WS7 No seasonal Dummies

*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: Wed, 18 Nov 2009 08:26:28 -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/18/t12585580900hdps5rzss71d9y.htm/, Retrieved Wed, 18 Nov 2009 16:28:22 +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/18/t12585580900hdps5rzss71d9y.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:

Dataseries X:

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7,55 42,97 7,55 42,98 7,59 43,01 7,59 43,09 7,59 43,14 7,57 43,39 7,57 43,46 7,59 43,54 7,6 43,62 7,64 44,01 7,64 44,5 7,76 44,73 7,76 44,89 7,76 45,09 7,77 45,17 7,83 45,24 7,94 45,42 7,94 45,67 7,94 45,68 8,09 46,56 8,18 46,72 8,26 47,01 8,28 47,26 8,28 47,49 8,28 47,51 8,29 47,52 8,3 47,66 8,3 47,71 8,31 47,87 8,33 48 8,33 48 8,34 48,05 8,48 48,25 8,59 48,72 8,67 48,94 8,67 49,16 8,67 49,18 8,71 49,25 8,72 49,34 8,72 49,49 8,72 49,57 8,74 49,63 8,74 49,67 8,74 49,7 8,74 49,8 8,79 50,09 8,85 50,49 8,86 50,73 8,87 51,12 8,92 51,15 8,96 51,41 8,97 51,61 8,99 52,06 8,98 52,17 8,98 52,18 9,01 52,19 9,01 52,74 9,03 53,05 9,05 53,38 9,05 53,78

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 0.462072666827835 + 0.164564293187078X[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) 0.462072666827835 0.178599 2.5872 0.012205 0.006102 X 0.164564293187078 0.003719 44.2541 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.985513176483913 R-squared 0.971236221023412 Adjusted R-squared 0.970740293799678 F-TEST (value) 1958.42489490720 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0884255780843264 Sum Squared Residuals 0.453506805853744 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.55 7.53340034507653 0.0165996549234734 2 7.55 7.53504598800843 0.0149540119915662 3 7.59 7.53998291680405 0.0500170831959535 4 7.59 7.55314806025901 0.0368519397409863 5 7.59 7.56137627491837 0.0286237250816329 6 7.57 7.60251734821514 -0.0325173482151362 7 7.57 7.61403684873823 -0.0440368487382316 8 7.59 7.6272019921932 -0.0372019921931979 9 7.6 7.64036713564816 -0.0403671356481641 10 7.64 7.70454720999112 -0.0645472099911245 11 7.64 7.7851837136528 -0.145183713652793 12 7.76 7.82303350108582 -0.0630335010858202 13 7.76 7.84936378799575 -0.0893637879957532 14 7.76 7.88227664663317 -0.122276646633169 15 7.77 7.89544179008814 -0.125441790088135 16 7.83 7.90696129061123 -0.0769612906112304 17 7.94 7.9365828633849 0.00341713661509587 18 7.94 7.97772393668167 -0.0377239366816736 19 7.94 7.97936957961354 -0.039369579613544 20 8.09 8.12418615761817 -0.0341861576181734 21 8.18 8.1505164445281 0.0294835554718946 22 8.26 8.19824008955236 0.0617599104476422 23 8.28 8.23938116284913 0.0406188371508723 24 8.28 8.27723095028216 0.00276904971784379 25 8.28 8.2805222361459 -0.000522236145897113 26 8.29 8.28216787907777 0.00783212092223105 27 8.3 8.30520688012396 -0.0052068801239572 28 8.3 8.31343509478331 -0.0134350947833118 29 8.31 8.33976538169324 -0.0297653816932439 30 8.33 8.36115873980756 -0.0311587398075649 31 8.33 8.36115873980756 -0.0311587398075649 32 8.34 8.36938695446692 -0.0293869544669185 33 8.48 8.40229981310434 0.077700186895666 34 8.59 8.47964503090226 0.110354969097739 35 8.67 8.51584917540342 0.154150824596582 36 8.67 8.55205331990457 0.117946680095425 37 8.67 8.55534460576832 0.114655394231683 38 8.71 8.56686410629141 0.143135893708589 39 8.72 8.58167489267825 0.138325107321751 40 8.72 8.60635953665631 0.113640463343689 41 8.72 8.61952468011128 0.100475319888724 42 8.74 8.6293985377025 0.110601462297498 43 8.74 8.63598110942998 0.104018890570015 44 8.74 8.6409180382256 0.0990819617744026 45 8.74 8.6573744675443 0.0826255324556958 46 8.79 8.70509811256856 0.0849018874314411 47 8.85 8.77092382984339 0.0790761701566106 48 8.86 8.81041926020829 0.0495807397917126 49 8.87 8.87459933455125 -0.00459933455124791 50 8.92 8.87953626334686 0.0404637366531402 51 8.96 8.9223229795755 0.0376770204245012 52 8.97 8.95523583821292 0.0147641617870849 53 8.99 9.0292897701471 -0.0392897701471009 54 8.98 9.04739184239768 -0.0673918423976791 55 8.98 9.04903748532955 -0.0690374853295497 56 9.01 9.05068312826142 -0.0406831282614207 57 9.01 9.14119348951431 -0.131193489514314 58 9.03 9.19220842040231 -0.162208420402308 59 9.05 9.24651463715404 -0.196514637154043 60 9.05 9.31234035442887 -0.262340354428874 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00708888224308033 0.0141777644861607 0.99291111775692 6 0.00538241578275043 0.0107648315655009 0.99461758421725 7 0.00117658931580066 0.00235317863160132 0.9988234106842 8 0.000242528932992321 0.000485057865984642 0.999757471067008 9 5.26515572399274e-05 0.000105303114479855 0.99994734844276 10 2.30703556182822e-05 4.61407112365645e-05 0.999976929644382 11 5.66955330510113e-06 1.13391066102023e-05 0.999994330446695 12 0.000214512221510069 0.000429024443020139 0.99978548777849 13 0.000138975499177488 0.000277950998354976 0.999861024500823 14 6.13106574933657e-05 0.000122621314986731 0.999938689342507 15 3.17593380445697e-05 6.35186760891394e-05 0.999968240661955 16 6.48119120065078e-05 0.000129623824013016 0.999935188087993 17 0.00274496621206301 0.00548993242412601 0.997255033787937 18 0.00443825265561581 0.00887650531123161 0.995561747344384 19 0.00559041476269672 0.0111808295253934 0.994409585237303 20 0.00937018664719278 0.0187403732943856 0.990629813352807 21 0.0263860764177195 0.052772152835439 0.97361392358228 22 0.0551376825583874 0.110275365116775 0.944862317441613 23 0.0571550125187659 0.114310025037532 0.942844987481234 24 0.0467307600493119 0.0934615200986238 0.953269239950688 25 0.0390727397032562 0.0781454794065125 0.960927260296744 26 0.0335925844657509 0.0671851689315018 0.96640741553425 27 0.0314304000403553 0.0628608000807106 0.968569599959645 28 0.0350204722769454 0.0700409445538908 0.964979527723055 29 0.0543710828964865 0.108742165792973 0.945628917103513 30 0.110710861466090 0.221421722932180 0.88928913853391 31 0.329647069494729 0.659294138989458 0.670352930505271 32 0.926902220195605 0.146195559608790 0.0730977798043948 33 0.996122504143895 0.00775499171220931 0.00387749585610466 34 0.999381689223823 0.0012366215523542 0.0006183107761771 35 0.999695291372814 0.000609417254371444 0.000304708627185722 36 0.999742152186266 0.000515695627467562 0.000257847813733781 37 0.999787592353527 0.000424815292946632 0.000212407646473316 38 0.9997139922892 0.000572015421598132 0.000286007710799066 39 0.999541425727756 0.000917148544488767 0.000458574272244383 40 0.99923681810867 0.00152636378266085 0.000763181891330424 41 0.99893163888457 0.00213672223086050 0.00106836111543025 42 0.99816095405038 0.00367809189923945 0.00183904594961972 43 0.997253275751602 0.00549344849679531 0.00274672424839766 44 0.99685553900742 0.00628892198515978 0.00314446099257989 45 0.998748714047074 0.00250257190585178 0.00125128595292589 46 0.99919746055997 0.00160507888006078 0.000802539440030392 47 0.998542659145361 0.00291468170927744 0.00145734085463872 48 0.998627865459997 0.00274426908000543 0.00137213454000271 49 0.99998640894854 2.71821029188654e-05 1.35910514594327e-05 50 0.999993734301918 1.25313961643341e-05 6.26569808216705e-06 51 0.999962663157502 7.46736849954911e-05 3.73368424977456e-05 52 0.999799967262917 0.00040006547416639 0.000200032737083195 53 0.999144040493766 0.00171191901246789 0.000855959506233943 54 0.99748364746192 0.00503270507615839 0.00251635253807919 55 0.996513628579552 0.00697274284089557 0.00348637142044779 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 35 0.686274509803922 NOK 5% type I error level 39 0.764705882352941 NOK 10% type I error level 45 0.88235294117647 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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