Voedingsmiddelen

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 20 Dec 2008 11:17:21 -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/Dec/20/t1229797100elcmaev4uul3z9x.htm/, Retrieved Sat, 20 Dec 2008 19:18:21 +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/2008/Dec/20/t1229797100elcmaev4uul3z9x.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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100,29 0 101,12 0 102,65 0 102,71 0 103,39 0 102,8 0 102,07 0 102,15 0 101,21 0 101,27 0 101,86 0 101,65 0 101,94 0 102,62 0 102,71 0 103,39 0 104,51 0 104,09 0 104,29 0 104,57 0 105,39 0 105,15 0 106,13 0 105,46 0 106,47 0 106,62 0 106,52 0 108,04 0 107,15 0 107,32 0 107,76 0 107,26 0 107,89 0 109,08 0 110,4 0 111,03 0 112,05 0 112,28 0 112,8 0 114,17 0 114,92 0 114,65 0 115,49 0 114,67 1 114,71 1 115,15 1 115,03 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Voedingsmiddelen[t] = + 106.170232558140 + 8.71976744186046Dummy[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) 106.170232558140 0.62994 168.5402 0 0 Dummy 8.71976744186046 2.159326 4.0382 0.000207 0.000104 Multiple Linear Regression - Regression Statistics Multiple R 0.515741072160679 R-squared 0.265988853513447 Adjusted R-squared 0.249677494702635 F-TEST (value) 16.3069709028246 F-TEST (DF numerator) 1 F-TEST (DF denominator) 45 p-value 0.000207090572747259 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.13079410626097 Sum Squared Residuals 767.855697674418 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.29 106.170232558139 -5.88023255813947 2 101.12 106.170232558140 -5.05023255813953 3 102.65 106.170232558140 -3.52023255813953 4 102.71 106.170232558140 -3.46023255813954 5 103.39 106.170232558140 -2.78023255813954 6 102.8 106.170232558140 -3.37023255813954 7 102.07 106.170232558140 -4.10023255813954 8 102.15 106.170232558140 -4.02023255813953 9 101.21 106.170232558140 -4.96023255813954 10 101.27 106.170232558140 -4.90023255813954 11 101.86 106.170232558140 -4.31023255813954 12 101.65 106.170232558140 -4.52023255813953 13 101.94 106.170232558140 -4.23023255813954 14 102.62 106.170232558140 -3.55023255813953 15 102.71 106.170232558140 -3.46023255813954 16 103.39 106.170232558140 -2.78023255813954 17 104.51 106.170232558140 -1.66023255813953 18 104.09 106.170232558140 -2.08023255813953 19 104.29 106.170232558140 -1.88023255813953 20 104.57 106.170232558140 -1.60023255813954 21 105.39 106.170232558140 -0.780232558139536 22 105.15 106.170232558140 -1.02023255813953 23 106.13 106.170232558140 -0.0402325581395413 24 105.46 106.170232558140 -0.710232558139543 25 106.47 106.170232558140 0.299767441860462 26 106.62 106.170232558140 0.449767441860468 27 106.52 106.170232558140 0.349767441860459 28 108.04 106.170232558140 1.86976744186047 29 107.15 106.170232558140 0.979767441860469 30 107.32 106.170232558140 1.14976744186046 31 107.76 106.170232558140 1.58976744186047 32 107.26 106.170232558140 1.08976744186047 33 107.89 106.170232558140 1.71976744186046 34 109.08 106.170232558140 2.90976744186046 35 110.4 106.170232558140 4.22976744186047 36 111.03 106.170232558140 4.85976744186046 37 112.05 106.170232558140 5.87976744186046 38 112.28 106.170232558140 6.10976744186046 39 112.8 106.170232558140 6.62976744186046 40 114.17 106.170232558140 7.99976744186046 41 114.92 106.170232558140 8.74976744186046 42 114.65 106.170232558140 8.47976744186047 43 115.49 106.170232558140 9.31976744186046 44 114.67 114.89 -0.219999999999998 45 114.71 114.89 -0.180000000000006 46 115.15 114.89 0.260000000000006 47 115.03 114.89 0.140000000000001 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0592164921675836 0.118432984335167 0.940783507832416 6 0.0202130913749886 0.0404261827499771 0.979786908625011 7 0.00592218704375994 0.0118443740875199 0.99407781295624 8 0.00164461442190182 0.00328922884380364 0.998355385578098 9 0.000663514594732519 0.00132702918946504 0.999336485405267 10 0.000257994136124644 0.000515988272249289 0.999742005863875 11 7.92384212672867e-05 0.000158476842534573 0.999920761578733 12 2.70720610437563e-05 5.41441220875127e-05 0.999972927938956 13 9.15799223096346e-06 1.83159844619269e-05 0.999990842007769 14 4.03381447059698e-06 8.06762894119396e-06 0.99999596618553 15 2.03823548198118e-06 4.07647096396237e-06 0.999997961764518 16 2.20699550698509e-06 4.41399101397018e-06 0.999997793004493 17 1.08785508309043e-05 2.17571016618086e-05 0.99998912144917 18 1.74575037065491e-05 3.49150074130982e-05 0.999982542496293 19 3.06578278306625e-05 6.1315655661325e-05 0.99996934217217 20 6.26038891063421e-05 0.000125207778212684 0.999937396110894 21 0.000216267507059992 0.000432535014119984 0.99978373249294 22 0.000479970594993944 0.000959941189987888 0.999520029405006 23 0.00160763765090461 0.00321527530180922 0.998392362349095 24 0.00324196705251369 0.00648393410502737 0.996758032947486 25 0.00835615189218388 0.0167123037843678 0.991643848107816 26 0.0186578427213165 0.0373156854426331 0.981342157278683 27 0.0373859483832213 0.0747718967664425 0.962614051616779 28 0.0803313491637568 0.160662698327514 0.919668650836243 29 0.135175787133309 0.270351574266618 0.864824212866691 30 0.222207029136756 0.444414058273512 0.777792970863244 31 0.346486329806125 0.69297265961225 0.653513670193875 32 0.572598383993066 0.854803232013867 0.427401616006934 33 0.82222089531509 0.355558209369818 0.177779104684909 34 0.951727014666648 0.0965459706667043 0.0482729853333521 35 0.98662637137566 0.0267472572486791 0.0133736286243395 36 0.996853754409112 0.00629249118177706 0.00314624559088853 37 0.99867692203193 0.00264615593614069 0.00132307796807035 38 0.999656598087618 0.00068680382476331 0.000343401912381655 39 0.99998232509711 3.53498057787717e-05 1.76749028893858e-05 40 0.999982080413045 3.58391739104836e-05 1.79195869552418e-05 41 0.999851856682272 0.000296286635454972 0.000148143317727486 42 0.999733976171468 0.00053204765706415 0.000266023828532075 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.631578947368421 NOK 5% type I error level 29 0.763157894736842 NOK 10% type I error level 31 0.81578947368421 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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