seizoensdummies bakmeel

*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: Thu, 16 Dec 2010 12:26:31 +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/16/t129250230074dbeapp5pxjqvp.htm/, Retrieved Thu, 16 Dec 2010 13:25:20 +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/Dec/16/t129250230074dbeapp5pxjqvp.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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0.81 0 0.81 0 0.81 0 0.79 0 0.78 0 0.78 0 0.77 0 0.78 0 0.77 0 0.78 0 0.79 0 0.79 0 0.79 0 0.79 0 0.79 0 0.8 0 0.8 0 0.8 1 0.8 1 0.81 1 0.8 1 0.82 1 0.85 1 0.85 1 0.86 1 0.85 1 0.83 1 0.81 1 0.82 1 0.82 1 0.78 1 0.78 1 0.73 1 0.68 1 0.65 1 0.62 1 0.6 1 0.6 1 0.59 1 0.6 1 0.6 1 0.6 1 0.59 1 0.58 1 0.56 1 0.55 1 0.54 1 0.55 1 0.55 1 0.54 1 0.54 1 0.54 1 0.53 1 0.53 1 0.53 1 0.53 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Bakmeel[t] = + 0.792598684210527 -0.120131578947369Dummy[t] + 0.00148026315789534M1[t] -0.00251973684210528M2[t] -0.00851973684210531M3[t] -0.0125197368421053M4[t] -0.0145197368421053M5[t] + 0.00950657894736838M6[t] -0.00249342105263159M7[t] -0.000493421052631561M8[t] + 0.0125M9[t] + 0.00499999999999997M10[t] + 0.00499999999999997M11[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) 0.792598684210527 0.06424 12.3381 0 0 Dummy -0.120131578947369 0.034775 -3.4545 0.001252 0.000626 M1 0.00148026315789534 0.078937 0.0188 0.985125 0.492563 M2 -0.00251973684210528 0.078937 -0.0319 0.974683 0.487341 M3 -0.00851973684210531 0.078937 -0.1079 0.914552 0.457276 M4 -0.0125197368421053 0.078937 -0.1586 0.874723 0.437361 M5 -0.0145197368421053 0.078937 -0.1839 0.854924 0.427462 M6 0.00950657894736838 0.078783 0.1207 0.904516 0.452258 M7 -0.00249342105263159 0.078783 -0.0316 0.974898 0.487449 M8 -0.000493421052631561 0.078783 -0.0063 0.995032 0.497516 M9 0.0125 0.083025 0.1506 0.881029 0.440514 M10 0.00499999999999997 0.083025 0.0602 0.952257 0.476128 M11 0.00499999999999997 0.083025 0.0602 0.952257 0.476128 Multiple Linear Regression - Regression Statistics Multiple R 0.470063994309785 R-squared 0.22096015874647 Adjusted R-squared 0.00355369141990347 F-TEST (value) 1.01634584041406 F-TEST (DF numerator) 12 F-TEST (DF denominator) 43 p-value 0.451409060296931 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.117414471853918 Sum Squared Residuals 0.592804802631579 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.81 0.794078947368419 0.0159210526315815 2 0.81 0.79007894736842 0.0199210526315791 3 0.81 0.784078947368421 0.0259210526315789 4 0.79 0.780078947368421 0.00992105263157892 5 0.78 0.778078947368421 0.00192105263157879 6 0.78 0.802105263157895 -0.0221052631578949 7 0.77 0.790105263157895 -0.0201052631578949 8 0.78 0.792105263157895 -0.0121052631578949 9 0.77 0.805098684210526 -0.0350986842105264 10 0.78 0.797598684210526 -0.0175986842105265 11 0.79 0.797598684210526 -0.00759868421052643 12 0.79 0.792598684210526 -0.00259868421052646 13 0.79 0.794078947368422 -0.00407894736842181 14 0.79 0.790078947368421 -7.89473684212328e-05 15 0.79 0.784078947368421 0.00592105263157885 16 0.8 0.780078947368421 0.0199210526315788 17 0.8 0.778078947368421 0.0219210526315788 18 0.8 0.681973684210526 0.118026315789474 19 0.8 0.669973684210526 0.130026315789474 20 0.81 0.671973684210526 0.138026315789474 21 0.8 0.684967105263158 0.115032894736842 22 0.82 0.677467105263158 0.142532894736842 23 0.85 0.677467105263158 0.172532894736842 24 0.85 0.672467105263158 0.177532894736842 25 0.86 0.673947368421053 0.186052631578947 26 0.85 0.669947368421053 0.180052631578947 27 0.83 0.663947368421053 0.166052631578947 28 0.81 0.659947368421053 0.150052631578947 29 0.82 0.657947368421053 0.162052631578947 30 0.82 0.681973684210526 0.138026315789474 31 0.78 0.669973684210526 0.110026315789474 32 0.78 0.671973684210526 0.108026315789474 33 0.73 0.684967105263158 0.0450328947368421 34 0.68 0.677467105263158 0.00253289473684221 35 0.65 0.677467105263158 -0.0274671052631578 36 0.62 0.672467105263158 -0.0524671052631579 37 0.6 0.673947368421053 -0.0739473684210532 38 0.6 0.669947368421053 -0.0699473684210527 39 0.59 0.663947368421053 -0.0739473684210526 40 0.6 0.659947368421053 -0.0599473684210526 41 0.6 0.657947368421053 -0.0579473684210526 42 0.6 0.681973684210526 -0.0819736842105263 43 0.59 0.669973684210526 -0.0799736842105263 44 0.58 0.671973684210526 -0.0919736842105263 45 0.56 0.684967105263158 -0.124967105263158 46 0.55 0.677467105263158 -0.127467105263158 47 0.54 0.677467105263158 -0.137467105263158 48 0.55 0.672467105263158 -0.122467105263158 49 0.55 0.673947368421053 -0.123947368421053 50 0.54 0.669947368421053 -0.129947368421053 51 0.54 0.663947368421053 -0.123947368421053 52 0.54 0.659947368421053 -0.119947368421053 53 0.53 0.657947368421053 -0.127947368421053 54 0.53 0.681973684210526 -0.151973684210526 55 0.53 0.669973684210526 -0.139973684210526 56 0.53 0.671973684210526 -0.141973684210526 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00140224242698842 0.00280448485397684 0.998597757573012 17 0.000188704121732213 0.000377408243464425 0.999811295878268 18 1.62622317284713e-05 3.25244634569426e-05 0.999983737768272 19 1.45305969378616e-06 2.90611938757232e-06 0.999998546940306 20 1.21474128230855e-07 2.42948256461709e-07 0.999999878525872 21 9.13303601456206e-09 1.82660720291241e-08 0.999999990866964 22 9.79455948947691e-10 1.95891189789538e-09 0.999999999020544 23 4.9613264402823e-10 9.9226528805646e-10 0.999999999503867 24 1.75568871353511e-10 3.51137742707022e-10 0.999999999824431 25 7.84487934192638e-11 1.56897586838528e-10 0.99999999992155 26 2.16465228817821e-11 4.32930457635642e-11 0.999999999978354 27 9.08160565619374e-12 1.81632113123875e-11 0.999999999990918 28 1.21045010754585e-11 2.42090021509171e-11 0.999999999987895 29 9.59471631917635e-12 1.91894326383527e-11 0.999999999990405 30 1.99716890729718e-11 3.99433781459437e-11 0.999999999980028 31 1.50549144252779e-10 3.01098288505559e-10 0.99999999984945 32 2.01542308840681e-08 4.03084617681361e-08 0.99999997984577 33 2.42439442809682e-05 4.84878885619364e-05 0.999975756055719 34 0.0274090668509318 0.0548181337018637 0.972590933149068 35 0.398001996083638 0.796003992167277 0.601998003916361 36 0.70136059508174 0.597278809836521 0.298639404918261 37 0.816704384460097 0.366591231079805 0.183295615539903 38 0.848664894796601 0.302670210406798 0.151335105203399 39 0.828102095440234 0.343795809119533 0.171897904559766 40 0.777882530530691 0.444234938938618 0.222117469469309 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.72 NOK 5% type I error level 18 0.72 NOK 10% type I error level 19 0.76 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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