095359667678 0.00412047679833839 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 21 0.411764705882353 NOK 5% type I error level 32 0.627450980392157 NOK 10% type I error level 34 0.666666666666667 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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