month

*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, 01 Dec 2010 21:21:06 +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/01/t129123846656v80jyrd6mc6r5.htm/, Retrieved Wed, 01 Dec 2010 22:21:16 +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/01/t129123846656v80jyrd6mc6r5.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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11 0 8 17 2 6 10 -2 3 23 3 7 9 -4 3 24 1 4 8 -4 7 27 1 3 7 -7 4 31 0 0 6 -9 -4 40 1 6 5 -13 -6 47 -1 3 4 -8 8 43 2 1 3 -13 2 60 2 6 2 -15 -1 64 0 5 1 -15 -2 65 1 7 12 -15 0 65 1 4 11 -10 10 55 3 3 10 -12 3 57 3 6 9 -11 6 57 1 6 8 -11 7 57 1 5 7 -17 -4 65 -2 2 6 -18 -5 69 1 3 5 -19 -7 70 1 -2 4 -22 -10 71 -1 -4 3 -24 -21 71 -4 0 2 -24 -22 73 -2 1 1 -20 -16 68 -1 4 12 -25 -25 65 -5 -3 11 -22 -22 57 -4 -3 10 -17 -22 41 -5 0 9 -9 -19 21 0 6 8 -11 -21 21 -2 -1 7 -13 -31 17 -4 0 6 -11 -28 9 -6 -1 5 -9 -23 11 -2 1 4 -7 -17 6 -2 -4 3 -3 -12 -2 -2 -1 2 -3 -14 0 1 -1 1 -6 -18 5 -2 0 12 -4 -16 3 0 3 11 -8 -22 7 -1 0 10 -1 -9 4 2 8 9 -2 -10 8 3 8 8 -2 -10 9 2 8 7 -1 0 14 3 8 6 1 3 12 4 11 5 2 2 12 5 13 4 2 4 7 5 5 3 -1 -3 15 4 12 2 1 0 14 5 13 1 -1 -1 19 6 9 12 -8 -7 39 4 11 11 1 2 12 6 7 10 2 3 11 6 12 9 -2 -3 17 3 11 8 -2 -5 16 5 10 7 -2 0 25 5 13 6 -2 -3 24 5 14 5 -6 -7 28 3 10 4 -4 -7 25 5 13 3 -5 -7 31 5 12 2 -2 -4 24 6 13 1 -1 -3 24 6 17 12 -5 -6 33 5 15

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation werkloosheid[t] = + 1.54451965078872 -0.112572244790880maand[t] -3.93284564582941indicator[t] + 1.00796554976765economie[t] + 0.995091256179224`financiën`[t] + 0.892220731906652spaarvermogen[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) 1.54451965078872 0.561517 2.7506 0.008078 0.004039 maand -0.112572244790880 0.044449 -2.5326 0.014261 0.00713 indicator -3.93284564582941 0.029754 -132.1801 0 0 economie 1.00796554976765 0.022118 45.5724 0 0 `financiën` 0.995091256179224 0.12856 7.7403 0 0 spaarvermogen 0.892220731906652 0.056435 15.8098 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.998822807707077 R-squared 0.99764700119585 Adjusted R-squared 0.997429130936206 F-TEST (value) 4579.08758555641 F-TEST (DF numerator) 5 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.17146454492620 Sum Squared Residuals 74.1057757210336 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 17 15.7134562600286 1.28654373997144 2 23 20.5392040357259 2.46079596427408 3 24 23.8506228640973 0.149377135902722 4 27 27.1028365760521 -0.102836576052094 5 31 32.318295657129 -1.31829565712902 6 40 38.5812504430566 1.41874955694335 7 47 47.7424294635515 -0.742429463551458 8 43 43.5031234806668 -0.503123480666781 9 60 61.693234315532 -1.69323431553206 10 64 63.7651979584137 0.234802041586297 11 65 65.6493373734295 -0.649337373429456 12 65 63.7503115845451 1.24968841545488 13 55 55.3762728783173 -0.376272878317263 14 57 58.9754397621134 -1.97543976211336 15 57 56.1888804980193 0.811119501980669 16 57 56.4171975606712 0.582802439328783 17 65 63.3772866687368 1.62271333126325 18 69 70.2922335100337 -1.29223351003371 19 70 67.8606166415854 2.13938335841457 20 71 72.9732051983898 -1.97320519838984 21 71 70.4474568464843 0.552543153515698 22 73 72.4344667857726 0.565533214227364 23 68 66.535203197751 1.46479680224902 24 65 65.663536638226 -0.663536638226006 25 57 57.9965598510108 -0.996559851010842 26 41 40.1264748061954 0.873525193804584 27 21 22.1289592059900 -1.12895920599002 28 21 19.8555640071994 1.1444359928006 29 17 16.6562102655208 0.343789734479206 30 9 9.04458462369071 -0.0445846236907088 31 11 12.0960998141912 -1.09609981419123 32 6 5.92967040639594 0.0703295936040589 33 -2 -1.9726499875726 -0.0273500124273982 34 0 -0.890735073779348 0.890735073779348 35 5 4.89545887279813 0.104541127201869 36 3 2.47424869605333 0.525751303946666 37 7 8.59865677365676 -1.59865677365676 38 4 4.40790126841214 -0.407901268412138 39 8 8.440444865444 -0.440444865443997 40 9 7.55792585405566 1.44207414594434 41 14 14.8123992068729 -0.812399206872864 42 12 13.7549302612071 -1.75493026120706 43 12 11.7062240303934 0.293775969606594 44 7 6.69696151946638 0.303038480533619 45 15 16.8027657205393 -1.80276572053927 46 14 13.9608553110602 0.0391446889398421 47 19 18.3573616262948 0.642638373705174 48 39 38.3954521072499 0.604547892750058 49 12 10.6054030722168 1.39459692778316 50 11 12.2541988804792 -1.25419888047923 51 17 18.1728659095375 -1.17286590953751 52 16 17.3674688352449 -1.36746883524489 53 25 25.196531024594 -0.196531024593982 54 24 23.1774273519886 0.822572648011439 55 28 29.4304545410414 -1.43045454104141 56 25 26.3441802022519 -1.34418020225188 57 31 29.4973773609655 1.50262263903448 58 24 22.722621305657 1.27737869434299 59 24 23.4791963820127 0.520803617987259 60 33 32.1688549033352 0.831145096664802 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.063776502110284 0.127553004220568 0.936223497889716 10 0.186488053118418 0.372976106236836 0.813511946881582 11 0.258483886650326 0.516967773300652 0.741516113349674 12 0.322406860403230 0.644813720806459 0.67759313959677 13 0.242432022881075 0.484864045762151 0.757567977118925 14 0.63607650385945 0.7278469922811 0.36392349614055 15 0.554123260112802 0.891753479774395 0.445876739887198 16 0.47017778564228 0.94035557128456 0.52982221435772 17 0.558057144638614 0.883885710722773 0.441942855361386 18 0.490162873142093 0.980325746284186 0.509837126857907 19 0.86571790775318 0.268564184493641 0.134282092246821 20 0.929278653657791 0.141442692684418 0.0707213463422089 21 0.896030367016752 0.207939265966495 0.103969632983248 22 0.852087026834692 0.295825946330617 0.147912973165308 23 0.848319740165321 0.303360519669358 0.151680259834679 24 0.871355751222342 0.257288497555317 0.128644248777658 25 0.881461287891455 0.23707742421709 0.118538712108545 26 0.860487105405771 0.279025789188457 0.139512894594229 27 0.905778122693089 0.188443754613822 0.094221877306911 28 0.897331522167967 0.205336955664066 0.102668477832033 29 0.860419900442157 0.279160199115686 0.139580099557843 30 0.843706954418072 0.312586091163856 0.156293045581928 31 0.833996608001866 0.332006783996267 0.166003391998133 32 0.780440256204385 0.439119487591231 0.219559743795616 33 0.737777449583709 0.524445100832582 0.262222550416291 34 0.69171313331715 0.616573733365701 0.308286866682850 35 0.670345802180619 0.659308395638762 0.329654197819381 36 0.654103059377893 0.691793881244213 0.345896940622107 37 0.673179920849219 0.653640158301562 0.326820079150781 38 0.600590131238947 0.798819737522106 0.399409868761053 39 0.553847068995049 0.892305862009902 0.446152931004951 40 0.817510437117653 0.364979125764693 0.182489562882347 41 0.787913377037938 0.424173245924124 0.212086622962062 42 0.801050114277732 0.397899771444535 0.198949885722268 43 0.769029014938004 0.461941970123991 0.230970985061996 44 0.697781100528196 0.604437798943609 0.302218899471805 45 0.653256848835485 0.693486302329031 0.346743151164515 46 0.582173247322013 0.835653505355975 0.417826752677987 47 0.483700336328202 0.967400672656403 0.516299663671798 48 0.373099429710948 0.746198859421896 0.626900570289052 49 0.480123960553188 0.960247921106376 0.519876039446812 50 0.394689869872242 0.789379739744485 0.605310130127758 51 0.381009874167565 0.76201974833513 0.618990125832435 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

Parameters (R input):

par1 = 4 ; 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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