Ws 8 - Regression analyse

*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: Mon, 29 Nov 2010 11:05:57 +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/Nov/29/t12910286904wz68w8r2odzi8j.htm/, Retrieved Mon, 29 Nov 2010 12:04:50 +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/2010/Nov/29/t12910286904wz68w8r2odzi8j.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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167.16 179.84 174.44 180.35 193.17 195.16 202.43 189.91 195.98 212.09 205.81 204.31 196.07 199.98 199.10 198.31 195.72 223.04 238.41 259.73 326.54 335.15 321.81 368.62 369.59 425.00 439.72 362.23 328.76 348.55 328.18 329.34 295.55 237.38 226.85 220.14 239.36 224.69 230.98 233.47 256.70 253.41 224.95 210.37 191.09 198.85 211.04 206.25 201.51 194.54 191.07 192.82 181.88 157.67 195.82 246.25 271.69 270.29

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Tarwe[t] = + 245.128295454545 -14.3083825757576M1[t] -4.39310606060605M2[t] -2.29782954545454M3[t] -16.0805530303030M4[t] -18.4272765151515M5[t] -14.264M6[t] -12.0287234848485M7[t] -3.02344696969697M8[t] + 5.86982954545454M9[t] + 0.295106060606054M10[t] -8.29577651515151M11[t] + 0.156723484848486t + 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) 245.128295454545 41.321677 5.9322 0 0 M1 -14.3083825757576 50.130717 -0.2854 0.776631 0.388315 M2 -4.39310606060605 50.099169 -0.0877 0.930514 0.465257 M3 -2.29782954545454 50.074619 -0.0459 0.963602 0.481801 M4 -16.0805530303030 50.057075 -0.3212 0.749513 0.374756 M5 -18.4272765151515 50.046546 -0.3682 0.714448 0.357224 M6 -14.264 50.043036 -0.285 0.776925 0.388463 M7 -12.0287234848485 50.046546 -0.2404 0.81115 0.405575 M8 -3.02344696969697 50.057075 -0.0604 0.952105 0.476052 M9 5.86982954545454 50.074619 0.1172 0.907206 0.453603 M10 0.295106060606054 50.099169 0.0059 0.995326 0.497663 M11 -8.29577651515151 52.753321 -0.1573 0.875747 0.437873 t 0.156723484848486 0.592734 0.2644 0.792673 0.396336 Multiple Linear Regression - Regression Statistics Multiple R 0.122409353781914 R-squared 0.0149840498933058 Adjusted R-squared -0.247686870135146 F-TEST (value) 0.057044951499324 F-TEST (DF numerator) 12 F-TEST (DF denominator) 45 p-value 0.999997131728267 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 74.599753247114 Sum Squared Residuals 250430.543303864 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 167.16 230.976636363637 -63.8166363636367 2 179.84 241.048636363636 -61.2086363636364 3 174.44 243.300636363636 -68.8606363636364 4 180.35 229.674636363636 -49.3246363636364 5 193.17 227.484636363636 -34.3146363636363 6 195.16 231.804636363636 -36.6446363636363 7 202.43 234.196636363636 -31.7666363636364 8 189.91 243.358636363636 -53.4486363636364 9 195.98 252.408636363636 -56.4286363636363 10 212.09 246.990636363636 -34.9006363636363 11 205.81 238.556477272727 -32.7464772727273 12 204.31 247.008977272727 -42.6989772727272 13 196.07 232.857318181818 -36.7873181818181 14 199.98 242.929318181818 -42.9493181818182 15 199.1 245.181318181818 -46.0813181818182 16 198.31 231.555318181818 -33.2453181818182 17 195.72 229.365318181818 -33.6453181818182 18 223.04 233.685318181818 -10.6453181818182 19 238.41 236.077318181818 2.33268181818182 20 259.73 245.239318181818 14.4906818181818 21 326.54 254.289318181818 72.2506818181818 22 335.15 248.871318181818 86.2786818181818 23 321.81 240.437159090909 81.3728409090909 24 368.62 248.889659090909 119.730340909091 25 369.59 234.738 134.852 26 425 244.81 180.19 27 439.72 247.062 192.658 28 362.23 233.436 128.794 29 328.76 231.246 97.514 30 348.55 235.566 112.984 31 328.18 237.958 90.222 32 329.34 247.12 82.22 33 295.55 256.17 39.38 34 237.38 250.752 -13.372 35 226.85 242.317840909091 -15.4678409090909 36 220.14 250.770340909091 -30.6303409090909 37 239.36 236.618681818182 2.74131818181828 38 224.69 246.690681818182 -22.0006818181818 39 230.98 248.942681818182 -17.9626818181818 40 233.47 235.316681818182 -1.84668181818184 41 256.7 233.126681818182 23.5733181818182 42 253.41 237.446681818182 15.9633181818182 43 224.95 239.838681818182 -14.8886818181818 44 210.37 249.000681818182 -38.6306818181818 45 191.09 258.050681818182 -66.9606818181818 46 198.85 252.632681818182 -53.7826818181818 47 211.04 244.198522727273 -33.1585227272727 48 206.25 252.651022727273 -46.4010227272727 49 201.51 238.499363636364 -36.9893636363636 50 194.54 248.571363636364 -54.0313636363637 51 191.07 250.823363636364 -59.7533636363637 52 192.82 237.197363636364 -44.3773636363637 53 181.88 235.007363636364 -53.1273636363636 54 157.67 239.327363636364 -81.6573636363637 55 195.82 241.719363636364 -45.8993636363637 56 246.25 250.881363636364 -4.63136363636365 57 271.69 259.931363636364 11.7586363636363 58 270.29 254.513363636364 15.7766363636364 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.000218982994096329 0.000437965988192657 0.999781017005904 17 0.000394720255906879 0.000789440511813759 0.999605279744093 18 7.74192489404122e-05 0.000154838497880824 0.99992258075106 19 3.38841821778283e-05 6.77683643556565e-05 0.999966115817822 20 0.000646383814350474 0.00129276762870095 0.99935361618565 21 0.0304537793493947 0.0609075586987894 0.969546220650605 22 0.0555007953060735 0.111001590612147 0.944499204693927 23 0.0564350383581313 0.112870076716263 0.943564961641869 24 0.121879271959093 0.243758543918185 0.878120728040907 25 0.166978935935551 0.333957871871102 0.833021064064449 26 0.390707520267352 0.781415040534704 0.609292479732648 27 0.735417798868002 0.529164402263996 0.264582201131998 28 0.742591570557475 0.514816858885051 0.257408429442525 29 0.694529849963583 0.610940300072833 0.305470150036417 30 0.742563938516959 0.514872122966082 0.257436061483041 31 0.780145554837273 0.439708890325454 0.219854445162727 32 0.809301021437305 0.381397957125390 0.190698978562695 33 0.848207597701678 0.303584804596645 0.151792402298322 34 0.908749037111417 0.182501925777167 0.0912509628885834 35 0.918556786449526 0.162886427100948 0.0814432135504739 36 0.923599381372174 0.152801237255651 0.0764006186278257 37 0.905379424345912 0.189241151308175 0.0946205756540876 38 0.883756915659881 0.232486168680237 0.116243084340118 39 0.843833957969048 0.312332084061905 0.156166042030952 40 0.77202249386086 0.455955012278279 0.227977506139140 41 0.7386578308101 0.522684338379801 0.261342169189900 42 0.878782040125896 0.242435919748207 0.121217959874104 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.185185185185185 NOK 5% type I error level 5 0.185185185185185 NOK 10% type I error level 6 0.222222222222222 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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