Multiple Regression - Broodprijs - Seasonal dummies and trend

*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: Tue, 14 Dec 2010 18:49:45 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t1292352473pyo5kf2rwjhp24r.htm/, Retrieved Tue, 14 Dec 2010 19:48:02 +0100

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@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/2010/Dec/14/t1292352473pyo5kf2rwjhp24r.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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Dataseries X:

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104.37 104.89 105.15 105.72 106.38 106.40 106.47 106.59 106.76 107.35 107.81 108.03 109.08 109.86 110.29 110.34 110.59 110.64 110.83 111.51 113.32 115.89 116.51 117.44 118.25 118.65 118.52 119.07 119.12 119.28 119.30 119.44 119.57 119.93 120.03 119.66 119.46 119.48 119.56 119.43 119.57 119.59 119.50 119.54 119.56 119.61 119.64 119.60 119.71 119.72 119.66 119.76 119.80 119.88 119.78 120.08 120.22

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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Broodprijs[t] = + 106.911785714286 -0.463380952380941M1[t] -0.426404761904755M2[t] -0.619428571428571M3[t] -0.700452380952378M4[t] -0.78147619047619M5[t] -1.02450000000000M6[t] -1.31552380952381M7[t] -1.36854761904761M8[t] -1.22357142857143M9[t] + 0.130547619047621M10[t] + 0.124023809523815M11[t] + 0.309023809523809t + 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) 106.911785714286 1.486722 71.9111 0 0 M1 -0.463380952380941 1.795913 -0.258 0.797595 0.398797 M2 -0.426404761904755 1.79473 -0.2376 0.813304 0.406652 M3 -0.619428571428571 1.793808 -0.3453 0.731503 0.365752 M4 -0.700452380952378 1.79315 -0.3906 0.697958 0.348979 M5 -0.78147619047619 1.792755 -0.4359 0.665035 0.332517 M6 -1.02450000000000 1.792623 -0.5715 0.570563 0.285281 M7 -1.31552380952381 1.792755 -0.7338 0.466963 0.233481 M8 -1.36854761904761 1.79315 -0.7632 0.449412 0.224706 M9 -1.22357142857143 1.793808 -0.6821 0.498746 0.249373 M10 0.130547619047621 1.890091 0.0691 0.945247 0.472624 M11 0.124023809523815 1.889716 0.0656 0.947969 0.473984 t 0.309023809523809 0.021732 14.2195 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.907342742855159 R-squared 0.823270853011923 Adjusted R-squared 0.775071994742447 F-TEST (value) 17.0807127506857 F-TEST (DF numerator) 12 F-TEST (DF denominator) 44 p-value 8.83182416089312e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.67228486432564 Sum Squared Residuals 314.208681428571 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 104.37 106.757428571429 -2.38742857142851 2 104.89 107.103428571429 -2.21342857142857 3 105.15 107.219428571429 -2.06942857142857 4 105.72 107.447428571429 -1.72742857142858 5 106.38 107.675428571429 -1.29542857142858 6 106.4 107.741428571429 -1.34142857142857 7 106.47 107.759428571429 -1.28942857142858 8 106.59 108.015428571429 -1.42542857142858 9 106.76 108.469428571429 -1.70942857142857 10 107.35 110.132571428571 -2.78257142857144 11 107.81 110.435071428571 -2.62507142857143 12 108.03 110.620071428571 -2.59007142857143 13 109.08 110.465714285714 -1.38571428571429 14 109.86 110.811714285714 -0.951714285714292 15 110.29 110.927714285714 -0.637714285714282 16 110.34 111.155714285714 -0.815714285714287 17 110.59 111.383714285714 -0.793714285714284 18 110.64 111.449714285714 -0.80971428571429 19 110.83 111.467714285714 -0.637714285714289 20 111.51 111.723714285714 -0.213714285714284 21 113.32 112.177714285714 1.14228571428571 22 115.89 113.840857142857 2.04914285714286 23 116.51 114.143357142857 2.36664285714286 24 117.44 114.328357142857 3.11164285714286 25 118.25 114.174 4.07599999999998 26 118.65 114.52 4.13 27 118.52 114.636 3.88399999999999 28 119.07 114.864 4.20599999999999 29 119.12 115.092 4.02800000000000 30 119.28 115.158 4.122 31 119.3 115.176 4.124 32 119.44 115.432 4.008 33 119.57 115.886 3.68400000000000 34 119.93 117.549142857143 2.38085714285715 35 120.03 117.851642857143 2.17835714285714 36 119.66 118.036642857143 1.62335714285714 37 119.46 117.882285714286 1.57771428571427 38 119.48 118.228285714286 1.25171428571429 39 119.56 118.344285714286 1.21571428571429 40 119.43 118.572285714286 0.857714285714295 41 119.57 118.800285714286 0.769714285714281 42 119.59 118.866285714286 0.72371428571429 43 119.5 118.884285714286 0.61571428571429 44 119.54 119.140285714286 0.399714285714294 45 119.56 119.594285714286 -0.0342857142857081 46 119.61 121.257428571429 -1.64742857142857 47 119.64 121.559928571429 -1.91992857142857 48 119.6 121.744928571429 -2.14492857142857 49 119.71 121.590571428571 -1.88057142857145 50 119.72 121.936571428571 -2.21657142857143 51 119.66 122.052571428571 -2.39257142857143 52 119.76 122.280571428571 -2.52057142857142 53 119.8 122.508571428571 -2.70857142857143 54 119.88 122.574571428571 -2.69457142857143 55 119.78 122.592571428571 -2.81257142857142 56 120.08 122.848571428571 -2.76857142857143 57 120.22 123.302571428571 -3.08257142857142 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.000711758411078018 0.00142351682215604 0.999288241588922 17 0.000548751110497066 0.00109750222099413 0.999451248889503 18 0.00024082349950649 0.00048164699901298 0.999759176500494 19 0.000120351888149118 0.000240703776298235 0.99987964811185 20 0.000201679518095747 0.000403359036191494 0.999798320481904 21 0.115964327761146 0.231928655522292 0.884035672238854 22 0.967739156888554 0.0645216862228915 0.0322608431114457 23 0.99998435332589 3.12933482197734e-05 1.56466741098867e-05 24 0.999999996306932 7.38613661568576e-09 3.69306830784288e-09 25 0.99999999981083 3.78337779341133e-10 1.89168889670566e-10 26 0.999999999853872 2.92255241606575e-10 1.46127620803288e-10 27 0.999999999975598 4.88048978936672e-11 2.44024489468336e-11 28 0.999999999884767 2.30465525303569e-10 1.15232762651784e-10 29 0.999999999491633 1.01673375893903e-09 5.08366879469517e-10 30 0.999999997128625 5.74274934984942e-09 2.87137467492471e-09 31 0.99999998120785 3.75842996495553e-08 1.87921498247776e-08 32 0.999999884838874 2.30322251359141e-07 1.15161125679571e-07 33 0.999999340400447 1.31919910594486e-06 6.59599552972431e-07 34 0.999999351312276 1.29737544724931e-06 6.48687723624653e-07 35 0.999999897923116 2.04153767742508e-07 1.02076883871254e-07 36 0.999999912374499 1.75251002715106e-07 8.76255013575532e-08 37 0.999999608809729 7.82380542561824e-07 3.91190271280912e-07 38 0.999997793185787 4.41362842620912e-06 2.20681421310456e-06 39 0.999993003271502 1.39934569956719e-05 6.99672849783594e-06 40 0.99992747611316 0.000145047773679456 7.25238868397279e-05 41 0.999445611800604 0.00110877639879158 0.000554388199395789 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.923076923076923 NOK 5% type I error level 24 0.923076923076923 NOK 10% type I error level 25 0.961538461538462 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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